Finite Group Databasebeta

← C2×#20252371 #27080739

Subgroups — C2×#20252371 #27080739

Order 12032.

1970 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×#15689651C211yesmaximal, characteristic
2#20252371C2116yesmaximal, direct product factor
3C2×#15689252C211yesmaximal, characteristic, complemented
4C2×#15689250C211yesmaximal, characteristic, complemented
5C2×#15689200C211yesmaximal, characteristic, complemented
6C2×#15689198C211yesmaximal, characteristic, complemented
7C2×#15689197C211yesmaximal, characteristic, complemented
8C2×#15689193C211yesmaximal, characteristic, complemented
9C2×#15689191C211yesmaximal, characteristic, complemented
10C2×#15689191C211yesmaximal, characteristic, complemented
11C2×#15689182C211yesmaximal, characteristic, complemented
12C2×#15689178C211yesmaximal, characteristic, complemented
13C2×#15689080C211yesmaximal, characteristic, complemented
14C2×#15689079C211yesmaximal, characteristic, complemented
15C2×C4×#10625324C211yesmaximal, characteristic, complemented
16C2×C47×#433C211yesmaximal, characteristic, complemented
17C22×#10625329C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×#10625324C2211yescharacteristic
21C23×C47⋊C8C2211yescharacteristic
22C22×C8×D47C2211yescharacteristic
23#15689651C418yes—
24#15689651C2218yes—
25C2×#13094019C411yescharacteristic
26C2×#13094017C411yescharacteristic
27C2×#13094014C411yescharacteristic
28C2×#13094010C411yescharacteristic
29C2×#13094009C411yescharacteristic
30C2×#13094006C411yescharacteristic
31C2×#13094002C411yescharacteristic
32C2×#13093997C411yescharacteristic
33C2×C4×Dic94C2211yescharacteristic
34C2×C4×D188C2211yescharacteristic
35C2×C4×C22⋊D47C2211yescharacteristic
36C2×C4×C22⋊D47C2211yescharacteristic
37C2×#13093981C2211yescharacteristic
38C2×C42×D47C2211yescharacteristic
39#15689252C2218yescomplemented
40#15689250C2218yescomplemented
41#15689200C2218yescomplemented
42#15689198C2218yescomplemented
43#15689197C2218yescomplemented
44#15689193C2218yescomplemented
45#15689191C2218yescomplemented
46#15689191C2218yescomplemented
47#15689182C2218yescomplemented
48#15689178C2218yescomplemented
49C2×Dic47⋊C8C2211yescharacteristic
50C2×Dic47⋊C8C2211yescharacteristic
51C2×Dic47⋊C8C2211yescharacteristic
52C2×Dic47⋊C8C2211yescharacteristic
53C2×(C2×D47)⋊C8C2211yescharacteristic
54C2×(C2×D47)⋊C8C2211yescharacteristic
55C2×(C2×D47)⋊C8C2211yescharacteristic
56C2×(C2×D47)⋊C8C2211yescharacteristic
57#15689080C2218yescomplemented
58#15689079C2218yescomplemented
59C4×#10625324C2218yescomplemented
60C2×#13093935C2211yescharacteristic
61C2×#13093935C2211yescharacteristic
62C2×#13093934C2211yescharacteristic
63C2×#13093934C2211yescharacteristic
64C2×#13093934C2211yescharacteristic
65C2×C4×C47⋊C8C2211yescharacteristic
66C2×C4×C47⋊C8C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
68C2×#117×C47C2211yescharacteristic
69C47×#433C2218yescomplemented
70C2×C4⋊C8×C47C2211yescharacteristic
71C2×C4⋊C8×C47C2211yescharacteristic
72C2×C22⋊C8×C47C2211yescharacteristic
73C2×C22⋊C8×C47C2211yescharacteristic
74C2×#97×C47C2211yescharacteristic
75C2×C4×C8×C47C2211yescharacteristic
76C22×Dic94C2×C411yescharacteristic
77C22×D188C2×C411yescharacteristic
78C22×C22⋊D47C2×C411yescharacteristic
79C22×C22⋊D47C2×C411yescharacteristic
80C22×C4×D47C2×C411yescharacteristic
