Finite Group Databasebeta

← #34305529

Subgroups — #34305529

Order 20224.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098567C211yesmaximal, characteristic
2C22⋊C4×D316C211yesmaximal, characteristic
3#23764096C211yesmaximal, characteristic, complemented
4#23764082C211yesmaximal, characteristic, complemented
5#23764027C211yesmaximal, characteristic, complemented
6#23764020C211yesmaximal, characteristic, complemented
7#23763660C211yesmaximal, characteristic, complemented
8#23763646C211yesmaximal, characteristic, complemented
9#23763495C211yesmaximal, characteristic, complemented
10#23763431C211yesmaximal, characteristic, complemented
11#23763330C211yesmaximal, characteristic
12#23763228C211yesmaximal, characteristic, complemented
13C4×#14579081C211yesmaximal, characteristic, complemented
14#23763184C211yesmaximal, characteristic, complemented
15C79×#2347C211yesmaximal, characteristic, complemented
16C23×D316C2211yescharacteristic
17C22×#11929608C2211yescharacteristic
18C2×C4×D316C2211yescharacteristic
19C2×C4×D316C2211yescharacteristic
20C2×C22⋊C4×D79—21no—
21C2×#14579094C2211yescharacteristic, complemented
22C2×#14579092C2211yescharacteristic, complemented
23#19098567C418yescomplemented
24C2×#14579081C2211yescharacteristic
25C2×#14579081C2211yescharacteristic
26C2×#14579081C2211yescharacteristic
27C2×#14579081C2211yescharacteristic
28C2×#14579081C2211yescharacteristic
29C2×#14579081C2211yescharacteristic
30C2×#14579081C2211yescharacteristic
31C2×#14579081C2211yescharacteristic
32C2×C22⋊(C79⋊C8)C2211yescharacteristic
33C2×#14579072C2211yescharacteristic, complemented
34C2×C4×C79⋊C8C2211yescharacteristic, complemented
35#19098465C2211yescharacteristic
36#19098465C2211yescharacteristic
37#19098441—21no—
38#19098441—21no—
39#19098423C2211yescharacteristic
40#19098418—21no—
41#19098325C2211yescharacteristic, complemented
42#19098325C2211yescharacteristic, complemented
43#19098325C2211yescharacteristic, complemented
44#19098325C2211yescharacteristic, complemented
45#19098325C2211yescharacteristic, complemented
46#19098325C2211yescharacteristic, complemented
47#19098318C2211yescharacteristic, complemented
48#19098318C2211yescharacteristic, complemented
49C2×#117×C79C2211yescharacteristic
50#389×C79C2211yescharacteristic, complemented
51#389×C79C2211yescharacteristic, complemented
52#388×C79—21no—
53#388×C79—21no—
54#383×C79—21no—
55#380×C79C2211yescharacteristic
56C4×C4⋊C4×C79—21no—
57C4×C4⋊C4×C79C2211yescharacteristic, complemented
58C4×C4⋊C4×C79C2211yescharacteristic, complemented
59C4×C22⋊C4×C79C2211yescharacteristic
60C24×D79—21no—
61C22×D316—22no—
62C22×D316—22no—
63C22×D316—21no—
64C22×D316—22no—
65C22×D316—41no—
66C22×D316—41no—
67C22×D316C2×C414yes—
68C22×D316C2311yescharacteristic
69C22×D316C2311yescharacteristic
70C22×C4×D79—21no—
71C22×C4×D79—21no—
72C2×#11929608—41no—
73C2×#11929608—41no—
