Finite Group Databasebeta

← #26139167

Subgroups — #26139167

Order 12032.

1750 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic94C211yesmaximal, characteristic
2C2×#15689027C211yesmaximal, characteristic
3C2×#15689027C211yesmaximal, characteristic
4C2×#15689018C211yesmaximal, characteristic
5C2×#15688987C211yesmaximal, characteristic
6#20241646C211yesmaximal, characteristic
7#20241645C211yesmaximal, characteristic
8#20241644C211yesmaximal, characteristic
9#20241643C211yesmaximal, characteristic
10#20241623C211yesmaximal, characteristic
11#20241621C211yesmaximal, characteristic
12#20241620C211yesmaximal, characteristic
13Dic47⋊#95C211yesmaximal, characteristic
14#95×Dic47C211yesmaximal, characteristic
15C47×#1436C211yesmaximal, characteristic
16C23×Dic94C2211yescharacteristic
17C2×C4×Dic94—24no—
18C2×C4×Dic94—24no—
19C2×C4×Dic94—24no—
20C22×C4⋊Dic47C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28C22×C4×Dic47C2211yescharacteristic
29C22×C4×Dic47C2211yescharacteristic
30#15689027—24no—
31#15689027C418yescomplemented
32#15689018—24no—
33#15688987—24no—
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2211yescharacteristic
38C2×C47⋊#95C2211yescharacteristic
39C2×C47⋊#95C2211yescharacteristic
40C2×C47⋊#95C2211yescharacteristic
41C2×C47⋊#95C2211yescharacteristic
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2211yescharacteristic
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C2×C47⋊#95C2211yescharacteristic
49C2×C47⋊#95C2211yescharacteristic
50C2×C47⋊#95C2211yescharacteristic
51C22×C4⋊C4×C47C2211yescharacteristic
52C22×C42×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C2×#95×C47C2211yescharacteristic
57C2×#95×C47C2211yescharacteristic
58C22×Dic94—22no—
59C22×Dic94—22no—
60C22×Dic94—22no—
61C22×Dic94—22no—
62C22×Dic94C2×C414yes—
63C22×Dic94D414yes—
64C22×Dic94Q814yes—
65C23×Dic47C2311yescharacteristic
66C23×Dic47C2311yescharacteristic
67C23×Dic47C2311yescharacteristic
68C23×Dic47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C4×Dic94—232no—
74C2×C4⋊Dic47—22no—
75C2×C4⋊Dic47—22no—
76C2×C4⋊Dic47—22no—
77C2×Dic47⋊C4—22no—
78C2×Dic47⋊C4—22no—
79C2×Dic47⋊C4—22no—
80C2×Dic47⋊C4—22no—
81C2×Dic47⋊C4—22no—
82C2×Dic47⋊C4—22no—
83C2×Dic47⋊C4—22no—
84C2×Dic47⋊C4—22no—
85C2×Dic47⋊C4—22no—
86C2×Dic47⋊C4—22no—
87C2×Dic47⋊C4—22no—
88C2×Dic47⋊C4—22no—
89C2×Dic47⋊C4—22no—
90C2×Dic47⋊C4C2×C414yes—
91C2×Dic47⋊C4D414yes—
92C2×C4×Dic47—22no—
93C2×C4×Dic47—22no—
94C2×C4×Dic47—22no—
95C2×C4×Dic47—22no—
96C2×C4×Dic47—22no—
97C2×C4×Dic47—22no—
98C2×C4×Dic47—22no—
99C2×C4×Dic47—22no—
100C2×C4×Dic47—22no—
101C2×C4×Dic47—22no—
102C2×C4×Dic47C2×C414yes—
103C2×C4×Dic47D414yes—
104C47⋊#95—22no—
105C47⋊#95—22no—
106C47⋊#95—22no—
107C47⋊#95—22no—
108C47⋊#95—22no—
109C47⋊#95—22no—
110C47⋊#95—22no—
111C47⋊#95—22no—
112C47⋊#95—22no—
113C47⋊#95—22no—
114C47⋊#95—22no—
115C47⋊#95—22no—
116C47⋊#95—22no—
117C47⋊#95—22no—
118C47⋊#95C2×C414yes—
119C47⋊#95C2×C414yes—
120C47⋊#95C2×C414yes—
121C23×C4×C47C2311yescharacteristic
122C23×C4×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C2×C4⋊C4×C47—22no—
129C2×C4⋊C4×C47—22no—
130C2×C4⋊C4×C47—22no—
131C2×C42×C47—22no—
132C2×C42×C47—22no—
133C2×C42×C47—22no—
134#95×C47—22no—
