Finite Group Databasebeta

← #35197299

Subgroups — #35197299

Order 20224.

7102 conjugacy classes of subgroups.

The subgroup lattice has 1574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777266C214yesmaximal, complemented
2#23777265C211yesmaximal, characteristic, complemented
3#23777264C212yesmaximal, complemented
4#23777261C214yesmaximal, complemented
5#23777254C211yesmaximal, characteristic, complemented
6#23777253C214yesmaximal, complemented
7#23777249C211yesmaximal, characteristic, complemented
8#23777248C214yesmaximal, complemented
9#23777245C212yesmaximal, complemented
10#23777118C214yesmaximal, complemented
11#23777114C214yesmaximal, complemented
12#23777112C214yesmaximal, complemented
13#23777108C214yesmaximal, complemented
14#23777105C214yesmaximal, complemented
15#23777100C214yesmaximal, complemented
16#23776810C214yesmaximal, complemented
17#23776808C214yesmaximal, complemented
18#23776803C211yesmaximal, characteristic, complemented
19#23776732C212yesmaximal, complemented
20#23776727C211yesmaximal, characteristic, complemented
21C2×#19099045C211yesmaximal, characteristic, complemented
22#520×D79C212yesmaximal, complemented
23C79×#3507C211yesmaximal, characteristic, complemented
24C22×#11929625C2211yescharacteristic
25C2×#41×D79C2212yes—
26#19099298C2214yescomplemented
27#19099298C2214yescomplemented
28#19099298C2212yescomplemented
29#19099296C2214yescomplemented
30#19099295C2214yescomplemented
31#19099295C2214yescomplemented
32#19099291C2212yescomplemented
33#19099288C2214yescomplemented
34#19099287C2212yescomplemented
35#19099287C2214yescomplemented
36#19099286C2212yescomplemented
37#19099286C2212yescomplemented
38#19099285C2218yescomplemented
39#19099285C2214yescomplemented
40#19099285C2214yescomplemented
41#19099284C2214yescomplemented
42#19099282C2214yescomplemented
43#19099280C2218yescomplemented
44#19099279C2212yescomplemented
45#19099278C2212yescomplemented
46#19099276C2218yescomplemented
47#19099276C2214yescomplemented
48#19099275C2218yescomplemented
49#19099273C2212yescomplemented
50#19099271C2214yescomplemented
51#19099269C2218yescomplemented
52#19099267C2218yescomplemented
53#19099266C2214yescomplemented
54#19099264C2218yescomplemented
55#19099264C2218yescomplemented
56#19099262C2218yescomplemented
57#19099261C2214yescomplemented
58#19099259C2214yescomplemented
59#19099258C2218yescomplemented
60#19099257C2214yescomplemented
61#19099255C2214yescomplemented
62#19099254C2214yescomplemented
63#19099249C2218yescomplemented
64#19099247C2214yescomplemented
65#19099246C2218yescomplemented
66#19099245C2218yescomplemented
67#19099245C2218yescomplemented
68#19099235C2212yescomplemented
69#19099234C2214yescomplemented
70#19099233C2212yescomplemented
71#19099217C2212yescomplemented
72#19099216C2212yescomplemented
73#19099215C2218yescomplemented
74#19099214C2214yescomplemented
75#19099211C2218yescomplemented
76#19099193C2212yescomplemented
77#19099193C2212yescomplemented
78#19099192C2212yescomplemented
79#19099192C2212yescomplemented
80#19099190C2212yescomplemented
81#19099190C2212yescomplemented
82#19099188C2212yes—
83#19099188C2212yes—
84#19099161C2218yescomplemented
85#19099161C2218yescomplemented
86#19099160C2214yescomplemented
87#19099159C2218yescomplemented
88#19099157C2218yescomplemented
89#19099154C2218yescomplemented
90#19099153C2214yescomplemented
91#19099152C2218yescomplemented
92#19099152C2218yescomplemented
93#19099150C2214yescomplemented
94#19099149C2218yescomplemented
95#19099147C2218yescomplemented
96#19099146C2218yescomplemented
97#19099143C2214yes—
98#19099143C2214yes—
99#19099140C2212yes—
100#19099140C2212yes—
101#19099138C2212yescomplemented
102#19099138C2214yescomplemented
103#19099137C2212yescomplemented
104#19099133C2212yescomplemented
105#19099132C2212yescomplemented
106#19099131C2212yescomplemented
107#19099131C2214yescomplemented
108#19099127C2212yescomplemented
109#19099126C2212yescomplemented
110#19099124C2218yes—
111#19099121C2212yes—
112#19099121C2212yes—
113#19099120C2211yescharacteristic, complemented
114#19099117C2214yescomplemented
115#19099117C2214yescomplemented
116#19099116C2212yescomplemented
117#19099114C2214yes—
118#19099113C2211yescharacteristic
119#19099112C2214yes—
120#19099109C2212yes—
121#19099100C2218yescomplemented
122#19099098C2218yescomplemented
123#19099097C2214yescomplemented
124#19099096C2218yescomplemented
125#19099091C2218yescomplemented
126#19099090C2218yescomplemented
127#19099076C2214yescomplemented
128#19099076C2218yescomplemented
129#19099076C2214yescomplemented
130#19099076C2214yescomplemented
131#19099075C2218yescomplemented
132#19099073C2214yescomplemented
133#19099072C2218yescomplemented
134#19099072C2218yescomplemented
135#19099072C2214yescomplemented
136#19099072C2214yescomplemented
137#19099071C2218yescomplemented
138#19099071C2218yescomplemented
139#19099046C2212yescomplemented
