Finite Group Databasebeta

← #26216091

Subgroups — #26216091

Order 12032.

1374 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689604C211yesmaximal, characteristic
2C2×#15689088C211yesmaximal, characteristic
3#20245977C211yesmaximal, characteristic
4#20243484C211yesmaximal, characteristic, complemented
5#20243482C211yesmaximal, characteristic, complemented
6#20243481C211yesmaximal, characteristic, complemented
7#20243480C211yesmaximal, characteristic, complemented
8#20243478C211yesmaximal, characteristic, complemented
9#20243477C211yesmaximal, characteristic, complemented
10#20243473C211yesmaximal, characteristic, complemented
11#20243106C211yesmaximal, characteristic, complemented
12#20243106C211yesmaximal, characteristic, complemented
13#20243103C211yesmaximal, characteristic, complemented
14#340×D47C211yesmaximal, characteristic, complemented
15C47×#1823C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19#15689604—24no—
20#15689604C418yescomplemented
21C2×#13093989—21no—
22C2×#13093986—21no—
23C2×C4×C22⋊D47—21no—
24C2×C4×C22⋊D47—21no—
25C2×#13093983C2211yescharacteristic
26C2×#13093982C2211yescharacteristic
27C2×#13093982C2211yescharacteristic
28C2×#13093982C2211yescharacteristic
29C2×C4⋊C4×D47C2211yescharacteristic
30C2×C4⋊C4×D47C2211yescharacteristic
31C2×C4⋊C4×D47C2211yescharacteristic
32#15689088—24no—
33C2×C22⋊(C47⋊C8)C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×(C2×D47)⋊C8C2211yescharacteristic
36#15689027—21no—
37#15689023—21no—
38#15689001—21no—
39#15688999—21no—
40#15688983C2211yescharacteristic
41#15688980C2211yescharacteristic
42#15688980C2211yescharacteristic
43#15688886C2211yescharacteristic
44#15688886C2211yescharacteristic
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55C22×C4⋊C4×C47C2211yescharacteristic
56C2×C22⋊C8×C47C2211yescharacteristic
57C47×#380C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C2×#10625350—22no—
63C2×#10625350—22no—
64C2×#10625350—22no—
65C2×#10625350—22no—
66C2×#10625350C2×C414yes—
67C2×#10625350D414yes—
68C22×Dic94D411yescharacteristic
69C22×D188D411yescharacteristic
70C22×C22⋊D47D411yescharacteristic
71C22×C22⋊D47D411yescharacteristic
72C22×C4×D47—21no—
73C22×C4×D47—21no—
74C22×C4×D47—21no—
75C22×C4×D47C2311yescharacteristic
76C22×C4×D47C2311yescharacteristic
77C2×#10625324—22no—
78C2×#10625324—22no—
79C2×#10625324—22no—
80C22×C47⋊C8C2311yescharacteristic
81C22×C47⋊C8C2311yescharacteristic
82C2×C8×D47—22no—
83C2×C8×D47—22no—
84C2×C8×D47—22no—
85#13093989—28no—
86#13093986—28no—
87C4×C22⋊D47—28no—
88C4×C22⋊D47—28no—
89#13093983—22no—
90#13093983C2×C414yescomplemented
91#13093982—22no—
92#13093982—22no—
93#13093982—22no—
94#13093982—22no—
95#13093982C2×C414yes—
96#13093982C2×C414yescomplemented
97C2×C4⋊Dic47C2311yescharacteristic
98C2×C4⋊Dic47C2311yescharacteristic
99C2×C4⋊Dic47C2311yescharacteristic
100C2×C4⋊Dic47C2311yescharacteristic
101C2×Dic47⋊C4—21no—
102C2×Dic47⋊C4—21no—
103C2×Dic47⋊C4—21no—
104C4⋊C4×D47—22no—
105C4⋊C4×D47—22no—
106C4⋊C4×D47—22no—
107C4⋊C4×D47—22no—
108C4⋊C4×D47C2×C414yes—
109C4⋊C4×D47C2×C414yescomplemented
110C2×C22⋊Dic47—21no—
111C2×C22⋊Dic47—21no—
