Finite Group Databasebeta

← #26377312

Subgroups — #26377312

Order 12032.

5050 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094072C211yesmaximal, characteristic
2C2×#15689599C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
4#20246228C213yesmaximal, complemented
5#20246226C211yesmaximal, characteristic, complemented
6#20246226C211yesmaximal, characteristic, complemented
7#20246225C213yesmaximal, complemented
8Q8×C22⋊Dic47C211yesmaximal, characteristic, complemented
9#20246222C213yesmaximal, complemented
10#20246222C213yesmaximal, complemented
11#20245979C213yesmaximal, complemented
12#20245977C213yesmaximal, complemented
13#20245877C213yesmaximal, complemented
14#20245874C213yesmaximal, complemented
15Q8×C22⋊C4×C47C211yesmaximal, characteristic, complemented
16C2×#13094072—28no—
17C2×#13094072—28no—
18C2×#13094072C4116yescomplemented
19C22×#10625354C2213yes—
20C22×#10625354C2211yescharacteristic
21C22×#10625350C2213yes—
22C22×#10625350C2213yes—
23C22×Q8×D47C2213yes—
24C22×Q8×D47C2211yescharacteristic
25#15689599—28no—
26C2×Q8×Dic47C2211yescharacteristic
27C2×Q8×Dic47C2211yescharacteristic
28C2×C4×Dic94C2213yes—
29C2×C4×Dic94C2213yes—
30C2×#13093989C2213yes—
31C2×#13093989C2213yes—
32C4×Q8×D47—28no—
33C2×#13093982C2213yes—
34C2×#13093981C2213yes—
35C2×C4⋊C4×D47C2213yes—
36C2×C42×D47C2213yes—
37#15689030C2213yes—
38#15689030C2213yes—
39#15689027C2213yes—
40#15689027C2213yes—
41#15689027C2216yes—
42#15689025C2213yes—
43#15689025C2213yes—
44#15689024C2213yes—
45#15689024C2213yes—
46#15689023C2213yes—
47#15689023C2213yes—
48#15689023C2216yes—
49#15689001C2213yes—
50#15689001C2213yes—
51#15689001C2216yes—
52#15688999C2211yescharacteristic
53#15688999C2213yes—
54#15688983C2213yes—
55#15688982C2216yes—
56#15688982C2216yes—
57#15688980C2213yes—
58#15688980C2213yes—
59C4×(C2×D47)⋊C4C2213yes—
60C4×(C2×D47)⋊C4C2213yes—
61C4×C22⋊Dic47C2213yes—
62#15688970C2216yes—
63#15688970C2216yes—
64C23×Q8×C47C2211yescharacteristic
65C2×C4×Q8×C47C2211yescharacteristic
66C2×C4×Q8×C47C2211yescharacteristic
67C47×#391C2213yes—
68C47×#391C2213yes—
69C47×#380C2213yes—
70C4×C22⋊C4×C47C2213yes—
71#13094072—2128no—
72C2×#10625354—24no—
73C2×#10625354—24no—
74C2×#10625354—212no—
75C2×#10625354—212no—
76C2×#10625354C2×C4124yes—
77C2×#10625354C2×C418yescomplemented
78C2×#10625350—212no—
79C2×#10625350—212no—
80C2×#10625350—212no—
81C2×#10625350—212no—
82C2×#10625350C2×C4124yes—
83C2×#10625350C2×C4124yescomplemented
84C22×Dic94C2313yes—
85C22×Dic94C2313yes—
86C2×Q8×D47—212no—
87C2×Q8×D47—212no—
88C2×Q8×D47C2×C418yes—
89C2×Q8×D47C2×C4124yescomplemented
90C2×Q8×D47D418yes—
91C2×Q8×D47D418yes—
92C22×D188C2313yes—
93C22×D188C2313yes—
94C22×C22⋊D47C2311yescharacteristic
95C22×C22⋊D47C2313yes—
