Finite Group Databasebeta

← #24988945

Subgroups — #24988945

Order 11008.

630 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19133305C211yesmaximal, characteristic, complemented
2#19133226C211yesmaximal, characteristic, complemented
3#19133068C211yesmaximal, characteristic, complemented
4#19133003C211yesmaximal, characteristic, complemented
5#19132964C211yesmaximal, characteristic, complemented
6#19132964C211yesmaximal, characteristic, complemented
7C43×#3564C211yesmaximal, characteristic
8#14582956C2211yescharacteristic
9#14582956C2211yescharacteristic
10#14582952C2211yescharacteristic
11#14582952C2211yescharacteristic
12#14582648—21no—
13#14582645—21no—
14#14582641—21no—
15#14582639—21no—
16Q8⋊(C43⋊C8)—21no—
17Q8⋊(C43⋊C8)—21no—
18Q8⋊(C43⋊C8)—21no—
19D4⋊(C43⋊C8)—21no—
20#14582625—21no—
21#14582625—21no—
22#14582623—21no—
23#14582623—21no—
24C43×#563—21no—
25C43×#563—21no—
26C43×#556—21no—
27C43×#554—21no—
28C43×#552—21no—
29C43×#552—21no—
30C43×#551—21no—
31C43×#551—21no—
32C43×#544C411yescharacteristic
33C43×#543C411yescharacteristic
34C43×#542—21no—
35C43×#541—21no—
36C43×#541—21no—
37C43×#539—21no—
38C43×#539C411yescharacteristic
39C43×#538C411yescharacteristic
40C43×#533C2211yescharacteristic
41C43×#529C2211yescharacteristic
42C2×#126×C43C2211yescharacteristic
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51#13063236—21no—
52#13063236—21no—
53C4×C43⋊C8—21no—
54C4×C43⋊C8—21no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43D411yescharacteristic
59C4⋊Q8×C43D411yescharacteristic
60#126×C43—21no—
61#126×C43—21no—
62#126×C43—21no—
63#126×C43—21no—
64#126×C43—21no—
65#126×C43—21no—
66#126×C43—21no—
67#126×C43—21no—
68#126×C43—21no—
69#126×C43—21no—
70#126×C43—21no—
71#126×C43—21no—
72#126×C43—21no—
73#125×C43—21no—
74#125×C43—21no—
75#125×C43—21no—
76#125×C43—21no—
77#125×C43—21no—
78#125×C43—21no—
79#125×C43—21no—
80#125×C43—21no—
81#125×C43—21no—
82#125×C43D411yescharacteristic
83#124×C43—21no—
84#124×C43—21no—
85#124×C43—21no—
86#124×C43D411yescharacteristic
87#123×C43—21no—
88#123×C43—21no—
89#123×C43—21no—
90#123×C43—21no—
91#123×C43—21no—
92#123×C43—21no—
93#123×C43—21no—
94#123×C43—21no—
95C22⋊Q8×C43—21no—
96C22⋊Q8×C43—21no—
97C22⋊Q8×C43—21no—
98C22⋊Q8×C43—21no—
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43—21no—
101C22⋊Q8×C43—21no—
102C22⋊Q8×C43—21no—
103C22⋊Q8×C43—21no—
104C22⋊Q8×C43—21no—
105C22⋊Q8×C43—21no—
106C22⋊Q8×C43—21no—
107C22⋊Q8×C43—21no—
108C22⋊Q8×C43—21no—
109C22⋊Q8×C43C2×C411yescharacteristic
110C22⋊Q8×C43C2×C411yescharacteristic
111C22⋊Q8×C43C2×C411yescharacteristic
112#121×C43—21no—
113#121×C43C2×C411yescharacteristic
114#120×C43—21no—
115C4×Q8×C43—21no—
116C4×Q8×C43—21no—
117C4×Q8×C43—21no—
118C4×Q8×C43D411yescharacteristic
119C4×Q8×C43D411yescharacteristic
120C4×Q8×C43D411yescharacteristic
121C4×D4×C43—21no—
122C4×D4×C43—21no—
123C4×D4×C43—21no—
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43D411yescharacteristic
127#117×C43—21no—
128#117×C43—21no—
129#117×C43—21no—
130#117×C43—21no—
131#117×C43—21no—
132#117×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2×C411yescharacteristic
135C2×C4⋊C4×C43D411yescharacteristic
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43C2×C411yescharacteristic
139C2×C22⋊C4×C43D411yescharacteristic
140C2×C22⋊C4×C43D411yescharacteristic
141C2×C42×C43C2311yescharacteristic
142C24×C43C22⋊C411yescharacteristic
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C22⋊C411yescharacteristic
147C2×Q8×C43C22⋊C411yescharacteristic
