Finite Group Databasebeta

← #34306455

Subgroups — #34306455

Order 20224.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098635C211yesmaximal, characteristic
2C2×#19098606C211yesmaximal, characteristic, complemented
3C22×#14579094C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic79C211yesmaximal, characteristic
5#23764166C211yesmaximal, characteristic, complemented
6#23764158C211yesmaximal, characteristic, complemented
7#23763599C211yesmaximal, characteristic, complemented
8#23763592C211yesmaximal, characteristic, complemented
9#23763588C211yesmaximal, characteristic, complemented
10#23763587C211yesmaximal, characteristic, complemented
11#23763569C211yesmaximal, characteristic, complemented
12#23763431C211yesmaximal, characteristic, complemented
13#23763423C211yesmaximal, characteristic, complemented
14#23763298C211yesmaximal, characteristic, complemented
15C79×#2352C211yesmaximal, characteristic
16C22×#11929608C2211yescharacteristic
17C23×C79⋊C8C2211yescharacteristic
18C2×D4×Dic79—21no—
19C22×C4⋊Dic79C2211yescharacteristic
20C22×C4⋊Dic79C2211yescharacteristic
21#19098635C418yescomplemented
22#19098606—24no—
23C2×#14579094—24no—
24C2×#14579094C2211yescharacteristic
25C2×#14579094C2211yescharacteristic
26C2×#14579094C2211yescharacteristic
27C2×#14579094C2211yescharacteristic
28C2×#14579094C2211yescharacteristic
29C2×#14579094C2211yescharacteristic
30C2×#14579092C2211yescharacteristic
31C2×#14579092C2211yescharacteristic
32C2×#14579092C2211yescharacteristic
33C2×#14579092C2211yescharacteristic
34C2×C4⋊(C79⋊C8)C2211yescharacteristic
35C2×C22⋊(C79⋊C8)C2211yescharacteristic
36C2×C22⋊(C79⋊C8)C2211yescharacteristic
37C2×#14579072C2211yescharacteristic
38#19098462—21no—
39#19098438—21no—
40#19098438—21no—
41#19098433C2211yescharacteristic
42#19098423C2211yescharacteristic
43#19098423C2211yescharacteristic
44C4×C4⋊Dic79C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51C2×C4×D4×C79C2211yescharacteristic
52C2×#117×C79C2211yescharacteristic
53C22×C4⋊C4×C79C2211yescharacteristic
54#388×C79—21no—
55#387×C79—21no—
56#386×C79—21no—
57#382×C79C2211yescharacteristic
58#380×C79C2211yescharacteristic
59#380×C79C2211yescharacteristic
60C4×C4⋊C4×C79C2211yescharacteristic
61C4×C22⋊C4×C79—21no—
62C23×Dic79—21no—
63C23×Dic79—21no—
64C2×#11929608—22no—
65C2×#11929608—22no—
66C2×#11929608C2×C414yescomplemented
67C22×C79⋊C8—22no—
68C22×C79⋊C8—22no—
69C22×C79⋊C8C2×C414yescomplemented
70C22×C79⋊C8C2311yescharacteristic
71C22×C79⋊C8C2311yescharacteristic
72C22×C79⋊C8C2311yescharacteristic
73C22×C79⋊C8C2311yescharacteristic
74D4×Dic79—44no—
