Finite Group Databasebeta

← #34298237

Subgroups — #34298237

Order 20224.

1078 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099184C211yesmaximal, characteristic
2C2×#19098590C211yesmaximal, characteristic, complemented
3#23764352C211yesmaximal, characteristic, complemented
4#23764348C211yesmaximal, characteristic, complemented
5#23764332C211yesmaximal, characteristic, complemented
6#23764332C211yesmaximal, characteristic, complemented
7#23763836C211yesmaximal, characteristic
8#23763831C211yesmaximal, characteristic, complemented
9#23763826C211yesmaximal, characteristic
10#23763821C211yesmaximal, characteristic, complemented
11#23763412C211yesmaximal, characteristic, complemented
12#23763407C211yesmaximal, characteristic, complemented
13#23763402C211yesmaximal, characteristic, complemented
14#23763397C211yesmaximal, characteristic, complemented
15C79×#2314C211yesmaximal, characteristic, complemented
16C22×#11929608C2211yescharacteristic
17C23×C79⋊C8C2211yescharacteristic
18#19099184—24no—
19#19099184C418yescomplemented
20C2×#14579161C2211yescharacteristic
21C2×#14579156—21no—
22C2×#14579149C2211yescharacteristic
23C2×#14579147—21no—
24C2×#14579143—21no—
25C2×#14579140C2211yescharacteristic
26C2×#14579139—21no—
27C2×#14579135C2211yescharacteristic
28C2×C4×Dic158C2211yescharacteristic
29C2×C4×D316C2211yescharacteristic
30#19098590—24no—
31C2×C4⋊(C79⋊C8)C2211yescharacteristic
32C2×C4⋊(C79⋊C8)C2211yescharacteristic
33C2×C4⋊(C79⋊C8)C2211yescharacteristic
34C2×C4⋊(C79⋊C8)C2211yescharacteristic
35C2×#14579084C2211yescharacteristic
36C2×#14579084C2211yescharacteristic
37C2×#14579084C2211yescharacteristic
38C2×#14579084C2211yescharacteristic
39C2×#14579081C2211yescharacteristic
40C2×#14579081C2211yescharacteristic
41C2×#14579081C2211yescharacteristic
42C2×#14579081C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51C2×#117×C79C2211yescharacteristic
52#388×C79—21no—
53#388×C79—21no—
54#387×C79—21no—
55#387×C79—21no—
56#384×C79C2211yescharacteristic
57#382×C79C2211yescharacteristic
58#380×C79C2211yescharacteristic
59#380×C79C2211yescharacteristic
60C4×C4⋊C4×C79C2211yescharacteristic
61C4×C4⋊C4×C79C2211yescharacteristic
62C22×Dic158—21no—
63C22×Dic158C2311yescharacteristic
64C22×D316C2311yescharacteristic
65C22×C22⋊D79—21no—
66C22×C4×D79—21no—
67C2×#11929608—22no—
68C2×#11929608—41no—
69C2×#11929608—41no—
70C22×C79⋊C8—22no—
71C22×C79⋊C8—41no—
72C22×C79⋊C8—41no—
73C22×C79⋊C8C2311yescharacteristic
74C22×C79⋊C8C2311yescharacteristic
75C22×C79⋊C8C2311yescharacteristic
76C22×C79⋊C8C2311yescharacteristic
77#14579161—22no—
78#14579161C2×C414yes—
79#14579156—28no—
80#14579149—22no—
81#14579149C2×C414yes—
82#14579147—28no—
83#14579143—28no—
84#14579140—22no—
85#14579140C2×C414yes—
86#14579139—28no—
87#14579135—22no—
88#14579135C2×C414yes—
89C4×Dic158—22no—
90C4×Dic158C2×C414yes—
91C4×D316—22no—
92C4×D316C2×C414yes—
93C2×C4⋊Dic79—21no—
94C2×C4⋊Dic79C2311yescharacteristic
