Finite Group Databasebeta

← #34448824

Subgroups — #34448824

Order 20224.

2698 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099075C211yesmaximal, characteristic
2#23766530C214yesmaximal, complemented
3#23766440C212yesmaximal, complemented
4#23766426C212yesmaximal, complemented
5#23766371C212yesmaximal, complemented
6#23766333C212yesmaximal, complemented
7#23766285C211yesmaximal, characteristic, complemented
8#23766240C211yesmaximal, characteristic, complemented
9#23766228C211yesmaximal, characteristic, complemented
10#23766053C214yesmaximal, complemented
11#23766031C212yesmaximal, complemented
12C4×#14579141C212yesmaximal, complemented
13#23765908C212yesmaximal, complemented
14#23765782C211yesmaximal, characteristic, complemented
15#23765760C212yesmaximal, complemented
16C4×C22⋊C4×D79C211yesmaximal, characteristic, complemented
17C79×#2347C211yesmaximal, characteristic, complemented
18C22×#11929624C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20#19099075C4116yescomplemented
21C2×#14579145C2212yes—
22C2×#14579141C2211yescharacteristic
23C2×#14579141C2211yescharacteristic
24C2×#14579136C2211yescharacteristic
25C2×#14579136C2211yescharacteristic
26C2×#14579131C2212yes—
27C2×C4×Dic158C2212yescomplemented
28C2×C4×D316C2212yes—
29C2×C4×D316C2212yes—
30C2×#14579123C2214yes—
31C2×#14579123C2212yescomplemented
32C2×#14579119C2212yes—
33C2×C22⋊C4×D79C2212yes—
34C2×C42×D79C2212yes—
35#19098468C2212yescomplemented
36#19098465C2214yes—
37#19098465C2212yescomplemented
38#19098463C2214yes—
39#19098462C2212yescomplemented
40#19098456C2214yes—
41#19098455C2214yescomplemented
42#19098453C2214yes—
43#19098453C2214yescomplemented
44#19098452C2214yes—
45#19098448C2214yescomplemented
46#19098446C2214yescomplemented
47#19098441C2214yes—
48#19098441C2214yes—
49#19098439C2214yes—
50#19098437C2214yes—
51#19098429C2212yescomplemented
52#19098425C2212yes—
53#19098425C2212yescomplemented
54#19098423C2211yescharacteristic
55#19098422C2212yescomplemented
56#19098420C2212yes—
57#19098418C2212yes—
58C4⋊C4×Dic79C2214yescomplemented
59C4⋊C4×Dic79C2212yescomplemented
60C4×C4⋊Dic79C2214yescomplemented
61C22⋊C4×Dic79C2212yes—
62C22⋊C4×Dic79C2212yes—
63C4×(C2×D79)⋊C4C2214yes—
64C4×(C2×D79)⋊C4C2212yes—
65C4×(C2×D79)⋊C4C2214yescomplemented
66C4×C22⋊Dic79C2211yescharacteristic
67#19098410C2212yes—
68#19098410C2211yescharacteristic
69#19098410C2211yescharacteristic
70#19098410C2212yescomplemented
71#19098410C2214yescomplemented
72#19098409C2212yescomplemented
73#95×D79C2211yescharacteristic
74#95×D79C2211yescharacteristic
75#95×D79C2212yescomplemented
76C2×#117×C79C2211yescharacteristic
77#389×C79C2212yescomplemented
