Finite Group Databasebeta

← C2×#20252508 #27081336

Subgroups — C2×#20252508 #27081336

Order 12032.

2210 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625352C211yesmaximal, characteristic
2#20252508C2116yesmaximal, direct product factor
3C2×#15689252C211yesmaximal, characteristic, complemented
4C2×#15689251C211yesmaximal, characteristic, complemented
5C2×#15689197C211yesmaximal, characteristic, complemented
6C2×#15689195C211yesmaximal, characteristic, complemented
7C2×#15689192C211yesmaximal, characteristic, complemented
8C2×C8×C22⋊D47C211yesmaximal, characteristic, complemented
9C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
10C2×#15689178C211yesmaximal, characteristic, complemented
11C2×#15689177C211yesmaximal, characteristic, complemented
12C2×#15689173C211yesmaximal, characteristic, complemented
13C2×#15689146C211yesmaximal, characteristic, complemented
14C22×Dic47⋊C8C211yesmaximal, characteristic, complemented
15C2×C4⋊C8×D47C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic, complemented
17C22×#10625352C411yescharacteristic
18C22×#10625329C2211yescharacteristic
19C23×C47⋊C8C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21C22×C8×D47C2211yescharacteristic
22C4×#10625352C418yes—
23C4×#10625352C2218yes—
24C2×C4×Dic94C2211yescharacteristic
25C2×#13093989C411yescharacteristic
26C2×D4×Dic47C411yescharacteristic
27C2×C4×C22⋊D47C2211yescharacteristic
28C2×C4×C22⋊D47C2211yescharacteristic
29C2×(C22⋊D47)⋊C4C411yescharacteristic
30C2×(C22⋊D47)⋊C4C411yescharacteristic
31C2×#13093982C411yescharacteristic
32C2×#13093980C411yescharacteristic
33C2×#13093980C411yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36C2×C42×D47C2211yescharacteristic
37#15689252C2218yescomplemented
38#15689251C2218yescomplemented
39#15689197C2218yescomplemented
40#15689195C2218yescomplemented
41#15689192C2218yescomplemented
42C8×C22⋊D47C2218yescomplemented
43(C22⋊D47)⋊C8C2218yescomplemented
44#15689178C2218yescomplemented
45#15689177C2218yescomplemented
46#15689173C2218yescomplemented
47#15689146C2218yescomplemented
48C2×C4⋊(C47⋊C8)C2211yescharacteristic
49C2×Dic47⋊C8C2211yescharacteristic
50C2×Dic47⋊C8C2211yescharacteristic
51C2×Dic47⋊C8C2211yescharacteristic
52C2×Dic47⋊C8C2211yescharacteristic
53C2×Dic47⋊C8C2211yescharacteristic
54C2×Dic47⋊C8C2211yescharacteristic
55C2×Dic47⋊C8C2211yescharacteristic
56C2×Dic47⋊C8C2211yescharacteristic
57C2×Dic47⋊C8C2218yescomplemented
58C4⋊C8×D47C2218yescomplemented
59C2×C22⋊(C47⋊C8)C2211yescharacteristic
60C2×C22⋊(C47⋊C8)C2211yescharacteristic
61C2×(C2×D47)⋊C8C2211yescharacteristic
62C2×(C2×D47)⋊C8C2211yescharacteristic
