Finite Group Databasebeta

← #25112014

Subgroups — #25112014

Order 11008.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C43⋊C8C211yesmaximal, characteristic, complemented
2C2×#14582895C211yesmaximal, characteristic, complemented
3C22×#13063246C211yesmaximal, characteristic, complemented
4#19137524C211yesmaximal, characteristic, complemented
5#19135528C211yesmaximal, characteristic, complemented
6#19135407C211yesmaximal, characteristic, complemented
7#19135024C211yesmaximal, characteristic, complemented
8#19135019C211yesmaximal, characteristic, complemented
9#19134918C211yesmaximal, characteristic, complemented
10#19134903C211yesmaximal, characteristic, complemented
11#19134605C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134526C211yesmaximal, characteristic, complemented
14C4×#13063246C211yesmaximal, characteristic, complemented
15C2×C43×#546C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic, complemented
18C2×#13063284C2211yescharacteristic, complemented
19C22×C4⋊Dic43C2211yescharacteristic
20D4×C43⋊C8—24no—
21C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
22#14582895—24no—
23C2×#13063249C2211yescharacteristic, complemented
24C2×#13063249C2211yescharacteristic, complemented
25C2×#13063249C2211yescharacteristic, complemented
26C2×#13063249C2211yescharacteristic, complemented
27C2×#13063246—24no—
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, complemented
38C2×C4×C43⋊C8C2211yescharacteristic, complemented
39#14582792—21no—
40#14582785—21no—
41#14582779—21no—
42#14582765C2211yescharacteristic, complemented
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic, complemented
45C4×C4⋊Dic43C2211yescharacteristic, complemented
46C22⋊C4×Dic43—21no—
47#14582661C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51C22×#41×C43C2211yescharacteristic
52C23×D4×C43C2211yescharacteristic
53C43×#546—24no—
54C43×#546C418yescomplemented
55C2×#124×C43C2211yescharacteristic
56C2×#123×C43—21no—
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#121×C43—21no—
59C2×#121×C43C2211yescharacteristic
60C2×#120×C43—21no—
61C2×C4×D4×C43C2211yescharacteristic
62C2×C4×D4×C43C2211yescharacteristic
63C22×C22⋊C4×C43—21no—
64C23×Dic43—21no—
65C22×C43⋊C8—22no—
66C22×C43⋊C8—22no—
67C22×C43⋊C8—22no—
68C22×C43⋊C8—22no—
69C22×C43⋊C8—41no—
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—41no—
93#13063249—41no—
94#13063246—22no—
95#13063246—22no—
96#13063246—22no—
97#13063246—22no—
98#13063246—22no—
99#13063246—41no—
100#13063246—41no—
101#13063246D414yescomplemented
102C22⋊(C43⋊C8)—22no—
103C22⋊(C43⋊C8)—22no—
104C4×C43⋊C8—22no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C25×C43—21no—
111C2×#41×C43—22no—
112C2×#41×C43—22no—
113C2×#41×C43—22no—
114C2×#41×C43—41no—
115C2×#41×C43—41no—
116C2×#41×C43C2×C414yescomplemented
117C22×Q8×C43C2311yescharacteristic
118C22×D4×C43—22no—
119C22×D4×C43—22no—
120C22×D4×C43—21no—
121C22×D4×C43—21no—
122C22×D4×C43—21no—
123C22×D4×C43—22no—
124C22×D4×C43—41no—
125C22×D4×C43—41no—
126C22×D4×C43C2×C414yes—
127C22×D4×C43D411yescharacteristic
128C22×D4×C43C2311yescharacteristic
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43—21no—
131C23×C4×C43—21no—
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134#124×C43—22no—
135#124×C43C2×C414yescomplemented
136#123×C43—28no—
137C22⋊Q8×C43—22no—
138C22⋊Q8×C43C2×C414yes—
139#121×C43—22no—
140#121×C43—28no—
141#121×C43C2×C414yescomplemented
142#120×C43—28no—
143C4×D4×C43—22no—
144C4×D4×C43C2×C414yes—
145C4×D4×C43C2×C414yescomplemented
146C4×D4×C43D414yes—
147C2×C4⋊C4×C43—21no—
148C2×C4⋊C4×C43D411yescharacteristic
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C22⋊C4×C43—21no—
151C2×C22⋊C4×C43—21no—
152C2×C22⋊C4×C43—21no—
153C2×C22⋊C4×C43—21no—
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43—28no—
156C2×C22⋊C4×C43D411yescharacteristic
157C2×C22⋊C4×C43D411yescharacteristic
158C2×C42×C43C2311yescharacteristic
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—24no—
162C24×C43—42no—
163C24×C43—42no—
164C24×C43—42no—
165C24×C43—42no—
166C24×C43—81no—
167C24×C43—81no—
168C24×C43C2×D411yescharacteristic
169C24×C43C2×D411yescharacteristic