148C2×Q8×C43C22⋊C411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43C22⋊C411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C22⋊C411yescharacteristic
159C22×C4×C43C22⋊C411yescharacteristic
160C22×C4×C43C22⋊C411yescharacteristic
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43C22⋊C411yescharacteristic
194C4⋊C4×C43C22⋊C411yescharacteristic
195C4⋊C4×C43C22⋊C411yescharacteristic
196C4⋊C4×C43C22⋊C411yescharacteristic
197C22⋊C4×C43—21no—
198C22⋊C4×C43—21no—
199C22⋊C4×C43—21no—
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—21no—
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43—21no—
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—21no—
217C22⋊C4×C43—21no—
218C42×C43—21no—
219C42×C43—21no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43—21no—
223C42×C43—21no—
224C42×C43—21no—
225C42×C43C2×D411yescharacteristic
226C42×C43C2×D411yescharacteristic
227C42×C43C2×D411yescharacteristic
228C42×C43C2×D411yescharacteristic
229C2×C43⋊C8—41no—
230C2×C43⋊C8—41no—
231C2×C43⋊C8—41no—
232C2×C43⋊C8—41no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43C2×C22⋊C411yescharacteristic
239Q8×C43—41no—
240Q8×C43—41no—
241Q8×C43—41no—
242Q8×C43—81no—
243Q8×C43—81no—
244Q8×C43—81no—
245D4×C43—41no—
246D4×C43—42no—
247D4×C43—81no—
248D4×C43—81no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—81no—
266C2×C4×C43—81no—
267C2×C4×C43—81no—
268C2×C4×C43—81no—
269C2×C4×C43—81no—
270C2×C4×C43C2×C22⋊C411yescharacteristic
271C2×C4×C43C2×C22⋊C411yescharacteristic
272C2×C4×C43#12011yescharacteristic
273C2×C4×C43#12011yescharacteristic
274C2×C4×C43#12011yescharacteristic
275C2×C4×C43#12011yescharacteristic
276C43⋊C8—81no—
277C43⋊C8—81no—
278C43⋊C8—81no—
279C43⋊C8—81no—
280#8490—431nomaximal, Sylow
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—161no—
291C22×C43#37911yescharacteristic
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—41no—
308#3564D4311yescharacteristic
309#1554—431no—
310#1535—431no—
311#1497—431no—
312#1482—431no—
313#1473—431no—
314#1473—431no—
315C2×C43—41no—
316C2×C43—81no—
317C2×C43—81no—
318C2×C43#179111yescharacteristic
319C2×C43#179411yescharacteristic
320C2×C43#179611yescharacteristic
321#563—21no—
322#563—21no—
323#556—21no—
324#554—21no—
325#552—21no—
326#552—21no—
327#551—21no—
328#551—21no—
329#544Dic4311yescharacteristic
330#543Dic4311yescharacteristic
331#542—21no—
332#541—21no—
333#541—21no—
334#539—21no—
335#539Dic4311yescharacteristic
336#538Dic4311yescharacteristic
337#533C2×D4311yescharacteristic
338#529C2×D4311yescharacteristic
339C2×#126C2×D4311yescharacteristic
340#432—431no—
341#432—431no—
342#431—431no—
343#431—431no—
344#333—861no—
345#332—861no—
346#330—861no—
347#329—861no—
348Q8⋊C8—861no—
349Q8⋊C8—861no—
350Q8⋊C8—861no—
351D4⋊C8—861no—
352#324—861no—
353#324—861no—
354#323—861no—
355#323—861no—
356C43#849011yescharacteristic, complemented, Sylow
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8C22⋊D4311yescharacteristic
361C4⋊Q8C22⋊D4311yescharacteristic
362#126—21no—
363#126—21no—
364#126—21no—
365#126—21no—
366#126—21no—
367#126—21no—
368#126—21no—
369#126—21no—
370#126—21no—
371#126—21no—
372#126—21no—
373#126—21no—
374#126—21no—
375#125—21no—
376#125—21no—
377#125—21no—
378#125—21no—
379#125—21no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125—21no—
384#125C22⋊D4311yescharacteristic
385#124—21no—
386#124—21no—
387#124—21no—
388#124C22⋊D4311yescharacteristic
389#123—21no—
390#123—21no—
391#123—21no—
392#123—21no—
393#123—21no—
394#123—21no—
395#123—21no—