96C22×C4×D47C2311yescharacteristic
97C22×C4×D47C2316yes—
98C22×C4×D47C2313yes—
99C22×C4×D47C2313yes—
100C22×C4×D47C2313yes—
101Q8×Dic47—24no—
102Q8×Dic47—24no—
103C4×Dic94—212no—
104C4×Dic94—212no—
105#13093989—212no—
106#13093989—212no—
107#13093982—212no—
108#13093981—212no—
109C2×C4⋊Dic47C2313yes—
110C2×C4⋊Dic47C2313yes—
111C2×Dic47⋊C4C2316yes—
112C2×Dic47⋊C4C2313yes—
113C2×Dic47⋊C4C2313yes—
114C4⋊C4×D47—212no—
115C2×C22⋊Dic47C2311yescharacteristic
116C2×C22⋊Dic47C2313yes—
117C2×(C2×D47)⋊C4C2313yes—
118C2×(C2×D47)⋊C4C2313yes—
119C2×(C2×D47)⋊C4C2311yescharacteristic
120C2×(C2×D47)⋊C4C2313yes—
121C2×(C2×D47)⋊C4C2316yes—
122C2×(C2×D47)⋊C4C2316yes—
123C2×(C2×D47)⋊C4C2313yes—
124C2×(C2×D47)⋊C4C2313yes—
125C2×C4×Dic47C2313yes—
126C2×C4×Dic47C2313yes—
127C2×C4×Dic47C2316yes—
128C2×C4×Dic47C2313yes—
129C2×C4×Dic47C2313yes—
130C42×D47—212no—
131C47⋊#95C2313yes—
132C47⋊#95C2316yes—
133C47⋊#95C2313yes—
134C47⋊#95C2311yescharacteristic
135C47⋊#95C2311yescharacteristic
136C47⋊#95C2313yes—
137C47⋊#95C2313yes—
138C22×Q8×C47—24no—
139C22×Q8×C47—24no—
140C22×Q8×C47C2×C418yescomplemented
141C22×Q8×C47C2313yes—
142C22×Q8×C47C2311yescharacteristic
143C23×C4×C47C2313yes—
144C4×Q8×C47—24no—
145C4×Q8×C47—24no—
146C2×C4⋊C4×C47C2313yes—
147C2×C4⋊C4×C47C2313yes—
148C2×C22⋊C4×C47C2311yescharacteristic
149C2×C22⋊C4×C47C2313yes—
150C2×C42×C47C2313yes—
151C2×C42×C47C2313yes—
152#95×C47C2313yes—
153#95×C47C2316yes—
154#95×C47C2313yes—
155C24×C47C2411yescharacteristic
156C23×D47C2413yes—
157C23×D47C2411yescharacteristic
158C2×Q8×C47—232no—
159C2×Q8×C47—26no—
160C2×Q8×C47—26no—
161C2×Q8×C47C22×C4112yes—
162C2×Q8×C47C22×C414yes—
163C2×Q8×C47C2×D414yes—
164C2×Q8×C47C2×D414yes—
165C22×C4×C47—26no—
166C22×C4×C47—26no—
167C22×C4×C47C22×C4112yes—
168C22×C4×C47C2411yescharacteristic
169C22×C4×C47C2413yes—
170C22×C4×C47C2413yes—
171C22×C4×C47C2413yes—
172C22×C4×C47C2411yescharacteristic
173C22×C4×C47C2413yes—
174C2×C22⋊D47—22no—
175C2×C22⋊D47—22no—
176C2×C22⋊D47—26no—
177C2×C22⋊D47—26no—
178C2×C22⋊D47C22×C414yes—
179C2×C22⋊D47C22×C4112yes—
180C22×Dic47C2411yescharacteristic
181C22×Dic47C2413yes—
182C22×Dic47C2413yes—
183C22×Dic47C2411yescharacteristic
184C22×Dic47C2411yescharacteristic
185C22×Dic47C2413yes—
186#10625354—232no—
187#10625354—296no—
188Q8×D47—296no—
189Q8×D47C22⋊C4164yescomplemented
190#10625350—296no—
191#10625350—296no—
192C2×D188—26no—
193C2×D188—26no—
194C2×D188—26no—
195C2×D188—26no—
196C2×D188C22×C4112yes—
197C2×D188C22×C4112yes—
198C2×C4×D47—22no—
199C2×C4×D47—26no—
200C2×C4×D47—26no—
201C2×C4×D47—22no—
202C2×C4×D47—212no—
203C2×C4×D47—212no—
204C2×C4×D47—22no—
205C2×C4×D47—26no—
206C2×C4×D47—43no—
207C2×C4×D47—43no—
208C2×C4×D47C22×C4112yes—
209C2×C4×D47C22×C4124yes—
210C2×C4×D47C22×C4112yes—
211C2×C4×D47C2×D4112yes—
