Finite Group Databasebeta

← #3538×D79 #35195509

Subgroups — #3538×D79 #35195509

Order 20224.

7162 conjugacy classes of subgroups.

The subgroup lattice has 1490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777649C211yesmaximal, characteristic, complemented
2#23777648C212yesmaximal, complemented
3#23777647C214yesmaximal, complemented
4#23777646C214yesmaximal, complemented
5#23777645C212yesmaximal, complemented
6#23777644C214yesmaximal, complemented
7#23777643C212yesmaximal, complemented
8#23777642C214yesmaximal, complemented
9#23777641C214yesmaximal, complemented
10#23777640C214yesmaximal, complemented
11#563×D79C214yesmaximal, complemented
12#552×D79C214yesmaximal, complemented
13#551×D79C214yesmaximal, complemented
14D4×Q8×D79C214yesmaximal, complemented
15#544×D79C214yesmaximal, complemented
16#541×D79C212yesmaximal, complemented
17#539×D79C214yesmaximal, complemented
18#536×D79C212yesmaximal, complemented
19#525×D79C211yesmaximal, characteristic
20C2×C22⋊Q8×D79C212yesmaximal, complemented
21C79×#3538C211yesmaximal, characteristic, complemented
22C2×#41×D79C2211yescharacteristic
23C22×Q8×D79C2212yes—
24C22×Q8×D79C2212yescomplemented
25C23×C4×D79C2211yescharacteristic
26#19099317C2218yescomplemented
27#19099316C2214yescomplemented
28#19099316C2214yescomplemented
29#19099315C2218yescomplemented
30#19099315C2218yescomplemented
31#19099314C2218yescomplemented
32#19099314C2218yescomplemented
33#19099313C2214yescomplemented
34#19099312C2218yescomplemented
35#19099255C2214yescomplemented
36#19099254C2214yescomplemented
37#19099253C2214yescomplemented
38#19099252C2214yescomplemented
39#19099251C2214yescomplemented
40#19099250C2218yescomplemented
41#19099249C2218yescomplemented
42#19099248C2214yescomplemented
43#19099247C2214yescomplemented
44#19099246C2218yescomplemented
45#19099245C2218yescomplemented
46#19099244C2214yescomplemented
47#19099243C2214yescomplemented
48#19099242C2218yescomplemented
49#19099241C2214yescomplemented
50#19099240C2218yescomplemented
51#19099239C2218yescomplemented
52#19099238C2218yescomplemented
53#19099237C2218yescomplemented
54#19099236C2218yescomplemented
55Q8×D316C2214yescomplemented
56D4×Dic158C2218yescomplemented
57D4×Dic158C2214yescomplemented
58#19099228C2214yescomplemented
59#19099228C2218yescomplemented
60Q8×C22⋊D79C2214yescomplemented
61Q8×C22⋊D79C2214yescomplemented
62#19099226C2214yescomplemented
63#19099226C2218yescomplemented
64#19099226C2218yescomplemented
65#19099226C2214yescomplemented
66#19099194C2214yescomplemented
67#19099193C2218yescomplemented
68#19099193C2218yescomplemented
69#19099192C2218yescomplemented
70#19099192C2214yescomplemented
71#19099192C2214yescomplemented
72#19099191C2218yescomplemented
73#19099190C2218yescomplemented
74#19099190C2218yescomplemented
75#19099176C2212yescomplemented
76#19099175C2212yescomplemented
77#19099174C2212yescomplemented
78#19099173C2214yescomplemented
79#19099172C2218yescomplemented
80#19099171C2214yescomplemented
81#19099170C2218yescomplemented
82#19099162C2214yescomplemented
83#19099161C2218yescomplemented
84#19099160C2214yescomplemented
85#19099159C2218yescomplemented
86#19099158C2214yescomplemented
87#19099157C2218yescomplemented
88#19099156C2218yescomplemented
89#19099155C2218yescomplemented
90#19099154C2218yescomplemented
91#19099139C2212yescomplemented
92#19099138C2214yescomplemented
93#19099137C2212yescomplemented
94#19099136C2214yescomplemented
95#19099136C2214yescomplemented
96#19099135C2214yescomplemented
97#19099135C2214yescomplemented
98#19099134C2212yescomplemented
99#19099133C2214yescomplemented
100C4⋊Q8×D79C2214yescomplemented
101C4⋊Q8×D79C2218yescomplemented
102C4⋊Q8×D79C2212yescomplemented
103#126×D79C2218yes—
104#126×D79C2218yescomplemented
105#125×D79C2218yescomplemented
106#125×D79C2218yescomplemented
107#125×D79C2212yescomplemented
108#124×D79C2214yes—
109#19099076C2212yes—
110#19099075C2211yescharacteristic
111#19099074C2211yescharacteristic
112#19099073C2212yes—
113#19099072C2214yes—
114#19099071C2212yes—
115#19099070C2211yescharacteristic
116#19099069C2212yes—
117#123×D79C2212yes—
118#123×D79C2218yes—
119#123×D79C2214yes—
120#123×D79C2214yescomplemented
121C2×#14579141C2212yescomplemented
122C2×#14579140C2212yescomplemented
123C2×#14579139C2214yescomplemented
124C2×#14579138C2214yescomplemented
125C2×#14579137C2212yescomplemented
126C22⋊Q8×D79C2212yes—
127C22⋊Q8×D79C2218yes—
128C22⋊Q8×D79C2214yes—
129C22⋊Q8×D79C2214yes—
130C22⋊Q8×D79C2214yes—
131C22⋊Q8×D79C2214yes—
132C22⋊Q8×D79C2214yescomplemented
133C22⋊Q8×D79C2214yescomplemented
134C22⋊Q8×D79C2214yescomplemented
135C22⋊Q8×D79C2214yescomplemented
136C22⋊Q8×D79C2214yescomplemented
137C22⋊Q8×D79C2218yescomplemented
138#121×D79C2212yes—
139#120×D79C2212yes—
140C4×Q8×D79C2214yescomplemented
141C4×D4×D79C2214yes—
142C4×D4×D79C2218yes—
143#117×D79C2218yes—
144#117×D79C2211yescharacteristic
145#117×D79C2212yescomplemented
146C2×C4⋊C4×D79C2214yes—
147C2×C4⋊C4×D79C2212yes—
