Finite Group Databasebeta

← #26217015

Subgroups — #26217015

Order 12032.

1558 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D47C211yesmaximal, characteristic
2C2×#15689164C211yesmaximal, characteristic, complemented
3C2×#15689162C211yesmaximal, characteristic, complemented
4C2×#15689085C211yesmaximal, characteristic
5#20245770C211yesmaximal, characteristic
6#20243590C211yesmaximal, characteristic, complemented
7#20243589C211yesmaximal, characteristic, complemented
8#20243588C211yesmaximal, characteristic, complemented
9#20243587C211yesmaximal, characteristic, complemented
10#20243586C211yesmaximal, characteristic, complemented
11#20243585C211yesmaximal, characteristic, complemented
12#20243584C211yesmaximal, characteristic, complemented
13#20243106C211yesmaximal, characteristic, complemented
14#20243106C211yesmaximal, characteristic, complemented
15C47×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C2×#13093983C2211yescharacteristic
20C2×#13093982C2211yescharacteristic
21C2×#13093982C2211yescharacteristic
22C2×#13093982C2211yescharacteristic
23C2×#13093982C2211yescharacteristic
24C2×#13093981—21no—
25C2×#13093980—21no—
26#117×D47—24no—
27#117×D47—24no—
28C2×C4⋊C4×D47C2211yescharacteristic
29C2×C4⋊C4×D47C2211yescharacteristic
30C2×C22⋊C4×D47—21no—
31C2×C42×D47—21no—
32#15689164—24no—
33#15689162—24no—
34C2×#13093958C2211yescharacteristic, complemented
35C2×#13093957C2211yescharacteristic, complemented
36C2×#13093957C2211yescharacteristic, complemented
37C2×#13093956C2211yescharacteristic, complemented
38C2×#13093955C2211yescharacteristic, complemented
39C2×#13093955C2211yescharacteristic, complemented
40#15689085C418yescomplemented
41C2×C22⋊(C47⋊C8)C2211yescharacteristic
42C2×(C2×D47)⋊C8C2211yescharacteristic
43C2×(C2×D47)⋊C8C2211yescharacteristic
44#15688985—21no—
45#15688983C2211yescharacteristic
46#15688980C2211yescharacteristic
47#15688980C2211yescharacteristic
48#15688978—21no—
49C22⋊C4×Dic47—21no—
50#15688970—21no—
51#15688886C2211yescharacteristic, complemented
52#15688886C2211yescharacteristic, complemented
53#15688885C2211yescharacteristic, complemented
54#15688885C2211yescharacteristic, complemented
55#15688885C2211yescharacteristic, complemented
56#15688885C2211yescharacteristic, complemented
57C2×#117×C47C2211yescharacteristic
58C2×#107×C47C2211yescharacteristic, complemented
59C2×#106×C47C2211yescharacteristic, complemented
60C2×C22⋊C8×C47C2211yescharacteristic
61C47×#380C2211yescharacteristic
62C47×#340C2211yescharacteristic, complemented
63C47×#340C2211yescharacteristic, complemented
64C24×D47D411yescharacteristic
65C23×Dic47D411yescharacteristic
66C22×C4×D47—22no—
67C22×C4×D47—22no—
68C22×C4×D47—22no—
69C22×C4×D47—22no—
70C22×C4×D47—21no—
71C22×C4×D47—21no—
72C22×C4×D47C2×C414yes—
73C22×C4×D47D411yescharacteristic
74C22×C4×D47D411yescharacteristic
75C22×C4×D47Q814yes—
76C22×C4×D47C2311yescharacteristic
77C22×C4×D47C2311yescharacteristic
