Finite Group Databasebeta

← C2×#23766532 #34447985

Subgroups — C2×#23766532 #34447985

Order 20224.

3094 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579146C211yesmaximal, characteristic
2#23766532C2116yesmaximal, direct product factor
3C2×#19098464C211yesmaximal, characteristic
4C2×#19098455C211yesmaximal, characteristic, complemented
5C2×#19098455C211yesmaximal, characteristic, complemented
6C2×#19098452C211yesmaximal, characteristic, complemented
7C2×#19098452C211yesmaximal, characteristic, complemented
8C2×#19098444C211yesmaximal, characteristic, complemented
9C2×#19098441C211yesmaximal, characteristic
10C2×C4⋊C4×Dic79C211yesmaximal, characteristic, complemented
11C2×#19098414C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D79)⋊C4C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D79)⋊C4C211yesmaximal, characteristic, complemented
14C2×#19098410C211yesmaximal, characteristic, complemented
15C2×#19098410C211yesmaximal, characteristic, complemented
16C2×#387×C79C211yesmaximal, characteristic, complemented
17C23×D316C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20C2×#14579146C4116yescomplemented
21C2×#14579146C2218yes—
22C22×C4⋊Dic79C2211yescharacteristic
23C22×Dic79⋊C4C2211yescharacteristic
24C22×Dic79⋊C4C2211yescharacteristic
25C22×(C2×D79)⋊C4C2211yescharacteristic
26C22×(C2×D79)⋊C4C2211yescharacteristic
27C22×(C2×D79)⋊C4C2211yescharacteristic
28C22×(C2×D79)⋊C4C2211yescharacteristic
29C22×(C2×D79)⋊C4C2211yescharacteristic
30C22×(C2×D79)⋊C4C2211yescharacteristic
31C22×(C2×D79)⋊C4C2211yescharacteristic
32C22×(C2×D79)⋊C4C2211yescharacteristic
33C22×(C2×D79)⋊C4C2211yescharacteristic
34C22×(C2×D79)⋊C4C2211yescharacteristic
35C22×C4×Dic79C2211yescharacteristic
36C22×C4×Dic79C2211yescharacteristic
37C22×C4×Dic79C2211yescharacteristic
38C22×C4×Dic79C2211yescharacteristic
39C22×C4×Dic79C2211yescharacteristic
40C22×C4×Dic79C2211yescharacteristic
41#19098464C2218yes—
42#19098455C2218yescomplemented
43#19098455C2218yescomplemented
44#19098452C2218yescomplemented
45#19098452C2218yescomplemented
46#19098444C2218yescomplemented
47#19098441C2218yes—
48C4⋊C4×Dic79C2218yescomplemented
49#19098414C2218yescomplemented
50C4×(C2×D79)⋊C4C2218yescomplemented
51C4×(C2×D79)⋊C4C2218yescomplemented
52#19098410C2218yescomplemented
53#19098410C2218yescomplemented
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C2×C79⋊#95C2211yescharacteristic
60C22×C4⋊C4×C79C2211yescharacteristic
61C22×C4⋊C4×C79C2211yescharacteristic
62C22×C42×C79C2211yescharacteristic
63#387×C79C2218yescomplemented
64C2×#95×C79C2211yescharacteristic
