Finite Group Databasebeta

← #34209685

Subgroups — #34209685

Order 20224.

2574 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D79C211yesmaximal, characteristic
2C2×#19098420C211yesmaximal, characteristic
3C2×C4⋊C4×Dic79C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Dic79C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D79)⋊C4C211yesmaximal, characteristic
6C2×#19098410C212yesmaximal
7#23761631C212yesmaximal, complemented
8#23761631C212yesmaximal, complemented
9#23761629C211yesmaximal, characteristic, complemented
10(C2×D79)⋊#95C212yesmaximal
11C79×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D79C2212yes—
13C23×C4×D79C2211yescharacteristic
14C22×C4⋊Dic79C2211yescharacteristic
15C22×C4⋊Dic79C2211yescharacteristic
16C22×Dic79⋊C4C2212yes—
17C2×C4⋊C4×D79—24no—
18C2×C4⋊C4×D79—24no—
19C2×C4⋊C4×D79C418yescomplemented
20C22×(C2×D79)⋊C4C2212yes—
21C22×(C2×D79)⋊C4C2211yescharacteristic
22C22×(C2×D79)⋊C4C2211yescharacteristic
23C22×C4×Dic79C2212yes—
24C22×C4×Dic79C2212yes—
25C22×C4×Dic79C2211yescharacteristic
26#19098420C418yescomplemented
27C4⋊C4×Dic79—24no—
28C4×C4⋊Dic79—24no—
29C4×(C2×D79)⋊C4C418yescomplemented
30#19098410—28no—
31C2×C79⋊#95C2212yes—
32C2×C79⋊#95C2212yes—
33C2×C79⋊#95C2212yes—
34C2×C79⋊#95C2212yes—
35C2×C79⋊#95C2212yes—
36C2×C79⋊#95C2211yescharacteristic
37C2×C79⋊#95C2211yescharacteristic
38C22×C4⋊C4×C79C2211yescharacteristic
39C22×C4⋊C4×C79C2211yescharacteristic
40C22×C42×C79C2211yescharacteristic
41C2×#95×C79C2212yes—
42C2×#95×C79C2212yes—
43C24×D79C2311yescharacteristic
44C23×Dic79C2311yescharacteristic
45C23×Dic79C2312yes—
46C23×Dic79C2311yescharacteristic
47C23×Dic79C2312yes—
48C23×Dic79C2311yescharacteristic
49C22×C4×D79—22no—
50C22×C4×D79—22no—
51C22×C4×D79—22no—
52C22×C4×D79—22no—
53C22×C4×D79—24no—
54C22×C4×D79—24no—
55C22×C4×D79—24no—
56C22×C4×D79—24no—
57C22×C4×D79—42no—
58C22×C4×D79—42no—
59C22×C4×D79C2×C418yes—
60C22×C4×D79C2×C414yes—
61C22×C4×D79C2×C414yes—
62C22×C4×D79C2×C414yes—
63C2×C4⋊Dic79—22no—
64C2×C4⋊Dic79—22no—
65C2×C4⋊Dic79C2×C414yes—
66C2×C4⋊Dic79C2×C414yescomplemented
67C2×C4⋊Dic79D414yes—
68C2×C4⋊Dic79D414yes—
69C2×Dic79⋊C4—24no—
70C2×Dic79⋊C4—24no—
71C2×Dic79⋊C4C2×C418yes—
72C4⋊C4×D79—232no—
73C2×(C2×D79)⋊C4—24no—
74C2×(C2×D79)⋊C4—22no—
75C2×(C2×D79)⋊C4—22no—
76C2×(C2×D79)⋊C4—24no—
77C2×(C2×D79)⋊C4C2×C414yes—
78C2×(C2×D79)⋊C4C2×C418yes—
79C2×(C2×D79)⋊C4C2×C414yes—
80C2×(C2×D79)⋊C4D414yes—
81C2×(C2×D79)⋊C4Q814yes—
82C2×C4×Dic79—22no—
83C2×C4×Dic79—22no—
84C2×C4×Dic79—24no—
85C2×C4×Dic79—24no—
86C2×C4×Dic79—24no—
87C2×C4×Dic79—24no—
88C2×C4×Dic79—42no—
89C2×C4×Dic79—42no—
90C2×C4×Dic79C2×C414yescomplemented
91C79⋊#95—24no—
92C79⋊#95—24no—
93C79⋊#95—24no—
94C79⋊#95—42no—
95C79⋊#95C2×C414yescomplemented
96C79⋊#95C2×C414yescomplemented
97C79⋊#95C2×C418yescomplemented
98C23×C4×C79C2311yescharacteristic
