Finite Group Databasebeta

← #26121846

Subgroups — #26121846

Order 12032.

1370 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093989C211yesmaximal, characteristic
2C22×#13093949C211yesmaximal, characteristic
3C22×#13093947C211yesmaximal, characteristic
4C2×#15688885C211yesmaximal, characteristic
5C2×#15688877C211yesmaximal, characteristic
6#20241617C211yesmaximal, characteristic
7C2×C47×#340C211yesmaximal, characteristic
8C23×Dic94C2211yescharacteristic
9C23×C47⋊C8C2211yescharacteristic
10C2×#13093989—22no—
11C2×#13093989—22no—
12C2×#13093989—22no—
13C2×#13093989—22no—
14C2×#13093989—22no—
15C2×#13093989C414yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×Dic47⋊C4—21no—
18C22×C4×Dic47—21no—
19C22×C4×Dic47C2211yescharacteristic
20C2×#13093949—22no—
21C2×#13093949—22no—
22C2×#13093949C414yescomplemented
23C2×#13093947—22no—
24C2×#13093947—22no—
25C2×#13093947C414yescomplemented
26C2×C47⋊#95—21no—
27C2×C47⋊#95—21no—
28#15688885—22no—
29#15688877—22no—
30C23×C8×C47C2211yescharacteristic
31C22×C4⋊C4×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C47×#340—22no—
34C22×Dic94—21no—
35C22×Dic94—21no—
36C22×Dic94—21no—
37C22×Dic94—21no—
38C22×Dic94—21no—
39C22×Dic94—21no—
40C22×Dic94—21no—
41C22×Dic94C2×C412yes—
42C22×Dic94C2×C412yes—
43C22×Dic94C2×C412yes—
44C22×Dic94D412yes—
45C22×Dic94D412yes—
46C22×Dic94D412yes—
47C22×Dic94Q812yes—
48C23×Dic47—21no—
49C23×Dic47—21no—
50C23×Dic47D411yescharacteristic
51C23×Dic47D411yescharacteristic
52C22×C47⋊C8—21no—
53C22×C47⋊C8—21no—
54C22×C47⋊C8—21no—
55C22×C47⋊C8—21no—
56C22×C47⋊C8—21no—
57C22×C47⋊C8—21no—
58C22×C47⋊C8C2×C412yes—
59#13093989—28no—
60#13093989—28no—
61#13093989—28no—
62#13093989—28no—
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47—21no—
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47—21no—
68C2×C4⋊Dic47C2×C412yes—
69C2×Dic47⋊C4—24no—
70C2×Dic47⋊C4—24no—
71C2×Dic47⋊C4—24no—
72C2×C4×Dic47—24no—
73C2×C4×Dic47—24no—
74C2×C4×Dic47—21no—
75C2×C4×Dic47—21no—
76C2×C4×Dic47—21no—
77C2×C4×Dic47—21no—
78C2×C4×Dic47—24no—
79C2×C4×Dic47C2×C412yes—
80C2×C4×Dic47D412yes—
81#13093949—28no—
82#13093947—28no—
83C47⋊#95—42no—
84C47⋊#95—42no—
85C23×C4×C47—21no—
86C23×C4×C47—21no—
87C23×C4×C47C2311yescharacteristic
88C22×C8×C47—21no—
89C22×C8×C47—21no—
90C22×C8×C47—21no—
91C22×C8×C47—21no—
92C22×C8×C47—21no—
93C22×C8×C47—21no—
94C22×C8×C47C2×C412yes—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47C2×C412yes—
104C2×C4⋊C4×C47C2×C412yes—
105C2×C4⋊C4×C47D412yes—
106C2×C4⋊C4×C47D412yes—
107C24×C47C2×D411yescharacteristic
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—41no—
113C22×C4×C47—41no—
114C22×C4×C47—41no—
115C22×C4×C47—41no—
116C22×C4×C47—41no—
117C22×C4×C47—41no—
118C22×C4×C47—41no—
119C22×C4×C47—41no—
120C22×C4×C47—41no—
121C22×C4×C47—41no—
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C22×C411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×Q811yescharacteristic
132C22×C4×C47#4111yescharacteristic
