Finite Group Databasebeta

← C2×#23766067 #34446995

Subgroups — C2×#23766067 #34446995

Order 20224.

3718 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579143C211yesmaximal, characteristic
2C22×C4×C22⋊D79C211yesmaximal, characteristic
3C22×C4⋊C4×D79C211yesmaximal, characteristic, complemented
4#23766067C2116yesmaximal, direct product factor
5C2×#19098460C211yesmaximal, characteristic, complemented
6C2×#19098459C211yesmaximal, characteristic, complemented
7C2×#19098456C211yesmaximal, characteristic, complemented
8C2×#19098451C211yesmaximal, characteristic, complemented
9C2×#19098448C211yesmaximal, characteristic, complemented
10C2×#19098444C211yesmaximal, characteristic, complemented
11C2×#19098439C211yesmaximal, characteristic
12C2×#19098436C211yesmaximal, characteristic, complemented
13C2×#19098434C211yesmaximal, characteristic, complemented
14C2×#19098425C211yesmaximal, characteristic, complemented
15C2×#19098410C211yesmaximal, characteristic, complemented
16C2×#385×C79C211yesmaximal, characteristic, complemented
17C23×C22⋊D79C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20C23×C4×D79C2211yescharacteristic
21C2×#14579143C4116yescomplemented
22C2×#14579143C2218yes—
23C2×C4×C22⋊D79—28no—
24C2×C4×C22⋊D79C2218yes—
25C22×C4⋊Dic79C2211yescharacteristic
26C22×C4⋊Dic79C2211yescharacteristic
27C22×Dic79⋊C4C2211yescharacteristic
28C22×Dic79⋊C4C2211yescharacteristic
29C22×Dic79⋊C4C2211yescharacteristic
30C22×Dic79⋊C4C2211yescharacteristic
31C22×Dic79⋊C4C2211yescharacteristic
32C2×C4⋊C4×D79—28no—
33C2×C4⋊C4×D79C2218yescomplemented
34C22×C22⋊Dic79C2211yescharacteristic
35C22×C22⋊Dic79C2211yescharacteristic
36C22×C22⋊Dic79C2211yescharacteristic
37C22×(C2×D79)⋊C4C2211yescharacteristic
38C22×(C2×D79)⋊C4C2211yescharacteristic
39C22×(C2×D79)⋊C4C2211yescharacteristic
40C22×C4×Dic79C2211yescharacteristic
41C22×C4×Dic79C2211yescharacteristic
42C22×C4×Dic79C2211yescharacteristic
43#19098460C2218yescomplemented
44#19098459C2218yescomplemented
45#19098456C2218yescomplemented
46#19098451C2218yescomplemented
47#19098448C2218yescomplemented
48#19098444C2218yescomplemented
49#19098439C2218yes—
50#19098436C2218yescomplemented
51#19098434C2218yescomplemented
52#19098425C2218yescomplemented
53#19098410C2218yescomplemented
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C2×C79⋊#95C2211yescharacteristic
60C2×C79⋊#95C2211yescharacteristic
61C2×C79⋊#95C2211yescharacteristic
62C24×C4×C79C2211yescharacteristic
63C22×C4⋊C4×C79C2211yescharacteristic
64C22×C4⋊C4×C79C2211yescharacteristic
65C22×C22⋊C4×C79C2211yescharacteristic
66C22×C22⋊C4×C79C2211yescharacteristic
67#385×C79C2218yescomplemented
68C2×#95×C79C2211yescharacteristic
69C2×#95×C79C2211yescharacteristic
70C24×D79C2311yescharacteristic
