Finite Group Databasebeta

← #14909437

Subgroups — #14909437

Order 2816.

496 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079268C211yesmaximal, characteristic, complemented
2#13079248C211yesmaximal, characteristic
3#13070901C211yesmaximal, characteristic, complemented
4#13070886C211yesmaximal, characteristic, complemented
5#13070846C211yesmaximal, characteristic, complemented
6#13070842C211yesmaximal, characteristic, complemented
7#13070727C211yesmaximal, characteristic
8#13070722C211yesmaximal, characteristic, complemented
9#13070707C211yesmaximal, characteristic, complemented
10#13070486C211yesmaximal, characteristic, complemented
11#13070481C211yesmaximal, characteristic, complemented
12#13070472C211yesmaximal, characteristic, complemented
13#13070471C211yesmaximal, characteristic, complemented
14#13070212C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic
16#10623156—21no—
17#10623134—21no—
18C2×C11×SD32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C11×#467C2211yescharacteristic
21C11×#466C2211yescharacteristic
22Q16×Dic11C2211yescharacteristic
23#10622794C2211yescharacteristic
24C2×#66893C2211yescharacteristic
25#10622768C2211yescharacteristic
26D8×Dic11C2211yescharacteristic
27C2×#66891C2211yescharacteristic
28#10622729C2211yescharacteristic
29#10622729C2211yescharacteristic
30#10622714C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32#10622665—21no—
33#10622655—21no—
34C2×Dic88C2211yescharacteristic
35#10622491C2211yescharacteristic
36#10622487C2211yescharacteristic
37#10622486C2211yescharacteristic
38#10622486C2211yescharacteristic
39#10622410—21no—
40#10622402—21no—
41#10622378—21no—
42#10622370—21no—
43C11×#367C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#357C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622142C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622140C2211yescharacteristic
52#10622140C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×D8C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C22⋊Q8—21no—
63C11×#121—21no—
64Q8×Dic11—21no—
65#66997—21no—
66C2×#4326—21no—
67#66989—21no—
68#66989—41no—
69#66988—41no—
70D4×Dic11—21no—
71C2×#4324—21no—
72#66979D411yescharacteristic
73#66977—21no—
74#66977—21no—
75C2×#4318D411yescharacteristic
76C2×Dic44C2311yescharacteristic
77C2×Dic44C2311yescharacteristic
78#66943—21no—
79#66943—41no—
80#66942—41no—
81#66941—21no—
82#66940—21no—
83#66940—21no—
84#66932—41no—
85#66932—41no—
86#66932—41no—
87#66931—41no—
88C11×SD32—22no—
89C2×C11×C16—22no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#103—21no—
95C11×#102—21no—
96#66899—21no—
97#66896—21no—
98#66893—22no—
99#66891—22no—
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66880—21no—
103#66880—21no—
104#66879D411yescharacteristic
105#66879D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C8×Dic11C2311yescharacteristic
108#66876—22no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111#66874—21no—
112#66874—21no—
113#66872—21no—
114#66871—21no—
115Dic88—22no—
116#33745—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C22×Dic11—41no—
122C2×Dic22—21no—
123C2×Dic22—21no—
124C2×Dic22—41no—
125C11×Q16—21no—
126C11×Q16—21no—
127C11×D8—21no—
128C11×D8—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2411yescharacteristic
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143C22⋊Dic11D811yescharacteristic
144C22⋊Dic11D811yescharacteristic
145#4326—42no—
146#4324—42no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C4⋊Dic11D811yescharacteristic
152C4⋊Dic11D811yescharacteristic
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163C4×Dic11—41no—
164C4×Dic11C2×D411yescharacteristic
165C4×Dic11C2×D411yescharacteristic
166#4318—22no—
167C2×C11⋊C8C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169Dic44—21no—
170Dic44—21no—
171Dic44—21no—
172Dic44—21no—
173C11×C16—21no—
174C11×C16#4112yes—
175C11⋊C16—21no—
176C11⋊C16#4112yes—
177#3177—111no—
178#3175—111no—
179#2255—111no—
180#2251—111no—
181#2242—111no—
182#2241—111no—
183#2220—111no—
184#2219—111no—
185#2217D1111yescharacteristic
186#2216—111no—
187#2176—111no—
188#2175—111no—
189C4×Q32—111no—
190C4×SD32—111no—
191#2108—111no—
192C23×C11—41no—
193C23×C11C2×D811yescharacteristic
194Q8×C11—41no—
195Q8×C11—41no—
196D4×C11—41no—
197D4×C11—41no—
198D4×C11—161no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—161no—
211C2×Dic11C2×D811yescharacteristic
212C2×Dic11C2×D811yescharacteristic
213C2×Dic11C2×D811yescharacteristic
214C2×Dic11C2×D811yescharacteristic
215Dic22—41no—
216Dic22—41no—
217Dic22—41no—
218Dic22—41no—
219Dic22—161no—
220C8×C11—21no—
221C8×C11C2×#4111yescharacteristic
222C8×C11C2×#4111yescharacteristic
223C11⋊C8—21no—
224C11⋊C8#13512yes—
225#542—221no—
226#541—221no—
227C2×Q32—111no—
228C2×Q32—111no—
