Finite Group Databasebeta

← #35197457

Subgroups — #35197457

Order 20224.

7310 conjugacy classes of subgroups.

The subgroup lattice has 1524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777505C214yesmaximal, complemented
2#23777434C214yesmaximal, complemented
3#23777424C218yesmaximal, complemented
4#23777404C214yesmaximal, complemented
5#23777344C214yesmaximal, complemented
6#23777330C218yesmaximal, complemented
7#23777323C212yesmaximal, complemented
8#23777320C211yesmaximal, characteristic, complemented
9#23777277C211yesmaximal, characteristic, complemented
10#23777272C212yesmaximal, complemented
11#23777221C211yesmaximal, characteristic, complemented
12#23777173C211yesmaximal, characteristic, complemented
13#23777137C212yesmaximal, complemented
14#23777133C214yesmaximal, complemented
15#23777061C212yesmaximal, complemented
16#23776820C214yesmaximal, complemented
17#23776816C212yesmaximal, complemented
18#23776791C212yesmaximal, complemented
19C2×#19099168C211yesmaximal, characteristic, complemented
20#540×D79C212yesmaximal, complemented
21C4×#14579207C212yesmaximal, complemented
22#23776601C211yesmaximal, characteristic, complemented
23C79×#3455C211yesmaximal, characteristic, complemented
24C2×#14579207C2212yes—
25C22×#11929624C2211yescharacteristic
26#19099298C2214yescomplemented
27#19099297C2218yescomplemented
28#19099291C2214yescomplemented
29#19099278C2214yescomplemented
30#19099275C2218yescomplemented
31#19099273C2214yescomplemented
32#19099267C2218yescomplemented
33#19099266C2218yescomplemented
34#19099264C2218yescomplemented
35#19099264C2218yescomplemented
36#19099264C2218yescomplemented
37#19099259C2214yescomplemented
38#19099259C2214yescomplemented
39#19099259C2214yescomplemented
40#19099258C2218yescomplemented
41#19099256C2218yescomplemented
42#19099253C2214yescomplemented
43#19099245C2218yescomplemented
44#19099240C2218yescomplemented
45#19099238C2218yescomplemented
46#19099236C2218yescomplemented
47#19099235C2214yescomplemented
48#19099234C2214yescomplemented
49#19099234C2214yescomplemented
50#19099231C2218yescomplemented
51#19099222C2214yescomplemented
52#19099217C2214yescomplemented
53#19099215C2218yescomplemented
54#19099209C2214yescomplemented
55#19099206C2218yescomplemented
56#19099205C2218yescomplemented
57#19099205C2218yescomplemented
58#19099205C2218yescomplemented
59#19099204C2218yescomplemented
60#19099202C2218yescomplemented
61#19099200C2218yescomplemented
62D4×D316C2214yescomplemented
63D4×D316C2214yescomplemented
64#19099197C2218yescomplemented
65#19099195C2218yescomplemented
66#19099191C2212yescomplemented
67#19099190C2214yescomplemented
68#19099186C2214yescomplemented
69#19099185C2214yescomplemented
70#19099184C2214yescomplemented
71#19099183C2218yescomplemented
72#19099174C2212yescomplemented
73#19099169C2212yescomplemented
74#19099169C2212yescomplemented
75#19099168C2212yescomplemented
76#19099168C2212yescomplemented
77#19099168C2214yescomplemented
78#19099168C2212yescomplemented
79#19099168C2214yescomplemented
80#19099168C2212yescomplemented
81#19099168C2214yescomplemented
82#19099167C2212yescomplemented
83#19099166C2214yescomplemented
84#19099165C2218yescomplemented
85#19099165C2218yescomplemented
86#19099164C2214yescomplemented
87#19099163C2218yescomplemented
88#19099161C2218yescomplemented
89#19099152C2218yescomplemented
90#19099152C2218yescomplemented
91#19099147C2218yescomplemented
92#19099146C2218yescomplemented
93#19099143C2214yescomplemented
94#19099141C2212yescomplemented
95#19099132C2212yescomplemented
96#19099131C2214yescomplemented
97#19099129C2214yescomplemented
98#19099127C2212yescomplemented
99#19099119C2212yescomplemented
100#19099114C2212yescomplemented
101#19099114C2214yescomplemented
102#19099113C2214yescomplemented
103#19099112C2218yescomplemented
104#19099110C2214yescomplemented
105#19099108C2214yescomplemented
106C2×#14579158C2211yescharacteristic, complemented
107#127×D79C2212yescomplemented
108#19099100C2214yescomplemented
109#19099099C2214yescomplemented
110#19099098C2218yescomplemented
111#19099097C2214yescomplemented
112#19099096C2218yescomplemented
113#19099096C2218yescomplemented
114#19099092C2214yescomplemented
115C2×#14579153C2211yescharacteristic, complemented
116#125×D79C2212yescomplemented
117#19099076C2214yescomplemented
118#19099076C2218yescomplemented
119#19099072C2218yescomplemented
120#19099071C2218yescomplemented
121C2×#14579146C2214yescomplemented
122#123×D79C2218yescomplemented
123C2×#14579135C2212yescomplemented
124C2×#14579134C2214yescomplemented
125#121×D79C2214yescomplemented
126#121×D79C2218yescomplemented
127#19099046C2212yescomplemented
128#19099045C2214yescomplemented
129#19099044C2214yescomplemented
130#19099043C2212yes—
131#19099043C2212yescomplemented
132#19099043C2212yescomplemented
133#19099043C2214yescomplemented
134#19099040C2212yescomplemented