71C22×C22⋊D79—24no—
72C22×C22⋊D79—24no—
73C22×C22⋊D79C2×C418yes—
74C22×C22⋊D79C2314yes—
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C23×Dic79C2311yescharacteristic
80C23×Dic79C2311yescharacteristic
81C23×Dic79C2311yescharacteristic
82C22×C4×D79—24no—
83C22×C4×D79—24no—
84C22×C4×D79—24no—
85C22×C4×D79—42no—
86C22×C4×D79—42no—
87C22×C4×D79—42no—
88C22×C4×D79—42no—
89C22×C4×D79C2×C418yescomplemented
90C22×C4×D79D418yes—
91C22×C4×D79C2314yes—
92C22×C4×D79C2314yes—
93C22×C4×D79C2314yes—
94#14579143C2×C4164yescomplemented
95C4×C22⋊D79—232no—
96C2×C4⋊Dic79—24no—
97C2×C4⋊Dic79C2×C418yescomplemented
98C2×C4⋊Dic79C2314yes—
99C2×C4⋊Dic79C2314yes—
100C2×Dic79⋊C4—24no—
101C2×Dic79⋊C4—24no—
102C2×Dic79⋊C4—24no—
103C2×Dic79⋊C4—42no—
104C2×Dic79⋊C4C2×C418yescomplemented
105C2×Dic79⋊C4C2314yes—
106C2×Dic79⋊C4C2314yes—
107C2×Dic79⋊C4C2314yes—
108C2×Dic79⋊C4C2314yes—
109C2×Dic79⋊C4C2314yes—
110C4⋊C4×D79—232no—
111C2×C22⋊Dic79—24no—
112C2×C22⋊Dic79—42no—
113C2×C22⋊Dic79C2×C418yescomplemented
114C2×C22⋊Dic79C2314yes—
115C2×C22⋊Dic79C2314yes—
116C2×C22⋊Dic79C2314yes—
117C2×(C2×D79)⋊C4—24no—
118C2×(C2×D79)⋊C4—24no—
119C2×(C2×D79)⋊C4C2×C418yescomplemented
120C2×(C2×D79)⋊C4C2314yes—
121C2×(C2×D79)⋊C4C2314yes—
122C2×(C2×D79)⋊C4C2314yes—
123C2×C4×Dic79—24no—
124C2×C4×Dic79—42no—
125C2×C4×Dic79—42no—
126C2×C4×Dic79C2314yes—
127C2×C4×Dic79C2314yes—
128C2×C4×Dic79C2314yes—
129C79⋊#95C2314yes—
130C79⋊#95C2314yes—
131C79⋊#95C2314yes—
132C79⋊#95C2314yes—
133C79⋊#95C2314yes—
134C79⋊#95C2314yes—
135C79⋊#95C2314yes—
136C79⋊#95C2314yes—
137C25×C79C2311yescharacteristic
138C23×C4×C79—24no—
139C23×C4×C79—42no—
140C23×C4×C79—42no—
141C23×C4×C79C2311yescharacteristic
142C23×C4×C79C2311yescharacteristic
143C23×C4×C79C2311yescharacteristic
144C23×C4×C79C2311yescharacteristic
145C23×C4×C79C2311yescharacteristic
146C23×C4×C79C2311yescharacteristic
147C23×C4×C79C2314yes—
148C2×C4⋊C4×C79—24no—
149C2×C4⋊C4×C79—42no—
150C2×C4⋊C4×C79C2314yes—
151C2×C4⋊C4×C79C2314yes—
152C2×C22⋊C4×C79—42no—
153C2×C22⋊C4×C79C2×C418yescomplemented
154C2×C22⋊C4×C79C2314yes—
155C2×C22⋊C4×C79C2314yes—
156#95×C79C2314yes—
157#95×C79C2314yes—
158C23×D79—22no—
159C23×D79—22no—
160C23×D79—22no—
161C23×D79—22no—
162C23×D79C22×C414yes—
163C23×D79C2×D414yes—
164C23×D79#4114yes—
165C23×D79C2412yes—
166C2×C22⋊D79—232no—
167C2×C22⋊D79—28no—
168C2×C22⋊D79—28no—
169C2×C22⋊D79C22×C4116yes—
170C22×Dic79—22no—
171C22×Dic79—22no—
172C22×Dic79—22no—
173C22×Dic79—22no—
174C22×Dic79—22no—
175C22×Dic79—22no—
176C22×Dic79—22no—
177C22×Dic79—22no—
178C22×Dic79—22no—
179C22×Dic79—22no—
180C22×Dic79—22no—
181C22×Dic79—22no—
182C22×Dic79—22no—
183C22×Dic79—22no—
184C22×Dic79—22no—
185C22×Dic79—22no—
186C22×Dic79—22no—
187C22×Dic79C22×C414yes—
188C22×Dic79C22×C414yes—
