Finite Group Databasebeta

← #14664482

Subgroups — #14664482

Order 2816.

680 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 87 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×#10622560C211yesmaximal, characteristic
2#13068690C211yesmaximal, characteristic
3#13066638C214yesmaximal, complemented
4C11×#1462C211yesmaximal, characteristic
5C23×Dic22C411yescharacteristic, complemented
6C22×C11×C22⋊C4C2211yescharacteristic
7C22×C22⋊Dic11—21no—
8C11×#407—21no—
9#10622860—21no—
10C2×C11⋊#95—21no—
11C2×C11⋊#95C411yescharacteristic, complemented
12#10622560—21no—
13#10622560—21no—
14#10622560C412yescomplemented
15#10622560C2212yes—
16C11×#323—21no—
17C11×#323C2212yes—
18#10622164—21no—
19#10622164C2212yes—
20C25×C11D411yescharacteristic
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11—21no—
24C23×Dic11—21no—
25C22×Dic22—21no—
26C22×Dic22—41no—
27C22×Dic22—41no—
28C22×Dic22—44no—
29C22×Dic22C2×C412yes—
30C2×C11×M16—41no—
31C2×C11×C22⋊C4—41no—
32C2×C11×C22⋊C4—41no—
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C22⋊Dic11—22no—
38C2×C22⋊Dic11—22no—
39C2×C22⋊Dic11—22no—
40C2×C22⋊Dic11—44no—
41C2×C22⋊Dic11—41no—
42C2×C22⋊Dic11—41no—
43C11×C22⋊C8—22no—
44C11×C22⋊C8—41no—
45C11⋊#95—21no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95C2×C412yes—
49#11808—111nomaximal, Sylow
50C24×C11—22no—
51C24×C11—21no—
52C24×C11—21no—
53C24×C11—41no—
54C24×C11—42no—
55C24×C11—42no—
56C24×C11C22⋊C411yescharacteristic
57C24×C11C22⋊C411yescharacteristic
58C24×C11C2×D411yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—24no—
70C22×Dic11—22no—
71C22×Dic11—22no—
72C22×Dic11—42no—
73C22×Dic11—42no—
74C22×Dic11—42no—
75C22×Dic11—42no—
76C22×Dic11—42no—
77C22×Dic11—41no—
78C22×Dic11—41no—
79C2×Dic22—42no—
80C2×Dic22—42no—
81C2×Dic22—44no—
82C2×Dic22—44no—
83C2×Dic22—48no—
84C2×Dic22—44no—
85C2×Dic22—44no—
86C11×M16—82no—
87C2×C8×C11—42no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C22⋊Dic11—42no—
93C22⋊Dic11—44no—
94C22⋊Dic11—44no—
95C22⋊Dic11—42no—
96C22⋊Dic11—82no—
97C22⋊Dic11—82no—
98C2×#393—111no—
99#1819—111no—
100#1462D1111yescharacteristic
101#1351—114no—
102C23×C11—22no—
103C23×C11—22no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—42no—
112C23×C11—42no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—48no—
118C23×C11—42no—
119C23×C11—42no—
120C23×C11—81no—
121C23×C11—81no—
122C23×C11—84no—
123C23×C11#9911yescharacteristic
124C23×C11#9911yescharacteristic
125C23×C11C2×C22⋊C411yescharacteristic
126C23×C11#13712yes—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—81no—
139C2×Dic11—24no—
140C2×Dic11—42no—
141C2×Dic11—44no—
142C2×Dic11—44no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—84no—
148C2×Dic11—82no—
149C2×Dic11—82no—
150C2×Dic11—82no—
151Dic22—44no—
152Dic22—48no—
153Dic22—44no—
154C8×C11—82no—
155C23×Q8—111no—
156C22×C22⋊C4—221no—
157C22×C22⋊C4C2×D1111yescharacteristic
158#407—21no—
159#393—112no—
160#393—112no—
161#393—221no—
162#393—221no—
163#379—221no—
164C2×#95—111no—
165C2×#95—221no—
166#342—112no—
167#342—221no—
168#323—21no—
169#323C2×D1112yes—
170C22×C11—24no—
171C22×C11—24no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—22no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—81no—
187C22×C11—84no—
188C22×C11—84no—
189C22×C11—81no—
190C22×C11AΣL(1,𝔽16)12yes—
191C22×C11#35412yes—
192C22×C11C2×#9911yescharacteristic
193C22×C11#41911yescharacteristic
194C22×C11#42111yescharacteristic
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199Dic11—44no—
200Dic11—82no—
