Finite Group Databasebeta

← #34448436

Subgroups — #34448436

Order 20224.

2914 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579123C211yesmaximal, characteristic
2#23766369C212yesmaximal, complemented
3#23766339C214yesmaximal, complemented
4#23766309C212yesmaximal, complemented
5#23766269C211yesmaximal, characteristic, complemented
6#23766250C212yesmaximal, complemented
7#23766242C212yesmaximal, complemented
8C22⋊C4×D316C211yesmaximal, characteristic
9#23766220C211yesmaximal, characteristic
10#23766039C212yesmaximal, complemented
11#23766032C214yesmaximal, complemented
12#23765795C211yesmaximal, characteristic, complemented
13#23765794C211yesmaximal, characteristic, complemented
14#23765779C212yesmaximal, complemented
15#381×D79C212yesmaximal, complemented
16#23765760C212yesmaximal, complemented
17C79×#2344C211yesmaximal, characteristic, complemented
18C23×D316C2211yescharacteristic
19C23×C4×D79C2212yes—
20C2×C4×D316C2212yes—
21C2×#14579123C4116yescomplemented
22C2×#14579123C2212yes—
23C2×#14579123C2211yescharacteristic
24C2×#14579123C2211yescharacteristic
25C2×#14579123C2212yes—
26C2×#14579123C2211yescharacteristic
27C2×#14579123C2212yes—
28C2×#14579123C2211yescharacteristic
29C2×#14579120C2212yes—
30C22×(C2×D79)⋊C4C2212yes—
31C2×C22⋊C4×D79C2212yes—
32C2×C22⋊C4×D79C2212yes—
33C22×C4×Dic79C2211yescharacteristic
34#19098465C2212yes—
35#19098464C2212yes—
36#19098462C2212yescomplemented
37#19098455C2214yescomplemented
38#19098454C2214yescomplemented
39#19098453C2214yescomplemented
40#19098452C2214yescomplemented
41#19098449C2214yescomplemented
42#19098441C2214yes—
43#19098441C2214yes—
44#19098437C2214yescomplemented
45#19098434C2214yescomplemented
46#19098430C2212yescomplemented
47#19098430C2212yescomplemented
48#19098428C2212yescomplemented
49#19098427C2212yescomplemented
50#19098426C2212yes—
51#19098425C2214yescomplemented
52#19098425C2214yescomplemented
53#19098424C2211yescharacteristic
54#19098424C2212yes—
55#19098424C2211yescharacteristic
56#19098423C2211yescharacteristic
57#19098421C2211yescharacteristic
58#19098421C2211yescharacteristic
59#19098420C2214yescomplemented
60#19098420C2214yescomplemented
61#19098418C2212yes—
62#19098418C2212yes—
63C4⋊C4×Dic79C2212yescomplemented
64C4⋊C4×Dic79C2212yescomplemented
65C4×Dic79⋊C4C2212yescomplemented
66C22⋊C4×Dic79C2212yes—
67C4×(C2×D79)⋊C4C2214yescomplemented
68C4×(C2×D79)⋊C4C2214yescomplemented
69C4×(C2×D79)⋊C4C2214yescomplemented
70C4×C22⋊Dic79C2211yescharacteristic
71#19098410C2214yescomplemented
72#19098409C2212yescomplemented
73#19098408C2212yescomplemented
74#95×D79C2214yescomplemented
