Finite Group Databasebeta

← #34215818

Subgroups — #34215818

Order 20224.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098466C211yesmaximal, characteristic
2C2×#19098426C211yesmaximal, characteristic, complemented
3#23761657C211yesmaximal, characteristic, complemented
4#23761649C211yesmaximal, characteristic, complemented
5#23761649C211yesmaximal, characteristic, complemented
6#23761645C211yesmaximal, characteristic, complemented
7#23761645C211yesmaximal, characteristic, complemented
8#23761641C211yesmaximal, characteristic
9#23761637C211yesmaximal, characteristic, complemented
10#23761637C211yesmaximal, characteristic, complemented
11#23761634C211yesmaximal, characteristic, complemented
12#23761634C211yesmaximal, characteristic, complemented
13#23761625C211yesmaximal, characteristic, complemented
14#23761623C211yesmaximal, characteristic, complemented
15C2×#386×C79C211yesmaximal, characteristic
16C22×C4⋊Dic79C2211yescharacteristic
17C22×C4⋊Dic79C2211yescharacteristic
18C22×C22⋊Dic79C2211yescharacteristic
19C22×C22⋊Dic79C2211yescharacteristic
20C22×C22⋊Dic79C2211yescharacteristic
21C22×C22⋊Dic79C2211yescharacteristic
22C22×C22⋊Dic79C2211yescharacteristic
23C22×C22⋊Dic79C2211yescharacteristic
24C22×C22⋊Dic79C2211yescharacteristic
25C22×C22⋊Dic79C2211yescharacteristic
26C22×C4×Dic79C2211yescharacteristic
27C22×C4×Dic79C2211yescharacteristic
28#19098466—24no—
29#19098426—24no—
30C2×C79⋊#95C2211yescharacteristic
31C2×C79⋊#95C2211yescharacteristic
32C2×C79⋊#95C2211yescharacteristic
33C2×C79⋊#95C2211yescharacteristic
34C2×C79⋊#95C2211yescharacteristic
35C2×C79⋊#95C2211yescharacteristic
36C2×C79⋊#95C2211yescharacteristic
37C2×C79⋊#95C2211yescharacteristic
38C2×C79⋊#95C2211yescharacteristic
39C2×C79⋊#95C2211yescharacteristic
40C2×C79⋊#95C2211yescharacteristic
41C2×C79⋊#95C2211yescharacteristic
42C2×C79⋊#95C2211yescharacteristic
43C2×C79⋊#95C2211yescharacteristic
44C2×C79⋊#95C2211yescharacteristic
45C2×C79⋊#95C2211yescharacteristic
46C23×D4×C79C2211yescharacteristic
47C24×C4×C79C2211yescharacteristic
48C22×C22⋊C4×C79C2211yescharacteristic
49C22×C22⋊C4×C79C2211yescharacteristic
50C22×C22⋊C4×C79C2211yescharacteristic
51#386×C79C418yescomplemented
52C2×#95×C79C2211yescharacteristic
53C2×#95×C79C2211yescharacteristic
54C23×Dic79C2311yescharacteristic
55C23×Dic79C2311yescharacteristic
56C23×Dic79C2311yescharacteristic
57C23×Dic79C2311yescharacteristic
58C23×Dic79C2311yescharacteristic
59C23×Dic79C2311yescharacteristic
60C23×Dic79C2311yescharacteristic
61C23×Dic79C2311yescharacteristic
62C2×C4⋊Dic79—22no—
63C2×C4⋊Dic79—22no—
64C2×C4⋊Dic79—22no—
65C2×C4⋊Dic79—41no—
66C2×C4⋊Dic79—41no—
67C2×C4⋊Dic79—41no—
68C2×C22⋊Dic79—22no—
69C2×C22⋊Dic79—22no—
70C2×C22⋊Dic79—22no—
71C2×C22⋊Dic79—22no—
72C2×C22⋊Dic79—22no—
73C2×C22⋊Dic79—22no—
74C2×C22⋊Dic79—22no—
75C2×C22⋊Dic79—22no—
