Finite Group Databasebeta

← C2×#20252051 #27080038

Subgroups — C2×#20252051 #27080038

Order 12032.

2178 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689591C211yesmaximal, characteristic
2#20252051C2116yesmaximal, direct product factor
3C2×#15689184C211yesmaximal, characteristic, complemented
4C2×#15689183C211yesmaximal, characteristic, complemented
5C2×#15689183C211yesmaximal, characteristic, complemented
6C2×#15689178C211yesmaximal, characteristic, complemented
7C2×#15689177C211yesmaximal, characteristic, complemented
8C2×#15689174C211yesmaximal, characteristic, complemented
9C2×#15689173C211yesmaximal, characteristic, complemented
10C2×#15689145C211yesmaximal, characteristic, complemented
11C2×C4⋊C8×D47C211yesmaximal, characteristic, complemented
12C2×#15689088C211yesmaximal, characteristic
13C2×#15689088C211yesmaximal, characteristic
14C2×#15689080C211yesmaximal, characteristic, complemented
15C2×#15689077C211yesmaximal, characteristic, complemented
16C2×C47×#433C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21C22×C8×D47C2211yescharacteristic
22#15689591C418yes—
23#15689591C2218yes—
24C2×#13093989C411yescharacteristic
25C2×#13093989C411yescharacteristic
26C2×#13093986C411yescharacteristic
27C2×#13093986C411yescharacteristic
28C2×(C22⋊D47)⋊C4C411yescharacteristic
29C2×(C22⋊D47)⋊C4C411yescharacteristic
30C2×(C22⋊D47)⋊C4C411yescharacteristic
31C2×(C22⋊D47)⋊C4C411yescharacteristic
32C2×#13093981C2211yescharacteristic
33C2×#13093981C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35C2×C42×D47C2211yescharacteristic
36C2×C42×D47C2211yescharacteristic
37#15689184C2218yescomplemented
38#15689183C2218yescomplemented
39#15689183C2218yescomplemented
40#15689178C2218yescomplemented
41#15689177C2218yescomplemented
42#15689174C2218yescomplemented
43#15689173C2218yescomplemented
44#15689145C2218yescomplemented
45C2×C4⋊(C47⋊C8)C2211yescharacteristic
46C2×C4⋊(C47⋊C8)C2211yescharacteristic
47C2×Dic47⋊C8C2211yescharacteristic
48C2×Dic47⋊C8C2211yescharacteristic
49C2×Dic47⋊C8C2211yescharacteristic
50C2×Dic47⋊C8C2211yescharacteristic
51C4⋊C8×D47C2218yescomplemented
52#15689088C2218yes—
53#15689088C2218yes—
54C2×C22⋊(C47⋊C8)C2211yescharacteristic
55C2×C22⋊(C47⋊C8)C2211yescharacteristic
56C2×(C2×D47)⋊C8C2211yescharacteristic
57C2×(C2×D47)⋊C8C2211yescharacteristic
58C2×(C2×D47)⋊C8C2211yescharacteristic
59C2×(C2×D47)⋊C8C2211yescharacteristic
60#15689080C2218yescomplemented
61#15689077C2218yescomplemented
62C2×#13093935C2211yescharacteristic
63C2×#13093934C2211yescharacteristic
64C2×#13093934C2211yescharacteristic
65C2×C4×C47⋊C8C2211yescharacteristic
66C2×C8×Dic47C2211yescharacteristic
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
76C2×#10625350—24no—
77C2×#10625350—24no—
78C2×#10625350C2×C414yes—
79C2×#10625350C2314yes—
80C22×Dic94C2×C411yescharacteristic
81C22×D188C2×C411yescharacteristic
