Finite Group Databasebeta

← #26222038

Subgroups — #26222038

Order 12032.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689603C211yesmaximal, characteristic
2C2×#15689283C211yesmaximal, characteristic
3C2×#15689228C211yesmaximal, characteristic, complemented
4C2×C4×#10625336C211yesmaximal, characteristic, complemented
5#20243732C211yesmaximal, characteristic, complemented
6#20243725C211yesmaximal, characteristic, complemented
7#20243696C211yesmaximal, characteristic, complemented
8#20243655C211yesmaximal, characteristic, complemented
9#20243648C211yesmaximal, characteristic, complemented
10#20243580C211yesmaximal, characteristic, complemented
11#20243326C211yesmaximal, characteristic
12#20243216C211yesmaximal, characteristic, complemented
13C4×#13093947C211yesmaximal, characteristic, complemented
14#20243154C211yesmaximal, characteristic, complemented
15C47×#2323C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C22×#10625337C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19#15689603—24no—
20#15689603—24no—
21C2×C4×Dic94C2211yescharacteristic
22C2×C4×Dic94C2211yescharacteristic
23C2×C4×D188C2211yescharacteristic
24C2×C4×D188C2211yescharacteristic
25C2×(C22⋊D47)⋊C4—21no—
26C2×(C22⋊D47)⋊C4—21no—
27C2×#13093982—21no—
28C22×C4⋊Dic47C2211yescharacteristic
29C2×C4⋊C4×D47—21no—
30#15689283C418yescomplemented
31#15689228—24no—
32C4×#10625336—24no—
33C2×#13093955C2211yescharacteristic
34C2×#13093955C2211yescharacteristic
35C2×#13093948C2211yescharacteristic
36C2×#13093948C2211yescharacteristic
37C2×#13093947C2211yescharacteristic
38C2×#13093947C2211yescharacteristic
39C2×#13093947C2211yescharacteristic
40C2×#13093944C2211yescharacteristic
41C2×#13093944C2211yescharacteristic
42C2×#13093944C2211yescharacteristic
43C2×C22⋊(C47⋊C8)C2211yescharacteristic
44C2×C22⋊(C47⋊C8)C2211yescharacteristic
45C2×#13093935C2211yescharacteristic
46C2×C4×C47⋊C8C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688878C2211yescharacteristic
52#15688878C2211yescharacteristic
53C2×C22⋊Q8×C47C2211yescharacteristic
54C2×C4×Q8×C47C2211yescharacteristic
55C2×#117×C47C2211yescharacteristic
56C47×#391C2211yescharacteristic
57C47×#389—21no—
58C47×#389C2211yescharacteristic
59C47×#388—21no—
60C47×#388—21no—
61C47×#387—21no—
62C47×#380C2211yescharacteristic
63C4×C4⋊C4×C47C2211yescharacteristic
64C2×#10625350—22no—
65C2×#10625350—22no—
66C2×#10625350—22no—
67C2×#10625350—22no—
68C2×#10625350—22no—
69C2×#10625350C2×C414yes—
70C22×Dic94C2311yescharacteristic
71C22×D188C2311yescharacteristic
72C22×C22⋊D47—21no—
73C23×Dic47—21no—
74C22×C4×D47—21no—
75C22×C4×D47—21no—
76C22×C4×D47—21no—
77C2×#10625337—22no—
78C2×#10625337—22no—
79C2×#10625337C2×C414yescomplemented
80C2×#10625336—22no—
81C2×#10625336—22no—
82C2×#10625336C2×C414yescomplemented
83C22×C47⋊C8C2311yescharacteristic
84C22×C47⋊C8C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86C22×C47⋊C8C2311yescharacteristic
87C4×Dic94—22no—
88C4×Dic94—22no—
89C4×Dic94—22no—
90C4×Dic94D414yes—
91C4×D188—22no—
92C4×D188—22no—
93C4×D188—22no—
94C4×D188D414yes—
95(C22⋊D47)⋊C4—28no—
96(C22⋊D47)⋊C4—28no—
97#13093982—28no—
98C2×C4⋊Dic47—21no—
