Finite Group Databasebeta

← #34196248

Subgroups — #34196248

Order 20224.

886 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579094C211yesmaximal, characteristic
2C2×#19098325C211yesmaximal, characteristic
3C2×#19098325C211yesmaximal, characteristic
4C2×#19098325C211yesmaximal, characteristic
5C2×#19098318C211yesmaximal, characteristic
6#23761630C211yesmaximal, characteristic
7C2×#389×C79C211yesmaximal, characteristic
8C23×C79⋊C8C2211yescharacteristic
9C23×C79⋊C8C2211yescharacteristic
10C22×C4⋊Dic79C2211yescharacteristic
11C22×C4⋊Dic79C2211yescharacteristic
12C2×#14579094—22no—
13C2×#14579094—22no—
14C2×#14579094C414yescomplemented
15C2×C79⋊#95—21no—
16C2×C79⋊#95—21no—
17#19098325—22no—
18#19098325—22no—
19#19098325—22no—
20#19098318—22no—
21C22×C4⋊C4×C79—21no—
22C22×C4⋊C4×C79C2211yescharacteristic
23C22×C4⋊C4×C79C2211yescharacteristic
24C22×C42×C79C2211yescharacteristic
25#389×C79—22no—
26#389×C79—22no—
27C2×#95×C79—21no—
28C23×Dic79—21no—
29C23×Dic79—21no—
30C22×C79⋊C8—21no—
31C22×C79⋊C8—21no—
32C22×C79⋊C8—21no—
33C22×C79⋊C8—21no—
34C22×C79⋊C8—21no—
35C22×C79⋊C8—21no—
36C22×C79⋊C8—21no—
37C22×C79⋊C8—21no—
38C22×C79⋊C8—21no—
39C22×C79⋊C8—21no—
40C22×C79⋊C8C2×C412yes—
41C22×C79⋊C8D412yes—
42C22×C79⋊C8Q812yes—
43C22×C79⋊C8Q812yes—
44C2×C4⋊Dic79—21no—
45C2×C4⋊Dic79—21no—
46C2×C4⋊Dic79—21no—
47C2×C4⋊Dic79—21no—
48C2×C4⋊Dic79—21no—
49C2×C4⋊Dic79—21no—
50C2×C4⋊Dic79—21no—
51C2×C4⋊Dic79—21no—
52C2×C4⋊Dic79—21no—
53C2×C4⋊Dic79—21no—
54C2×C4⋊Dic79C2×C412yes—
55C2×C4⋊Dic79Q812yes—
56#14579094—28no—
57C79⋊#95—42no—
58C79⋊#95—42no—
59C23×C4×C79—21no—
60C23×C4×C79—21no—
61C23×C4×C79D411yescharacteristic
62C23×C4×C79D411yescharacteristic
63C23×C4×C79C2311yescharacteristic
64C2×C4⋊C4×C79—21no—
65C2×C4⋊C4×C79—21no—
66C2×C4⋊C4×C79—21no—
67C2×C4⋊C4×C79—21no—
68C2×C4⋊C4×C79—21no—
69C2×C4⋊C4×C79—21no—
70C2×C4⋊C4×C79—21no—
71C2×C4⋊C4×C79—24no—
72C2×C4⋊C4×C79—21no—
73C2×C4⋊C4×C79—42no—
74C2×C4⋊C4×C79—42no—
75C2×C4⋊C4×C79C2×C412yes—
76C2×C4⋊C4×C79D412yes—
77C2×C4⋊C4×C79D412yes—
78C2×C4⋊C4×C79D412yes—
79C2×C42×C79—21no—
80C2×C42×C79—21no—
81C2×C42×C79—21no—
82C2×C42×C79—21no—
83C2×C42×C79—21no—
84C2×C42×C79—21no—
85#95×C79—24no—
86C22×Dic79—22no—
87C22×Dic79—22no—
88C22×Dic79—41no—
89C22×Dic79—41no—
90C22×Dic79—41no—
91C22×Dic79—41no—
92C22×Dic79—41no—
93C22×Dic79—41no—
94C22×Dic79—41no—
95C22×Dic79—41no—
96C22×Dic79—41no—
97C22×Dic79—41no—
98C22×Dic79—41no—
99C22×Dic79—41no—
100C2×C79⋊C8—22no—
101C2×C79⋊C8—22no—
102C2×C79⋊C8—22no—
103C2×C79⋊C8—22no—
104C2×C79⋊C8—22no—
105C2×C79⋊C8—22no—
106C2×C79⋊C8—22no—
107C2×C79⋊C8—22no—
108C2×C79⋊C8—22no—
109C2×C79⋊C8—41no—
110C2×C79⋊C8—41no—
111C2×C79⋊C8—41no—
112C2×C79⋊C8—41no—
113C2×C79⋊C8C4⋊C414yescomplemented