78C2×#10625324—22no—
79C2×#10625324—22no—
80C2×#10625324—22no—
81C2×#10625324—22no—
82C2×#10625324C2×C414yes—
83C2×#10625324C2×C414yes—
84C22×C47⋊C8C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86#13093983—22no—
87#13093983—22no—
88#13093982—22no—
89#13093982—22no—
90#13093982—22no—
91#13093982—22no—
92#13093982—22no—
93#13093982—22no—
94#13093982—22no—
95#13093982—22no—
96#13093981—28no—
97#13093980—28no—
98C2×C4⋊Dic47C2311yescharacteristic
99C2×C4⋊Dic47C2311yescharacteristic
100C2×C4⋊Dic47C2311yescharacteristic
101C2×C4⋊Dic47C2311yescharacteristic
102C2×Dic47⋊C4—21no—
103C2×Dic47⋊C4—21no—
104C4⋊C4×D47—22no—
105C4⋊C4×D47—22no—
106C4⋊C4×D47D414yes—
107C4⋊C4×D47D414yes—
108C2×C22⋊Dic47—21no—
109C2×C22⋊Dic47—21no—
110C2×(C2×D47)⋊C4—21no—
111C2×(C2×D47)⋊C4—21no—
112C2×(C2×D47)⋊C4—21no—
113C2×(C2×D47)⋊C4—21no—
114C2×(C2×D47)⋊C4—21no—
115C2×(C2×D47)⋊C4—21no—
116C22⋊C4×D47—28no—
117C2×C4×Dic47—21no—
118C2×C4×Dic47—21no—
119C2×C4×Dic47—21no—
120C2×C4×Dic47—21no—
121C2×C4×Dic47—21no—
122C42×D47—28no—
123#13093958—22no—
124#13093957—22no—
125#13093957—22no—
126#13093956—22no—
127#13093955—22no—
128#13093955—22no—
129C22⋊(C47⋊C8)C2×C414yescomplemented
130(C2×D47)⋊C8C2×C414yescomplemented
131(C2×D47)⋊C8C2×C414yescomplemented
132C47⋊#95—21no—
133C47⋊#95—21no—
134C47⋊#95—21no—
135C23×C4×C47C2311yescharacteristic
136C22×C8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138#117×C47—22no—
139#117×C47—22no—
140C2×C4⋊C4×C47C2311yescharacteristic
141C2×C4⋊C4×C47C2311yescharacteristic
142C2×C4⋊C4×C47C2311yescharacteristic
143C2×C4⋊C4×C47C2311yescharacteristic
144C2×C22⋊C4×C47—21no—
145C2×C22⋊C4×C47—21no—
146C2×C42×C47—21no—
147#107×C47—22no—
148#106×C47—22no—
149C22⋊C8×C47C2×C414yescomplemented
150#95×C47—21no—
151C24×C47C2×D411yescharacteristic
152C23×D47—22no—
153C23×D47—22no—
154C23×D47—41no—
155C23×D47—41no—
156C23×D47—41no—
157C23×D47—41no—
158C23×D47C4⋊C414yes—
159C23×D47C2×D411yescharacteristic
160C23×D47C2×D411yescharacteristic
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×C47C22×C412yes—
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×Q812yes—
172C22×C4×C47C2411yescharacteristic
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47C4⋊C414yes—
180C22×Dic47C2×D411yescharacteristic
181C22×Dic47C2×D411yescharacteristic
182C2×C4×D47—22no—
183C2×C4×D47—22no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—21no—
187C2×C4×D47—21no—
188C2×C4×D47—22no—
189C2×C4×D47—22no—
190C2×C4×D47—28no—
191C2×C4×D47—28no—
192C2×C4×D47—28no—
193C2×C4×D47—28no—
194C2×C4×D47—24no—
195C2×C4×D47—24no—
196C2×C4×D47—42no—
197C2×C4×D47—42no—
198C2×C4×D47—42no—
199C2×C4×D47—42no—
200C2×C4×D47C4⋊C414yes—
201C2×C4×D47C4⋊C414yes—
202C2×C4×D47C22×C412yes—
203C2×C4×D47C22×C412yes—
204C2×C4×D47C2×D412yes—
205C2×C4×D47C2×D412yes—
206C2×C4×D47C2×Q812yes—
207C2×C4×D47C2×Q812yes—
208C2×C4×D47#4112yes—
209C2×C4×D47#4112yes—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47C22×C412yes—