112C2×(C2×D47)⋊C4—21no—
113C2×(C2×D47)⋊C4—21no—
114C2×(C2×D47)⋊C4—21no—
115C2×(C2×D47)⋊C4—21no—
116C2×(C2×D47)⋊C4—21no—
117C2×C4×Dic47—21no—
118C2×C4×Dic47—21no—
119C2×C4×Dic47—21no—
120C2×C4×Dic47—21no—
121C22⋊(C47⋊C8)—22no—
122(C2×D47)⋊C8—22no—
123(C2×D47)⋊C8—22no—
124C47⋊#95—21no—
125C47⋊#95—21no—
126C47⋊#95—21no—
127C23×C4×C47—21no—
128C23×C4×C47C2311yescharacteristic
129C22×C8×C47C2311yescharacteristic
130C22×C8×C47C2311yescharacteristic
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47—22no—
133C2×C4⋊C4×C47C2×C414yescomplemented
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47C2311yescharacteristic
137C2×C4⋊C4×C47C2311yescharacteristic
138C2×C22⋊C4×C47—21no—
139C22⋊C8×C47—22no—
140#95×C47—21no—
141C24×C47C2×D411yescharacteristic
142C23×D47C2×D411yescharacteristic
143C23×D47C2×D411yescharacteristic
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—24no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—81no—
154C22×C4×C47—81no—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2411yescharacteristic
159C2×C22⋊D47—22no—
160C2×C22⋊D47—22no—
161C2×C22⋊D47—22no—
162C2×C22⋊D47—22no—
163C2×C22⋊D47C22⋊C414yes—
164C2×C22⋊D47C22⋊C414yes—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47C2×D411yescharacteristic
170C22×Dic47C2×D411yescharacteristic
171#10625350—28no—
172#10625350—28no—
173#10625350—28no—
174#10625350—28no—
175C2×D188—22no—
176C2×D188—22no—
177C2×D188C22⋊C414yes—
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—24no—
183C2×C4×D47—24no—
184C2×C4×D47—42no—
185C2×C4×D47—81no—
186C2×C4×D47—81no—
187C2×C4×D47—81no—
188C2×C4×D47—81no—
189C2×C4×D47—81no—
190C2×C4×D47—81no—
191C2×C4×D47C22×C412yes—
192C2×C4×D47C22×C412yes—
193C2×C4×D47C2×D412yes—
194C2×C4×D47C2×D412yes—
195C2×C4×D47#4112yes—
196C2×C4×D47#4112yes—
197C2×C4×D47#4112yes—
198C2×C4×D47#4112yes—
199C2×Dic94—22no—
200C2×Dic94—22no—
201C2×Dic94C22⋊C414yes—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C4⋊C4×C47—24no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—21no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47C22×C412yes—
216C4⋊C4×C47C22×C412yes—
217C22⋊C4×C47—81no—
218C22⋊Dic47—24no—
219C22⋊Dic47—81no—
220(C2×D47)⋊C4—24no—
221(C2×D47)⋊C4—24no—
222(C2×D47)⋊C4—42no—
223(C2×D47)⋊C4—81no—
224(C2×D47)⋊C4—81no—
225C4⋊Dic47—21no—
226C4⋊Dic47—21no—
227C4⋊Dic47—21no—
228C4⋊Dic47—21no—
229C4⋊Dic47—21no—
230C4⋊Dic47—21no—
231C4⋊Dic47C22×C412yes—
232C4⋊Dic47C22×C412yes—
233Dic47⋊C4—24no—
234Dic47⋊C4—24no—
235Dic47⋊C4—42no—
236C4×Dic47—24no—
237C4×Dic47—24no—
238C4×Dic47—24no—
239C4×Dic47—42no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—21no—
243C2×C47⋊C8—21no—
244C2×C47⋊C8—21no—
245C2×C47⋊C8—21no—
246#10625324—44no—
247C8×D47—44no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47C2×C22⋊C412yes—
255C23×C47C22×D411yescharacteristic
256C22×D47—21no—
257C22×D47—21no—
258C22×D47—21no—
259C22×D47—21no—
260C22×D47—21no—
261C22×D47—21no—
262C22×D47—21no—
263C22×D47—21no—
264C22×D47—21no—
265C22×D47—21no—
266C22×D47C2×C22⋊C412yes—
267C22×D47C2×C22⋊C412yes—
268C22×D47#12312yes—
269C22×D47#12312yes—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—84no—
