Finite Group Databasebeta

← #14909828

Subgroups — #14909828

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#13079110C211yesmaximal, characteristic
2#13070885C211yesmaximal, characteristic, complemented
3#13070868C211yesmaximal, characteristic, complemented
4#13070863C211yesmaximal, characteristic, complemented
5#13070850C211yesmaximal, characteristic, complemented
6#13070678C212yesmaximal, complemented
7#13070666C212yesmaximal, complemented
8#13070554C212yesmaximal
9#13070549C212yesmaximal, complemented
10#13070423C211yesmaximal, characteristic, complemented
11C11×#3177C211yesmaximal, characteristic, complemented
12C11×#541—21no—
13C2×#66962—21no—
14C22×Dic44C2211yescharacteristic
15C2×#66957C2211yescharacteristic
16#10623057—21no—
17C11×#499C2211yescharacteristic
18C11×#494C2211yescharacteristic
19C11×#491—21no—
20C11×#470—21no—
21C11×#467C2212yes—
22C11×#441—21no—
23C4×C11×Q16C2212yes—
24C11×#405C2211yescharacteristic
25C2×#66893C2212yes—
26C2×#66893C2212yes—
27C2×#66893C2212yes—
28C2×#66892C2212yes—
29#10622328—21no—
30#10622328—21no—
31#10622312C2211yescharacteristic
32#10622312C2211yescharacteristic
33#10622309C2211yescharacteristic
34#10622309C2211yescharacteristic
35C22⋊(C11⋊C16)C2212yes—
36#10622130C2212yes—
37#10622130C2212yes—
38#10622130C2212yes—
39#10622129C2212yes—
40C4⋊(C11⋊C16)C2212yes—
41#10622099C2211yescharacteristic
42C4×C11⋊C16C2211yescharacteristic
43C2×#4339—21no—
44C22×Dic22—21no—
45C2×C11×Q16—21no—
46C2×C11×Q16C2312yes—
47C2×C11×M16D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×C4⋊Q8—21no—
50C11×#126—42no—
51C11×#125—21no—
52C11×#125—42no—
53C11×C22⋊Q8—22no—
54C4×Q8×C11—22no—
55C11×#117D411yescharacteristic
56#66962—44no—
57C2×Dic44—21no—
58C2×Dic44—21no—
59C2×Dic44—21no—
60C2×Dic44—42no—
61C2×Dic44C2311yescharacteristic
62C2×Dic44C2311yescharacteristic
63C2×Dic44C2311yescharacteristic
64#66957—42no—
65C2×D88C2311yescharacteristic
66C2×#4314—21no—
67C2×#4314—21no—
68C2×#4314—21no—
69#66950—42no—
70#66939—42no—
71#66928—21no—
72#66928—21no—
73#66922—21no—
74#66922—21no—
75C11×#107C2312yes—
76C11×#106—21no—
77C11×#103—22no—
78C11×#103—22no—
79C11×#97D411yescharacteristic
80C11×#97D411yescharacteristic
81C4×C8×C11C2311yescharacteristic
82C4×C8×C11C2311yescharacteristic
83#66893—42no—
84#66893—42no—
85#66893—42no—
86#66892—42no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33789—111nomaximal, Sylow
90C2×Q8×C11—22no—
91C22×C4×C11C2×D411yescharacteristic
92C2×C22⋊D11—41no—
93C22×Dic11—41no—
94#4339—42no—
95#4339—42no—
96C2×D44—21no—
97C2×C4×D11—41no—
98C2×Dic22—21no—
99C2×Dic22—21no—
100C2×Dic22—21no—
101C2×Dic22—42no—
102C2×Dic22—42no—
103C2×Dic22—41no—
104C11×Q16—22no—
105C11×Q16—22no—
106C11×Q16—42no—
107C11×M16—22no—
108C2×C8×C11—22no—
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2411yescharacteristic
113C11×C4⋊C4—22no—
114C11×C4⋊C4—42no—
115C11×C4⋊C4—42no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4D812yes—
119C11×C22⋊C4—42no—
120C11×C22⋊C4D812yes—
121C42×C11—42no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124(C2×D11)⋊C4—42no—
125(C2×D11)⋊C4—42no—
126C4⋊Dic11—42no—
127C4⋊Dic11—42no—
128Dic44—22no—
129Dic44—22no—
130Dic44—22no—
131Dic44—42no—
132Dic44—42no—
133Dic44—42no—
134D88—22no—
135#4314—42no—
136#4314—42no—
137#4314—42no—
138C11⋊C16—22no—
139C11⋊C16—22no—
140#3177D1111yescharacteristic, complemented
141#3156—111no—
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×C11C2×D811yescharacteristic
152C22×D11—41no—
153Q8×C11—42no—
154Q8×C11—42no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11C2×D812yes—
160C2×C4×C11C2×D812yes—
161C2×C4×C11C2×D811yescharacteristic
162C2×C4×C11C22×D411yescharacteristic
163C22⋊D11—82no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—82no—
168D44—41no—
169D44—41no—
170C4×D11—82no—
171Dic22—41no—
172Dic22—41no—
173Dic22—41no—
174Dic22—41no—
175Dic22—41no—
176Dic22—41no—
177Dic22—82no—
178C8×C11—21no—
179C8×C11—21no—
180C8×C11AGL(1,ℤ/8)12yes—
181C8×C11H(5,𝔽2)12yes—
182C2×#137—221no—
183C2×#135—111no—
184C22×Q16—111no—
185#541—21no—
186#536—221no—
187C2×Q32—112no—
188C2×Q32—112no—
189C2×Q32—112no—