75#95×D79C2214yescomplemented
76C2×#117×C79C2212yes—
77C22×C4⋊C4×C79C2211yescharacteristic
78#389×C79C2212yescomplemented
79#387×C79C2214yescomplemented
80#381×C79C2212yes—
81#380×C79C2211yescharacteristic
82C4×C4⋊C4×C79C2212yescomplemented
83C4×C22⋊C4×C79C2211yescharacteristic
84C24×D79C2312yes—
85C22×D316—28no—
86C22×D316C2×C418yes—
87C22×D316C2312yes—
88C22×D316C2311yescharacteristic
89C22×D316C2311yescharacteristic
90C23×Dic79C2311yescharacteristic
91C23×Dic79C2311yescharacteristic
92C22×C4×D79—44no—
93C22×C4×D79—44no—
94C22×C4×D79C2×C4116yescomplemented
95C22×C4×D79C2314yes—
96C22×C4×D79C2314yes—
97C22×C4×D79C2312yes—
98C22×C4×D79C2312yes—
99C22×C4×D79C2312yes—
100C22×C4×D79C2312yes—
101C4×D316—28no—
102#14579123—28no—
103#14579123C2×C418yes—
104#14579123C2×C418yes—
105#14579123C2×C418yescomplemented
106#14579123C2×C418yescomplemented
107#14579123C2×C4116yescomplemented
108#14579123C2×C4116yescomplemented
109#14579120—44no—
110C2×C4⋊Dic79C2312yes—
111C2×C4⋊Dic79C2314yes—
112C2×Dic79⋊C4C2312yes—
113C2×Dic79⋊C4C2312yes—
114C2×C22⋊Dic79C2311yescharacteristic
115C2×C22⋊Dic79C2311yescharacteristic
116C2×C22⋊Dic79C2312yes—
117C2×(C2×D79)⋊C4C2×C4116yescomplemented
118C2×(C2×D79)⋊C4C2314yes—
119C2×(C2×D79)⋊C4C2314yes—
120C2×(C2×D79)⋊C4C2314yes—
121C2×(C2×D79)⋊C4C2314yes—
122C2×(C2×D79)⋊C4C2314yes—
123C2×(C2×D79)⋊C4C2314yes—
124C2×(C2×D79)⋊C4C2312yes—
125C2×(C2×D79)⋊C4C2312yes—
126C2×(C2×D79)⋊C4C2312yes—
127C2×(C2×D79)⋊C4C2312yes—
128C22⋊C4×D79—44no—
129C22⋊C4×D79—44no—
130C2×C4×Dic79C2×C418yescomplemented
131C2×C4×Dic79C2312yes—
132C2×C4×Dic79C2314yes—
133C2×C4×Dic79C2314yes—
134C2×C4×Dic79C2311yescharacteristic
135C2×C4×Dic79C2311yescharacteristic
136C2×C4×Dic79C2311yescharacteristic
137C2×C4×Dic79C2311yescharacteristic
138C79⋊#95C2312yes—
139C79⋊#95C2312yes—
140C79⋊#95C2314yes—
141C79⋊#95C2314yes—
142C79⋊#95C2314yes—
143C79⋊#95C2314yes—
144C79⋊#95C2312yes—
145C79⋊#95C2312yes—
146C79⋊#95C2312yes—
147C79⋊#95C2312yes—
148C79⋊#95C2312yes—
149C79⋊#95C2312yes—
150C79⋊#95C2314yes—
151C23×C4×C79C2311yescharacteristic
152C23×C4×C79C2312yes—
153#117×C79—44no—
154C2×C4⋊C4×C79C2×C418yescomplemented
155C2×C4⋊C4×C79C2312yes—
156C2×C4⋊C4×C79C2314yes—
157C2×C4⋊C4×C79C2311yescharacteristic
158C2×C4⋊C4×C79C2312yes—
159C2×C4⋊C4×C79C2311yescharacteristic
160C2×C22⋊C4×C79C2312yes—
161C2×C22⋊C4×C79C2311yescharacteristic
162C2×C22⋊C4×C79C2311yescharacteristic
163C2×C42×C79C2312yes—
164C2×C42×C79C2314yes—
165#95×C79C2314yes—
166#95×C79C2314yes—
167#95×C79C2312yes—
168#95×C79C2312yes—
169C23×D79—24no—
170C23×D79—24no—
171C23×D79—28no—
172C23×D79—44no—
173C23×D79C22×C418yes—
174C23×D79C2412yes—