189C22×Dic79C22×C414yes—
190C22×Dic79C2×D414yes—
191C22×Dic79C2412yes—
192C22×Dic79C2412yes—
193C22×Dic79C2412yes—
194C22×Dic79C2412yes—
195C22×Dic79C2412yes—
196C22×Dic79C2412yes—
197C22×Dic79C2412yes—
198C2×C4×D79—232no—
199C2×C4×D79—28no—
200C2×C4×D79—28no—
201C2×C4×D79—28no—
202C2×C4×D79—416no—
203C2×C4×D79—44no—
204C2×C4×D79—44no—
205C2×C4×D79—44no—
206C2×C4×D79—44no—
207C2×C4×D79—416no—
208C2×C4×D79C22×C4116yescomplemented
209C2×C4×D79C2×D4116yes—
210C4⋊Dic79—28no—
211C4⋊Dic79C22×C4116yescomplemented
212Dic79⋊C4—28no—
213Dic79⋊C4—28no—
214Dic79⋊C4—28no—
215Dic79⋊C4—44no—
216Dic79⋊C4C22×C4116yescomplemented
217C22⋊Dic79—28no—
218C22⋊Dic79—44no—
219C22⋊Dic79C22×C4116yescomplemented
220(C2×D79)⋊C4—28no—
221(C2×D79)⋊C4—28no—
222(C2×D79)⋊C4C22×C4116yescomplemented
223C4×Dic79—28no—
224C4×Dic79—44no—
225C4×Dic79—44no—
226C24×C79—22no—
227C24×C79—22no—
228C24×C79—22no—
229C24×C79—22no—
230C24×C79—22no—
231C24×C79—22no—
232C24×C79C22×C414yes—
233C24×C79C2412yes—
234C24×C79C2411yescharacteristic
235C22×C4×C79—22no—
236C22×C4×C79—22no—
237C22×C4×C79—22no—
238C22×C4×C79—22no—
239C22×C4×C79—22no—
240C22×C4×C79—22no—
241C22×C4×C79—22no—
242C22×C4×C79—22no—
243C22×C4×C79—22no—
244C22×C4×C79—22no—
245C22×C4×C79—22no—
246C22×C4×C79—22no—
247C22×C4×C79—22no—
248C22×C4×C79—22no—
249C22×C4×C79—22no—
250C22×C4×C79—28no—
251C22×C4×C79—44no—
252C22×C4×C79—44no—
253C22×C4×C79—416no—
254C22×C4×C79C22×C414yes—
255C22×C4×C79C22×C414yes—
256C22×C4×C79C2×D414yes—
257C22×C4×C79C2412yes—
258C22×C4×C79C2412yes—
259C22×C4×C79C2412yes—
260C22×C4×C79C2412yes—
261C22×C4×C79C2412yes—
262C22×C4×C79C2412yes—
263C4⋊C4×C79—28no—
264C4⋊C4×C79—44no—
265C22⋊C4×C79—44no—
266C22⋊C4×C79C22×C4116yescomplemented
267C23×C79—28no—
268C23×C79—28no—
269C23×C79—28no—
270C23×C79—22no—
271C23×C79—22no—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—22no—
276C23×C79—44no—
277C23×C79—44no—
278C23×C79—44no—
279C23×C79—44no—
280C23×C79C23×C414yes—
281C23×C79C23×C412yes—
282C23×C79C22×D412yes—
283C23×C79C2×#4112yes—
284C23×C79H(5,𝔽2)12yes—
285C23×C79H(5,𝔽2)12yes—
286C23×C792−1+412yes—
287C23×C792−1+412yes—
288C23×C79C2511yescharacteristic
289C22×D79—28no—
290C22×D79—28no—
291C22×D79—28no—
292C22×D79—28no—
293C22×D79—28no—
294C22×D79—28no—
295C22×D79—22no—
296C22×D79—22no—
297C22×D79—22no—
298C22×D79—22no—
299C22×D79C4×D4116yes—
300C22×D79C23×C414yes—
301C22×D79C22×D414yes—
302C22×D79C2×#4114yes—
303C2×C4×C79—28no—
304C2×C4×C79—28no—
305C2×C4×C79—28no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—22no—
313C2×C4×C79—22no—
314C2×C4×C79—22no—
315C2×C4×C79—22no—
316C2×C4×C79—22no—
317C2×C4×C79—22no—
318C2×C4×C79—22no—
319C2×C4×C79—22no—
320C2×C4×C79—22no—
321C2×C4×C79—416no—
322C2×C4×C79—44no—
323C2×C4×C79—44no—
324C2×C4×C79—44no—
