Finite Group Databasebeta

← #14646830

Subgroups — #14646830

Order 2816.

454 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C11⋊C8C211yesmaximal, characteristic
2#13068775C211yesmaximal, characteristic
3#13068621C211yesmaximal, characteristic
4C2×#10622117C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic
6#13066499C211yesmaximal, characteristic
7C11×#1803C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×#103—21no—
11C11×#384C2211yescharacteristic
12C2×#66899—21no—
13Q8×C11⋊C8—22no—
14Q8×C11⋊C8C414yescomplemented
15C2×#66871—21no—
16C2×#66871—21no—
17#10622548C2211yescharacteristic
18C2×C4⋊(C11⋊C8)—21no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8—21no—
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×#340—21no—
24#10622167—21no—
25#10622117—22no—
26C22×Q8×C11D411yescharacteristic
27C22×C8×C11—21no—
28C4×Q8×C11—21no—
29C4×Q8×C11—21no—
30C4×Q8×C11C2×C412yes—
31C4×Q8×C11Q812yes—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C22×C11⋊C8—21no—
43C22×C11⋊C8—21no—
44C22×C11⋊C8D411yescharacteristic
45C22×C11⋊C8D411yescharacteristic
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×#103—42no—
49#66899—42no—
50#66871—42no—
51#66871—42no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—24no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)C2×C412yes—
57C4×C11⋊C8—24no—
58C4×C11⋊C8C2×C412yes—
59C4×C11⋊C8D412yes—
60#8645—111nomaximal, Sylow
61C2×Q8×C11—21no—
62C2×Q8×C11—21no—
63C2×Q8×C11—21no—
64C2×Q8×C11C4⋊C412yes—
65C2×Q8×C11D812yes—
66C2×Q8×C11Q1612yes—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—41no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—81no—
85C11×C4⋊C4C4⋊C412yes—
86C42×C11—22no—
87C42×C11—22no—
88C42×C11C22×C411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×Q811yescharacteristic
91C42×C11#4111yescharacteristic
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—81no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8C22⋊C412yes—
106C2×C11⋊C8C22⋊C412yes—
107C2×C11⋊C8SD1612yes—
108C2×C11⋊C8Q1612yes—
109C2×C8×Q8—111no—
110#1845—111no—
111#1803—111no—
112#1803D1111yescharacteristic
113C2×#335—111no—
114#1296—111no—
115#1296—111no—
116C23×C11#12111yescharacteristic
117Q8×C11—22no—
118Q8×C11—22no—
119Q8×C11—22no—
120Q8×C11#10714yescomplemented
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—22no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11C2×C22⋊C411yescharacteristic
133C2×C4×C11C2×C4⋊C411yescharacteristic
134C2×C4×C11#11711yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11C22⋊Q811yescharacteristic
137C2×C4×C11C22⋊Q811yescharacteristic
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×SD1611yescharacteristic
140C2×C4×C11C2×Q1611yescharacteristic
141C2×C4×C11C2×Q1611yescharacteristic
142C2×C4×C11#13511yescharacteristic
143C2×C4×C11#13511yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×Dic11—81no—
147C2×Dic11—81no—
148C2×Dic11—81no—
149C8×C11—81no—
150C11⋊C8—22no—
151C11⋊C8—42no—
152C11⋊C8—81no—
153C11⋊C8#10314yescomplemented
154C2×C4×Q8C2×D1111yescharacteristic
155C8×Q8—114no—
156C8×Q8—222no—
157C2×#107—221no—
158C2×#107—221no—
159C2×C4⋊C8—111no—
160C2×C4⋊C8—111no—
161C2×C4⋊C8—221no—
162C2×C4⋊C8C2×D1111yescharacteristic
163C2×#103—21no—
164C2×#103—221no—
165C2×C4×C8—111no—
166C2×C4×C8—221no—
167#384—111no—
168#384C2×D1111yescharacteristic
169#340—21no—
170#340—221no—
171#335—222no—
172C22×C11#38011yescharacteristic
173C22×C11#46011yescharacteristic
174C22×C11#46211yescharacteristic
175C22×C11#46611yescharacteristic
176C22×C11#46711yescharacteristic
177C22×C11#47211yescharacteristic
178C22×C11#47311yescharacteristic
179C4×C11—24no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—42no—
183C4×C11—161no—
184C4×C11C2×#10311yescharacteristic
185C4×C11#41711yescharacteristic
186C4×C11C2×#10711yescharacteristic
187C4×C11#42711yescharacteristic
