Finite Group Databasebeta

← #26376741

Subgroups — #26376741

Order 12032.

2422 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D47C211yesmaximal, characteristic
2#20246475C212yesmaximal, complemented
3#20246474C212yesmaximal, complemented
4#20246445C212yesmaximal, complemented
5#20246442C212yesmaximal, complemented
6#20246264C212yesmaximal
7#20246261C212yesmaximal
8#20246222C212yesmaximal
9Q8×(C2×D47)⋊C4C212yesmaximal
10#20246135C212yesmaximal, complemented
11#20246132C212yesmaximal, complemented
12#20246003C212yesmaximal
13C4⋊Q8×Dic47C211yesmaximal, characteristic, complemented
14C4×#13094024C211yesmaximal, characteristic, complemented
15#20245955C211yesmaximal, characteristic, complemented
16#20245793C211yesmaximal, characteristic
17#20245742C212yesmaximal
18C4×#13093981C211yesmaximal, characteristic
19C4×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
20C22×Q8×D47C2212yes—
21C2×#13094024C2211yescharacteristic
22C2×#13094023C2212yes—
23C2×#13094023C2212yes—
24C2×#13094022C2212yes—
25C4⋊Q8×D47C4116yescomplemented
26C2×Q8×Dic47C2212yes—
27C2×C4×Dic94C2212yes—
28C2×#13093989C2212yes—
29C2×#13093982C2212yes—
30C2×#13093981C2211yescharacteristic
31C2×#13093981C2211yescharacteristic
32C2×C4⋊C4×D47C2212yes—
33C2×C4⋊C4×D47C2212yes—
34C2×C42×D47C2211yescharacteristic
35#15689030C2212yes—
36#15689029C2214yes—
37#15689029C2212yes—
38#15689028C2214yes—
39#15689028C2212yes—
40#15689027C2214yes—
41#15689027C2214yes—
42#15689022C2212yes—
43#15689022C2212yes—
44#15689021C2212yes—
45#15689021C2212yes—
46#15689020C2214yes—
47#15689019C2212yes—
48#15689019C2212yes—
49#15689018C2214yes—
50#15689010C2214yes—
51#15689007C2214yes—
52#15689005C2214yes—
53#15689004C2214yes—
54#15688993C2211yescharacteristic
55#15688988C2212yes—
56#15688982C2214yes—
57#15688980C2212yes—
58#15688980C2212yes—
59#15688980C2214yes—
60C4⋊C4×Dic47C2212yes—
61C4⋊C4×Dic47C2212yes—
62C4⋊C4×Dic47C2212yes—
63C4⋊C4×Dic47C2212yes—
64C4⋊C4×Dic47C2212yes—
65C4⋊C4×Dic47C2212yes—
66C4×Dic47⋊C4C2211yescharacteristic
67C4×Dic47⋊C4C2214yes—
68C4×Dic47⋊C4C2211yescharacteristic
69C4×Dic47⋊C4C2211yescharacteristic
70C4×Dic47⋊C4C2211yescharacteristic
71C4×C4⋊Dic47C2212yes—
72C4×C4⋊Dic47C2212yes—
73#15688974C2214yes—
74C4×(C2×D47)⋊C4C2211yescharacteristic
75C4×(C2×D47)⋊C4C2214yes—
76C4×(C2×D47)⋊C4C2211yescharacteristic
77C4×(C2×D47)⋊C4C2211yescharacteristic
78C4×(C2×D47)⋊C4C2211yescharacteristic
79#15688970C2214yes—
80#15688969C2211yescharacteristic
81#15688969C2211yescharacteristic
82C42×Dic47C2211yescharacteristic
