Finite Group Databasebeta

← #25112165

Subgroups — #25112165

Order 11008.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583562C211yesmaximal, characteristic
2C2×#14582967C211yesmaximal, characteristic
3C2×#14582906C211yesmaximal, characteristic, complemented
4C22×#13063248C211yesmaximal, characteristic, complemented
5#19137520C211yesmaximal, characteristic
6#19135516C211yesmaximal, characteristic, complemented
7#19135413C211yesmaximal, characteristic, complemented
8#19135027C211yesmaximal, characteristic, complemented
9#19135019C211yesmaximal, characteristic, complemented
10#19134906C211yesmaximal, characteristic, complemented
11#19134609C211yesmaximal, characteristic, complemented
12#19134531C211yesmaximal, characteristic, complemented
13#19134528C211yesmaximal, characteristic, complemented
14#19134424C211yesmaximal, characteristic, complemented
15C43×#1872C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20#14583562—24no—
21#14583562C418yescomplemented
22C2×#13063324—21no—
23C2×#13063323C2211yescharacteristic
24C2×#13063305C2211yescharacteristic
25C2×#13063303—21no—
26C2×#13063302—21no—
27C2×#13063290C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×(C22⋊D43)⋊C4—21no—
30C2×#13063283C2211yescharacteristic
31#14582967—24no—
32C2×Dic43⋊C8C2211yescharacteristic
33#14582906—24no—
34C2×#13063250C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063248—24no—
41C2×#13063248C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×#13063248C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×#13063235C2211yescharacteristic
47#14582789—21no—
48#14582780—21no—
49#14582778—21no—
50#14582764C2211yescharacteristic
51#14582759C2211yescharacteristic
52#14582756C2211yescharacteristic
53C4⋊C4×Dic43C2211yescharacteristic
54C4×C22⋊Dic43—21no—
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C22×C4⋊C4×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—22no—
67C22×Dic86—21no—
68C22×Dic86—21no—
69C22×Dic86—41no—
70C22×Dic86—41no—
71C22×Dic86C2×C414yes—
72C22×Dic86C2311yescharacteristic
73C22×Dic86C2311yescharacteristic
74C2×Q8×D43—22no—
75C2×Q8×D43—22no—
76C2×Q8×D43—22no—
77C2×Q8×D43—41no—
78C2×Q8×D43—41no—
79C2×Q8×D43C2×C414yescomplemented
80C22×C22⋊D43D411yescharacteristic
81C23×Dic43—21no—
82C22×C4×D43—21no—
83C22×C4×D43C2311yescharacteristic
84C2×#10621872—22no—
85C2×#10621872—22no—
86C2×#10621872—41no—
87C22×C43⋊C8—22no—
88C22×C43⋊C8—22no—
89C22×C43⋊C8—41no—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92#13063324—28no—
93#13063323—22no—
94#13063323C2×C414yescomplemented
95#13063305—22no—
96#13063305C2×C414yescomplemented
97#13063303—28no—
98#13063302—28no—
99#13063290—22no—
100#13063290C2×C414yescomplemented
101C4×C22⋊D43C2×C414yes—
102C4×C22⋊D43D414yes—
103(C22⋊D43)⋊C4—28no—
104#13063283—22no—
105#13063283—41no—
106C2×C4⋊Dic43—21no—
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4D411yescharacteristic
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)⋊C4D411yescharacteristic
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43C2311yescharacteristic
123Dic43⋊C8—22no—
124#13063250—22no—
125#13063250—22no—
126#13063250—41no—
127#13063250—41no—
128#13063249—22no—
129#13063249—41no—
130#13063248—22no—
131#13063248—22no—
132#13063248—22no—
133#13063248D414yescomplemented
134(C2×D43)⋊C8—22no—
135#13063235—22no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C43⋊#95—21no—
139C43⋊#95—21no—
140C43⋊#95—21no—
141C22×Q8×C43C2311yescharacteristic
142C23×C4×C43—21no—
143C23×C4×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146C22⋊Q8×C43—22no—
147C22⋊Q8×C43C2×C414yes—
148C2×C4⋊C4×C43—21no—
149C2×C4⋊C4×C43—22no—
150C2×C4⋊C4×C43—21no—
151C2×C4⋊C4×C43—41no—
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C22⋊C4×C43—21no—
156#103×C43—22no—
157#103×C43—41no—
158C22⋊C8×C43—22no—
159C24×C43C2×D411yescharacteristic
160C23×D43C2×D411yescharacteristic