133C22×C4×C47#4111yescharacteristic
134C22×C4×C47#4111yescharacteristic
135C22×C4×C47#4111yescharacteristic
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47—22no—
154C22×Dic47—41no—
155C22×Dic47—41no—
156C22×Dic47—41no—
157C22×Dic47—41no—
158C22×Dic47—41no—
159C22×Dic47—41no—
160C22×Dic47C22⋊C412yes—
161C22×Dic47C22⋊C412yes—
162C22×Dic47SD1612yes—
163C22×Dic47Q1612yes—
164C2×Dic94—22no—
165C2×Dic94—22no—
166C2×Dic94—22no—
167C2×Dic94—22no—
168C2×Dic94—22no—
169C2×Dic94—22no—
170C2×Dic94—22no—
171C2×Dic94—22no—
172C2×Dic94—22no—
173C2×Dic94—22no—
174C2×Dic94—22no—
175C2×Dic94—22no—
176C2×Dic94—22no—
177C2×Dic94—22no—
178C2×Dic94—22no—
179C2×Dic94—22no—
180C2×Dic94—22no—
181C2×Dic94—22no—
182C2×Dic94—22no—
183C2×Dic94—22no—
184C2×Dic94—22no—
185C2×Dic94C4214yes—
186C2×Dic94C22⋊C414yes—
187C2×Dic94C22⋊C414yes—
188C2×Dic94C22⋊C414yes—
189C2×Dic94C4⋊C414yes—
190C2×Dic94C4⋊C414yes—
191C2×Dic94C4⋊C414yes—
192C2×C8×C47—22no—
193C2×C8×C47—22no—
194C2×C8×C47—22no—
195C2×C8×C47—41no—
196C2×C8×C47—41no—
197C2×C8×C47—41no—
198C2×C8×C47—41no—
199C4⋊C4×C47—22no—
200C4⋊C4×C47—22no—
201C4⋊C4×C47—22no—
202C4⋊C4×C47—22no—
203C4⋊C4×C47—22no—
204C4⋊C4×C47—41no—
205C4⋊C4×C47—41no—
206C4⋊C4×C47C22⋊C414yes—
207C4⋊Dic47—22no—
208C4⋊Dic47—22no—
209C4⋊Dic47—41no—
210C4⋊Dic47—41no—
211Dic47⋊C4—216no—
212C4×Dic47—216no—
213C4×Dic47—22no—
214C4×Dic47—22no—
215C4×Dic47—22no—
216C4×Dic47—22no—
217C2×C47⋊C8—22no—
218C2×C47⋊C8—22no—
219C2×C47⋊C8—22no—
220C2×C47⋊C8—41no—
221C2×C47⋊C8—41no—
222C2×C47⋊C8—41no—
223C2×C47⋊C8—41no—
224C23×C47C2×C22⋊C411yescharacteristic
225C23×C47C4×D411yescharacteristic
226C23×C47C4×D411yescharacteristic
227C23×C47#12011yescharacteristic
228C23×C47#12011yescharacteristic
229C23×C47#12111yescharacteristic
230C23×C47C22⋊Q811yescharacteristic
231C23×C47C2×SD1611yescharacteristic
232C23×C47C2×Q1611yescharacteristic
233C23×C47#13511yescharacteristic
234C23×C47#13511yescharacteristic
235C23×C47AGL(1,ℤ/8)11yescharacteristic
236C23×C47#13711yescharacteristic
237C23×C47#13711yescharacteristic
238C23×C47#13711yescharacteristic
239C2×C4×C47—24no—
240C2×C4×C47—42no—
241C2×C4×C47—42no—
242C2×C4×C47—42no—
243C2×C4×C47—42no—
244C2×C4×C47—42no—
245C2×C4×C47—42no—
246C2×C4×C47—42no—
247C2×C4×C47—42no—
248C2×C4×C47—42no—
249C2×C4×C47—81no—
250C2×C4×C47—81no—
251C2×C4×C47—81no—
252C2×C4×C47—81no—
253C2×C4×C47C2×C4211yescharacteristic
254C2×C4×C47C2×C22⋊C411yescharacteristic
255C2×C4×C47C2×C22⋊C411yescharacteristic
256C2×C4×C47C2×C22⋊C411yescharacteristic
257C2×C4×C47C2×C22⋊C411yescharacteristic
258C2×C4×C47C2×C4⋊C411yescharacteristic
259C2×C4×C47C2×C4⋊C411yescharacteristic
260C2×C4×C47C2×C4⋊C411yescharacteristic
261C2×C4×C47#11711yescharacteristic
262C2×C4×C47#11711yescharacteristic
263C2×C4×C47C4×D411yescharacteristic
264C2×C4×C47C4×D411yescharacteristic
265C2×C4×C47C4×D411yescharacteristic
266C2×C4×C47C4×D411yescharacteristic
267C2×C4×C47C4×D411yescharacteristic
268C2×C4×C47C4×D411yescharacteristic