99C23×C4×C79C2312yes—
100C23×C4×C79C2312yes—
101C23×C4×C79C2311yescharacteristic
102C23×C4×C79C2311yescharacteristic
103C2×C4⋊C4×C79—22no—
104C2×C4⋊C4×C79—22no—
105C2×C4⋊C4×C79—22no—
106C2×C4⋊C4×C79—22no—
107C2×C4⋊C4×C79C2×C414yes—
108C2×C4⋊C4×C79C2×C414yescomplemented
109C2×C42×C79—22no—
110C2×C42×C79—22no—
111C2×C42×C79C2×C414yescomplemented
112#95×C79—24no—
113#95×C79—42no—
114C23×D79—21no—
115C23×D79—21no—
116C23×D79—21no—
117C23×D79—21no—
118C23×D79—21no—
119C23×D79—21no—
120C23×D79—21no—
121C23×D79—21no—
122C23×D79C22×C412yes—
123C23×D79C22×C412yes—
124C23×D79C22×C412yes—
125C23×D79C2×D412yes—
126C23×D79C2×Q812yes—
127C23×D79#4112yes—
128C23×D79#4112yes—
129C22×Dic79—21no—
130C22×Dic79—22no—
131C22×Dic79—21no—
132C22×Dic79—21no—
133C22×Dic79—21no—
134C22×Dic79—22no—
135C22×Dic79—22no—
136C22×Dic79—21no—
137C22×Dic79—22no—
138C22×Dic79—21no—
139C22×Dic79—21no—
140C22×Dic79—21no—
141C22×Dic79—21no—
142C22×Dic79—21no—
143C22×Dic79—22no—
144C22×Dic79—22no—
145C22×Dic79—21no—
146C22×Dic79—22no—
147C22×Dic79—22no—
148C22×Dic79—21no—
149C22×Dic79—22no—
150C22×Dic79—21no—
151C22×Dic79—21no—
152C22×Dic79—22no—
153C22×Dic79C22×C412yes—
154C22×Dic79C22×C414yes—
155C22×Dic79C22×C412yes—
156C22×Dic79C22×C412yes—
157C22×Dic79C22×C412yes—
158C22×Dic79C22×C414yes—
159C22×Dic79C22×C412yes—
160C22×Dic79C2×D414yes—
161C22×Dic79C2×D414yes—
162C22×Dic79C2×D412yes—
163C22×Dic79C2×Q812yes—
164C2×C4×D79—216no—
165C2×C4×D79—216no—
166C2×C4×D79—28no—
167C2×C4×D79—28no—
168C2×C4×D79—28no—
169C2×C4×D79—28no—
170C2×C4×D79—28no—
171C2×C4×D79—28no—
172C2×C4×D79—48no—
173C2×C4×D79—48no—
174C2×C4×D79—48no—
175C2×C4×D79—48no—
176C2×C4×D79—48no—
177C2×C4×D79C42116yescomplemented
178C4⋊Dic79—28no—
179C4⋊Dic79C22⋊C4116yescomplemented
180Dic79⋊C4—216no—
181(C2×D79)⋊C4—28no—
182(C2×D79)⋊C4—216no—
183(C2×D79)⋊C4C4⋊C4116yescomplemented
184C4×Dic79—28no—
185C4×Dic79—48no—
186C4×Dic79—48no—
187C24×C79C2411yescharacteristic
188C22×C4×C79—21no—
189C22×C4×C79—21no—
190C22×C4×C79—21no—
191C22×C4×C79—21no—
192C22×C4×C79—22no—
193C22×C4×C79—22no—
194C22×C4×C79—21no—
195C22×C4×C79—22no—
196C22×C4×C79—22no—
197C22×C4×C79—22no—
198C22×C4×C79—21no—
199C22×C4×C79—22no—
200C22×C4×C79—21no—
201C22×C4×C79—21no—
202C22×C4×C79—22no—
203C22×C4×C79—22no—
204C22×C4×C79—21no—
205C22×C4×C79—22no—
206C22×C4×C79—22no—
207C22×C4×C79—22no—
208C22×C4×C79—22no—
209C22×C4×C79—21no—
210C22×C4×C79C22×C412yes—
211C22×C4×C79C22×C414yes—
212C22×C4×C79C22×C414yes—
213C22×C4×C79C22×C412yes—
214C22×C4×C79C22×C412yes—
215C22×C4×C79C22×C412yes—
216C22×C4×C79C22×C412yes—
217C22×C4×C79C2×D412yes—
218C22×C4×C79C2×D412yes—
219C22×C4×C79C2×D412yes—
220C22×C4×C79C2×Q812yes—
221C22×C4×C79#4112yes—
222C22×C4×C79#4112yes—
223C4⋊C4×C79—28no—
224C4⋊C4×C79—28no—
225C42×C79—28no—
226C23×C79C23×C411yescharacteristic