289C2×C4×C47C2×C22⋊C412yes—
290C2×C4×C47C23×C411yescharacteristic
291C2×C4×C47C22×D411yescharacteristic
292C2×C4×C47C2×#4111yescharacteristic
293C2×C4×C47C2×#4111yescharacteristic
294C2×C4×C47C2×#4111yescharacteristic
295C2×C4×C47C2×#4111yescharacteristic
296C22⋊D47—28no—
297C22⋊D47—28no—
298C2×Dic47—21no—
299C2×Dic47—21no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—41no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47—41no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311C2×Dic47—41no—
312C2×Dic47C2×C22⋊C412yes—
313C2×Dic47C2×C22⋊C412yes—
314C2×Dic47#12312yes—
315C2×Dic47#12312yes—
316D188—28no—
317C4×D47—22no—
318C4×D47—22no—
319C4×D47—22no—
320C4×D47—22no—
321C4×D47—84no—
322C4×D47—84no—
323C4×D47—84no—
324C4×D47#11714yes—
325C4×D47#11714yes—
326C4×D47#12314yes—
327C4×D47#12314yes—
328Dic94—28no—
329C8×C47—41no—
330C8×C47—41no—
331C47⋊C8—41no—
332C47⋊C8—41no—
333#20703—471nomaximal, Sylow
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47C22×C22⋊C411yescharacteristic
342C22×C47C2×#12311yescharacteristic
343C22×C47C2×#12311yescharacteristic
344C22×C47#57611yescharacteristic
345C22×C47#57711yescharacteristic
346C22×C47#57711yescharacteristic
347C22×C47#57811yescharacteristic
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—22no—
351C2×D47—22no—
352C2×D47—22no—
353C2×D47—22no—
354C2×D47—22no—
355C2×D47—22no—
356C2×D47—22no—
357C2×D47—41no—
358C2×D47—41no—
359C2×D47—41no—
360C2×D47—41no—
361C2×D47#38114yes—
362C4×C47—22no—
363C4×C47—42no—
364C4×C47—42no—
365C4×C47—81no—
366C4×C47—81no—
367C4×C47C2×#11711yescharacteristic
368C4×C47C2×#11711yescharacteristic
369C4×C47C2×#12311yescharacteristic
370C4×C47C2×#12311yescharacteristic
371Dic47—22no—
372Dic47—42no—
373Dic47—42no—
374Dic47—81no—
375Dic47—81no—
376Dic47#38114yes—
377C2×#520—471no—
378C2×#408—471no—
379#2311—471no—
380#1825—471no—
381#1825—471no—
382#1825—471no—
383#1825—471no—
384#1824—471no—
385#1824—471no—
386#1823—471no—
387#1823D4711yescharacteristic, complemented
388#1736—471no—
389#1736—471no—
390#1735—471no—
391C2×#340—471no—
392C2×C47—42no—
393C2×C47C2×#38111yescharacteristic
394C2×C47#289711yescharacteristic
395C2×C47#289811yescharacteristic
396C2×C47#309611yescharacteristic
397C2×C47#309711yescharacteristic
398C2×C47#309811yescharacteristic
399C2×C47#309911yescharacteristic
400D47—24no—
401D47—42no—
402C22×#41—471no—
403C22×M16—471no—
404C23×C8—471no—
405#520—478no—
406#520—944no—
407C2×C4×Q8—941no—
408C2×C4×D4—941no—
409C2×C4×D4—941no—
410C2×C4×D4—941no—
411C2×#117—471no—
412C2×#117—471no—
413C2×#117—471no—
414C2×#117—471no—
415C22×C4⋊C4—471no—
416C22×C4⋊C4—471no—
417C22×C4⋊C4—471no—
418C22×C4⋊C4C2×D4711yescharacteristic
419#408—944no—
420C2×C22⋊C8—471no—
421C2×C22⋊C8—471no—
422C2×C22⋊C8—471no—
423C2×C22⋊C8C2×D4711yescharacteristic
424#391—941no—
425#390—941no—
426#386—941no—
427#386—941no—
428#380—471no—
429#380—471no—
430#380—471no—
431#380C2×D4711yescharacteristic
432#340—471no—
433#340—471no—
434#340—471no—
435#340—471no—
436#340—471no—
437#340—471no—
438#340—471no—
439#340—471no—
440#340—471no—
441#340—471no—