229C2×SD32—111no—
230C2×SD32C2×D1111yescharacteristic
231C2×M32—111no—
232C22×C16C2×D1111yescharacteristic
233#500—111no—
234#499—111no—
235#495—111no—
236#494—111no—
237#491—221no—
238#489—221no—
239#470—221no—
240#468—221no—
241#467—111no—
242#467—111no—
243#467C2×D1111yescharacteristic
244#466C2×D1111yescharacteristic
245#441—221no—
246#440—221no—
247C4×Q16—111no—
248C4×Q16—111no—
249C4×Q16—111no—
250C4×D8—111no—
251#405—111no—
252#367—111no—
253#367C2×D1111yescharacteristic
254#366—111no—
255#366—111no—
256#358—111no—
257#358—111no—
258#358—111no—
259#358—111no—
260#358—111no—
261#358C2×D1111yescharacteristic
262#357—111no—
263#357C2×D1111yescharacteristic
264#346—111no—
265#346—111no—
266C4×C16—111no—
267C4×C16—111no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11C22×D811yescharacteristic
275C4×C11—21no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11#53211yescharacteristic
280C4×C11C2×#13511yescharacteristic
281Dic11—21no—
282Dic11—21no—
283Dic11—21no—
284Dic11—21no—
285Dic11—81no—
286Dic11—81no—
287Dic11—81no—
288Dic11—81no—
289C2×Q16—111no—
290C2×Q16—111no—
291C2×Q16—221no—
292C2×Q16C22×D1111yescharacteristic
293C2×SD16—221no—
294C2×D8C22×D1111yescharacteristic
295C2×M16—111no—
296C22×C8C22×D1111yescharacteristic
297C4⋊Q8—221no—
298C4⋊Q8—221no—
299#126—441no—
300#126—441no—
301#126—441no—
302#125—221no—
303#125—441no—
304#125—441no—
305#124—221no—
306#124—441no—
307#123—441no—
308C22⋊Q8—21no—
309C22⋊Q8—221no—
310C22⋊Q8—221no—
311C22⋊Q8—441no—
312#121—21no—
313C4×Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×D4—221no—
317#117—111no—
318Q32—222no—
319Q32—222no—
320SD32—22no—
321SD32—222no—
322M32—222no—
323C2×C16—22no—
324C2×C16—111no—
325C2×C16—111no—
326C2×C16C22×D1111yescharacteristic
327C2×C16C22×D1111yescharacteristic
328#107—111no—
329#107—111no—
330#107—221no—
331#107C22×D1111yescharacteristic
332#107C22×D1111yescharacteristic
333#106—221no—
334#103—21no—
335#103—221no—
336#103—221no—
337#103—221no—
338#103—221no—
339#103—221no—
340#102—21no—
341#102—221no—
342#97—111no—
343#97—111no—
344C4×C8—111no—
345C4×C8—111no—
346C2×C11—41no—
347C2×C11—161no—
348C2×C11#316911yescharacteristic
349C2×C11#341611yescharacteristic
350C2×C11#341711yescharacteristic
351C2×Q8—21no—
352C2×Q8—221no—
353C2×Q8—221no—
354C2×Q8—441no—
355C2×D4—21no—
356C2×D4—41no—
357C22×C4—441no—
358C22×C4D4×D1111yescharacteristic
359Q16—21no—
360Q16—21no—
361Q16—221no—
362Q16—221no—
363Q16—221no—
364Q16—221no—
365Q16—442no—
366SD16—442no—
367D8—21no—
368D8—21no—
369M16—222no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—111no—
373C2×C8—111no—
374C2×C8D4×D1111yescharacteristic
375C2×C8C23×D1111yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—111no—
380C4⋊C4—111no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—111no—
396C22⋊C4—111no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C42—111no—
403C42—111no—
404C42—441no—
405C42—441no—
406C42—441no—
407C16—21no—
408C16—112no—
409C16—221no—
410C16#434112yes—
411C11#3374511yescharacteristic, complemented, Sylow
412C23—41no—
413C23D8×D1111yescharacteristic
414Q8—41no—
415Q8—41no—
416Q8—441no—
417Q8—441no—
418Q8—441no—
419Q8—441no—
420Q8—1761no—
421D4—41no—
422D4—41no—
423D4—161no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—111no—
430C2×C4—111no—
431C2×C4—111no—
432C2×C4—111no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—1761no—
438C2×C4D8×D1111yescharacteristic
439C2×C4C2×D4×D1111yescharacteristic
440C8—21no—
441C8—112no—
442C8—221no—
443C8C2×#434111yescharacteristic
444C8#41×D1111yescharacteristic
445C22—21no—
446C22—21no—
447C22—21no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22C2×D8×D1111yescharacteristic
452C4—21no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4—221no—
457C4—221no—
458C4—221no—
459C4—221no—
460C4—881no—
461C4—881no—
462C4—881no—
463C4—881no—
464C4#1062312711yescharacteristic
465C4D11×#13511yescharacteristic
466C2—41no—
467C2—161no—
468C2#1307919011yescharacteristic
469C2#1308175811yescharacteristic
470C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
prime radicalC11×#466C22
hypercenter#2217D11
hypocenterC11#33745
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. #13079268C2semidirect
3. #13070901C2semidirect
4. #13070886C2semidirect
5. #13070846C2semidirect
6. #13070842C2semidirect
8. #13070722C2semidirect
9. #13070707C2semidirect
10. #13070486C2semidirect
11. #13070481C2semidirect
12. #13070472C2semidirect
13. #13070471C2semidirect
14. #13070212C2semidirect
411. C11#33745semidirect

Maximal subgroups

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

subgroupindex
#130792682
#130792482
#130709012
#130708862
#130708462
#130708422
#130707272
#130707222
#130707072
#130704862
#130704812
#130704722
#130704712
#130702122
C11×#22172
#3374511