83C2×C4⋊Q8×C47C2211yescharacteristic
84C2×C4×Q8×C47C2212yes—
85C47×#391C2212yes—
86C47×#389C2212yes—
87C47×#389C2212yes—
88C47×#384C2211yescharacteristic
89C4×C4⋊C4×C47C2212yes—
90C4×C4⋊C4×C47C2212yes—
91C43×C47C2211yescharacteristic
92C22×Dic94C2312yes—
93C22×Dic94C2314yes—
94C2×Q8×D47—44no—
95C2×Q8×D47—44no—
96C2×Q8×D47C2×C4116yes—
97C22×C4×D47C2311yescharacteristic
98C22×C4×D47C2311yescharacteristic
99C22×C4×D47C2314yes—
100C22×C4×D47C2311yescharacteristic
101#13094024C2×C418yes—
102#13094023C2×C4116yes—
103#13094023C2×C4116yes—
104#13094022C2×C4116yes—
105Q8×Dic47—44no—
106C4×Dic94—44no—
107#13093989—44no—
108#13093982—28no—
109#13093981—24no—
110#13093981Q818yescomplemented
111C2×C4⋊Dic47C2312yes—
112C2×C4⋊Dic47C2312yes—
113C2×C4⋊Dic47C2312yes—
114C2×C4⋊Dic47C2314yes—
115C2×C4⋊Dic47C2312yes—
116C2×C4⋊Dic47C2312yes—
117C2×Dic47⋊C4C2311yescharacteristic
118C2×Dic47⋊C4C2311yescharacteristic
119C2×Dic47⋊C4C2314yes—
120C2×Dic47⋊C4C2314yes—
121C2×Dic47⋊C4C2314yes—
122C2×Dic47⋊C4C2314yes—
123C2×Dic47⋊C4C2311yescharacteristic
124C2×Dic47⋊C4C2311yescharacteristic
125C4⋊C4×D47C2×C4116yes—
126C4⋊C4×D47C2×C4116yes—
127C2×(C2×D47)⋊C4C2314yes—
128C2×(C2×D47)⋊C4C2311yescharacteristic
129C2×(C2×D47)⋊C4C2311yescharacteristic
130C2×(C2×D47)⋊C4C2311yescharacteristic
131C2×(C2×D47)⋊C4C2311yescharacteristic
132C2×C4×Dic47C2311yescharacteristic
133C2×C4×Dic47C2311yescharacteristic
134C2×C4×Dic47C2311yescharacteristic
135C2×C4×Dic47C2311yescharacteristic
136C2×C4×Dic47C2311yescharacteristic
137C2×C4×Dic47C2314yes—
138C2×C4×Dic47C2314yes—
139C2×C4×Dic47C2314yes—
140C2×C4×Dic47C2314yes—
141C2×C4×Dic47C2311yescharacteristic
142C2×C4×Dic47C2311yescharacteristic
143C2×C4×Dic47C2311yescharacteristic
144C2×C4×Dic47C2311yescharacteristic
145C42×D47C2×C418yes—
146C47⋊#95C2311yescharacteristic
147C47⋊#95C2311yescharacteristic
148C47⋊#95C2311yescharacteristic
149C47⋊#95C2311yescharacteristic
150C47⋊#95C2311yescharacteristic
151C47⋊#95C2311yescharacteristic
152C47⋊#95C2311yescharacteristic
153C47⋊#95C2311yescharacteristic
154C47⋊#95C2314yes—
155C47⋊#95C2314yes—
156C47⋊#95C2314yes—
157C47⋊#95C2314yes—
158C47⋊#95C2314yes—
159C47⋊#95C2314yes—
160C47⋊#95C2314yes—
161C47⋊#95C2314yes—
162C22×Q8×C47C2312yes—
163C4⋊Q8×C47C2×C418yes—
164C4×Q8×C47—44no—
165C2×C4⋊C4×C47C2312yes—
166C2×C4⋊C4×C47C2312yes—
167C2×C4⋊C4×C47C2312yes—
168C2×C4⋊C4×C47C2314yes—
169C2×C4⋊C4×C47C2312yes—
170C2×C4⋊C4×C47C2312yes—
171C2×C42×C47C2311yescharacteristic
172C2×C42×C47C2311yescharacteristic
173C2×C42×C47C2311yescharacteristic
174C2×C42×C47C2311yescharacteristic
