Finite Group Databasebeta

← #14658298

Subgroups — #14658298

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#13069567C211yesmaximal, characteristic
2#13069417C211yesmaximal, characteristic
3#13069372C211yesmaximal, characteristic
4#13069332C211yesmaximal, characteristic
5C2×#10622118C211yesmaximal, characteristic
6C2×#10622120C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C2×Dic11⋊C8—21no—
13C2×#66874—21no—
14C2×#66874—21no—
15C2×#66871—21no—
16C4×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19#10622189—21no—
20#10622189—21no—
21#10622188—21no—
22#10622167—21no—
23#10622120—22no—
24#10622118—22no—
25C22×Dic22—21no—
26C22×C8×C11—21no—
27C22×C8×C11—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11D411yescharacteristic
35C2×C4⋊Dic11D411yescharacteristic
36C2×C4×Dic11—21no—
37C22×C11⋊C8—21no—
38C22×C11⋊C8D411yescharacteristic
39C22×C11⋊C8D411yescharacteristic
40#66922—21no—
41#66922—21no—
42#66922—21no—
43#66922Q812yes—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11⋊#95—21no—
49Dic11⋊C8—42no—
50#66874—42no—
51#66874—42no—
52#66871—42no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)D412yes—
55C4×C11⋊C8—21no—
56C4×C11⋊C8—21no—
57#10588—111nomaximal, Sylow
58C22×C4×C11—41no—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C22×Dic11—21no—
63C22×Dic11—21no—
64C22×Dic11—41no—
65C2×Dic22—22no—
66C2×Dic22—41no—
67C2×Dic22—41no—
68C2×Dic22—41no—
69C2×Dic22—41no—
70C2×Dic22—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—81no—
82C42×C11C2×D411yescharacteristic
83C42×C11C2×Q811yescharacteristic
84C42×C11#4111yescharacteristic
85C42×C11#4111yescharacteristic
86C4⋊Dic11—22no—
87C4⋊Dic11—22no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11SD1612yes—
94C4×Dic11—41no—
95C4×Dic11—41no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8D812yes—
105#1988—111no—
106#1956—111no—
107#1947—111no—
108#1939—111no—
109C2×#334—111no—
110C2×#332—111no—
111#1296D1111yescharacteristic
112C23×C11#12111yescharacteristic
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11—81no—
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12111yescharacteristic
120C2×C4×C11C22⋊Q811yescharacteristic
121C2×C4×C11C22⋊Q811yescharacteristic
122C2×C4×C11C22⋊Q811yescharacteristic
123C2×C4×C11#12611yescharacteristic
124C2×C4×C11C2×D811yescharacteristic
125C2×C4×C11C2×SD1611yescharacteristic
126C2×C4×C11#13511yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×Dic11—22no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—42no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—81no—
140C2×Dic11—81no—
141Dic22—42no—
142Dic22—42no—
143Dic22—81no—
144Dic22—81no—
145C8×C11—81no—
146C8×C11—81no—
147C11⋊C8—22no—
148C11⋊C8—42no—
149C11⋊C8—41no—
150C2×C4⋊Q8—111no—
151C2×#107—221no—
152C2×C4⋊C8—111no—
153C2×C4⋊C8—221no—
154C2×C4⋊C8C2×D1111yescharacteristic
155C2×C4⋊C8C2×D1111yescharacteristic
156C2×#103—221no—
157C2×#103—221no—
158C2×C4×C8—111no—
159#384C2×D1111yescharacteristic
160C4×C4⋊C4—111no—
161#340—221no—
162#340—221no—
163#340—221no—
164#336—221no—
165#334—222no—
166#332—222no—
167C22×C11#39611yescharacteristic
168C22×C11#45911yescharacteristic
169C22×C11#46411yescharacteristic
170C22×C11#46511yescharacteristic
171C22×C11#47011yescharacteristic
172C22×C11#47111yescharacteristic
173C22×C11#47311yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—161no—
177C4×C11#46111yescharacteristic
178C4×C11#46411yescharacteristic
179C4×C11#46611yescharacteristic
180C4×C11#46811yescharacteristic
181C4×C11#47411yescharacteristic
182C4×C11#47511yescharacteristic
183C4×C11#47811yescharacteristic
