Finite Group Databasebeta

← #34196183

Subgroups — #34196183

Order 20224.

870 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098462C211yesmaximal, characteristic
2C2×#19098428C211yesmaximal, characteristic
3C2×#19098326C211yesmaximal, characteristic
4C2×#19098325C211yesmaximal, characteristic
5C2×#19098325C211yesmaximal, characteristic
6C2×#19098317C211yesmaximal, characteristic
7C2×#340×C79C211yesmaximal, characteristic
8C23×C79⋊C8C2211yescharacteristic
9C22×C4⋊Dic79—21no—
10C22×C4⋊Dic79C2211yescharacteristic
11C22×C4⋊Dic79C2211yescharacteristic
12C22×C4×Dic79C2211yescharacteristic
13#19098462—22no—
14#19098462C414yescomplemented
15#19098428—22no—
16#19098428—22no—
17C2×C79⋊#95—21no—
18C2×C79⋊#95—21no—
19C2×C79⋊#95—21no—
20#19098326—22no—
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⋊Dic79—21no—
48C2×C4⋊Dic79—21no—
49C2×C4⋊Dic79—24no—
50C2×C4⋊Dic79—42no—
51C2×C4⋊Dic79—42no—
52C2×C4⋊Dic79C2×C412yes—
53C2×C4⋊Dic79D412yes—
54C2×C4×Dic79—21no—
55C2×C4×Dic79—21no—
56C2×C4×Dic79—21no—
57C2×C4×Dic79—21no—
58C2×C4×Dic79C2×C412yes—
59C2×C4×Dic79D412yes—
60C79⋊#95—24no—
61C79⋊#95—24no—
62C79⋊#95—24no—
63C23×C4×C79—21no—
64C23×C4×C79—21no—
65C23×C4×C79C2311yescharacteristic
66C22×C8×C79—21no—
67C22×C8×C79—21no—
68C22×C8×C79—21no—
69C22×C8×C79—21no—
70C22×C8×C79—21no—
71C22×C8×C79—21no—
72C22×C8×C79Q812yes—
73C2×C4⋊C4×C79—21no—
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×C79C2×C412yes—
82C2×C4⋊C4×C79D412yes—
83C2×C4⋊C4×C79D412yes—
84C2×C4⋊C4×C79Q812yes—
85C22×Dic79—22no—
86C22×Dic79—21no—
87C22×Dic79—21no—
88C22×Dic79—22no—
89C22×Dic79—21no—
90C22×Dic79—21no—
91C22×Dic79—21no—
92C22×Dic79—21no—
93C22×Dic79—21no—
94C22×Dic79—21no—
95C22×Dic79—21no—
96C22×Dic79—21no—
97C22×Dic79—21no—
98C22×Dic79—21no—
99C22×Dic79—41no—
100C22×Dic79—41no—
101C22×Dic79—41no—
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×Dic79C22⋊C412yes—
112C22×Dic79C22⋊C412yes—
113C2×C79⋊C8—22no—
114C2×C79⋊C8—22no—
115C2×C79⋊C8—22no—
116C2×C79⋊C8—41no—
117C2×C79⋊C8—41no—
118C2×C79⋊C8—41no—
119C2×C79⋊C8—41no—
120C4⋊Dic79—22no—
121C4⋊Dic79—22no—
122C4⋊Dic79—22no—
123C4⋊Dic79—22no—
124C4⋊Dic79—48no—
125C4⋊Dic79—41no—
126C4⋊Dic79—41no—
127C4⋊Dic79—41no—
128C4⋊Dic79—41no—
129C4×Dic79—22no—
130C4×Dic79—22no—
131C4×Dic79—22no—
132C4×Dic79—22no—
133C24×C79C2×D411yescharacteristic
134C22×C4×C79—22no—
135C22×C4×C79—22no—
136C22×C4×C79—22no—
137C22×C4×C79—22no—
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×C79C22×C411yescharacteristic
149C22×C4×C79C2×D411yescharacteristic
150C22×C4×C79C2×D411yescharacteristic
151C22×C4×C79C2×D411yescharacteristic
152C22×C4×C79C2×D411yescharacteristic
153C22×C4×C79C2×Q811yescharacteristic
154C22×C4×C79C2×Q811yescharacteristic
155C22×C4×C79C2×Q811yescharacteristic
156C22×C4×C79#4111yescharacteristic
157C22×C4×C79#4111yescharacteristic
158C22×C4×C79#4111yescharacteristic
159C22×C4×C79#4111yescharacteristic
