Finite Group Databasebeta

← #34210544

Subgroups — #34210544

Order 20224.

1774 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098462C211yesmaximal, characteristic
2C2×#19098461C211yesmaximal, characteristic
3C2×#19098459C211yesmaximal, characteristic
4C2×#19098432C212yesmaximal
5C2×#19098432C211yesmaximal, characteristic
6C2×C4⋊C4×Dic79C211yesmaximal, characteristic
7C2×C4×Dic79⋊C4C211yesmaximal, characteristic
8#23761664C212yesmaximal
9#23761663C212yesmaximal
10Dic79⋊#95C212yesmaximal
11C2×#389×C79C211yesmaximal, characteristic
12C22×C4⋊Dic79C2211yescharacteristic
13C22×C4⋊Dic79C2212yes—
14C22×C4⋊Dic79C2211yescharacteristic
15C22×Dic79⋊C4C2212yes—
16C22×Dic79⋊C4C2212yes—
17C22×Dic79⋊C4C2212yes—
18C22×Dic79⋊C4C2211yescharacteristic
19C22×Dic79⋊C4C2211yescharacteristic
20C22×Dic79⋊C4C2212yes—
21C22×C4×Dic79C2211yescharacteristic
22C22×C4×Dic79C2212yes—
23C22×C4×Dic79C2211yescharacteristic
24#19098462—24no—
25#19098461—24no—
26#19098459—24no—
27#19098432—28no—
28#19098432—24no—
29C4⋊C4×Dic79C418yescomplemented
30C4×Dic79⋊C4—24no—
31C2×C79⋊#95C2211yescharacteristic
32C2×C79⋊#95C2212yes—
33C2×C79⋊#95C2212yes—
34C2×C79⋊#95C2212yes—
35C2×C79⋊#95C2211yescharacteristic
36C2×C79⋊#95C2212yes—
37C22×C4⋊C4×C79C2211yescharacteristic
38C22×C4⋊C4×C79C2212yes—
39C22×C4⋊C4×C79C2211yescharacteristic
40C22×C42×C79C2211yescharacteristic
41#389×C79—24no—
42C2×#95×C79C2212yes—
43C23×Dic79C2312yes—
44C23×Dic79C2311yescharacteristic
45C23×Dic79C2311yescharacteristic
46C23×Dic79C2311yescharacteristic
47C23×Dic79C2312yes—
48C23×Dic79C2311yescharacteristic
49C2×C4⋊Dic79—22no—
50C2×C4⋊Dic79—22no—
51C2×C4⋊Dic79—24no—
52C2×C4⋊Dic79—22no—
53C2×C4⋊Dic79—24no—
54C2×C4⋊Dic79—42no—
55C2×C4⋊Dic79C2×C414yes—
56C2×C4⋊Dic79D414yes—
57C2×C4⋊Dic79Q814yes—
58C2×Dic79⋊C4—22no—
59C2×Dic79⋊C4—22no—
60C2×Dic79⋊C4—22no—
61C2×Dic79⋊C4—22no—
62C2×Dic79⋊C4—24no—
63C2×Dic79⋊C4—24no—
64C2×Dic79⋊C4—24no—
65C2×Dic79⋊C4—24no—
66C2×Dic79⋊C4—24no—
67C2×Dic79⋊C4—24no—
68C2×Dic79⋊C4—24no—
69C2×Dic79⋊C4—24no—
70C2×Dic79⋊C4—42no—
71C2×Dic79⋊C4—42no—
72C2×Dic79⋊C4—42no—
73C2×Dic79⋊C4—42no—
74C2×Dic79⋊C4D414yes—
75C2×Dic79⋊C4Q814yes—
76C2×C4×Dic79—24no—
77C2×C4×Dic79—24no—
78C2×C4×Dic79—22no—
79C2×C4×Dic79—22no—
80C2×C4×Dic79—22no—
81C2×C4×Dic79C2×C418yes—
82C2×C4×Dic79C2×C414yes—
83C2×C4×Dic79D414yes—
84C2×C4×Dic79Q814yes—
85C79⋊#95—24no—
86C79⋊#95—22no—
87C79⋊#95—22no—
88C79⋊#95—24no—
89C79⋊#95—24no—
90C79⋊#95C2×C418yes—
91C23×C4×C79C2312yes—
92C23×C4×C79C2311yescharacteristic
93C23×C4×C79C2311yescharacteristic
94C23×C4×C79C2312yes—
95C23×C4×C79C2311yescharacteristic
96C2×C4⋊C4×C79—24no—
97C2×C4⋊C4×C79—22no—
98C2×C4⋊C4×C79—22no—
99C2×C4⋊C4×C79—24no—
100C2×C4⋊C4×C79—22no—
101C2×C4⋊C4×C79—42no—
102C2×C4⋊C4×C79C2×C414yes—
103C2×C4⋊C4×C79D414yes—