269C2×C4×C47#12011yescharacteristic
270C2×C4×C47#12011yescharacteristic
271C2×C4×C47#12111yescharacteristic
272C2×C4×C47#12111yescharacteristic
273C2×C4×C47#12111yescharacteristic
274C2×C4×C47C22⋊Q811yescharacteristic
275C2×C4×C47C22⋊Q811yescharacteristic
276C2×C4×C47C22⋊Q811yescharacteristic
277C2×C4×C47#12311yescharacteristic
278C2×C4×C47#12311yescharacteristic
279C2×C4×C47#12311yescharacteristic
280C2×C4×C47#12311yescharacteristic
281C2×Dic47—24no—
282C2×Dic47—22no—
283C2×Dic47—24no—
284C2×Dic47—24no—
285C2×Dic47—24no—
286C2×Dic47—24no—
287C2×Dic47—24no—
288C2×Dic47—24no—
289C2×Dic47—22no—
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—42no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47—81no—
305C2×Dic47—81no—
306C2×Dic47—81no—
307C2×Dic47—81no—
308C2×Dic47#10314yescomplemented
309Dic94—24no—
310Dic94—24no—
311Dic94—24no—
312Dic94—24no—
313Dic94—24no—
314Dic94—24no—
315Dic94—24no—
316Dic94#9518yescomplemented
317C8×C47—42no—
318C47⋊C8—42no—
319#10789—471nomaximal, Sylow
320C22×C47C4×C22⋊C411yescharacteristic
321C22×C47#37911yescharacteristic
322C22×C47#38011yescharacteristic
323C22×C47#38511yescharacteristic
324C22×C47#38511yescharacteristic
325C22×C47#38611yescharacteristic
326C22×C47#38611yescharacteristic
327C22×C47C2×#10311yescharacteristic
328C22×C47#41611yescharacteristic
329C22×C47#41711yescharacteristic
330C22×C47#41911yescharacteristic
331C22×C47C4×SD1611yescharacteristic
332C22×C47C4×SD1611yescharacteristic
333C22×C47C4×Q1611yescharacteristic
334C22×C47C4×Q1611yescharacteristic
335C22×C47#44011yescharacteristic
336C22×C47#44011yescharacteristic
337C22×C47#44111yescharacteristic
338C22×C47#44111yescharacteristic
339C22×C47#44811yescharacteristic
340C22×C47#44811yescharacteristic
341C22×C47#44911yescharacteristic
342C22×C47#44911yescharacteristic
343C22×C47#45111yescharacteristic
344C22×C47#45111yescharacteristic
345C22×C47#45211yescharacteristic
346C22×C47#45211yescharacteristic
347C22×C47#46011yescharacteristic
348C22×C47#46211yescharacteristic
349C22×C47#46411yescharacteristic
350C22×C47#46411yescharacteristic
351C22×C47#47511yescharacteristic
352C22×C47#47711yescharacteristic
353C22×C47#47911yescharacteristic
354C22×C47#47911yescharacteristic
355C4×C47—44no—
356C4×C47—82no—
357C4×C47C2×#9511yescharacteristic
358C4×C47C4×C22⋊C411yescharacteristic
359C4×C47#38011yescharacteristic
360C4×C47#38111yescharacteristic
361C4×C47#38511yescharacteristic
362C4×C47#38511yescharacteristic
363C4×C47#38611yescharacteristic
364C4×C47#38611yescharacteristic
365Dic47—28no—
366Dic47—24no—
367Dic47—42no—
368Dic47—82no—
369C22×C4×Q8—471no—
370C22×#103—471no—
371C22×#103—471no—
372C2×#340—471no—
373C2×#340D4711yescharacteristic
374C2×#336—471no—
375C4⋊#95—471no—
376C2×C47C22⋊#9511yescharacteristic
377C2×C47C4×#10311yescharacteristic
378C2×C47#176311yescharacteristic
379C2×C47#178711yescharacteristic
380C2×C47#178811yescharacteristic
381C2×C47#180311yescharacteristic
