Finite Group Databasebeta

← #15617229

Subgroups — #15617229

Order 2816.

4874 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623350C211yesmaximal, characteristic, complemented
2C22×#67001C211yesmaximal, characteristic, complemented
3#13077065C2116yesmaximal, complemented
4#13077061C216yesmaximal, complemented
5C2×#10622847C216yesmaximal, complemented
6C2×C11×#585C211yesmaximal, characteristic
7C11×#585—28no—
8C11×#585—28no—
9C2×C11×2−1+4C414yes—
10C2×C11×2−1+4C412yes—
11C2×C11×H(5,𝔽2)C414yes—
12C2×C11×H(5,𝔽2)C416yes—
13C22×C11×#41C2216yes—
14C22×C11×#41C2218yes—
15C22×C11×#41C2211yescharacteristic
16#10623350—28no—
17C2×#67001—28no—
18C2×#67001C2218yescomplemented
19C2×#67001C2218yescomplemented
20C22×#4318C2216yescomplemented
21C22×#4318C2213yescomplemented
22C23×C11⋊C8C2213yescomplemented
23#10622847C2214yescomplemented
24#10622847C22112yescomplemented
25#10622847C22124yescomplemented
26#10622847C22124yescomplemented
27#10622820C22124yescomplemented
28C2×C22⋊(C11⋊C8)C22124yescomplemented
29C11×2−1+4—232no—
30C11×2−1+4—216no—
31C11×H(5,𝔽2)—232no—
32C11×H(5,𝔽2)—248no—
33C2×C11×#41—232no—
34C2×C11×#41—232no—
35C2×C11×#41—224no—
36C2×C11×#41—224no—
37C2×C11×#41C2×C418yes—
38C2×C11×#41C2×C4124yes—
39C2×C11×#41C2×C4112yes—
40C2×C11×#41C2×C4112yes—
41C2×C11×#41C2×C414yes—
42C2×C11×#41D418yes—
43C2×C11×#41D418yes—
44C2×C11×#41C2314yes—
45C2×C11×#41C23112yes—
46C2×C11×#41C2314yes—
47C22×Q8×C11C2×C418yes—
48C22×Q8×C11C2×C416yes—
49C22×Q8×C11C2×C411yescharacteristic
50C22×D4×C11C2×C4112yes—
51C22×D4×C11C2×C4124yes—
52C22×D4×C11C2×C416yes—
53C22×D4×C11C2×C413yes—
54C23×C4×C11C23112yes—
55C23×C4×C11C2313yes—
56#67001—232no—
57#67001—232no—
58C2×#4318—212no—
59C2×#4318—224no—
60C2×#4318C2314yes—
61C2×#4318C23112yes—
62C2×#4318C23112yes—
63C22×C11⋊C8—212no—
64C22×C11⋊C8C2311yescharacteristic
65C22×C11⋊C8C2313yes—
66C22×C11⋊C8C23112yes—
67C22×C11⋊C8C23112yes—
68C22⋊(C11⋊C8)C23116yes—
69C22⋊(C11⋊C8)C23148yes—
70#60065—111nomaximal, Sylow
71C24×C11C22×C4112yes—
72C24×C11C22×C413yes—
73C11×#41—232no—
74C11×#41—296no—
75C11×#41—248no—
76C11×#41—248no—
77C11×#41—28no—
78C11×#41—224no—
79C11×#41—224no—
80C11×#41—28no—
81C11×#41C22⋊C4132yes—
82C11×#41C2×D4116yes—
83C11×#41C2×D4116yes—
84C2×Q8×C11—232no—
85C2×Q8×C11—224no—
86C2×Q8×C11C22⋊C418yes—
87C2×Q8×C11C22×C4112yes—
88C2×Q8×C11C22×C414yes—
89C2×Q8×C11C22×C414yes—
90C2×D4×C11—248no—
91C2×D4×C11—296no—
92C2×D4×C11—224no—
93C2×D4×C11C22⋊C4124yes—
94C2×D4×C11C22×C4124yes—
95C2×D4×C11C22×C418yes—
96C2×D4×C11C22×C4112yes—
97C2×D4×C11C22×C414yes—
98C2×D4×C11C22×C4112yes—
99C22×C4×C11—224no—
100C22×C4×C11—224no—
101C22×C4×C11C22×C4112yes—
102C22×C4×C11C22×C4124yes—
103C22×C4×C11C22×C416yes—
104C22×C4×C11C22×C413yes—
105C22×C4×C11C2×D4112yes—
106C22×C4×C11C2×D4112yes—
107C22×C4×C11C2418yes—
108C22×C4×C11C2411yescharacteristic
109C22×C4×C11C2416yes—
110#4318—28no—
111#4318—224no—