175C2×C42×C47C2311yescharacteristic
176C2×C42×C47C2314yes—
177C2×C42×C47C2311yescharacteristic
178C2×C42×C47C2311yescharacteristic
179#95×C47C2314yes—
180#95×C47C2314yes—
181C23×D47C2411yescharacteristic
182C2×Q8×C47—24no—
183C2×Q8×C47—24no—
184C2×Q8×C47C22×C418yes—
185C22×C4×C47C2411yescharacteristic
186C22×C4×C47C2411yescharacteristic
187C22×C4×C47C2414yes—
188C22×C4×C47C2414yes—
189C22×C4×C47C2411yescharacteristic
190C22×C4×C47C2411yescharacteristic
191C22×C4×C47C2411yescharacteristic
192C22×C4×C47C2411yescharacteristic
193C22×C4×C47C2411yescharacteristic
194C22×Dic47C2411yescharacteristic
195C22×Dic47C2411yescharacteristic
196C22×Dic47C2414yes—
197C22×Dic47C2411yescharacteristic
198C22×Dic47C2411yescharacteristic
199C22×Dic47C2414yes—
200C22×Dic47C2411yescharacteristic
201C22×Dic47C2411yescharacteristic
202C22×Dic47C2411yescharacteristic
203Q8×D47—432no—
204C2×C4×D47—22no—
205C2×C4×D47—22no—
206C2×C4×D47—22no—
207C2×C4×D47—22no—
208C2×C4×D47—44no—
209C2×C4×D47—44no—
210C2×C4×D47C22×C414yes—
211C2×C4×D47C22×C414yes—
212C2×C4×D47C22×C4116yes—
213C2×C4×D47C22×C414yes—
214C2×C4×D47C2×Q814yes—
215C2×C4×D47#4114yes—
216C2×Dic94—24no—
217C2×Dic94—24no—
218C2×Dic94—44no—
219C2×Dic94—44no—
220C2×Dic94C22×C418yes—
221C2×Dic94C22×C4116yes—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—24no—
224C4⋊C4×C47—24no—
225C4⋊C4×C47—44no—
226C4⋊C4×C47C22×C418yes—
227C4⋊C4×C47C22×C418yes—
228C42×C47—22no—
229C42×C47—22no—
230C42×C47—22no—
231C42×C47—22no—
232C42×C47—22no—
233C42×C47—44no—
234C42×C47C22×C414yes—
235C42×C47C2×Q814yescomplemented
236(C2×D47)⋊C4—22no—
237(C2×D47)⋊C4—22no—
238(C2×D47)⋊C4—28no—
239(C2×D47)⋊C4C2×Q814yes—
240(C2×D47)⋊C4C2×Q814yes—
241C4⋊Dic47—24no—
242C4⋊Dic47—24no—
243C4⋊Dic47—24no—
244C4⋊Dic47—44no—
245C4⋊Dic47C22×C418yes—
246C4⋊Dic47C22×C418yes—
247Dic47⋊C4—22no—
248Dic47⋊C4—22no—
249Dic47⋊C4—44no—
250Dic47⋊C4—44no—
251Dic47⋊C4C22×C4116yes—
252Dic47⋊C4C22×C4116yes—
253Dic47⋊C4C2×Q814yescomplemented
254Dic47⋊C4C2×Q814yescomplemented
255C4×Dic47—22no—
256C4×Dic47—22no—
257C4×Dic47—22no—
258C4×Dic47—22no—
259C4×Dic47—22no—
260C4×Dic47—28no—
261C4×Dic47—44no—
262C4×Dic47—44no—
263C4×Dic47—44no—
264C4×Dic47C22×C414yes—
265C4×Dic47C22×C414yes—
266C4×Dic47C22×C414yes—
267C4×Dic47C2×Q814yescomplemented
268C23×C47C2511yescharacteristic
269C22×D47—21no—
270C22×D47—21no—
271C22×D47—21no—
272C22×D47—21no—
273C22×D47C23×C412yes—
274C22×D47C22×Q812yes—
275C22×D47C2×#4112yes—
276Q8×C47—216no—
277C2×C4×C47—21no—
278C2×C4×C47—24no—
279C2×C4×C47—21no—
