Finite Group Databasebeta

← #34215575

Subgroups — #34215575

Order 20224.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098456C211yesmaximal, characteristic, complemented
2C2×#19098443C211yesmaximal, characteristic
3C2×#19098438C211yesmaximal, characteristic, complemented
4C2×#19098423C211yesmaximal, characteristic, complemented
5#23761668C211yesmaximal, characteristic, complemented
6#23761653C211yesmaximal, characteristic, complemented
7#23761653C211yesmaximal, characteristic, complemented
8#23761649C211yesmaximal, characteristic, complemented
9#23761645C211yesmaximal, characteristic, complemented
10#23761641C211yesmaximal, characteristic
11#23761637C211yesmaximal, characteristic, complemented
12#23761629C211yesmaximal, characteristic, complemented
13#23761623C211yesmaximal, characteristic, complemented
14#23761622C211yesmaximal, characteristic, complemented
15C22×#123×C79C211yesmaximal, characteristic
16C24×Dic79C2211yescharacteristic
17C22×C4⋊Dic79C2211yescharacteristic
18C22×C4⋊Dic79C2211yescharacteristic
19C22×C4⋊Dic79C2211yescharacteristic
20C22×C22⋊Dic79C2211yescharacteristic
21C22×C22⋊Dic79C2211yescharacteristic
22C22×C22⋊Dic79C2211yescharacteristic
23C22×C22⋊Dic79C2211yescharacteristic
24C22×C22⋊Dic79C2211yescharacteristic
25C22×C22⋊Dic79C2211yescharacteristic
26C22×C22⋊Dic79C2211yescharacteristic
27C22×C4×Dic79C2211yescharacteristic
28#19098456—24no—
29#19098443—24no—
30#19098438—24no—
31#19098423—24no—
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
46C2×C79⋊#95C2211yescharacteristic
47C2×C79⋊#95C2211yescharacteristic
48C23×D4×C79C2211yescharacteristic
49C24×C4×C79C2211yescharacteristic
50C2×#123×C79—24no—
51C2×#123×C79—24no—
52C2×#123×C79C418yescomplemented
53C22×C4⋊C4×C79C2211yescharacteristic
54C22×C4⋊C4×C79C2211yescharacteristic
55C22×C22⋊C4×C79C2211yescharacteristic
56C22×C22⋊C4×C79C2211yescharacteristic
57C22×C22⋊C4×C79C2211yescharacteristic
58C23×Dic79—22no—
59C23×Dic79—22no—
60C23×Dic79—22no—
61C23×Dic79—41no—
62C23×Dic79—41no—
63C23×Dic79—41no—
64C23×Dic79—41no—
65C23×Dic79C2311yescharacteristic
66C23×Dic79C2311yescharacteristic
67C23×Dic79C2311yescharacteristic
68C23×Dic79C2311yescharacteristic
69C23×Dic79C2311yescharacteristic
70C23×Dic79C2311yescharacteristic
71C23×Dic79C2311yescharacteristic
72C23×Dic79C2311yescharacteristic
73C2×C4⋊Dic79—22no—
74C2×C4⋊Dic79—22no—
75C2×C4⋊Dic79—22no—
76C2×C4⋊Dic79—22no—
77C2×C4⋊Dic79—22no—
78C2×C4⋊Dic79—22no—
79C2×C4⋊Dic79—41no—
80C2×C4⋊Dic79—41no—
81C2×C4⋊Dic79—41no—
82C2×C22⋊Dic79—22no—
83C2×C22⋊Dic79—22no—
84C2×C22⋊Dic79—22no—
85C2×C22⋊Dic79—22no—
86C2×C22⋊Dic79—22no—
87C2×C22⋊Dic79—22no—
88C2×C22⋊Dic79—22no—
89C2×C22⋊Dic79—22no—
90C2×C22⋊Dic79—22no—
91C2×C22⋊Dic79—22no—
92C2×C22⋊Dic79—41no—
93C2×C22⋊Dic79—41no—
94C2×C22⋊Dic79—41no—