160C22×C4×C79#4111yescharacteristic
161C22×C4×C79#4111yescharacteristic
162C2×C8×C79—22no—
163C2×C8×C79—22no—
164C2×C8×C79—22no—
165C2×C8×C79—41no—
166C2×C8×C79—41no—
167C2×C8×C79—41no—
168C2×C8×C79—41no—
169C4⋊C4×C79—22no—
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×C79C4⋊C414yes—
177C23×C79C2×C22⋊C411yescharacteristic
178C23×C79#12011yescharacteristic
179C23×C79#12111yescharacteristic
180C23×C79C22⋊Q811yescharacteristic
181C23×C79#12311yescharacteristic
182C23×C79#12411yescharacteristic
183C23×C79C4⋊Q811yescharacteristic
184C23×C79#13511yescharacteristic
185C23×C79#13511yescharacteristic
186C23×C79#13511yescharacteristic
187C23×C79#13511yescharacteristic
188C23×C79AGL(1,ℤ/8)11yescharacteristic
189C23×C79AGL(1,ℤ/8)11yescharacteristic
190C23×C79#13711yescharacteristic
191C23×C79#13711yescharacteristic
192C2×C4×C79—24no—
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—42no—
200C2×C4×C79—42no—
201C2×C4×C79—42no—
202C2×C4×C79—81no—
203C2×C4×C79—81no—
204C2×C4×C79—81no—
205C2×C4×C79—81no—
206C2×C4×C79C2×C4⋊C411yescharacteristic
207C2×C4×C79#11711yescharacteristic
208C2×C4×C79C4×D411yescharacteristic
209C2×C4×C79C4×D411yescharacteristic
210C2×C4×C79C4×Q811yescharacteristic
211C2×C4×C79C4×Q811yescharacteristic
212C2×C4×C79#12111yescharacteristic
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#12511yescharacteristic
227C2×C4×C79#12511yescharacteristic
228C2×C4×C79#12511yescharacteristic
229C2×C4×C79#12511yescharacteristic
230C2×C4×C79#12611yescharacteristic
231C2×C4×C79#12611yescharacteristic
232C2×C4×C79C4⋊Q811yescharacteristic
233C2×C4×C79C4⋊Q811yescharacteristic
234C2×Dic79—22no—
235C2×Dic79—22no—
236C2×Dic79—22no—
237C2×Dic79—22no—
238C2×Dic79—22no—
239C2×Dic79—22no—
240C2×Dic79—41no—
241C2×Dic79—41no—
242C2×Dic79—41no—
243C2×Dic79—41no—
244C2×Dic79—41no—
245C2×Dic79—41no—
246C2×Dic79—41no—
247C2×Dic79—41no—
248C2×Dic79—42no—
249C2×Dic79—42no—
250C2×Dic79—42no—
251C2×Dic79—42no—
252C2×Dic79—42no—
253C2×Dic79—42no—
254C2×Dic79—81no—
255C2×Dic79—81no—
256C2×Dic79—81no—
257C2×Dic79—81no—
258C2×Dic79—81no—
259C2×Dic79—81no—
260C2×Dic79—81no—
261C2×Dic79—81no—
262C8×C79—42no—
263C79⋊C8—42no—
264C22×C79#38011yescharacteristic
265C22×C79#38611yescharacteristic
266C22×C79#39111yescharacteristic
267C22×C79#39411yescharacteristic
268C22×C79#39511yescharacteristic
269C22×C79#39811yescharacteristic
270C22×C79#40011yescharacteristic
271C22×C79#41611yescharacteristic
272C22×C79#41611yescharacteristic
273C22×C79#41811yescharacteristic
274C22×C79#41911yescharacteristic
275C22×C79#44911yescharacteristic
276C22×C79#44911yescharacteristic
277C22×C79#45211yescharacteristic
278C22×C79#45211yescharacteristic
279C22×C79#46311yescharacteristic
280C22×C79#46311yescharacteristic
281C22×C79#46411yescharacteristic
282C22×C79#46411yescharacteristic
283C22×C79#47811yescharacteristic
284C22×C79#47811yescharacteristic
285C22×C79#47911yescharacteristic