76C2×C22⋊Dic79—22no—
77C2×C22⋊Dic79—41no—
78C2×C22⋊Dic79—41no—
79C2×C22⋊Dic79—41no—
80C2×C22⋊Dic79—41no—
81C2×C22⋊Dic79—41no—
82C2×C22⋊Dic79—41no—
83C2×C22⋊Dic79—41no—
84C2×C22⋊Dic79—41no—
85C2×C22⋊Dic79—41no—
86C2×C22⋊Dic79—41no—
87C2×C22⋊Dic79—41no—
88C2×C22⋊Dic79—41no—
89C2×C22⋊Dic79—41no—
90C2×C22⋊Dic79—41no—
91C2×C22⋊Dic79D414yes—
92C2×C4×Dic79—22no—
93C2×C4×Dic79—22no—
94C2×C4×Dic79—41no—
95C2×C4×Dic79—41no—
96C2×C4×Dic79—41no—
97C2×C4×Dic79—41no—
98C79⋊#95—22no—
99C79⋊#95—22no—
100C79⋊#95—22no—
101C79⋊#95—22no—
102C79⋊#95—22no—
103C79⋊#95—22no—
104C79⋊#95—22no—
105C79⋊#95—41no—
106C79⋊#95—41no—
107C79⋊#95—41no—
108C79⋊#95—41no—
109C79⋊#95—41no—
110C79⋊#95—41no—
111C79⋊#95—41no—
112C79⋊#95—41no—
113C79⋊#95—41no—
114C25×C79C2311yescharacteristic
115C25×C79C2311yescharacteristic
116C22×D4×C79—22no—
117C22×D4×C79—22no—
118C22×D4×C79—22no—
119C22×D4×C79—22no—
120C22×D4×C79—41no—
121C22×D4×C79—41no—
122C22×D4×C79C2×C414yes—
123C23×C4×C79—22no—
124C23×C4×C79—22no—
125C23×C4×C79—41no—
126C23×C4×C79—41no—
127C23×C4×C79—41no—
128C23×C4×C79—41no—
129C23×C4×C79C2×C414yes—
130C23×C4×C79C2311yescharacteristic
131C23×C4×C79C2311yescharacteristic
132C23×C4×C79C2311yescharacteristic
133C23×C4×C79C2311yescharacteristic
134C23×C4×C79C2311yescharacteristic
135C2×C22⋊C4×C79—41no—
136C2×C22⋊C4×C79—41no—
137C2×C22⋊C4×C79—41no—
138C2×C22⋊C4×C79—41no—
139C2×C22⋊C4×C79—41no—
140C2×C22⋊C4×C79—41no—
141C2×C22⋊C4×C79C2×C414yes—
142C2×C22⋊C4×C79C2×C414yes—
143C2×C22⋊C4×C79C2×C414yes—
144#95×C79C2×C414yes—
145#95×C79C2×C414yes—
146C22×Dic79—21no—
147C22×Dic79—21no—
148C22×Dic79—21no—
149C22×Dic79—21no—
150C22×Dic79—21no—
151C22×Dic79—21no—
152C22×Dic79—21no—
153C22×Dic79—21no—
154C22×Dic79—21no—
155C22×Dic79—21no—
156C22×Dic79—21no—
157C22×Dic79—21no—
158C22×Dic79—21no—
159C22×Dic79—21no—
160C22×Dic79—21no—
161C22×Dic79—21no—
162C22×Dic79—21no—
163C22×Dic79—21no—
164C22×Dic79—21no—
165C22×Dic79—21no—
166C22×Dic79—21no—
167C22×Dic79—21no—
168C22×Dic79—21no—
169C22×Dic79—21no—
170C22×Dic79—21no—
171C22×Dic79—21no—
172C22×Dic79—21no—
173C22×Dic79—21no—
174C22×Dic79—21no—
175C22×Dic79—21no—
176C22×Dic79—21no—
177C22×Dic79—21no—
178C22×Dic79—21no—
179C22×Dic79—21no—
180C22×Dic79—21no—
181C22×Dic79—21no—
182C22×Dic79—21no—
183C22×Dic79—21no—
184C22×Dic79—21no—
185C22×Dic79—21no—
186C22×Dic79—21no—
187C22×Dic79—21no—
188C22×Dic79—21no—
189C22×Dic79—21no—
190C22×Dic79—21no—
191C22×Dic79—21no—
192C22×Dic79—21no—
193C22×Dic79—21no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79C2×D412yes—
199C22×Dic79C2×D412yes—
200C22×Dic79#4112yes—
201C22×Dic79#4112yes—
202C4⋊Dic79—44no—
203C4⋊Dic79—44no—
204C22⋊Dic79—44no—
205C22⋊Dic79—44no—
206C22⋊Dic79—44no—
207C22⋊Dic79—44no—
208C22⋊Dic79—44no—
209C22⋊Dic79—44no—
210C22⋊Dic79—44no—
211C22⋊Dic79—44no—
212C4×Dic79—44no—
213C4×Dic79—44no—
