Finite Group Databasebeta

← #25130587

Subgroups — #25130587

Order 11008.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583196C211yesmaximal, characteristic, complemented
2C2×C4×#10621884C211yesmaximal, characteristic, complemented
3#19139496C211yesmaximal, characteristic
4#19135795C211yesmaximal, characteristic, complemented
5#19135788C211yesmaximal, characteristic, complemented
6#19135596C211yesmaximal, characteristic, complemented
7#19135596C211yesmaximal, characteristic, complemented
8#19135561C211yesmaximal, characteristic, complemented
9#19135390C211yesmaximal, characteristic, complemented
10#19134917C211yesmaximal, characteristic, complemented
11#19134912C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134788C211yesmaximal, characteristic, complemented
14#19134610C211yesmaximal, characteristic, complemented
15C2×C43×#552C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20#14583196—24no—
21C4×#10621884—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37#14582825—21no—
38#14582807—21no—
39#14582775—21no—
40#14582775—21no—
41#14582765C2211yescharacteristic
42#14582759C2211yescharacteristic
43#14582759C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50C43×#552—24no—
51C43×#552—24no—
52C2×#126×C43—21no—
53C2×#125×C43—21no—
54C2×#125×C43C2211yescharacteristic
55C2×#123×C43—21no—
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×C4×Q8×C43C2211yescharacteristic
59C2×C4×D4×C43C2211yescharacteristic
60C2×#117×C43—21no—
61C2×#117×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063299—22no—
75#13063299—22no—
76#13063299—41no—
77#13063299—41no—
78C4×D172—22no—
79C4×D172—22no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88#13063258—22no—
89#13063256—22no—
90#13063256—22no—
91C4⋊(C43⋊C8)—22no—
92#13063249—22no—
93#13063249—41no—
94#13063249—41no—
95#13063245—22no—
96#13063245—22no—
97#13063245—22no—
98C22⋊(C43⋊C8)—22no—
99C22⋊(C43⋊C8)—22no—
100C22⋊(C43⋊C8)—41no—
101C22⋊(C43⋊C8)—41no—
102C4×C43⋊C8—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C22×Q8×C43C2311yescharacteristic
108C22×D4×C43D411yescharacteristic
109C23×C4×C43—21no—
110C23×C4×C43C2311yescharacteristic
111C23×C4×C43C2311yescharacteristic
112#126×C43—28no—
113#125×C43—28no—
114#125×C43—22no—
115#125×C43D414yescomplemented
116#123×C43—28no—
117C22⋊Q8×C43—22no—
118C22⋊Q8×C43—22no—
119C22⋊Q8×C43—22no—
120C22⋊Q8×C43—22no—
121C4×Q8×C43—22no—
122C4×Q8×C43D414yescomplemented
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125#117×C43—28no—
126#117×C43—22no—
127#117×C43—22no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—22no—
135C2×C4⋊C4×C43—22no—
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43D411yescharacteristic
144C2×C22⋊C4×C43D411yescharacteristic
145C2×C42×C43—21no—
146C2×C42×C43—21no—
147C2×C42×C43C2311yescharacteristic
148C24×C43C2×D411yescharacteristic
149C24×C43C2×D411yescharacteristic
150C23×D43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43C2×D412yes—
157C2×D4×C43—22no—
158C2×D4×C43—22no—
159C2×D4×C43—41no—
160C22×C4×C43—24no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
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—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—42no—
178C22×C4×C43—42no—
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2411yescharacteristic
184C2×C22⋊D43—42no—
185C2×C22⋊D43—42no—
186C2×C22⋊D43—42no—
187C2×C22⋊D43—42no—
188C2×C22⋊D43—81no—
189C2×C22⋊D43—81no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172#4112yes—
199C2×C4×D43—42no—
200C2×C4×D43—81no—
201C2×C4×D43—81no—
202C4⋊C4×C43—24no—
203C4⋊C4×C43—24no—
204C4⋊C4×C43—24no—
205C4⋊C4×C43—24no—
206C4⋊C4×C43—24no—
207C4⋊C4×C43—24no—
208C4⋊C4×C43—22no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43C2×D412yes—
213C4⋊C4×C43C2×D412yes—
214C4⋊C4×C43C2×D412yes—
215C22⋊C4×C43—24no—
216C22⋊C4×C43—24no—
217C22⋊C4×C43—24no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—22no—
220C42×C43—24no—
221C42×C43—24no—
222C42×C43C2×D412yes—
223C42×C43C2×D412yes—
224C22⋊Dic43—81no—
225C22⋊Dic43—81no—
226#10621884—28no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—42no—
229(C2×D43)⋊C4—42no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8#4112yes—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43#13512yes—