135#19099037C2214yescomplemented
136#19099037C2212yescomplemented
137#19099037C2212yescomplemented
138#19099036C2214yescomplemented
139#19099035C2218yescomplemented
140#19099035C2214yescomplemented
141C4×#11929625C2214yescomplemented
142C4×#11929624C2211yescharacteristic
143C4×#11929624C2211yescharacteristic
144C4×#11929624C2211yescharacteristic, complemented
145C4×#11929624C2211yescharacteristic, complemented
146C4×#11929624C2214yescomplemented
147#19099031C2212yescomplemented
148#19099031C2212yescomplemented
149C2×C4×D316C2212yescomplemented
150C2×C4×D316C2214yescomplemented
151C4×D4×D79C2218yescomplemented
152C4×D4×D79C2214yescomplemented
153C2×#14579120C2211yescharacteristic, complemented
154#117×D79C2212yescomplemented
155#117×D79C2212yescomplemented
156#542×C79C2212yescomplemented
157#542×C79C2212yescomplemented
158#541×C79C2211yescharacteristic, complemented
159#541×C79C2211yescharacteristic, complemented
160#540×C79C2211yescharacteristic, complemented
161#540×C79C2211yescharacteristic, complemented
162#539×C79C2214yescomplemented
163#538×C79C2214yescomplemented
164#533×C79C2211yescharacteristic, complemented
165#532×C79C2211yescharacteristic, complemented
166#529×C79C2214yescomplemented
167#529×C79C2214yescomplemented
168#525×C79C2212yescomplemented
169C4×#41×C79C2212yescomplemented
170C2×#117×C79C2211yescharacteristic, complemented
171#14579207—216no—
172C2×#11929625C2314yes—
173C2×#11929625C2318yes—
174C2×#11929624—28no—
175C2×#11929624C2314yes—
176C2×#11929624C2311yescharacteristic
177C2×#11929624C2312yes—
178C2×#11929624C2312yes—
179C2×#11929624C2311yescharacteristic
180C2×#11929624C2311yescharacteristic
181C2×#11929624C2318yes—
182C2×#11929624C2311yescharacteristic
183C2×#11929623C2318yes—
184C22×Dic158C2311yescharacteristic
185C22×D316C2314yes—
186C22×D316C2312yes—
187C22×D316C2311yescharacteristic
188C22×D316C2314yes—
189C22×C22⋊D79C2312yes—
190C22×C22⋊D79C2314yes—
191C2×D4×D79C2318yes—
192C2×D4×D79C2314yes—
193C2×D4×D79C2318yes—
194C2×D4×D79C2318yes—
195C22×C4×D79C2312yes—
196C22×C4×D79C2318yes—
197C22×C4×D79C2314yes—
198#14579161C2314yes—
199#14579160C2314yes—
200#14579159C2318yes—
201#14579158C2312yes—
202#14579158C2314yes—
203#14579158C2312yes—
204#14579158C2314yes—
205#14579157C2318yes—
206#14579157C2314yes—
207#14579157C2318yes—
208#14579156C2318yes—
209#14579156C2318yes—
210#14579156C2318yes—
211#14579156C2318yes—
212#14579155C2318yes—
213#14579154C2318yes—
214#14579153C2312yes—
215#14579153C2312yes—
216#14579153C2314yes—
217#14579153C2314yes—
218#14579152C2314yes—
219#14579151C2318yes—
220#14579151C2318yes—
221#14579151C2318yes—
222#14579150C2318yes—
223#14579150C2314yes—
224#14579149C2318yes—
225#14579149C2314yes—
226#14579147C2318yes—
227#14579147C2318yes—
228#14579147C2318yes—
229#14579147C2318yes—
230#14579146C2318yes—
231#14579146C2318yes—
232#14579146C2318yes—
233#14579146C2318yes—
234#14579146C2318yes—
235#14579146C2318yes—
236#14579146C2318yes—
237#14579146C2318yes—
238#14579146C2318yes—
239#14579145C2318yes—
240#14579145C2318yes—
241#14579144C2318yes—
242#14579143C2318yes—
243#14579143C2318yes—
244#14579143C2318yes—
245#14579143C2318yes—
246#14579142C2318yes—
247#14579141C2318yes—
248#14579140C2314yes—
249#14579139C2318yes—
250#14579139C2318yes—
251#14579139C2318yes—
252#14579139C2318yes—
253#14579138C2318yes—
254#14579137C2314yes—
255#14579137C2318yes—
256#14579136C2318yes—
257#14579136C2314yes—
258#14579136C2318yes—
259#14579136C2318yes—
260#14579136C2318yes—
261#14579136C2318yes—
262#14579136C2314yes—
263#14579135C2314yes—
264#14579135C2314yes—
265#14579135C2318yes—
266#14579135C2314yes—
267#14579135C2314yes—
268#14579135C2314yes—
269#14579135C2314yes—
270#14579135C2314yes—
271#14579134C2318yes—
272#14579134C2318yes—
273#14579134C2318yes—
274#14579134C2318yes—
275#14579134C2318yes—
276#14579134C2318yes—
277#14579134C2318yes—
278#14579134C2318yes—
279#14579134C2318yes—
280#14579134C2318yes—
281#14579134C2318yes—
282#14579133C2318yes—
283#14579133C2318yes—
284#14579133C2318yes—
285#14579133C2318yes—
286#14579133C2318yes—
287#14579132C2314yes—
288#14579132C2318yes—
289#14579131C2318yes—
290#14579131C2318yes—
291#14579131C2318yes—
292#14579131C2318yes—
293#14579131C2318yes—
294#14579129C2318yes—
295#14579129C2318yes—
296Q8×Dic79C2314yes—
297C4×Dic158C2312yes—
298C4×Dic158C2314yes—
299C4×Dic158C2312yes—
300C4×Dic158C2312yes—
301C4×Dic158C2312yes—
302#14579126C2314yes—
303#14579126C2318yes—
304#14579126C2314yes—
305C4×D316C2318yes—
306C4×D316C2314yes—
307C4×D316C2314yes—
308C4×D316C2314yes—
309C4×D316C2314yes—
310C4×D316C2312yes—
311C4×D316C2312yes—
312C4×D316C2314yes—
313C4×D316C2318yes—
314C4×D316C2318yes—
315C4×D316C2314yes—
316C4×D316C2312yes—
317C4×D316C2314yes—
318C4×D316C2312yes—
319D4×Dic79C2314yes—
320D4×Dic79C2318yes—
321#14579123C2314yes—
322#14579123C2318yes—
323#14579123C2314yes—
324#14579123C2314yes—