81C22×C4×D47C2×C411yescharacteristic
82C22×C4×D47C2311yescharacteristic
83C22×C4×D47C2311yescharacteristic
84C2×#10625329—24no—
85C2×#10625329C2314yes—
86C2×#10625324—24no—
87C2×#10625324—24no—
88C2×#10625324—24no—
89C2×#10625324C2314yes—
90C2×#10625324C2314yes—
91C2×#10625324C2314yes—
92C22×C47⋊C8—24no—
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2314yes—
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2311yescharacteristic
98C2×C8×D47—24no—
99C2×C8×D47C2314yes—
100#13094019C2×C418yes—
101#13094017C2×C418yes—
102#13094014C2×C418yes—
103#13094010C2×C418yes—
104#13094009C2×C418yes—
105#13094006C2×C418yes—
106#13094002C2×C418yes—
107#13093997C2×C418yes—
108C4×Dic94C2×C414yes—
109C4×Dic94C2314yes—
110C4×D188C2×C414yes—
111C4×D188C2314yes—
112C4×C22⋊D47C2×C414yes—
113C4×C22⋊D47C2×C414yes—
114C4×C22⋊D47C2314yes—
115C4×C22⋊D47C2314yes—
116#13093981C2×C414yes—
117#13093981C2314yes—
118C2×C4⋊Dic47C2×C411yescharacteristic
119C2×C4⋊Dic47C2×C411yescharacteristic
120C2×Dic47⋊C4C2×C411yescharacteristic
121C2×Dic47⋊C4C2×C411yescharacteristic
122C2×Dic47⋊C4C2×C411yescharacteristic
123C2×Dic47⋊C4C2×C411yescharacteristic
124C2×Dic47⋊C4C2×C411yescharacteristic
125C2×Dic47⋊C4C2×C411yescharacteristic
126C2×C22⋊Dic47C2×C411yescharacteristic
127C2×C22⋊Dic47C2×C411yescharacteristic
128C2×(C2×D47)⋊C4C2×C411yescharacteristic
129C2×(C2×D47)⋊C4C2×C411yescharacteristic
130C2×(C2×D47)⋊C4C2×C411yescharacteristic
131C2×(C2×D47)⋊C4C2×C411yescharacteristic
132C2×(C2×D47)⋊C4C2×C411yescharacteristic
133C2×(C2×D47)⋊C4C2×C411yescharacteristic
134C2×C4×Dic47C2×C411yescharacteristic
135C2×C4×Dic47C2×C411yescharacteristic
136C2×C4×Dic47C2311yescharacteristic
137C2×C4×Dic47C2311yescharacteristic
138C42×D47C2×C414yes—
139C42×D47C2314yes—
140Dic47⋊C8C2314yes—
141Dic47⋊C8C2314yes—
142Dic47⋊C8C2314yes—
143Dic47⋊C8C2314yes—
144(C2×D47)⋊C8C2314yes—
145(C2×D47)⋊C8C2314yes—
146(C2×D47)⋊C8C2314yes—
147(C2×D47)⋊C8C2314yes—
148#13093935C2314yes—
149#13093935C2314yes—
150#13093934C2314yes—
151#13093934C2314yes—
152#13093934C2314yes—
153C4×C47⋊C8C2314yes—
154C4×C47⋊C8C2314yes—
155C8×Dic47C2314yes—
156C23×C4×C47C2311yescharacteristic
157C22×C8×C47C2311yescharacteristic
158C22×C8×C47C2311yescharacteristic
159C22×C8×C47C2311yescharacteristic
160C22×C8×C47C2311yescharacteristic
161#117×C47C2×C414yes—
162#117×C47C2314yes—
163C2×C4⋊C4×C47C2×C411yescharacteristic
164C2×C4⋊C4×C47C2×C411yescharacteristic
165C2×C22⋊C4×C47C2×C411yescharacteristic
166C2×C22⋊C4×C47C2×C411yescharacteristic
167C2×C42×C47C2311yescharacteristic
168C2×C42×C47C2311yescharacteristic
169C4⋊C8×C47C2314yes—
170C4⋊C8×C47C2314yes—
171C22⋊C8×C47C2314yes—
172C22⋊C8×C47C2314yes—
173#97×C47C2314yes—
174C4×C8×C47C2314yes—
175C24×C47C22×C411yescharacteristic
176C23×D47C22×C411yescharacteristic
177C23×D47C22×C411yescharacteristic
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47C22×C411yescharacteristic
181C22×C4×C47C22×C411yescharacteristic
182C22×C4×C47C22×C411yescharacteristic
183C22×C4×C47C22×C411yescharacteristic
184C22×C4×C47C22×C411yescharacteristic
185C22×C4×C47C22×C412yes—
186C22×C4×C47C2412yes—
187C22×C4×C47C2411yescharacteristic
188C2×C22⋊D47—42no—
189C2×C22⋊D47—42no—
190C2×C22⋊D47C22×C414yes—
191C2×C22⋊D47C22×C414yes—
192C22×Dic47C22×C411yescharacteristic
193C22×Dic47C22×C411yescharacteristic