227C23×C79C23×C411yescharacteristic
228C23×C79C23×C411yescharacteristic
229C23×C79C22×D411yescharacteristic
230C23×C79C22×D411yescharacteristic
231C23×C79C22×D411yescharacteristic
232C23×C79C22×Q811yescharacteristic
233C23×C79C2×#4111yescharacteristic
234C23×C79C2×#4111yescharacteristic
235C23×C79C2×#4111yescharacteristic
236C23×C79C2×#4111yescharacteristic
237C23×C79H(5,𝔽2)11yescharacteristic
238C23×C79H(5,𝔽2)11yescharacteristic
239C23×C792−1+411yescharacteristic
240C23×C792−1+411yescharacteristic
241C22×D79—22no—
242C22×D79—22no—
243C22×D79—22no—
244C22×D79—22no—
245C22×D79—22no—
246C22×D79—22no—
247C22×D79—22no—
248C22×D79—22no—
249C22×D79—22no—
250C22×D79—22no—
251C22×D79—22no—
252C22×D79—22no—
253C22×D79—22no—
254C22×D79—22no—
255C22×D79—22no—
256C22×D79—22no—
257C22×D79—22no—
258C22×D79—22no—
259C22×D79—22no—
260C22×D79—22no—
261C22×D79—22no—
262C22×D79—22no—
263C22×D79—22no—
264C22×D79—22no—
265C22×D79—22no—
266C22×D79—22no—
267C22×D79—22no—
268C22×D79—22no—
269C22×D79C2×C4214yes—
270C22×D79C2×C4⋊C414yes—
271C22×D79#11714yes—
272C22×D79C4×D414yes—
273C22×D79C4×D414yes—
274C22×D79C4×Q814yes—
275C22×D79C4×Q814yes—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—24no—
283C2×C4×C79—22no—
284C2×C4×C79—24no—
285C2×C4×C79—24no—
286C2×C4×C79—22no—
287C2×C4×C79—24no—
288C2×C4×C79—24no—
289C2×C4×C79—24no—
290C2×C4×C79—22no—
291C2×C4×C79—42no—
292C2×C4×C79—42no—
293C2×C4×C79—42no—
294C2×C4×C79—42no—
295C2×C4×C79—42no—
296C2×C4×C79—41no—
297C2×C4×C79—42no—
298C2×C4×C79—42no—
299C2×C4×C79—41no—
300C2×C4×C79—41no—
301C2×C4×C79—41no—
302C2×C4×C79—42no—
303C2×C4×C79C2×C4214yes—
304C2×C4×C79C2×C22⋊C414yes—
305C2×C4×C79C2×C4⋊C414yescomplemented
306C2×C4×C79#11714yes—
307C2×C4×C79C4×D414yes—
308C2×C4×C79C4×D414yes—
309C2×C4×C79C4×D414yes—
310C2×C4×C79C4×D414yes—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—24no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—24no—
320C2×Dic79—22no—
321C2×Dic79—22no—
322C2×Dic79—24no—
323C2×Dic79—24no—
324C2×Dic79—24no—
325C2×Dic79—24no—
326C2×Dic79—22no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—22no—
330C2×Dic79—22no—
331C2×Dic79—24no—
332C2×Dic79—24no—
333C2×Dic79—22no—
334C2×Dic79—24no—
335C2×Dic79—42no—
336C2×Dic79—41no—
337C2×Dic79—42no—
338C2×Dic79—41no—
339C2×Dic79—42no—
340C2×Dic79—41no—
341C2×Dic79—41no—
342C2×Dic79—42no—
343C2×Dic79C2×C4214yes—
344C2×Dic79C2×C22⋊C418yes—
345C2×Dic79C2×C4⋊C414yescomplemented
346C4×D79—232no—
347C4×D79—432no—
348C22×C79C22×C4211yescharacteristic
349C22×C79C22×C22⋊C411yescharacteristic
350C22×C79C22×C4⋊C411yescharacteristic
351C22×C79C2×#11711yescharacteristic
352C22×C79C2×#11711yescharacteristic
353C22×C79C2×C4×D411yescharacteristic
354C22×C79C2×C4×D411yescharacteristic
355C22×C79C2×C4×D411yescharacteristic
356C22×C79C2×C4×D411yescharacteristic
357C22×C79C2×C4×D411yescharacteristic