140#19099045C2214yescomplemented
141#19099045C2214yescomplemented
142#19099045C2214yescomplemented
143#19099045C2214yescomplemented
144#19099045C2214yescomplemented
145#19099044C2214yescomplemented
146#19099044C2212yescomplemented
147#19099043C2214yescomplemented
148#19099043C2212yescomplemented
149#19099042C2218yescomplemented
150#19099042C2214yescomplemented
151C2×Q8×Dic79C2211yescharacteristic, complemented
152C4×Q8×D79C2214yescomplemented
153C2×C4×D316C2212yes—
154C2×C4×D316C2211yescharacteristic, complemented
155C2×#14579123C2212yes—
156C2×#14579123C2211yescharacteristic, complemented
157C4×D4×D79C2218yes—
158C4×D4×D79C2214yescomplemented
159C2×#14579118C2211yescharacteristic
160C2×#14579118C2212yescomplemented
161#117×D79C2212yes—
162#117×D79C2214yescomplemented
163C2×C4⋊C4×D79C2211yescharacteristic
164C2×C4⋊C4×D79C2214yescomplemented
165C2×C4⋊C4×D79C2212yescomplemented
166#559×C79C2212yescomplemented
167#557×C79C2212yescomplemented
168#556×C79C2212yescomplemented
169#556×C79C2214yescomplemented
170#554×C79C2212yescomplemented
171#552×C79C2214yescomplemented
172#539×C79C2214yescomplemented
173#536×C79C2212yescomplemented
174#533×C79C2211yescharacteristic, complemented
175#532×C79C2211yescharacteristic
176#529×C79C2214yescomplemented
177#520×C79C2212yescomplemented
178C2×C4×Q8×C79C2211yescharacteristic, complemented
179C2×#11929625—28no—
180C2×#11929625C2314yes—
181C2×#11929625C2312yes—
182C2×#11929625C2314yes—
183C2×#11929625C2314yes—
184C2×#11929624C2312yes—
185C2×#11929624C2314yes—
186C2×#11929624C2318yes—
187C2×#11929623C2314yes—
188C2×#11929623C2312yes—
189C2×#11929623C2314yes—
190#41×D79—216no—
191C2×Q8×D79C2312yes—
192C22×D316C2312yes—
193C22×D316C2311yescharacteristic
194C2×D4×D79C2314yes—
195C2×D4×D79C2312yes—
196C22×C4×D79C2314yes—
197C22×C4×D79C2312yes—
198C22×C4×D79C2312yes—
199C22×C4×D79C2318yes—
200C22×C4×D79C2312yes—
201C22×C4×D79C2312yes—
202C22×C4×D79C2311yescharacteristic
203#14579161C2311yescharacteristic
204#14579161C2311yescharacteristic
205#14579161C2311yescharacteristic
206#14579160C2312yes—
207#14579160C2312yes—
208#14579160C2314yes—
209#14579160C2314yes—
210#14579159C2314yes—
211#14579159C2312yes—
212#14579159C2314yes—
213#14579159C2314yes—
214#14579158C2314yes—
215#14579158C2311yescharacteristic
216#14579157C2314yes—
217#14579157C2312yes—
218#14579156C2318yes—
219#14579156C2318yes—
220#14579156C2318yes—
221#14579156C2318yes—
222#14579156C2318yes—
223#14579156C2318yes—
224#14579155C2318yes—
225#14579155C2318yes—
226#14579154C2318yes—
227#14579154C2318yes—
228#14579153C2314yes—
229#14579153C2312yes—
230#14579152C2318yes—
231#14579152C2312yes—
232#14579152C2312yes—
233#14579151C2318yes—
234#14579151C2318yes—
235#14579151C2318yes—
236#14579151C2314yes—
237#14579151C2314yes—
238#14579151C2314yes—
239#14579151C2314yes—
240#14579150C2314yes—
241#14579150C2314yes—
242#14579150C2312yes—
243#14579150C2318yes—
244#14579149C2312yes—
245#14579149C2314yes—
246#14579149C2318yes—
247#14579149C2314yes—
248#14579148C2312yes—
249#14579147C2318yes—
250#14579147C2318yes—
251#14579147C2318yes—
252#14579146C2318yes—
253#14579146C2318yes—
254#14579146C2314yes—
255#14579146C2314yes—
256#14579146C2318yes—
257#14579146C2318yes—
258#14579146C2318yes—
259#14579146C2318yes—
260#14579146C2318yes—
261#14579145C2318yes—
262#14579145C2318yes—
263#14579144C2318yes—
264#14579144C2318yes—
265#14579143C2318yes—
266#14579143C2318yes—
267#14579143C2318yes—
268#14579143C2314yes—
269#14579143C2314yes—
270#14579141C2314yes—
271#14579141C2314yes—
272#14579141C2318yes—
273#14579141C2314yes—
274#14579140C2312yes—
275#14579140C2312yes—
276#14579139C2314yes—
277#14579139C2314yes—
278#14579139C2318yes—
279#14579139C2318yes—
280#14579139C2314yes—
281#14579139C2314yes—
282#14579139C2318yes—
283#14579139C2318yes—
284#14579139C2314yes—
285#14579139C2314yes—
286#14579138C2314yes—
287#14579138C2314yes—
288#14579138C2314yes—
289#14579138C2318yes—
290#14579138C2314yes—
291#14579137C2314yes—
292#14579137C2314yes—
293#14579137C2314yes—
294#14579137C2314yes—
295#14579137C2314yes—
296#14579136C2318yes—
297#14579136C2318yes—
298#14579136C2314yes—
299#14579136C2314yes—
300#14579136C2314yes—
301#14579136C2318yes—
302#14579135C2312yes—
303#14579135C2312yes—
304#14579135C2314yes—
305#14579135C2314yes—
306#14579135C2318yes—
307#14579134C2314yes—
308#14579134C2314yes—
309#14579134C2318yes—
310#14579134C2318yes—
311#14579134C2318yes—
312#14579134C2318yes—
313#14579134C2318yes—
314#14579134C2318yes—
315#14579133C2314yes—
316#14579133C2314yes—
317#14579133C2314yes—
318#14579133C2314yes—
319#14579133C2318yes—
320#14579132C2314yes—
321#14579131C2318yes—
322#14579131C2318yes—
323#14579131C2318yes—
324#14579131C2314yes—
325#14579131C2314yes—
326#14579129C2318yes—
327#14579129C2314yes—
328#14579129C2314yes—
329Q8×Dic79C2314yes—
330Q8×Dic79C2314yes—
331Q8×Dic79C2314yes—
332C4×Dic158C2312yes—
333C4×Dic158C2314yes—