170#41×C43—28no—
171#41×C43—44no—
172#41×C43—44no—
173#41×C43—44no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43C22×C412yes—
180C2×D4×C43—24no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—24no—
186C2×D4×C43—24no—
187C2×D4×C43—22no—
188C2×D4×C43—22no—
189C2×D4×C43—28no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—42no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
197C2×D4×C43—42no—
198C2×D4×C43—44no—
199C2×D4×C43—44no—
200C2×D4×C43—44no—
201C2×D4×C43—81no—
202C2×D4×C43—81no—
203C2×D4×C43C22⋊C414yes—
204C2×D4×C43C22×C412yes—
205C2×D4×C43C22×C412yes—
206C2×D4×C43C2×D412yes—
207C2×D4×C43#4112yes—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
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—24no—
217C22×C4×C43—24no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—42no—
221C22×C4×C43—42no—
222C22×C4×C43—81no—
223C22×C4×C43—81no—
224C22×C4×C43C22×C412yes—
225C22×C4×C43C22×C412yes—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2411yescharacteristic
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—42no—
238C22×Dic43—42no—
239C22×Dic43—81no—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43C22⋊C414yes—
243C4⋊C4×C43C22×C412yes—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—24no—
247C22⋊C4×C43—24no—
248C22⋊C4×C43—24no—
249C22⋊C4×C43C22⋊C414yes—
250C22⋊C4×C43C22⋊C414yes—
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—
267C2×C43⋊C8—21no—
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—44no—
279C2×C43⋊C8—44no—
280C2×C43⋊C8C2×D412yes—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—22no—
286C23×C43—21no—
287C23×C43—22no—
288C23×C43—21no—
289C23×C43—22no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—22no—
295C23×C43—48no—
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—48no—
307C23×C43—84no—
308C23×C43—84no—
309C23×C43—84no—
310C23×C43—84no—
311C23×C43—84no—
312C23×C43C2×C22⋊C412yes—
313C23×C43C2×C22⋊C412yes—
314C23×C43#13512yes—
315C23×C43#13512yes—
316C23×C43C22×D411yescharacteristic
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—41no—
320Q8×C43—41no—
321D4×C43—28no—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—22no—
325D4×C43—22no—
326D4×C43—22no—
327D4×C43—48no—
328D4×C43—48no—
329D4×C43—41no—
330D4×C43—41no—
331D4×C43—84no—
332D4×C43C4×D414yes—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
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—22no—
350C2×C4×C43—22no—
351C2×C4×C43—48no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—84no—
357C2×C4×C43C2×C22⋊C412yes—
358C2×C4×C43C2×C22⋊C412yes—
359C2×C4×C43C2×C22⋊C412yes—
360C2×C4×C43C2×C22⋊C412yes—
361C2×C4×C43C23×C411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C2×#4111yescharacteristic
365C2×C4×C43H(5,𝔽2)11yescharacteristic
366C2×C4×C43H(5,𝔽2)11yescharacteristic
367C2×Dic43—22no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43—41no—
376C2×Dic43—41no—
377C2×Dic43—41no—
378C2×Dic43—41no—
379C2×Dic43—84no—
380C43⋊C8—22no—
381C43⋊C8—41no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384#22414—431nomaximal, Sylow
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—24no—
392C22×C43—22no—
393C22×C43—22no—
394C22×C43—22no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—41no—
398C22×C43—42no—
399C22×C43—41no—
400C22×C43—42no—
401C22×C43—41no—
402C22×C43—42no—
403C22×C43—41no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—42no—
407C22×C43—42no—
408C22×C43—816no—
409C22×C43—81no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43—81no—
413C22×C43#41614yescomplemented
414C22×C43C22×C22⋊C411yescharacteristic
415C22×C43D4211yescharacteristic
416C22×C43#54611yescharacteristic
417C22×C43C2×#13511yescharacteristic
418C22×C43C2×#13511yescharacteristic
419C22×C43#57611yescharacteristic
420C22×C43#57711yescharacteristic
421C4×C43—22no—
422C4×C43—22no—
423C4×C43—22no—
424C4×C43—22no—
425C4×C43—42no—
426C4×C43—42no—
427C4×C43C2×C4×D411yescharacteristic
428C4×C43#51811yescharacteristic
429C4×C43D4211yescharacteristic
430C4×C43#54611yescharacteristic
431Dic43—42no—
432Dic43—81no—
433Dic43—81no—
434Dic43—81no—
435C2×#546D4311yescharacteristic