358C22×C79C2×C4×D411yescharacteristic
359C22×C79C2×C4×Q811yescharacteristic
360C22×C79C2×C4×Q811yescharacteristic
361C22×C79#51811yescharacteristic
362C22×C79#51911yescharacteristic
363C22×C79#52011yescharacteristic
364C22×C79#52011yescharacteristic
365C22×C79#52011yescharacteristic
366C22×C79#52011yescharacteristic
367C22×C79D4211yescharacteristic
368C22×C79D4211yescharacteristic
369C22×C79#54611yescharacteristic
370C22×C79#54611yescharacteristic
371C22×C79#54711yescharacteristic
372C22×C79#54711yescharacteristic
373C22×C79#54811yescharacteristic
374C22×C79#54811yescharacteristic
375C22×C79D4×Q811yescharacteristic
376C22×C79D4×Q811yescharacteristic
377C22×C79#55211yescharacteristic
378C22×C79#55211yescharacteristic
379C22×C79#55311yescharacteristic
380C22×C79#55311yescharacteristic
381C22×C79#55411yescharacteristic
382C22×C79#55411yescharacteristic
383C2×D79—24no—
384C2×D79—24no—
385C2×D79—24no—
386C2×D79—24no—
387C2×D79—24no—
388C2×D79—24no—
389C2×D79—24no—
390C2×D79—24no—
391C2×D79—24no—
392C2×D79—24no—
393C2×D79—24no—
394C2×D79—24no—
395C2×D79—24no—
396C2×D79—24no—
397C2×D79C4×C4⋊C418yescomplemented
398C4×C79—24no—
399C4×C79—44no—
400C4×C79—42no—
401C4×C79—44no—
402C4×C79C4×C22⋊C418yescomplemented
403Dic79—28no—
404Dic79—24no—
405Dic79—24no—
406Dic79—42no—
407Dic79—44no—
408C22⋊C4×C4⋊C4—791nomaximal, Sylow
409C2×C79C2×C4×C22⋊C411yescharacteristic
410C2×C79C2×C4×C4⋊C411yescharacteristic
411C2×C79#227411yescharacteristic
412C2×C79D4×C22⋊C411yescharacteristic
413C2×C79Q8×C22⋊C411yescharacteristic
414C2×C79#234411yescharacteristic
415C2×C79#234511yescharacteristic
416C2×C79D4×C4⋊C411yescharacteristic
417C2×C79D4×C4⋊C411yescharacteristic
418C2×C79#235211yescharacteristic
419C2×C79#235211yescharacteristic
420C2×C79#236011yescharacteristic
421C2×C79#236011yescharacteristic
422C2×C79#236111yescharacteristic
423C2×C79#236111yescharacteristic
424D79—28no—
425C23×C4⋊C4—791no—
426C2×#380—791no—
427C2×C4×C4⋊C4—791no—
428C2×C4×C4⋊C4—791no—
429C2×C4×C22⋊C4—791no—
430C2×C4×C22⋊C4—792no—
431#1436—792no—
432#1436—792no—
433C4⋊#95—791no—
434C4⋊#95D7911yescharacteristic, complemented
435C22⋊#95—792no—
436C79C22⋊C4×C4⋊C411yescharacteristic, complemented, Sylow
437C24×C4—792no—
438C24×C4—791no—
439C22×C4⋊C4—791no—
440C22×C4⋊C4—792no—
441C22×C4⋊C4—791no—
442C22×C4⋊C4—798no—
443C22×C4⋊C4—1584no—
444C22×C4⋊C4—1584no—
445C22×C4⋊C4C2×D7911yescharacteristic
446C22×C4⋊C4C2×D7911yescharacteristic
447C22×C22⋊C4—791no—
448C22×C22⋊C4—791no—
449C22×C22⋊C4—792no—
450C22×C42—792no—
451C22×C42—792no—
452C22×C42—791no—
453C22×C42C2×D7911yescharacteristic
454#380—798no—
455C4×C4⋊C4—1584no—
456C4×C4⋊C4—1584no—
457C4×C22⋊C4—798no—
458C4×C22⋊C4—1588no—
459C2×#95—792no—
460C2×#95—791no—
461C2×#95—791no—
462C2×#95—792no—
463C2×#95—792no—
464C2×#95—792no—
465C2×#95—792no—
466C2×#95C2×D7912yes—