74C2×#11929608C2×C414yescomplemented
75C22×C79⋊C8C2311yescharacteristic
76C22×C79⋊C8C2311yescharacteristic
77C22×C79⋊C8C2311yescharacteristic
78C22×C79⋊C8C2311yescharacteristic
79C4×D316—22no—
80C4×D316—22no—
81C4×D316—41no—
82C4×D316—41no—
83C2×C4⋊Dic79C2311yescharacteristic
84C2×C4⋊Dic79C2311yescharacteristic
85C2×C22⋊Dic79—21no—
86C2×(C2×D79)⋊C4—21no—
87C2×(C2×D79)⋊C4—21no—
88C2×(C2×D79)⋊C4—21no—
89C2×(C2×D79)⋊C4—21no—
90C2×(C2×D79)⋊C4—21no—
91C2×(C2×D79)⋊C4—21no—
92C22⋊C4×D79—44no—
93#14579094—41no—
94#14579092—41no—
95#14579081—22no—
96#14579081—22no—
97#14579081—41no—
98#14579081—41no—
99#14579081C2×C414yes—
100#14579081C2×C414yes—
101#14579081C2×C414yescomplemented
102#14579081C2×C414yescomplemented
103C22⋊(C79⋊C8)—22no—
104#14579072—41no—
105C4×C79⋊C8—41no—
106C79⋊#95—21no—
107C23×C4×C79C2311yescharacteristic
108#117×C79—22no—
109#117×C79C2×C414yescomplemented
110C2×C4⋊C4×C79—21no—
111C2×C4⋊C4×C79—21no—
112C2×C4⋊C4×C79C2311yescharacteristic
113C2×C4⋊C4×C79C2311yescharacteristic
114C2×C4⋊C4×C79C2311yescharacteristic
115C2×C4⋊C4×C79C2311yescharacteristic
116C2×C22⋊C4×C79—21no—
117C2×C22⋊C4×C79—21no—
118C2×C22⋊C4×C79D411yescharacteristic
119C2×C22⋊C4×C79D411yescharacteristic
120C2×C42×C79—21no—
121C2×C42×C79—21no—
122C2×C42×C79—21no—
123C2×C42×C79C2311yescharacteristic
124C2×C42×C79C2311yescharacteristic
125#95×C79—21no—
126#95×C79—21no—
127#95×C79—21no—
128#95×C79—21no—
129#95×C79—21no—
130#95×C79D411yescharacteristic
131#95×C79D411yescharacteristic
132C23×D79—21no—
133C23×D79—21no—
134C23×D79—24no—
135C23×D79—42no—
136C23×D79—42no—
137C23×D79—42no—
138C23×D79—42no—
139C23×D79—81no—
140C23×D79—81no—
141C2×D316—28no—
142C2×D316—24no—
143C2×D316—21no—
144C2×D316—21no—
145C2×D316—21no—
146C2×D316—21no—
147C2×D316—21no—
148C2×D316—21no—
149C2×D316—21no—
150C2×D316—21no—
151C2×D316—42no—
152C2×D316—42no—
153C2×D316—44no—
154C2×D316—44no—
155C2×D316—44no—
156C2×D316C22×C412yes—
157C2×D316C22×C412yes—
158C2×D316#4112yes—
159C2×D316#4112yes—
160C22×Dic79—21no—
161C22×Dic79—21no—
162C2×C4×D79—42no—
163C2×C4×D79—42no—
164C2×C4×D79—42no—
165C2×C4×D79—42no—
166C2×C4×D79—81no—
167C2×C4×D79—81no—
168#11929608—44no—
169C2×C79⋊C8—21no—
170C2×C79⋊C8—21no—
171C2×C79⋊C8—21no—
172C2×C79⋊C8—21no—
173C2×C79⋊C8—21no—
174C2×C79⋊C8—21no—
175C2×C79⋊C8—21no—
176C2×C79⋊C8—21no—
177C2×C79⋊C8—21no—
178C2×C79⋊C8—21no—
179C2×C79⋊C8C22×C412yes—
180C2×C79⋊C8C22×C412yes—
181C4⋊Dic79—21no—
182C4⋊Dic79—21no—
183C4⋊Dic79—21no—
184C4⋊Dic79—21no—
185C22⋊Dic79—42no—
186(C2×D79)⋊C4—42no—
187(C2×D79)⋊C4—42no—
188(C2×D79)⋊C4—42no—
189(C2×D79)⋊C4—42no—
190(C2×D79)⋊C4—81no—
191(C2×D79)⋊C4—81no—
192C24×C79C2×D411yescharacteristic
193C22×C4×C79—21no—
194C22×C4×C79—21no—
195C22×C4×C79—21no—
196C22×C4×C79—21no—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—21no—
200C22×C4×C79—21no—
201C22×C4×C79C22×C412yes—
202C22×C4×C79C2×D411yescharacteristic
203C22×C4×C79C2×D411yescharacteristic
