Finite Group Databasebeta

← #25149964

Subgroups — #25149964

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×#14583584C211yesmaximal, characteristic
2C2×#14583266C211yesmaximal, characteristic, complemented
3C2×#14583108C211yesmaximal, characteristic, complemented
4#19139545C211yesmaximal, characteristic
5#19135606C211yesmaximal, characteristic, complemented
6#19135605C211yesmaximal, characteristic, complemented
7#19135604C211yesmaximal, characteristic, complemented
8#19135603C211yesmaximal, characteristic, complemented
9#19135549C211yesmaximal, characteristic, complemented
10#19135391C211yesmaximal, characteristic
11#19134906C211yesmaximal, characteristic, complemented
12#19134904C211yesmaximal, characteristic, complemented
13#19134902C211yesmaximal, characteristic, complemented
14#19134424C211yesmaximal, characteristic, complemented
15C43×#1872C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18#14583584—24no—
19#14583584—24no—
20C2×#13063323C2211yescharacteristic
21C2×#13063320—21no—
22C2×#13063316C2211yescharacteristic
23C2×#13063315—21no—
24C2×#13063308—21no—
25C2×#13063305C2211yescharacteristic
26C2×#13063305C2211yescharacteristic
27C2×#13063304C2211yescharacteristic
28C2×#13063304C2211yescharacteristic
29C2×#13063301C2211yescharacteristic
30C2×#13063290C2211yescharacteristic
31C2×C4×C22⋊D43C2211yescharacteristic
32C2×#13063284—21no—
33C2×#13063283C2211yescharacteristic
34#14583266—24no—
35#14583108—24no—
36C2×Dic43⋊C8C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×#13063235C2211yescharacteristic
47#14582835—21no—
48#14582834—21no—
49#14582799—21no—
50#14582768—21no—
51C4⋊C4×Dic43C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C22×C4⋊C4×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×Dic86C2311yescharacteristic
65C22×C22⋊D43D411yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C2×Dic172—22no—
68C2×Dic172—41no—
69C2×Dic172—41no—
70C2×#10621885—22no—
71C2×#10621885—41no—
72C2×#10621885—41no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063323—22no—
76#13063323—22no—
77#13063320—28no—
78#13063316—22no—
79#13063316D414yes—
80#13063315—28no—
81#13063308—28no—
82#13063305—22no—
83#13063305—22no—
84#13063305—22no—
85#13063305—41no—
86#13063304—22no—
87#13063304—22no—
88#13063304—22no—
89#13063304—41no—
90#13063301—22no—
91#13063301—41no—
92#13063290—22no—
93#13063290D414yes—
94C4×C22⋊D43—22no—
95C4×C22⋊D43—22no—
96#13063284—28no—
97#13063283—22no—
98#13063283—22no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4D411yescharacteristic
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43D411yescharacteristic
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4D411yescharacteristic
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43—21no—
123C2×C4×Dic43C2311yescharacteristic
124Dic43⋊C8—22no—
125#13063250—22no—
126#13063250—22no—
127#13063249—22no—
128#13063248—22no—
129#13063248—22no—
130#13063248—22no—
131C22⋊(C43⋊C8)—41no—
132(C2×D43)⋊C8—41no—
133(C2×D43)⋊C8—41no—
134#13063235—22no—
135C43⋊#95—21no—
136C22×Q8×C43C2311yescharacteristic
137C23×C4×C43—21no—
138C23×C4×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C22⋊Q8×C43—22no—
142C22⋊Q8×C43—41no—
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43—22no—
145C2×C4⋊C4×C43—22no—
146C2×C4⋊C4×C43—21no—
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C4⋊C4×C43C2311yescharacteristic
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—
162C22×C4×C43—24no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—42no—
174C22×C4×C43—42no—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2411yescharacteristic
177C2×C22⋊D43—22no—
178C2×C22⋊D43—22no—
179C2×C22⋊D43—41no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86C2×D412yes—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C4⋊C4×C43—24no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—42no—
216C4⋊C4×C43C2×D412yes—
217C4⋊C4×C43C2×D412yes—
218C4⋊C4×C43#4112yes—
219C22⋊C4×C43—42no—
220C22⋊Dic43—24no—
221C22⋊Dic43—22no—
222C22⋊Dic43—42no—
223#10621885—44no—
224(C2×D43)⋊C4—24no—
225(C2×D43)⋊C4—24no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—42no—
229C4⋊Dic43—24no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—24no—
233C4⋊Dic43—42no—
234C4⋊Dic43C2×D412yes—
235C4⋊Dic43#4112yes—
236Dic43⋊C4—24no—
237Dic43⋊C4—24no—
238Dic43⋊C4—24no—
239Dic43⋊C4—22no—
240Dic43⋊C4—42no—
241Dic43⋊C4—42no—
242Dic43⋊C4—42no—
243Dic43⋊C4—42no—
244C4×Dic43—24no—
245C4×Dic43—24no—
246C4×Dic43—42no—
247C4×Dic43C2×D412yes—
248C4×Dic43C2×D412yes—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255Dic172—44no—
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—41no—
272Q8×C43—41no—
273Q8×C43—41no—
274Q8×C43—41no—
275C2×C4×C43—22no—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—21no—
279C2×C4×C43—22no—
280C2×C4×C43—21no—
