Finite Group Databasebeta

← #14909834

Subgroups — #14909834

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079275C211yesmaximal, characteristic, complemented
2#13070888C211yesmaximal, characteristic, complemented
3#13070868C211yesmaximal, characteristic, complemented
4#13070861C211yesmaximal, characteristic, complemented
5#13070847C211yesmaximal, characteristic, complemented
6#13070675C212yesmaximal, complemented
7#13070663C212yesmaximal, complemented
8#13070556C212yesmaximal
9#13070550C212yesmaximal, complemented
10#13070423C211yesmaximal, characteristic, complemented
11C11×#3156C211yesmaximal, characteristic
12C2×C11×#137—21no—
13C2×C11×#135C2211yescharacteristic
14C22×C11×Q16C2211yescharacteristic
15C11×#536—21no—
16#10623049—21no—
17C11×#497—21no—
18C11×#497—21no—
19C11×#495C2211yescharacteristic
20C11×#495C2211yescharacteristic
21C11×#494C2211yescharacteristic
22C11×#494C2211yescharacteristic
23C11×#405C2211yescharacteristic
24C2×#66893C2212yes—
25C2×#66893C2212yes—
26C2×#66893C2212yes—
27C2×#66891C2212yes—
28#10622750—21no—
29#10622729C2212yes—
30#10622329—21no—
31#10622316—21no—
32#10622312C2211yescharacteristic
33C4×Dic44C2212yes—
34#10622296C2211yescharacteristic
35#10622202C2212yes—
36#10622202C2212yes—
37#10622202C2212yes—
38#10622200C2212yes—
39C22⋊(C11⋊C16)C2212yes—
40C4⋊(C11⋊C16)C2212yes—
41#10622099C2211yescharacteristic
42C4×C11⋊C16C2211yescharacteristic
43C2×C11×#41—21no—
44C22×Q8×C11—21no—
45C11×#137—44no—
46C11×#135—42no—
47C2×C11×Q16—21no—
48C2×C11×Q16—21no—
49C2×C11×Q16—21no—
50C2×C11×Q16—42no—
51C2×C11×Q16C2311yescharacteristic
52C2×C11×Q16C2311yescharacteristic
53C2×C11×Q16C2311yescharacteristic
54C2×C11×SD16—21no—
55C2×C11×SD16—21no—
56C2×C11×SD16—21no—
57C2×C11×D8C2311yescharacteristic
58C2×C11×M16D411yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—21no—
62C11×#124—21no—
63C11×#124—21no—
64C11×#123—42no—
65C11×C22⋊Q8—42no—
66C11×#117D411yescharacteristic
67#66977—22no—
68C2×Dic44—21no—
69C2×Dic44C2312yes—
70#66942—42no—
71#66932—42no—
72#66923—21no—
73#66922—21no—
74C4×Dic22—22no—
75C11×#97D411yescharacteristic
76C11×#97D411yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C4×C8×C11C2311yescharacteristic
79#66893—42no—
80#66893—42no—
81#66893—42no—
82#66891—42no—
83#66882C2312yes—
84#66881—21no—
85#66880—22no—
86#66880—22no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33789—111nomaximal, Sylow
90C11×#41—42no—
91C11×#41—42no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11—41no—
98C2×D4×C11—21no—
99C2×D4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11C2×D411yescharacteristic
103C2×Dic22—22no—
104C11×Q16—22no—
105C11×Q16—22no—
106C11×Q16—22no—
107C11×Q16—42no—
108C11×Q16—42no—
109C11×Q16—42no—
110C11×SD16—42no—
111C11×SD16—42no—
112C11×SD16—42no—
113C11×D8—22no—
114C11×M16—22no—
115C2×C8×C11—22no—
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2411yescharacteristic
120C11×C4⋊C4—42no—
121C11×C4⋊C4—42no—
122C11×C4⋊C4D812yes—
123C11×C22⋊C4—42no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4D812yes—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C22⋊Dic11—42no—
129C4⋊Dic11—22no—
130C4⋊Dic11—42no—
131Dic11⋊C4—42no—
132Dic11⋊C4—42no—
133Dic11⋊C4—42no—
134C4×Dic11—42no—
135Dic44—22no—
136Dic44—22no—
137Dic44—42no—
138C11⋊C16—22no—
139C11⋊C16—22no—
140#3177—111no—
141#3156D1111yescharacteristic
142#2251—111no—
143#2247—111no—
144#2245—111no—
145#2242—111no—
146#2211—112no—
147#2209—112no—
148#2189—112no—
149#2188—112no—
150#2164—111no—
151C23×C11—41no—
152C23×C11C2×D811yescharacteristic
153Q8×C11—41no—
154Q8×C11—41no—
155Q8×C11—41no—
156Q8×C11—41no—
157Q8×C11—41no—
158Q8×C11—41no—
159Q8×C11—82no—
160D4×C11—41no—
161D4×C11—41no—
162D4×C11—82no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—82no—
169C2×C4×C11—82no—
170C2×C4×C11C2×D812yes—
171C2×C4×C11C2×D811yescharacteristic
172C2×C4×C11C2×D812yes—
173C2×C4×C11C22×D411yescharacteristic
174C2×Dic11—42no—
175C2×Dic11—42no—
176Dic22—42no—
177Dic22—42no—
178C8×C11—21no—
179C8×C11—21no—
180C8×C11AGL(1,ℤ/8)12yes—
181C8×C11H(5,𝔽2)12yes—
182C2×#137—21no—
183C2×#135C2×D1111yescharacteristic
184C22×Q16C2×D1111yescharacteristic
185#541—221no—
186#536—21no—
187C2×Q32—112no—
188C2×Q32—112no—
189C2×Q32—112no—
190C2×SD32—112no—
191#499—111no—
192#497—21no—