95C2×C22⋊Dic79—41no—
96C2×C22⋊Dic79—41no—
97C2×C22⋊Dic79—41no—
98C2×C22⋊Dic79—41no—
99C2×C22⋊Dic79—41no—
100C2×C22⋊Dic79—41no—
101C2×C22⋊Dic79—41no—
102C2×C22⋊Dic79D414yes—
103C2×C4×Dic79—22no—
104C2×C4×Dic79—22no—
105C2×C4×Dic79—41no—
106C79⋊#95—22no—
107C79⋊#95—22no—
108C79⋊#95—22no—
109C79⋊#95—22no—
110C79⋊#95—22no—
111C79⋊#95—22no—
112C79⋊#95—22no—
113C79⋊#95—22no—
114C79⋊#95—41no—
115C79⋊#95—41no—
116C79⋊#95—41no—
117C79⋊#95—41no—
118C79⋊#95—41no—
119C79⋊#95—41no—
120C79⋊#95—41no—
121C79⋊#95—41no—
122C25×C79C2311yescharacteristic
123C25×C79C2311yescharacteristic
124C22×D4×C79—22no—
125C22×D4×C79—22no—
126C22×D4×C79—22no—
127C22×D4×C79—22no—
128C22×D4×C79—41no—
129C22×D4×C79—41no—
130C22×D4×C79C2×C414yes—
131C23×C4×C79—22no—
132C23×C4×C79—22no—
133C23×C4×C79—22no—
134C23×C4×C79—22no—
135C23×C4×C79—41no—
136C23×C4×C79—41no—
137C23×C4×C79C2×C414yescomplemented
138C23×C4×C79C2311yescharacteristic
139C23×C4×C79C2311yescharacteristic
140C23×C4×C79C2311yescharacteristic
141C23×C4×C79C2311yescharacteristic
142C23×C4×C79C2311yescharacteristic
143#123×C79—232no—
144C2×C4⋊C4×C79—22no—
145C2×C4⋊C4×C79—22no—
146C2×C4⋊C4×C79—22no—
147C2×C4⋊C4×C79—22no—
148C2×C4⋊C4×C79C2×C414yescomplemented
149C2×C4⋊C4×C79C2×C414yescomplemented
150C2×C22⋊C4×C79—22no—
151C2×C22⋊C4×C79—22no—
152C2×C22⋊C4×C79—22no—
153C2×C22⋊C4×C79—22no—
154C2×C22⋊C4×C79C2×C414yes—
155C2×C22⋊C4×C79C2×C414yes—
156C2×C22⋊C4×C79C2×C414yescomplemented
157C2×C22⋊C4×C79D414yes—
158C2×C22⋊C4×C79D414yes—
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×Dic79—21no—
199C22×Dic79—21no—
200C22×Dic79—21no—
201C22×Dic79—21no—
202C22×Dic79—21no—
203C22×Dic79—21no—
204C22×Dic79—21no—
205C22×Dic79—21no—
206C22×Dic79—21no—
207C22×Dic79—21no—
208C22×Dic79—21no—
209C22×Dic79—21no—
210C22×Dic79—21no—
211C22×Dic79—44no—
212C22×Dic79—44no—
213C22×Dic79—44no—
214C22×Dic79—44no—
215C22×Dic79—44no—
216C22×Dic79—44no—
217C22×Dic79—44no—
218C22×Dic79C2×D412yes—
219C22×Dic79C2×D412yes—
220C22×Dic79#4112yes—
221C22×Dic79#4112yes—
222C4⋊Dic79—44no—
223C4⋊Dic79—44no—
224C4⋊Dic79—44no—
225C22⋊Dic79—44no—
226C22⋊Dic79—44no—
227C22⋊Dic79—44no—
228C22⋊Dic79—44no—
229C22⋊Dic79—44no—
230C22⋊Dic79—44no—
231C22⋊Dic79—44no—
232C4×Dic79—44no—
233C24×C79—21no—
234C24×C79—21no—
235C24×C79—21no—
236C24×C79—21no—
237C24×C79—21no—
238C24×C79—21no—
239C24×C79—21no—
240C24×C79—21no—
241C24×C79—21no—
242C24×C79—21no—
243C24×C79—21no—
244C24×C79—21no—
245C24×C79—21no—
246C24×C79—21no—
247C24×C79—21no—
248C24×C79—21no—
249C24×C79—21no—
250C24×C79—21no—
251C24×C79—21no—
252C24×C79—21no—
253C24×C79—21no—
254C24×C79—21no—
255C24×C79—21no—
256C24×C79—21no—
257C24×C79C22×C412yes—
258C24×C79C22×C412yes—
259C24×C79C2×D412yes—
260C24×C79C2×D412yes—
261C24×C79C2×D412yes—
262C24×C79#4112yes—
263C24×C79C2411yescharacteristic