63C2×#13093935C2211yescharacteristic
64C2×#13093934C2211yescharacteristic
65C2×#13093934C2211yescharacteristic
66C2×C8×Dic47C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
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
76C2×#10625352—28no—
77C2×#10625352C2×C418yes—
78C22×Dic94C2×C411yescharacteristic
79C22×C22⋊D47C2×C411yescharacteristic
80C22×C22⋊D47C2×C411yescharacteristic
81C23×Dic47C2×C411yescharacteristic
82C23×Dic47C2×C411yescharacteristic
83C23×Dic47C2×C411yescharacteristic
84C23×Dic47C2×C411yescharacteristic
85C22×C4×D47C2×C411yescharacteristic
86C22×C4×D47C2×C411yescharacteristic
87C22×C4×D47C2311yescharacteristic
88C2×#10625329—42no—
89C2×#10625329C2314yes—
90C22×C47⋊C8—42no—
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2314yes—
96C2×C8×D47—42no—
97C2×C8×D47—42no—
98C2×C8×D47C2314yes—
99C2×C8×D47C2314yes—
100C4×Dic94C2×C414yes—
101C4×Dic94C2314yes—
102#13093989C2×C418yes—
103D4×Dic47C2×C418yes—
104C4×C22⋊D47C2×C414yes—
105C4×C22⋊D47C2×C414yes—
106C4×C22⋊D47C2314yes—
107C4×C22⋊D47C2314yes—
108(C22⋊D47)⋊C4C2×C418yes—
109(C22⋊D47)⋊C4C2×C418yes—
110#13093982C2×C418yes—
111#13093980C2×C418yes—
112#13093980C2×C418yes—
113C2×C4⋊Dic47C2×C411yescharacteristic
114C2×Dic47⋊C4C2×C411yescharacteristic
115C2×Dic47⋊C4C2×C411yescharacteristic
116C2×Dic47⋊C4C2×C411yescharacteristic
117C2×Dic47⋊C4C2×C411yescharacteristic
118C2×C22⋊Dic47C2×C411yescharacteristic
119C2×C22⋊Dic47C2×C411yescharacteristic
120C2×(C2×D47)⋊C4C2×C411yescharacteristic
121C2×(C2×D47)⋊C4C2×C411yescharacteristic
122C2×C4×Dic47C2×C411yescharacteristic
123C2×C4×Dic47C2×C411yescharacteristic
124C2×C4×Dic47C2×C411yescharacteristic
125C2×C4×Dic47C2×C411yescharacteristic
126C2×C4×Dic47C2×C411yescharacteristic
127C2×C4×Dic47C2×C411yescharacteristic
128C2×C4×Dic47C2×C414yes—
129C2×C4×Dic47C2×C414yes—
130C2×C4×Dic47C2311yescharacteristic
131C2×C4×Dic47C2311yescharacteristic
132C2×C4×Dic47C2311yescharacteristic
133C2×C4×Dic47C2314yes—
134C2×C4×Dic47C2314yes—
135C42×D47C2×C414yes—
136C42×D47C2314yes—
137C4⋊(C47⋊C8)C2314yes—
138Dic47⋊C8C2314yes—
139Dic47⋊C8C2314yes—
140Dic47⋊C8C2314yes—
141Dic47⋊C8C2314yes—
142Dic47⋊C8C2314yes—
143Dic47⋊C8C2314yes—
144Dic47⋊C8C2314yes—
145Dic47⋊C8C2314yes—
146C22⋊(C47⋊C8)C2314yes—
147C22⋊(C47⋊C8)C2314yes—
148(C2×D47)⋊C8C2314yes—
149(C2×D47)⋊C8C2314yes—
150#13093935C2314yes—
151#13093934C2314yes—
152#13093934C2314yes—
153C8×Dic47C2314yes—
154C8×Dic47C2314yes—
155C22×D4×C47C2×C411yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2311yescharacteristic
158C2×M16×C47—42no—
159C2×M16×C47C2314yes—
160C22×C8×C47—42no—
161C22×C8×C47C2311yescharacteristic
