Finite Group Databasebeta

← #25112007

Subgroups — #25112007

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×#14583537C211yesmaximal, characteristic
2C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
3C2×#14582895C211yesmaximal, characteristic, complemented
4C2×#102×D43C211yesmaximal, characteristic, complemented
5#19137517C211yesmaximal, characteristic, complemented
6#19135524C211yesmaximal, characteristic, complemented
7#19135403C211yesmaximal, characteristic, complemented
8#19135021C211yesmaximal, characteristic, complemented
9#19135015C211yesmaximal, characteristic, complemented
10#19134915C211yesmaximal, characteristic, complemented
11#19134899C211yesmaximal, characteristic, complemented
12#19134603C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic, complemented
18C22×C8×D43C2211yescharacteristic
19#14583537—24no—
20#14583537C418yescomplemented
21C2×#13063314C2211yescharacteristic
22C2×#13063308—21no—
23C2×#13063301C2211yescharacteristic
24C2×#13063299C2211yescharacteristic
25C2×#13063297—21no—
26C2×#13063293—21no—
27C2×D4×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063284C2211yescharacteristic, complemented
30C2×C4⋊C4×D43C2211yescharacteristic
31C22×(C2×D43)⋊C4—21no—
32(C22⋊D43)⋊C8—24no—
33C2×Dic43⋊C8C2211yescharacteristic, complemented
34#14582895—24no—
35C2×#13063249C2211yescharacteristic, complemented
36C2×#13063249C2211yescharacteristic, complemented
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43#102×D43—24no—
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic, complemented
46#14582787—21no—
47#14582781—21no—
48#14582775—21no—
49#14582764C2211yescharacteristic, complemented
50#14582756C2211yescharacteristic
51C4⋊C4×Dic43C2211yescharacteristic, complemented
52#14582746—21no—
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C22×#41×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic, complemented
59C2×#103×C43C2211yescharacteristic, complemented
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic, complemented
63C43×#380C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C22×C22⋊D43D411yescharacteristic
69C2×D4×D43—22no—
70C2×D4×D43—22no—
71C2×D4×D43—22no—
72C2×D4×D43—41no—
73C2×D4×D43—41no—
74C2×D4×D43C2×C414yes—
75C23×Dic43—21no—
76C22×C4×D43—21no—
77C22×C4×D43C2311yescharacteristic
78C22×C43⋊C8—22no—
79C22×C43⋊C8—22no—
80C22×C43⋊C8—41no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C2×C8×D43—22no—
84C2×C8×D43—22no—
85C2×C8×D43—41no—
86#13063314—22no—
87#13063314C2×C414yescomplemented
88#13063308—28no—
89#13063301—22no—
90#13063301C2×C414yes—
91#13063299—22no—
92#13063299C2×C414yescomplemented
93#13063297—28no—
94#13063293—28no—
95D4×Dic43—22no—
96D4×Dic43C2×C414yescomplemented
97C4×C22⋊D43C2×C414yes—
98C4×C22⋊D43D414yes—
99#13063284—22no—
100#13063284—41no—
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4D411yescharacteristic
107C4⋊C4×D43—22no—
108C4⋊C4×D43—41no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43D411yescharacteristic
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—28no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4D411yescharacteristic
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43C2311yescharacteristic
122Dic43⋊C8—22no—
123#13063249—22no—
124#13063249—22no—
125#13063247—22no—
126#13063247—41no—
127#13063246—22no—
128#13063246D414yescomplemented
129#13063245—22no—
130#13063245—41no—
131(C2×D43)⋊C8—22no—
132C8×Dic43—22no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C2×#41×C43—22no—
138C2×#41×C43—22no—
139C2×#41×C43—22no—
140C2×#41×C43—41no—
141C2×#41×C43—41no—
142C2×#41×C43C2×C414yescomplemented
143C22×Q8×C43C2311yescharacteristic
144C22×D4×C43—21no—
145C22×D4×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—41no—
154#103×C43—41no—
155#102×C43—22no—
156#102×C43—22no—
157C22⋊C8×C43—22no—
158#95×C43—21no—
159C24×C43—21no—
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C23×D43—24no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—81no—
168C23×D43—81no—