184C4×C11#47911yescharacteristic
185Dic11—42no—
186Dic11—82no—
187Dic11—81no—
188C22×Q8—221no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—111no—
192C22×C8—111no—
193C22×C8—221no—
194C4⋊Q8—112no—
195C4⋊Q8—221no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C42—221no—
206C2×C42C22×D1111yescharacteristic
207#107—442no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—112no—
213C4⋊C8—221no—
214C4⋊C8—442no—
215#103—442no—
216#103—442no—
217C4×C8—221no—
218C4×C8—221no—
219#95—221no—
220C2×C11#166511yescharacteristic
221C2×C11#168011yescharacteristic
222C2×C11#168911yescharacteristic
223C2×C11#170411yescharacteristic
224C2×C11#206411yescharacteristic
225C2×C11#206611yescharacteristic
226C2×C11#206711yescharacteristic
227C2×Q8—222no—
228C2×Q8—441no—
229C2×Q8—441no—
230C2×Q8—441no—
231C2×Q8—441no—
232C2×Q8—441no—
233C22×C4—41no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4—441no—
237C22×C4#433911yescharacteristic
238C22×C4D4×D1111yescharacteristic
239C22×C4D4×D1111yescharacteristic
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—112no—
247C2×C8—221no—
248C2×C8—221no—
249C2×C8—221no—
250C2×C8—222no—
251C2×C8—221no—
252C2×C8—221no—
253C2×C8—441no—
254C2×C8—441no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—81no—
260C4⋊C4—112no—
261C4⋊C4—221no—
262C4⋊C4—222no—
263C4⋊C4—222no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C42—441no—
269C42—441no—
270C42#433911yescharacteristic
271C42#433911yescharacteristic
272C42D4×D1111yescharacteristic
273C42Q8×D1111yescharacteristic
274C11#1058811yescharacteristic, complemented, Sylow
275C23#6693711yescharacteristic
276Q8—442no—
277Q8—442no—
278Q8—881no—
279Q8—881no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—222no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—442no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—881no—
293C2×C4—881no—
294C2×C4#6692911yescharacteristic
295C2×C4#6693711yescharacteristic
296C2×C4#6693711yescharacteristic
297C2×C4#6694911yescharacteristic
298C2×C4#6694911yescharacteristic
299C2×C4#6694911yescharacteristic
300C2×C4D8×D1111yescharacteristic
301C2×C4#6696511yescharacteristic
302C2×C4SD16×D1111yescharacteristic
303C2×C4#6696711yescharacteristic
304C2×C4#6696811yescharacteristic
305C2×C4#6696911yescharacteristic
306C2×C4#6697111yescharacteristic
307C2×C4#6697111yescharacteristic
308C8—81no—
309C8—81no—
310C8—222no—
311C8—441no—
312C8—442no—
313C22#1062228911yescharacteristic
314C22#1062236111yescharacteristic
315C22#1062236811yescharacteristic
316C22#1062239111yescharacteristic
317C22#1062239911yescharacteristic
318C22#1062241111yescharacteristic
319C22#1062242911yescharacteristic
320C4—21no—
321C4—21no—
322C4—161no—
323C4—442no—
324C4—881no—
325C4—882no—
326C4#1062238011yescharacteristic
327C4#1062238811yescharacteristic
328C4#1062242511yescharacteristic
329C4#1062243111yescharacteristic
330C4#1062246711yescharacteristic
331C4#1062248411yescharacteristic
332C4#1062249011yescharacteristic
333C4#1062250311yescharacteristic
334C2#1306795611yescharacteristic
335C2#1306804911yescharacteristic
336C2#1306810411yescharacteristic
337C2#1306820111yescharacteristic
338C2#1306998411yescharacteristic
339C2#1306999811yescharacteristic
340C2#1307000511yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socle, prime radicalC23×C11#121
hypercenter#1296D11
hypocenterC11#10588
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
274. C11#10588semidirect

Maximal subgroups

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

subgroupindex
#130695672
#130694172
#130693722
#130693322
C2×#106221182
C2×#106221202
C11×#12962
#1058811