286C22×C79#47911yescharacteristic
287C22×C79#48211yescharacteristic
288C22×C79#48211yescharacteristic
289C22×C79#48511yescharacteristic
290C22×C79#48511yescharacteristic
291C22×C79#48811yescharacteristic
292C22×C79#48811yescharacteristic
293C22×C79#48911yescharacteristic
294C22×C79#48911yescharacteristic
295C22×C79#49911yescharacteristic
296C22×C79#49911yescharacteristic
297C22×C79#50111yescharacteristic
298C22×C79#50111yescharacteristic
299C4×C79—44no—
300C4×C79—82no—
301C4×C79#38711yescharacteristic
302C4×C79#38711yescharacteristic
303C4×C79#38911yescharacteristic
304C4×C79#38911yescharacteristic
305C4×C79#39611yescharacteristic
306C4×C79#39611yescharacteristic
307C4×C79#39811yescharacteristic
308C4×C79#39811yescharacteristic
309Dic79—42no—
310Dic79—42no—
311Dic79—82no—
312Dic79—82no—
313#11208—791nomaximal, Sylow
314C2×C79#144111yescharacteristic
315C2×C79#180411yescharacteristic
316C2×C79#180511yescharacteristic
317C2×C79#187311yescharacteristic
318C2×C79#187511yescharacteristic
319C2×C79#199111yescharacteristic
320C2×C79#199311yescharacteristic
321C2×C79#204211yescharacteristic
322C2×C79#204211yescharacteristic
323C2×C79#205911yescharacteristic
324C2×C79#205911yescharacteristic
325C2×C79#208511yescharacteristic
326C2×C79#208511yescharacteristic
327C2×C79#210111yescharacteristic
328C2×C79#210111yescharacteristic
329C2×#389—791no—
330C2×#382—791no—
331C2×#340—791no—
332C2×#340—791no—
333C2×#340—791no—
334C2×#340D7911yescharacteristic
335C2×#336—791no—
336C79#1120811yescharacteristic, complemented, Sylow
337C23×C8—791no—
338C23×C8C2×D7911yescharacteristic
339C22×C4⋊C4—791no—
340C22×C4⋊C4—791no—
341C22×C4⋊C4—1581no—
342C22×C4⋊C4C2×D7911yescharacteristic
343C22×C4⋊C4C2×D7911yescharacteristic
344C22×C42—791no—
345#389—794no—
346#389—1582no—
347#382—1582no—
348#382—1582no—
349C2×#95—1581no—
350C2×#95—1581no—
351C2×#95—1581no—
352#340—22no—
353#340—1582no—
354#340—1582no—
355#340—1582no—
356#336—1582no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—791no—
360C23×C4—791no—
361C23×C4—1581no—
362C23×C4—1581no—
363C23×C4C22×D7911yescharacteristic
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—792no—
371C22×C8—1581no—
372C22×C8—1581no—
373C22×C8—1581no—
374C22×C8—1581no—
375C22×C8—1581no—
376C22×C8—1581no—
377C22×C8Dic15812yes—
378C2×C4⋊C4—21no—
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—3162no—
387C2×C4⋊C4—3162no—
388C2×C4⋊C4—792no—
389C2×C4⋊C4—792no—
390C2×C4⋊C4—1584no—
391C2×C4⋊C4—1581no—
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⋊C4Dic15812yes—
402C2×C4⋊C4C4×D7912yes—
403C2×C4⋊C4D31612yes—
404C2×C4⋊C4C22⋊D7912yes—
405C2×C42—792no—
406C2×C42—792no—
407C2×C42—1581no—
408C2×C42—1581no—
409C2×C42—1581no—
410C2×C42—1581no—
411#95—1584no—
412#95—1584no—
413#95—1584no—
414C24D4×D7911yescharacteristic
415C22×C4—22no—
416C22×C4—22no—
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—3161no—
430C22×C4—3161no—