75C2×C4⋊Dic79—22no—
76C2×C4⋊Dic79—22no—
77C2×C4⋊Dic79—21no—
78C2×C4⋊Dic79—21no—
79C2×C4⋊Dic79—21no—
80C2×C4⋊Dic79—21no—
81C2×C4⋊Dic79—41no—
82C2×C4⋊Dic79—41no—
83C2×C4⋊Dic79C2311yescharacteristic
84C2×C4⋊Dic79C2311yescharacteristic
85C2×C4⋊Dic79C2311yescharacteristic
86C2×C4⋊Dic79C2311yescharacteristic
87C2×C22⋊Dic79—21no—
88C2×C22⋊Dic79—21no—
89C2×C4×Dic79—21no—
90#14579094—22no—
91#14579094—22no—
92#14579094—22no—
93#14579094—22no—
94#14579094—41no—
95#14579094D414yescomplemented
96#14579092—22no—
97#14579092—22no—
98#14579092—22no—
99#14579092—41no—
100C4⋊(C79⋊C8)C2×C414yescomplemented
101C22⋊(C79⋊C8)C2×C414yescomplemented
102C22⋊(C79⋊C8)C2×C414yescomplemented
103#14579072C2×C414yescomplemented
104C79⋊#95—21no—
105C79⋊#95—21no—
106C79⋊#95—21no—
107C22×D4×C79D411yescharacteristic
108C23×C4×C79—21no—
109C23×C4×C79C2311yescharacteristic
110C23×C4×C79C2311yescharacteristic
111C4×D4×C79C2×C414yes—
112C4×D4×C79Q814yes—
113#117×C79—22no—
114#117×C79—41no—
115C2×C4⋊C4×C79—22no—
116C2×C4⋊C4×C79—21no—
117C2×C4⋊C4×C79—41no—
118C2×C4⋊C4×C79D411yescharacteristic
119C2×C4⋊C4×C79C2311yescharacteristic
120C2×C4⋊C4×C79C2311yescharacteristic
121C2×C4⋊C4×C79C2311yescharacteristic
122C2×C4⋊C4×C79C2311yescharacteristic
123C2×C22⋊C4×C79—21no—
124C2×C22⋊C4×C79—21no—
125C2×C22⋊C4×C79—21no—
126C2×C22⋊C4×C79D411yescharacteristic
127C2×C22⋊C4×C79D411yescharacteristic
128C2×C42×C79—21no—
129C2×C42×C79—21no—
130C2×C42×C79C2311yescharacteristic
131#95×C79—21no—
132#95×C79—21no—
133#95×C79—21no—
134#95×C79—21no—
135#95×C79—21no—
136C22×Dic79—21no—
137C22×Dic79—21no—
138C22×Dic79—21no—
139C22×Dic79—21no—
140C22×Dic79—42no—
141C22×Dic79—42no—
142C22×Dic79—42no—
143C22×Dic79—42no—
144C22×Dic79—81no—
145C22×Dic79—81no—
146#11929608—28no—
147C2×C79⋊C8—28no—
148C2×C79⋊C8—21no—
149C2×C79⋊C8—21no—
150C2×C79⋊C8—21no—
151C2×C79⋊C8—21no—
152C2×C79⋊C8—21no—
153C2×C79⋊C8—21no—
154C2×C79⋊C8C22×C412yes—
155C2×C79⋊C8C22×C412yes—
156C2×C79⋊C8C22×C412yes—
157C2×C79⋊C8C22×C412yes—
158C2×C79⋊C8C2×D412yes—
159C2×C79⋊C8#4112yes—
160C4⋊Dic79—21no—
161C4⋊Dic79—21no—
162C4⋊Dic79—21no—
163C4⋊Dic79—21no—
164C4⋊Dic79—21no—
165C4⋊Dic79—21no—
166C4⋊Dic79—21no—
167C4⋊Dic79—42no—
168C4⋊Dic79—42no—
169C4⋊Dic79—42no—
170C4⋊Dic79—81no—
171C4⋊Dic79C2×D412yes—
172C22⋊Dic79—42no—
173C22⋊Dic79—42no—
174C4×Dic79—42no—
175C24×C79C2×D411yescharacteristic
176C24×C79C2×D411yescharacteristic
177C2×D4×C79—22no—
178C2×D4×C79—22no—
179C2×D4×C79C4⋊C414yes—
180C22×C4×C79—21no—
181C22×C4×C79—21no—
182C22×C4×C79—21no—
183C22×C4×C79—21no—
184C22×C4×C79—21no—
185C22×C4×C79—21no—
186C22×C4×C79—21no—
187C22×C4×C79—21no—