112#4318—224no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—26no—
115C2×C11⋊C8—224no—
116C2×C11⋊C8—224no—
117C2×C11⋊C8C2412yes—
118C2×C11⋊C8C2418yes—
119C2×C11⋊C8C2416yes—
120C2×#585D1111yescharacteristic
121C2×#568—111no—
122C22×#131—111no—
123#2880—1116no—
124#2879—116no—
125C2×#408—116no—
126C23×C11—224no—
127C23×C11—46no—
128C23×C11—424no—
129C23×C11C2×C22⋊C4112yes—
130C23×C11C23×C418yes—
131C23×C11C23×C416yes—
132C23×C11C23×C411yescharacteristic
133Q8×C11—224no—
134Q8×C11—28no—
135Q8×C11C2×C22⋊C4116yes—
136D4×C11—248no—
137D4×C11—216no—
138D4×C11—224no—
139D4×C11—28no—
140D4×C11C2×C22⋊C4148yes—
141C2×C4×C11—224no—
142C2×C4×C11—248no—
143C2×C4×C11—28no—
144C2×C4×C11—28no—
145C2×C4×C11C2×C22⋊C4124yes—
146C2×C4×C11C2×C22⋊C4112yes—
147C2×C4×C11C23×C418yes—
148C2×C4×C11C23×C416yes—
149C2×C4×C11C23×C411yescharacteristic
150C2×C4×C11C22×D412yes—
151C2×C4×C11C22×D4112yes—
152C2×C4×C11C22×D4112yes—
153C2×C4×C11C22×D412yes—
154C2×C4×C11C2511yescharacteristic
155C11⋊C8—22no—
156C11⋊C8—26no—
157C11⋊C8—28no—
158#585—28no—
159#585—28no—
160C2×2−1+4Dic1114yes—
161C2×2−1+4Dic1112yes—
162C2×H(5,𝔽2)Dic1114yes—
163C2×H(5,𝔽2)Dic1116yes—
164C22×#41C2×D1116yes—
165C22×#41C2×D1118yes—
166C22×#41C2×D1111yescharacteristic
167#568—228no—
168C2×#131—118no—
169C2×#131—118no—
170C2×#131—228no—
171C22×M16—116no—
172C22×M16—113no—
173C23×C8—113no—
174#408—114no—
175#408—1112no—
176#408—1124no—
177#408—1124no—
178#407—1124no—
179C2×C22⋊C8—1124no—
180C22×C11—22no—
181C22×C11—212no—
182C22×C11—28no—
183C22×C11—216no—
184C22×C11—412no—
185C22×C11—824no—
186C22×C11C22×C22⋊C4112yes—
187C22×C11C22×C22⋊C412yes—
188C22×C11C24×C411yescharacteristic
189C4×C11—28no—
190C4×C11C22×C22⋊C4112yes—
191C4×C11C22×C22⋊C412yes—
192C4×C11C23×D411yescharacteristic
193C4×C11C23×D411yescharacteristic
1942−1+4—232no—
1952−1+4—216no—
196H(5,𝔽2)—232no—
197H(5,𝔽2)—248no—
198C2×#41—232no—
199C2×#41—232no—
200C2×#41—224no—
201C2×#41—224no—
202C2×#41C2×Dic1118yes—
203C2×#41C2×Dic11124yes—
204C2×#41C2×Dic11112yes—
205C2×#41C2×Dic11112yes—
206C2×#41C2×Dic1114yes—
207C2×#41C22⋊D1118yes—
208C2×#41C22⋊D1118yes—
209C2×#41C22×D1114yes—
210C2×#41C22×D11112yes—
211C2×#41C22×D1114yes—
212C22×Q8C2×Dic1118yes—
213C22×Q8C2×Dic1116yes—
214C22×Q8C2×Dic1111yescharacteristic
215C22×D4C2×Dic11112yes—
216C22×D4C2×Dic11124yes—
217C22×D4C2×Dic1116yes—
218C22×D4C2×Dic1113yes—
219C23×C4C22×D11112yes—
220C23×C4C22×D1113yes—
221#131—2232no—
222#131—2232no—
223C2×M16—114no—
224C2×M16—1112no—
225C2×M16—1112no—
226C2×M16—2212no—
227C2×M16—2224no—
228C22×C8—111no—
229C22×C8—113no—
230C22×C8—1112no—
231C22×C8—1112no—
232C22×C8—2212no—
233C22⋊C8—1116no—
234C22⋊C8—1148no—
235C2×C11—22no—
236C2×C11—212no—
237C2×C11—48no—
238C2×C11C23×C22⋊C411yescharacteristic
239C2×C11#357312yes—
240C24C22×Dic11112yes—
241C24C22×Dic1113yes—
242#41—232no—
243#41—296no—
244#41—248no—
245#41—248no—
246#41—28no—
247#41—224no—
248#41—224no—