78#388×C79C2214yes—
79#383×C79C2212yescomplemented
80#380×C79C2211yescharacteristic
81C4×C4⋊C4×C79C2212yescomplemented
82C4×C4⋊C4×C79C2212yescomplemented
83C4×C22⋊C4×C79C2211yescharacteristic
84C24×D79C2311yescharacteristic
85C2×#11929624—44no—
86C2×#11929624C2×C418yescomplemented
87C22×Dic158C2311yescharacteristic
88C22×D316C2312yes—
89C22×D316C2311yescharacteristic
90C22×D316C2312yes—
91C22×C22⋊D79C2312yes—
92C23×Dic79C2311yescharacteristic
93C22×C4×D79—44no—
94C22×C4×D79C2×C418yescomplemented
95C22×C4×D79C2311yescharacteristic
96C22×C4×D79C2311yescharacteristic
97C22×C4×D79C2312yes—
98C22×C4×D79C2314yes—
99C22×C4×D79C2311yescharacteristic
100C22×C4×D79C2312yes—
101C22×C4×D79C2311yescharacteristic
102C22×C4×D79C2312yes—
103#14579145C2×C4116yescomplemented
104#14579141C2×C418yescomplemented
105#14579141C2×C418yescomplemented
106#14579136C2×C418yes—
107#14579136C2×C418yescomplemented
108#14579131C2×C4116yescomplemented
109C4×Dic158—44no—
110C4×D316C2×C4116yescomplemented
111C4×D316C2×C4116yescomplemented
112#14579123—216no—
113#14579123—44no—
114#14579119—44no—
115C2×C4⋊Dic79C2312yes—
116C2×C4⋊Dic79C2314yes—
117C2×C4⋊Dic79C2312yes—
118C2×C4⋊Dic79C2312yes—
119C2×Dic79⋊C4C2314yes—
120C2×C22⋊Dic79C2312yes—
121C2×C22⋊Dic79C2312yes—
122C2×(C2×D79)⋊C4C2314yes—
123C2×(C2×D79)⋊C4C2312yes—
124C2×(C2×D79)⋊C4C2312yes—
125C2×(C2×D79)⋊C4C2314yes—
126C2×(C2×D79)⋊C4C2314yes—
127C2×(C2×D79)⋊C4C2314yes—
128C2×(C2×D79)⋊C4C2314yes—
129C2×(C2×D79)⋊C4C2312yes—
130C2×(C2×D79)⋊C4C2312yes—
131C2×(C2×D79)⋊C4C2312yes—
132C2×(C2×D79)⋊C4C2312yes—
133C22⋊C4×D79—28no—
134C2×C4×Dic79C2314yes—
135C2×C4×Dic79C2312yes—
136C2×C4×Dic79C2312yes—
137C2×C4×Dic79C2314yes—
138C2×C4×Dic79C2312yes—
139C2×C4×Dic79C2314yes—
140C42×D79—44no—
141C79⋊#95C2311yescharacteristic
142C79⋊#95C2311yescharacteristic
143C79⋊#95C2312yes—
144C79⋊#95C2312yes—
145C79⋊#95C2314yes—
146C79⋊#95C2312yes—
147C79⋊#95C2314yes—
148C79⋊#95C2314yes—
149C79⋊#95C2314yes—
150C79⋊#95C2314yes—
151C23×C4×C79C2311yescharacteristic
152#117×C79C2×C418yescomplemented
153C2×C4⋊C4×C79C2314yes—
154C2×C4⋊C4×C79C2312yes—
155C2×C4⋊C4×C79C2311yescharacteristic
156C2×C4⋊C4×C79C2311yescharacteristic
157C2×C22⋊C4×C79C2312yes—
158C2×C22⋊C4×C79C2312yes—
159C2×C22⋊C4×C79C2312yes—
160C2×C42×C79C2312yes—
161C2×C42×C79C2314yes—
162C2×C42×C79C2312yes—
163#95×C79C2311yescharacteristic
164#95×C79C2311yescharacteristic
165#95×C79C2312yes—
166#95×C79C2314yes—
167#95×C79C2314yes—
168C23×D79—24no—
169C23×D79—41no—
170C23×D79—41no—
171C23×D79—42no—
172C23×D79C22×C414yes—
173C23×D79C2411yescharacteristic
174C23×D79C2412yes—
175C23×D79C2411yescharacteristic
176#11929624—416no—