135#95×C47—22no—
136#95×C47—22no—
137#95×C47—22no—
138#95×C47C2×C414yes—
139C24×C47C2411yescharacteristic
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47C22×C412yes—
180C22×C4×C47C22×C412yes—
181C22×C4×C47C22×C412yes—
182C22×C4×C47C2×D412yes—
183C22×C4×C47C2×D412yes—
184C22×C4×C47C2×D412yes—
185C22×C4×C47C2×Q812yes—
186C22×C4×C47#4112yes—
187C22×C4×C47#4112yes—
188C22×C4×C47#4112yes—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47C22×C412yes—
231C22×Dic47C22×C412yes—
232C22×Dic47C22×C412yes—
233C22×Dic47C22×C412yes—
234C22×Dic47C2×D412yes—
235C22×Dic47C2×D412yes—
236C22×Dic47C2×D412yes—
237C22×Dic47C2×D412yes—
238C22×Dic47C2×D412yes—
239C22×Dic47C2×D412yes—
240C22×Dic47C2×Q812yes—
241C22×Dic47C2×Q812yes—
242C22×Dic47#4112yes—
243C22×Dic47#4112yes—
244C22×Dic47#4112yes—
245C2×Dic94—28no—
246C2×Dic94—28no—
247C2×Dic94—28no—
248C2×Dic94—28no—
249C2×Dic94—28no—
250C2×Dic94—28no—
251C2×Dic94C4⋊C4116yescomplemented
252C4⋊C4×C47—44no—
253C42×C47—28no—
254C4⋊Dic47—28no—
255Dic47⋊C4—28no—
256Dic47⋊C4—28no—
257Dic47⋊C4—28no—
258Dic47⋊C4—44no—
259Dic47⋊C4—44no—
260C4×Dic47—28no—
261C4×Dic47—28no—
262C4×Dic47—28no—
263C4×Dic47—44no—
264C23×C47C23×C411yescharacteristic
265C23×C47C22×D411yescharacteristic
266C23×C47C22×D411yescharacteristic
267C23×C47C22×D411yescharacteristic
268C23×C47C22×Q811yescharacteristic
269C23×C47C2×#4111yescharacteristic
270C23×C47C2×#4111yescharacteristic
271C23×C47C2×#4111yescharacteristic
272C23×C47C2×#4111yescharacteristic
273C23×C47C2×#4111yescharacteristic
274C23×C47C2×#4111yescharacteristic
275C23×C472−1+411yescharacteristic
276C23×C472−1+411yescharacteristic
277C23×C472−1+411yescharacteristic
278C23×C472−1+411yescharacteristic
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47C2×C4⋊C414yes—
327C2×C4×C47#12414yes—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—41no—
350C2×Dic47—41no—
351C2×Dic47—41no—
352C2×Dic47—41no—
353C2×Dic47—41no—
354C2×Dic47—41no—
355C2×Dic47—41no—
356C2×Dic47—41no—
357C2×Dic47—41no—
358C2×Dic47—41no—
359C2×Dic47—41no—
360C2×Dic47—41no—
361C2×Dic47—41no—
362C2×Dic47—41no—
363C2×Dic47—41no—
364C2×Dic47—41no—
365C2×Dic47—41no—
366C2×Dic47—41no—
367C2×Dic47—41no—
368C2×Dic47—41no—
369C2×Dic47—41no—
370C2×Dic47—41no—
371C2×Dic47—41no—
372C2×Dic47—41no—
373C2×Dic47—41no—
374C2×Dic47—41no—
375C2×Dic47—41no—
376C2×Dic47C2×C4⋊C414yes—
377C2×Dic47C2×C4⋊C414yes—
378C2×Dic47C4×D414yes—
379C2×Dic47C4×D414yes—
380C2×Dic47#12014yes—
381C2×Dic47C22⋊Q814yes—
382C2×Dic47C22⋊Q814yes—
383C2×Dic47#12314yes—
384Dic94—232no—
385#13978—471nomaximal, Sylow
386C22×C47C22×C4⋊C411yescharacteristic
387C22×C47C2×C4×D411yescharacteristic
388C22×C47C2×C4×D411yescharacteristic
389C22×C47C4×#4111yescharacteristic
390C22×C47C4×#4111yescharacteristic
391C22×C47#51911yescharacteristic
392C22×C47#51911yescharacteristic
393C22×C47C2×#12011yescharacteristic
394C22×C47C2×C22⋊Q811yescharacteristic
395C22×C47C2×C22⋊Q811yescharacteristic
396C22×C47C2×#12311yescharacteristic
397C22×C47C2×#12411yescharacteristic
398C22×C47#52911yescharacteristic
399C22×C47#52911yescharacteristic
400C22×C47#53211yescharacteristic
401C22×C47#53611yescharacteristic
402C22×C47#53611yescharacteristic