162C22×C8×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2314yes—
166C4×D4×C47C2×C414yes—
167C4×D4×C47C2314yes—
168C2×C4⋊C4×C47C2×C411yescharacteristic
169C2×C22⋊C4×C47C2×C411yescharacteristic
170C2×C22⋊C4×C47C2×C411yescharacteristic
171C2×C42×C47C2311yescharacteristic
172C4⋊C8×C47C2314yes—
173C22⋊C8×C47C2314yes—
174C22⋊C8×C47C2314yes—
175#97×C47C2314yes—
176C24×C47C22×C411yescharacteristic
177C24×C47C22×C411yescharacteristic
178C23×D47C22×C411yescharacteristic
179C2×D4×C47—24no—
180C2×D4×C47C22×C414yes—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47C22×C411yescharacteristic
186C22×C4×C47C22×C411yescharacteristic
187C22×C4×C47C22×C411yescharacteristic
188C22×C4×C47C22×C411yescharacteristic
189C22×C4×C47C22×C412yes—
190C22×C4×C47C22×C412yes—
191C22×C4×C47C2412yes—
192C22×C4×C47C2412yes—
193C22×C4×C47C2411yescharacteristic
194C2×C22⋊D47—24no—
195C2×C22⋊D47M1618yescomplemented
196C2×C22⋊D47C22×C414yes—
197C2×C22⋊D47C22×C414yes—
198C22×Dic47—24no—
199C22×Dic47—24no—
200C22×Dic47—24no—
201C22×Dic47—24no—
202C22×Dic47C22×C411yescharacteristic
203C22×Dic47C22×C411yescharacteristic
204C22×Dic47C22×C411yescharacteristic
205C22×Dic47C22×C411yescharacteristic
206C22×Dic47C22×C411yescharacteristic
207C22×Dic47C22×C414yes—
208C22×Dic47C22×C414yes—
209C22×Dic47C22×C414yes—
210C22×Dic47C22×C414yes—
211C22×Dic47C22×C411yescharacteristic
212C22×Dic47C22×C411yescharacteristic
213#10625352—232no—
214C2×C4×D47—24no—
215C2×C4×D47—22no—
216C2×C4×D47—22no—
217C2×C4×D47—24no—
218C2×C4×D47C22×C412yes—
219C2×C4×D47C22×C414yes—
220C2×C4×D47C22×C414yes—
221C2×C4×D47C2412yes—
222C2×Dic94—24no—
223C2×Dic94C22×C414yes—
224M16×C47—44no—
225C2×C8×C47—22no—
226C2×C8×C47—22no—
227C2×C8×C47—22no—
228C2×C8×C47—22no—
229C2×C8×C47—44no—
230C2×C8×C47C2412yes—
231C2×C8×C47C2412yes—
232C2×C8×C47C2412yes—
233C2×C8×C47C2412yes—
234C4⋊C4×C47C22×C414yes—
235C22⋊C4×C47C22×C414yes—
236C22⋊C4×C47C22×C414yes—
237C42×C47C22×C412yes—
238C42×C47C2412yes—
239C22⋊Dic47C22×C414yes—
240C22⋊Dic47C22×C414yes—
241(C2×D47)⋊C4C22×C414yes—
242(C2×D47)⋊C4C22×C414yes—
243C4⋊Dic47C22×C414yes—
244Dic47⋊C4C22×C414yes—
245Dic47⋊C4C22×C414yes—
246Dic47⋊C4C22×C414yes—
247Dic47⋊C4C22×C414yes—
248C4×Dic47C22×C412yes—
249C4×Dic47C22×C414yes—
250C4×Dic47C22×C414yes—
251C4×Dic47C22×C414yes—
252C4×Dic47C22×C414yes—
253C4×Dic47C22×C414yes—
254C4×Dic47C22×C414yes—
255C4×Dic47C22×C412yes—
256C4×Dic47C22×C412yes—
257C4×Dic47C2412yes—
258C4×Dic47C2412yes—
259C4×Dic47C2412yes—
260#10625329—44no—
261C2×C47⋊C8—22no—
262C2×C47⋊C8—22no—
263C2×C47⋊C8—22no—
264C2×C47⋊C8—22no—
265C2×C47⋊C8—44no—
266C2×C47⋊C8C2412yes—
267C2×C47⋊C8C2412yes—
268C2×C47⋊C8C2412yes—
