Finite Group Databasebeta

← #14664886

Subgroups — #14664886

Order 2816.

390 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 79 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
1D11×#467C211yesmaximal, characteristic
2#13070225C211yesmaximal, characteristic
3#13068653C211yesmaximal, characteristic
4#13066635C211yesmaximal, characteristic, complemented
5#13066634C211yesmaximal, characteristic, complemented
6#13066633C211yesmaximal, characteristic, complemented
7C11×#1350C211yesmaximal, characteristic, complemented
8C2×Q16×D11C411yescharacteristic
9C22×C8×D11C2211yescharacteristic
10D11×C22⋊Q8—21no—
11C11×#467C2211yescharacteristic
12#10622801C411yescharacteristic
13#10622739—21no—
14C2×#66886—21no—
15#10622729C2211yescharacteristic
16#10622664—21no—
17C2×#66862—21no—
18#10622500C411yescharacteristic
19D11×#107C411yescharacteristic
20#10622426—21no—
21D11×#103—21no—
22C11×C22⋊C16C2211yescharacteristic
23C11×#341C2211yescharacteristic
24#10622190C2211yescharacteristic
25C22⋊(C11⋊C16)C2211yescharacteristic
26(C2×D11)⋊C16—21no—
27C2×Q8×D11—21no—
28C22×C4×D11D411yescharacteristic
29C2×C11×Q16C2×C411yescharacteristic
30C2×C11×M16—21no—
31C22×C8×C11C2311yescharacteristic
32C11×C22⋊Q8—21no—
33#66999—21no—
34C2×#4326—21no—
35#66977—21no—
36C2×#4318—21no—
37C22×C11⋊C8D411yescharacteristic
38Q16×D11—42no—
39C2×Dic44C2×C411yescharacteristic
40C2×C8×D11—42no—
41C2×C8×D11C2×C411yescharacteristic
42C2×C8×D11C2×C411yescharacteristic
43C2×C8×D11D411yescharacteristic
44C2×C8×D11D411yescharacteristic
45#66950—21no—
46#66949—41no—
47C4⋊C4×D11—21no—
48C4⋊C4×D11—41no—
49C22⋊C4×D11—41no—
50#66931—41no—
51C2×C11×C16—21no—
52C11×#107C2×C411yescharacteristic
53C11×#103—21no—
54#66899—21no—
55#66886—42no—
56(C2×D11)⋊C8—41no—
57(C2×D11)⋊C8—41no—
58#66882C2×C411yescharacteristic
59#66880—21no—
60C2×C11⋊C16—21no—
61#66874—21no—
62#66871—21no—
63#66862—42no—
64#11896—111nomaximal, Sylow
65C23×D11SD1611yescharacteristic
66C2×Q8×C11—21no—
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11SD1611yescharacteristic
69Q8×D11—42no—
70Q8×D11—42no—
71C2×C4×D11—41no—
72C2×C4×D11—41no—
73C2×C4×D11—41no—
74C2×C4×D11—41no—
75C2×C4×D11C22⋊C411yescharacteristic
76C2×C4×D11C22⋊C411yescharacteristic
77C2×C4×D11D811yescharacteristic
78C2×C4×D11D811yescharacteristic
79C2×Dic22—21no—
80C2×Dic22—41no—
81C11×Q16—41no—
82C11×M16—41no—
83C11×M16—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11C22×C411yescharacteristic
87C2×C8×C11C2×D411yescharacteristic
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C22⋊Dic11—41no—
92#4326—42no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95C4⋊Dic11—21no—
96C4⋊Dic11—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99Dic11⋊C4—41no—
100#4318—41no—
101#4318—41no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8C22⋊C411yescharacteristic
105C2×C11⋊C8C22⋊C411yescharacteristic
106Dic44—41no—
107C8×D11—22no—
108C8×D11—22no—
109C8×D11—41no—
110C8×D11—41no—
111C11×C16—41no—
112C11⋊C16—41no—
113C2×#467—111no—
114#2112—111no—
115#1810—111no—
116#1350—111no—
117#1350—111no—
118#1350—111no—
119#1350D1111yescharacteristic, complemented
120C23×C11C2×SD1611yescharacteristic
121C22×D11—22no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11#10211yescharacteristic
125C22×D11#10211yescharacteristic
126Q8×C11—41no—
127Q8×C11—41no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11C2×C22⋊C411yescharacteristic
133C2×C4×C11C2×D811yescharacteristic
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11#10211yescharacteristic
138C2×Dic11#10211yescharacteristic
139C4×D11—21no—
140C4×D11—21no—
141C4×D11—21no—
142C4×D11—21no—
143C4×D11—41no—
144C4×D11—41no—
145C4×D11—82no—
146C4×D11—82no—
147Dic22—41no—
148Dic22—41no—
149Dic22—82no—
150C8×C11—21no—
151C8×C11—21no—
152C8×C11—81no—
153C11⋊C8—21no—
154C11⋊C8—81no—
155C11⋊C8#9912yes—
156C22×Q16—111no—
157C23×C8—111no—
158C2×C22⋊Q8—221no—
