Finite Group Databasebeta

← #14658367

Subgroups — #14658367

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#13069578C211yesmaximal, characteristic
2#13069379C211yesmaximal, characteristic
3#13069335C211yesmaximal, characteristic
4C2×#10622118C211yesmaximal, characteristic
5C2×#10622185C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic
7C11×#1981C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×#103—21no—
11C2×C11×#103—21no—
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66872—21no—
14#10622548C2211yescharacteristic
15C2×C4⋊(C11⋊C8)—21no—
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19#10622185—22no—
20#10622167—21no—
21#10622167—21no—
22#10622167—21no—
23#10622162—21no—
24#10622118—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×#103—42no—
47C11×#103—42no—
48C11×#95—21no—
49#66872—42no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—42no—
54C4⋊(C11⋊C8)D412yes—
55C4×C11⋊C8—21no—
56C4×C11⋊C8—21no—
57#10598—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—21no—
65C22×C4×C11—21no—
66C22×C4×C11—41no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C22×Dic11—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4SD1612yes—
82C42×C11—41no—
83C42×C11—41no—
84C42×C11C2×D411yescharacteristic
85C42×C11C2×Q811yescharacteristic
86C42×C11#4111yescharacteristic
87C42×C11#4111yescharacteristic
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—81no—
93C2×C11⋊C8—21no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8SD1612yes—
105#1990—111no—
106#1981D1111yescharacteristic
107#1948—111no—
108#1939—111no—
109C2×#334—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—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11C22⋊Q811yescharacteristic
131C2×C4×C11C22⋊Q811yescharacteristic
132C2×C4×C11C22⋊Q811yescharacteristic
133C2×C4×C11#12611yescharacteristic
134C2×C4×C11C2×SD1611yescharacteristic
135C2×C4×C11C2×SD1611yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11#13511yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×Dic11—81no—
143C2×Dic11—81no—
144C2×Dic11—81no—
145C8×C11—81no—
146C11⋊C8—22no—
147C11⋊C8—42no—
148C11⋊C8—41no—
149C11⋊C8—81no—
150C2×C4⋊Q8C2×D1111yescharacteristic
151C2×#106—221no—
152C2×C4⋊C8—111no—
153C2×C4⋊C8—111no—
154C2×C4⋊C8—221no—
155C2×C4⋊C8C2×D1111yescharacteristic
156C2×#103—21no—
157C2×#103—21no—
158C2×C4×C8—111no—
159#384—111no—
160C4×C4⋊C4C2×D1111yescharacteristic
161#340—221no—
162#340—221no—
163#340—221no—
164#336—221no—
165#334—222no—
166#332—222no—
167C22×C11#39611yescharacteristic
168C22×C11#46111yescharacteristic
169C22×C11#46411yescharacteristic
170C22×C11#46511yescharacteristic
171C22×C11#46911yescharacteristic
172C22×C11#47111yescharacteristic
173C22×C11#47311yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—42no—
177C4×C11—82no—
178C4×C11—81no—
179C4×C11#46011yescharacteristic
180C4×C11#46311yescharacteristic
181C4×C11#46511yescharacteristic
182C4×C11#47011yescharacteristic
183C4×C11#47511yescharacteristic
184C4×C11#47611yescharacteristic
185C4×C11#47811yescharacteristic
186C4×C11#47911yescharacteristic
187Dic11—161no—
188C22×Q8—21no—
189C22×C8—21no—
190C22×C8—111no—
191C22×C8—111no—
192C22×C8—221no—
193C22×C8—221no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8Dic2212yes—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4C22⋊D1111yescharacteristic
204C2×C4⋊C4C22⋊D1111yescharacteristic
205C2×C42—21no—
206C2×C42C22×D1111yescharacteristic
207#106—442no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—112no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214C4⋊C8—442no—
215#103—42no—
216#103—42no—
217C4×C8—221no—
218C4×C8—221no—
219#95—21no—
220C2×C11#167111yescharacteristic
221C2×C11#168011yescharacteristic
222C2×C11#169311yescharacteristic
223C2×C11#170211yescharacteristic
224C2×C11#206411yescharacteristic
225C2×C11#206511yescharacteristic
226C2×C11#206611yescharacteristic
227C2×Q8—22no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—41no—
236C22×C4—441no—
237C22×C4D4×D1111yescharacteristic
238C22×C4#434111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—112no—
244C2×C8—221no—
245C2×C8—221no—
246C2×C8—221no—
247C2×C8—221no—
248C2×C8—221no—
249C2×C8—222no—
250C2×C8—441no—
251C2×C8—441no—
252C2×C8—441no—
253C2×C8—441no—
254C2×C8—441no—
255C4⋊C4—21no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—881no—
267C4⋊C4#432412yes—
268C42—41no—
269C42—41no—
270C42C2×Dic2211yescharacteristic
271C42#433911yescharacteristic
272C42D4×D1111yescharacteristic
273C42#434111yescharacteristic
274C11#1059811yescharacteristic, complemented, Sylow
275C23#6699211yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—881no—
292C2×C4—881no—
293C2×C4—881no—
294C2×C4#6693111yescharacteristic
295C2×C4#6693111yescharacteristic
296C2×C4#6693211yescharacteristic
297C2×C4#6693711yescharacteristic
298C2×C4SD16×D1111yescharacteristic
299C2×C4#6696811yescharacteristic
300C2×C4#6697111yescharacteristic
301C2×C4#6697211yescharacteristic
302C2×C4#6697711yescharacteristic
303C2×C4#6698511yescharacteristic
304C2×C4C2×#432411yescharacteristic
305C2×C4#6699111yescharacteristic
306C2×C4#6700211yescharacteristic
307C2×C4#6700311yescharacteristic
308C8—81no—
309C8—222no—
310C8—442no—
311C8—441no—
312C8—881no—
313C22#1062256111yescharacteristic
314C22#1062265211yescharacteristic
315C22#1062265411yescharacteristic
316C22#1062277511yescharacteristic
317C22#1062279811yescharacteristic
318C22#1062281611yescharacteristic
319C22#1062281711yescharacteristic
320C4—21no—
321C4—21no—
322C4—42no—
323C4—81no—
324C4—82no—
325C4—1761no—
326C4#1062240411yescharacteristic
327C4#1062240911yescharacteristic
328C4#1062242011yescharacteristic
329C4#1062242911yescharacteristic
330C4#1062262111yescharacteristic
331C4#1062262211yescharacteristic
332C4#1062267011yescharacteristic
333C4#1062268811yescharacteristic
334C2#1306798911yescharacteristic
335C2#1306804811yescharacteristic
336C2#1306812711yescharacteristic
337C2#1306818611yescharacteristic
338C2#1306998311yescharacteristic
339C2#1306999011yescharacteristic
340C2#1306999311yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1981C2
socle, prime radicalC23×C11#121
hypercenter#1981D11
hypocenterC11#10598
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
274. C11#10598semidirect

Maximal subgroups

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

subgroupindex
#130695782
#130693792
#130693352
C2×#106221182
C2×#106221852
#130665002
C11×#19812
#1059811