Finite Group Databasebeta

← #26232828

Subgroups — #26232828

Order 12032.

1114 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689832C211yesmaximal, characteristic
2#20246260C212yesmaximal, complemented
3#20244372C212yesmaximal, complemented
4#20244371C212yesmaximal, complemented
5#20244371C212yesmaximal, complemented
6#20243374C211yesmaximal, characteristic
7#20243374C211yesmaximal, characteristic
8#99×Dic47C211yesmaximal, characteristic
9#99×Dic47C211yesmaximal, characteristic
10C4×#13093939C211yesmaximal, characteristic
11C47×#1799C211yesmaximal, characteristic
12#15689832—22no—
13#15689832—22no—
14#15689832—22no—
15#15689832—22no—
16C2×#13094023C411yescharacteristic, complemented
17C2×#13094016C411yescharacteristic, complemented
18C2×#13094015C411yescharacteristic, complemented
19C2×#13094003C411yescharacteristic, complemented
20C2×#13094003C2211yescharacteristic
21C2×#13094001C411yescharacteristic, complemented
22C2×#13094001C411yescharacteristic, complemented
23C2×#13094001C2211yescharacteristic
24C2×#13094001C2211yescharacteristic
25C2×C4×Dic94C411yescharacteristic, complemented
26C2×D4×Dic47C2211yescharacteristic
27C2×D4×Dic47C2211yescharacteristic
28C22×Dic47⋊C4C411yescharacteristic, complemented
29C22×Dic47⋊C4C2211yescharacteristic
30C2×#13093939C2211yescharacteristic
31C2×#13093939C2211yescharacteristic
32#15689018—22no—
33#15689005—22no—
34#15689004—22no—
35#15688981C2212yes—
36#15688981C2212yes—
37#15688974—22no—
38C22⋊C4×Dic47C2212yes—
39C22⋊C4×Dic47C2212yes—
40C4×C22⋊Dic47C2212yes—
41#15688890C2212yes—
42#15688889C2212yes—
43#15688889C2212yes—
44#15688889C2212yes—
45#15688889C2212yes—
46C2×C4×D4×C47C2211yescharacteristic
47C2×#99×C47C2211yescharacteristic
48C2×#99×C47C2211yescharacteristic
49C47×#380C2212yes—
50C47×#342C2212yes—
51C22×Dic94C2×C411yescharacteristic
52C22×Dic94C2×C411yescharacteristic
53C22×Dic94C2×C411yescharacteristic
54C23×Dic47C2×C411yescharacteristic
55C23×Dic47C2×C411yescharacteristic
56C23×Dic47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58#13094023—22no—
59#13094023—22no—
60#13094016—22no—
61#13094016—22no—
62#13094015—22no—
63#13094015—22no—
64#13094003—22no—
65#13094003—22no—
66#13094003—22no—
67#13094003—22no—
68#13094001—22no—
69#13094001—22no—
70#13094001—22no—
71#13094001—22no—
72#13094001—22no—
73#13094001—22no—
74#13094001—22no—
75#13094001—22no—
76C4×Dic94—21no—
77C4×Dic94—21no—
78C4×Dic94—21no—
79C4×Dic94—21no—
80D4×Dic47—22no—
81D4×Dic47—22no—
82D4×Dic47—22no—
83D4×Dic47—22no—
84C2×C4⋊Dic47C2×C411yescharacteristic
85C2×C4⋊Dic47C2×C411yescharacteristic
86C2×C4⋊Dic47C2×C411yescharacteristic
