Finite Group Databasebeta

← #14641986

Subgroups — #14641986

Order 2816.

462 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071185C211yesmaximal, characteristic
2#13068758C211yesmaximal, characteristic
3#13068468C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic
6#13066441C211yesmaximal, characteristic
7C11×#1272C211yesmaximal, characteristic
8C2×Q8×Dic11C411yescharacteristic
9C2×#66997C411yescharacteristic
10C2×#66940C411yescharacteristic
11C11×#391C2211yescharacteristic
12C2×#66879—21no—
13C2×Dic11⋊C8—21no—
14#10622589C411yescharacteristic
15C42×Dic11C2211yescharacteristic
16#10622542C2211yescharacteristic
17#10622262—21no—
18#10622262—21no—
19#10622260—21no—
20#10622260—21no—
21C11×#336C2211yescharacteristic
22C11×#336C2211yescharacteristic
23#10622188—21no—
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11C2×C411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33Q8×Dic11—42no—
34#66997—22no—
35#66997—22no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11C2×C411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C2×C4×Dic11D411yescharacteristic
51C22×C11⋊C8—21no—
52C22×C11⋊C8—21no—
53#66940—42no—
54C11×#95—21no—
55C11×#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58#66879—42no—
59Dic11⋊C8—24no—
60#7624—111nomaximal, Sylow
61C2×Q8×C11—21no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C2×Q8×C11M1612yes—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C2×Dic22—21no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22M1612yes—
80C2×C8×C11—22no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—41no—
87C42×C11—41no—
88C4⋊Dic11—41no—
89C4⋊Dic11—42no—
90Dic11⋊C4—24no—
91Dic11⋊C4—24no—
92Dic11⋊C4—42no—
93Dic11⋊C4—42no—
94Dic11⋊C4—42no—
95C4×Dic11—22no—
96C4×Dic11—22no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—41no—
102C4×Dic11—42no—
103C4×Dic11—42no—
104C4×Dic11SD1612yes—
105C4×Dic11Q1612yes—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C4×C4⋊Q8—111no—
113#1839—111no—
114#1767—111no—
115#1272—111no—
116#1272—111no—
117#1272—111no—
118#1272D1111yescharacteristic
119C23×C11C2×C22⋊C411yescharacteristic
120Q8×C11—42no—
121Q8×C11—42no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11C2×M1611yescharacteristic
135C2×C4×C11C2×M1611yescharacteristic
136C2×C4×C11C2×SD1611yescharacteristic
137C2×C4×C11C2×Q1611yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—22no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11#10012yes—
155C2×Dic11#10312yes—
156C2×Dic11#10312yes—
157C2×Dic11#10412yes—
158Dic22—42no—
159Dic22—42no—
160C8×C11—42no—
161C8×C11—81no—
162C11⋊C8—42no—
163C11⋊C8—81no—
164C2×C4⋊Q8—111no—
165C2×C4×Q8—111no—
166C2×C4×Q8—111no—
167C2×C4⋊C8—221no—
168C2×#97—221no—
169#391—111no—
170#391C2×D1111yescharacteristic
171#389—221no—
172#389—221no—
173#384—111no—
174C4×C4⋊C4—221no—
175C4×C4⋊C4—221no—
176C43—111no—
177#336—111no—
178#336—111no—
179#336—221no—
180#336—221no—
181#336C2×D1111yescharacteristic
182#336C2×D1111yescharacteristic
183C22×C11#40711yescharacteristic
184C22×C11#41011yescharacteristic
185C22×C11C2×#10011yescharacteristic
186C22×C11C2×#10311yescharacteristic
187C22×C11#41911yescharacteristic
188C22×C11C2×#10411yescharacteristic
189C22×C11#42111yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—42no—
197C4×C11—81no—
198Dic11—22no—
199Dic11—22no—
200Dic11—22no—
201Dic11—22no—
202Dic11—42no—
203Dic11—81no—
204C22×Q8—111no—
205C22×Q8C4×D1111yescharacteristic
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—221no—
209C22×C8—221no—
210C4⋊Q8—222no—
211C4⋊Q8—222no—
212C4×Q8—442no—
213C4×Q8—442no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4C4×D1111yescharacteristic
222C2×C42—111no—
223C2×C42—111no—
224C2×C42—111no—
225C2×C42—111no—
226C2×C42—111no—
227C2×C42—111no—
228C2×C42—221no—
229C2×C42—221no—
230C2×C42C22×D1111yescharacteristic
231C4⋊C8—224no—
232#97—442no—
233#95—21no—
234#95—21no—
235#95—221no—
236#95—221no—
237C2×C11#146611yescharacteristic
238C2×C11#148711yescharacteristic
239C2×C11#149111yescharacteristic
240C2×C11#150311yescharacteristic
241C2×C11#151511yescharacteristic
242C2×C11#153011yescharacteristic
243C2×C11#154811yescharacteristic
244C2×Q8—21no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—112no—
248C2×Q8—221no—
249C2×Q8—441no—
250C2×Q8—441no—
251C2×Q8#431312yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—111no—
257C22×C4—111no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4C2×C4×D1111yescharacteristic
261C22×C4D4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—222no—
270C2×C8—441no—
271C2×C8—441no—
272C2×C8—441no—
273C2×C8—441no—
274C2×C8—441no—
275C4⋊C4—41no—
276C4⋊C4—224no—
277C4⋊C4—224no—
278C4⋊C4—441no—
279C4⋊C4—442no—
280C4⋊C4—442no—
281C4⋊C4—442no—
282C4⋊C4—442no—
283C42—41no—
284C42—112no—
285C42—112no—
286C42—222no—
287C42—222no—
288C42—221no—
289C42—221no—
290C42—221no—
291C42—221no—
292C42—441no—
293C42—442no—
294C42—442no—
295C11#762411yescharacteristic, complemented, Sylow
296C23C22⋊C4×D1111yescharacteristic
297Q8—42no—
298Q8—42no—
299Q8—442no—
300Q8—442no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—112no—
314C2×C4—112no—
315C2×C4—112no—
316C2×C4—112no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—222no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4C2×#431311yescharacteristic
332C2×C4M16×D1111yescharacteristic
333C2×C4SD16×D1111yescharacteristic
334C2×C4#6696811yescharacteristic
335C2×C4Q16×D1111yescharacteristic
336C2×C4#6697111yescharacteristic
337C8—42no—
338C8—81no—
339C8—442no—
340C8—881no—
341C22#1062233911yescharacteristic
342C22#1062235311yescharacteristic
343C22D11×#10011yescharacteristic
344C22D11×#10311yescharacteristic
345C22#1062241511yescharacteristic
346C22D11×#10411yescharacteristic
347C22#1062243411yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—81no—
356C4—222no—
357C4—222no—
358C4—222no—
359C4—222no—
360C4—442no—
361C4—881no—
362C2#1306695511yescharacteristic
363C2#1306704311yescharacteristic
364C2#1306706111yescharacteristic
365C2#1306711311yescharacteristic
366C2#1306716511yescharacteristic
367C2#1306722511yescharacteristic
368C2#1306729511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1272D11
hypocenterC11#7624
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
295. C11#7624semidirect

Maximal subgroups

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

subgroupindex
#130711852
#130687582
#130684682
#130664422
#130664412
C11×#12722
#762411