Finite Group Databasebeta

← #34196250

Subgroups — #34196250

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×#14579095C211yesmaximal, characteristic
2C2×#19098459C211yesmaximal, characteristic
3C2×#19098325C211yesmaximal, characteristic
4C2×#19098325C211yesmaximal, characteristic
5C2×#19098317C211yesmaximal, characteristic
6#23761629C211yesmaximal, characteristic
7C2×#340×C79C211yesmaximal, characteristic
8C23×C79⋊C8C2211yescharacteristic
9C22×C4⋊Dic79C2211yescharacteristic
10C22×C4⋊Dic79C2211yescharacteristic
11C22×Dic79⋊C4—21no—
12C22×C4×Dic79C2211yescharacteristic
13C2×#14579095—22no—
14C2×#14579095—22no—
15C2×#14579095C414yescomplemented
16#19098459—22no—
17#19098459—22no—
18C2×C79⋊#95—21no—
19C2×C79⋊#95—21no—
20C2×C79⋊#95—21no—
21#19098325—22no—
22#19098325—22no—
23#19098317—22no—
24C23×C8×C79C2211yescharacteristic
25C22×C4⋊C4×C79C2211yescharacteristic
26C22×C4⋊C4×C79C2211yescharacteristic
27#340×C79—22no—
28C23×Dic79—21no—
29C23×Dic79—21no—
30C23×Dic79D411yescharacteristic
31C23×Dic79D411yescharacteristic
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⋊C8Q812yes—
39C2×C4⋊Dic79—21no—
40C2×C4⋊Dic79—21no—
41C2×C4⋊Dic79—21no—
42C2×C4⋊Dic79—21no—
43C2×C4⋊Dic79—21no—
44C2×C4⋊Dic79—21no—
45C2×C4⋊Dic79—21no—
46C2×C4⋊Dic79—21no—
47C2×C4⋊Dic79C2×C412yes—
48C2×C4⋊Dic79C2×C412yes—
49C2×C4⋊Dic79D412yes—
50C2×C4⋊Dic79D412yes—
51C2×Dic79⋊C4—24no—
52C2×Dic79⋊C4—42no—
53C2×Dic79⋊C4—42no—
54C2×C4×Dic79—21no—
55C2×C4×Dic79—21no—
56C2×C4×Dic79—21no—
57C2×C4×Dic79—21no—
58C2×C4×Dic79—21no—
59C2×C4×Dic79—21no—
60#14579095—28no—
61C79⋊#95—24no—
62C79⋊#95—42no—
63C79⋊#95—42no—
64C23×C4×C79—21no—
65C23×C4×C79—21no—
66C23×C4×C79C2311yescharacteristic
67C22×C8×C79—21no—
68C22×C8×C79—21no—
69C22×C8×C79—21no—
70C22×C8×C79—21no—
71C22×C8×C79C2×C412yes—
72C22×C8×C79D412yes—
73C22×C8×C79Q812yes—
74C2×C4⋊C4×C79—21no—
75C2×C4⋊C4×C79—21no—
76C2×C4⋊C4×C79—21no—
77C2×C4⋊C4×C79—21no—
78C2×C4⋊C4×C79—21no—
79C2×C4⋊C4×C79—21no—
80C2×C4⋊C4×C79—21no—
81C2×C4⋊C4×C79—21no—
82C2×C4⋊C4×C79—21no—
83C2×C4⋊C4×C79—21no—
84C2×C4⋊C4×C79D412yes—
85C2×C4⋊C4×C79Q812yes—
86C22×Dic79—22no—
87C22×Dic79—22no—
88C22×Dic79—21no—
89C22×Dic79—22no—
90C22×Dic79—21no—
91C22×Dic79—21no—
92C22×Dic79—21no—
93C22×Dic79—22no—
94C22×Dic79—21no—
95C22×Dic79—21no—
96C22×Dic79—21no—
97C22×Dic79—21no—
98C22×Dic79—21no—
99C22×Dic79—21no—
100C22×Dic79—21no—
101C22×Dic79—21no—
102C22×Dic79—41no—
103C22×Dic79—41no—
104C22×Dic79—41no—
105C22×Dic79—41no—
106C22×Dic79—41no—
107C22×Dic79—41no—
108C22×Dic79—41no—
109C22×Dic79—41no—
110C22×Dic79—41no—
111C22×Dic79—41no—
112C22×Dic79D812yes—
113C22×Dic79Q1612yes—
114C2×C79⋊C8—22no—
115C2×C79⋊C8—22no—
116C2×C79⋊C8—22no—
117C2×C79⋊C8—41no—
118C2×C79⋊C8—41no—
119C2×C79⋊C8—41no—
120C2×C79⋊C8—41no—
121C4⋊Dic79—22no—
122C4⋊Dic79—22no—
123C4⋊Dic79—22no—