148C2×C22⋊C4×D79C2214yes—
149#563×C79C2214yescomplemented
150#552×C79C2214yescomplemented
151#551×C79C2214yescomplemented
152D4×Q8×C79C2214yescomplemented
153#544×C79C2214yescomplemented
154#541×C79C2212yescomplemented
155#539×C79C2214yescomplemented
156#536×C79C2212yescomplemented
157#525×C79C2211yescharacteristic
158C2×C22⋊Q8×C79C2212yescomplemented
159C24×D79C2311yescharacteristic
160C2×#11929625C2311yescharacteristic
161C2×#11929624C2311yescharacteristic
162C2×#11929624C2312yes—
163C2×#11929623C2312yes—
164C2×#11929623C2311yescharacteristic
165#41×D79—44no—
166C22×Dic158C2314yes—
167C22×Dic158C2312yes—
168C22×Dic158C2312yescomplemented
169C22×Dic158C2314yescomplemented
170C2×Q8×D79—48no—
171C2×Q8×D79—48no—
172C2×Q8×D79C2314yes—
173C2×Q8×D79C2314yes—
174C2×Q8×D79C2314yes—
175C2×Q8×D79C2314yes—
176C2×Q8×D79C2314yes—
177C2×Q8×D79C2311yescharacteristic
178C2×Q8×D79C2314yescomplemented
179C2×Q8×D79C2314yescomplemented
180C2×D4×D79C2314yes—
181C2×D4×D79C2312yes—
182C2×D4×D79C2311yescharacteristic
183C23×Dic79C2311yescharacteristic
184C22×C4×D79—44no—
185C22×C4×D79C2314yes—
186C22×C4×D79C2312yes—
187C22×C4×D79C2311yescharacteristic
188C22×C4×D79C2312yes—
189C22×C4×D79C2314yes—
190C22×C4×D79C2312yes—
191C22×C4×D79C2314yes—
192C22×C4×D79C2311yescharacteristic
193C22×C4×D79C2311yescharacteristic
194C22×C4×D79C2311yescharacteristic
195C22×C4×D79C2312yes—
196C22×C4×D79C2312yes—
197#14579161C2314yescomplemented
198#14579161C2312yescomplemented
199#14579161C2318yescomplemented
200#14579160C2318yescomplemented
201#14579160C2318yescomplemented
202#14579160C2318yescomplemented
203#14579160C2318yescomplemented
204#14579160C2318yescomplemented
205#14579160C2318yescomplemented
206#14579160C2318yescomplemented
207#14579159C2314yescomplemented
208#14579159C2314yescomplemented
209#14579159C2314yescomplemented
210#14579159C2318yescomplemented
211#14579159C2318yescomplemented
212#14579156C2318yes—
213#14579156C2318yes—
214#14579156C2318yes—
215#14579156C2318yescomplemented
216#14579156C2318yescomplemented
217#14579156C2318yescomplemented
218#14579155C2318yes—
219#14579155C2318yescomplemented
220#14579154C2318yes—
221#14579154C2318yes—
222#14579154C2318yes—
223#14579154C2318yescomplemented
224#14579154C2318yescomplemented
225#14579154C2318yescomplemented
226#14579153C2318yescomplemented
227#14579153C2312yescomplemented
228#14579153C2318yescomplemented
229#14579152C2318yescomplemented
230#14579152C2318yescomplemented
231#14579152C2314yescomplemented
232#14579152C2318yescomplemented
233#14579152C2318yescomplemented
234#14579151C2318yescomplemented
235#14579151C2318yescomplemented
236#14579151C2318yescomplemented
237#14579151C2318yescomplemented
238#14579151C2318yescomplemented
239#14579151C2318yescomplemented
240#14579151C2318yescomplemented
241#14579151C2318yescomplemented
242#14579151C2318yescomplemented
243#14579150C2314yes—
244#14579149C2314yes—
245#14579148C2314yes—
246#14579147C2318yes—
247#14579147C2318yes—
248#14579146C2318yes—
249#14579146C2318yes—
250#14579146C2318yes—
251#14579146C2314yes—
252#14579146C2318yescomplemented
253#14579145C2314yes—
254#14579145C2318yes—
255#14579145C2312yes—
256#14579145C2314yescomplemented
257#14579144C2314yes—
258#14579144C2318yes—
259#14579144C2312yes—
260#14579144C2314yescomplemented
261#14579143C2318yes—
262#14579143C2318yes—
263#14579143C2318yes—
264#14579143C2314yes—
265#14579143C2318yescomplemented
266#14579142C2318yes—
267#14579142C2314yes—
268#14579142C2312yes—
269#14579142C2314yescomplemented
270#14579141C2314yes—
271#14579141C2314yes—
272#14579141C2312yes—
273#14579141C2318yes—
274#14579141C2314yes—
275#14579141C2314yes—
276#14579141C2314yescomplemented
277#14579141C2318yescomplemented
278#14579140C2314yes—
279#14579140C2314yes—
280#14579140C2312yes—
281#14579140C2318yes—
282#14579140C2314yes—
283#14579140C2314yes—
284#14579140C2314yescomplemented
285#14579140C2318yescomplemented
286#14579139C2318yes—
287#14579139C2318yes—
288#14579139C2314yes—
289#14579139C2318yes—
290#14579139C2318yes—
291#14579139C2318yes—
292#14579139C2318yes—
293#14579139C2318yescomplemented
294#14579139C2318yescomplemented
295#14579139C2318yescomplemented
296#14579138C2318yes—
297#14579138C2318yes—
298#14579138C2314yes—
299#14579138C2318yes—
300#14579138C2318yes—
301#14579138C2318yes—
302#14579138C2318yes—
303#14579138C2318yescomplemented
304#14579138C2318yescomplemented
305#14579138C2318yescomplemented
306#14579137C2314yes—
307#14579137C2314yes—
308#14579137C2312yes—
309#14579137C2318yes—
310#14579137C2314yes—
311#14579137C2314yes—
312#14579137C2314yescomplemented
313#14579137C2318yescomplemented
314#14579136C2312yes—
315#14579135C2312yes—
316#14579134C2314yes—
317#14579133C2314yes—
318#14579132C2312yes—
319#14579131C2314yes—
320#14579131C2312yes—
321#14579130C2312yes—
322#14579129C2314yes—
323#14579129C2312yes—
324Q8×Dic79C2314yescomplemented
325C4×Dic158C2318yescomplemented
326C4×Dic158C2314yescomplemented
