Finite Group Databasebeta

← #26215802

Subgroups — #26215802

Order 12032.

1462 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689605C211yesmaximal, characteristic
2C2×#15689148C211yesmaximal, characteristic, complemented
3C2×#15689123C211yesmaximal, characteristic
4C2×#15689118C211yesmaximal, characteristic
5#20246009C211yesmaximal, characteristic, complemented
6#20243403C211yesmaximal, characteristic, complemented
7#20243401C211yesmaximal, characteristic, complemented
8#20243399C211yesmaximal, characteristic, complemented
9#20243397C211yesmaximal, characteristic, complemented
10#20243391C211yesmaximal, characteristic, complemented
11#20243387C211yesmaximal, characteristic, complemented
12#20243385C211yesmaximal, characteristic, complemented
13#20243106C211yesmaximal, characteristic, complemented
14#340×D47C211yesmaximal, characteristic, complemented
15C47×#1803C211yesmaximal, characteristic, complemented
16C22×#10625354C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19#15689605—24no—
20#15689605C418yescomplemented
21C2×Q8×Dic47C2211yescharacteristic
22C2×C4×D188—21no—
23C2×C4×D188C2211yescharacteristic
24C2×#13093986—21no—
25C2×#13093986C2211yescharacteristic
26C2×#13093982C2211yescharacteristic
27C2×#13093981—21no—
28C2×#13093981C2211yescharacteristic
29C2×C4⋊C4×D47—21no—
30C2×C4⋊C4×D47C2211yescharacteristic
31C2×C4⋊C4×D47C2211yescharacteristic
32#15689148—24no—
33C2×C4⋊(C47⋊C8)C2211yescharacteristic
34C2×Dic47⋊C8C2211yescharacteristic
35C2×Dic47⋊C8C2211yescharacteristic
36#15689123—24no—
37#15689118—24no—
38C2×#13093948C2211yescharacteristic
39C2×#13093948C2211yescharacteristic
40C2×#13093946C2211yescharacteristic
41C2×#13093946C2211yescharacteristic
42C2×#13093944C2211yescharacteristic
43C2×#13093944C2211yescharacteristic
44#15689018—21no—
45#15689018—21no—
46#15688994—21no—
47#15688994—21no—
48#15688992C2211yescharacteristic
49#15688989C2211yescharacteristic
50#15688988C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55#15688885C2211yescharacteristic
56#15688885C2211yescharacteristic
57C2×C4×Q8×C47C2211yescharacteristic
58C2×C4⋊C8×C47C2211yescharacteristic
59C2×#103×C47C2211yescharacteristic
60C2×#103×C47C2211yescharacteristic
61C47×#384C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C47×#340C2211yescharacteristic
64C2×#10625354—22no—
65C2×#10625354—22no—
66C2×#10625354—22no—
67C2×#10625354C2×C414yes—
68C2×#10625354D414yes—
69C2×#10625354Q814yes—
70C22×D188—21no—
71C22×D188C2311yescharacteristic
72C22×C4×D47—21no—
73C22×C4×D47—21no—
74C22×C4×D47—21no—
75C22×C4×D47—21no—
76C22×C4×D47—21no—
77C22×C4×D47C2311yescharacteristic
78C2×#10625324—22no—
79C2×#10625324—22no—
80C2×#10625324—22no—
81C22×C47⋊C8C2311yescharacteristic
82C22×C47⋊C8C2311yescharacteristic
