Finite Group Databasebeta

← #25150222

Subgroups — #25150222

Order 11008.

1158 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583281C211yesmaximal, characteristic, complemented
2C2×#14583261C211yesmaximal, characteristic, complemented
3#19140352C211yesmaximal, characteristic, complemented
4#19135603C211yesmaximal, characteristic, complemented
5#19135598C211yesmaximal, characteristic, complemented
6#19135596C211yesmaximal, characteristic, complemented
7#19135591C211yesmaximal, characteristic
8#19135557C211yesmaximal, characteristic, complemented
9#19135412C211yesmaximal, characteristic, complemented
10#19134950C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic, complemented
12#19134936C211yesmaximal, characteristic, complemented
13#19134929C211yesmaximal, characteristic, complemented
14#19134361C211yesmaximal, characteristic, complemented
15C2×C43×#542C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C2×#13063313C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23#14583281—24no—
24#14583261—24no—
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063236C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37#14582821—21no—
38#14582821—21no—
39#14582815—21no—
40#14582815—21no—
41#14582805C2211yescharacteristic
42#14582801C2211yescharacteristic
43#14582769C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C43×#542—24no—
51C43×#542—24no—
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×#126×C43—21no—
54C2×#124×C43—21no—
55C2×#124×C43C2211yescharacteristic
56C2×#123×C43—21no—
57C2×C22⋊Q8×C43—21no—
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#121×C43C2211yescharacteristic
60C2×C4×Q8×C43C2211yescharacteristic
61C2×C4×D4×C43C2211yescharacteristic
62C2×#117×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C2×#10621885—22no—
67C2×#10621885—22no—
68C2×#10621885—41no—
69C2×#10621883—22no—
70C2×#10621883—22no—
71C2×#10621883—41no—
72C2×#10621884—22no—
73C2×#10621884—22no—
74C2×#10621884—41no—
75C2×#10621882—22no—
76C2×#10621882—22no—
77C2×#10621882—41no—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063313—22no—
83#13063313—22no—
84#13063304—41no—
85#13063304—41no—
86#13063299—41no—
87#13063299—41no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×C22⋊Dic43—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99#13063249—41no—
100#13063249—41no—
101#13063248—22no—
102#13063248—22no—
103#13063246—41no—
104#13063246—41no—
105#13063245—22no—
106#13063245—22no—
107C22⋊(C43⋊C8)—22no—
108C22⋊(C43⋊C8)—22no—
109#13063236—22no—
110C4×C43⋊C8—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×Q8×C43—21no—
114C22×Q8×C43C2311yescharacteristic
115C22×D4×C43—21no—
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C23×C4×C43C2311yescharacteristic
119C4⋊Q8×C43—22no—
120C4⋊Q8×C43D414yescomplemented
121#126×C43—28no—
122#124×C43—28no—
123#124×C43—22no—
124#124×C43D414yescomplemented
125#123×C43—28no—
126C22⋊Q8×C43—28no—
127C22⋊Q8×C43—22no—
128C22⋊Q8×C43—22no—
129#121×C43—22no—
130#121×C43—22no—
131C4×Q8×C43—22no—
132C4×Q8×C43—22no—
133C4×D4×C43—22no—
134C4×D4×C43—22no—
135#117×C43—22no—
136#117×C43—22no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43D411yescharacteristic
141C2×C4⋊C4×C43D411yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
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×C43C2311yescharacteristic
153C2×C42×C43C2311yescharacteristic
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C23×D43—21no—