99C2×C4⋊Dic47—22no—
100C2×C4⋊Dic47—22no—
101C2×C4⋊Dic47C2311yescharacteristic
102C2×C4⋊Dic47C2311yescharacteristic
103C2×Dic47⋊C4—21no—
104C2×Dic47⋊C4—21no—
105C4⋊C4×D47—28no—
106C2×(C2×D47)⋊C4—21no—
107C2×(C2×D47)⋊C4—21no—
108C2×C4×Dic47—21no—
109C2×C4×Dic47—21no—
110#13093955—22no—
111#13093955—22no—
112#13093948—22no—
113#13093948—22no—
114#13093947—22no—
115#13093947—22no—
116#13093947C2×C414yescomplemented
117#13093944—22no—
118#13093944—22no—
119#13093944C2×C414yescomplemented
120C22⋊(C47⋊C8)—22no—
121C22⋊(C47⋊C8)C2×C414yescomplemented
122#13093935—22no—
123C4×C47⋊C8—22no—
124C22×Q8×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C22⋊Q8×C47—22no—
127C22⋊Q8×C47C2×C414yescomplemented
128C4×Q8×C47—22no—
129C4×Q8×C47—22no—
130#117×C47—22no—
131#117×C47—22no—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47—21no—
135C2×C4⋊C4×C47D411yescharacteristic
136C2×C4⋊C4×C47D411yescharacteristic
137C2×C4⋊C4×C47C2311yescharacteristic
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C4⋊C4×C47C2311yescharacteristic
140C2×C22⋊C4×C47—21no—
141C2×C22⋊C4×C47—21no—
142C2×C22⋊C4×C47D411yescharacteristic
143C2×C22⋊C4×C47D411yescharacteristic
144C2×C42×C47—21no—
145C2×C42×C47—21no—
146C2×C42×C47C2311yescharacteristic
147C2×C42×C47C2311yescharacteristic
148#95×C47—21no—
149#95×C47—21no—
150#95×C47—21no—
151#95×C47—21no—
152#95×C47—21no—
153C24×C47C2×D411yescharacteristic
154C23×D47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47C22×C412yes—
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×D411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47#4112yes—
176C22×C4×C47C2411yescharacteristic
177C2×C22⋊D47—24no—
178C2×C22⋊D47—24no—
179C2×C22⋊D47—24no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—24no—
184C22×Dic47—81no—
185C22×Dic47—81no—
186#10625350—28no—
187#10625350—28no—
188#10625350—28no—
189#10625350—28no—
190C2×D188—21no—
191C2×D188—21no—
192C2×D188—21no—
193C2×D188C22×C412yes—
194C2×D188C2×D412yes—
195C2×D188#4112yes—
196C2×C4×D47—24no—
197C2×C4×D47—24no—
198C2×C4×D47—24no—
199C2×C4×D47—24no—
200C2×C4×D47—24no—
201C2×C4×D47—81no—
202C2×C4×D47—81no—
203C2×C4×D47—81no—
204C2×C4×D47—81no—
205C2×Dic94—21no—
206C2×Dic94—21no—
207C2×Dic94—21no—
208C2×Dic94C22×C412yes—
209C2×Dic94C2×D412yes—
210C2×Dic94#4112yes—
211C4⋊C4×C47—24no—
212C4⋊C4×C47—22no—
213C4⋊C4×C47—22no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—42no—
220C4⋊C4×C47—81no—
221C4⋊C4×C47C22×C412yes—
222C22⋊C4×C47—24no—
223C22⋊C4×C47—22no—
224C22⋊C4×C47—22no—
225C22⋊C4×C47—81no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47—42no—
229C42×C47—81no—
230C42×C47C2×D412yes—
231C42×C47C2×D412yes—
232#10625337—28no—
233#10625336—28no—
234(C2×D47)⋊C4—24no—
235(C2×D47)⋊C4—24no—
236C4⋊Dic47—24no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47C2×D412yes—
240C4⋊Dic47C2×D412yes—
241Dic47⋊C4—24no—
242Dic47⋊C4—24no—
243C4×Dic47—24no—
244C4×Dic47—24no—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8C22×C412yes—
256C2×C47⋊C8C22×C412yes—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47C4×D412yes—
264C23×C47C22×D411yescharacteristic
265C22×D47—22no—
266C22×D47—22no—
267C22×D47—22no—