325C2×C4×C79C23×C414yes—
326C2×C4×C79C23×C414yes—
327C2×C4×C79C22×D414yes—
328C22⋊D79—232no—
329C2×Dic79—28no—
330C2×Dic79—28no—
331C2×Dic79—28no—
332C2×Dic79—28no—
333C2×Dic79—22no—
334C2×Dic79—22no—
335C2×Dic79—22no—
336C2×Dic79—22no—
337C2×Dic79—22no—
338C2×Dic79—22no—
339C2×Dic79—22no—
340C2×Dic79—22no—
341C2×Dic79—22no—
342C2×Dic79—22no—
343C2×Dic79—22no—
344C2×Dic79—22no—
345C2×Dic79—22no—
346C2×Dic79—22no—
347C2×Dic79—22no—
348C2×Dic79—22no—
349C2×Dic79—22no—
350C2×Dic79—44no—
351C2×Dic79—44no—
352C2×Dic79—44no—
353C2×Dic79C23×C414yes—
354C2×Dic79C23×C414yes—
355C2×Dic79C23×C414yes—
356C2×Dic79C22×D414yes—
357C4×D79—232no—
358C4×D79—416no—
359C4×D79—416no—
360C22×C79—24no—
361C22×C79—24no—
362C22×C79—24no—
363C22×C79—416no—
364C22×C79—42no—
365C22×C79—42no—
366C22×C79—42no—
367C22×C79—42no—
368C22×C79C2×C4×D414yes—
369C22×C79#52014yes—
370C22×C79#52014yes—
371C22×C79#53414yes—
372C22×C79#53614yes—
373C22×C79#53914yes—
374C22×C79#53914yes—
375C22×C79C24×C411yescharacteristic
376C22×C79C23×D411yescharacteristic
377C22×C79C22×#4111yescharacteristic
378C22×C79C2×H(5,𝔽2)11yescharacteristic
379C22×C79C2×H(5,𝔽2)11yescharacteristic
380C22×C79C2×2−1+411yescharacteristic
381C22×C79C2×2−1+411yescharacteristic
382C2×D79—232no—
383C2×D79—24no—
384C2×D79—24no—
385C2×D79—24no—
386C2×D79—24no—
387C2×D79—24no—
388C2×D79—24no—
389C2×D79C2×C4×D418yes—
390C4×C79—24no—
391C4×C79—24no—
392C4×C79—24no—
393C4×C79—42no—
394C4×C79—42no—
395C4×C79—42no—
396Dic79—24no—
397Dic79—24no—
398Dic79—24no—
399Dic79—24no—
400Dic79—42no—
401Dic79—42no—
402Dic79—42no—
403C2×#2322—791nomaximal, Sylow
404C2×C79—44no—
405C2×C79#232218yescomplemented
406C2×C79C22×C4×D411yescharacteristic
407C2×C79C2×#52011yescharacteristic
408C2×C79C2×#52011yescharacteristic
409C2×C79C2×#53411yescharacteristic
410C2×C79C2×#53611yescharacteristic
411C2×C79C2×#53911yescharacteristic
412C2×C79C2×#53911yescharacteristic
413D79—28no—
414C22×#123—791no—
415C22×C4×D4—791no—
416C23×C4⋊C4—791no—
417#2322—7916no—
418C2×#389—791no—
419C2×#389—791no—
420C2×#388—791no—
421C2×#388—791no—
422C2×#387—791no—
423C2×#387—791no—
424C2×#386—791no—
425C2×#385—791no—
426C2×#385—791no—
427C2×#385D7911yescharacteristic, complemented
428C2×#381—791no—
429C2×C4×C22⋊C4—791no—
430C79C2×#232211yescharacteristic, complemented, Sylow
431C23×D4—791no—
432C24×C4—791no—
433C24×C4—791no—
434C24×C4—791no—
435C24×C4C2×D7911yescharacteristic
436C2×#123—798no—
437C2×#123—7916no—
438C2×C4×D4—798no—
439C2×C4×D4—1588no—
440C22×C4⋊C4—791no—
441C22×C4⋊C4—791no—
442C22×C4⋊C4—791no—
443C22×C4⋊C4—791no—
444C22×C4⋊C4—791no—
445C22×C4⋊C4—791no—
446C22×C4⋊C4—791no—
447C22×C4⋊C4—798no—
448C22×C4⋊C4—1588no—
449C22×C4⋊C4C2×D7911yescharacteristic
450C22×C4⋊C4C2×D7911yescharacteristic
