Finite Group Databasebeta

← #34298042

Subgroups — #34298042

Order 20224.

1086 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099184C211yesmaximal, characteristic
2C2×#19098624C211yesmaximal, characteristic, complemented
3#23764372C211yesmaximal, characteristic, complemented
4#23764360C211yesmaximal, characteristic, complemented
5#23764214C211yesmaximal, characteristic, complemented
6#23764209C211yesmaximal, characteristic, complemented
7#23763722C211yesmaximal, characteristic
8#23763717C211yesmaximal, characteristic
9#23763712C211yesmaximal, characteristic, complemented
10#23763707C211yesmaximal, characteristic, complemented
11#23763412C211yesmaximal, characteristic, complemented
12#23763407C211yesmaximal, characteristic, complemented
13#23763402C211yesmaximal, characteristic, complemented
14#23763397C211yesmaximal, characteristic, complemented
15C79×#2317C211yesmaximal, characteristic, complemented
16#19099184—24no—
17#19099184C418yescomplemented
18C2×#14579161C2211yescharacteristic
19C2×#14579156—21no—
20C2×#14579149C2211yescharacteristic
21C2×#14579147—21no—
22C2×#14579143—21no—
23C2×#14579140C2211yescharacteristic
24C2×#14579139—21no—
25C2×#14579135C2211yescharacteristic
26C2×C4×Dic158C2211yescharacteristic
27C2×C4×D316C2211yescharacteristic
28#19098624—24no—
29C2×C4⋊(C79⋊C8)C2211yescharacteristic
30C2×C4⋊(C79⋊C8)C2211yescharacteristic
31C2×#14579084C2211yescharacteristic
32C2×#14579084C2211yescharacteristic
33C2×#14579084C2211yescharacteristic
34C2×#14579084C2211yescharacteristic
35C2×#14579081C2211yescharacteristic
36C2×#14579081C2211yescharacteristic
37C2×#14579081C2211yescharacteristic
38C2×#14579081C2211yescharacteristic
39C2×C22⋊(C79⋊C8)C2211yescharacteristic
40C2×C22⋊(C79⋊C8)C2211yescharacteristic
41C2×#14579072C2211yescharacteristic
42C2×C4×C79⋊C8C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51C2×#117×C79C2211yescharacteristic
52C2×#117×C79C2211yescharacteristic
53C22×C4⋊C4×C79C2211yescharacteristic
54#389×C79—21no—
55#389×C79—21no—
56#385×C79—21no—
57#385×C79—21no—
58#384×C79C2211yescharacteristic
59#384×C79C2211yescharacteristic
60#382×C79C2211yescharacteristic
61#382×C79C2211yescharacteristic
62C22×Dic158—21no—
63C22×Dic158C2311yescharacteristic
64C22×D316C2311yescharacteristic
65C22×C22⋊D79—21no—
66C22×C4×D79—21no—
67C22×C79⋊C8C2311yescharacteristic
68C22×C79⋊C8C2311yescharacteristic
69C22×C79⋊C8C2311yescharacteristic
70C22×C79⋊C8C2311yescharacteristic
71#14579161—22no—
72#14579161C2×C414yescomplemented
73#14579156—28no—
74#14579149—22no—
75#14579149C2×C414yescomplemented
76#14579147—28no—
77#14579143—28no—
78#14579140—22no—