249#41—28no—
250#41C22⋊Dic11132yes—
251#41C2×C22⋊D11116yes—
252#41C2×C22⋊D11116yes—
253C2×Q8—232no—
254C2×Q8—224no—
255C2×Q8C22⋊Dic1118yes—
256C2×Q8C22×Dic11112yes—
257C2×Q8C22×Dic1114yes—
258C2×Q8C22×Dic1114yes—
259C2×D4—248no—
260C2×D4—296no—
261C2×D4—224no—
262C2×D4C22⋊Dic11124yes—
263C2×D4C22×Dic11124yes—
264C2×D4C22×Dic1118yes—
265C2×D4C22×Dic11112yes—
266C2×D4C22×Dic1114yes—
267C2×D4C22×Dic11112yes—
268C22×C4—224no—
269C22×C4—224no—
270C22×C4C22×Dic11112yes—
271C22×C4C22×Dic11124yes—
272C22×C4C22×Dic1116yes—
273C22×C4C22×Dic1113yes—
274C22×C4C2×C22⋊D11112yes—
275C22×C4C2×C22⋊D11112yes—
276C22×C4C23×D1118yes—
277C22×C4C23×D1111yescharacteristic
278C22×C4C23×D1116yes—
279M16—228no—
280M16—2224no—
281M16—2224no—
282C2×C8—112no—
283C2×C8—118no—
284C2×C8—116no—
285C2×C8—222no—
286C2×C8—226no—
287C2×C8—2224no—
288C2×C8—2224no—
289C11#6006511yescharacteristic, complemented, Sylow
290C23—224no—
291C23—46no—
292C23—424no—
293C23C2×C22⋊Dic11112yes—
294C23C23×Dic1118yes—
295C23C23×Dic1116yes—
296C23C23×Dic1111yescharacteristic
297Q8—224no—
298Q8—28no—
299Q8C2×C22⋊Dic11116yes—
300D4—248no—
301D4—216no—
302D4—224no—
303D4—28no—
304D4C2×C22⋊Dic11148yes—
305C2×C4—224no—
306C2×C4—248no—
307C2×C4—28no—
308C2×C4—28no—
309C2×C4C2×C22⋊Dic11124yes—
310C2×C4C2×C22⋊Dic11112yes—
311C2×C4C23×Dic1118yes—
312C2×C4C23×Dic1116yes—
313C2×C4C23×Dic1111yescharacteristic
314C2×C4C22×C22⋊D1112yes—
315C2×C4C22×C22⋊D11112yes—
316C2×C4C22×C22⋊D11112yes—
317C2×C4C22×C22⋊D1112yes—
318C2×C4C24×D1111yescharacteristic
319C8—222no—
320C8—226no—
321C8—228no—
322C22—22no—
323C22—212no—
324C22—28no—
325C22—216no—
326C22—412no—
327C22—824no—
328C22C22×C22⋊Dic11112yes—
329C22C22×C22⋊Dic1112yes—
330C22C24×Dic1111yescharacteristic
331C4—28no—
332C4C22×C22⋊Dic11112yes—
333C4C22×C22⋊Dic1112yes—
334C4C23×C22⋊D1111yescharacteristic
335C4C23×C22⋊D1111yescharacteristic
336C2—22no—
337C2—212no—
338C2—48no—
339C2C23×C22⋊Dic1111yescharacteristic
340C2#1308332812yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
Fitting, prime radicalC2×C11×#585C2
cosocleC2×C4×C11C25
hypercenterC2×#585D11
hypocenterC11#60065
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#585

Complements

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

NH ≅ G/Ntype
1. C2×#10623350C2semidirect
2. C22×#67001C2semidirect
3. #13077065C2semidirect
4. #13077061C2semidirect
5. C2×#10622847C2semidirect
18. C2×#67001C22semidirect
19. C2×#67001C22semidirect
20. C22×#4318C22semidirect
21. C22×#4318C22semidirect
22. C23×C11⋊C8C22semidirect
23. #10622847C22semidirect
24. #10622847C22semidirect
25. #10622847C22semidirect
26. #10622847C22semidirect
27. #10622820C22semidirect
28. C2×C22⋊(C11⋊C8)C22semidirect
289. C11#60065semidirect

Maximal subgroups

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

subgroupindex
C2×#106233502
C22×#670012
#130770652
#130770612
C2×#106228472
C2×C11×#5852
#6006511