204C22×C4×C79C2×D411yescharacteristic
205C22×C4×C79C2×D411yescharacteristic
206C22×C4×C79C2×D411yescharacteristic
207C22×C4×C79#4112yes—
208C22×C4×C79C2411yescharacteristic
209C4⋊C4×C79—21no—
210C4⋊C4×C79—21no—
211C4⋊C4×C79—21no—
212C4⋊C4×C79—21no—
213C4⋊C4×C79—21no—
214C4⋊C4×C79—21no—
215C4⋊C4×C79—42no—
216C4⋊C4×C79—42no—
217C4⋊C4×C79C22×C412yes—
218C4⋊C4×C79C22×C412yes—
219C22⋊C4×C79—24no—
220C22⋊C4×C79—22no—
221C22⋊C4×C79—41no—
222C22⋊C4×C79—81no—
223C42×C79—24no—
224C42×C79—21no—
225C42×C79—21no—
226C42×C79—21no—
227C42×C79—21no—
228C42×C79—81no—
229C42×C79—81no—
230C23×C79—21no—
231C23×C79—21no—
232C23×C79—21no—
233C23×C79—21no—
234C23×C79—21no—
235C23×C79—21no—
236C23×C79C4×D412yes—
237C23×C79C22×D411yescharacteristic
238C22×D79—22no—
239C22×D79—22no—
240C22×D79—22no—
241C22×D79—22no—
242C22×D79—48no—
243C22×D79—41no—
244C22×D79—41no—
245C22×D79—41no—
246C22×D79—41no—
247C22×D79—48no—
248C22×D79—41no—
249C22×D79—41no—
250C22×D79—41no—
251C22×D79—41no—
252C22×D79—41no—
253C22×D79—41no—
254C22×D79—84no—
255C22×D79—84no—
256C22×D79—84no—
257C22×D79—84no—
258C22×D79—84no—
259C2×C4×C79—21no—
260C2×C4×C79—21no—
261C2×C4×C79—21no—
262C2×C4×C79—21no—
263C2×C4×C79—22no—
264C2×C4×C79—22no—
265C2×C4×C79—22no—
266C2×C4×C79—22no—
267C2×C4×C79—22no—
268C2×C4×C79—22no—
269C2×C4×C79—21no—
270C2×C4×C79—21no—
271C2×C4×C79—21no—
272C2×C4×C79—21no—
273C2×C4×C79—21no—
274C2×C4×C79—21no—
275C2×C4×C79—21no—
276C2×C4×C79—21no—
277C2×C4×C79—21no—
278C2×C4×C79—41no—
279C2×C4×C79—41no—
280C2×C4×C79—41no—
281C2×C4×C79—41no—
282C2×C4×C79—41no—
283C2×C4×C79—41no—
284C2×C4×C79—41no—
285C2×C4×C79—41no—
286C2×C4×C79—41no—
287C2×C4×C79—41no—
288C2×C4×C79C4×D412yes—
289C2×C4×C79AGL(1,ℤ/8)12yes—
290C2×C4×C79C23×C411yescharacteristic
291C2×C4×C79C2×#4111yescharacteristic
292C2×C4×C79C2×#4111yescharacteristic
293C2×C4×C79C2×#4111yescharacteristic
294C2×C4×C79H(5,𝔽2)11yescharacteristic
295C2×C4×C79H(5,𝔽2)11yescharacteristic
296C2×Dic79—41no—
297C2×Dic79—41no—
298C2×Dic79—41no—
299C2×Dic79—41no—
300C2×Dic79—41no—
301C2×Dic79—41no—
302D316—22no—
303D316—22no—
304D316—22no—
305D316—22no—
306D316—22no—
307D316—48no—
308D316—41no—
309D316—41no—
310D316#11714yes—
311C4×D79—84no—
312C4×D79—84no—
313C79⋊C8—22no—
314C79⋊C8—22no—
315C79⋊C8—41no—
316C79⋊C8—41no—
317C22×C79—22no—
318C22×C79—22no—
319C22×C79—22no—
320C22×C79—41no—
321C22×C79—41no—
322C22×C79—41no—
323C22×C79—41no—
324C22×C79C2×C4×D411yescharacteristic
325C22×C79#54611yescharacteristic
326C22×C79#54611yescharacteristic
327C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
328C22×C79#57511yescharacteristic
329C22×C79#57611yescharacteristic
330C22×C79#57711yescharacteristic
331C2×D79—24no—
332C2×D79—42no—
333C2×D79—42no—
334C2×D79—42no—
335C2×D79—42no—
336C2×D79—42no—
337C2×D79—42no—
338C2×D79—42no—
339C2×D79—42no—
340C2×D79—42no—
341C2×D79—816no—
342C2×D79—81no—
343C2×D79—81no—