268C22×D47—41no—
269C22×D47—41no—
270C22×D47—41no—
271C22×D47—41no—
272Q8×C47—22no—
273Q8×C47—22no—
274Q8×C47—41no—
275Q8×C47—41no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
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—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—41no—
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×C47C4×D412yes—
305C2×C4×C47#12012yes—
306C2×C4×C47#12012yes—
307C2×C4×C47C23×C411yescharacteristic
308C2×C4×C47C22×D411yescharacteristic
309C2×C4×C47C22×D411yescharacteristic
310C2×C4×C47C2×#4111yescharacteristic
311C2×C4×C47C2×#4111yescharacteristic
312C2×C4×C47C2×#4111yescharacteristic
313C22⋊D47—216no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—41no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—84no—
324D188—22no—
325D188—22no—
326D188—22no—
327D188C4×D414yes—
328C4×D47—216no—
329C4×D47—84no—
330C4×D47—84no—
331Dic94—22no—
332Dic94—22no—
333Dic94—22no—
334Dic94C4×D414yes—
335C47⋊C8—22no—
336C47⋊C8—22no—
337C47⋊C8—41no—
338C47⋊C8—41no—
339#21461—471nomaximal, Sylow
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47C2×C4×D411yescharacteristic
348C22×C47C2×#12011yescharacteristic
349C22×C47#52511yescharacteristic
350C22×C47#57711yescharacteristic
351C22×C47#57711yescharacteristic
352C22×C47#57711yescharacteristic
353C22×C47#57811yescharacteristic
354C2×D47—24no—
355C2×D47—42no—
356C2×D47—42no—
357C2×D47—42no—
358C2×D47—42no—
359C2×D47—42no—
360C2×D47—42no—
361C4×C47—22no—
362C4×C47—22no—
363C4×C47—22no—
364C4×C47—42no—
365C4×C47—41no—
366C4×C47—41no—
367C4×C47—42no—
368C4×C47—81no—
369C4×C47—81no—
370C4×C47C2×C4×D411yescharacteristic
371C4×C47C2×C4×D411yescharacteristic
372C4×C47#52511yescharacteristic
373C4×C47#52511yescharacteristic
374Dic47—24no—
375Dic47—42no—
376Dic47—42no—
377C2×#520—471no—
378C2×#452—471no—
379C2×#441—471no—
380C2×C4×SD16—471no—
381#2323D4711yescharacteristic, complemented
382#1878—471no—
383#1877—471no—
384#1872—471no—
385#1865—471no—
386#1864—471no—
387#1853—471no—
388#1788—471no—
389#1762—471no—
390C4×#103—471no—
391#1750—471no—
392C2×C47—42no—
393C2×C47C4×#12011yescharacteristic
394C2×C47#294711yescharacteristic
395C2×C47#295211yescharacteristic
396C2×C47#300911yescharacteristic
397C2×C47#301311yescharacteristic
398C2×C47#312011yescharacteristic
399C2×C47#312511yescharacteristic
400D47—44no—
401C22×#41—471no—
402C22×Q16—471no—
403C22×SD16—471no—
404C2×C22⋊Q8C2×D4711yescharacteristic
405#520—944no—
406#520—944no—
407C2×C4×Q8—471no—
408C2×C4×Q8—471no—
409C2×C4×Q8C2×D4711yescharacteristic
410C2×C4×D4—471no—
411C2×C4×D4—471no—
412C2×C4×D4—941no—
413C2×C4×D4—941no—
414C2×#117—941no—
415C2×#117C2×D4711yescharacteristic
416C22×C4⋊C4—471no—
417C22×C4⋊C4—941no—
418#452—478no—
419#441—944no—
420C4×SD16—944no—
421C2×#106—471no—
422C2×#106—471no—
423C2×#103—471no—
424C2×#103—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#102—471no—
429C2×#102—471no—
430C2×#102—471no—
431C2×C22⋊C8—471no—
432C2×C22⋊C8—471no—
433C2×#97—471no—
434C2×C4×C8—471no—
435#391C2×D4711yescharacteristic
436#389—21no—
437#389C2×D4711yescharacteristic
438#388—21no—
439#388—21no—
440#387—21no—