280C2×C4×C47—24no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—24no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—24no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—24no—
292C2×C4×C47C23×C418yes—
293C2×C4×C47C23×C412yes—
294C2×C4×C47C23×C412yes—
295C2×C4×C47C23×C412yes—
296C2×C4×C47C22×Q812yes—
297C2×C4×C47C22×Q812yes—
298C2×C4×C47C22×Q812yes—
299C2×C4×C47C2×#4112yes—
300C2×C4×C47H(5,𝔽2)12yes—
301C2×C4×C47H(5,𝔽2)12yes—
302C2×C4×C472−1+412yes—
303C2×C4×C472−1+412yes—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—24no—
307C2×Dic47—24no—
308C2×Dic47—21no—
309C2×Dic47—21no—
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47—21no—
315C2×Dic47—21no—
316C2×Dic47—24no—
317C2×Dic47—21no—
318C2×Dic47—21no—
319C2×Dic47—24no—
320C2×Dic47—21no—
321C2×Dic47—21no—
322C2×Dic47—24no—
323C2×Dic47C23×C412yes—
324C2×Dic47C23×C412yes—
325C2×Dic47C23×C418yes—
326C2×Dic47C23×C412yes—
327C2×Dic47C22×Q812yes—
328C2×Dic47C22×Q812yes—
329C2×Dic47C22×Q812yes—
330C2×Dic47C2×#4112yes—
331C4×D47—28no—
332C4×D47—28no—
333C4×D47—416no—
334C4×D47C4×Q8116yescomplemented
335Dic94—216no—
336Dic94—416no—
337#34216—471nomaximal, Sylow
338C22×C47C24×C411yescharacteristic
339C22×C47C23×Q811yescharacteristic
340C22×C47C22×#4111yescharacteristic
341C22×C47C2×H(5,𝔽2)11yescharacteristic
342C22×C47C2×H(5,𝔽2)11yescharacteristic
343C22×C47C2×2−1+411yescharacteristic
344C22×C47C2×2−1+411yescharacteristic
345C2×D47—22no—
346C2×D47—22no—
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—22no—
351C2×D47C2×C4×Q814yes—
352C4×C47—28no—
353C4×C47—22no—
354C4×C47—22no—
355C4×C47—44no—
356C4×C47—41no—
357C4×C47—41no—
358C4×C47C2×C4×Q814yes—
359C4×C47#51814yes—
360C4×C47#51914yes—
361Dic47—28no—
362Dic47—22no—
363Dic47—22no—
364Dic47—22no—
365Dic47—22no—
366Dic47—41no—
367Dic47—41no—
368Dic47—44no—
369Dic47C2×C4×Q814yes—
370C22×C4⋊Q8—471no—
371#2369—472no—
372#2369—472no—
373#2365—472no—
374#2365—472no—
375#2345—472no—
376#2345—472no—
377Q8×C22⋊C4—472no—
378Q8×C22⋊C4—472no—
379#2331—472no—
380#2331—472no—
381#2316—472no—
382C4×C4⋊Q8—471no—
383C4×C4⋊Q8—471no—
384C4×C4⋊Q8—471no—
385C4×C4⋊Q8D4711yescharacteristic, complemented
386#2285—471no—
387#2274—472no—
388C4×#117—471no—
389C2×C47C22×C4×Q811yescharacteristic
390C2×C47C2×#51811yescharacteristic
391C2×C47C2×#51911yescharacteristic
392C2×C47#350311yescharacteristic
393C2×C47#350311yescharacteristic
394C2×C47#351111yescharacteristic
395C2×C47#351111yescharacteristic
396D47—24no—
397C23×Q8—472no—
398C2×C4⋊Q8—472no—
399C2×C4⋊Q8—4716no—
400C2×C4⋊Q8—472no—
401C2×C4⋊Q8—472no—