264C2×D4×C79—28no—
265C2×D4×C79—28no—
266C2×D4×C79—44no—
267C2×D4×C79—44no—
268C2×D4×C79—44no—
269C2×D4×C79—44no—
270C2×D4×C79—44no—
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—28no—
280C22×C4×C79—21no—
281C22×C4×C79—21no—
282C22×C4×C79—21no—
283C22×C4×C79—21no—
284C22×C4×C79—21no—
285C22×C4×C79—21no—
286C22×C4×C79—21no—
287C22×C4×C79—21no—
288C22×C4×C79—21no—
289C22×C4×C79—21no—
290C22×C4×C79—21no—
291C22×C4×C79—21no—
292C22×C4×C79—21no—
293C22×C4×C79—21no—
294C22×C4×C79—21no—
295C22×C4×C79—21no—
296C22×C4×C79—21no—
297C22×C4×C79—21no—
298C22×C4×C79—28no—
299C22×C4×C79—44no—
300C22×C4×C79—44no—
301C22×C4×C79—44no—
302C22×C4×C79—44no—
303C22×C4×C79—44no—
304C22×C4×C79C22×C412yes—
305C22×C4×C79C22×C412yes—
306C22×C4×C79C22×C412yes—
307C22×C4×C79C22×C412yes—
308C22×C4×C79C22×C412yes—
309C22×C4×C79C2×D412yes—
310C22×C4×C79C2×D412yes—
311C22×C4×C79C2×D412yes—
312C22×C4×C79C2×D412yes—
313C4⋊C4×C79—28no—
314C4⋊C4×C79—28no—
315C22⋊C4×C79—28no—
316C22⋊C4×C79—28no—
317C22⋊C4×C79C22⋊C4116yescomplemented
318C23×C79—22no—
319C23×C79—22no—
320C23×C79—22no—
321C23×C79—22no—
322C23×C79—22no—
323C23×C79—22no—
324C23×C79—22no—
325C23×C79—22no—
326C23×C79—22no—
327C23×C79—22no—
328C23×C79—22no—
329C23×C79—22no—
330C23×C79—22no—
331C23×C79—22no—
332C23×C79—22no—
333C23×C79—22no—
334C23×C79—22no—
335C23×C79—22no—
336C23×C79—22no—
337C23×C79—22no—
338C23×C79—22no—
339C23×C79—22no—
340C23×C79—22no—
341C23×C79—22no—
342C23×C79—22no—
343C23×C79—22no—
344C23×C79—22no—
345C23×C79—22no—
346C23×C79—22no—
347C23×C79—22no—
348C23×C79—22no—
349C23×C79—22no—
350C23×C79—22no—
351C23×C79—22no—
352C23×C79—22no—
353C23×C79—22no—
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×C79—41no—
367C23×C79—41no—
368C23×C79—41no—
369C23×C79—41no—
370C23×C79—41no—
371C23×C79—41no—
372C23×C79—41no—
373C23×C79—41no—
374C23×C79—41no—
375C23×C79—41no—
376C23×C79—41no—
377C23×C79—41no—
378C23×C79—41no—
379C23×C79—41no—
380C23×C79—41no—
381C23×C79—41no—
382C23×C79—41no—
383C23×C79—41no—
384C23×C79—41no—
385C23×C79—41no—
386C23×C79C2×C22⋊C414yes—
387C23×C79C4×D414yes—
388C23×C79C23×C411yescharacteristic
389C23×C79C22×D411yescharacteristic
390C23×C79C22×D411yescharacteristic
391C23×C79C22×D411yescharacteristic
392C23×C79C2×#4111yescharacteristic
393C23×C79C2×#4111yescharacteristic
394C23×C79C2×#4111yescharacteristic
395C23×C79H(5,𝔽2)11yescharacteristic
396C23×C79H(5,𝔽2)11yescharacteristic
397C23×C79H(5,𝔽2)11yescharacteristic
398C23×C79H(5,𝔽2)11yescharacteristic
399C23×C79H(5,𝔽2)11yescharacteristic
400C23×C792−1+411yescharacteristic
401C23×C792−1+411yescharacteristic
402C23×C792−1+411yescharacteristic
403D4×C79—416no—
404C2×C4×C79—22no—
405C2×C4×C79—22no—
406C2×C4×C79—22no—
407C2×C4×C79—22no—
408C2×C4×C79—22no—
409C2×C4×C79—22no—
410C2×C4×C79—22no—
411C2×C4×C79—22no—