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C2×#95×C79C2211yescharacteristic
68C24×D79C2311yescharacteristic
69C24×D79C2311yescharacteristic
70C22×D316—42no—
71C22×D316—42no—
72C22×D316C2×C418yes—
73C22×D316C2314yes—
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C23×Dic79C2311yescharacteristic
80C22×C4×D79—24no—
81C22×C4×D79—24no—
82C22×C4×D79—42no—
83C22×C4×D79—42no—
84C22×C4×D79—42no—
85C22×C4×D79C2×C418yescomplemented
86C22×C4×D79C2314yes—
87C22×C4×D79C2314yes—
88#14579146C2×C4164yescomplemented
89C2×C4⋊Dic79—24no—
90C2×C4⋊Dic79C2314yes—
91C2×Dic79⋊C4—24no—
92C2×Dic79⋊C4C2×C418yescomplemented
93C2×Dic79⋊C4C2314yes—
94C2×Dic79⋊C4C2314yes—
95C2×(C2×D79)⋊C4—24no—
96C2×(C2×D79)⋊C4—24no—
97C2×(C2×D79)⋊C4—24no—
98C2×(C2×D79)⋊C4—24no—
99C2×(C2×D79)⋊C4—24no—
100C2×(C2×D79)⋊C4—24no—
101C2×(C2×D79)⋊C4—42no—
102C2×(C2×D79)⋊C4C2×C418yes—
103C2×(C2×D79)⋊C4C2×C418yes—
104C2×(C2×D79)⋊C4C2×C418yescomplemented
105C2×(C2×D79)⋊C4C2314yes—
106C2×(C2×D79)⋊C4C2314yes—
107C2×(C2×D79)⋊C4C2314yes—
108C2×(C2×D79)⋊C4C2314yes—
109C2×(C2×D79)⋊C4C2314yes—
110C2×(C2×D79)⋊C4C2314yes—
111C2×(C2×D79)⋊C4C2314yes—
112C2×(C2×D79)⋊C4C2314yes—
113C2×(C2×D79)⋊C4C2314yes—
114C2×(C2×D79)⋊C4C2314yes—
115C2×C4×Dic79—24no—
116C2×C4×Dic79—24no—
117C2×C4×Dic79—42no—
118C2×C4×Dic79—42no—
119C2×C4×Dic79—42no—
120C2×C4×Dic79—42no—
121C2×C4×Dic79C2314yes—
122C2×C4×Dic79C2314yes—
123C2×C4×Dic79C2314yes—
124C2×C4×Dic79C2314yes—
125C2×C4×Dic79C2314yes—
126C2×C4×Dic79C2314yes—
127C79⋊#95C2314yes—
128C79⋊#95C2314yes—
129C79⋊#95C2314yes—
130C79⋊#95C2314yes—
131C79⋊#95C2314yes—
132C79⋊#95C2314yes—
133C23×C4×C79C2311yescharacteristic
134C23×C4×C79C2311yescharacteristic
135C23×C4×C79C2311yescharacteristic
136C23×C4×C79C2311yescharacteristic
137C23×C4×C79C2311yescharacteristic
138C23×C4×C79C2311yescharacteristic
139C23×C4×C79C2311yescharacteristic
140C2×C4⋊C4×C79—42no—
141C2×C4⋊C4×C79C2×C418yescomplemented
142C2×C4⋊C4×C79C2314yes—
143C2×C4⋊C4×C79C2314yes—
144C2×C42×C79—42no—
145C2×C42×C79C2314yes—
146#95×C79C2314yes—
147#95×C79C2314yes—
148#95×C79C2314yes—
149#95×C79C2314yes—
150C23×D79—22no—
151C23×D79—22no—
152C23×D79—22no—
153C23×D79—22no—
154C23×D79—22no—
155C23×D79—22no—
156C23×D79—22no—
157C23×D79—22no—
158C23×D79—22no—
159C23×D79—22no—
160C23×D79—22no—
161C23×D79—22no—
162C23×D79C22×C414yes—
163C23×D79C22×C414yes—
164C23×D79C2412yes—
165C23×D79C2412yes—
166C2×D316—416no—
167C2×D316—44no—
168C2×D316—44no—
169C2×D316C22×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×Dic79C22×C414yes—
184C22×Dic79C22×C414yes—
185C22×Dic79#4114yes—
186C22×Dic79#4114yes—