402C2×C4⋊Q8—471no—
403C2×C4⋊Q8C2×D4711yescharacteristic
404C2×C4×Q8—472no—
405C2×C4×Q8—472no—
406C2×C4×Q8—472no—
407C2×C4×Q8C2×D4712yes—
408C2×#117—472no—
409C2×#117—471no—
410C2×#117—471no—
411C22×C4⋊C4—472no—
412C22×C4⋊C4—472no—
413C22×C42—471no—
414#391—472no—
415#391—472no—
416#391—474no—
417#391—472no—
418#391—474no—
419#391—474no—
420#391—474no—
421#391C2×D4712yes—
422#389—472no—
423#389—472no—
424#389—472no—
425#389—472no—
426#389—474no—
427#389—472no—
428#389—472no—
429#389—474no—
430#389C2×D4712yes—
431#389C2×D4712yes—
432#387—474no—
433#387—474no—
434#387—474no—
435#387—474no—
436#384—471no—
437#384C2×D4711yescharacteristic
438#382—472no—
439#380—474no—
440#380—472no—
441#380—472no—
442#380—474no—
443C4×C4⋊C4—472no—
444C4×C4⋊C4—472no—
445C4×C4⋊C4—472no—
446C4×C4⋊C4—472no—
447C4×C4⋊C4—472no—
448C4×C4⋊C4—472no—
449C4×C4⋊C4—472no—
450C4×C4⋊C4—472no—
451C4×C4⋊C4—471no—
452C4×C4⋊C4—471no—
453C4×C4⋊C4—474no—
454C4×C4⋊C4—471no—
455C4×C4⋊C4—471no—
456C4×C4⋊C4—474no—
457C4×C4⋊C4C2×D4712yes—
458C4×C4⋊C4C2×D4712yes—
459C4×C22⋊C4—471no—
460C4×C22⋊C4—471no—
461C4×C22⋊C4—474no—
462C4×C22⋊C4—471no—
463C4×C22⋊C4—471no—
464C4×C22⋊C4—474no—
465#376—471no—
466#376—471no—
467C43—471no—
468C43C2×D4711yescharacteristic
469C47#3421611yescharacteristic, complemented, Sylow
470C22×Q8—4716no—
471C22×Q8—472no—
472C22×Q8—474no—
473C22×Q8—1884no—
474C22×Q8—1884no—
475C22×Q8C22×D4712yes—
476C23×C4—471no—
477C23×C4—471no—
478C23×C4—471no—
479C23×C4—474no—
480C4⋊Q8—4716no—
481C4⋊Q8—4716no—
482C4⋊Q8—4716no—
483C4⋊Q8—478no—
484C4⋊Q8C4×D4718yes—
485C4×Q8—44no—
486C4×Q8—1884no—
487C4×Q8—1884no—
488C4×Q8—1884no—
489#117—478no—
490#117—944no—
491#117—948no—
492C2×C4⋊C4—474no—
493C2×C4⋊C4—474no—
494C2×C4⋊C4—472no—
495C2×C4⋊C4—472no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—4716no—
499C2×C4⋊C4—4716no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—472no—
503C2×C4⋊C4—472no—
504C2×C4⋊C4—472no—
505C2×C4⋊C4—474no—
506C2×C4⋊C4—474no—
507C2×C4⋊C4—474no—
508C2×C4⋊C4C22×D4712yes—
509C2×C4⋊C4C22×D4712yes—
510C2×C4⋊C4C22×D4712yes—
511C2×C4⋊C4C22×D4714yes—
512C2×C4⋊C4C22×D4712yes—
513C2×C4⋊C4C22×D4712yes—
514C2×C22⋊C4—471no—
515C2×C22⋊C4—471no—
516C2×C22⋊C4—471no—
517C2×C22⋊C4—474no—
518C2×C22⋊C4—471no—
519C2×C42—471no—
520C2×C42—471no—
521C2×C42—471no—
522C2×C42—471no—
523C2×C42—478no—
524C2×C42—471no—
525C2×C42—474no—
526C2×C42—471no—
527C2×C42—471no—
528C2×C42—471no—
529C2×C42—471no—
530C2×C42—474no—
531C2×C42—474no—
532C2×C42—474no—
533C2×C42C22×D4711yescharacteristic
534C2×C42C22×D4711yescharacteristic