441#380C2×D4711yescharacteristic
442C4×C4⋊C4C2×D4711yescharacteristic
443#340—471no—
444#340—471no—
445#340—471no—
446#340—471no—
447#336—471no—
448#336—471no—
449C47#2146111yescharacteristic, complemented, Sylow
450C2×#41—474no—
451C2×#41—942no—
452C2×#41—942no—
453C2×#41—942no—
454C2×#41—942no—
455C2×#41—942no—
456C22×Q8—471no—
457C22×Q8C22×D4711yescharacteristic
458C22×D4—471no—
459C22×D4—941no—
460C23×C4—941no—
461C23×C4—941no—
462C23×C4—941no—
463C23×C4—941no—
464C23×C4C22×D4711yescharacteristic
465C2×Q16—474no—
466C2×Q16—942no—
467C2×Q16—942no—
468C2×SD16—474no—
469C2×SD16—942no—
470C2×SD16—942no—
471C22×C8—471no—
472C22×C8—471no—
473C22×C8—471no—
474C22×C8—471no—
475C22⋊Q8—22no—
476C22⋊Q8C4×D4714yescomplemented
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—474no—
480C4×Q8—942no—
481C4×Q8—942no—
482C4×Q8—942no—
483C4×D4—474no—
484C4×D4—942no—
485C4×D4—942no—
486C4×D4—948no—
487C4×D4—948no—
488C4×D4—942no—
489#117—22no—
490#117—22no—
491#117—948no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—948no—
498C2×C4⋊C4—942no—
499C2×C4⋊C4—942no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4C22⋊D4711yescharacteristic
504C2×C4⋊C4C22⋊D4711yescharacteristic
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4C22⋊D4711yescharacteristic
513C2×C22⋊C4C22⋊D4711yescharacteristic
514C2×C42—21no—
515C2×C42—21no—
516C2×C42—941no—
517C2×C42—941no—
518C2×C42C22×D4711yescharacteristic
519C2×C42C22×D4711yescharacteristic
520#106—942no—
521#106—942no—
522#103—474no—
523#103—942no—
524#103—942no—
525#103—942no—
526#103—942no—
527#102—474no—
528#102—942no—
529#102—942no—
530C22⋊C8—474no—
531C22⋊C8—942no—
532#97—942no—
533C4×C8—942no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539C24—941no—
540C24C2×C22⋊D4711yescharacteristic
541#41—948no—
542#41—948no—
543#41—948no—
544#41—948no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—472no—
551C2×Q8—472no—
552C2×Q8—472no—
553C2×Q8—941no—
554C2×Q8—941no—
555C2×Q8—941no—
556C2×Q8C2×C4×D4712yes—
557C2×D4—472no—
558C2×D4—472no—
559C2×D4—472no—
560C2×D4—944no—
561C2×D4—944no—
562C2×D4—944no—
563C2×D4—941no—
564C2×D4—941no—
565C2×D4—941no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—944no—
575C22×C4—944no—
576C22×C4—944no—
577C22×C4—941no—
578C22×C4—944no—
579C22×C4—944no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—944no—
583C22×C4—3761no—
584C22×C4—3761no—
585C22×C4—3761no—
586C22×C4—3761no—
587C22×C4—3761no—
588C22×C4—3761no—
589C22×C4C2×C4×D4712yes—
590C22×C4#1062535012yes—
591C22×C4C2×C22⋊D4711yescharacteristic
592C22×C4C2×C22⋊D4711yescharacteristic
593C22×C4C2×C22⋊D4711yescharacteristic
594C22×C4C2×C22⋊D4711yescharacteristic
595C22×C4C2×C22⋊D4711yescharacteristic
596C22×C4C23×D4711yescharacteristic
597Q16—948no—
598SD16—948no—
599C2×C8—472no—
600C2×C8—472no—
601C2×C8—941no—
602C2×C8—941no—
603C2×C8—941no—
604C2×C8—941no—
605C2×C8—941no—
606C2×C8—941no—
607C2×C8—941no—
608C2×C8—941no—
609C2×C8—941no—
610C2×C8—941no—
611C4⋊C4—24no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—42no—
620C4⋊C4—81no—
621C4⋊C4—472no—
622C4⋊C4—472no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—941no—
627C4⋊C4—941no—