451C22×C22⋊C4—791no—
452C22×C22⋊C4—791no—
453C22×C22⋊C4—791no—
454C22×C22⋊C4—791no—
455C22×C22⋊C4—791no—
456C22×C22⋊C4—791no—
457C22×C22⋊C4C2×D7911yescharacteristic
458C22×C22⋊C4C2×D7911yescharacteristic
459C22×C42—791no—
460C22×C42—791no—
461C22×C42—791no—
462#389—798no—
463#389—798no—
464#388—798no—
465#388—798no—
466#387—798no—
467#387—798no—
468#386—798no—
469#385—798no—
470#385—798no—
471#385C2×D7918yescomplemented
472#381—798no—
473C4×C22⋊C4—798no—
474C2×#95—791no—
475C2×#95—791no—
476C2×#95—791no—
477C2×#95—791no—
478C2×#95—791no—
479C2×#95—791no—
480C2×#95—791no—
481C2×#95—791no—
482C2×#95C2×D7911yescharacteristic
483C2×#95C2×D7911yescharacteristic
484C25—791no—
485C25C22×D7911yescharacteristic
486C22×D4—798no—
487C22×D4—794no—
488C22×D4—1584no—
489C22×D4—1584no—
490C23×C4—24no—
491C23×C4—42no—
492C23×C4—42no—
493C23×C4—3162no—
494C23×C4—3162no—
495C23×C4—3162no—
496C23×C4—3162no—
497C23×C4—798no—
498C23×C4—794no—
499C23×C4—794no—
500C23×C4—791no—
501C23×C4—791no—
502C23×C4—791no—
503C23×C4—791no—
504C23×C4—798no—
505C23×C4—794no—
506C23×C4—791no—
507C23×C4—791no—
508C23×C4—791no—
509C23×C4—1584no—
510C23×C4—1584no—
511C23×C4—1584no—
512C23×C4C22×D7911yescharacteristic
513C23×C4C22×D7911yescharacteristic
514C23×C4C22×D7911yescharacteristic
515C23×C4C22×D7911yescharacteristic
516C23×C4C22×D7911yescharacteristic
517C23×C4C22×D7911yescharacteristic
518C23×C4C22×D7914yes—
519#123—7964no—
520C4×D4—15832no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—42no—
523C2×C4⋊C4—3162no—
524C2×C4⋊C4—794no—
525C2×C4⋊C4—798no—
526C2×C4⋊C4—798no—
527C2×C4⋊C4—794no—
528C2×C4⋊C4—794no—
529C2×C4⋊C4—794no—
530C2×C4⋊C4—794no—
531C2×C4⋊C4—794no—
532C2×C4⋊C4—794no—
533C2×C4⋊C4—15832no—
534C2×C4⋊C4—1584no—
535C2×C4⋊C4—1584no—
536C2×C4⋊C4—1584no—
537C2×C4⋊C4—1584no—
538C2×C4⋊C4C22×D7914yes—
539C2×C4⋊C4C22×D7914yes—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—3162no—
542C2×C22⋊C4—794no—
543C2×C22⋊C4—798no—
544C2×C22⋊C4—794no—
545C2×C22⋊C4—798no—
546C2×C22⋊C4—794no—
547C2×C22⋊C4—794no—
548C2×C22⋊C4—794no—
549C2×C22⋊C4—794no—
550C2×C22⋊C4—1584no—
551C2×C22⋊C4—1584no—
552C2×C22⋊C4—1584no—
553C2×C22⋊C4C4×D7918yescomplemented
554C2×C22⋊C4C22×D7914yes—
555C2×C22⋊C4C22×D7914yes—
556C2×C42—3162no—
557C2×C42—3162no—
558C2×C42—794no—
559C2×C42—794no—
560C2×C42—794no—
561C2×C42—1584no—
562#95—794no—
563#95—794no—
564#95—794no—
565#95—794no—
566#95—794no—
567#95—794no—
568#95—794no—
569#95—794no—
570#95C22×D7914yes—
571#95C22×D7914yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—794no—
579C24—792no—
580C24—794no—
581C24—794no—
582C24—1582no—
583C24—1582no—
584C24—1582no—
585C24—1582no—
586C24C2×C4×D7914yes—
587C24C23×D7912yes—
588C24C23×D7911yescharacteristic
589C2×D4—7916no—
590C2×D4—1588no—