194C22×Dic47C22×C411yescharacteristic
195C22×Dic47C22×C411yescharacteristic
196C22×Dic47C22×C411yescharacteristic
197C22×Dic47C22×C411yescharacteristic
198C2×D188—42no—
199C2×D188C22×C414yes—
200C2×C4×D47—22no—
201C2×C4×D47—22no—
202C2×C4×D47—22no—
203C2×C4×D47—22no—
204C2×C4×D47—42no—
205C2×C4×D47—42no—
206C2×C4×D47C22×C412yes—
207C2×C4×D47C22×C412yes—
208C2×C4×D47C22×C414yes—
209C2×C4×D47C22×C414yes—
210C2×C4×D47C2412yes—
211C2×C4×D47C2412yes—
212C2×Dic94—42no—
213C2×Dic94C22×C414yes—
214C2×C8×C47—22no—
215C2×C8×C47—22no—
216C2×C8×C47—22no—
217C2×C8×C47—22no—
218C2×C8×C47C2412yes—
219C2×C8×C47C2412yes—
220C2×C8×C47C2412yes—
221C2×C8×C47C2412yes—
222C4⋊C4×C47C22×C414yes—
223C4⋊C4×C47C22×C414yes—
224C22⋊C4×C47C22×C414yes—
225C22⋊C4×C47C22×C414yes—
226C42×C47C22×C412yes—
227C42×C47C22×C412yes—
228C42×C47C2412yes—
229C42×C47C2412yes—
230C22⋊Dic47C22×C414yes—
231C22⋊Dic47C22×C414yes—
232(C2×D47)⋊C4C22×C414yes—
233(C2×D47)⋊C4C22×C414yes—
234(C2×D47)⋊C4C22×C414yes—
235(C2×D47)⋊C4C22×C414yes—
236(C2×D47)⋊C4C22×C414yes—
237(C2×D47)⋊C4C22×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×C414yes—
248C4×Dic47C22×C414yes—
249C4×Dic47C22×C412yes—
250C4×Dic47C2412yes—
251C4×Dic47C2412yes—
252#10625329—28no—
253C2×C47⋊C8—22no—
254C2×C47⋊C8—22no—
255C2×C47⋊C8—28no—
256C2×C47⋊C8#4114yes—
257C2×C47⋊C8#4114yes—
258C2×C47⋊C8C2412yes—
259C2×C47⋊C8C2412yes—
260C2×C47⋊C8C2412yes—
261C2×C47⋊C8C2412yes—
262#10625324—28no—
263#10625324—28no—
264#10625324—28no—
265C8×D47—28no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47C23×C412yes—
270C23×C47C23×C411yescharacteristic
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D47C23×C412yes—
278C22×D47C23×C412yes—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—24no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47C23×C412yes—
288C2×C4×C47C23×C412yes—
289C2×C4×C47C23×C412yes—
290C2×C4×C47C23×C412yes—
291C2×C4×C47C23×C412yes—
292C2×C4×C47C23×C411yescharacteristic
293C2×C4×C47C2×#4112yes—
294C2×C4×C47C2×#4112yes—
295C2×C4×C47C2511yescharacteristic
296C22⋊D47—44no—
297C22⋊D47—44no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47C23×C412yes—
305C2×Dic47C23×C412yes—
306C2×Dic47C23×C412yes—
307C2×Dic47C23×C412yes—
308C2×Dic47C23×C412yes—
309C2×Dic47C23×C412yes—
310D188—44no—
311C4×D47—24no—
312C4×D47—24no—
313C4×D47—22no—
314C4×D47—22no—
315C4×D47—22no—
316C4×D47—22no—
317C4×D47—44no—
318C4×D47—44no—
319Dic94—44no—
320C8×C47—22no—
321C8×C47—22no—
322C8×C47—22no—
323C8×C47—22no—
324C47⋊C8—22no—
325C47⋊C8—22no—
326C47⋊C8C2×#4114yes—
327C47⋊C8C2×#4114yes—
328C2×#2967—471nomaximal, Sylow
329C22×C47—22no—
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—44no—
333C22×C47C4×#4112yes—
334C22×C47#56812yes—
335C22×C47#56812yes—
336C22×C47C24×C411yescharacteristic
337C2×D47—22no—
338C2×D47—22no—
339C2×D47—22no—
340C2×D47—22no—
341C2×D47—22no—
342C2×D47—22no—
343C2×D47—44no—
344C2×D47—44no—
345C4×C47—22no—
346C4×C47—22no—
347C4×C47—22no—
348C4×C47—22no—
349C4×C47—22no—
350C4×C47C4×#4112yes—
351C4×C47C22×#4111yescharacteristic
352C4×C47C22×#4111yescharacteristic
353Dic47—22no—
354Dic47—22no—
355Dic47—22no—
356Dic47—22no—
357Dic47—22no—
358Dic47—22no—
359C2×#529—471no—
360#2967—4716no—
361C2×#446—471no—
362C2×#446—471no—
363C2×#436—471no—
364C2×#436—471no—