79#14579140C2×C414yes—
80#14579139—28no—
81#14579135—22no—
82#14579135C2×C414yes—
83C4×Dic158—22no—
84C4×Dic158C2×C414yescomplemented
85C4×D316—22no—
86C4×D316C2×C414yescomplemented
87C2×C4⋊Dic79—21no—
88C2×C4⋊Dic79C2311yescharacteristic
89C2×C4⋊Dic79C2311yescharacteristic
90C2×Dic79⋊C4—21no—
91C2×Dic79⋊C4—21no—
92C2×C22⋊Dic79—21no—
93C2×(C2×D79)⋊C4—21no—
94C2×(C2×D79)⋊C4—21no—
95C2×(C2×D79)⋊C4—21no—
96C2×(C2×D79)⋊C4—21no—
97C2×C4×Dic79—21no—
98C4⋊(C79⋊C8)—22no—
99C4⋊(C79⋊C8)—22no—
100#14579084—41no—
101#14579084—41no—
102#14579084—41no—
103#14579084—41no—
104#14579081—41no—
105#14579081—41no—
106#14579081—41no—
107#14579081—41no—
108C22⋊(C79⋊C8)—22no—
109C22⋊(C79⋊C8)—22no—
110#14579072—22no—
111C4×C79⋊C8—22no—
112C23×C4×C79—21no—
113C23×C4×C79C2311yescharacteristic
114#117×C79—41no—
115#117×C79—41no—
116#117×C79C2×C414yes—
117#117×C79D414yes—
118C2×C4⋊C4×C79—21no—
119C2×C4⋊C4×C79—21no—
120C2×C4⋊C4×C79—21no—
121C2×C4⋊C4×C79—21no—
122C2×C4⋊C4×C79—21no—
123C2×C4⋊C4×C79—41no—
124C2×C4⋊C4×C79—41no—
125C2×C4⋊C4×C79D411yescharacteristic
126C2×C4⋊C4×C79D411yescharacteristic
127C2×C4⋊C4×C79C2311yescharacteristic
128C2×C4⋊C4×C79C2311yescharacteristic
129C2×C4⋊C4×C79C2311yescharacteristic
130C2×C4⋊C4×C79C2311yescharacteristic
131C2×C22⋊C4×C79—21no—
132C2×C22⋊C4×C79D411yescharacteristic
133C2×C22⋊C4×C79D411yescharacteristic
134C2×C42×C79—21no—
135C2×C42×C79C2311yescharacteristic
136C2×C42×C79C2311yescharacteristic
137#95×C79—21no—
138#95×C79—21no—
139#95×C79—21no—
140#95×C79—21no—
141C23×D79—21no—
142C2×Dic158—24no—
143C2×Dic158—21no—
144C2×Dic158—21no—
145C2×Dic158—21no—
146C2×Dic158—21no—
147C2×Dic158—21no—
148C2×Dic158—81no—
149C2×Dic158—81no—
150C2×Dic158C22×C412yes—
151C2×D316—21no—
152C2×D316—21no—
153C2×D316—21no—
154C2×D316—21no—
155C2×D316—21no—
156C2×D316C22×C412yes—
157C2×C22⋊D79—24no—
158C2×C22⋊D79—81no—
159C2×C22⋊D79—81no—
160C22×Dic79—21no—
161C22×Dic79—21no—
162C22×Dic79—21no—
163C2×C4×D79—24no—
164C2×C4×D79—81no—
165C2×C4×D79—81no—
166C2×C79⋊C8—21no—
167C2×C79⋊C8—21no—
168C2×C79⋊C8—21no—
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—
178C4⋊Dic79—24no—
179C4⋊Dic79—21no—
180C4⋊Dic79—21no—
181C4⋊Dic79C22×C412yes—
182C4⋊Dic79C22×C412yes—
183Dic79⋊C4—24no—
184Dic79⋊C4—24no—
185C22⋊Dic79—24no—
186(C2×D79)⋊C4—24no—
187(C2×D79)⋊C4—24no—
188(C2×D79)⋊C4—24no—
189(C2×D79)⋊C4—24no—
190C4×Dic79—24no—
191C24×C79C2×D411yescharacteristic
192C22×C4×C79—21no—
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—42no—
201C22×C4×C79—81no—
202C22×C4×C79—81no—
203C22×C4×C79C22×C412yes—
204C22×C4×C79C2×D411yescharacteristic
205C22×C4×C79C2×D411yescharacteristic
