Finite Group Databasebeta

← #14764189

Subgroups — #14764189

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622612C211yesmaximal, characteristic
2#13071225C211yesmaximal, characteristic
3#13069384C212yesmaximal, complemented
4#13069382C212yesmaximal, complemented
5#13069379C212yesmaximal, complemented
6#13069377C212yesmaximal, complemented
7#13068647C212yesmaximal
8#13068639C212yesmaximal
9C11×#2314C211yesmaximal, characteristic
10C2×C11×#117C2211yescharacteristic
11C22×#4318C2211yescharacteristic
12C23×C11⋊C8C2211yescharacteristic
13C11×#388—22no—
14C11×#387—22no—
15C11×#384C2211yescharacteristic
16C11×#382C2211yescharacteristic
17C11×#380C2212yes—
18C4×C11×C4⋊C4C2212yes—
19#10622825C2212yes—
20#10622612C418yescomplemented
21#10622594—22no—
22C2×#66872C2212yes—
23C2×#66872C2212yes—
24C2×#66872C2212yes—
25C2×#66871C2212yes—
26#10622564—22no—
27#10622549C2211yescharacteristic
28#10622548C2211yescharacteristic
29C4×C4⋊Dic11C2212yes—
30C2×C4⋊(C11⋊C8)C2212yes—
31C2×C4⋊(C11⋊C8)C2212yes—
32#10622167C2212yes—
33#10622167C2212yes—
34#10622167C2212yes—
35#10622167C2212yes—
36C23×C4×C11C2311yescharacteristic
37C11×#117C2×C414yes—
38C11×#117Q814yes—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4D412yes—
41C2×C11×C4⋊C4C2312yes—
42C2×C11×C4⋊C4C2312yes—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4D412yes—
45C2×C42×C11—22no—
46C2×C42×C11C2311yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C22⋊Dic11—22no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11C2312yes—
51C2×C4⋊Dic11C2312yes—
52C2×C4×Dic11—22no—
53C2×#4318—41no—
54C2×#4318—41no—
55C2×#4318C2×C414yes—
56C22×C11⋊C8—41no—
57C22×C11⋊C8—41no—
58C22×C11⋊C8C2×C414yes—
59C22×C11⋊C8C2312yes—
60C22×C11⋊C8C2312yes—
61C11×#95—22no—
62C11×#95—22no—
63C11×#95—22no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C11⋊#95—22no—
67#66872—42no—
68#66872—42no—
69#66872—42no—
70#66871—42no—
71C4⋊(C11⋊C8)C2×C418yes—
72C4⋊(C11⋊C8)C2×C418yes—
73#21967—111nomaximal, Sylow
74C24×C11C2×D411yescharacteristic
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11C22×C412yes—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×D412yes—
85C22×C4×C11C2×Q812yes—
86C22×C4×C11C2411yescharacteristic
87C22×Dic11—22no—
88C22×Dic11—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—82no—
94C11×C4⋊C4C4⋊C418yes—
95C11×C22⋊C4—82no—
96C11×C22⋊C4C4⋊C418yes—
97C42×C11—82no—
98C42×C11C22×C412yes—
99C42×C11C22×C412yes—
100C42×C11C2×Q812yes—
101C42×C11C2×Q812yes—
102C22⋊Dic11—82no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11—22no—
107C4⋊Dic11—82no—
108C4×Dic11—82no—
109#4318—44no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—44no—
115C2×C11⋊C8C22×C414yes—
116C2×C11⋊C8C22×C414yes—
117C2×#424—111no—
118#2314—111no—
119#2314D1111yescharacteristic
120#1949—112no—
121#1949—112no—
122#1948—112no—
123#1948—112no—
124#1809—112no—
125#1807—112no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—22no—
129C23×C11—22no—
130C23×C11C2×C4⋊C412yes—
131C23×C11C22×D411yescharacteristic
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11C2×C4⋊C414yes—
149C2×C4×C11C2×C4⋊C414yes—
150C2×C4×C11C2×C4⋊C412yes—
151C2×C4×C11C23×C411yescharacteristic
152C2×C4×C11C22×Q811yescharacteristic
153C2×C4×C11H(5,𝔽2)11yescharacteristic
154C2×C4×C11H(5,𝔽2)11yescharacteristic
155C2×C4×C112−1+411yescharacteristic
156C2×C4×C112−1+411yescharacteristic
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C11⋊C8—24no—
164C11⋊C8—24no—
165C22×M16—111no—
166C23×C8—111no—
167C2×#117C2×D1111yescharacteristic
168C2×#107—112no—
169C2×#106—112no—
170C2×#106—112no—
171C2×#106—112no—
172#424—118no—
173C2×C4⋊C8—112no—
174C2×C4⋊C8—112no—
175#388—22no—
176#388—222no—
177#387—22no—
178#387—222no—
179#384—111no—
180#384C2×D1111yescharacteristic
181#382—111no—
182#382C2×D1111yescharacteristic
183#380—112no—
184#380C2×D1112yes—
185C4×C4⋊C4—112no—
186C4×C4⋊C4C2×D1112yes—