325#14579123C2318yes—
326#14579123C2318yes—
327#14579123C2314yes—
328#14579123C2318yes—
329#14579123C2318yes—
330C4×C22⋊D79C2314yes—
331C4×C22⋊D79C2318yes—
332C4×C22⋊D79C2314yes—
333C4×C22⋊D79C2318yes—
334C4×C22⋊D79C2314yes—
335C4×C22⋊D79C2318yes—
336C4×C22⋊D79C2314yes—
337(C22⋊D79)⋊C4C2314yes—
338(C22⋊D79)⋊C4C2318yes—
339(C22⋊D79)⋊C4C2314yes—
340(C22⋊D79)⋊C4C2318yes—
341(C22⋊D79)⋊C4C2318yes—
342(C22⋊D79)⋊C4C2318yes—
343(C22⋊D79)⋊C4C2314yes—
344(C22⋊D79)⋊C4C2318yes—
345(C22⋊D79)⋊C4C2318yes—
346(C22⋊D79)⋊C4C2314yes—
347(C22⋊D79)⋊C4C2318yes—
348#14579120C2312yes—
349#14579120C2311yescharacteristic
350#14579120C2312yes—
351#14579120C2314yes—
352#14579120C2312yes—
353#14579120C2311yescharacteristic
354#14579119C2314yes—
355#14579119C2318yes—
356#14579119C2314yes—
357#14579119C2318yes—
358#14579119C2314yes—
359#14579118C2312yes—
360#14579118C2312yes—
361#14579118C2312yes—
362#14579118C2318yes—
363#14579118C2318yes—
364#14579118C2312yes—
365#14579117C2314yes—
366#14579117C2318yes—
367#14579117C2314yes—
368C2×C4⋊Dic79C2312yes—
369C2×C4⋊Dic79C2312yes—
370C2×C4⋊Dic79C2314yes—
371C2×Dic79⋊C4C2314yes—
372C4⋊C4×D79C2314yes—
373C4⋊C4×D79C2314yes—
374C4⋊C4×D79C2314yes—
375C4⋊C4×D79C2318yes—
376C4⋊C4×D79C2318yes—
377C2×C22⋊Dic79C2312yes—
378C2×(C2×D79)⋊C4C2314yes—
379C2×(C2×D79)⋊C4C2318yes—
380C2×(C2×D79)⋊C4C2314yes—
381C22⋊C4×D79C2318yes—
382C22⋊C4×D79C2314yes—
383C22⋊C4×D79C2318yes—
384C22⋊C4×D79C2318yes—
385C22⋊C4×D79C2314yes—
386C22⋊C4×D79C2318yes—
387C2×C4×Dic79C2312yes—
388C42×D79C2312yes—
389C42×D79C2312yes—
390C42×D79C2312yes—
391C42×D79C2312yes—
392C42×D79C2318yes—
393C2×#41×C79C2312yes—
394C23×C4×C79C2311yescharacteristic
395C4⋊Q8×C79C2311yescharacteristic
396C4⋊Q8×C79C2312yes—
397#127×C79C2311yescharacteristic
398#126×C79C2314yes—
399#126×C79C2314yes—
400#126×C79C2314yes—
401#126×C79C2314yes—
402#125×C79C2314yes—
403#125×C79C2311yescharacteristic
404#125×C79C2311yescharacteristic
405#125×C79C2314yes—
406#124×C79C2314yes—
407#124×C79C2314yes—
408#124×C79C2312yes—
409#123×C79C2314yes—
410#123×C79C2314yes—
411#123×C79C2314yes—
412#123×C79C2314yes—
413#123×C79C2314yes—
414C22⋊Q8×C79C2312yes—
415C22⋊Q8×C79C2314yes—
416C22⋊Q8×C79C2312yes—
417C22⋊Q8×C79C2314yes—
418C22⋊Q8×C79C2314yes—
419#121×C79C2314yes—
420#121×C79C2312yes—
421#121×C79C2314yes—
422#121×C79C2314yes—
423#121×C79C2312yes—
424#120×C79C2314yes—
425C4×Q8×C79C2312yes—
426C4×Q8×C79C2314yes—
427C4×Q8×C79C2312yes—
428C4×D4×C79C2314yes—
429C4×D4×C79C2312yes—
430C4×D4×C79C2314yes—
431C4×D4×C79C2314yes—
432C4×D4×C79C2314yes—
433C4×D4×C79C2314yes—
434C4×D4×C79C2312yes—
435#117×C79C2312yes—
436#117×C79C2312yes—
437#117×C79C2311yescharacteristic
438#117×C79C2311yescharacteristic
439#117×C79C2311yescharacteristic
440#117×C79C2311yescharacteristic
441#117×C79C2314yes—
442#117×C79C2312yes—
443C2×C4⋊C4×C79C2312yes—
444C2×C22⋊C4×C79C2312yes—
445C2×C42×C79C2311yescharacteristic
446C2×C42×C79C2311yescharacteristic
447C2×C42×C79C2314yes—
448C23×D79C2412yes—
449C23×D79C2418yes—
450C23×D79C2414yes—
451#11929625—216no—
452#11929625—88no—
453#11929624—24no—
454#11929624—28no—
455#11929624—24no—
456#11929624—216no—
457#11929624—24no—
458#11929624—28no—
459#11929624—88no—
460#11929624#4118yescomplemented
461#11929623—88no—
462C2×Dic158—24no—
463C2×Dic158C2412yes—
464C2×Dic158C2411yescharacteristic
465C2×Dic158C2418yes—
466C2×Dic158C2411yescharacteristic
467C2×D316—24no—
468C2×D316—216no—
469C2×D316—28no—
470C2×D316—84no—
471C2×D316C2412yes—
472C2×D316C2411yescharacteristic
473C2×D316C2414yes—
474C2×D316C2418yes—
475C2×D316C2414yes—
476C2×D316C2418yes—
477C2×D316C2418yes—
478C2×D316C2418yes—
479C2×D316C2418yes—
480C2×D316C2411yescharacteristic
481C2×C22⋊D79—28no—
482C2×C22⋊D79—84no—
483C2×C22⋊D79C2412yes—
484C2×C22⋊D79C2412yes—
485C2×C22⋊D79C2412yes—
486C2×C22⋊D79C2418yes—
487C2×C22⋊D79C2418yes—
488C2×C22⋊D79C2418yes—
489C2×C22⋊D79C2418yes—
490C2×C22⋊D79C2418yes—
491C2×C22⋊D79C2418yes—
492C2×C22⋊D79C2412yes—
493D4×D79—216no—
494D4×D79—232no—
495D4×D79—88no—
496D4×D79—88no—
497C22×Dic79C2412yes—
498C22×Dic79C2414yes—
499C22×Dic79C2418yes—
500C22×Dic79C2414yes—
501C2×C4×D79—28no—
502C2×C4×D79—88no—
503C2×C4×D79—84no—
504C2×C4×D79C2412yes—
505C2×C4×D79C2412yes—
506C2×C4×D79C2412yes—
507C2×C4×D79C2418yes—
508C2×C4×D79C2418yes—
509C2×C4×D79C2414yes—
510C2×C4×D79C2418yes—
511C2×C4×D79C2414yes—
512C2×C4×D79C2418yes—
513C2×C4×D79C2414yes—
514C2×C4×D79C2414yes—
515C2×C4×D79C2418yes—
516C2×C4×D79C2418yes—
517C2×C4×D79C2412yes—
518C4⋊Dic79C2414yes—
519C4⋊Dic79C2414yes—
520C4⋊Dic79C2418yes—
521C4⋊Dic79C2418yes—
522C4⋊Dic79C2412yes—
523C4⋊Dic79C2414yes—
524C4⋊Dic79C2412yes—
525Dic79⋊C4C2414yes—
526Dic79⋊C4C2418yes—
527Dic79⋊C4C2418yes—
528Dic79⋊C4C2414yes—
529Dic79⋊C4C2414yes—
530Dic79⋊C4C2414yes—
531Dic79⋊C4C2418yes—
532Dic79⋊C4C2418yes—
533Dic79⋊C4C2418yes—
534Dic79⋊C4C2418yes—
535C22⋊Dic79C2412yes—
536C22⋊Dic79C2414yes—
537C22⋊Dic79C2418yes—