206C22×C4×C79C2×D411yescharacteristic
207C22×C4×C79C2×D411yescharacteristic
208C22×C4×C79C2×D411yescharacteristic
209C22×C4×C79C2×D412yes—
210C22×C4×C79C2411yescharacteristic
211C4⋊C4×C79—21no—
212C4⋊C4×C79—21no—
213C4⋊C4×C79—21no—
214C4⋊C4×C79—21no—
215C4⋊C4×C79—21no—
216C4⋊C4×C79—21no—
217C4⋊C4×C79—21no—
218C4⋊C4×C79—21no—
219C4⋊C4×C79—42no—
220C4⋊C4×C79—81no—
221C4⋊C4×C79—81no—
222C4⋊C4×C79—81no—
223C4⋊C4×C79—81no—
224C4⋊C4×C79C22⋊C414yes—
225C4⋊C4×C79C22⋊C414yes—
226C22⋊C4×C79—42no—
227C22⋊C4×C79C22⋊C414yes—
228C22⋊C4×C79C22⋊C414yes—
229C42×C79—42no—
230C42×C79C22×C412yes—
231C42×C79C22×C412yes—
232C42×C79C2×D412yes—
233C42×C79C2×D412yes—
234C23×C79—21no—
235C23×C79—21no—
236C23×C79—21no—
237C23×C79—21no—
238C23×C79—21no—
239C23×C79—21no—
240C23×C79C2×C22⋊C412yes—
241C23×C79C22×D411yescharacteristic
242C22×D79—22no—
243C22×D79—41no—
244C22×D79—41no—
245C22×D79—41no—
246C22×D79—41no—
247C22×D79—41no—
248C22×D79—41no—
249C2×C4×C79—21no—
250C2×C4×C79—21no—
251C2×C4×C79—21no—
252C2×C4×C79—21no—
253C2×C4×C79—21no—
254C2×C4×C79—21no—
255C2×C4×C79—21no—
256C2×C4×C79—21no—
257C2×C4×C79—21no—
258C2×C4×C79—21no—
259C2×C4×C79—22no—
260C2×C4×C79—22no—
261C2×C4×C79—22no—
262C2×C4×C79—22no—
263C2×C4×C79—41no—
264C2×C4×C79—41no—
265C2×C4×C79—41no—
266C2×C4×C79—41no—
267C2×C4×C79—41no—
268C2×C4×C79—41no—
269C2×C4×C79—41no—
270C2×C4×C79—41no—
271C2×C4×C79—41no—
272C2×C4×C79—41no—
273C2×C4×C79—41no—
274C2×C4×C79—41no—
275C2×C4×C79—84no—
276C2×C4×C79C2×C22⋊C412yes—
277C2×C4×C79C2×C22⋊C412yes—
278C2×C4×C79C2×C22⋊C412yes—
279C2×C4×C79C2×C22⋊C412yes—
280C2×C4×C79C2×C22⋊C412yes—
281C2×C4×C79C23×C411yescharacteristic
282C2×C4×C79C22×D411yescharacteristic
283C2×C4×C79H(5,𝔽2)11yescharacteristic
284C2×C4×C79H(5,𝔽2)11yescharacteristic
285C2×C4×C792−1+411yescharacteristic
286C2×C4×C792−1+411yescharacteristic
287C22⋊D79—84no—
288C2×Dic79—22no—
289C2×Dic79—22no—
290C2×Dic79—22no—
291C2×Dic79—41no—
292C2×Dic79—41no—
293C2×Dic79—41no—
294C2×Dic79—41no—
295C2×Dic79—41no—
296C2×Dic79—41no—
297D316—22no—
298D316—22no—
299D316—41no—
300D316—41no—
301C4×D79—84no—
302Dic158—22no—
303Dic158—22no—
304Dic158—41no—
305Dic158—41no—
306Dic158—84no—
307C79⋊C8—41no—
308C79⋊C8—41no—
309C79⋊C8—41no—
310C79⋊C8—41no—
311C22×C79—22no—
312C22×C79—22no—
313C22×C79—22no—
314C22×C79—41no—
315C22×C79—41no—
316C22×C79—41no—
317C22×C79—41no—
318C22×C79C22×C22⋊C411yescharacteristic
319C22×C79#53511yescharacteristic
320C22×C79#53611yescharacteristic
321C22×C79#57611yescharacteristic
322C22×C79#57711yescharacteristic
323C22×C79#57711yescharacteristic
324C22×C79#57811yescharacteristic
325C2×D79—42no—
326C2×D79—42no—