403C22×C47#54111yescharacteristic
404C22×C47#54111yescharacteristic
405C22×C47#54711yescharacteristic
406C22×C47#54711yescharacteristic
407C22×C47#54811yescharacteristic
408C22×C47#54811yescharacteristic
409C22×C47#54811yescharacteristic
410C22×C47#54811yescharacteristic
411C22×C47#54811yescharacteristic
412C22×C47#54811yescharacteristic
413C22×C47#55211yescharacteristic
414C22×C47#55211yescharacteristic
415C22×C47#55611yescharacteristic
416C22×C47#55611yescharacteristic
417C22×C47#55711yescharacteristic
418C22×C47#55711yescharacteristic
419C22×C47#55711yescharacteristic
420C22×C47#55711yescharacteristic
421C4×C47—24no—
422C4×C47—24no—
423C4×C47—42no—
424C4×C47—42no—
425C4×C47—42no—
426C4×C47—42no—
427C4×C47—81no—
428Dic47—24no—
429Dic47—42no—
430Dic47—42no—
431Dic47—42no—
432Dic47—42no—
433Dic47—42no—
434Dic47—81no—
435Dic47#38518yes—
436C22×C4×Q8—471no—
437C2×#391—471no—
438C2×#391—471no—
439C2×#389—471no—
440C2×#382—471no—
441#1442—471no—
442#1442—471no—
443#1442—471no—
444#1442—471no—
445#1436—471no—
446#1436—471no—
447#1436—471no—
448#1436D4711yescharacteristic
449C4⋊#95—471no—
450C4×#95—471no—
451C2×C47C2×#38511yescharacteristic
452C2×C47C4×#12411yescharacteristic
453C2×C47#232711yescharacteristic
454C2×C47#235111yescharacteristic
455C2×C47#235111yescharacteristic
456C2×C47#236211yescharacteristic
457C2×C47#236211yescharacteristic
458C2×C47#242111yescharacteristic
459C2×C47#242111yescharacteristic
460C2×C47#243211yescharacteristic
461C2×C47#243611yescharacteristic
462C2×C47#245311yescharacteristic
463C2×C47#245311yescharacteristic
464C2×C47#256511yescharacteristic
465C2×C47#256811yescharacteristic
466C23×Q8—471no—
467C2×C4×Q8—944no—
468C2×C4×Q8—944no—
469C2×C4×Q8—944no—
470C22×C4⋊C4—471no—
471C22×C4⋊C4—471no—
472C22×C4⋊C4—471no—
473C22×C4⋊C4—471no—
474C22×C4⋊C4—471no—
475C22×C4⋊C4—471no—
476C22×C4⋊C4C2×D4711yescharacteristic
477C22×C42—471no—
478C22×C42—471no—
479C22×C42—471no—
480C22×C42—471no—
481C22×C42C2×D4711yescharacteristic
482#391—478no—
483#391—944no—
484#389—944no—
485#382—944no—
486C2×#95—471no—
487C2×#95—471no—
488C2×#95—471no—
489C2×#95—471no—
490C2×#95—471no—
491C2×#95—471no—
492C2×#95—471no—
493C2×#95—471no—
494C2×#95—471no—
495C2×#95—471no—
496C2×#95—471no—
497C2×#95—471no—
498C2×#95—471no—
499C2×#95—471no—
500C2×#95—471no—
501C2×#95—471no—
502C2×#95—471no—
503C2×#95C2×D4711yescharacteristic
504C2×#95C2×D4711yescharacteristic
505C2×#95C2×D4711yescharacteristic
506C2×#95C2×D4711yescharacteristic
507C2×#95C2×D4711yescharacteristic
508C47#1397811yescharacteristic, complemented, Sylow
509C22×Q8—474no—
510C22×Q8—474no—
511C22×Q8—474no—
512C22×Q8—942no—
513C22×Q8—942no—
514C22×Q8—942no—
515C22×Q8—942no—
516C23×C4—471no—
517C23×C4—471no—
518C23×C4—471no—
519C23×C4—471no—
520C23×C4—471no—
521C23×C4—471no—
522C23×C4—471no—
523C23×C4—471no—
524C23×C4C22×D4711yescharacteristic
525C23×C4C22×D4711yescharacteristic
526C23×C4C22×D4711yescharacteristic
527C23×C4C22×D4711yescharacteristic
528C23×C4C22×D4711yescharacteristic
529C23×C4C22×D4711yescharacteristic
530C23×C4C22×D4711yescharacteristic
531C4×Q8—9432no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—474no—
536C2×C4⋊C4—474no—
537C2×C4⋊C4—942no—
538C2×C4⋊C4—942no—