214C24×C79—21no—
215C24×C79—21no—
216C24×C79—21no—
217C24×C79—21no—
218C24×C79—21no—
219C24×C79—21no—
220C24×C79—21no—
221C24×C79—21no—
222C24×C79—21no—
223C24×C79—21no—
224C24×C79—21no—
225C24×C79—21no—
226C24×C79—21no—
227C24×C79—21no—
228C24×C79—21no—
229C24×C79—21no—
230C24×C79—21no—
231C24×C79—21no—
232C24×C79—21no—
233C24×C79—21no—
234C24×C79—21no—
235C24×C79—21no—
236C24×C79—21no—
237C24×C79—21no—
238C24×C79—21no—
239C24×C79—21no—
240C24×C79C22×C412yes—
241C24×C79C22×C412yes—
242C24×C79C2×D412yes—
243C24×C79#4112yes—
244C24×C79C2411yescharacteristic
245C2×D4×C79—28no—
246C2×D4×C79—28no—
247C2×D4×C79—44no—
248C2×D4×C79—44no—
249C2×D4×C79—44no—
250C2×D4×C79—44no—
251C2×D4×C79—44no—
252C22×C4×C79—21no—
253C22×C4×C79—21no—
254C22×C4×C79—21no—
255C22×C4×C79—21no—
256C22×C4×C79—28no—
257C22×C4×C79—21no—
258C22×C4×C79—21no—
259C22×C4×C79—21no—
260C22×C4×C79—21no—
261C22×C4×C79—21no—
262C22×C4×C79—21no—
263C22×C4×C79—21no—
264C22×C4×C79—21no—
265C22×C4×C79—21no—
266C22×C4×C79—21no—
267C22×C4×C79—21no—
268C22×C4×C79—21no—
269C22×C4×C79—21no—
270C22×C4×C79—21no—
271C22×C4×C79—21no—
272C22×C4×C79—21no—
273C22×C4×C79—21no—
274C22×C4×C79—21no—
275C22×C4×C79—21no—
276C22×C4×C79—21no—
277C22×C4×C79—21no—
278C22×C4×C79—21no—
279C22×C4×C79—21no—
280C22×C4×C79—21no—
281C22×C4×C79—44no—
282C22×C4×C79—44no—
283C22×C4×C79—44no—
284C22×C4×C79—44no—
285C22×C4×C79—44no—
286C22×C4×C79—44no—
287C22×C4×C79C22×C412yes—
288C22×C4×C79C22×C412yes—
289C22×C4×C79C22×C412yes—
290C22×C4×C79C22×C412yes—
291C22×C4×C79C22×C412yes—
292C22×C4×C79#4112yes—
293C22×C4×C79#4112yes—
294C22⋊C4×C79—44no—
295C22⋊C4×C79—44no—
296C22⋊C4×C79—44no—
297C23×C79—22no—
298C23×C79—22no—
299C23×C79—22no—
300C23×C79—22no—
301C23×C79—22no—
302C23×C79—22no—
303C23×C79—22no—
304C23×C79—22no—
305C23×C79—22no—
306C23×C79—22no—
307C23×C79—22no—
308C23×C79—22no—
309C23×C79—22no—
310C23×C79—22no—
311C23×C79—22no—
312C23×C79—22no—
313C23×C79—22no—
314C23×C79—22no—
315C23×C79—22no—
316C23×C79—22no—
317C23×C79—22no—
318C23×C79—22no—
319C23×C79—22no—
320C23×C79—22no—
321C23×C79—22no—
322C23×C79—41no—
323C23×C79—41no—
324C23×C79—41no—
325C23×C79—41no—
326C23×C79—41no—
327C23×C79—41no—
328C23×C79—41no—
329C23×C79—41no—
330C23×C79—41no—
331C23×C79—41no—
332C23×C79—41no—
333C23×C79—41no—
334C23×C79—41no—
335C23×C79—41no—
336C23×C79—41no—
337C23×C79—41no—
338C23×C79—41no—
339C23×C79—41no—
340C23×C79—41no—
341C23×C79—41no—
342C23×C79—41no—
343C23×C79—41no—
344C23×C79—41no—
345C23×C79—41no—
346C23×C79—41no—
347C23×C79—41no—
348C23×C79—41no—
349C23×C79—41no—
350C23×C79—41no—
351C23×C79—41no—
352C23×C79—41no—
353C23×C79—41no—
354C23×C79—41no—
355C23×C79—41no—
356C23×C79—41no—
357C23×C79—41no—
358C23×C79—41no—
359C23×C79—41no—
360C23×C79—41no—
361C23×C79—41no—
362C23×C79—41no—
363C23×C79—41no—
364C23×C79—41no—
365C23×C79—41no—