412C2×C4×C79—22no—
413C2×C4×C79—22no—
414C2×C4×C79—22no—
415C2×C4×C79—22no—
416C2×C4×C79—22no—
417C2×C4×C79—22no—
418C2×C4×C79—22no—
419C2×C4×C79—22no—
420C2×C4×C79—22no—
421C2×C4×C79—22no—
422C2×C4×C79—22no—
423C2×C4×C79—22no—
424C2×C4×C79—22no—
425C2×C4×C79—416no—
426C2×C4×C79—41no—
427C2×C4×C79—41no—
428C2×C4×C79—41no—
429C2×C4×C79—41no—
430C2×C4×C79—41no—
431C2×C4×C79—41no—
432C2×C4×C79—41no—
433C2×C4×C79—41no—
434C2×C4×C79—41no—
435C2×C4×C79—41no—
436C2×C4×C79—41no—
437C2×C4×C79—41no—
438C2×C4×C79C2×C22⋊C414yes—
439C2×C4×C79C2×C22⋊C414yes—
440C2×Dic79—22no—
441C2×Dic79—22no—
442C2×Dic79—22no—
443C2×Dic79—22no—
444C2×Dic79—22no—
445C2×Dic79—22no—
446C2×Dic79—22no—
447C2×Dic79—22no—
448C2×Dic79—22no—
449C2×Dic79—22no—
450C2×Dic79—22no—
451C2×Dic79—22no—
452C2×Dic79—416no—
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—
475C2×Dic79—41no—
476C2×Dic79—41no—
477C2×Dic79—41no—
478C2×Dic79—41no—
479C2×Dic79—41no—
480C2×Dic79—41no—
481C2×Dic79—41no—
482C2×Dic79—41no—
483C2×Dic79—41no—
484C2×Dic79—41no—
485C2×Dic79—41no—
486C2×Dic79—41no—
487C2×Dic79—41no—
488C2×Dic79—41no—
489C2×Dic79—41no—
490C2×Dic79—41no—
491C2×Dic79—41no—
492C2×Dic79—41no—
493C2×Dic79—41no—
494C2×Dic79—41no—
495C2×Dic79—41no—
496C2×Dic79—41no—
497C22×C79—24no—
498C22×C79—24no—
499C22×C79—24no—
500C22×C79—24no—
501C22×C79—24no—
502C22×C79—24no—
503C22×C79—42no—
504C22×C79—42no—
505C22×C79—42no—
506C22×C79—42no—
507C22×C79—42no—
508C22×C79—42no—
509C22×C79—42no—
510C22×C79—42no—
511C22×C79—42no—
512C22×C79—42no—
513C22×C79—42no—
514C22×C79—42no—
515C22×C79—42no—
516C22×C79—42no—
517C22×C79—42no—
518C22×C79—42no—
519C22×C79—42no—
520C22×C79—42no—
521C22×C79—42no—
522C22×C79—42no—
523C22×C79—42no—
524C22×C79—42no—
525C22×C79—42no—
526C22×C79—42no—
527C22×C79C22×C22⋊C411yescharacteristic
528C22×C79C2×C4×D411yescharacteristic
529C22×C79C4×#4111yescharacteristic
530C22×C79#51811yescharacteristic
531C22×C79#52011yescharacteristic
532C22×C79#52011yescharacteristic
533C22×C79#52011yescharacteristic
534C22×C79#53411yescharacteristic
535C22×C79#53511yescharacteristic
536C22×C79#53611yescharacteristic
537C22×C79#53611yescharacteristic
538C22×C79#53711yescharacteristic
539C22×C79#53711yescharacteristic
540C22×C79#53811yescharacteristic
541C22×C79#53911yescharacteristic
542C22×C79#53911yescharacteristic
543C22×C79#53911yescharacteristic
544C22×C79#54011yescharacteristic
545C22×C79#54211yescharacteristic
546C22×C79D4211yescharacteristic
547C22×C79D4211yescharacteristic
548C22×C79#54611yescharacteristic
549C22×C79#54611yescharacteristic
550C22×C79#54611yescharacteristic
551C22×C79#54611yescharacteristic
552C22×C79#54611yescharacteristic
553C22×C79#54711yescharacteristic
554C22×C79#54711yescharacteristic
555C22×C79#54711yescharacteristic
