Finite Group Databasebeta

← C2×#20252358 #27080725

Subgroups — C2×#20252358 #27080725

Order 12032.

2070 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689653C211yesmaximal, characteristic
2#20252358C2116yesmaximal, direct product factor
3C2×#15689251C211yesmaximal, characteristic, complemented
4C2×#15689247C211yesmaximal, characteristic, complemented
5C2×#15689199C211yesmaximal, characteristic, complemented
6C2×#15689194C211yesmaximal, characteristic, complemented
7C2×D4×C47⋊C8C211yesmaximal, characteristic, complemented
8C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
9C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
10C2×#15689183C211yesmaximal, characteristic, complemented
11C2×#15689181C211yesmaximal, characteristic, complemented
12C2×#15689177C211yesmaximal, characteristic, complemented
13C2×#15689081C211yesmaximal, characteristic, complemented
14C2×#15689080C211yesmaximal, characteristic, complemented
15C22×C8×Dic47C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic, complemented
17C22×#10625324C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19C23×C47⋊C8C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689653C418yes—
22#15689653C2218yes—
23C2×#13094019C411yescharacteristic
24C2×#13094017C411yescharacteristic
25C2×#13094014C411yescharacteristic
26C2×#13094010C411yescharacteristic
27C2×#13094008C411yescharacteristic
28C2×#13094005C411yescharacteristic
29C2×#13094001C411yescharacteristic
30C2×#13093996C411yescharacteristic
31C2×C4×Dic94C2211yescharacteristic
32C2×C4×C22⋊D47C2211yescharacteristic
33C2×C4×C22⋊D47C2211yescharacteristic
34C2×#13093983C2211yescharacteristic
35C2×#13093981C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37#15689251C2218yescomplemented
38#15689247C2218yescomplemented
39#15689199C2218yescomplemented
40#15689194C2218yescomplemented
41D4×C47⋊C8C2218yescomplemented
42(C22⋊D47)⋊C8C2218yescomplemented
43(C22⋊D47)⋊C8C2218yescomplemented
44#15689183C2218yescomplemented
45#15689181C2218yescomplemented
46#15689177C2218yescomplemented
47C2×C4⋊(C47⋊C8)C2211yescharacteristic
48C2×Dic47⋊C8C2211yescharacteristic
49C2×Dic47⋊C8C2211yescharacteristic
50C2×Dic47⋊C8C2211yescharacteristic
51C2×Dic47⋊C8C2211yescharacteristic
52C2×C22⋊(C47⋊C8)C2211yescharacteristic
53C2×C22⋊(C47⋊C8)C2211yescharacteristic
54C2×(C2×D47)⋊C8C2211yescharacteristic
55C2×(C2×D47)⋊C8C2211yescharacteristic
56#15689081C2218yescomplemented
57#15689080C2218yescomplemented
58C2×#13093934C2211yescharacteristic
59C2×#13093934C2211yescharacteristic
60C2×#13093934C2211yescharacteristic
61C2×C4×C47⋊C8C2211yescharacteristic
62C2×C8×Dic47C2211yescharacteristic
63C2×C8×Dic47C2211yescharacteristic
64C2×C8×Dic47C2211yescharacteristic
65C2×C8×Dic47C2211yescharacteristic
66C2×C8×Dic47C2211yescharacteristic
67C2×C8×Dic47C2218yescomplemented
68C22×M16×C47C2211yescharacteristic
69C23×C8×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C47×#435C2218yescomplemented
72C2×C4⋊C8×C47C2211yescharacteristic
73C2×C22⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×#97×C47C2211yescharacteristic
