Finite Group Databasebeta

← #14670839

Subgroups — #14670839

Order 2816.

526 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622202C211yesmaximal, characteristic, complemented
3C2×#10622200C211yesmaximal, characteristic
4#13069483C211yesmaximal, characteristic
5#13066708C211yesmaximal, characteristic, complemented
6#13066693C211yesmaximal, characteristic, complemented
7C22×C11×SD32C211yesmaximal, characteristic
8C22×C11×Q16C2211yescharacteristic
9C22×C11×D8C2211yescharacteristic
10C2×Q8×Dic11—21no—
11C2×C11×SD32—22no—
12C2×C11×SD32—22no—
13C2×C11×SD32C414yescomplemented
14C22×C11×C16C2211yescharacteristic
15C2×#66899—21no—
16#10622834—21no—
17C2×#66896—21no—
18Q16×Dic11—22no—
19Q16×Dic11—22no—
20C2×#66882C2211yescharacteristic
21C2×#66882C2211yescharacteristic
22C2×C8×Dic11C2211yescharacteristic
23C22×C11⋊C16C2211yescharacteristic
24#10622202—22no—
25#10622200—22no—
26C22×Q8×C11—21no—
27C22×D4×C11—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16—21no—
30C2×C11×Q16—21no—
31C2×C11×Q16C2×C412yes—
32C2×C11×Q16D412yes—
33C2×C11×Q16D412yes—
34C2×C11×D8—21no—
35C2×C11×D8—21no—
36C2×C11×D8—21no—
37C2×C11×D8—21no—
38C2×C11×D8—21no—
39C2×C11×D8C2×C412yes—
40C22×C8×C11C2311yescharacteristic
41C2×C22⋊Dic11—41no—
42C2×C22⋊Dic11—41no—
43Q8×Dic11—24no—
44Q8×Dic11—42no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—41no—
48C2×C4×Dic11—41no—
49C2×C4×Dic11D411yescharacteristic
50C22×C11⋊C8D411yescharacteristic
51C11×SD32—28no—
52C2×C11×C16—21no—
53C2×C11×C16—21no—
54C2×C11×C16C2×C412yes—
55#66899—24no—
56#66896—42no—
57#66882—21no—
58#66882—21no—
59#66882—21no—
60#66882D412yes—
61C8×Dic11—21no—
62C8×Dic11—21no—
63C2×C11⋊C16—21no—
64C2×C11⋊C16—21no—
65C2×C11⋊C16—21no—
66#13013—111nomaximal, Sylow
67C24×C11—41no—
68C2×Q8×C11—22no—
69C2×Q8×C11—22no—
70C2×Q8×C11—22no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×D4×C11—22no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—41no—
83C22×Dic11—41no—
84C22×Dic11D811yescharacteristic
85C22×Dic11D811yescharacteristic
86C11×Q16—22no—
87C11×Q16—22no—
88C11×Q16—22no—
89C11×Q16C22⋊C414yescomplemented
90C11×D8—22no—
91C11×D8—22no—
92C11×D8—41no—
93C11×D8—41no—
94C2×C8×C11C22×C411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C22⋊Dic11—82no—
101C22⋊Dic11—82no—
102C4⋊Dic11—22no—
103C4⋊Dic11—44no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—44no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C11×C16—22no—
114C11⋊C16—41no—
115C22×SD32D1111yescharacteristic
116C2×C4×Q16—111no—
117C2×#358—111no—
118C2×#357—111no—
119#1970—111no—
120#1380—111no—
121#1374—111no—
122C23×C11—42no—
123C23×C11—81no—
124C23×C11—81no—
125C23×C11—81no—
126C23×C11—81no—
127C23×C11—81no—
128C23×C11—81no—
129C23×C11C2×D811yescharacteristic
130Q8×C11—24no—
131Q8×C11—42no—
132Q8×C11—42no—
133Q8×C11—42no—
134D4×C11—42no—
135D4×C11—42no—
136D4×C11—81no—
137D4×C11—81no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—42no—
153C2×Dic11—81no—
154C2×Dic11—81no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158C2×Dic11SD3212yescomplemented
159C8×C11C2×C22⋊C411yescharacteristic
160C8×C11C4×D411yescharacteristic
161C8×C11#12111yescharacteristic
162C8×C11#12311yescharacteristic
163C11⋊C8—41no—
164C22×Q16C2×D1111yescharacteristic
165C22×D8C2×D1111yescharacteristic
166C2×C4×Q8—221no—
167C2×SD32—22no—
168C2×SD32—22no—
169C2×SD32Dic1114yescomplemented
170C22×C16—111no—
171C22×C16C2×D1111yescharacteristic
172C4×Q16—222no—
173C4×Q16—222no—
174C2×#107—111no—
175C2×#107—111no—
176C2×#103—221no—
177C2×#102—221no—
178C2×C4×C8—111no—
179#390—221no—
180#358—222no—
181#357—222no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11—82no—
185C22×C11—161no—
186C22×C11—161no—
187C22×C11—161no—
188C22×C11—161no—
189C22×C11C4×D811yescharacteristic
190C22×C11#44711yescharacteristic
191C22×C11#45911yescharacteristic
192C22×C11C2×SD3211yescharacteristic
193C22×C11#50811yescharacteristic
194C22×C11#50911yescharacteristic
195C22×C11#51011yescharacteristic
196C4×C11—44no—
197C4×C11#38611yescharacteristic
198C4×C11#44211yescharacteristic
199C4×C11#44911yescharacteristic
200C4×C11#46311yescharacteristic
201Dic11—22no—
202Dic11—41no—
203Dic11—82no—
204Dic11—161no—
