Finite Group Databasebeta

← #25112122

Subgroups — #25112122

Order 11008.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582971C211yesmaximal, characteristic, complemented
2C2×#14582900C211yesmaximal, characteristic, complemented
3C2×#14582895C211yesmaximal, characteristic, complemented
4#19137524C211yesmaximal, characteristic, complemented
5#19135523C211yesmaximal, characteristic, complemented
6#19135420C211yesmaximal, characteristic, complemented
7#19135034C211yesmaximal, characteristic, complemented
8#19135024C211yesmaximal, characteristic, complemented
9#19134918C211yesmaximal, characteristic, complemented
10#19134913C211yesmaximal, characteristic, complemented
11#19134610C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134425C211yesmaximal, characteristic, complemented
15C2×C43×#550C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20#14582971—24no—
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22#14582900—24no—
23#14582895—24no—
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×#13063236C2211yescharacteristic
39#14582792—21no—
40#14582785—21no—
41#14582779—21no—
42#14582765C2211yescharacteristic
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46C22⋊C4×Dic43—21no—
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51C22×#41×C43C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C43×#550—24no—
54C43×#550C418yescomplemented
55C2×#127×C43—21no—
56C2×#127×C43C2211yescharacteristic
57C2×#121×C43—21no—
58C2×#121×C43—21no—
59C2×#121×C43C2211yescharacteristic
60C2×#121×C43C2211yescharacteristic
61C2×C4×Q8×C43C2211yescharacteristic
62C2×C4×D4×C43—21no—
63C2×C4×D4×C43C2211yescharacteristic
64C23×Dic43—21no—
65C2×#10621877—22no—
66C2×#10621877—22no—
67C2×#10621877—41no—
68C22×C43⋊C8—22no—
69C22×C43⋊C8—22no—
70C22×C43⋊C8—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063284—22no—
76#13063284—41no—
77C2×C4⋊Dic43—22no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—41no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C4⋊(C43⋊C8)—22no—
90#13063249—22no—
91#13063249—22no—
92#13063249—22no—
93#13063249D414yescomplemented
94#13063246—22no—
95#13063246—22no—
96#13063246—22no—
97#13063246—22no—
98#13063246—41no—
99#13063246—41no—
100#13063246—41no—
101#13063246—41no—
102C22⋊(C43⋊C8)—22no—
103C22⋊(C43⋊C8)—22no—
104#13063236—22no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C2×#41×C43—22no—
111C2×#41×C43—22no—
112C2×#41×C43—22no—
113C2×#41×C43—22no—
114C2×#41×C43—22no—
115C2×#41×C43—22no—
116C2×#41×C43—41no—
117C2×#41×C43—41no—
118C2×#41×C43—41no—
119C2×#41×C43—41no—
120C2×#41×C43C2×C414yes—
121C2×#41×C43C2×C414yescomplemented
122C22×Q8×C43C2311yescharacteristic
123C22×D4×C43—21no—
124C22×D4×C43—21no—
125C22×D4×C43—21no—
126C22×D4×C43—21no—
127C22×D4×C43—21no—
128C22×D4×C43—21no—
129C22×D4×C43D411yescharacteristic
130C22×D4×C43C2311yescharacteristic
131C22×D4×C43C2311yescharacteristic
132C23×C4×C43—21no—
133C23×C4×C43—21no—
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136#127×C43—28no—
137#127×C43—22no—
138#127×C43C2×C414yescomplemented
139#121×C43—22no—
140#121×C43—22no—
141#121×C43—28no—
142#121×C43—28no—
143#121×C43C2×C414yes—
144#121×C43C2×C414yescomplemented
145C4×Q8×C43—22no—
146C4×Q8×C43C2×C414yescomplemented
147C4×D4×C43—28no—
148C4×D4×C43C2×C414yes—
149C4×D4×C43D414yes—
150C2×C4⋊C4×C43—21no—
151C2×C4⋊C4×C43D411yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43D411yescharacteristic
156C2×C22⋊C4×C43D411yescharacteristic
157C2×C42×C43—21no—
158C2×C42×C43C2311yescharacteristic
159C24×C43—21no—
160C24×C43—21no—
161C24×C43C2×D411yescharacteristic