82C22×C22⋊D47C2×C411yescharacteristic
83C22×C22⋊D47C2×C411yescharacteristic
84C23×Dic47C2×C411yescharacteristic
85C23×Dic47C2×C411yescharacteristic
86C22×C4×D47C2×C411yescharacteristic
87C22×C4×D47C2×C411yescharacteristic
88C22×C4×D47C2×C411yescharacteristic
89C22×C4×D47C2×C411yescharacteristic
90C22×C4×D47C2311yescharacteristic
91C22×C4×D47C2311yescharacteristic
92C2×#10625324—24no—
93C2×#10625324—24no—
94C2×#10625324C2314yes—
95C2×#10625324C2314yes—
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2311yescharacteristic
98C22×C47⋊C8C2311yescharacteristic
99C22×C47⋊C8C2311yescharacteristic
100C2×C8×D47—24no—
101C2×C8×D47—24no—
102C2×C8×D47C2314yes—
103C2×C8×D47C2314yes—
104#13093989C2×C418yes—
105#13093989C2×C418yes—
106#13093986C2×C418yes—
107#13093986C2×C418yes—
108(C22⋊D47)⋊C4C2×C418yes—
109(C22⋊D47)⋊C4C2×C418yes—
110(C22⋊D47)⋊C4C2×C418yes—
111(C22⋊D47)⋊C4C2×C418yes—
112#13093981C2×C414yes—
113#13093981C2×C414yes—
114#13093981C2314yes—
115#13093981C2314yes—
116C2×Dic47⋊C4C2×C411yescharacteristic
117C2×Dic47⋊C4C2×C411yescharacteristic
118C2×Dic47⋊C4C2×C411yescharacteristic
119C2×Dic47⋊C4C2×C411yescharacteristic
120C2×(C2×D47)⋊C4C2×C411yescharacteristic
121C2×(C2×D47)⋊C4C2×C411yescharacteristic
122C2×(C2×D47)⋊C4C2×C411yescharacteristic
123C2×(C2×D47)⋊C4C2×C411yescharacteristic
124C2×C4×Dic47C2×C411yescharacteristic
125C2×C4×Dic47C2×C411yescharacteristic
126C2×C4×Dic47C2×C411yescharacteristic
127C2×C4×Dic47C2×C411yescharacteristic
128C2×C4×Dic47C2×C411yescharacteristic
129C2×C4×Dic47C2×C411yescharacteristic
130C2×C4×Dic47C2×C414yes—
131C2×C4×Dic47C2311yescharacteristic
132C2×C4×Dic47C2311yescharacteristic
133C2×C4×Dic47C2314yes—
134C42×D47C2×C414yes—
135C42×D47C2×C414yes—
136C42×D47C2314yes—
137C42×D47C2314yes—
138C4⋊(C47⋊C8)C2314yes—
139C4⋊(C47⋊C8)C2314yes—
140Dic47⋊C8C2314yes—
141Dic47⋊C8C2314yes—
142Dic47⋊C8C2314yes—
143Dic47⋊C8C2314yes—
144C22⋊(C47⋊C8)C2314yes—
145C22⋊(C47⋊C8)C2314yes—
146(C2×D47)⋊C8C2314yes—
147(C2×D47)⋊C8C2314yes—
148(C2×D47)⋊C8C2314yes—
149(C2×D47)⋊C8C2314yes—
150#13093935C2314yes—
151#13093934C2314yes—
152#13093934C2314yes—
153C4×C47⋊C8C2314yes—
154C8×Dic47C2314yes—
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—24no—
189C2×C22⋊D47—24no—
190C2×C22⋊D47C22×C414yes—
191C2×C22⋊D47C22×C414yes—
192C22×Dic47—24no—
193C22×Dic47—42no—
194C22×Dic47C22×C411yescharacteristic
195C22×Dic47C22×C411yescharacteristic
196C22×Dic47C22×C411yescharacteristic
197C22×Dic47C22×C411yescharacteristic
198C22×Dic47C22×C414yes—
199C22×Dic47C22×C414yes—
200C22×Dic47C22×C411yescharacteristic
201C22×Dic47C22×C411yescharacteristic
202#10625350—216no—
203#10625350—28no—
204#10625350—28no—
205C2×D188—24no—
206C2×D188C22×C414yes—
207C2×C4×D47—22no—
208C2×C4×D47—22no—
209C2×C4×D47—24no—
210C2×C4×D47—24no—
211C2×C4×D47—42no—
212C2×C4×D47—42no—
213C2×C4×D47C22×C412yes—
214C2×C4×D47C22×C414yes—
215C2×C4×D47C22×C414yes—
