Finite Group Databasebeta

← #25116948

Subgroups — #25116948

Order 11008.

1174 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583011C211yesmaximal, characteristic, complemented
2C2×#14582895C211yesmaximal, characteristic, complemented
3#19137637C211yesmaximal, characteristic, complemented
4#19137425C211yesmaximal, characteristic, complemented
5#19135478C211yesmaximal, characteristic, complemented
6#19135287C211yesmaximal, characteristic, complemented
7#19135231C211yesmaximal, characteristic, complemented
8#19135024C211yesmaximal, characteristic, complemented
9#19134945C211yesmaximal, characteristic, complemented
10#19134931C211yesmaximal, characteristic, complemented
11#19134844C211yesmaximal, characteristic, complemented
12#19134796C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic, complemented
14#19134374C211yesmaximal, characteristic, complemented
15C2×C43×#449C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14583011—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24#14582895—24no—
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582806C2211yescharacteristic
35#14582802—21no—
36#14582802C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582792—21no—
39#14582779—21no—
40#14582779—21no—
41#14582779—21no—
42#14582762—21no—
43#14582759C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C22⋊C4×Dic43—21no—
46C4×C22⋊Dic43C2211yescharacteristic
47C2×C43⋊#95—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×#41×C43C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C22×D8×C43C2211yescharacteristic
57C2×#121×C43C2211yescharacteristic
58C43×#449C418yescomplemented
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C23×Dic43—21no—
63C23×Dic43—21no—
64C23×Dic43—21no—
65C22×C43⋊C8—22no—
66C22×C43⋊C8—22no—
67C22×C43⋊C8—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70D4×Dic43—22no—
71D4×Dic43—22no—
72D4×Dic43—22no—
73D4×Dic43—41no—
74D4×Dic43—41no—
75D4×Dic43—41no—
76#13063284—22no—
77#13063284—41no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43D411yescharacteristic
91C2×C22⋊Dic43D411yescharacteristic
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063259—41no—
97#13063257—22no—
98#13063249—22no—
99#13063249—22no—
100#13063246—22no—
101#13063246—22no—
102#13063246—41no—
103#13063246D414yescomplemented
104#13063235—22no—
105#13063235—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C2×#41×C43—22no—
116C2×#41×C43—22no—
117C2×#41×C43—22no—
118C2×#41×C43—41no—
119C2×#41×C43—41no—
120C2×#41×C43C2×C414yescomplemented
121C22×Q8×C43C2311yescharacteristic
122C22×D4×C43—21no—
123C22×D4×C43—21no—
124C22×D4×C43C2311yescharacteristic
125C22×D4×C43C2311yescharacteristic
126C23×C4×C43—21no—
127C23×C4×C43C2311yescharacteristic
128C2×SD16×C43—41no—
129C2×SD16×C43—41no—
130C2×SD16×C43C2×C414yescomplemented
131C2×D8×C43—22no—
132C2×D8×C43—22no—
133C2×D8×C43C2×C414yes—
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136#121×C43—22no—
137#121×C43C2×C414yescomplemented
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140#103×C43C2×C414yescomplemented
141#102×C43C2×C414yescomplemented
142C22⋊C8×C43C2×C414yescomplemented
143C24×C43—21no—
144C24×C43—21no—
145C24×C43C2×D411yescharacteristic
146#41×C43—28no—
147#41×C43—44no—
148#41×C43—44no—
149#41×C43—44no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43C22×C412yes—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—24no—
161C2×D4×C43—24no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43—81no—
169C2×D4×C43—81no—
170C2×D4×C43C22×C412yes—
171C2×D4×C43C22×C412yes—
172C2×D4×C43C2×D412yes—
173C2×D4×C43#4112yes—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—24no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—42no—
182C22×C4×C43—42no—
183C22×C4×C43C22×C412yes—
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43#4112yes—
186C22×C4×C43C2411yescharacteristic
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—42no—
192C22×Dic43—42no—
193C22×Dic43—42no—
194C22×Dic43—42no—
195C22×Dic43—42no—
196C22×Dic43—42no—
197C22×Dic43—81no—
198C22×Dic43—81no—
199C22×Dic43—81no—
200C22×Dic43C2×D411yescharacteristic
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204SD16×C43—44no—
205D8×C43—28no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43C22×C412yes—
211C2×C8×C43C22×C412yes—
212C4⋊C4×C43—21no—
213C4⋊C4×C43C22×C412yes—
214C22⋊C4×C43—24no—
215C22⋊Dic43—41no—
216C22⋊Dic43—41no—
217C22⋊Dic43—42no—
218C22⋊Dic43—42no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—81no—
223C22⋊Dic43—81no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—81no—
232C4⋊Dic43C2×D412yes—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—42no—