366C23×C79C4×D414yes—
367C23×C79C23×C411yescharacteristic
368C23×C79C22×D411yescharacteristic
369C23×C79C2×#4111yescharacteristic
370C23×C79C2×#4111yescharacteristic
371C23×C79C2×#4111yescharacteristic
372C23×C79C2×#4111yescharacteristic
373C23×C79C2×#4111yescharacteristic
374C23×C79H(5,𝔽2)11yescharacteristic
375C23×C79H(5,𝔽2)11yescharacteristic
376C23×C79H(5,𝔽2)11yescharacteristic
377C23×C79H(5,𝔽2)11yescharacteristic
378C23×C79H(5,𝔽2)11yescharacteristic
379C23×C79H(5,𝔽2)11yescharacteristic
380C23×C79H(5,𝔽2)11yescharacteristic
381C23×C792−1+411yescharacteristic
382D4×C79—416no—
383C2×C4×C79—22no—
384C2×C4×C79—22no—
385C2×C4×C79—22no—
386C2×C4×C79—22no—
387C2×C4×C79—22no—
388C2×C4×C79—22no—
389C2×C4×C79—22no—
390C2×C4×C79—22no—
391C2×C4×C79—22no—
392C2×C4×C79—22no—
393C2×C4×C79—22no—
394C2×C4×C79—22no—
395C2×C4×C79—22no—
396C2×C4×C79—22no—
397C2×C4×C79—22no—
398C2×C4×C79—22no—
399C2×C4×C79—22no—
400C2×C4×C79—22no—
401C2×C4×C79—416no—
402C2×C4×C79—41no—
403C2×C4×C79—41no—
404C2×C4×C79—41no—
405C2×C4×C79—41no—
406C2×C4×C79—41no—
407C2×C4×C79—41no—
408C2×C4×C79—41no—
409C2×C4×C79—41no—
410C2×C4×C79—41no—
411C2×C4×C79—41no—
412C2×C4×C79—41no—
413C2×C4×C79—41no—
414C2×C4×C79—41no—
415C2×C4×C79—41no—
416C2×C4×C79—41no—
417C2×C4×C79—41no—
418C2×C4×C79#11714yes—
419C2×Dic79—22no—
420C2×Dic79—22no—
421C2×Dic79—22no—
422C2×Dic79—22no—
423C2×Dic79—22no—
424C2×Dic79—22no—
425C2×Dic79—22no—
426C2×Dic79—22no—
427C2×Dic79—22no—
428C2×Dic79—22no—
429C2×Dic79—22no—
430C2×Dic79—22no—
431C2×Dic79—41no—
432C2×Dic79—41no—
433C2×Dic79—41no—
434C2×Dic79—41no—
435C2×Dic79—41no—
436C2×Dic79—41no—
437C2×Dic79—41no—
438C2×Dic79—41no—
439C2×Dic79—41no—
440C2×Dic79—41no—
441C2×Dic79—41no—
442C2×Dic79—41no—
443C2×Dic79—41no—
444C2×Dic79—41no—
445C2×Dic79—41no—
446C2×Dic79—41no—
447C2×Dic79—41no—
448C2×Dic79—41no—
449C2×Dic79—41no—
450C2×Dic79—41no—
451C2×Dic79—41no—
452C2×Dic79—41no—
453C2×Dic79—41no—
454C2×Dic79—41no—
455C2×Dic79—41no—
456C2×Dic79—41no—
457C2×Dic79—41no—
458C2×Dic79—41no—
459C2×Dic79—41no—
460C2×Dic79—41no—
461C2×Dic79—41no—
462C2×Dic79—41no—
463C2×Dic79—41no—
464C2×Dic79—41no—
465C2×Dic79—41no—
466C2×Dic79—41no—
467C2×Dic79—41no—
468C2×Dic79—41no—
469C2×Dic79—41no—
470C2×Dic79—41no—
471C2×Dic79—41no—
472C2×Dic79—41no—
473C2×Dic79—41no—
474C2×Dic79—41no—
475C22×C79—24no—
476C22×C79—24no—
477C22×C79—24no—
478C22×C79—42no—
479C22×C79—42no—
480C22×C79—42no—
481C22×C79—42no—
482C22×C79—42no—
483C22×C79—42no—
484C22×C79—42no—
485C22×C79—42no—
486C22×C79—42no—
487C22×C79—42no—
488C22×C79—42no—
489C22×C79—42no—
490C22×C79—42no—
491C22×C79—42no—
492C22×C79—42no—
493C22×C79—42no—
494C22×C79—42no—
495C22×C79—42no—
496C22×C79—42no—
497C22×C79—81no—
498C22×C79—81no—
499C22×C79—81no—
500C22×C79—81no—
501C22×C79—81no—
502C22×C79—81no—
503C22×C79—81no—
504C22×C79—81no—