327#14579126C2318yescomplemented
328#14579126C2314yescomplemented
329C4×D316C2318yes—
330C4×D316C2314yes—
331D4×Dic79C2318yes—
332D4×Dic79C2314yes—
333#14579123C2318yes—
334#14579123C2314yes—
335C4×C22⋊D79C2318yes—
336C4×C22⋊D79C2318yes—
337C4×C22⋊D79C2314yes—
338C4×C22⋊D79C2314yes—
339(C22⋊D79)⋊C4C2318yes—
340(C22⋊D79)⋊C4C2318yes—
341(C22⋊D79)⋊C4C2314yes—
342(C22⋊D79)⋊C4C2314yes—
343#14579120C2311yescharacteristic
344#14579120C2318yes—
345#14579120C2312yescomplemented
346#14579119C2312yes—
347#14579119C2318yes—
348#14579119C2318yes—
349#14579119C2314yescomplemented
350#14579118C2312yes—
351#14579118C2318yes—
352#14579118C2318yes—
353#14579118C2314yescomplemented
354#14579117C2312yes—
355#14579117C2318yes—
356#14579117C2318yes—
357#14579117C2314yescomplemented
358C2×C4⋊Dic79C2314yes—
359C2×C4⋊Dic79C2312yes—
360C2×Dic79⋊C4C2314yes—
361C2×Dic79⋊C4C2314yes—
362C2×Dic79⋊C4C2314yes—
363C4⋊C4×D79C2318yes—
364C4⋊C4×D79C2318yes—
365C4⋊C4×D79C2314yes—
366C4⋊C4×D79C2314yes—
367C4⋊C4×D79C2314yes—
368C4⋊C4×D79C2318yes—
369C4⋊C4×D79C2318yes—
370C4⋊C4×D79C2314yes—
371C4⋊C4×D79C2312yes—
372C4⋊C4×D79C2318yes—
373C4⋊C4×D79C2318yes—
374C4⋊C4×D79C2318yes—
375C4⋊C4×D79C2314yes—
376C4⋊C4×D79C2318yes—
377C2×C22⋊Dic79C2314yes—
378C2×(C2×D79)⋊C4C2314yes—
379C2×(C2×D79)⋊C4C2314yes—
380C22⋊C4×D79C2318yes—
381C22⋊C4×D79C2318yes—
382C22⋊C4×D79C2318yes—
383C22⋊C4×D79C2318yes—
384C22⋊C4×D79C2314yes—
385C22⋊C4×D79C2312yes—
386C22⋊C4×D79C2314yes—
387C22⋊C4×D79C2314yes—
388C22⋊C4×D79C2318yes—
389C42×D79C2314yes—
390C42×D79C2312yes—
391C42×D79C2318yes—
392C2×#41×C79C2311yescharacteristic
393C22×Q8×C79C2312yes—
394C22×Q8×C79C2312yescomplemented
395C23×C4×C79C2311yescharacteristic
396C4⋊Q8×C79C2314yescomplemented
397C4⋊Q8×C79C2312yescomplemented
398C4⋊Q8×C79C2318yescomplemented
399#126×C79C2318yes—
400#126×C79C2318yescomplemented
401#125×C79C2318yescomplemented
402#125×C79C2312yescomplemented
403#125×C79C2318yescomplemented
404#124×C79C2314yes—
405#123×C79C2318yes—
406#123×C79C2314yes—
407#123×C79C2312yes—
408#123×C79C2314yescomplemented
409C22⋊Q8×C79C2314yes—
410C22⋊Q8×C79C2314yes—
411C22⋊Q8×C79C2312yes—
412C22⋊Q8×C79C2318yes—
413C22⋊Q8×C79C2314yes—
414C22⋊Q8×C79C2314yes—
415C22⋊Q8×C79C2314yescomplemented
416C22⋊Q8×C79C2318yescomplemented
417#121×C79C2312yes—
418#120×C79C2312yes—
419C4×Q8×C79C2314yescomplemented
420C4×D4×C79C2318yes—
421C4×D4×C79C2314yes—
422#117×C79C2311yescharacteristic
423#117×C79C2318yes—
424#117×C79C2312yescomplemented
425C2×C4⋊C4×C79C2314yes—
426C2×C4⋊C4×C79C2312yes—
427C2×C22⋊C4×C79C2314yes—
428C23×D79—28no—
429C23×D79—42no—
430C23×D79C2411yescharacteristic
431C23×D79C2412yes—
432C23×D79C2411yescharacteristic
433C23×D79C2412yes—
434C23×D79C2412yes—
435#11929625—42no—
436#11929624—42no—
437#11929624—44no—
438#11929623—42no—
439#11929623—44no—
440C2×Dic158—44no—
441C2×Dic158—44no—
442C2×Dic158—48no—
443C2×Dic158—48no—
444C2×Dic158C2418yes—
445C2×Dic158C2414yes—
446C2×Dic158C2418yes—
447C2×Dic158C2414yes—
448C2×Dic158C2414yes—
449C2×Dic158C2418yes—
450C2×Dic158C2412yes—
451C2×Dic158C2411yescharacteristic
452Q8×D79—216no—
453Q8×D79—48no—
454Q8×D79—48no—
455Q8×D79—48no—
456Q8×D79—48no—
457Q8×D79—48no—
458Q8×D79—48no—
459Q8×D79—42no—
460C2×D316C2414yes—
461C2×D316C2412yes—
462C2×D316C2411yescharacteristic
463C2×C22⋊D79C2414yes—
464C2×C22⋊D79C2414yes—
465C2×C22⋊D79C2412yes—
466C2×C22⋊D79C2412yes—
467C2×C22⋊D79C2412yes—
468D4×D79—216no—
469D4×D79—42no—
470D4×D79—44no—
471C22×Dic79—42no—
472C22×Dic79C2412yes—
473C22×Dic79C2412yes—
474C22×Dic79C2411yescharacteristic
475C22×Dic79C2414yes—
476C22×Dic79C2414yes—
477C22×Dic79C2414yes—
478C22×Dic79C2412yes—
479C22×Dic79C2411yescharacteristic
480C2×C4×D79—28no—
481C2×C4×D79—28no—
482C2×C4×D79—24no—
483C2×C4×D79—216no—
484C2×C4×D79—44no—
485C2×C4×D79—42no—
486C2×C4×D79—48no—
487C2×C4×D79—48no—
488C2×C4×D79—44no—
489C2×C4×D79—42no—
490C2×C4×D79—42no—
491C2×C4×D79—44no—
492C2×C4×D79C2412yes—
493C2×C4×D79C2418yes—
494C2×C4×D79C2412yes—
495C2×C4×D79C2412yes—
496C2×C4×D79C2412yes—
497C2×C4×D79C2411yescharacteristic
498C2×C4×D79C2412yes—
499C2×C4×D79C2412yes—
500C2×C4×D79C2411yescharacteristic
501C2×C4×D79C2411yescharacteristic
502C2×C4×D79C2414yes—
503C2×C4×D79C2418yes—
504C2×C4×D79C2418yes—
505C2×C4×D79C2418yes—
506C2×C4×D79C2418yes—
507C2×C4×D79C2412yes—
508C2×C4×D79C2412yes—
509C2×C4×D79C2412yes—
510C2×C4×D79C2411yescharacteristic
511C4⋊Dic79C2414yes—
512C4⋊Dic79C2414yes—
513C4⋊Dic79C2418yes—
514C4⋊Dic79C2418yes—
515C4⋊Dic79C2412yes—
516C4⋊Dic79C2418yes—
517C4⋊Dic79C2418yes—
518C4⋊Dic79C2418yes—
519C4⋊Dic79C2414yes—
520C4⋊Dic79C2418yes—
521Dic79⋊C4C2418yes—
522Dic79⋊C4C2418yes—
523Dic79⋊C4C2418yes—
524Dic79⋊C4C2418yes—
525Dic79⋊C4C2418yes—
526Dic79⋊C4C2418yes—
527Dic79⋊C4C2414yes—
528Dic79⋊C4C2418yes—
529Dic79⋊C4C2418yes—
530Dic79⋊C4C2418yes—
531Dic79⋊C4C2418yes—
532Dic79⋊C4C2418yes—
533Dic79⋊C4C2414yes—
534Dic79⋊C4C2418yes—
535Dic79⋊C4C2414yes—
536Dic79⋊C4C2418yes—
537Dic79⋊C4C2418yes—
538C22⋊Dic79C2418yes—
539C22⋊Dic79C2418yes—