216C2×C4×D47C22×C414yes—
217C2×C4×D47C22×C414yes—
218C2×C4×D47C22×C412yes—
219C2×C4×D47#4114yes—
220C2×C4×D47#4114yes—
221C2×C4×D47C2412yes—
222C2×C4×D47C2412yes—
223C2×Dic94—24no—
224C2×Dic94C22×C414yes—
225C2×C8×C47—22no—
226C2×C8×C47—22no—
227C2×C8×C47—22no—
228C2×C8×C47—22no—
229C2×C8×C47C2412yes—
230C2×C8×C47C2412yes—
231C2×C8×C47C2412yes—
232C2×C8×C47C2412yes—
233C4⋊C4×C47C22×C414yes—
234C4⋊C4×C47C22×C414yes—
235C22⋊C4×C47C22×C414yes—
236C22⋊C4×C47C22×C414yes—
237C42×C47C22×C412yes—
238C42×C47C22×C412yes—
239C42×C47C2412yes—
240C42×C47C2412yes—
241(C2×D47)⋊C4C22×C414yes—
242(C2×D47)⋊C4C22×C414yes—
243(C2×D47)⋊C4C22×C414yes—
244(C2×D47)⋊C4C22×C414yes—
245Dic47⋊C4C22×C414yes—
246Dic47⋊C4C22×C414yes—
247Dic47⋊C4C22×C414yes—
248Dic47⋊C4C22×C414yes—
249C4×Dic47C22×C412yes—
250C4×Dic47C22×C414yes—
251C4×Dic47C22×C414yes—
252C4×Dic47C22×C414yes—
253C4×Dic47C22×C414yes—
254C4×Dic47C22×C412yes—
255C4×Dic47C22×C414yes—
256C4×Dic47C22×C414yes—
257C4×Dic47C2412yes—
258C4×Dic47C2412yes—
259C2×C47⋊C8—22no—
260C2×C47⋊C8—22no—
261C2×C47⋊C8—22no—
262C2×C47⋊C8—22no—
263C2×C47⋊C8C2412yes—
264C2×C47⋊C8C2412yes—
265C2×C47⋊C8C2412yes—
266C2×C47⋊C8C2412yes—
267#10625324—28no—
268#10625324—28no—
269C8×D47—28no—
270C8×D47—28no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47C23×C412yes—
275C23×C47C23×C411yescharacteristic
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47#11714yes—
282C22×D47C23×C412yes—
283C22×D47C23×C412yes—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—24no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47C23×C412yes—
293C2×C4×C47C23×C412yes—
294C2×C4×C47C23×C412yes—
295C2×C4×C47C23×C412yes—
296C2×C4×C47C23×C412yes—
297C2×C4×C47C23×C411yescharacteristic
298C2×C4×C47C2×#4112yes—
299C2×C4×C47C2×#4112yes—
300C2×C4×C47C2511yescharacteristic
301C22⋊D47—28no—
302C22⋊D47—28no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—28no—
308C2×Dic47—44no—
309C2×Dic47#11714yes—
310C2×Dic47#13114yes—
311C2×Dic47C23×C412yes—
312C2×Dic47C23×C412yes—
313C2×Dic47C23×C412yes—
314C2×Dic47C23×C412yes—
315C2×Dic47C23×C412yes—
316C2×Dic47C23×C412yes—
317D188—28no—
318C4×D47—24no—
319C4×D47—22no—
320C4×D47—22no—
321C4×D47—28no—
322C4×D47—28no—
323C4×D47—44no—
324C4×D47—44no—
325C4×D47#11718yes—
326C4×D47C2×#4114yes—
327C4×D47C2×#4114yes—
328Dic94—28no—
329C8×C47—22no—
330C8×C47—22no—
331C8×C47—22no—
332C8×C47—22no—
333C47⋊C8—22no—
334C47⋊C8—22no—
335C47⋊C8—22no—
336C47⋊C8—22no—
337C2×#2925—471nomaximal, Sylow
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—44no—
342C22×C47C2×#11712yes—
343C22×C47C2×#13112yes—
344C22×C47#56812yes—
345C22×C47C24×C411yescharacteristic
346C2×D47—28no—
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—22no—
351C2×D47—22no—
352C2×D47—44no—
353C2×D47C2×#11714yes—
354C4×C47—22no—
355C4×C47—22no—
356C4×C47—22no—
357C4×C47—22no—
358C4×C47—22no—
359C4×C47C2×#11712yes—