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—1581no—
447C22×C4—1581no—
448C22×C4—1581no—
449C22×C4—1581no—
450C22×C4—1581no—
451C22×C4—1581no—
452C22×C4—1581no—
453C22×C4—1581no—
454C22×C4—1581no—
455C22×C4—1581no—
456C22×C4—1581no—
457C22×C4C2×C4×D7911yescharacteristic
458C22×C4D4×D7911yescharacteristic
459C22×C4D4×D7911yescharacteristic
460C22×C4C2×C22⋊D7911yescharacteristic
461C22×C4C2×D31611yescharacteristic
462C22×C4Q8×D7911yescharacteristic
463C22×C4C2×Dic15811yescharacteristic
464C22×C4C2×Dic15811yescharacteristic
465C22×C4#1192962311yescharacteristic
466C22×C4#1192962311yescharacteristic
467C22×C4#1192962311yescharacteristic
468C22×C4#1192962411yescharacteristic
469C22×C4#1192962411yescharacteristic
470C22×C4#1192962511yescharacteristic
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—3161no—
479C2×C8—3161no—
480C2×C8—3161no—
481C2×C8—3161no—
482C2×C8—1582no—
483C2×C8—1582no—
484C2×C8—1582no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—3168no—
493C4⋊C4—3161no—
494C4⋊C4—3161no—
495C4⋊C4—3161no—
496C4⋊C4—3161no—
497C4⋊C4—1582no—
498C4⋊C4—1582no—
499C4⋊C4—1582no—
500C4⋊C4—1582no—
501C4⋊C4Dic79⋊C414yes—
502C42—1582no—
503C42—1582no—
504C42—1582no—
505C42—1582no—
506C23C22⋊C4×D7911yescharacteristic
507C23#1457913111yescharacteristic
508C23#1457913311yescharacteristic
509C23#1457913811yescharacteristic
510C23#1457914611yescharacteristic
511C23#1457914711yescharacteristic
512C23#1457916011yescharacteristic
513C23#1457918011yescharacteristic
514C23#1457918211yescharacteristic
515C23#1457918211yescharacteristic
516C23#1457918411yescharacteristic
517C23#1457918511yescharacteristic
518C23#1457918811yescharacteristic
519C23#1457919011yescharacteristic
520C23#1457919311yescharacteristic
521C2×C4—24no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—3161no—
536C2×C4—3161no—
537C2×C4—3161no—
538C2×C4—3161no—
539C2×C4—3161no—
540C2×C4—3161no—
541C2×C4—3161no—
542C2×C4—3161no—
543C2×C4—3162no—
544C2×C4—3162no—
545C2×C4—3162no—
546C2×C4—3162no—
547C2×C4—3162no—
548C2×C4—3162no—
549C2×C4—6321no—
550C2×C4—6321no—
551C2×C4—6321no—
552C2×C4—6321no—
553C2×C4—6321no—
554C2×C4—6321no—
555C2×C4—6321no—
556C2×C4—6321no—
557C2×C4—1582no—
558C2×C4—1582no—
559C2×C4—1582no—
560C2×C4—1582no—
561C2×C4—1582no—
562C2×C4—1582no—
563C2×C4C2×Dic79⋊C411yescharacteristic
564C2×C4#1457911711yescharacteristic
565C2×C4#1457912311yescharacteristic
566C2×C4C4×D31611yescharacteristic
567C2×C4#1457912611yescharacteristic
568C2×C4C4×Dic15811yescharacteristic
569C2×C4#1457913211yescharacteristic
570C2×C4#1457913311yescharacteristic
571C2×C4#1457913411yescharacteristic
572C2×C4#1457913511yescharacteristic
573C2×C4#1457913611yescharacteristic
574C2×C4#1457913711yescharacteristic
575C2×C4#1457913811yescharacteristic
576C2×C4#1457913811yescharacteristic
577C2×C4#1457913811yescharacteristic
578C2×C4#1457913911yescharacteristic
579C2×C4#1457914011yescharacteristic