382C2×C47#180511yescharacteristic
383C2×C47#186311yescharacteristic
384C2×C47#186311yescharacteristic
385C2×C47#186511yescharacteristic
386C2×C47#186511yescharacteristic
387C2×C47#187811yescharacteristic
388C2×C47#187811yescharacteristic
389C2×C47#188011yescharacteristic
390C2×C47#188011yescharacteristic
391C23×Q8—471no—
392C23×C8—471no—
393C23×C8C2×D4711yescharacteristic
394C2×C4×Q8—474no—
395C2×C4×Q8—942no—
396C2×C4×Q8—942no—
397C2×C4×Q8—942no—
398C2×C4×Q8—942no—
399C2×C4×Q8—942no—
400C22×C4⋊C4—471no—
401C22×C4⋊C4—941no—
402C22×C4⋊C4C2×D4711yescharacteristic
403C22×C4⋊C4C2×D4711yescharacteristic
404C22×C42—471no—
405C22×C42—941no—
406C2×#103—474no—
407C2×#103—474no—
408C2×#103—942no—
409C2×#103—942no—
410C2×#103—942no—
411C2×#103—942no—
412C2×#95—941no—
413C2×#95—941no—
414#340—22no—
415#340—942no—
416#336—942no—
417C47#1078911yescharacteristic, complemented, Sylow
418C22×Q8—472no—
419C22×Q8—472no—
420C22×Q8—472no—
421C22×Q8—472no—
422C22×Q8—472no—
423C22×Q8—472no—
424C22×Q8—472no—
425C22×Q8—941no—
426C22×Q8—941no—
427C22×Q8—941no—
428C22×Q8—941no—
429C22×Q8—941no—
430C22×Q8—941no—
431C22×Q8—941no—
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—471no—
435C23×C4—471no—
436C23×C4—941no—
437C23×C4—941no—
438C23×C4C22×D4711yescharacteristic
439C22×C8—21no—
440C22×C8—21no—
441C22×C8—21no—
442C22×C8—21no—
443C22×C8—21no—
444C22×C8—21no—
445C22×C8—472no—
446C22×C8—941no—
447C22×C8—941no—
448C22×C8—941no—
449C22×C8—941no—
450C22×C8—941no—
451C22×C8—941no—
452C22×C8C4×D4712yes—
453C4×Q8—948no—
454C4×Q8—948no—
455C4×Q8—948no—
456C4×Q8—948no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—472no—
466C2×C4⋊C4—944no—
467C2×C4⋊C4—944no—
468C2×C4⋊C4—944no—
469C2×C4⋊C4—941no—
470C2×C4⋊C4—941no—
471C2×C4⋊C4—941no—
472C2×C4⋊C4—941no—
473C2×C4⋊C4—941no—
474C2×C4⋊C4C4×D4712yes—
475C2×C4⋊C4C4×D4712yes—
476C2×C4⋊C4D18812yes—
477C2×C4⋊C4C22⋊D4712yes—
478C2×C42—472no—
479C2×C42—472no—
480C2×C42—944no—
481C2×C42—944no—
482C2×C42—944no—
483C2×C42—941no—
484C2×C42—941no—
485C2×C42—941no—
486C2×C42—941no—
487#103—948no—
488#103—948no—
489#95—1882no—
490#95—1882no—
491C24D4×D4711yescharacteristic
492C2×Q8—474no—
493C2×Q8—474no—
494C2×Q8—474no—
495C2×Q8—474no—
496C2×Q8—474no—
497C2×Q8—474no—
498C2×Q8—474no—
499C2×Q8—942no—
500C2×Q8—942no—
501C2×Q8—942no—
502C2×Q8—942no—
503C2×Q8—942no—
504C2×Q8—942no—
505C2×Q8—942no—
506C2×Q8—942no—
507C2×Q8—942no—
508C2×Q8—942no—
509C2×Q8—942no—
510C2×Q8—942no—
511C2×Q8—942no—
512C2×Q8—942no—
513C2×Q8—942no—
514C2×Q8—942no—
515C2×Q8—942no—
516C2×Q8—942no—
517C2×Q8—942no—
518C2×Q8—942no—
519C2×Q8—942no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—472no—
535C22×C4—472no—
536C22×C4—472no—
537C22×C4—472no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4—941no—
542C22×C4—942no—
543C22×C4—941no—
544C22×C4—942no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—941no—
548C22×C4—941no—
549C22×C4—941no—
550C22×C4—941no—
551C22×C4—941no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4—942no—