538C22⋊Dic79C2418yes—
539C22⋊Dic79C2412yes—
540(C2×D79)⋊C4C2414yes—
541(C2×D79)⋊C4C2418yes—
542(C2×D79)⋊C4C2418yes—
543(C2×D79)⋊C4C2418yes—
544(C2×D79)⋊C4C2418yes—
545(C2×D79)⋊C4C2418yes—
546(C2×D79)⋊C4C2414yes—
547(C2×D79)⋊C4C2414yes—
548(C2×D79)⋊C4C2414yes—
549(C2×D79)⋊C4C2418yes—
550(C2×D79)⋊C4C2418yes—
551(C2×D79)⋊C4C2418yes—
552(C2×D79)⋊C4C2418yes—
553(C2×D79)⋊C4C2418yes—
554(C2×D79)⋊C4C2418yes—
555(C2×D79)⋊C4C2418yes—
556C4×Dic79C2414yes—
557C4×Dic79C2412yes—
558C4×Dic79C2412yes—
559C4×Dic79C2414yes—
560C4×Dic79C2414yes—
561C4×Dic79C2418yes—
562C4×Dic79C2414yes—
563C4×Dic79C2418yes—
564C4×Dic79C2414yes—
565C24×C79C2411yescharacteristic
566#41×C79—28no—
567C2×Q8×C79C2412yes—
568C2×Q8×C79C2414yes—
569C2×D4×C79C2414yes—
570C2×D4×C79C2412yes—
571C2×D4×C79C2414yes—
572C2×D4×C79C2414yes—
573C2×D4×C79C2414yes—
574C22×C4×C79—24no—
575C22×C4×C79C2411yescharacteristic
576C22×C4×C79C2411yescharacteristic
577C22×C4×C79C2411yescharacteristic
578C22×C4×C79C2411yescharacteristic
579C22×C4×C79C2414yes—
580C22×C4×C79C2411yescharacteristic
581C22×C4×C79C2414yes—
582C22×C4×C79C2412yes—
583C22×C4×C79C2412yes—
584C22×C4×C79C2414yes—
585C22×C4×C79C2411yescharacteristic
586C4⋊C4×C79C2412yes—
587C4⋊C4×C79C2412yes—
588C4⋊C4×C79C2412yes—
589C4⋊C4×C79C2412yes—
590C4⋊C4×C79C2412yes—
591C4⋊C4×C79C2412yes—
592C4⋊C4×C79C2414yes—
593C4⋊C4×C79C2414yes—
594C4⋊C4×C79C2414yes—
595C4⋊C4×C79C2414yes—
596C4⋊C4×C79C2414yes—
597C4⋊C4×C79C2414yes—
598C4⋊C4×C79C2414yes—
599C4⋊C4×C79C2414yes—
600C22⋊C4×C79C2412yes—
601C22⋊C4×C79C2412yes—
602C22⋊C4×C79C2412yes—
603C22⋊C4×C79C2412yes—
604C22⋊C4×C79C2414yes—
605C22⋊C4×C79C2414yes—
606C22⋊C4×C79C2414yes—
607C22⋊C4×C79C2414yes—
608C22⋊C4×C79C2414yes—
609C22⋊C4×C79C2414yes—
610C22⋊C4×C79C2414yes—
611C22⋊C4×C79C2414yes—
612C22⋊C4×C79C2414yes—
613C42×C79C2412yes—
614C42×C79C2411yescharacteristic
615C42×C79C2411yescharacteristic
616C42×C79C2414yes—
617C42×C79C2412yes—
618C42×C79C2411yescharacteristic
619C42×C79C2411yescharacteristic
620C42×C79C2414yes—
621C42×C79C2414yes—
622C23×C79—22no—
623C23×C79—42no—
624C23×C79C2511yescharacteristic
625C23×C79C2514yes—
626C23×C79C2511yescharacteristic
627C23×C79C2511yescharacteristic
628C22×D79—28no—
629C22×D79—24no—
630C22×D79—216no—
631C22×D79—48no—
632C22×D79—44no—
633C22×D79—48no—
634C22×D79—44no—
635C22×D79—44no—
636C22×D79C2518yes—
637C22×D79C2512yes—
638C22×D79C2512yes—
639Q8×C79—24no—
640Q8×C79—44no—
641D4×C79—28no—
642D4×C79—24no—
643D4×C79—44no—
644D4×C79—44no—
645D4×C79—44no—
646C2×C4×C79—22no—
647C2×C4×C79—22no—
648C2×C4×C79—22no—
649C2×C4×C79—28no—
650C2×C4×C79—22no—
651C2×C4×C79—22no—
652C2×C4×C79—42no—
653C2×C4×C79—44no—
654C2×C4×C79—42no—
655C2×C4×C79—44no—
656C2×C4×C79C2×#4114yes—
657C2×C4×C79C2511yescharacteristic
658C2×C4×C79C2514yes—
659C2×C4×C79C2512yes—
660C2×C4×C79C2512yes—
661C2×C4×C79C2514yes—
662C2×C4×C79C2512yes—
663C2×C4×C79C2512yes—
664C2×C4×C79C2511yescharacteristic
665C2×C4×C79C2514yes—
666C2×C4×C79C2511yescharacteristic
667C2×C4×C79C2511yescharacteristic
668C22⋊D79—24no—
669C22⋊D79—24no—
670C22⋊D79—216no—
671C22⋊D79—24no—
672C22⋊D79—48no—
673C22⋊D79—48no—
674C22⋊D79—48no—
675C22⋊D79—48no—
676C22⋊D79—48no—
677C22⋊D79C2×#4118yes—
678C2×Dic79—24no—
679C2×Dic79—44no—
680C2×Dic79—48no—
681C2×Dic79—44no—
682C2×Dic79C2514yes—
683C2×Dic79C2512yes—
684C2×Dic79C2514yes—
685C2×Dic79C2518yes—
686C2×Dic79C2512yes—
687D316—216no—
688D316—24no—
689D316—28no—
690D316—28no—
691D316—22no—
692D316—48no—
693D316—48no—
694D316—48no—
695D316—48no—
696D316C2×#4114yes—
697C4×D79—24no—
698C4×D79—24no—
699C4×D79—24no—
700C4×D79—216no—
701C4×D79—48no—
702C4×D79—44no—
703C4×D79—48no—
704C4×D79—48no—
705C4×D79—48no—
706C4×D79—44no—
707C4×D79—48no—
708C4×D79—44no—
709C4×D79—44no—
710C4×D79C2×#4118yes—
711Dic158—22no—
712Dic158—24no—
713Dic158—48no—
714Dic158C2×#4114yes—
715C22×C79—22no—
716C22×C79—21no—
717C22×C79—24no—
718C22×C79—21no—
719C22×C79—24no—
720C22×C79—22no—
721C22×C79—22no—
722C22×C79—24no—
723C22×C79—82no—
724C22×C79C22×#4112yes—
725C22×C79C2611yescharacteristic
726C2×D79—24no—
727C2×D79—22no—
728C2×D79—28no—
729C2×D79—28no—
730C2×D79—24no—
731C2×D79—28no—
732C2×D79—84no—
733C2×D79—816no—
734C2×D79—88no—
735C2×D79C22×#4114yes—
736C4×C79—21no—
737C4×C79—21no—
738C4×C79—24no—
739C4×C79—22no—
740C4×C79—22no—
741C4×C79—22no—
742C4×C79—24no—
743C4×C79—24no—
744C4×C79—22no—
745C4×C79C22×#4112yes—
746C4×C79C22×#4112yes—
747Dic79—22no—
748Dic79—24no—
749Dic79—28no—
750Dic79—24no—
751Dic79C22×#4114yes—
752#62858—791nomaximal, Sylow
753C2×C79—22no—
754C2×C79—44no—
755C2×C79—41no—
756C2×C79—41no—
757C2×C79C23×#4111yescharacteristic
758C2×C79H(7,𝔽2)12yes—
759D79—24no—
760D79—42no—
761D79—48no—
762#3524—794no—
763#3519—798no—
764#3519—794no—
765#3517—794no—
766#3513—798no—
767#3513—794no—
768#3512—792no—
769#3512—791no—
770#3508—792no—
771#3508—791no—
772#3504—791no—
773#3498—791no—
774#3494—794no—