175C23×D79C2412yes—
176C2×D316—232no—
177C2×D316—28no—
178C2×D316—24no—
179C2×D316C22×C418yes—
180C2×D316C22×C414yes—
181C2×D316C22×C414yes—
182C2×D316#4118yes—
183C22×Dic79—22no—
184C22×Dic79—22no—
185C22×Dic79—42no—
186C22×Dic79C22×C414yes—
187C22×Dic79C22×C414yes—
188C22×Dic79C2412yes—
189C22×Dic79C2414yes—
190C22×Dic79C2412yes—
191C22×Dic79C2411yescharacteristic
192C22×Dic79C2411yescharacteristic
193C22×Dic79C2411yescharacteristic
194C22×Dic79C2411yescharacteristic
195C2×C4×D79—28no—
196C2×C4×D79—28no—
197C2×C4×D79—432no—
198C2×C4×D79—42no—
199C2×C4×D79—42no—
200C2×C4×D79—42no—
201C2×C4×D79—42no—
202C2×C4×D79—42no—
203C2×C4×D79—42no—
204C2×C4×D79—42no—
205C2×C4×D79—42no—
206C2×C4×D79—44no—
207C2×C4×D79—44no—
208C2×C4×D79—44no—
209C2×C4×D79—44no—
210C2×C4×D79C22×C418yes—
211C2×C4×D79C22×C418yes—
212C2×C4×D79C22×C418yes—
213C2×C4×D79C22×C418yes—
214C4⋊Dic79—24no—
215C4⋊Dic79—44no—
216Dic79⋊C4—42no—
217Dic79⋊C4—42no—
218C22⋊Dic79—22no—
219C22⋊Dic79—24no—
220C22⋊Dic79—22no—
221(C2×D79)⋊C4—28no—
222(C2×D79)⋊C4—28no—
223(C2×D79)⋊C4—44no—
224(C2×D79)⋊C4—44no—
225(C2×D79)⋊C4—44no—
226(C2×D79)⋊C4—44no—
227(C2×D79)⋊C4C22×C418yes—
228(C2×D79)⋊C4C22×C418yes—
229(C2×D79)⋊C4C22×C418yes—
230(C2×D79)⋊C4C22×C418yes—
231C4×Dic79—24no—
232C4×Dic79—44no—
233C4×Dic79—44no—
234C4×Dic79C22×C414yes—
235C4×Dic79C22×C414yes—
236C4×Dic79C22×C414yes—
237C4×Dic79C22×C414yes—
238C24×C79C2411yescharacteristic
239C22×C4×C79—24no—
240C22×C4×C79—24no—
241C22×C4×C79—24no—
242C22×C4×C79C22×C414yes—
243C22×C4×C79C22×C418yes—
244C22×C4×C79C2412yes—
245C22×C4×C79C2414yes—
246C22×C4×C79C2412yes—
247C22×C4×C79C2411yescharacteristic
248C22×C4×C79C2412yes—
249C22×C4×C79C2412yes—
250C22×C4×C79C2411yescharacteristic
251C4⋊C4×C79—24no—
252C4⋊C4×C79—44no—
253C4⋊C4×C79C22×C414yes—
254C4⋊C4×C79C22×C414yes—
255C4⋊C4×C79C22×C418yes—
256C22⋊C4×C79—22no—
257C22⋊C4×C79—24no—
258C22⋊C4×C79—22no—
259C42×C79—24no—
260C42×C79—44no—
261C23×C79—22no—
262C23×C79—22no—
263C23×C79C23×C412yes—
264C23×C79H(5,𝔽2)12yes—
265C23×C79H(5,𝔽2)12yes—
266C23×C79C2511yescharacteristic
267C22×D79—22no—
268C22×D79—22no—
269C22×D79—24no—
270C22×D79—216no—
271C22×D79—24no—
272C22×D79—22no—
273C22×D79—22no—
274C22×D79—24no—
275C22×D79—216no—
276C22×D79—48no—
277C22×D79—416no—
278C22×D79—416no—
279C22×D79C23×C414yes—
280C22×D79C23×C414yes—
281C22×D79C2×#4118yes—
282C2×C4×C79—216no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—28no—
289C2×C4×C79—22no—
290C2×C4×C79—24no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—24no—
294C2×C4×C79—22no—
295C2×C4×C79—24no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79C23×C412yes—