238C4×Dic43—81no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—44no—
245C2×C43⋊C8C2×D412yes—
246C23×C43—22no—
247C23×C43—21no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—22no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43C4×D412yes—
267C23×C43C22×D411yescharacteristic
268Q8×C43—22no—
269Q8×C43—22no—
270Q8×C43—41no—
271Q8×C43—41no—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—22no—
275D4×C43—22no—
276D4×C43—22no—
277D4×C43—48no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—84no—
281D4×C43C4×D414yes—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—48no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43C4×D412yes—
296C2×C4×C43C23×C411yescharacteristic
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43H(5,𝔽2)11yescharacteristic
301C2×C4×C43H(5,𝔽2)11yescharacteristic
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—22no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—41no—
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—41no—
326C2×Dic43—84no—
327C2×Dic43—84no—
328C2×Dic43—84no—
329C8×C43—22no—
330C8×C43—22no—
331C43⋊C8—22no—
332C43⋊C8—41no—
333#22860—431nomaximal, Sylow
334C22×C43—24no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—41no—
341C22×C43—42no—
342C22×C43—41no—
343C22×C43—42no—
344C22×C43—41no—
345C22×C43—42no—
346C22×C43—41no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43C2×C4×D411yescharacteristic
356C22×C43D4211yescharacteristic
357C22×C43#54611yescharacteristic
358C22×C43#57511yescharacteristic
359C22×C43#57511yescharacteristic
360C22×C43#57611yescharacteristic
361C22×C43#57711yescharacteristic
362C4×C43—22no—
363C4×C43—42no—
364C4×C43—42no—
365C4×C43C2×C4×D411yescharacteristic
366C4×C43#51811yescharacteristic
367C4×C43#54611yescharacteristic
368C4×C43#55111yescharacteristic
369Dic43—41no—
370Dic43—42no—
371Dic43—41no—
372Dic43—41no—
373Dic43—41no—
374Dic43—81no—
375Dic43—81no—
376Dic43—81no—
377C2×#449D4311yescharacteristic
378C2×#442—431no—
379C2×#416—431no—
380#2363—431no—
381#2339—431no—
382#1973—431no—
383#1935—431no—
384#1927—431no—
385#1893—431no—
386#1879—431no—
387#1877—431no—
388#1862—431no—
389#1854—431no—
390#1762—431no—
391#1752—431no—
392C2×C43—42no—
393C2×C43—44no—
394C2×C43—82no—
395C2×C43#235811yescharacteristic
396C2×C43#294311yescharacteristic
397C2×C43#294611yescharacteristic
398C2×C43#326711yescharacteristic
399C2×C43#326811yescharacteristic
400C2×C43#330711yescharacteristic
401C2×C43#331911yescharacteristic
402C22×#41C2×D4311yescharacteristic
403C22×SD16C2×D4311yescharacteristic
404C22×D8C2×D4311yescharacteristic
405C23×C8—431no—
406C2×#121C2×D4311yescharacteristic
407C2×C4×D4—431no—
408C2×C4×D4—431no—
409C2×C4×D4—431no—
410C2×#117—431no—
411#449Dic4318yescomplemented
412#442—864no—
413C2×#107—431no—
414C2×#106—431no—
415#416—864no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#103C2×D4311yescharacteristic
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102C2×D4311yescharacteristic
424C2×C22⋊C8C2×D4311yescharacteristic
425C2×#97—431no—
426C2×#97—431no—
427#391—431no—
428#391—431no—
429#390—431no—
430#390—861no—
431#389—431no—
432#388—861no—
433#386—861no—
434#386—861no—
435#386—861no—
436#381—861no—
437#380—431no—
438C4×C4⋊C4—431no—
439C4×C22⋊C4—431no—
440C4×C22⋊C4—861no—
441C2×#95—861no—
442#340—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446#336—431no—
447#336—431no—
448C43#2286011yescharacteristic, complemented, Sylow
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—41no—
453C2×#41—41no—
454C2×#41C2×Dic4314yescomplemented
455C22×Q8C22×D4311yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4C22×D4311yescharacteristic
459C22×D4C22×D4311yescharacteristic
460C23×C4—21no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4—861no—
464C23×C4C22×D4311yescharacteristic
465C2×SD16—41no—
466C2×SD16—41no—
467C2×SD16C2×Dic4314yescomplemented
468C2×D8—22no—
469C2×D8—22no—
470C2×D8C2×Dic4314yes—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8—862no—
474C22×C8—862no—
475C22×C8—1721no—
476C22×C8C22×D4311yescharacteristic
477C22×C8C22×D4311yescharacteristic
478#121—22no—
479#121C2×Dic4314yescomplemented
480C4×D4—862no—
481C4×D4—862no—
482C4×D4—862no—
483C4×D4—1721no—
484C4×D4—1721no—
485C4×D4—1721no—
486#117—862no—
487#117—1721no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4C22×D4311yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—431no—
496C2×C22⋊C4—431no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C42—431no—
505C2×C42—431no—
506C2×C42—861no—
507C2×C42—861no—
508#107—1721no—
509#106—862no—
510#103—862no—
511#103—862no—
512#103C2×Dic4314yescomplemented
513#102—434no—
514#102—862no—
515#102—862no—