215C2×C8×C47C22×C412yes—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47C2×D412yes—
223C4⋊C4×C47C2×D412yes—
224C22⋊C4×C47—24no—
225C22⋊C4×C47—42no—
226C42×C47—24no—
227C22⋊Dic47—24no—
228C22⋊Dic47—42no—
229(C2×D47)⋊C4—24no—
230(C2×D47)⋊C4—24no—
231(C2×D47)⋊C4—42no—
232(C2×D47)⋊C4—42no—
233(C2×D47)⋊C4—42no—
234(C2×D47)⋊C4—42no—
235C4⋊Dic47—21no—
236C4⋊Dic47—21no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47—21no—
241C4⋊Dic47C2×D412yes—
242C4⋊Dic47C2×D412yes—
243Dic47⋊C4—24no—
244Dic47⋊C4—24no—
245C4×Dic47—24no—
246C4×Dic47—24no—
247C4×Dic47—24no—
248C4×Dic47—42no—
249C4×Dic47—42no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8C22×C412yes—
255C2×C47⋊C8C22×C412yes—
256#10625324—28no—
257#10625324—28no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47C2×C4⋊C412yes—
265C23×C47C22×D411yescharacteristic
266C22×D47—21no—
267C22×D47—21no—
268C22×D47—21no—
269C22×D47—21no—
270C22×D47—21no—
271C22×D47—21no—
272C22×D47—21no—
273C22×D47—21no—
274C22×D47—21no—
275C22×D47—21no—
276C22×D47—28no—
277C22×D47—44no—
278C22×D47—44no—
279C22×D47—44no—
280C22×D47—44no—
281C22×D47—44no—
282C22×D47—44no—
283C22×D47C2×C4⋊C412yes—
284C22×D47C2×C4⋊C412yes—
285C22×D47#12012yes—
286C22×D47#12312yes—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
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—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47C2×C4⋊C412yes—
306C2×C4×C47C23×C411yescharacteristic
307C2×C4×C47C22×D411yescharacteristic
308C2×C4×C47C22×D411yescharacteristic
309C2×C4×C47C22×Q811yescharacteristic
310C2×C4×C47C2×#4111yescharacteristic
311C2×C4×C47C2×#4111yescharacteristic
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47—28no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—41no—
318C2×Dic47—41no—
319C2×Dic47—41no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327C2×Dic47C2×C4⋊C412yes—
328C2×Dic47C2×C4⋊C412yes—
329C2×Dic47#12012yes—
330C2×Dic47#12312yes—
331C4×D47—28no—
332C4×D47—22no—
333C4×D47—22no—
334C4×D47—22no—
335C4×D47—22no—
336C4×D47—28no—
337C4×D47—48no—
338C4×D47—48no—
339C4×D47C4×D414yes—
340C4×D47C4×D414yes—
341C4×D47C22⋊Q814yes—
342C4×D47C22⋊Q814yes—
343C8×C47—22no—
344C8×C47—22no—
345C47⋊C8—22no—
346C47⋊C8—22no—
347#20845—471nomaximal, Sylow
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47C22×C4⋊C411yescharacteristic
356C22×C47C2×#12011yescharacteristic
357C22×C47C2×#12311yescharacteristic
358C22×C47#57511yescharacteristic
359C22×C47#57511yescharacteristic
360C22×C47#57511yescharacteristic
361C22×C47#57511yescharacteristic
362C2×D47—22no—
363C2×D47—22no—
364C2×D47—22no—
365C2×D47—22no—
366C2×D47—22no—
367C2×D47—22no—
368C2×D47—22no—
369C2×D47—22no—
370C2×D47—22no—
371C2×D47—416no—
372C2×D47—41no—
373C2×D47—41no—
374C2×D47—41no—
375C2×D47—41no—
376C2×D47#38514yes—
377C4×C47—22no—
378C4×C47—42no—
379C4×C47—42no—
380C4×C47—81no—
381C4×C47—81no—
382C4×C47C2×C4×D411yescharacteristic