187C22×Dic79#4114yes—
188C22×Dic79C2412yes—
189C22×Dic79C2412yes—
190C22×Dic79C2412yes—
191C22×Dic79C2412yes—
192C22×Dic79C2412yes—
193C22×Dic79C2412yes—
194C2×C4×D79—28no—
195C2×C4×D79—28no—
196C2×C4×D79—416no—
197C2×C4×D79—44no—
198C2×C4×D79—44no—
199C2×C4×D79—44no—
200C2×C4×D79—416no—
201C2×C4×D79C22×C4116yescomplemented
202C4⋊Dic79—28no—
203Dic79⋊C4—28no—
204Dic79⋊C4C22×C4116yescomplemented
205(C2×D79)⋊C4—28no—
206(C2×D79)⋊C4—28no—
207(C2×D79)⋊C4—28no—
208(C2×D79)⋊C4—28no—
209(C2×D79)⋊C4—28no—
210(C2×D79)⋊C4—28no—
211(C2×D79)⋊C4—44no—
212(C2×D79)⋊C4C22×C4116yes—
213(C2×D79)⋊C4C22×C4116yes—
214(C2×D79)⋊C4C22×C4116yescomplemented
215C4×Dic79—28no—
216C4×Dic79—28no—
217C4×Dic79—44no—
218C4×Dic79—44no—
219C4×Dic79—44no—
220C4×Dic79—44no—
221C24×C79C2411yescharacteristic
222C22×C4×C79—22no—
223C22×C4×C79—22no—
224C22×C4×C79—22no—
225C22×C4×C79—22no—
226C22×C4×C79—22no—
227C22×C4×C79—22no—
228C22×C4×C79—22no—
229C22×C4×C79—22no—
230C22×C4×C79—22no—
231C22×C4×C79—22no—
232C22×C4×C79—22no—
233C22×C4×C79—22no—
234C22×C4×C79—22no—
235C22×C4×C79—22no—
236C22×C4×C79—22no—
237C22×C4×C79—22no—
238C22×C4×C79—22no—
239C22×C4×C79C22×C414yes—
240C22×C4×C79C22×C414yes—
241C22×C4×C79C22×C414yes—
242C22×C4×C79#4114yes—
243C22×C4×C79C2412yes—
244C22×C4×C79C2412yes—
245C22×C4×C79C2412yes—
246C22×C4×C79C2412yes—
247C22×C4×C79C2412yes—
248C22×C4×C79C2412yes—
249C22×C4×C79C2412yes—
250C4⋊C4×C79—44no—
251C4⋊C4×C79C22×C4116yescomplemented
252C42×C79—44no—
253C23×C79C23×C412yes—
254C23×C79C2×#4112yes—
255C23×C79C2×#4112yes—
256C23×C79C2×#4112yes—
257C23×C79C2×#4112yes—
258C23×C79H(5,𝔽2)12yes—
259C23×C79H(5,𝔽2)12yes—
260C23×C79C2511yescharacteristic
261C22×D79—28no—
262C22×D79—28no—
263C22×D79—28no—
264C22×D79—28no—
265C22×D79—28no—
266C22×D79—28no—
267C22×D79—22no—
268C22×D79—22no—
269C22×D79—22no—
270C22×D79—22no—
271C22×D79—22no—
272C22×D79—22no—
273C22×D79—22no—
274C22×D79—22no—
275C22×D79—22no—
276C22×D79—22no—
277C22×D79—22no—
278C22×D79—22no—
279C22×D79—44no—
280C22×D79—44no—
281C22×D79—44no—
282C22×D79—44no—
283C22×D79—44no—
284C22×D79—44no—
285C22×D79—44no—
286C22×D79—44no—
287C22×D79C23×C414yes—
288C22×D79C23×C414yes—
289C2×C4×C79—28no—
290C2×C4×C79—28no—
291C2×C4×C79—28no—
292C2×C4×C79—28no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—22no—
302C2×C4×C79—22no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—44no—
311C2×C4×C79—44no—
312C2×C4×C79—44no—
313C2×C4×C79C23×C414yes—
314C2×C4×C79C23×C414yes—
315C2×C4×C79C23×C414yes—
316C2×C4×C79C2×#4114yes—
317C2×Dic79—28no—
318C2×Dic79—28no—
319C2×Dic79—28no—
320C2×Dic79—28no—