344C2×D79—81no—
345C2×D79—81no—
346C4×C79—22no—
347C4×C79—22no—
348C4×C79—42no—
349C4×C79—42no—
350C4×C79—41no—
351C4×C79—41no—
352C4×C79—41no—
353C4×C79—81no—
354C4×C79—81no—
355C4×C79C2×#11711yescharacteristic
356C4×C79#51811yescharacteristic
357C4×C79#55111yescharacteristic
358C4×C79#55111yescharacteristic
359Dic79—81no—
360Dic79—81no—
361#22580—791nomaximal, Sylow
362C2×C79—42no—
363C2×C79#234211yescharacteristic
364C2×C79C4×AGL(1,ℤ/8)11yescharacteristic
365C2×C79#294611yescharacteristic
366C2×C79#331111yescharacteristic
367C2×C79#331811yescharacteristic
368C2×C79#332211yescharacteristic
369C2×C79#332411yescharacteristic
370D79—44no—
371D79—82no—
372C2×#418—791no—
373#2347D7911yescharacteristic, complemented
374D4×C22⋊C4—791no—
375#1936—791no—
376#1934—791no—
377#1926—791no—
378#1925—791no—
379#1864—791no—
380#1862—791no—
381#1825—791no—
382#1809—791no—
383#1786—791no—
384#1762—791no—
385C4×#102—791no—
386#1753—791no—
387C79#2258011yescharacteristic, complemented, Sylow
388C23×D4—791no—
389C22×M16—791no—
390C2×C4×D4—791no—
391C2×C4×D4—791no—
392C2×#117C2×D7911yescharacteristic
393C22×C22⋊C4—1581no—
394C2×#107—791no—
395C2×#106—791no—
396#418—798no—
397C2×#102—791no—
398C2×#102—791no—
399C2×#102—791no—
400C2×#102—791no—
401C2×#102—791no—
402C2×#102—791no—
403C2×#102—791no—
404C2×#102—791no—
405C2×C22⋊C8—791no—
406C2×#97—791no—
407C2×C4×C8—791no—
408#390—791no—
409#390—791no—
410#389C2×D7911yescharacteristic, complemented
411#389C2×D7911yescharacteristic, complemented
412#388—21no—
413#388—21no—
414#386—1581no—
415#386—1581no—
416#383—21no—
417#380—791no—
418#380C2×D7911yescharacteristic
419#379—1581no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4C2×D7911yescharacteristic, complemented
422C4×C4⋊C4C2×D7911yescharacteristic, complemented
423C4×C22⋊C4C2×D7911yescharacteristic
424#340—791no—
425#340—791no—
426#340—791no—
427#340—791no—
428#340—791no—
429#340—791no—
430#336—791no—
431#336—791no—
432C25—1581no—
433C22×D4—3161no—
434C22×D4—3161no—
435C22×D4—794no—
436C22×D4—791no—
437C22×D4—791no—
438C22×D4—1582no—
439C22×D4—1582no—
440C22×D4—1581no—
441C22×D4—1582no—
442C23×C4—1581no—
443C23×C4—1581no—
444C23×C4C22×D7911yescharacteristic
445C2×M16—3161no—
446C2×M16—3161no—
447C2×M16—794no—
448C22×C8—791no—
449C22×C8—791no—
450C22×C8—791no—
451C22×C8—791no—
452C4×D4—3161no—
453C4×D4—3161no—
454C4×D4—1582no—
455C4×D4—1582no—
456#117—22no—
457#117C4×D7914yescomplemented
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—791no—
461C2×C4⋊C4—791no—
462C2×C4⋊C4C22×D7911yescharacteristic
463C2×C4⋊C4C22×D7911yescharacteristic
464C2×C4⋊C4C22×D7911yescharacteristic
465C2×C4⋊C4C22×D7911yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—3164no—
469C2×C22⋊C4—1581no—
470C2×C22⋊C4—1581no—
471C2×C22⋊C4—1581no—
472C2×C22⋊C4—1581no—
473C2×C22⋊C4—1581no—
474C2×C22⋊C4—1581no—
475C2×C22⋊C4—1581no—
476C2×C22⋊C4C22⋊D7911yescharacteristic