540C22⋊Dic79C2414yes—
541C22⋊Dic79C2412yes—
542C22⋊Dic79C2414yes—
543C22⋊Dic79C2414yes—
544C22⋊Dic79C2418yes—
545(C2×D79)⋊C4C2418yes—
546(C2×D79)⋊C4C2418yes—
547(C2×D79)⋊C4C2418yes—
548(C2×D79)⋊C4C2418yes—
549(C2×D79)⋊C4C2414yes—
550(C2×D79)⋊C4C2414yes—
551(C2×D79)⋊C4C2414yes—
552(C2×D79)⋊C4C2418yes—
553(C2×D79)⋊C4C2414yes—
554(C2×D79)⋊C4C2418yes—
555(C2×D79)⋊C4C2414yes—
556(C2×D79)⋊C4C2418yes—
557C4×Dic79C2414yes—
558C4×Dic79C2418yes—
559C4×Dic79C2414yes—
560C4×Dic79C2418yes—
561C4×Dic79C2418yes—
562C4×Dic79C2418yes—
563C4×Dic79C2412yes—
564C24×C79C2411yescharacteristic
565#41×C79—42no—
566C2×Q8×C79—44no—
567C2×Q8×C79—44no—
568C2×Q8×C79C2414yes—
569C2×Q8×C79C2414yes—
570C2×Q8×C79C2414yes—
571C2×Q8×C79C2411yescharacteristic
572C2×D4×C79C2414yes—
573C2×D4×C79C2412yes—
574C2×D4×C79C2411yescharacteristic
575C22×C4×C79—42no—
576C22×C4×C79C2412yes—
577C22×C4×C79C2412yes—
578C22×C4×C79C2411yescharacteristic
579C22×C4×C79C2414yes—
580C22×C4×C79C2414yes—
581C22×C4×C79C2414yes—
582C22×C4×C79C2412yes—
583C22×C4×C79C2411yescharacteristic
584C4⋊C4×C79C2414yes—
585C4⋊C4×C79C2418yes—
586C4⋊C4×C79C2418yes—
587C4⋊C4×C79C2414yes—
588C4⋊C4×C79C2412yes—
589C4⋊C4×C79C2418yes—
590C4⋊C4×C79C2418yes—
591C4⋊C4×C79C2418yes—
592C4⋊C4×C79C2414yes—
593C4⋊C4×C79C2418yes—
594C22⋊C4×C79C2418yes—
595C22⋊C4×C79C2418yes—
596C22⋊C4×C79C2414yes—
597C22⋊C4×C79C2412yes—
598C22⋊C4×C79C2414yes—
599C22⋊C4×C79C2414yes—
600C22⋊C4×C79C2418yes—
601C42×C79C2414yes—
602C42×C79C2412yes—
603C42×C79C2418yes—
604C23×C79—24no—
605C23×C79—41no—
606C23×C79C2511yescharacteristic
607C23×C79C2512yes—
608C23×C79C2512yes—
609C22×D79—24no—
610C22×D79—24no—
611C22×D79—24no—
612C22×D79—24no—
613C22×D79—22no—
614C22×D79—28no—
615C22×D79—24no—
616C22×D79—24no—
617C22×D79—24no—
618C22×D79—41no—
619C22×D79—42no—
620C22×D79—416no—
621C22×D792−1+418yes—
622C22×D79C2511yescharacteristic
623C22×D79C2512yes—
624C22×D79C2512yes—
625C22×D79C2511yescharacteristic
626Q8×C79—28no—
627Q8×C79—44no—
628Q8×C79—44no—
629Q8×C79—41no—
630D4×C79—28no—
631D4×C79—41no—
632D4×C79—42no—
633C2×C4×C79—28no—
634C2×C4×C79—24no—
635C2×C4×C79—22no—
636C2×C4×C79—24no—
637C2×C4×C79—42no—
638C2×C4×C79—41no—
639C2×C4×C79—44no—
640C2×C4×C79—44no—
641C2×C4×C79C2514yes—
642C2×C4×C79C2518yes—
643C2×C4×C79C2512yes—
644C2×C4×C79C2518yes—
645C2×C4×C79C2512yes—
646C2×C4×C79C2511yescharacteristic
647C2×C4×C79C2511yescharacteristic
648C22⋊D79—28no—
649C22⋊D79—28no—
650C22⋊D79—42no—
651C22⋊D79—42no—
652C22⋊D79—42no—
653C2×Dic79—28no—
654C2×Dic79—24no—
655C2×Dic79—22no—
656C2×Dic79—24no—
657C2×Dic79—42no—
658C2×Dic79—41no—
659C2×Dic79—44no—
660C2×Dic79—44no—
661C2×Dic79C2514yes—
662C2×Dic79C2518yes—
663C2×Dic79C2512yes—
664C2×Dic79C2518yes—
665C2×Dic79C2512yes—
666C2×Dic79C2511yescharacteristic
667C2×Dic79C2511yescharacteristic
668D316—28no—
669D316—41no—
670D316—42no—
671C4×D79—22no—
672C4×D79—24no—
673C4×D79—24no—
674C4×D79—216no—
675C4×D79—216no—
676C4×D79—216no—
677C4×D79—28no—
678C4×D79—24no—
679C4×D79—22no—
680C4×D79—24no—
681C4×D79—24no—
682C4×D79—22no—
683C4×D79—24no—
684C4×D79—42no—
685C4×D79—42no—
686C4×D79—42no—
687C4×D79—48no—
688C4×D79—48no—
689C4×D79H(5,𝔽2)14yes—
690Dic158—28no—
691Dic158—216no—
692Dic158—48no—
693Dic158—44no—
694Dic158—44no—
695Dic158—48no—
696Dic158—41no—
697Dic158—42no—
698C22×C79—22no—
699C22×C79—22no—
700C22×C79—22no—
701C22×C79—21no—
702C22×C79—24no—
703C22×C79—22no—
704C22×C79—44no—
705C22×C79C2×2−1+414yes—
706C22×C79C2611yescharacteristic
707C2×D79—22no—
708C2×D79—22no—
709C2×D79—216no—
710C2×D79—21no—
711C2×D79—22no—
712C2×D79—24no—
713C2×D79—22no—
714C2×D79—44no—
715C2×D79—48no—
716C2×D79—48no—
717C2×D79—44no—
718C2×D79C2×H(5,𝔽2)12yes—
719C2×D79C2×2−1+414yes—
720C2×D79C2×2−1+414yes—
721C4×C79—21no—
722C4×C79—22no—
723C4×C79—22no—
724C4×C79—28no—
725C4×C79—28no—
726C4×C79—24no—
727C4×C79C2×H(5,𝔽2)12yes—
728Dic79—22no—
729Dic79—21no—
730Dic79—28no—
731Dic79—22no—
732Dic79—24no—
733Dic79—28no—
734Dic79C2×H(5,𝔽2)12yes—
735C2×#3538—791nomaximal, Sylow
736C2×C79—24no—
737C2×C79—41no—
738C2×C79—42no—
739C2×C79C22×H(5,𝔽2)11yescharacteristic
740C2×C79C22×2−1+412yes—
741D79—24no—
742D79—42no—
743D79—41no—
744D79#353814yesdirect product factor
745#3538—794no—
746#3538—794no—
747#3538—794no—
748#3538—794no—
749#3538—794no—
750#3538—792no—
751#3538—794no—
752#3538—792no—
753#3538—791no—
754#3538—792no—
755#3538D7911yescharacteristic, direct product factor
756C2×#563—794no—
757C2×#552—794no—
758C2×#551—794no—
759C2×D4×Q8—794no—
760C2×#544—794no—
761C2×#541—792no—
762C2×#539—794no—
763C2×#536—792no—
764C2×#525—791no—
765C22×C22⋊Q8—792no—
766C79C2×#353811yescharacteristic, complemented, Sylow
767C22×#41—791no—
768C23×Q8—792no—
769C23×Q8—792no—
770C24×C4—791no—
771#563—798no—
772#563—798no—
773#563—798no—
774#563—798no—
775#563—794no—
776#563—794no—
777#563—794no—
778#563—798no—
779#563—798no—
780#563C2×D7914yescomplemented
781#552—798no—
782#552—798no—
783#552—794no—
784#552—798no—
785#552—794no—
