Finite Group Databasebeta

← #14737474

Subgroups — #14737474

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079953C211yesmaximal, characteristic
2#13079357C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic
4#13068193C211yesmaximal, characteristic, complemented
5#13068161C211yesmaximal, characteristic, complemented
6#13068124C211yesmaximal, characteristic, complemented
7#13068108C211yesmaximal, characteristic, complemented
8#13068076C211yesmaximal, characteristic, complemented
9#13068044C211yesmaximal, characteristic, complemented
10#13067993C211yesmaximal, characteristic, complemented
11#13067979C211yesmaximal, characteristic, complemented
12#13067369C211yesmaximal, characteristic, complemented
13#13067280C211yesmaximal, characteristic, complemented
14#13067273C211yesmaximal, characteristic, complemented
15C11×#3233C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#499—21no—
20C11×#488—21no—
21C11×#485—21no—
22C11×#482—21no—
23C11×#477C2211yescharacteristic
24C11×#476C2211yescharacteristic
25C11×#475C2211yescharacteristic
26C11×#474C2211yescharacteristic
27C11×#431C2211yescharacteristic
28#10622706C2211yescharacteristic
29#10622705C2211yescharacteristic
30#10622694C2211yescharacteristic
31#10622692C2211yescharacteristic
32#10622676—21no—
33#10622667—21no—
34#10622665—21no—
35#10622665—21no—
36#10622664—21no—
37#10622654—21no—
38#10622644C2211yescharacteristic
39#10622643—21no—
40#10622643—21no—
41#10622637C2211yescharacteristic
42Q8×C11⋊C8C2211yescharacteristic
43#10622633C2211yescharacteristic
44#10622632C2211yescharacteristic
45#10622625—21no—
46#10622625C2211yescharacteristic
47#10622624—21no—
48D4×C11⋊C8C2211yescharacteristic
49#10622620C2211yescharacteristic
50#10622613—21no—
51#10622610—21no—
52#10622538C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C11×C4⋊Q8C2311yescharacteristic
68C11×C4⋊Q8C2311yescharacteristic
69C11×#126—21no—
70C11×#125—21no—
71C11×#125D411yescharacteristic
72C11×#124D411yescharacteristic
73C11×#123—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8D411yescharacteristic
77C11×#121D411yescharacteristic
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11C2311yescharacteristic
83C11×#117—21no—
84C11×#117—21no—
85C2×C42×C11C2311yescharacteristic
86C2×#4326—21no—
87C2×#4326—21no—
88C2×#4326—21no—
89C2×#4324—21no—
90#66979—21no—
91#66977—21no—
92#66977—21no—
93C2×#4318—21no—
94C2×#4318D411yescharacteristic
95C2×#4318D411yescharacteristic
96C22×C11⋊C8—21no—
97C22×C11⋊C8—21no—
98#66923—21no—
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101C4×Dic22—21no—
102C4×Dic22—21no—
103C11×#107—21no—
104C11×#107—21no—
105C11×#106—21no—
106C11×#106—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103—21no—
110C11×#103—21no—
111C11×#102—21no—
112C11×#102—21no—
113C11×C22⋊C8—21no—
114C4×C8×C11—21no—
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66896—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66874—21no—
123#66874—21no—
124#66874—21no—
125#66874—21no—
126#66872—21no—
127#66872—21no—
128#66872—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19249—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4C2×D411yescharacteristic
169C11×C4⋊C4C2×D411yescharacteristic
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—41no—
176C42×C11—21no—
177C42×C11—41no—
178C42×C11C2×D411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11#4111yescharacteristic
181C42×C11C2411yescharacteristic
182C22⋊Dic11—41no—
183#4326—42no—
184#4326—42no—
185#4326—81no—
186#4324—81no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191Dic11⋊C4—41no—
192Dic11⋊C4—41no—
193C4×Dic11—41no—
194#4318—22no—
195#4318—41no—
196#4318—42no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—42no—
202C2×C11⋊C8—81no—
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207#3248—111no—
208#3233D1111yescharacteristic
209#3185—111no—
210#2969—111no—
211#1703—111no—
212#1699—111no—
213#1692—111no—
214#1690—111no—
215#1684—111no—
216#1680—111no—
217#1671—111no—
218#1669—111no—
219#1565—111no—
220#1544—111no—
221#1542—111no—
222C23×C11—21no—
223C23×C11#12111yescharacteristic
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—81no—
229D4×C11—21no—
230D4×C11—21no—
231D4×C11—81no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×Dic11—41no—
251C2×Dic11—41no—
252Dic22—41no—
253Dic22—41no—
254Dic22—41no—
255Dic22—41no—
256C8×C11—41no—
257C8×C11—41no—
258C11⋊C8—21no—
259C11⋊C8—21no—
260C11⋊C8—21no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265C11⋊C8#13512yes—
266#533—111no—
267#533C2×D1111yescharacteristic
268#529C2×D1111yescharacteristic
269#499—21no—
270#498—111no—
271#494—111no—
272#488—21no—
273#487—111no—
274#487—111no—
275#485—21no—
276#482—21no—
277#479—221no—
278#477C2×D1111yescharacteristic
279#476C2×D1111yescharacteristic
280#475—111no—
281#475C2×D1111yescharacteristic
282#474—111no—
283#474C2×D1111yescharacteristic
284#470—221no—
285#470—221no—
286#467—221no—
287#465—221no—
288#464—221no—
289#462—111no—
290#461—111no—
291#446—111no—