269C2×C47⋊C8C2412yes—
270C8×D47—44no—
271C8×D47—44no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47C2×M1614yes—
278C23×C47C23×C412yes—
279C23×C47C23×C412yes—
280C23×C47C23×C411yescharacteristic
281C22×D47—22no—
282C22×D47—22no—
283C22×D47C2×M1614yes—
284C22×D47C23×C412yes—
285D4×C47—28no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—24no—
291C2×C4×C47—24no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47C23×C412yes—
297C2×C4×C47C23×C412yes—
298C2×C4×C47C23×C412yes—
299C2×C4×C47C23×C412yes—
300C2×C4×C47C23×C411yescharacteristic
301C2×C4×C47H(5,𝔽2)12yes—
302C2×C4×C472−1+412yes—
303C2×C4×C47C2511yescharacteristic
304C22⋊D47—28no—
305C22⋊D47C2×M16116yescomplemented
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—28no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—28no—
313C2×Dic47—28no—
314C2×Dic47—28no—
315C2×Dic47C2×M1614yes—
316C2×Dic47#13114yes—
317C2×Dic47C23×C412yes—
318C2×Dic47C23×C412yes—
319C2×Dic47C23×C412yes—
320C2×Dic47C23×C412yes—
321C2×Dic47C23×C412yes—
322C2×Dic47C23×C412yes—
323C2×Dic47C23×C412yes—
324C4×D47—28no—
325C4×D47—24no—
326C4×D47—22no—
327C4×D47—22no—
328C4×D47—28no—
329Dic94—28no—
330C8×C47—22no—
331C8×C47—22no—
332C8×C47—22no—
333C8×C47—22no—
334C47⋊C8—22no—
335C47⋊C8—22no—
336C47⋊C8—22no—
337C47⋊C8—22no—
338C2×#2990—471nomaximal, Sylow
339C22×C47—22no—
340C22×C47—28no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—44no—
346C22×C47#52012yes—
347C22×C47C22×M1614yes—
348C22×C47C22×M1612yes—
349C22×C47C2×#13112yes—
350C22×C47C24×C411yescharacteristic
351C2×D47—22no—
352C2×D47—28no—
353C2×D47—22no—
354C2×D47C22×M1614yes—
355C4×C47—22no—
356C4×C47—22no—
357C4×C47—22no—
358C4×C47—22no—
359C4×C47#52012yes—
360C4×C47C2×H(5,𝔽2)11yescharacteristic
361C4×C47C2×2−1+411yescharacteristic
362Dic47—22no—
363Dic47—22no—
364Dic47—22no—
365Dic47—22no—
366Dic47—22no—
367Dic47C22×M1614yes—
368Dic47C2×#13114yes—
369C2×C4×#41—471no—
370#2990—4716no—
371C2×#446—471no—
372C2×#446—471no—
373C2×#435—471no—
374C2×#435—471no—
375C2×#435—471no—
376C2×#435D4711yescharacteristic, complemented
377C2×C8×D4—471no—
378C2×C8×D4—471no—
379C2×#432—471no—
380C2×#432—471no—
381C2×#431—471no—
382C2×#423—471no—
383C22×C4⋊C8—471no—
384C22×C4⋊C8—471no—
385C2×C47—24no—
386C2×C47—42no—
387C2×C47#299014yescomplemented
388C2×C47C2×#52011yescharacteristic
389C2×C47C23×M1611yescharacteristic
390C2×C47C22×#13111yescharacteristic
391D47—24no—
392C22×#41—471no—
393C22×M16—471no—
394C22×M16C2×D4711yescharacteristic
395C23×C8—471no—
396C23×C8—471no—
397C23×C8—471no—
398C23×C8C2×D4711yescharacteristic
399C4×#41—478no—
400C4×#41—478no—
401C2×C4×Q8—471no—