159C2×M32—221no—
160#467—111no—
161#467—111no—
162#467—111no—
163#467—221no—
164#467—221no—
165#467C2×D1111yescharacteristic
166C2×#108—221no—
167C2×#107—111no—
168C2×#103—221no—
169#407—221no—
170C22⋊C16—111no—
171C22⋊C16—221no—
172C22⋊C16C2×D1111yescharacteristic
173#341—111no—
174#341C2×D1111yescharacteristic
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11C2×#10211yescharacteristic
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—44no—
185C2×D11#36212yes—
186C4×C11—21no—
187C4×C11—81no—
188C4×C11—81no—
189C4×C11C2×#9911yescharacteristic
190C4×C11#42111yescharacteristic
191Dic11—21no—
192Dic11—21no—
193Dic11—81no—
194Dic11—81no—
195C22×Q8—221no—
196C23×C4—111no—
197C2×Q16—111no—
198C2×Q16—221no—
199C2×Q16—442no—
200C2×Q16C4×D1111yescharacteristic
201C2×M16—21no—
202C2×M16—221no—
203C22×C8—111no—
204C22×C8—111no—
205C22×C8—111no—
206C22×C8—111no—
207C22×C8—111no—
208C22×C8—442no—
209C22×C8C22×D1111yescharacteristic
210C22⋊Q8—21no—
211C22⋊Q8—221no—
212C22⋊Q8—221no—
213C22⋊Q8—221no—
214C22⋊Q8—441no—
215C22⋊Q8—441no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—441no—
218C2×C22⋊C4—441no—
219M32—442no—
220C2×C16—21no—
221C2×C16—221no—
222#108—442no—
223#107—111no—
224#107—221no—
225#107C4×D1111yescharacteristic
226#103—21no—
227#103—221no—
228#103—221no—
229#103—221no—
230C22⋊C8—441no—
231C22⋊C8—441no—
232C2×C11—41no—
233C2×C11#151911yescharacteristic
234C2×C11#214311yescharacteristic
235C2×C11C2×#36211yescharacteristic
236D11—22no—
237D11—41no—
238C24—111no—
239C2×Q8—21no—
240C2×Q8—221no—
241C2×Q8—441no—
242C2×Q8—442no—
243C2×Q8—442no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—441no—
250C22×C4—441no—
251C22×C4—441no—
252C22×C4—441no—
253C22×C4D4×D1111yescharacteristic
254Q16—41no—
255Q16—441no—
256Q16—442no—
257M16—41no—
258M16—41no—
259M16—441no—
260M16—441no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—111no—
264C2×C8—111no—
265C2×C8—222no—
266C2×C8—222no—
267C2×C8—222no—
268C2×C8—441no—
269C2×C8—441no—
270C2×C8—441no—
271C2×C8C2×C4×D1111yescharacteristic
272C2×C8D4×D1111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—221no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C22⋊C4—41no—
281C22⋊C4—441no—
282C22⋊C4—441no—
283C22⋊C4—441no—
284C16—41no—
285C16—441no—
286C11#1189611yescharacteristic, complemented, Sylow
287C23—111no—
288C23—111no—
289C23—222no—
290C23—441no—
291C23—441no—
292C23SD16×D1111yescharacteristic
293Q8—41no—
294Q8—41no—
295Q8—441no—
296Q8—441no—
297Q8—882no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—111no—
303C2×C4—111no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—882no—
314C2×C4—882no—
315C2×C4C22⋊C4×D1111yescharacteristic
316C2×C4D8×D1111yescharacteristic
317C8—21no—
318C8—21no—
319C8—81no—
320C8—112no—
321C8—221no—
322C8—881no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—112no—
327C22—221no—
328C22—221no—
329C22—221no—
330C22—221no—
331C22—221no—
332C22—444no—
333C22D11×#10211yescharacteristic
334C4—21no—
335C4—81no—
336C4—81no—
337C4—221no—
338C4—221no—
339C4—881no—
340C4—881no—
341C4D11×#9911yescharacteristic
342C4#1062243411yescharacteristic
343C2—41no—
344C2—222no—
345C2—441no—
346C2#1306718211yescharacteristic
347C2#1307034211yescharacteristic
348C2D11×#36211yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1350C2
socleC22×C11C2×#102
prime radicalC23×D11SD16
cosocleC22×C8×C11C23
hypercenter#1350D11
hypocenterC11#11896
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1350

Complements

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

NH ≅ G/Ntype
4. #13066635C2semidirect
5. #13066634C2semidirect
6. #13066633C2semidirect
7. C11×#1350C2semidirect
119. #1350D11semidirect
286. C11#11896semidirect

Maximal subgroups

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

subgroupindex
D11×#4672
#130702252
#130686532
#130666352
#130666342
#130666332
C11×#13502
#1189611