477C2×C22⋊C4C22⋊D7911yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42C22×D7911yescharacteristic
482C2×C42C22×D7911yescharacteristic
483#107—3161no—
484#106—3161no—
485#102—3161no—
486#102—3161no—
487#102—794no—
488#102—794no—
489#102—794no—
490#102—794no—
491#102—1582no—
492#102—1582no—
493C22⋊C8—1582no—
494#97—3161no—
495C4×C8—3161no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—1581no—
502#95C22⋊D7911yescharacteristic
503#95C22⋊D7911yescharacteristic
504C24—3162no—
505C24—3162no—
506C24—3162no—
507C24—3162no—
508C24—6321no—
509C24—6321no—
510C24—1581no—
511C24—1584no—
512C24—1581no—
513C24C2×C22⋊D7911yescharacteristic
514C2×D4—3162no—
515C2×D4—3162no—
516C2×D4—3164no—
517C2×D4—3164no—
518C2×D4—3164no—
519C2×D4—792no—
520C2×D4—792no—
521C2×D4—792no—
522C2×D4—792no—
523C2×D4—1588no—
524C2×D4—1581no—
525C2×D4—1581no—
526C2×D4—1581no—
527C2×D4—1581no—
528C2×D4—1581no—
529C2×D4—1581no—
530C2×D4—1581no—
531C2×D4—1581no—
532C2×D4—1584no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—3162no—
542C22×C4—3162no—
543C22×C4—3162no—
544C22×C4—3162no—
545C22×C4—6321no—
546C22×C4—6321no—
547C22×C4—1581no—
548C22×C4—1581no—
549C22×C4C2×C4×D7912yes—
550C22×C4C2×C22⋊D7911yescharacteristic
551C22×C4C2×C22⋊D7911yescharacteristic
552C22×C4C2×C22⋊D7911yescharacteristic
553C22×C4C2×C22⋊D7911yescharacteristic
554C22×C4C2×C22⋊D7911yescharacteristic
555C22×C4#1192962412yes—
556C22×C4C23×D7911yescharacteristic
557M16—3164no—
558C2×C8—792no—
559C2×C8—792no—
560C2×C8—1581no—
561C2×C8—1581no—
562C2×C8—1581no—
563C2×C8—1581no—
564C2×C8—1581no—
565C2×C8—1581no—
566C2×C8—1581no—
567C2×C8—1581no—
568C2×C8—1581no—
569C2×C8—1581no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—1581no—
579C4⋊C4—1581no—
580C4⋊C4—1581no—
581C4⋊C4—1581no—
582C4⋊C4C2×C4×D7912yes—
583C4⋊C4C2×C4×D7912yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—81no—
588C22⋊C4—3162no—
589C22⋊C4—3162no—
590C22⋊C4—3162no—
591C22⋊C4—3162no—
592C22⋊C4—3162no—
593C22⋊C4—6321no—
594C22⋊C4—6321no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—24no—
600C42—81no—
601C42—81no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—3168no—
609C23—3168no—
610C23—3161no—
611C23—3161no—
612C23—3161no—
613C23—3161no—
614C23—3161no—
615C23—3161no—
616C23—3161no—
617C23—3161no—
618C23—3161no—
619C23—3161no—
620C23—6324no—
621C23—6324no—
622C23—6324no—
623C23—6324no—
624C23—6324no—
625C23—1582no—
626C23—1582no—
627C23—1582no—
628C23—1582no—
629C23C4×C22⋊D7912yes—
630C23C22×C22⋊D7911yescharacteristic
631D4—3168no—
632D4—3161no—
633D4—3161no—
634D4—794no—
635D4—1582no—
636D4—1582no—
637D4—1582no—
638D4—1582no—
639D4—1582no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—3161no—
670C2×C4—3161no—
671C2×C4—3161no—
672C2×C4—3161no—
673C2×C4—3161no—
674C2×C4—3161no—
675C2×C4—6324no—
676C2×C4—6324no—
677C2×C4C4×C22⋊D7912yes—
678C2×C4#1457918612yes—
679C2×C4C22×C4×D7911yescharacteristic
