Finite Group Databasebeta

← C2×#23766395 #34447775

Subgroups — C2×#23766395 #34447775

Order 20224.

3830 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×#14579119C211yesmaximal, characteristic, complemented
4#23766395C2116yesmaximal, direct product factor
5C2×#19098458C211yesmaximal, characteristic, complemented
6C2×#19098457C211yesmaximal, characteristic, complemented
7C2×#19098456C211yesmaximal, characteristic, complemented
8C2×#19098450C211yesmaximal, characteristic, complemented
9C2×#19098448C211yesmaximal, characteristic, complemented
10C2×#19098439C211yesmaximal, characteristic
11C2×#19098434C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic79C211yesmaximal, characteristic, complemented
13C2×C4×C22⋊Dic79C211yesmaximal, characteristic, complemented
14C2×#19098410C211yesmaximal, characteristic, complemented
15C2×#95×D79C211yesmaximal, 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—
25C2×#14579119—28no—
26C2×#14579119C2218yescomplemented
27C22×C4⋊Dic79C2211yescharacteristic
28C22×C4⋊Dic79C2211yescharacteristic
29C22×Dic79⋊C4C2211yescharacteristic
30C22×Dic79⋊C4C2211yescharacteristic
31C22×Dic79⋊C4C2211yescharacteristic
32C22×C22⋊Dic79C2211yescharacteristic
33C22×C22⋊Dic79C2211yescharacteristic
34C22×C22⋊Dic79C2211yescharacteristic
35C22×(C2×D79)⋊C4C2211yescharacteristic
36C22×(C2×D79)⋊C4C2211yescharacteristic
37C22×(C2×D79)⋊C4C2211yescharacteristic
38C22×C4×Dic79C2211yescharacteristic
39C22×C4×Dic79C2211yescharacteristic
40C22×C4×Dic79C2211yescharacteristic
41C22×C4×Dic79C2211yescharacteristic
42C22×C4×Dic79C2211yescharacteristic
43#19098458C2218yescomplemented
44#19098457C2218yescomplemented
45#19098456C2218yescomplemented
46#19098450C2218yescomplemented
47#19098448C2218yescomplemented
48#19098439C2218yes—
49#19098434C2218yescomplemented
50C4⋊C4×Dic79C2218yescomplemented
51C4×C22⋊Dic79C2218yescomplemented
52#19098410C2218yescomplemented
53C2×C79⋊#95C2211yescharacteristic
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C2×C79⋊#95C2211yescharacteristic
60C2×C79⋊#95C2211yescharacteristic
61#95×D79C2218yescomplemented
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—24no—
86C22×C4×D79—24no—
87C22×C4×D79—24no—
88C22×C4×D79—42no—
89C22×C4×D79—42no—
90C22×C4×D79C2×C418yescomplemented
91C22×C4×D79C2314yes—
92C22×C4×D79C2314yes—
93C22×C4×D79C2314yes—
94#14579143C2×C4164yescomplemented
95C4×C22⋊D79—232no—
96#14579119—232no—
97C2×C4⋊Dic79—24no—
98C2×C4⋊Dic79C2×C418yescomplemented
99C2×C4⋊Dic79C2314yes—
100C2×C4⋊Dic79C2314yes—
101C2×Dic79⋊C4—24no—
102C2×Dic79⋊C4—42no—
103C2×Dic79⋊C4C2×C418yescomplemented
104C2×Dic79⋊C4C2314yes—
105C2×Dic79⋊C4C2314yes—
106C2×Dic79⋊C4C2314yes—
107C2×C22⋊Dic79—24no—
108C2×C22⋊Dic79—24no—
109C2×C22⋊Dic79C2×C418yescomplemented
110C2×C22⋊Dic79C2314yes—
111C2×C22⋊Dic79C2314yes—
112C2×C22⋊Dic79C2314yes—
113C2×(C2×D79)⋊C4—24no—
114C2×(C2×D79)⋊C4C2×C418yescomplemented
