Finite Group Databasebeta

← C2×#20244371 #26220916

Subgroups — C2×#20244371 #26220916

Order 12032.

1698 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094001C211yesmaximal, characteristic
2C2×#15688981C211yesmaximal, characteristic
3C2×C22⋊C4×Dic47C211yesmaximal, characteristic
4#20244371C218yesmaximal, direct product factor
5C2×#15688890C211yesmaximal, characteristic
6C2×#15688889C211yesmaximal, characteristic
7C2×#15688889C211yesmaximal, characteristic
8C2×C47×#342C211yesmaximal, characteristic
9C23×Dic94C411yescharacteristic, complemented
10C24×Dic47C2211yescharacteristic
11C2×#13094001—21no—
12C2×#13094001—21no—
13C2×#13094001—21no—
14C2×#13094001—21no—
15C2×#13094001—22no—
16C2×#13094001—22no—
17C2×#13094001C414yescomplemented
18C2×#13094001C2214yes—
19C22×C4⋊Dic47C411yescharacteristic, complemented
20C22×Dic47⋊C4—21no—
21C22×Dic47⋊C4C411yescharacteristic, complemented
22C22×Dic47⋊C4C411yescharacteristic, complemented
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C4×Dic47—21no—
27#15688981—22no—
28#15688981C2214yes—
29C22⋊C4×Dic47—22no—
30C22⋊C4×Dic47C2214yes—
31C2×C47⋊#95—21no—
32C2×C47⋊#95—21no—
33#15688890C2214yes—
34#15688889C2214yes—
35#15688889C2214yes—
36C22×C22⋊C4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47C2211yescharacteristic
39C47×#342C2214yes—
40C22×Dic94—21no—
41C22×Dic94—22no—
42C22×Dic94—21no—
43C22×Dic94—44no—
44C22×Dic94C2×C414yescomplemented
45C23×Dic47—21no—
46C23×Dic47—21no—
47C23×Dic47—44no—
48C23×Dic47C2×C411yescharacteristic
49C23×Dic47C2×C411yescharacteristic
50C23×Dic47C2×C411yescharacteristic
51C23×Dic47C2×C411yescharacteristic
52C23×Dic47C2×C412yes—
53C23×Dic47D411yescharacteristic
54C23×Dic47D411yescharacteristic
55C23×Dic47D411yescharacteristic
56C23×Dic47D411yescharacteristic
57C23×Dic47D412yes—
58C23×Dic47D412yes—
59C23×Dic47C2312yes—
60#13094001—24no—
61#13094001—24no—
62#13094001—24no—
63#13094001—24no—
64#13094001—24no—
65#13094001—24no—
66#13094001—24no—
67#13094001—24no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47—21no—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47C2×C414yescomplemented
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×Dic47⋊C4—22no—
76C2×Dic47⋊C4—22no—
77C2×Dic47⋊C4—21no—
78C2×Dic47⋊C4—24no—
79C2×Dic47⋊C4—44no—
80C2×Dic47⋊C4C2×C414yescomplemented
81C2×Dic47⋊C4C2×C414yescomplemented
82C2×C22⋊Dic47—21no—
83C2×C22⋊Dic47—21no—
84C2×C22⋊Dic47—21no—
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C22⋊Dic47—22no—
88C2×C22⋊Dic47—22no—
89C2×C22⋊Dic47—22no—
90C2×C22⋊Dic47—21no—
91C2×C22⋊Dic47C2×C412yes—
92C2×C22⋊Dic47Q814yescomplemented
93C2×C22⋊Dic47C2312yes—
94C2×C22⋊Dic47C2312yes—
95C2×C22⋊Dic47C2312yes—