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43C22×C412yes—
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—42no—
176C22×C4×C43—42no—
177C22×C4×C43—81no—
178C22×C4×C43C22×C412yes—
179C22×C4×C43C2×D412yes—
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2411yescharacteristic
182C2×C22⋊D43—22no—
183C2×C22⋊D43—22no—
184C2×C22⋊D43C22⋊C414yes—
185C22×Dic43—24no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—42no—
191C22×Dic43—42no—
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195Q8×D43—28no—
196Q8×D43—44no—
197Q8×D43—44no—
198Q8×D43—44no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—24no—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43C22×C412yes—
207C2×C4×D43C2×D412yes—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—28no—
216C2×Dic86—24no—
217C2×Dic86—21no—
218C2×Dic86—24no—
219C2×Dic86—44no—
220C2×Dic86—44no—
221C2×Dic86—44no—
222C2×Dic86—42no—
223C2×Dic86—42no—
224C2×Dic86—42no—
225C2×Dic86—42no—
226C2×Dic86C22×C412yes—
227C2×Dic86C22×C412yes—
228C2×Dic86C2×D412yes—
229C2×Dic86#4112yes—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C4⋊C4×C43—24no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—42no—
242C4⋊C4×C43C22×C412yes—
243C4⋊C4×C43C2×D412yes—
244C22⋊C4×C43—24no—
245C22⋊Dic43—42no—
246C22⋊Dic43C22⋊C414yes—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—42no—
249(C2×D43)⋊C4—81no—
250(C2×D43)⋊C4C22⋊C414yes—
251C4⋊Dic43—24no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4C22⋊C414yes—
260C4×Dic43—24no—
261C4×Dic43—42no—
262C4×Dic43—81no—
263C4×Dic43C22×C412yes—
264C4×Dic43C2×D412yes—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—44no—
271C2×C43⋊C8C2×D412yes—
272#10621872—44no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43C2×C22⋊C412yes—
278C23×C43#13712yes—
279C23×C43#13712yes—
280C23×C43C22×D411yescharacteristic
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43C2×C22⋊C412yes—
288Q8×C43—22no—
289Q8×C43—22no—
290Q8×C43—41no—
291Q8×C43—41no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—84no—
311C2×C4×C43C2×C22⋊C412yes—
312C2×C4×C43C23×C411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43H(5,𝔽2)11yescharacteristic
317C2×C4×C43H(5,𝔽2)11yescharacteristic
318C22⋊D43—28no—
319C2×Dic43—22no—
320C2×Dic43—21no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—22no—
329C2×Dic43—48no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43C2×C22⋊C412yes—
339C2×Dic43C2×C22⋊C412yes—
340C2×Dic43C2×C22⋊C412yes—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—48no—
346Dic86—22no—
347Dic86—22no—
348Dic86—22no—
349Dic86—22no—
350Dic86—22no—
351Dic86—48no—
352Dic86—48no—
353Dic86—41no—
354Dic86—41no—
355Dic86C4×D414yes—
356C8×C43—41no—
357C8×C43—41no—
358C43⋊C8—22no—
359C43⋊C8—41no—
360#22425—431nomaximal, Sylow
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—22no—
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—22no—
367C22×C43#41914yescomplemented
368C22×C43C22×C22⋊C411yescharacteristic
369C22×C43D4211yescharacteristic
370C22×C43#54611yescharacteristic
371C22×C43C2×#13711yescharacteristic
372C22×C43C2×#13711yescharacteristic
373C22×C43#57711yescharacteristic
374C22×C43#57811yescharacteristic
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—41no—
379C2×D43—41no—
380C2×D43—41no—
381C2×D43—41no—
382C4×C43—22no—
383C4×C43—42no—
384C4×C43—42no—
385C4×C43—42no—
386C4×C43—81no—
387C4×C43C2×C4×D411yescharacteristic
388C4×C43#51811yescharacteristic
389C4×C43D4211yescharacteristic
390C4×C43#54611yescharacteristic
391Dic43—24no—
392Dic43—22no—
393Dic43—22no—
394Dic43—22no—
395Dic43—42no—
396Dic43—81no—
397Dic43—81no—
398C2×D4×Q8—431no—
399C2×#435—431no—
400C2×#419—431no—
401C22×#103—431no—
402#2352—431no—
403#1981—431no—
404#1960—431no—
405#1894—431no—
406#1892—431no—
407#1873—431no—
408#1872D4311yescharacteristic, complemented
409#1805—431no—
410#1787—431no—
411#1787—431no—
412#1763—431no—