321C2×Dic79—28no—
322C2×Dic79—22no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—22no—
330C2×Dic79—22no—
331C2×Dic79—22no—
332C2×Dic79—22no—
333C2×Dic79—22no—
334C2×Dic79—22no—
335C2×Dic79—44no—
336C2×Dic79C23×C414yes—
337C2×Dic79C23×C414yes—
338C2×Dic79C2×#4114yes—
339C2×Dic79C2×#4114yes—
340C2×Dic79C2×#4114yes—
341D316—416no—
342C4×D79—416no—
343C4×D79—416no—
344C22×C79C4×#4114yes—
345C22×C79C4×#4114yes—
346C22×C79#51814yes—
347C22×C79#55114yes—
348C22×C79#55314yes—
349C22×C79#55314yes—
350C22×C79#55914yes—
351C22×C79C24×C411yescharacteristic
352C22×C79C22×#4111yescharacteristic
353C22×C79C22×#4111yescharacteristic
354C22×C79C22×#4111yescharacteristic
355C22×C79C22×#4111yescharacteristic
356C22×C79C2×H(5,𝔽2)11yescharacteristic
357C22×C79C2×H(5,𝔽2)11yescharacteristic
358C2×D79—24no—
359C2×D79—24no—
360C2×D79—24no—
361C2×D79—24no—
362C2×D79—24no—
363C2×D79—24no—
364C2×D79—416no—
365C2×D79—416no—
366C2×D79—42no—
367C2×D79—42no—
368C2×D79—42no—
369C2×D79—42no—
370C2×D79—42no—
371C2×D79—42no—
372C2×D79—42no—
373C2×D79—42no—
374C4×C79—24no—
375C4×C79—24no—
376C4×C79—24no—
377C4×C79—24no—
378C4×C79—42no—
379C4×C79—42no—
380C4×C79—42no—
381Dic79—24no—
382Dic79—24no—
383Dic79—24no—
384Dic79—24no—
385Dic79—24no—
386Dic79—42no—
387C2×#2374—791nomaximal, Sylow
388C2×C79#237418yescomplemented
389C2×C79C2×C4×#4111yescharacteristic
390C2×C79C2×C4×#4111yescharacteristic
391C2×C79C2×#51811yescharacteristic
392C2×C79C2×#55111yescharacteristic
393C2×C79C2×#55311yescharacteristic
394C2×C79C2×#55311yescharacteristic
395C2×C79C2×#55911yescharacteristic
396D79—44no—
397D79—44no—
398C22×#123—791no—
399#2374—7916no—
400C2×#390—791no—
401C2×#388—791no—
402C2×#388—791no—
403C2×#388—791no—
404C2×#388—791no—
405C2×#387—791no—
406C2×#387D7911yescharacteristic, complemented
407C2×#386—791no—
408C2×C4×C4⋊C4—791no—
409C2×C4×C4⋊C4—791no—
410C2×C4×C22⋊C4—791no—
411C2×C4×C22⋊C4—791no—
412C2×C4×C22⋊C4—791no—
413C2×C4×C22⋊C4—791no—
414C79C2×#237411yescharacteristic, complemented, Sylow
415C23×D4—791no—
416C24×C4—791no—
417C24×C4—791no—
418C2×#123—798no—
419C2×#123—7916no—
420C22×C4⋊C4—791no—
421C22×C4⋊C4—791no—
422C22×C4⋊C4—791no—
423C22×C4⋊C4C2×D7911yescharacteristic
424C22×C4⋊C4C2×D7911yescharacteristic
425C22×C22⋊C4—791no—
426C22×C22⋊C4—791no—
427C22×C22⋊C4—791no—
428C22×C22⋊C4—791no—
429C22×C22⋊C4—791no—
430C22×C22⋊C4—791no—
431C22×C22⋊C4—791no—
432C22×C22⋊C4—791no—
433C22×C22⋊C4—791no—
434C22×C22⋊C4—791no—
435C22×C42—791no—
436C22×C42—791no—
437C22×C42—791no—
438C22×C42—791no—
439C22×C42—791no—
440C22×C42—791no—
441C22×C42C2×D7911yescharacteristic