327C2×D79—42no—
328C2×D79—81no—
329C2×D79—81no—
330C2×D79—81no—
331C2×D79—81no—
332C4×C79—22no—
333C4×C79—22no—
334C4×C79—22no—
335C4×C79—22no—
336C4×C79—22no—
337C4×C79—81no—
338C4×C79—81no—
339C4×C79—81no—
340C4×C79—81no—
341C4×C79#52011yescharacteristic
342C4×C79#52011yescharacteristic
343C4×C79#53711yescharacteristic
344C4×C79#53711yescharacteristic
345Dic79—42no—
346Dic79—42no—
347Dic79—42no—
348#21871—791nomaximal, Sylow
349C2×C79—42no—
350C2×C79#231111yescharacteristic
351C2×C79#289711yescharacteristic
352C2×C79#289811yescharacteristic
353C2×C79#322411yescharacteristic
354C2×C79#322511yescharacteristic
355C2×C79#324311yescharacteristic
356C2×C79#324411yescharacteristic
357D79—82no—
358C2×#542—791no—
359C2×#433—791no—
360#2317D7911yescharacteristic, complemented
361#1993—791no—
362#1990—791no—
363#1959—791no—
364#1958—791no—
365#1875—791no—
366#1874—791no—
367#1873—791no—
368#1872—791no—
369#1805—791no—
370#1804—791no—
371#1803—791no—
372#1802—791no—
373C79#2187111yescharacteristic, complemented, Sylow
374#542—798no—
375#542—1584no—
376C2×C4⋊Q8—791no—
377C2×#126—1581no—
378C2×#124—791no—
379C2×#124—1581no—
380C2×#123—1581no—
381C2×C22⋊Q8—791no—
382C2×C22⋊Q8—1581no—
383C2×#121—791no—
384C2×C4×Q8—791no—
385C2×C4×D4—791no—
386C2×#117C2×D7911yescharacteristic
387C2×#117C2×D7911yescharacteristic
388C22×C4⋊C4C2×D7911yescharacteristic
389#433—1584no—
390C2×C4⋊C8—791no—
391C2×C4⋊C8—791no—
392C2×#103—791no—
393C2×#103—791no—
394C2×#103—791no—
395C2×#103—791no—
396C2×#102—791no—
397C2×#102—791no—
398C2×#102—791no—
399C2×#102—791no—
400C2×C22⋊C8—791no—
401C2×C22⋊C8—791no—
402C2×#97—791no—
403C2×C4×C8—791no—
404#389—21no—
405#389—21no—
406#385—21no—
407#385—21no—
408#384C2×D7911yescharacteristic
409#384C2×D7911yescharacteristic
410#382C2×D7911yescharacteristic
411#382C2×D7911yescharacteristic
412#340—791no—
413#340—791no—
414#340—791no—
415#340—791no—
416#340—791no—
417#340—791no—
418#340—791no—
419#340—791no—
420C22×Q8—791no—
421C22×Q8—1581no—
422C22×D4—791no—
423C22×D4—1581no—
424C23×C4—21no—
425C23×C4—1581no—
426C23×C4C22×D7911yescharacteristic
427C22×C8—791no—
428C22×C8—791no—
429C22×C8—791no—
430C22×C8—791no—
431C4⋊Q8—794no—
432C4⋊Q8—1582no—
433#126—1588no—
434#124—794no—
435#124—1588no—
436#124—1582no—
437#123—1588no—
438C22⋊Q8—794no—
439C22⋊Q8—1582no—
440C22⋊Q8—1588no—
441#121—794no—
442#121—1582no—
443C4×Q8—794no—
444C4×Q8—1582no—
445C4×D4—794no—
446C4×D4—1582no—
447#117—41no—
448#117—41no—
449#117C4×D7914yes—
450#117D31614yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—791no—
459C2×C4⋊C4—791no—
460C2×C4⋊C4—1581no—
461C2×C4⋊C4—1581no—
462C2×C4⋊C4—1581no—