177C2×Dic158—24no—
178C2×Dic158C22×C414yes—
179C2×D316—28no—
180C2×D316—24no—
181C2×D316—42no—
182C2×D316—42no—
183C2×D316C22×C414yes—
184C2×D316C22×C418yes—
185C2×D316C22×C418yes—
186C2×C22⋊D79—44no—
187C2×C22⋊D79C22×C418yes—
188C22×Dic79—42no—
189C22×Dic79C22×C414yes—
190C22×Dic79C2412yes—
191C22×Dic79C2414yes—
192C22×Dic79C2412yes—
193C22×Dic79C2411yescharacteristic
194C22×Dic79C2411yescharacteristic
195C22×Dic79C2412yes—
196C2×C4×D79—28no—
197C2×C4×D79—24no—
198C2×C4×D79—24no—
199C2×C4×D79—24no—
200C2×C4×D79—44no—
201C2×C4×D79—42no—
202C2×C4×D79—42no—
203C2×C4×D79—42no—
204C2×C4×D79—42no—
205C2×C4×D79—42no—
206C2×C4×D79—42no—
207C2×C4×D79—44no—
208C2×C4×D79—44no—
209C2×C4×D79—416no—
210C2×C4×D79C22×C414yes—
211C2×C4×D79C22×C414yes—
212C2×C4×D79C22×C418yes—
213C2×C4×D79C22×C414yes—
214C2×C4×D79C22×C414yes—
215C2×C4×D79#4118yescomplemented
216C4⋊Dic79—24no—
217C4⋊Dic79—44no—
218C4⋊Dic79C22×C418yes—
219C4⋊Dic79C22×C418yes—
220Dic79⋊C4—44no—
221C22⋊Dic79—24no—
222C22⋊Dic79—42no—
223(C2×D79)⋊C4—24no—
224(C2×D79)⋊C4—28no—
225(C2×D79)⋊C4—24no—
226(C2×D79)⋊C4—28no—
227(C2×D79)⋊C4—44no—
228(C2×D79)⋊C4—44no—
229(C2×D79)⋊C4—44no—
230(C2×D79)⋊C4C22×C418yes—
231(C2×D79)⋊C4C22×C418yes—
232(C2×D79)⋊C4C22×C418yes—
233(C2×D79)⋊C4C22×C418yes—
234C4×Dic79—28no—
235C4×Dic79—24no—
236C4×Dic79—42no—
237C4×Dic79—42no—
238C4×Dic79—44no—
239C4×Dic79—44no—
240C24×C79C2411yescharacteristic
241C22×C4×C79—24no—
242C22×C4×C79C22×C414yes—
243C22×C4×C79C2412yes—
244C22×C4×C79C2414yes—
245C22×C4×C79C2411yescharacteristic
246C22×C4×C79C2412yes—
247C22×C4×C79C2412yes—
248C22×C4×C79C2412yes—
249C22×C4×C79C2411yescharacteristic
250C4⋊C4×C79—28no—
251C4⋊C4×C79—24no—
252C4⋊C4×C79C22×C414yes—
253C4⋊C4×C79C22×C414yes—
254C22⋊C4×C79—24no—
255C22⋊C4×C79—42no—
256C22⋊C4×C79C22×C418yes—
257C42×C79—24no—
258C42×C79—44no—
259C42×C79C22×C418yes—
260C23×C79—22no—
261C23×C79—22no—
262C23×C79—21no—
263C23×C79—21no—
264C23×C79C23×C412yes—
265C23×C79C2511yescharacteristic
266C22×D79—22no—
267C22×D79—21no—
268C22×D79—21no—
269C22×D79—22no—
270C22×D79—24no—
271C22×D79—22no—
272C22×D79—24no—
273C22×D79—22no—
274C22×D79—22no—
275C22×D79—21no—
276C22×D79—21no—
277C22×D79—28no—
278C22×D79—44no—
279C22×D79—44no—
280C22×D79—48no—
281C22×D79—48no—
282C22×D79C23×C412yes—
283C22×D79C23×C414yes—
284C22×D79C23×C412yes—
285C22×D79C2×#4114yes—
286C2×C4×C79—24no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—28no—
293C2×C4×C79—22no—
294C2×C4×C79—24no—
295C2×C4×C79—24no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—24no—
299C2×C4×C79C23×C414yes—
300C2×C4×C79C23×C414yes—
301C2×C4×C79C23×C412yes—
302C2×C4×C79C23×C412yes—
