Finite Group Databasebeta

← #14658348

Subgroups — #14658348

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#13069418C211yesmaximal, characteristic
3#13069380C211yesmaximal, characteristic
4#13069334C211yesmaximal, characteristic
5C2×#10622124C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic
7C2×C11×#334C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66881—21no—
13C2×#66880—21no—
14C2×#66880—21no—
15C2×Dic11⋊C8—21no—
16#10622548C2211yescharacteristic
17C4×C4⋊Dic11C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C11×#334—22no—
20#10622189—21no—
21#10622189—21no—
22#10622189—21no—
23#10622188—21no—
24#10622124—22no—
25C22×Dic22—21no—
26C22×C8×C11—21no—
27C22×C8×C11—21no—
28C22×C8×C11D411yescharacteristic
29C22×C8×C11D411yescharacteristic
30C2×C42×C11C2311yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4×Dic11—21no—
39C22×C11⋊C8—21no—
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⋊C8D412yes—
48C4×C8×C11—21no—
49C4×C8×C11—21no—
50C11⋊#95—21no—
51#66881—42no—
52#66880—42no—
53#66880—42no—
54Dic11⋊C8—42no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57#10596—111nomaximal, Sylow
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11#4111yescharacteristic
61C22×Dic11—21no—
62C22×Dic11—21no—
63C22×Dic11—41no—
64C22×Dic11—41no—
65C2×Dic22—22no—
66C2×Dic22—41no—
67C2×Dic22—41no—
68C2×Dic22—41no—
69C2×Dic22—41no—
70C2×Dic22—41no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—22no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—21no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11SD1612yes—
83C42×C11C2×D411yescharacteristic
84C42×C11C2×Q811yescharacteristic
85C42×C11#4111yescharacteristic
86C42×C11#4111yescharacteristic
87C4⋊Dic11—22no—
88C4⋊Dic11—22no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—81no—
99C4⋊Dic11SD1612yes—
100C4×Dic11—41no—
101C4×Dic11—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#1988—111no—
106#1956—111no—
107#1948—111no—
108#1939—111no—
109C2×#334D1111yescharacteristic
110C2×#332—111no—
111#1296—111no—
112C23×C11#12111yescharacteristic
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11#12111yescharacteristic
116C2×C4×C11#12111yescharacteristic
117C2×C4×C11C22⋊Q811yescharacteristic
118C2×C4×C11C22⋊Q811yescharacteristic
119C2×C4×C11C22⋊Q811yescharacteristic
120C2×C4×C11#12611yescharacteristic
121C2×C4×C11C2×SD1611yescharacteristic
122C2×C4×C11C2×SD1611yescharacteristic
123C2×C4×C11#13511yescharacteristic
124C2×C4×C11#13511yescharacteristic
125C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C11#13711yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×Dic11—22no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—42no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—81no—
137C2×Dic11—81no—
138C2×Dic11—81no—
139C2×Dic11—81no—
140C2×Dic11—81no—
141Dic22—42no—
142Dic22—42no—
143Dic22—81no—
144Dic22—81no—
145C8×C11—22no—
146C8×C11—42no—
147C8×C11—41no—
148C8×C11—81no—
149C11⋊C8—81no—
150C2×C4⋊Q8—111no—
151C2×#106—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×C8C2×D1111yescharacteristic
159#384—111no—
160C4×C4⋊C4—111no—
161#340—221no—
162#340—221no—
163#340—221no—
164#336—221no—
165#334—22no—
166#332—222no—
167C22×C11#39611yescharacteristic
168C22×C11#46011yescharacteristic
169C22×C11#46311yescharacteristic
170C22×C11#46511yescharacteristic
171C22×C11#47011yescharacteristic
172C22×C11#47111yescharacteristic
173C22×C11#47311yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11#46111yescharacteristic
177C4×C11#46411yescharacteristic
178C4×C11#46511yescharacteristic
179C4×C11#46911yescharacteristic
180C4×C11#47511yescharacteristic
181C4×C11#47611yescharacteristic