205C22×Q8—21no—
206C22×D4—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16C2×Dic1112yes—
211C2×Q16C22⋊D1112yes—
212C2×Q16C22⋊D1112yes—
213C2×D8—21no—
214C2×D8—21no—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8C2×Dic1112yes—
219C22×C8—111no—
220C22×C8C22×D1111yescharacteristic
221C4×Q8—224no—
222C4×Q8—442no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—441no—
226C2×C22⋊C4—441no—
227C2×C22⋊C4—441no—
228C2×C42—111no—
229C2×C42—441no—
230SD32—28no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—221no—
234C2×C16—221no—
235C2×C16—221no—
236C2×C16C2×Dic1112yes—
237#107—112no—
238#107—221no—
239#107—221no—
240#107—221no—
241#103—224no—
242#102—442no—
243C4×C8—221no—
244C4×C8—221no—
245C2×C11—162no—
246C2×C11#187911yescharacteristic
247C2×C11C4×SD3211yescharacteristic
248C2×C11#217511yescharacteristic
249C2×C11#218511yescharacteristic
250C2×C11#218611yescharacteristic
251C2×C11#220711yescharacteristic
252C2×C11#221111yescharacteristic
253C24—41no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×D4—22no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C22×C4—41no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—441no—
270C22×C4—441no—
271C22×C4D4×D1111yescharacteristic
272Q16—22no—
273Q16—22no—
274Q16—22no—
275Q16C22⋊Dic1114yescomplemented
276D8—22no—
277D8—22no—
278D8—41no—
279D8—41no—
280C2×C8—221no—
281C2×C8—221no—
282C2×C8—221no—
283C2×C8D4×D1111yescharacteristic
284C2×C8#434111yescharacteristic
285C2×C8#434111yescharacteristic
286C2×C8C22×Dic1111yescharacteristic
287C2×C8C2×C22⋊D1111yescharacteristic
288C2×C8C2×C22⋊D1111yescharacteristic
289C4⋊C4—222no—
290C4⋊C4—444no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C22⋊C4—882no—
295C22⋊C4—882no—
296C42—221no—
297C42—221no—
298C42—444no—
299C16—22no—
300C16—441no—
301C11#1301311yescharacteristic, complemented, Sylow
302C23—42no—
303C23—81no—
304C23—81no—
305C23—81no—
306C23—81no—
307C23—81no—
308C23—81no—
309C23D8×D1111yescharacteristic
310Q8—24no—
311Q8—42no—
312Q8—42no—
313Q8—42no—
314D4—42no—
315D4—42no—
316D4—81no—
317D4—81no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—112no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—442no—
328C2×C4—881no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4—881no—
332C2×C4—881no—
333C2×C4#6696411yescharacteristic
334C2×C4#6696411yescharacteristic
335C2×C4#6696511yescharacteristic
336C2×C4D4×Dic1111yescharacteristic
337C2×C4#6699011yescharacteristic
338C2×C4#6699211yescharacteristic
339C8—441no—
340C8D4×Dic1111yescharacteristic
341C8#6698811yescharacteristic
342C8#6699211yescharacteristic
343C8C2×C22⋊Dic1111yescharacteristic
344C22—82no—
345C22—82no—
346C22—82no—
347C22—161no—
348C22—161no—
349C22—161no—
350C22—161no—
351C22D11×SD3211yescharacteristic
352C22#1062252711yescharacteristic
353C22#1062252811yescharacteristic
354C22#1062252911yescharacteristic
355C22D8×Dic1111yescharacteristic
356C22#1062276311yescharacteristic
357C22#1062276911yescharacteristic
358C4—44no—
359C4—222no—
360C4—441no—
361C4—882no—
362C4—1761no—
363C4#1062276511yescharacteristic
364C4#1062276611yescharacteristic
365C4#1062277111yescharacteristic
366C4#1062283311yescharacteristic
367C2—162no—
368C2#1306896611yescharacteristic
369C2SD32×Dic1111yescharacteristic
370C2#1307048111yescharacteristic
371C2#1307053111yescharacteristic
372C2#1307053811yescharacteristic
373C2#1307065411yescharacteristic
374C2#1307067611yescharacteristic
subgroupG/H
centerC23D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC22×C11×SD32C2
socleC23×C11C2×D8
prime radicalC22×C11×D8C22
cosocleC22×C8×C11C23
hypercenterC22×SD32D11
hypocenterC11#13013
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

Complements

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

NH ≅ G/Ntype
1. C2×Q16×Dic11C2semidirect
2. C2×#10622202C2semidirect
5. #13066708C2semidirect
6. #13066693C2semidirect
13. C2×C11×SD32C4semidirect
89. C11×Q16C22⋊C4semidirect
158. C2×Dic11SD32semidirect
169. C2×SD32Dic11semidirect
275. Q16C22⋊Dic11semidirect
301. C11#13013semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×Dic112
C2×#106222022
C2×#106222002
#130694832
#130667082
#130666932
C22×C11×SD322
#1301311