556C22×C79#55111yescharacteristic
557C22×C79#55211yescharacteristic
558C22×C79#56011yescharacteristic
559C22×C79#56211yescharacteristic
560C22×C79#56211yescharacteristic
561C22×C79#56311yescharacteristic
562C4×C79—24no—
563C4×C79—24no—
564C4×C79—42no—
565C4×C79—42no—
566C4×C79—42no—
567Dic79—42no—
568Dic79—42no—
569Dic79—42no—
570Dic79—42no—
571Dic79—81no—
572Dic79—81no—
573Dic79—81no—
574Dic79—81no—
575#14359—791nomaximal, Sylow
576C2×C79—44no—
577C2×C79—44no—
578C2×C79#231111yescharacteristic
579C2×C79#232211yescharacteristic
580C2×C79#233511yescharacteristic
581C2×C79D4×C22⋊C411yescharacteristic
582C2×C79#233911yescharacteristic
583C2×C79#235911yescharacteristic
584C2×C79#237611yescharacteristic
585C2×C79#267111yescharacteristic
586C2×C79#267211yescharacteristic
587C2×C79#267811yescharacteristic
588C2×C79#268011yescharacteristic
589C2×C79#268711yescharacteristic
590C2×C79#269311yescharacteristic
591C2×C79#269511yescharacteristic
592C2×C79#270611yescharacteristic
593C22×#123D7911yescharacteristic
594C2×#388—791no—
595C2×#386—791no—
596C2×#385—791no—
597C2×#380—791no—
598#1445—791no—
599#1441—791no—
600#1441—791no—
601#1440—791no—
602#1439—791no—
603#1438—791no—
604#1437—791no—
605C4⋊#95—791no—
606C22⋊#95—791no—
607C22⋊#95—791no—
608C79#1435911yescharacteristic, complemented, Sylow
609C23×D4C2×D7911yescharacteristic
610C24×C4—791no—
611C24×C4C2×D7911yescharacteristic
612C2×#123—24no—
613C2×#123—24no—
614C2×#123Dic7918yescomplemented
615C22×C4⋊C4—791no—
616C22×C4⋊C4—791no—
617C22×C4⋊C4—791no—
618C22×C4⋊C4C2×D7911yescharacteristic
619C22×C4⋊C4C2×D7911yescharacteristic
620C22×C22⋊C4—791no—
621C22×C22⋊C4—791no—
622C22×C22⋊C4—791no—
623C22×C22⋊C4—791no—
624C22×C22⋊C4—791no—
625C22×C22⋊C4—791no—
626C22×C22⋊C4—791no—
627C22×C22⋊C4C2×D7911yescharacteristic
628C22×C22⋊C4C2×D7911yescharacteristic
629C22×C22⋊C4C2×D7911yescharacteristic
630C22×C42—791no—
631#388—1584no—
632#386—1584no—
633#385—1584no—
634#380—1584no—
635C2×#95—791no—
636C2×#95—791no—
637C2×#95—791no—
638C2×#95—791no—
639C2×#95—791no—
640C2×#95—791no—
641C2×#95—791no—
642C2×#95—791no—
643C2×#95—791no—
644C2×#95—791no—
645C2×#95—791no—
646C2×#95—791no—
647C2×#95—791no—
648C2×#95—791no—
649C2×#95—791no—
650C2×#95—791no—
651C25C22×D7911yescharacteristic
652C25C22×D7911yescharacteristic
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—41no—
658C22×D4—41no—
659C22×D4C2×Dic7914yes—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—41no—
665C23×C4—41no—
666C23×C4—3161no—
667C23×C4—3161no—
668C23×C4—3161no—
669C23×C4—3161no—
670C23×C4—791no—
671C23×C4—791no—
672C23×C4—791no—
673C23×C4—791no—
674C23×C4—791no—
675C23×C4—791no—
676C23×C4—791no—
677C23×C4—791no—
678C23×C4—1582no—
679C23×C4—1582no—
680C23×C4—1582no—
681C23×C4C2×Dic7914yescomplemented
682C23×C4C22×D7911yescharacteristic
