Finite Group Databasebeta

← #25112161

Subgroups — #25112161

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×D4×Dic86C211yesmaximal, characteristic
2C2×#14582971C211yesmaximal, characteristic
3C2×#14582907C211yesmaximal, characteristic, complemented
4C22×#13063248C211yesmaximal, characteristic, complemented
5#19135518C211yesmaximal, characteristic, complemented
6#19135414C211yesmaximal, characteristic, complemented
7#19135026C211yesmaximal, characteristic, complemented
8#19135016C211yesmaximal, characteristic, complemented
9#19134907C211yesmaximal, characteristic, complemented
10#19134902C211yesmaximal, characteristic, complemented
11#19134607C211yesmaximal, characteristic, complemented
12#19134529C211yesmaximal, characteristic, complemented
13#19134529C211yesmaximal, characteristic, complemented
14#19134428C211yesmaximal, characteristic, complemented
15C43×#2352C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C23×Dic86C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20D4×Dic86—24no—
21D4×Dic86C418yescomplemented
22C2×#13063325C2211yescharacteristic
23C2×#13063324—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063304C2211yescharacteristic
26C2×#13063302—21no—
27C2×#13063302—21no—
28C2×C4×Dic86C2211yescharacteristic
29C2×D4×Dic43—21no—
30#14582971—24no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32#14582907—24no—
33C2×#13063248—24no—
34C2×#13063248C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×#13063248C2211yescharacteristic
45C2×#13063248C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47C2×C22⋊(C43⋊C8)C2211yescharacteristic
48C2×#13063236C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C43×#388—21no—
57C43×#387—21no—
58C43×#386—21no—
59C43×#382C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C4×C4⋊C4×C43C2211yescharacteristic
63C4×C22⋊C4×C43—21no—
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—22no—
67C22×Dic86—22no—
68C22×Dic86—22no—
69C22×Dic86—22no—
70C22×Dic86—21no—
71C22×Dic86—21no—
72C22×Dic86—41no—
73C22×Dic86—41no—
74C22×Dic86—41no—
75C22×Dic86—41no—
76C22×Dic86C2×C414yes—
77C22×Dic86C2×C414yescomplemented
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×Dic86C2311yescharacteristic
81C23×Dic43—21no—
82C23×Dic43—21no—
83C2×#10621877—22no—
84C2×#10621877—22no—
85C2×#10621877—41no—
86C22×C43⋊C8—22no—
87C22×C43⋊C8—22no—
88C22×C43⋊C8—41no—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93#13063325—22no—
94#13063325C2×C414yescomplemented
95#13063324—28no—
96#13063304—22no—
97#13063304—22no—
98#13063304C2×C414yes—
99#13063304C2×C414yescomplemented
100#13063302—28no—
101#13063302—28no—
102C4×Dic86—22no—
103C4×Dic86C2×C414yescomplemented
104D4×Dic43—28no—
105C2×C4⋊Dic43—21no—
106C2×C4⋊Dic43—21no—
107C2×C4⋊Dic43C2311yescharacteristic
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C4×Dic43—21no—
114C4⋊(C43⋊C8)—22no—
115#13063248—22no—
116#13063248—22no—
117#13063248—22no—
118#13063248—22no—
119#13063248—22no—
120#13063248—22no—
121#13063248—22no—
122#13063248—41no—
123#13063248—41no—
124#13063248—41no—
125#13063248—41no—
126#13063248D414yescomplemented
127C22⋊(C43⋊C8)—22no—
128C22⋊(C43⋊C8)—22no—
129#13063236—22no—
130C22×D4×C43D411yescharacteristic
131C23×C4×C43—21no—
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C4×D4×C43C2×C414yes—
135C4×D4×C43D414yes—
136#117×C43—22no—
137#117×C43—41no—
138C2×C4⋊C4×C43—22no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43—41no—
141C2×C4⋊C4×C43D411yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43D411yescharacteristic
150C2×C22⋊C4×C43D411yescharacteristic
151C2×C42×C43—21no—
152C2×C42×C43—21no—
153C2×C42×C43C2311yescharacteristic