162C24×C43C2×D411yescharacteristic
163#41×C43—28no—
164#41×C43—28no—
165#41×C43—44no—
166#41×C43—44no—
167#41×C43—44no—
168#41×C43—44no—
169#41×C43—44no—
170#41×C43—44no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43C22×C412yes—
175C2×Q8×C43C2×D412yes—
176C2×Q8×C43#4112yes—
177C2×D4×C43—24no—
178C2×D4×C43—24no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—24no—
182C2×D4×C43—24no—
183C2×D4×C43—24no—
184C2×D4×C43—24no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—41no—
194C2×D4×C43—41no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
197C2×D4×C43—42no—
198C2×D4×C43—42no—
199C2×D4×C43—42no—
200C2×D4×C43—42no—
201C2×D4×C43—81no—
202C2×D4×C43—81no—
203C2×D4×C43—81no—
204C2×D4×C43—81no—
205C2×D4×C43—81no—
206C2×D4×C43—81no—
207C2×D4×C43C22⋊C414yes—
208C2×D4×C43C22×C412yes—
209C2×D4×C43C22×C412yes—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—24no—
219C22×C4×C43—24no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—42no—
223C22×C4×C43—42no—
224C22×C4×C43—42no—
225C22×C4×C43—42no—
226C22×C4×C43C22×C412yes—
227C22×C4×C43C22×C412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D412yes—
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2411yescharacteristic
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—42no—
240C22×Dic43—42no—
241C22×Dic43—81no—
242C4⋊C4×C43—24no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43C22⋊C414yes—
245C4⋊C4×C43C22×C412yes—
246C22⋊C4×C43—24no—
247C22⋊C4×C43—24no—
248C22⋊C4×C43C22⋊C414yes—
249C22⋊C4×C43C22⋊C414yes—
250C42×C43—24no—
251C42×C43C22×C412yes—
252C42×C43C2×D412yes—
253C22⋊Dic43—42no—
254C22⋊Dic43—42no—
255C22⋊Dic43—81no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—42no—
264C4⋊Dic43C2×D412yes—
265C4×Dic43—42no—
266C4×Dic43—81no—
267#10621877—44no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—44no—
280C2×C43⋊C8C2×D412yes—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43C2×C22⋊C412yes—
308C23×C43C2×C22⋊C412yes—
309C23×C43C22×D411yescharacteristic
310Q8×C43—22no—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43C4×D414yes—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—22no—
318D4×C43—44no—
319D4×C43—48no—
320D4×C43—48no—
321D4×C43—48no—
322D4×C43—41no—
323D4×C43—41no—
324D4×C43—41no—
325D4×C43—41no—
326D4×C43—84no—
327D4×C43—84no—
328D4×C43—84no—
329C2×C4×C43—22no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—22no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—22no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—48no—
350C2×C4×C43—48no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43C2×C22⋊C412yes—
354C2×C4×C43C2×C22⋊C412yes—
355C2×C4×C43C2×C22⋊C412yes—
356C2×C4×C43C2×C22⋊C412yes—
357C2×C4×C43C23×C411yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C2×#4111yescharacteristic
361C2×C4×C43H(5,𝔽2)11yescharacteristic
362C2×C4×C43H(5,𝔽2)11yescharacteristic
363C2×Dic43—22no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43—84no—
376C43⋊C8—22no—
377C43⋊C8—41no—
378C43⋊C8—41no—
379C43⋊C8—41no—
380#22422—431nomaximal, Sylow
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43—81no—
407C22×C43—81no—
408C22×C43—81no—
409C22×C43C22×C22⋊C411yescharacteristic
410C22×C43D4211yescharacteristic
411C22×C43#54611yescharacteristic
412C22×C43#57511yescharacteristic
413C22×C43#57511yescharacteristic
414C22×C43#57611yescharacteristic
415C22×C43#57711yescharacteristic
416C4×C43—22no—
417C4×C43—22no—
418C4×C43—24no—
419C4×C43—22no—
420C4×C43—22no—
421C4×C43—42no—
422C4×C43C2×C4×D411yescharacteristic
423C4×C43#51811yescharacteristic
424C4×C43D4211yescharacteristic
