Finite Group Databasebeta

← #14643751

Subgroups — #14643751

Order 2816.

522 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077245C211yesmaximal, characteristic
2#13077245C211yesmaximal, characteristic
3C2×#10622332C211yesmaximal, characteristic
4#13066493C211yesmaximal, characteristic
5#13066492C211yesmaximal, characteristic
6#13066492C211yesmaximal, characteristic
7C11×#1293C211yesmaximal, characteristic
8C22×C4×Dic11C2211yescharacteristic
9C11×#407C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12#10622820C2211yescharacteristic
13#10622820C2211yescharacteristic
14C2×C22⋊(C11⋊C8)C2211yescharacteristic
15#10622731—21no—
16#10622731—21no—
17M16×Dic11—21no—
18M16×Dic11—21no—
19C2×#66879C412yes—
20C2×Dic11⋊C8C412yes—
21#10622332—21no—
22#10622332—21no—
23#10622332—21no—
24#10622332—21no—
25#10622332—21no—
26#10622332—21no—
27#10622332C412yes—
28#10622332C412yes—
29#10622331—21no—
30#10622331—21no—
31#10622331C412yes—
32#10622331C412yes—
33C23×C4×C11C2311yescharacteristic
34C23×Dic11Q811yescharacteristic
35C23×Dic11Q811yescharacteristic
36C2×C11×M16—21no—
37C2×C11×M16—21no—
38C22×C8×C11C2×C412yes—
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11C2×C411yescharacteristic
41C2×C4×Dic11C2×C411yescharacteristic
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11C2×C411yescharacteristic
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C2×C4×Dic11D411yescharacteristic
51C2×#4318—21no—
52C2×#4318—21no—
53C22×C11⋊C8C2×C412yes—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8C2×C412yes—
59C11×C22⋊C8C2×C412yes—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)C2×C412yes—
65C22⋊(C11⋊C8)C2×C412yes—
66#66879—22no—
67#66879—22no—
68#66879—22no—
69#66879—22no—
70Dic11⋊C8—22no—
71Dic11⋊C8—22no—
72Dic11⋊C8—22no—
73Dic11⋊C8—22no—
74Dic11⋊C8—22no—
75Dic11⋊C8—22no—
76C8×Dic11—22no—
77C8×Dic11—22no—
78#8010—111nomaximal, Sylow
79C24×C11C2×Q811yescharacteristic
80C22×C4×C11—42no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—42no—
88C22×Dic11—42no—
89C22×Dic11C4⋊C411yescharacteristic
90C22×Dic11C4⋊C411yescharacteristic
91C22×Dic11C4⋊C411yescharacteristic
92C22×Dic11C4⋊C411yescharacteristic
93C22×Dic11C4⋊C411yescharacteristic
94C22×Dic11C4⋊C411yescharacteristic
95C22×Dic11C4⋊C411yescharacteristic
96C22×Dic11C4⋊C411yescharacteristic
97C22×Dic11C4⋊C411yescharacteristic
98C22×Dic11C4⋊C411yescharacteristic
99C22×Dic11C4⋊C411yescharacteristic
100C22×Dic11C4⋊C411yescharacteristic
101C11×M16—42no—
102C11×M16—42no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—42no—
107C4×Dic11C4211yescharacteristic
108C4×Dic11C4211yescharacteristic
109C4×Dic11C4211yescharacteristic
110C4×Dic11C4211yescharacteristic
111C4×Dic11C22⋊C411yescharacteristic
112C4×Dic11C22⋊C411yescharacteristic
113C4×Dic11C22⋊C411yescharacteristic
114C4×Dic11C22⋊C411yescharacteristic
115C4×Dic11C22⋊C411yescharacteristic
116C4×Dic11C22⋊C411yescharacteristic
117C4×Dic11C22⋊C411yescharacteristic
118C4×Dic11C22⋊C411yescharacteristic
119C4×Dic11C22⋊C411yescharacteristic
120C4×Dic11C22⋊C411yescharacteristic
121C4×Dic11C22⋊C411yescharacteristic
122C4×Dic11C22⋊C411yescharacteristic
123#4318—42no—
124#4318—42no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—42no—
129#2920—111no—
130#2920—111no—
131C2×#432—111no—
132#1293—111no—
133#1293—111no—
134#1293—111no—
135#1293D1111yescharacteristic
136C23×C11—22no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11C2×C4⋊C411yescharacteristic
140C23×C11C2×C4⋊C411yescharacteristic
141C23×C11C2×C4⋊C411yescharacteristic
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11C2×C4211yescharacteristic
149C2×C4×C11C2×C22⋊C411yescharacteristic
150C2×C4×C11C2×C22⋊C411yescharacteristic
151C2×C4×C11C2×C22⋊C411yescharacteristic
152C2×Dic11—22no—
153C2×Dic11—22no—
154C2×Dic11—22no—
155C2×Dic11—22no—
156C2×Dic11—22no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11#9511yescharacteristic
165C2×Dic11#9511yescharacteristic
166C2×Dic11#9511yescharacteristic
167C2×Dic11#9511yescharacteristic
168C2×Dic11#9511yescharacteristic
169C2×Dic11#9511yescharacteristic
170C2×Dic11#9511yescharacteristic
171C2×Dic11#9511yescharacteristic
172C8×C11—42no—
173C8×C11—42no—
174C8×C11—42no—
175C11⋊C8—42no—
176C11⋊C8—42no—
177C11⋊C8—42no—
