Finite Group Databasebeta

← #25112231

Subgroups — #25112231

Order 11008.

1426 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D43C211yesmaximal, characteristic
2C2×#14582974C211yesmaximal, characteristic
3C2×#14582908C211yesmaximal, characteristic, complemented
4C2×#14582906C211yesmaximal, characteristic, complemented
5#19137539C211yesmaximal, characteristic
6#19135516C211yesmaximal, characteristic, complemented
7#19135395C211yesmaximal, characteristic, complemented
8#19135026C211yesmaximal, characteristic, complemented
9#19135025C211yesmaximal, characteristic, complemented
10#19134905C211yesmaximal, characteristic, complemented
11#19134904C211yesmaximal, characteristic, complemented
12#19134598C211yesmaximal, characteristic, complemented
13#19134528C211yesmaximal, characteristic, complemented
14#103×Dic43C211yesmaximal, characteristic, complemented
15C43×#1787C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19Q8×C22⋊D43—24no—
20Q8×C22⋊D43C418yescomplemented
21C2×#13063323—21no—
22C2×#13063323C2211yescharacteristic
23C2×#13063304—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063301—21no—
26C2×#13063301C2211yescharacteristic
27C2×Q8×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43—21no—
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×#13063284C2211yescharacteristic
31C2×#13063283C2211yescharacteristic
32#14582974—24no—
33C2×Dic43⋊C8C2211yescharacteristic
34#14582908—24no—
35#14582906—24no—
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063249C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic
46#14582799—21no—
47#14582793—21no—
48#14582788—21no—
49#14582768C2211yescharacteristic
50#14582756C2211yescharacteristic
51C4⋊C4×Dic43C2211yescharacteristic
52#14582750—21no—
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57C23×Q8×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C22×Dic86—21no—
65C22×Dic86C2311yescharacteristic
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—41no—
70C2×Q8×D43—41no—
71C2×Q8×D43C2×C414yes—
72C22×C22⋊D43D411yescharacteristic
73C22×C4×D43—21no—
74C22×C4×D43C2311yescharacteristic
75C2×#10621877—22no—
76C2×#10621877—22no—
77C2×#10621877—41no—
78C2×#10621872—22no—
79C2×#10621872—22no—
80C2×#10621872—41no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063323—28no—
84#13063323—22no—
85#13063323C2×C414yes—
86#13063304—22no—
87#13063304—28no—
88#13063304C2×C414yes—
89#13063301—22no—
90#13063301—28no—
91#13063301C2×C414yes—
92Q8×Dic43—22no—
93Q8×Dic43C2×C414yes—
94C4×C22⋊D43—28no—
95C4×C22⋊D43C2×C414yes—
96C4×C22⋊D43D414yes—
97#13063284—22no—
98#13063284—41no—
99#13063283—22no—
100#13063283—41no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
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)⋊C4D411yescharacteristic
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43—21no—
123C2×C4×Dic43C2311yescharacteristic
124Dic43⋊C8—22no—
125#13063250—22no—
126#13063250—41no—
127#13063249—22no—
128#13063249—22no—
129#13063249—22no—
130#13063249D414yescomplemented
131#13063248—22no—
132#13063248—41no—
133(C2×D43)⋊C8—22no—
134C8×Dic43—22no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C22×Q8×C43—22no—
138C22×Q8×C43—21no—
139C22×Q8×C43—22no—
140C22×Q8×C43—22no—
141C22×Q8×C43—41no—
142C22×Q8×C43—41no—
143C22×Q8×C43C2×C414yes—
144C22×Q8×C43C2311yescharacteristic
145C22×Q8×C43C2311yescharacteristic
146C23×C4×C43—21no—
147C23×C4×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C22⋊C4×C43—21no—
153#103×C43—22no—
154#103×C43—22no—
155#103×C43—41no—
156#103×C43—41no—
157C22⋊C8×C43—22no—
158#95×C43—21no—
159C24×C43C2×D411yescharacteristic