303C2×C4×C79C2×#4114yes—
304C2×C4×C79H(5,𝔽2)14yes—
305C22⋊D79—48no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—24no—
310C2×Dic79—22no—
311C2×Dic79—24no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—24no—
315C2×Dic79—24no—
316C2×Dic79—22no—
317C2×Dic79—44no—
318C2×Dic79C23×C412yes—
319C2×Dic79C23×C412yes—
320C2×Dic79C23×C414yes—
321C2×Dic79C2×#4114yes—
322D316—216no—
323D316—28no—
324D316—48no—
325C4×D79—28no—
326C4×D79—28no—
327C4×D79—44no—
328C4×D79—44no—
329C4×D79—48no—
330C4×D79—48no—
331C4×D79—48no—
332C4×D79—88no—
333Dic158—28no—
334C22×C79—22no—
335C22×C79—22no—
336C22×C79—22no—
337C22×C79—42no—
338C22×C79—42no—
339C22×C79C24×C411yescharacteristic
340C22×C79C22×#4112yes—
341C22×C79C2×H(5,𝔽2)12yes—
342C22×C79#58511yescharacteristic
343C22×C79#58511yescharacteristic
344C2×D79—22no—
345C2×D79—22no—
346C2×D79—24no—
347C2×D79—24no—
348C2×D79—22no—
349C2×D79—24no—
350C2×D79—24no—
351C2×D79—22no—
352C2×D79—22no—
353C2×D79—24no—
354C2×D79—416no—
355C2×D79—42no—
356C2×D79—44no—
357C2×D79—44no—
358C2×D79—42no—
359C2×D79C4×#4114yes—
360C4×C79—24no—
361C4×C79—22no—
362C4×C79—24no—
363C4×C79—24no—
364C4×C79—44no—
365C4×C79—42no—
366C4×C79#51814yes—
367Dic79—24no—
368Dic79—22no—
369Dic79—22no—
370Dic79—24no—
371Dic79—42no—
372Dic79—44no—
373#34223—791nomaximal, Sylow
374C2×C79—42no—
375C2×C79C2×C4×#4111yescharacteristic
376C2×C79C2×#51811yescharacteristic
377C2×C79#342811yescharacteristic
378C2×C79#350512yes—
379C2×C79#350612yes—
380D79—24no—
381D79—44no—
382D79—42no—
383C2×#525—791no—
384#2374—794no—
385#2363—792no—
386#2362—792no—
387#2357—792no—
388#2353—792no—
389#2347D7911yescharacteristic, complemented
390#2346—791no—
391#2341—791no—
392#2339—791no—
393#2321—794no—
394#2318—792no—
395C4×C22⋊Q8—792no—
396C4×#121—792no—
397#2280—791no—
398#2275—792no—
399C2×C4×C22⋊C4—791no—
400C79#3422311yescharacteristic, complemented, Sylow
401C22×#41—791no—
402C24×C4—791no—
403#525—7916no—
404C2×#123—792no—
405C2×C22⋊Q8—791no—
406C2×C22⋊Q8—791no—
407C2×#121—791no—
408C2×#121—791no—
409C2×#120—792no—
410C2×C4×Q8—792no—
411C2×C4×D4—792no—
412C2×C4×D4—794no—
413C2×C4×D4—792no—
414C2×C4×D4—792no—
415C2×#117—792no—
416C2×#117C2×D7911yescharacteristic
417C22×C22⋊C4—792no—
418C22×C42—792no—
419#391—792no—
420#390—794no—
421#390—794no—
422#390—792no—
423#389—792no—
424#389C2×D7912yescomplemented
425#388—794no—
426#388—794no—
427#388—794no—
428#388—794no—
429#388—794no—
430#388C2×D7914yes—
431#387—794no—
432#387—794no—
433#386—794no—
434#386—794no—
435#386—794no—
436#385—794no—
437#383C2×D7912yescomplemented
438#382—792no—
439#381—792no—
440#381—792no—
441#380—791no—
442#380—792no—
443#380—792no—