96C2×C4×Dic47—24no—
97C2×C4×Dic47—44no—
98C47⋊#95—24no—
99C47⋊#95—24no—
100C25×C47C2311yescharacteristic
101C23×C4×C47—21no—
102C23×C4×C47—21no—
103C23×C4×C47C2×C411yescharacteristic
104C23×C4×C47C2×C411yescharacteristic
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—22no—
111C2×C22⋊C4×C47—22no—
112C2×C22⋊C4×C47—22no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47C2×C412yes—
115C2×C22⋊C4×C47Q814yescomplemented
116C2×C22⋊C4×C47C2312yes—
117C2×C22⋊C4×C47C2312yes—
118C2×C22⋊C4×C47C2312yes—
119C24×C47—42no—
120C24×C47—42no—
121C24×C47C22×C411yescharacteristic
122C24×C47C22×C411yescharacteristic
123C24×C47C2×D411yescharacteristic
124C24×C47C2×D411yescharacteristic
125C24×C47C2×D411yescharacteristic
126C24×C47C2×D411yescharacteristic
127C24×C47C2×Q812yes—
128C24×C47C2×Q812yes—
129C24×C47#4112yes—
130C24×C47#4112yes—
131C24×C47C2411yescharacteristic
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—24no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—42no—
140C22×C4×C47—42no—
141C22×C4×C47—42no—
142C22×C4×C47—42no—
143C22×C4×C47—42no—
144C22×C4×C47—42no—
145C22×C4×C47—42no—
146C22×C4×C47C22×C412yes—
147C22×C4×C47C22×C412yes—
148C22×Dic47—24no—
149C22×Dic47—24no—
150C22×Dic47—24no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—24no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—44no—
159C22×Dic47—44no—
160C22×Dic47—44no—
161C22×Dic47—44no—
162C22×Dic47—42no—
163C22×Dic47—42no—
164C22×Dic47—42no—
165C22×Dic47—42no—
166C22×Dic47—42no—
167C22×Dic47—42no—
168C22×Dic47—42no—
169C22×Dic47—42no—
170C22×Dic47—42no—
171C22×Dic47—42no—
172C22×Dic47C22⋊C411yescharacteristic
173C22×Dic47C22⋊C411yescharacteristic
174C22×Dic47C22⋊C411yescharacteristic
175C22×Dic47C22⋊C412yes—
176C22×Dic47C22⋊C412yes—
177C22×Dic47C22⋊C412yes—
178C22×Dic47C22⋊C412yes—
179C22×Dic47C22⋊C412yes—
180C22×Dic47C22⋊C412yes—
181C22×Dic47C22⋊C411yescharacteristic
182C22×Dic47C22×C412yes—
183C22×Dic47C22×C412yes—
184C22×Dic47C22×C412yes—
185C22×Dic47C22×C412yes—
186C22×Dic47C2×D412yes—
187C22×Dic47C2×D412yes—
188C22×Dic47C2×D412yes—
189C22×Dic47C2×D412yes—
190C2×Dic94—24no—
191C2×Dic94—24no—
192C2×Dic94—44no—
193C2×Dic94—48no—
194C2×Dic94—44no—
195C2×Dic94—48no—
196C22⋊C4×C47—22no—
197C22⋊C4×C47—22no—
198C22⋊C4×C47—24no—
199C22⋊C4×C47—22no—
200C22⋊C4×C47—22no—
201C22⋊C4×C47—22no—
202C22⋊C4×C47—22no—
203C22⋊C4×C47—22no—
204C22⋊C4×C47—42no—
205C22⋊C4×C47C2×Q814yescomplemented
206C22⋊Dic47—22no—
207C22⋊Dic47—22no—
208C22⋊Dic47—24no—
209C22⋊Dic47—22no—
210C22⋊Dic47—22no—
211C22⋊Dic47—22no—
212C22⋊Dic47—22no—
213C22⋊Dic47—22no—
214C22⋊Dic47—42no—
215C22⋊Dic47C2×Q814yescomplemented
216C4⋊Dic47—24no—
217C4⋊Dic47—24no—
