Finite Group Databasebeta

← #14645260

Subgroups — #14645260

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3C2×#10622185C214yesmaximal, complemented
4C22×C11×C4⋊Q8C211yesmaximal, characteristic
5C23×Q8×C11—21no—
6C2×C11×C4⋊Q8—28no—
7C2×C11×C4⋊Q8—21no—
8C2×C11×C4⋊Q8—21no—
9C2×C11×C4⋊Q8C412yes—
10C2×C11×C4⋊Q8C2212yes—
11C22×C11×C4⋊C4—21no—
12C22×C11×C4⋊C4C412yes—
13C22×C42×C11C2211yescharacteristic
14C2×C22⋊(C11⋊C8)—21no—
15C2×C22⋊(C11⋊C8)—21no—
16C2×C4⋊(C11⋊C8)C2212yes—
17C2×C4⋊(C11⋊C8)C2212yes—
18#10622185—28no—
19#10622162—21no—
20#10622162—21no—
21C22×Q8×C11—28no—
22C22×Q8×C11—22no—
23C22×Q8×C11—22no—
24C22×Q8×C11—44no—
25C22×Q8×C11—42no—
26C22×Q8×C11—42no—
27C23×C4×C11—22no—
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C11×C4⋊Q8—28no—
32C11×C4⋊Q8—28no—
33C11×C4⋊Q8—28no—
34C11×C4⋊Q8—24no—
35C11×C4⋊Q8D418yes—
36C2×C11×C4⋊C4—28no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—28no—
41C2×C11×C4⋊C4C2×C414yes—
42C2×C42×C11—24no—
43C2×C42×C11C2×C411yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C2×C42×C11C2311yescharacteristic
47C22×C11⋊C8—22no—
48C22×C11⋊C8—22no—
49C22⋊(C11⋊C8)—42no—
50C22⋊(C11⋊C8)—42no—
51C4⋊(C11⋊C8)—24no—
52C4⋊(C11⋊C8)—24no—
53#8340—111nomaximal, Sylow
54C24×C11C22⋊C411yescharacteristic
55C2×Q8×C11—28no—
56C2×Q8×C11—28no—
57C2×Q8×C11—44no—
58C2×Q8×C11—416no—
59C2×Q8×C11—416no—
60C2×Q8×C11—44no—
61C2×Q8×C11—42no—
62C2×Q8×C11—42no—
63C2×Q8×C11—44no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—28no—
72C22×C4×C11—24no—
73C22×C4×C11—44no—
74C22×C4×C11—44no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11D812yes—
79C22×C4×C11SD1612yes—
80C22×C4×C11SD1612yes—
81C22×C4×C11Q1612yes—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C11×C4⋊C4—28no—
86C11×C4⋊C4—28no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—28no—
89C11×C4⋊C4C22⋊C418yes—
90C42×C11—22no—
91C42×C11—22no—
92C42×C11—22no—
93C42×C11C2×D414yes—
94C2×C11⋊C8—42no—
95C2×C11⋊C8—42no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—42no—
99C2×C11⋊C8—42no—
100C22×C4⋊Q8D1111yescharacteristic
101#1797—111no—
102#1797—111no—
103C2×#332—114no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11#10112yes—
109C23×C11#10212yes—
110C23×C11#10312yes—
111C23×C11C2×C22⋊C411yescharacteristic
112Q8×C11—416no—
113Q8×C11—48no—
114Q8×C11—48no—
115C2×C4×C11—28no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—24no—
125C2×C4×C11—24no—
126C2×C4×C11—24no—
127C2×C4×C11—24no—
128C2×C4×C11—28no—
129C2×C4×C11—416no—
130C2×C4×C11—44no—
131C2×C4×C11—44no—
132C2×C4×C11#10112yes—
133C2×C4×C11#10212yes—
134C2×C4×C11#10312yes—
135C2×C4×C11C2×C22⋊C412yes—
136C2×C4×C11#12012yes—
137C2×C4×C11#12012yes—
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×SD1611yescharacteristic
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11C2×Q1611yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)12yes—
143C2×C4×C11#13712yes—
144C11⋊C8—82no—
145C11⋊C8—82no—
146C23×Q8—21no—
147C2×C4⋊Q8—28no—
148C2×C4⋊Q8—21no—
149C2×C4⋊Q8—21no—
150C2×C4⋊Q8Dic1112yes—
151C2×C4⋊Q8C2×D1112yes—
152C22×C4⋊C4—21no—
153C22×C4⋊C4Dic1112yes—
154C22×C42C2×D1111yescharacteristic
155C2×C4⋊C8—112no—
156C2×C4⋊C8—112no—
157C2×C22⋊C8—221no—
158C2×C22⋊C8—221no—
159#336—221no—
160#336—221no—
161#332—228no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—22no—
165C22×C11—22no—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11#33214yescomplemented
169C22×C11#37911yescharacteristic
170C22×C11C2×#10111yescharacteristic
171C22×C11C2×#10111yescharacteristic
172C22×C11C2×#10211yescharacteristic
173C22×C11C2×#10311yescharacteristic
174C22×C11#41811yescharacteristic
175C22×C11#41911yescharacteristic
176C4×C11—22no—
177C4×C11—22no—