444#380C2×D7911yescharacteristic
445#379—792no—
446C4×C4⋊C4—792no—
447C4×C4⋊C4—794no—
448C4×C4⋊C4—794no—
449C4×C4⋊C4C2×D7912yescomplemented
450C4×C4⋊C4C2×D7912yescomplemented
451C4×C22⋊C4—791no—
452C4×C22⋊C4—792no—
453C4×C22⋊C4—792no—
454C4×C22⋊C4—794no—
455C4×C22⋊C4—792no—
456C4×C22⋊C4—794no—
457C4×C22⋊C4—792no—
458C4×C22⋊C4—792no—
459C4×C22⋊C4—791no—
460C4×C22⋊C4—791no—
461C4×C22⋊C4—794no—
462C4×C22⋊C4C2×D7911yescharacteristic
463#376—792no—
464C2×#95—791no—
465C2×#95—792no—
466C2×#95—791no—
467C25—791no—
468C2×#41—3164no—
469C2×#41—798no—
470C22×Q8—791no—
471C22×D4—792no—
472C22×D4—792no—
473C22×D4—792no—
474C22×D4—791no—
475C23×C4—3164no—
476C23×C4—791no—
477C23×C4—798no—
478C23×C4—792no—
479C23×C4—791no—
480C23×C4—791no—
481C23×C4—792no—
482C23×C4—792no—
483C23×C4—794no—
484C23×C4—791no—
485C23×C4—791no—
486C23×C4C22×D7911yescharacteristic
487#123—7916no—
488C22⋊Q8—798no—
489C22⋊Q8—798no—
490#121—798no—
491#121—798no—
492#120—7916no—
493C4×Q8—3164no—
494C4×D4—3164no—
495C4×D4—7916no—
496C4×D4—7916no—
497C4×D4—15816no—
498#117—3164no—
499#117C4×D7918yescomplemented
500C2×C4⋊C4—794no—
501C2×C4⋊C4—794no—
502C2×C4⋊C4—792no—
503C2×C4⋊C4—792no—
504C2×C4⋊C4—792no—
505C2×C4⋊C4C22×D7912yes—
506C2×C4⋊C4C22×D7914yes—
507C2×C4⋊C4C22×D7911yescharacteristic
508C2×C4⋊C4C22×D7911yescharacteristic
509C2×C22⋊C4—792no—
510C2×C22⋊C4—794no—
511C2×C22⋊C4—794no—
512C2×C22⋊C4—794no—
513C2×C22⋊C4—792no—
514C2×C22⋊C4—792no—
515C2×C22⋊C4—792no—
516C2×C22⋊C4—792no—
517C2×C22⋊C4—792no—
518C2×C22⋊C4—792no—
519C2×C22⋊C4—792no—
520C2×C22⋊C4—794no—
521C2×C22⋊C4—794no—
522C2×C22⋊C4—1588no—
523C2×C22⋊C4C22×D7912yes—
524C2×C22⋊C4C22×D7912yes—
525C2×C22⋊C4C22×D7912yes—
526C2×C42—3164no—
527C2×C42—794no—
528C2×C42—794no—
529C2×C42—792no—
530C2×C42—792no—
531C2×C42—794no—
532C2×C42—792no—
533C2×C42C22×D7912yes—
534C2×C42C22×D7914yes—
535C2×C42C22×D7912yes—
536#95—791no—
537#95—792no—
538#95—791no—
539#95—792no—
540#95—794no—
541#95—792no—
542#95—794no—
543#95—794no—
544#95—794no—
545#95—794no—
546#95C22×D7911yescharacteristic
547#95C22×D7911yescharacteristic
548#95C22×D7912yes—
549#95C22×D7914yes—
550#95C22×D7914yes—
551C24—3162no—
552C24—3161no—
553C24—3161no—
554C24—794no—
555C24—791no—
556C24—791no—
557C24—792no—
558C24—1584no—
559C24C23×D7911yescharacteristic
560#41—31616no—
561C2×Q8—794no—
562C2×Q8—1584no—
563C2×D4—3162no—
564C2×D4—3162no—
565C2×D4—3164no—
566C2×D4—798no—
567C2×D4—798no—
568C2×D4—798no—
569C2×D4—794no—
570C2×D4—1588no—
571C2×D4—1584no—
572C22×C4—24no—
573C22×C4—3162no—
574C22×C4—3162no—
575C22×C4—3162no—
576C22×C4—3162no—
577C22×C4—3162no—
578C22×C4—3162no—
579C22×C4—3164no—
580C22×C4—31616no—