413C2×C43—24no—
414C2×C43D4×C22⋊C411yescharacteristic
415C2×C43C2×#41911yescharacteristic
416C2×C43#289811yescharacteristic
417C2×C43#326611yescharacteristic
418C2×C43#327011yescharacteristic
419C2×C43#331211yescharacteristic
420C2×C43#332011yescharacteristic
421D43—42no—
422C23×Q8—431no—
423C23×Q8—431no—
424C22×M16—431no—
425C23×C8—431no—
426D4×Q8—438no—
427D4×Q8—864no—
428C2×C4⋊Q8—431no—
429C2×C4⋊Q8—861no—
430C2×C22⋊Q8—431no—
431C2×C22⋊Q8—861no—
432C2×C22⋊Q8—861no—
433C2×C22⋊Q8C2×D4311yescharacteristic
434C2×C4×Q8—431no—
435C2×C4×D4—431no—
436C2×C4×D4—861no—
437C2×#117—431no—
438C22×C4⋊C4C2×D4311yescharacteristic
439#435—864no—
440C2×C4⋊C8—431no—
441#419—864no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#103—431no—
445C2×#103—431no—
446C2×#103—431no—
447C2×#103—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#103—864no—
453C2×#103C2×D4311yescharacteristic
454C2×#103C2×D4311yescharacteristic
455C2×C22⋊C8—431no—
456C2×C22⋊C8C2×D4311yescharacteristic
457C2×#97—431no—
458#388—861no—
459#387—861no—
460#386—861no—
461#382—431no—
462#380—431no—
463#380—431no—
464C4×C4⋊C4—431no—
465C4×C22⋊C4—861no—
466#340—431no—
467#340—431no—
468#340C2×D4311yescharacteristic
469#340C2×D4311yescharacteristic
470C43#2242511yescharacteristic, complemented, Sylow
471C22×Q8—434no—
472C22×Q8—434no—
473C22×Q8—431no—
474C22×Q8—431no—
475C22×Q8—861no—
476C22×Q8—862no—
477C22×Q8—862no—
478C22×Q8—862no—
479C22×Q8—861no—
480C22×Q8—862no—
481C22×Q8—862no—
482C22×Q8—862no—
483C22×Q8—1721no—
484C22×Q8—1721no—
485C22×Q8—1721no—
486C22×Q8—1721no—
487C22×Q8C22×D4311yescharacteristic
488C22×D4—431no—
489C23×C4—21no—
490C23×C4—431no—
491C23×C4—861no—
492C23×C4—861no—
493C23×C4C22×D4311yescharacteristic
494C2×M16—862no—
495C2×M16—862no—
496C2×M16—1721no—
497C22×C8—431no—
498C22×C8—431no—
499C22×C8—862no—
500C22×C8—862no—
501C22×C8—1721no—
502C22×C8C22×D4311yescharacteristic
503C22×C8C22×D4311yescharacteristic
504C4⋊Q8—434no—
505C4⋊Q8—862no—
506C4⋊Q8—868no—
507C22⋊Q8—22no—
508C22⋊Q8—434no—
509C22⋊Q8—868no—
510C22⋊Q8—868no—
511C22⋊Q8—862no—
512C22⋊Q8C4×D4314yes—
513C4×Q8—434no—
514C4×Q8—862no—
515C4×D4—434no—
516C4×D4—434no—
517C4×D4—868no—
518#117—862no—
519#117—1721no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—41no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4—431no—
526C2×C4⋊C4—431no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4C22×D4311yescharacteristic
532C2×C4⋊C4C22×D4311yescharacteristic
533C2×C4⋊C4C22×D4311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—431no—
536C2×C22⋊C4—431no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C42—431no—
542C2×C42—861no—
543C2×C42—861no—
544C2×C42—861no—
545C4⋊C8—862no—
546#103—22no—
547#103—41no—
548#103—434no—
549#103—862no—
550#103—862no—
551#103—862no—
552#103—862no—
553#103—862no—
554#103—862no—
555#103—1721no—
556#103—1721no—
557#103—1721no—
558C22⋊C8—22no—
559C22⋊C8—862no—
560#97—862no—
561#95—861no—
562#95—861no—
563#95—861no—
564#95—861no—
565#95—861no—
566C24—431no—
567C24D4×D4311yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—432no—
574C2×Q8—432no—
575C2×Q8—432no—
576C2×Q8—432no—
577C2×Q8—864no—
578C2×Q8—868no—
579C2×Q8—864no—
580C2×Q8—861no—
581C2×Q8—861no—
582C2×Q8—861no—
583C2×Q8—861no—
584C2×Q8—868no—
585C2×Q8—861no—
586C2×Q8—861no—
587C2×Q8—861no—
588C2×Q8—861no—
589C2×Q8—1722no—
590C2×Q8—1722no—
591C2×Q8—1724no—
592C2×Q8—1724no—
593C2×Q8—1724no—
594C2×Q8—1722no—
595C2×Q8—1722no—
596C2×Q8—1724no—
597C2×Q8—1724no—
598C2×Q8—1724no—
599C2×Q8C2×C4×D4312yes—
600C2×D4—434no—
601C2×D4—862no—
602C2×D4—862no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—81no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—432no—
618C22×C4—432no—
619C22×C4—864no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—864no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—1722no—
630C22×C4—1722no—
631C22×C4—1722no—
632C22×C4—1722no—