124C4⋊Dic79—22no—
125C4⋊Dic79—22no—
126C4⋊Dic79—41no—
127C4⋊Dic79—41no—
128C4⋊Dic79C22⋊C414yes—
129Dic79⋊C4—48no—
130C4×Dic79—41no—
131C4×Dic79—41no—
132C4×Dic79—41no—
133C4×Dic79—41no—
134C24×C79C2×D411yescharacteristic
135C22×C4×C79—22no—
136C22×C4×C79—22no—
137C22×C4×C79—41no—
138C22×C4×C79—41no—
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×C79C22×C411yescharacteristic
150C22×C4×C79C2×D411yescharacteristic
151C22×C4×C79C2×D411yescharacteristic
152C22×C4×C79C2×D411yescharacteristic
153C22×C4×C79C2×D411yescharacteristic
154C22×C4×C79C2×Q811yescharacteristic
155C22×C4×C79C2×Q811yescharacteristic
156C22×C4×C79C2×Q811yescharacteristic
157C22×C4×C79#4111yescharacteristic
158C22×C4×C79#4111yescharacteristic
159C22×C4×C79#4111yescharacteristic
160C22×C4×C79#4111yescharacteristic
161C22×C4×C79#4111yescharacteristic
162C22×C4×C79#4111yescharacteristic
163C2×C8×C79—22no—
164C2×C8×C79—22no—
165C2×C8×C79—22no—
166C2×C8×C79—22no—
167C2×C8×C79—22no—
168C2×C8×C79—22no—
169C2×C8×C79C4⋊C414yescomplemented
170C4⋊C4×C79—22no—
171C4⋊C4×C79—22no—
172C4⋊C4×C79—22no—
173C4⋊C4×C79—22no—
174C4⋊C4×C79—41no—
175C4⋊C4×C79—41no—
176C4⋊C4×C79—41no—
177C4⋊C4×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—42no—
194C2×C4×C79—42no—
195C2×C4×C79—42no—
196C2×C4×C79—42no—
197C2×C4×C79—42no—
198C2×C4×C79—42no—
199C2×C4×C79—81no—
200C2×C4×C79—81no—
201C2×C4×C79—81no—
202C2×C4×C79—81no—
203C2×C4×C79—81no—
204C2×C4×C79—81no—
205C2×C4×C79—81no—
206C2×C4×C79—81no—
207C2×C4×C79C2×C22⋊C411yescharacteristic
208C2×C4×C79C2×C4⋊C411yescharacteristic
209C2×C4×C79#11711yescharacteristic
210C2×C4×C79C4×D411yescharacteristic
211C2×C4×C79C4×Q811yescharacteristic
212C2×C4×C79C4×Q811yescharacteristic
213C2×C4×C79#12111yescharacteristic
214C2×C4×C79#12111yescharacteristic
215C2×C4×C79#12111yescharacteristic
216C2×C4×C79#12111yescharacteristic
217C2×C4×C79C22⋊Q811yescharacteristic
218C2×C4×C79C22⋊Q811yescharacteristic
219C2×C4×C79C22⋊Q811yescharacteristic
220C2×C4×C79C22⋊Q811yescharacteristic
221C2×C4×C79C22⋊Q811yescharacteristic
222C2×C4×C79C22⋊Q811yescharacteristic
223C2×C4×C79C22⋊Q811yescharacteristic
224C2×C4×C79#12311yescharacteristic
225C2×C4×C79#12311yescharacteristic
226C2×C4×C79#12411yescharacteristic
227C2×C4×C79#12511yescharacteristic
228C2×C4×C79#12511yescharacteristic
229C2×C4×C79#12511yescharacteristic
230C2×C4×C79#12511yescharacteristic
231C2×C4×C79#12611yescharacteristic
232C2×C4×C79#12611yescharacteristic
233C2×C4×C79C4⋊Q811yescharacteristic
234C2×C4×C79C4⋊Q811yescharacteristic
235C2×Dic79—24no—
236C2×Dic79—22no—
237C2×Dic79—22no—
238C2×Dic79—22no—
239C2×Dic79—22no—
240C2×Dic79—22no—
241C2×Dic79—22no—
242C2×Dic79—41no—
243C2×Dic79—41no—
244C2×Dic79—42no—
245C2×Dic79—42no—
246C2×Dic79—42no—
247C2×Dic79—41no—
248C2×Dic79—42no—
249C2×Dic79—41no—
250C2×Dic79—42no—