786#552—794no—
787#552—794no—
788#552—794no—
789#552—798no—
790#552—794no—
791#552—794no—
792#552C2×D7914yescomplemented
793#551—798no—
794#551—794no—
795#551—798no—
796#551—794no—
797#551—798no—
798#551—794no—
799#551—798no—
800#551—798no—
801#551—798no—
802#551C2×D7914yescomplemented
803D4×Q8—794no—
804D4×Q8—794no—
805D4×Q8—798no—
806D4×Q8—794no—
807D4×Q8—794no—
808D4×Q8—798no—
809D4×Q8—794no—
810D4×Q8—798no—
811D4×Q8—794no—
812D4×Q8—798no—
813D4×Q8—794no—
814D4×Q8C2×D7914yescomplemented
815#544—798no—
816#544—798no—
817#544—798no—
818#544—798no—
819#544—794no—
820#544—794no—
821#544—798no—
822#544—798no—
823#544—794no—
824#544C2×D7914yescomplemented
825#541—792no—
826#541—798no—
827#541—798no—
828#541—792no—
829#541—794no—
830#541—794no—
831#541—792no—
832#541C2×D7912yescomplemented
833#539—798no—
834#539—798no—
835#539—798no—
836#539—798no—
837#539—794no—
838#539—798no—
839#539—794no—
840#539—798no—
841#539—794no—
842#539C2×D7914yescomplemented
843#536—792no—
844#536—792no—
845#536—794no—
846#536—794no—
847#536—794no—
848#536—794no—
849#536—794no—
850#536—794no—
851#536—792no—
852#536C2×D7912yescomplemented
853C2×C4⋊Q8—794no—
854C2×C4⋊Q8—792no—
855C2×C4⋊Q8—798no—
856C2×#126—798no—
857C2×#126—798no—
858C2×#125—798no—
859C2×#125—792no—
860C2×#125—798no—
861C2×#124—794no—
862#525—791no—
863#525—791no—
864#525—792no—
865#525—792no—
866#525—792no—
867#525—792no—
868#525—794no—
869#525—791no—
870#525C2×D7911yescharacteristic
871C2×#123—792no—
872C2×#123—794no—
873C2×#123—798no—
874C2×#123—794no—
875C2×C22⋊Q8—792no—
876C2×C22⋊Q8—792no—
877C2×C22⋊Q8—794no—
878C2×C22⋊Q8—794no—
879C2×C22⋊Q8—794no—
880C2×C22⋊Q8—794no—
881C2×C22⋊Q8—794no—
882C2×C22⋊Q8—794no—
883C2×C22⋊Q8—794no—
884C2×C22⋊Q8—794no—
885C2×C22⋊Q8—792no—
886C2×C22⋊Q8—798no—
887C2×C22⋊Q8—794no—
888C2×C22⋊Q8—798no—
889C2×C22⋊Q8—794no—
890C2×C22⋊Q8—792no—
891C2×C22⋊Q8—794no—
892C2×C22⋊Q8C2×D7912yescomplemented
893C2×#121—792no—
894C2×#120—792no—
895C2×C4×Q8—794no—
896C2×C4×D4—794no—
897C2×C4×D4—798no—
898C2×#117—791no—
899C2×#117—798no—
900C2×#117—792no—
901C22×C4⋊C4—794no—
902C22×C4⋊C4—792no—
903C22×C22⋊C4—794no—
904C25—791no—
905C2×#41—3164no—
906C2×#41—791no—
907C2×#41—791no—
908C2×#41—792no—
909C2×#41—791no—
910C2×#41—792no—
911C2×#41C22×D7911yescharacteristic
912C22×Q8—3168no—
913C22×Q8—3168no—
914C22×Q8—794no—
915C22×Q8—794no—
916C22×Q8—791no—
917C22×Q8—794no—
918C22×Q8—794no—
919C22×Q8—794no—
920C22×Q8—794no—
921C22×Q8—794no—
922C22×Q8—792no—
923C22×Q8—794no—
924C22×Q8—792no—
925C22×Q8—794no—
926C22×Q8C22×D7912yes—
927C22×Q8C22×D7912yescomplemented
928C22×D4—792no—
929C22×D4—791no—
930C22×D4—794no—
931C23×C4—3164no—
932C23×C4—791no—
933C23×C4—794no—
934C23×C4—792no—
935C23×C4—794no—
936C23×C4—791no—
937C23×C4—792no—
938C23×C4—791no—
939C23×C4—791no—
940C23×C4—792no—
941C23×C4—794no—
942C23×C4—792no—
943C23×C4—792no—
944C23×C4—791no—
945C23×C4C22×D7911yescharacteristic
946C4⋊Q8—794no—
947C4⋊Q8—794no—
948C4⋊Q8—794no—
949C4⋊Q8—798no—
950C4⋊Q8—798no—
951C4⋊Q8—798no—
952C4⋊Q8—798no—
953C4⋊Q8—798no—
954C4⋊Q8—798no—
955C4⋊Q8—798no—
956C4⋊Q8—798no—
957C4⋊Q8—798no—
958C4⋊Q8—794no—
959C4⋊Q8—792no—
960C4⋊Q8—798no—
961C4⋊Q8C22×D7914yescomplemented
962C4⋊Q8C22×D7912yescomplemented
963C4⋊Q8C22×D7918yescomplemented
964#126—798no—
965#126—798no—
966#126—798no—
967#126—798no—
968#126—798no—
969#126—798no—
970#126—798no—
971#126—798no—
972#126—798no—
973#126—798no—
974#126—798no—
975#126—798no—
976#126—798no—
977#126—798no—
978#126C22×D7918yes—
979#126C22×D7918yescomplemented
980#125—798no—
981#125—798no—
982#125—798no—
983#125—798no—
984#125—798no—
985#125—798no—
986#125—798no—
987#125—794no—
988#125—798no—
989#125—798no—
990#125—798no—
991#125—798no—
992#125—798no—
993#125—798no—
994#125—798no—
995#125—792no—
996#125—798no—
997#125C22×D7918yescomplemented
998#125C22×D7912yescomplemented
999#125C22×D7918yescomplemented
1000#124—794no—
1001#124—794no—
1002#124—798no—
1003#124—798no—
1004#124—794no—
1005#124C22×D7914yes—
1006#123—792no—
1007#123—794no—
1008#123—794no—
1009#123—798no—
1010#123—792no—
1011#123—794no—
1012#123—794no—
1013#123—798no—
1014#123—794no—
1015#123—798no—
1016#123—798no—
1017#123—798no—
1018#123—798no—
1019#123—794no—
1020#123—792no—
1021#123—798no—
1022#123—794no—
1023#123—798no—
1024#123—794no—
1025#123—798no—
1026#123—798no—
1027#123—798no—
1028#123C22×D7912yes—
1029#123C22×D7914yes—
1030#123C22×D7918yes—
1031#123C22×D7914yescomplemented
1032C22⋊Q8—794no—
1033C22⋊Q8—794no—
1034C22⋊Q8—794no—
1035C22⋊Q8—794no—
1036C22⋊Q8—792no—
1037C22⋊Q8—794no—
1038C22⋊Q8—798no—
1039C22⋊Q8—798no—
1040C22⋊Q8—794no—
1041C22⋊Q8—794no—
1042C22⋊Q8—794no—
1043C22⋊Q8—794no—
1044C22⋊Q8—792no—
1045C22⋊Q8—794no—
1046C22⋊Q8—798no—
1047C22⋊Q8—798no—
1048C22⋊Q8—798no—
1049C22⋊Q8—794no—
1050C22⋊Q8—798no—
1051C22⋊Q8—794no—
1052C22⋊Q8—798no—
1053C22⋊Q8—794no—
1054C22⋊Q8—798no—
1055C22⋊Q8—794no—
1056C22⋊Q8—794no—
1057C22⋊Q8—792no—
1058C22⋊Q8—798no—
1059C22⋊Q8—794no—
1060C22⋊Q8—798no—
1061C22⋊Q8—798no—