505C22×C79C2×#11711yescharacteristic
506C22×C79C2×C4×D411yescharacteristic
507C22×C79C4×#4111yescharacteristic
508C22×C79#51811yescharacteristic
509C22×C79#51811yescharacteristic
510C22×C79#51811yescharacteristic
511C22×C79#52011yescharacteristic
512C22×C79#53411yescharacteristic
513C22×C79#53511yescharacteristic
514C22×C79#53811yescharacteristic
515C22×C79#53811yescharacteristic
516C22×C79#53811yescharacteristic
517C22×C79#53811yescharacteristic
518C22×C79#54011yescharacteristic
519C22×C79#54011yescharacteristic
520C22×C79#54011yescharacteristic
521C22×C79#54011yescharacteristic
522C22×C79#54211yescharacteristic
523C22×C79#54211yescharacteristic
524C22×C79#54611yescharacteristic
525C22×C79#54611yescharacteristic
526C22×C79#54611yescharacteristic
527C22×C79#54711yescharacteristic
528C22×C79#55111yescharacteristic
529C22×C79#55111yescharacteristic
530C22×C79#55111yescharacteristic
531C22×C79#55211yescharacteristic
532C22×C79#55311yescharacteristic
533C22×C79#55311yescharacteristic
534C22×C79#55911yescharacteristic
535C22×C79#55911yescharacteristic
536C22×C79#56011yescharacteristic
537C22×C79#56011yescharacteristic
538C22×C79#56211yescharacteristic
539C22×C79#56211yescharacteristic
540C4×C79—24no—
541C4×C79—42no—
542C4×C79—42no—
543C4×C79—42no—
544C4×C79—42no—
545Dic79—42no—
546Dic79—42no—
547Dic79—42no—
548Dic79—42no—
549Dic79—81no—
550Dic79—81no—
551Dic79—81no—
552Dic79—81no—
553#14376—791nomaximal, Sylow
554C2×C79—44no—
555C2×C79—82no—
556C2×C79#231911yescharacteristic
557C2×C79#232111yescharacteristic
558C2×C79#233311yescharacteristic
559C2×C79#234211yescharacteristic
560C2×C79#235711yescharacteristic
561C2×C79#235911yescharacteristic
562C2×C79#237711yescharacteristic
563C2×C79#270111yescharacteristic
564C2×C79#270311yescharacteristic
565C2×C79#270911yescharacteristic
566C2×C79#271011yescharacteristic
567C2×C79#274911yescharacteristic
568C2×C79#275111yescharacteristic
569C2×C79#275211yescharacteristic
570C2×C79#276111yescharacteristic
571C2×#390—791no—
572C2×#386D7911yescharacteristic
573C2×#381—791no—
574#1442—791no—
575#1440—791no—
576#1440—791no—
577#1439—791no—
578#1439—791no—
579#1438—791no—
580#1437—791no—
581#1437—791no—
582#1436—791no—
583#1436—791no—
584#1434—791no—
585C22⋊#95—791no—
586C79#1437611yescharacteristic, complemented, Sylow
587C23×D4C2×D7911yescharacteristic
588C24×C4C2×D7911yescharacteristic
589C22×C4⋊C4—791no—
590C22×C4⋊C4—791no—
591C22×C22⋊C4—791no—
592C22×C22⋊C4—791no—
593C22×C22⋊C4—791no—
594C22×C22⋊C4—791no—
595C22×C22⋊C4—791no—
596C22×C22⋊C4—791no—
597C22×C22⋊C4—791no—
598C22×C22⋊C4—791no—
599C22×C22⋊C4C2×D7911yescharacteristic
600C22×C22⋊C4C2×D7911yescharacteristic
601C22×C22⋊C4C2×D7911yescharacteristic
602C22×C42—791no—
603C22×C42—791no—
604#390—1584no—
605#386Dic7918yescomplemented
606#381—1584no—
607C2×#95—791no—
608C2×#95—791no—