157C2×Q8×C43—24no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—81no—
164C2×Q8×C43—81no—
165C2×Q8×C43C2×D412yes—
166C2×D4×C43—24no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—81no—
173C2×D4×C43—81no—
174C2×D4×C43C2×D412yes—
175C22×C4×C43—24no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—81no—
186C22×C4×C43—81no—
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2411yescharacteristic
193C2×C22⋊D43—42no—
194C2×C22⋊D43—81no—
195C2×C22⋊D43—81no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C4⋊C4×C43—24no—
212C4⋊C4×C43—24no—
213C4⋊C4×C43—24no—
214C4⋊C4×C43—22no—
215C4⋊C4×C43—22no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43C2×D412yes—
219C4⋊C4×C43C2×D412yes—
220C22⋊C4×C43—24no—
221C22⋊C4×C43—24no—
222C22⋊C4×C43—24no—
223C22⋊C4×C43—24no—
224C22⋊C4×C43—24no—
225C22⋊C4×C43—22no—
226C22⋊C4×C43—22no—
227C42×C43—24no—
228C42×C43—21no—
229C42×C43—21no—
230C42×C43C2×D412yes—
231C42×C43C2×D412yes—
232C22⋊Dic43—42no—
233#10621885—44no—
234#10621884—44no—
235#10621883—44no—
236#10621882—44no—
237(C2×D43)⋊C4—42no—
238(C2×D43)⋊C4—42no—
239(C2×D43)⋊C4—42no—
240(C2×D43)⋊C4—81no—
241(C2×D43)⋊C4—81no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—81no—
247C4⋊Dic43—81no—
248Dic43⋊C4—42no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8#4112yes—
260C2×C43⋊C8#4112yes—
261C23×C43—21no—
262C23×C43—22no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43C22×D411yescharacteristic
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283Q8×C43—22no—
284Q8×C43—22no—
285Q8×C43—41no—
286Q8×C43—41no—
287Q8×C43—84no—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—84no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—22no—
299C2×C4×C43—21no—
300C2×C4×C43—22no—
301C2×C4×C43—21no—
302C2×C4×C43—22no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
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—41no—
318C2×C4×C43—41no—
319C2×C4×C43—84no—
320C2×C4×C43#12012yes—
321C2×C4×C43#12012yes—
322C2×C4×C43C22×D411yescharacteristic
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C2×#4111yescharacteristic
325C2×C4×C43C2×#4111yescharacteristic
326C2×C4×C43H(5,𝔽2)11yescharacteristic
327C2×C4×C43H(5,𝔽2)11yescharacteristic
328C22⋊D43—84no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338D172—41no—
339D172—41no—
340D172—41no—
341D172—41no—
342Dic86—41no—
343Dic86—41no—
344Dic86—41no—
345Dic86—41no—
346C43⋊C8—22no—
347C43⋊C8—22no—
348C43⋊C8—41no—
349C43⋊C8—41no—
350#25610—431nomaximal, Sylow
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—42no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—42no—
359C22×C43—41no—
360C22×C43—42no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43C2×#12011yescharacteristic
366C22×C43#53211yescharacteristic
367C22×C43#53511yescharacteristic
368C22×C43#57611yescharacteristic
369C22×C43#57711yescharacteristic
370C22×C43#57711yescharacteristic
371C22×C43#57811yescharacteristic
372C2×D43—81no—
373C2×D43—81no—
374C2×D43—81no—
375C2×D43—81no—
376C2×D43—81no—
377C2×D43—81no—
378C2×D43—81no—
379C4×C43—22no—
380C4×C43—22no—
381C4×C43—41no—
382C4×C43—42no—
383C4×C43—41no—
384C4×C43—42no—
385C4×C43—42no—
386C4×C43—41no—
387C4×C43#54611yescharacteristic
388C4×C43#54611yescharacteristic
389C4×C43#55011yescharacteristic
390C4×C43#55011yescharacteristic
391Dic43—81no—
392Dic43—81no—
393Dic43—81no—
394C2×#542D4311yescharacteristic, complemented
395C2×#495—431no—
396C2×#489—431no—
397#2620—431no—
398#2001—431no—
399#2000—431no—