775#3494—792no—
776#3488—792no—
777#3460—794no—
778#3460—792no—
779#3455—792no—
780#3455D7911yescharacteristic, complemented
781C2×#540—792no—
782C2×#540—791no—
783C4×H(5,𝔽2)—792no—
784#3428—791no—
785C79#6285811yescharacteristic, complemented, Sylow
786C2×H(5,𝔽2)—792no—
787C22×#41—791no—
788#559—798no—
789#559—794no—
790#557—794no—
791#555—798no—
792#555—794no—
793#554—798no—
794#554—794no—
795#553—798no—
796#553—798no—
797#553—798no—
798#553—798no—
799#553—798no—
800#553—798no—
801#553—794no—
802#553—794no—
803#553—794no—
804#552—798no—
805#552—794no—
806#551—798no—
807#551—798no—
808#551—798no—
809#550—798no—
810#550—794no—
811#550—794no—
812#550—794no—
813#548—794no—
814#547—798no—
815#547—794no—
816#546—798no—
817#546—798no—
818#546—798no—
819#546—798no—
820#546—798no—
821#546—798no—
822#546—798no—
823#546—794no—
824D42—798no—
825D42—798no—
826D42—794no—
827D42—794no—
828#544—794no—
829#544—792no—
830#542—798no—
831#542—794no—
832#542—794no—
833#542—794no—
834#542C2×D7912yescomplemented
835#542C2×D7912yescomplemented
836#541—792no—
837#541C2×D7911yescharacteristic, complemented
838#541C2×D7911yescharacteristic, complemented
839#540—792no—
840#540—792no—
841#540—792no—
842#540—798no—
843#540—798no—
844#540—798no—
845#540—794no—
846#540—794no—
847#540—792no—
848#540—792no—
849#540—792no—
850#540—792no—
851#540—794no—
852#540—794no—
853#540—794no—
854#540C2×D7911yescharacteristic, complemented
855#540C2×D7911yescharacteristic, complemented
856#539—798no—
857#539C2×D7914yescomplemented
858#538—798no—
859#538—798no—
860#538—798no—
861#538—798no—
862#538C2×D7914yescomplemented
863#537—792no—
864#537—794no—
865#535—792no—
866#535—794no—
867#535—794no—
868#535—792no—
869#533—792no—
870#533C2×D7911yescharacteristic, complemented
871#532—792no—
872#532—794no—
873#532—798no—
874#532—794no—
875#532—794no—
876#532—794no—
877#532C2×D7911yescharacteristic, complemented
878C2×#127—792no—
879C2×#127—791no—
880#529—798no—
881#529—798no—
882#529—798no—
883#529—794no—
884#529—794no—
885#529—794no—
886#529—794no—
887#529C2×D7914yescomplemented
888#529C2×D7914yescomplemented
889C2×#125—792no—
890C2×#125—791no—
891#525—798no—
892#525—794no—
893#525—798no—
894#525—798no—
895#525C2×D7912yescomplemented
896C2×#123—798no—
897C2×#123—794no—
898C2×#121—792no—
899C2×#121—794no—
900C2×#121—798no—
901C2×#121—794no—
902#520—792no—
903#520—794no—
904#520—792no—
905#520—792no—
906#520—792no—
907#520—794no—
908#520—794no—
909#519—792no—
910#518—794no—
911#518—798no—
912#518—792no—
913#518—792no—
914#518—794no—
915#518—794no—
916C4×#41—794no—
917C4×#41—792no—
918C4×#41—792no—
919C4×#41—791no—
920C4×#41—791no—
921C4×#41—791no—
922C4×#41—791no—
923C4×#41—794no—
924C4×#41C2×D7912yescomplemented
925C2×C4×D4—794no—
926C2×C4×D4—798no—
927C2×C4×D4—792no—
928C2×C4×D4—794no—
929C2×#117—791no—
930C2×#117—792no—
931C2×#117—792no—
932C2×#117C2×D7911yescharacteristic, complemented
933H(5,𝔽2)—15816no—
934C2×#41—798no—
935C2×#41—794no—
936C2×#41—798no—
937C2×#41—791no—
938C2×#41—798no—
939C2×#41—792no—
940C2×#41—791no—
941C2×#41—794no—
942C2×#41—791no—
943C2×#41—792no—
944C2×#41—791no—
945C2×#41—1588no—
946C2×#41C22×D7912yes—
947C22×Q8—791no—
948C22×D4—794no—
949C22×D4—792no—
950C22×D4—798no—
951C22×D4—798no—
952C22×D4—794no—
953C22×D4—798no—
954C22×D4—794no—
955C22×D4—792no—
956C22×D4—794no—
957C22×D4—791no—
958C23×C4—794no—
959C23×C4—798no—
960C23×C4—792no—
961C23×C4C22×D7911yescharacteristic
962C4⋊Q8—798no—
963C4⋊Q8—794no—
964C4⋊Q8—794no—
965C4⋊Q8C22×D7911yescharacteristic
966C4⋊Q8C22×D7912yes—
967#127—794no—
968#127—798no—
969#127—798no—
970#127—792no—
971#127—792no—
972#127—794no—
973#127—794no—
974#127C22×D7911yescharacteristic
975#126—798no—
976#126—798no—
977#126—798no—
978#126—798no—
979#126—798no—
980#126—798no—
981#126C22×D7914yes—
982#126C22×D7914yes—
983#126C22×D7914yes—
984#126C22×D7914yes—
985#125—794no—
986#125—798no—
987#125—798no—
988#125—798no—
989#125—792no—
990#125—792no—
991#125—794no—
992#125—794no—
993#125C22×D7911yescharacteristic
994#125C22×D7914yes—
995#125C22×D7914yes—
996#125C22×D7911yescharacteristic
997#124—794no—
998#124—798no—
999#124—798no—
1000#124—798no—
1001#124—798no—
1002#124—798no—
1003#124—798no—
1004#124—794no—
1005#124C22×D7912yes—
1006#124C22×D7914yes—
1007#124C22×D7914yes—
1008#123—798no—
1009#123—798no—
1010#123—798no—
1011#123—798no—
1012#123—798no—
1013#123—798no—
1014#123—798no—
1015#123—798no—
1016#123—798no—
1017#123—798no—
1018#123—798no—
1019#123—798no—
1020#123—798no—
1021#123—798no—
1022#123—798no—
1023#123—798no—
1024#123—798no—
1025#123C22×D7914yes—
1026#123C22×D7914yes—
1027#123C22×D7914yes—
1028#123C22×D7914yes—
1029#123C22×D7914yes—
1030C22⋊Q8—794no—
1031C22⋊Q8—798no—
1032C22⋊Q8—794no—
1033C22⋊Q8—798no—
1034C22⋊Q8—798no—
1035C22⋊Q8—798no—
1036C22⋊Q8—798no—
1037C22⋊Q8—798no—
1038C22⋊Q8—798no—
1039C22⋊Q8C22×D7912yes—
1040C22⋊Q8C22×D7914yes—
