Finite Group Databasebeta

← #14658332

Subgroups — #14658332

Order 2816.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069578C211yesmaximal, characteristic
2#13069374C211yesmaximal, characteristic
3#13069335C211yesmaximal, characteristic
4C2×#10622117C211yesmaximal, characteristic
5C2×#10622184C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic
7C11×#1987C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C4×C11×C4⋊C4C2211yescharacteristic
11C2×#66871—21no—
12#10622548C2211yescharacteristic
13C2×C4⋊(C11⋊C8)—21no—
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×C4×C11⋊C8C2211yescharacteristic
17C11×#340—21no—
18C11×#340—21no—
19#10622184—22no—
20#10622167—21no—
21#10622167—21no—
22#10622167—21no—
23#10622162—21no—
24#10622117—22no—
25C22×Q8×C11—21no—
26C22×C8×C11—21no—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8Q812yes—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C22×C11⋊C8—21no—
41C22×C11⋊C8—21no—
42C22×C11⋊C8D411yescharacteristic
43C22×C11⋊C8D411yescharacteristic
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×#95—21no—
47#66871—42no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—42no—
52C4⋊(C11⋊C8)D412yes—
53C4×C11⋊C8—21no—
54C4×C11⋊C8—21no—
55#10593—111nomaximal, Sylow
56C2×Q8×C11—22no—
57C2×Q8×C11—41no—
58C2×Q8×C11—81no—
59C2×Q8×C11—81no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11#4111yescharacteristic
66C22×Dic11—41no—
67C2×C8×C11—41no—
68C2×C8×C11—41no—
69C2×C8×C11—41no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4Q1612yes—
78C42×C11—41no—
79C42×C11—41no—
80C42×C11C2×D411yescharacteristic
81C42×C11C2×Q811yescharacteristic
82C42×C11#4111yescharacteristic
83C42×C11#4111yescharacteristic
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11—81no—
89C2×C11⋊C8—21no—
90C2×C11⋊C8—21no—
91C2×C11⋊C8—22no—
92C2×C11⋊C8—21no—
93C2×C11⋊C8—21no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8Q1612yes—
101#1990—111no—
102#1987D1111yescharacteristic
103#1947—111no—
104#1939—111no—
105C2×#335—111no—
106C2×#333—111no—
107#1296—111no—
108C23×C11#12111yescharacteristic
109Q8×C11—82no—
110Q8×C11—82no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11#12111yescharacteristic
123C2×C4×C11#12111yescharacteristic
124C2×C4×C11C22⋊Q811yescharacteristic
125C2×C4×C11C22⋊Q811yescharacteristic
126C2×C4×C11C22⋊Q811yescharacteristic
127C2×C4×C11#12611yescharacteristic
128C2×C4×C11C2×Q1611yescharacteristic
129C2×C4×C11C2×Q1611yescharacteristic
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×Dic11—81no—
137C2×Dic11—81no—
138C2×Dic11—81no—
139C8×C11—81no—
140C11⋊C8—22no—
141C11⋊C8—42no—
142C11⋊C8—41no—
143C11⋊C8—81no—
144C2×C4⋊Q8C2×D1111yescharacteristic
145C2×#107—221no—
146C2×C4⋊C8—111no—
147C2×C4⋊C8—111no—
148C2×C4⋊C8—221no—
149C2×C4⋊C8C2×D1111yescharacteristic
150C2×C4×C8—111no—
151#384—111no—
152C4×C4⋊C4C2×D1111yescharacteristic
153#340—21no—
154#340—21no—
155#340—221no—
156#340—221no—
157#340—221no—
158#336—221no—
159#335—222no—
160#333—222no—
161C22×C11#39611yescharacteristic
162C22×C11#46211yescharacteristic
163C22×C11#46311yescharacteristic
164C22×C11#46711yescharacteristic
165C22×C11#46811yescharacteristic
166C22×C11#47111yescharacteristic
167C22×C11#47211yescharacteristic
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—42no—
171C4×C11—82no—
172C4×C11—81no—
173C4×C11#46211yescharacteristic
174C4×C11#46311yescharacteristic
175C4×C11#46711yescharacteristic
176C4×C11#46811yescharacteristic
177C4×C11#47711yescharacteristic
178C4×C11#47711yescharacteristic