628C4⋊C4C2×C4×D4712yes—
629C22⋊C4—24no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—81no—
633C22⋊C4—944no—
634C22⋊C4—944no—
635C42—21no—
636C42—21no—
637C42—42no—
638C42—81no—
639C42—944no—
640C42—944no—
641C42D4×D4712yes—
642C42D4×D4712yes—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—942no—
650C23—942no—
651C23—942no—
652C23—1881no—
653C23—1881no—
654C23—1881no—
655C23—1881no—
656C23C4×C22⋊D4712yes—
657C23C22×C22⋊D4711yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662Q8—474no—
663Q8—942no—
664Q8—942no—
665Q8—942no—
666D4—474no—
667D4—9416no—
668D4—942no—
669D4—942no—
670D4—942no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—9416no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—3764no—
706C2×C4—3764no—
707C2×C4—3764no—
708C2×C4—1881no—
709C2×C4—1881no—
710C2×C4—1881no—
711C2×C4—1881no—
712C2×C4C4×C22⋊D4712yes—
713C2×C4#1309399212yes—
714C2×C4#1309399212yes—
715C2×C4C22×C4×D4711yescharacteristic
716C2×C4C2×D4×D4711yescharacteristic
717C2×C4C2×D4×D4711yescharacteristic
718C2×C4#41×D4711yescharacteristic
719C2×C4#41×D4711yescharacteristic
720C2×C4C2×#1062535011yescharacteristic
721C8—942no—
722C8—942no—
723C8—1881no—
724C8—1881no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—944no—
733C22—1882no—
734C22—1882no—
735C22—1882no—
736C22—1882no—
737C22—1882no—
738C22—1882no—
739C22C2×C4×C22⋊D4711yescharacteristic
740C22C2×#1309399211yescharacteristic
741C22#1568963011yescharacteristic
742C22#1568993111yescharacteristic
743C22#1568993111yescharacteristic
744C22#1568993411yescharacteristic
745C22#1568993811yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—42no—
751C4—42no—
752C4—41no—
753C4—81no—
754C4—81no—
755C4—944no—
756C4—1882no—
757C4—1882no—
758C4C4×D4×D4711yescharacteristic
759C4C4×D4×D4711yescharacteristic
760C4#1568963211yescharacteristic
761C4#1568963211yescharacteristic
762C2—42no—
763C2—1884no—
764C2C4×#1309399211yescharacteristic
765C2#2025223111yescharacteristic
766C2#2025226911yescharacteristic
767C2#2025266311yescharacteristic
768C2#2025270011yescharacteristic
769C2#2025359611yescharacteristic
770C2#2025365911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2323C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenter#2323D47
hypocenterC47#21461
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
3. C2×#15689228C2semidirect
4. C2×C4×#10625336C2semidirect
5. #20243732C2semidirect
6. #20243725C2semidirect
7. #20243696C2semidirect
8. #20243655C2semidirect
9. #20243648C2semidirect
10. #20243580C2semidirect
12. #20243216C2semidirect
13. C4×#13093947C2semidirect
14. #20243154C2semidirect
15. C47×#2323C2semidirect
30. #15689283C4semidirect
79. C2×#10625337C2×C4semidirect
82. C2×#10625336C2×C4semidirect
116. #13093947C2×C4semidirect
119. #13093944C2×C4semidirect
121. C22⋊(C47⋊C8)C2×C4semidirect
127. C22⋊Q8×C47C2×C4semidirect
381. #2323D47semidirect
449. C47#21461semidirect
476. C22⋊Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896032
C2×#156892832
C2×#156892282
C2×C4×#106253362
#202437322
#202437252
#202436962
#202436552
#202436482
#202435802
#202433262
#202432162
C4×#130939472
#202431542
C47×#23232
#2146147