442#390—798no—
443#388—798no—
444#388—798no—
445#388—798no—
446#388—798no—
447#387—798no—
448#387C2×D7918yescomplemented
449#386—798no—
450C4×C4⋊C4—798no—
451C4×C4⋊C4—798no—
452C4×C22⋊C4—798no—
453C4×C22⋊C4—798no—
454C4×C22⋊C4—798no—
455C4×C22⋊C4—798no—
456C2×#95—791no—
457C2×#95—791no—
458C2×#95—791no—
459C2×#95—791no—
460C2×#95—791no—
461C2×#95—791no—
462C2×#95C2×D7911yescharacteristic
463C2×#95C2×D7911yescharacteristic
464C2×#95C2×D7911yescharacteristic
465C2×#95C2×D7911yescharacteristic
466C25—791no—
467C25—791no—
468C22×D4—3162no—
469C22×D4—3162no—
470C22×D4—798no—
471C22×D4—794no—
472C23×C4—3162no—
473C23×C4—3162no—
474C23×C4—3162no—
475C23×C4—798no—
476C23×C4—794no—
477C23×C4—794no—
478C23×C4—791no—
479C23×C4—791no—
480C23×C4—791no—
481C23×C4—791no—
482C23×C4—791no—
483C23×C4—791no—
484C23×C4—1584no—
485C23×C4—1584no—
486C23×C4C22×D7911yescharacteristic
487C23×C4C22×D7911yescharacteristic
488C23×C4C22×D7911yescharacteristic
489C23×C4C22×D7911yescharacteristic
490C23×C4C22×D7911yescharacteristic
491C23×C4C22×D7911yescharacteristic
492C23×C4C22×D7911yescharacteristic
493#123—7964no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—798no—
496C2×C4⋊C4—794no—
497C2×C4⋊C4—794no—
498C2×C4⋊C4—794no—
499C2×C4⋊C4—1584no—
500C2×C4⋊C4—1584no—
501C2×C4⋊C4C4×D7918yescomplemented
502C2×C4⋊C4C22×D7914yes—
503C2×C4⋊C4C22×D7914yes—
504C2×C22⋊C4—3162no—
505C2×C22⋊C4—794no—
506C2×C22⋊C4—798no—
507C2×C22⋊C4—798no—
508C2×C22⋊C4—798no—
509C2×C22⋊C4—794no—
510C2×C22⋊C4—794no—
511C2×C22⋊C4—794no—
512C2×C22⋊C4—794no—
513C2×C22⋊C4—794no—
514C2×C22⋊C4—794no—
515C2×C22⋊C4—794no—
516C2×C22⋊C4—794no—
517C2×C22⋊C4—794no—
518C2×C22⋊C4—1584no—
519C2×C22⋊C4—1584no—
520C2×C22⋊C4—1584no—
521C2×C22⋊C4—1584no—
522C2×C22⋊C4—1584no—
523C2×C22⋊C4—1584no—
524C2×C42—42no—
525C2×C42—3162no—
526C2×C42—3162no—
527C2×C42—3162no—
528C2×C42—3162no—
529C2×C42—794no—
530C2×C42—794no—
531C2×C42—794no—
532C2×C42—794no—
533C2×C42—794no—
534C2×C42—794no—
535C2×C42—1584no—
536C2×C42—1584no—
537C2×C42C22×D7914yes—
538#95—794no—
539#95—794no—
540#95—794no—
541#95—794no—
542#95—794no—
543#95—794no—
544#95C22×D7914yes—
545#95C22×D7914yes—
546#95C22×D7914yes—
547#95C22×D7914yes—
548C24—792no—
549C24—792no—
550C24—794no—
551C24—794no—
552C24—1582no—
553C24—1582no—
554C24—1582no—
555C24—1582no—
556C24—1582no—
557C24—1582no—
558C24—1582no—
559C24—1582no—
560C24—1582no—
561C24—1582no—
562C24—1582no—
563C24—1582no—
564C24C23×D7911yescharacteristic
565C2×D4—3164no—
566C2×D4—3164no—
567C2×D4—31616no—
568C2×D4—7916no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—31616no—