299C2×C4×C79C23×C414yes—
300C2×C4×C79C23×C414yes—
301C2×C4×C79C23×C412yes—
302C2×C4×C79C2×#4114yes—
303C2×Dic79—28no—
304C2×Dic79—21no—
305C2×Dic79—21no—
306C2×Dic79—21no—
307C2×Dic79—21no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—24no—
313C2×Dic79—22no—
314C2×Dic79—24no—
315C2×Dic79—22no—
316C2×Dic79—24no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—44no—
320C2×Dic79C23×C412yes—
321C2×Dic79C23×C412yes—
322C2×Dic79C23×C412yes—
323C2×Dic79C23×C412yes—
324D316—216no—
325D316—28no—
326D316#117116yescomplemented
327C4×D79—48no—
328C4×D79—48no—
329C4×D79—48no—
330C4×D79—48no—
331C4×D79—88no—
332C4×D79—88no—
333C22×C79—22no—
334C22×C79—22no—
335C22×C79—24no—
336C22×C79—24no—
337C22×C79#51814yes—
338C22×C79C24×C411yescharacteristic
339C22×C79C22×#4112yes—
340C22×C79C2×H(5,𝔽2)11yescharacteristic
341C22×C79C2×H(5,𝔽2)11yescharacteristic
342C22×C79#58512yes—
343C2×D79—24no—
344C2×D79—24no—
345C2×D79—28no—
346C2×D79—28no—
347C2×D79—24no—
348C2×D79—24no—
349C2×D79—24no—
350C2×D79—432no—
351C2×D79—44no—
352C2×D79—44no—
353C2×D79C2×#11718yes—
354C4×C79—22no—
355C4×C79—24no—
356C4×C79—24no—
357C4×C79—42no—
358C4×C79—44no—
359C4×C79—42no—
360C4×C79C2×#11714yes—
361Dic79—22no—
362Dic79—22no—
363Dic79—22no—
364Dic79—22no—
365Dic79—42no—
366Dic79—44no—
367Dic79—42no—
368#34190—791nomaximal, Sylow
369C2×C79—24no—
370C2×C79C22×#11711yescharacteristic
371C2×C79C2×#51811yescharacteristic
372C2×C79#342811yescharacteristic
373C2×C79#351312yes—
374C2×C79#351312yes—
375D79—28no—
376D79—44no—
377C22×C4×D4—791no—
378#2357—792no—
379#2353—794no—
380#2349—792no—
381#2344—791no—
382#2344D7911yescharacteristic, complemented
383#2342—792no—
384#2342—792no—
385D4×C22⋊C4—791no—
386D4×C22⋊C4—791no—
387#2319—792no—
388#2318—794no—
389#2283—791no—
390#2283—791no—
391#2280—792no—
392C2×#381—792no—
393#2275—792no—
394C79#3419011yescharacteristic, complemented, Sylow
395C23×D4—791no—
396C24×C4—792no—
397C2×C4×D4—792no—
398C2×C4×D4—791no—
399C2×C4×D4—791no—
400C2×C4×D4—792no—
401C2×C4×D4—791no—
402C2×C4×D4—791no—
403C2×C4×D4—792no—
404C2×C4×D4—7916no—
405C2×C4×D4—792no—
406C2×#117—792no—
407C2×#117C2×D7912yes—
408C22×C4⋊C4C2×D7911yescharacteristic
409C22×C22⋊C4—792no—
410C22×C22⋊C4—792no—
411C22×C22⋊C4—792no—
412C22×C42—791no—
413#390—792no—
414#390—792no—
415#389—792no—
416#389C2×D7912yescomplemented
417#388—794no—
418#388—794no—
419#388—794no—
420#388—794no—
421#387—794no—
422#387C2×D7914yescomplemented
423#386—794no—
424#386—794no—
425#385—794no—
426#385—794no—
427#383—792no—
428#383—792no—
429#382—792no—
430#382—792no—
431#381—792no—
432#381—791no—
433#381—792no—
434#381—791no—