95C2×C4⋊Dic79C2311yescharacteristic
96C2×Dic79⋊C4—21no—
97C2×Dic79⋊C4—21no—
98C2×C22⋊Dic79—21no—
99C2×(C2×D79)⋊C4—21no—
100C2×(C2×D79)⋊C4—21no—
101C2×(C2×D79)⋊C4—21no—
102C2×(C2×D79)⋊C4—21no—
103C2×C4×Dic79—21no—
104C4⋊(C79⋊C8)—22no—
105C4⋊(C79⋊C8)—22no—
106C4⋊(C79⋊C8)—22no—
107C4⋊(C79⋊C8)—22no—
108#14579084—41no—
109#14579084—41no—
110#14579084—41no—
111#14579084—41no—
112#14579081—41no—
113#14579081—41no—
114#14579081—41no—
115#14579081—41no—
116C23×C4×C79C2311yescharacteristic
117#117×C79C2×C414yes—
118#117×C79D414yes—
119C2×C4⋊C4×C79—21no—
120C2×C4⋊C4×C79—21no—
121C2×C4⋊C4×C79D411yescharacteristic
122C2×C4⋊C4×C79D411yescharacteristic
123C2×C4⋊C4×C79C2311yescharacteristic
124C2×C4⋊C4×C79C2311yescharacteristic
125C2×C4⋊C4×C79C2311yescharacteristic
126C2×C4⋊C4×C79C2311yescharacteristic
127C2×C22⋊C4×C79—21no—
128C2×C22⋊C4×C79—21no—
129C2×C22⋊C4×C79D411yescharacteristic
130C2×C22⋊C4×C79D411yescharacteristic
131C2×C42×C79—21no—
132C2×C42×C79—21no—
133C2×C42×C79C2311yescharacteristic
134C2×C42×C79C2311yescharacteristic
135#95×C79—21no—
136#95×C79—21no—
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—
166#11929608—44no—
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—
178C2×C79⋊C8—21no—
179C2×C79⋊C8—44no—
180C4⋊Dic79—24no—
181C4⋊Dic79—21no—
182C4⋊Dic79—21no—
183C4⋊Dic79C22×C412yes—
184C4⋊Dic79C22×C412yes—
185Dic79⋊C4—24no—
186Dic79⋊C4—24no—
187C22⋊Dic79—24no—
188(C2×D79)⋊C4—24no—
189(C2×D79)⋊C4—24no—
190(C2×D79)⋊C4—24no—
191(C2×D79)⋊C4—24no—
192C4×Dic79—24no—
193C24×C79C2×D411yescharacteristic
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×C79—21no—
202C22×C4×C79C22×C412yes—
203C22×C4×C79C2×D411yescharacteristic
204C22×C4×C79C2×D411yescharacteristic
205C22×C4×C79C2×D411yescharacteristic
206C22×C4×C79C2×D411yescharacteristic
207C22×C4×C79C2×D411yescharacteristic
208C22×C4×C79C2×D412yes—
209C22×C4×C79C2411yescharacteristic
210C4⋊C4×C79—21no—
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—81no—
219C4⋊C4×C79—81no—
220C4⋊C4×C79C22⋊C414yes—
221C4⋊C4×C79C22⋊C414yes—
222C22⋊C4×C79—81no—
223C22⋊C4×C79—81no—
224C22⋊C4×C79C22⋊C414yes—
225C22⋊C4×C79C22⋊C414yes—
226C42×C79—81no—
227C42×C79—81no—
228C42×C79C22×C412yes—
229C42×C79C22×C412yes—
230C42×C79C2×D412yes—
231C42×C79C2×D412yes—
232C23×C79—21no—
233C23×C79—21no—
234C23×C79—21no—
235C23×C79—21no—
236C23×C79—21no—
237C23×C79—21no—
238C23×C79C2×C22⋊C412yes—
239C23×C79C22×D411yescharacteristic
240C22×D79—22no—
241C22×D79—41no—
242C22×D79—41no—
243C22×D79—41no—
244C22×D79—41no—
245C22×D79—41no—
246C22×D79—41no—
247C2×C4×C79—21no—
248C2×C4×C79—21no—
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—22no—
258C2×C4×C79—22no—
259C2×C4×C79—22no—
260C2×C4×C79—22no—
261C2×C4×C79—41no—
262C2×C4×C79—41no—
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×C79C2×C22⋊C412yes—
274C2×C4×C79C2×C22⋊C412yes—
275C2×C4×C79C2×C22⋊C412yes—
276C2×C4×C79C2×C22⋊C412yes—
277C2×C4×C79C2×C22⋊C412yes—
278C2×C4×C79C23×C411yescharacteristic