609C2×#95—791no—
610C2×#95—791no—
611C2×#95—791no—
612C2×#95—791no—
613C2×#95—791no—
614C2×#95—791no—
615C2×#95—791no—
616C2×#95—791no—
617C2×#95—791no—
618C2×#95—791no—
619C2×#95—791no—
620C2×#95—791no—
621C2×#95—791no—
622C2×#95—791no—
623C2×#95C2×D7911yescharacteristic
624C2×#95C2×D7911yescharacteristic
625C25C22×D7911yescharacteristic
626C25C22×D7911yescharacteristic
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—41no—
632C22×D4—41no—
633C22×D4C2×Dic7914yes—
634C23×C4—22no—
635C23×C4—22no—
636C23×C4—41no—
637C23×C4—41no—
638C23×C4—41no—
639C23×C4—41no—
640C23×C4—791no—
641C23×C4—791no—
642C23×C4—791no—
643C23×C4—791no—
644C23×C4—791no—
645C23×C4—791no—
646C23×C4—791no—
647C23×C4—791no—
648C23×C4C2×Dic7914yes—
649C23×C4C22×D7911yescharacteristic
650C23×C4C22×D7911yescharacteristic
651C23×C4C22×D7911yescharacteristic
652C23×C4C22×D7911yescharacteristic
653C23×C4C22×D7911yescharacteristic
654C2×C4⋊C4—3161no—
655C2×C4⋊C4—3161no—
656C2×C4⋊C4—3161no—
657C2×C4⋊C4—1582no—
658C2×C4⋊C4—1582no—
659C2×C4⋊C4—1582no—
660C2×C22⋊C4—41no—
661C2×C22⋊C4—41no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—3161no—
667C2×C22⋊C4—3161no—
668C2×C22⋊C4—3161no—
669C2×C22⋊C4—3161no—
670C2×C22⋊C4—3161no—
671C2×C22⋊C4—3161no—
672C2×C22⋊C4—3161no—
673C2×C22⋊C4—3161no—
674C2×C22⋊C4—3161no—
675C2×C22⋊C4—3161no—
676C2×C22⋊C4—3161no—
677C2×C22⋊C4—3161no—
678C2×C22⋊C4—3161no—
679C2×C22⋊C4—3161no—
680C2×C22⋊C4—794no—
681C2×C22⋊C4—1582no—
682C2×C22⋊C4—1582no—
683C2×C22⋊C4—1582no—
684C2×C22⋊C4—1582no—
685C2×C22⋊C4—1582no—
686C2×C22⋊C4—1582no—
687C2×C22⋊C4—1582no—
688C2×C22⋊C4—1582no—
689C2×C22⋊C4—1582no—
690C2×C22⋊C4C2×Dic7914yes—
691C2×C22⋊C4C2×Dic7914yes—
692C2×C22⋊C4C2×Dic7914yes—
693C2×C42—3161no—
694C2×C42—3161no—
695C2×C42—3161no—
696C2×C42—3161no—
697C2×C42—1582no—
698C2×C42—1582no—
699#95—3161no—
700#95—3161no—
701#95—3161no—
702#95—3161no—
703#95—3161no—
704#95—3161no—
705#95—3161no—
706#95—3161no—
707#95—3161no—
708#95—1582no—
709#95—1582no—
710#95—1582no—
711#95—1582no—
712#95—1582no—
713#95—1582no—
714#95—1582no—
715#95C2×Dic7914yes—
716#95C2×Dic7914yes—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24C22×Dic7912yes—
744C24C22×Dic7912yes—
745C24D4×D7912yes—
746C24#1192962312yes—
747C24C23×D7911yescharacteristic
748C2×D4—28no—
749C2×D4—28no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—28no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—792no—
791C22×C4—792no—
792C22×C4—792no—
793C22×C4—792no—
794C22×C4—1581no—
795C22×C4—1581no—
796C22×C4—1581no—
797C22×C4—1581no—
798C22×C4—1581no—
799C22×C4—1581no—
800C22×C4—1581no—
801C22×C4—1581no—
802C22×C4—1581no—
803C22×C4—1581no—
804C22×C4—1581no—
805C22×C4—1581no—
806C22×C4—1581no—
807C22×C4—1581no—
808C22×C4—1581no—
809C22×C4—1581no—
810C22×C4—1581no—
811C22×C4—1581no—
812C22×C4—1581no—
813C22×C4—1581no—