436C2×C8×D4—431no—
437C2×#416—431no—
438C22×#102—431no—
439#2352—431no—
440#1983—431no—
441#1958—431no—
442#1893—431no—
443#1892—431no—
444#1875—431no—
445#1872—431no—
446#1804—431no—
447#1788—431no—
448#1786—431no—
449C4×#102—431no—
450C2×C43—24no—
451C2×C43—42no—
452C2×C43—44no—
453C2×C43—82no—
454C2×C43D4×C22⋊C411yescharacteristic
455C2×C43C2×#41611yescharacteristic
456C2×C43#289711yescharacteristic
457C2×C43#328011yescharacteristic
458C2×C43#328211yescharacteristic
459C2×C43#329611yescharacteristic
460C2×C43#329711yescharacteristic
461C22×#41C2×D4311yescharacteristic
462C23×D4C2×D4311yescharacteristic
463C23×C8—431no—
464C23×C8—431no—
465#546—24no—
466#546Dic4318yescomplemented
467C2×#124C2×D4311yescharacteristic
468C2×#123—21no—
469C2×C22⋊Q8C2×D4311yescharacteristic
470C2×#121—21no—
471C2×#121C2×D4311yescharacteristic
472C2×#120—21no—
473C2×C4×D4C2×D4311yescharacteristic
474C2×C4×D4C2×D4311yescharacteristic
475C2×#117—431no—
476C22×C4⋊C4—431no—
477C22×C22⋊C4—21no—
478C8×D4—864no—
479C2×C4⋊C8—431no—
480#416—864no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—431no—
492C2×#102—431no—
493C2×#102—864no—
494C2×C22⋊C8—431no—
495C2×C22⋊C8—431no—
496C2×C4×C8—431no—
497#388—861no—
498#387—861no—
499#386—861no—
500#382—431no—
501#380—431no—
502#380—431no—
503C4×C4⋊C4—431no—
504C4×C22⋊C4—861no—
505#340—431no—
506#340—431no—
507#340—431no—
508#340—431no—
509C43#2241411yescharacteristic, complemented, Sylow
510C25—21no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C2×Dic4314yescomplemented
517C22×Q8C22×D4311yescharacteristic
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×Dic4314yes—
527C22×D4C22⋊D4311yescharacteristic
528C22×D4C22×D4311yescharacteristic
529C22×D4C22×D4311yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—861no—
533C23×C4C22×D4311yescharacteristic
534C23×C4C22×D4311yescharacteristic
535C22×C8—431no—
536C22×C8—431no—
537C22×C8—431no—
538C22×C8—431no—
539C22×C8—862no—
540C22×C8—862no—
541C22×C8—862no—
542C22×C8—862no—
543C22×C8—1721no—
544C22×C8—1721no—
545#124—22no—
546#124C2×Dic4314yescomplemented
547#123—28no—
548C22⋊Q8—22no—
549C22⋊Q8C2×Dic4314yes—
550#121—22no—
551#121—28no—
552#121C2×Dic4314yescomplemented
553#120—28no—
554C4×D4—22no—
555C4×D4C2×Dic4314yes—
556C4×D4C2×Dic4314yescomplemented
557C4×D4C22⋊D4314yes—
558#117—862no—
559#117—1721no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—862no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—1721no—
568C2×C4⋊C4C22⋊D4311yescharacteristic
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—28no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4C22⋊D4311yescharacteristic
580C2×C22⋊C4C22⋊D4311yescharacteristic
581C2×C42—861no—
582C2×C42—861no—
583C2×C42C22×D4311yescharacteristic
584C4⋊C8—862no—
585#103—862no—
586#103—862no—
587#103—1721no—
588#103—1721no—
589#102—434no—
590#102—862no—
591#102—862no—
592#102—862no—
593#102—862no—
594#102—862no—
595#102—1721no—
596#102—1721no—
597C22⋊C8—862no—
598C22⋊C8—862no—
599C4×C8—862no—
600#95—861no—
601#95—861no—
602#95—861no—
603#95—861no—
604#95—861no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24C2×C22⋊D4311yescharacteristic
615C24C2×C22⋊D4311yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22×Dic4312yes—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—28no—
629C2×D4—24no—
630C2×D4—24no—
631C2×D4—24no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—44no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4C22⋊Dic4314yes—
650C2×D4D4×D4312yes—
651C2×D4#1062190012yes—
652C2×D4C22×Dic4312yes—
653C2×D4C22×Dic4312yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—81no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—3441no—
675C22×C4—1722no—
676C22×C4—1722no—
677C22×C4C22×Dic4312yes—
678C22×C4C22×Dic4312yes—
679C22×C4C2×C22⋊D4311yescharacteristic
680C22×C4C2×C22⋊D4311yescharacteristic
681C22×C4C2×C22⋊D4311yescharacteristic
682C22×C4C2×C22⋊D4311yescharacteristic
683C22×C4C2×C22⋊D4312yes—
684C22×C4C2×C22⋊D4312yes—
685C22×C4C23×D4311yescharacteristic
686C2×C8—432no—
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—861no—
697C2×C8—861no—
698C2×C8—1724no—
