Finite Group Databasebeta

← #14772098

Subgroups — #14772098

Order 2816.

898 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622329C211yesmaximal, characteristic
2C2×#10622466C211yesmaximal, characteristic
3C2×#10622486C211yesmaximal, characteristic
4#13071535C212yesmaximal
5#13069355C211yesmaximal, characteristic
6#13068871C212yesmaximal
7#13068869C212yesmaximal
8#13068777C211yesmaximal, characteristic
9#13068630C212yesmaximal
10#13068484C211yesmaximal, characteristic
11C11×#1943C211yesmaximal, characteristic
12C22×Dic44C2211yescharacteristic
13C2×#66940C2212yes—
14C2×#66940C2212yes—
15C2×C4×Dic22C2212yes—
16C2×C11×#107C2211yescharacteristic
17C2×C11×#106C2211yescharacteristic
18C2×C11×#97C2211yescharacteristic
19C11×#389C2212yes—
20C2×#66881C2211yescharacteristic
21C2×#66880C2212yes—
22C2×#66879C2211yescharacteristic
23C2×Dic11⋊C8C2211yescharacteristic
24C2×C8×Dic11C2211yescharacteristic
25#10622598C2212yes—
26#10622590C2212yes—
27C4⋊C4×Dic11—22no—
28#10622585—22no—
29C2×#66874C2212yes—
30C2×#66874C2212yes—
31C2×#66871C2212yes—
32C4×Dic11⋊C4C2211yescharacteristic
33#10622486C418yescomplemented
34#10622466—24no—
35#10622329—24no—
36#10622263—22no—
37#10622260—22no—
38C11×#340C2212yes—
39#10622188C2211yescharacteristic
40#10622167C2212yes—
41#10622162C2211yescharacteristic
42C22×Dic22C2312yes—
43C22×C8×C11C2311yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4C2312yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C42×C11C2311yescharacteristic
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11C2312yes—
51C2×Dic11⋊C4—22no—
52C2×Dic11⋊C4—22no—
53C2×Dic11⋊C4—22no—
54C2×Dic11⋊C4D412yes—
55C2×C4×Dic11—22no—
56C2×C4×Dic11—22no—
57C2×C4×Dic11—22no—
58C2×C4×Dic11C2311yescharacteristic
59C2×C4×Dic11C2311yescharacteristic
60C22×C11⋊C8C2311yescharacteristic
61C22×C11⋊C8C2311yescharacteristic
62C2×Dic44C2×C414yes—
63C2×Dic44D414yes—
64C2×Dic44Q814yes—
65#66940—24no—
66#66940—24no—
67#66940—42no—
68#66940C2×C418yes—
69C4×Dic22—24no—
70C4×Dic22—42no—
71C11×#107C2×C414yes—
72C11×#106—22no—
73C11×#97—22no—
74C11×#95—22no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C11⋊#95D412yes—
79#66881—22no—
80#66880—24no—
81#66879—22no—
82Dic11⋊C8—22no—
83C8×Dic11C2×C414yes—
84#66874—24no—
85#66874C2×C418yes—
86#66871—42no—
87#22675—111nomaximal, Sylow
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2411yescharacteristic
92C22×Dic11—22no—
93C22×Dic11—22no—
94C22×Dic11C2×D412yes—
95C22×Dic11C2×D411yescharacteristic
96C22×Dic11C2×D411yescharacteristic
97C2×Dic22—22no—
98C2×Dic22—22no—
99C2×Dic22—22no—
100C2×Dic22C22×C414yes—
101C2×Dic22C2×D414yes—
102C2×Dic22C2×Q814yes—
103C2×C8×C11—21no—
104C2×C8×C11—21no—
105C2×C8×C11—21no—
106C2×C8×C11C22×C412yes—
107C2×C8×C11C2×D412yes—
108C2×C8×C11C2×Q812yes—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—44no—
113C11×C4⋊C4C22×C414yes—
114C42×C11—21no—
115C42×C11—21no—
116C4⋊Dic11—22no—