365C2×#435—471no—
366C2×#435—471no—
367C2×#435—471no—
368C2×#435—471no—
369C2×#433—471no—
370C2×#433D4711yescharacteristic, complemented
371C2×#432—471no—
372C2×#405—471no—
373C2×#405—471no—
374C2×C4×M16—471no—
375C2×C47—42no—
376C2×C47#296714yescomplemented
377C2×C47C2×C4×#4111yescharacteristic
378C2×C47C2×#56811yescharacteristic
379C2×C47C2×#56811yescharacteristic
380D47—42no—
381D47—42no—
382C22×M16—471no—
383C22×M16—471no—
384C22×M16—471no—
385C22×M16—471no—
386C23×C8—471no—
387C23×C8—471no—
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×D4—471no—
402C2×#117—471no—
403C2×#117C2×D4711yescharacteristic
404C22×C42—471no—
405#446—478no—
406#446—478no—
407#436—478no—
408#436—478no—
409#435—478no—
410#435—478no—
411#435—478no—
412#435—478no—
413#433—478no—
414#433C2×D4718yescomplemented
415#432—478no—
416C2×C4⋊C8—471no—
417C2×C4⋊C8—471no—
418C2×C4⋊C8—471no—
419C2×C4⋊C8—471no—
420C2×C4⋊C8C2×D4711yescharacteristic
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—
430C4×M16—478no—
431C2×#97—471no—
432C2×#97—471no—
433C2×#97—471no—
434C2×#97—471no—
435C2×#97—471no—
436C2×#97C2×D4711yescharacteristic
437C2×C4×C8—471no—
438C2×C4×C8—471no—
439C2×C4×C8—471no—
440C2×C4×C8C2×D4711yescharacteristic
441C47C2×#296711yescharacteristic, complemented, Sylow
442C22×Q8—471no—
443C22×D4—471no—
444C22×D4—471no—
445C22×D4—471no—
446C23×C4—471no—
447C23×C4—471no—
448C23×C4—471no—
449C23×C4—471no—
450C23×C4C22×D4711yescharacteristic
451C2×M16—474no—
452C2×M16—474no—
453C2×M16—474no—
454C2×M16—474no—
455C2×M16—944no—
456C2×M16—944no—
457C2×M16—944no—
458C2×M16—944no—
459C22×C8—471no—
460C22×C8—471no—
461C22×C8—474no—
462C22×C8—471no—
463C22×C8—471no—
464C22×C8—474no—
465C22×C8—944no—
466C22×C8—944no—
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×D4—474no—
486C4×D4—474no—
487#117—474no—
488#117—474no—
489#117C4×D4714yes—
490#117C22×D4714yes—
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⋊C4C4×D4711yescharacteristic
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—471no—
514C2×C42—471no—
515C2×C42—474no—
516C2×C42—474no—
517C2×C42C22×D4711yescharacteristic
518C2×C42C22×D4711yescharacteristic
519C4⋊C8—474no—
520C4⋊C8—474no—
521C4⋊C8—474no—
522C4⋊C8—474no—
523C4⋊C8C22×D4714yes—
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#97—474no—
535#97—474no—
536#97C22×D4714yes—
537C4×C8—474no—
538C4×C8—474no—
539C4×C8—474no—
540C4×C8C22×D4714yes—
541C24—471no—
542C24—471no—
543C24C2×C4×D4711yescharacteristic
544C2×Q8—474no—
545C2×Q8—1882no—
546C2×D4—474no—
547C2×D4—474no—
548C2×D4—474no—
549C2×D4—1882no—
550C2×D4—1882no—
551C2×D4—1882no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—471no—
555C22×C4—471no—
556C22×C4—471no—
557C22×C4—471no—
558C22×C4—471no—
559C22×C4—471no—
560C22×C4—472no—
561C22×C4—472no—
562C22×C4—472no—
563C22×C4—472no—
564C22×C4—474no—
565C22×C4—474no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—1882no—
571C22×C4—1882no—
572C22×C4C2×C4×D4711yescharacteristic
573C22×C4C2×C4×D4711yescharacteristic
574C22×C4C2×C4×D4711yescharacteristic
575C22×C4C2×C4×D4711yescharacteristic
576C22×C4C2×C4×D4711yescharacteristic
577C22×C4C2×C4×D4712yes—
578C22×C4C23×D4712yes—
579C22×C4C23×D4711yescharacteristic
580M16—948no—
581M16—948no—
582M16—948no—
583M16—948no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—474no—