402C2×C4×Q8—471no—
403C2×C4×D4—471no—
404C2×C4×D4—471no—
405C2×C4×D4—471no—
406C2×C4×D4—471no—
407C2×C4×D4—471no—
408C2×C4×D4C2×D4711yescharacteristic
409C2×#117—471no—
410C2×#117—471no—
411C2×#117—471no—
412C22×C42—471no—
413C22×C42—471no—
414C22×C42—471no—
415#446—478no—
416#446—478no—
417#435—478no—
418#435—478no—
419#435—478no—
420#435C2×D4718yescomplemented
421C8×D4—478no—
422C8×D4—478no—
423#432—478no—
424#432—478no—
425#431—478no—
426#423—478no—
427C2×C4⋊C8—471no—
428C2×C4⋊C8—471no—
429C2×C4⋊C8—471no—
430C2×C4⋊C8—471no—
431C2×C4⋊C8—471no—
432C2×C4⋊C8—478no—
433C2×C4⋊C8—471no—
434C2×C4⋊C8—471no—
435C2×C4⋊C8—471no—
436C2×C4⋊C8—471no—
437C2×C4⋊C8—478no—
438C2×C4⋊C8C2×D4711yescharacteristic
439C2×C22⋊C8—471no—
440C2×C22⋊C8—471no—
441C2×C22⋊C8—471no—
442C2×C22⋊C8—471no—
443C2×C22⋊C8C2×D4711yescharacteristic
444C2×C22⋊C8C2×D4711yescharacteristic
445C2×#97—471no—
446C2×#97—471no—
447C2×#97—471no—
448C2×#97C2×D4711yescharacteristic
449C2×C4×C8—471no—
450C2×C4×C8—471no—
451C47C2×#299011yescharacteristic, complemented, Sylow
452C2×#41—478no—
453C2×#41—948no—
454C22×Q8—471no—
455C22×D4—471no—
456C22×D4—471no—
457C22×D4C4×D4711yescharacteristic
458C23×C4—471no—
459C23×C4—471no—
460C23×C4—471no—
461C23×C4—471no—
462C23×C4—471no—
463C23×C4—471no—
464C23×C4—471no—
465C23×C4C22×D4711yescharacteristic
466C23×C4C22×D4711yescharacteristic
467C2×M16—42no—
468C2×M16—474no—
469C2×M16—1882no—
470C2×M16C22×D4714yes—
471C22×C8—42no—
472C22×C8—471no—
473C22×C8—471no—
474C22×C8—471no—
475C22×C8—471no—
476C22×C8—474no—
477C22×C8—474no—
478C22×C8—474no—
479C22×C8—1882no—
480C22×C8—1882no—
481C22×C8—1882no—
482C22×C8C22×D4711yescharacteristic
483C22×C8C22×D4711yescharacteristic
484C22×C8C22×D4711yescharacteristic
485C22×C8C22×D4711yescharacteristic
486C22×C8C22×D4714yes—
487C4×Q8—478no—
488C4×Q8—474no—
489C4×Q8—474no—
490C4×D4—478no—
491C4×D4—474no—
492C4×D4—474no—
493C4×D4—474no—
494C4×D4—474no—
495C4×D4—478no—
496C4×D4—478no—
497C4×D4C4×D4714yes—
498C4×D4C22×D4714yes—
499#117—478no—
500#117—478no—
501#117—478no—
502C2×C4⋊C4—471no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4C4×D4711yescharacteristic
508C2×C22⋊C4—471no—
509C2×C22⋊C4—471no—
510C2×C22⋊C4—471no—
511C2×C22⋊C4—471no—
512C2×C22⋊C4C4×D4711yescharacteristic
513C2×C22⋊C4C4×D4711yescharacteristic
514C2×C42—471no—
515C2×C42—471no—
516C2×C42—471no—
517C2×C42—471no—
518C2×C42—471no—
519C2×C42—471no—
520C2×C42—474no—
521C2×C42—474no—
522C2×C42—474no—
523C2×C42—474no—
524C2×C42—471no—
525C2×C42—471no—
526C2×C42—471no—
527C2×C42—474no—
528C2×C42—474no—
529C2×C42C22×D4711yescharacteristic
530C4⋊C8—474no—
531C4⋊C8—474no—