169C23×D43C2×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—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—24no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43C22×C412yes—
187C2×D4×C43C2×D412yes—
188C2×D4×C43#4112yes—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—24no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—42no—
198C22×C4×C43—42no—
199C22×C4×C43C22×C412yes—
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—22no—
206C2×C22⋊D43—22no—
207C2×C22⋊D43—42no—
208C2×C22⋊D43—42no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43—81no—
211C2×C22⋊D43C22⋊C414yes—
212C22×Dic43—24no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—81no—
217C22×Dic43—81no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221D4×D43—28no—
222D4×D43—44no—
223D4×D43—44no—
224D4×D43—44no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—21no—
230C2×D172C22×C412yes—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—42no—
236C2×C4×D43—42no—
237C2×C4×D43—81no—
238C2×C4×D43C22×C412yes—
239C2×C4×D43C2×D412yes—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C22⋊C4×C43—81no—
251C22⋊Dic43—24no—
252C22⋊Dic43—42no—
253C22⋊Dic43C22⋊C414yes—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—42no—
259(C2×D43)⋊C4C22⋊C414yes—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43C22×C412yes—
265C4⋊Dic43C2×D412yes—
266Dic43⋊C4—24no—
267Dic43⋊C4—42no—
268Dic43⋊C4C22⋊C414yes—
269C4×Dic43—42no—
270C4×Dic43—81no—
271C4×Dic43C22×C412yes—
272C4×Dic43C2×D412yes—
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⋊C8C2×D412yes—
280C8×D43—44no—
281C23×C43—22no—
282C23×C43—21no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43C2×C22⋊C412yes—
295C23×C43C22×D411yescharacteristic
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—22no—
301C22×D43—48no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—48no—
309C22×D43—84no—
310C22×D43—84no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43C2×C22⋊C412yes—
315C22×D43#13512yes—
316C22×D43#13512yes—
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—41no—
320Q8×C43—41no—
321D4×C43—22no—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—48no—
325D4×C43C4×D414yes—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—48no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43C2×C22⋊C412yes—
343C2×C4×C43C23×C411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C2×#4111yescharacteristic
347C2×C4×C43H(5,𝔽2)11yescharacteristic
348C2×C4×C43H(5,𝔽2)11yescharacteristic
349C22⋊D43—28no—
350C22⋊D43—48no—
351C22⋊D43—84no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—84no—
368C2×Dic43C2×C22⋊C412yes—
369C2×Dic43C2×C22⋊C412yes—
370C2×Dic43C2×C22⋊C412yes—
371D172—22no—
372D172—22no—
373D172—41no—
374D172—41no—
375C4×D43—22no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—84no—
380C8×C43—41no—
381C8×C43—41no—
382C43⋊C8—22no—
383C43⋊C8—41no—
384#22414—431nomaximal, Sylow
385C22×C43—24no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—42no—
392C22×C43—41no—
393C22×C43—42no—
394C22×C43—41no—
395C22×C43—42no—
396C22×C43—41no—
397C22×C43—42no—
398C22×C43—41no—
399C22×C43C22×C22⋊C411yescharacteristic
400C22×C43D4211yescharacteristic
401C22×C43#54611yescharacteristic
402C22×C43C2×#13511yescharacteristic
403C22×C43C2×#13511yescharacteristic
404C22×C43#57611yescharacteristic
405C22×C43#57711yescharacteristic
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—22no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—816no—
416C2×D43—81no—
417C2×D43—81no—
418C2×D43—81no—
419C2×D43—81no—
420C2×D43#41614yescomplemented
421C4×C43—22no—
422C4×C43—42no—
423C4×C43—81no—
424C4×C43—81no—
425C4×C43C2×C4×D411yescharacteristic
426C4×C43#51811yescharacteristic
427C4×C43D4211yescharacteristic
428C4×C43#54611yescharacteristic
429Dic43—22no—
430Dic43—22no—
431Dic43—22no—
432Dic43—42no—
433Dic43—42no—
434Dic43—81no—
435C2×#546—431no—
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#1788D4311yescharacteristic, complemented
448#1786—431no—
449C4×#102—431no—