589C2×C8—474no—
590C2×C8—472no—
591C2×C8—472no—
592C2×C8—472no—
593C2×C8—472no—
594C2×C8—948no—
595C2×C8—948no—
596C2×C8—942no—
597C2×C8—942no—
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⋊C4C2×C4×D4714yes—
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—474no—
624C42—474no—
625C42—472no—
626C42—472no—
627C42—472no—
628C42C2×C4×D4712yes—
629C42C2×C4×D4712yes—
630C42C23×D4712yes—
631C42C23×D4712yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—472no—
636C23—472no—
637C23—942no—
638C23—942no—
639C23—942no—
640C23—942no—
641C23—942no—
642C23—942no—
643C23C22×C4×D4712yes—
644C23C22×C4×D4711yescharacteristic
645Q8—1884no—
646D4—1884no—
647D4—1884no—
648D4—1884no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—472no—
658C2×C4—472no—
659C2×C4—472no—
660C2×C4—472no—
661C2×C4—472no—
662C2×C4—472no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—944no—
670C2×C4—944no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—1884no—
676C2×C4—1884no—
677C2×C4C22×C4×D4712yes—
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×C4#41×D4712yes—
685C2×C4C24×D4711yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C8—474no—
691C8—474no—
692C8—942no—
693C8—942no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—942no—
699C22—942no—
700C22—942no—
701C22—942no—
702C22—942no—
703C22—942no—
704C22—1884no—
705C22—1884no—
706C22#1568959112yes—
707C22#1568988812yes—
708C22#1568988812yes—
709C22C23×C4×D4711yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—942no—
716C4—942no—
717C4—942no—
718C4—942no—
719C4—942no—
720C4—942no—
721C4#1568959112yes—
722C4C2×#41×D4711yescharacteristic
723C4C2×#41×D4711yescharacteristic
724C2—42no—
725C2—1882no—
726C2—1882no—
727C2#2025237114yesdirect product factor
728C2C2×#1568959111yescharacteristic
729C2C2×#1568988811yescharacteristic
730C2C2×#1568988811yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#433C2
socleC23×C47C23×C4
prime radicalC2×#13093997C4
cosocleC2×C4×C47C25
hypercenterC2×#433D47
hypocenterC47C2×#2967
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #20252371C2direct (N × H)
3. C2×#15689252C2semidirect
4. C2×#15689250C2semidirect
5. C2×#15689200C2semidirect
6. C2×#15689198C2semidirect
7. C2×#15689197C2semidirect
8. C2×#15689193C2semidirect
9. C2×#15689191C2semidirect
10. C2×#15689191C2semidirect
11. C2×#15689182C2semidirect
12. C2×#15689178C2semidirect
13. C2×#15689080C2semidirect
14. C2×#15689079C2semidirect
15. C2×C4×#10625324C2semidirect
16. C2×C47×#433C2semidirect
39. #15689252C22semidirect
40. #15689250C22semidirect
41. #15689200C22semidirect
42. #15689198C22semidirect
43. #15689197C22semidirect
44. #15689193C22semidirect
45. #15689191C22semidirect
46. #15689191C22semidirect
47. #15689182C22semidirect
48. #15689178C22semidirect
57. #15689080C22semidirect
58. #15689079C22semidirect
59. C4×#10625324C22semidirect
69. C47×#433C22semidirect
370. C2×#433D47semidirect
376. C2×C47#2967semidirect
414. #433C2×D47semidirect
441. C47C2×#2967semidirect
727. C2#20252371direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896512
#202523712
C2×#156892522
C2×#156892502
C2×#156892002
C2×#156891982
C2×#156891972
C2×#156891932
C2×#156891912
C2×#156891822
C2×#156891782
C2×#156890802
C2×#156890792
C2×C4×#106253242
C2×C47×#4332
C2×#296747