400#2000—431no—
401#1999—431no—
402#1990—431no—
403#1959—431no—
404#1880—431no—
405#1879—431no—
406#1878—431no—
407#1877—431no—
408#1750—431no—
409C2×C43—81no—
410C2×C43—82no—
411C2×C43#243111yescharacteristic
412C2×C43#301211yescharacteristic
413C2×C43#301311yescharacteristic
414C2×C43#317311yescharacteristic
415C2×C43#317511yescharacteristic
416C2×C43#322411yescharacteristic
417C2×C43#322511yescharacteristic
418D43—161no—
419C22×Q16—431no—
420C22×SD16—431no—
421C22×SD16—431no—
422C22×D8—431no—
423#542—24no—
424#542—24no—
425C2×C4⋊Q8C2×D4311yescharacteristic
426C2×#126—21no—
427C2×#124—21no—
428C2×#124—431no—
429C2×#124C2×D4311yescharacteristic
430C2×#123—21no—
431C2×C22⋊Q8—21no—
432C2×C22⋊Q8—431no—
433C2×C22⋊Q8C2×D4311yescharacteristic
434C2×#121—431no—
435C2×#121C2×D4311yescharacteristic
436C2×C4×Q8C2×D4311yescharacteristic
437C2×C4×D4C2×D4311yescharacteristic
438C2×#117C2×D4311yescharacteristic
439#495—864no—
440#489—864no—
441C2×#103—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#103—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×C22⋊C8—431no—
450C2×C22⋊C8—431no—
451C2×#97—431no—
452C2×C4×C8—431no—
453#396—861no—
454#396—861no—
455#394—861no—
456#394—861no—
457#391—431no—
458#390—431no—
459#384—431no—
460#340—431no—
461#340—431no—
462#340—431no—
463#340—431no—
464#336—431no—
465#336—431no—
466C43#2561011yescharacteristic, complemented, Sylow
467C22×Q8—21no—
468C22×Q8—431no—
469C22×Q8C22×D4311yescharacteristic
470C22×D4—21no—
471C22×D4—431no—
472C22×D4—861no—
473C22×D4C22×D4311yescharacteristic
474C23×C4—21no—
475C23×C4C22×D4311yescharacteristic
476C2×Q16—862no—
477C2×Q16—862no—
478C2×Q16—1721no—
479C2×SD16—862no—
480C2×SD16—862no—
481C2×SD16—862no—
482C2×SD16—862no—
483C2×SD16—1721no—
484C2×SD16—1721no—
485C2×D8—862no—
486C2×D8—862no—
487C2×D8—1721no—
488C22×C8—431no—
489C22×C8—431no—
490C22×C8—431no—
491C22×C8—431no—
492C4⋊Q8—22no—
493C4⋊Q8C22⋊D4314yescomplemented
494#126—28no—
495#124—28no—
496#124—22no—
497#124—862no—
498#124—862no—
499#124C22⋊D4314yescomplemented
500#123—28no—
501C22⋊Q8—28no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8—1721no—
505C22⋊Q8—1721no—
506#121—22no—
507#121—22no—
508#121—1721no—
509#121—1721no—
510C4×Q8—22no—
511C4×Q8—22no—
512C4×D4—22no—
513C4×D4—22no—
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4C22⋊D4311yescharacteristic
525C2×C4⋊C4C22⋊D4311yescharacteristic
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4C22⋊D4311yescharacteristic
540C2×C22⋊C4C22⋊D4311yescharacteristic
541C2×C42—21no—
542C2×C42C22×D4311yescharacteristic
543C2×C42C22×D4311yescharacteristic
544#103—862no—
545#103—862no—
546#103—1721no—
547#103—1721no—
548#102—862no—
549#102—862no—
550#102—1721no—
551#102—1721no—
552C22⋊C8—862no—
553C22⋊C8—862no—
554#97—862no—
555C4×C8—862no—
556#95—861no—
557#95—861no—
558C24—21no—
559C24—861no—
560C24C2×C22⋊D4311yescharacteristic
561C2×Q8—24no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—81no—
568C2×Q8—81no—
569C2×Q8—861no—
570C2×Q8—861no—
571C2×Q8—861no—
572C2×Q8—861no—
573C2×Q8—861no—
574C2×Q8—861no—
575C2×Q8C2×C22⋊D4312yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—3441no—
591C2×D4—3441no—
592C2×D4—1722no—
593C2×D4C2×C22⋊D4312yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—24no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4C2×C22⋊D4311yescharacteristic
610C22×C4C2×C22⋊D4311yescharacteristic
611C22×C4C2×C22⋊D4311yescharacteristic
612C22×C4C2×C22⋊D4311yescharacteristic