435#381—794no—
436#381—794no—
437#381C2×D7912yes—
438#380—791no—
439#380—794no—
440#380—794no—
441#380—791no—
442#380—791no—
443#380C2×D7911yescharacteristic
444#379—792no—
445#379—792no—
446C4×C4⋊C4—792no—
447C4×C4⋊C4—792no—
448C4×C4⋊C4—792no—
449C4×C4⋊C4C2×D7912yescomplemented
450C4×C22⋊C4—791no—
451C4×C22⋊C4—792no—
452C4×C22⋊C4—794no—
453C4×C22⋊C4—794no—
454C4×C22⋊C4—794no—
455C4×C22⋊C4—794no—
456C4×C22⋊C4C2×D7911yescharacteristic
457#376—792no—
458#376—792no—
459C2×#95—794no—
460C2×#95—794no—
461C25—792no—
462C22×D4—798no—
463C22×D4—791no—
464C22×D4—792no—
465C22×D4—791no—
466C22×D4—1588no—
467C23×C4—3164no—
468C23×C4—3164no—
469C23×C4—791no—
470C23×C4—7916no—
471C23×C4—792no—
472C23×C4—792no—
473C23×C4—792no—
474C23×C4—792no—
475C23×C4—794no—
476C23×C4—794no—
477C23×C4—791no—
478C23×C4C22×D7912yes—
479C23×C4C22×D7911yescharacteristic
480C4×D4—798no—
481C4×D4—798no—
482C4×D4—7916no—
483C4×D4—798no—
484C4×D4—7916no—
485C4×D4—798no—
486C4×D4—1588no—
487C4×D4—1588no—
488#117—44no—
489#117—3164no—
490C2×C4⋊C4—794no—
491C2×C4⋊C4—792no—
492C2×C4⋊C4—792no—
493C2×C4⋊C4—792no—
494C2×C4⋊C4C4×D7918yescomplemented
495C2×C4⋊C4C22×D7912yes—
496C2×C4⋊C4C22×D7914yes—
497C2×C4⋊C4C22×D7911yescharacteristic
498C2×C4⋊C4C22×D7912yes—
499C2×C4⋊C4C22×D7911yescharacteristic
500C2×C22⋊C4—3164no—
501C2×C22⋊C4—3164no—
502C2×C22⋊C4—794no—
503C2×C22⋊C4—794no—
504C2×C22⋊C4—794no—
505C2×C22⋊C4—794no—
506C2×C22⋊C4—7916no—
507C2×C22⋊C4—792no—
508C2×C22⋊C4—792no—
509C2×C22⋊C4—792no—
510C2×C22⋊C4—792no—
511C2×C22⋊C4—791no—
512C2×C22⋊C4—792no—
513C2×C22⋊C4—791no—
514C2×C22⋊C4—794no—
515C2×C22⋊C4—794no—
516C2×C22⋊C4C22×D7911yescharacteristic
517C2×C22⋊C4C22×D7912yes—
518C2×C22⋊C4C22×D7911yescharacteristic
519C2×C42—794no—
520C2×C42—794no—
521C2×C42—798no—
522C2×C42—791no—
523C2×C42—791no—
524C2×C42—791no—
525C2×C42—791no—
526C2×C42—792no—
527C2×C42C22×D7912yes—
528C2×C42C22×D7914yes—
529#95—792no—
530#95—792no—
531#95—794no—
532#95—794no—
533#95—794no—
534#95—794no—
535#95—792no—
536#95—792no—
537#95—792no—
538#95—792no—
539#95—792no—
540#95—794no—
541#95—792no—
542#95C22×D7914yes—
543#95C22×D7914yes—
544#95C22×D7912yes—
545#95C22×D7912yes—
546C24—3164no—
547C24—798no—
548C24—792no—
549C24—792no—
550C24—1588no—
551C24—1584no—
552C24—1584no—
553C24C23×D7911yescharacteristic
554C2×D4—798no—
555C2×D4—794no—
556C2×D4—798no—
557C2×D4—794no—
558C2×D4—15832no—
559C2×D4—1588no—
560C2×D4—1584no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—3162no—
565C22×C4—3162no—
566C22×C4—3162no—
567C22×C4—3162no—
568C22×C4—3162no—
569C22×C4—3162no—
570C22×C4—3162no—
571C22×C4—3162no—
572C22×C4—31632no—