516#102—1721no—
517#102C2×Dic4314yescomplemented
518C22⋊C8C2×Dic4314yescomplemented
519#97—862no—
520#97—1721no—
521#95—431no—
522#95—431no—
523#95—861no—
524#95—861no—
525#95—861no—
526#95—861no—
527#95—861no—
528#95—861no—
529#95—861no—
530C24—21no—
531C24—21no—
532C24D4×D4311yescharacteristic
533#41—28no—
534#41—44no—
535#41—44no—
536#41—44no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8C22×Dic4312yes—
543C2×D4—24no—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4D4×D4312yes—
558C2×D4#1062190012yes—
559C2×D4C22×Dic4312yes—
560C2×D4C22×Dic4312yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—431no—
571C22×C4—431no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—3441no—
579C22×C4—3441no—
580C22×C4—3441no—
581C22×C4—1722no—
582C22×C4—1722no—
583C22×C4—1722no—
584C22×C4—1722no—
585C22×C4—1722no—
586C22×C4—1722no—
587C22×C4D4×D4311yescharacteristic
588C22×C4#1062190012yes—
589C22×C4C22×Dic4312yes—
590C22×C4C23×D4311yescharacteristic
591SD16—44no—
592D8—28no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—432no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—1724no—
604C2×C8C22×Dic4312yes—
605C2×C8C22×Dic4312yes—
606C4⋊C4—21no—
607C4⋊C4—432no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—3441no—
616C4⋊C4C22×Dic4312yes—
617C22⋊C4—24no—
618C22⋊C4—3441no—
619C22⋊C4—3441no—
620C22⋊C4—1721no—
621C22⋊C4—1721no—
622C22⋊C4—1722no—
623C22⋊C4—1722no—
624C22⋊C4—1722no—
625C22⋊C4—1722no—
626C22⋊C4—1722no—
627C42—861no—
628C42—861no—
629C42—861no—
630C42—861no—
631C42—3441no—
632C42—1722no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—22no—
641C23—21no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23D4×Dic4312yes—
654C23C2×D4×D4311yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—41no—
658Q8—41no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—48no—
665D4—41no—
666D4—41no—
667D4—84no—
668D4D4×Dic4314yes—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—48no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—862no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—3444no—
696C2×C4—3444no—
697C2×C4—3444no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
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×C4D4×Dic4312yes—
710C2×C4C23×Dic4311yescharacteristic
711C2×C4C2×D4×D4311yescharacteristic
712C2×C4C2×#1062190011yescharacteristic
713C2×C4C2×#1062190011yescharacteristic
714C2×C4#1306337011yescharacteristic
715C2×C4#1306337011yescharacteristic
716C8—22no—
717C8—22no—
718C8—862no—
719C8—1721no—
720C22—22no—
721C22—22no—
722C22—24no—
723C22—22no—
724C22—42no—
725C22—41no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22C2×D4×Dic4311yescharacteristic
742C22#1458353111yescharacteristic
743C22#1458353611yescharacteristic
744C22#1458369611yescharacteristic
745C22#1458369611yescharacteristic
746C22#1458370311yescharacteristic
747C22#1458370911yescharacteristic
748C4—22no—
749C4—42no—
750C4—42no—
751C4—3441no—
752C4—3441no—
753C4—3441no—
754C4—1721no—
755C4—1721no—
756C4—1721no—
757C4—1722no—
758C4—1721no—
759C4C2×D4×Dic4311yescharacteristic
760C4#1458337411yescharacteristic
761C4#1458353611yescharacteristic
762C4#1458358011yescharacteristic
763C2—42no—
764C2—44no—
765C2—82no—
766C2#1913757911yescharacteristic
767C2#1914339611yescharacteristic
768C2#1914342811yescharacteristic
769C2#1914611311yescharacteristic
770C2#1914613911yescharacteristic
771C2#1914657511yescharacteristic
772C2#1914675511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#449C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC2×#449D43
hypocenterC43#22860
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#14583011C2semidirect
2. C2×#14582895C2semidirect
3. #19137637C2semidirect
4. #19137425C2semidirect
5. #19135478C2semidirect
6. #19135287C2semidirect
7. #19135231C2semidirect
8. #19135024C2semidirect
9. #19134945C2semidirect
10. #19134931C2semidirect
11. #19134844C2semidirect
12. #19134796C2semidirect
13. #19134422C2semidirect
14. #19134374C2semidirect
58. C43×#449C4semidirect
103. #13063246D4semidirect
120. C2×#41×C43C2×C4semidirect
130. C2×SD16×C43C2×C4semidirect
137. #121×C43C2×C4semidirect
140. #103×C43C2×C4semidirect
141. #102×C43C2×C4semidirect
142. C22⋊C8×C43C2×C4semidirect
411. #449Dic43semidirect
448. C43#22860semidirect
454. C2×#41C2×Dic43semidirect
467. C2×SD16C2×Dic43semidirect
479. #121C2×Dic43semidirect
512. #103C2×Dic43semidirect
517. #102C2×Dic43semidirect
518. C22⋊C8C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830112
C2×#145828952
#191376372
#191374252
#191354782
#191352872
#191352312
#191350242
#191349452
#191349312
#191348442
#191347962
#191344222
#191343742
C2×C43×#4492
#2286043