218Dic47⋊C4—24no—
219Dic47⋊C4—24no—
220Dic47⋊C4—24no—
221Dic47⋊C4—24no—
222Dic47⋊C4—48no—
223C4×Dic47—48no—
224C23×C47—22no—
225C23×C47—22no—
226C23×C47—22no—
227C23×C47—22no—
228C23×C47—22no—
229C23×C47—22no—
230C23×C47—41no—
231C23×C47—41no—
232C23×C47—41no—
233C23×C47—41no—
234C23×C47—41no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—44no—
238C23×C47—44no—
239C23×C47—44no—
240C23×C47—44no—
241C23×C47—41no—
242C23×C47C2×C22⋊C411yescharacteristic
243C23×C47C2×C22⋊C411yescharacteristic
244C23×C47C2×C22⋊C411yescharacteristic
245C23×C47C2×C22⋊C411yescharacteristic
246C23×C47C4×Q812yes—
247C23×C47C4×Q812yes—
248C23×C47C4×Q812yes—
249C23×C47C4×Q812yes—
250C23×C47C22⋊Q812yes—
251C23×C47C22⋊Q812yes—
252C23×C47C22⋊Q812yes—
253C23×C47C22⋊Q812yes—
254C23×C47#12412yes—
255C23×C47#12412yes—
256C23×C47C4⋊Q812yes—
257C23×C47C4⋊Q812yes—
258C23×C47C23×C411yescharacteristic
259C23×C47C22×D411yescharacteristic
260C23×C47C22×D411yescharacteristic
261C23×C47C22×Q811yescharacteristic
262C23×C47C22×Q811yescharacteristic
263C23×C47C2×#4111yescharacteristic
264C23×C47C2×#4111yescharacteristic
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—24no—
268C2×C4×C47—42no—
269C2×C4×C47—42no—
270C2×C4×C47—42no—
271C2×C4×C47—48no—
272C2×C4×C47—42no—
273C2×C4×C47—42no—
274C2×C4×C47—42no—
275C2×C4×C47—42no—
276C2×C4×C47—42no—
277C2×C4×C47—42no—
278C2×C4×C47—42no—
279C2×C4×C47—42no—
280C2×C4×C47—84no—
281C2×Dic47—22no—
282C2×Dic47—22no—
283C2×Dic47—22no—
284C2×Dic47—24no—
285C2×Dic47—24no—
286C2×Dic47—24no—
287C2×Dic47—24no—
288C2×Dic47—24no—
289C2×Dic47—24no—
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—24no—
293C2×Dic47—42no—
294C2×Dic47—42no—
295C2×Dic47—42no—
296C2×Dic47—42no—
297C2×Dic47—42no—
298C2×Dic47—42no—
299C2×Dic47—42no—
300C2×Dic47—42no—
301C2×Dic47—42no—
302C2×Dic47—48no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—84no—
312C2×Dic47#9914yes—
313C2×Dic47C2×C22⋊C412yes—
314C2×Dic47C2×C22⋊C412yes—
315C2×Dic47C2×C22⋊C412yes—
316C2×Dic47C2×C22⋊C412yes—
317Dic94—48no—
318Dic94—48no—
319C2×#1996—471nomaximal, Sylow
320C22×C47—21no—
321C22×C47—21no—
322C22×C47—21no—
323C22×C47—21no—
324C22×C47—21no—
325C22×C47—21no—
326C22×C47—21no—
327C22×C47—21no—
328C22×C47—21no—
329C22×C47—21no—
330C22×C47—21no—
331C22×C47—21no—
332C22×C47—24no—
333C22×C47—24no—
334C22×C47—24no—
335C22×C47—24no—
336C22×C47—24no—
337C22×C47—24no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47#39112yes—
349C22×C47#39112yes—
350C22×C47#39112yes—
351C22×C47#39112yes—
352C22×C47C2×#9912yes—
353C22×C47#41012yes—
354C22×C47C22×C22⋊C411yescharacteristic
355C22×C47C2×C4×Q811yescharacteristic
356C22×C47C2×C4×Q811yescharacteristic