334C4×Dic158C2318yes—
335C4×Dic158C2314yes—
336C4×Dic158C2314yes—
337C4×Dic158C2314yes—
338C4×Dic158C2312yes—
339#14579126C2318yes—
340#14579126C2318yes—
341#14579126C2314yes—
342C4×D316C2318yes—
343C4×D316C2318yes—
344C4×D316C2318yes—
345C4×D316C2312yes—
346C4×D316C2312yes—
347C4×D316C2312yes—
348C4×D316C2312yes—
349C4×D316C2314yes—
350C4×D316C2312yes—
351C4×D316C2318yes—
352C4×D316C2314yes—
353C4×D316C2312yes—
354D4×Dic79C2318yes—
355D4×Dic79C2314yes—
356#14579123C2318yes—
357#14579123C2318yes—
358#14579123C2318yes—
359#14579123C2314yes—
360#14579123C2318yes—
361#14579123C2314yes—
362#14579123C2314yes—
363#14579123C2318yes—
364#14579123C2318yes—
365C4×C22⋊D79C2318yes—
366C4×C22⋊D79C2318yes—
367C4×C22⋊D79C2314yes—
368C4×C22⋊D79C2318yes—
369C4×C22⋊D79C2314yes—
370C4×C22⋊D79C2318yes—
371(C22⋊D79)⋊C4C2318yes—
372(C22⋊D79)⋊C4C2318yes—
373(C22⋊D79)⋊C4C2318yes—
374(C22⋊D79)⋊C4C2318yes—
375(C22⋊D79)⋊C4C2318yes—
376(C22⋊D79)⋊C4C2318yes—
377(C22⋊D79)⋊C4C2318yes—
378#14579120C2312yes—
379#14579120C2314yes—
380#14579119C2312yes—
381#14579119C2312yes—
382#14579119C2314yes—
383#14579119C2318yes—
384#14579119C2314yes—
385#14579119C2314yes—
386#14579119C2314yes—
387#14579118C2314yes—
388#14579118C2312yes—
389#14579118C2312yes—
390#14579118C2312yes—
391#14579118C2318yes—
392#14579118C2318yes—
393#14579118C2318yes—
394#14579118C2318yes—
395#14579118C2318yes—
396#14579118C2312yes—
397#14579117C2314yes—
398#14579117C2318yes—
399#14579117C2318yes—
400C2×C4⋊Dic79C2312yes—
401C2×C4⋊Dic79C2314yes—
402C2×C4⋊Dic79C2311yescharacteristic
403C2×Dic79⋊C4C2311yescharacteristic
404C2×Dic79⋊C4C2311yescharacteristic
405C2×Dic79⋊C4C2318yes—
406C2×Dic79⋊C4C2312yes—
407C4⋊C4×D79C2312yes—
408C4⋊C4×D79C2312yes—
409C4⋊C4×D79C2318yes—
410C4⋊C4×D79C2318yes—
411C4⋊C4×D79C2314yes—
412C4⋊C4×D79C2318yes—
413C4⋊C4×D79C2318yes—
414C4⋊C4×D79C2314yes—
415C4⋊C4×D79C2314yes—
416C4⋊C4×D79C2314yes—
417C2×(C2×D79)⋊C4C2312yes—
418C2×(C2×D79)⋊C4C2312yes—
419C2×(C2×D79)⋊C4C2311yescharacteristic
420C2×(C2×D79)⋊C4C2311yescharacteristic
421C22⋊C4×D79C2318yes—
422C22⋊C4×D79C2314yes—
423C2×C4×Dic79C2311yescharacteristic
424C2×C4×Dic79C2312yes—
425C42×D79C2314yes—
426C42×D79C2318yes—
427C2×#41×C79C2312yes—
428C22×Q8×C79C2311yescharacteristic
429C4⋊Q8×C79C2311yescharacteristic
430C4⋊Q8×C79C2314yes—
431C4⋊Q8×C79C2311yescharacteristic
432C4⋊Q8×C79C2311yescharacteristic
433#127×C79C2311yescharacteristic
434#126×C79C2318yes—
435#126×C79C2318yes—
436#125×C79C2314yes—
437#125×C79C2318yes—
438#125×C79C2312yes—
439#124×C79C2314yes—
440#124×C79C2312yes—
441#124×C79C2314yes—
442#123×C79C2318yes—
443#123×C79C2318yes—
444C22⋊Q8×C79C2314yes—
445C22⋊Q8×C79C2314yes—
446C22⋊Q8×C79C2312yes—
447C22⋊Q8×C79C2318yes—
448C22⋊Q8×C79C2312yes—
449#121×C79C2312yes—
450#121×C79C2312yes—
451C4×Q8×C79C2312yes—
452C4×Q8×C79C2312yes—
453C4×Q8×C79C2312yes—
454C4×Q8×C79C2312yes—
455C4×Q8×C79C2312yes—
456C4×Q8×C79C2314yes—
457C4×Q8×C79C2314yes—
458C4×Q8×C79C2312yes—
459C4×D4×C79C2318yes—
460C4×D4×C79C2312yes—
461C4×D4×C79C2314yes—
462C4×D4×C79C2314yes—
463C4×D4×C79C2312yes—
464#117×C79C2312yes—
465#117×C79C2314yes—
466#117×C79C2318yes—
467C2×C4⋊C4×C79C2312yes—
468C2×C4⋊C4×C79C2314yes—
469C2×C4⋊C4×C79C2311yescharacteristic
470C2×C42×C79C2312yes—
471C2×C42×C79C2311yescharacteristic
472C23×D79C2414yes—
473C23×D79C2412yes—
474C23×D79C2411yescharacteristic
475#11929625—28no—
476#11929625—216no—
477#11929625—216no—
478#11929625—84no—
479#11929624—216no—
480#11929624—28no—
481#11929624—88no—
482#11929623—216no—
483#11929623—28no—
484#11929623—84no—
485C2×Dic158C2414yes—
486C2×Dic158C2412yes—
487C2×Dic158C2412yes—
488C2×Dic158C2414yes—
489C2×Dic158C2414yes—
490C2×Dic158C2412yes—
491Q8×D79—28no—
492C2×D316—28no—
493C2×D316—24no—
494C2×D316C2414yes—
495C2×D316C2412yes—
496C2×D316C2418yes—
497C2×D316C2412yes—
498C2×D316C2412yes—
499C2×D316C2418yes—
500C2×D316C2412yes—
501C2×D316C2418yes—
502C2×D316C2412yes—
503C2×C22⋊D79C2414yes—
504C2×C22⋊D79C2414yes—
505C2×C22⋊D79C2414yes—
506C2×C22⋊D79C2418yes—
507C2×C22⋊D79C2414yes—
508C2×C22⋊D79C2418yes—
509C2×C22⋊D79C2414yes—
510D4×D79—28no—
511D4×D79—216no—
512C22×Dic79C2414yes—
513C22×Dic79C2418yes—
514C22×Dic79C2411yescharacteristic
515C22×Dic79C2412yes—
516C22×Dic79C2411yescharacteristic
517C22×Dic79C2411yescharacteristic
518C2×C4×D79—28no—
519C2×C4×D79—216no—
520C2×C4×D79—82no—
521C2×C4×D79—82no—
522C2×C4×D79—82no—
523C2×C4×D79—88no—
524C2×C4×D79#4118yescomplemented
525C2×C4×D79C2414yes—
526C2×C4×D79C2414yes—
527C2×C4×D79C2414yes—
528C2×C4×D79C2418yes—
529C2×C4×D79C2414yes—
530C2×C4×D79C2418yes—
531C2×C4×D79C2418yes—
532C2×C4×D79C2418yes—
533C2×C4×D79C2414yes—
534C2×C4×D79C2414yes—
535C2×C4×D79C2418yes—
536C2×C4×D79C2414yes—
537C2×C4×D79C2412yes—
538C2×C4×D79C2412yes—
539C4⋊Dic79C2412yes—
540C4⋊Dic79C2412yes—
541C4⋊Dic79C2412yes—
542C4⋊Dic79C2418yes—
543C4⋊Dic79C2418yes—
544C4⋊Dic79C2412yes—
545C4⋊Dic79C2412yes—