83C2×C8×D47—22no—
84C2×C8×D47—22no—
85C2×C8×D47—22no—
86Q8×Dic47—22no—
87Q8×Dic47C2×C414yescomplemented
88C4×D188—22no—
89C4×D188—28no—
90C4×D188C2×C414yescomplemented
91#13093986—28no—
92#13093986—22no—
93#13093986C2×C414yescomplemented
94#13093982—22no—
95#13093982—22no—
96#13093981—28no—
97#13093981C2×C414yes—
98#13093981D414yes—
99C2×C4⋊Dic47—21no—
100C2×C4⋊Dic47C2311yescharacteristic
101C2×C4⋊Dic47C2311yescharacteristic
102C2×C4⋊Dic47C2311yescharacteristic
103C2×Dic47⋊C4—21no—
104C2×Dic47⋊C4—21no—
105C2×Dic47⋊C4—21no—
106C2×Dic47⋊C4—21no—
107C2×Dic47⋊C4D411yescharacteristic
108C2×Dic47⋊C4D411yescharacteristic
109C4⋊C4×D47—22no—
110C4⋊C4×D47—28no—
111C4⋊C4×D47—22no—
112C4⋊C4×D47—22no—
113C4⋊C4×D47C2×C414yes—
114C2×(C2×D47)⋊C4—21no—
115C2×(C2×D47)⋊C4—21no—
116C2×(C2×D47)⋊C4—21no—
117C2×(C2×D47)⋊C4D411yescharacteristic
118C2×(C2×D47)⋊C4D411yescharacteristic
119C2×C4×Dic47—21no—
120C2×C4×Dic47—21no—
121C2×C4×Dic47C2311yescharacteristic
122C4⋊(C47⋊C8)—22no—
123Dic47⋊C8—22no—
124Dic47⋊C8—22no—
125#13093948—22no—
126#13093948—22no—
127#13093946—22no—
128#13093946—22no—
129#13093944—22no—
130#13093944—22no—
131C47⋊#95—21no—
132C47⋊#95—21no—
133C47⋊#95—21no—
134C47⋊#95—21no—
135C22×Q8×C47C2311yescharacteristic
136C22×C8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C4×Q8×C47—22no—
139C4×Q8×C47C2×C414yescomplemented
140C2×C4⋊C4×C47—21no—
141C2×C4⋊C4×C47—21no—
142C2×C4⋊C4×C47—21no—
143C2×C4⋊C4×C47C2311yescharacteristic
144C2×C4⋊C4×C47C2311yescharacteristic
145C2×C4⋊C4×C47C2311yescharacteristic
146C2×C42×C47—21no—
147C2×C42×C47C2311yescharacteristic
148C4⋊C8×C47—22no—
149#103×C47—22no—
150#103×C47—22no—
151C23×D47—21no—
152C23×D47C2×D411yescharacteristic
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47C22×C412yes—
157C2×Q8×C47C2×D412yes—
158C2×Q8×C47C2×Q812yes—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47C2411yescharacteristic
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47C2×D411yescharacteristic
170C22×Dic47C2×D411yescharacteristic
171C22×Dic47C2×D411yescharacteristic
172#10625354—28no—
173#10625354—28no—
174#10625354—28no—
175#10625354C4⋊C4116yescomplemented
176C2×D188—24no—
177C2×D188—24no—
178C2×D188—24no—
179C2×D188—21no—
180C2×D188—21no—
181C2×D188—21no—
182C2×D188C22×C412yes—
183C2×D188C2×D412yes—
184C2×D188C2×Q812yes—
185C2×C4×D47—24no—
186C2×C4×D47—24no—
187C2×C4×D47—24no—
188C2×C4×D47—24no—
189C2×C4×D47—24no—
190C2×C4×D47—24no—
191C2×C4×D47—42no—
192C2×C4×D47—81no—
193C2×C4×D47—81no—
194C2×C4×D47—81no—
195C2×C4×D47—81no—
196C2×C4×D47—81no—
197C2×C4×D47—81no—
198C2×C4×D47—81no—
199C2×C4×D47—81no—
200C2×C4×D47C22×C412yes—
201C2×C4×D47C2×D412yes—
202C2×C4×D47C2×D412yes—
203C2×C4×D47C2×Q812yes—
204C2×C4×D47#4112yes—