104C2×C4⋊C4×C79Q814yes—
105C2×C42×C79—22no—
106C2×C42×C79—22no—
107C2×C42×C79—22no—
108#95×C79—24no—
109C22×Dic79—22no—
110C22×Dic79—21no—
111C22×Dic79—21no—
112C22×Dic79—21no—
113C22×Dic79—21no—
114C22×Dic79—21no—
115C22×Dic79—21no—
116C22×Dic79—22no—
117C22×Dic79—22no—
118C22×Dic79—22no—
119C22×Dic79—22no—
120C22×Dic79—22no—
121C22×Dic79—21no—
122C22×Dic79—21no—
123C22×Dic79—22no—
124C22×Dic79—21no—
125C22×Dic79—21no—
126C22×Dic79—22no—
127C22×Dic79—21no—
128C22×Dic79—21no—
129C22×Dic79—22no—
130C22×Dic79—22no—
131C22×Dic79—21no—
132C22×Dic79—21no—
133C22×Dic79—22no—
134C22×Dic79—21no—
135C22×Dic79—21no—
136C22×Dic79C22×C412yes—
137C22×Dic79C22×C414yes—
138C22×Dic79C22×C412yes—
139C22×Dic79C2×D412yes—
140C22×Dic79C2×D412yes—
141C22×Dic79C2×D414yes—
142C22×Dic79C2×D412yes—
143C22×Dic79C2×D412yes—
144C22×Dic79C2×Q812yes—
145C22×Dic79C2×Q812yes—
146C22×Dic79C2×Q814yes—
147C22×Dic79C2×Q812yes—
148C22×Dic79C2×Q812yes—
149C22×Dic79#4112yes—
150C22×Dic79#4112yes—
151C4⋊Dic79—48no—
152C4⋊Dic79—44no—
153C4⋊Dic79C4⋊C4116yescomplemented
154Dic79⋊C4—28no—
155Dic79⋊C4—28no—
156Dic79⋊C4—48no—
157Dic79⋊C4—48no—
158Dic79⋊C4—48no—
159Dic79⋊C4—48no—
160C4×Dic79—216no—
161C4×Dic79—44no—
162C4×Dic79C4⋊C4116yescomplemented
163C24×C79C2411yescharacteristic
164C22×C4×C79—22no—
165C22×C4×C79—22no—
166C22×C4×C79—22no—
167C22×C4×C79—22no—
168C22×C4×C79—21no—
169C22×C4×C79—21no—
170C22×C4×C79—21no—
171C22×C4×C79—21no—
172C22×C4×C79—21no—
173C22×C4×C79—21no—
174C22×C4×C79—21no—
175C22×C4×C79—21no—
176C22×C4×C79—21no—
177C22×C4×C79—21no—
178C22×C4×C79—21no—
179C22×C4×C79—21no—
180C22×C4×C79—22no—
181C22×C4×C79—22no—
182C22×C4×C79—22no—
183C22×C4×C79—22no—
184C22×C4×C79—22no—
185C22×C4×C79—22no—
186C22×C4×C79—22no—
187C22×C4×C79C22×C414yes—
188C22×C4×C79C22×C412yes—
189C22×C4×C79C2×D412yes—
190C22×C4×C79C2×D414yes—
191C22×C4×C79C2×D412yes—
192C22×C4×C79C2×D412yes—
193C22×C4×C79C2×D412yes—
194C22×C4×C79C2×Q812yes—
195C22×C4×C79C2×Q814yes—
196C22×C4×C79C2×Q812yes—
197C22×C4×C79C2×Q812yes—
198C22×C4×C79C2×Q812yes—
199C4⋊C4×C79—48no—
200C4⋊C4×C79—44no—
201C4⋊C4×C79C4⋊C4116yescomplemented
202C42×C79—44no—
203C23×C79C23×C411yescharacteristic
204C23×C79C22×D411yescharacteristic
205C23×C79C22×D411yescharacteristic
206C23×C79C22×D411yescharacteristic
207C23×C79C22×D411yescharacteristic
208C23×C79C22×Q811yescharacteristic
209C23×C79C22×Q811yescharacteristic
210C23×C79C22×Q811yescharacteristic
211C23×C79C22×Q811yescharacteristic
212C23×C79C2×#4111yescharacteristic
213C23×C79C2×#4111yescharacteristic
214C23×C79H(5,𝔽2)11yescharacteristic
215C23×C79H(5,𝔽2)11yescharacteristic
216C23×C792−1+411yescharacteristic
217C23×C792−1+411yescharacteristic
218C2×C4×C79—24no—
219C2×C4×C79—24no—
220C2×C4×C79—24no—
221C2×C4×C79—24no—
222C2×C4×C79—24no—
223C2×C4×C79—24no—