450C2×C43—44no—
451C2×C43—42no—
452C2×C43D4×C22⋊C411yescharacteristic
453C2×C43C2×#41611yescharacteristic
454C2×C43#289711yescharacteristic
455C2×C43#328011yescharacteristic
456C2×C43#328211yescharacteristic
457C2×C43#329611yescharacteristic
458C2×C43#329711yescharacteristic
459D43—24no—
460D43—82no—
461C22×#41C2×D4311yescharacteristic
462C23×D4—431no—
463C23×C8—431no—
464C23×C8—431no—
465#546—438no—
466#546—864no—
467C2×#124—431no—
468C2×#123—861no—
469C2×C22⋊Q8—431no—
470C2×#121—431no—
471C2×#121—861no—
472C2×#120—861no—
473C2×C4×D4—431no—
474C2×C4×D4—431no—
475C2×#117—431no—
476C22×C4⋊C4—431no—
477C22×C22⋊C4—861no—
478C8×D4—864no—
479C2×C4⋊C8—431no—
480#416—864no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103C2×D4311yescharacteristic, complemented
484C2×#103C2×D4311yescharacteristic, complemented
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—864no—
492C2×#102C2×D4311yescharacteristic
493C2×#102C2×D4311yescharacteristic
494C2×C22⋊C8—431no—
495C2×C22⋊C8C2×D4311yescharacteristic, complemented
496C2×C4×C8—431no—
497#388—861no—
498#387—861no—
499#386—861no—
500#382—431no—
501#380—431no—
502#380C2×D4311yescharacteristic, complemented
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—861no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C4×D4314yescomplemented
517C22×Q8C22×D4311yescharacteristic
518C22×D4—21no—
519C22×D4—431no—
520C22×D4—434no—
521C22×D4—431no—
522C22×D4—862no—
523C22×D4—861no—
524C22×D4—862no—
525C22×D4—862no—
526C22×D4—861no—
527C22×D4—1721no—
528C22×D4—1721no—
529C22×D4C22×D4311yescharacteristic
530C23×C4—21no—
531C23×C4—431no—
532C23×C4—861no—
533C23×C4—861no—
534C23×C4C22×D4311yescharacteristic
535C22×C8—431no—
536C22×C8—431no—
537C22×C8—862no—
538C22×C8—862no—
539C22×C8—862no—
540C22×C8—862no—
541C22×C8—1721no—
542C22×C8—1721no—
543C22×C8C22×D4311yescharacteristic
544C22×C8C22×D4311yescharacteristic
545#124—434no—
546#124—862no—
547#123—868no—
548C22⋊Q8—434no—
549C22⋊Q8—862no—
550#121—434no—
551#121—868no—
552#121—862no—
553#120—868no—
554C4×D4—434no—
555C4×D4—434no—
556C4×D4—434no—
557C4×D4—862no—
558#117—862no—
559#117—1721no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—862no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—1721no—
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—868no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C42—431no—
582C2×C42—861no—
583C2×C42—861no—
584C4⋊C8—862no—
585#103—41no—
586#103—41no—
587#103—862no—
588#103—862no—
589#102—22no—
590#102—22no—
591#102—434no—
592#102—862no—
593#102—862no—
594#102—862no—
595#102—1721no—
596#102—1721no—
597C22⋊C8—22no—
598C22⋊C8—862no—
599C4×C8—862no—
600#95—21no—
601#95—861no—
602#95—861no—
603#95—861no—
604#95—861no—
605C24—21no—
606C24—431no—
607C24—864no—
608C24—861no—
609C24—3441no—
610C24—3441no—
611C24—1722no—
612C24—1722no—
613C24—1722no—
614C24—1722no—
615C24D4×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×Q8C2×C4×D4312yes—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—434no—
633C2×D4—432no—
634C2×D4—864no—
635C2×D4—862no—
636C2×D4—862no—
637C2×D4—868no—
638C2×D4—864no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—3441no—
645C2×D4—3441no—
646C2×D4—1724no—
647C2×D4—1724no—
648C2×D4—1724no—
649C2×D4—1722no—
650C2×D4—1722no—
651C2×D4C2×C4×D4312yes—
652C2×D4D4×D4312yes—
653C2×D4#1062190012yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—432no—
668C22×C4—432no—
669C22×C4—864no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—3441no—
678C22×C4—3441no—
679C22×C4—3441no—
680C22×C4—1722no—
681C22×C4—1722no—
682C22×C4C2×C4×D4312yes—
683C22×C4D4×D4311yescharacteristic
684C22×C4D4×D4312yes—
685C22×C4C23×D4311yescharacteristic
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—432no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—1724no—
699C2×C8—1724no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—434no—
705C4⋊C4—432no—
706C4⋊C4—432no—
707C4⋊C4—864no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4—1722no—
713C22⋊C4—81no—