360C4×C47C22×#4111yescharacteristic
361C4×C47C22×#4111yescharacteristic
362Dic47—22no—
363Dic47—22no—
364Dic47—22no—
365Dic47—22no—
366Dic47C2×#11714yes—
367Dic47C2×#13114yes—
368C2×C4×#41—471no—
369#2925—4716no—
370C2×#433—471no—
371C2×#433—471no—
372C2×#433—471no—
373C2×#433D4711yescharacteristic, complemented
374C2×#432—471no—
375C2×#432—471no—
376C2×#431—471no—
377C2×#431—471no—
378C2×#423—471no—
379C22×C4⋊C8—471no—
380C2×#408—471no—
381C2×#408—471no—
382C2×#405—471no—
383C2×#405—471no—
384C2×C47—42no—
385C2×C47#292514yescomplemented
386C2×C47C22×#11711yescharacteristic
387C2×C47C22×#13111yescharacteristic
388C2×C47C2×#56811yescharacteristic
389D47—24no—
390D47—42no—
391C22×#41—471no—
392C22×M16—471no—
393C22×M16—471no—
394C23×C8—471no—
395C23×C8—471no—
396C4×#41—478no—
397C4×#41—478no—
398C2×C4×Q8—471no—
399C2×C4×Q8—471no—
400C2×C4×D4—471no—
401C2×C4×D4—471no—
402C2×C4×D4—471no—
403C2×C4×D4—471no—
404C2×C4×D4—471no—
405C2×C4×D4—471no—
406C2×#117—471no—
407C2×#117—471no—
408C2×#117C2×D4711yescharacteristic
409C22×C42—471no—
410C22×C42—471no—
411C22×C42—471no—
412#433—478no—
413#433—478no—
414#433—478no—
415#433C2×D4718yescomplemented
416#432—478no—
417#432—478no—
418#431—478no—
419#431—478no—
420#423—478no—
421C2×C4⋊C8—471no—
422C2×C4⋊C8—471no—
423C2×C4⋊C8—471no—
424C2×C4⋊C8—471no—
425C2×C4⋊C8—471no—
426C2×C4⋊C8—471no—
427C2×C4⋊C8—478no—
428C2×C4⋊C8C2×D4711yescharacteristic
429C2×C4⋊C8C2×D4711yescharacteristic
430#408—478no—
431#408—478no—
432C2×C22⋊C8—471no—
433C2×C22⋊C8—471no—
434C2×C22⋊C8—471no—
435C2×C22⋊C8—471no—
436C2×C22⋊C8—471no—
437C2×C22⋊C8—471no—
438C2×C22⋊C8C2×D4711yescharacteristic
439C2×C22⋊C8C2×D4711yescharacteristic
440#405—478no—
441#405—478no—
442C2×#97—471no—
443C2×#97—471no—
444C2×#97—471no—
445C2×#97C2×D4711yescharacteristic
446C2×C4×C8—471no—
447C2×C4×C8—471no—
448C2×C4×C8—471no—
449C2×C4×C8C2×D4711yescharacteristic
450C47C2×#292511yescharacteristic, complemented, Sylow
451C2×#41—474no—
452C2×#41—474no—
453C2×#41—944no—
454C2×#41—944no—
455C22×Q8—471no—
456C22×D4—471no—
457C22×D4—471no—
458C22×D4—471no—
459C23×C4—471no—
460C23×C4—471no—
461C23×C4—471no—
462C23×C4—471no—
463C23×C4—471no—
464C23×C4—471no—
465C23×C4—471no—
466C23×C4—471no—
467C23×C4C22×D4711yescharacteristic
468C2×M16—474no—
469C2×M16—474no—
470C2×M16—944no—
471C2×M16—944no—
472C22×C8—471no—
473C22×C8—471no—
474C22×C8—471no—
475C22×C8—471no—
476C22×C8—474no—
477C22×C8—474no—
478C22×C8—944no—
479C22×C8—944no—
480C22×C8C22×D4711yescharacteristic
481C22×C8C22×D4711yescharacteristic
482C22×C8C22×D4711yescharacteristic
483C22×C8C22×D4711yescharacteristic
484C4×Q8—478no—
485C4×Q8—478no—
486C4×D4—478no—
487C4×D4—478no—
488C4×D4—478no—
489C4×D4—478no—
490C4×D4—478no—
491C4×D4—478no—
492#117—474no—
493#117—474no—
494#117—474no—
495#117—474no—
496#117C4×D4714yes—
497#117C22×D4714yes—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4C4×D4711yescharacteristic