160C23×D43C2×D411yescharacteristic
161C2×Q8×C43—24no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—28no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—42no—
172C2×Q8×C43—42no—
173C2×Q8×C43—44no—
174C2×Q8×C43—44no—
175C2×Q8×C43—44no—
176C2×Q8×C43C22×C412yes—
177C2×Q8×C43C22×C412yes—
178C2×Q8×C43C2×D412yes—
179C2×Q8×C43#4112yes—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—24no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—42no—
190C22×C4×C43—42no—
191C22×C4×C43C22×C412yes—
192C22×C4×C43C2×D412yes—
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C2×C22⋊D43—22no—
196C2×C22⋊D43—22no—
197C2×C22⋊D43C22⋊C414yes—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205Q8×D43—28no—
206Q8×D43—44no—
207Q8×D43—44no—
208Q8×D43—44no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43—21no—
213C2×C4×D43—24no—
214C2×C4×D43—42no—
215C2×C4×D43—42no—
216C2×C4×D43C22×C412yes—
217C2×C4×D43C2×D412yes—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86—24no—
224C2×Dic86—42no—
225C2×Dic86—42no—
226C2×Dic86C22×C412yes—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C22⋊C4×C43—81no—
238C22⋊Dic43—24no—
239C22⋊Dic43—42no—
240C22⋊Dic43C22⋊C414yes—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—42no—
243(C2×D43)⋊C4—81no—
244(C2×D43)⋊C4C22⋊C414yes—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—24no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43C22×C412yes—
251C4⋊Dic43C2×D412yes—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—42no—
257Dic43⋊C4—81no—
258Dic43⋊C4C22⋊C414yes—
259C4×Dic43—24no—
260C4×Dic43—42no—
261C4×Dic43—42no—
262C4×Dic43—42no—
263C4×Dic43C22×C412yes—
264C4×Dic43C2×D412yes—
265#10621877—44no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8C2×D412yes—
272#10621872—44no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43C2×C22⋊C412yes—
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—22no—
291Q8×C43—22no—
292Q8×C43—22no—
293Q8×C43—48no—
294Q8×C43—41no—
295Q8×C43—41no—
296Q8×C43C4×D414yes—
297C2×C4×C43—22no—
298C2×C4×C43—21no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—21no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—48no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43C2×C22⋊C412yes—
317C2×C4×C43C23×C411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C22⋊D43—28no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43C2×C22⋊C412yes—
341C2×Dic43C2×C22⋊C412yes—
342C2×Dic43C2×C22⋊C412yes—
343C2×Dic43#13712yes—
344C2×Dic43#13712yes—
345C4×D43—22no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—22no—
349C4×D43—48no—
350Dic86—22no—
351Dic86—22no—
352Dic86—48no—
353Dic86—41no—
354Dic86—41no—
355C8×C43—41no—
356C8×C43—41no—
357C43⋊C8—22no—
358C43⋊C8—41no—
359#22430—431nomaximal, Sylow
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43C22×C22⋊C411yescharacteristic
368C22×C43D4211yescharacteristic
369C22×C43#54611yescharacteristic
370C22×C43C2×#13711yescharacteristic
371C22×C43C2×#13711yescharacteristic
372C22×C43#57711yescharacteristic
373C22×C43#57811yescharacteristic
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—41no—
378C2×D43—41no—
379C2×D43—41no—
380C2×D43—41no—
381C4×C43—24no—
382C4×C43—22no—
383C4×C43—42no—
384C4×C43—81no—
385C4×C43—81no—
386C4×C43C2×C4×D411yescharacteristic
387C4×C43#51811yescharacteristic
388C4×C43D4211yescharacteristic
389C4×C43#54611yescharacteristic
390Dic43—22no—
391Dic43—22no—
392Dic43—42no—
393Dic43—42no—
394Dic43—42no—
395Dic43—81no—
396Dic43#41914yescomplemented
397C2×D4×Q8—431no—
398C2×#436—431no—
399C2×#419—431no—
400C2×#419—431no—
401#2354—431no—
402#1981—431no—