587C22×C4—3164no—
588C22×C4—3164no—
589C22×C4—3164no—
590C22×C4—31616no—
591C22×C4—7916no—
592C22×C4—794no—
593C22×C4—794no—
594C22×C4—794no—
595C22×C4—792no—
596C22×C4—792no—
597C22×C4—792no—
598C22×C4—792no—
599C22×C4—792no—
600C22×C4—794no—
601C22×C4—794no—
602C22×C4—792no—
603C22×C4—1588no—
604C22×C4—1582no—
605C22×C4—1582no—
606C22×C4—1582no—
607C22×C4—1588no—
608C22×C4—1582no—
609C22×C4—1582no—
610C22×C4—1582no—
611C22×C4—1582no—
612C22×C4—1582no—
613C22×C4—1582no—
614C22×C4—1582no—
615C22×C4—1582no—
616C22×C4—1582no—
617C22×C4—1582no—
618C22×C4C2×C4×D7914yes—
619C22×C4C2×C4×D7914yes—
620C22×C4C2×C4×D7914yes—
621C22×C4#1192962514yes—
622C22×C4C23×D7912yes—
623C22×C4C23×D7912yes—
624C22×C4C23×D7912yes—
625C22×C4C23×D7912yes—
626C22×C4C23×D7912yes—
627C22×C4C23×D7912yes—
628C22×C4C23×D7912yes—
629C4⋊C4—44no—
630C4⋊C4—7916no—
631C4⋊C4—1588no—
632C4⋊C4—1588no—
633C4⋊C4C2×C4×D79116yescomplemented
634C22⋊C4—3164no—
635C22⋊C4—7916no—
636C22⋊C4—7916no—
637C22⋊C4—7916no—
638C22⋊C4—1588no—
639C22⋊C4—1588no—
640C22⋊C4—1588no—
641C22⋊C4—1588no—
642C22⋊C4—1588no—
643C22⋊C4—1588no—
644C42—44no—
645C42—3164no—
646C42—3164no—
647C42—3164no—
648C42—3164no—
649C42—1588no—
650C42—1588no—
651C23—3164no—
652C23—3164no—
653C23—3164no—
654C23—3164no—
655C23—3164no—
656C23—3164no—
657C23—3164no—
658C23—3164no—
659C23—794no—
660C23—794no—
661C23—1582no—
662C23—1582no—
663C23—1582no—
664C23—1582no—
665C23—1588no—
666C23—1588no—
667C23—1588no—
668C23—1588no—
669C23—1588no—
670C23—1588no—
671C23—1582no—
672C23—1582no—
673C23—1582no—
674C23—1582no—
675C23—1582no—
676C23—1582no—
677C23—1582no—
678C23—1582no—
679C23C22×C4×D7912yes—
680C23#41×D7912yes—
681C23#41×D7912yes—
682C23#41×D7912yes—
683C23C2×#1192962512yes—
684C23#1457920612yes—
685C23#1457920712yes—
686C23C24×D7911yescharacteristic
687D4—31616no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—31616no—
713C2×C4—31616no—
714C2×C4—3164no—
715C2×C4—794no—
716C2×C4—794no—
717C2×C4—794no—
718C2×C4—794no—
719C2×C4—794no—
720C2×C4—1582no—
721C2×C4—1582no—
722C2×C4—1582no—
723C2×C4—1582no—
724C2×C4—1582no—
725C2×C4—1582no—
726C2×C4—1582no—
727C2×C4—1582no—
728C2×C4—1588no—
729C2×C4—1588no—
730C2×C4—1588no—
731C2×C4—1588no—
732C2×C4—1588no—
733C2×C4—1582no—
734C2×C4—1582no—
735C2×C4—1582no—
736C2×C4—1582no—
737C2×C4—1582no—
738C2×C4C22×C4×D7914yes—
739C2×C4C22×C4×D7914yes—
740C2×C4C22×C4×D7914yes—
741C2×C4C2×#1192962514yes—
742C22—31616no—
743C22—31616no—
744C22—3162no—
745C22—3162no—
746C22—3162no—
747C22—3162no—
748C22—3162no—
749C22—3162no—
750C22—3162no—
751C22—3162no—
752C22—1584no—
753C22—1584no—