205C2×C4×D47#4112yes—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C4⋊C4×C47—24no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—81no—
219C4⋊C4×C47—81no—
220C4⋊C4×C47C22×C412yes—
221C42×C47—24no—
222C42×C47C22×C412yes—
223C42×C47C2×D412yes—
224(C2×D47)⋊C4—24no—
225(C2×D47)⋊C4—24no—
226(C2×D47)⋊C4—42no—
227(C2×D47)⋊C4C22⋊C414yes—
228(C2×D47)⋊C4C22⋊C414yes—
229C4⋊Dic47—21no—
230C4⋊Dic47—24no—
231C4⋊Dic47—21no—
232C4⋊Dic47—21no—
233C4⋊Dic47—21no—
234C4⋊Dic47—21no—
235C4⋊Dic47C22×C412yes—
236Dic47⋊C4—24no—
237Dic47⋊C4—42no—
238Dic47⋊C4—81no—
239Dic47⋊C4—81no—
240Dic47⋊C4C22⋊C414yes—
241Dic47⋊C4C22⋊C414yes—
242C4×Dic47—24no—
243C4×Dic47—42no—
244C4×Dic47C22×C412yes—
245C4×Dic47C2×D412yes—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252#10625324—44no—
253C8×D47—44no—
254C23×C47C22×D411yescharacteristic
255C22×D47—21no—
256C22×D47—21no—
257C22×D47—21no—
258C22×D47—21no—
259C22×D47—22no—
260C22×D47—22no—
261C22×D47—22no—
262C22×D47—41no—
263C22×D47—41no—
264C22×D47—41no—
265C22×D47—41no—
266C22×D47C2×C22⋊C412yes—
267C22×D47#12112yes—
268C22×D47C22⋊Q812yes—
269Q8×C47—22no—
270Q8×C47—22no—
271Q8×C47—22no—
272Q8×C47C2×C4⋊C414yes—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—22no—
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—41no—
289C2×C4×C47C2×C22⋊C412yes—
290C2×C4×C47C2×C22⋊C412yes—
291C2×C4×C47C23×C411yescharacteristic
292C2×C4×C47C22×D411yescharacteristic
293C2×C4×C47C22×D411yescharacteristic
294C2×C4×C47C22×Q811yescharacteristic
295C2×C4×C47C2×#4111yescharacteristic
296C2×C4×C47C2×#4111yescharacteristic
297C2×Dic47—21no—
298C2×Dic47—21no—
299C2×Dic47—21no—
300C2×Dic47—21no—
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×Dic47C2×C22⋊C412yes—
311C2×Dic47C2×C22⋊C412yes—
312C2×Dic47C2×C22⋊C412yes—
313C2×Dic47#12112yes—
314C2×Dic47C22⋊Q812yes—
315D188—216no—
316D188—22no—
317D188—22no—
318D188—22no—
319D188C2×C4⋊C414yes—
320C4×D47—216no—
321C4×D47—84no—
322C4×D47—84no—
323C4×D47—84no—
324C4×D47—84no—
325C4×D47C2×C4⋊C414yes—
326C4×D47#11714yes—
327C4×D47#12114yes—
328C4×D47C22⋊Q814yes—
329C8×C47—41no—
330C8×C47—41no—
331C47⋊C8—41no—
332C47⋊C8—41no—
333#20652—471nomaximal, Sylow
334C22×C47C22×C22⋊C411yescharacteristic
335C22×C47C2×#12111yescharacteristic
336C22×C47C2×C22⋊Q811yescharacteristic
337C22×C47#57611yescharacteristic
338C22×C47#57711yescharacteristic
339C22×C47#57711yescharacteristic
340C22×C47#57811yescharacteristic
341C2×D47—22no—
342C2×D47—22no—
343C2×D47—22no—
344C2×D47—22no—
345C2×D47—22no—
346C2×D47—22no—
347C2×D47—24no—
348C2×D47—42no—
349C2×D47—42no—
350C2×D47—42no—
351C2×D47—42no—
352C2×D47—42no—
353C2×D47—42no—
354C2×D47#38014yes—
355C4×C47—22no—
356C4×C47—22no—
357C4×C47—24no—
358C4×C47—42no—
359C4×C47—81no—
360C4×C47—81no—
