Finite Group Databasebeta

← #14652805

Subgroups — #14652805

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077012C211yesmaximal, characteristic
2#13068767C211yesmaximal, characteristic
3C4⋊C8×Dic11C211yesmaximal, characteristic
4C2×#10622120C211yesmaximal, characteristic
5C2×#10622185C211yesmaximal, characteristic
6C2×#10622124C211yesmaximal, characteristic
7C2×C11×#332C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66997—22no—
10C2×#66922C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×Dic11⋊C8—22no—
14C2×C8×Dic11—21no—
15#10622589—21no—
16#10622589—21no—
17#10622589C414yes—
18C42×Dic11C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C11×#332—22no—
22#10622188—21no—
23#10622185—22no—
24#10622124—22no—
25#10622120—22no—
26C22×Q8×C11—21no—
27C22×Dic22—21no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C412yes—
36C2×C42×C11C2311yescharacteristic
37#66997—44no—
38#66997—44no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11C2×C412yes—
41C2×Dic11⋊C4—24no—
42C2×Dic11⋊C4—24no—
43C2×C4×Dic11C2×C412yes—
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D412yes—
46C2×C4×Dic11D411yescharacteristic
47C22×C11⋊C8—21no—
48C22×C11⋊C8—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8D412yes—
57Dic11⋊C8—44no—
58C8×Dic11—42no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)D412yes—
63#9692—111nomaximal, Sylow
64C2×Q8×C11—41no—
65C2×Q8×C11—41no—
66C2×Q8×C11—42no—
67C2×Q8×C11—42no—
68C22×C4×C11—22no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—22no—
73C22×Dic11C22⋊C412yes—
74C22×Dic11C22⋊C412yes—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—42no—
78C2×Dic22—42no—
79C2×C8×C11—22no—
80C2×C8×C11—41no—
81C2×C8×C11—42no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11#4111yescharacteristic
91C42×C11#4111yescharacteristic
92C4⋊Dic11—22no—
93C4⋊Dic11—22no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96Dic11⋊C4—48no—
97Dic11⋊C4—48no—
98C4×Dic11—24no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11D814yes—
102C4×Dic11SD1614yes—
103C4×Dic11SD1612yes—
104C4×Dic11Q1612yes—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—42no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110#2868—111no—
111#1842—111no—
112C4×C4⋊C8—111no—
113C2×#332—111no—
114C2×#332—111no—
115C2×#332—111no—
116C2×#332D1111yescharacteristic
117C23×C11C2×C22⋊C411yescharacteristic
118Q8×C11—82no—
119Q8×C11—81no—
120Q8×C11—81no—
121C2×C4×C11—22no—
122C2×C4×C11—42no—
123C2×C4×C11—44no—
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11C4×D411yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12411yescharacteristic
129C2×C4×C11#12711yescharacteristic
130C2×C4×C11C2×D812yes—
131C2×C4×C11C2×SD1611yescharacteristic
132C2×C4×C11C2×SD1612yes—
133C2×C4×C11C2×Q1611yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×Dic11—22no—
137C2×Dic11—22no—
138C2×Dic11—42no—
139C2×Dic11—44no—
140C2×Dic11#10114yes—
141C2×Dic11#10214yes—
142C2×Dic11#10214yes—
143C2×Dic11#10314yes—
144Dic22—82no—
145Dic22—81no—
146Dic22—81no—
147C8×C11—42no—
148C8×C11—81no—
149C11⋊C8—42no—
150C11⋊C8—81no—
151C2×C4⋊Q8—111no—
152C2×C4⋊Q8—222no—
153C2×C4⋊Q8C2×D1111yescharacteristic
154C2×C4⋊C8—111no—
155C2×C4⋊C8—111no—
156C2×C4⋊C8—222no—
157C2×C4⋊C8C2×D1111yescharacteristic
158C2×C4⋊C8C2×D1111yescharacteristic
159C2×C4×C8—221no—
160#384—114no—
161#384—221no—
162#384—221no—
163C43—111no—
164#336—221no—
165#332—22no—
166#332—222no—
167#332—222no—
168#332—222no—
169C22×C11#39011yescharacteristic
170C22×C11C2×#10112yes—
171C22×C11C2×#10212yes—
172C22×C11C2×#10311yescharacteristic
173C22×C11#41911yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—82no—
177C4×C11#46111yescharacteristic