754C22—1584no—
755C22—1584no—
756C22—1584no—
757C22—1584no—
758C22#1909903114yes—
759C22C4×#1192962514yes—
760C22#1909903514yes—
761C22#1909924014yes—
762C22#1909926414yes—
763C22#1909926614yes—
764C22#1909929714yes—
765C22C23×C4×D7911yescharacteristic
766C22C2×#41×D7911yescharacteristic
767C22C2×#41×D7911yescharacteristic
768C22C2×#41×D7911yescharacteristic
769C22C22×#1192962511yescharacteristic
770C22C2×#1457920611yescharacteristic
771C22C2×#1457920711yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—3162no—
780C4—1584no—
781C4—1584no—
782C4—1584no—
783C4—1584no—
784C4—1584no—
785C2—3164no—
786C2—3164no—
787C2#2376653218yesdirect product factor
788C2C2×#1909903111yescharacteristic
789C2C2×C4×#1192962511yescharacteristic
790C2C2×#1909903511yescharacteristic
791C2C2×#1909924011yescharacteristic
792C2C2×#1909926411yescharacteristic
793C2C2×#1909926611yescharacteristic
794C2C2×#1909929711yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×#387×C79C2
socleC24×C79C24
prime radicalC23×D316C22
cosocleC23×C79C25
hypercenterC2×#387D79
hypocenterC79C2×#2374
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #23766532C2direct (N × H)
4. C2×#19098455C2semidirect
5. C2×#19098455C2semidirect
6. C2×#19098452C2semidirect
7. C2×#19098452C2semidirect
8. C2×#19098444C2semidirect
10. C2×C4⋊C4×Dic79C2semidirect
11. C2×#19098414C2semidirect
12. C2×C4×(C2×D79)⋊C4C2semidirect
13. C2×C4×(C2×D79)⋊C4C2semidirect
14. C2×#19098410C2semidirect
15. C2×#19098410C2semidirect
16. C2×#387×C79C2semidirect
20. C2×#14579146C4semidirect
42. #19098455C22semidirect
43. #19098455C22semidirect
44. #19098452C22semidirect
45. #19098452C22semidirect
46. #19098444C22semidirect
48. C4⋊C4×Dic79C22semidirect
49. #19098414C22semidirect
50. C4×(C2×D79)⋊C4C22semidirect
51. C4×(C2×D79)⋊C4C22semidirect
52. #19098410C22semidirect
53. #19098410C22semidirect
63. #387×C79C22semidirect
85. C22×C4×D79C2×C4semidirect
88. #14579146C2×C4semidirect
92. C2×Dic79⋊C4C2×C4semidirect
104. C2×(C2×D79)⋊C4C2×C4semidirect
141. C2×C4⋊C4×C79C2×C4semidirect
201. C2×C4×D79C22×C4semidirect
204. Dic79⋊C4C22×C4semidirect
214. (C2×D79)⋊C4C22×C4semidirect
251. C4⋊C4×C79C22×C4semidirect
388. C2×C79#2374semidirect
406. C2×#387D79semidirect
414. C79C2×#2374semidirect
448. #387C2×D79semidirect
501. C2×C4⋊C4C4×D79semidirect
633. C4⋊C4C2×C4×D79semidirect
787. C2#23766532direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791462
#237665322
C2×#190984642
C2×#190984552
C2×#190984522
C2×#190984442
C2×#190984412
C2×C4⋊C4×Dic792
C2×#190984142
C2×C4×(C2×D79)⋊C42
C2×#190984102
C2×#387×C792
C2×#237479