251C2×Dic79—42no—
252C2×Dic79—41no—
253C2×Dic79—41no—
254C2×Dic79—41no—
255C2×Dic79—41no—
256C2×Dic79—42no—
257C2×Dic79—42no—
258C2×Dic79—42no—
259C2×Dic79—81no—
260C2×Dic79—81no—
261C2×Dic79—81no—
262C2×Dic79—81no—
263C8×C79—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—82no—
301C4×C79—82no—
302C4×C79#38011yescharacteristic
303C4×C79#38711yescharacteristic
304C4×C79#38911yescharacteristic
305C4×C79#39111yescharacteristic
306C4×C79#39611yescharacteristic
307C4×C79#39811yescharacteristic
308C4×C79#39811yescharacteristic
309C4×C79#40011yescharacteristic
310Dic79—44no—
311Dic79—42no—
312Dic79—42no—
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×#389—791no—
332C2×#340—791no—
333C2×#340—791no—
334C2×#340D7911yescharacteristic
335C2×#336—791no—
336C4⋊#95—791no—
337C79#1121911yescharacteristic, complemented, Sylow
338C23×C8—791no—
339C23×C8C2×D7911yescharacteristic
340C22×C4⋊C4—791no—
341C22×C4⋊C4—791no—
342C22×C4⋊C4—1581no—
343C22×C4⋊C4C2×D7911yescharacteristic
344C22×C4⋊C4C2×D7911yescharacteristic
345C22×C42—791no—
346C2×#107—794no—
347C2×#107—1582no—
348C2×#107—1582no—
349#389—1582no—
350#389—1582no—
351C2×#95—1581no—
352C2×#95—1581no—
353C2×#95—1581no—
354#340—22no—
355#340—1582no—
356#340—1582no—
357#336—1582no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—791no—
361C23×C4—791no—
362C23×C4—1581no—
363C23×C4—1581no—
364C23×C4C22×D7911yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—792no—
370C22×C8—1581no—
371C22×C8—1581no—
372C22×C8—1581no—
373C22×C8—1581no—
374C22×C8—1581no—
375C22×C8—1581no—
376C22×C8Dic15812yes—
377C22×C8C4×D7912yes—
378C22×C8C22⋊D7912yes—
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—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—3162no—
390C2×C4⋊C4—3162no—
391C2×C4⋊C4—792no—
392C2×C4⋊C4—792no—
393C2×C4⋊C4—792no—
394C2×C4⋊C4—792no—
395C2×C4⋊C4—1584no—
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⋊C4—1581no—
403C2×C4⋊C4—1581no—
404C2×C4⋊C4Dic15812yes—
405C2×C4⋊C4D31612yes—
406C2×C42—1581no—
407C2×C42—1581no—
408C2×C42—1581no—
409C2×C42—1581no—
410C2×C42—1581no—
411C2×C42—1581no—
412#107—1588no—
413#95—3162no—
414#95—3162no—
415#95—1584no—
416C24D4×D7911yescharacteristic
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—3161no—
432C22×C4—3161no—
433C22×C4—3161no—
434C22×C4—3161no—
435C22×C4—3161no—
436C22×C4—3161no—
437C22×C4—3161no—
438C22×C4—3161no—
439C22×C4—3161no—
440C22×C4—3161no—
441C22×C4—792no—
442C22×C4—792no—
443C22×C4—1582no—
444C22×C4—1582no—
445C22×C4—1581no—
446C22×C4—1582no—
447C22×C4—1581no—
448C22×C4—1581no—
449C22×C4—1581no—
450C22×C4—1582no—
451C22×C4—1581no—
452C22×C4—1581no—
453C22×C4—1581no—
454C22×C4—1581no—
455C22×C4—1581no—
456C22×C4—1581no—
457C22×C4—1581no—
458C22×C4—1581no—
459C22×C4C2×C4×D7911yescharacteristic
460C22×C4D4×D7911yescharacteristic