117C4⋊Dic11—22no—
118C4⋊Dic11—44no—
119Dic11⋊C4—28no—
120Dic11⋊C4—42no—
121Dic11⋊C4—44no—
122Dic11⋊C4—44no—
123C4×Dic11—28no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C4×Dic11—44no—
127C4×Dic11—44no—
128C4×Dic11C22×C412yes—
129C4×Dic11#4112yes—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8C22×C412yes—
136Dic44C4⋊C4116yescomplemented
137C2×#441—111no—
138C2×#441—111no—
139C2×C4×Q16—111no—
140#2351—112no—
141#1943—111no—
142#1943D1111yescharacteristic
143#1863—112no—
144#1863—112no—
145#1846—111no—
146#1805—112no—
147#1770—111no—
148C23×C11C22×D411yescharacteristic
149C2×C4×C11—24no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11C23×C411yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C22×Q811yescharacteristic
161C2×C4×C11C2×#4111yescharacteristic
162C2×C4×C11H(5,𝔽2)11yescharacteristic
163C2×C4×C112−1+411yescharacteristic
164C2×Dic11—24no—
165C2×Dic11—24no—
166C2×Dic11—24no—
167C2×Dic11—22no—
168C2×Dic11—22no—
169C2×Dic11—22no—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11C4×D412yes—
176C2×Dic11C4×D412yes—
177Dic22—24no—
178Dic22—24no—
179Dic22—24no—
180Dic22C2×C4⋊C418yes—
181C8×C11—41no—
182C8×C11C2×C4⋊C414yes—
183C11⋊C8—22no—
184C11⋊C8—41no—
185C22×Q16—111no—
186C2×C4×Q8—112no—
187C2×C4×Q8—112no—
188C2×C4×Q8—112no—
189#441—224no—
190#441—224no—
191C4×Q16—118no—
192C2×#107—112no—
193C2×#107C2×D1111yescharacteristic
194C2×#106—111no—
195C2×#106C2×D1111yescharacteristic
196C2×C4⋊C8—111no—
197C2×#103—112no—
198C2×#103—112no—
199C2×#103—112no—
200C2×#97—111no—
201C2×#97C2×D1111yescharacteristic
202C2×C4×C8—111no—
203#389—112no—
204#389—222no—
205#389—222no—
206#389C2×D1112yes—
207#382—112no—
208#382—222no—
209C4×C4⋊C4—111no—
210C4×C4⋊C4—222no—
211#340—112no—
212#340C2×D1112yes—
213#336—111no—
214#336—111no—
215C22×C11C2×C4×D411yescharacteristic
216C22×C11D4211yescharacteristic
217C22×C11D4×Q811yescharacteristic
218C22×C11#57512yes—
219C22×C11#57812yes—
220C4×C11—44no—
221C4×C11—42no—
222C4×C11—82no—
223C4×C11C22×C4⋊C411yescharacteristic
224C4×C11#52011yescharacteristic
225C4×C11#54711yescharacteristic
226C4×C11#55411yescharacteristic
227Dic11—28no—
228Dic11—22no—
229Dic11—22no—
230Dic11—42no—
231Dic11—82no—
232C22×Q8—112no—
233C2×Q16—114no—
234C2×Q16—114no—
235C2×Q16—114no—
236C22×C8—111no—
237C22×C8—111no—
238C22×C8C22×D1111yescharacteristic
239C22×C8C22×D1111yescharacteristic
240C4×Q8—118no—
241C4×Q8—224no—
242C4×Q8—224no—
243C4×Q8—224no—
244C4×Q8—442no—
245C4×Q8—442no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—112no—
248C2×C4⋊C4—112no—
249C2×C4⋊C4—222no—
250C2×C4⋊C4—222no—
251C2×C4⋊C4—222no—
252C2×C4⋊C4—222no—
253C2×C4⋊C4C22×D1112yes—
254C2×C4⋊C4C22×D1112yes—
255C2×C42—111no—
256C2×C42—111no—
257C2×C42—222no—
258C2×C42—222no—
259C2×C42—222no—
260C2×C42C22×D1111yescharacteristic
261#107—442no—
262#107C4×D1114yes—
263#106—22no—
264#106—222no—
265C4⋊C8—222no—
266#103—118no—