539C2×C4⋊C4—942no—
540C2×C4⋊C4—942no—
541C2×C4⋊C4—942no—
542C2×C4⋊C4—942no—
543C2×C4⋊C4—942no—
544C2×C4⋊C4—942no—
545C2×C4⋊C4—942no—
546C2×C4⋊C4—942no—
547C2×C4⋊C4—942no—
548C2×C4⋊C4—942no—
549C2×C4⋊C4—942no—
550C2×C4⋊C4—942no—
551C2×C4⋊C4—942no—
552C2×C4⋊C4—942no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—474no—
557C2×C42—474no—
558C2×C42—942no—
559C2×C42—942no—
560C2×C42—942no—
561C2×C42—942no—
562C2×C42—942no—
563C2×C42—942no—
564C2×C42—942no—
565C2×C42—942no—
566C2×C42—942no—
567C2×C42—942no—
568#95—22no—
569#95—22no—
570#95—22no—
571#95—22no—
572#95—474no—
573#95—474no—
574#95—474no—
575#95—942no—
576#95—942no—
577#95—942no—
578#95—942no—
579#95—942no—
580#95—942no—
581#95—942no—
582#95—942no—
583#95—942no—
584#95—942no—
585#95—942no—
586#95—942no—
587#95—942no—
588#95—942no—
589#95C4×D4714yes—
590C24C23×D4711yescharacteristic
591C2×Q8—4716no—
592C2×Q8—948no—
593C2×Q8—948no—
594C2×Q8—948no—
595C2×Q8—948no—
596C2×Q8—948no—
597C2×Q8—948no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—472no—
638C22×C4—472no—
639C22×C4—472no—
640C22×C4—472no—
641C22×C4—472no—
642C22×C4—472no—
643C22×C4—472no—
644C22×C4—472no—
645C22×C4—472no—
646C22×C4—472no—
647C22×C4—472no—
648C22×C4—472no—
649C22×C4—472no—
650C22×C4—472no—
651C22×C4—472no—
652C22×C4—941no—
653C22×C4—941no—
654C22×C4—941no—
655C22×C4—941no—
656C22×C4—941no—
657C22×C4—941no—
658C22×C4—941no—
659C22×C4—941no—
660C22×C4—941no—
661C22×C4—941no—
662C22×C4—941no—
663C22×C4—941no—
664C22×C4—941no—
665C22×C4—941no—
666C22×C4—941no—
667C22×C4—941no—
668C22×C4—941no—
669C22×C4—941no—
670C22×C4—941no—
671C22×C4—941no—
672C22×C4—941no—
673C22×C4—941no—
674C22×C4—941no—
675C22×C4—941no—
676C22×C4—941no—
677C22×C4—941no—
678C22×C4—941no—
679C22×C4—941no—
680C22×C4—941no—
681C22×C4—941no—
682C22×C4—941no—
683C22×C4—941no—
684C22×C4—941no—
685C22×C4—941no—
686C22×C4—941no—
687C22×C4—941no—
688C22×C4—941no—
689C22×C4—941no—
690C22×C4—941no—
691C22×C4—941no—
692C22×C4—941no—
693C22×C4C2×C4×D4712yes—
694C22×C4C2×C4×D4712yes—
695C22×C4C2×C4×D4712yes—
696C22×C4#1062535012yes—
697C22×C4#1062535012yes—
698C22×C4D4×D4712yes—
699C22×C4D4×D4712yes—
700C22×C4D4×D4712yes—
701C22×C4#1062535212yes—
702C22×C4Q8×D4712yes—
703C4⋊C4—44no—
704C4⋊C4—948no—
705C4⋊C4—948no—
706C4⋊C4—948no—
707C4⋊C4—948no—
708C4⋊C4—1884no—
709C4⋊C4—1884no—
710C42—28no—
711C42—948no—
712C42—948no—
713C42—948no—
714C42—1884no—
715C23C22×C4×D4711yescharacteristic
716C23C2×D4×D4711yescharacteristic
717C23C2×D4×D4711yescharacteristic
718C23C2×D4×D4711yescharacteristic
719C23C2×Q8×D4711yescharacteristic
720C23#41×D4711yescharacteristic
721C23#41×D4711yescharacteristic
722C23#41×D4711yescharacteristic
723C23C2×#1062535211yescharacteristic
724C23C2×#1062535011yescharacteristic
725C23C2×#1062535011yescharacteristic
726C23#1309407111yescharacteristic
727C23#1309407111yescharacteristic
728C23#1309407111yescharacteristic
729C23#1309407211yescharacteristic
730Q8—9432no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—474no—
779C2×C4—474no—
780C2×C4—474no—
781C2×C4—474no—
782C2×C4—474no—
783C2×C4—474no—
784C2×C4—474no—
785C2×C4—474no—
786C2×C4—942no—
787C2×C4—942no—
788C2×C4—942no—
789C2×C4—942no—
790C2×C4—942no—