680C2×C4#41×D7911yescharacteristic
681C2×C4#41×D7911yescharacteristic
682C2×C4C2×#1192962411yescharacteristic
683C2×C4#1457920711yescharacteristic
684C2×C4#1457920711yescharacteristic
685C8—3161no—
686C8—3161no—
687C8—1582no—
688C8—1582no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—3162no—
697C22—3162no—
698C22—3162no—
699C22—3162no—
700C22—3162no—
701C22—3162no—
702C22—3162no—
703C22—3162no—
704C22—3162no—
705C22—63216no—
706C22—6321no—
707C22—6321no—
708C22—6321no—
709C22—6321no—
710C22—1584no—
711C22C2×C4×C22⋊D7911yescharacteristic
712C22#1909920111yescharacteristic
713C22#1909920111yescharacteristic
714C22C2×#1457918611yescharacteristic
715C22#1909936111yescharacteristic
716C22#1909936611yescharacteristic
717C22#1909937111yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—81no—
726C4—81no—
727C4—6321no—
728C4—6321no—
729C4#117×D7911yescharacteristic
730C4#1909903711yescharacteristic
731C4#1909923711yescharacteristic
732C4#1909923711yescharacteristic
733C2—42no—
734C2—3164no—
735C2—6322no—
736C2#2376625011yescharacteristic
737C2C4×#1457918611yescharacteristic
738C2#2377222811yescharacteristic
739C2#2377543011yescharacteristic
740C2#2377553511yescharacteristic
741C2#2377559511yescharacteristic
742C2#2377562511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2347C2
socleC23×C79C22×D4
prime radicalC23×D316C22
cosocleC22×C4×C79C24
hypercenter#2347D79
hypocenterC79#22580
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2347

Complements

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

NH ≅ G/Ntype
3. #23764096C2semidirect
4. #23764082C2semidirect
5. #23764027C2semidirect
6. #23764020C2semidirect
7. #23763660C2semidirect
8. #23763646C2semidirect
9. #23763495C2semidirect
10. #23763431C2semidirect
12. #23763228C2semidirect
13. C4×#14579081C2semidirect
14. #23763184C2semidirect
15. C79×#2347C2semidirect
21. C2×#14579094C22semidirect
22. C2×#14579092C22semidirect
23. #19098567C4semidirect
33. C2×#14579072C22semidirect
34. C2×C4×C79⋊C8C22semidirect
41. #19098325C22semidirect
42. #19098325C22semidirect
43. #19098325C22semidirect
44. #19098325C22semidirect
45. #19098325C22semidirect
46. #19098325C22semidirect
47. #19098318C22semidirect
48. #19098318C22semidirect
50. #389×C79C22semidirect
51. #389×C79C22semidirect
57. C4×C4⋊C4×C79C22semidirect
58. C4×C4⋊C4×C79C22semidirect
74. C2×#11929608C2×C4semidirect
101. #14579081C2×C4semidirect
102. #14579081C2×C4semidirect
109. #117×C79C2×C4semidirect
373. #2347D79semidirect
387. C79#22580semidirect
410. #389C2×D79semidirect
411. #389C2×D79semidirect
421. C4×C4⋊C4C2×D79semidirect
422. C4×C4⋊C4C2×D79semidirect
457. #117C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190985672
C22⋊C4×D3162
#237640962
#237640822
#237640272
#237640202
#237636602
#237636462
#237634952
#237634312
#237633302
#237632282
C4×#145790812
#237631842
C79×#23472
#2258079