396#123—21no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8C2×Dic4311yescharacteristic
412C22⋊Q8C2×Dic4311yescharacteristic
413C22⋊Q8C2×Dic4311yescharacteristic
414#121—21no—
415#121C2×Dic4311yescharacteristic
416#120—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8C22⋊D4311yescharacteristic
421C4×Q8C22⋊D4311yescharacteristic
422C4×Q8C22⋊D4311yescharacteristic
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4C22⋊D4311yescharacteristic
429#117—21no—
430#117—21no—
431#117—21no—
432#117—21no—
433#117—21no—
434#117—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4C2×Dic4311yescharacteristic
437C2×C4⋊C4C22⋊D4311yescharacteristic
438C2×C4⋊C4C22⋊D4311yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4C2×Dic4311yescharacteristic
441C2×C22⋊C4C22⋊D4311yescharacteristic
442C2×C22⋊C4C22⋊D4311yescharacteristic
443C2×C42C22×D4311yescharacteristic
444C4⋊C8—861no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447C4⋊C8—861no—
448C22⋊C8—861no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452#97—861no—
453#97—861no—
454C4×C8—861no—
455C4×C8—861no—
456C24C22⋊Dic4311yescharacteristic
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C22⋊Dic4311yescharacteristic
461C2×Q8C22⋊Dic4311yescharacteristic
462C2×Q8C22⋊Dic4311yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4C22⋊Dic4311yescharacteristic
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4C22⋊Dic4311yescharacteristic
473C22×C4C22⋊Dic4311yescharacteristic
474C22×C4C22⋊Dic4311yescharacteristic
475C22×C4C22×Dic4311yescharacteristic
476C22×C4C2×C22⋊D4311yescharacteristic
477C22×C4C2×C22⋊D4311yescharacteristic
478C2×C8—1721no—
479C2×C8—1721no—
480C2×C8—1721no—
481C2×C8—1721no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4C22⋊Dic4311yescharacteristic
512C4⋊C4C22⋊Dic4311yescharacteristic
513C4⋊C4C22⋊Dic4311yescharacteristic
514C4⋊C4C22⋊Dic4311yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42C2×C22⋊D4311yescharacteristic
544C42C2×C22⋊D4311yescharacteristic
545C42C2×C22⋊D4311yescharacteristic
546C42C2×C22⋊D4311yescharacteristic
547C23—21no—
548C23—21no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C2×C22⋊Dic4311yescharacteristic
553Q8—41no—
554Q8—41no—
555Q8—41no—
556Q8—81no—
557Q8—81no—
558Q8—81no—
559D4—41no—
560D4—42no—
561D4—81no—
562D4—81no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—81no—
583C2×C4—81no—
584C2×C4C2×C22⋊Dic4311yescharacteristic
585C2×C4C2×C22⋊Dic4311yescharacteristic
586C2×C4#1306329411yescharacteristic
587C2×C4#1306329411yescharacteristic
588C2×C4#1306329411yescharacteristic
589C2×C4#1306329411yescharacteristic
590C8—3441no—
591C8—3441no—
592C8—3441no—
593C8—3441no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—161no—
604C22#1458275511yescharacteristic
605C4—21no—
606C4—21no—
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C2—41no—
622C2—81no—
623C2—81no—
624C2#1913454611yescharacteristic
625C2#1913455911yescharacteristic
626C2#1913457011yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3564C2
socleC22×C43#379
prime radicalC43×#538C4
cosocleC2×C42×C43C23
hypercenter#3564D43
hypocenterC43#8490
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3564

Complements

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

NH ≅ G/Ntype
1. #19133305C2semidirect
2. #19133226C2semidirect
3. #19133068C2semidirect
4. #19133003C2semidirect
5. #19132964C2semidirect
6. #19132964C2semidirect
356. C43#8490semidirect

Maximal subgroups

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

subgroupindex
#191333052
#191332262
#191330682
#191330032
#191329642
C43×#35642
#849043