76C22×Dic94C2×C411yescharacteristic
77C22×C22⋊D47C2×C411yescharacteristic
78C22×C22⋊D47C2×C411yescharacteristic
79C23×Dic47C2×C411yescharacteristic
80C23×Dic47C2×C411yescharacteristic
81C22×C4×D47C2311yescharacteristic
82C2×#10625324—24no—
83C2×#10625324C2314yes—
84C22×C47⋊C8—24no—
85C22×C47⋊C8—24no—
86C22×C47⋊C8C2311yescharacteristic
87C22×C47⋊C8C2314yes—
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90C22×C47⋊C8C2314yes—
91C22×C47⋊C8C2311yescharacteristic
92C2×C8×D47—24no—
93C2×C8×D47C2314yes—
94#13094019C2×C418yes—
95#13094017C2×C418yes—
96#13094014C2×C418yes—
97#13094010C2×C418yes—
98#13094008C2×C418yes—
99#13094005C2×C418yes—
100#13094001C2×C418yes—
101#13093996C2×C418yes—
102C4×Dic94C2×C414yes—
103C4×Dic94C2314yes—
104C4×C22⋊D47C2×C414yes—
105C4×C22⋊D47C2×C414yes—
106C4×C22⋊D47C2314yes—
107C4×C22⋊D47C2314yes—
108#13093983C2×C414yes—
109#13093983C2314yes—
110#13093981C2×C414yes—
111#13093981C2314yes—
112C2×C4⋊Dic47C2×C411yescharacteristic
113C2×C4⋊Dic47C2×C411yescharacteristic
114C2×C4⋊Dic47C2×C411yescharacteristic
115C2×Dic47⋊C4C2×C411yescharacteristic
116C2×Dic47⋊C4C2×C411yescharacteristic
117C2×Dic47⋊C4C2×C411yescharacteristic
118C2×Dic47⋊C4C2×C411yescharacteristic
119C2×Dic47⋊C4C2×C411yescharacteristic
120C2×Dic47⋊C4C2×C411yescharacteristic
121C2×C22⋊Dic47C2×C411yescharacteristic
122C2×C22⋊Dic47C2×C411yescharacteristic
123C2×C22⋊Dic47C2×C411yescharacteristic
124C2×C22⋊Dic47C2×C411yescharacteristic
125C2×(C2×D47)⋊C4C2×C411yescharacteristic
126C2×(C2×D47)⋊C4C2×C411yescharacteristic
127C2×(C2×D47)⋊C4C2×C411yescharacteristic
128C2×(C2×D47)⋊C4C2×C411yescharacteristic
129C2×C4×Dic47C2×C411yescharacteristic
130C2×C4×Dic47C2×C411yescharacteristic
131C2×C4×Dic47C2×C414yes—
132C2×C4×Dic47C2311yescharacteristic
133C2×C4×Dic47C2311yescharacteristic
134C2×C4×Dic47C2314yes—
135C2×C4×Dic47C2311yescharacteristic
136C4⋊(C47⋊C8)C2314yes—
137Dic47⋊C8C2314yes—
138Dic47⋊C8C2314yes—
139Dic47⋊C8C2314yes—
140Dic47⋊C8C2314yes—
141C22⋊(C47⋊C8)C2314yes—
142C22⋊(C47⋊C8)C2314yes—
143(C2×D47)⋊C8C2314yes—
144(C2×D47)⋊C8C2314yes—
145#13093934C2314yes—
146#13093934C2314yes—
147#13093934C2314yes—
148C4×C47⋊C8C2314yes—
149C8×Dic47C2314yes—
150C8×Dic47C2314yes—
151C8×Dic47C2314yes—
152C8×Dic47C2314yes—
153C8×Dic47C2314yes—
154C22×D4×C47C2×C411yescharacteristic
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C2×M16×C47—24no—
158C2×M16×C47C2314yes—
159C22×C8×C47—24no—
160C22×C8×C47C2311yescharacteristic
161C22×C8×C47C2311yescharacteristic
162C22×C8×C47C2314yes—
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C4×D4×C47C2×C414yes—
166C4×D4×C47C2314yes—
167C2×C4⋊C4×C47C2×C411yescharacteristic
168C2×C22⋊C4×C47C2×C411yescharacteristic
169C2×C22⋊C4×C47C2×C411yescharacteristic
170C2×C42×C47C2311yescharacteristic
171C4⋊C8×C47C2314yes—
172C22⋊C8×C47C2314yes—
173C22⋊C8×C47C2314yes—
174#97×C47C2314yes—
175C24×C47C22×C411yescharacteristic
176C24×C47C22×C411yescharacteristic
177C23×D47C22×C411yescharacteristic
178C2×D4×C47—24no—