591C2×D4—15832no—
592C2×D4—1588no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—416no—
612C22×C4—3164no—
613C22×C4—3164no—
614C22×C4—31616no—
615C22×C4—3164no—
616C22×C4—3164no—
617C22×C4—31616no—
618C22×C4—7916no—
619C22×C4—792no—
620C22×C4—792no—
621C22×C4—792no—
622C22×C4—792no—
623C22×C4—794no—
624C22×C4—794no—
625C22×C4—794no—
626C22×C4—794no—
627C22×C4—7916no—
628C22×C4—792no—
629C22×C4—792no—
630C22×C4—792no—
631C22×C4—1588no—
632C22×C4—1588no—
633C22×C4—15832no—
634C22×C4—1588no—
635C22×C4—1582no—
636C22×C4—1582no—
637C22×C4—1582no—
638C22×C4—1582no—
639C22×C4—1582no—
640C22×C4—1582no—
641C22×C4—1582no—
642C22×C4—1582no—
643C22×C4—1582no—
644C22×C4—1582no—
645C22×C4—1582no—
646C22×C4—1582no—
647C22×C4—1582no—
648C22×C4—1582no—
649C22×C4—1582no—
650C22×C4—1582no—
651C22×C4—1582no—
652C22×C4C2×C4×D7914yes—
653C22×C4C2×C4×D7914yes—
654C22×C4D4×D7914yes—
655C22×C4C23×D7912yes—
656C22×C4C23×D7912yes—
657C22×C4C23×D7912yes—
658C22×C4C23×D7912yes—
659C22×C4C23×D7912yes—
660C22×C4C23×D7912yes—
661C4⋊C4—28no—
662C4⋊C4—44no—
663C4⋊C4—3164no—
664C4⋊C4—7916no—
665C4⋊C4—7916no—
666C4⋊C4—1588no—
667C4⋊C4—1588no—
668C4⋊C4—1588no—
669C4⋊C4—1588no—
670C22⋊C4—44no—
671C22⋊C4—3164no—
672C22⋊C4—7916no—
673C22⋊C4—7916no—
674C22⋊C4—1588no—
675C22⋊C4—1588no—
676C22⋊C4—1588no—
677C22⋊C4C2×C4×D79116yescomplemented
678C42—3164no—
679C42—3164no—
680C42—1588no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—28no—
686C23—28no—
687C23—28no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—7916no—
695C23—794no—
696C23—794no—
697C23—794no—
698C23—1588no—
699C23—1582no—
700C23—1582no—
701C23—1582no—
702C23—1582no—
703C23—1588no—
704C23—1588no—
705C23—1588no—
706C23—1588no—
707C23—1588no—
708C23C22×C4×D7914yes—
709C23C22×C4×D7912yes—
710C23C2×D4×D7912yes—
711C23#41×D7912yes—
712C23#1457920612yes—
713C23#1457920612yes—
714C23#1457920812yes—
715C23#1457920912yes—
716C23C24×D7911yescharacteristic
717D4—15832no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—28no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—31616no—
741C2×C4—31616no—
742C2×C4—3164no—
743C2×C4—3164no—
744C2×C4—3164no—
745C2×C4—794no—
746C2×C4—794no—
747C2×C4—794no—
748C2×C4—794no—
749C2×C4—15832no—
750C2×C4—1582no—
751C2×C4—1582no—
752C2×C4—1582no—
753C2×C4—1582no—
754C2×C4—1582no—
755C2×C4—1582no—
756C2×C4—1582no—
757C2×C4—1582no—
758C2×C4—1582no—
759C2×C4—1582no—
760C2×C4—1582no—
761C2×C4—1582no—
762C2×C4—1582no—
763C2×C4—1588no—
764C2×C4—1588no—
765C2×C4—1588no—
766C2×C4—1588no—
767C2×C4—1582no—
768C2×C4—1582no—
769C2×C4—1582no—
770C2×C4—1582no—
771C2×C4C22×C4×D7914yes—
772C2×C4C22×C4×D7914yes—
773C2×C4C2×D4×D7914yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—798no—
783C22—15832no—
784C22—1584no—
785C22—1584no—