535C2×C42C22×D4711yescharacteristic
536C2×C42C22×D4711yescharacteristic
537C2×C42C22×D4711yescharacteristic
538C2×C42C22×D4714yes—
539C2×C42C22×D4711yescharacteristic
540C2×C42C22×D4711yescharacteristic
541#95—471no—
542#95—471no—
543#95—471no—
544#95—471no—
545#95—471no—
546#95—471no—
547#95—471no—
548#95—471no—
549#95—474no—
550#95—474no—
551#95—474no—
552#95—474no—
553#95—474no—
554#95—474no—
555#95—474no—
556#95—474no—
557#95C22×D4714yes—
558#95C22×D4714yes—
559C24—471no—
560C2×Q8—24no—
561C2×Q8—24no—
562C2×Q8—478no—
563C2×Q8—4716no—
564C2×Q8—944no—
565C2×Q8—944no—
566C2×Q8—1884no—
567C2×Q8—1884no—
568C2×Q8—18832no—
569C2×Q8C2×C4×D4718yes—
570C22×C4—471no—
571C22×C4—474no—
572C22×C4—474no—
573C22×C4—474no—
574C22×C4—471no—
575C22×C4—471no—
576C22×C4—471no—
577C22×C4—471no—
578C22×C4—474no—
579C22×C4—474no—
580C22×C4—474no—
581C22×C4—4716no—
582C22×C4—471no—
583C22×C4—471no—
584C22×C4—474no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—1884no—
590C22×C4—1884no—
591C22×C4C23×D4711yescharacteristic
592C22×C4C23×D4714yes—
593C22×C4C23×D4711yescharacteristic
594C22×C4C23×D4714yes—
595C22×C4C23×D4711yescharacteristic
596C22×C4C23×D4711yescharacteristic
597C22×C4C23×D4711yescharacteristic
598C22×C4C23×D4711yescharacteristic
599C22×C4C23×D4711yescharacteristic
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—44no—
604C4⋊C4—4716no—
605C4⋊C4—4716no—
606C4⋊C4—478no—
607C4⋊C4—478no—
608C4⋊C4—474no—
609C4⋊C4—474no—
610C4⋊C4—942no—
611C4⋊C4—942no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—1884no—
616C4⋊C4—1884no—
617C4⋊C4—1884no—
618C4⋊C4C2×C4×D4718yes—
619C4⋊C4C2×C4×D4718yes—
620C22⋊C4—474no—
621C22⋊C4—474no—
622C22⋊C4—942no—
623C22⋊C4—942no—
624C22⋊C4—948no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—44no—
631C42—474no—
632C42—474no—
633C42—474no—
634C42—474no—
635C42—948no—
636C42—942no—
637C42—942no—
638C42—942no—
639C42—942no—
640C42—942no—
641C42—1884no—
642C42—1884no—
643C42—1884no—
644C42C2×C4×D4714yes—
645C42Q8×D4714yescomplemented
646C23—472no—
647C23—472no—
648C23—472no—
649C23—941no—
650C23—941no—
651C23—941no—
652C23—941no—
653C23C24×D4711yescharacteristic
654Q8—216no—
655Q8—9416no—
656Q8—18816no—
657C2×C4—21no—
658C2×C4—24no—
659C2×C4—21no—
660C2×C4—24no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—24no—
666C2×C4—21no—
667C2×C4—24no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—24no—
671C2×C4—21no—
672C2×C4—472no—
673C2×C4—472no—
674C2×C4—472no—
675C2×C4—4716no—
676C2×C4—472no—
677C2×C4—472no—
678C2×C4—478no—
679C2×C4—472no—