613C22×C4C2×C22⋊D4311yescharacteristic
614C22×C4C23×D4311yescharacteristic
615Q16—1724no—
616SD16—1724no—
617SD16—1724no—
618D8—1724no—
619C2×C8—432no—
620C2×C8—432no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C2×C8—861no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—861no—
639C4⋊C4—861no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C4⋊C4—3441no—
643C4⋊C4—3441no—
644C4⋊C4—1722no—
645C4⋊C4C2×C22⋊D4312yes—
646C4⋊C4C2×C22⋊D4312yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—3441no—
655C22⋊C4—3441no—
656C22⋊C4—1722no—
657C22⋊C4—1722no—
658C22⋊C4—1722no—
659C22⋊C4—1722no—
660C42—24no—
661C42—21no—
662C42—21no—
663C42C2×C22⋊D4312yes—
664C42C2×C22⋊D4312yes—
665C23—21no—
666C23—22no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—1721no—
680C23—1721no—
681C23—1721no—
682C23—1721no—
683C23—1721no—
684C23—1721no—
685C23—1721no—
686C23C22×C22⋊D4311yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—41no—
690Q8—41no—
691Q8—84no—
692Q8—1721no—
693Q8—1721no—
694Q8—1721no—
695Q8—1721no—
696D4—22no—
697D4—22no—
698D4—41no—
699D4—41no—
700D4—84no—
701D4—3444no—
702D4—1721no—
703D4—1721no—
704D4—1721no—
705D4—1721no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—84no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4#1306329412yes—
743C2×C4#1306329412yes—
744C2×C4C22×C22⋊D4311yescharacteristic
745C2×C4C22×C22⋊D4311yescharacteristic
746C2×C4#41×D4311yescharacteristic
747C2×C4#41×D4311yescharacteristic
748C2×C4#1306337111yescharacteristic
749C2×C4#1306337111yescharacteristic
750C8—862no—
751C8—862no—
752C8—1721no—
753C8—1721no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—3441no—
769C22—3441no—
770C22—3441no—
771C22—3441no—
772C22—3441no—
773C22—3441no—
774C22—3441no—
775C22C2×#1306329411yescharacteristic
776C22#1458344511yescharacteristic
777C22#1458346311yescharacteristic
778C22#1458370211yescharacteristic
779C22#1458370711yescharacteristic
780C22#1458371011yescharacteristic
781C22#1458371411yescharacteristic
782C4—22no—
783C4—22no—
784C4—41no—
785C4—42no—
786C4—41no—
787C4—42no—
788C4—42no—
789C4—41no—
790C4—3441no—
791C4—3441no—
792C4—3441no—
793C4#1458353711yescharacteristic
794C4#1458353711yescharacteristic
795C4#1458356811yescharacteristic
796C4#1458356811yescharacteristic
797C2—81no—
798C2—82no—
799C2—6881no—
800C2#1913821011yescharacteristic
801C2#1914389911yescharacteristic
802C2#1914391011yescharacteristic
803C2#1914520611yescharacteristic
804C2#1914522811yescharacteristic
805C2#1914568311yescharacteristic
806C2#1914569811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#542C2
socleC23×C43C22×D4
prime radical#19135591C2
hypercenterC2×#542D43
hypocenterC43#25610
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#14583281C2semidirect
2. C2×#14583261C2semidirect
3. #19140352C2semidirect
4. #19135603C2semidirect
5. #19135598C2semidirect
6. #19135596C2semidirect
8. #19135557C2semidirect
9. #19135412C2semidirect
10. #19134950C2semidirect
11. #19134943C2semidirect
12. #19134936C2semidirect
13. #19134929C2semidirect
14. #19134361C2semidirect
15. C2×C43×#542C2semidirect
120. C4⋊Q8×C43D4semidirect
124. #124×C43D4semidirect
394. C2×#542D43semidirect
466. C43#25610semidirect
493. C4⋊Q8C22⋊D43semidirect
499. #124C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832812
C2×#145832612
#191403522
#191356032
#191355982
#191355962
#191355912
#191355572
#191354122
#191349502
#191349432
#191349362
#191349292
#191343612
C2×C43×#5422
#2561043