461C22×C4D4×D7911yescharacteristic
462C22×C4C2×C22⋊D7911yescharacteristic
463C22×C4C2×D31611yescharacteristic
464C22×C4Q8×D7911yescharacteristic
465C22×C4C2×Dic15811yescharacteristic
466C22×C4C2×Dic15811yescharacteristic
467C22×C4#1192962311yescharacteristic
468C22×C4#1192962311yescharacteristic
469C22×C4#1192962311yescharacteristic
470C22×C4#1192962411yescharacteristic
471C22×C4#1192962411yescharacteristic
472C22×C4#1192962511yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—3161no—
480C2×C8—3161no—
481C2×C8—3161no—
482C2×C8—3161no—
483C2×C8—1582no—
484C2×C8—1582no—
485C2×C8—1582no—
486C2×C8Dic79⋊C414yescomplemented
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—3168no—
496C4⋊C4—3161no—
497C4⋊C4—3161no—
498C4⋊C4—794no—
499C4⋊C4—1582no—
500C4⋊C4—1582no—
501C4⋊C4—1582no—
502C4⋊C4—1582no—
503C4⋊C4—1582no—
504C42—3161no—
505C42—3161no—
506C42—3161no—
507C42—3161no—
508C23#1457912311yescharacteristic
509C23#1457913111yescharacteristic
510C23#1457913211yescharacteristic
511C23#1457913411yescharacteristic
512C23#1457913811yescharacteristic
513C23#1457914311yescharacteristic
514C23#1457916011yescharacteristic
515C23D8×D7911yescharacteristic
516C23Q16×D7911yescharacteristic
517C23#1457918011yescharacteristic
518C23#1457918411yescharacteristic
519C23#1457918811yescharacteristic
520C23#1457918811yescharacteristic
521C23#1457919011yescharacteristic
522C23#1457919011yescharacteristic
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—3161no—
538C2×C4—3162no—
539C2×C4—3161no—
540C2×C4—3162no—
541C2×C4—3162no—
542C2×C4—3162no—
543C2×C4—3161no—
544C2×C4—3161no—
545C2×C4—3161no—
546C2×C4—3161no—
547C2×C4—3162no—
548C2×C4—3162no—
549C2×C4—3161no—
550C2×C4—3161no—
551C2×C4—3162no—
552C2×C4—3162no—
553C2×C4—3162no—
554C2×C4—6321no—
555C2×C4—6321no—
556C2×C4—6321no—
557C2×C4—6321no—
558C2×C4—1582no—
559C2×C4—1584no—
560C2×C4—1582no—
561C2×C4—1582no—
562C2×C4—1582no—
563C2×C4—1582no—
564C2×C4—1582no—
565C2×C4C22⋊C4×D7911yescharacteristic
566C2×C4C2×Dic79⋊C411yescharacteristic
567C2×C4#1457911711yescharacteristic
568C2×C4C4×D31611yescharacteristic
569C2×C4#1457912611yescharacteristic
570C2×C4C4×Dic15811yescharacteristic
571C2×C4#1457913311yescharacteristic
572C2×C4#1457913311yescharacteristic
573C2×C4#1457913511yescharacteristic
574C2×C4#1457913611yescharacteristic
575C2×C4#1457913711yescharacteristic
576C2×C4#1457913811yescharacteristic
577C2×C4#1457913811yescharacteristic
578C2×C4#1457913811yescharacteristic
579C2×C4#1457913911yescharacteristic
580C2×C4#1457914011yescharacteristic
581C2×C4#1457914111yescharacteristic
582C2×C4#1457914511yescharacteristic
583C2×C4#1457914611yescharacteristic
584C2×C4#1457914711yescharacteristic
585C2×C4#1457915111yescharacteristic
586C2×C4#1457915211yescharacteristic
587C2×C4#1457915211yescharacteristic
