Finite Group Databasebeta

← #14764191

Subgroups — #14764191

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622732C211yesmaximal, characteristic
2#13071223C212yesmaximal
3#13069387C212yesmaximal, complemented
4#13069381C212yesmaximal, complemented
5#13069378C212yesmaximal, complemented
6#13069376C212yesmaximal, complemented
7#13068649C211yesmaximal, characteristic
8#13068639C212yesmaximal
9C11×#1809C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C2×#66979C2211yescharacteristic
12C23×C11⋊C8C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14C2×C11×#106C2211yescharacteristic
15C11×#380C2212yes—
16#10622825C2212yes—
17#10622732C418yescomplemented
18C2×#66882C2211yescharacteristic
19C2×#66881C2211yescharacteristic
20C2×Dic11⋊C8C2212yes—
21C2×Dic11⋊C8C2212yes—
22#10622590C2212yes—
23#10622589C2212yes—
24C4⋊C4×Dic11C2212yes—
25C4⋊C4×Dic11C2212yes—
26C2×#66872C2212yes—
27C2×#66872C2212yes—
28#10622558—22no—
29#10622557—22no—
30#10622267—22no—
31#10622266—22no—
32C11×#340C2212yes—
33#10622189C2212yes—
34#10622167C2212yes—
35#10622167C2212yes—
36C23×C4×C11C2311yescharacteristic
37C2×C11×M16—41no—
38C2×C11×M16—41no—
39C2×C11×M16C2×C414yes—
40C22×C8×C11C2311yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C2×C11×C4⋊C4C2312yes—
43C2×C11×C4⋊C4C2312yes—
44C2×C11×C22⋊C4—22no—
45C2×C22⋊Dic11—22no—
46C2×C22⋊Dic11D411yescharacteristic
47C2×C22⋊Dic11D411yescharacteristic
48#66979C2×C414yes—
49#66979Q814yes—
50C2×C4⋊Dic11D412yes—
51C2×C4⋊Dic11C2312yes—
52C2×C4⋊Dic11C2312yes—
53C2×Dic11⋊C4—22no—
54C2×Dic11⋊C4—22no—
55C2×C4×Dic11—22no—
56C2×C4×Dic11—22no—
57C2×C4×Dic11C2312yes—
58C22×C11⋊C8—41no—
59C22×C11⋊C8—41no—
60C22×C11⋊C8C2×C414yes—
61C22×C11⋊C8C2312yes—
62C11×#107—41no—
63C11×#106—41no—
64C11×#95—22no—
65C11⋊#95—22no—
66C11⋊#95—22no—
67C11⋊#95—22no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70#66882—41no—
71#66881—41no—
72Dic11⋊C8C2×C418yes—
73Dic11⋊C8C2×C418yes—
74#66872—42no—
75#66872—42no—
76#21967—111nomaximal, Sylow
77C24×C11C2×D411yescharacteristic
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11C22×C412yes—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×Q812yes—
87C22×C4×C11C2411yescharacteristic
88C22×Dic11—22no—
89C22×Dic11—22no—
90C22×Dic11C2×D412yes—
91C22×Dic11C2×D412yes—
92C11×M16—44no—
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—21no—
97C2×C8×C11C22×C412yes—
98C2×C8×C11C22×C412yes—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C22⋊C4—82no—
104C22⋊Dic11—82no—
105C22⋊Dic11C4⋊C414yes—
106C22⋊Dic11C4⋊C414yes—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11C4⋊C418yes—
112Dic11⋊C4—82no—
113Dic11⋊C4—82no—
114C4×Dic11—82no—
115C4×Dic11—82no—
116C4×Dic11C22×C414yes—
117C4×Dic11C2×Q814yes—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—44no—
121C2×C11⋊C8C22×C414yes—
122C2×#424—111no—
123#2314—112no—
124#1949—112no—
125#1949—112no—
126#1948—112no—
127#1948—112no—
128#1809—111no—
129#1809D1111yescharacteristic
130#1807—112no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11C2×C4⋊C412yes—
136C23×C11C22×D411yescharacteristic
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11C2×C4⋊C412yes—
150C2×C4×C11C23×C411yescharacteristic
151C2×C4×C11C22×Q811yescharacteristic
152C2×C4×C11H(5,𝔽2)11yescharacteristic
153C2×C4×C11H(5,𝔽2)11yescharacteristic
154C2×C4×C112−1+411yescharacteristic
155C2×C4×C112−1+411yescharacteristic
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—22no—
159C2×Dic11—22no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11C2×C4⋊C414yes—
167C2×Dic11C2×C4⋊C414yes—
168C8×C11—22no—
169C8×C11—22no—
170C11⋊C8—24no—
171C22×M16C2×D1111yescharacteristic
172C23×C8—111no—
173C2×#117—111no—
174C2×#107—111no—
175C2×#107C2×D1111yescharacteristic
176C2×#106—111no—
177C2×#106—112no—
178C2×#106—112no—
179C2×#106C2×D1111yescharacteristic
180#424—118no—
181C2×C4⋊C8—112no—
182C2×C4⋊C8—112no—
183#388—222no—
184#388—222no—
185#387—222no—
186#387—222no—
187#384—112no—
188#382—112no—
189#380—112no—
190#380C2×D1112yes—