154#95×C43—21no—
155#95×C43—21no—
156#95×C43—21no—
157#95×C43—21no—
158#95×C43—21no—
159C24×C43C2×D411yescharacteristic
160C24×C43C2×D411yescharacteristic
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C2×D4×C43C22⋊C414yes—
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—42no—
177C22×C4×C43—42no—
178C22×C4×C43—81no—
179C22×C4×C43C22×C412yes—
180C22×C4×C43C22×C412yes—
181C22×C4×C43C2×D412yes—
182C22×C4×C43C2×D412yes—
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2411yescharacteristic
188C22×Dic43—24no—
189C22×Dic43—24no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—42no—
195C22×Dic43—42no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—28no—
210C2×Dic86—28no—
211C2×Dic86—24no—
212C2×Dic86—24no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—44no—
216C2×Dic86—44no—
217C2×Dic86—44no—
218C2×Dic86—44no—
219C2×Dic86—44no—
220C2×Dic86—44no—
221C2×Dic86—42no—
222C2×Dic86—42no—
223C2×Dic86—42no—
224C2×Dic86—42no—
225C2×Dic86C22×C412yes—
226C2×Dic86C22×C412yes—
227C2×Dic86C22×C412yes—
228C2×Dic86C2×D412yes—
229C2×Dic86#4112yes—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—42no—
238C4⋊C4×C43C22⋊C414yes—
239C4⋊C4×C43C2×D412yes—
240C22⋊C4×C43—42no—
241C22⋊C4×C43—42no—
242C22⋊C4×C43—81no—
243C22⋊C4×C43C22⋊C414yes—
244C22⋊C4×C43C22⋊C414yes—
245C42×C43—42no—
246C42×C43—81no—
247C42×C43C22×C412yes—
248C42×C43C2×D412yes—
249C22⋊Dic43—24no—
250C22⋊Dic43—24no—
251C4⋊Dic43—24no—
252C4⋊Dic43—24no—
253C4⋊Dic43—21no—
254C4⋊Dic43C22×C412yes—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258C4×Dic43—24no—
259#10621877—44no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—44no—
272C2×C43⋊C8C2×D412yes—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43C2×C22⋊C412yes—
284C23×C43C2×C22⋊C412yes—
285C23×C43#13712yes—
286C23×C43#13712yes—
287C23×C43C22×D411yescharacteristic
288D4×C43—28no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
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×C43—41no—
317C2×C4×C43—84no—
318C2×C4×C43C2×C22⋊C412yes—
319C2×C4×C43C2×C22⋊C412yes—
320C2×C4×C43C2×C22⋊C412yes—
321C2×C4×C43C2×C22⋊C412yes—
322C2×C4×C43C23×C411yescharacteristic
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C2×#4111yescharacteristic
326C2×C4×C43H(5,𝔽2)11yescharacteristic
327C2×C4×C43H(5,𝔽2)11yescharacteristic
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—48no—
335C2×Dic43—48no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342Dic86—22no—
343Dic86—22no—
344Dic86—22no—
345Dic86—22no—
346Dic86—22no—
347Dic86—22no—
348Dic86—22no—
349Dic86—48no—
350Dic86—48no—
351Dic86—41no—
352Dic86—41no—
353Dic86—41no—
354Dic86—41no—
355Dic86C4×D414yes—
356C43⋊C8—22no—
357C43⋊C8—41no—
358C43⋊C8—41no—
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—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43#41914yescomplemented
375C22×C43C22×C22⋊C411yescharacteristic
376C22×C43D4211yescharacteristic
377C22×C43#54611yescharacteristic
378C22×C43C2×#13711yescharacteristic
379C22×C43C2×#13711yescharacteristic
380C22×C43#57711yescharacteristic
381C22×C43#57811yescharacteristic
382C4×C43—22no—
383C4×C43—22no—
384C4×C43—22no—
385C4×C43—22no—
386C4×C43—42no—
387C4×C43—81no—
388C4×C43—81no—
389C4×C43—81no—
390C4×C43C2×C4×D411yescharacteristic
391C4×C43#51811yescharacteristic
392C4×C43D4211yescharacteristic
393C4×C43#54611yescharacteristic
394Dic43—24no—
395Dic43—42no—
396Dic43—42no—
397Dic43—42no—
398C2×D4×Q8—431no—
399C2×#435—431no—
400C2×#419—431no—
401C22×#103—431no—
402#2352D4311yescharacteristic
403#1981—431no—
404#1960—431no—
405#1894—431no—
406#1892—431no—
407#1873—431no—
408#1872—431no—
409#1805—431no—
410#1787—431no—
411#1787—431no—