357C22×C47C2×C22⋊Q811yescharacteristic
358C22×C47C2×C22⋊Q811yescharacteristic
359C22×C47C2×#12411yescharacteristic
360C22×C47C2×C4⋊Q811yescharacteristic
361C4×C47—44no—
362C4×C47—42no—
363C4×C47—42no—
364C4×C47—82no—
365Dic47—22no—
366Dic47—22no—
367Dic47—22no—
368Dic47—44no—
369Dic47—42no—
370Dic47—42no—
371Dic47—82no—
372Dic47C2×#9914yes—
373C22×C22⋊Q8—471no—
374C2×#380—471no—
375C2×C4×C22⋊C4—471no—
376#1996—478no—
377C2×#342—471no—
378C2×#342—471no—
379C2×#342—471no—
380C2×#342D4711yescharacteristic
381C2×C47—21no—
382C2×C47—21no—
383C2×C47—21no—
384C2×C47—21no—
385C2×C47—21no—
386C2×C47—21no—
387C2×C47—22no—
388C2×C47—22no—
389C2×C47—22no—
390C2×C47#199614yescomplemented
391C2×C47C2×#39111yescharacteristic
392C2×C47C22×#9911yescharacteristic
393C2×C47C2×#41011yescharacteristic
394C23×Q8—471no—
395C24×C4—471no—
396C2×C22⋊Q8—474no—
397C2×C22⋊Q8—474no—
398C2×C22⋊Q8—941no—
399C2×C22⋊Q8—941no—
400C2×C22⋊Q8—941no—
401C2×C22⋊Q8—941no—
402C2×C22⋊Q8—942no—
403C2×C22⋊Q8—942no—
404C22×C4⋊C4—471no—
405C22×C4⋊C4—471no—
406C22×C4⋊C4—471no—
407C22×C4⋊C4—941no—
408C22×C22⋊C4—471no—
409C22×C22⋊C4—471no—
410C22×C22⋊C4—471no—
411C22×C22⋊C4C2×D4711yescharacteristic
412C22×C22⋊C4C2×D4711yescharacteristic
413C22×C22⋊C4C2×D4711yescharacteristic
414C22×C42—941no—
415#380—474no—
416#380—942no—
417C4×C22⋊C4—474no—
418C4×C22⋊C4—942no—
419C2×#95—941no—
420C2×#95—941no—
421#342—474no—
422#342—474no—
423#342—474no—
424#342C2×D4714yes—
425C47C2×#199611yescharacteristic, complemented, Sylow
426C25C22×D4711yescharacteristic
427C22×Q8—474no—
428C22×Q8—942no—
429C22×Q8—941no—
430C22×Q8—941no—
431C22×Q8—1884no—
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—471no—
435C23×C4—471no—
436C23×C4—471no—
437C23×C4—471no—
438C23×C4—472no—
439C23×C4—471no—
440C23×C4—471no—
441C23×C4—472no—
442C23×C4—472no—
443C23×C4—472no—
444C23×C4—471no—
445C23×C4—471no—
446C23×C4—941no—
447C23×C4—941no—
448C23×C4—1884no—
449C23×C4C4×D4711yescharacteristic
450C23×C4C4×D4711yescharacteristic
451C22⋊Q8—944no—
452C22⋊Q8—944no—
453C22⋊Q8—944no—
454C22⋊Q8—944no—
455C22⋊Q8—944no—
456C22⋊Q8—944no—
457C22⋊Q8—944no—
458C22⋊Q8—944no—
459C2×C4⋊C4—474no—
460C2×C4⋊C4—474no—
461C2×C4⋊C4—474no—
462C2×C4⋊C4—942no—
463C2×C4⋊C4—942no—
464C2×C4⋊C4—941no—
465C2×C4⋊C4—941no—
466C2×C4⋊C4—941no—
467C2×C4⋊C4—941no—
468C2×C4⋊C4—942no—
469C2×C4⋊C4—941no—
470C2×C4⋊C4—941no—
471C2×C4⋊C4—944no—
472C2×C4⋊C4—1884no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—474no—
483C2×C22⋊C4—472no—
484C2×C22⋊C4—472no—
485C2×C22⋊C4—472no—
486C2×C22⋊C4—472no—
487C2×C22⋊C4—942no—
488C2×C22⋊C4—941no—
489C2×C22⋊C4—941no—
490C2×C22⋊C4—941no—
491C2×C22⋊C4—941no—
492C2×C22⋊C4—941no—
493C2×C22⋊C4—942no—