463C2×C4⋊C4C22⋊D7911yescharacteristic
464C2×C4⋊C4C22⋊D7911yescharacteristic
465C2×C4⋊C4C22×D7911yescharacteristic
466C2×C4⋊C4C22×D7911yescharacteristic
467C2×C4⋊C4C22×D7911yescharacteristic
468C2×C4⋊C4C22×D7911yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—1581no—
471C2×C22⋊C4—1581no—
472C2×C22⋊C4—1581no—
473C2×C22⋊C4—1581no—
474C2×C22⋊C4—1581no—
475C2×C22⋊C4C22⋊D7911yescharacteristic
476C2×C22⋊C4C22⋊D7911yescharacteristic
477C2×C42—21no—
478C2×C42—1581no—
479C2×C42C22×D7911yescharacteristic
480C2×C42C22×D7911yescharacteristic
481C4⋊C8—1582no—
482C4⋊C8—1582no—
483#103—3161no—
484#103—3161no—
485#103—3161no—
486#103—3161no—
487#102—3161no—
488#102—3161no—
489#102—3161no—
490#102—3161no—
491C22⋊C8—1582no—
492C22⋊C8—1582no—
493#97—1582no—
494C4×C8—1582no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C24—1581no—
500C24C2×C22⋊D7911yescharacteristic
501C2×Q8—792no—
502C2×Q8—6321no—
503C2×Q8—6321no—
504C2×Q8—1581no—
505C2×Q8—1581no—
506C2×Q8—1581no—
507C2×Q8—1581no—
508C2×Q8—1584no—
509C2×Q8—1581no—
510C2×D4—792no—
511C2×D4—6321no—
512C2×D4—6321no—
513C2×D4—1584no—
514C2×D4—1581no—
515C2×D4—1581no—
516C2×D4—1581no—
517C2×D4—1581no—
518C2×D4—1581no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—6321no—
531C22×C4—6321no—
532C22×C4—1581no—
533C22×C4—1581no—
534C22×C4—1581no—
535C22×C4—1584no—
536C22×C4C2×C4×D7912yes—
537C22×C4C2×C22⋊D7911yescharacteristic
538C22×C4C2×C22⋊D7911yescharacteristic
539C22×C4C2×C22⋊D7911yescharacteristic
540C22×C4C2×C22⋊D7911yescharacteristic
541C22×C4C2×C22⋊D7911yescharacteristic
542C22×C4C2×D31612yes—
543C22×C4C23×D7911yescharacteristic
544C2×C8—1581no—
545C2×C8—1581no—
546C2×C8—1581no—
547C2×C8—1581no—
548C2×C8—1581no—
549C2×C8—1581no—
550C2×C8—1581no—
551C2×C8—1581no—
552C2×C8—1581no—
553C2×C8—1581no—
554C2×C8—1581no—
555C2×C8—1581no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—42no—
565C4⋊C4—81no—
566C4⋊C4—81no—
567C4⋊C4—81no—
568C4⋊C4—81no—
569C4⋊C4—792no—
570C4⋊C4—792no—
571C4⋊C4—1584no—
572C4⋊C4—1584no—
573C4⋊C4—1584no—
574C4⋊C4—1581no—
575C4⋊C4—1581no—
576C4⋊C4(C2×D79)⋊C414yes—
577C4⋊C4(C2×D79)⋊C414yes—
578C22⋊C4—42no—
579C22⋊C4—1584no—
580C22⋊C4—1584no—
581C22⋊C4—1584no—
582C22⋊C4—1584no—
583C22⋊C4—1584no—
584C22⋊C4(C2×D79)⋊C414yes—
585C22⋊C4(C2×D79)⋊C414yes—
586C42—42no—
587C42—1584no—
588C42C2×C4×D7912yes—
589C42C2×C4×D7912yes—
590C42C2×D31612yes—
591C42C2×D31612yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—3161no—
599C23—3161no—
600C23—3161no—
601C23—3161no—
602C23—3161no—
603C23—3161no—
604C23—1582no—
605C23C2×(C2×D79)⋊C412yes—
606C23C22×C22⋊D7911yescharacteristic
607Q8—3161no—