573C22×C4—3164no—
574C22×C4—3164no—
575C22×C4—3164no—
576C22×C4—3164no—
577C22×C4—3162no—
578C22×C4—794no—
579C22×C4—798no—
580C22×C4—798no—
581C22×C4—798no—
582C22×C4—798no—
583C22×C4—791no—
584C22×C4—791no—
585C22×C4—791no—
586C22×C4—791no—
587C22×C4—794no—
588C22×C4—792no—
589C22×C4—794no—
590C22×C4—792no—
591C22×C4—1588no—
592C22×C4—1588no—
593C22×C4—1582no—
594C22×C4—1582no—
595C22×C4C2×C4×D7914yes—
596C22×C4C2×C4×D7918yes—
597C22×C4C23×D7912yes—
598C22×C4C23×D7914yes—
599C22×C4C23×D7912yes—
600C22×C4C23×D7911yescharacteristic
601C22×C4C23×D7912yes—
602C22×C4C23×D7912yes—
603C22×C4C23×D7911yescharacteristic
604C4⋊C4—24no—
605C4⋊C4—44no—
606C4⋊C4—3162no—
607C4⋊C4—3162no—
608C4⋊C4—3164no—
609C4⋊C4—1584no—
610C4⋊C4C2×C4×D7918yes—
611C4⋊C4C2×C4×D7914yes—
612C4⋊C4C2×C4×D7914yes—
613C22⋊C4—24no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—3164no—
617C22⋊C4—3164no—
618C22⋊C4—3164no—
619C22⋊C4—3164no—
620C22⋊C4—798no—
621C22⋊C4—798no—
622C22⋊C4—798no—
623C22⋊C4—798no—
624C22⋊C4—1588no—
625C22⋊C4—1588no—
626C22⋊C4—1582no—
627C22⋊C4—1584no—
628C22⋊C4—1582no—
629C42—24no—
630C42—44no—
631C42—3164no—
632C42—3164no—
633C42—794no—
634C42—794no—
635C42—794no—
636C42—794no—
637C42—1584no—
638C23—22no—
639C23—22no—
640C23—31616no—
641C23—31616no—
642C23—3168no—
643C23—794no—
644C23—798no—
645C23—794no—
646C23—15816no—
647C23—1582no—
648C23—1582no—
649C23—1584no—
650C23—15816no—
651C23—1584no—
652C23—1582no—
653C23—1582no—
654C23—1584no—
655C23C22×C4×D7912yes—
656C23#1457920612yes—
657C23#1457920712yes—
658C23C24×D7911yescharacteristic
659D4—7916no—
660D4—15816no—
661D4—1588no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—216no—
667C2×C4—22no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—3168no—
679C2×C4—3168no—
680C2×C4—3168no—
681C2×C4—3168no—
682C2×C4—3164no—
683C2×C4—792no—
684C2×C4—792no—
685C2×C4—792no—
686C2×C4—792no—
687C2×C4—6328no—
688C2×C4—6328no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4—1584no—
692C2×C4—1584no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4—1584no—
698C2×C4—1581no—
699C2×C4—1581no—
700C2×C4—1581no—
701C2×C4—1581no—
702C2×C4—1582no—
703C2×C4—1582no—
704C2×C4—1588no—
705C2×C4C22×C4×D7912yes—
706C2×C4C22×C4×D7914yes—
707C2×C4C22×C4×D7914yes—
708C2×C4C22×C4×D7912yes—
709C2×C4#41×D7914yes—
710C22—22no—
711C22—24no—
712C22—24no—
713C22—22no—
714C22—31632no—
715C22—3164no—
716C22—3164no—
717C22—798no—
718C22—1584no—
719C22—1584no—
720C22—1584no—
721C22—1588no—
722C22—1588no—
723C22—1584no—
724C22—1584no—
725C22#1909903514yes—
726C22C23×C4×D7911yescharacteristic
727C22C2×#41×D7912yes—
728C22C2×#1457920611yescharacteristic