467C2×#95C2×D7912yes—
468C25—791no—
469C23×C4—3162no—
470C23×C4—3162no—
471C23×C4—798no—
472C23×C4—791no—
473C23×C4—791no—
474C23×C4—792no—
475C23×C4—794no—
476C23×C4—794no—
477C23×C4—794no—
478C23×C4—792no—
479C23×C4—791no—
480C23×C4—1584no—
481C23×C4—1584no—
482C23×C4—1584no—
483C23×C4—1584no—
484C23×C4—1582no—
485C23×C4—1582no—
486C23×C4—1582no—
487C23×C4—1582no—
488C23×C4C22×D7912yes—
489C23×C4C22×D7911yescharacteristic
490C23×C4C22×D7912yes—
491C23×C4C22×D7911yescharacteristic
492C23×C4C22×D7911yescharacteristic
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—794no—
498C2×C4⋊C4—794no—
499C2×C4⋊C4—794no—
500C2×C4⋊C4—798no—
501C2×C4⋊C4—794no—
502C2×C4⋊C4—15832no—
503C2×C4⋊C4—1584no—
504C2×C4⋊C4—1584no—
505C2×C4⋊C4—1582no—
506C2×C4⋊C4—1582no—
507C2×C4⋊C4C4×D7914yes—
508C2×C4⋊C4C4×D7914yescomplemented
509C2×C22⋊C4—794no—
510C2×C22⋊C4—794no—
511C2×C22⋊C4—794no—
512C2×C22⋊C4—794no—
513C2×C22⋊C4—798no—
514C2×C22⋊C4—1584no—
515C2×C22⋊C4—1582no—
516C2×C22⋊C4—1584no—
517C2×C22⋊C4—1582no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—3162no—
521C2×C42—3162no—
522C2×C42—794no—
523C2×C42—1584no—
524C2×C42—1584no—
525C2×C42—1584no—
526C2×C42—1584no—
527C2×C42—1582no—
528C2×C42—1582no—
529C2×C42C4×D7914yescomplemented
530#95—24no—
531#95—42no—
532#95—3162no—
533#95—794no—
534#95—794no—
535#95—798no—
536#95—1584no—
537#95—1584no—
538#95—1584no—
539C24—792no—
540C24—792no—
541C24—792no—
542C24—792no—
543C24—792no—
544C24—792no—
545C24—792no—
546C24—1581no—
547C24—1581no—
548C24—1581no—
549C24—1581no—
550C24—1581no—
551C24—1581no—
552C24—1581no—
553C24—1581no—
554C24C23×D7911yescharacteristic
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—3168no—
578C22×C4—3168no—
579C22×C4—3168no—
580C22×C4—3168no—
581C22×C4—3168no—
582C22×C4—792no—
583C22×C4—792no—
584C22×C4—792no—
585C22×C4—792no—
586C22×C4—792no—
587C22×C4—794no—
588C22×C4—792no—
589C22×C4—794no—
590C22×C4—794no—
591C22×C4—7916no—
592C22×C4—792no—
593C22×C4—794no—
594C22×C4—15816no—
595C22×C4—15816no—
596C22×C4—1581no—
597C22×C4—1581no—
598C22×C4—1582no—
599C22×C4—1581no—
600C22×C4—1582no—
601C22×C4—1581no—
602C22×C4—1582no—
603C22×C4—1581no—
604C22×C4—1582no—
605C22×C4—1581no—
606C22×C4—1582no—
607C22×C4—1582no—
608C22×C4—1582no—
609C22×C4—1581no—
610C22×C4—1581no—
611C22×C4—1581no—
612C22×C4—1581no—
613C22×C4—1582no—
614C22×C4—1582no—
615C22×C4—1581no—
616C22×C4—1581no—
617C22×C4—1582no—
618C22×C4—1581no—
619C22×C4—1581no—
620C22×C4—1588no—
621C22×C4—1588no—
622C22×C4—1588no—
623C22×C4—1588no—
624C22×C4—1588no—
625C22×C4—1588no—
626C22×C4C2×C4×D7912yes—
627C22×C4C2×C4×D7914yes—
628C22×C4C2×C4×D7914yes—
629C22×C4C2×C4×D7912yes—
630C22×C4C2×C4×D7912yes—
631C22×C4C2×C4×D7912yes—
632C22×C4C2×C4×D7912yes—
633C22×C4D4×D7912yes—
634C22×C4D4×D7912yes—
635C22×C4D4×D7912yes—
636C22×C4Q8×D7912yes—