279C2×C4×C79C22×D411yescharacteristic
280C2×C4×C79H(5,𝔽2)11yescharacteristic
281C2×C4×C79H(5,𝔽2)11yescharacteristic
282C2×C4×C792−1+411yescharacteristic
283C2×C4×C792−1+411yescharacteristic
284C22⋊D79—84no—
285C2×Dic79—22no—
286C2×Dic79—22no—
287C2×Dic79—22no—
288C2×Dic79—41no—
289C2×Dic79—41no—
290C2×Dic79—41no—
291C2×Dic79—41no—
292C2×Dic79—41no—
293C2×Dic79—41no—
294D316—22no—
295D316—22no—
296D316—41no—
297D316—41no—
298C4×D79—84no—
299Dic158—22no—
300Dic158—22no—
301Dic158—41no—
302Dic158—41no—
303Dic158—84no—
304C79⋊C8—41no—
305C79⋊C8—41no—
306C79⋊C8—41no—
307C79⋊C8—41no—
308C22×C79—22no—
309C22×C79—22no—
310C22×C79—22no—
311C22×C79—41no—
312C22×C79—41no—
313C22×C79—41no—
314C22×C79—41no—
315C22×C79C22×C22⋊C411yescharacteristic
316C22×C79#53711yescharacteristic
317C22×C79#53711yescharacteristic
318C22×C79#57611yescharacteristic
319C22×C79#57711yescharacteristic
320C22×C79#57711yescharacteristic
321C22×C79#57811yescharacteristic
322C2×D79—42no—
323C2×D79—42no—
324C2×D79—42no—
325C2×D79—81no—
326C2×D79—81no—
327C2×D79—81no—
328C2×D79—81no—
329C4×C79—22no—
330C4×C79—22no—
331C4×C79—22no—
332C4×C79—22no—
333C4×C79—22no—
334C4×C79—81no—
335C4×C79—81no—
336C4×C79—81no—
337C4×C79—81no—
338C4×C79#52011yescharacteristic
339C4×C79#52011yescharacteristic
340C4×C79#53511yescharacteristic
341C4×C79#53611yescharacteristic
342Dic79—42no—
343Dic79—42no—
344Dic79—42no—
345#21896—791nomaximal, Sylow
346C2×C79—42no—
347C2×C79#231111yescharacteristic
348C2×C79#289711yescharacteristic
349C2×C79#289811yescharacteristic
350C2×C79#325711yescharacteristic
351C2×C79#325811yescharacteristic
352C2×C79#326211yescharacteristic
353C2×C79#326311yescharacteristic
354D79—82no—
355C2×#542—791no—
356C2×#424—791no—
357#2314D7911yescharacteristic, complemented
358#1988—791no—
359#1987—791no—
360#1983—791no—
361#1983—791no—
362#1895—791no—
363#1894—791no—
364#1893—791no—
365#1892—791no—
366#1805—791no—
367#1804—791no—
368#1803—791no—
369#1802—791no—
370C79#2189611yescharacteristic, complemented, Sylow
371C22×M16—791no—
372C23×C8—791no—
373#542—798no—
374#542—1584no—
375C2×C4⋊Q8—791no—
376C2×#126—1581no—
377C2×#124—791no—
378C2×#124—1581no—
379C2×#123—1581no—
380C2×C22⋊Q8—791no—
381C2×C22⋊Q8—1581no—
382C2×#121—791no—
383C2×C4×Q8—791no—
384C2×C4×D4—791no—
385C2×#117C2×D7911yescharacteristic
386#424—1584no—
387C2×C4⋊C8—791no—
388C2×C4⋊C8—791no—
389C2×C4⋊C8—791no—
390C2×C4⋊C8—791no—
391C2×#103—791no—
392C2×#103—791no—
393C2×#103—791no—
394C2×#103—791no—
395C2×#102—791no—
396C2×#102—791no—
397C2×#102—791no—
398C2×#102—791no—
399#388—21no—
400#388—21no—
401#387—21no—
402#387—21no—
403#384C2×D7911yescharacteristic
404#382C2×D7911yescharacteristic
405#380C2×D7911yescharacteristic
406#380C2×D7911yescharacteristic
407C4×C4⋊C4C2×D7911yescharacteristic
408C4×C4⋊C4C2×D7911yescharacteristic
409#340—791no—
410#340—791no—
411#340—791no—
412#340—791no—
413#340—791no—
414#340—791no—
415#340—791no—
416#340—791no—