556C22×C4—1881no—
557C22×C4—1881no—
558C22×C4—1881no—
559C22×C4—1881no—
560C22×C4—1881no—
561C22×C4—1881no—
562C22×C4C2×C4×D4711yescharacteristic
563C22×C4C2×C4×D4711yescharacteristic
564C22×C4C2×C4×D4711yescharacteristic
565C22×C4C2×D18811yescharacteristic
566C22×C4#1062535011yescharacteristic
567C22×C4#1062535011yescharacteristic
568C22×C4D4×D4711yescharacteristic
569C22×C4D4×D4711yescharacteristic
570C22×C4D4×D4711yescharacteristic
571C22×C4D4×D4711yescharacteristic
572C22×C4#1062535211yescharacteristic
573C22×C4Q8×D4711yescharacteristic
574C22×C4#1062535411yescharacteristic
575C22×C4C2×C22⋊D4711yescharacteristic
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—942no—
584C2×C8—942no—
585C2×C8—942no—
586C2×C8—1881no—
587C2×C8—1881no—
588C2×C8—1881no—
589C2×C8—1881no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—9416no—
598C4⋊C4—942no—
599C4⋊C4—942no—
600C4⋊C4—1881no—
601C4⋊C4—1881no—
602C4⋊C4(C2×D47)⋊C414yes—
603C42—9416no—
604C42—942no—
605C42—942no—
606C42—942no—
607C42—942no—
608C23C22⋊C4×D4711yescharacteristic
609C23(C22⋊D47)⋊C411yescharacteristic
610C23#1309398611yescharacteristic
611C23#1309399211yescharacteristic
612C23#1309399411yescharacteristic
613C23#1309399711yescharacteristic
614C23#1309400211yescharacteristic
615C23SD16×D4711yescharacteristic
616C23Q16×D4711yescharacteristic
617C23#1309404311yescharacteristic
618C23#1309404511yescharacteristic
619C23#1309404811yescharacteristic
620C23#1309405311yescharacteristic
621C23#1309405311yescharacteristic
622C23#1309405611yescharacteristic
623Q8—478no—
624Q8—944no—
625Q8—944no—
626Q8—944no—
627Q8—944no—
628Q8—944no—
629Q8—944no—
630Q8—944no—
631C2×C4—24no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4—474no—
646C2×C4—944no—
647C2×C4—942no—
648C2×C4—944no—
649C2×C4—944no—
650C2×C4—944no—
651C2×C4—944no—
652C2×C4—944no—
653C2×C4—944no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—942no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—3761no—
663C2×C4—3761no—
664C2×C4—3761no—
665C2×C4—3761no—
666C2×C4—1882no—
667C2×C4—1882no—
668C2×C4—1882no—
669C2×C4—1881no—
670C2×C4—1881no—
671C2×C4—1881no—
672C2×C4—1881no—
673C2×C4C42×D4711yescharacteristic
674C2×C4C22⋊C4×D4711yescharacteristic
675C2×C4C22⋊C4×D4711yescharacteristic
676C2×C4C22⋊C4×D4711yescharacteristic
677C2×C4C2×(C2×D47)⋊C411yescharacteristic
678C2×C4C4⋊C4×D4711yescharacteristic
679C2×C4C4⋊C4×D4711yescharacteristic
680C2×C4C4⋊C4×D4711yescharacteristic
681C2×C4#1309398111yescharacteristic
682C2×C4#1309398211yescharacteristic
683C2×C4(C22⋊D47)⋊C411yescharacteristic
684C2×C4C4×C22⋊D4711yescharacteristic
685C2×C4C4×C22⋊D4711yescharacteristic
686C2×C4#1309398611yescharacteristic
687C2×C4C4×D18811yescharacteristic
688C2×C4C4×D18811yescharacteristic
689C2×C4#1309399211yescharacteristic
690C2×C4#1309399411yescharacteristic
691C2×C4#1309399511yescharacteristic
692C2×C4#1309399711yescharacteristic
693C2×C4#1309399911yescharacteristic