115C2×(C2×D79)⋊C4D418yes—
116C2×(C2×D79)⋊C4C2314yes—
117C2×(C2×D79)⋊C4C2314yes—
118C2×(C2×D79)⋊C4C2314yes—
119C2×C4×Dic79—24no—
120C2×C4×Dic79—24no—
121C2×C4×Dic79—24no—
122C2×C4×Dic79—24no—
123C2×C4×Dic79—42no—
124C2×C4×Dic79C2314yes—
125C2×C4×Dic79C2314yes—
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—24no—
140C23×C4×C79—42no—
141C23×C4×C79C2311yescharacteristic
142C23×C4×C79C2311yescharacteristic
143C23×C4×C79C2314yes—
144C23×C4×C79C2311yescharacteristic
145C23×C4×C79C2311yescharacteristic
146C23×C4×C79C2311yescharacteristic
147C23×C4×C79C2311yescharacteristic
148C2×C4⋊C4×C79—24no—
149C2×C4⋊C4×C79—24no—
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×Dic79C22×C414yes—
187C22×Dic79C22×C414yes—
188C22×Dic79C22×C414yes—
189C22×Dic79C2×D414yes—
190C22×Dic79#4114yes—
191C22×Dic79C2412yes—
192C22×Dic79C2412yes—
193C22×Dic79C2412yes—
194C22×Dic79C2412yes—
195C22×Dic79C2412yes—
196C22×Dic79C2412yes—
197C22×Dic79C2412yes—
198C2×C4×D79—28no—
199C2×C4×D79—232no—
200C2×C4×D79—28no—
201C2×C4×D79—28no—
202C2×C4×D79—28no—
203C2×C4×D79—28no—
204C2×C4×D79—28no—
205C2×C4×D79—44no—
206C2×C4×D79—44no—
207C2×C4×D79—416no—
208C2×C4×D79—416no—
209C2×C4×D79C22×C4116yescomplemented
210C4⋊Dic79—28no—
211C4⋊Dic79C22×C4116yescomplemented
212Dic79⋊C4—28no—
213Dic79⋊C4—44no—
214Dic79⋊C4C22×C4116yescomplemented
215C22⋊Dic79—28no—
216C22⋊Dic79—28no—
217C22⋊Dic79C22×C4116yescomplemented
218(C2×D79)⋊C4—28no—
219(C2×D79)⋊C4C22×C4116yescomplemented
220(C2×D79)⋊C4C2×D4116yes—
221C4×Dic79—28no—
222C4×Dic79—28no—
223C4×Dic79—28no—
224C4×Dic79—28no—
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—28no—
250C22×C4×C79—28no—
251C22×C4×C79—44no—
252C22×C4×C79—416no—
253C22×C4×C79C22×C414yes—
254C22×C4×C79C22×C414yes—
255C22×C4×C79C2×D414yes—
256C22×C4×C79#4114yes—
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—28no—
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×C79C2×#4112yes—
285C23×C79C2×#4112yes—
286C23×C79H(5,𝔽2)12yes—
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—28no—
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×C79C23×C414yes—
325C2×C4×C79C23×C414yes—
326C2×C4×C79C22×D414yes—
327C2×C4×C79C2×#4114yes—
328C22⋊D79—232no—
329C2×Dic79—28no—
330C2×Dic79—28no—
331C2×Dic79—28no—
332C2×Dic79—28no—
333C2×Dic79—28no—
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×Dic79C23×C414yes—
353C2×Dic79C23×C414yes—
354C2×Dic79C23×C414yes—
355C2×Dic79C22×D414yes—
356C2×Dic79C2×#4114yes—
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×C79C4×#4114yes—
370C22×C79#52014yes—
371C22×C79#54614yes—
372C22×C79#54714yes—
373C22×C79#55114yes—
374C22×C79#55214yes—
375C22×C79C24×C411yescharacteristic
376C22×C79C23×D411yescharacteristic
377C22×C79C22×#4111yescharacteristic
378C22×C79C22×#4111yescharacteristic
379C22×C79C22×#4111yescharacteristic
380C22×C79C2×H(5,𝔽2)11yescharacteristic
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—24no—