1041C22⋊Q8C22×D7912yes—
1042C22⋊Q8C22×D7914yes—
1043C22⋊Q8C22×D7914yes—
1044#121—794no—
1045#121—798no—
1046#121—798no—
1047#121—798no—
1048#121—798no—
1049#121—798no—
1050#121—798no—
1051#121—794no—
1052#121—798no—
1053#121—794no—
1054#121—794no—
1055#121—794no—
1056#121—794no—
1057#121—794no—
1058#121—794no—
1059#121—794no—
1060#121—798no—
1061#121—794no—
1062#121—798no—
1063#121—798no—
1064#121—798no—
1065#121—798no—
1066#121—798no—
1067#121—798no—
1068#121—798no—
1069#121—798no—
1070#121—798no—
1071#121—798no—
1072#121—798no—
1073#121—798no—
1074#121—798no—
1075#121—798no—
1076#121—798no—
1077#121C22×D7912yes—
1078#121C22×D7914yes—
1079#121C22×D7912yes—
1080#121C22×D7914yes—
1081#121C22×D7914yes—
1082#120—798no—
1083#120—798no—
1084#120—798no—
1085#120—798no—
1086#120—798no—
1087#120—798no—
1088#120—798no—
1089#120C22×D7914yes—
1090C4×Q8—794no—
1091C4×Q8—794no—
1092C4×Q8—794no—
1093C4×Q8—798no—
1094C4×Q8—792no—
1095C4×Q8—792no—
1096C4×Q8—792no—
1097C4×Q8—792no—
1098C4×Q8—794no—
1099C4×Q8C22×D7912yes—
1100C4×Q8C22×D7912yes—
1101C4×Q8C22×D7914yes—
1102C4×D4—794no—
1103C4×D4—798no—
1104C4×D4—794no—
1105C4×D4—798no—
1106C4×D4—798no—
1107C4×D4—794no—
1108C4×D4—794no—
1109C4×D4—794no—
1110C4×D4—798no—
1111C4×D4—794no—
1112C4×D4—798no—
1113C4×D4—798no—
1114C4×D4—794no—
1115C4×D4—794no—
1116C4×D4—794no—
1117C4×D4—798no—
1118C4×D4—798no—
1119C4×D4—798no—
1120C4×D4—798no—
1121C4×D4—798no—
1122C4×D4—798no—
1123C4×D4—794no—
1124C4×D4—794no—
1125C4×D4—794no—
1126C4×D4—794no—
1127C4×D4—798no—
1128C4×D4—798no—
1129C4×D4—798no—
1130C4×D4—798no—
1131C4×D4—792no—
1132C4×D4—798no—
1133C4×D4—794no—
1134C4×D4—794no—
1135C4×D4—794no—
1136C4×D4—794no—
1137C4×D4—794no—
1138C4×D4—798no—
1139C4×D4—794no—
1140C4×D4—794no—
1141C4×D4—792no—
1142C4×D4—792no—
1143C4×D4—792no—
1144C4×D4—798no—
1145C4×D4C22×D7914yes—
1146C4×D4C22×D7912yes—
1147C4×D4C22×D7914yes—
1148C4×D4C22×D7912yes—
1149C4×D4C22×D7914yes—
1150C4×D4C22×D7914yes—
1151C4×D4C22×D7914yes—
1152#117—792no—
1153#117—791no—
1154#117—791no—
1155#117—792no—
1156#117—792no—
1157#117—794no—
1158#117—794no—
1159#117—794no—
1160#117—794no—
1161#117—798no—
1162#117—798no—
1163#117—794no—
1164#117—794no—
1165#117—798no—
1166#117—792no—
1167#117—792no—
1168#117—792no—
1169#117—792no—
1170#117—798no—
1171#117—798no—
1172#117C22×D7911yescharacteristic
1173#117C22×D7911yescharacteristic
1174#117C22×D7911yescharacteristic
1175#117C22×D7911yescharacteristic
1176#117C22×D7912yes—
1177#117C22×D7912yes—
1178#117C22×D7912yes—
1179#117C22×D7914yes—
1180C2×C4⋊C4—792no—
1181C2×C4⋊C4—792no—
1182C2×C4⋊C4—794no—
1183C2×C4⋊C4—794no—
1184C2×C4⋊C4—794no—
1185C2×C4⋊C4—794no—
1186C2×C4⋊C4—794no—
1187C2×C4⋊C4—798no—
1188C2×C4⋊C4—798no—
1189C2×C4⋊C4C22×D7912yes—
1190C2×C22⋊C4—792no—
1191C2×C22⋊C4—794no—
1192C2×C22⋊C4—798no—
1193C2×C22⋊C4—794no—
1194C2×C22⋊C4—794no—
1195C2×C22⋊C4—794no—
1196C2×C22⋊C4—798no—
1197C2×C22⋊C4—798no—
1198C2×C22⋊C4—798no—
1199C2×C22⋊C4—798no—
1200C2×C22⋊C4C22×D7912yes—
1201C2×C42—792no—
1202C2×C42—792no—
1203C2×C42—792no—
1204C2×C42—792no—
1205C2×C42—792no—
1206C2×C42—798no—
1207C2×C42C22×D7911yescharacteristic
1208C2×C42C22×D7911yescharacteristic
1209C2×C42C22×D7914yes—
1210C24—798no—
1211C24—794no—
1212C24—792no—
1213C24C23×D7911yescharacteristic
1214#41—28no—
1215#41—798no—
1216#41—6328no—
1217#41—6328no—
1218#41—6328no—
1219#41—1588no—
1220#41—1588no—
1221#41—1584no—
1222#41—1584no—
1223#41—15816no—
1224#41—15816no—
1225#41—1584no—
1226C2×Q8—798no—
1227C2×Q8—791no—
1228C2×Q8—792no—
1229C2×Q8—791no—
1230C2×Q8—1584no—
1231C2×Q8C23×D7912yes—
1232C2×Q8C23×D7914yes—
1233C2×D4—798no—
1234C2×D4—798no—
1235C2×D4—798no—
1236C2×D4—798no—
1237C2×D4—798no—
1238C2×D4—792no—
1239C2×D4—792no—
1240C2×D4—792no—
1241C2×D4—798no—
1242C2×D4—792no—
1243C2×D4—798no—
1244C2×D4—798no—
1245C2×D4—798no—
1246C2×D4—798no—
1247C2×D4—791no—
1248C2×D4—792no—
1249C2×D4—798no—
1250C2×D4—794no—
1251C2×D4—794no—
1252C2×D4—791no—
1253C2×D4—6324no—
1254C2×D4—6328no—
1255C2×D4—6328no—
1256C2×D4—6324no—
1257C2×D4—1584no—
1258C2×D4—15816no—
1259C2×D4—15816no—
1260C2×D4—15832no—
1261C2×D4—1588no—
1262C2×D4—1588no—
1263C2×D4C23×D7914yes—
1264C2×D4C23×D7912yes—
1265C2×D4C23×D7914yes—
1266C2×D4C23×D7914yes—
1267C2×D4C23×D7914yes—
1268C22×C4—24no—
1269C22×C4—794no—
1270C22×C4—794no—
1271C22×C4—798no—
1272C22×C4—794no—
1273C22×C4—798no—
1274C22×C4—794no—
1275C22×C4—794no—
1276C22×C4—794no—
1277C22×C4—798no—
1278C22×C4—798no—
1279C22×C4—798no—
1280C22×C4—798no—
1281C22×C4—792no—
1282C22×C4—792no—
1283C22×C4—792no—
1284C22×C4—798no—
1285C22×C4—792no—
1286C22×C4—792no—
1287C22×C4—6328no—
1288C22×C4—6324no—
1289C22×C4—1588no—
1290C22×C4C23×D7911yescharacteristic
1291C22×C4C23×D7914yes—
1292C22×C4C23×D7911yescharacteristic
1293C22×C4C23×D7911yescharacteristic
1294C22×C4C23×D7911yescharacteristic
1295C22×C4C23×D7911yescharacteristic
1296C22×C4C23×D7912yes—