114C4⋊Dic79—22no—
115C4⋊Dic79—22no—
116C4⋊Dic79—22no—
117C4⋊Dic79—22no—
118C4⋊Dic79—41no—
119C4⋊Dic79—41no—
120C4⋊Dic79—41no—
121C4⋊Dic79—41no—
122C24×C79C2×D411yescharacteristic
123C22×C4×C79—22no—
124C22×C4×C79—21no—
125C22×C4×C79—22no—
126C22×C4×C79—21no—
127C22×C4×C79—21no—
128C22×C4×C79—21no—
129C22×C4×C79—22no—
130C22×C4×C79—21no—
131C22×C4×C79—21no—
132C22×C4×C79—21no—
133C22×C4×C79—21no—
134C22×C4×C79—21no—
135C22×C4×C79—21no—
136C22×C4×C79—21no—
137C22×C4×C79—21no—
138C22×C4×C79—22no—
139C22×C4×C79—41no—
140C22×C4×C79—41no—
141C22×C4×C79—41no—
142C22×C4×C79—41no—
143C22×C4×C79—41no—
144C22×C4×C79—41no—
145C22×C4×C79—41no—
146C22×C4×C79—41no—
147C22×C4×C79—41no—
148C22×C4×C79—41no—
149C22×C4×C79D812yes—
150C22×C4×C79Q1612yes—
151C22×C4×C79C22×C411yescharacteristic
152C22×C4×C79C2×D411yescharacteristic
153C22×C4×C79C2×D411yescharacteristic
154C22×C4×C79C2×D411yescharacteristic
155C22×C4×C79C2×D411yescharacteristic
156C22×C4×C79C2×Q811yescharacteristic
157C22×C4×C79C2×Q811yescharacteristic
158C22×C4×C79C2×Q811yescharacteristic
159C22×C4×C79#4111yescharacteristic
160C22×C4×C79#4111yescharacteristic
161C22×C4×C79#4111yescharacteristic
162C22×C4×C79#4111yescharacteristic
163C22×C4×C79#4111yescharacteristic
164C22×C4×C79#4111yescharacteristic
165C4⋊C4×C79—22no—
166C4⋊C4×C79—22no—
167C4⋊C4×C79—22no—
168C4⋊C4×C79—22no—
169C4⋊C4×C79—22no—
170C4⋊C4×C79—48no—
171C4⋊C4×C79—41no—
172C4⋊C4×C79—41no—
173C4⋊C4×C79C22⋊C414yes—
174C42×C79—41no—
175C42×C79—41no—
176C42×C79—41no—
177C42×C79—41no—
178C23×C79C4×D411yescharacteristic
179C23×C79#12011yescharacteristic
180C23×C79#12111yescharacteristic
181C23×C79#12111yescharacteristic
182C23×C79C22⋊Q811yescharacteristic
183C23×C79#12311yescharacteristic
184C23×C79C4⋊Q811yescharacteristic
185C23×C79C2×D811yescharacteristic
186C23×C79C2×Q1611yescharacteristic
187C23×C79#13511yescharacteristic
188C23×C79#13511yescharacteristic
189C23×C79AGL(1,ℤ/8)11yescharacteristic
190C23×C79AGL(1,ℤ/8)11yescharacteristic
191C23×C79#13711yescharacteristic
192C23×C79#13711yescharacteristic
193C2×C4×C79—24no—
194C2×C4×C79—22no—
195C2×C4×C79—22no—
196C2×C4×C79—22no—
197C2×C4×C79—22no—
198C2×C4×C79—22no—
199C2×C4×C79—22no—
200C2×C4×C79—41no—
201C2×C4×C79—41no—
202C2×C4×C79—42no—
203C2×C4×C79—42no—
204C2×C4×C79—42no—
205C2×C4×C79—41no—
206C2×C4×C79—42no—
207C2×C4×C79—41no—
208C2×C4×C79—42no—
209C2×C4×C79—42no—
210C2×C4×C79—41no—
211C2×C4×C79—41no—
212C2×C4×C79—41no—
213C2×C4×C79—41no—
214C2×C4×C79—42no—
215C2×C4×C79—42no—
216C2×C4×C79—42no—
217C2×C4×C79—81no—
218C2×C4×C79—81no—
219C2×C4×C79—81no—
220C2×C4×C79—81no—
221C2×C4×C79C2×C22⋊C411yescharacteristic
222C2×C4×C79C2×C4⋊C411yescharacteristic
223C2×C4×C79#11711yescharacteristic