581C22×C4—3164no—
582C22×C4—3164no—
583C22×C4—3162no—
584C22×C4—794no—
585C22×C4—798no—
586C22×C4—794no—
587C22×C4—794no—
588C22×C4—798no—
589C22×C4—792no—
590C22×C4—791no—
591C22×C4—791no—
592C22×C4—792no—
593C22×C4—794no—
594C22×C4—794no—
595C22×C4—792no—
596C22×C4—794no—
597C22×C4—1584no—
598C22×C4—1588no—
599C22×C4—1584no—
600C22×C4—1584no—
601C22×C4C2×C4×D7914yes—
602C22×C4C23×D7914yes—
603C22×C4C23×D7912yes—
604C22×C4C23×D7912yes—
605C22×C4C23×D7911yescharacteristic
606C22×C4C23×D7912yes—
607C22×C4C23×D7912yes—
608C22×C4C23×D7911yescharacteristic
609C4⋊C4—28no—
610C4⋊C4—24no—
611C4⋊C4—3164no—
612C4⋊C4—3164no—
613C4⋊C4—798no—
614C4⋊C4—798no—
615C4⋊C4—1584no—
616C4⋊C4C2×C4×D7914yes—
617C4⋊C4C2×C4×D7914yes—
618C22⋊C4—24no—
619C22⋊C4—42no—
620C22⋊C4—3164no—
621C22⋊C4—3164no—
622C22⋊C4—3164no—
623C22⋊C4—3162no—
624C22⋊C4—798no—
625C22⋊C4—798no—
626C22⋊C4—798no—
627C22⋊C4—798no—
628C22⋊C4—1584no—
629C22⋊C4—1588no—
630C22⋊C4—1584no—
631C22⋊C4—1584no—
632C22⋊C4—1588no—
633C22⋊C4C2×C4×D7918yes—
634C42—24no—
635C42—44no—
636C42—3162no—
637C42—3162no—
638C42—3164no—
639C42—3164no—
640C42—1588no—
641C42—1584no—
642C42C2×C4×D7918yes—
643C23—22no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—3164no—
648C23—3164no—
649C23—3168no—
650C23—3168no—
651C23—792no—
652C23—794no—
653C23—792no—
654C23—794no—
655C23—1588no—
656C23—1582no—
657C23—1584no—
658C23—1582no—
659C23—1581no—
660C23—1582no—
661C23—1581no—
662C23—1582no—
663C23—1584no—
664C23—1582no—
665C23—1581no—
666C23—1581no—
667C23C22×C4×D7912yes—
668C23C24×D7911yescharacteristic
669Q8—1588no—
670D4—3168no—
671D4—3168no—
672D4—15816no—
673D4—1588no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—28no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—3164no—
688C2×C4—3164no—
689C2×C4—3168no—
690C2×C4—3168no—
691C2×C4—3168no—
692C2×C4—3164no—
693C2×C4—792no—
694C2×C4—792no—
695C2×C4—794no—
696C2×C4—794no—
697C2×C4—6328no—
698C2×C4—1584no—
699C2×C4—1582no—
700C2×C4—1584no—
701C2×C4—1582no—
702C2×C4—1584no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4—1584no—
708C2×C4—1582no—
709C2×C4—1588no—
710C2×C4—1588no—
711C2×C4C22×C4×D7912yes—
712C2×C4C22×C4×D7914yes—
713C2×C4C22×C4×D7914yes—
714C2×C4C22×C4×D7912yes—
715C2×C4#41×D7914yes—
716C2×C4#1457920714yes—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—42no—
721C22—42no—
722C22—31616no—
723C22—3164no—
724C22—3162no—
725C22—3162no—
726C22—3164no—
727C22—794no—
728C22—1584no—
729C22—1582no—
730C22—1582no—
731C22—1584no—
732C22—1582no—
733C22—1584no—
734C22—1582no—
735C22—1582no—
736C22—1584no—
737C22—1584no—
738C22C23×C4×D7911yescharacteristic
739C22C2×#41×D7912yes—