212C2×C4×D47C2×D4112yes—
213C2×Dic94—26no—
214C2×Dic94—26no—
215C2×Dic94C22×C4112yes—
216C2×Dic94C22×C4112yes—
217C2×Dic94C2×D4112yes—
218C2×Dic94C2×D4112yes—
219C4⋊C4×C47—26no—
220C4⋊C4×C47—26no—
221C22⋊C4×C47—22no—
222C22⋊C4×C47—43no—
223C42×C47—26no—
224C42×C47—26no—
225C22⋊Dic47—22no—
226C22⋊Dic47—43no—
227(C2×D47)⋊C4—22no—
228(C2×D47)⋊C4—26no—
229(C2×D47)⋊C4—26no—
230(C2×D47)⋊C4—26no—
231(C2×D47)⋊C4—43no—
232(C2×D47)⋊C4—46no—
233(C2×D47)⋊C4—46no—
234(C2×D47)⋊C4—43no—
235C4⋊Dic47—26no—
236C4⋊Dic47—26no—
237Dic47⋊C4—212no—
238Dic47⋊C4—26no—
239Dic47⋊C4—26no—
240C4×Dic47—26no—
241C4×Dic47—26no—
242C4×Dic47—26no—
243C4×Dic47—26no—
244C4×Dic47—212no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47C23×C412yes—
252C23×C47C2511yescharacteristic
253C22×D47—21no—
254C22×D47—21no—
255C22×D47—21no—
256C22×D47—21no—
257C22×D47—23no—
258C22×D47—23no—
259C22×D47—23no—
260C22×D47—23no—
261C22×D47—23no—
262C22×D47—23no—
263C22×D47C23×C416yes—
264C22×D47C23×C412yes—
265C22×D47C22×D412yes—
266C22×D47C22×D412yes—
267Q8×C47—224no—
268Q8×C47C2×C22⋊C4116yes—
269C2×C4×C47—21no—
270C2×C4×C47—23no—
271C2×C4×C47—23no—
272C2×C4×C47—21no—
273C2×C4×C47—224no—
274C2×C4×C47—23no—
275C2×C4×C47—23no—
276C2×C4×C47—21no—
277C2×C4×C47—23no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—23no—
281C2×C4×C47—23no—
282C2×C4×C47—23no—
283C2×C4×C47C23×C416yes—
284C2×C4×C47C23×C416yes—
285C2×C4×C47C22×D416yes—
286C2×C4×C47C22×D416yes—
287C2×C4×C472−1+412yescomplemented
288C22⋊D47—28no—
289C22⋊D47—224no—
290C2×Dic47—21no—
291C2×Dic47—21no—
292C2×Dic47—21no—
293C2×Dic47—21no—
294C2×Dic47—21no—
295C2×Dic47—23no—
296C2×Dic47—23no—
297C2×Dic47—23no—
298C2×Dic47—21no—
299C2×Dic47—21no—
300C2×Dic47—23no—
301C2×Dic47—23no—
302C2×Dic47—23no—
303C2×Dic47C23×C412yes—
304C2×Dic47C23×C416yes—
305C2×Dic47C22×D416yes—
306C2×Dic47C22×D416yes—
307C2×Dic472−1+412yescomplemented
308D188—224no—
309D188—224no—
310C4×D47—28no—
311C4×D47—224no—
312C4×D47—248no—
313C4×D47—412no—
314C4×D47C2×C22⋊C4148yes—
315Dic94—224no—
316Dic94C2×C22⋊C4148yes—
317#34257—471nomaximal, Sylow
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47—41no—
324C22×C47—41no—
325C22×C47C24×C411yescharacteristic
326C22×C47C23×D411yescharacteristic
327C22×C47C23×D411yescharacteristic
328C22×C47C2×2−1+411yescharacteristic
329C22×C47C2×2−1+411yescharacteristic
330C22×C47#58511yescharacteristic
331C22×C47#58511yescharacteristic
332C2×D47—22no—
333C2×D47—22no—
334C2×D47—22no—
335C2×D47—22no—
336C2×D47—22no—
337C2×D47—22no—
338C2×D47—26no—
339C2×D47—26no—
340C2×D47—26no—
341C2×D47—43no—
342C2×D47—43no—
343C2×D47—43no—
344C2×D47—43no—
345C2×D47C22×C22⋊C414yes—
346C4×C47—26no—
347C4×C47—22no—
348C4×C47—43no—
349C4×C47—43no—
350C4×C47—41no—