361C4×C47C22×C4⋊C411yescharacteristic
362C4×C47C2×#11711yescharacteristic
363C4×C47C2×#12111yescharacteristic
364C4×C47C2×C22⋊Q811yescharacteristic
365Dic47—22no—
366Dic47—22no—
367Dic47—42no—
368Dic47—81no—
369Dic47—81no—
370Dic47#38014yes—
371C2×#520—471no—
372C2×#424—471no—
373C2×#417—471no—
374C2×#416—471no—
375#2317—471no—
376#1805—471no—
377#1805—471no—
378#1804—471no—
379#1804—471no—
380#1803—471no—
381#1803D4711yescharacteristic, complemented
382#1802—471no—
383#1802—471no—
384#1736—471no—
385C2×#340—471no—
386C2×C47C2×#38011yescharacteristic
387C2×C47#289711yescharacteristic
388C2×C47#289811yescharacteristic
389C2×C47#304511yescharacteristic
390C2×C47#304611yescharacteristic
391C2×C47#308311yescharacteristic
392C2×C47#308411yescharacteristic
393D47—24no—
394D47—44no—
395C22×#41—471no—
396C22×M16—471no—
397C23×C8—471no—
398#520—478no—
399#520—944no—
400C2×C4×Q8—471no—
401C2×C4×Q8C2×D4711yescharacteristic
402C2×C4×D4—471no—
403C2×C4×D4—471no—
404C2×C4×D4—941no—
405C2×C4×D4—941no—
406C2×#117—471no—
407C2×#117—471no—
408C2×#117—941no—
409C22×C4⋊C4—471no—
410C22×C4⋊C4—471no—
411C22×C4⋊C4—941no—
412#424—944no—
413C2×C4⋊C8—471no—
414C2×C4⋊C8—471no—
415C2×C4⋊C8—471no—
416C2×C4⋊C8C2×D4711yescharacteristic
417#417—944no—
418#416—944no—
419C2×#103—471no—
420C2×#103—471no—
421C2×#103C2×D4711yescharacteristic
422C2×#103C2×D4711yescharacteristic
423C2×#102—471no—
424C2×#102—471no—
425C2×#102—471no—
426C2×#102—471no—
427#389—941no—
428#389—941no—
429#385—941no—
430#385—941no—
431#384—471no—
432#384C2×D4711yescharacteristic
433#382—471no—
434#382—471no—
435#340—471no—
436#340—471no—
437#340—471no—
438#340—471no—
439#340—471no—
440#340—471no—
441#340C2×D4711yescharacteristic
442#340C2×D4711yescharacteristic
443C47#2065211yescharacteristic, complemented, Sylow
444C2×#41—474no—
445C2×#41—474no—
446C2×#41—474no—
447C2×#41—942no—
448C2×#41—942no—
449C2×#41—942no—
450C22×Q8C22×D4711yescharacteristic
451C22×D4—471no—
452C22×D4—941no—
453C23×C4—471no—
454C23×C4—941no—
455C23×C4—941no—
456C23×C4—941no—
457C23×C4—941no—
458C23×C4—941no—
459C2×M16—942no—
460C2×M16—942no—
461C2×M16—942no—
462C22×C8—471no—
463C22×C8—471no—
464C22×C8—942no—
465C22×C8—942no—
466C22×C8—942no—
467C22×C8C22×D4711yescharacteristic
468C22×C8C22×D4711yescharacteristic
469C4×Q8—22no—
470C4×Q8—474no—
471C4×Q8—942no—
472C4×Q8C4×D4714yescomplemented
473C4×D4—474no—
474C4×D4—474no—
475C4×D4—948no—
476C4×D4—942no—
477C4×D4—948no—
478C4×D4—942no—
479#117—474no—
480#117—474no—
481#117—948no—
482#117—942no—
483#117—942no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—471no—
488C2×C4⋊C4—471no—
489C2×C4⋊C4—471no—
490C2×C4⋊C4—474no—
491C2×C4⋊C4—471no—
492C2×C4⋊C4—471no—
493C2×C4⋊C4—948no—
494C2×C4⋊C4—942no—
495C2×C4⋊C4—942no—