292C8×Q8—111no—
293#441—221no—
294#441—221no—
295#436—111no—
296#436—221no—
297#435—221no—
298C8×D4—111no—
299#433—221no—
300#431—111no—
301#431C2×D1111yescharacteristic
302C2×C4⋊C8—111no—
303#405—221no—
304C4×M16—111no—
305#335—111no—
306#335—111no—
307#334—111no—
308#334—111no—
309#333—111no—
310#333—111no—
311#332—111no—
312#332—111no—
313#332—111no—
314#332—111no—
315#332—111no—
316#332—111no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11C2×#12111yescharacteristic
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11C2×#13511yescharacteristic
334C4×C11#57511yescharacteristic
335C4×C11#57711yescharacteristic
336C4×C11#57811yescharacteristic
337Dic11—81no—
338Dic11—81no—
339C2×Q16—221no—
340C2×Q16—221no—
341C2×Q16—221no—
342C2×SD16—221no—
343C2×M16—111no—
344C2×M16—111no—
345C2×M16—221no—
346C22×C8—221no—
347C22×C8—221no—
348C4⋊Q8—111no—
349C4⋊Q8—111no—
350C4⋊Q8C22×D1111yescharacteristic
351C4⋊Q8C22×D1111yescharacteristic
352#126—21no—
353#125—21no—
354#125—221no—
355#125C22⋊D1111yescharacteristic
356#124C22⋊D1111yescharacteristic
357#123—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—221no—
361C22⋊Q8—221no—
362C22⋊Q8C22⋊D1111yescharacteristic
363#121C22⋊D1111yescharacteristic
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—221no—
367C4×Q8—221no—
368C4×Q8C22×D1111yescharacteristic
369C4×D4—21no—
370C4×D4C22×D1111yescharacteristic
371#117—21no—
372#117—21no—
373#117—221no—
374C2×C42C22×D1111yescharacteristic
375#107—21no—
376#107—21no—
377#107—221no—
378#106—21no—
379#106—21no—
380#106—221no—
381#106—221no—
382#106—221no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8C22×D1111yescharacteristic
391C4⋊C8C22×D1111yescharacteristic
392#103—21no—
393#103—21no—
394#103—221no—
395#103—221no—
396#103—221no—
397#103—221no—
398#103—221no—
399#103—221no—
400#103—221no—
401#102—21no—
402#102—21no—
403#102—221no—
404C22⋊C8—21no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408#97—111no—
409#97—111no—
410#97—221no—
411C4×C8—21no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—221no—
415C4×C8—221no—
416C2×C11—41no—
417C2×C11—81no—
418C2×C11#303511yescharacteristic
419C2×C11#306311yescharacteristic
420C2×C11#306911yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8C2×C22⋊D1111yescharacteristic
426C2×D4—21no—
427C2×D4C2×C22⋊D1111yescharacteristic
428C22×C4—21no—
429C22×C4D4×D1111yescharacteristic
430C22×C4#434111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432Q16—442no—
433Q16—442no—
434Q16—881no—
435SD16—881no—
436M16—222no—
437M16—441no—
438M16—442no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—111no—
442C2×C8—111no—
443C2×C8—111no—
444C2×C8—111no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—442no—
450C2×C8—881no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—441no—
466C4⋊C4—441no—
467C4⋊C4C2×C22⋊D1111yescharacteristic
468C4⋊C4C2×C22⋊D1111yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—41no—
475C22⋊C4—441no—
476C42—21no—
477C42—41no—
478C42—441no—
479C42D4×D1111yescharacteristic
480C42#434111yescharacteristic
481C42C2×C22⋊D1111yescharacteristic
482C42C23×D1111yescharacteristic
483C11#1924911yescharacteristic, complemented, Sylow
484C23—21no—
485C23#6699211yescharacteristic
486Q8—21no—
487Q8—21no—
488Q8—41no—
489Q8—41no—
490Q8—81no—
491Q8—441no—
492Q8—441no—
493Q8—441no—
494Q8—441no—
495D4—21no—
496D4—21no—
497D4—81no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4#6699211yescharacteristic
513C2×C4#6699211yescharacteristic
514C2×C4#6699211yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4C2×#434111yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—41no—
519C8—41no—
520C8—112no—
521C8—221no—
522C8—221no—
523C8—221no—
524C8—441no—
525C8—441no—
526C8—441no—
527C8—441no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22C2×#6699211yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—881no—
545C4—881no—
546C4D11×#13511yescharacteristic
547C4#1062329911yescharacteristic
548C4#1062336811yescharacteristic
549C4#1062336911yescharacteristic
550C2—41no—
551C2—81no—
552C2#1307806711yescharacteristic
553C2#1307830311yescharacteristic
554C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3233C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#3233D11
hypocenterC11#19249
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3233

Complements

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

NH ≅ G/Ntype
2. #13079357C2semidirect
4. #13068193C2semidirect
5. #13068161C2semidirect
6. #13068124C2semidirect
7. #13068108C2semidirect
8. #13068076C2semidirect
9. #13068044C2semidirect
10. #13067993C2semidirect
11. #13067979C2semidirect
12. #13067369C2semidirect
13. #13067280C2semidirect
14. #13067273C2semidirect
483. C11#19249semidirect

Maximal subgroups

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

subgroupindex
#130799532
#130793572
#130776212
#130681932
#130681612
#130681242
#130681082
#130680762
#130680442
#130679932
#130679792
#130673692
#130672802
#130672732
C11×#32332
#1924911