224C2×C4×C79—22no—
225C2×C4×C79—22no—
226C2×C4×C79—22no—
227C2×C4×C79—22no—
228C2×C4×C79—22no—
229C2×C4×C79—22no—
230C2×C4×C79—41no—
231C2×C4×C79—41no—
232C2×C4×C79—41no—
233C2×C4×C79—41no—
234C2×C4×C79—41no—
235C2×C4×C79—41no—
236C2×C4×C79—41no—
237C2×C4×C79—41no—
238C2×C4×C79—42no—
239C2×C4×C79—42no—
240C2×C4×C79—42no—
241C2×C4×C79—42no—
242C2×C4×C79—42no—
243C2×C4×C79—42no—
244C2×C4×C79—42no—
245C2×C4×C79C2×C4⋊C414yes—
246C2×C4×C79C2×C4⋊C414yes—
247C2×C4×C79C2×C4⋊C418yes—
248C2×C4×C79C2×C4⋊C414yes—
249C2×C4×C79#12714yes—
250C2×C4×C79C4⋊Q814yes—
251C2×C4×C79C4⋊Q814yes—
252C2×C4×C79C4⋊Q814yes—
253C2×Dic79—24no—
254C2×Dic79—22no—
255C2×Dic79—22no—
256C2×Dic79—24no—
257C2×Dic79—22no—
258C2×Dic79—22no—
259C2×Dic79—22no—
260C2×Dic79—22no—
261C2×Dic79—24no—
262C2×Dic79—24no—
263C2×Dic79—24no—
264C2×Dic79—24no—
265C2×Dic79—22no—
266C2×Dic79—22no—
267C2×Dic79—22no—
268C2×Dic79—22no—
269C2×Dic79—22no—
270C2×Dic79—22no—
271C2×Dic79—41no—
272C2×Dic79—41no—
273C2×Dic79—41no—
274C2×Dic79—41no—
275C2×Dic79—41no—
276C2×Dic79—41no—
277C2×Dic79—41no—
278C2×Dic79—41no—
279C2×Dic79—42no—
280C2×Dic79—42no—
281C2×Dic79—42no—
282C2×Dic79—42no—
283C2×Dic79—42no—
284C2×Dic79—42no—
285C2×Dic79—42no—
286C2×Dic79C2×C4⋊C414yes—
287C2×Dic79C2×C4⋊C418yes—
288C2×Dic79C2×C4⋊C414yes—
289C2×Dic79C4×D414yes—
290C2×Dic79C4×Q814yes—
291C2×Dic79#12114yes—
292C2×Dic79C22⋊Q814yes—
293C2×Dic79#12514yes—
294C2×Dic79C4⋊Q814yes—
295C22×C79C22×C4⋊C411yescharacteristic
296C22×C79C22×C4⋊C411yescharacteristic
297C22×C79C22×C4⋊C411yescharacteristic
298C22×C79C2×C4×D411yescharacteristic
299C22×C79C2×C4×Q811yescharacteristic
300C22×C79#52011yescharacteristic
301C22×C79#52011yescharacteristic
302C22×C79C2×#12111yescharacteristic
303C22×C79C2×C22⋊Q811yescharacteristic
304C22×C79C2×#12511yescharacteristic
305C22×C79C2×#12711yescharacteristic
306C22×C79C2×C4⋊Q811yescharacteristic
307C22×C79C2×C4⋊Q811yescharacteristic
308C22×C79C2×C4⋊Q811yescharacteristic
309C22×C79C2×C4⋊Q811yescharacteristic
310C22×C79#53511yescharacteristic
311C22×C79#53611yescharacteristic
312C22×C79#54411yescharacteristic
313C22×C79#54411yescharacteristic
314C22×C79D4211yescharacteristic
315C22×C79D4211yescharacteristic
316C22×C79#54711yescharacteristic
317C22×C79#54711yescharacteristic
318C22×C79D4×Q811yescharacteristic
319C22×C79D4×Q811yescharacteristic
320C22×C79D4×Q811yescharacteristic
321C22×C79D4×Q811yescharacteristic
322C22×C79#55011yescharacteristic
323C22×C79#55011yescharacteristic
324C22×C79#55411yescharacteristic
325C22×C79#55411yescharacteristic
326C22×C79#55711yescharacteristic
327C22×C79#55711yescharacteristic
328C22×C79Q8211yescharacteristic
329C22×C79Q8211yescharacteristic
330C4×C79—28no—
331C4×C79—42no—
332C4×C79—42no—
333C4×C79—82no—
334C4×C79#38418yescomplemented