496C2×C4⋊C4—942no—
497C2×C4⋊C4—941no—
498C2×C4⋊C4—941no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4C22×D4711yescharacteristic
503C2×C4⋊C4C22×D4711yescharacteristic
504C2×C4⋊C4C22×D4711yescharacteristic
505C2×C22⋊C4—471no—
506C2×C22⋊C4—471no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—941no—
510C2×C42—21no—
511C2×C42—471no—
512C2×C42—941no—
513C2×C42—941no—
514C2×C42C22×D4711yescharacteristic
515C4⋊C8—22no—
516C4⋊C8—942no—
517C4⋊C8—942no—
518C4⋊C8—942no—
519#103—22no—
520#103—22no—
521#103—942no—
522#103—942no—
523#102—942no—
524#102—942no—
525#102—942no—
526#102—942no—
527#95—941no—
528#95—941no—
529#95—941no—
530#95—941no—
531C24—471no—
532C24—941no—
533#41—4716no—
534#41—948no—
535#41—948no—
536#41—948no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8C2×C4×D4712yes—
541C2×Q8D4×D4712yes—
542C2×Q8Q8×D4712yes—
543C2×D4—472no—
544C2×D4—472no—
545C2×D4—472no—
546C2×D4—944no—
547C2×D4—944no—
548C2×D4—944no—
549C2×D4—941no—
550C2×D4—941no—
551C2×D4—941no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—471no—
557C22×C4—472no—
558C22×C4—472no—
559C22×C4—472no—
560C22×C4—472no—
561C22×C4—472no—
562C22×C4—472no—
563C22×C4—471no—
564C22×C4—471no—
565C22×C4—944no—
566C22×C4—944no—
567C22×C4—944no—
568C22×C4—944no—
569C22×C4—944no—
570C22×C4—941no—
571C22×C4—944no—
572C22×C4—941no—
573C22×C4—941no—
574C22×C4—3761no—
575C22×C4—3761no—
576C22×C4—3761no—
577C22×C4—3761no—
578C22×C4—3761no—
579C22×C4—3761no—
580C22×C4—3761no—
581C22×C4—3761no—
582C22×C4—1882no—
583C22×C4D4×D4711yescharacteristic
584C22×C4D4×D4711yescharacteristic
585C22×C4C23×D4711yescharacteristic
586M16—1884no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—941no—
594C2×C8—941no—
595C2×C8—941no—
596C2×C8—941no—
597C2×C8—941no—
598C2×C8—941no—
599C2×C8—1884no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—81no—
607C4⋊C4—81no—
608C4⋊C4—474no—
609C4⋊C4—474no—
610C4⋊C4—472no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4—941no—
614C4⋊C4—941no—
615C4⋊C4—941no—
616C4⋊C4—941no—
617C4⋊C4—941no—
618C4⋊C4—3761no—
619C4⋊C4—3761no—
620C4⋊C4—1882no—
621C4⋊C4C2×C4×D4712yes—
622C22⋊C4—474no—
623C22⋊C4—474no—
624C22⋊C4—944no—
625C22⋊C4—944no—
626C22⋊C4—1882no—
627C42—24no—
628C42—472no—
629C42—472no—
630C42—944no—
631C42—1882no—
632C42C2×C4×D4712yes—
633C42D4×D4712yes—
634C23—472no—
635C23—472no—
636C23—472no—
637C23—941no—
638C23—941no—
639C23—941no—
640C23—941no—
641C23—942no—
642C23—942no—
643C23—942no—
644C23—1881no—
645C23—1881no—
646C23—1881no—
647C23—1881no—
648C23C2×D4×D4711yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8C4⋊C4×D4714yes—
653D4—474no—
654D4—9416no—
655D4—942no—
656D4—942no—
657D4—942no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—472no—