1062C22⋊Q8—798no—
1063C22⋊Q8—798no—
1064C22⋊Q8—798no—
1065C22⋊Q8—798no—
1066C22⋊Q8—798no—
1067C22⋊Q8—798no—
1068C22⋊Q8—798no—
1069C22⋊Q8—798no—
1070C22⋊Q8—794no—
1071C22⋊Q8—798no—
1072C22⋊Q8—798no—
1073C22⋊Q8—798no—
1074C22⋊Q8—798no—
1075C22⋊Q8—798no—
1076C22⋊Q8C22×D7914yes—
1077C22⋊Q8C22×D7914yes—
1078C22⋊Q8C22×D7914yes—
1079C22⋊Q8C22×D7914yes—
1080C22⋊Q8C22×D7912yes—
1081C22⋊Q8C22×D7918yes—
1082C22⋊Q8C22×D7914yescomplemented
1083C22⋊Q8C22×D7918yescomplemented
1084#121—792no—
1085#121—794no—
1086#121—792no—
1087#121—792no—
1088#121—794no—
1089#121C22×D7912yes—
1090#120—792no—
1091#120—794no—
1092#120—792no—
1093#120—792no—
1094#120—794no—
1095#120C22×D7912yes—
1096C4×Q8—794no—
1097C4×Q8—798no—
1098C4×Q8—794no—
1099C4×Q8—798no—
1100C4×Q8—794no—
1101C4×Q8C22×D7914yescomplemented
1102C4×D4—794no—
1103C4×D4—798no—
1104C4×D4—794no—
1105C4×D4—794no—
1106C4×D4—798no—
1107C4×D4—798no—
1108C4×D4—794no—
1109C4×D4—798no—
1110C4×D4—794no—
1111C4×D4—794no—
1112C4×D4—798no—
1113C4×D4—798no—
1114C4×D4—794no—
1115C4×D4—798no—
1116C4×D4C22×D7914yes—
1117C4×D4C22×D7918yes—
1118#117—791no—
1119#117—792no—
1120#117—798no—
1121#117—792no—
1122#117—794no—
1123#117—798no—
1124#117—798no—
1125#117—792no—
1126#117—794no—
1127#117—798no—
1128#117—798no—
1129#117—792no—
1130#117—794no—
1131#117—798no—
1132#117—798no—
1133#117C22×D7911yescharacteristic
1134#117C22×D7918yes—
1135#117C22×D7912yescomplemented
1136C2×C4⋊C4—794no—
1137C2×C4⋊C4—794no—
1138C2×C4⋊C4—794no—
1139C2×C4⋊C4—794no—
1140C2×C4⋊C4—792no—
1141C2×C4⋊C4—794no—
1142C2×C4⋊C4—798no—
1143C2×C4⋊C4—798no—
1144C2×C4⋊C4—794no—
1145C2×C4⋊C4—798no—
1146C2×C4⋊C4—798no—
1147C2×C4⋊C4—794no—
1148C2×C4⋊C4—794no—
1149C2×C4⋊C4—792no—
1150C2×C4⋊C4—798no—
1151C2×C4⋊C4—798no—
1152C2×C4⋊C4—798no—
1153C2×C4⋊C4—794no—
1154C2×C4⋊C4—798no—
1155C2×C4⋊C4C22×D7914yes—
1156C2×C4⋊C4C22×D7912yes—
1157C2×C22⋊C4—794no—
1158C2×C22⋊C4—794no—
1159C2×C22⋊C4—794no—
1160C2×C22⋊C4—798no—
1161C2×C22⋊C4—798no—
1162C2×C22⋊C4—798no—
1163C2×C22⋊C4—798no—
1164C2×C22⋊C4—794no—
1165C2×C22⋊C4—792no—
1166C2×C22⋊C4—794no—
1167C2×C22⋊C4—794no—
1168C2×C22⋊C4—798no—
1169C2×C22⋊C4C22×D7914yes—
1170C2×C42—794no—
1171C2×C42—792no—
1172C2×C42—798no—
1173C24—3162no—
1174C24—791no—
1175C24—792no—
1176C24—792no—
1177C24—791no—
1178C24—792no—
1179C24—1588no—
1180C24C23×D7911yescharacteristic
1181#41—42no—
1182#41—3162no—
1183#41—3164no—
1184#41—3162no—
1185#41—3164no—
1186#41—3162no—
1187C2×Q8—44no—
1188C2×Q8—44no—
1189C2×Q8—3164no—
1190C2×Q8—3164no—
1191C2×Q8—3168no—
1192C2×Q8—3168no—
1193C2×Q8—3168no—
1194C2×Q8—3168no—
1195C2×Q8—3168no—
1196C2×Q8—3168no—
1197C2×Q8—3168no—
1198C2×Q8—3168no—
1199C2×Q8—3162no—
1200C2×Q8—794no—
1201C2×Q8—798no—
1202C2×Q8—798no—
1203C2×Q8—794no—
1204C2×Q8—791no—
1205C2×Q8—792no—
1206C2×Q8—798no—
1207C2×Q8—794no—
1208C2×Q8—15816no—
1209C2×Q8C23×D7914yes—
1210C2×Q8C23×D7914yes—
1211C2×Q8C23×D7914yes—
1212C2×Q8C23×D7911yescharacteristic
1213C2×D4—3162no—
1214C2×D4—3164no—
1215C2×D4—792no—
1216C2×D4—792no—
1217C2×D4—792no—
1218C2×D4—794no—
1219C2×D4—794no—
1220C2×D4—792no—
1221C2×D4—791no—
1222C2×D4—794no—
1223C2×D4—15816no—
1224C2×D4C23×D7914yes—
1225C2×D4C23×D7912yes—
1226C2×D4C23×D7911yescharacteristic
1227C22×C4—42no—
1228C22×C4—3164no—
1229C22×C4—3162no—
1230C22×C4—3164no—
1231C22×C4—3162no—
1232C22×C4—3168no—
1233C22×C4—3168no—
1234C22×C4—3162no—
1235C22×C4—3164no—
1236C22×C4—3162no—
1237C22×C4—794no—
1238C22×C4—792no—
1239C22×C4—794no—
1240C22×C4—791no—
1241C22×C4—798no—
1242C22×C4—792no—
1243C22×C4—792no—
1244C22×C4—798no—
1245C22×C4—792no—
1246C22×C4—791no—
1247C22×C4—794no—
1248C22×C4—792no—
1249C22×C4—792no—
1250C22×C4—791no—
1251C22×C4—794no—
1252C22×C4—798no—
1253C22×C4—792no—
1254C22×C4—798no—
1255C22×C4—792no—
1256C22×C4—798no—
1257C22×C4—791no—
1258C22×C4—792no—
1259C22×C4—792no—
1260C22×C4—792no—
1261C22×C4—792no—
1262C22×C4—791no—
1263C22×C4—791no—
1264C22×C4—1588no—
1265C22×C4—1584no—
1266C22×C4—1588no—
1267C22×C4—15816no—
1268C22×C4C23×D7914yes—
1269C22×C4C23×D7912yes—
1270C22×C4C23×D7911yescharacteristic
1271C22×C4C23×D7912yes—
1272C22×C4C23×D7914yes—
1273C22×C4C23×D7912yes—
1274C22×C4C23×D7914yes—
1275C22×C4C23×D7911yescharacteristic
1276C4⋊C4—798no—
1277C4⋊C4—798no—
1278C4⋊C4—798no—
1279C4⋊C4—798no—
1280C4⋊C4—798no—
1281C4⋊C4—798no—
1282C4⋊C4—794no—
1283C4⋊C4—798no—
1284C4⋊C4—798no—
1285C4⋊C4—798no—
1286C4⋊C4—798no—
1287C4⋊C4—798no—
1288C4⋊C4—798no—
1289C4⋊C4—794no—
1290C4⋊C4—794no—
1291C4⋊C4—798no—
1292C4⋊C4—798no—
1293C4⋊C4—794no—
1294C4⋊C4—798no—
1295C4⋊C4—798no—
1296C4⋊C4—794no—
1297C4⋊C4—792no—
1298C4⋊C4—798no—
1299C4⋊C4—798no—
1300C4⋊C4—798no—
1301C4⋊C4—794no—
1302C4⋊C4—798no—
1303C4⋊C4C23×D7914yes—
1304C4⋊C4C23×D7918yes—
1305C4⋊C4C23×D7918yes—
1306C4⋊C4C23×D7914yes—
1307C4⋊C4C23×D7912yes—
1308C4⋊C4C23×D7918yes—
1309C4⋊C4C23×D7918yes—
1310C4⋊C4C23×D7918yes—
1311C4⋊C4C23×D7914yes—
1312C4⋊C4C23×D7918yes—
1313C22⋊C4—798no—
1314C22⋊C4—798no—
1315C22⋊C4—794no—
1316C22⋊C4—792no—
1317C22⋊C4—794no—