179C2×D4×C47C22×C414yes—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47C22×C411yescharacteristic
185C22×C4×C47C22×C411yescharacteristic
186C22×C4×C47C22×C411yescharacteristic
187C22×C4×C47C22×C411yescharacteristic
188C22×C4×C47C22×C412yes—
189C22×C4×C47C22×C412yes—
190C22×C4×C47C2412yes—
191C22×C4×C47C2412yes—
192C22×C4×C47C2411yescharacteristic
193C2×C22⋊D47—24no—
194C2×C22⋊D47—24no—
195C2×C22⋊D47C22×C414yes—
196C2×C22⋊D47C22×C414yes—
197C22×Dic47—24no—
198C22×Dic47—24no—
199C22×Dic47C22×C411yescharacteristic
200C22×Dic47C22×C411yescharacteristic
201C22×Dic47C22×C411yescharacteristic
202C22×Dic47C22×C414yes—
203C22×Dic47C22×C414yes—
204C22×Dic47C22×C411yescharacteristic
205C22×Dic47C22×C411yescharacteristic
206C22×Dic47C22×C411yescharacteristic
207C22×Dic47C22×C411yescharacteristic
208C2×C4×D47—22no—
209C2×C4×D47—22no—
210C2×C4×D47C22×C412yes—
211C2×C4×D47C2412yes—
212C2×Dic94—24no—
213C2×Dic94C22×C414yes—
214M16×C47—28no—
215C2×C8×C47—22no—
216C2×C8×C47—22no—
217C2×C8×C47—22no—
218C2×C8×C47—28no—
219C2×C8×C47#4114yes—
220C2×C8×C47C2412yes—
221C2×C8×C47C2412yes—
222C2×C8×C47C2412yes—
223C2×C8×C47C2412yes—
224C4⋊C4×C47C22×C414yes—
225C22⋊C4×C47C22×C414yes—
226C22⋊C4×C47C22×C414yes—
227C42×C47C22×C412yes—
228C42×C47C2412yes—
229C22⋊Dic47C22×C414yes—
230C22⋊Dic47C22×C414yes—
231C22⋊Dic47C22×C414yes—
232C22⋊Dic47C22×C414yes—
233(C2×D47)⋊C4C22×C414yes—
234(C2×D47)⋊C4C22×C414yes—
235(C2×D47)⋊C4C22×C414yes—
236(C2×D47)⋊C4C22×C414yes—
237C4⋊Dic47C22×C414yes—
238C4⋊Dic47C22×C414yes—
239C4⋊Dic47C22×C414yes—
240Dic47⋊C4C22×C414yes—
241Dic47⋊C4C22×C414yes—
242Dic47⋊C4C22×C414yes—
243Dic47⋊C4C22×C414yes—
244Dic47⋊C4C22×C414yes—
245Dic47⋊C4C22×C414yes—
246C4×Dic47C22×C412yes—
247C4×Dic47C22×C412yes—
248C4×Dic47C22×C414yes—
249C4×Dic47C22×C414yes—
250C4×Dic47C22×C412yes—
251C4×Dic47C2412yes—
252C4×Dic47C2412yes—
253C4×Dic47C2412yes—
254C2×C47⋊C8—22no—
255C2×C47⋊C8—22no—
256C2×C47⋊C8—22no—
257C2×C47⋊C8—28no—
258C2×C47⋊C8—28no—
259C2×C47⋊C8#4114yes—
260C2×C47⋊C8C2412yes—
261C2×C47⋊C8C2412yes—
262C2×C47⋊C8C2412yes—
263C2×C47⋊C8C2412yes—
264#10625324—28no—
265C8×D47—28no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47#13114yes—
272C23×C47C23×C412yes—
273C23×C47C23×C412yes—
274C23×C47C23×C411yescharacteristic
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47C23×C412yes—
279D4×C47—28no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—24no—
285C2×C4×C47—24no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47C23×C412yes—
291C2×C4×C47C23×C412yes—
292C2×C4×C47C23×C412yes—
293C2×C4×C47C23×C412yes—
294C2×C4×C47C23×C411yescharacteristic
295C2×C4×C47C2×#4112yes—
296C2×C4×C47C2×#4112yes—
297C2×C4×C47C2511yescharacteristic
298C22⋊D47—28no—
299C22⋊D47—28no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—28no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—28no—
308C2×Dic47#13114yes—
309C2×Dic47C23×C412yes—
310C2×Dic47C23×C412yes—
311C2×Dic47C23×C412yes—
312C2×Dic47C23×C412yes—
313C2×Dic47C23×C412yes—
314C2×Dic47C23×C412yes—
315C2×Dic47C23×C412yes—
316C4×D47—24no—
317C4×D47—22no—
318C4×D47—22no—