403#1956—431no—
404#1894—431no—
405#1894—431no—
406#1873—431no—
407#1873—431no—
408#1803—431no—
409#1787—431no—
410#1787D4311yescharacteristic, complemented
411C4×#103—431no—
412C2×C43—42no—
413C2×C43D4×C22⋊C411yescharacteristic
414C2×C43C2×#41911yescharacteristic
415C2×C43#289811yescharacteristic
416C2×C43#327611yescharacteristic
417C2×C43#327811yescharacteristic
418C2×C43#332811yescharacteristic
419C2×C43#332911yescharacteristic
420D43—42no—
421C23×Q8—431no—
422C23×Q8C2×D4311yescharacteristic
423C22×M16—431no—
424C22×M16—431no—
425D4×Q8—438no—
426D4×Q8—864no—
427C2×C4⋊Q8—431no—
428C2×C4⋊Q8—861no—
429C2×C22⋊Q8—431no—
430C2×C22⋊Q8—431no—
431C2×C22⋊Q8—861no—
432C2×C22⋊Q8—861no—
433C2×C4×Q8—431no—
434C2×C4×D4—431no—
435C2×C4×D4—861no—
436C2×#117—431no—
437C2×#117—431no—
438#436—864no—
439C2×C4⋊C8—431no—
440#419—864no—
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×#103C2×D4311yescharacteristic
451C2×#103C2×D4311yescharacteristic
452C2×#103C2×D4311yescharacteristic
453C2×#103C2×D4311yescharacteristic
454C2×C22⋊C8—431no—
455C2×C22⋊C8C2×D4311yescharacteristic
456C2×C4×C8—431no—
457#390—861no—
458#388—861no—
459#388—861no—
460#384—431no—
461#380—431no—
462#380C2×D4311yescharacteristic
463C4×C4⋊C4—431no—
464C4×C4⋊C4—861no—
465#340—431no—
466#340—431no—
467#340—431no—
468#340—431no—
469C43#2243011yescharacteristic, complemented, Sylow
470C22×Q8—21no—
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—41no—
475C22×Q8—41no—
476C22×Q8—434no—
477C22×Q8—431no—
478C22×Q8—861no—
479C22×Q8—862no—
480C22×Q8—862no—
481C22×Q8—862no—
482C22×Q8—1721no—
483C22×Q8—1721no—
484C22×Q8C4×D4314yes—
485C22×Q8C22×D4311yescharacteristic
486C22×Q8C22×D4311yescharacteristic
487C22×D4—431no—
488C23×C4—21no—
489C23×C4—431no—
490C23×C4—861no—
491C23×C4C22×D4311yescharacteristic
492C2×M16—862no—
493C2×M16—862no—
494C2×M16—862no—
495C2×M16—862no—
496C2×M16—1721no—
497C2×M16—1721no—
498C22×C8—431no—
499C22×C8—431no—
500C22×C8C22×D4311yescharacteristic
501C22×C8C22×D4311yescharacteristic
502C4⋊Q8—434no—
503C4⋊Q8—862no—
504C4⋊Q8—868no—
505C22⋊Q8—434no—
506C22⋊Q8—434no—
507C22⋊Q8—868no—
508C22⋊Q8—868no—
509C22⋊Q8—862no—
510C22⋊Q8—862no—
511C4×Q8—434no—
512C4×Q8—862no—
513C4×D4—434no—
514C4×D4—434no—
515C4×D4—868no—
516#117—862no—
517#117—862no—
518#117—1721no—
519#117—1721no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
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×C22⋊C4—21no—
534C2×C22⋊C4—431no—
535C2×C22⋊C4—431no—
536C2×C22⋊C4—861no—
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—
545C2×C42—861no—
546C4⋊C8—862no—
547#103—22no—
548#103—22no—
549#103—41no—
550#103—41no—
551#103—434no—
552#103—862no—
553#103—862no—
554#103—862no—
555#103—862no—
556#103—862no—
557#103—1721no—
558#103—1721no—
559C22⋊C8—22no—
560C22⋊C8—862no—
561C4×C8—862no—
562#95—21no—
563#95—861no—
564#95—861no—
565C24—431no—
566C24D4×D4311yescharacteristic
567C2×Q8—24no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—28no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—42no—
578C2×Q8—42no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—432no—
583C2×Q8—864no—
584C2×Q8—861no—
585C2×Q8—868no—
586C2×Q8—861no—
587C2×Q8—861no—
588C2×Q8—861no—
589C2×Q8—861no—
590C2×Q8—1722no—
591C2×Q8—1722no—
592C2×Q8—1724no—
593C2×Q8—1724no—
594C2×Q8—1724no—
595C2×Q8C2×C4×D4312yes—
596C2×Q8C2×C4×D4312yes—
597C2×Q8D4×D4312yes—
598C2×Q8#1062190012yes—
599C2×D4—434no—
600C2×D4—862no—
601C2×D4—862no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—432no—
617C22×C4—432no—
618C22×C4—864no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—1722no—
628C22×C4—1722no—