188C22×C4×C79—21no—
189C22×C4×C79—21no—
190C22×C4×C79—21no—
191C22×C4×C79—21no—
192C22×C4×C79—42no—
193C22×C4×C79—42no—
194C22×C4×C79—81no—
195C22×C4×C79C22×C412yes—
196C22×C4×C79C22×C412yes—
197C22×C4×C79C2×D411yescharacteristic
198C22×C4×C79C2×D411yescharacteristic
199C22×C4×C79C2×D411yescharacteristic
200C22×C4×C79C2×D411yescharacteristic
201C22×C4×C79C2×Q812yes—
202C22×C4×C79C2×Q812yes—
203C22×C4×C79C2411yescharacteristic
204C4⋊C4×C79—21no—
205C4⋊C4×C79—21no—
206C4⋊C4×C79—21no—
207C4⋊C4×C79—21no—
208C4⋊C4×C79—21no—
209C4⋊C4×C79—21no—
210C4⋊C4×C79—21no—
211C4⋊C4×C79—42no—
212C4⋊C4×C79C4⋊C414yes—
213C4⋊C4×C79C2×D412yes—
214C22⋊C4×C79—42no—
215C22⋊C4×C79—42no—
216C22⋊C4×C79—81no—
217C22⋊C4×C79C4⋊C414yes—
218C22⋊C4×C79C4⋊C414yes—
219C42×C79—42no—
220C42×C79—81no—
221C42×C79C22×C412yes—
222C42×C79C2×Q812yes—
223C23×C79—21no—
224C23×C79—21no—
225C23×C79—21no—
226C23×C79—21no—
227C23×C79—21no—
228C23×C79—21no—
229C23×C79—21no—
230C23×C79—21no—
231C23×C79—21no—
232C23×C79—21no—
233C23×C79C2×C4⋊C412yes—
234C23×C79C2×C4⋊C412yes—
235C23×C79AGL(1,ℤ/8)12yes—
236C23×C79#13712yes—
237C23×C79C22×D411yescharacteristic
238D4×C79—28no—
239C2×C4×C79—21no—
240C2×C4×C79—21no—
241C2×C4×C79—21no—
242C2×C4×C79—21no—
243C2×C4×C79—21no—
244C2×C4×C79—21no—
245C2×C4×C79—21no—
246C2×C4×C79—21no—
247C2×C4×C79—22no—
248C2×C4×C79—22no—
249C2×C4×C79—22no—
250C2×C4×C79—22no—
251C2×C4×C79—22no—
252C2×C4×C79—22no—
253C2×C4×C79—22no—
254C2×C4×C79—22no—
255C2×C4×C79—22no—
256C2×C4×C79—41no—
257C2×C4×C79—41no—
258C2×C4×C79—41no—
259C2×C4×C79—41no—
260C2×C4×C79—41no—
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—84no—
268C2×C4×C79C2×C4⋊C412yes—
269C2×C4×C79C2×C4⋊C412yes—
270C2×C4×C79C2×C4⋊C412yes—
271C2×C4×C79C2×C4⋊C412yes—
272C2×C4×C79C23×C411yescharacteristic
273C2×C4×C79C22×D411yescharacteristic
274C2×C4×C79C22×Q811yescharacteristic
275C2×C4×C79C2×#4111yescharacteristic
276C2×C4×C79H(5,𝔽2)11yescharacteristic
277C2×C4×C792−1+411yescharacteristic
278C2×Dic79—22no—
279C2×Dic79—41no—
280C2×Dic79—41no—
281C2×Dic79—41no—
282C2×Dic79—41no—
283C2×Dic79—41no—
284C2×Dic79—41no—
285C2×Dic79—41no—
286C2×Dic79—41no—
287C2×Dic79—41no—
288C2×Dic79—41no—
289C2×Dic79—41no—
290C2×Dic79—84no—
291C2×Dic79—84no—
292C79⋊C8—22no—
293C79⋊C8—22no—
294C79⋊C8—22no—
295C79⋊C8C4×D414yescomplemented
296C22×C79—22no—
297C22×C79—22no—
298C22×C79—22no—
299C22×C79—22no—
300C22×C79—22no—
301C22×C79—22no—
302C22×C79—22no—
303C22×C79—22no—
304C22×C79—22no—
305C22×C79—41no—
306C22×C79—41no—
307C22×C79—41no—
308C22×C79—41no—
309C22×C79#42814yescomplemented
310C22×C79C22×C4⋊C411yescharacteristic
311C22×C79D4211yescharacteristic