224C2×C4×C79C4×D411yescharacteristic
225C2×C4×C79C4×Q811yescharacteristic
226C2×C4×C79C4×Q811yescharacteristic
227C2×C4×C79#12111yescharacteristic
228C2×C4×C79#12111yescharacteristic
229C2×C4×C79#12111yescharacteristic
230C2×C4×C79#12111yescharacteristic
231C2×C4×C79C22⋊Q811yescharacteristic
232C2×C4×C79C22⋊Q811yescharacteristic
233C2×C4×C79C22⋊Q811yescharacteristic
234C2×C4×C79C22⋊Q811yescharacteristic
235C2×C4×C79C22⋊Q811yescharacteristic
236C2×C4×C79C22⋊Q811yescharacteristic
237C2×C4×C79C22⋊Q811yescharacteristic
238C2×C4×C79#12311yescharacteristic
239C2×C4×C79#12311yescharacteristic
240C2×C4×C79#12411yescharacteristic
241C2×C4×C79#12511yescharacteristic
242C2×C4×C79#12511yescharacteristic
243C2×C4×C79#12511yescharacteristic
244C2×C4×C79#12511yescharacteristic
245C2×C4×C79#12611yescharacteristic
246C2×C4×C79#12611yescharacteristic
247C2×C4×C79C4⋊Q811yescharacteristic
248C2×C4×C79C4⋊Q811yescharacteristic
249C2×Dic79—42no—
250C2×Dic79—42no—
251C2×Dic79—42no—
252C2×Dic79—42no—
253C2×Dic79—42no—
254C2×Dic79—42no—
255C2×Dic79—81no—
256C2×Dic79—81no—
257C2×Dic79—81no—
258C2×Dic79—81no—
259C2×Dic79—81no—
260C2×Dic79—81no—
261C2×Dic79—81no—
262C2×Dic79—81no—
263C79⋊C8—24no—
264C79⋊C8—42no—
265C22×C79#38611yescharacteristic
266C22×C79#38711yescharacteristic
267C22×C79#38911yescharacteristic
268C22×C79#39411yescharacteristic
269C22×C79#39511yescharacteristic
270C22×C79#39611yescharacteristic
271C22×C79#39811yescharacteristic
272C22×C79C4×D811yescharacteristic
273C22×C79C4×Q1611yescharacteristic
274C22×C79#44111yescharacteristic
275C22×C79#44211yescharacteristic
276C22×C79#44711yescharacteristic
277C22×C79#44911yescharacteristic
278C22×C79#45111yescharacteristic
279C22×C79#45211yescharacteristic
280C22×C79#45911yescharacteristic
281C22×C79#46211yescharacteristic
282C22×C79#46311yescharacteristic
283C22×C79#46411yescharacteristic
284C22×C79#46611yescharacteristic
285C22×C79#46711yescharacteristic
286C22×C79#46811yescharacteristic
287C22×C79#46811yescharacteristic
288C22×C79#47411yescharacteristic
289C22×C79#47711yescharacteristic
290C22×C79#47811yescharacteristic
291C22×C79#47911yescharacteristic
292C22×C79#48011yescharacteristic
293C22×C79#48211yescharacteristic
294C22×C79#48411yescharacteristic
295C22×C79#48511yescharacteristic
296C22×C79#49911yescharacteristic
297C22×C79#50011yescharacteristic
298C22×C79#50111yescharacteristic
299C22×C79#50111yescharacteristic
300C4×C79—44no—
301C4×C79—42no—
302C4×C79—42no—
303C4×C79—82no—
304C4×C79#38011yescharacteristic
305C4×C79#38711yescharacteristic
306C4×C79#38911yescharacteristic
307C4×C79#39111yescharacteristic
308C4×C79#39611yescharacteristic
309C4×C79#39811yescharacteristic