319Dic94—28no—
320C8×C47—22no—
321C8×C47—22no—
322C8×C47—22no—
323C8×C47C2×#4114yes—
324C47⋊C8—22no—
325C47⋊C8—22no—
326C47⋊C8—22no—
327C47⋊C8C2×#4114yes—
328C2×#2966—471nomaximal, Sylow
329C22×C47—22no—
330C22×C47—28no—
331C22×C47—22no—
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—44no—
336C22×C47C4×#4112yes—
337C22×C47C2×#13112yes—
338C22×C47C2×#13114yes—
339C22×C47C2×#13112yes—
340C22×C47C24×C411yescharacteristic
341C2×D47—22no—
342C2×D47—22no—
343C2×D47—22no—
344C2×D47—44no—
345C4×C47—22no—
346C4×C47—22no—
347C4×C47—22no—
348C4×C47—22no—
349C4×C47C4×#4112yes—
350C4×C47C22×#4111yescharacteristic
351C4×C47C22×#4111yescharacteristic
352Dic47—22no—
353Dic47—22no—
354Dic47—22no—
355Dic47—22no—
356Dic47—22no—
357Dic47—22no—
358Dic47C2×#13114yes—
359C2×#529—471no—
360#2966—4716no—
361C2×#446—471no—
362C2×C8×Q8—471no—
363C2×#436—471no—
364C2×#435—471no—
365C2×#435D4711yescharacteristic, complemented
366C2×C8×D4—471no—
367C2×C8×D4—471no—
368C2×C8×D4—471no—
369C2×#433—471no—
370C2×#433—471no—
371C2×#432—471no—
372C2×#405—471no—
373C2×#405—471no—
374C22×C4×C8—471no—
375C2×C47—24no—
376C2×C47—42no—
377C2×C47#296614yescomplemented
378C2×C47C2×C4×#4111yescharacteristic
379C2×C47C22×#13111yescharacteristic
380C2×C47C22×#13111yescharacteristic
381D47—42no—
382C22×M16—471no—
383C22×M16C2×D4711yescharacteristic
384C23×C8—471no—
385C23×C8—471no—
386C23×C8—471no—
387C23×C8C2×D4711yescharacteristic
388#529—478no—
389#529—478no—
390C2×#126—471no—
391C2×#126—471no—
392C2×#125—471no—
393C2×#124—471no—
394C2×#123—471no—
395C2×#123—471no—
396C2×C22⋊Q8—471no—
397C2×#121—471no—
398C2×C4×Q8—471no—
399C2×C4×D4—471no—
400C2×C4×D4—471no—
401C2×C4×D4C2×D4711yescharacteristic
402C2×#117—471no—
403C2×#117—471no—
404C22×C42—471no—
405#446—478no—
406C8×Q8—478no—
407#436—478no—
408#435—478no—
409#435C2×D4718yescomplemented
410C8×D4—478no—
411C8×D4—478no—
412C8×D4—478no—
413#433—478no—
414#433—478no—
415#432—478no—
416C2×C4⋊C8—471no—
417C2×C4⋊C8—471no—
418C2×C4⋊C8—471no—
419C2×C4⋊C8—471no—
420C2×C4⋊C8—471no—
421C2×C4⋊C8C2×D4711yescharacteristic
422C2×C22⋊C8—471no—
423C2×C22⋊C8—471no—
424C2×C22⋊C8—471no—
425C2×C22⋊C8—471no—
426C2×C22⋊C8C2×D4711yescharacteristic
427C2×C22⋊C8C2×D4711yescharacteristic
428#405—478no—
429#405—478no—
430C2×#97—471no—
431C2×#97—471no—
432C2×#97—471no—
433C2×#97C2×D4711yescharacteristic
434C2×C4×C8—471no—
435C2×C4×C8—471no—
436C2×C4×C8—471no—
437C2×C4×C8—471no—
438C2×C4×C8—478no—
439C2×C4×C8—471no—
440C2×C4×C8—471no—
441C47C2×#296611yescharacteristic, complemented, Sylow
442C22×Q8—471no—
443C22×D4—471no—
444C22×D4—471no—
445C22×D4C4×D4711yescharacteristic
446C23×C4—471no—
447C23×C4—471no—
448C23×C4—471no—
449C23×C4C22×D4711yescharacteristic
450C23×C4C22×D4711yescharacteristic
451C2×M16—24no—
452C2×M16—474no—
453C2×M16—944no—
454C2×M16C22×D4714yes—
455C22×C8—24no—
456C22×C8—471no—
457C22×C8—474no—
458C22×C8—474no—
459C22×C8—471no—
460C22×C8—471no—
461C22×C8—471no—
462C22×C8—474no—
463C22×C8—944no—
464C22×C8—944no—
465C22×C8—944no—
466C22×C8C22×D4714yes—
