Finite Group Databasebeta

← #25149961

Subgroups — #25149961

Order 11008.

1126 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×#14583591C211yesmaximal, characteristic
2C2×#14583266C211yesmaximal, characteristic, complemented
3C2×#14583107C211yesmaximal, characteristic, complemented
4#19139545C211yesmaximal, characteristic
5#19135604C211yesmaximal, characteristic, complemented
6#19135603C211yesmaximal, characteristic, complemented
7#19135602C211yesmaximal, characteristic, complemented
8#19135551C211yesmaximal, characteristic, complemented
9#19135391C211yesmaximal, characteristic
10#19134906C211yesmaximal, characteristic, complemented
11#19134904C211yesmaximal, characteristic, complemented
12#19134903C211yesmaximal, characteristic, complemented
13#19134900C211yesmaximal, characteristic, complemented
14#19134427C211yesmaximal, characteristic, complemented
15C43×#2001C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17#14583591—24no—
18#14583591—24no—
19C2×#13063323C2211yescharacteristic
20C2×#13063320—21no—
21C2×#13063316—21no—
22C2×#13063316C2211yescharacteristic
23C2×#13063309—21no—
24C2×#13063305C2211yescharacteristic
25C2×#13063304C2211yescharacteristic
26C2×#13063301C2211yescharacteristic
27C2×#13063301C2211yescharacteristic
28C2×Q8×Dic43C2211yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×#13063283C2211yescharacteristic
31C2×#13063281—21no—
32C22×C4⋊Dic43C2211yescharacteristic
33#14583266—24no—
34#14583107—24no—
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×#13063235C2211yescharacteristic
46#14582835—21no—
47#14582834—21no—
48#14582799—21no—
49#14582768—21no—
50C4⋊C4×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C22×Q16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×C22⋊D43D411yescharacteristic
65C23×Dic43—21no—
66C22×C4×D43C2311yescharacteristic
67C2×#10621885—22no—
68C2×#10621885—41no—
69C2×#10621885—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063323—22no—
73#13063323—22no—
74#13063320—28no—
75#13063316—28no—
76#13063316—22no—
77#13063316D414yes—
78#13063309—28no—
79#13063305—22no—
80#13063305—41no—
81#13063304—22no—
82#13063304—41no—
83#13063301—22no—
84#13063301—22no—
85#13063301—22no—
86#13063301—41no—
87Q8×Dic43—22no—
88Q8×Dic43D414yes—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—22no—
91#13063283—22no—
92#13063283—22no—
93#13063281—28no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43—22no—
98C2×C4⋊Dic43—22no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4D411yescharacteristic
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43D411yescharacteristic
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4D411yescharacteristic
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43C2311yescharacteristic
121Dic43⋊C8—22no—
122#13063250—22no—
123#13063250—22no—
124#13063249—22no—
125#13063249—22no—
126#13063249—22no—
127#13063248—22no—
128C22⋊(C43⋊C8)—41no—
129(C2×D43)⋊C8—41no—
130(C2×D43)⋊C8—41no—
131#13063235—22no—
132C43⋊#95—21no—
133C22×Q8×C43C2311yescharacteristic
134C22×Q8×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C2×Q16×C43—22no—
137C2×Q16×C43—41no—
138C2×Q16×C43—41no—
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C22⋊Q8×C43—22no—
142C22⋊Q8×C43—22no—
143C22⋊Q8×C43—22no—
144C22⋊Q8×C43—41no—
145C2×C4⋊C4×C43—21no—
146C2×C4⋊C4×C43—21no—
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43—21no—
151#103×C43—22no—
152#103×C43—22no—
153C22⋊C8×C43—41no—
154C24×C43C2×D411yescharacteristic
155C23×D43C2×D411yescharacteristic
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43C2×D412yes—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180C2×C22⋊D43—22no—
181C2×C22⋊D43—22no—
182C2×C22⋊D43—41no—
183C22×Dic43—24no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205Q16×C43—44no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C4⋊C4×C43—24no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—42no—
216C4⋊C4×C43C2×D412yes—
217C4⋊C4×C43#4112yes—
218C22⋊C4×C43—24no—
219C22⋊C4×C43—42no—
220C22⋊Dic43—22no—
221C22⋊Dic43—42no—
222#10621885—44no—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—24no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—42no—
227(C2×D43)⋊C4—42no—