412#1763—431no—
413C2×C43—24no—
414C2×C43—42no—
415C2×C43D4×C22⋊C411yescharacteristic
416C2×C43C2×#41911yescharacteristic
417C2×C43#289811yescharacteristic
418C2×C43#326611yescharacteristic
419C2×C43#327011yescharacteristic
420C2×C43#331211yescharacteristic
421C2×C43#332011yescharacteristic
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—431no—
432C2×C22⋊Q8—861no—
433C2×C22⋊Q8—861no—
434C2×C4×Q8—431no—
435C2×C4×D4—861no—
436C2×C4×D4C2×D4311yescharacteristic
437C2×#117C2×D4311yescharacteristic
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—431no—
453C2×#103—431no—
454C2×#103—864no—
455C2×C22⋊C8—431no—
456C2×C22⋊C8—431no—
457C2×#97—431no—
458#388—21no—
459#387—21no—
460#386—21no—
461#382C2×D4311yescharacteristic
462#380C2×D4311yescharacteristic
463#380C2×D4311yescharacteristic
464C4×C4⋊C4C2×D4311yescharacteristic
465C4×C22⋊C4—21no—
466#340—431no—
467#340—431no—
468#340—431no—
469#340—431no—
470C43#2242511yescharacteristic, complemented, Sylow
471C22×Q8—434no—
472C22×Q8—434no—
473C22×Q8—431no—
474C22×Q8—431no—
475C22×Q8—431no—
476C22×Q8—862no—
477C22×Q8—862no—
478C22×Q8—862no—
479C22×Q8—862no—
480C22×Q8—862no—
481C22×Q8—862no—
482C22×Q8—861no—
483C22×Q8—861no—
484C22×Q8—1721no—
485C22×Q8—1721no—
486C22×Q8—1721no—
487C22×Q8—1721no—
488C22×D4C22⋊D4311yescharacteristic
489C23×C4—21no—
490C23×C4—861no—
491C23×C4—861no—
492C23×C4C22×D4311yescharacteristic
493C23×C4C22×D4311yescharacteristic
494C2×M16—862no—
495C2×M16—862no—
496C2×M16—1721no—
497C22×C8—431no—
498C22×C8—431no—
499C22×C8—431no—
500C22×C8—431no—
501C22×C8—862no—
502C22×C8—862no—
503C22×C8—1721no—
504C4⋊Q8—434no—
505C4⋊Q8—868no—
506C4⋊Q8—862no—
507C22⋊Q8—434no—
508C22⋊Q8—434no—
509C22⋊Q8—862no—
510C22⋊Q8—862no—
511C22⋊Q8—868no—
512C22⋊Q8—868no—
513C4×Q8—434no—
514C4×Q8—862no—
515C4×D4—868no—
516C4×D4C4×D4314yes—
517C4×D4D17214yes—
518#117—22no—
519#117—41no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—41no—
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⋊C4C22⋊D4311yescharacteristic
530C2×C4⋊C4C22×D4311yescharacteristic
531C2×C4⋊C4C22×D4311yescharacteristic
532C2×C4⋊C4C22×D4311yescharacteristic
533C2×C4⋊C4C22×D4311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4C22⋊D4311yescharacteristic
540C2×C22⋊C4C22⋊D4311yescharacteristic
541C2×C42—21no—
542C2×C42—21no—
543C2×C42—861no—
544C2×C42C22×D4311yescharacteristic
545C4⋊C8—862no—
546#103—434no—
547#103—862no—
548#103—862no—
549#103—862no—
550#103—862no—
551#103—862no—
552#103—862no—
553#103—862no—
554#103—1721no—
555#103—1721no—
556#103—1721no—
557#103—1721no—
558C22⋊C8—862no—
559C22⋊C8—862no—
560#97—862no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95—21no—
566C24C2×C22⋊D4311yescharacteristic
567C24C2×C22⋊D4311yescharacteristic
568C2×Q8—432no—
569C2×Q8—432no—
570C2×Q8—432no—
571C2×Q8—432no—
572C2×Q8—432no—
573C2×Q8—868no—
574C2×Q8—868no—
575C2×Q8—864no—
576C2×Q8—864no—
577C2×Q8—861no—
578C2×Q8—861no—
579C2×Q8—861no—
580C2×Q8—861no—
581C2×Q8—861no—
582C2×Q8—861no—
583C2×Q8—861no—
584C2×Q8—861no—
585C2×Q8—861no—
586C2×Q8—861no—
587C2×Q8—861no—
588C2×Q8—861no—
589C2×Q8—861no—
590C2×Q8—1722no—
591C2×Q8—1722no—
592C2×Q8—1722no—
593C2×Q8—1722no—
594C2×Q8—1724no—
595C2×Q8—1724no—
596C2×Q8—1724no—
597C2×Q8—1724no—
598C2×Q8—1724no—
599C2×Q8—1724no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4(C2×D43)⋊C414yes—
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—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—81no—
618C22×C4—861no—
619C22×C4—864no—
620C22×C4—864no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4—1722no—
627C22×C4—1722no—
628C22×C4C2×C4×D4312yes—
629C22×C4C2×C4×D4312yes—
630C22×C4C2×D17212yes—