425C4×C43#54611yescharacteristic
426Dic43—42no—
427Dic43—81no—
428Dic43—81no—
429Dic43—81no—
430C2×#550D4311yescharacteristic
431C2×#435—431no—
432C2×#417—431no—
433C2×#416—431no—
434#2352—431no—
435#1982—431no—
436#1961—431no—
437#1895—431no—
438#1893—431no—
439#1875—431no—
440#1874—431no—
441#1805—431no—
442#1788—431no—
443#1788—431no—
444#1763—431no—
445C2×C43—42no—
446C2×C43—42no—
447C2×C43—82no—
448C2×C43—82no—
449C2×C43D4×C22⋊C411yescharacteristic
450C2×C43#289611yescharacteristic
451C2×C43#289711yescharacteristic
452C2×C43#326811yescharacteristic
453C2×C43#327111yescharacteristic
454C2×C43#330911yescharacteristic
455C2×C43#331711yescharacteristic
456C22×#41C2×D4311yescharacteristic
457C22×#41C2×D4311yescharacteristic
458C22×M16—431no—
459C23×C8—431no—
460#550—24no—
461#550Dic4318yescomplemented
462C2×#127—21no—
463C2×#127C2×D4311yescharacteristic
464C2×#121—21no—
465C2×#121—21no—
466C2×#121C2×D4311yescharacteristic
467C2×#121C2×D4311yescharacteristic
468C2×C4×Q8C2×D4311yescharacteristic
469C2×C4×D4—21no—
470C2×C4×D4C2×D4311yescharacteristic
471C2×#117—431no—
472C22×C4⋊C4—431no—
473#435—864no—
474C2×C4⋊C8—431no—
475#417—864no—
476#416—864no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103—431no—
480C2×#103—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×#102—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×C22⋊C8—431no—
490C2×C22⋊C8—431no—
491C2×#97—431no—
492#388—861no—
493#387—861no—
494#386—861no—
495#382—431no—
496#380—431no—
497#380—431no—
498C4×C4⋊C4—431no—
499C4×C22⋊C4—861no—
500#340—431no—
501#340—431no—
502#340—431no—
503#340—431no—
504C43#2242211yescharacteristic, complemented, Sylow
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×Dic4314yes—
516C2×#41C2×Dic4314yescomplemented
517C22×Q8C22×D4311yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4C22⋊D4311yescharacteristic
525C22×D4C22×D4311yescharacteristic
526C22×D4C22×D4311yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—861no—
530C23×C4C22×D4311yescharacteristic
531C23×C4C22×D4311yescharacteristic
532C2×M16—862no—
533C2×M16—862no—
534C2×M16—1721no—
535C22×C8—431no—
536C22×C8—431no—
537C22×C8—431no—
538C22×C8—431no—
539C22×C8—862no—
540C22×C8—862no—
541C22×C8—1721no—
542#127—28no—
543#127—22no—
544#127C2×Dic4314yescomplemented
545#121—22no—
546#121—22no—
547#121—28no—
548#121—28no—
549#121C2×Dic4314yes—
550#121C2×Dic4314yescomplemented
551C4×Q8—22no—
552C4×Q8C2×Dic4314yescomplemented
553C4×D4—28no—
554C4×D4C2×Dic4314yes—
555C4×D4C22⋊D4314yes—
556#117—862no—
557#117—1721no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—862no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—1721no—
566C2×C4⋊C4C22⋊D4311yescharacteristic
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4C22⋊D4311yescharacteristic
574C2×C22⋊C4C22⋊D4311yescharacteristic
575C2×C42—21no—
576C2×C42—861no—
577C2×C42—861no—
578C2×C42C22×D4311yescharacteristic
579C4⋊C8—862no—
580#103—434no—
581#103—862no—
582#103—862no—
583#103—862no—
584#102—862no—
585#102—862no—
586#102—862no—
587#102—862no—
588#102—1721no—
589#102—1721no—
590#102—1721no—
591#102—1721no—
592C22⋊C8—862no—
593C22⋊C8—862no—
594#97—862no—
595#95—861no—
596#95—861no—
597#95—861no—
598#95—861no—
599#95—861no—
600C24—21no—
601C24—21no—
602C24C2×C22⋊D4311yescharacteristic
603C24C2×C22⋊D4311yescharacteristic
604#41—28no—
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8D4×D4312yes—
616C2×Q8#1062190012yes—
617C2×Q8C22×Dic4312yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic4314yes—
649C2×D4C22×Dic4312yes—
650C2×D4C22×Dic4312yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—3441no—