791C2×C4—942no—
792C2×C4—942no—
793C2×C4—942no—
794C2×C4—942no—
795C2×C4—942no—
796C2×C4—942no—
797C2×C4—942no—
798C2×C4—942no—
799C2×C4—942no—
800C2×C4—942no—
801C2×C4—942no—
802C2×C4—942no—
803C2×C4—942no—
804C2×C4—942no—
805C2×C4—942no—
806C2×C4—942no—
807C2×C4—1881no—
808C2×C4—1881no—
809C2×C4—1881no—
810C2×C4—1881no—
811C2×C4—1881no—
812C2×C4—1881no—
813C2×C4—1881no—
814C2×C4—1881no—
815C2×C4—1881no—
816C2×C4—1881no—
817C2×C4—1881no—
818C2×C4—1881no—
819C2×C4—1881no—
820C2×C4—1881no—
821C2×C4—1881no—
822C2×C4—1881no—
823C2×C4—1881no—
824C2×C4—1881no—
825C2×C4—1881no—
826C2×C4—1881no—
827C2×C4—1881no—
828C2×C4—1881no—
829C2×C4—1881no—
830C2×C4—1881no—
831C2×C4—1881no—
832C2×C4—1881no—
833C2×C4—1881no—
834C2×C4C4⋊C4×D4714yes—
835C2×C4#1309401014yes—
836C22C2×C4⋊C4×D4711yescharacteristic
837C22C4×D4×D4711yescharacteristic
838C22C4×D4×D4711yescharacteristic
839C22C4×#1062535211yescharacteristic
840C22C4×#1062535011yescharacteristic
841C22#1568959911yescharacteristic
842C22#1568960011yescharacteristic
843C22#120×D4711yescharacteristic
844C22C22⋊Q8×D4711yescharacteristic
845C22C22⋊Q8×D4711yescharacteristic
846C22#123×D4711yescharacteristic
847C22C2×#1309401011yescharacteristic
848C22#1568965111yescharacteristic
849C22#1568965311yescharacteristic
850C22#1568967011yescharacteristic
851C22#1568969511yescharacteristic
852C22#1568969611yescharacteristic
853C22#1568973011yescharacteristic
854C22#1568973211yescharacteristic
855C22#1568977111yescharacteristic
856C22#1568977411yescharacteristic
857C22#1568977911yescharacteristic
858C22#1568977911yescharacteristic
859C22#1568978211yescharacteristic
860C22#1568978211yescharacteristic
861C22#1568978211yescharacteristic
862C22#1568978311yescharacteristic
863C22#1568980611yescharacteristic
864C22#1568980911yescharacteristic
865C22#1568984211yescharacteristic
866C22#1568984511yescharacteristic
867C22#1568984811yescharacteristic
868C22#1568985011yescharacteristic
869C22#1568985111yescharacteristic
870C22#1568985111yescharacteristic
871C4—24no—
872C4—24no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—81no—
878C4—478no—
879C4—944no—
880C4—3761no—
881C4—1882no—
882C4—1882no—
883C4—1882no—
884C4—1882no—
885C4—1882no—
886C2#385×D4711yescharacteristic
887C2C4×#1309401011yescharacteristic
888C2#2024610311yescharacteristic
889C2#2024630711yescharacteristic
890C2#2024630811yescharacteristic
891C2#2024641611yescharacteristic
892C2#2024641811yescharacteristic
893C2#2024688811yescharacteristic
894C2#2024689011yescharacteristic
895C2#2024701411yescharacteristic
896C2#2024704411yescharacteristic
897C2#2024724611yescharacteristic
898C2#2024724811yescharacteristic
899C2#2024857711yescharacteristic
900C2#2024860211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1436C2
socle, prime radical, cosocleC24×C47C24
hypercenter#1436D47
hypocenterC47#13978
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
31. #15689027C4semidirect
251. C2×Dic94C4⋊C4semidirect
508. C47#13978semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic942
C2×#156890272
C2×#156890182
C2×#156889872
#202416462
#202416452
#202416442
#202416432
#202416232
#202416212
#202416202
Dic47⋊#952
#95×Dic472
C47×#14362
#1397847