633C22×C4C2×C4×D4312yes—
634C22×C4D4×D4311yescharacteristic
635C22×C4D4×D4312yes—
636C22×C4C23×D4311yescharacteristic
637M16—1724no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—432no—
645C2×C8—861no—
646C2×C8—861no—
647C2×C8—861no—
648C2×C8—861no—
649C2×C8—861no—
650C2×C8—1724no—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4—434no—
658C4⋊C4—864no—
659C4⋊C4—864no—
660C4⋊C4—864no—
661C4⋊C4—864no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4C2×C4×D4312yes—
667C4⋊C4D4×D4312yes—
668C22⋊C4—24no—
669C22⋊C4—434no—
670C22⋊C4—434no—
671C22⋊C4—864no—
672C22⋊C4—3441no—
673C22⋊C4—1722no—
674C22⋊C4—1722no—
675C42—432no—
676C42—432no—
677C42—864no—
678C42—3441no—
679C42—1722no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—432no—
685C23—861no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—861no—
690C23—861no—
691C23C22⋊C4×D4312yes—
692C23#1306335412yes—
693C23#1306335712yes—
694C23C2×D4×D4311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—41no—
698Q8—41no—
699Q8—434no—
700Q8—862no—
701Q8—862no—
702Q8—862no—
703Q8—862no—
704Q8—862no—
705Q8—1728no—
706Q8—1728no—
707Q8—1721no—
708Q8—1721no—
709D4—868no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—84no—
729C2×C4—432no—
730C2×C4—432no—
731C2×C4—432no—
732C2×C4—862no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—861no—
738C2×C4—862no—
739C2×C4—861no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—1728no—
747C2×C4—1728no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4C22⋊C4×D4312yes—
757C2×C4C22×C4×D4311yescharacteristic
758C2×C4C2×D4×D4311yescharacteristic
759C2×C4C2×D4×D4311yescharacteristic
760C2×C4#41×D4311yescharacteristic
761C2×C4#1306337011yescharacteristic
762C2×C4#1306337111yescharacteristic
763C8—41no—
764C8—41no—
765C8—862no—
766C8—1721no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—862no—
774C22—862no—
775C22—862no—
776C22—1721no—
777C22—1721no—
778C22—1721no—
779C22—1721no—
780C22#1458290614yescomplemented
781C22C2×C22⋊C4×D4311yescharacteristic
782C22#1458353111yescharacteristic
783C22#1458354111yescharacteristic
784C22C2×#1306335411yescharacteristic
785C22C2×#1306335711yescharacteristic
786C22#1458370911yescharacteristic
787C22#1458371511yescharacteristic
788C4—22no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—81no—
793C4—862no—
794C4—864no—
795C4—862no—
796C4—862no—
797C4—3441no—
798C4—3441no—
799C4—1722no—
800C4C4×D4×D4311yescharacteristic
801C4#1458337111yescharacteristic
802C4#1458353311yescharacteristic
803C4#1458353811yescharacteristic
804C2—24no—
805C2—1722no—
806C2#1913741311yescharacteristic
807C2C2×#1458290611yescharacteristic
808C2#1914312611yescharacteristic
809C2#1914610911yescharacteristic
810C2#1914616911yescharacteristic
811C2#1914664411yescharacteristic
812C2#1914676411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1872C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
cosocleC22×C4×C43C24
hypercenter#1872D43
hypocenterC43#22425
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. C2×#14582906C2semidirect
4. C22×#13063248C2semidirect
6. #19135516C2semidirect
7. #19135413C2semidirect
8. #19135027C2semidirect
9. #19135019C2semidirect
10. #19134906C2semidirect
11. #19134609C2semidirect
12. #19134531C2semidirect
13. #19134528C2semidirect
14. #19134424C2semidirect
15. C43×#1872C2semidirect
21. #14583562C4semidirect
79. C2×Q8×D43C2×C4semidirect
94. #13063323C2×C4semidirect
96. #13063305C2×C4semidirect
100. #13063290C2×C4semidirect
133. #13063248D4semidirect
367. C22×C43#419semidirect
408. #1872D43semidirect
470. C43#22425semidirect
780. C22#14582906semidirect

Maximal subgroups

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

subgroupindex
C2×#145835622
C2×#145829672
C2×#145829062
C22×#130632482
#191375202
#191355162
#191354132
#191350272
#191350192
#191349062
#191346092
#191345312
#191345282
#191344242
C43×#18722
#2242543