680C2×C4—472no—
681C2×C4—941no—
682C2×C4—944no—
683C2×C4—941no—
684C2×C4—941no—
685C2×C4—944no—
686C2×C4—941no—
687C2×C4—941no—
688C2×C4—941no—
689C2×C4—941no—
690C2×C4—941no—
691C2×C4—948no—
692C2×C4—948no—
693C2×C4—941no—
694C2×C4—941no—
695C2×C4—944no—
696C2×C4—941no—
697C2×C4—941no—
698C2×C4—944no—
699C2×C4—941no—
700C2×C4—941no—
701C2×C4—944no—
702C2×C4—18816no—
703C2×C4C22×C4×D4718yes—
704C2×C4C22×C4×D4712yes—
705C2×C4C22×C4×D4712yes—
706C2×C4C22×C4×D4712yes—
707C2×C4C2×Q8×D4712yes—
708C2×C4C2×Q8×D4712yes—
709C2×C4C2×Q8×D4712yes—
710C2×C4#41×D4712yes—
711C2×C4#1309406912yes—
712C2×C4#1309407012yes—
713C2×C4#1309407112yes—
714C2×C4#1309407212yes—
715C22—474no—
716C22—942no—
717C22—942no—
718C22—942no—
719C22—942no—
720C22—942no—
721C22—942no—
722C22C23×C4×D4711yescharacteristic
723C22C22×Q8×D4711yescharacteristic
724C22C2×#41×D4711yescharacteristic
725C22C2×#1309406911yescharacteristic
726C22C2×#1309407011yescharacteristic
727C22C2×#1309407111yescharacteristic
728C22C2×#1309407211yescharacteristic
729C4—28no—
730C4—22no—
731C4—22no—
732C4—41no—
733C4—44no—
734C4—41no—
735C4—474no—
736C4—942no—
737C4—948no—
738C4—942no—
739C4—942no—
740C4—942no—
741C4—1881no—
742C4—1881no—
743C4—1884no—
744C4C4×Q8×D4714yes—
745C4#1568959514yes—
746C4#1568959914yes—
747C2—944no—
748C2C2×C4×Q8×D4711yescharacteristic
749C2C2×#1568959511yescharacteristic
750C2C2×#1568959911yescharacteristic
751C2#2025720011yescharacteristic
752C2#2025720411yescharacteristic
753C2#2025728911yescharacteristic
754C2#2025730011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC4×C4⋊Q8×C47C2
socle, cosocleC23×C47C25
prime radicalC23×D47C24
hypercenterC4×C4⋊Q8D47
hypocenterC47#34216
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #20246475C2semidirect
3. #20246474C2semidirect
4. #20246445C2semidirect
5. #20246442C2semidirect
10. #20246135C2semidirect
11. #20246132C2semidirect
13. C4⋊Q8×Dic47C2semidirect
14. C4×#13094024C2semidirect
15. #20245955C2semidirect
19. C4×C4⋊Q8×C47C2semidirect
25. C4⋊Q8×D47C4semidirect
110. #13093981Q8semidirect
235. C42×C47C2×Q8semidirect
253. Dic47⋊C4C2×Q8semidirect
254. Dic47⋊C4C2×Q8semidirect
267. C4×Dic47C2×Q8semidirect
334. C4×D47C4×Q8semidirect
385. C4×C4⋊Q8D47semidirect
469. C47#34216semidirect
645. C42Q8×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D472
#202464752
#202464742
#202464452
#202464422
#202462642
#202462612
#202462222
Q8×(C2×D47)⋊C42
#202461352
#202461322
#202460032
C4⋊Q8×Dic472
C4×#130940242
#202459552
#202457932
#202457422
C4×#130939812
C4×C4⋊Q8×C472
#3421647