312C22×C79#54711yescharacteristic
313C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C79C2×#13711yescharacteristic
315C22×C79#57611yescharacteristic
316C22×C79#57811yescharacteristic
317C4×C79—22no—
318C4×C79—22no—
319C4×C79—22no—
320C4×C79—22no—
321C4×C79—42no—
322C4×C79—81no—
323C4×C79—81no—
324C4×C79—81no—
325C4×C79C2×C4×D411yescharacteristic
326C4×C79#52011yescharacteristic
327C4×C79D4×Q811yescharacteristic
328C4×C79#55411yescharacteristic
329Dic79—42no—
330Dic79—81no—
331Dic79—81no—
332Dic79—81no—
333#22661—791nomaximal, Sylow
334C2×C79—24no—
335C2×C79—42no—
336C2×C79D4×C4⋊C411yescharacteristic
337C2×C79C2×#42811yescharacteristic
338C2×C79#291311yescharacteristic
339C2×C79#326411yescharacteristic
340C2×C79#327011yescharacteristic
341C2×C79#334311yescharacteristic
342C2×C79#334611yescharacteristic
343C2×#435—791no—
344C2×#428—791no—
345C22×#107—791no—
346#2352D7911yescharacteristic
347D4×C4⋊C4—791no—
348#1949—791no—
349#1947—791no—
350#1854—791no—
351#1853—791no—
352#1852—791no—
353#1852—791no—
354#1847—791no—
355#1809—791no—
356#1807—791no—
357#1776—791no—
358C79#2266111yescharacteristic, complemented, Sylow
359C22×M16—791no—
360C23×C8—791no—
361C2×C4×D4—1581no—
362C2×C4×D4C2×D7911yescharacteristic
363C2×#117C2×D7911yescharacteristic
364C22×C4⋊C4—791no—
365C22×C4⋊C4—791no—
366C22×C4⋊C4C2×D7911yescharacteristic
367#435—798no—
368#428—1584no—
369C2×#107—791no—
370C2×#107—791no—
371C2×#107—791no—
372C2×#107—791no—
373C2×#107—791no—
374C2×#107—791no—
375C2×#107—1584no—
376C2×#106—791no—
377C2×#106—791no—
378C2×#106—791no—
379C2×#106—791no—
380C2×C4⋊C8—791no—
381C2×C22⋊C8—791no—
382C2×C22⋊C8—791no—
383C2×#97—791no—
384#389—1581no—
385#388—21no—
386#387—21no—
387#386—21no—
388#385—1581no—
389#385—1581no—
390#384—791no—
391#382C2×D7911yescharacteristic
392#380—791no—
393#380—791no—
394#380C2×D7911yescharacteristic
395#380C2×D7911yescharacteristic
396C4×C4⋊C4—791no—
397C4×C4⋊C4C2×D7911yescharacteristic
398C4×C22⋊C4—21no—
399#340—791no—
400#340—791no—
401#340—791no—
402#340—791no—
403#340—791no—
404#340—791no—
405C22×D4C22⋊D7911yescharacteristic
406C23×C4—21no—
407C23×C4—1581no—
408C23×C4—1581no—
409C23×C4C22×D7911yescharacteristic
410C23×C4C22×D7911yescharacteristic
411C2×M16—794no—
412C2×M16—1582no—
413C2×M16—1582no—
414C22×C8—791no—
415C22×C8—794no—
416C22×C8—791no—
417C22×C8—791no—
418C22×C8—791no—
419C22×C8—1582no—
420C22×C8—1582no—
421C4×D4—3164no—
422C4×D4Dic15814yes—
423C4×D4C4×D7914yes—
424#117—22no—
425#117—41no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4—3161no—
430C2×C4⋊C4—3161no—
431C2×C4⋊C4—791no—