786C22—1584no—
787C22—1584no—
788C22—1584no—
789C22—1584no—
790C22C4×D4×D7914yes—
791C22#1909904214yes—
792C22#1909904414yes—
793C22#1909912314yes—
794C22#1909913614yes—
795C22#1909915614yes—
796C22#1909915914yes—
797C22C23×C4×D7911yescharacteristic
798C22C22×D4×D7911yescharacteristic
799C22C2×#41×D7911yescharacteristic
800C22C2×#1457920611yescharacteristic
801C22C2×#1457920611yescharacteristic
802C22C2×#1457920811yescharacteristic
803C22C2×#1457920911yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—3162no—
811C4—3162no—
812C4—3162no—
813C4—1584no—
814C4—1584no—
815C4—1584no—
816C4—1584no—
817C2—44no—
818C2—1588no—
819C2#2376606718yesdirect product factor
820C2C2×C4×D4×D7911yescharacteristic
821C2C2×#1909904211yescharacteristic
822C2C2×#1909904411yescharacteristic
823C2C2×#1909912311yescharacteristic
824C2C2×#1909913611yescharacteristic
825C2C2×#1909915611yescharacteristic
826C2C2×#1909915911yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×#385×C79C2
socleC24×C79C24
prime radicalC23×C22⋊D79C22
cosocleC23×C79C25
hypercenterC2×#385D79
hypocenterC79C2×#2322
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D79C2semidirect
4. #23766067C2direct (N × H)
5. C2×#19098460C2semidirect
6. C2×#19098459C2semidirect
7. C2×#19098456C2semidirect
8. C2×#19098451C2semidirect
9. C2×#19098448C2semidirect
10. C2×#19098444C2semidirect
12. C2×#19098436C2semidirect
13. C2×#19098434C2semidirect
14. C2×#19098425C2semidirect
15. C2×#19098410C2semidirect
16. C2×#385×C79C2semidirect
21. C2×#14579143C4semidirect
33. C2×C4⋊C4×D79C22semidirect
43. #19098460C22semidirect
44. #19098459C22semidirect
45. #19098456C22semidirect
46. #19098451C22semidirect
47. #19098448C22semidirect
48. #19098444C22semidirect
50. #19098436C22semidirect
51. #19098434C22semidirect
52. #19098425C22semidirect
53. #19098410C22semidirect
67. #385×C79C22semidirect
89. C22×C4×D79C2×C4semidirect
94. #14579143C2×C4semidirect
97. C2×C4⋊Dic79C2×C4semidirect
104. C2×Dic79⋊C4C2×C4semidirect
113. C2×C22⋊Dic79C2×C4semidirect
119. C2×(C2×D79)⋊C4C2×C4semidirect
153. C2×C22⋊C4×C79C2×C4semidirect
208. C2×C4×D79C22×C4semidirect
211. C4⋊Dic79C22×C4semidirect
216. Dic79⋊C4C22×C4semidirect
219. C22⋊Dic79C22×C4semidirect
222. (C2×D79)⋊C4C22×C4semidirect
266. C22⋊C4×C79C22×C4semidirect
405. C2×C79#2322semidirect
427. C2×#385D79semidirect
430. C79C2×#2322semidirect
471. #385C2×D79semidirect
553. C2×C22⋊C4C4×D79semidirect
677. C22⋊C4C2×C4×D79semidirect
819. C2#23766067direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791432
C22×C4×C22⋊D792
C22×C4⋊C4×D792
#237660672
C2×#190984602
C2×#190984592
C2×#190984562
C2×#190984512
C2×#190984482
C2×#190984442
C2×#190984392
C2×#190984362
C2×#190984342
C2×#190984252
C2×#190984102
C2×#385×C792
C2×#232279