442#340—471no—
443#340—471no—
444#340C2×D4711yescharacteristic
445#340C2×D4711yescharacteristic
446#340C2×D4711yescharacteristic
447#340C2×D4711yescharacteristic
448C47#2070311yescharacteristic, complemented, Sylow
449C2×#41—474no—
450C2×#41—474no—
451C2×#41—942no—
452C2×#41—942no—
453C2×#41—942no—
454C2×#41—942no—
455C22×Q8—471no—
456C22×D4—471no—
457C22×D4—471no—
458C22×D4—471no—
459C23×C4—21no—
460C23×C4—471no—
461C23×C4—471no—
462C23×C4—941no—
463C23×C4—941no—
464C23×C4—941no—
465C23×C4C22×D4711yescharacteristic
466C2×M16—942no—
467C2×M16—942no—
468C2×M16—942no—
469C22×C8—471no—
470C22×C8—471no—
471C22×C8—942no—
472C22×C8—942no—
473C22×C8—942no—
474C22×C8C22×D4711yescharacteristic
475C22×C8C22×D4711yescharacteristic
476C4×Q8—948no—
477C4×D4—948no—
478C4×D4—948no—
479C4×D4—948no—
480#117—474no—
481#117—474no—
482#117—474no—
483#117—942no—
484#117—942no—
485#117—942no—
486#117—942no—
487#117—942no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—471no—
491C2×C4⋊C4—471no—
492C2×C4⋊C4—474no—
493C2×C4⋊C4—474no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—942no—
497C2×C4⋊C4—942no—
498C2×C4⋊C4—942no—
499C2×C4⋊C4—942no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4C4×D4714yescomplemented
504C2×C4⋊C4C22×D4711yescharacteristic
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C22⋊C4—941no—
515C2×C22⋊C4—941no—
516C2×C42—941no—
517C2×C42—941no—
518C2×C42—941no—
519C2×C42—941no—
520C22⋊C8—22no—
521C22⋊C8—942no—
522C22⋊C8—942no—
523C22⋊C8—942no—
524#95—21no—
525#95—941no—
526#95—941no—
527#95—941no—
528C24—471no—
529C24—471no—
530C24D4×D4711yescharacteristic
531#41—948no—
532#41—948no—
533#41—948no—
534#41—948no—
535C2×Q8—474no—
536C2×Q8—942no—
537C2×Q8—942no—
538C2×D4—474no—
539C2×D4—474no—
540C2×D4—474no—
541C2×D4—942no—
542C2×D4—942no—
543C2×D4—942no—
544C2×D4—942no—
545C2×D4—942no—
546C2×D4—942no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—471no—
559C22×C4—472no—
560C22×C4—472no—
561C22×C4—472no—
562C22×C4—472no—
563C22×C4—472no—
564C22×C4—472no—
565C22×C4—471no—
566C22×C4—472no—
567C22×C4—472no—
568C22×C4—944no—
569C22×C4—944no—
570C22×C4—941no—
571C22×C4—941no—
572C22×C4—941no—
573C22×C4—941no—
574C22×C4—941no—
575C22×C4—941no—
576C22×C4—941no—
577C22×C4—941no—
578C22×C4—3761no—
579C22×C4—3761no—
580C22×C4—3761no—
581C22×C4—3761no—
582C22×C4—3761no—
583C22×C4—3761no—
584C22×C4—1882no—
585C22×C4C2×C4×D4712yes—
586C22×C4D4×D4711yescharacteristic
587C22×C4D4×D4712yes—
588C22×C4C23×D4711yescharacteristic
589M16—1884no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—941no—
597C2×C8—941no—
598C2×C8—941no—
599C2×C8—941no—
600C2×C8—941no—
601C2×C8—941no—
602C2×C8—1884no—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—472no—
611C4⋊C4—472no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—941no—
615C4⋊C4—941no—
616C4⋊C4—941no—
617C4⋊C4—941no—
618C4⋊C4—941no—
619C4⋊C4—941no—
620C4⋊C4—1882no—
621C4⋊C4C2×C4×D4712yes—
622C4⋊C4C2×C4×D4712yes—
623C22⋊C4—81no—
624C22⋊C4—944no—
625C22⋊C4—944no—
626C22⋊C4—944no—
627C22⋊C4—3761no—
628C22⋊C4—3761no—
629C22⋊C4—3761no—
630C22⋊C4—1882no—
631C42—944no—
632C42—944no—