494C2×C22⋊C4—942no—
495C2×C22⋊C4—941no—
496C2×C22⋊C4Dic9414yescomplemented
497C2×C22⋊C4C4×D4712yes—
498C2×C22⋊C4C22×D4712yes—
499C2×C22⋊C4C22×D4712yes—
500C2×C22⋊C4C22×D4712yes—
501C2×C42—944no—
502C2×C42—1884no—
503#95—944no—
504#95—944no—
505C24—42no—
506C24—42no—
507C24C2×Dic9412yes—
508C24C2×C4×D4711yescharacteristic
509C24C2×C4×D4711yescharacteristic
510C24#1062535012yes—
511C24D4×D4711yescharacteristic
512C24D4×D4711yescharacteristic
513C24D4×D4711yescharacteristic
514C24D4×D4711yescharacteristic
515C24#1062535212yes—
516C24Q8×D4712yes—
517C24C23×D4711yescharacteristic
518C2×Q8—944no—
519C2×Q8—944no—
520C2×Q8—1884no—
521C2×Q8—1888no—
522C2×Q8—1888no—
523C2×Q8—1884no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—471no—
539C22×C4—472no—
540C22×C4—472no—
541C22×C4—472no—
542C22×C4—471no—
543C22×C4—471no—
544C22×C4—471no—
545C22×C4—472no—
546C22×C4—472no—
547C22×C4—472no—
548C22×C4—472no—
549C22×C4—472no—
550C22×C4—472no—
551C22×C4—472no—
552C22×C4—472no—
553C22×C4—472no—
554C22×C4—472no—
555C22×C4—472no—
556C22×C4—944no—
557C22×C4—944no—
558C22×C4—944no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—944no—
564C22×C4—942no—
565C22×C4—942no—
566C22×C4—1884no—
567C22×C4—1884no—
568C22×C4—1884no—
569C22×C4—1884no—
570C22×C4—1882no—
571C22×C4—1882no—
572C22×C4—1882no—
573C22×C4—1882no—
574C22×C4—1882no—
575C22×C4—1882no—
576C22×C4—1882no—
577C22×C4—1882no—
578C22×C4—1882no—
579C22×C4—1882no—
580C22×C4C2×C4×D4712yes—
581C22×C4C2×C4×D4712yes—
582C4⋊C4—944no—
583C4⋊C4—944no—
584C4⋊C4—944no—
585C4⋊C4—944no—
586C4⋊C4—944no—
587C4⋊C4—944no—
588C4⋊C4—1888no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—24no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—42no—
598C22⋊C4—474no—
599C22⋊C4—942no—
600C22⋊C4—942no—
601C22⋊C4—944no—
602C22⋊C4—942no—
603C22⋊C4—942no—
604C22⋊C4—942no—
605C22⋊C4—942no—
606C22⋊C4—942no—
607C22⋊C4—1882no—
608C22⋊C4C2×Dic9414yescomplemented
609C42—1888no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—44no—
621C23—41no—
622C23—44no—
623C23—41no—
624C23—41no—
625C23—44no—
626C23—44no—
627C23—41no—
628C23C22⋊C4×D4711yescharacteristic
629C23C22⋊C4×D4711yescharacteristic
630C23C22⋊C4×D4711yescharacteristic
631C23C22⋊C4×D4711yescharacteristic
632C23#1309398912yes—
633C23#1309398912yes—
634C23C4×Dic9412yes—
635C23C4×Dic9412yes—
636C23#1309400112yes—
637C23#1309400112yes—
638C23#1309400212yes—
639C23#1309400212yes—
640C23#1309401012yes—
641C23#1309401012yes—
642C23#1309402312yes—
643C23#1309402312yes—
644C23C22×C4×D4711yescharacteristic
645C23C2×D4×D4711yescharacteristic
646C23C2×D4×D4711yescharacteristic
647C23C2×Q8×D4711yescharacteristic
648C23C22×Dic9411yescharacteristic