417C22×Q8—791no—
418C22×Q8—1581no—
419C22×D4—791no—
420C22×D4—1581no—
421C23×C4—1581no—
422C23×C4C22×D7911yescharacteristic
423C2×M16—3161no—
424C2×M16—3161no—
425C2×M16—1582no—
426C22×C8—3161no—
427C22×C8—3161no—
428C22×C8—791no—
429C22×C8—791no—
430C22×C8—791no—
431C22×C8—791no—
432C22×C8—1582no—
433C4⋊Q8—794no—
434C4⋊Q8—1582no—
435#126—1588no—
436#124—794no—
437#124—1588no—
438#124—1582no—
439#123—1588no—
440C22⋊Q8—794no—
441C22⋊Q8—1582no—
442C22⋊Q8—1588no—
443#121—794no—
444#121—1582no—
445C4×Q8—794no—
446C4×Q8—1582no—
447C4×D4—794no—
448C4×D4—1582no—
449#117C4×D7914yes—
450#117D31614yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—791no—
454C2×C4⋊C4—791no—
455C2×C4⋊C4—1581no—
456C2×C4⋊C4—1581no—
457C2×C4⋊C4—1581no—
458C2×C4⋊C4C22⋊D7911yescharacteristic
459C2×C4⋊C4C22⋊D7911yescharacteristic
460C2×C4⋊C4C22×D7911yescharacteristic
461C2×C4⋊C4C22×D7911yescharacteristic
462C2×C4⋊C4C22×D7911yescharacteristic
463C2×C4⋊C4C22×D7911yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—1581no—
467C2×C22⋊C4—1581no—
468C2×C22⋊C4—1581no—
469C2×C22⋊C4—1581no—
470C2×C22⋊C4—1581no—
471C2×C22⋊C4C22⋊D7911yescharacteristic
472C2×C22⋊C4C22⋊D7911yescharacteristic
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—1581no—
476C2×C42C22×D7911yescharacteristic
477C2×C42C22×D7911yescharacteristic
478C4⋊C8—1582no—
479C4⋊C8—1582no—
480C4⋊C8—1582no—
481C4⋊C8—1582no—
482#103—3161no—
483#103—3161no—
484#103—3161no—
485#103—3161no—
486#102—3161no—
487#102—3161no—
488#102—3161no—
489#102—3161no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496C24—1581no—
497C24C2×C22⋊D7911yescharacteristic
498C2×Q8—792no—
499C2×Q8—6321no—
500C2×Q8—6321no—
501C2×Q8—1581no—
502C2×Q8—1581no—
503C2×Q8—1581no—
504C2×Q8—1581no—
505C2×Q8—1584no—
506C2×Q8—1581no—
507C2×D4—792no—
508C2×D4—6321no—
509C2×D4—6321no—
510C2×D4—1584no—
511C2×D4—1581no—
512C2×D4—1581no—
513C2×D4—1581no—
514C2×D4—1581no—
515C2×D4—1581no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—6321no—
525C22×C4—6321no—
526C22×C4—1581no—
527C22×C4—1581no—
528C22×C4—1581no—
529C22×C4—1584no—
530C22×C4C2×C4×D7912yes—
531C22×C4C2×C22⋊D7911yescharacteristic
532C22×C4C2×C22⋊D7911yescharacteristic
533C22×C4C2×C22⋊D7911yescharacteristic
534C22×C4C2×C22⋊D7911yescharacteristic
535C22×C4C2×C22⋊D7911yescharacteristic
536C22×C4C2×D31612yes—
537C22×C4C23×D7911yescharacteristic
538M16—3164no—
539C2×C8—3164no—
540C2×C8—1581no—
541C2×C8—1581no—
542C2×C8—1581no—
543C2×C8—1581no—
544C2×C8—1581no—
545C2×C8—1581no—
546C2×C8—1581no—
547C2×C8—1581no—
548C2×C8—1581no—
549C2×C8—1581no—
550C2×C8—1581no—
551C2×C8—1581no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—81no—
561C4⋊C4—81no—
562C4⋊C4—792no—
563C4⋊C4—792no—
564C4⋊C4—1584no—
565C4⋊C4—1584no—
566C4⋊C4—1584no—
567C4⋊C4—1581no—
568C4⋊C4—1581no—
569C4⋊C4(C2×D79)⋊C414yes—
570C4⋊C4(C2×D79)⋊C414yes—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—1584no—
574C22⋊C4—1584no—
575C22⋊C4—1584no—