683C23×C4C22×D7911yescharacteristic
684C23×C4C22×D7911yescharacteristic
685C23×C4C22×D7911yescharacteristic
686C23×C4C22×D7911yescharacteristic
687#123—232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—3161no—
693C2×C4⋊C4—3161no—
694C2×C4⋊C4—3161no—
695C2×C4⋊C4—1582no—
696C2×C4⋊C4—1582no—
697C2×C4⋊C4—1582no—
698C2×C4⋊C4—1582no—
699C2×C4⋊C4—1582no—
700C2×C4⋊C4—1582no—
701C2×C4⋊C4C2×Dic7914yescomplemented
702C2×C4⋊C4C2×Dic7914yescomplemented
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—3161no—
708C2×C22⋊C4—3161no—
709C2×C22⋊C4—3161no—
710C2×C22⋊C4—3161no—
711C2×C22⋊C4—3161no—
712C2×C22⋊C4—3161no—
713C2×C22⋊C4—3161no—
714C2×C22⋊C4—3161no—
715C2×C22⋊C4—3161no—
716C2×C22⋊C4—3161no—
717C2×C22⋊C4—794no—
718C2×C22⋊C4—1582no—
719C2×C22⋊C4—1582no—
720C2×C22⋊C4—1582no—
721C2×C22⋊C4—1582no—
722C2×C22⋊C4—1582no—
723C2×C22⋊C4—1582no—
724C2×C22⋊C4—1582no—
725C2×C22⋊C4—1582no—
726C2×C22⋊C4—1582no—
727C2×C22⋊C4—1582no—
728C2×C22⋊C4C2×Dic7914yes—
729C2×C22⋊C4C2×Dic7914yes—
730C2×C22⋊C4C2×Dic7914yescomplemented
731C2×C22⋊C4C22⋊D7914yes—
732C2×C22⋊C4C22⋊D7914yes—
733C2×C42—3161no—
734C2×C42—1582no—
735C2×C42—1582no—
736#95—3161no—
737#95—3161no—
738#95—3161no—
739#95—3161no—
740#95—3161no—
741#95—3161no—
742#95—3161no—
743#95—3161no—
744#95—1582no—
745#95—1582no—
746#95—1582no—
747#95—1582no—
748#95—1582no—
749#95—1582no—
750#95—1582no—
751#95—1582no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24C22×Dic7912yes—
777C24C22×Dic7912yes—
778C24D4×D7912yes—
779C24C2×C22⋊D7912yes—
780C24C2×C22⋊D7912yes—
781C24#1192962312yes—
782C24C23×D7911yescharacteristic
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—28no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—28no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—3164no—
824C22×C4—3164no—
825C22×C4—3164no—
826C22×C4—3164no—
827C22×C4—3164no—
828C22×C4—3164no—
829C22×C4—3164no—
830C22×C4—792no—
831C22×C4—792no—
832C22×C4—792no—
833C22×C4—792no—
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×C4—1581no—
847C22×C4—1581no—
848C22×C4—1581no—
849C22×C4—1581no—
850C22×C4—1581no—
851C22×C4—1581no—
852C22×C4—1581no—
853C22×C4—1581no—
854C22×C4—1581no—
855C22×C4—1581no—
856C22×C4—1581no—
857C22×C4—1581no—
858C22×C4—1581no—
859C22×C4—1581no—
860C22×C4—1581no—
861C22×C4—1581no—
862C22×C4—1581no—
863C22×C4—1581no—
864C22×C4—1581no—
865C22×C4—1581no—
866C22×C4—1581no—
867C22×C4—1581no—
868C22×C4—1581no—
869C22×C4—1581no—
870C22×C4—1581no—
871C22×C4—1581no—
872C22×C4—1581no—
873C22×C4—1581no—
874C22×C4—1581no—
875C22×C4—1581no—
876C22×C4—1581no—
877C22×C4—1581no—
878C22×C4—1581no—
879C22×C4—1581no—
880C22×C4—1581no—
881C22×C4—1581no—
882C22×C4—1581no—
883C22×C4—1581no—
884C22×C4—1581no—
885C22×C4—1581no—
886C22×C4C22×Dic7912yes—
887C22×C4C22×Dic7912yes—