193#497—21no—
194#495C2×D1111yescharacteristic
195#495C2×D1111yescharacteristic
196#494—111no—
197#494C2×D1111yescharacteristic
198#494C2×D1111yescharacteristic
199#491—221no—
200#470—221no—
201#467—112no—
202#441—221no—
203C4×Q16—112no—
204#405C2×D1111yescharacteristic
205C4⋊C16—112no—
206#358—112no—
207#358—112no—
208#358—112no—
209#357—112no—
210C22⋊C16—112no—
211#346—111no—
212C4×C16—111no—
213C22×C11—22no—
214C22×C11—21no—
215C22×C11—82no—
216C22×C11—81no—
217C22×C11C22×D811yescharacteristic
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—21no—
221C4×C11—81no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11#53511yescharacteristic
225C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
226Dic11—82no—
227Dic11—82no—
228C2×#41—21no—
229C22×Q8—21no—
230#137—44no—
231#135—42no—
232C2×Q16—21no—
233C2×Q16—21no—
234C2×Q16—21no—
235C2×Q16—42no—
236C2×Q16—112no—
237C2×Q16—221no—
238C2×Q16C22×D1111yescharacteristic
239C2×Q16C22×D1111yescharacteristic
240C2×Q16C22×D1111yescharacteristic
241C2×SD16—21no—
242C2×SD16—21no—
243C2×SD16—21no—
244C2×D8C22×D1111yescharacteristic
245C2×M16C22⋊D1111yescharacteristic
246C22×C8C22×D1111yescharacteristic
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—221no—
250#126—442no—
251#125—221no—
252#125—442no—
253#124—21no—
254#124—21no—
255#123—42no—
256C22⋊Q8—42no—
257C22⋊Q8—222no—
258C4×Q8—222no—
259#117C22⋊D1111yescharacteristic
260Q32—442no—
261Q32—442no—
262Q32—442no—
263SD32—442no—
264C2×C16—112no—
265C2×C16—112no—
266#107—112no—
267#106—221no—
268#103—222no—
269#103—222no—
270#97C22⋊D1111yescharacteristic
271#97C22⋊D1111yescharacteristic
272C4×C8C22×D1111yescharacteristic
273C4×C8C22×D1111yescharacteristic
274C2×C11—41no—
275C2×C11—161no—
276C2×C11#320511yescharacteristic
277C2×C11#341712yes—
278#41—42no—
279#41—42no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×Q8—41no—
286C2×Q8—222no—
287C2×D4—21no—
288C2×D4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4C2×C22⋊D1111yescharacteristic
292Q16—22no—
293Q16—22no—
294Q16—22no—
295Q16—42no—
296Q16—42no—
297Q16—42no—
298Q16—222no—
299Q16—222no—
300Q16—442no—
301SD16—42no—
302SD16—42no—
303SD16—42no—
304D8—22no—
305M16—22no—
306C2×C8—22no—
307C2×C8C2×C22⋊D1111yescharacteristic
308C2×C8C2×C22⋊D1111yescharacteristic
309C2×C8C2×C22⋊D1111yescharacteristic
310C2×C8C23×D1111yescharacteristic
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—222no—
314C4⋊C4—442no—
315C4⋊C4—442no—
316C4⋊C4—442no—
317C4⋊C4—442no—
318C4⋊C4#432312yes—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—442no—
322C22⋊C4#432312yes—
323C42—442no—
324C42C2×C22⋊D1111yescharacteristic
325C42C2×C22⋊D1111yescharacteristic
326C16—222no—
327C16—222no—
328C11#3378911yescharacteristic, complemented, Sylow
329C23—41no—
330C23C2×#432311yescharacteristic
331Q8—41no—
332Q8—41no—
333Q8—41no—
334Q8—41no—
335Q8—41no—
336Q8—41no—
337Q8—82no—
338Q8—442no—
339Q8—442no—
340D4—41no—
341D4—41no—
342D4—82no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4C2×#432312yes—
353C2×C4C2×#432312yes—
354C2×C4C2×#432311yescharacteristic
355C2×C4C22×C22⋊D1111yescharacteristic
356C8—21no—
357C8—21no—
358C8#6698512yes—
359C8#6703712yes—
360C22—22no—
361C22—21no—
362C22—82no—
363C22—81no—
364C22C22×#432311yescharacteristic
365C4—22no—
366C4—22no—
367C4—21no—
368C4—81no—
369C4—81no—
370C4—81no—
371C4—882no—
372C4—882no—
373C4C2×#6698511yescharacteristic
374C4#1062333611yescharacteristic
375C2—41no—
376C2—161no—
377C2#1307953411yescharacteristic
378C2#1308176712yes—
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3156C2
socleC22×C11C22×D8
prime radicalC2×C11×#135C22
hypercenter#3156D11
hypocenterC11#33789
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3156

Complements

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

NH ≅ G/Ntype
1. #13079275C2semidirect
2. #13070888C2semidirect
3. #13070868C2semidirect
4. #13070861C2semidirect
5. #13070847C2semidirect
6. #13070675C2semidirect
7. #13070663C2semidirect
9. #13070550C2semidirect
10. #13070423C2semidirect
328. C11#33789semidirect

Maximal subgroups

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

subgroupindex
#130792752
#130708882
#130708682
#130708612
#130708472
#130706752
#130706632
#130705562
#130705502
#130704232
C11×#31562
#3378911