394C4×C79—42no—
395C4×C79—42no—
396Dic79—24no—
397Dic79—24no—
398Dic79—24no—
399Dic79—24no—
400Dic79—24no—
401Dic79—42no—
402Dic79—42no—
403C2×#2359—791nomaximal, Sylow
404C2×C79—44no—
405C2×C79#235918yescomplemented
406C2×C79C22×C4×D411yescharacteristic
407C2×C79C2×C4×#4111yescharacteristic
408C2×C79C2×#52011yescharacteristic
409C2×C79C2×#54611yescharacteristic
410C2×C79C2×#54711yescharacteristic
411C2×C79C2×#55111yescharacteristic
412C2×C79C2×#55211yescharacteristic
413D79—28no—
414C22×#123—791no—
415C22×C4×D4—791no—
416C22×#117—791no—
417#2359—7916no—
418C2×#389—791no—
419C2×#388—791no—
420C2×#388—791no—
421C2×#387—791no—
422C2×#387—791no—
423C2×#386—791no—
424C2×#385—791no—
425C2×#385D7911yescharacteristic, complemented
426C2×C4×C4⋊C4—791no—
427C2×C4×C22⋊C4—791no—
428C2×C4×C22⋊C4—791no—
429C22×#95—791no—
430C79C2×#235911yescharacteristic, 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—
440C2×#117—798no—
441C2×#117—1588no—
442C22×C4⋊C4—791no—
443C22×C4⋊C4—791no—
444C22×C4⋊C4—791no—
445C22×C4⋊C4—791no—
446C22×C4⋊C4—791no—
447C22×C4⋊C4C2×D7911yescharacteristic
448C22×C4⋊C4C2×D7911yescharacteristic
449C22×C22⋊C4—791no—
450C22×C22⋊C4—791no—
451C22×C22⋊C4—791no—
452C22×C22⋊C4—791no—
453C22×C22⋊C4—791no—
454C22×C22⋊C4—791no—
455C22×C22⋊C4C2×D7911yescharacteristic
456C22×C22⋊C4C2×D7911yescharacteristic
457C22×C42—791no—
458C22×C42—791no—
459C22×C42—791no—
460C22×C42—791no—
461C22×C42—791no—
462#389—798no—
463#388—798no—
464#388—798no—
465#387—798no—
466#387—798no—
467#386—798no—
468#385—798no—
469#385C2×D7918yescomplemented
470C4×C4⋊C4—798no—
471C4×C22⋊C4—798no—
472C4×C22⋊C4—798no—
473C2×#95—791no—
474C2×#95—791no—
475C2×#95—791no—
476C2×#95—791no—
477C2×#95—791no—
478C2×#95—791no—
479C2×#95—791no—
480C2×#95—791no—
481C2×#95—798no—
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—24no—
492C23×C4—42no—
493C23×C4—3162no—
494C23×C4—3162no—
495C23×C4—794no—
496C23×C4—794no—
497C23×C4—791no—
498C23×C4—791no—
499C23×C4—791no—
500C23×C4—791no—
501C23×C4—791no—
502C23×C4—798no—
503C23×C4—794no—
504C23×C4—791no—
505C23×C4—791no—
506C23×C4—1584no—
507C23×C4—1584no—
508C23×C4—1584no—
509C23×C4—1584no—
510C23×C4—1584no—
511C23×C4—1584no—
512C23×C4C22×D7911yescharacteristic
513C23×C4C22×D7911yescharacteristic
514C23×C4C22×D7914yes—
515C23×C4C22×D7911yescharacteristic
516C23×C4C22×D7911yescharacteristic
517C23×C4C22×D7911yescharacteristic
518C23×C4C22×D7911yescharacteristic
519#123—7964no—
520C4×D4—15832no—
521#117—15832no—
522C2×C4⋊C4—24no—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—3162no—
525C2×C4⋊C4—794no—
526C2×C4⋊C4—798no—
527C2×C4⋊C4—798no—
528C2×C4⋊C4—794no—
529C2×C4⋊C4—794no—
530C2×C4⋊C4—794no—
531C2×C4⋊C4—794no—
532C2×C4⋊C4—1584no—
533C2×C4⋊C4—1584no—
534C2×C4⋊C4C22×D7914yes—
535C2×C4⋊C4C22×D7914yes—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—798no—
538C2×C22⋊C4—794no—