281C2×C4×C43—48no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43H(5,𝔽2)11yescharacteristic
300C2×C4×C43H(5,𝔽2)11yescharacteristic
301C22⋊D43—44no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43#12012yes—
322C2×Dic43#12012yes—
323C4×D43—41no—
324C4×D43—41no—
325C4×D43—41no—
326C4×D43—41no—
327Dic86—22no—
328Dic86—22no—
329Dic86—41no—
330Dic86—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—42no—
373Dic43—41no—
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#2001—431no—
385#1989—431no—
386#1955—431no—
387#1873—431no—
388#1873—431no—
389#1872—431no—
390#1872D4311yescharacteristic, complemented
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×Q16—431no—
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⋊Q8—431no—
415C2×C22⋊Q8C2×D4311yescharacteristic
416C2×C4×Q8—431no—
417C2×C4×D4—431no—
418C2×#117—431no—
419C2×#117—861no—
420C22×C4⋊C4C2×D4311yescharacteristic
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#340C2×D4311yescharacteristic
447#340C2×D4311yescharacteristic
448C43#2558411yescharacteristic, complemented, Sylow
449C22×Q8—431no—
450C22×Q8—431no—
451C22×Q8C22×D4311yescharacteristic
452C22×D4—431no—
453C23×C4—21no—
454C23×C4—431no—
455C23×C4C22×D4311yescharacteristic
456C2×Q16—862no—
457C2×Q16—862no—
458C2×Q16—1721no—
459C2×Q16—1721no—
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—41no—
475C22⋊Q8—862no—
476C22⋊Q8—862no—
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—862no—
490#117—868no—
491#117—862no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—861no—
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⋊C4C22×D4311yescharacteristic
510C2×C4⋊C4C22×D4311yescharacteristic
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—431no—
514C2×C22⋊C4—431no—
515C2×C22⋊C4—861no—
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—432no—
549C2×Q8—861no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×Q8—861no—
560C2×D4—862no—
561C2×D4—862no—
562C2×D4—1721no—
563C22×C4—24no—
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—21no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—431no—
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—861no—
588C22×C4—861no—
589C22×C4D4×D4311yescharacteristic
590C22×C4C23×D4311yescharacteristic
591Q16—1724no—
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—21no—
609C4⋊C4—42no—
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—1722no—
621C4⋊C4—1722no—
622C4⋊C4—1722no—
623C4⋊C4—1722no—
624C4⋊C4—1722no—
625C4⋊C4#1062189812yes—
626C4⋊C4D4×D4312yes—
627C4⋊C4D4×D4312yes—
628C22⋊C4—42no—
629C22⋊C4—862no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4—862no—
633C22⋊C4—864no—
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#1306335412yes—
656C23C2×D4×D4311yescharacteristic
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—862no—
662Q8—862no—
663Q8—1721no—
664Q8—1721no—
665Q8—1721no—
666Q8—1721no—
667Q8—1721no—
668Q8—1721no—
669D4—1724no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—48no—
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—41no—
690C2×C4—432no—
691C2×C4—432no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—861no—
700C2×C4—862no—
701C2×C4—861no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
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×#1062189811yescharacteristic
719C2×C4#1306337011yescharacteristic
720C2×C4#1306337111yescharacteristic
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#1458353911yescharacteristic
741C22#1458354111yescharacteristic
742C22C2×#1306335411yescharacteristic
743C22#1458369511yescharacteristic
744C22#1458371211yescharacteristic
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#1458344611yescharacteristic
759C4#1458346511yescharacteristic
760C4#1458356711yescharacteristic
761C4#1458357011yescharacteristic
762C2—42no—
763C2—3441no—
764C2#1913821211yescharacteristic
765C2#1914385011yescharacteristic
766C2#1914388511yescharacteristic
767C2#1914664211yescharacteristic
768C2#1914664411yescharacteristic
769C2#1914669211yescharacteristic
770C2#1914669411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1872C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#1872D43
hypocenterC43#25584
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#14583266C2semidirect
3. C2×#14583108C2semidirect
5. #19135606C2semidirect
6. #19135605C2semidirect
7. #19135604C2semidirect
8. #19135603C2semidirect
9. #19135549C2semidirect
11. #19134906C2semidirect
12. #19134904C2semidirect
13. #19134902C2semidirect
14. #19134424C2semidirect
15. C43×#1872C2semidirect
390. #1872D43semidirect
448. C43#25584semidirect

Maximal subgroups

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

subgroupindex
C2×#145835842
C2×#145832662
C2×#145831082
#191395452
#191356062
#191356052
#191356042
#191356032
#191355492
#191353912
#191349062
#191349042
#191349022
#191344242
C43×#18722
#2558443