576C22⋊C4—1584no—
577C22⋊C4—1584no—
578C22⋊C4(C2×D79)⋊C414yes—
579C22⋊C4(C2×D79)⋊C414yes—
580C42—81no—
581C42—81no—
582C42—1584no—
583C42C2×C4×D7912yes—
584C42C2×C4×D7912yes—
585C42C2×D31612yes—
586C42C2×D31612yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—3161no—
594C23—3161no—
595C23—3161no—
596C23—3161no—
597C23—3161no—
598C23—3161no—
599C23—1582no—
600C23C2×(C2×D79)⋊C412yes—
601C23C22×C22⋊D7911yescharacteristic
602Q8—3161no—
603Q8—3161no—
604Q8—6324no—
605Q8—1582no—
606Q8—1582no—
607D4—3161no—
608D4—3161no—
609D4—6324no—
610D4—1582no—
611D4—1582no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—3161no—
639C2×C4—3161no—
640C2×C4—3161no—
641C2×C4—3161no—
642C2×C4—3161no—
643C2×C4—3161no—
644C2×C4—6324no—
645C2×C4—1582no—
646C2×C4—1582no—
647C2×C4—1582no—
648C2×C4C2×(C2×D79)⋊C412yes—
649C2×C4C2×(C2×D79)⋊C412yes—
650C2×C4C2×(C2×D79)⋊C412yes—
651C2×C4C2×(C2×D79)⋊C412yes—
652C2×C4C2×(C2×D79)⋊C412yes—
653C2×C4C22×C4×D7911yescharacteristic
654C2×C4C22×D31611yescharacteristic
655C2×C4#1457920711yescharacteristic
656C2×C4#1457920711yescharacteristic
657C2×C4#1457920811yescharacteristic
658C2×C4#1457920811yescharacteristic
659C8—3161no—
660C8—3161no—
661C8—3161no—
662C8—3161no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—3162no—
671C22—3162no—
672C22—3162no—
673C22—6321no—
674C22—6321no—
675C22—6321no—
676C22—6321no—
677C22C22×(C2×D79)⋊C411yescharacteristic
678C22#1909914111yescharacteristic
679C22#1909914111yescharacteristic
680C22#1909936611yescharacteristic
681C22#1909937111yescharacteristic
682C22#1909937411yescharacteristic
683C22#1909937811yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—3162no—
694C4—3162no—
695C4—3162no—
696C4#1909904311yescharacteristic
697C4#1909904311yescharacteristic
698C4#1909913211yescharacteristic
699C4#1909913911yescharacteristic
700C2—42no—
701C2—6322no—
702C2#2376598811yescharacteristic
703C2#2377192311yescharacteristic
704C2#2377193011yescharacteristic
705C2#2377480511yescharacteristic
706C2#2377482011yescharacteristic
707C2#2377485611yescharacteristic
708C2#2377486511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2314C2
socleC23×C79C22×D4
prime radicalC2×#14579135C22
cosocleC22×C4×C79C24
hypercenter#2314D79
hypocenterC79#21896
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. C2×#19098590C2semidirect
3. #23764352C2semidirect
4. #23764348C2semidirect
5. #23764332C2semidirect
6. #23764332C2semidirect
8. #23763831C2semidirect
10. #23763821C2semidirect
11. #23763412C2semidirect
12. #23763407C2semidirect
13. #23763402C2semidirect
14. #23763397C2semidirect
15. C79×#2314C2semidirect
19. #19099184C4semidirect
357. #2314D79semidirect
370. C79#21896semidirect

Maximal subgroups

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

subgroupindex
C2×#190991842
C2×#190985902
#237643522
#237643482
#237643322
#237638362
#237638312
#237638262
#237638212
#237634122
#237634072
#237634022
#237633972
C79×#23142
#2189679