888C22×C4C22×Dic7912yes—
889C22×C4C22×Dic7912yes—
890C22×C4C22×Dic7912yes—
891C22×C4C2×C22⋊D7912yes—
892C22×C4C2×C22⋊D7912yes—
893C22×C4C2×C22⋊D7912yes—
894C22×C4C2×C22⋊D7912yes—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—3164no—
898C4⋊C4—3164no—
899C4⋊C4—3164no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—3164no—
903C22⋊C4—3164no—
904C22⋊C4—3164no—
905C22⋊C4—3164no—
906C22⋊C4—3164no—
907C22⋊C4—3164no—
908C22⋊C4—3164no—
909C22⋊C4C22⋊Dic79116yescomplemented
910C42—3164no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23C2×C22⋊Dic7914yes—
980C23D4×Dic7914yes—
981C23C23×Dic7911yescharacteristic
982C23C2×D4×D7911yescharacteristic
983C23C22×C22⋊D7911yescharacteristic
984C23C22×C22⋊D7911yescharacteristic
985C23#41×D7911yescharacteristic
986C23#41×D7911yescharacteristic
987C23C2×#1192962311yescharacteristic
988C23#1457920611yescharacteristic
989C23#1457920611yescharacteristic
990C23#1457920711yescharacteristic
991C23#1457920711yescharacteristic
992C23#1457920711yescharacteristic
993C23#1457920811yescharacteristic
994C23#1457920811yescharacteristic
995C23#1457920811yescharacteristic
996D4—416no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—416no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—31616no—
1032C2×C4—3161no—
1033C2×C4—3161no—
1034C2×C4—3161no—
1035C2×C4—3161no—
1036C2×C4—3161no—
1037C2×C4—3161no—
1038C2×C4—3161no—
1039C2×C4—3161no—
1040C2×C4—3161no—
1041C2×C4—3161no—
1042C2×C4—3161no—
1043C2×C4—3161no—
1044C2×C4—3161no—
1045C2×C4—3161no—
1046C2×C4—3161no—
1047C2×C4—3161no—
1048C2×C4—3161no—
1049C2×C4—3161no—
1050C2×C4—3161no—
1051C2×C4—3161no—
1052C2×C4—3161no—
1053C2×C4—3161no—
1054C2×C4—3161no—
1055C2×C4—3161no—
1056C2×C4—3161no—
1057C2×C4—3161no—
1058C2×C4—3161no—
1059C2×C4—3161no—
1060C2×C4—3161no—
1061C2×C4—3161no—
1062C2×C4—3161no—
1063C2×C4—3161no—
1064C2×C4—3161no—
1065C2×C4—3161no—
1066C2×C4—3161no—
1067C2×C4—3161no—
1068C2×C4—3161no—
1069C2×C4—3161no—
1070C2×C4—3161no—
1071C2×C4—3161no—
1072C2×C4—3161no—
1073C2×C4—3161no—
1074C2×C4—3161no—
1075C2×C4—3161no—
1076C2×C4—1582no—
1077C2×C4—1582no—
1078C2×C4—1582no—
1079C2×C4—1582no—
1080C2×C4—1582no—
1081C2×C4—1582no—
1082C2×C4—1582no—
1083C2×C4—1582no—
1084C2×C4—1582no—
1085C2×C4—1582no—
1086C2×C4—1582no—
1087C2×C4—1582no—
1088C2×C4C2×C22⋊Dic7914yes—
1089C2×C4C2×C22⋊Dic7914yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C22×C22⋊Dic7911yescharacteristic
1121C22C2×D4×Dic7911yescharacteristic
1122C22#41×Dic7911yescharacteristic
1123C22#1909903811yescharacteristic
1124C22#1909904611yescharacteristic
1125C22#1909904611yescharacteristic
1126C22#1909904611yescharacteristic
1127C22#1909912411yescharacteristic
1128C22#1909912711yescharacteristic
1129C22#1909913411yescharacteristic
1130C22#1909913511yescharacteristic