335Dic79—24no—
336Dic79—28no—
337Dic79—42no—
338Dic79—42no—
339Dic79—82no—
340Dic79#38918yescomplemented
341#13910—791nomaximal, Sylow
342C2×C79C2×#38411yescharacteristic
343C2×C79C2×#38911yescharacteristic
344C2×C79#231711yescharacteristic
345C2×C79D4×C4⋊C411yescharacteristic
346C2×C79D4×C4⋊C411yescharacteristic
347C2×C79Q8×C4⋊C411yescharacteristic
348C2×C79Q8×C4⋊C411yescharacteristic
349C2×C79#254111yescharacteristic
350C2×C79#254211yescharacteristic
351C2×C79#254611yescharacteristic
352C2×C79#255111yescharacteristic
353C2×C79#255111yescharacteristic
354C2×C79#255211yescharacteristic
355C2×C79#255211yescharacteristic
356C2×C79#256711yescharacteristic
357C2×#389—791no—
358C2×#389—791no—
359C2×#389—791no—
360C2×#389D7911yescharacteristic
361C2×#384—791no—
362C2×#384—792no—
363C2×C4×C4⋊C4—791no—
364C2×C4×C4⋊C4—791no—
365#1444—792no—
366#1444—792no—
367C4⋊#95—792no—
368C79#1391011yescharacteristic, complemented, Sylow
369C22×C4⋊C4—792no—
370C22×C4⋊C4—792no—
371C22×C4⋊C4—792no—
372C22×C4⋊C4—792no—
373C22×C4⋊C4—791no—
374C22×C4⋊C4—791no—
375C22×C4⋊C4—791no—
376C22×C4⋊C4—792no—
377C22×C4⋊C4—791no—
378C22×C4⋊C4C2×D7911yescharacteristic
379C22×C4⋊C4C2×D7912yes—
380C22×C4⋊C4C2×D7911yescharacteristic
381C22×C42—791no—
382C22×C42—792no—
383C22×C42—791no—
384C22×C42C2×D7911yescharacteristic
385#389—24no—
386#389—1584no—
387#389—1584no—
388#389—1584no—
389#384—1584no—
390#384—1588no—
391C4×C4⋊C4—798no—
392C4×C4⋊C4—1584no—
393C2×#95—792no—
394C2×#95—792no—
395C2×#95—792no—
396C2×#95—792no—
397C2×#95—791no—
398C2×#95—791no—
399C2×#95C2×D7912yes—
400C23×C4—791no—
401C23×C4—792no—
402C23×C4—791no—
403C23×C4—791no—
404C23×C4—791no—
405C23×C4—792no—
406C23×C4C22×D7912yes—
407C23×C4C22×D7911yescharacteristic
408C23×C4C22×D7911yescharacteristic
409C23×C4C22×D7912yes—
410C23×C4C22×D7911yescharacteristic
411C2×C4⋊C4—24no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4—3162no—
418C2×C4⋊C4—3162no—
419C2×C4⋊C4—3162no—
420C2×C4⋊C4—3162no—
421C2×C4⋊C4—3162no—
422C2×C4⋊C4—794no—
423C2×C4⋊C4—794no—
424C2×C4⋊C4—794no—
425C2×C4⋊C4—794no—
426C2×C4⋊C4—794no—
427C2×C4⋊C4—1584no—
428C2×C4⋊C4—1584no—
429C2×C4⋊C4—1584no—
430C2×C4⋊C4—1584no—
431C2×C4⋊C4—1584no—
432C2×C4⋊C4—1584no—
433C2×C4⋊C4—1584no—
434C2×C4⋊C4—1584no—
435C2×C4⋊C4—1584no—
436C2×C4⋊C4—1582no—
437C2×C4⋊C4—1582no—
438C2×C4⋊C4—1584no—
439C2×C4⋊C4—1582no—
440C2×C4⋊C4—1582no—
441C2×C4⋊C4—1582no—
442C2×C4⋊C4—1582no—
443C2×C4⋊C4—1582no—
444C2×C4⋊C4Dic15814yes—
445C2×C4⋊C4C4×D7914yes—
446C2×C4⋊C4C22⋊D7914yes—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—794no—
451C2×C42—794no—
452C2×C42—794no—
453C2×C42—798no—
454C2×C42—1582no—
455C2×C42—1582no—
456C2×C42—1582no—
457C2×C42—1584no—
458C2×C42—1584no—
459#95—24no—
460#95—798no—
461#95—1582no—
462#95—1582no—
463#95—1584no—