1297C22×C4C23×D7914yes—
1298C22×C4C23×D7912yes—
1299C22×C4C23×D7914yes—
1300C22×C4C23×D7911yescharacteristic
1301C4⋊C4—794no—
1302C4⋊C4—798no—
1303C4⋊C4—798no—
1304C4⋊C4—794no—
1305C4⋊C4—794no—
1306C4⋊C4—794no—
1307C4⋊C4—798no—
1308C4⋊C4—798no—
1309C4⋊C4—798no—
1310C4⋊C4—798no—
1311C4⋊C4—792no—
1312C4⋊C4—794no—
1313C4⋊C4—794no—
1314C4⋊C4—794no—
1315C4⋊C4—798no—
1316C4⋊C4—792no—
1317C4⋊C4—798no—
1318C4⋊C4C23×D7912yes—
1319C4⋊C4C23×D7912yes—
1320C4⋊C4C23×D7912yes—
1321C4⋊C4C23×D7914yes—
1322C4⋊C4C23×D7914yes—
1323C4⋊C4C23×D7912yes—
1324C4⋊C4C23×D7912yes—
1325C4⋊C4C23×D7912yes—
1326C4⋊C4C23×D7914yes—
1327C4⋊C4C23×D7914yes—
1328C4⋊C4C23×D7914yes—
1329C4⋊C4C23×D7914yes—
1330C4⋊C4C23×D7914yes—
1331C4⋊C4C23×D7914yes—
1332C22⋊C4—792no—
1333C22⋊C4—794no—
1334C22⋊C4—798no—
1335C22⋊C4—792no—
1336C22⋊C4—798no—
1337C22⋊C4—794no—
1338C22⋊C4—798no—
1339C22⋊C4—798no—
1340C22⋊C4—798no—
1341C22⋊C4—798no—
1342C22⋊C4—798no—
1343C22⋊C4—798no—
1344C22⋊C4—794no—
1345C22⋊C4—794no—
1346C22⋊C4—794no—
1347C22⋊C4—798no—
1348C22⋊C4—798no—
1349C22⋊C4—798no—
1350C22⋊C4—798no—
1351C22⋊C4—798no—
1352C22⋊C4—798no—
1353C22⋊C4C23×D7912yes—
1354C22⋊C4C23×D7912yes—
1355C22⋊C4C23×D7914yes—
1356C22⋊C4C23×D7914yes—
1357C22⋊C4C23×D7914yes—
1358C22⋊C4C23×D7914yes—
1359C22⋊C4C23×D7912yes—
1360C22⋊C4C23×D7912yes—
1361C22⋊C4C23×D7914yes—
1362C22⋊C4C23×D7914yes—
1363C22⋊C4C23×D7914yes—
1364C22⋊C4C23×D7914yes—
1365C22⋊C4C23×D7914yes—
1366C42—794no—
1367C42—792no—
1368C42—792no—
1369C42—798no—
1370C42—794no—
1371C42—794no—
1372C42—794no—
1373C42—798no—
1374C42—794no—
1375C42C23×D7911yescharacteristic
1376C42C23×D7911yescharacteristic
1377C42C23×D7911yescharacteristic
1378C42C23×D7911yescharacteristic
1379C42C23×D7914yes—
1380C42C23×D7912yes—
1381C42C23×D7914yes—
1382C42C23×D7914yes—
1383C42C23×D7912yes—
1384C23—22no—
1385C23—42no—
1386C23—3164no—
1387C23—3168no—
1388C23—3164no—
1389C23—3168no—
1390C23—3164no—
1391C23—792no—
1392C23—798no—
1393C23—792no—
1394C23—1584no—
1395C23—15816no—
1396C23—1588no—
1397C23C24×D7911yescharacteristic
1398C23C24×D7914yes—
1399C23C24×D7911yescharacteristic
1400C23C24×D7911yescharacteristic
1401Q8—24no—
1402Q8—44no—
1403Q8—3168no—
1404Q8—794no—
1405Q8—1584no—
1406Q8—1582no—
1407D4—28no—
1408D4—24no—
1409D4—44no—
1410D4—44no—
1411D4—44no—
1412D4—3168no—
1413D4—3168no—
1414D4—3168no—
1415D4—3168no—
1416D4—3168no—
1417D4—3168no—
1418D4—3168no—
1419D4—3168no—
1420D4—3168no—
1421D4—798no—
1422D4—794no—
1423D4—15816no—
1424D4—1584no—
1425D4—15816no—
1426D4—1584no—
1427D4—1584no—
1428D4—1584no—
1429D4—1588no—
1430D4—1588no—
1431D4—1582no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—28no—
1438C2×C4—42no—
1439C2×C4—44no—
1440C2×C4—42no—
1441C2×C4—44no—
1442C2×C4—3164no—
1443C2×C4—3168no—
1444C2×C4—3168no—
1445C2×C4—3168no—
1446C2×C4—3168no—
1447C2×C4—3164no—
1448C2×C4—3164no—
1449C2×C4—3168no—
1450C2×C4—3164no—
1451C2×C4—3164no—
1452C2×C4—3168no—
1453C2×C4—3164no—
1454C2×C4—792no—
1455C2×C4—798no—
1456C2×C4—794no—
1457C2×C4—792no—
1458C2×C4—794no—
1459C2×C4—798no—
1460C2×C4—1584no—
1461C2×C4—15816no—
1462C2×C4—1584no—
1463C2×C4—1584no—
1464C2×C4—1584no—
1465C2×C4#41×D7914yes—
1466C2×C4C24×D7911yescharacteristic
1467C2×C4C24×D7912yes—
1468C2×C4C24×D7912yes—
1469C2×C4C24×D7914yes—
1470C2×C4C24×D7914yes—
1471C2×C4C24×D7912yes—
1472C2×C4C24×D7912yes—
1473C2×C4C24×D7914yes—
1474C2×C4C24×D7911yescharacteristic
1475C2×C4C24×D7911yescharacteristic
1476C2×C4C24×D7911yescharacteristic
1477C22—22no—
1478C22—21no—
1479C22—21no—
1480C22—24no—
1481C22—24no—
1482C22—24no—
1483C22—22no—
1484C22—22no—
1485C22—82no—
1486C22—794no—
1487C22—6328no—
1488C22—6324no—
1489C22—63216no—
1490C22—1582no—
1491C22—1588no—
1492C22—1588no—
1493C22—1584no—
1494C22—1588no—
1495C22—1584no—
1496C22C2×#41×D7912yes—
1497C22C25×D7911yescharacteristic
1498C4—21no—
1499C4—21no—
1500C4—24no—
1501C4—22no—
1502C4—22no—
1503C4—24no—
1504C4—22no—
1505C4—24no—
1506C4—22no—
1507C4—794no—
1508C4—1582no—
1509C4—1584no—
1510C4—1588no—
1511C4—1584no—
1512C4C2×#41×D7912yes—
1513C4C2×#41×D7912yes—
1514C2—22no—
1515C2—41no—
1516C2—41no—
1517C2—44no—
1518C2—3168no—
1519C2—3162no—
1520C2—1584no—
1521C2C22×#41×D7911yescharacteristic
1522C2#2377821112yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3455C2
hypercenter#3455D79
hypocenterC79#62858
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3455

Complements

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

NH ≅ G/Ntype
1. #23777505C2semidirect
2. #23777434C2semidirect
3. #23777424C2semidirect
4. #23777404C2semidirect
5. #23777344C2semidirect
6. #23777330C2semidirect
7. #23777323C2semidirect
8. #23777320C2semidirect
9. #23777277C2semidirect
10. #23777272C2semidirect
11. #23777221C2semidirect
12. #23777173C2semidirect
13. #23777137C2semidirect
14. #23777133C2semidirect
15. #23777061C2semidirect
16. #23776820C2semidirect
17. #23776816C2semidirect