187#340—112no—
188#340—112no—
189#340—112no—
190#340—112no—
191C22×C11—22no—
192C22×C11—24no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—42no—
196C22×C11C22×C4⋊C411yescharacteristic
197C22×C11#53711yescharacteristic
198C22×C11#53711yescharacteristic
199C22×C11#57712yes—
200C22×C11#57712yes—
201C4×C11—22no—
202C4×C11—24no—
203C4×C11—24no—
204C4×C11—82no—
205C4×C11—82no—
206C4×C11#51811yescharacteristic
207C4×C11#51911yescharacteristic
208C4×C11#54411yescharacteristic
209C4×C11#54411yescharacteristic
210Dic11—82no—
211Dic11—82no—
212C23×C4C22×D1111yescharacteristic
213C2×M16—114no—
214C2×M16—441no—
215C2×M16—441no—
216C22×C8—112no—
217C22×C8—112no—
218C22×C8—114no—
219C22×C8—441no—
220C22×C8—441no—
221#117Dic2214yes—
222#117C4×D1114yes—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—112no—
225C2×C4⋊C4—112no—
226C2×C4⋊C4—222no—
227C2×C4⋊C4C22⋊D1112yes—
228C2×C4⋊C4C22×D1112yes—
229C2×C4⋊C4C22×D1112yes—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—222no—
232C2×C22⋊C4C22⋊D1112yes—
233C2×C42—22no—
234C2×C42—222no—
235C2×C42C22×D1111yescharacteristic
236C2×C42C22×D1111yescharacteristic
237#107—442no—
238#106—442no—
239#106—442no—
240#106—442no—
241C4⋊C8—118no—
242C4⋊C8—118no—
243#95—22no—
244#95—22no—
245#95—22no—
246#95—222no—
247#95—222no—
248#95—222no—
249C2×C11—42no—
250C2×C11#231611yescharacteristic
251C2×C11#291212yes—
252C2×C11#326011yescharacteristic
253C2×C11#326011yescharacteristic
254C2×C11#326312yes—
255C24C2×C22⋊D1111yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—222no—
263C22×C4—222no—
264C22×C4C2×Dic2212yes—
265C22×C4C2×C4×D1112yes—
266C22×C4C2×C22⋊D1111yescharacteristic
267C22×C4C2×C22⋊D1112yes—
268C22×C4C2×C22⋊D1112yes—
269C22×C4C23×D1111yescharacteristic
270M16—444no—
271C2×C8—114no—
272C2×C8—114no—
273C2×C8—222no—
274C2×C8—222no—
275C2×C8—222no—
276C2×C8—222no—
277C2×C8—444no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—82no—
283C4⋊C4—222no—
284C4⋊C4—222no—
285C4⋊C4—222no—
286C4⋊C4—222no—
287C4⋊C4—882no—
288C4⋊C4Dic11⋊C418yes—
289C22⋊C4—82no—
290C22⋊C4—882no—
291C22⋊C4Dic11⋊C418yes—
292C42—82no—
293C42—882no—
294C42C2×Dic2212yes—
295C42C2×Dic2212yes—
296C42C2×C4×D1112yes—
297C42C2×C4×D1112yes—
298C11#2196711yescharacteristic, complemented, Sylow
299C23—21no—
300C23—21no—
301C23—22no—
302C23—22no—
303C23C2×Dic11⋊C412yes—
304C23C22×C22⋊D1111yescharacteristic
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4C2×Dic11⋊C414yes—
328C2×C4C2×Dic11⋊C414yes—
329C2×C4C2×Dic11⋊C412yes—
330C2×C4C22×Dic2211yescharacteristic
331C2×C4C22×C4×D1111yescharacteristic
332C2×C4#6704211yescharacteristic
333C2×C4#6704211yescharacteristic
334C2×C4#6704311yescharacteristic
335C2×C4#6704311yescharacteristic
336C8—224no—
337C8—224no—
338C22—22no—
339C22—24no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22C22×Dic11⋊C411yescharacteristic
344C22#1062336411yescharacteristic
345C22#1062336411yescharacteristic
346C22#1062336712yes—
347C22#1062336812yes—
348C4—22no—
349C4—24no—
350C4—24no—
351C4—82no—
352C4—82no—
353C4—882no—
354C4—882no—
355C4#1062304711yescharacteristic
356C4#1062305011yescharacteristic
357C4#1062305011yescharacteristic
358C4#1062305211yescharacteristic
359C2—42no—
360C2#1307123211yescharacteristic
361C2#1307720912yes—
362C2#1308005711yescharacteristic
363C2#1308006211yescharacteristic
364C2#1308008112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2314C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2314D11
hypocenterC11#21967
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
3. #13069384C2semidirect
4. #13069382C2semidirect
5. #13069379C2semidirect
6. #13069377C2semidirect
20. #10622612C4semidirect
298. C11#21967semidirect

Maximal subgroups

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

subgroupindex
C2×#106226122
#130712252
#130693842
#130693822
#130693792
#130693772
#130686472
#130686392
C11×#23142
#2196711