182C4×C11#47811yescharacteristic
183C4×C11#47911yescharacteristic
184Dic11—42no—
185Dic11—82no—
186Dic11—81no—
187Dic11—161no—
188C22×Q8—221no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—221no—
192C22×C8D4411yescharacteristic
193C22×C8D4411yescharacteristic
194C4⋊Q8—112no—
195C4⋊Q8—221no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C42—221no—
206C2×C42C22×D1111yescharacteristic
207#106—442no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213C4⋊C8—442no—
214C4⋊C8C22⋊D1112yes—
215#103—442no—
216#103—442no—
217C4×C8—21no—
218C4×C8—21no—
219#95—221no—
220C2×C11#166611yescharacteristic
221C2×C11#167911yescharacteristic
222C2×C11#169011yescharacteristic
223C2×C11#170311yescharacteristic
224C2×C11#206411yescharacteristic
225C2×C11#206511yescharacteristic
226C2×C11#206611yescharacteristic
227C2×Q8—222no—
228C2×Q8—441no—
229C2×Q8—441no—
230C2×Q8—441no—
231C2×Q8—441no—
232C2×Q8—441no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—441no—
236C22×C4—441no—
237C22×C4C2×D4411yescharacteristic
238C22×C4D4×D1111yescharacteristic
239C22×C4#434311yescharacteristic
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—441no—
252C2×C8—441no—
253C2×C8—441no—
254C2×C8#431412yes—
255C4⋊C4—112no—
256C4⋊C4—221no—
257C4⋊C4—222no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—222no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—881no—
268C42—441no—
269C42—441no—
270C42#433911yescharacteristic
271C42#434111yescharacteristic
272C42Q8×D1111yescharacteristic
273C42C2×C22⋊D1111yescharacteristic
274C11#1059611yescharacteristic, complemented, Sylow
275C23#6694811yescharacteristic
276Q8—442no—
277Q8—442no—
278Q8—881no—
279Q8—881no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—222no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—442no—
288C2×C4—441no—
289C2×C4—881no—
290C2×C4—881no—
291C2×C4—881no—
292C2×C4—881no—
293C2×C4—881no—
294C2×C4#6694911yescharacteristic
295C2×C4#6695011yescharacteristic
296C2×C4#6695111yescharacteristic
297C2×C4C2×#431411yescharacteristic
298C2×C4#6695711yescharacteristic
299C2×C4#6696111yescharacteristic
300C2×C4#6696111yescharacteristic
301C2×C4SD16×D1111yescharacteristic
302C2×C4#6696811yescharacteristic
303C2×C4#6696811yescharacteristic
304C2×C4#6696911yescharacteristic
305C2×C4#6698311yescharacteristic
306C2×C4#6699211yescharacteristic
307C2×C4#6699911yescharacteristic
308C8—22no—
309C8—41no—
310C8—42no—
311C8—81no—
312C8—881no—
313C22#1062245711yescharacteristic
314C22#1062246111yescharacteristic
315C22#1062247711yescharacteristic
316C22#1062248111yescharacteristic
317C22#1062250911yescharacteristic
318C22#1062251111yescharacteristic
319C22#1062260711yescharacteristic
320C4—21no—
321C4—21no—
322C4—442no—
323C4—881no—
324C4—882no—
325C4—1761no—
326C4#1062245511yescharacteristic
327C4#1062246011yescharacteristic
328C4#1062246711yescharacteristic
329C4#1062247011yescharacteristic
330C4#1062272711yescharacteristic
331C4#1062274811yescharacteristic
332C4#1062277511yescharacteristic
333C4#1062277911yescharacteristic
334C2#1306796511yescharacteristic
335C2#1306804011yescharacteristic
336C2#1306811111yescharacteristic
337C2#1306819211yescharacteristic
338C2#1306997811yescharacteristic
339C2#1306998911yescharacteristic
340C2#1306999211yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#334C2
socle, prime radicalC23×C11#121
hypercenterC2×#334D11
hypocenterC11#10596
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
274. C11#10596semidirect

Maximal subgroups

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

subgroupindex
#130695672
#130694182
#130693802
#130693342
C2×#106221242
#130665002
C2×C11×#3342
#1059611