464#95—1584no—
465#95—1584no—
466C24C23×D7911yescharacteristic
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—792no—
491C22×C4—792no—
492C22×C4—792no—
493C22×C4—792no—
494C22×C4—792no—
495C22×C4—792no—
496C22×C4—792no—
497C22×C4—792no—
498C22×C4—794no—
499C22×C4—792no—
500C22×C4—794no—
501C22×C4—792no—
502C22×C4—794no—
503C22×C4—792no—
504C22×C4—792no—
505C22×C4—1582no—
506C22×C4—1582no—
507C22×C4—1582no—
508C22×C4—1582no—
509C22×C4—1582no—
510C22×C4—1582no—
511C22×C4—1582no—
512C22×C4—1581no—
513C22×C4—1581no—
514C22×C4—1581no—
515C22×C4—1581no—
516C22×C4—1581no—
517C22×C4—1581no—
518C22×C4—1581no—
519C22×C4—1581no—
520C22×C4—1581no—
521C22×C4—1581no—
522C22×C4—1581no—
523C22×C4—1581no—
524C22×C4—1582no—
525C22×C4—1581no—
526C22×C4—1581no—
527C22×C4—1582no—
528C22×C4—1581no—
529C22×C4—1581no—
530C22×C4—1582no—
531C22×C4—1582no—
532C22×C4C2×C4×D7914yes—
533C22×C4C2×C4×D7912yes—
534C22×C4D4×D7912yes—
535C22×C4D4×D7912yes—
536C22×C4D4×D7912yes—
537C22×C4C2×C22⋊D7914yes—
538C22×C4C2×C22⋊D7912yes—
539C22×C4Q8×D7912yes—
540C22×C4Q8×D7912yes—
541C22×C4Q8×D7912yes—
542C22×C4C2×Dic15814yes—
543C22×C4C2×Dic15812yes—
544C4⋊C4—48no—
545C4⋊C4—44no—
546C4⋊C4—3168no—
547C4⋊C4—3168no—
548C4⋊C4—3168no—
549C4⋊C4—3168no—
550C4⋊C4—3168no—
551C4⋊C4—3164no—
552C4⋊C4—7916no—
553C4⋊C4—1588no—
554C4⋊C4—1588no—
555C4⋊C4Dic79⋊C4116yescomplemented
556C42—44no—
557C42—3164no—
558C42—7916no—
559C42—15816no—
560C23C22×C4×D7911yescharacteristic
561C23C2×D4×D7911yescharacteristic
562C23C2×D4×D7911yescharacteristic
563C23C2×D4×D7911yescharacteristic
564C23C22×C22⋊D7911yescharacteristic
565C23C2×Q8×D7911yescharacteristic
566C23C2×Q8×D7911yescharacteristic
567C23C2×Q8×D7911yescharacteristic
568C23C22×Dic15811yescharacteristic
569C23#41×D7911yescharacteristic
570C23#41×D7911yescharacteristic
571C23#1457920611yescharacteristic
572C23#1457920711yescharacteristic
573C23#1457920811yescharacteristic
574C23#1457920911yescharacteristic
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—3161no—
603C2×C4—3161no—
604C2×C4—3161no—
605C2×C4—3161no—
606C2×C4—3161no—
607C2×C4—3161no—
608C2×C4—3161no—
609C2×C4—3161no—
610C2×C4—3162no—
611C2×C4—3162no—
612C2×C4—3162no—
613C2×C4—3162no—
614C2×C4—3162no—
615C2×C4—3162no—
616C2×C4—3162no—
617C2×C4—794no—
618C2×C4—794no—
619C2×C4—794no—
620C2×C4—794no—
621C2×C4—794no—
622C2×C4—794no—
623C2×C4—794no—
624C2×C4—794no—
625C2×C4—798no—
626C2×C4—1582no—
627C2×C4—1582no—
628C2×C4—1582no—
629C2×C4—1582no—
630C2×C4—1582no—
631C2×C4—1582no—
632C2×C4—1582no—
633C2×C4—1582no—
634C2×C4—1582no—
635C2×C4—1584no—
636C2×C4—1584no—
637C2×C4—1584no—
638C2×C4—1584no—
639C2×C4—1584no—
640C2×C4—1582no—
641C2×C4—1582no—
642C2×C4—1584no—
643C2×C4—1582no—
644C2×C4C4⋊C4×D7914yes—
645C2×C4C4⋊C4×D7914yes—
646C2×C4C2×Dic79⋊C418yes—