262C23×C43C22×D411yescharacteristic
263C22×D43—22no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270Q8×C43—22no—
271Q8×C43—22no—
272Q8×C43—41no—
273Q8×C43—41no—
274D4×C43—44no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—22no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—48no—
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×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43#12012yes—
307C2×C4×C43#12012yes—
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43C2×#4111yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C2×C4×C432−1+411yescharacteristic
314C22⋊D43—84no—
315C22⋊D43—84no—
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—
325D172—22no—
326D172—22no—
327D172—41no—
328D172—41no—
329C4×D43—84no—
330C43⋊C8—22no—
331C43⋊C8—41no—
332C43⋊C8—41no—
333C43⋊C8—41no—
334#24125—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43C2×#12011yescharacteristic
350C22×C43#54611yescharacteristic
351C22×C43#54711yescharacteristic
352C22×C43C2×#13511yescharacteristic
353C22×C43#57511yescharacteristic
354C22×C43#57711yescharacteristic
355C22×C43#57711yescharacteristic
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—81no—
360C2×D43—81no—
361C2×D43—81no—
362C2×D43—81no—
363C4×C43—22no—
364C4×C43—22no—
365C4×C43—41no—
366C4×C43—41no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43—42no—
370C4×C43—42no—
371C4×C43#52511yescharacteristic
372C4×C43#53711yescharacteristic
373C4×C43#54811yescharacteristic
374C4×C43#55011yescharacteristic
375Dic43—81no—
376Dic43—81no—
377Dic43—81no—
378C2×#552D4311yescharacteristic, complemented
379C2×#478—431no—
380C2×C4×SD16—431no—
381#2535—431no—
382#2036—431no—
383#2035—431no—
384#2000—431no—
385#2000—431no—
386#1991—431no—
387#1954—431no—
388#1875—431no—
389#1874—431no—
390#1854—431no—
391#1853—431no—
392#1805—431no—
393C2×C43—42no—
394C2×C43—81no—
395C2×C43#240711yescharacteristic
396C2×C43#300211yescharacteristic
397C2×C43#301011yescharacteristic
398C2×C43#329611yescharacteristic
399C2×C43#332311yescharacteristic
400C2×C43#333711yescharacteristic
401C2×C43#335111yescharacteristic
402D43—82no—
403C22×SD16—431no—
404#552—24no—
405#552—24no—
406C2×#126—21no—
407C2×#125—21no—
408C2×#125C2×D4311yescharacteristic
409C2×#123—21no—
410C2×C22⋊Q8C2×D4311yescharacteristic
411C2×C22⋊Q8C2×D4311yescharacteristic
412C2×#121—431no—
413C2×#121—431no—
414C2×C4×Q8C2×D4311yescharacteristic
415C2×C4×D4—431no—
416C2×C4×D4C2×D4311yescharacteristic
417C2×#117—21no—
418C2×#117C2×D4311yescharacteristic
419C22×C4⋊C4C2×D4311yescharacteristic
420#478—864no—
421C4×SD16—864no—
422C2×#107—431no—
423C2×#106—431no—
424C2×#106—431no—
425C2×C4⋊C8—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×C22⋊C8—431no—
433C2×C22⋊C8—431no—
434C2×C22⋊C8—431no—
435C2×C22⋊C8—431no—
436C2×C4×C8—431no—
437#397—861no—
438#392—861no—
439#386—861no—
440#386—861no—
441#382—431no—
442#380—431no—
443#380—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#340—431no—
448#340—431no—
449#340—431no—
450C43#2412511yescharacteristic, complemented, Sylow
451C22×Q8C22×D4311yescharacteristic
452C22×D4—431no—
453C22×D4—861no—
454C22×D4—861no—
455C22×D4C22⋊D4311yescharacteristic
456C23×C4—21no—
457C23×C4—861no—
458C23×C4C22×D4311yescharacteristic
459C23×C4C22×D4311yescharacteristic
460C2×SD16—862no—
461C2×SD16—862no—
462C2×SD16—862no—
463C22×C8—431no—
464C22×C8—431no—
465C22×C8—431no—
466C22×C8—431no—
467#126—28no—
468#125—28no—
469#125—22no—
470#125C22⋊D4314yescomplemented
471#123—28no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476#121—862no—
477#121—862no—
478#121—1721no—
479#121—1721no—
480C4×Q8—22no—
481C4×Q8C22⋊D4314yescomplemented
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—862no—
485C4×D4—862no—
486#117—28no—
487#117—22no—
488#117—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4C22⋊D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C4⋊C4C22×D4311yescharacteristic
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4C22⋊D4311yescharacteristic
513C2×C22⋊C4C22⋊D4311yescharacteristic
514C2×C42—21no—
515C2×C42—21no—
516C2×C42C22×D4311yescharacteristic
517#107—862no—