383C4×C47C2×C4×D411yescharacteristic
384C4×C47C2×C22⋊Q811yescharacteristic
385C4×C47C2×C22⋊Q811yescharacteristic
386Dic47—22no—
387Dic47—42no—
388Dic47—42no—
389Dic47—81no—
390Dic47—81no—
391Dic47#38514yes—
392C22×#117—471no—
393C2×#428—471no—
394C2×#428—471no—
395C2×#407—471no—
396#2280—471no—
397#1854—471no—
398#1854—471no—
399#1854—471no—
400#1854—471no—
401#1854—471no—
402#1854—471no—
403#1854—471no—
404#1854D4711yescharacteristic, complemented
405#1736—471no—
406#1736—471no—
407C2×C47—42no—
408C2×C47C2×#38511yescharacteristic
409C2×C47#291111yescharacteristic
410C2×C47#291111yescharacteristic
411C2×C47#300511yescharacteristic
412C2×C47#300511yescharacteristic
413C2×C47#309311yescharacteristic
414C2×C47#309311yescharacteristic
415D47—24no—
416D47—42no—
417C24×C4—471no—
418C22×M16—471no—
419C22×M16—471no—
420C2×#117—471no—
421C2×#117—471no—
422C2×#117—471no—
423C2×#117—471no—
424C2×#117—471no—
425C2×#117—941no—
426C2×#117—941no—
427C2×#117—944no—
428C2×#117—944no—
429C2×#117C2×D4711yescharacteristic
430C22×C4⋊C4—471no—
431C22×C4⋊C4—471no—
432C22×C22⋊C4—941no—
433C22×C42—941no—
434#428—944no—
435#428—944no—
436C2×#107—471no—
437C2×#107—471no—
438C2×#107—471no—
439C2×#107C2×D4711yescharacteristic, complemented
440C2×#106—471no—
441C2×#106—471no—
442C2×#106—471no—
443C2×#106C2×D4711yescharacteristic, complemented
444#407—478no—
445C2×C22⋊C8—471no—
446C2×C22⋊C8—471no—
447C2×C22⋊C8—471no—
448C2×C22⋊C8C2×D4711yescharacteristic
449#381—941no—
450#380—471no—
451#380—471no—
452#380—471no—
453#380C2×D4711yescharacteristic
454#379—941no—
455C4×C22⋊C4—941no—
456C4×C22⋊C4—941no—
457#340—471no—
458#340—471no—
459#340—471no—
460#340—471no—
461#340—471no—
462#340—471no—
463#340C2×D4711yescharacteristic, complemented
464#340C2×D4711yescharacteristic, complemented
465C47#2084511yescharacteristic, complemented, Sylow
466C25—471no—
467C23×C4—471no—
468C23×C4—471no—
469C23×C4—474no—
470C23×C4—471no—
471C23×C4—471no—
472C23×C4—474no—
473C23×C4—471no—
474C23×C4—942no—
475C23×C4—942no—
476C23×C4—942no—
477C23×C4—942no—
478C23×C4—941no—
479C23×C4—941no—
480C23×C4C22×D4711yescharacteristic
481C2×M16—474no—
482C2×M16—474no—
483C2×M16—942no—
484C2×M16—942no—
485C2×M16—942no—
486C2×M16—942no—
487C22×C8—471no—
488C22×C8—471no—
489C22×C8C22×D4711yescharacteristic
490C22×C8C22×D4711yescharacteristic
491#117—22no—
492#117—22no—
493#117—948no—
494#117—948no—
495#117—942no—
496#117—942no—
497#117—942no—
498#117—942no—
499#117—942no—
500#117—942no—
501#117—942no—
502#117—942no—
503#117—942no—
504#117—942no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—474no—
508C2×C4⋊C4—474no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—471no—
511C2×C4⋊C4—942no—
512C2×C4⋊C4—942no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4C22×D4711yescharacteristic
516C2×C4⋊C4C22×D4711yescharacteristic
517C2×C4⋊C4C22×D4711yescharacteristic
518C2×C4⋊C4C22×D4711yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—948no—