310C4×C79#39811yescharacteristic
311C4×C79#40011yescharacteristic
312Dic79—82no—
313Dic79—82no—
314#11219—791nomaximal, Sylow
315C2×C79#144111yescharacteristic
316C2×C79#187811yescharacteristic
317C2×C79#187911yescharacteristic
318C2×C79#191811yescharacteristic
319C2×C79#192111yescharacteristic
320C2×C79#194211yescharacteristic
321C2×C79#194311yescharacteristic
322C2×C79#203311yescharacteristic
323C2×C79#203611yescharacteristic
324C2×C79#205711yescharacteristic
325C2×C79#205911yescharacteristic
326C2×C79#206711yescharacteristic
327C2×C79#206811yescharacteristic
328C2×C79#208311yescharacteristic
329C2×C79#208511yescharacteristic
330C22×#107—791no—
331C2×#389D7911yescharacteristic
332C2×#340—791no—
333C2×#340—791no—
334C2×#340—791no—
335C2×#336—791no—
336C4⋊#95—791no—
337C79#1121911yescharacteristic, complemented, Sylow
338C23×C8—791no—
339C23×C8—791no—
340C22×C4⋊C4—21no—
341C22×C4⋊C4—791no—
342C22×C4⋊C4—791no—
343C22×C4⋊C4C2×D7911yescharacteristic
344C22×C4⋊C4C2×D7911yescharacteristic
345C22×C42C2×D7911yescharacteristic
346C2×#107—794no—
347C2×#107—1582no—
348C2×#107—1582no—
349#389—22no—
350#389—22no—
351C2×#95—21no—
352C2×#95—1581no—
353C2×#95—1581no—
354#340—1582no—
355#340—1582no—
356#340—1582no—
357#336—1582no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—1581no—
361C23×C4—1581no—
362C23×C4C22⋊D7911yescharacteristic
363C23×C4C22⋊D7911yescharacteristic
364C23×C4C22×D7911yescharacteristic
365C22×C8—792no—
366C22×C8—792no—
367C22×C8—792no—
368C22×C8—792no—
369C22×C8—1581no—
370C22×C8—1581no—
371C22×C8—1581no—
372C22×C8—1581no—
373C22×C8—1581no—
374C22×C8—1581no—
375C22×C8—1581no—
376C22×C8—1581no—
377C22×C8—1581no—
378C22×C8—1581no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—792no—
391C2×C4⋊C4—792no—
392C2×C4⋊C4—1581no—
393C2×C4⋊C4—1581no—
394C2×C4⋊C4—1581no—
395C2×C4⋊C4—1581no—
396C2×C4⋊C4—1581no—
397C2×C4⋊C4—1581no—
398C2×C4⋊C4—1581no—
399C2×C4⋊C4—1581no—
400C2×C4⋊C4—1581no—
401C2×C4⋊C4—1581no—
402C2×C4⋊C4C4×D7912yes—
403C2×C4⋊C4D31612yes—
404C2×C4⋊C4C22⋊D7912yes—
405C2×C4⋊C4C22⋊D7912yes—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412#107—1588no—
413#95—24no—
414#95—3162no—
415#95—3162no—
416C24C2×C22⋊D7911yescharacteristic
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—3161no—
444C22×C4—3161no—
445C22×C4—3161no—
446C22×C4—3161no—
447C22×C4—3161no—
448C22×C4—3161no—
449C22×C4—3161no—
450C22×C4—3161no—
451C22×C4—3161no—
452C22×C4—3161no—
453C22×C4—3161no—
454C22×C4—3161no—
455C22×C4—1582no—
456C22×C4—1582no—
457C22×C4#1192960912yes—
458C22×C4#1192961412yes—
459C22×C4C2×C4×D7911yescharacteristic
460C22×C4D4×D7911yescharacteristic
461C22×C4C2×C22⋊D7911yescharacteristic
462C22×C4C2×C22⋊D7911yescharacteristic
