Finite Group Databasebeta

← #14652034

Subgroups — #14652034

Order 2816.

466 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069411C211yesmaximal, characteristic
2#13069332C211yesmaximal, characteristic, complemented
3C4×#66896C211yesmaximal, characteristic
4C2×C8×C11⋊C8C211yesmaximal, characteristic, complemented
5#13066456C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×D4⋊C8C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66896C411yescharacteristic
12C2×#66896C411yescharacteristic
13C2×C22⋊(C11⋊C8)—21no—
14C2×C22⋊(C11⋊C8)—21no—
15C2×Dic11⋊C8—21no—
16C4×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19C2×C4×C11⋊C8C2211yescharacteristic
20C11×D4⋊C8—22no—
21#10622188—21no—
22#10622167C411yescharacteristic
23#10622167C411yescharacteristic
24C8×C11⋊C8—22no—
25C22×D4×C11C2×C411yescharacteristic
26C23×C4×C11—21no—
27C22×C8×C11—21no—
28C22×C8×C11—21no—
29C4×D4×C11—21no—
30C4×D4×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4×Dic11—21no—
39C22×C11⋊C8—21no—
40C22×C11⋊C8C2×C411yescharacteristic
41C22×C11⋊C8C2×C411yescharacteristic
42C22×C11⋊C8D411yescharacteristic
43C22×C11⋊C8D411yescharacteristic
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C4×C8×C11—21no—
47C4×C8×C11D412yes—
48#66896—22no—
49#66896C814yescomplemented
50C11⋊#95—21no—
51C22⋊(C11⋊C8)—42no—
52C22⋊(C11⋊C8)—42no—
53Dic11⋊C8—42no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4×C11⋊C8—21no—
57C4×C11⋊C8—21no—
58C4×C11⋊C8—21no—
59C4×C11⋊C8—21no—
60#9554—111nomaximal, Sylow
61C24×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11C2×C812yes—
68C22×C4×C11—21no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×Dic11—21no—
79C22×Dic11—21no—
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11—22no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11C2×C812yes—
98C4×Dic11—41no—
99C4×Dic11—41no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8C2×C812yes—
112C2×C11⋊C8M1612yes—
113C2×C11⋊C8D812yes—
114C2×C11⋊C8SD1612yes—
115#1954—111no—
116#1939—111no—
117C4×#102—111no—
118C2×D4⋊C8D1111yescharacteristic
119C2×C82—111no—
120#1279—111no—
121#1277—111no—
122C23×C11—22no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11C4×D411yescharacteristic
130D4×C11—22no—
131D4×C11—22no—
132D4×C11—41no—
133D4×C11—41no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11#11711yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11#12411yescharacteristic
148C2×C4×C11#12611yescharacteristic
149C2×C4×C11C22×C811yescharacteristic
150C2×C4×C11C2×M1611yescharacteristic
151C2×C4×C11#13111yescharacteristic
152C2×C4×C11#13111yescharacteristic
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11C2×SD1611yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×Dic11—22no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C8×C11—24no—
164C8×C11—81no—
165C11⋊C8—22no—
166C11⋊C8—22no—
167C11⋊C8—22no—
168C11⋊C8—22no—
169C11⋊C8—81no—
170C2×C4×D4C2×D1111yescharacteristic
171C2×C4⋊C8—111no—
172C2×C4⋊C8—221no—
173C2×C4⋊C8C2×D1111yescharacteristic
174C2×#102—111no—
175C2×#102—111no—
176C2×C22⋊C8—221no—
177C2×C22⋊C8—221no—
178C2×C4×C8—111no—
179C2×C4×C8—111no—
180C2×C4×C8C2×D1111yescharacteristic
181C4×C4⋊C4—111no—
182#340—111no—
183#340—111no—
184#336—221no—
185D4⋊C8—22no—
186C82—222no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11#38811yescharacteristic
195C22×C11C8×D411yescharacteristic
196C22×C11#43611yescharacteristic
197C22×C11C4×D811yescharacteristic
198C22×C11C4×SD1611yescharacteristic
199C22×C11#44311yescharacteristic
200C22×C11#44311yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11#43111yescharacteristic
205C4×C11#43311yescharacteristic
206C4×C11C8×D411yescharacteristic
207C4×C11#43511yescharacteristic
208C4×C11#46511yescharacteristic
209C4×C11#46611yescharacteristic
210C4×C11#48611yescharacteristic
211C4×C11#48811yescharacteristic
212Dic11—42no—
213Dic11—81no—
214C22×D4C4×D1111yescharacteristic