228C4⋊Dic43—24no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—24no—
233C4⋊Dic43—24no—
234C4⋊Dic43—42no—
235C4⋊Dic43C2×D412yes—
236C4⋊Dic43C2×D412yes—
237C4⋊Dic43#4112yes—
238Dic43⋊C4—24no—
239Dic43⋊C4—24no—
240Dic43⋊C4—22no—
241Dic43⋊C4—42no—
242Dic43⋊C4—42no—
243Dic43⋊C4—42no—
244Dic43⋊C4—42no—
245C4×Dic43—24no—
246C4×Dic43—24no—
247C4×Dic43—42no—
248C4×Dic43C2×D412yes—
249C4×Dic43C2×D412yes—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43#13712yes—
263C23×C43C22×D411yescharacteristic
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271Q8×C43—22no—
272Q8×C43—22no—
273Q8×C43—41no—
274Q8×C43—41no—
275Q8×C43—41no—
276Q8×C43—41no—
277Q8×C43—41no—
278Q8×C43—41no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—22no—
284C2×C4×C43—21no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C22⋊D43—44no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—48no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43#12012yes—
326C2×Dic43#12012yes—
327C4×D43—41no—
328C4×D43—41no—
329C4×D43—41no—
330C4×D43—41no—
331Dic86—41no—
332Dic86—41no—
333Dic86—41no—
334Dic86—41no—
335C8×C43—41no—
336C8×C43—41no—
337C43⋊C8—41no—
338C43⋊C8—41no—
339#25584—431nomaximal, Sylow
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43C2×#12011yescharacteristic
348C22×C43#54611yescharacteristic
349C22×C43#54611yescharacteristic
350C22×C43C2×#13711yescharacteristic
351C22×C43#57511yescharacteristic
352C22×C43#57811yescharacteristic
353C22×C43#57811yescharacteristic
354C2×D43—41no—
355C2×D43—41no—
356C2×D43—41no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C4×C43—41no—
362C4×C43—42no—
363C4×C43—42no—
364C4×C43—42no—
365C4×C43—81no—
366C4×C43#53211yescharacteristic
367C4×C43#53511yescharacteristic
368C4×C43#55011yescharacteristic
369C4×C43#55011yescharacteristic
370Dic43—22no—
371Dic43—22no—
372Dic43—41no—
373Dic43—42no—
374Dic43—42no—
375Dic43—42no—
376Dic43—81no—
377C2×#552—431no—
378C2×#491—431no—
379C2×#462—431no—
380#2542—431no—
381#2001—431no—
382#2001—431no—
383#2001—431no—
384#2001D4311yescharacteristic, complemented
385#1989—431no—
386#1955—431no—
387#1873—431no—
388#1873—431no—
389#1872—431no—
390#1872—431no—
391#1763—431no—
392C2×C43—42no—
393C2×C43#243111yescharacteristic
394C2×C43#300711yescharacteristic
395C2×C43#301111yescharacteristic
396C2×C43#331211yescharacteristic
397C2×C43#331211yescharacteristic
398C2×C43#331511yescharacteristic
399C2×C43#331511yescharacteristic
400D43—81no—
401C22×Q16—431no—
402C22×Q16C2×D4311yescharacteristic
403#552—864no—
404#552—864no—
405C2×C4⋊Q8—431no—
406C2×#126—861no—
407C2×#125—431no—
408C2×#125—861no—
409C2×#123—861no—
410C2×C22⋊Q8—431no—
411C2×C22⋊Q8—431no—
412C2×C22⋊Q8—431no—
413C2×C22⋊Q8—431no—
414C2×C22⋊Q8C2×D4311yescharacteristic
415C2×C22⋊Q8C2×D4311yescharacteristic
416C2×C4×Q8—431no—
417C2×C4×D4—431no—
418C2×#117—431no—
419C2×#117—861no—
420C22×C4⋊C4—431no—
421#491—864no—
422#462—864no—
423C2×C4⋊C8—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103C2×D4311yescharacteristic
431C2×#103C2×D4311yescharacteristic
432C2×C22⋊C8—431no—
433C2×C22⋊C8—431no—
434C2×C22⋊C8—431no—
435C2×C22⋊C8C2×D4311yescharacteristic
436C2×#97—431no—
437#399—861no—
438#399—861no—
439#390—861no—
440#384—861no—
441C4×C4⋊C4—431no—
442#340—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#340C2×D4311yescharacteristic
448C43#2558411yescharacteristic, complemented, Sylow
449C22×Q8—431no—
450C22×Q8C22×D4311yescharacteristic
451C22×Q8C22×D4311yescharacteristic
452C22×D4—431no—
453C23×C4—431no—
454C23×C4—861no—
455C23×C4C22×D4311yescharacteristic
456C2×Q16—22no—
457C2×Q16—41no—
458C2×Q16—41no—
459C2×Q16—862no—
460C2×Q16—1721no—
461C2×Q16—1721no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8C22×D4311yescharacteristic
465C22×C8C22×D4311yescharacteristic
466C4⋊Q8—862no—
467C4⋊Q8—862no—
468#126—868no—
469#125—434no—
470#125—862no—
471#125—868no—
472#123—868no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—41no—
477C22⋊Q8—862no—
478C22⋊Q8—862no—
479C22⋊Q8—862no—
480C22⋊Q8—862no—
481C22⋊Q8—862no—
482C22⋊Q8—1721no—
483C22⋊Q8—1721no—
484C22⋊Q8—1721no—
485C4×Q8—434no—
486C4×Q8—862no—
487C4×D4—862no—
488C4×D4—862no—
489#117—868no—
490#117—862no—
491#117—862no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—862no—