87C2×C4⋊Dic47C2×C411yescharacteristic
88C2×C4⋊Dic47C2×C411yescharacteristic
89C2×Dic47⋊C4—21no—
90C2×Dic47⋊C4—21no—
91C2×Dic47⋊C4—21no—
92C2×Dic47⋊C4—21no—
93C2×Dic47⋊C4—22no—
94C2×Dic47⋊C4—22no—
95C2×Dic47⋊C4C2×C411yescharacteristic
96C2×Dic47⋊C4C2×C411yescharacteristic
97C2×Dic47⋊C4C2×C411yescharacteristic
98C2×Dic47⋊C4C2×C411yescharacteristic
99C2×Dic47⋊C4C2×C411yescharacteristic
100C2×Dic47⋊C4C2×C411yescharacteristic
101C2×Dic47⋊C4C2×C411yescharacteristic
102C2×Dic47⋊C4C2×C411yescharacteristic
103C2×Dic47⋊C4C2×C411yescharacteristic
104C2×Dic47⋊C4C2×C411yescharacteristic
105C2×Dic47⋊C4D412yes—
106C2×Dic47⋊C4D412yes—
107C2×Dic47⋊C4D412yes—
108C2×Dic47⋊C4D412yes—
109C2×C22⋊Dic47C2×C411yescharacteristic
110C2×C22⋊Dic47C2×C411yescharacteristic
111C2×C22⋊Dic47C2312yes—
112C2×C22⋊Dic47C2311yescharacteristic
113C2×C22⋊Dic47C2311yescharacteristic
114C2×C22⋊Dic47C2312yes—
115C2×C4×Dic47—22no—
116C2×C4×Dic47—22no—
117C2×C4×Dic47—22no—
118C2×C4×Dic47C2×C411yescharacteristic
119C2×C4×Dic47C2×C411yescharacteristic
120#13093939—22no—
121#13093939Q814yescomplemented
122C47⋊#95—22no—
123C47⋊#95—22no—
124C47⋊#95—22no—
125C47⋊#95—22no—
126C47⋊#95—22no—
127C22×D4×C47C2311yescharacteristic
128C23×C4×C47C2×C411yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C4×D4×C47—22no—
131C4×D4×C47—22no—
132C2×C4⋊C4×C47—22no—
133C2×C4⋊C4×C47C2×C411yescharacteristic
134C2×C22⋊C4×C47C2×C411yescharacteristic
135C2×C22⋊C4×C47C2312yes—
136C2×C22⋊C4×C47C2312yes—
137C2×C22⋊C4×C47C2311yescharacteristic
138C2×C42×C47C2×C411yescharacteristic
139#99×C47—22no—
140#99×C47—22no—
141#95×C47—22no—
142C24×C47C22×C411yescharacteristic
143C24×C47C2411yescharacteristic
144C2×D4×C47—22no—
145C2×D4×C47—22no—
146C2×D4×C47C2×Q812yes—
147C2×D4×C47#4112yes—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—81no—
153C22×C4×C47—81no—
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C22×C411yescharacteristic
157C22×C4×C47C22×C411yescharacteristic
158C22×C4×C47C22×C411yescharacteristic
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×D412yes—
161C22×Dic47—22no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—22no—
167C22×Dic47—42no—
168C22×Dic47—42no—
169C22×Dic47—81no—
170C22×Dic47—81no—
171C22×Dic47C22×C411yescharacteristic
172C22×Dic47C22×C411yescharacteristic
173C22×Dic47C22×C411yescharacteristic
174C22×Dic47C22×C411yescharacteristic
175C22×Dic47C22×C411yescharacteristic
176C22×Dic47C22×C411yescharacteristic
177C22×Dic47C22×C411yescharacteristic
178C22×Dic47C22×C411yescharacteristic
179C22×Dic47C2×D412yes—
180C22×Dic47C2×D412yes—
181C22×Dic47C2×D412yes—
182C22×Dic47C2×D412yes—
183C2×Dic94—21no—