351C4×C47C22×C22⋊C4112yes—
352Dic47—22no—
353Dic47—22no—
354Dic47—43no—
355Dic47—41no—
356Dic47—43no—
357Dic47C22×C22⋊C4112yes—
358C22×2−1+4—471no—
359C2×#519—471no—
360C22×C4×Q8—471no—
361#2341—473no—
362#2341—473no—
363#2341—471no—
364#2341—471no—
365Q8×C22⋊C4—473no—
366Q8×C22⋊C4—473no—
367Q8×C22⋊C4—471no—
368Q8×C22⋊C4D4711yescharacteristic, complemented
369#2311—473no—
370#2311—473no—
371#2297—473no—
372#2297—473no—
373C2×C47—42no—
374C2×C47C23×C22⋊C411yescharacteristic
375C2×C47C4×2−1+411yescharacteristic
376C2×C47C4×2−1+411yescharacteristic
377C2×C47#348611yescharacteristic
378C2×C47#348711yescharacteristic
379C2×C47#349711yescharacteristic
380C2×C47#349711yescharacteristic
381D47—24no—
382D47—46no—
383C2×2−1+4—4716no—
384C2×2−1+4—948no—
385C2×2−1+4—948no—
386C22×#41—473no—
387C22×#41—471no—
388C22×#41—473no—
389C22×#41—473no—
390C23×Q8—471no—
391C23×Q8—473no—
392C23×Q8C2×D4711yescharacteristic
393#519—948no—
394C2×C4×Q8—471no—
395C2×C4×Q8—471no—
396C2×C4×Q8—473no—
397C2×C4×Q8—473no—
398C2×C4×Q8—473no—
399C2×C4×Q8—473no—
400C2×C4×Q8—948no—
401C2×C4×Q8C2×D4711yescharacteristic
402C2×C4×Q8C2×D4711yescharacteristic
403C2×#117—473no—
404C2×#117—473no—
405C22×C4⋊C4—473no—
406C22×C42—473no—
407#391—473no—
408#391—473no—
409#391—476no—
410#391—473no—
411#391—473no—
412#391C2×D4713yes—
413#391C2×D4713yes—
414#390—473no—
415#390—473no—
416#390—476no—
417#390—473no—
418#390—473no—
419#390—473no—
420#390—473no—
421#386—473no—
422#386—471no—
423#386—476no—
424#386—473no—
425#386—473no—
426#380—473no—
427#380—473no—
428#380—473no—
429#380—476no—
430#380—476no—
431#380C2×D4713yes—
432C4×C22⋊C4—473no—
433C4×C22⋊C4—473no—
434C4×C22⋊C4—473no—
435C4×C22⋊C4—476no—
436C4×C22⋊C4—476no—
437C4×C22⋊C4C2×D4713yes—
438C47#3425711yescharacteristic, complemented, Sylow
4392−1+4—94128no—
440C2×#41—4724no—
441C2×#41—478no—
442C2×#41—4724no—
443C2×#41—4724no—
444C2×#41—9412no—
445C2×#41—9412no—
446C2×#41—9412no—
447C2×#41—9412no—
448C2×#41—9412no—
449C2×#41—9412no—
450C2×#41—944no—
451C2×#41—944no—
452C22×Q8—24no—
453C22×Q8—24no—
454C22×Q8—478no—
455C22×Q8—478no—
456C22×Q8—478no—
457C22×Q8—4724no—
458C22×Q8—473no—
459C22×Q8—473no—
460C22×Q8—9412no—
461C22×Q8—9412no—
462C22×Q8C4×D4718yescomplemented
463C22×Q8C22×D4713yes—
464C22×Q8C22×D4711yescharacteristic
465C22×D4—471no—
466C22×D4—473no—
467C22×D4—473no—
468C22×D4—473no—
469C23×C4—473no—
470C23×C4—476no—
471C23×C4—473no—
472C23×C4—471no—
473C23×C4—473no—
474C23×C4C22×D4713yes—
475C4×Q8—24no—
476C4×Q8—24no—
477C4×Q8—9412no—
478C4×Q8—9412no—
479C4×Q8—9412no—
480C4×Q8—9412no—
481C4×Q8—944no—
482C4×Q8—944no—
483#117—9412no—
484#117—9412no—
485C2×C4⋊C4—476no—
486C2×C4⋊C4—473no—
487C2×C4⋊C4—473no—
488C2×C4⋊C4—473no—
489C2×C4⋊C4—473no—
490C2×C4⋊C4—9412no—
491C2×C4⋊C4C22×D4713yes—