699C2×C8—1724no—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—432no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—1722no—
711C4⋊C4C22⋊Dic4314yes—
712C4⋊C4C22×Dic4312yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—3441no—
719C22⋊C4—1722no—
720C22⋊C4—1722no—
721C22⋊C4C22⋊Dic4314yes—
722C22⋊C4C22⋊Dic4314yes—
723C42—3441no—
724C42—1722no—
725C42C22×Dic4312yes—
726C42C2×C22⋊D4312yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—21no—
739C23—22no—
740C23—22no—
741C23—48no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—48no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23C2×C22⋊Dic4312yes—
759C23C2×C22⋊Dic4312yes—
760C23#1306334512yes—
761C23#1306334512yes—
762C23C22×C22⋊D4311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—28no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—22no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4D4×Dic4314yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—84no—
803C2×C4—862no—
804C2×C4—3444no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4C2×C22⋊Dic4312yes—
817C2×C4C2×C22⋊Dic4312yes—
818C2×C4C2×C22⋊Dic4312yes—
819C2×C4C2×C22⋊Dic4312yes—
820C2×C4C23×Dic4311yescharacteristic
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C22×C22⋊D4311yescharacteristic
823C2×C4C2×#1062190011yescharacteristic
824C2×C4#1306337011yescharacteristic
825C2×C4#1306337011yescharacteristic
826C8—862no—
827C8—1721no—
828C8—1721no—
829C8—1721no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—24no—
838C22—22no—
839C22—22no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—42no—
845C22—41no—
846C22—42no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—816no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22#1458289514yescomplemented
859C22C22×C22⋊Dic4311yescharacteristic
860C22D4×C22⋊D4311yescharacteristic
861C22#1458354311yescharacteristic
862C22C2×#1306334511yescharacteristic
863C22C2×#1306334511yescharacteristic
864C22#1458370211yescharacteristic
865C22#1458371011yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—3441no—
873C4—3441no—
874C4—3441no—
875C4—1722no—
876C4C2×D4×Dic4311yescharacteristic
877C4#1458337411yescharacteristic
878C4D4×C22⋊D4311yescharacteristic
879C4#1458354311yescharacteristic
880C2—24no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊Dic4311yescharacteristic
885C2C2×#1458289511yescharacteristic
886C2#1914312111yescharacteristic
887C2#1914627611yescharacteristic
888C2#1914629811yescharacteristic
889C2#1914643011yescharacteristic
890C2#1914644511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#546C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC2×#546D43
hypocenterC43#22414
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×D4×C43⋊C8C2semidirect
2. C2×#14582895C2semidirect
3. C22×#13063246C2semidirect
4. #19137524C2semidirect
5. #19135528C2semidirect
6. #19135407C2semidirect
7. #19135024C2semidirect
8. #19135019C2semidirect
9. #19134918C2semidirect
10. #19134903C2semidirect
11. #19134605C2semidirect
12. #19134535C2semidirect
13. #19134526C2semidirect
14. C4×#13063246C2semidirect
17. C23×C43⋊C8C22semidirect
18. C2×#13063284C22semidirect
21. C2×C4⋊(C43⋊C8)C22semidirect
23. C2×#13063249C22semidirect
24. C2×#13063249C22semidirect
25. C2×#13063249C22semidirect
26. C2×#13063249C22semidirect
37. C2×C22⋊(C43⋊C8)C22semidirect
38. C2×C4×C43⋊C8C22semidirect
42. #14582765C22semidirect
44. #14582759C22semidirect
45. C4×C4⋊Dic43C22semidirect
47. #14582661C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
54. C43×#546C4semidirect
101. #13063246D4semidirect
116. C2×#41×C43C2×C4semidirect
135. #124×C43C2×C4semidirect
141. #121×C43C2×C4semidirect
145. C4×D4×C43C2×C4semidirect
413. C22×C43#416semidirect
466. #546Dic43semidirect
509. C43#22414semidirect
516. C2×#41C2×Dic43semidirect
546. #124C2×Dic43semidirect
552. #121C2×Dic43semidirect
556. C4×D4C2×Dic43semidirect
858. C22#14582895semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C43⋊C82
C2×#145828952
C22×#130632462
#191375242
#191355282
#191354072
#191350242
#191350192
#191349182
#191349032
#191346052
#191345352
#191345262
C4×#130632462
C2×C43×#5462
#2241443