215C23×C4—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—111no—
219C22×C8—111no—
220C22×C8—111no—
221C22×C8—111no—
222C22×C8—221no—
223C4×D4—21no—
224C4×D4—21no—
225C4×D4—21no—
226C4×D4—21no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4C4×D1111yescharacteristic
230C2×C22⋊C4—21no—
231C2×C42—221no—
232C2×C42C22×D1111yescharacteristic
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—221no—
236C4⋊C8—221no—
237C4⋊C8—442no—
238#102—114no—
239#102—222no—
240C22⋊C8—442no—
241C22⋊C8—442no—
242C4×C8—21no—
243C4×C8—221no—
244C4×C8—221no—
245C4×C8—221no—
246C4×C8—221no—
247C4×C8C22⋊D1112yes—
248#95—221no—
249C2×C11—82no—
250C2×C11C8×D811yescharacteristic
251C2×C11C8×SD1611yescharacteristic
252C2×C11#158911yescharacteristic
253C2×C11#159011yescharacteristic
254C2×C11#192311yescharacteristic
255C2×C11#193411yescharacteristic
256C2×C11#193711yescharacteristic
257C24—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4C8×D1112yes—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4C2×C4×D1111yescharacteristic
274C22×C4D4×D1111yescharacteristic
275C22×C4#434111yescharacteristic
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—112no—
283C2×C8—112no—
284C2×C8—112no—
285C2×C8—112no—
286C2×C8—221no—
287C2×C8—221no—
288C2×C8—221no—
289C2×C8—221no—
290C2×C8—221no—
291C2×C8—221no—
292C2×C8—221no—
293C2×C8—221no—
294C2×C8—441no—
295C2×C8—441no—
296C2×C8—441no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—112no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C42—441no—
306C42—441no—
307C42#433911yescharacteristic
308C42#434111yescharacteristic
309C42#434111yescharacteristic
310C42C2×C22⋊D1111yescharacteristic
311C11#955411yescharacteristic, complemented, Sylow
312C23—22no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23(C22⋊D11)⋊C411yescharacteristic
320D4—22no—
321D4—22no—
322D4—41no—
323D4—41no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—222no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4#6693011yescharacteristic
340C2×C4#6693211yescharacteristic
341C2×C4#6693811yescharacteristic
342C2×C4C2×C8×D1111yescharacteristic
343C2×C4#6695411yescharacteristic
344C2×C4M16×D1111yescharacteristic
345C2×C4#6696011yescharacteristic
346C2×C4D8×D1111yescharacteristic
347C2×C4#6696511yescharacteristic
348C2×C4SD16×D1111yescharacteristic
349C2×C4#6696911yescharacteristic
350C2×C4C4×C22⋊D1111yescharacteristic
351C2×C4#6698811yescharacteristic
352C2×C4#6699111yescharacteristic
353C8—24no—
354C8—81no—
355C8—222no—
356C8—222no—
357C8—222no—
358C8—222no—
359C8—881no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22(C22⋊D11)⋊C811yescharacteristic
368C22#1062234211yescharacteristic
369C22#1062236911yescharacteristic
370C22#1062237111yescharacteristic
371C22#1062243711yescharacteristic
372C22#1062243711yescharacteristic
373C22#1062255711yescharacteristic
374C4—21no—
375C4—21no—
376C4—81no—
377C4—442no—
378C4—881no—
379C4#1062233111yescharacteristic
380C4#1062233311yescharacteristic
381C4#1062237311yescharacteristic
382C4#1062238111yescharacteristic
383C4C8×C22⋊D1111yescharacteristic
384C4#1062274011yescharacteristic
385C4#1062277011yescharacteristic
386C4#1062278411yescharacteristic
387C2—82no—
388C2#1306740811yescharacteristic
389C2#1306741911yescharacteristic
390C2#1306749811yescharacteristic
391C2#1306750911yescharacteristic
392C2#1306921911yescharacteristic
393C2#1306929611yescharacteristic
394C2#1306931711yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11C4×D4
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenterC2×D4⋊C8D11
hypocenterC11#9554
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13069332C2semidirect
4. C2×C8×C11⋊C8C2semidirect
5. #13066456C2semidirect
6. #13066450C2semidirect
49. #66896C8semidirect
311. C11#9554semidirect

Maximal subgroups

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

subgroupindex
#130694112
#130693322
C4×#668962
C2×C8×C11⋊C82
#130664562
#130664502
C2×C11×D4⋊C82
#955411