499C2×C4⋊C4—862no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4C22×D4311yescharacteristic
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—431no—
515C2×C22⋊C4—431no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C42—431no—
522C2×C42—861no—
523C2×C42—861no—
524C2×C42—861no—
525C4⋊C8—862no—
526#103—22no—
527#103—22no—
528#103—862no—
529#103—862no—
530#103—862no—
531#103—862no—
532#103—862no—
533#103—862no—
534C22⋊C8—41no—
535C22⋊C8—1721no—
536C22⋊C8—1721no—
537C22⋊C8—1721no—
538#97—862no—
539#95—861no—
540C24—431no—
541C24D4×D4311yescharacteristic
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×Q8D4×D4312yes—
560C2×D4—862no—
561C2×D4—862no—
562C2×D4—1721no—
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—21no—
572C22×C4—21no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—431no—
576C22×C4—864no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—1722no—
588C22×C4—1722no—
589C22×C4D4×D4311yescharacteristic
590C22×C4C23×D4311yescharacteristic
591Q16—44no—
592Q16—1724no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—42no—
609C4⋊C4—432no—
610C4⋊C4—432no—
611C4⋊C4—432no—
612C4⋊C4—862no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—1722no—
622C4⋊C4—1722no—
623C4⋊C4—1722no—
624C4⋊C4—1722no—
625C4⋊C4—1722no—
626C4⋊C4D4×D4312yes—
627C4⋊C4#1062190012yes—
628C22⋊C4—24no—
629C22⋊C4—42no—
630C22⋊C4—862no—
631C22⋊C4—864no—
632C22⋊C4—864no—
633C22⋊C4—862no—
634C22⋊C4—1722no—
635C22⋊C4—1722no—
636C22⋊C4—1722no—
637C42—432no—
638C42—432no—
639C42—864no—
640C42—864no—
641C42—1722no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—861no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23#1306335712yes—
656C23C2×D4×D4311yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—1721no—
666Q8—1721no—
667Q8—1721no—
668Q8—1721no—
669D4—1724no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—432no—
690C2×C4—432no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—862no—
696C2×C4—861no—
697C2×C4—862no—
698C2×C4—861no—
699C2×C4—862no—
700C2×C4—861no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1728no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4C2×D4×D4311yescharacteristic
716C2×C4C2×D4×D4311yescharacteristic
717C2×C4#41×D4311yescharacteristic
718C2×C4C2×#1062190011yescharacteristic
719C2×C4#1306337011yescharacteristic
720C2×C4#1306337011yescharacteristic
721C8—41no—
722C8—41no—
723C8—1721no—
724C8—1721no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—1721no—
733C22—1721no—
734C22—1721no—
735C22—1721no—
736C22—1721no—
737C22—1721no—
738C22—1721no—
739C22#120×D4311yescharacteristic
740C22#1458353611yescharacteristic
741C22#1458353811yescharacteristic
742C22C2×#1306335711yescharacteristic
743C22#1458369811yescharacteristic
744C22#1458371311yescharacteristic
745C22#1458371511yescharacteristic
746C4—41no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—81no—
751C4—862no—
752C4—862no—
753C4—3441no—
754C4—1721no—
755C4—1722no—
756C4—1722no—
757C4—1722no—
758C4#1458344411yescharacteristic
759C4#1458346411yescharacteristic
760C4#1458356711yescharacteristic
761C4#1458356911yescharacteristic
762C2—42no—
763C2—3441no—
764C2#1913820911yescharacteristic
765C2#1914385411yescharacteristic
766C2#1914388711yescharacteristic
767C2#1914665011yescharacteristic
768C2#1914665211yescharacteristic
769C2#1914668411yescharacteristic
770C2#1914668611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2001C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#2001D43
hypocenterC43#25584
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. C2×#14583266C2semidirect
3. C2×#14583107C2semidirect
5. #19135604C2semidirect
6. #19135603C2semidirect
7. #19135602C2semidirect
8. #19135551C2semidirect
10. #19134906C2semidirect
11. #19134904C2semidirect
12. #19134903C2semidirect
13. #19134900C2semidirect
14. #19134427C2semidirect
15. C43×#2001C2semidirect
384. #2001D43semidirect
448. C43#25584semidirect

Maximal subgroups

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

subgroupindex
C2×#145835912
C2×#145832662
C2×#145831072
#191395452
#191356042
#191356032
#191356022
#191355512
#191353912
#191349062
#191349042
#191349032
#191349002
#191344272
C43×#20012
#2558443