184C2×Dic94—21no—
185C2×Dic94—22no—
186C2×Dic94—22no—
187C2×Dic94—42no—
188C2×Dic94—81no—
189C2×Dic94—81no—
190C4⋊C4×C47—22no—
191C4⋊C4×C47—82no—
192C22⋊C4×C47—22no—
193C22⋊C4×C47—22no—
194C22⋊C4×C47—22no—
195C22⋊C4×C47—22no—
196C22⋊C4×C47—22no—
197C22⋊C4×C47—22no—
198C42×C47—21no—
199C42×C47—21no—
200C22⋊Dic47—22no—
201C22⋊Dic47—22no—
202C22⋊Dic47—22no—
203C22⋊Dic47—22no—
204C22⋊Dic47—22no—
205C22⋊Dic47—22no—
206C22⋊Dic47—22no—
207C22⋊Dic47C2×Q814yes—
208C4⋊Dic47—22no—
209C4⋊Dic47—22no—
210C4⋊Dic47—22no—
211C4⋊Dic47—21no—
212C4⋊Dic47—21no—
213C4⋊Dic47—22no—
214Dic47⋊C4—21no—
215Dic47⋊C4—21no—
216Dic47⋊C4—21no—
217Dic47⋊C4—21no—
218Dic47⋊C4—21no—
219Dic47⋊C4—21no—
220Dic47⋊C4—21no—
221Dic47⋊C4—21no—
222Dic47⋊C4—22no—
223Dic47⋊C4—22no—
224Dic47⋊C4—44no—
225Dic47⋊C4—82no—
226Dic47⋊C4C22⋊C411yescharacteristic
227Dic47⋊C4C22⋊C411yescharacteristic
228Dic47⋊C4C22⋊C411yescharacteristic
229Dic47⋊C4C22⋊C411yescharacteristic
230Dic47⋊C4C22⋊C412yes—
231Dic47⋊C4C22⋊C412yes—
232Dic47⋊C4C22⋊C412yes—
233Dic47⋊C4C22⋊C412yes—
234Dic47⋊C4C22⋊C412yes—
235Dic47⋊C4C22⋊C412yes—
236C4×Dic47—21no—
237C4×Dic47—21no—
238C4×Dic47—21no—
239C4×Dic47—21no—
240C4×Dic47—44no—
241C4×Dic47—82no—
242C4×Dic47—82no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47C4×Q812yes—
250C23×C47C23×C411yescharacteristic
251C23×C47C22×D412yes—
252C23×C47C22×Q811yescharacteristic
253C23×C47C2×#4111yescharacteristic
254C23×C472−1+412yes—
255D4×C47—24no—
256D4×C47—24no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—42no—
262C2×C4×C47—42no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—42no—
268C2×C4×C47—42no—
269C2×C4×C47—42no—
270C2×C4×C47—42no—
271C2×C4×C47—42no—
272C2×C4×C47—42no—
273C2×C4×C47—81no—
274C2×C4×C47—81no—
275C2×C4×C47C2×C22⋊C411yescharacteristic
276C2×C4×C47C2×C22⋊C411yescharacteristic
277C2×C4×C47C2×C22⋊C412yes—
278C2×C4×C47C4×Q812yes—
279C2×Dic47—24no—
280C2×Dic47—22no—
281C2×Dic47—21no—
282C2×Dic47—21no—
283C2×Dic47—21no—
284C2×Dic47—21no—
285C2×Dic47—24no—
286C2×Dic47—42no—
287C2×Dic47—42no—
288C2×Dic47—41no—
289C2×Dic47—41no—
290C2×Dic47—42no—
291C2×Dic47—41no—
292C2×Dic47—42no—
293C2×Dic47—42no—
294C2×Dic47—42no—
295C2×Dic47—42no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—42no—
301C2×Dic47—42no—
302C2×Dic47—42no—
303C2×Dic47—81no—
304C2×Dic47—81no—
305C2×Dic47C2×C22⋊C411yescharacteristic
306C2×Dic47C2×C22⋊C411yescharacteristic
307C2×Dic47C2×C22⋊C411yescharacteristic
308C2×Dic47C2×C22⋊C412yes—
309C2×Dic47C2×C22⋊C412yes—
310C2×Dic47C2×C22⋊C411yescharacteristic
311Dic94—42no—
312Dic94—42no—
313Dic94—82no—
314Dic94—82no—
315#22513—471nomaximal, Sylow
316C22×C47—22no—