672C22×C4—1722no—
673C22×C4—1722no—
674C22×C4C22×Dic4312yes—
675C22×C4C22×Dic4312yes—
676C22×C4C2×C22⋊D4311yescharacteristic
677C22×C4C2×C22⋊D4311yescharacteristic
678C22×C4C2×C22⋊D4311yescharacteristic
679C22×C4C2×C22⋊D4311yescharacteristic
680C22×C4C2×C22⋊D4312yes—
681C22×C4C2×C22⋊D4312yes—
682C22×C4C23×D4311yescharacteristic
683M16—1724no—
684C2×C8—432no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—1724no—
697C4⋊C4—24no—
698C4⋊C4—21no—
699C4⋊C4—432no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—1722no—
708C4⋊C4C22⋊Dic4314yes—
709C4⋊C4C22×Dic4312yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—3441no—
713C22⋊C4—1722no—
714C22⋊C4—1722no—
715C22⋊C4C22⋊Dic4314yes—
716C22⋊C4C22⋊Dic4314yes—
717C42—24no—
718C42—3441no—
719C42—1722no—
720C42C22×Dic4312yes—
721C42C2×C22⋊D4312yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23C2×C22⋊Dic4312yes—
749C23C2×C22⋊Dic4312yes—
750C23C22×C22⋊D4311yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8D4×Dic4314yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—84no—
768D4—84no—
769D4—84no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—48no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—862no—
795C2×C4—3444no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4C2×C22⋊Dic4312yes—
808C2×C4C2×C22⋊Dic4312yes—
809C2×C4C2×C22⋊Dic4312yes—
810C2×C4C2×C22⋊Dic4312yes—
811C2×C4C23×Dic4311yescharacteristic
812C2×C4C2×D4×D4311yescharacteristic
813C2×C4C22×C22⋊D4311yescharacteristic
814C2×C4C2×#1062190011yescharacteristic
815C2×C4#1306337011yescharacteristic
816C2×C4#1306337011yescharacteristic
817C8—862no—
818C8—1721no—
819C8—1721no—
820C8—1721no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22C22×C22⋊Dic4311yescharacteristic
850C22D4×C22⋊D4311yescharacteristic
851C22#1458354311yescharacteristic
852C22#1458369711yescharacteristic
853C22#1458369711yescharacteristic
854C22#1458370211yescharacteristic
855C22#1458371011yescharacteristic
856C4—22no—
857C4—22no—
858C4—24no—
859C4—22no—
860C4—22no—
861C4—42no—
862C4—3441no—
863C4—3441no—
864C4—3441no—
865C4—1722no—
866C4C2×D4×Dic4311yescharacteristic
867C4#1458337411yescharacteristic
868C4D4×C22⋊D4311yescharacteristic
869C4#1458354311yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2D4×C22⋊Dic4311yescharacteristic
875C2#1914311411yescharacteristic
876C2#1914312111yescharacteristic
877C2#1914613611yescharacteristic
878C2#1914617611yescharacteristic
879C2#1914660111yescharacteristic
880C2#1914672111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#550C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC2×#550D43
hypocenterC43#22422
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#14582971C2semidirect
2. C2×#14582900C2semidirect
3. C2×#14582895C2semidirect
4. #19137524C2semidirect
5. #19135523C2semidirect
6. #19135420C2semidirect
7. #19135034C2semidirect
8. #19135024C2semidirect
9. #19134918C2semidirect
10. #19134913C2semidirect
11. #19134610C2semidirect
12. #19134535C2semidirect
13. #19134535C2semidirect
14. #19134425C2semidirect
54. C43×#550C4semidirect
93. #13063249D4semidirect
121. C2×#41×C43C2×C4semidirect
138. #127×C43C2×C4semidirect
144. #121×C43C2×C4semidirect
146. C4×Q8×C43C2×C4semidirect
461. #550Dic43semidirect
504. C43#22422semidirect
516. C2×#41C2×Dic43semidirect
544. #127C2×Dic43semidirect
550. #121C2×Dic43semidirect
552. C4×Q8C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829712
C2×#145829002
C2×#145828952
#191375242
#191355232
#191354202
#191350342
#191350242
#191349182
#191349132
#191346102
#191345352
#191344252
C2×C43×#5502
#2242243