546C4⋊Dic79C2412yes—
547C4⋊Dic79C2414yes—
548C4⋊Dic79C2414yes—
549C4⋊Dic79C2412yes—
550C4⋊Dic79C2412yes—
551Dic79⋊C4C2418yes—
552Dic79⋊C4C2412yes—
553Dic79⋊C4C2412yes—
554Dic79⋊C4C2414yes—
555Dic79⋊C4C2418yes—
556Dic79⋊C4C2418yes—
557Dic79⋊C4C2414yes—
558Dic79⋊C4C2412yes—
559Dic79⋊C4C2412yes—
560Dic79⋊C4C2414yes—
561Dic79⋊C4C2418yes—
562Dic79⋊C4C2414yes—
563Dic79⋊C4C2414yes—
564Dic79⋊C4C2414yes—
565Dic79⋊C4C2414yes—
566Dic79⋊C4C2414yes—
567Dic79⋊C4C2418yes—
568Dic79⋊C4C2414yes—
569Dic79⋊C4C2414yes—
570C22⋊Dic79C2414yes—
571C22⋊Dic79C2418yes—
572C22⋊Dic79C2414yes—
573C22⋊Dic79C2414yes—
574(C2×D79)⋊C4C2414yes—
575(C2×D79)⋊C4C2418yes—
576(C2×D79)⋊C4C2414yes—
577(C2×D79)⋊C4C2418yes—
578(C2×D79)⋊C4C2412yes—
579(C2×D79)⋊C4C2412yes—
580(C2×D79)⋊C4C2418yes—
581(C2×D79)⋊C4C2412yes—
582(C2×D79)⋊C4C2412yes—
583(C2×D79)⋊C4C2414yes—
584(C2×D79)⋊C4C2414yes—
585(C2×D79)⋊C4C2414yes—
586(C2×D79)⋊C4C2418yes—
587(C2×D79)⋊C4C2418yes—
588(C2×D79)⋊C4C2418yes—
589(C2×D79)⋊C4C2414yes—
590(C2×D79)⋊C4C2418yes—
591(C2×D79)⋊C4C2418yes—
592(C2×D79)⋊C4C2418yes—
593(C2×D79)⋊C4C2414yes—
594(C2×D79)⋊C4C2414yes—
595C4×Dic79C2418yes—
596C4×Dic79C2418yes—
597C4×Dic79C2414yes—
598C4×Dic79C2414yes—
599C4×Dic79C2418yes—
600C4×Dic79C2414yes—
601C4×Dic79C2418yes—
602C4×Dic79C2412yes—
603C4×Dic79C2412yes—
604#41×C79—28no—
605C2×Q8×C79—24no—
606C2×Q8×C79C2412yes—
607C2×Q8×C79C2412yes—
608C2×Q8×C79C2412yes—
609C2×Q8×C79C2412yes—
610C2×Q8×C79C2412yes—
611C2×D4×C79C2414yes—
612C2×D4×C79C2412yes—
613C2×D4×C79C2412yes—
614C2×D4×C79C2412yes—
615C22×C4×C79C2414yes—
616C22×C4×C79C2412yes—
617C22×C4×C79C2418yes—
618C22×C4×C79C2411yescharacteristic
619C22×C4×C79C2412yes—
620C22×C4×C79C2411yescharacteristic
621C22×C4×C79C2411yescharacteristic
622C4⋊C4×C79C2412yes—
623C4⋊C4×C79C2412yes—
624C4⋊C4×C79C2412yes—
625C4⋊C4×C79C2418yes—
626C4⋊C4×C79C2414yes—
627C4⋊C4×C79C2414yes—
628C4⋊C4×C79C2412yes—
629C4⋊C4×C79C2414yes—
630C4⋊C4×C79C2418yes—
631C4⋊C4×C79C2412yes—
632C4⋊C4×C79C2412yes—
633C4⋊C4×C79C2412yes—
634C4⋊C4×C79C2414yes—
635C4⋊C4×C79C2418yes—
636C4⋊C4×C79C2412yes—
637C22⋊C4×C79C2414yes—
638C22⋊C4×C79C2414yes—
639C22⋊C4×C79C2418yes—
640C22⋊C4×C79C2418yes—
641C22⋊C4×C79C2414yes—
642C22⋊C4×C79C2418yes—
643C42×C79C2414yes—
644C42×C79C2411yescharacteristic
645C42×C79C2411yescharacteristic
646C42×C79C2414yes—
647C42×C79C2411yescharacteristic
648C42×C79C2411yescharacteristic
649C42×C79C2418yes—
650C42×C79C2414yes—
651C23×C79C2514yes—
652C23×C79C2511yescharacteristic
653C22×D79—24no—
654C22×D79—28no—
655C22×D79—41no—
656C22×D79—44no—
657C22×D79—42no—
658C22×D79—41no—
659C22×D79—44no—
660C22×D79—42no—
661C22×D79C2×#4114yes—
662C22×D79C2514yes—
663C22×D79C2514yes—
664C22×D79C2512yes—
665Q8×C79—24no—
666Q8×C79—24no—
667Q8×C79—24no—
668Q8×C79—42no—
669Q8×C79—42no—
670D4×C79—28no—
671D4×C79—24no—
672D4×C79—42no—
673D4×C79—42no—
674C2×C4×C79—24no—
675C2×C4×C79—28no—
676C2×C4×C79—42no—
677C2×C4×C79—41no—
678C2×C4×C79—48no—
679C2×C4×C79—41no—
680C2×C4×C79C2×#4114yes—
681C2×C4×C79C2514yes—
682C2×C4×C79C2514yes—
683C2×C4×C79C2514yes—
684C2×C4×C79C2514yes—
685C2×C4×C79C2514yes—
686C2×C4×C79C2511yescharacteristic
687C2×C4×C79C2511yescharacteristic
688C2×C4×C79C2511yescharacteristic
689C2×C4×C79C2511yescharacteristic
690C2×C4×C79C2511yescharacteristic
691C2×C4×C79C2511yescharacteristic
692C22⋊D79—28no—
693C22⋊D79—28no—
694C22⋊D79—28no—
695C22⋊D79—48no—
696C22⋊D79—44no—
697C22⋊D79—48no—
698C22⋊D79—44no—
699C2×Dic79—28no—
700C2×Dic79—41no—
701C2×Dic79—42no—
702C2×Dic79—48no—
703C2×Dic79—41no—
704C2×Dic79C2×#4114yes—
705C2×Dic79C2512yes—
706C2×Dic79C2514yes—
707C2×Dic79C2514yes—
708C2×Dic79C2514yes—
709C2×Dic79C2514yes—
710C2×Dic79C2512yes—
711C2×Dic79C2512yes—
712D316—28no—
713D316—216no—
714D316—24no—
715D316—24no—
716D316—24no—
717D316—42no—
718D316—48no—
719D316—48no—
720D316—42no—
721C4×D79—28no—
722C4×D79—28no—
723C4×D79—28no—
724C4×D79—216no—
725C4×D79—44no—
726C4×D79—48no—
727C4×D79—44no—
728C4×D79—48no—
729C4×D79—48no—
730C4×D79—48no—
731C4×D79—44no—
732C4×D79—44no—
733C4×D79C2×#4118yes—
734C4×D79C2×#4118yes—
735Dic158—24no—
736Dic158—28no—
737Dic158—42no—
738Dic158—44no—
739Dic158—42no—
740Dic158—44no—
741C22×C79—21no—
742C22×C79—21no—
743C22×C79—24no—
744C22×C79—24no—
745C22×C79—24no—
746C22×C79C22×#4112yes—
747C22×C79C2611yescharacteristic
748C2×D79—22no—
749C2×D79—22no—
750C2×D79—24no—
751C2×D79—24no—
752C2×D79—24no—
753C2×D79—24no—
754C2×D79—24no—
755C2×D79—24no—
756C2×D79—44no—
757C2×D79—416no—
758C2×D79—48no—
759C2×D79C22×#4114yes—
760C4×C79—24no—
761C4×C79—24no—
762C4×C79—24no—
763C4×C79—24no—
764C4×C79—21no—
765C4×C79—21no—
766C4×C79—21no—
767C4×C79—21no—
768C4×C79—24no—
769C4×C79C22×#4112yes—
770C4×C79C22×#4112yes—
771Dic79—24no—
772Dic79—22no—
773Dic79—24no—
774Dic79—24no—
775Dic79—24no—
776Dic79—22no—
777Dic79C22×#4114yes—
778#62845—791nomaximal, Sylow
779C2×C79—22no—
780C2×C79—44no—
781C2×C79C23×#4111yescharacteristic