532C4⋊C8—474no—
533C4⋊C8—474no—
534C4⋊C8—474no—
535C4⋊C8—474no—
536C4⋊C8—474no—
537C4⋊C8—474no—
538C4⋊C8—474no—
539C4⋊C8C22×D4714yes—
540C22⋊C8—474no—
541C22⋊C8—474no—
542C22⋊C8—474no—
543C22⋊C8—474no—
544C22⋊C8C22×D4714yes—
545C22⋊C8C22×D4714yes—
546#97—474no—
547#97—474no—
548#97—474no—
549#97C22×D4714yes—
550C4×C8—474no—
551C4×C8—474no—
552C24—471no—
553C24C2×C4×D4711yescharacteristic
554C24C2×C4×D4711yescharacteristic
555#41—9432no—
556C2×Q8—474no—
557C2×Q8—944no—
558C2×D4—24no—
559C2×D4—478no—
560C2×D4—474no—
561C2×D4—474no—
562C2×D4—944no—
563C2×D4C2×C4×D4714yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—471no—
569C22×C4—471no—
570C22×C4—471no—
571C22×C4—471no—
572C22×C4—471no—
573C22×C4—471no—
574C22×C4—471no—
575C22×C4—474no—
576C22×C4—474no—
577C22×C4—474no—
578C22×C4—474no—
579C22×C4—474no—
580C22×C4—474no—
581C22×C4—472no—
582C22×C4—472no—
583C22×C4—944no—
584C22×C4—944no—
585C22×C4—944no—
586C22×C4—944no—
587C22×C4—944no—
588C22×C4—944no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4C2×C4×D4711yescharacteristic
592C22×C4C2×C4×D4711yescharacteristic
593C22×C4C2×C4×D4712yes—
594C22×C4C2×C4×D4712yes—
595C22×C4C2×C4×D4711yescharacteristic
596C22×C4C2×C4×D4711yescharacteristic
597C22×C4C23×D4712yes—
598C22×C4C23×D4712yes—
599C22×C4C23×D4711yescharacteristic
600M16—44no—
601M16—1884no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—44no—
607C2×C8—472no—
608C2×C8—472no—
609C2×C8—472no—
610C2×C8—472no—
611C2×C8—942no—
612C2×C8—942no—
613C2×C8—942no—
614C2×C8—942no—
615C2×C8—1884no—
616C2×C8—1884no—
617C2×C8—1884no—
618C2×C8C23×D4712yes—
619C2×C8C23×D4712yes—
620C2×C8C23×D4712yes—
621C2×C8C23×D4712yes—
622C4⋊C4—474no—
623C4⋊C4—474no—
624C4⋊C4—474no—
625C4⋊C4—474no—
626C4⋊C4—474no—
627C4⋊C4C2×C4×D4714yes—
628C22⋊C4—474no—
629C22⋊C4—474no—
630C22⋊C4—474no—
631C22⋊C4—474no—
632C22⋊C4C2×C4×D4714yes—
633C22⋊C4C2×C4×D4714yes—
634C42—472no—
635C42—474no—
636C42—474no—
637C42—474no—
638C42—474no—
639C42—474no—
640C42—474no—
641C42—472no—
642C42—472no—
643C42—472no—
644C42—472no—
645C42—472no—
646C42C2×C4×D4712yes—
647C42C23×D4712yes—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—474no—
654C23—472no—
655C23—942no—
656C23—942no—
657C23M16×D4714yes—
658C23C22×C4×D4712yes—
659C23C22×C4×D4712yes—
660C23C22×C4×D4711yescharacteristic
661Q8—948no—
662D4—28no—
663D4—4716no—
664D4—948no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—474no—
676C2×C4—474no—
677C2×C4—472no—
678C2×C4—472no—
679C2×C4—472no—
680C2×C4—472no—
681C2×C4—472no—
682C2×C4—472no—
683C2×C4—472no—
684C2×C4—948no—
685C2×C4—948no—
686C2×C4—948no—
687C2×C4—948no—