317C22×C47—21no—
318C22×C47—22no—
319C22×C47—21no—
320C22×C47—22no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47—42no—
324C22×C47—42no—
325C22×C47—42no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47C22×C22⋊C411yescharacteristic
329C22×C47C2×C4×Q811yescharacteristic
330C22×C47#51911yescharacteristic
331C22×C47#54812yes—
332C22×C47D4×Q812yes—
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—21no—
336C4×C47—21no—
337C4×C47—41no—
338C4×C47—41no—
339C4×C47—82no—
340C4×C47—82no—
341Dic47—21no—
342Dic47—22no—
343Dic47—22no—
344Dic47—21no—
345Dic47—21no—
346Dic47—44no—
347Dic47—41no—
348Dic47—41no—
349Dic47—41no—
350Dic47—41no—
351Dic47—82no—
352Dic47#41012yes—
353C2×#554—471no—
354#2345—472no—
355#1996—472no—
356#1996—472no—
357#1996—472no—
358#1799—471no—
359#1799—471no—
360#1799D4711yescharacteristic
361C4×#99—471no—
362C4×#99—471no—
363C4×#99—471no—
364C2×C47—22no—
365C2×C47—22no—
366C2×C47—21no—
367C2×C47—21no—
368C2×C47—42no—
369C2×C47Q8×C22⋊C411yescharacteristic
370C2×C47C2×#41011yescharacteristic
371C2×C47#288311yescharacteristic
372#554—942no—
373#554—942no—
374#554—942no—
375#554—942no—
376C2×C4⋊Q8—471no—
377C2×#125—471no—
378C2×#125—471no—
379C2×C22⋊Q8—471no—
380C2×C22⋊Q8—471no—
381C2×C22⋊Q8—471no—
382C2×C22⋊Q8—471no—
383C2×C22⋊Q8—471no—
384C2×C22⋊Q8—471no—
385C2×C4×Q8—471no—
386C2×C4×D4—471no—
387C2×C4×D4—471no—
388C2×C4×D4C2×D4711yescharacteristic
389C22×C4⋊C4—471no—
390C22×C4⋊C4—471no—
391C2×#99—471no—
392C2×#99—471no—
393C2×#99C2×D4711yescharacteristic
394C2×#99C2×D4711yescharacteristic
395#389—942no—
396#387—942no—
397#387—942no—
398#380—472no—
399#380—472no—
400#380C2×D4712yes—
401C4×C4⋊C4—942no—
402C4×C22⋊C4—472no—
403C4×C22⋊C4—472no—
404C4×C22⋊C4—472no—
405#342—472no—
406#342—472no—
407#342—472no—
408#342—472no—
409#342—472no—
410#342C2×D4712yes—
411C47#2251311yescharacteristic, complemented, Sylow
412C22×Q8—471no—
413C22×Q8—471no—
414C22×Q8—471no—
415C22×D4C22×D4711yescharacteristic
416C23×C4—471no—
417C23×C4—471no—
418C23×C4—471no—
419C23×C4—471no—
420C23×C4C4×D4711yescharacteristic
421C23×C4C22×D4711yescharacteristic
422C4⋊Q8—942no—
423C4⋊Q8—942no—
424#125—942no—
425#125—942no—
426#125—942no—
427#125—942no—
428C22⋊Q8—942no—
429C22⋊Q8—942no—
430C22⋊Q8—942no—
431C22⋊Q8—942no—
432C22⋊Q8—942no—
433C22⋊Q8—942no—
434C22⋊Q8—942no—
435C22⋊Q8—942no—
436C22⋊Q8—942no—
437C22⋊Q8—942no—
438C22⋊Q8—942no—
439C22⋊Q8—942no—
440C4×Q8—941no—
441C4×Q8—941no—
442C4×Q8—941no—
443C4×Q8—941no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—942no—
447C4×D4—942no—
448C4×D4—942no—
449C4×D4—942no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—471no—