782C2×C79H(7,𝔽2)11yescharacteristic
783C2×C792−1+611yescharacteristic
784D79—24no—
785D79—44no—
786D79—44no—
787#3507—794no—
788#3507—794no—
789#3507—792no—
790#3507—791no—
791#3507D7911yescharacteristic, complemented
792#3506—794no—
793#3506—794no—
794#3506—791no—
795#3506—791no—
796#3506—792no—
797#3493—794no—
798#3493—794no—
799#3493—794no—
800#3492—794no—
801#3492—794no—
802#3492—794no—
803#3459—794no—
804#3459—794no—
805#3458—791no—
806#3449—792no—
807#3449—791no—
808C2×#520—792no—
809C2×#520—791no—
810C79#6284511yescharacteristic, complemented, Sylow
811C22×#41—792no—
812C22×#41—791no—
813#559—794no—
814#559—794no—
815#559—794no—
816#559—792no—
817#559—794no—
818#559—794no—
819#559C2×D7912yescomplemented
820#557—794no—
821#557—792no—
822#557C2×D7912yescomplemented
823#556—794no—
824#556—792no—
825#556—798no—
826#556—794no—
827#556—794no—
828#556—798no—
829#556—794no—
830#556—794no—
831#556—792no—
832#556—792no—
833#556C2×D7912yescomplemented
834#556C2×D7914yescomplemented
835#555—792no—
836#555—798no—
837#555—792no—
838#555—794no—
839#555—798no—
840#554—798no—
841#554—798no—
842#554—794no—
843#554—792no—
844#554C2×D7912yescomplemented
845#553—798no—
846#553—798no—
847#553—794no—
848#553—798no—
849#553—794no—
850#553—798no—
851#553—794no—
852#553—794no—
853#552—798no—
854#552—798no—
855#552—798no—
856#552—794no—
857#552—794no—
858#552—794no—
859#552—798no—
860#552C2×D7914yescomplemented
861#550—792no—
862#550—792no—
863#550—794no—
864#547—792no—
865#547—798no—
866#547—798no—
867#547—792no—
868#547—794no—
869#544—792no—
870#544—792no—
871#544—792no—
872#544—792no—
873#544—792no—
874#544—792no—
875#543—792no—
876#543—792no—
877#539—798no—
878#539—798no—
879#539—798no—
880#539—798no—
881#539—798no—
882#539—794no—
883#539C2×D7914yescomplemented
884#538—798no—
885#538—798no—
886#538—798no—
887#538—798no—
888#538—794no—
889#538—794no—
890#538—798no—
891#537—794no—
892#537—794no—
893#537—792no—
894#537—792no—
895#536—792no—
896#536—794no—
897#536—792no—
898#536—792no—
899#536C2×D7912yescomplemented
900#535—792no—
901#535—792no—
902#535—794no—
903#535—792no—
904#535—792no—
905#534—798no—
906#534—792no—
907#534—792no—
908#533—794no—
909#533—794no—
910#533—792no—
911#533—791no—
912#533C2×D7911yescharacteristic, complemented
913#532—792no—
914#532—794no—
915#532—794no—
916#532—791no—
917#532C2×D7911yescharacteristic
918#529—798no—
919#529—798no—
920#529—798no—
921#529—798no—
922#529—798no—
923#529—794no—
924#529C2×D7914yescomplemented
925#525—798no—
926#525—798no—
927#525—794no—
928#525—794no—
929#525—798no—
930#525—794no—
931#525—794no—
932#525—794no—
933#525—794no—
934#525—798no—
935#525—798no—
936#525—798no—
937#520—792no—
938#520—794no—
939#520—794no—
940#520—794no—
941#520—794no—
942#520—794no—
943#520—798no—
944#520—794no—
945#520—794no—
946#520—792no—
947#520—794no—
948#520—792no—
949#520C2×D7912yescomplemented
950C2×C4×Q8—791no—
951C2×C4×Q8—794no—
952C2×C4×Q8C2×D7911yescharacteristic, complemented
953C2×C4×D4—798no—
954C2×C4×D4—794no—
955C2×C4×D4—792no—
956C2×C4×D4—791no—
957C2×C4×D4—792no—
958C2×C4×D4—791no—
959C2×#117—792no—
960C2×#117—794no—
961C2×#117—791no—
962C2×#117—792no—
963C22×C4⋊C4—791no—
964C22×C4⋊C4—792no—
965C22×C4⋊C4—794no—
966C2×#41—794no—
967C2×#41—794no—
968C2×#41—792no—
969C2×#41—794no—
970C2×#41—794no—
971C2×#41—794no—
972C2×#41—792no—
973C2×#41—798no—
974C2×#41—794no—
975C2×#41—792no—
976C2×#41—1588no—
977C2×#41—15816no—
978C2×#41C22×D7912yes—
979C22×Q8—792no—
980C22×Q8C22×D7911yescharacteristic
981C22×D4—794no—
982C22×D4—792no—
983C22×D4—792no—
984C22×D4—791no—
985C23×C4—791no—
986C23×C4—792no—
987C23×C4—792no—
988C23×C4—792no—
989C23×C4—798no—
990C23×C4—792no—
991C23×C4—794no—
992C4⋊Q8—792no—
993C4⋊Q8—794no—
994C4⋊Q8—794no—
995C4⋊Q8—794no—
996C4⋊Q8—794no—
997C4⋊Q8—792no—
998C4⋊Q8—794no—
999C4⋊Q8—792no—
1000C4⋊Q8—791no—
1001C4⋊Q8—791no—
1002C4⋊Q8—791no—
1003C4⋊Q8C22×D7914yes—
1004C4⋊Q8C22×D7911yescharacteristic
1005C4⋊Q8C22×D7911yescharacteristic
1006C4⋊Q8C22×D7911yescharacteristic
1007#127—792no—
1008#127—794no—
1009#127—794no—
1010#127—791no—
1011#127C22×D7911yescharacteristic
1012#126—798no—
1013#126—798no—
1014#126—798no—
1015#126—798no—
1016#126—798no—
1017#126—798no—
1018#126—798no—
1019#126—798no—
1020#126—798no—
1021#126—798no—
1022#126C22×D7918yes—
1023#126C22×D7918yes—
1024#125—798no—
1025#125—798no—
1026#125—798no—
1027#125—798no—
1028#125—794no—
1029#125—794no—
1030#125—794no—
1031#125—794no—
1032#125—792no—
1033#125—792no—
1034#125—794no—
1035#125—792no—
1036#125C22×D7918yes—
1037#125C22×D7914yes—
1038#125C22×D7912yes—
1039#124—798no—
1040#124—792no—
1041#124—794no—
1042#124—794no—
1043#124—792no—
1044#124—798no—
1045#124—798no—
1046#124—798no—
1047#124—798no—
1048#124—794no—
1049#124—794no—
1050#124—792no—
1051#124C22×D7914yes—
1052#124C22×D7914yes—
1053#124C22×D7912yes—
1054#123—798no—
1055#123—798no—
1056#123—798no—
1057#123—794no—