580C2×C4#1457914111yescharacteristic
581C2×C4#1457914311yescharacteristic
582C2×C4#1457914511yescharacteristic
583C2×C4#1457915111yescharacteristic
584C2×C4#1457915211yescharacteristic
585C2×C4#1457915211yescharacteristic
586C2×C4#1457915311yescharacteristic
587C2×C4#1457915411yescharacteristic
588C2×C4#1457915611yescharacteristic
589C2×C4#1457916011yescharacteristic
590C2×C4#1457916111yescharacteristic
591C8—42no—
592C8—3162no—
593C22#1909842111yescharacteristic
594C22#1909844111yescharacteristic
595C22#1909846711yescharacteristic
596C22#1909847911yescharacteristic
597C22#1909848411yescharacteristic
598C22#1909849611yescharacteristic
599C22#1909850511yescharacteristic
600C22#1909855611yescharacteristic
601C22#1909855811yescharacteristic
602C22#1909856611yescharacteristic
603C22#1909857011yescharacteristic
604C22#1909870911yescharacteristic
605C22#1909871111yescharacteristic
606C22#1909872611yescharacteristic
607C22#1909872811yescharacteristic
608C22#1909877611yescharacteristic
609C22#1909878011yescharacteristic
610C22#1909878311yescharacteristic
611C22#1909878711yescharacteristic
612C22#1909886111yescharacteristic
613C22#1909886511yescharacteristic
614C22#1909886811yescharacteristic
615C22#1909887211yescharacteristic
616C22#1909888911yescharacteristic
617C22#1909889011yescharacteristic
618C22#1909890611yescharacteristic
619C22#1909890711yescharacteristic
620C22#1909891611yescharacteristic
621C22#1909891911yescharacteristic
622C22#1909892111yescharacteristic
623C22#1909892411yescharacteristic
624C22#1909896311yescharacteristic
625C22#1909896411yescharacteristic
626C22#1909897011yescharacteristic
627C22#1909897111yescharacteristic
628C4—44no—
629C4—82no—
630C4—3162no—
631C4—3162no—
632C4—6322no—
633C4—6322no—
634C4#1909844611yescharacteristic
635C4#1909844811yescharacteristic
636C4#1909845911yescharacteristic
637C4#1909846111yescharacteristic
638C4#1909848511yescharacteristic
639C4#1909848611yescharacteristic
640C4#1909849511yescharacteristic
641C4#1909849711yescharacteristic
642C2#2376165211yescharacteristic
643C2#2376340811yescharacteristic
644C2#2376341311yescharacteristic
645C2#2376371111yescharacteristic
646C2#2376372111yescharacteristic
647C2#2376436311yescharacteristic
648C2#2376437111yescharacteristic
649C2#2376463811yescharacteristic
650C2#2376464011yescharacteristic
651C2#2376473711yescharacteristic
652C2#2376474111yescharacteristic
653C2#2376488411yescharacteristic
654C2#2376488511yescharacteristic
655C2#2376497111yescharacteristic
656C2#2376497311yescharacteristic
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#11208
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
14. #19098462C4semidirect
336. C79#11208semidirect

Maximal subgroups

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

subgroupindex
C2×#190984622
C2×#190984282
C2×#190983262
C2×#190983252
C2×#190983172
C2×#340×C792
#1120879