1131C22#1909914111yescharacteristic
1132C22#1909914111yescharacteristic
1133C22#1909914911yescharacteristic
1134C22#1909915611yescharacteristic
1135C22#1909915711yescharacteristic
1136C22#1909915711yescharacteristic
1137C22#1909916511yescharacteristic
1138C22#1909918111yescharacteristic
1139C22D4×C22⋊D7911yescharacteristic
1140C22D4×C22⋊D7911yescharacteristic
1141C22#1909920111yescharacteristic
1142C22#1909920111yescharacteristic
1143C22#1909920511yescharacteristic
1144C22#1909920711yescharacteristic
1145C22#1909920711yescharacteristic
1146C22#1909921111yescharacteristic
1147C22#1909921211yescharacteristic
1148C22#1909921211yescharacteristic
1149C22#1909923611yescharacteristic
1150C22#1909925011yescharacteristic
1151C22#1909930311yescharacteristic
1152C22#1909931011yescharacteristic
1153C22#1909931011yescharacteristic
1154C22#1909931611yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—3162no—
1161C4—3162no—
1162C4—3162no—
1163C4—3162no—
1164C4—6321no—
1165C4—6321no—
1166C4—6321no—
1167C4—6321no—
1168C2—44no—
1169C2—44no—
1170C2#2376599211yescharacteristic
1171C2#2376607211yescharacteristic
1172C2#2376619411yescharacteristic
1173C2D4×C22⋊Dic7911yescharacteristic
1174C2#2376623011yescharacteristic
1175C2#2376639611yescharacteristic
1176C2#2376654811yescharacteristic
1177C2#2376963611yescharacteristic
1178C2#2376965111yescharacteristic
1179C2#2376971911yescharacteristic
1180C2#2376973711yescharacteristic
1181C2#2376981511yescharacteristic
1182C2#2376990511yescharacteristic
1183C2#2376993111yescharacteristic
1184C2#2377008411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D79
commutatorC23×C79C23×C4
FittingC22×#123×C79C2
socle, cosocleC24×C79C24
prime radicalC23×D4×C79C22
hypercenterC22×#123D79
hypocenterC79#14359
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C2×#19098456C2semidirect
3. C2×#19098438C2semidirect
4. C2×#19098423C2semidirect
5. #23761668C2semidirect
6. #23761653C2semidirect
7. #23761653C2semidirect
8. #23761649C2semidirect
9. #23761645C2semidirect
11. #23761637C2semidirect
12. #23761629C2semidirect
13. #23761623C2semidirect
14. #23761622C2semidirect
52. C2×#123×C79C4semidirect
137. C23×C4×C79C2×C4semidirect
148. C2×C4⋊C4×C79C2×C4semidirect
149. C2×C4⋊C4×C79C2×C4semidirect
156. C2×C22⋊C4×C79C2×C4semidirect
317. C22⋊C4×C79C22⋊C4semidirect
608. C79#14359semidirect
614. C2×#123Dic79semidirect
681. C23×C4C2×Dic79semidirect
701. C2×C4⋊C4C2×Dic79semidirect
702. C2×C4⋊C4C2×Dic79semidirect
730. C2×C22⋊C4C2×Dic79semidirect
909. C22⋊C4C22⋊Dic79semidirect

Maximal subgroups

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

subgroupindex
C2×#190984562
C2×#190984432
C2×#190984382
C2×#190984232
#237616682
#237616532
#237616492
#237616452
#237616412
#237616372
#237616292
#237616232
#237616222
C22×#123×C792
#1435979