608Q8—3161no—
609Q8—6324no—
610Q8—1582no—
611Q8—1582no—
612D4—3161no—
613D4—3161no—
614D4—6324no—
615D4—1582no—
616D4—1582no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4—3161no—
645C2×C4—3161no—
646C2×C4—3161no—
647C2×C4—3161no—
648C2×C4—3161no—
649C2×C4—3161no—
650C2×C4—6324no—
651C2×C4—1582no—
652C2×C4—1582no—
653C2×C4—1582no—
654C2×C4C2×(C2×D79)⋊C412yes—
655C2×C4C2×(C2×D79)⋊C412yes—
656C2×C4C2×(C2×D79)⋊C412yes—
657C2×C4C2×(C2×D79)⋊C412yes—
658C2×C4C2×(C2×D79)⋊C412yes—
659C2×C4C22×C4×D7911yescharacteristic
660C2×C4C22×D31611yescharacteristic
661C2×C4#1457920611yescharacteristic
662C2×C4#1457920611yescharacteristic
663C2×C4#1457920911yescharacteristic
664C2×C4#1457920911yescharacteristic
665C8—3161no—
666C8—3161no—
667C8—3161no—
668C8—3161no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—3162no—
677C22—3162no—
678C22—3162no—
679C22—6321no—
680C22—6321no—
681C22—6321no—
682C22—6321no—
683C22C22×(C2×D79)⋊C411yescharacteristic
684C22#1909913011yescharacteristic
685C22#1909913711yescharacteristic
686C22#1909936611yescharacteristic
687C22#1909937111yescharacteristic
688C22#1909937411yescharacteristic
689C22#1909937811yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—3162no—
700C4—3162no—
701C4—3162no—
702C4#1909904411yescharacteristic
703C4#1909904411yescharacteristic
704C4#1909914411yescharacteristic
705C4#1909914411yescharacteristic
706C2—42no—
707C2—6322no—
708C2#2376599311yescharacteristic
709C2#2377192311yescharacteristic
710C2#2377193011yescharacteristic
711C2#2377449411yescharacteristic
712C2#2377450911yescharacteristic
713C2#2377468311yescharacteristic
714C2#2377469811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2317C2
socleC23×C79C22×D4
prime radicalC2×#14579135C22
cosocleC22×C4×C79C24
hypercenter#2317D79
hypocenterC79#21871
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. C2×#19098624C2semidirect
3. #23764372C2semidirect
4. #23764360C2semidirect
5. #23764214C2semidirect
6. #23764209C2semidirect
9. #23763712C2semidirect
10. #23763707C2semidirect
11. #23763412C2semidirect
12. #23763407C2semidirect
13. #23763402C2semidirect
14. #23763397C2semidirect
15. C79×#2317C2semidirect
17. #19099184C4semidirect
72. #14579161C2×C4semidirect
75. #14579149C2×C4semidirect
84. C4×Dic158C2×C4semidirect
86. C4×D316C2×C4semidirect
360. #2317D79semidirect
373. C79#21871semidirect

Maximal subgroups

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

subgroupindex
C2×#190991842
C2×#190986242
#237643722
#237643602
#237642142
#237642092
#237637222
#237637172
#237637122
#237637072
#237634122
#237634072
#237634022
#237633972
C79×#23172
#2187179