178C4×C11#46111yescharacteristic
179C4×C11#46211yescharacteristic
180C4×C11#46211yescharacteristic
181C4×C11#48612yes—
182C4×C11#49211yescharacteristic
183C4×C11#49311yescharacteristic
184Dic11—24no—
185Dic11—82no—
186Dic11#33218yescomplemented
187C22×Q8—21no—
188C22×Q8—221no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—221no—
192C22×C8—221no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—221no—
198C4⋊Q8—221no—
199C4⋊Q8—221no—
200C4⋊Q8—221no—
201C4⋊Q8—444no—
202C4⋊Q8—444no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—112no—
205C2×C4⋊C4—224no—
206C2×C4⋊C4—224no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4C4×D1112yes—
209C2×C42—112no—
210C2×C42—111no—
211C2×C42—112no—
212C2×C42—111no—
213C2×C42C22×D1111yescharacteristic
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—112no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221C4⋊C8—444no—
222C4⋊C8C22⋊D1112yes—
223C4×C8—442no—
224C2×C11C2×#33212yes—
225C2×C11#154612yes—
226C2×C11#195711yescharacteristic
227C2×C11#196611yescharacteristic
228C2×C11#198111yescharacteristic
229C2×Q8—41no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—41no—
233C2×Q8—441no—
234C2×Q8—442no—
235C2×Q8—442no—
236C2×Q8—441no—
237C22×C4—22no—
238C22×C4—112no—
239C22×C4—112no—
240C22×C4—222no—
241C22×C4C2×C4×D1111yescharacteristic
242C22×C4D4×D1111yescharacteristic
243C22×C4D4×D1111yescharacteristic
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—42no—
248C2×C8—41no—
249C2×C8—222no—
250C2×C8—441no—
251C2×C8—441no—
252C2×C8—442no—
253C2×C8—441no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—222no—
259C4⋊C4—222no—
260C4⋊C4—448no—
261C4⋊C4—448no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C42—114no—
265C42—112no—
266C42—114no—
267C42—112no—
268C42—224no—
269C42—221no—
270C42—221no—
271C42#433911yescharacteristic
272C42D4×D1111yescharacteristic
273C42#434111yescharacteristic
274C42C2×C22⋊D1111yescharacteristic
275C11#969211yescharacteristic, complemented, Sylow
276C23C22⋊C4×D1111yescharacteristic
277Q8—81no—
278Q8—81no—
279Q8—82no—
280Q8—881no—
281Q8—881no—
282Q8—882no—
283C2×C4—22no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—114no—
287C2×C4—114no—
288C2×C4—114no—
289C2×C4—114no—
290C2×C4—222no—
291C2×C4—222no—
292C2×C4—442no—
293C2×C4—444no—
294C2×C4(C22⋊D11)⋊C411yescharacteristic
295C2×C4#6693711yescharacteristic
296C2×C4#6693811yescharacteristic
297C2×C4D8×D1112yes—
298C2×C4SD16×D1111yescharacteristic
299C2×C4SD16×D1112yes—
300C2×C4#6696811yescharacteristic
301C2×C4Q16×D1111yescharacteristic
302C2×C4#6697111yescharacteristic
303C2×C4C4×C22⋊D1111yescharacteristic
304C2×C4#6699211yescharacteristic
305C2×C4#6699311yescharacteristic
306C8—42no—
307C8—81no—
308C8—442no—
309C8—881no—
310C22D11×#10112yes—
311C22D11×#10212yes—
312C22D11×#10311yescharacteristic
313C22#1062241511yescharacteristic
314C22#1062257011yescharacteristic
315C4—21no—
316C4—21no—
317C4—82no—
318C4—118no—
319C4—224no—
320C4—882no—
321C4#1062237312yes—
322C4#1062240611yescharacteristic
323C4#1062243111yescharacteristic
324C4#1062276411yescharacteristic
325C4#1062277511yescharacteristic
326C4#1062278811yescharacteristic
327C4#1062279511yescharacteristic
328C2D11×#33212yes—
329C2#1306728612yes—
330C2#1306942011yescharacteristic
331C2#1306945811yescharacteristic
332C2#1306953711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#332D11
hypocenterC11#9692
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
186. Dic11#332semidirect
275. C11#9692semidirect

Maximal subgroups

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

subgroupindex
#130770122
#130687672
C4⋊C8×Dic112
C2×#106221202
C2×#106221852
C2×#106221242
C2×C11×#3322
#969211