539C2×C22⋊C4—798no—
540C2×C22⋊C4—798no—
541C2×C22⋊C4—794no—
542C2×C22⋊C4—794no—
543C2×C22⋊C4—794no—
544C2×C22⋊C4—794no—
545C2×C22⋊C4—794no—
546C2×C22⋊C4—1584no—
547C2×C22⋊C4—1584no—
548C2×C22⋊C4—1584no—
549C2×C22⋊C4C4×D7918yescomplemented
550C2×C22⋊C4C22×D7914yes—
551C2×C22⋊C4C22×D7914yes—
552C2×C42—3162no—
553C2×C42—794no—
554C2×C42—794no—
555C2×C42—794no—
556C2×C42—794no—
557C2×C42—794no—
558C2×C42—1584no—
559C2×C42—1584no—
560C2×C42—1584no—
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—28no—
608C22×C4—28no—
609C22×C4—44no—
610C22×C4—416no—
611C22×C4—31616no—
612C22×C4—3164no—
613C22×C4—3164no—
614C22×C4—31616no—
615C22×C4—794no—
616C22×C4—792no—
617C22×C4—792no—
618C22×C4—792no—
619C22×C4—792no—
620C22×C4—792no—
621C22×C4—794no—
622C22×C4—794no—
623C22×C4—794no—
624C22×C4—794no—
625C22×C4—7916no—
626C22×C4—792no—
627C22×C4—792no—
628C22×C4—1588no—
629C22×C4—1588no—
630C22×C4—1588no—
631C22×C4—1588no—
632C22×C4—15832no—
633C22×C4—1588no—
634C22×C4—1582no—
635C22×C4—1582no—
636C22×C4—1582no—
637C22×C4—1582no—
638C22×C4—1582no—
639C22×C4—1582no—
640C22×C4—1588no—
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×C4C2×C4×D7914yes—
652C22×C4C2×C4×D7914yes—
653C22×C4D4×D7914yes—
654C22×C4#1192962314yes—
655C22×C4C23×D7912yes—
656C22×C4C23×D7912yes—
657C22×C4C23×D7912yes—
658C22×C4C23×D7912yes—
659C22×C4C23×D7912yes—
660C22×C4C23×D7912yes—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—3164no—
664C4⋊C4—7916no—
665C4⋊C4—7916no—
666C4⋊C4—1588no—
667C4⋊C4—1588no—
668C22⋊C4—44no—
669C22⋊C4—7916no—
670C22⋊C4—7916no—
671C22⋊C4—7916no—
672C22⋊C4—1588no—
673C22⋊C4—1588no—
674C22⋊C4—1588no—
675C22⋊C4C2×C4×D79116yescomplemented
676C42—3164no—
677C42—1588no—
678C42—1588no—
679C42—1588no—
680C42—1588no—
681C23—22no—
682C23—22no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—7916no—
695C23—794no—
696C23—794no—
697C23—794no—
698C23—1582no—
699C23—1582no—
700C23—1588no—
701C23—1588no—
702C23—1588no—
703C23—1588no—
704C23—1588no—
705C23—1588no—
706C23—1582no—
707C23—1582no—
708C23C22×C4×D7914yes—
709C23C22×C4×D7912yes—
710C23C2×D4×D7912yes—
711C23#41×D7912yes—
712C23#41×D7912yes—
713C23C2×#1192962312yes—
714C23#1457920612yes—
715C23#1457920912yes—
716C23C24×D7911yescharacteristic
717D4—15832no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—22no—
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—31616no—
740C2×C4—31616no—
741C2×C4—3164no—
742C2×C4—3164no—
743C2×C4—794no—
744C2×C4—794no—
745C2×C4—794no—
746C2×C4—794no—
747C2×C4—794no—
748C2×C4—15832no—
749C2×C4—1582no—
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—1588no—
760C2×C4—1588no—
761C2×C4—1588no—
762C2×C4—1588no—
763C2×C4—1588no—
764C2×C4—1582no—
765C2×C4—1582no—
766C2×C4—1582no—
767C2×C4—1582no—
768C2×C4—1582no—
769C2×C4—1582no—
770C2×C4C22×C4×D7914yes—
771C2×C4C22×C4×D7914yes—
772C2×C4C2×D4×D7914yes—