522C2×C22⋊C4—941no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4—941no—
529C2×C22⋊C4—941no—
530C2×C42—21no—
531C2×C42—948no—
532C2×C42—941no—
533C2×C42—941no—
534C2×C42—941no—
535C2×C42—941no—
536C2×C42—941no—
537#107—22no—
538#107—942no—
539#107—942no—
540#107—942no—
541#106—22no—
542#106—942no—
543#106—942no—
544#106—942no—
545C22⋊C8—474no—
546C22⋊C8—474no—
547C22⋊C8—474no—
548C22⋊C8C4×D4714yescomplemented
549#95—21no—
550#95—941no—
551#95—941no—
552#95—941no—
553C24—471no—
554C24—471no—
555C24—474no—
556C24—942no—
557C24—942no—
558C24—1881no—
559C24—1881no—
560C24—1881no—
561C24—1881no—
562C24D4×D4711yescharacteristic
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—471no—
572C22×C4—472no—
573C22×C4—472no—
574C22×C4—472no—
575C22×C4—472no—
576C22×C4—472no—
577C22×C4—472no—
578C22×C4—474no—
579C22×C4—471no—
580C22×C4—474no—
581C22×C4—474no—
582C22×C4—472no—
583C22×C4—472no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—948no—
587C22×C4—948no—
588C22×C4—948no—
589C22×C4—948no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—944no—
593C22×C4—944no—
594C22×C4—942no—
595C22×C4—942no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—1882no—
605C22×C4—1882no—
606C22×C4—1882no—
607C22×C4—1882no—
608C22×C4C2×C4×D4712yes—
609C22×C4D4×D4711yescharacteristic
610C22×C4Q8×D4712yes—
611C22×C4C23×D4711yescharacteristic
612M16—948no—
613M16—948no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—472no—
619C2×C8—472no—
620C2×C8—941no—
621C2×C8—941no—
622C2×C8—941no—
623C2×C8—941no—
624C2×C8C2×C4×D4712yes—
625C2×C8C2×C4×D4712yes—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—472no—
633C4⋊C4—472no—
634C4⋊C4—944no—
635C4⋊C4—944no—
636C4⋊C4—941no—
637C4⋊C4—941no—
638C4⋊C4—941no—
639C4⋊C4—941no—
640C4⋊C4—941no—
641C4⋊C4—941no—
642C4⋊C4D4×D4712yes—
643C4⋊C4D4×D4712yes—
644C22⋊C4—24no—
645C22⋊C4—42no—
646C22⋊C4—944no—
647C22⋊C4—944no—
648C22⋊C4—944no—
649C22⋊C4—1882no—
650C22⋊C4—1882no—
651C22⋊C4—1882no—
652C22⋊C4—1882no—
653C22⋊C4—1882no—
654C42—24no—
655C42—944no—
656C42—944no—
657C42—944no—
658C42—1882no—
659C42—1882no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—472no—
667C23—472no—
668C23—472no—
669C23—472no—
670C23—948no—
671C23—941no—
672C23—941no—
673C23—941no—
674C23—941no—
675C23—941no—
676C23—941no—
677C23—941no—
678C23—941no—
679C23—941no—
680C23—941no—
681C23—1884no—
682C23—1884no—
683C23—1884no—
684C23—1884no—
685C23—1884no—
686C23—1884no—
687C23C4⋊C4×D4712yes—
688C23C2×D4×D4711yescharacteristic
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—472no—
708C2×C4—472no—
709C2×C4—472no—
710C2×C4—474no—
711C2×C4—474no—
712C2×C4—474no—
713C2×C4—474no—
714C2×C4—472no—
715C2×C4—948no—
716C2×C4—948no—
717C2×C4—948no—
718C2×C4—941no—
719C2×C4—941no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—1888no—
727C2×C4—1888no—
728C2×C4—1881no—
729C2×C4—1881no—
730C2×C4—1881no—
731C2×C4—1881no—
732C2×C4—1881no—
733C2×C4—1881no—