729C22C2×#1457920711yescharacteristic
730C22#1909940012yes—
731C4—22no—
732C4—24no—
733C4—24no—
734C4—44no—
735C4—42no—
736C4—42no—
737C4—3162no—
738C4—3164no—
739C4—3162no—
740C4—1582no—
741C4—1582no—
742C4—1582no—
743C4—1582no—
744C4#117×D7914yes—
745C2—24no—
746C2—3164no—
747C2—1588no—
748C2C2×#117×D7911yescharacteristic
749C2C2×#1909903511yescharacteristic
750C2#2377660211yescharacteristic
751C2#2377733512yes—
752C2#2377734512yes—
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingC79×#2344C2
socle, cosocleC23×C79C25
prime radicalC23×D316C22
hypercenter#2344D79
hypocenterC79#34190
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. #23766369C2semidirect
3. #23766339C2semidirect
4. #23766309C2semidirect
5. #23766269C2semidirect
6. #23766250C2semidirect
7. #23766242C2semidirect
10. #23766039C2semidirect
11. #23766032C2semidirect
12. #23765795C2semidirect
13. #23765794C2semidirect
14. #23765779C2semidirect
15. #381×D79C2semidirect
16. #23765760C2semidirect
17. C79×#2344C2semidirect
21. C2×#14579123C4semidirect
36. #19098462C22semidirect
37. #19098455C22semidirect
38. #19098454C22semidirect
39. #19098453C22semidirect
40. #19098452C22semidirect
41. #19098449C22semidirect
44. #19098437C22semidirect
45. #19098434C22semidirect
46. #19098430C22semidirect
47. #19098430C22semidirect
48. #19098428C22semidirect
49. #19098427C22semidirect
51. #19098425C22semidirect
52. #19098425C22semidirect
59. #19098420C22semidirect
60. #19098420C22semidirect
63. C4⋊C4×Dic79C22semidirect
64. C4⋊C4×Dic79C22semidirect
65. C4×Dic79⋊C4C22semidirect
67. C4×(C2×D79)⋊C4C22semidirect
68. C4×(C2×D79)⋊C4C22semidirect
69. C4×(C2×D79)⋊C4C22semidirect
71. #19098410C22semidirect
72. #19098409C22semidirect
73. #19098408C22semidirect
74. #95×D79C22semidirect
75. #95×D79C22semidirect
78. #389×C79C22semidirect
79. #387×C79C22semidirect
82. C4×C4⋊C4×C79C22semidirect
94. C22×C4×D79C2×C4semidirect
105. #14579123C2×C4semidirect
106. #14579123C2×C4semidirect
107. #14579123C2×C4semidirect
108. #14579123C2×C4semidirect
117. C2×(C2×D79)⋊C4C2×C4semidirect
130. C2×C4×Dic79C2×C4semidirect
154. C2×C4⋊C4×C79C2×C4semidirect
326. D316#117semidirect
382. #2344D79semidirect
394. C79#34190semidirect
416. #389C2×D79semidirect
422. #387C2×D79semidirect
449. C4×C4⋊C4C2×D79semidirect
494. C2×C4⋊C4C4×D79semidirect

Maximal subgroups

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

subgroupindex
C22×#145791232
#237663692
#237663392
#237663092
#237662692
#237662502
#237662422
C22⋊C4×D3162
#237662202
#237660392
#237660322
#237657952
#237657942
#237657792
#381×D792
#237657602
C79×#23442
#3419079