773C2×C4C2×#1192962314yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—416no—
780C22—42no—
781C22—42no—
782C22—798no—
783C22—1584no—
784C22—1584no—
785C22—1584no—
786C22—1584no—
787C22—15832no—
788C22—1584no—
789C22—1584no—
790C22C4×D4×D7914yes—
791C22C4×#1192962314yes—
792C22#1909904414yes—
793C22#1909920014yes—
794C22#1909921514yes—
795C22#1909924114yes—
796C22#1909924714yes—
797C22C23×C4×D7911yescharacteristic
798C22C22×D4×D7911yescharacteristic
799C22C2×#41×D7911yescharacteristic
800C22C2×#41×D7911yescharacteristic
801C22C22×#1192962311yescharacteristic
802C22C2×#1457920611yescharacteristic
803C22C2×#1457920911yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—3162no—
811C4—3162no—
812C4—1584no—
813C4—1584no—
814C4—1584no—
815C4—1584no—
816C4—1584no—
817C2—44no—
818C2—1588no—
819C2#2376639518yesdirect product factor
820C2C2×C4×D4×D7911yescharacteristic
821C2C2×C4×#1192962311yescharacteristic
822C2C2×#1909904411yescharacteristic
823C2C2×#1909920011yescharacteristic
824C2C2×#1909921511yescharacteristic
825C2C2×#1909924111yescharacteristic
826C2C2×#1909924711yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×#385×C79C2
socleC24×C79C24
prime radicalC23×C22⋊D79C22
cosocleC23×C79C25
hypercenterC2×#385D79
hypocenterC79C2×#2359
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C22×#14579119C2semidirect
4. #23766395C2direct (N × H)
5. C2×#19098458C2semidirect
6. C2×#19098457C2semidirect
7. C2×#19098456C2semidirect
8. C2×#19098450C2semidirect
9. C2×#19098448C2semidirect
11. C2×#19098434C2semidirect
12. C2×C4⋊C4×Dic79C2semidirect
13. C2×C4×C22⋊Dic79C2semidirect
14. C2×#19098410C2semidirect
15. C2×#95×D79C2semidirect
16. C2×#385×C79C2semidirect
21. C2×#14579143C4semidirect
26. C2×#14579119C22semidirect
43. #19098458C22semidirect
44. #19098457C22semidirect
45. #19098456C22semidirect
46. #19098450C22semidirect
47. #19098448C22semidirect
49. #19098434C22semidirect
50. C4⋊C4×Dic79C22semidirect
51. C4×C22⋊Dic79C22semidirect
52. #19098410C22semidirect
61. #95×D79C22semidirect
67. #385×C79C22semidirect
90. C22×C4×D79C2×C4semidirect
94. #14579143C2×C4semidirect
98. C2×C4⋊Dic79C2×C4semidirect
103. C2×Dic79⋊C4C2×C4semidirect
109. C2×C22⋊Dic79C2×C4semidirect
114. C2×(C2×D79)⋊C4C2×C4semidirect
153. C2×C22⋊C4×C79C2×C4semidirect
209. C2×C4×D79C22×C4semidirect
211. C4⋊Dic79C22×C4semidirect
214. Dic79⋊C4C22×C4semidirect
217. C22⋊Dic79C22×C4semidirect
219. (C2×D79)⋊C4C22×C4semidirect
266. C22⋊C4×C79C22×C4semidirect
405. C2×C79#2359semidirect
425. C2×#385D79semidirect
430. C79C2×#2359semidirect
469. #385C2×D79semidirect
549. C2×C22⋊C4C4×D79semidirect
675. C22⋊C4C2×C4×D79semidirect
819. C2#23766395direct (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×#145791192
#237663952
C2×#190984582
C2×#190984572
C2×#190984562
C2×#190984502
C2×#190984482
C2×#190984392
C2×#190984342
C2×C4⋊C4×Dic792
C2×C4×C22⋊Dic792
C2×#190984102
C2×#95×D792
C2×#385×C792
C2×#235979