492C2×C4⋊C4C22×D4713yes—
493C2×C22⋊C4—471no—
494C2×C22⋊C4—473no—
495C2×C22⋊C4—471no—
496C2×C22⋊C4—473no—
497C2×C22⋊C4—473no—
498C2×C22⋊C4—473no—
499C2×C22⋊C4—476no—
500C2×C22⋊C4—473no—
501C2×C22⋊C4—476no—
502C2×C22⋊C4—473no—
503C2×C22⋊C4C22×D4711yescharacteristic
504C2×C22⋊C4C22×D4713yes—
505C2×C42—476no—
506C2×C42—473no—
507C2×C42—473no—
508C2×C42—473no—
509C2×C42—473no—
510C2×C42—9412no—
511C2×C42C22×D4713yes—
512C2×C42C22×D4713yes—
513#95—471no—
514#95—471no—
515#95—473no—
516#95—473no—
517#95—473no—
518#95—476no—
519#95—473no—
520#95C22×D4713yes—
521#95C22×D4716yes—
522#95C22×D4713yes—
523C24—471no—
524C24—473no—
525C24C23×D4711yescharacteristic
526#41—9496no—
527#41—9496no—
528#41—9496no—
529#41—9432no—
530C2×Q8—232no—
531C2×Q8—26no—
532C2×Q8—26no—
533C2×Q8—4764no—
534C2×Q8—4712no—
535C2×Q8—4712no—
536C2×Q8—4712no—
537C2×Q8—4712no—
538C2×Q8—946no—
539C2×Q8—946no—
540C2×Q8—9496no—
541C2×Q8C2×C4×D47112yes—
542C2×Q8C2×C4×D4714yes—
543C2×Q8D4×D4714yes—
544C2×Q8D4×D4714yes—
545C2×D4—4712no—
546C2×D4—474no—
547C2×D4—4712no—
548C2×D4—4712no—
549C2×D4—946no—
550C2×D4—946no—
551C2×D4—946no—
552C2×D4—946no—
553C2×D4—942no—
554C2×D4—942no—
555C2×D4—946no—
556C2×D4—946no—
557C22×C4—26no—
558C22×C4—26no—
559C22×C4—473no—
560C22×C4—4712no—
561C22×C4—4712no—
562C22×C4—4712no—
563C22×C4—471no—
564C22×C4—471no—
565C22×C4—4724no—
566C22×C4—4712no—
567C22×C4—471no—
568C22×C4—473no—
569C22×C4—473no—
570C22×C4—942no—
571C22×C4—9412no—
572C22×C4—9412no—
573C22×C4—942no—
574C22×C4—946no—
575C22×C4—946no—
576C22×C4—946no—
577C22×C4—942no—
578C22×C4—1883no—
579C22×C4—1883no—
580C22×C4C2×C4×D47112yes—
581C22×C4C23×D4713yes—
582C22×C4C23×D4713yes—
583C22×C4C23×D4711yescharacteristic
584C22×C4C23×D4713yes—
585C22×C4C23×D4711yescharacteristic
586C22×C4C23×D4713yes—
587C4⋊C4—26no—
588C4⋊C4—26no—
589C4⋊C4—9412no—
590C4⋊C4—946no—
591C4⋊C4—946no—
592C4⋊C4—946no—
593C4⋊C4—946no—
594C22⋊C4—22no—
595C22⋊C4—43no—
596C22⋊C4—946no—
597C22⋊C4—942no—
598C22⋊C4—946no—
599C22⋊C4—942no—
600C22⋊C4—946no—
601C22⋊C4—1886no—
602C22⋊C4—1883no—
603C22⋊C4—1883no—
604C22⋊C4—1886no—
605C22⋊C4—1883no—
606C42—26no—
607C42—26no—
608C42—946no—
609C42—946no—
610C42—9412no—
611C42—946no—
612C42—946no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—472no—
620C23—472no—
621C23—472no—
622C23—476no—
623C23—941no—
624C23—941no—
625C23—941no—
626C23—941no—
627C23—943no—
628C23—943no—
629C23—943no—
630C23—943no—
631C23—943no—
632C23—943no—
633C23C22×C4×D4712yes—
634C23C24×D4711yescharacteristic
635Q8—224no—
636Q8—4748no—
637Q8—9424no—
638Q8C22⋊C4×D47116yes—
639D4—9424no—
640D4—9424no—
641D4—948no—
642D4—9424no—
643C2×C4—21no—
644C2×C4—23no—
645C2×C4—23no—
646C2×C4—21no—
647C2×C4—224no—
648C2×C4—21no—
649C2×C4—23no—
650C2×C4—23no—