503C2×C4⋊C4C4×D4711yescharacteristic
504C2×C22⋊C4—471no—
505C2×C22⋊C4—471no—
506C2×C22⋊C4—471no—
507C2×C22⋊C4—471no—
508C2×C22⋊C4C4×D4711yescharacteristic
509C2×C22⋊C4C4×D4711yescharacteristic
510C2×C42—471no—
511C2×C42—471no—
512C2×C42—471no—
513C2×C42—471no—
514C2×C42—471no—
515C2×C42—471no—
516C2×C42—474no—
517C2×C42—474no—
518C2×C42—471no—
519C2×C42—471no—
520C2×C42—474no—
521C2×C42—474no—
522C2×C42—474no—
523C2×C42—474no—
524C2×C42C22×D4711yescharacteristic
525C2×C42C22×D4711yescharacteristic
526C4⋊C8—474no—
527C4⋊C8—474no—
528C4⋊C8—474no—
529C4⋊C8—474no—
530C4⋊C8—474no—
531C4⋊C8—474no—
532C4⋊C8C22×D4714yes—
533C4⋊C8C22×D4714yes—
534C22⋊C8—474no—
535C22⋊C8—474no—
536C22⋊C8—474no—
537C22⋊C8—474no—
538C22⋊C8—474no—
539C22⋊C8—474no—
540C22⋊C8C22×D4714yes—
541C22⋊C8C22×D4714yes—
542#97—474no—
543#97—474no—
544#97—474no—
545#97C22×D4714yes—
546C4×C8—474no—
547C4×C8—474no—
548C4×C8—474no—
549C4×C8C22×D4714yes—
550C24—471no—
551C24—471no—
552C24C2×C4×D4711yescharacteristic
553#41—9416no—
554#41—948no—
555#41—948no—
556C2×Q8—474no—
557C2×Q8—944no—
558C2×D4—474no—
559C2×D4—474no—
560C2×D4—474no—
561C2×D4—944no—
562C2×D4—944no—
563C2×D4—944no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—471no—
567C22×C4—471no—
568C22×C4—472no—
569C22×C4—474no—
570C22×C4—474no—
571C22×C4—472no—
572C22×C4—471no—
573C22×C4—471no—
574C22×C4—471no—
575C22×C4—471no—
576C22×C4—474no—
577C22×C4—474no—
578C22×C4—472no—
579C22×C4—474no—
580C22×C4—474no—
581C22×C4—472no—
582C22×C4—474no—
583C22×C4—474no—
584C22×C4—944no—
585C22×C4—944no—
586C22×C4—944no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—1882no—
590C22×C4—1882no—
591C22×C4—1882no—
592C22×C4C2×C4×D4711yescharacteristic
593C22×C4C2×C4×D4712yes—
594C22×C4C2×C4×D4711yescharacteristic
595C22×C4C2×C4×D4711yescharacteristic
596C22×C4C2×C4×D4711yescharacteristic
597C22×C4C2×C4×D4711yescharacteristic
598C22×C4C23×D4712yes—
599C22×C4C23×D4711yescharacteristic
600M16—948no—
601M16—948no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—472no—
607C2×C8—472no—
608C2×C8—472no—
609C2×C8—472no—
610C2×C8—948no—
611C2×C8—948no—
612C2×C8—942no—
613C2×C8—942no—
614C2×C8—942no—
615C2×C8—942no—
616C2×C8C23×D4712yes—
617C2×C8C23×D4712yes—
618C2×C8C23×D4712yes—
619C2×C8C23×D4712yes—
620C4⋊C4—474no—
621C4⋊C4—474no—
622C4⋊C4—474no—
623C4⋊C4—474no—
624C4⋊C4C2×C4×D4714yes—
625C4⋊C4C2×C4×D4714yes—
626C22⋊C4—474no—
627C22⋊C4—474no—
628C22⋊C4—474no—
629C22⋊C4—474no—
630C22⋊C4C2×C4×D4714yes—
631C22⋊C4C2×C4×D4714yes—
632C42—472no—
633C42—472no—
634C42—474no—
635C42—474no—
636C42—474no—
637C42—474no—
638C42—474no—
639C42—474no—
640C42—472no—
641C42—472no—
642C42C2×C4×D4712yes—
643C42C2×C4×D4712yes—
644C42C23×D4712yes—
645C42C23×D4712yes—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—474no—
650C23—472no—
651C23—472no—
652C23—942no—
653C23—942no—
654C23—942no—