432C2×C4⋊C4—791no—
433C2×C4⋊C4—791no—
434C2×C4⋊C4—791no—
435C2×C4⋊C4—1581no—
436C2×C4⋊C4—1581no—
437C2×C4⋊C4—1581no—
438C2×C4⋊C4—1582no—
439C2×C4⋊C4—1582no—
440C2×C4⋊C4—1581no—
441C2×C4⋊C4C22⋊D7911yescharacteristic
442C2×C4⋊C4C22×D7911yescharacteristic
443C2×C4⋊C4C22×D7911yescharacteristic
444C2×C4⋊C4C22×D7911yescharacteristic
445C2×C4⋊C4C22×D7911yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—1581no—
450C2×C22⋊C4—1581no—
451C2×C22⋊C4C22⋊D7911yescharacteristic
452C2×C22⋊C4C22⋊D7911yescharacteristic
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—1581no—
456C2×C42C22×D7911yescharacteristic
457#107—3161no—
458#107—794no—
459#107—1582no—
460#107—1582no—
461#107—1582no—
462#107—1582no—
463#106—3161no—
464#106—1582no—
465#106—1582no—
466#106—1582no—
467C4⋊C8—794no—
468C22⋊C8—794no—
469C22⋊C8—794no—
470#97—794no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—1581no—
477#95—1581no—
478#95—1581no—
479C24C2×C22⋊D7911yescharacteristic
480C24C2×C22⋊D7911yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4Dic79⋊C414yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4—3162no—
500C22×C4—3162no—
501C22×C4—3162no—
502C22×C4—3162no—
503C22×C4—6321no—
504C22×C4—6321no—
505C22×C4—1581no—
506C22×C4—1581no—
507C22×C4—1581no—
508C22×C4—1581no—
509C22×C4C2×C4×D7912yes—
510C22×C4C2×C4×D7912yes—
511C22×C4C2×C22⋊D7911yescharacteristic
512C22×C4C2×C22⋊D7911yescharacteristic
513C22×C4C2×C22⋊D7911yescharacteristic
514C22×C4C2×C22⋊D7911yescharacteristic
515C22×C4C2×Dic15812yes—
516C22×C4C2×Dic15812yes—
517C22×C4C23×D7911yescharacteristic
518M16—1588no—
519C2×C8—792no—
520C2×C8—792no—
521C2×C8—792no—
522C2×C8—792no—
523C2×C8—792no—
524C2×C8—792no—
525C2×C8—1588no—
526C2×C8—1581no—
527C2×C8—1581no—
528C2×C8—1581no—
529C2×C8—1581no—
530C2×C8—1581no—
531C2×C8—1581no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—3162no—
541C4⋊C4—3162no—
542C4⋊C4—3162no—
543C4⋊C4—792no—
544C4⋊C4—6321no—
545C4⋊C4—1581no—
546C4⋊C4—1581no—
547C4⋊C4—1581no—
548C4⋊C4—1581no—
549C4⋊C4—1581no—
550C4⋊C4—1581no—
551C4⋊C4—1581no—
552C4⋊C4Dic79⋊C414yes—
553C4⋊C4D4×D7912yes—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C22⋊C4—3162no—
558C22⋊C4—3162no—
559C22⋊C4Dic79⋊C414yes—
560C22⋊C4Dic79⋊C414yes—
561C42—42no—
562C42—81no—
563C42—3162no—
564C42C2×C4×D7912yes—
565C42C2×Dic15812yes—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×Dic79⋊C412yes—
577C23C2×Dic79⋊C412yes—
578C23#1457918612yes—
579C23#1457919112yes—
580C23C22×C22⋊D7911yescharacteristic
581D4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—84no—
611C2×C4—3161no—
612C2×C4—3161no—
613C2×C4—3161no—