452C2×C4⋊C4—471no—
453C2×C4⋊C4—471no—
454C2×C4⋊C4—471no—
455C2×C4⋊C4—472no—
456C2×C4⋊C4—472no—
457C2×C4⋊C4—472no—
458C2×C4⋊C4—472no—
459C2×C4⋊C4—471no—
460C2×C4⋊C4—471no—
461C2×C4⋊C4—471no—
462C2×C4⋊C4—471no—
463C2×C4⋊C4—471no—
464C2×C4⋊C4—471no—
465C2×C4⋊C4—471no—
466C2×C4⋊C4—471no—
467C2×C4⋊C4—471no—
468C2×C4⋊C4—471no—
469C2×C4⋊C4—471no—
470C2×C4⋊C4—941no—
471C2×C4⋊C4—941no—
472C2×C4⋊C4—941no—
473C2×C4⋊C4—941no—
474C2×C4⋊C4—942no—
475C2×C4⋊C4—942no—
476C2×C4⋊C4C4×D4711yescharacteristic
477C2×C22⋊C4—472no—
478C2×C22⋊C4—471no—
479C2×C22⋊C4—471no—
480C2×C22⋊C4—471no—
481C2×C22⋊C4—471no—
482C2×C22⋊C4—472no—
483C2×C22⋊C4C4×D4711yescharacteristic
484C2×C22⋊C4C22×D4712yes—
485C2×C22⋊C4C22×D4712yes—
486C2×C22⋊C4C22×D4711yescharacteristic
487C2×C42—471no—
488C2×C42—471no—
489C2×C42—942no—
490C2×C42—942no—
491C2×C42—942no—
492C2×C42C4×D4711yescharacteristic
493#99—22no—
494#99—22no—
495#99—474no—
496#99—942no—
497#95—22no—
498#95—942no—
499#95—942no—
500#95—942no—
501#95—942no—
502#95—942no—
503C24C2×C4×D4711yescharacteristic
504C24C23×D4711yescharacteristic
505C2×Q8—942no—
506C2×Q8—941no—
507C2×Q8—941no—
508C2×Q8—942no—
509C2×Q8—3761no—
510C2×Q8—3761no—
511C2×Q8—1882no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4#1062535212yes—
515C2×D4Q8×D4712yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—471no—
523C22×C4—472no—
524C22×C4—471no—
525C22×C4—471no—
526C22×C4—471no—
527C22×C4—472no—
528C22×C4—472no—
529C22×C4—472no—
530C22×C4—471no—
531C22×C4—471no—
532C22×C4—471no—
533C22×C4—471no—
534C22×C4—941no—
535C22×C4—941no—
536C22×C4—941no—
537C22×C4—941no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—3761no—
541C22×C4—3761no—
542C22×C4—1882no—
543C22×C4—1882no—
544C22×C4C2×C4×D4711yescharacteristic
545C22×C4C2×C4×D4711yescharacteristic
546C22×C4C2×C4×D4711yescharacteristic
547C22×C4C2×C4×D4711yescharacteristic
548C22×C4C2×C4×D4711yescharacteristic
549C22×C4D4×D4712yes—
550C22×C4D4×D4712yes—
551C4⋊C4—22no—
552C4⋊C4—82no—
553C4⋊C4—471no—
554C4⋊C4—471no—
555C4⋊C4—471no—
556C4⋊C4—471no—
557C4⋊C4—472no—
558C4⋊C4—472no—
559C4⋊C4—472no—
560C4⋊C4—472no—
561C4⋊C4—472no—
562C4⋊C4—472no—
563C4⋊C4—941no—
564C4⋊C4—941no—
565C4⋊C4—941no—
566C4⋊C4—941no—
567C4⋊C4—942no—
568C4⋊C4—942no—
569C4⋊C4—942no—
570C4⋊C4—942no—
571C4⋊C4—941no—
572C4⋊C4—941no—
573C4⋊C4—942no—
574C4⋊C4—941no—
575C4⋊C4—941no—
576C4⋊C4—941no—
577C4⋊C4—941no—
578C4⋊C4—942no—
579C4⋊C4—3762no—
580C4⋊C4—1884no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—474no—
588C22⋊C4—942no—
589C22⋊C4—942no—
590C22⋊C4—942no—
591C22⋊C4—942no—
592C22⋊C4—942no—
593C22⋊C4—942no—
594C22⋊C4—942no—