637C22×C4#1192962312yes—
638C22×C4#1192962512yes—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—7916no—
642C4⋊C4—15816no—
643C4⋊C4—1588no—
644C22⋊C4—7916no—
645C22⋊C4—1588no—
646C22⋊C4—15816no—
647C42—28no—
648C42—3168no—
649C42—3168no—
650C42—1588no—
651C23—794no—
652C23—794no—
653C23—794no—
654C23—794no—
655C23—794no—
656C23—794no—
657C23—794no—
658C23—1582no—
659C23—1582no—
660C23—1582no—
661C23—1582no—
662C23—1582no—
663C23—1582no—
664C23—1582no—
665C23—1582no—
666C23—1582no—
667C23—1582no—
668C23—1582no—
669C23—1582no—
670C23—1582no—
671C23—1582no—
672C23—1582no—
673C23—1582no—
674C23—1582no—
675C23—1582no—
676C23—1582no—
677C23—1582no—
678C23—1582no—
679C23—1582no—
680C23—1582no—
681C23—1582no—
682C23—1582no—
683C23—1582no—
684C23—1582no—
685C23—1582no—
686C23C22×C4×D7911yescharacteristic
687C23C22×C4×D7911yescharacteristic
688C23C22×C4×D7911yescharacteristic
689C23C2×D4×D7911yescharacteristic
690C23C2×D4×D7911yescharacteristic
691C23C2×D4×D7911yescharacteristic
692C23C2×Q8×D7911yescharacteristic
693C23#41×D7911yescharacteristic
694C23#41×D7911yescharacteristic
695C23C2×#1192962311yescharacteristic
696C23C2×#1192962511yescharacteristic
697C23#1457920611yescharacteristic
698C23#1457920711yescharacteristic
699C23#1457920811yescharacteristic
700C23#1457920911yescharacteristic
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—31632no—
729C2×C4—3162no—
730C2×C4—3161no—
731C2×C4—3162no—
732C2×C4—3161no—
733C2×C4—3162no—
734C2×C4—3161no—
735C2×C4—3161no—
736C2×C4—3162no—
737C2×C4—794no—
738C2×C4—798no—
739C2×C4—794no—
740C2×C4—1582no—
741C2×C4—1584no—
742C2×C4—1582no—
743C2×C4—1584no—
744C2×C4—1582no—
745C2×C4—1584no—
746C2×C4—1584no—
747C2×C4—1582no—
748C2×C4—1584no—
749C2×C4—1584no—
750C2×C4—1584no—
751C2×C4—1582no—
752C2×C4—1582no—
753C2×C4—1582no—
754C2×C4—1582no—
755C2×C4—1582no—
756C2×C4—1584no—
757C2×C4—1582no—
758C2×C4—1582no—
759C2×C4—1582no—
760C2×C4—1582no—
761C2×C4—1582no—
762C2×C4—1584no—
763C2×C4—1582no—
764C2×C4—15832no—
765C2×C4C42×D7914yes—
766C2×C4C22⋊C4×D7914yes—
767C2×C4C4⋊C4×D7914yescomplemented
768C2×C4#1457911914yes—
769C2×C4(C22⋊D79)⋊C414yes—
770C2×C4(C22⋊D79)⋊C414yes—
771C2×C4#1457912314yes—
772C2×C4#1457912314yes—
773C22—798no—
774C22—1584no—
775C22—1584no—
776C22—1584no—
777C22—1584no—
778C22—1584no—
779C22—1584no—
780C22—1584no—
781C22—1584no—
782C22—1584no—
783C22—1584no—
784C22—1584no—
785C22—1584no—
786C22—1584no—
787C22—1584no—
788C22C2×C42×D7911yescharacteristic
789C22C2×C22⋊C4×D7911yescharacteristic
790C22C2×C4⋊C4×D7911yescharacteristic
791C22#117×D7911yescharacteristic
792C22C2×#1457911911yescharacteristic
793C22C4×D4×D7911yescharacteristic
794C22C4×D4×D7911yescharacteristic
795C22C2×(C22⋊D79)⋊C411yescharacteristic
796C22C2×(C22⋊D79)⋊C411yescharacteristic
797C22C2×#1457912311yescharacteristic