734C2×C4—1881no—
735C2×C4—1881no—
736C2×C4—1881no—
737C2×C4—1881no—
738C2×C4C4⋊C4×D4712yes—
739C2×C4C22×C4×D4711yescharacteristic
740C2×C4C2×D4×D4711yescharacteristic
741C2×C4C2×D4×D4711yescharacteristic
742C2×C4C2×Q8×D4711yescharacteristic
743C2×C4#41×D4711yescharacteristic
744C2×C4#41×D4711yescharacteristic
745C8—22no—
746C8—22no—
747C8—942no—
748C8—942no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—474no—
757C22—942no—
758C22—942no—
759C22—942no—
760C22—942no—
761C22—942no—
762C22—942no—
763C22—942no—
764C22—942no—
765C22—942no—
766C22—18816no—
767C22—1881no—
768C22—1881no—
769C22—1881no—
770C22—1881no—
771C22C2×C4⋊C4×D4711yescharacteristic
772C22#120×D4711yescharacteristic
773C22#123×D4711yescharacteristic
774C22#1568991911yescharacteristic
775C22#1568992011yescharacteristic
776C22#1568992011yescharacteristic
777C22#1568992211yescharacteristic
778C4—22no—
779C4—42no—
780C4—42no—
781C4—81no—
782C4—81no—
783C4—474no—
784C4—942no—
785C4—3761no—
786C4—3761no—
787C4—1882no—
788C4—1882no—
789C4C4×D4×D4711yescharacteristic
790C4C4×D4×D4711yescharacteristic
791C4C22⋊Q8×D4711yescharacteristic
792C4C22⋊Q8×D4711yescharacteristic
793C2—42no—
794C2—944no—
795C2—1882no—
796C2#385×D4711yescharacteristic
797C2#2025197511yescharacteristic
798C2#2025197611yescharacteristic
799C2#2025262611yescharacteristic
800C2#2025263111yescharacteristic
801C2#2025331611yescharacteristic
802C2#2025332011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1854C2
socleC23×C47C22×D4
prime radicalC24×D47D4
cosocleC22×C4×C47C24
hypercenter#1854D47
hypocenterC47#20845
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#15689164C2semidirect
3. C2×#15689162C2semidirect
6. #20243590C2semidirect
7. #20243589C2semidirect
8. #20243588C2semidirect
9. #20243587C2semidirect
10. #20243586C2semidirect
11. #20243585C2semidirect
12. #20243584C2semidirect
13. #20243106C2semidirect
14. #20243106C2semidirect
15. C47×#1854C2semidirect
34. C2×#13093958C22semidirect
35. C2×#13093957C22semidirect
36. C2×#13093957C22semidirect
37. C2×#13093956C22semidirect
38. C2×#13093955C22semidirect
39. C2×#13093955C22semidirect
40. #15689085C4semidirect
51. #15688886C22semidirect
52. #15688886C22semidirect
53. #15688885C22semidirect
54. #15688885C22semidirect
55. #15688885C22semidirect
56. #15688885C22semidirect
58. C2×#107×C47C22semidirect
59. C2×#106×C47C22semidirect
62. C47×#340C22semidirect
63. C47×#340C22semidirect
129. C22⋊(C47⋊C8)C2×C4semidirect
130. (C2×D47)⋊C8C2×C4semidirect
131. (C2×D47)⋊C8C2×C4semidirect
149. C22⋊C8×C47C2×C4semidirect
404. #1854D47semidirect
439. C2×#107C2×D47semidirect
443. C2×#106C2×D47semidirect
463. #340C2×D47semidirect
464. #340C2×D47semidirect
465. C47#20845semidirect
548. C22⋊C8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D472
C2×#156891642
C2×#156891622
C2×#156890852
#202457702
#202435902
#202435892
#202435882
#202435872
#202435862
#202435852
#202435842
#202431062
C47×#18542
#2084547