651C2×C4—23no—
652C2×C4—21no—
653C2×C4—23no—
654C2×C4—23no—
655C2×C4—21no—
656C2×C4—23no—
657C2×C4—476no—
658C2×C4—476no—
659C2×C4—476no—
660C2×C4—4748no—
661C2×C4—472no—
662C2×C4—472no—
663C2×C4—9448no—
664C2×C4—948no—
665C2×C4—941no—
666C2×C4—941no—
667C2×C4—941no—
668C2×C4—941no—
669C2×C4—9424no—
670C2×C4—941no—
671C2×C4—943no—
672C2×C4—943no—
673C2×C4—941no—
674C2×C4—943no—
675C2×C4—941no—
676C2×C4—943no—
677C2×C4—943no—
678C2×C4—943no—
679C2×C4—18812no—
680C2×C4C22×C4×D4716yes—
681C2×C4C22×C4×D4716yes—
682C2×C4C2×D4×D4716yes—
683C2×C4C2×D4×D4716yes—
684C2×C4#1309407212yescomplemented
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—474no—
693C22—942no—
694C22—942no—
695C22—942no—
696C22—942no—
697C22—942no—
698C22—942no—
699C22—946no—
700C22—946no—
701C22—946no—
702C22—1883no—
703C22—1883no—
704C22—1883no—
705C22—1883no—
706C22C23×C4×D4711yescharacteristic
707C22C22×D4×D4711yescharacteristic
708C22C22×D4×D4711yescharacteristic
709C222−1+4×D4711yescharacteristic
710C22C2×#1309407211yescharacteristic
711C22#1568995911yescharacteristic
712C22#1568996011yescharacteristic
713C4—22no—
714C4—26no—
715C4—43no—
716C4—43no—
717C4—41no—
718C4—4712no—
719C4—942no—
720C4—942no—
721C4—1883no—
722C4—1881no—
723C4—1883no—
724C4C2×C22⋊C4×D47112yes—
725C2—42no—
726C2—944no—
727C2—1886no—
728C2C22×C22⋊C4×D4711yescharacteristic
729C2#2025659711yescharacteristic
730C2C4×#1309407211yescharacteristic
731C2#2025703811yescharacteristic
732C2#2025704511yescharacteristic
733C2#2025715611yescharacteristic
734C2#2025715811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingQ8×C22⋊C4×C47C2
socle, cosocleC23×C47C25
prime radicalC22×#13094072C2
hypercenterQ8×C22⋊C4D47
hypocenterC47#34257
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#15689599C2semidirect
3. C2×C4×Q8×D47C2semidirect
4. #20246228C2semidirect
5. #20246226C2semidirect
6. #20246226C2semidirect
7. #20246225C2semidirect
8. Q8×C22⋊Dic47C2semidirect
9. #20246222C2semidirect
10. #20246222C2semidirect
11. #20245979C2semidirect
12. #20245977C2semidirect
13. #20245877C2semidirect
14. #20245874C2semidirect
15. Q8×C22⋊C4×C47C2semidirect
18. C2×#13094072C4semidirect
77. C2×#10625354C2×C4semidirect
83. C2×#10625350C2×C4semidirect
89. C2×Q8×D47C2×C4semidirect
140. C22×Q8×C47C2×C4semidirect
189. Q8×D47C22⋊C4semidirect
287. C2×C4×C472−1+4semidirect
307. C2×Dic472−1+4semidirect
368. Q8×C22⋊C4D47semidirect
438. C47#34257semidirect
462. C22×Q8C4×D47semidirect
684. C2×C4#13094072semidirect

Maximal subgroups

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

subgroupindex
C22×#130940722
C2×#156895992
C2×C4×Q8×D472
#202462282
#202462262
#202462252
Q8×C22⋊Dic472
#202462222
#202459792
#202459772
#202458772
#202458742
Q8×C22⋊C4×C472
#3425747