518#106—862no—
519#106—862no—
520C4⋊C8—862no—
521#103—862no—
522#103—1721no—
523#103—1721no—
524#102—862no—
525#102—862no—
526#102—862no—
527C22⋊C8—862no—
528C22⋊C8—862no—
529C22⋊C8—1721no—
530C22⋊C8—1721no—
531C4×C8—862no—
532#95—861no—
533#95—861no—
534#95—861no—
535#95—861no—
536C24—861no—
537C24C2×C22⋊D4311yescharacteristic
538C24C2×C22⋊D4311yescharacteristic
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8C2×C22⋊D4312yes—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—41no—
548C2×D4—432no—
549C2×D4—861no—
550C2×D4—861no—
551C2×D4—861no—
552C2×D4—861no—
553C2×D4—861no—
554C2×D4—3441no—
555C2×D4—3441no—
556C2×D4—1722no—
557C2×D4—1722no—
558C2×D4—1722no—
559C2×D4—1722no—
560C22×C4—24no—
561C22×C4—21no—
562C22×C4—21no—
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—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—3441no—
583C22×C4—3441no—
584C22×C4—1722no—
585C22×C4C2×C22⋊D4311yescharacteristic
586C22×C4C2×C22⋊D4311yescharacteristic
587C22×C4C2×C22⋊D4311yescharacteristic
588C22×C4C2×C22⋊D4311yescharacteristic
589C22×C4C23×D4311yescharacteristic
590SD16—868no—
591C2×C8—432no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4C2×C22⋊D4312yes—
620C4⋊C4C2×C22⋊D4312yes—
621C4⋊C4C2×C22⋊D4312yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—3441no—
628C22⋊C4—3441no—
629C22⋊C4—1722no—
630C22⋊C4—1722no—
631C22⋊C4—1722no—
632C42—24no—
633C42—24no—
634C42C2×C22⋊D4312yes—
635C42C2×C22⋊D4312yes—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—862no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23#1306334512yes—
657C23C22×C22⋊D4311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662D4—44no—
663D4—862no—
664D4—862no—
665D4—3444no—
666D4—3444no—
667D4—1721no—
668D4—1721no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—48no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
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—41no—
700C2×C4—3444no—
701C2×C4—1721no—
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#1306329412yes—
711C2×C4#1306329412yes—
712C2×C4C22×C22⋊D4311yescharacteristic
713C2×C4C22×C22⋊D4311yescharacteristic
714C2×C4#41×D4311yescharacteristic
715C2×C4#41×D4311yescharacteristic
716C2×C4#1306337111yescharacteristic
717C2×C4#1306337211yescharacteristic
718C8—862no—
719C8—1721no—
720C8—1721no—
721C8—1721no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—3441no—
737C22—3441no—
738C22—3441no—
739C22—3441no—
740C22—1722no—
741C22—1722no—
742C22—1722no—
743C22C2×#1306329411yescharacteristic
744C22#1458353711yescharacteristic
745C22#1458354811yescharacteristic
746C22C2×#1306334511yescharacteristic
747C22#1458369711yescharacteristic
748C22#1458370711yescharacteristic
749C22#1458370711yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—41no—
755C4—41no—
756C4—42no—
757C4—42no—
758C4—3441no—
759C4—3441no—
760C4—3441no—
761C4#1458340611yescharacteristic
762C4#1458347711yescharacteristic
763C4#1458355611yescharacteristic
764C4#1458356811yescharacteristic
765C2—42no—
766C2—81no—
767C2—3442no—
768C2#1913793411yescharacteristic
769C2#1914381311yescharacteristic
770C2#1914388111yescharacteristic
771C2#1914642411yescharacteristic
772C2#1914680511yescharacteristic
773C2#1914697411yescharacteristic
774C2#1914715511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#552C2
socleC23×C43C22×D4
prime radical#19139496C2
hypercenterC2×#552D43
hypocenterC43#24125
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#14583196C2semidirect
2. C2×C4×#10621884C2semidirect
4. #19135795C2semidirect
5. #19135788C2semidirect
6. #19135596C2semidirect
7. #19135596C2semidirect
8. #19135561C2semidirect
9. #19135390C2semidirect
10. #19134917C2semidirect
11. #19134912C2semidirect
12. #19134794C2semidirect
13. #19134788C2semidirect
14. #19134610C2semidirect
15. C2×C43×#552C2semidirect
115. #125×C43D4semidirect
122. C4×Q8×C43D4semidirect
378. C2×#552D43semidirect
450. C43#24125semidirect
470. #125C22⋊D43semidirect
481. C4×Q8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831962
C2×C4×#106218842
#191394962
#191357952
#191357882
#191355962
#191355612
#191353902
#191349172
#191349122
#191347942
#191347882
#191346102
C2×C43×#5522
#2412543