1318C22⋊C4—794no—
1319C22⋊C4—798no—
1320C22⋊C4—798no—
1321C22⋊C4—798no—
1322C22⋊C4—798no—
1323C22⋊C4—798no—
1324C22⋊C4—794no—
1325C22⋊C4—794no—
1326C22⋊C4—794no—
1327C22⋊C4—798no—
1328C22⋊C4—794no—
1329C22⋊C4—794no—
1330C22⋊C4—798no—
1331C22⋊C4—798no—
1332C22⋊C4C23×D7918yes—
1333C22⋊C4C23×D7918yes—
1334C22⋊C4C23×D7914yes—
1335C22⋊C4C23×D7912yes—
1336C22⋊C4C23×D7914yes—
1337C22⋊C4C23×D7914yes—
1338C22⋊C4C23×D7918yes—
1339C42—794no—
1340C42—798no—
1341C42—794no—
1342C42—792no—
1343C42—798no—
1344C42—798no—
1345C42—798no—
1346C42C23×D7914yes—
1347C42C23×D7912yes—
1348C42C23×D7918yes—
1349C23—24no—
1350C23—41no—
1351C23—3162no—
1352C23—3161no—
1353C23—31616no—
1354C23—791no—
1355C23—798no—
1356C23—792no—
1357C23—791no—
1358C23—792no—
1359C23—1584no—
1360C23—1582no—
1361C23—1588no—
1362C23—1584no—
1363C23—1584no—
1364C23—1584no—
1365C23—1584no—
1366C23—1584no—
1367C23—1584no—
1368C23C24×D7911yescharacteristic
1369C23C24×D7912yes—
1370C23C24×D7912yes—
1371Q8—28no—
1372Q8—44no—
1373Q8—44no—
1374Q8—41no—
1375Q8—3164no—
1376Q8—3164no—
1377Q8—3168no—
1378Q8—3168no—
1379Q8—3161no—
1380Q8—3162no—
1381Q8—15816no—
1382Q8—1588no—
1383D4—28no—
1384D4—41no—
1385D4—42no—
1386D4—3161no—
1387D4—3162no—
1388D4—3162no—
1389D4—3162no—
1390D4—3162no—
1391D4—1588no—
1392D4—1588no—
1393D4—1588no—
1394C2×C4—28no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—24no—
1398C2×C4—42no—
1399C2×C4—41no—
1400C2×C4—44no—
1401C2×C4—44no—
1402C2×C4—3162no—
1403C2×C4—3162no—
1404C2×C4—3162no—
1405C2×C4—3168no—
1406C2×C4—3168no—
1407C2×C4—3162no—
1408C2×C4—3161no—
1409C2×C4—3164no—
1410C2×C4—3164no—
1411C2×C4—791no—
1412C2×C4—794no—
1413C2×C4—794no—
1414C2×C4—798no—
1415C2×C4—792no—
1416C2×C4—798no—
1417C2×C4—792no—
1418C2×C4—791no—
1419C2×C4—1584no—
1420C2×C4—1582no—
1421C2×C4—1584no—
1422C2×C4—1582no—
1423C2×C4—1584no—
1424C2×C4—15816no—
1425C2×C4—1584no—
1426C2×C4—15816no—
1427C2×C4—15816no—
1428C2×C4—1588no—
1429C2×C4—1584no—
1430C2×C4—1582no—
1431C2×C4—1584no—
1432C2×C4—1588no—
1433C2×C4—1584no—
1434C2×C4—1582no—
1435C2×C4—1584no—
1436C2×C4C24×D7914yes—
1437C2×C4C24×D7918yes—
1438C2×C4C24×D7912yes—
1439C2×C4C24×D7918yes—
1440C2×C4C24×D7912yes—
1441C2×C4C24×D7911yescharacteristic
1442C2×C4C24×D7911yescharacteristic
1443C22—22no—
1444C22—22no—
1445C22—22no—
1446C22—21no—
1447C22—24no—
1448C22—22no—
1449C22—44no—
1450C22—3168no—
1451C22—3164no—
1452C22—3168no—
1453C22—3164no—
1454C22—792no—
1455C22—794no—
1456C22—794no—
1457C22—15816no—
1458C22—1582no—
1459C22—1581no—
1460C22—1584no—
1461C22—1582no—
1462C22—1582no—
1463C22—1582no—
1464C222−1+4×D7914yes—
1465C22C25×D7911yescharacteristic
1466C4—21no—
1467C4—22no—
1468C4—22no—
1469C4—28no—
1470C4—28no—
1471C4—24no—
1472C4—792no—
1473C4—1581no—
1474C4—1582no—
1475C4—1588no—
1476C4—1582no—
1477C4—1588no—
1478C4—1584no—
1479C4H(5,𝔽2)×D7912yes—
1480C2—24no—
1481C2—41no—
1482C2—42no—
1483C2—3161no—
1484C2—3162no—
1485C2—794no—
1486C2—1584no—
1487C2C2×H(5,𝔽2)×D7911yescharacteristic
1488C2C2×2−1+4×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3538C2
prime radical#525×D79C2
hypercenter#3538D79
hypocenterC79C2×#3538
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3538

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777649C2semidirect
2. #23777648C2semidirect
3. #23777647C2semidirect
4. #23777646C2semidirect
5. #23777645C2semidirect
6. #23777644C2semidirect
7. #23777643C2semidirect
8. #23777642C2semidirect
9. #23777641C2semidirect
10. #23777640C2semidirect
11. #563×D79C2semidirect
12. #552×D79C2semidirect
13. #551×D79C2semidirect
14. D4×Q8×D79C2semidirect
15. #544×D79C2semidirect
16. #541×D79C2semidirect
17. #539×D79C2semidirect
18. #536×D79C2semidirect
20. C2×C22⋊Q8×D79C2semidirect
21. C79×#3538C2semidirect
24. C22×Q8×D79C22semidirect
26. #19099317C22semidirect
27. #19099316C22semidirect
28. #19099316C22semidirect
29. #19099315C22semidirect
30. #19099315C22semidirect
31. #19099314C22semidirect
32. #19099314C22semidirect
33. #19099313C22semidirect
34. #19099312C22semidirect
35. #19099255C22semidirect
36. #19099254C22semidirect
37. #19099253C22semidirect
38. #19099252C22semidirect
39. #19099251C22semidirect
40. #19099250C22semidirect
41. #19099249C22semidirect
42. #19099248C22semidirect
43. #19099247C22semidirect
44. #19099246C22semidirect
45. #19099245C22semidirect
46. #19099244C22semidirect
47. #19099243C22semidirect
48. #19099242C22semidirect
49. #19099241C22semidirect
50. #19099240C22semidirect
51. #19099239C22semidirect
52. #19099238C22semidirect
53. #19099237C22semidirect
54. #19099236C22semidirect
55. Q8×D316C22semidirect
56. D4×Dic158C22semidirect
57. D4×Dic158C22semidirect
58. #19099228C22semidirect
59. #19099228C22semidirect
60. Q8×C22⋊D79C22semidirect
61. Q8×C22⋊D79C22semidirect
62. #19099226C22semidirect
63. #19099226C22semidirect
64. #19099226C22semidirect
65. #19099226C22semidirect
66. #19099194C22semidirect
67. #19099193C22semidirect
68. #19099193C22semidirect
69. #19099192C22semidirect