694C2×C4#1309400011yescharacteristic
695C2×C4#1309400211yescharacteristic
696C2×C4#1309400411yescharacteristic
697C2×C4#1309400611yescharacteristic
698C2×C4#1309400611yescharacteristic
699C2×C4#1309400911yescharacteristic
700C2×C4#1309400911yescharacteristic
701C8—42no—
702C8—1882no—
703C22#1568897011yescharacteristic
704C22#1568897811yescharacteristic
705C22#1568898211yescharacteristic
706C22#1568899411yescharacteristic
707C22#1568899711yescharacteristic
708C22#1568899911yescharacteristic
709C22#1568900111yescharacteristic
710C22#103×D4711yescharacteristic
711C22#1568911611yescharacteristic
712C22#1568912111yescharacteristic
713C22#1568913011yescharacteristic
714C22#1568921011yescharacteristic
715C22#1568921411yescharacteristic
716C22#1568921511yescharacteristic
717C22#1568921711yescharacteristic
718C22#1568922011yescharacteristic
719C22#1568922211yescharacteristic
720C22#1568922711yescharacteristic
721C22#1568922911yescharacteristic
722C22#1568926011yescharacteristic
723C22#1568926311yescharacteristic
724C22#1568926511yescharacteristic
725C22#1568926911yescharacteristic
726C22#1568927711yescharacteristic
727C22#1568928011yescharacteristic
728C22#1568928211yescharacteristic
729C22#1568928611yescharacteristic
730C22#1568932211yescharacteristic
731C22#1568933211yescharacteristic
732C22#1568934411yescharacteristic
733C22#1568934811yescharacteristic
734C22#1568940711yescharacteristic
735C22#1568941711yescharacteristic
736C22#1568942911yescharacteristic
737C22#1568943311yescharacteristic
738C4—44no—
739C4—82no—
740C4—944no—
741C4—948no—
742C4—3762no—
743C4—1882no—
744C4#95×D4711yescharacteristic
745C4C4×(C2×D47)⋊C411yescharacteristic
746C4#1568898011yescharacteristic
747C4#1568898511yescharacteristic
748C4#1568899411yescharacteristic
749C4#1568899711yescharacteristic
750C4#1568899911yescharacteristic
751C4#1568900111yescharacteristic
752C2(C2×D47)⋊#9511yescharacteristic
753C2#2024320711yescharacteristic
754C2#2024321711yescharacteristic
755C2#2024332111yescharacteristic
756C2#2024332511yescharacteristic
757C2#2024339211yescharacteristic
758C2#2024340211yescharacteristic
759C2#2024363911yescharacteristic
760C2#2024364311yescharacteristic
761C2#2024365311yescharacteristic
762C2#2024365711yescharacteristic
763C2#2024372611yescharacteristic
764C2#2024373011yescharacteristic
765C2#2024374011yescharacteristic
766C2#2024374411yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#340C2
socle, prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC2×#340D47
hypocenterC47#10789
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
15. C2×#13093989C4semidirect
22. C2×#13093949C4semidirect
25. C2×#13093947C4semidirect
308. C2×Dic47#103semidirect
316. Dic94#95semidirect
417. C47#10789semidirect

Maximal subgroups

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

subgroupindex
C22×#130939892
C22×#130939492
C22×#130939472
C2×#156888852
C2×#156888772
#202416172
C2×C47×#3402
#1078947