631C22×C4C2×D17212yes—
632C22×C4C2×C22⋊D4311yescharacteristic
633C22×C4C2×C22⋊D4311yescharacteristic
634C22×C4C2×C22⋊D4311yescharacteristic
635C22×C4C2×C22⋊D4311yescharacteristic
636C22×C4C23×D4311yescharacteristic
637M16—1724no—
638C2×C8—432no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—861no—
644C2×C8—861no—
645C2×C8—861no—
646C2×C8—861no—
647C2×C8—861no—
648C2×C8—861no—
649C2×C8—861no—
650C2×C8—1724no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—42no—
659C4⋊C4—432no—
660C4⋊C4—864no—
661C4⋊C4—864no—
662C4⋊C4—864no—
663C4⋊C4—864no—
664C4⋊C4—864no—
665C4⋊C4—861no—
666C4⋊C4(C2×D43)⋊C414yes—
667C4⋊C4D4×D4312yes—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—81no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C22⋊C4(C2×D43)⋊C414yes—
674C22⋊C4(C2×D43)⋊C414yes—
675C42—42no—
676C42—81no—
677C42—864no—
678C42C2×C4×D4312yes—
679C42C2×D17212yes—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23C2×(C2×D43)⋊C412yes—
691C23C2×(C2×D43)⋊C412yes—
692C23#1306335512yes—
693C23#1306335512yes—
694C23C22×C22⋊D4311yescharacteristic
695Q8—434no—
696Q8—862no—
697Q8—862no—
698Q8—862no—
699Q8—862no—
700Q8—862no—
701Q8—862no—
702Q8—862no—
703Q8—1728no—
704Q8—1728no—
705Q8—1721no—
706Q8—1721no—
707Q8—1721no—
708Q8—1721no—
709D4—28no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—1728no—
746C2×C4—1728no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4C2×(C2×D43)⋊C412yes—
754C2×C4C2×(C2×D43)⋊C412yes—
755C2×C4C2×(C2×D43)⋊C412yes—
756C2×C4C2×(C2×D43)⋊C412yes—
757C2×C4C22×C4×D4311yescharacteristic
758C2×C4C2×D4×D4311yescharacteristic
759C2×C4C22×D17211yescharacteristic
760C2×C4#41×D4311yescharacteristic
761C2×C4#1306337011yescharacteristic
762C2×C4#1306337111yescharacteristic
763C8—862no—
764C8—1721no—
765C8—1721no—
766C8—1721no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22#1458290714yescomplemented
781C22C22×(C2×D43)⋊C411yescharacteristic
782C22D4×C22⋊D4311yescharacteristic
783C22#1458353711yescharacteristic
784C22C2×#1306335511yescharacteristic
785C22C2×#1306335511yescharacteristic
786C22#1458371011yescharacteristic
787C22#1458371411yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—42no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4—864no—
797C4—1722no—
798C4—1722no—
799C4—1722no—
800C4C4×D4×D4311yescharacteristic
801C4#1458337111yescharacteristic
802C4D4×D17211yescharacteristic
803C4#1458354411yescharacteristic
804C2—24no—
805C2—42no—
806C2D4×(C2×D43)⋊C411yescharacteristic
807C2C2×#1458290711yescharacteristic
808C2#1914312511yescharacteristic
809C2#1914610111yescharacteristic
810C2#1914616111yescharacteristic
811C2#1914664011yescharacteristic
812C2#1914676011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2352C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
cosocleC22×C4×C43C24
hypercenter#2352D43
hypocenterC43#22425
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. C2×#14582907C2semidirect
4. C22×#13063248C2semidirect
5. #19135518C2semidirect
6. #19135414C2semidirect
7. #19135026C2semidirect
8. #19135016C2semidirect
9. #19134907C2semidirect
10. #19134902C2semidirect
11. #19134607C2semidirect
12. #19134529C2semidirect
13. #19134529C2semidirect
14. #19134428C2semidirect
21. D4×Dic86C4semidirect
77. C22×Dic86C2×C4semidirect
94. #13063325C2×C4semidirect
99. #13063304C2×C4semidirect
103. C4×Dic86C2×C4semidirect
126. #13063248D4semidirect
374. C22×C43#419semidirect
470. C43#22425semidirect
780. C22#14582907semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic862
C2×#145829712
C2×#145829072
C22×#130632482
#191355182
#191354142
#191350262
#191350162
#191349072
#191349022
#191346072
#191345292
#191344282
C43×#23522
#2242543