688C2×C4—948no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—948no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—944no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4C22×C4×D4712yes—
699C2×C4C22×C4×D4712yes—
700C2×C4C22×C4×D4712yes—
701C2×C4C22×C4×D4712yes—
702C2×C4C22×C4×D4711yescharacteristic
703C2×C4#1309406912yes—
704C2×C4#1309407112yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C8—942no—
711C8—942no—
712C8—942no—
713C8—942no—
714C22—22no—
715C22—22no—
716C22—28no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—44no—
721C22—474no—
722C22—942no—
723C22—942no—
724C22—948no—
725C22#1568960212yes—
726C22C2×M16×D4714yes—
727C22C2×M16×D4712yes—
728C22#131×D4712yes—
729C22C23×C4×D4711yescharacteristic
730C4—22no—
731C4—22no—
732C4—22no—
733C4—22no—
734C4—474no—
735C4—474no—
736C4—942no—
737C4—942no—
738C4—942no—
739C4—942no—
740C4—942no—
741C4#1568960212yes—
742C4C2×#1309406911yescharacteristic
743C4C2×#1309407111yescharacteristic
744C2—24no—
745C2—42no—
746C2—944no—
747C2#2025250814yesdirect product factor
748C2C2×#1568960211yescharacteristic
749C2C22×M16×D4711yescharacteristic
750C2C2×#131×D4711yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C23×C4
prime radicalC22×#10625352C4
cosocleC2×C4×C47C25
hypercenterC2×#435D47
hypocenterC47C2×#2990
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #20252508C2direct (N × H)
3. C2×#15689252C2semidirect
4. C2×#15689251C2semidirect
5. C2×#15689197C2semidirect
6. C2×#15689195C2semidirect
7. C2×#15689192C2semidirect
8. C2×C8×C22⋊D47C2semidirect
9. C2×(C22⋊D47)⋊C8C2semidirect
10. C2×#15689178C2semidirect
11. C2×#15689177C2semidirect
12. C2×#15689173C2semidirect
13. C2×#15689146C2semidirect
14. C22×Dic47⋊C8C2semidirect
15. C2×C4⋊C8×D47C2semidirect
16. C2×C47×#435C2semidirect
37. #15689252C22semidirect
38. #15689251C22semidirect
39. #15689197C22semidirect
40. #15689195C22semidirect
41. #15689192C22semidirect
42. C8×C22⋊D47C22semidirect
43. (C22⋊D47)⋊C8C22semidirect
44. #15689178C22semidirect
45. #15689177C22semidirect
46. #15689173C22semidirect
47. #15689146C22semidirect
57. C2×Dic47⋊C8C22semidirect
58. C4⋊C8×D47C22semidirect
71. C47×#435C22semidirect
195. C2×C22⋊D47M16semidirect
305. C22⋊D47C2×M16semidirect
376. C2×#435D47semidirect
387. C2×C47#2990semidirect
420. #435C2×D47semidirect
451. C47C2×#2990semidirect
747. C2#20252508direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#106253522
#202525082
C2×#156892522
C2×#156892512
C2×#156891972
C2×#156891952
C2×#156891922
C2×C8×C22⋊D472
C2×(C22⋊D47)⋊C82
C2×#156891782
C2×#156891772
C2×#156891732
C2×#156891462
C22×Dic47⋊C82
C2×C4⋊C8×D472
C2×C47×#4352
C2×#299047