1058#123—794no—
1059#123—798no—
1060#123—798no—
1061#123—798no—
1062#123—798no—
1063#123—798no—
1064#123—798no—
1065#123—794no—
1066#123—794no—
1067#123—798no—
1068#123—798no—
1069#123—798no—
1070#123—798no—
1071#123—798no—
1072#123C22×D7918yes—
1073#123C22×D7918yes—
1074C22⋊Q8—794no—
1075C22⋊Q8—794no—
1076C22⋊Q8—794no—
1077C22⋊Q8—794no—
1078C22⋊Q8—794no—
1079C22⋊Q8—792no—
1080C22⋊Q8—792no—
1081C22⋊Q8—794no—
1082C22⋊Q8—794no—
1083C22⋊Q8—794no—
1084C22⋊Q8—794no—
1085C22⋊Q8—798no—
1086C22⋊Q8—798no—
1087C22⋊Q8—794no—
1088C22⋊Q8—798no—
1089C22⋊Q8—798no—
1090C22⋊Q8—794no—
1091C22⋊Q8—798no—
1092C22⋊Q8—794no—
1093C22⋊Q8—794no—
1094C22⋊Q8—794no—
1095C22⋊Q8—794no—
1096C22⋊Q8—794no—
1097C22⋊Q8—794no—
1098C22⋊Q8—798no—
1099C22⋊Q8—794no—
1100C22⋊Q8C22×D7912yes—
1101C22⋊Q8C22×D7914yes—
1102C22⋊Q8C22×D7914yes—
1103C22⋊Q8C22×D7918yes—
1104C22⋊Q8C22×D7912yes—
1105#121—794no—
1106#121—794no—
1107#121—794no—
1108#121—794no—
1109#121—798no—
1110#121—794no—
1111#121—792no—
1112#121—794no—
1113#121—794no—
1114#121—798no—
1115#121—792no—
1116#121—798no—
1117#121—794no—
1118#121—794no—
1119#121—794no—
1120#121—798no—
1121#121—798no—
1122#121—798no—
1123#121—798no—
1124#121—794no—
1125#121—798no—
1126#121—794no—
1127#121—798no—
1128#121—798no—
1129#121—798no—
1130#121C22×D7912yes—
1131#121C22×D7912yes—
1132#120—798no—
1133#120—794no—
1134#120—794no—
1135#120—798no—
1136#120—794no—
1137#120—798no—
1138#120—794no—
1139#120—798no—
1140C4×Q8—794no—
1141C4×Q8—794no—
1142C4×Q8—794no—
1143C4×Q8—798no—
1144C4×Q8—794no—
1145C4×Q8—798no—
1146C4×Q8—798no—
1147C4×Q8—794no—
1148C4×Q8—794no—
1149C4×Q8—794no—
1150C4×Q8—792no—
1151C4×Q8—794no—
1152C4×Q8—792no—
1153C4×Q8C22×D7914yes—
1154C4×Q8C22×D7912yes—
1155C4×Q8C22×D7912yes—
1156C4×Q8C22×D7912yes—
1157C4×Q8C22×D7912yes—
1158C4×Q8C22×D7914yes—
1159C4×Q8C22×D7912yes—
1160C4×Q8C22×D7912yes—
1161C4×D4—798no—
1162C4×D4—794no—
1163C4×D4—798no—
1164C4×D4—798no—
1165C4×D4—798no—
1166C4×D4—798no—
1167C4×D4—794no—
1168C4×D4—794no—
1169C4×D4—798no—
1170C4×D4—798no—
1171C4×D4—798no—
1172C4×D4—794no—
1173C4×D4—794no—
1174C4×D4—794no—
1175C4×D4—798no—
1176C4×D4—798no—
1177C4×D4—798no—
1178C4×D4—798no—
1179C4×D4—798no—
1180C4×D4—798no—
1181C4×D4—798no—
1182C4×D4—798no—
1183C4×D4—798no—
1184C4×D4—798no—
1185C4×D4—798no—
1186C4×D4—798no—
1187C4×D4—798no—
1188C4×D4—792no—
1189C4×D4—792no—
1190C4×D4—794no—
1191C4×D4—792no—
1192C4×D4—792no—
1193C4×D4—798no—
1194C4×D4—794no—
1195C4×D4—792no—
1196C4×D4—792no—
1197C4×D4C22×D7918yes—
1198C4×D4C22×D7914yes—
1199C4×D4C22×D7914yes—
1200C4×D4C22×D7912yes—
1201C4×D4C22×D7912yes—
1202#117—792no—
1203#117—794no—
1204#117—792no—
1205#117—792no—
1206#117—794no—
1207#117—794no—
1208#117—794no—
1209#117—794no—
1210#117—798no—
1211#117—794no—
1212#117—798no—
1213#117—798no—
1214#117—792no—
1215#117—792no—
1216#117—794no—
1217#117—792no—
1218#117—792no—
1219#117—798no—
1220#117—798no—
1221#117—798no—
1222#117—798no—
1223#117—798no—
1224#117C22×D7912yes—
1225#117C22×D7914yes—
1226#117C22×D7918yes—
1227C2×C4⋊C4—792no—
1228C2×C4⋊C4—791no—
1229C2×C4⋊C4—791no—
1230C2×C4⋊C4—792no—
1231C2×C4⋊C4—798no—
1232C2×C4⋊C4—794no—
1233C2×C4⋊C4—791no—
1234C2×C4⋊C4—794no—
1235C2×C4⋊C4—792no—
1236C2×C4⋊C4—794no—
1237C2×C4⋊C4—798no—
1238C2×C4⋊C4—798no—
1239C2×C4⋊C4—798no—
1240C2×C4⋊C4—798no—
1241C2×C4⋊C4—794no—
1242C2×C4⋊C4—794no—
1243C2×C4⋊C4—792no—
1244C2×C4⋊C4C22×D7911yescharacteristic
1245C2×C4⋊C4C22×D7912yes—
1246C2×C4⋊C4C22×D7914yes—
1247C2×C22⋊C4—791no—
1248C2×C22⋊C4—791no—
1249C2×C22⋊C4—792no—
1250C2×C22⋊C4—792no—
1251C2×C22⋊C4—794no—
1252C2×C22⋊C4—798no—
1253C2×C42—792no—
1254C2×C42—791no—
1255C2×C42—798no—
1256C2×C42—794no—
1257C2×C42C22×D7912yes—
1258C2×C42C22×D7911yescharacteristic
1259C24—791no—
1260C24—794no—
1261C24—792no—
1262#41—28no—
1263#41—6328no—
1264#41—6324no—
1265#41—6324no—
1266#41—15816no—
1267#41—15816no—
1268#41—1588no—
1269#41—15816no—
1270#41—15816no—
1271#41—1588no—
1272#41—1588no—
1273C2×Q8—24no—
1274C2×Q8—794no—
1275C2×Q8—792no—
1276C2×Q8—794no—
1277C2×Q8—792no—
1278C2×Q8—794no—
1279C2×Q8—792no—
1280C2×Q8—1588no—
1281C2×Q8C23×D7912yes—
1282C2×Q8C23×D7912yes—
1283C2×Q8C23×D7912yes—
1284C2×Q8C23×D7912yes—
1285C2×Q8C23×D7912yes—
1286C2×D4—798no—
1287C2×D4—794no—
1288C2×D4—798no—
1289C2×D4—794no—
1290C2×D4—794no—
1291C2×D4—794no—
1292C2×D4—794no—
1293C2×D4—798no—
1294C2×D4—792no—
1295C2×D4—798no—
1296C2×D4—792no—
1297C2×D4—794no—
1298C2×D4—798no—
1299C2×D4—792no—
1300C2×D4—792no—
1301C2×D4—792no—
1302C2×D4—1588no—
1303C2×D4—1588no—
1304C2×D4—15816no—
1305C2×D4—1584no—
1306C2×D4C23×D7914yes—
1307C2×D4C23×D7912yes—
1308C2×D4C23×D7912yes—
1309C2×D4C23×D7912yes—
1310C22×C4—791no—
1311C22×C4—792no—
1312C22×C4—791no—
1313C22×C4—798no—
1314C22×C4—794no—
1315C22×C4—798no—
1316C22×C4—794no—
1317C22×C4—798no—
1318C22×C4—794no—
1319C22×C4—794no—
1320C22×C4—798no—
1321C22×C4—798no—
1322C22×C4—791no—
1323C22×C4—798no—
1324C22×C4—792no—