633C42—944no—
634C42—1882no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—472no—
642C23—472no—
643C23—472no—
644C23—472no—
645C23—941no—
646C23—941no—
647C23—941no—
648C23—941no—
649C23—941no—
650C23—941no—
651C23—941no—
652C23—941no—
653C23—941no—
654C23—941no—
655C23C22⋊C4×D4712yes—
656C23C2×D4×D4711yescharacteristic
657Q8—948no—
658D4—948no—
659D4—948no—
660D4—948no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—84no—
680C2×C4—472no—
681C2×C4—472no—
682C2×C4—472no—
683C2×C4—474no—
684C2×C4—474no—
685C2×C4—474no—
686C2×C4—474no—
687C2×C4—472no—
688C2×C4—941no—
689C2×C4—941no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—3764no—
697C2×C4—3764no—
698C2×C4—3764no—
699C2×C4—1881no—
700C2×C4—1881no—
701C2×C4—1881no—
702C2×C4—1881no—
703C2×C4—1881no—
704C2×C4—1881no—
705C2×C4—1881no—
706C2×C4—1881no—
707C2×C4—1881no—
708C2×C4—1881no—
709C2×C4C22⋊C4×D4712yes—
710C2×C4C22×C4×D4711yescharacteristic
711C2×C4C2×D4×D4711yescharacteristic
712C2×C4#41×D4711yescharacteristic
713C2×C4#41×D4711yescharacteristic
714C2×C4#41×D4711yescharacteristic
715C2×C4#41×D4711yescharacteristic
716C8—41no—
717C8—41no—
718C8—1881no—
719C8—1881no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—474no—
728C22—942no—
729C22—942no—
730C22—942no—
731C22—942no—
732C22—942no—
733C22—942no—
734C22—942no—
735C22—942no—
736C22—942no—
737C22—1881no—
738C22—1881no—
739C22—1881no—
740C22—1881no—
741C22C2×C22⋊C4×D4711yescharacteristic
742C22#123×D4711yescharacteristic
743C22#123×D4711yescharacteristic
744C22#1568992411yescharacteristic
745C22#1568992911yescharacteristic
746C22#1568993211yescharacteristic
747C22#1568993911yescharacteristic
748C4—22no—
749C4—42no—
750C4—42no—
751C4—81no—
752C4—81no—
753C4—474no—
754C4—942no—
755C4—3761no—
756C4—3761no—
757C4—1882no—
758C4—1882no—
759C4#117×D4711yescharacteristic
760C4#117×D4711yescharacteristic
761C4#123×D4711yescharacteristic
762C4#123×D4711yescharacteristic
763C2—42no—
764C2—944no—
765C2—1882no—
766C2#381×D4711yescharacteristic
767C2#2025190911yescharacteristic
768C2#2025192011yescharacteristic
769C2#2025333911yescharacteristic
770C2#2025335011yescharacteristic
771C2#2025336111yescharacteristic
772C2#2025337211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1823C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenter#1823D47
hypocenterC47#20703
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #20243484C2semidirect
5. #20243482C2semidirect
6. #20243481C2semidirect
7. #20243480C2semidirect
8. #20243478C2semidirect
9. #20243477C2semidirect
10. #20243473C2semidirect
11. #20243106C2semidirect
12. #20243106C2semidirect
13. #20243103C2semidirect
14. #340×D47C2semidirect
15. C47×#1823C2semidirect
20. #15689604C4semidirect
90. #13093983C2×C4semidirect
96. #13093982C2×C4semidirect
109. C4⋊C4×D47C2×C4semidirect
133. C2×C4⋊C4×C47C2×C4semidirect
387. #1823D47semidirect
448. C47#20703semidirect
503. C2×C4⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896042
C2×#156890882
#202459772
#202434842
#202434822
#202434812
#202434802
#202434782
#202434772
#202434732
#202431062
#202431032
#340×D472
C47×#18232
#2070347