179C4×C11#47911yescharacteristic
180C4×C11#47911yescharacteristic
181Dic11—161no—
182C22×Q8—21no—
183C22×C8—21no—
184C22×C8—111no—
185C22×C8—111no—
186C22×C8—221no—
187C22×C8—221no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8Dic2212yes—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4C22⋊D1111yescharacteristic
198C2×C4⋊C4C22⋊D1111yescharacteristic
199C2×C42—21no—
200C2×C42C22×D1111yescharacteristic
201#107—442no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—112no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208C4⋊C8—442no—
209C4×C8—221no—
210C4×C8—221no—
211#95—21no—
212C2×C11#167611yescharacteristic
213C2×C11#168311yescharacteristic
214C2×C11#169211yescharacteristic
215C2×C11#169711yescharacteristic
216C2×C11#206311yescharacteristic
217C2×C11#206811yescharacteristic
218C2×C11#206811yescharacteristic
219C2×Q8—22no—
220C2×Q8—41no—
221C2×Q8—81no—
222C2×Q8—81no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—41no—
226C22×C4—441no—
227C22×C4D4×D1111yescharacteristic
228C22×C4#434111yescharacteristic
229C22×C4C2×C22⋊D1111yescharacteristic
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—112no—
234C2×C8—221no—
235C2×C8—221no—
236C2×C8—221no—
237C2×C8—221no—
238C2×C8—221no—
239C2×C8—222no—
240C2×C8—441no—
241C2×C8—441no—
242C2×C8—441no—
243C2×C8—441no—
244C2×C8—441no—
245C4⋊C4—21no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—881no—
257C4⋊C4#432612yes—
258C42—41no—
259C42—41no—
260C42C2×Dic2211yescharacteristic
261C42#433911yescharacteristic
262C42D4×D1111yescharacteristic
263C42#434111yescharacteristic
264C11#1059311yescharacteristic, complemented, Sylow
265C23#6699211yescharacteristic
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—881no—
280C2×C4—881no—
281C2×C4—881no—
282C2×C4#6693111yescharacteristic
283C2×C4#6693111yescharacteristic
284C2×C4#6693211yescharacteristic
285C2×C4#6693711yescharacteristic
286C2×C4#6696711yescharacteristic
287C2×C4#6696911yescharacteristic
288C2×C4Q16×D1111yescharacteristic
289C2×C4#6697111yescharacteristic
290C2×C4#6697711yescharacteristic
291C2×C4#6699111yescharacteristic
292C2×C4#6699511yescharacteristic
293C2×C4C2×#432611yescharacteristic
294C2×C4#6700211yescharacteristic
295C2×C4#6700311yescharacteristic
296C8—81no—
297C8—222no—
298C8—442no—
299C8—441no—
300C8—881no—
301C22#1062256111yescharacteristic
302C22#1062266211yescharacteristic
303C22#1062266411yescharacteristic
304C22#1062277811yescharacteristic
305C22#1062279511yescharacteristic
306C22#1062281211yescharacteristic
307C22#1062281311yescharacteristic
308C4—21no—
309C4—21no—
310C4—42no—
311C4—81no—
312C4—82no—
313C4—1761no—
314C4#1062240711yescharacteristic
315C4#1062241211yescharacteristic
316C4#1062242511yescharacteristic
317C4#1062242611yescharacteristic
318C4#1062263411yescharacteristic
319C4#1062263511yescharacteristic
320C4#1062267011yescharacteristic
321C4#1062270311yescharacteristic
322C2#1306801811yescharacteristic
323C2#1306806911yescharacteristic
324C2#1306812411yescharacteristic
325C2#1306815111yescharacteristic
326C2#1306997611yescharacteristic
327C2#1307000711yescharacteristic
328C2#1307001111yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1987C2
socle, prime radicalC23×C11#121
hypercenter#1987D11
hypocenterC11#10593
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
264. C11#10593semidirect

Maximal subgroups

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

subgroupindex
#130695782
#130693742
#130693352
C2×#106221172
C2×#106221842
#130665002
C11×#19872
#1059311