814C22×C4—1581no—
815C22×C4—1581no—
816C22×C4—1581no—
817C22×C4—1581no—
818C22×C4—1581no—
819C22×C4—1581no—
820C22×C4—1581no—
821C22×C4—1581no—
822C22×C4—1581no—
823C22×C4—1581no—
824C22×C4—1581no—
825C22×C4—1581no—
826C22×C4—1581no—
827C22×C4—1581no—
828C22×C4—1581no—
829C22×C4—1581no—
830C22×C4—1581no—
831C22×C4—1581no—
832C22×C4—1581no—
833C22×C4—1581no—
834C22×C4—1581no—
835C22×C4—1581no—
836C22×C4—1581no—
837C22×C4—1581no—
838C22×C4—1581no—
839C22×C4—1581no—
840C22×C4—1581no—
841C22×C4—1581no—
842C22×C4—1581no—
843C22×C4—1581no—
844C22×C4—1581no—
845C22×C4—1581no—
846C22×C4C22×Dic7912yes—
847C22×C4C22×Dic7912yes—
848C22×C4C22×Dic7912yes—
849C22×C4C22×Dic7912yes—
850C22×C4C22×Dic7912yes—
851C22×C4#1192962412yes—
852C22×C4#1192962412yes—
853C4⋊C4—3164no—
854C4⋊C4—3164no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—3164no—
859C22⋊C4—3164no—
860C22⋊C4—3164no—
861C22⋊C4—3164no—
862C22⋊C4—3164no—
863C22⋊C4—3164no—
864C22⋊C4—3164no—
865C22⋊C4—3164no—
866C42—3164no—
867C42—3164no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23D4×Dic7914yes—
938C23C23×Dic7911yescharacteristic
939C23C2×D4×D7911yescharacteristic
940C23#41×D7911yescharacteristic
941C23#41×D7911yescharacteristic
942C23C2×#1192962311yescharacteristic
943C23C2×#1192962411yescharacteristic
944C23C2×#1192962411yescharacteristic
945C23#1457920611yescharacteristic
946C23#1457920611yescharacteristic
947C23#1457920611yescharacteristic
948C23#1457920611yescharacteristic
949C23#1457920611yescharacteristic
950C23#1457920611yescharacteristic
951C23#1457920711yescharacteristic
952C23#1457920811yescharacteristic
953D4—416no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—416no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—3161no—
990C2×C4—3161no—
991C2×C4—3161no—
992C2×C4—3161no—
993C2×C4—3161no—
994C2×C4—3161no—
995C2×C4—3161no—
996C2×C4—3161no—
997C2×C4—3161no—
998C2×C4—3161no—
999C2×C4—3161no—
1000C2×C4—3161no—
1001C2×C4—3161no—
1002C2×C4—3161no—
1003C2×C4—3161no—
1004C2×C4—3161no—
1005C2×C4—3161no—
1006C2×C4—3161no—
1007C2×C4—3161no—
1008C2×C4—3161no—
1009C2×C4—3161no—
1010C2×C4—3161no—
1011C2×C4—3161no—
1012C2×C4—3161no—
1013C2×C4—3161no—
1014C2×C4—3161no—
1015C2×C4—3161no—
1016C2×C4—3161no—
1017C2×C4—3161no—
1018C2×C4—3161no—
1019C2×C4—3161no—
1020C2×C4—3161no—
1021C2×C4—3161no—
1022C2×C4—3161no—
1023C2×C4—3161no—
1024C2×C4—3161no—
1025C2×C4—3161no—
1026C2×C4—3161no—
1027C2×C4—3161no—
1028C2×C4—3161no—
1029C2×C4—3161no—
1030C2×C4—3161no—
1031C2×C4—3161no—
1032C2×C4—3161no—
1033C2×C4—1582no—
1034C2×C4—1582no—
1035C2×C4—1582no—
1036C2×C4—1582no—
1037C2×C4—1582no—
1038C2×C4—1582no—
1039C2×C4—1582no—
1040C2×C4—1582no—
1041C2×C4—1582no—
1042C2×C4—1582no—
1043C2×C4—1582no—
1044C2×C4—1582no—
1045C2×C4#1457912014yes—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22C2×#1457912011yescharacteristic