714C22⋊C4—434no—
715C22⋊C4—434no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—864no—
721C22⋊C4—1722no—
722C22⋊C4—1722no—
723C42—432no—
724C42—432no—
725C42—3441no—
726C42—1722no—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—432no—
741C23—432no—
742C23—432no—
743C23—861no—
744C23—861no—
745C23—861no—
746C23—861no—
747C23—862no—
748C23—3444no—
749C23—3444no—
750C23—3444no—
751C23—3444no—
752C23—3444no—
753C23—1728no—
754C23—1728no—
755C23—1721no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23—1721no—
761C23C22⋊C4×D4312yes—
762C23C2×D4×D4311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—48no—
771D4—868no—
772D4—862no—
773D4—862no—
774D4—3444no—
775D4—1728no—
776D4—1721no—
777D4—1721no—
778D4(C22⋊D43)⋊C414yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—48no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—432no—
796C2×C4—432no—
797C2×C4—432no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—3444no—
811C2×C4—3444no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4C22⋊C4×D4312yes—
820C2×C4C22×C4×D4311yescharacteristic
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C2×D4×D4311yescharacteristic
823C2×C4C2×#1062190011yescharacteristic
824C2×C4#1306337011yescharacteristic
825C2×C4#1306337011yescharacteristic
826C8—41no—
827C8—41no—
828C8—862no—
829C8—1721no—
830C22—22no—
831C22—24no—
832C22—22no—
833C22—22no—
834C22—41no—
835C22—42no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—434no—
845C22—862no—
846C22—862no—
847C22—862no—
848C22—862no—
849C22—862no—
850C22—862no—
851C22—34416no—
852C22—3441no—
853C22—3441no—
854C22—3441no—
855C22—3441no—
856C22—1722no—
857C22—1722no—
858C22—1722no—
859C22C2×C22⋊C4×D4311yescharacteristic
860C22#1458353111yescharacteristic
861C22#1458353611yescharacteristic
862C22#135×D4311yescharacteristic
863C22#135×D4311yescharacteristic
864C22#1458370311yescharacteristic
865C22#1458370811yescharacteristic
866C4—22no—
867C4—42no—
868C4—81no—
869C4—81no—
870C4—862no—
871C4—862no—
872C4—862no—
873C4—3441no—
874C4—1722no—
875C4—1722no—
876C4C2×(C22⋊D43)⋊C411yescharacteristic
877C4#1458337211yescharacteristic
878C4#1458353111yescharacteristic
879C4#1458353611yescharacteristic
880C2—42no—
881C2—44no—
882C2—864no—
883C2—3442no—
884C2#1913741111yescharacteristic
885C2#416×D4311yescharacteristic
886C2#1914311911yescharacteristic
887C2#1914627811yescharacteristic
888C2#1914630011yescharacteristic
889C2#1914642311yescharacteristic
890C2#1914643811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583537C2
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#22414
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D43)⋊C8C2semidirect
3. C2×#14582895C2semidirect
4. C2×#102×D43C2semidirect
5. #19137517C2semidirect
6. #19135524C2semidirect
7. #19135403C2semidirect
8. #19135021C2semidirect
9. #19135015C2semidirect
10. #19134915C2semidirect
11. #19134899C2semidirect
12. #19134603C2semidirect
13. #19134524C2semidirect
14. #102×Dic43C2semidirect
15. C43×#1788C2semidirect
17. C23×C43⋊C8C22semidirect
20. #14583537C4semidirect
29. C2×#13063284C22semidirect
33. C2×Dic43⋊C8C22semidirect
35. C2×#13063249C22semidirect
36. C2×#13063249C22semidirect
45. C2×C8×Dic43C22semidirect
49. #14582764C22semidirect
51. C4⋊C4×Dic43C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
58. C2×#103×C43C22semidirect
59. C2×#103×C43C22semidirect
62. C2×C22⋊C8×C43C22semidirect
63. C43×#380C22semidirect
87. #13063314C2×C4semidirect
92. #13063299C2×C4semidirect
96. D4×Dic43C2×C4semidirect
128. #13063246D4semidirect
142. C2×#41×C43C2×C4semidirect
420. C2×D43#416semidirect
447. #1788D43semidirect
483. C2×#103C2×D43semidirect
484. C2×#103C2×D43semidirect
495. C2×C22⋊C8C2×D43semidirect
502. #380C2×D43semidirect
509. C43#22414semidirect
516. C2×#41C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835372
C2×(C22⋊D43)⋊C82
C2×#145828952
C2×#102×D432
#191375172
#191355242
#191354032
#191350212
#191350152
#191349152
#191348992
#191346032
#191345242
#102×Dic432
C43×#17882
#2241443