675C2×C4—472no—
676C2×C4—472no—
677C2×C4—474no—
678C2×C4—474no—
679C2×C4—474no—
680C2×C4—474no—
681C2×C4—472no—
682C2×C4—472no—
683C2×C4—9416no—
684C2×C4—941no—
685C2×C4—941no—
686C2×C4—941no—
687C2×C4—941no—
688C2×C4—942no—
689C2×C4—3764no—
690C2×C4—3764no—
691C2×C4—3764no—
692C2×C4—3764no—
693C2×C4—1881no—
694C2×C4—1881no—
695C2×C4—1881no—
696C2×C4—1881no—
697C2×C4—1881no—
698C2×C4—1881no—
699C2×C4—1881no—
700C2×C4—1881no—
701C2×C4C22⋊C4×D4712yes—
702C2×C4C22⋊C4×D4712yes—
703C2×C4C22×C4×D4711yescharacteristic
704C2×C4C2×D4×D4711yescharacteristic
705C2×C4C2×D4×D4711yescharacteristic
706C2×C4C2×Q8×D4711yescharacteristic
707C2×C4#41×D4711yescharacteristic
708C2×C4#41×D4711yescharacteristic
709C8—41no—
710C8—41no—
711C8—1881no—
712C8—1881no—
713C22—474no—
714C22—942no—
715C22—942no—
716C22—942no—
717C22—942no—
718C22—942no—
719C22—942no—
720C22—944no—
721C22—1882no—
722C22—1882no—
723C22—1882no—
724C22—1882no—
725C22—1882no—
726C22—1882no—
727C22C2×C22⋊C4×D4711yescharacteristic
728C22#121×D4711yescharacteristic
729C22C22⋊Q8×D4711yescharacteristic
730C22#1568992711yescharacteristic
731C22#1568992911yescharacteristic
732C22#1568993211yescharacteristic
733C22#1568993611yescharacteristic
734C4—22no—
735C4—22no—
736C4—24no—
737C4—42no—
738C4—81no—
739C4—81no—
740C4—474no—
741C4—942no—
742C4—942no—
743C4—3761no—
744C4—3761no—
745C4—1882no—
746C4C2×C4⋊C4×D4711yescharacteristic
747C4#117×D4711yescharacteristic
748C4#121×D4711yescharacteristic
749C4C22⋊Q8×D4711yescharacteristic
750C2—944no—
751C2—1884no—
752C2#380×D4711yescharacteristic
753C2#2025191211yescharacteristic
754C2#2025191611yescharacteristic
755C2#2025292411yescharacteristic
756C2#2025293511yescharacteristic
757C2#2025323611yescharacteristic
758C2#2025324711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1803C2
socleC23×C47C22×D4
prime radicalC22×#10625354C22
cosocleC22×C4×C47C24
hypercenter#1803D47
hypocenterC47#20652
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. C2×#15689148C2semidirect
5. #20246009C2semidirect
6. #20243403C2semidirect
7. #20243401C2semidirect
8. #20243399C2semidirect
9. #20243397C2semidirect
10. #20243391C2semidirect
11. #20243387C2semidirect
12. #20243385C2semidirect
13. #20243106C2semidirect
14. #340×D47C2semidirect
15. C47×#1803C2semidirect
20. #15689605C4semidirect
87. Q8×Dic47C2×C4semidirect
90. C4×D188C2×C4semidirect
93. #13093986C2×C4semidirect
139. C4×Q8×C47C2×C4semidirect
175. #10625354C4⋊C4semidirect
381. #1803D47semidirect
443. C47#20652semidirect
472. C4×Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896052
C2×#156891482
C2×#156891232
C2×#156891182
#202460092
#202434032
#202434012
#202433992
#202433972
#202433912
#202433872
#202433852
#202431062
#340×D472
C47×#18032
#2065247