655C23—942no—
656C23—942no—
657C23C22×C4×D4712yes—
658C23C22×C4×D4711yescharacteristic
659Q8—948no—
660D4—948no—
661D4—948no—
662D4—948no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—474no—
672C2×C4—474no—
673C2×C4—472no—
674C2×C4—472no—
675C2×C4—478no—
676C2×C4—474no—
677C2×C4—474no—
678C2×C4—472no—
679C2×C4—472no—
680C2×C4—472no—
681C2×C4—472no—
682C2×C4—948no—
683C2×C4—948no—
684C2×C4—948no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—944no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—1884no—
693C2×C4—1884no—
694C2×C4—1884no—
695C2×C4C22×C4×D4712yes—
696C2×C4C22×C4×D4712yes—
697C2×C4C22×C4×D4712yes—
698C2×C4C22×C4×D4712yes—
699C2×C4C22×C4×D4712yes—
700C2×C4C22×C4×D4711yescharacteristic
701C2×C4#41×D4712yes—
702C2×C4#41×D4712yes—
703C2×C4C24×D4711yescharacteristic
704C8—22no—
705C8—22no—
706C8—22no—
707C8—22no—
708C8—942no—
709C8—942no—
710C8—942no—
711C8—942no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—44no—
716C22—474no—
717C22—942no—
718C22—942no—
719C22—948no—
720C22—942no—
721C22—942no—
722C22—942no—
723C22—1884no—
724C22#117×D4712yes—
725C22#131×D4712yes—
726C22#1568988812yes—
727C22C23×C4×D4711yescharacteristic
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—22no—
733C4—474no—
734C4—474no—
735C4—942no—
736C4—942no—
737C4—942no—
738C4—942no—
739C4#117×D4712yes—
740C4C2×#41×D4711yescharacteristic
741C4C2×#41×D4711yescharacteristic
742C2—42no—
743C2—944no—
744C2—1882no—
745C2#2025205114yesdirect product factor
746C2C2×#117×D4711yescharacteristic
747C2C2×#131×D4711yescharacteristic
748C2C2×#1568988811yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#433C2
socleC23×C47C23×C4
prime radicalC22×#10625350C22
cosocleC2×C4×C47C25
hypercenterC2×#433D47
hypocenterC47C2×#2925
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #20252051C2direct (N × H)
3. C2×#15689184C2semidirect
4. C2×#15689183C2semidirect
5. C2×#15689183C2semidirect
6. C2×#15689178C2semidirect
7. C2×#15689177C2semidirect
8. C2×#15689174C2semidirect
9. C2×#15689173C2semidirect
10. C2×#15689145C2semidirect
11. C2×C4⋊C8×D47C2semidirect
14. C2×#15689080C2semidirect
15. C2×#15689077C2semidirect
16. C2×C47×#433C2semidirect
37. #15689184C22semidirect
38. #15689183C22semidirect
39. #15689183C22semidirect
40. #15689178C22semidirect
41. #15689177C22semidirect
42. #15689174C22semidirect
43. #15689173C22semidirect
44. #15689145C22semidirect
51. C4⋊C8×D47C22semidirect
60. #15689080C22semidirect
61. #15689077C22semidirect
69. C47×#433C22semidirect
373. C2×#433D47semidirect
385. C2×C47#2925semidirect
415. #433C2×D47semidirect
450. C47C2×#2925semidirect
745. C2#20252051direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156895912
#202520512
C2×#156891842
C2×#156891832
C2×#156891782
C2×#156891772
C2×#156891742
C2×#156891732
C2×#156891452
C2×C4⋊C8×D472
C2×#156890882
C2×#156890802
C2×#156890772
C2×C47×#4332
C2×#292547