18. #23776791C2semidirect
19. C2×#19099168C2semidirect
20. #540×D79C2semidirect
21. C4×#14579207C2semidirect
22. #23776601C2semidirect
23. C79×#3455C2semidirect
26. #19099298C22semidirect
27. #19099297C22semidirect
28. #19099291C22semidirect
29. #19099278C22semidirect
30. #19099275C22semidirect
31. #19099273C22semidirect
32. #19099267C22semidirect
33. #19099266C22semidirect
34. #19099264C22semidirect
35. #19099264C22semidirect
36. #19099264C22semidirect
37. #19099259C22semidirect
38. #19099259C22semidirect
39. #19099259C22semidirect
40. #19099258C22semidirect
41. #19099256C22semidirect
42. #19099253C22semidirect
43. #19099245C22semidirect
44. #19099240C22semidirect
45. #19099238C22semidirect
46. #19099236C22semidirect
47. #19099235C22semidirect
48. #19099234C22semidirect
49. #19099234C22semidirect
50. #19099231C22semidirect
51. #19099222C22semidirect
52. #19099217C22semidirect
53. #19099215C22semidirect
54. #19099209C22semidirect
55. #19099206C22semidirect
56. #19099205C22semidirect
57. #19099205C22semidirect
58. #19099205C22semidirect
59. #19099204C22semidirect
60. #19099202C22semidirect
61. #19099200C22semidirect
62. D4×D316C22semidirect
63. D4×D316C22semidirect
64. #19099197C22semidirect
65. #19099195C22semidirect
66. #19099191C22semidirect
67. #19099190C22semidirect
68. #19099186C22semidirect
69. #19099185C22semidirect
70. #19099184C22semidirect
71. #19099183C22semidirect
72. #19099174C22semidirect
73. #19099169C22semidirect
74. #19099169C22semidirect
75. #19099168C22semidirect
76. #19099168C22semidirect
77. #19099168C22semidirect
78. #19099168C22semidirect
79. #19099168C22semidirect
80. #19099168C22semidirect
81. #19099168C22semidirect
82. #19099167C22semidirect
83. #19099166C22semidirect
84. #19099165C22semidirect
85. #19099165C22semidirect
86. #19099164C22semidirect
87. #19099163C22semidirect
88. #19099161C22semidirect
89. #19099152C22semidirect
90. #19099152C22semidirect
91. #19099147C22semidirect
92. #19099146C22semidirect
93. #19099143C22semidirect
94. #19099141C22semidirect
95. #19099132C22semidirect
96. #19099131C22semidirect
97. #19099129C22semidirect
98. #19099127C22semidirect
99. #19099119C22semidirect
100. #19099114C22semidirect
101. #19099114C22semidirect
102. #19099113C22semidirect
103. #19099112C22semidirect
104. #19099110C22semidirect
105. #19099108C22semidirect
106. C2×#14579158C22semidirect
107. #127×D79C22semidirect
108. #19099100C22semidirect
109. #19099099C22semidirect
110. #19099098C22semidirect
111. #19099097C22semidirect
112. #19099096C22semidirect
113. #19099096C22semidirect
114. #19099092C22semidirect
115. C2×#14579153C22semidirect
116. #125×D79C22semidirect
117. #19099076C22semidirect
118. #19099076C22semidirect
119. #19099072C22semidirect
120. #19099071C22semidirect
121. C2×#14579146C22semidirect
122. #123×D79C22semidirect
123. C2×#14579135C22semidirect
124. C2×#14579134C22semidirect
125. #121×D79C22semidirect
126. #121×D79C22semidirect
127. #19099046C22semidirect
128. #19099045C22semidirect
129. #19099044C22semidirect
131. #19099043C22semidirect
132. #19099043C22semidirect
133. #19099043C22semidirect
134. #19099040C22semidirect
135. #19099037C22semidirect
136. #19099037C22semidirect
137. #19099037C22semidirect
138. #19099036C22semidirect
139. #19099035C22semidirect
140. #19099035C22semidirect
141. C4×#11929625C22semidirect
144. C4×#11929624C22semidirect
145. C4×#11929624C22semidirect
146. C4×#11929624C22semidirect
147. #19099031C22semidirect
148. #19099031C22semidirect
149. C2×C4×D316C22semidirect
150. C2×C4×D316C22semidirect
151. C4×D4×D79C22semidirect
152. C4×D4×D79C22semidirect
153. C2×#14579120C22semidirect
154. #117×D79C22semidirect
155. #117×D79C22semidirect
156. #542×C79C22semidirect
157. #542×C79C22semidirect
158. #541×C79C22semidirect
159. #541×C79C22semidirect
160. #540×C79C22semidirect
161. #540×C79C22semidirect
162. #539×C79C22semidirect
163. #538×C79C22semidirect
164. #533×C79C22semidirect
165. #532×C79C22semidirect
166. #529×C79C22semidirect
167. #529×C79C22semidirect
168. #525×C79C22semidirect
169. C4×#41×C79C22semidirect
170. C2×#117×C79C22semidirect
460. #11929624#41semidirect
780. #3455D79semidirect
785. C79#62858semidirect
834. #542C2×D79semidirect
835. #542C2×D79semidirect
837. #541C2×D79semidirect
838. #541C2×D79semidirect
854. #540C2×D79semidirect
855. #540C2×D79semidirect
857. #539C2×D79semidirect
862. #538C2×D79semidirect
870. #533C2×D79semidirect
877. #532C2×D79semidirect
887. #529C2×D79semidirect
888. #529C2×D79semidirect
895. #525C2×D79semidirect
924. C4×#41C2×D79semidirect
932. C2×#117C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237775052
#237774342
#237774242
#237774042
#237773442
#237773302
#237773232
#237773202
#237772772
#237772722
#237772212
#237771732
#237771372
#237771332
#237770612
#237768202
#237768162
#237767912
C2×#190991682
#540×D792
C4×#145792072
#237766012
C79×#34552
#6285879