588C2×C4#1457915311yescharacteristic
589C2×C4#1457915411yescharacteristic
590C2×C4#1457915611yescharacteristic
591C2×C4#1457916011yescharacteristic
592C2×C4#1457916111yescharacteristic
593C8—24no—
594C8—3162no—
595C22#1909844111yescharacteristic
596C22#1909844611yescharacteristic
597C22#1909845911yescharacteristic
598C22#1909847911yescharacteristic
599C22#1909848411yescharacteristic
600C22#1909848611yescharacteristic
601C22#1909849711yescharacteristic
602C22#1909864511yescharacteristic
603C22#1909865711yescharacteristic
604C22#1909866911yescharacteristic
605C22#1909867411yescharacteristic
606C22#1909869811yescharacteristic
607C22#1909871111yescharacteristic
608C22#1909872011yescharacteristic
609C22#1909872611yescharacteristic
610C22#1909875711yescharacteristic
611C22#1909877211yescharacteristic
612C22#1909878111yescharacteristic
613C22#1909878411yescharacteristic
614C22#1909879611yescharacteristic
615C22#1909880111yescharacteristic
616C22#1909880611yescharacteristic
617C22#1909880611yescharacteristic
618C22#1909884111yescharacteristic
619C22#1909885611yescharacteristic
620C22#1909886111yescharacteristic
621C22#1909887211yescharacteristic
622C22#1909887511yescharacteristic
623C22#1909888511yescharacteristic
624C22#1909889711yescharacteristic
625C22#1909890311yescharacteristic
626C22#1909896411yescharacteristic
627C22#1909896711yescharacteristic
628C22#1909897011yescharacteristic
629C22#1909897011yescharacteristic
630C4—82no—
631C4—82no—
632C4—3164no—
633C4—3162no—
634C4—3162no—
635C4—6322no—
636C4#1909842111yescharacteristic
637C4#1909844811yescharacteristic
638C4#1909846111yescharacteristic
639C4#1909846711yescharacteristic
640C4#1909848511yescharacteristic
641C4#1909849511yescharacteristic
642C4#1909849611yescharacteristic
643C4#1909850511yescharacteristic
644C2#2376165211yescharacteristic
645C2#2376374211yescharacteristic
646C2#2376374911yescharacteristic
647C2#2376397011yescharacteristic
648C2#2376399111yescharacteristic
649C2#2376413111yescharacteristic
650C2#2376413611yescharacteristic
651C2#2376458111yescharacteristic
652C2#2376460211yescharacteristic
653C2#2376472711yescharacteristic
654C2#2376474111yescharacteristic
655C2#2376478611yescharacteristic
656C2#2376479311yescharacteristic
657C2#2376487511yescharacteristic
658C2#2376488711yescharacteristic
subgroupG/H
centerC24D4×D79
commutatorC22×C4×C79C22×C4
FrattiniC23×C4C22×D79
FittingC2×#340×C79C2
socle, prime radicalC24×C79C2×D4
cosocleC23×C4×C79C23
hypercenterC2×#340D79
hypocenterC79#11219
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
15. C2×#14579095C4semidirect
169. C2×C8×C79C4⋊C4semidirect
337. C79#11219semidirect
486. C2×C8Dic79⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#145790952
C2×#190984592
C2×#190983252
C2×#190983172
#237616292
C2×#340×C792
#1121979