1325C22×C4—792no—
1326C22×C4—794no—
1327C22×C4—794no—
1328C22×C4—794no—
1329C22×C4—798no—
1330C22×C4—794no—
1331C22×C4—6322no—
1332C22×C4—6322no—
1333C22×C4—6322no—
1334C22×C4—6328no—
1335C22×C4—1588no—
1336C22×C4—15816no—
1337C22×C4C23×D7912yes—
1338C22×C4C23×D7914yes—
1339C22×C4C23×D7911yescharacteristic
1340C22×C4C23×D7912yes—
1341C22×C4C23×D7911yescharacteristic
1342C22×C4C23×D7918yes—
1343C22×C4C23×D7911yescharacteristic
1344C4⋊C4—798no—
1345C4⋊C4—794no—
1346C4⋊C4—792no—
1347C4⋊C4—792no—
1348C4⋊C4—798no—
1349C4⋊C4—798no—
1350C4⋊C4—794no—
1351C4⋊C4—792no—
1352C4⋊C4—792no—
1353C4⋊C4—794no—
1354C4⋊C4—798no—
1355C4⋊C4—794no—
1356C4⋊C4—794no—
1357C4⋊C4—794no—
1358C4⋊C4—794no—
1359C4⋊C4—794no—
1360C4⋊C4—794no—
1361C4⋊C4—794no—
1362C4⋊C4—798no—
1363C4⋊C4—792no—
1364C4⋊C4—792no—
1365C4⋊C4—792no—
1366C4⋊C4—798no—
1367C4⋊C4—798no—
1368C4⋊C4—792no—
1369C4⋊C4—792no—
1370C4⋊C4—794no—
1371C4⋊C4—792no—
1372C4⋊C4—794no—
1373C4⋊C4—792no—
1374C4⋊C4—792no—
1375C4⋊C4C23×D7912yes—
1376C4⋊C4C23×D7912yes—
1377C4⋊C4C23×D7912yes—
1378C4⋊C4C23×D7914yes—
1379C4⋊C4C23×D7914yes—
1380C4⋊C4C23×D7918yes—
1381C4⋊C4C23×D7912yes—
1382C4⋊C4C23×D7912yes—
1383C4⋊C4C23×D7912yes—
1384C4⋊C4C23×D7918yes—
1385C4⋊C4C23×D7914yes—
1386C4⋊C4C23×D7914yes—
1387C4⋊C4C23×D7918yes—
1388C4⋊C4C23×D7912yes—
1389C4⋊C4C23×D7912yes—
1390C22⋊C4—794no—
1391C22⋊C4—798no—
1392C22⋊C4—794no—
1393C22⋊C4—794no—
1394C22⋊C4—794no—
1395C22⋊C4—792no—
1396C22⋊C4—792no—
1397C22⋊C4—794no—
1398C22⋊C4—792no—
1399C22⋊C4—792no—
1400C22⋊C4—798no—
1401C22⋊C4—798no—
1402C22⋊C4—798no—
1403C22⋊C4—794no—
1404C22⋊C4—794no—
1405C22⋊C4—798no—
1406C22⋊C4—794no—
1407C22⋊C4—798no—
1408C22⋊C4—798no—
1409C22⋊C4—794no—
1410C22⋊C4—798no—
1411C22⋊C4—794no—
1412C22⋊C4—798no—
1413C22⋊C4—794no—
1414C22⋊C4—798no—
1415C22⋊C4C23×D7914yes—
1416C22⋊C4C23×D7918yes—
1417C22⋊C4C23×D7918yes—
1418C22⋊C4C23×D7914yes—
1419C22⋊C4C23×D7918yes—
1420C22⋊C4C23×D7914yes—
1421C42—798no—
1422C42—798no—
1423C42—798no—
1424C42—798no—
1425C42—794no—
1426C42—794no—
1427C42—792no—
1428C42—794no—
1429C42—792no—
1430C42C23×D7918yes—
1431C42C23×D7914yes—
1432C42C23×D7914yes—
1433C42C23×D7914yes—
1434C42C23×D7911yescharacteristic
1435C42C23×D7911yescharacteristic
1436C42C23×D7911yescharacteristic
1437C42C23×D7911yescharacteristic
1438C23—3162no—
1439C23—3161no—
1440C23—3164no—
1441C23—3162no—
1442C23—3161no—
1443C23—3164no—
1444C23—794no—
1445C23—792no—
1446C23—794no—
1447C23—794no—
1448C23—1588no—
1449C23—1584no—
1450C23C24×D7914yes—
1451C23C24×D7911yescharacteristic
1452Q8—24no—
1453Q8—24no—
1454Q8—24no—
1455Q8—42no—
1456Q8—42no—
1457Q8—3164no—
1458Q8—3162no—
1459Q8—3162no—
1460Q8—3164no—
1461Q8—1588no—
1462Q8—1584no—
1463D4—28no—
1464D4—24no—
1465D4—42no—
1466D4—42no—
1467D4—3168no—
1468D4—3162no—
1469D4—3162no—
1470D4—3168no—
1471D4—3168no—
1472D4—3164no—
1473D4—3168no—
1474D4—3164no—
1475D4—1588no—
1476D4—15816no—
1477D4—1588no—
1478D4—1588no—
1479D4—1588no—
1480D4—1584no—
1481D4—1584no—
1482D4—1584no—
1483C2×C4—24no—
1484C2×C4—28no—
1485C2×C4—42no—
1486C2×C4—41no—
1487C2×C4—48no—
1488C2×C4—41no—
1489C2×C4—3168no—
1490C2×C4—3164no—
1491C2×C4—3168no—
1492C2×C4—3168no—
1493C2×C4—3168no—
1494C2×C4—3164no—
1495C2×C4—3164no—
1496C2×C4—3164no—
1497C2×C4—3162no—
1498C2×C4—3161no—
1499C2×C4—3168no—
1500C2×C4—3161no—
1501C2×C4—792no—
1502C2×C4—794no—
1503C2×C4—798no—
1504C2×C4—798no—
1505C2×C4—794no—
1506C2×C4—792no—
1507C2×C4—794no—
1508C2×C4—794no—
1509C2×C4—794no—
1510C2×C4—792no—
1511C2×C4—1588no—
1512C2×C4—15816no—
1513C2×C4—1588no—
1514C2×C4—1588no—
1515C2×C4—1588no—
1516C2×C4#41×D7914yes—
1517C2×C4C24×D7914yes—
1518C2×C4C24×D7914yes—
1519C2×C4C24×D7914yes—
1520C2×C4C24×D7914yes—
1521C2×C4C24×D7914yes—
1522C2×C4C24×D7911yescharacteristic
1523C2×C4C24×D7911yescharacteristic
1524C2×C4C24×D7911yescharacteristic
1525C2×C4C24×D7911yescharacteristic
1526C2×C4C24×D7911yescharacteristic
1527C2×C4C24×D7911yescharacteristic
1528C22—21no—
1529C22—21no—
1530C22—24no—
1531C22—24no—
1532C22—24no—
1533C22—3168no—
1534C22—3164no—
1535C22—31616no—
1536C22—794no—
1537C22—1584no—
1538C22—1584no—
1539C22—1584no—
1540C22—1584no—
1541C22—1584no—
1542C22—1584no—
1543C22—1582no—
1544C22—1582no—
1545C22C2×#41×D7912yes—
1546C22C25×D7911yescharacteristic
1547C4—24no—
1548C4—24no—
1549C4—24no—
1550C4—24no—
1551C4—21no—
1552C4—21no—
1553C4—21no—
1554C4—21no—
1555C4—24no—
1556C4—794no—
1557C4—1584no—
1558C4—1584no—
1559C4—1584no—
1560C4—1582no—
1561C4—1584no—
1562C4—1582no—
1563C4C2×#41×D7912yes—
1564C4C2×#41×D7912yes—
1565C2—22no—
1566C2—44no—
1567C2—3164no—
1568C2—3164no—
1569C2—1584no—
1570C2C22×#41×D7911yescharacteristic
1571C2#2377821111yescharacteristic
1572C2#2377821211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3507C2
hypercenter#3507D79
hypocenterC79#62845
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. #23777266C2semidirect
2. #23777265C2semidirect
3. #23777264C2semidirect
4. #23777261C2semidirect