178C22×C42—111no—
179#432—112no—
180#432—112no—
181#432—221no—
182#432—221no—
183#432—221no—
184#432—221no—
185#432—221no—
186#432—221no—
187#431—112no—
188#431—112no—
189#431—221no—
190#431—221no—
191#423—221no—
192#423—221no—
193C2×C4⋊C8—112no—
194#407—111no—
195#407—111no—
196#407C2×D1111yescharacteristic
197#407C2×D1111yescharacteristic
198C2×C22⋊C8—111no—
199C2×C22⋊C8C2×D1111yescharacteristic
200C4×M16—221no—
201C4×M16—221no—
202C2×#97—112no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—44no—
212C22×C11C2×#9511yescharacteristic
213C22×C11#43012yes—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11#41012yes—
218Dic11—21no—
219Dic11—21no—
220Dic11—21no—
221Dic11—21no—
222Dic11—21no—
223Dic11—21no—
224Dic11—21no—
225Dic11#33812yes—
226C23×C4—111no—
227C23×C4—111no—
228C23×C4C22×D1111yescharacteristic
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—221no—
232C2×M16—221no—
233C22×C8—112no—
234C22×C8C4×D1112yes—
235C2×C42—111no—
236C2×C42—111no—
237C2×C42—111no—
238C2×C42—111no—
239C2×C42—111no—
240C2×C42—111no—
241C2×C42—111no—
242C2×C42—111no—
243C2×C42—111no—
244C2×C42—111no—
245C2×C42—111no—
246C2×C42—111no—
247C4⋊C8—222no—
248C4⋊C8—222no—
249C4⋊C8—222no—
250C4⋊C8—222no—
251C4⋊C8—222no—
252C4⋊C8—222no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—112no—
258C22⋊C8—112no—
259C22⋊C8—221no—
260C22⋊C8—221no—
261C22⋊C8—221no—
262C22⋊C8—221no—
263C22⋊C8C4×D1112yes—
264C22⋊C8C4×D1112yes—
265#97—222no—
266#97—222no—
267#97—222no—
268#97—222no—
269C4×C8—222no—
270C4×C8—222no—
271C2×C11—22no—
272C2×C11—41no—
273C2×C11—41no—
274C2×C11C2×#33811yescharacteristic
275C2×C11#173811yescharacteristic
276C2×C11#174011yescharacteristic
277C24Q8×D1111yescharacteristic
278C22×C4—42no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—111no—
282C22×C4—111no—
283C22×C4—111no—
284C22×C4—111no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—111no—
291C22×C4—442no—
292C22×C4—442no—
293C22×C4C2×C4×D1111yescharacteristic
294C22×C4C2×C4×D1111yescharacteristic
295C22×C4C2×C4×D1111yescharacteristic
296C22×C4D4×D1111yescharacteristic
297C22×C4D4×D1111yescharacteristic
298C22×C4D4×D1111yescharacteristic
299M16—42no—
300M16—42no—
301M16—442no—
302M16—442no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—42no—
307C2×C8—222no—
308C2×C8—222no—
309C2×C8—222no—
310C2×C8—442no—
311C42—111no—
312C42—111no—
313C42—111no—
314C42—111no—
315C42—111no—
316C42—111no—
317C42—111no—
318C42—111no—
319C42—111no—
320C42—111no—
321C42—111no—
322C42—111no—
323C42—111no—
324C42—111no—
325C42—111no—
326C42—111no—
327C11#801011yescharacteristic, complemented, Sylow
328C23—22no—
329C23—41no—
330C23—41no—
331C23C4⋊C4×D1111yescharacteristic
332C23C4⋊C4×D1111yescharacteristic
333C23C4⋊C4×D1111yescharacteristic
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—111no—
341C2×C4—111no—
342C2×C4—111no—
343C2×C4—111no—
344C2×C4—111no—
345C2×C4—111no—
346C2×C4—111no—
347C2×C4—111no—
348C2×C4—222no—
349C2×C4—222no—
350C2×C4—222no—
351C2×C4—222no—
352C2×C4—222no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4C42×D1111yescharacteristic
361C2×C4C22⋊C4×D1111yescharacteristic
362C2×C4C22⋊C4×D1111yescharacteristic
363C2×C4C22⋊C4×D1111yescharacteristic
364C8—42no—
365C8—42no—
366C8—42no—
367C8—442no—
368C8—442no—
369C8—442no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—44no—
379C22D11×#9511yescharacteristic
380C22#1062250612yes—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—112no—
385C4—221no—
386C4—221no—
387C4—221no—
388C4—221no—
389C4—221no—
390C4—221no—
391C4—221no—
392C4#1062235312yes—
393C2—22no—
394C2—41no—
395C2—41no—
396C2D11×#33811yescharacteristic
397C2#1306834111yescharacteristic
398C2#1306834711yescharacteristic
subgroupG/H
centerC22D11×#95
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1293C2
socleC22×C11C2×#95
prime radicalC24×C11C2×Q8
cosocleC23×C4×C11C23
hypercenter#1293D11
hypocenterC11#8010
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1293

Complements

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

NH ≅ G/Ntype
327. C11#8010semidirect

Maximal subgroups

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

subgroupindex
#130772452
C2×#106223322
#130664932
#130664922
C11×#12932
#801011