188C4×C11#46611yescharacteristic
189C4×C11#46711yescharacteristic
190C4×C11#47511yescharacteristic
191C4×C11#47711yescharacteristic
192Dic11—161no—
193C22×Q8C22⋊D1111yescharacteristic
194C22×C8—21no—
195C22×C8—111no—
196C22×C8—111no—
197C22×C8—221no—
198C22×C8—221no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8Dic2212yes—
202C4×Q8C4×D1112yes—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4C22⋊D1111yescharacteristic
211C2×C42—21no—
212C2×C42C22×D1111yescharacteristic
213#107—442no—
214#107—442no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—112no—
218C4⋊C8—224no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221C4⋊C8—221no—
222#103—42no—
223#103—442no—
224C4×C8—112no—
225C4×C8—112no—
226C4×C8—224no—
227C2×C11#166811yescharacteristic
228C2×C11#167011yescharacteristic
229C2×C11#167411yescharacteristic
230C2×C11#167611yescharacteristic
231C2×C11#180311yescharacteristic
232C2×C11#180811yescharacteristic
233C2×C11#181611yescharacteristic
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8Dic11⋊C412yes—
238C2×Q8#432312yes—
239C2×Q8#432612yes—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—41no—
243C22×C4—441no—
244C22×C4D4×D1111yescharacteristic
245C22×C4#434111yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—112no—
251C2×C8—112no—
252C2×C8—112no—
253C2×C8—112no—
254C2×C8—221no—
255C2×C8—221no—
256C2×C8—222no—
257C2×C8—441no—
258C2×C8—441no—
259C2×C8—441no—
260C2×C8—441no—
261C2×C8—441no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—81no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—881no—
275C4⋊C4Dic11⋊C412yes—
276C42—22no—
277C42—22no—
278C42C2×Dic2211yescharacteristic
279C42C2×C4×D1111yescharacteristic
280C42D4×D1111yescharacteristic
281C42#434111yescharacteristic
282C11#864511yescharacteristic, complemented, Sylow
283C23#6699211yescharacteristic
284Q8—22no—
285Q8—22no—
286Q8—22no—
287Q8#6687114yescomplemented
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4—881no—
302C2×C4#6693011yescharacteristic
303C2×C4#6693111yescharacteristic
304C2×C4#6693111yescharacteristic
305C2×C4C22⋊C4×D1111yescharacteristic
306C2×C4SD16×D1111yescharacteristic
307C2×C4#6696711yescharacteristic
308C2×C4Q16×D1111yescharacteristic
309C2×C4#6697111yescharacteristic
310C2×C4C2×Dic11⋊C411yescharacteristic
311C2×C4C2×#432311yescharacteristic
312C2×C4#6699211yescharacteristic
313C2×C4C2×#432611yescharacteristic
314C2×C4#6700311yescharacteristic
315C2×C4#6700311yescharacteristic
316C8—81no—
317C8—114no—
318C8—222no—
319C8—442no—
320C8—881no—
321C22#1062255511yescharacteristic
322C22#1062265111yescharacteristic
323C22#1062266411yescharacteristic
324C22#1062277611yescharacteristic
325C22#1062279511yescharacteristic
326C22#1062281211yescharacteristic
327C22#1062281711yescharacteristic
328C4—24no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—161no—
333C4—1761no—
334C4#1062240411yescharacteristic
335C4#1062240711yescharacteristic
336C4D11×#10311yescharacteristic
337C4#1062241611yescharacteristic
338C4C2×#6687111yescharacteristic
339C4#1062261111yescharacteristic
340C4#1062265111yescharacteristic
341C4#1062266411yescharacteristic
342C2#1306797411yescharacteristic
343C2#1306798411yescharacteristic
344C2#1306800811yescharacteristic
345C2#1306801811yescharacteristic
346C2#1306861911yescharacteristic
347C2#1306864311yescharacteristic
348C2#1306867811yescharacteristic
subgroupG/H
centerC23#66992
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1803C2
socle, prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1803D11
hypocenterC11#8645
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
14. Q8×C11⋊C8C4semidirect
120. Q8×C11#107semidirect
153. C11⋊C8#103semidirect
282. C11#8645semidirect
287. Q8#66871semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C11⋊C82
#130687752
#130686212
C2×#106221172
#130665002
#130664992
C11×#18032
#864511