5. #23777254C2semidirect
6. #23777253C2semidirect
7. #23777249C2semidirect
8. #23777248C2semidirect
9. #23777245C2semidirect
10. #23777118C2semidirect
11. #23777114C2semidirect
12. #23777112C2semidirect
13. #23777108C2semidirect
14. #23777105C2semidirect
15. #23777100C2semidirect
16. #23776810C2semidirect
17. #23776808C2semidirect
18. #23776803C2semidirect
19. #23776732C2semidirect
20. #23776727C2semidirect
21. C2×#19099045C2semidirect
22. #520×D79C2semidirect
23. C79×#3507C2semidirect
26. #19099298C22semidirect
27. #19099298C22semidirect
28. #19099298C22semidirect
29. #19099296C22semidirect
30. #19099295C22semidirect
31. #19099295C22semidirect
32. #19099291C22semidirect
33. #19099288C22semidirect
34. #19099287C22semidirect
35. #19099287C22semidirect
36. #19099286C22semidirect
37. #19099286C22semidirect
38. #19099285C22semidirect
39. #19099285C22semidirect
40. #19099285C22semidirect
41. #19099284C22semidirect
42. #19099282C22semidirect
43. #19099280C22semidirect
44. #19099279C22semidirect
45. #19099278C22semidirect
46. #19099276C22semidirect
47. #19099276C22semidirect
48. #19099275C22semidirect
49. #19099273C22semidirect
50. #19099271C22semidirect
51. #19099269C22semidirect
52. #19099267C22semidirect
53. #19099266C22semidirect
54. #19099264C22semidirect
55. #19099264C22semidirect
56. #19099262C22semidirect
57. #19099261C22semidirect
58. #19099259C22semidirect
59. #19099258C22semidirect
60. #19099257C22semidirect
61. #19099255C22semidirect
62. #19099254C22semidirect
63. #19099249C22semidirect
64. #19099247C22semidirect
65. #19099246C22semidirect
66. #19099245C22semidirect
67. #19099245C22semidirect
68. #19099235C22semidirect
69. #19099234C22semidirect
70. #19099233C22semidirect
71. #19099217C22semidirect
72. #19099216C22semidirect
73. #19099215C22semidirect
74. #19099214C22semidirect
75. #19099211C22semidirect
76. #19099193C22semidirect
77. #19099193C22semidirect
78. #19099192C22semidirect
79. #19099192C22semidirect
80. #19099190C22semidirect
81. #19099190C22semidirect
84. #19099161C22semidirect
85. #19099161C22semidirect
86. #19099160C22semidirect
87. #19099159C22semidirect
88. #19099157C22semidirect
89. #19099154C22semidirect
90. #19099153C22semidirect
91. #19099152C22semidirect
92. #19099152C22semidirect
93. #19099150C22semidirect
94. #19099149C22semidirect
95. #19099147C22semidirect
96. #19099146C22semidirect
101. #19099138C22semidirect
102. #19099138C22semidirect
103. #19099137C22semidirect
104. #19099133C22semidirect
105. #19099132C22semidirect
106. #19099131C22semidirect
107. #19099131C22semidirect
108. #19099127C22semidirect
109. #19099126C22semidirect
113. #19099120C22semidirect
114. #19099117C22semidirect
115. #19099117C22semidirect
116. #19099116C22semidirect
121. #19099100C22semidirect
122. #19099098C22semidirect
123. #19099097C22semidirect
124. #19099096C22semidirect
125. #19099091C22semidirect
126. #19099090C22semidirect
127. #19099076C22semidirect
128. #19099076C22semidirect
129. #19099076C22semidirect
130. #19099076C22semidirect
131. #19099075C22semidirect
132. #19099073C22semidirect
133. #19099072C22semidirect
134. #19099072C22semidirect
135. #19099072C22semidirect
136. #19099072C22semidirect
137. #19099071C22semidirect
138. #19099071C22semidirect
139. #19099046C22semidirect
140. #19099045C22semidirect
141. #19099045C22semidirect
142. #19099045C22semidirect
143. #19099045C22semidirect
144. #19099045C22semidirect
145. #19099044C22semidirect
146. #19099044C22semidirect
147. #19099043C22semidirect
148. #19099043C22semidirect
149. #19099042C22semidirect
150. #19099042C22semidirect
151. C2×Q8×Dic79C22semidirect
152. C4×Q8×D79C22semidirect
154. C2×C4×D316C22semidirect
156. C2×#14579123C22semidirect
158. C4×D4×D79C22semidirect
160. C2×#14579118C22semidirect
162. #117×D79C22semidirect
164. C2×C4⋊C4×D79C22semidirect
165. C2×C4⋊C4×D79C22semidirect
166. #559×C79C22semidirect
167. #557×C79C22semidirect
168. #556×C79C22semidirect
169. #556×C79C22semidirect
170. #554×C79C22semidirect
171. #552×C79C22semidirect
172. #539×C79C22semidirect
173. #536×C79C22semidirect
174. #533×C79C22semidirect
176. #529×C79C22semidirect
177. #520×C79C22semidirect
178. C2×C4×Q8×C79C22semidirect
524. C2×C4×D79#41semidirect
791. #3507D79semidirect
810. C79#62845semidirect
819. #559C2×D79semidirect
822. #557C2×D79semidirect
833. #556C2×D79semidirect
834. #556C2×D79semidirect
844. #554C2×D79semidirect
860. #552C2×D79semidirect
883. #539C2×D79semidirect
899. #536C2×D79semidirect
912. #533C2×D79semidirect
924. #529C2×D79semidirect
949. #520C2×D79semidirect
952. C2×C4×Q8C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237772662
#237772652
#237772642
#237772612
#237772542
#237772532
#237772492
#237772482
#237772452
#237771182
#237771142
#237771122
#237771082
#237771052
#237771002
#237768102
#237768082
#237768032
#237767322
#237767272
C2×#190990452
#520×D792
C79×#35072
#6284579