463C22×C4C2×D31611yescharacteristic
464C22×C4Q8×D7911yescharacteristic
465C22×C4Q8×D7911yescharacteristic
466C22×C4Q8×D7911yescharacteristic
467C22×C4#1192962311yescharacteristic
468C22×C4#1192962311yescharacteristic
469C22×C4#1192962311yescharacteristic
470C22×C4#1192962411yescharacteristic
471C22×C4#1192962411yescharacteristic
472C22×C4#1192962511yescharacteristic
473C2×C8—3161no—
474C2×C8—3161no—
475C2×C8—3161no—
476C2×C8—3161no—
477C2×C8—794no—
478C2×C8—1582no—
479C2×C8—1582no—
480C2×C8—1582no—
481C2×C8—1582no—
482C2×C8—1582no—
483C2×C8—1582no—
484C2×C8—1582no—
485C2×C8—1582no—
486C2×C8—1582no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—48no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—3161no—
496C4⋊C4—3161no—
497C4⋊C4—3161no—
498C4⋊C4—3161no—
499C4⋊C4—1582no—
500C4⋊C4—1582no—
501C4⋊C4—1582no—
502C4⋊C4—1582no—
503C4⋊C4(C2×D79)⋊C414yes—
504C42—41no—
505C42—41no—
506C42—41no—
507C42—41no—
508C23C4×C22⋊D7911yescharacteristic
509C23#1457913011yescharacteristic
510C23#1457913311yescharacteristic
511C23#1457913511yescharacteristic
512C23#1457913711yescharacteristic
513C23#1457914211yescharacteristic
514C23#1457915911yescharacteristic
515C23C2×#1192960911yescharacteristic
516C23C2×#1192961411yescharacteristic
517C23#1457918111yescharacteristic
518C23#1457918111yescharacteristic
519C23#1457918611yescharacteristic
520C23#1457918711yescharacteristic
521C23#1457919111yescharacteristic
522C23#1457919211yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—3162no—
552C2×C4—3162no—
553C2×C4—3162no—
554C2×C4—3162no—
555C2×C4—3162no—
556C2×C4—3162no—
557C2×C4—6321no—
558C2×C4—6321no—
559C2×C4—6321no—
560C2×C4—6321no—
561C2×C4—6321no—
562C2×C4—6321no—
563C2×C4—6321no—
564C2×C4—6321no—
565C2×C4C2×(C2×D79)⋊C411yescharacteristic
566C2×C4C4⋊C4×D7911yescharacteristic
567C2×C4#1457911911yescharacteristic
568C2×C4C4×C22⋊D7911yescharacteristic
569C2×C4#1457912611yescharacteristic
570C2×C4#1457912611yescharacteristic
571C2×C4#1457913211yescharacteristic
572C2×C4#1457913311yescharacteristic
573C2×C4#1457913511yescharacteristic
574C2×C4#1457913611yescharacteristic
575C2×C4#1457913711yescharacteristic
576C2×C4#1457913711yescharacteristic
577C2×C4#1457913911yescharacteristic
578C2×C4#1457913911yescharacteristic
579C2×C4#1457914111yescharacteristic
580C2×C4#1457914111yescharacteristic
581C2×C4#1457914111yescharacteristic
582C2×C4#1457914211yescharacteristic
583C2×C4#1457914411yescharacteristic
584C2×C4#1457914811yescharacteristic
585C2×C4#1457915111yescharacteristic
586C2×C4#1457915111yescharacteristic
587C2×C4#1457915111yescharacteristic
588C2×C4#1457915111yescharacteristic
589C2×C4#1457915611yescharacteristic
590C2×C4#1457915611yescharacteristic
