Finite Group Databasebeta

← #14658337

Subgroups — #14658337

Order 2816.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069540C211yesmaximal, characteristic
2#13069372C211yesmaximal, characteristic
3#13069334C211yesmaximal, characteristic
4C2×#10622096C211yesmaximal, characteristic
5C2×#10622185C211yesmaximal, characteristic
6#13066499C211yesmaximal, characteristic
7C11×#1990C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×C8×C11C2211yescharacteristic
10C11×#384C2211yescharacteristic
11C2×#66899—21no—
12C2×#66899—21no—
13C2×Dic11⋊C8—21no—
14C2×#66871—21no—
15C4×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C11×#340—21no—
20C11×#340—21no—
21#10622188—21no—
22#10622185—22no—
23#10622167—21no—
24#10622096—22no—
25C22×Q8×C11—21no—
26C22×C8×C11D411yescharacteristic
27C22×C8×C11D411yescharacteristic
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8Q812yes—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4×Dic11—21no—
41C22×C11⋊C8—21no—
42C22×C11⋊C8—21no—
43C22×C11⋊C8—21no—
44C4×C8×C11—21no—
45C4×C8×C11—21no—
46#66899—42no—
47#66899—42no—
48C11⋊#95—21no—
49Dic11⋊C8—42no—
50#66871—42no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)D412yes—
57#10594—111nomaximal, Sylow
58C2×Q8×C11—22no—
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11Q1612yes—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—81no—
86C42×C11C2×D411yescharacteristic
87C42×C11C2×Q811yescharacteristic
88C42×C11#4111yescharacteristic
89C42×C11#4111yescharacteristic
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11D812yes—
94C4×Dic11—41no—
95C4×Dic11—41no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#1990D1111yescharacteristic
106#1981—111no—
107#1947—111no—
108#1939—111no—
109C2×#335—111no—
110C2×#332—111no—
111#1296—111no—
112C23×C11#12111yescharacteristic
113Q8×C11—42no—
114Q8×C11—42no—
115Q8×C11—81no—
116Q8×C11—81no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—42no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C2×C4×C11C22⋊Q811yescharacteristic
129C2×C4×C11C22⋊Q811yescharacteristic
130C2×C4×C11#12611yescharacteristic
131C2×C4×C11C2×D811yescharacteristic
132C2×C4×C11C2×Q1611yescharacteristic
133C2×C4×C11#13511yescharacteristic
134C2×C4×C11#13511yescharacteristic
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C2×Dic11—22no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C8×C11—22no—
146C8×C11—41no—
147C11⋊C8—42no—
148C11⋊C8—81no—
149C11⋊C8—81no—
150C2×C4⋊Q8C2×D1111yescharacteristic
151C2×#107—221no—
152C2×C4⋊C8—111no—
153C2×C4⋊C8—111no—
154C2×C4⋊C8—111no—
155C2×C4⋊C8—221no—
156C2×#103—221no—
157C2×#103—221no—
158C2×C4×C8C2×D1111yescharacteristic
159#384C2×D1111yescharacteristic
160C4×C4⋊C4—111no—
161#340—21no—
162#340—21no—
163#340—221no—
164#336—221no—
165#335—222no—
166#332—222no—
167C22×C11#39611yescharacteristic
168C22×C11#46211yescharacteristic
169C22×C11#46311yescharacteristic
170C22×C11#46611yescharacteristic
171C22×C11#46811yescharacteristic
172C22×C11#47111yescharacteristic
173C22×C11#47311yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—82no—
177C4×C11—161no—
178C4×C11#45911yescharacteristic
179C4×C11#46411yescharacteristic
180C4×C11#46711yescharacteristic
181C4×C11#46811yescharacteristic
182C4×C11#47411yescharacteristic
183C4×C11#47711yescharacteristic
184C4×C11#47811yescharacteristic
185C4×C11#47911yescharacteristic
186Dic11—42no—
187Dic11—81no—
188C22×Q8—21no—
189C22×C8—221no—
190C22×C8—221no—
191C22×C8—221no—
192C22×C8C22⋊D1111yescharacteristic
193C22×C8C22⋊D1111yescharacteristic
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8Dic2212yes—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—111no—
205C2×C42—221no—
206C2×C42C22×D1111yescharacteristic
207#107—442no—
208C4⋊C8—112no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214C4⋊C8—442no—
215#103—442no—
216#103—442no—
217C4×C8—21no—
218C4×C8—21no—
219#95—221no—
220C2×C11#167411yescharacteristic
221C2×C11#168111yescharacteristic
222C2×C11#169211yescharacteristic
223C2×C11#169911yescharacteristic
224C2×C11#206411yescharacteristic
225C2×C11#206711yescharacteristic
226C2×C11#206811yescharacteristic
227C2×Q8—22no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4D4×D1111yescharacteristic
238C22×C4#434111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—222no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C2×C8—441no—
250C2×C8—441no—
251C2×C8—441no—
252C2×C8—441no—
253C2×C8—441no—
254C2×C8#432612yes—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—112no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C42—441no—
269C42—441no—
270C42C2×Dic2211yescharacteristic
271C42#433911yescharacteristic
272C42D4×D1111yescharacteristic
273C42#434111yescharacteristic
274C11#1059411yescharacteristic, complemented, Sylow
275C23#6699111yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—222no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4#6693111yescharacteristic
295C2×C4#6693111yescharacteristic
296C2×C4#6693211yescharacteristic
297C2×C4#6693711yescharacteristic
298C2×C4D8×D1111yescharacteristic
299C2×C4#6696511yescharacteristic
300C2×C4#6696711yescharacteristic
301C2×C4#6696811yescharacteristic
302C2×C4#6697711yescharacteristic
303C2×C4#6699211yescharacteristic
304C2×C4#6699511yescharacteristic
305C2×C4C2×#432611yescharacteristic
306C2×C4#6700211yescharacteristic
307C2×C4#6700311yescharacteristic
308C8—22no—
309C8—41no—
310C8—442no—
311C8—881no—
312C8—881no—
313C22#1062256111yescharacteristic
314C22#1062267011yescharacteristic
315C22#1062270311yescharacteristic
316C22#1062277011yescharacteristic
317C22#1062278711yescharacteristic
318C22#1062279011yescharacteristic
319C22#1062280511yescharacteristic
320C4—21no—
321C4—21no—
322C4—82no—
323C4—161no—
324C4—442no—
325C4—881no—
326C4#1062237211yescharacteristic
327C4#1062237911yescharacteristic
328C4#1062238011yescharacteristic
329C4#1062239911yescharacteristic
330C4#1062263411yescharacteristic
331C4#1062263511yescharacteristic
332C4#1062266211yescharacteristic
333C4#1062266411yescharacteristic
334C2#1306800711yescharacteristic
335C2#1306805011yescharacteristic
336C2#1306811911yescharacteristic
337C2#1306816011yescharacteristic
338C2#1306998111yescharacteristic
339C2#1307000211yescharacteristic
340C2#1307001111yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1990C2
socle, prime radicalC23×C11#121
hypercenter#1990D11
hypocenterC11#10594
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
274. C11#10594semidirect

Maximal subgroups

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

subgroupindex
#130695402
#130693722
#130693342
C2×#106220962
C2×#106221852
#130664992
C11×#19902
#1059411