740C22C2×#1457920712yes—
741C22#1909939811yescharacteristic
742C22#1909940011yescharacteristic
743C4—24no—
744C4—22no—
745C4—24no—
746C4—24no—
747C4—44no—
748C4—42no—
749C4—3162no—
750C4—3164no—
751C4—1582no—
752C4—1582no—
753C4—1584no—
754C4—1584no—
755C4#1909903714yes—
756C2—42no—
757C2—3162no—
758C2—3164no—
759C2—1584no—
760C2C4×#41×D7911yescharacteristic
761C2C2×#1909903711yescharacteristic
762C2#2377660011yescharacteristic
763C2#2377722912yes—
764C2#2377725312yes—
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingC79×#2347C2
socle, cosocleC23×C79C25
prime radicalC2×#19099075C2
hypercenter#2347D79
hypocenterC79#34223
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2347

Complements

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

NH ≅ G/Ntype
2. #23766530C2semidirect
3. #23766440C2semidirect
4. #23766426C2semidirect
5. #23766371C2semidirect
6. #23766333C2semidirect
7. #23766285C2semidirect
8. #23766240C2semidirect
9. #23766228C2semidirect
10. #23766053C2semidirect
11. #23766031C2semidirect
12. C4×#14579141C2semidirect
13. #23765908C2semidirect
14. #23765782C2semidirect
15. #23765760C2semidirect
16. C4×C22⋊C4×D79C2semidirect
17. C79×#2347C2semidirect
20. #19099075C4semidirect
27. C2×C4×Dic158C22semidirect
31. C2×#14579123C22semidirect
35. #19098468C22semidirect
37. #19098465C22semidirect
39. #19098462C22semidirect
41. #19098455C22semidirect
43. #19098453C22semidirect
45. #19098448C22semidirect
46. #19098446C22semidirect
51. #19098429C22semidirect
53. #19098425C22semidirect
55. #19098422C22semidirect
58. C4⋊C4×Dic79C22semidirect
59. C4⋊C4×Dic79C22semidirect
60. C4×C4⋊Dic79C22semidirect
65. C4×(C2×D79)⋊C4C22semidirect
70. #19098410C22semidirect
71. #19098410C22semidirect
72. #19098409C22semidirect
75. #95×D79C22semidirect
77. #389×C79C22semidirect
79. #383×C79C22semidirect
81. C4×C4⋊C4×C79C22semidirect
82. C4×C4⋊C4×C79C22semidirect
86. C2×#11929624C2×C4semidirect
94. C22×C4×D79C2×C4semidirect
103. #14579145C2×C4semidirect
104. #14579141C2×C4semidirect
105. #14579141C2×C4semidirect
107. #14579136C2×C4semidirect
108. #14579131C2×C4semidirect
110. C4×D316C2×C4semidirect
111. C4×D316C2×C4semidirect
152. #117×C79C2×C4semidirect
215. C2×C4×D79#41semidirect
389. #2347D79semidirect
400. C79#34223semidirect
424. #389C2×D79semidirect
437. #383C2×D79semidirect
449. C4×C4⋊C4C2×D79semidirect
450. C4×C4⋊C4C2×D79semidirect
499. #117C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190990752
#237665302
#237664402
#237664262
#237663712
#237663332
#237662852
#237662402
#237662282
#237660532
#237660312
C4×#145791412
#237659082
#237657822
#237657602
C4×C22⋊C4×D792
C79×#23472
#3422379