267#103—224no—
268#103—224no—
269#97—22no—
270#97—222no—
271C4×C8—114no—
272#95—22no—
273#95—112no—
274#95—222no—
275#95—222no—
276#95—222no—
277C2×C11D4×C4⋊C411yescharacteristic
278C2×C11#294311yescharacteristic
279C2×C11#295011yescharacteristic
280C2×C11#327712yes—
281C2×C11#339012yes—
282C2×Q8—114no—
283C2×Q8—114no—
284C2×Q8—114no—
285C2×Q8—222no—
286C2×Q8—222no—
287C2×Q8—222no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—111no—
291C22×C4—111no—
292C22×C4—112no—
293C22×C4—222no—
294C22×C4—222no—
295C22×C4D4×D1112yes—
296C22×C4C23×D1111yescharacteristic
297Q16—1116no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—112no—
302C2×C8—221no—
303C2×C8—221no—
304C2×C8—221no—
305C2×C8—221no—
306C2×C8—221no—
307C2×C8C2×C4×D1112yes—
308C2×C8D4×D1112yes—
309C2×C8Q8×D1112yes—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—44no—
314C4⋊C4—228no—
315C4⋊C4—222no—
316C4⋊C4—222no—
317C4⋊C4—442no—
318C4⋊C4—444no—
319C4⋊C4—444no—
320C4⋊C4—444no—
321C4⋊C4C2×C4×D1114yes—
322C42—21no—
323C42—21no—
324C42—112no—
325C42—112no—
326C42—228no—
327C42—221no—
328C42—221no—
329C42—444no—
330C42—444no—
331C11#2267511yescharacteristic, complemented, Sylow
332C23C2×D4×D1111yescharacteristic
333Q8—118no—
334Q8—224no—
335Q8—224no—
336Q8—224no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—112no—
347C2×C4—112no—
348C2×C4—224no—
349C2×C4—222no—
350C2×C4—222no—
351C2×C4—224no—
352C2×C4—224no—
353C2×C4—222no—
354C2×C4—222no—
355C2×C4—222no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4C22×C4×D1111yescharacteristic
360C2×C4C2×D4×D1111yescharacteristic
361C2×C4C2×Q8×D1111yescharacteristic
362C2×C4#6704011yescharacteristic
363C2×C4#41×D1111yescharacteristic
364C2×C4#6704211yescharacteristic
365C8—41no—
366C8—222no—
367C8—441no—
368C8C4⋊C4×D1114yes—
369C22C4×D4×D1111yescharacteristic
370C22#1062314011yescharacteristic
371C22#1062325811yescharacteristic
372C22#1062330412yes—
373C22#1062331012yes—
374C4—44no—
375C4—42no—
376C4—82no—
377C4—228no—
378C4—222no—
379C4—222no—
380C4—442no—
381C4—882no—
382C4C2×C4⋊C4×D1111yescharacteristic
383C4#1062310511yescharacteristic
384C4#1062316211yescharacteristic
385C4#1062322111yescharacteristic
386C2#1307151711yescharacteristic
387C2#1307741311yescharacteristic
388C2#1307748111yescharacteristic
389C2#1308027012yes—
390C2#1308158012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1943C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1943D11
hypocenterC11#22675
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

Complements

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

NH ≅ G/Ntype
33. #10622486C4semidirect
136. Dic44C4⋊C4semidirect
331. C11#22675semidirect

Maximal subgroups

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

subgroupindex
C2×#106223292
C2×#106224662
C2×#106224862
#130715352
#130693552
#130688712
#130688692
#130687772
#130686302
#130684842
C11×#19432
#2267511