201Dic11—162no—
202C25D4411yescharacteristic
203C22×Q8—112no—
204C22×Q8—221no—
205C22×Q8—441no—
206C22×Q8—441no—
207C22×Q8—444no—
208C23×C4—221no—
209C23×C4—221no—
210C23×C4C4×D1111yescharacteristic
211C23×C4C22⋊D1111yescharacteristic
212C2×M16—41no—
213C2×C22⋊C4—41no—
214C2×C22⋊C4—41no—
215C2×C22⋊C4—222no—
216C2×C22⋊C4—222no—
217C2×C22⋊C4—222no—
218C2×C22⋊C4—444no—
219C2×C22⋊C4—441no—
220C2×C22⋊C4—441no—
221C2×C22⋊C4C4×D1111yescharacteristic
222C2×C22⋊C4D4411yescharacteristic
223C2×C22⋊C4C22⋊D1111yescharacteristic
224C2×C22⋊C4C22×D1111yescharacteristic
225C22⋊C8—22no—
226C22⋊C8—41no—
227#95—112no—
228#95—221no—
229#95—222no—
230#95—222no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11—22no—
234C2×C11—22no—
235C2×C11—42no—
236C2×C11—81no—
237C2×C11#151111yescharacteristic
238C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
239C2×C11C2×#35411yescharacteristic
240C24—22no—
241C24—21no—
242C24—21no—
243C24—41no—
244C24—42no—
245C24—42no—
246C24(C2×D11)⋊C411yescharacteristic
247C24(C2×D11)⋊C411yescharacteristic
248C24C2×D4411yescharacteristic
249C2×Q8—442no—
250C2×Q8—442no—
251C2×Q8—444no—
252C2×Q8—444no—
253C2×Q8—448no—
254C2×Q8—444no—
255C2×Q8—444no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—224no—
263C22×C4—222no—
264C22×C4—222no—
265C22×C4—442no—
266C22×C4—441no—
267C22×C4—441no—
268C22×C4—442no—
269C22×C4—442no—
270C22×C4—442no—
271C22×C4—442no—
272C22×C4(C2×D11)⋊C411yescharacteristic
273C22×C4(C2×D11)⋊C411yescharacteristic
274C22×C4C2×C4×D1111yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276M16—82no—
277C2×C8—42no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—444no—
283C22⋊C4—444no—
284C22⋊C4—442no—
285C22⋊C4—442no—
286C22⋊C4—882no—
287C22⋊C4—882no—
288C11#1180811yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—22no—
292C23—22no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—42no—
299C23—42no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—48no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—81no—
309C23—84no—
310C23#6687011yescharacteristic
311C23#6687011yescharacteristic
312C23#6696212yes—
313C23C2×(C2×D11)⋊C411yescharacteristic
314Q8—444no—
315Q8—448no—
316Q8—444no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—224no—
330C2×C4—442no—
331C2×C4—444no—
332C2×C4—442no—
333C2×C4—444no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—884no—
338C2×C4—882no—
339C2×C4—882no—
340C2×C4—882no—
341C8—82no—
342C22—24no—
343C22—24no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—42no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—84no—
360C22—84no—
361C22—81no—
362C22#1062211112yes—
363C22#1062211312yes—
364C22C2×#6687011yescharacteristic
365C22#1062273311yescharacteristic
366C22#1062275211yescharacteristic
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—444no—
372C4—882no—
373C4—1762no—
374C2—21no—
375C2—21no—
376C2—22no—
377C2—22no—
378C2—42no—
379C2—81no—
380C2#1306715011yescharacteristic
381C2C2×#1062211311yescharacteristic
382C2C2×#1062211111yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1462C2
socleC22×C11C2×#99
prime radicalC25×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1462D11
hypocenterC11#11808
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
3. #13066638C2semidirect
5. C23×Dic22C4semidirect
11. C2×C11⋊#95C4semidirect
14. #10622560C4semidirect
288. C11#11808semidirect

Maximal subgroups

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

subgroupindex
C2×#106225602
#130686902
#130666382
C11×#14622
#1180811