595C42—21no—
596C42—21no—
597C42—941no—
598C42—941no—
599C42—941no—
600C42—941no—
601C42—3762no—
602C42—3762no—
603C42—1884no—
604C23—21no—
605C23—21no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23#1309398912yes—
611C23C22×C4×D4711yescharacteristic
612C23C2×D4×D4712yes—
613C23C2×Q8×D4711yescharacteristic
614C23C2×#1062535211yescharacteristic
615C23#1309407112yes—
616Q8—3762no—
617Q8—3762no—
618Q8—1882no—
619Q8—1882no—
620D4—24no—
621D4—24no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—81no—
639C2×C4—81no—
640C2×C4—471no—
641C2×C4—471no—
642C2×C4—471no—
643C2×C4—471no—
644C2×C4—472no—
645C2×C4—472no—
646C2×C4—944no—
647C2×C4—942no—
648C2×C4—944no—
649C2×C4—941no—
650C2×C4—941no—
651C2×C4—941no—
652C2×C4—941no—
653C2×C4—3761no—
654C2×C4—3761no—
655C2×C4—1882no—
656C2×C4—1882no—
657C2×C4—1882no—
658C2×C4—1881no—
659C2×C4—1881no—
660C2×C4—1882no—
661C2×C4—1881no—
662C2×C4—1882no—
663C2×C4—1882no—
664C2×C4—1882no—
665C2×C4—1882no—
666C2×C4—1882no—
667C2×C4—1882no—
668C2×C4—1881no—
669C2×C4—1881no—
670C2×C4—1881no—
671C2×C4—1881no—
672C2×C4C22⋊C4×D4711yescharacteristic
673C2×C4C22⋊C4×D4711yescharacteristic
674C2×C4C22⋊C4×D4712yes—
675C2×C4#1309398912yes—
676C22—22no—
677C22—21no—
678C22—22no—
679C22—21no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—41no—
687C22—41no—
688C22C2×C22⋊C4×D4711yescharacteristic
689C22C2×#1309398911yescharacteristic
690C22#1568960011yescharacteristic
691C22#1568977912yes—
692C22#1568978612yes—
693C4—21no—
694C4—21no—
695C4—22no—
696C4—22no—
697C4—41no—
698C4—41no—
699C4—82no—
700C4—82no—
701C4—472no—
702C4—941no—
703C4—942no—
704C4—941no—
705C4—941no—
706C4—942no—
707C4—3762no—
708C4—1884no—
709C4—1881no—
710C4—1881no—
711C4—1881no—
712C4—1881no—
713C2—22no—
714C2—22no—
715C2—21no—
716C2—21no—
717C2—42no—
718C2#2024622011yescharacteristic
719C2#410×D4711yescharacteristic
720C2#2025184611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#1799C2
socleC22×C47C22×C22⋊C4
prime radicalC22×D4×C47C23
cosocleC24×C47C24
hypercenter#1799D47
hypocenterC47#22513
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #20246260C2semidirect
3. #20244372C2semidirect
4. #20244371C2semidirect
5. #20244371C2semidirect
16. C2×#13094023C4semidirect
17. C2×#13094016C4semidirect
18. C2×#13094015C4semidirect
19. C2×#13094003C4semidirect
21. C2×#13094001C4semidirect
22. C2×#13094001C4semidirect
25. C2×C4×Dic94C4semidirect
28. C22×Dic47⋊C4C4semidirect
121. #13093939Q8semidirect
411. C47#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#156898322
#202462602
#202443722
#202443712
#202433742
#99×Dic472
C4×#130939392
C47×#17992
#2251347