1077C22C2×D4×Dic7911yescharacteristic
1078C22#41×Dic7911yescharacteristic
1079C22#1909903811yescharacteristic
1080C22#1909903811yescharacteristic
1081C22#1909903811yescharacteristic
1082C22#1909904611yescharacteristic
1083C22#1909912311yescharacteristic
1084C22#1909912811yescharacteristic
1085C22#1909914511yescharacteristic
1086C22#1909914511yescharacteristic
1087C22#1909914811yescharacteristic
1088C22#1909914811yescharacteristic
1089C22#1909916311yescharacteristic
1090C22#1909916311yescharacteristic
1091C22#1909916411yescharacteristic
1092C22#1909916411yescharacteristic
1093C22#1909917811yescharacteristic
1094C22#1909917811yescharacteristic
1095C22#1909920311yescharacteristic
1096C22#1909920311yescharacteristic
1097C22#1909920511yescharacteristic
1098C22#1909921111yescharacteristic
1099C22#1909923611yescharacteristic
1100C22#1909923911yescharacteristic
1101C22#1909923911yescharacteristic
1102C22#1909925011yescharacteristic
1103C22#1909926311yescharacteristic
1104C22#1909926311yescharacteristic
1105C22#1909929611yescharacteristic
1106C22#1909929611yescharacteristic
1107C22#1909930111yescharacteristic
1108C22#1909930111yescharacteristic
1109C22#1909930811yescharacteristic
1110C22#1909930811yescharacteristic
1111C4—24no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—3162no—
1117C4—3162no—
1118C4—3162no—
1119C4—3162no—
1120C4—6321no—
1121C4—6321no—
1122C4—6321no—
1123C4—6321no—
1124C2—44no—
1125C2—82no—
1126C2#2376604311yescharacteristic
1127C2#2376606111yescharacteristic
1128C2#2376616711yescharacteristic
1129C2#2376624911yescharacteristic
1130C2#2376637311yescharacteristic
1131C2#2376639611yescharacteristic
1132C2#2376655711yescharacteristic
1133C2#2377001611yescharacteristic
1134C2#2377004611yescharacteristic
1135C2#2377013111yescharacteristic
1136C2#2377014211yescharacteristic
1137C2#2377062711yescharacteristic
1138C2#2377065311yescharacteristic
1139C2#2377066711yescharacteristic
1140C2#2377078711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D79
commutatorC23×C79C23×C4
FittingC2×#386×C79C2
socle, cosocleC24×C79C24
prime radicalC23×D4×C79C22
hypercenterC2×#386D79
hypocenterC79#14376
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#19098426C2semidirect
3. #23761657C2semidirect
4. #23761649C2semidirect
5. #23761649C2semidirect
6. #23761645C2semidirect
7. #23761645C2semidirect
9. #23761637C2semidirect
10. #23761637C2semidirect
11. #23761634C2semidirect
12. #23761634C2semidirect
13. #23761625C2semidirect
14. #23761623C2semidirect
51. #386×C79C4semidirect
586. C79#14376semidirect
605. #386Dic79semidirect

Maximal subgroups

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

subgroupindex
C2×#190984662
C2×#190984262
#237616572
#237616492
#237616452
#237616412
#237616372
#237616342
#237616252
#237616232
C2×#386×C792
#1437679