647C2×C4C2×Dic79⋊C414yes—
648C2×C4#1457915714yes—
649C2×C4#1457915914yes—
650C2×C4#1457916014yes—
651C2×C4#1457916014yes—
652C22C2×C4⋊C4×D7911yescharacteristic
653C22C2×C4⋊C4×D7911yescharacteristic
654C22C22×Dic79⋊C411yescharacteristic
655C22C4×D4×D7911yescharacteristic
656C22C4×Q8×D7911yescharacteristic
657C22#1909904211yescharacteristic
658C22#1909904511yescharacteristic
659C22#121×D7911yescharacteristic
660C22C22⋊Q8×D7911yescharacteristic
661C22#125×D7911yescharacteristic
662C22C2×#1457915711yescharacteristic
663C22C4⋊Q8×D7911yescharacteristic
664C22C2×#1457915911yescharacteristic
665C22C2×#1457916011yescharacteristic
666C22C2×#1457916011yescharacteristic
667C22#1909912911yescharacteristic
668C22#1909913611yescharacteristic
669C22#1909919011yescharacteristic
670C22#1909919311yescharacteristic
671C22D4×C22⋊D7911yescharacteristic
672C22#1909919711yescharacteristic
673C22#1909921211yescharacteristic
674C22#1909921511yescharacteristic
675C22#1909922611yescharacteristic
676C22Q8×C22⋊D7911yescharacteristic
677C22#1909922811yescharacteristic
678C22D4×Dic15811yescharacteristic
679C22#1909923111yescharacteristic
680C22#1909923211yescharacteristic
681C22#1909926911yescharacteristic
682C22#1909927211yescharacteristic
683C22#1909928911yescharacteristic
684C22#1909929011yescharacteristic
685C22#1909929311yescharacteristic
686C22Q8×Dic15811yescharacteristic
687C4—28no—
688C4—42no—
689C4—42no—
690C4—82no—
691C4—3162no—
692C4—3162no—
693C4—798no—
694C4—6322no—
695C4—1584no—
696C4—1588no—
697C4#1909843218yescomplemented
698C2C2×#1909843211yescharacteristic
699C2#389×D7911yescharacteristic
700C2#2376602211yescharacteristic
701C2D4×Dic79⋊C411yescharacteristic
702C2#2376630111yescharacteristic
703C2Q8×Dic79⋊C411yescharacteristic
704C2#2376631411yescharacteristic
705C2#2376834311yescharacteristic
706C2#2376835011yescharacteristic
707C2#2376838711yescharacteristic
708C2#2376842711yescharacteristic
709C2#2376842811yescharacteristic
710C2#2376843211yescharacteristic
711C2#2376843711yescharacteristic
712C2#2376860711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D79
commutatorC23×C79C23×C4
FittingC2×#389×C79C2
socle, prime radical, cosocleC24×C79C24
hypercenterC2×#389D79
hypocenterC79#13910
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
29. C4⋊C4×Dic79C4semidirect
153. C4⋊Dic79C4⋊C4semidirect
162. C4×Dic79C4⋊C4semidirect
201. C4⋊C4×C79C4⋊C4semidirect
334. C4×C79#384semidirect
340. Dic79#389semidirect
368. C79#13910semidirect
555. C4⋊C4Dic79⋊C4semidirect
697. C4#19098432semidirect

Maximal subgroups

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

subgroupindex
C2×#190984622
C2×#190984612
C2×#190984592
C2×#190984322
C2×C4⋊C4×Dic792
C2×C4×Dic79⋊C42
#237616642
#237616632
Dic79⋊#952
C2×#389×C792
#1391079