614C2×C4—3161no—
615C2×C4—3161no—
616C2×C4—3161no—
617C2×C4—3161no—
618C2×C4—3161no—
619C2×C4—3161no—
620C2×C4—3161no—
621C2×C4—3161no—
622C2×C4—6324no—
623C2×C4—6324no—
624C2×C4—1582no—
625C2×C4C2×Dic79⋊C412yes—
626C2×C4C2×Dic79⋊C412yes—
627C2×C4C2×Dic79⋊C412yes—
628C2×C4C2×Dic79⋊C412yes—
629C2×C4C22×C4×D7911yescharacteristic
630C2×C4C2×D4×D7911yescharacteristic
631C2×C4C22×Dic15811yescharacteristic
632C2×C4#41×D7911yescharacteristic
633C2×C4#1457920611yescharacteristic
634C2×C4#1457920811yescharacteristic
635C8—794no—
636C8—1582no—
637C8—1582no—
638C8—1582no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22#1909860614yescomplemented
653C22C22×Dic79⋊C411yescharacteristic
654C22D4×C22⋊D7911yescharacteristic
655C22#1909921211yescharacteristic
656C22C2×#1457918611yescharacteristic
657C22C2×#1457919111yescharacteristic
658C22#1909936611yescharacteristic
659C22#1909937811yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—42no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—3162no—
669C4—6321no—
670C4—6321no—
671C4—6321no—
672C4C4×D4×D7911yescharacteristic
673C4#1909904211yescharacteristic
674C4D4×Dic15811yescharacteristic
675C4#1909927211yescharacteristic
676C2—24no—
677C2—42no—
678C2D4×Dic79⋊C411yescharacteristic
679C2C2×#1909860611yescharacteristic
680C2#2377199811yescharacteristic
681C2#2377488111yescharacteristic
682C2#2377496611yescharacteristic
683C2#2377584011yescharacteristic
684C2#2377588511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2352C2
socleC23×C79C22×D4
prime radicalC22×D4×C79D4
cosocleC22×C4×C79C24
hypercenter#2352D79
hypocenterC79#22661
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#19098606C2semidirect
3. C22×#14579094C2semidirect
5. #23764166C2semidirect
6. #23764158C2semidirect
7. #23763599C2semidirect
8. #23763592C2semidirect
9. #23763588C2semidirect
10. #23763587C2semidirect
11. #23763569C2semidirect
12. #23763431C2semidirect
13. #23763423C2semidirect
14. #23763298C2semidirect
21. #19098635C4semidirect
66. C2×#11929608C2×C4semidirect
69. C22×C79⋊C8C2×C4semidirect
95. #14579094D4semidirect
100. C4⋊(C79⋊C8)C2×C4semidirect
101. C22⋊(C79⋊C8)C2×C4semidirect
102. C22⋊(C79⋊C8)C2×C4semidirect
103. #14579072C2×C4semidirect
295. C79⋊C8C4×D4semidirect
309. C22×C79#428semidirect
358. C79#22661semidirect
652. C22#19098606semidirect

Maximal subgroups

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

subgroupindex
C2×#190986352
C2×#190986062
C22×#145790942
D4×C4⋊Dic792
#237641662
#237641582
#237635992
#237635922
#237635882
#237635872
#237635692
#237634312
#237634232
#237632982
C79×#23522
#2266179