649C23C2×#1062535211yescharacteristic
650C23C2×#1062535011yescharacteristic
651Q8—1888no—
652Q8—1888no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—42no—
657C2×C4—48no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—84no—
669C2×C4—472no—
670C2×C4—474no—
671C2×C4—472no—
672C2×C4—472no—
673C2×C4—472no—
674C2×C4—944no—
675C2×C4—944no—
676C2×C4—944no—
677C2×C4—944no—
678C2×C4—944no—
679C2×C4—944no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—944no—
686C2×C4—3764no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4—1882no—
690C2×C4—1882no—
691C2×C4—1882no—
692C2×C4—1882no—
693C2×C4—1882no—
694C2×C4—1882no—
695C2×C4—1882no—
696C2×C4—1882no—
697C2×C4—1888no—
698C2×C4—1882no—
699C2×C4—1882no—
700C2×C4—1882no—
701C2×C4—1882no—
702C2×C4—1882no—
703C2×C4—1882no—
704C2×C4—1882no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—24no—
710C22—24no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22#1568902712yes—
734C22#1568902712yes—
735C22#1568902712yes—
736C22#1568902712yes—
737C22#99×D4712yes—
738C22#1568909512yes—
739C22C2×C22⋊C4×D4711yescharacteristic
740C22C2×#1309398911yescharacteristic
741C22C2×C4×Dic9411yescharacteristic
742C22C2×#1309400111yescharacteristic
743C22C2×#1309400211yescharacteristic
744C22C2×#1309401011yescharacteristic
745C22C2×#1309402311yescharacteristic
746C4—44no—
747C4—42no—
748C4—42no—
749C4—82no—
750C4—474no—
751C4—942no—
752C4—942no—
753C4—942no—
754C4—3762no—
755C4—1884no—
756C4—1882no—
757C4—1882no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—22no—
762C2—22no—
763C2—22no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2#2024437114yesdirect product factor
768C2C2×#1568902711yescharacteristic
769C2C2×#99×D4711yescharacteristic
770C2C2×#1568909511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC2×C47×#342C2
socleC23×C47C2×C22⋊C4
prime radicalC25×C47C23
cosocleC24×C47C24
hypercenterC2×#342D47
hypocenterC47C2×#1996
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. #20244371C2direct (N × H)
9. C23×Dic94C4semidirect
17. C2×#13094001C4semidirect
19. C22×C4⋊Dic47C4semidirect
21. C22×Dic47⋊C4C4semidirect
22. C22×Dic47⋊C4C4semidirect
44. C22×Dic94C2×C4semidirect
71. C2×C4⋊Dic47C2×C4semidirect
80. C2×Dic47⋊C4C2×C4semidirect
81. C2×Dic47⋊C4C2×C4semidirect
92. C2×C22⋊Dic47Q8semidirect
115. C2×C22⋊C4×C47Q8semidirect
205. C22⋊C4×C47C2×Q8semidirect
215. C22⋊Dic47C2×Q8semidirect
390. C2×C47#1996semidirect
425. C47C2×#1996semidirect
496. C2×C22⋊C4Dic94semidirect
608. C22⋊C4C2×Dic94semidirect
767. C2#20244371direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940012
C2×#156889812
C2×C22⋊C4×Dic472
#202443712
C2×#156888902
C2×#156888892
C2×C47×#3422
C2×#199647