467C22×C8C22×D4711yescharacteristic
468C22×C8C22×D4711yescharacteristic
469C22×C8C22×D4711yescharacteristic
470C22×C8C22×D4711yescharacteristic
471#126—478no—
472#126—478no—
473#125—478no—
474#124—478no—
475#123—478no—
476#123—478no—
477C22⋊Q8—478no—
478#121—478no—
479C4×Q8—474no—
480C4×Q8—474no—
481C4×D4—474no—
482C4×D4—474no—
483C4×D4—474no—
484C4×D4—474no—
485C4×D4C4×D4714yes—
486C4×D4C22×D4714yes—
487#117—474no—
488#117—474no—
489#117—474no—
490#117—474no—
491C2×C4⋊C4—471no—
492C2×C4⋊C4—471no—
493C2×C4⋊C4—471no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4C4×D4711yescharacteristic
501C2×C22⋊C4—471no—
502C2×C22⋊C4—471no—
503C2×C22⋊C4—471no—
504C2×C22⋊C4—471no—
505C2×C22⋊C4—471no—
506C2×C22⋊C4—471no—
507C2×C22⋊C4—471no—
508C2×C22⋊C4—471no—
509C2×C22⋊C4C4×D4711yescharacteristic
510C2×C22⋊C4C4×D4711yescharacteristic
511C2×C42—471no—
512C2×C42—471no—
513C2×C42—474no—
514C2×C42—474no—
515C2×C42—471no—
516C2×C42—471no—
517C2×C42—471no—
518C2×C42C22×D4711yescharacteristic
519C4⋊C8—474no—
520C4⋊C8—474no—
521C4⋊C8—474no—
522C4⋊C8—474no—
523C4⋊C8—474no—
524C4⋊C8C22×D4714yes—
525C22⋊C8—474no—
526C22⋊C8—474no—
527C22⋊C8—474no—
528C22⋊C8—474no—
529C22⋊C8C22×D4714yes—
530C22⋊C8C22×D4714yes—
531#97—474no—
532#97—474no—
533#97—474no—
534#97C22×D4714yes—
535C4×C8—474no—
536C4×C8—474no—
537C4×C8—474no—
538C4×C8—474no—
539C4×C8—474no—
540C4×C8—474no—
541C24—471no—
542C24C2×C4×D4711yescharacteristic
543C24C2×C4×D4711yescharacteristic
544C2×Q8—474no—
545C2×Q8—944no—
546C2×D4—24no—
547C2×D4—474no—
548C2×D4—474no—
549C2×D4—944no—
550C2×D4—944no—
551C2×D4C2×C4×D4714yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—471no—
557C22×C4—471no—
558C22×C4—471no—
559C22×C4—471no—
560C22×C4—474no—
561C22×C4—474no—
562C22×C4—471no—
563C22×C4—471no—
564C22×C4—471no—
565C22×C4—472no—
566C22×C4—472no—
567C22×C4—944no—
568C22×C4—944no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4C2×C4×D4711yescharacteristic
572C22×C4C2×C4×D4712yes—
573C22×C4C2×C4×D4711yescharacteristic
574C22×C4C2×C4×D4711yescharacteristic
575C22×C4C2×C4×D4711yescharacteristic
576C22×C4C2×C4×D4712yes—
577C22×C4C23×D4712yes—
578C22×C4C23×D4712yes—
579C22×C4C23×D4711yescharacteristic
580M16—28no—
581M16—948no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—28no—
586C2×C8—474no—
587C2×C8—472no—
588C2×C8—472no—
589C2×C8—472no—
590C2×C8—472no—
591C2×C8—948no—
592C2×C8—948no—
593C2×C8—948no—
594C2×C8—942no—
595C2×C8—942no—
596C2×C8—942no—
597C2×C8#1062535214yes—
598C2×C8C23×D4712yes—
599C2×C8C23×D4712yes—
600C2×C8C23×D4712yes—
601C2×C8C23×D4712yes—
602C4⋊C4—474no—
603C4⋊C4—474no—
604C4⋊C4—474no—
605C4⋊C4—474no—
606C4⋊C4—474no—
607C4⋊C4—474no—
608C4⋊C4—474no—
609C4⋊C4—474no—
610C4⋊C4—474no—
611C4⋊C4C2×C4×D4714yes—
612C22⋊C4—474no—
613C22⋊C4—474no—
614C22⋊C4—474no—
615C22⋊C4—474no—
616C22⋊C4—474no—
617C22⋊C4—474no—
618C22⋊C4—474no—
619C22⋊C4—474no—
620C22⋊C4C2×C4×D4714yes—
621C22⋊C4C2×C4×D4714yes—
622C42—472no—
623C42—472no—
624C42—474no—
625C42—474no—
626C42—472no—
627C42—472no—
628C42—472no—
629C42—472no—
630C42C2×C4×D4712yes—
