Finite Group Databasebeta

← #14669255

Subgroups — #14669255

Order 2816.

976 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 976 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622177C214yesmaximal, complemented
2#13068544C211yesmaximal, characteristic
3#13068534C211yesmaximal, characteristic
4C2×C11×#536C211yesmaximal, characteristic
5C22×C11×#41C2211yescharacteristic
6C23×Q8×C11C411yescharacteristic, complemented
7C11×#536—28no—
8C2×C11×C4⋊Q8—21no—
9C2×C11×#124—21no—
10C2×C11×#123C412yescomplemented
11C2×C11×#123C2212yes—
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×#117C411yescharacteristic, complemented
15C2×#66900—21no—
16C2×#66898—21no—
17C2×#66898C2212yes—
18C2×#66897C2212yes—
19#10622824—21no—
20#10622820—21no—
21#10622177—28no—
22C2×C11×#41—24no—
23C2×C11×#41—42no—
24C2×C11×#41—42no—
25C22×Q8×C11—21no—
26C22×Q8×C11—21no—
27C22×Q8×C11—24no—
28C22×Q8×C11—42no—
29C22×Q8×C11—42no—
30C22×Q8×C11D411yescharacteristic
31C22×D4×C11C2×C411yescharacteristic
32C22×D4×C11D411yescharacteristic
33C22×D4×C11C2311yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11C2×C412yes—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C11×C4⋊Q8—28no—
39C11×#124—28no—
40C11×#123—24no—
41C11×#123—24no—
42C11×#123—24no—
43C11×#123D418yes—
44C11×C22⋊Q8—28no—
45C11×C22⋊Q8—28no—
46C11×#117—24no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4C2×C412yes—
53C2×C42×C11—21no—
54C2×C22⋊Dic11—22no—
55C2×#4318—22no—
56#66900—42no—
57#66898—24no—
58#66898—42no—
59#66897—24no—
60C11⋊#95—42no—
61C22⋊(C11⋊C8)—42no—
62#12692—111nomaximal, Sylow
63C24×C11C22⋊C411yescharacteristic
64C24×C11C22×C411yescharacteristic
65C24×C11C2×D411yescharacteristic
66C11×#41—416no—
67C2×Q8×C11—24no—
68C2×Q8×C11—24no—
69C2×Q8×C11—22no—
70C2×Q8×C11—22no—
71C2×Q8×C11—41no—
72C2×Q8×C11—416no—
73C2×Q8×C11—42no—
74C2×Q8×C11—42no—
75C2×Q8×C11—42no—
76C2×Q8×C11—42no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11C2×D414yes—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11C22⋊C411yescharacteristic
101C22×C4×C11C22⋊C411yescharacteristic
102C22×C4×C11C22⋊C411yescharacteristic
103C22×C4×C11C22⋊C414yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×Dic11—42no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—28no—
108C11×C4⋊C4—28no—
109C11×C22⋊C4—28no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—28no—
112C11×C22⋊C4C22⋊C414yes—
113C42×C11—24no—
114C22⋊Dic11—42no—
115C22⋊Dic11—42no—
116#4318—42no—
117#4318—42no—
118C2×C11⋊C8—42no—
119C2×#536D1111yescharacteristic
120C2×#352—114no—
121#1785—111no—
122#1782—111no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—42no—
133C23×C11C2×C22⋊C411yescharacteristic
134C23×C11C2×C22⋊C412yes—
135C23×C11#12012yes—
136Q8×C11—44no—
137Q8×C11—48no—
138Q8×C11—48no—
139D4×C11—44no—
140D4×C11—44no—
141D4×C11—44no—
142C2×C4×C11—28no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—44no—
155C2×C4×C11—44no—
156C2×C4×C11—44no—
157C2×C4×C11—44no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—44no—
161C2×C4×C11#9912yes—
162C2×C4×C11#9912yes—
163C2×C4×C11#12012yes—
164C2×Dic11—82no—
165C2×Dic11—84no—
166C11⋊C8—82no—
167C22×#41C2×D1111yescharacteristic
168C23×Q8Dic1111yescharacteristic, complemented
169#536—28no—
170C2×C4⋊Q8—21no—
171C2×#124—21no—
172C2×#123Dic1112yescomplemented
173C2×#123C2×D1112yes—
174C2×C22⋊Q8—21no—
175C2×C22⋊Q8—21no—
176C2×#117Dic1111yescharacteristic, complemented
177C2×#101—221no—
178C2×#100—112no—
179C2×#99—112no—
180C2×#99—221no—
181#407—221no—
182#381—221no—