629C22×C4C2×C4×D4312yes—
630C22×C4D4×D4311yescharacteristic
631C22×C4D4×D4312yes—
632C22×C4C23×D4311yescharacteristic
633M16—1724no—
634M16—1724no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—432no—
642C2×C8—861no—
643C2×C8—861no—
644C2×C8—861no—
645C2×C8—861no—
646C2×C8—861no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—434no—
652C4⋊C4—432no—
653C4⋊C4—432no—
654C4⋊C4—864no—
655C4⋊C4—864no—
656C4⋊C4—864no—
657C4⋊C4—864no—
658C4⋊C4—864no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—3441no—
664C4⋊C4—1722no—
665C22⋊C4—81no—
666C22⋊C4—434no—
667C22⋊C4—434no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C22⋊C4—3441no—
671C22⋊C4—1722no—
672C22⋊C4—1722no—
673C42—432no—
674C42—432no—
675C42—864no—
676C42—1722no—
677C42—1722no—
678C42—1722no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—432no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—861no—
690C23—861no—
691C23—861no—
692C23C22⋊C4×D4312yes—
693C23C2×D4×D4311yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—48no—
700Q8—41no—
701Q8—41no—
702Q8—862no—
703Q8—862no—
704Q8—1728no—
705Q8—1721no—
706Q8—1721no—
707Q8(C22⋊D43)⋊C414yes—
708D4—868no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—48no—
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—432no—
729C2×C4—432no—
730C2×C4—432no—
731C2×C4—432no—
732C2×C4—432no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—1728no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4C22⋊C4×D4312yes—
755C2×C4C22×C4×D4311yescharacteristic
756C2×C4C2×D4×D4311yescharacteristic
757C2×C4C2×D4×D4311yescharacteristic
758C2×C4C2×#1062190011yescharacteristic
759C2×C4#1306337011yescharacteristic
760C2×C4#1306337011yescharacteristic
761C8—41no—
762C8—41no—
763C8—862no—
764C8—1721no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—862no—
773C22—862no—
774C22—862no—
775C22—1721no—
776C22—1721no—
777C22—1721no—
778C22—1721no—
779C22C2×C22⋊C4×D4311yescharacteristic
780C22#1458353111yescharacteristic
781C22#1458353611yescharacteristic
782C22#137×D4311yescharacteristic
783C22#137×D4311yescharacteristic
784C22#1458370511yescharacteristic
785C22#1458371211yescharacteristic
786C4—22no—
787C4—24no—
788C4—42no—
789C4—81no—
790C4—81no—
791C4—434no—
792C4—862no—
793C4—862no—
794C4—3441no—
795C4—1722no—
796C4—1722no—
797C4—1722no—
798C4C2×(C22⋊D43)⋊C411yescharacteristic
799C4#1458337211yescharacteristic
800C4#1458353111yescharacteristic
801C4#1458353611yescharacteristic
802C2—42no—
803C2—1722no—
804C2#1913741111yescharacteristic
805C2#419×D4311yescharacteristic
806C2#1914312311yescharacteristic
807C2#1914623411yescharacteristic
808C2#1914625911yescharacteristic
809C2#1914687111yescharacteristic
810C2#1914688211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1787C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
cosocleC22×C4×C43C24
hypercenter#1787D43
hypocenterC43#22430
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
3. C2×#14582908C2semidirect
4. C2×#14582906C2semidirect
6. #19135516C2semidirect
7. #19135395C2semidirect
8. #19135026C2semidirect
9. #19135025C2semidirect
10. #19134905C2semidirect
11. #19134904C2semidirect
12. #19134598C2semidirect
13. #19134528C2semidirect
14. #103×Dic43C2semidirect
15. C43×#1787C2semidirect
20. Q8×C22⋊D43C4semidirect
130. #13063249D4semidirect
396. Dic43#419semidirect
410. #1787D43semidirect
469. C43#22430semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D432
C2×#145829742
C2×#145829082
C2×#145829062
#191375392
#191355162
#191353952
#191350262
#191350252
#191349052
#191349042
#191345982
#191345282
#103×Dic432
C43×#17872
#2243043