631C42C23×D4712yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—472no—
638C23—942no—
639C23—942no—
640C23—942no—
641C23#1309403214yes—
642C23C22×C4×D4712yes—
643C23C22×C4×D4712yes—
644C23C22×C4×D4711yescharacteristic
645Q8—948no—
646D4—28no—
647D4—948no—
648D4—948no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—474no—
660C2×C4—472no—
661C2×C4—472no—
662C2×C4—472no—
663C2×C4—472no—
664C2×C4—472no—
665C2×C4—472no—
666C2×C4—472no—
667C2×C4—948no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—948no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—944no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4C22×C4×D4712yes—
679C2×C4C22×C4×D4712yes—
680C2×C4C22×C4×D4712yes—
681C2×C4C22×C4×D4712yes—
682C2×C4C22×C4×D4711yescharacteristic
683C2×C4#41×D4712yes—
684C2×C4C2×#1062535212yes—
685C2×C4C24×D4711yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—474no—
690C8—942no—
691C8—942no—
692C8—942no—
693C8C2×#1062535214yes—
694C22—22no—
695C22—22no—
696C22—28no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—942no—
702C22—942no—
703C22—942no—
704C22—1884no—
705C22C4×#1062535212yes—
706C22#131×D4712yes—
707C22C2×#1309403214yes—
708C22C2×#1309403212yes—
709C22C23×C4×D4711yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—474no—
715C4—942no—
716C4—942no—
717C4—942no—
718C4—942no—
719C4—942no—
720C4—942no—
721C4C4×#1062535212yes—
722C4C2×#41×D4711yescharacteristic
723C4C22×#1062535211yescharacteristic
724C2—24no—
725C2—42no—
726C2—1882no—
727C2#2025235814yesdirect product factor
728C2C2×C4×#1062535211yescharacteristic
729C2C2×#131×D4711yescharacteristic
730C2C22×#1309403211yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C23×C4
prime radicalC2×#13093996C4
cosocleC2×C4×C47C25
hypercenterC2×#435D47
hypocenterC47C2×#2966
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #20252358C2direct (N × H)
3. C2×#15689251C2semidirect
4. C2×#15689247C2semidirect
5. C2×#15689199C2semidirect
6. C2×#15689194C2semidirect
7. C2×D4×C47⋊C8C2semidirect
8. C2×(C22⋊D47)⋊C8C2semidirect
9. C2×(C22⋊D47)⋊C8C2semidirect
10. C2×#15689183C2semidirect
11. C2×#15689181C2semidirect
12. C2×#15689177C2semidirect
13. C2×#15689081C2semidirect
14. C2×#15689080C2semidirect
15. C22×C8×Dic47C2semidirect
16. C2×C47×#435C2semidirect
37. #15689251C22semidirect
38. #15689247C22semidirect
39. #15689199C22semidirect
40. #15689194C22semidirect
41. D4×C47⋊C8C22semidirect
42. (C22⋊D47)⋊C8C22semidirect
43. (C22⋊D47)⋊C8C22semidirect
44. #15689183C22semidirect
45. #15689181C22semidirect
46. #15689177C22semidirect
56. #15689081C22semidirect
57. #15689080C22semidirect
67. C2×C8×Dic47C22semidirect
71. C47×#435C22semidirect
365. C2×#435D47semidirect
377. C2×C47#2966semidirect
409. #435C2×D47semidirect
441. C47C2×#2966semidirect
727. C2#20252358direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896532
#202523582
C2×#156892512
C2×#156892472
C2×#156891992
C2×#156891942
C2×D4×C47⋊C82
C2×(C22⋊D47)⋊C82
C2×#156891832
C2×#156891812
C2×#156891772
C2×#156890812
C2×#156890802
C22×C8×Dic472
C2×C47×#4352
C2×#296647