798C22C2×#1457912311yescharacteristic
799C22C4×Q8×D7911yescharacteristic
800C22C4×Q8×D7911yescharacteristic
801C22#1909903511yescharacteristic
802C22#1909903911yescharacteristic
803C22#1909904211yescharacteristic
804C22#1909904311yescharacteristic
805C22#1909904411yescharacteristic
806C22#1909904511yescharacteristic
807C22#1909919711yescharacteristic
808C22#1909919811yescharacteristic
809C22#1909920611yescharacteristic
810C22#1909921011yescharacteristic
811C22#1909921311yescharacteristic
812C22#1909921611yescharacteristic
813C22#1909922111yescharacteristic
814C22#1909922311yescharacteristic
815C22#1909922611yescharacteristic
816C22#1909922811yescharacteristic
817C22#1909924711yescharacteristic
818C22#1909925111yescharacteristic
819C22#1909926011yescharacteristic
820C22#1909926611yescharacteristic
821C22#1909927111yescharacteristic
822C22#1909927411yescharacteristic
823C4—24no—
824C4—42no—
825C4—44no—
826C4—44no—
827C4—3162no—
828C4—3164no—
829C4—1584no—
830C4—1588no—
831C4—1584no—
832C4#1909841018yescomplemented
833C2—1588no—
834C2C2×#1909841011yescharacteristic
835C2C4×C4⋊C4×D7911yescharacteristic
836C2#2376575411yescharacteristic
837C2#2376622111yescharacteristic
838C2#2376623411yescharacteristic
839C2#2376626811yescharacteristic
840C2#2376627611yescharacteristic
841C2#2376629611yescharacteristic
842C2#2376630011yescharacteristic
843C2#2376632211yescharacteristic
844C2#2376632611yescharacteristic
845C2#2376640411yescharacteristic
846C2#2376641011yescharacteristic
847C2#2376641511yescharacteristic
848C2#2376642111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D79
commutatorC22×C79C22×C42
FittingC79×C4⋊#95C2
socle, cosocleC24×C79C24
prime radicalC24×D79C23
hypercenterC4⋊#95D79
hypocenterC79C22⋊C4×C4⋊C4
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic79C2semidirect
4. C2×C4×C4⋊Dic79C2semidirect
7. #23761631C2semidirect
8. #23761631C2semidirect
9. #23761629C2semidirect
11. C79×C4⋊#95C2semidirect
19. C2×C4⋊C4×D79C4semidirect
26. #19098420C4semidirect
29. C4×(C2×D79)⋊C4C4semidirect
66. C2×C4⋊Dic79C2×C4semidirect
90. C2×C4×Dic79C2×C4semidirect
95. C79⋊#95C2×C4semidirect
96. C79⋊#95C2×C4semidirect
97. C79⋊#95C2×C4semidirect
108. C2×C4⋊C4×C79C2×C4semidirect
111. C2×C42×C79C2×C4semidirect
177. C2×C4×D79C42semidirect
179. C4⋊Dic79C22⋊C4semidirect
183. (C2×D79)⋊C4C4⋊C4semidirect
305. C2×C4×C79C2×C4⋊C4semidirect
345. C2×Dic79C2×C4⋊C4semidirect
397. C2×D79C4×C4⋊C4semidirect
402. C4×C79C4×C22⋊C4semidirect
434. C4⋊#95D79semidirect
436. C79C22⋊C4×C4⋊C4semidirect
508. C2×C4⋊C4C4×D79semidirect
529. C2×C42C4×D79semidirect
767. C2×C4C4⋊C4×D79semidirect
832. C4#19098410semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D792
C2×#190984202
C2×C4⋊C4×Dic792
C2×C4×C4⋊Dic792
C2×C4×(C2×D79)⋊C42
C2×#190984102
#237616312
#237616292
(C2×D79)⋊#952
C79×C4⋊#952
C22⋊C4×C4⋊C479