591C2×C4#1457915911yescharacteristic
592C2×C4#1457915911yescharacteristic
593C8—3162no—
594C8—1584no—
595C22#1909844211yescharacteristic
596C22#1909844411yescharacteristic
597C22#1909845811yescharacteristic
598C22#1909847711yescharacteristic
599C22#1909848211yescharacteristic
600C22#1909848511yescharacteristic
601C22#1909849311yescharacteristic
602C22C4×#1192960911yescharacteristic
603C22C4×#1192961411yescharacteristic
604C22#1909866811yescharacteristic
605C22#1909867311yescharacteristic
606C22#1909869711yescharacteristic
607C22#1909870811yescharacteristic
608C22#1909871911yescharacteristic
609C22#1909872511yescharacteristic
610C22#1909875811yescharacteristic
611C22#1909877311yescharacteristic
612C22#1909877811yescharacteristic
613C22#1909878511yescharacteristic
614C22#1909879711yescharacteristic
615C22#1909880211yescharacteristic
616C22#1909880711yescharacteristic
617C22#1909881111yescharacteristic
618C22#1909884011yescharacteristic
619C22#1909885511yescharacteristic
620C22#1909886011yescharacteristic
621C22#1909886711yescharacteristic
622C22#1909887411yescharacteristic
623C22#1909888411yescharacteristic
624C22#1909889611yescharacteristic
625C22#1909890111yescharacteristic
626C22#1909896211yescharacteristic
627C22#1909896611yescharacteristic
628C22#1909896911yescharacteristic
629C22#1909897311yescharacteristic
630C4—44no—
631C4—42no—
632C4—42no—
633C4—82no—
634C4—6322no—
635C4—6322no—
636C4#1909842011yescharacteristic
637C4#1909844411yescharacteristic
638C4#1909845811yescharacteristic
639C4#1909846811yescharacteristic
640C4#1909848511yescharacteristic
641C4#1909849311yescharacteristic
642C4#1909849411yescharacteristic
643C4#1909850111yescharacteristic
644C2#2376165011yescharacteristic
645C2#2376374111yescharacteristic
646C2#2376374811yescharacteristic
647C2#2376396811yescharacteristic
648C2#2376398911yescharacteristic
649C2#2376413011yescharacteristic
650C2#2376413511yescharacteristic
651C2#2376457911yescharacteristic
652C2#2376460011yescharacteristic
653C2#2376472511yescharacteristic
654C2#2376473511yescharacteristic
655C2#2376478511yescharacteristic
656C2#2376479211yescharacteristic
657C2#2376487111yescharacteristic
658C2#2376488111yescharacteristic
subgroupG/H
centerC24C2×C22⋊D79
commutatorC22×C4×C79C22×C4
FrattiniC23×C4C22×D79
FittingC2×#389×C79C2
socle, prime radicalC24×C79C2×D4
cosocleC23×C4×C79C23
hypercenterC2×#389D79
hypocenterC79#11219
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
14. C2×#14579094C4semidirect
113. C2×C79⋊C8C4⋊C4semidirect
337. C79#11219semidirect

Maximal subgroups

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

subgroupindex
C22×#145790942
C2×#190983252
C2×#190983182
#237616302
C2×#389×C792
#1121979