190C2×SD32—112no—
191#499C2×D1111yescharacteristic
192#497—221no—
193#497—221no—
194#495—111no—
195#495—111no—
196#494—111no—
197#494—111no—
198#494C2×D1111yescharacteristic
199#491—21no—
200#470—21no—
201#467C2×D1112yes—
202#441—21no—
203C4×Q16C2×D1112yes—
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×C11C22×D811yescharacteristic
216C2×D11—82no—
217C2×D11—81no—
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—21no—
221C4×C11—82no—
222C4×C11—82no—
223C4×C11#53511yescharacteristic
224C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
225Dic11—81no—
226Dic11—81no—
227Dic11—81no—
228C2×#41—221no—
229C22×Q8—221no—
230#137—444no—
231#135—442no—
232C2×Q16—21no—
233C2×Q16—111no—
234C2×Q16—111no—
235C2×Q16—111no—
236C2×Q16—221no—
237C2×Q16—221no—
238C2×Q16—221no—
239C2×Q16—442no—
240C2×Q16C22×D1112yes—
241C2×SD16—221no—
242C2×SD16—221no—
243C2×SD16—221no—
244C2×D8—111no—
245C2×M16C22⋊D1111yescharacteristic
246C22×C8C22×D1111yescharacteristic
247C4⋊Q8—21no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250#126—42no—
251#125—21no—
252#125—42no—
253#124—221no—
254#124—221no—
255#123—442no—
256C22⋊Q8—22no—
257C22⋊Q8—442no—
258C4×Q8—22no—
259#117C22⋊D1111yescharacteristic
260Q32—442no—
261Q32—442no—
262Q32—442no—
263SD32—442no—
264C2×C16—112no—
265C2×C16—112no—
266#107C22×D1112yes—
267#106—21no—
268#103—22no—
269#103—22no—
270#97C22⋊D1111yescharacteristic
271#97C22⋊D1111yescharacteristic
272C4×C8C22×D1111yescharacteristic
273C4×C8C22×D1111yescharacteristic
274C2×C11—41no—
275C2×C11#320511yescharacteristic
276C2×C11#341712yes—
277D11—161no—
278#41—442no—
279#41—442no—
280C2×Q8—22no—
281C2×Q8—221no—
282C2×Q8—221no—
283C2×Q8—221no—
284C2×Q8—442no—
285C2×Q8—442no—
286C2×Q8—441no—
287C2×D4—221no—
288C2×D4—441no—
289C22×C4—441no—
290C22×C4—441no—
291C22×C4C2×C22⋊D1111yescharacteristic
292Q16—22no—
293Q16—22no—
294Q16—42no—
295Q16—222no—
296Q16—222no—
297Q16—222no—
298Q16—442no—
299Q16—442no—
300Q16—442no—
301SD16—442no—
302SD16—442no—
303SD16—442no—
304D8—222no—
305M16—22no—
306C2×C8—22no—
307C2×C8C2×C22⋊D1111yescharacteristic
308C2×C8C2×C22⋊D1111yescharacteristic
309C2×C8C2×C22⋊D1111yescharacteristic
310C2×C8C23×D1111yescharacteristic
311C4⋊C4—22no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—442no—
317C4⋊C4—442no—
318C4⋊C4#432312yes—
319C22⋊C4—42no—
320C22⋊C4—442no—
321C22⋊C4—442no—
322C22⋊C4#432312yes—
323C42—42no—
324C42C2×C22⋊D1111yescharacteristic
325C42C2×C22⋊D1111yescharacteristic
326C16—222no—
327C16—222no—
328C11#3378911yescharacteristic, complemented, Sylow
329C23—441no—
330C23C2×#432311yescharacteristic
331Q8—42no—
332Q8—42no—
333Q8—441no—
334Q8—441no—
335Q8—441no—
336Q8—441no—
337Q8—441no—
338Q8—441no—
339Q8—882no—
340D4—441no—
341D4—441no—
342D4—882no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—882no—
351C2×C4—882no—
352C2×C4C2×#432312yes—
353C2×C4C2×#432312yes—
354C2×C4C2×#432311yescharacteristic
355C2×C4C22×C22⋊D1111yescharacteristic
356C8—21no—
357C8—21no—
358C8#6700212yes—
359C8#6704212yes—
360C22—22no—
361C22—21no—
362C22—882no—
363C22—881no—
364C22C22×#432311yescharacteristic
365C4—22no—
366C4—22no—
367C4—21no—
368C4—82no—
369C4—82no—
370C4—881no—
371C4—881no—
372C4—881no—
373C4C2×#6700211yescharacteristic
374C4#1062336111yescharacteristic
375C2—41no—
376C2—1761no—
377C2#1307953111yescharacteristic
378C2#1308176712yes—
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3177C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#3177D11
hypocenterC11#33789
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3177

Complements

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

NH ≅ G/Ntype
2. #13070885C2semidirect
3. #13070868C2semidirect
4. #13070863C2semidirect
5. #13070850C2semidirect
6. #13070678C2semidirect
7. #13070666C2semidirect
9. #13070549C2semidirect
10. #13070423C2semidirect
11. C11×#3177C2semidirect
140. #3177D11semidirect
328. C11#33789semidirect

Maximal subgroups

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

subgroupindex
#130791102
#130708852
#130708682
#130708632
#130708502
#130706782
#130706662
#130705542
#130705492
#130704232
C11×#31772
#3378911