70. #19099192C22semidirect
71. #19099192C22semidirect
72. #19099191C22semidirect
73. #19099190C22semidirect
74. #19099190C22semidirect
75. #19099176C22semidirect
76. #19099175C22semidirect
77. #19099174C22semidirect
78. #19099173C22semidirect
79. #19099172C22semidirect
80. #19099171C22semidirect
81. #19099170C22semidirect
82. #19099162C22semidirect
83. #19099161C22semidirect
84. #19099160C22semidirect
85. #19099159C22semidirect
86. #19099158C22semidirect
87. #19099157C22semidirect
88. #19099156C22semidirect
89. #19099155C22semidirect
90. #19099154C22semidirect
91. #19099139C22semidirect
92. #19099138C22semidirect
93. #19099137C22semidirect
94. #19099136C22semidirect
95. #19099136C22semidirect
96. #19099135C22semidirect
97. #19099135C22semidirect
98. #19099134C22semidirect
99. #19099133C22semidirect
100. C4⋊Q8×D79C22semidirect
101. C4⋊Q8×D79C22semidirect
102. C4⋊Q8×D79C22semidirect
104. #126×D79C22semidirect
105. #125×D79C22semidirect
106. #125×D79C22semidirect
107. #125×D79C22semidirect
120. #123×D79C22semidirect
121. C2×#14579141C22semidirect
122. C2×#14579140C22semidirect
123. C2×#14579139C22semidirect
124. C2×#14579138C22semidirect
125. C2×#14579137C22semidirect
132. C22⋊Q8×D79C22semidirect
133. C22⋊Q8×D79C22semidirect
134. C22⋊Q8×D79C22semidirect
135. C22⋊Q8×D79C22semidirect
136. C22⋊Q8×D79C22semidirect
137. C22⋊Q8×D79C22semidirect
140. C4×Q8×D79C22semidirect
145. #117×D79C22semidirect
149. #563×C79C22semidirect
150. #552×C79C22semidirect
151. #551×C79C22semidirect
152. D4×Q8×C79C22semidirect
153. #544×C79C22semidirect
154. #541×C79C22semidirect
155. #539×C79C22semidirect
156. #536×C79C22semidirect
158. C2×C22⋊Q8×C79C22semidirect
168. C22×Dic158C23semidirect
169. C22×Dic158C23semidirect
178. C2×Q8×D79C23semidirect
179. C2×Q8×D79C23semidirect
197. #14579161C23semidirect
198. #14579161C23semidirect
199. #14579161C23semidirect
200. #14579160C23semidirect
201. #14579160C23semidirect
202. #14579160C23semidirect
203. #14579160C23semidirect
204. #14579160C23semidirect
205. #14579160C23semidirect
206. #14579160C23semidirect
207. #14579159C23semidirect
208. #14579159C23semidirect
209. #14579159C23semidirect
210. #14579159C23semidirect
211. #14579159C23semidirect
215. #14579156C23semidirect
216. #14579156C23semidirect
217. #14579156C23semidirect
219. #14579155C23semidirect
223. #14579154C23semidirect
224. #14579154C23semidirect
225. #14579154C23semidirect
226. #14579153C23semidirect
227. #14579153C23semidirect
228. #14579153C23semidirect
229. #14579152C23semidirect
230. #14579152C23semidirect
231. #14579152C23semidirect
232. #14579152C23semidirect
233. #14579152C23semidirect
234. #14579151C23semidirect
235. #14579151C23semidirect
236. #14579151C23semidirect
237. #14579151C23semidirect
238. #14579151C23semidirect
239. #14579151C23semidirect
240. #14579151C23semidirect
241. #14579151C23semidirect
242. #14579151C23semidirect
252. #14579146C23semidirect
256. #14579145C23semidirect
260. #14579144C23semidirect
265. #14579143C23semidirect
269. #14579142C23semidirect
276. #14579141C23semidirect
277. #14579141C23semidirect
284. #14579140C23semidirect
285. #14579140C23semidirect
293. #14579139C23semidirect
294. #14579139C23semidirect
295. #14579139C23semidirect
303. #14579138C23semidirect
304. #14579138C23semidirect
305. #14579138C23semidirect
312. #14579137C23semidirect
313. #14579137C23semidirect
324. Q8×Dic79C23semidirect
325. C4×Dic158C23semidirect
326. C4×Dic158C23semidirect
327. #14579126C23semidirect
328. #14579126C23semidirect
345. #14579120C23semidirect
349. #14579119C23semidirect
353. #14579118C23semidirect
357. #14579117C23semidirect
394. C22×Q8×C79C23semidirect
396. C4⋊Q8×C79C23semidirect
397. C4⋊Q8×C79C23semidirect
398. C4⋊Q8×C79C23semidirect
400. #126×C79C23semidirect
401. #125×C79C23semidirect
402. #125×C79C23semidirect
403. #125×C79C23semidirect
408. #123×C79C23semidirect
415. C22⋊Q8×C79C23semidirect
416. C22⋊Q8×C79C23semidirect
419. C4×Q8×C79C23semidirect
424. #117×C79C23semidirect
744. D79#3538direct (N × H)
755. #3538D79direct (N × H)
766. C79C2×#3538semidirect
780. #563C2×D79semidirect
792. #552C2×D79semidirect
802. #551C2×D79semidirect
814. D4×Q8C2×D79semidirect
824. #544C2×D79semidirect
832. #541C2×D79semidirect
842. #539C2×D79semidirect
852. #536C2×D79semidirect
892. C2×C22⋊Q8C2×D79semidirect
927. C22×Q8C22×D79semidirect
961. C4⋊Q8C22×D79semidirect
962. C4⋊Q8C22×D79semidirect
963. C4⋊Q8C22×D79semidirect
979. #126C22×D79semidirect
997. #125C22×D79semidirect
998. #125C22×D79semidirect
999. #125C22×D79semidirect
1031. #123C22×D79semidirect
1082. C22⋊Q8C22×D79semidirect
1083. C22⋊Q8C22×D79semidirect
1101. C4×Q8C22×D79semidirect
1135. #117C22×D79semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237776492
#237776482
#237776472
#237776462
#237776452
#237776442
#237776432
#237776422
#237776412
#237776402
#563×D792
#552×D792
#551×D792
D4×Q8×D792
#544×D792
#541×D792
#539×D792
#536×D792
#525×D792
C2×C22⋊Q8×D792
C79×#35382
C2×#353879