183#352—228no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—42no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11—42no—
194C22×C11—41no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#37911yescharacteristic
198C22×C11C2×#9911yescharacteristic
199C22×C11C2×#9911yescharacteristic
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—44no—
204C4×C11—41no—
205C4×C11—44no—
206Dic11—162no—
207C2×#41—24no—
208C2×#41—42no—
209C2×#41—42no—
210C22×Q8—21no—
211C22×Q8—24no—
212C22×Q8—21no—
213C22×Q8—42no—
214C22×Q8—42no—
215C22×Q8C22⋊D1111yescharacteristic
216C22×D4C2×Dic1111yescharacteristic
217C22×D4C22⋊D1111yescharacteristic
218C22×D4C22×D1111yescharacteristic
219C23×C4C2×Dic1111yescharacteristic
220C23×C4C2×Dic1112yes—
221C23×C4C22⋊D1111yescharacteristic
222C23×C4C22⋊D1111yescharacteristic
223C2×M16—222no—
224C4⋊Q8—28no—
225#124—28no—
226#123—24no—
227#123—24no—
228#123—24no—
229#123C22⋊D1118yes—
230C22⋊Q8—28no—
231C22⋊Q8—28no—
232#117—24no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—222no—
239C2×C22⋊C4C2×Dic1112yes—
240C2×C42—21no—
241#101—442no—
242#100—224no—
243#99—224no—
244#99—442no—
245C22⋊C8—442no—
246#95—442no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—42no—
250C2×C11—42no—
251C2×C11—81no—
252C2×C11#178111yescharacteristic
253C2×C11#212312yes—
254C24C22⋊Dic1111yescharacteristic
255C24C22×Dic1111yescharacteristic
256C24C2×C22⋊D1111yescharacteristic
257#41—416no—
258C2×Q8—24no—
259C2×Q8—24no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—41no—
263C2×Q8—416no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4C2×C22⋊D1114yes—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—442no—
292C22×C4C22⋊Dic1111yescharacteristic
293C22×C4C22⋊Dic1111yescharacteristic
294C22×C4C22⋊Dic1114yes—
295C22×C4C22⋊Dic1111yescharacteristic
296C22×C4C2×C22⋊D1111yescharacteristic
297M16—442no—
298M16—442no—
299C2×C8—442no—
300C4⋊C4—24no—
301C4⋊C4—28no—
302C4⋊C4—28no—
303C22⋊C4—28no—
304C22⋊C4—22no—
305C22⋊C4—28no—
306C22⋊C4—442no—
307C22⋊C4—442no—
308C22⋊C4C22⋊Dic1114yes—
309C42—24no—
310C11#1269211yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23C2×C22⋊Dic1111yescharacteristic
322C23C2×C22⋊Dic1112yes—
323C23#6700612yes—
324Q8—44no—
325Q8—48no—
326Q8—48no—
327D4—44no—
328D4—44no—
329D4—44no—
330C2×C4—28no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—21no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—882no—
350C2×C4—884no—
351C2×C4#6689812yes—
352C2×C4#6689812yes—
353C2×C4#6700612yes—
354C8—882no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—41no—
366C22—81no—
367C22—81no—
368C22C2×#6689811yescharacteristic
369C22C2×#6689811yescharacteristic
370C22#1062286011yescharacteristic
371C4—22no—
372C4—22no—
373C4—22no—
374C4—44no—
375C4—41no—
376C4—44no—
377C4—1762no—
378C2—21no—
379C2—21no—
380C2—42no—
381C2—42no—
382C2—81no—
383C2#1306853111yescharacteristic
384C2#1307027012yes—
subgroupG/H
centerC22C2×#66898
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC2×C11×#536C2
socleC22×C11C2×#99
prime radicalC22×C11×#41C22
cosocleC22×D4×C11C23
hypercenterC2×#536D11
hypocenterC11#12692
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#10622177C2semidirect
6. C23×Q8×C11C4semidirect
10. C2×C11×#123C4semidirect
14. C2×C11×#117C4semidirect
168. C23×Q8Dic11semidirect
172. C2×#123Dic11semidirect
176. C2×#117Dic11semidirect
310. C11#12692semidirect

Maximal subgroups

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

subgroupindex
C2×#106221772
#130685442
#130685342
C2×C11×#5362
#1269211