178C4×C11—22no—
179C4×C11—22no—
180C4×C11—48no—
181C4×C11#44712yes—
182C4×C11#44812yes—
183C4×C11#45012yes—
184C4×C11#45112yes—
185C22×Q8—28no—
186C22×Q8—22no—
187C22×Q8—22no—
188C22×Q8—44no—
189C22×Q8—42no—
190C22×Q8—42no—
191C23×C4—22no—
192C23×C4C2×Dic1111yescharacteristic
193C23×C4C22⋊D1111yescharacteristic
194C23×C4C22⋊D1111yescharacteristic
195C22×C8—222no—
196C22×C8—222no—
197C4⋊Q8—28no—
198C4⋊Q8—28no—
199C4⋊Q8—28no—
200C4⋊Q8—24no—
201C4⋊Q8C22⋊D1118yes—
202C2×C4⋊C4—28no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—28no—
207C2×C4⋊C4C2×Dic1114yes—
208C2×C42—24no—
209C2×C42C2×Dic1111yescharacteristic
210C2×C42C22⋊D1111yescharacteristic
211C2×C42C22⋊D1111yescharacteristic
212C2×C42C22×D1111yescharacteristic
213C4⋊C8—224no—
214C4⋊C8—224no—
215C22⋊C8—442no—
216C22⋊C8—442no—
217C2×C11—24no—
218C2×C11C2×#33211yescharacteristic
219C2×C11#154611yescharacteristic
220C2×C11#154911yescharacteristic
221C2×C11#155611yescharacteristic
222C2×C11#178411yescharacteristic
223C2×C11#178611yescharacteristic
224C2×C11#178711yescharacteristic
225C24C22⋊Dic1111yescharacteristic
226C2×Q8—28no—
227C2×Q8—28no—
228C2×Q8—44no—
229C2×Q8—416no—
230C2×Q8—416no—
231C2×Q8—44no—
232C2×Q8—42no—
233C2×Q8—44no—
234C2×Q8—42no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—28no—
243C22×C4—24no—
244C22×C4—44no—
245C22×C4—44no—
246C22×C4#432312yes—
247C22×C4#432412yes—
248C22×C4#432512yes—
249C22×C4#432612yes—
250C22×C4C22⋊Dic1111yescharacteristic
251C22×C4C22⋊Dic1111yescharacteristic
252C22×C4C22⋊Dic1111yescharacteristic
253C22×C4C22×Dic1111yescharacteristic
254C22×C4C2×C22⋊D1111yescharacteristic
255C22×C4C2×C22⋊D1111yescharacteristic
256C2×C8—442no—
257C2×C8—442no—
258C2×C8—442no—
259C2×C8—442no—
260C2×C8—442no—
261C2×C8—442no—
262C4⋊C4—28no—
263C4⋊C4—28no—
264C4⋊C4—24no—
265C4⋊C4—28no—
266C4⋊C4C22⋊Dic1118yes—
267C42—22no—
268C42—22no—
269C42—22no—
270C42C2×C22⋊D1114yes—
271C11#834011yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23#6689612yes—
277C23#6689912yes—
278C23#6690012yes—
279C23C2×C22⋊Dic1111yescharacteristic
280Q8—416no—
281Q8—48no—
282Q8—48no—
283C2×C4—28no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—28no—
297C2×C4—416no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4#6689612yes—
301C2×C4#6689912yes—
302C2×C4#6690012yes—
303C2×C4C2×#432311yescharacteristic
304C2×C4#6698512yes—
305C2×C4C2×#432411yescharacteristic
306C2×C4C2×#432511yescharacteristic
307C2×C4#6699512yes—
308C2×C4C2×#432611yescharacteristic
309C2×C4C2×C22⋊Dic1112yes—
310C2×C4#6700612yes—
311C2×C4#6700612yes—
312C8—882no—
313C8—882no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22#1062218514yescomplemented
321C22C2×#6689611yescharacteristic
322C22#1062282811yescharacteristic
323C22C2×#6689911yescharacteristic
324C22#1062283811yescharacteristic
325C22C2×#6690011yescharacteristic
326C22C2×#6690011yescharacteristic
327C22#1062286011yescharacteristic
328C4—22no—
329C4—22no—
330C4—22no—
331C4—22no—
332C4—48no—
333C4#1062283012yes—
334C4#1062283112yes—
335C4#1062284012yes—
336C4#1062284112yes—
337C2—24no—
338C2C2×#1062218511yescharacteristic
339C2#1306728811yescharacteristic
340C2#1306730111yescharacteristic
341C2#1306733311yescharacteristic
342C2#1306854011yescharacteristic
343C2#1306854711yescharacteristic
344C2#1306855111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC22×C11×C4⋊Q8C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC22×C4⋊Q8D11
hypocenterC11#8340
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#10622185C2semidirect
168. C22×C11#332semidirect
271. C11#8340semidirect
320. C22#10622185semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221852
C22×C11×C4⋊Q82
#834011