191C4×C4⋊C4—112no—
192C4×C4⋊C4—112no—
193#340—112no—
194#340—112no—
195#340—112no—
196#340C2×D1112yes—
197C22×C11—22no—
198C22×C11—24no—
199C22×C11—42no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11C22×C4⋊C411yescharacteristic
203C22×C11#53711yescharacteristic
204C22×C11#53711yescharacteristic
205C22×C11#57712yes—
206C22×C11#57712yes—
207C4×C11—22no—
208C4×C11—82no—
209C4×C11—82no—
210C4×C11#51811yescharacteristic
211C4×C11#51911yescharacteristic
212C4×C11#54411yescharacteristic
213C4×C11#54411yescharacteristic
214Dic11—24no—
215Dic11—24no—
216Dic11—82no—
217Dic11—82no—
218C23×C4C22×D1111yescharacteristic
219C2×M16—41no—
220C2×M16—41no—
221C2×M16C4×D1114yes—
222C22×C8—112no—
223C22×C8—114no—
224C22×C8—441no—
225C22×C8—441no—
226C22×C8C22×D1111yescharacteristic
227C22×C8C22×D1111yescharacteristic
228#117—114no—
229#117—114no—
230C2×C4⋊C4—112no—
231C2×C4⋊C4—112no—
232C2×C4⋊C4—112no—
233C2×C4⋊C4—222no—
234C2×C4⋊C4—222no—
235C2×C4⋊C4C22×D1112yes—
236C2×C4⋊C4C22×D1112yes—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—111no—
239C2×C22⋊C4—111no—
240C2×C22⋊C4—222no—
241C2×C42—112no—
242C2×C42—222no—
243C2×C42—222no—
244#107—41no—
245#107—441no—
246#106—41no—
247#106—442no—
248#106—442no—
249#106—441no—
250C4⋊C8—118no—
251C4⋊C8—118no—
252#95—22no—
253#95—222no—
254#95—222no—
255#95—222no—
256#95—222no—
257#95—222no—
258C2×C11—42no—
259C2×C11#231611yescharacteristic
260C2×C11#291212yes—
261C2×C11#326012yes—
262C2×C11#326311yescharacteristic
263C2×C11#326311yescharacteristic
264C24D4×D1111yescharacteristic
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—112no—
272C22×C4—112no—
273C22×C4—222no—
274C22×C4—222no—
275C22×C4C2×C4×D1112yes—
276C22×C4D4×D1111yescharacteristic
277C22×C4Q8×D1112yes—
278C22×C4C23×D1111yescharacteristic
279M16—44no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—114no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8—444no—
288C2×C8C2×C4×D1112yes—
289C2×C8C2×C4×D1112yes—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—118no—
295C4⋊C4—222no—
296C4⋊C4—222no—
297C4⋊C4—222no—
298C4⋊C4—222no—
299C4⋊C4—882no—
300C4⋊C4—882no—
301C22⋊C4—82no—
302C22⋊C4—114no—
303C22⋊C4—114no—
304C22⋊C4—882no—
305C42—114no—
306C42—114no—
307C42—882no—
308C42—882no—
309C11#2196711yescharacteristic, complemented, Sylow
310C23—22no—
311C23—22no—
312C23—21no—
313C23—21no—
314C23C4⋊C4×D1112yes—
315C23C2×D4×D1111yescharacteristic
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—114no—
329C2×C4—114no—
330C2×C4—222no—
331C2×C4—222no—
332C2×C4—222no—
333C2×C4—222no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4C4⋊C4×D1112yes—
341C2×C4C22×C4×D1111yescharacteristic
342C2×C4#6703711yescharacteristic
343C2×C4#6703711yescharacteristic
344C2×C4C2×Q8×D1111yescharacteristic
345C2×C4#6704311yescharacteristic
346C2×C4#6704311yescharacteristic
347C8—22no—
348C8—22no—
349C8—224no—
350C22—22no—
351C22—24no—
352C22—41no—
353C22—41no—
354C22—42no—
355C22C2×C4⋊C4×D1111yescharacteristic
356C22#1062312811yescharacteristic
357C22#1062312811yescharacteristic
358C22#1062330612yes—
359C22#1062330912yes—
360C4—22no—
361C4—82no—
362C4—82no—
363C4—224no—
364C4—224no—
365C4—882no—
366C4—882no—
367C4#1062301711yescharacteristic
368C4#1062304711yescharacteristic
369C4#1062315411yescharacteristic
370C4#1062315411yescharacteristic
371C2—42no—
372C2#1307123311yescharacteristic
373C2#1307721012yes—
374C2#1308005812yes—
375C2#1308008211yescharacteristic
376C2#1308008611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1809C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1809D11
hypocenterC11#21967
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
3. #13069387C2semidirect
4. #13069381C2semidirect
5. #13069378C2semidirect
6. #13069376C2semidirect
17. #10622732C4semidirect
309. C11#21967semidirect

Maximal subgroups

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

subgroupindex
C2×#106227322
#130712232
#130693872
#130693812
#130693782
#130693762
#130686492
#130686392
C11×#18092
#2196711