Finite Group Databasebeta

← #14647893

Subgroups — #14647893

Order 2816.

380 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077755C211yesmaximal, characteristic
2#13068770C211yesmaximal, characteristic, complemented
3#13067401C211yesmaximal, characteristic, complemented
4#13067029C211yesmaximal, characteristic
5#13066509C211yesmaximal, characteristic, complemented
6#13066465C211yesmaximal, characteristic, complemented
7C11×#1500C211yesmaximal, characteristic
8C11×#529C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#376C2211yescharacteristic
11#10622637—21no—
12#10622624—21no—
13#10622624—21no—
14D4×C11⋊C8—21no—
15#10622613—21no—
16#10622612—21no—
17#10622539C2211yescharacteristic
18C2×C4⋊(C11⋊C8)—21no—
19C2×C4⋊(C11⋊C8)—21no—
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C4×#4318C2211yescharacteristic
23C11×#328C411yescharacteristic
24C11×#328C411yescharacteristic
25C11×#327C411yescharacteristic
26C11×#327C411yescharacteristic
27Q8⋊(C11⋊C8)—21no—
28D4⋊(C11⋊C8)—21no—
29#10622096—21no—
30#10622095—21no—
31C11×#126—21no—
32C11×#125Q811yescharacteristic
33C11×#124Q811yescharacteristic
34C11×#123—21no—
35C11×C22⋊Q8C2×C411yescharacteristic
36C11×#121C2×C411yescharacteristic
37C4×Q8×C11D411yescharacteristic
38C4×D4×C11—21no—
39C4×D4×C11D411yescharacteristic
40C11×#117—21no—
41C2×C42×C11—21no—
42C2×C42×C11C2311yescharacteristic
43C2×#4318—21no—
44C2×#4318—21no—
45C22×C11⋊C8—21no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8D411yescharacteristic
48C22×C11⋊C8D411yescharacteristic
49C11×C4⋊C8—21no—
50C11×C22⋊C8C2×C411yescharacteristic
51C11×C22⋊C8C2×C411yescharacteristic
52C4×C8×C11—21no—
53C11×#95—21no—
54C11×#95C2×C411yescharacteristic
55C11×#95C2×C411yescharacteristic
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58C22⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—42no—
66C4⋊(C11⋊C8)—42no—
67C4⋊(C11⋊C8)D411yescharacteristic
68C4⋊(C11⋊C8)D411yescharacteristic
69#66867—21no—
70#66867—21no—
71#66867—21no—
72C4×C11⋊C8—21no—
73C4×C11⋊C8—21no—
74#8876—111nomaximal, Sylow
75C2×Q8×C11C4⋊C411yescharacteristic
76C2×D4×C11—21no—
77C2×D4×C11C4⋊C411yescharacteristic
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4C4⋊C411yescharacteristic
91C11×C4⋊C4C4⋊C411yescharacteristic
92C11×C22⋊C4—21no—
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C11×C22⋊C4—21no—
96C11×C22⋊C4—21no—
97C42×C11—22no—
98C42×C11—22no—
99C42×C11—21no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×Q811yescharacteristic
103C42×C11#4111yescharacteristic
104#4318—22no—
105#4318—41no—
106#4318—81no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—81no—
118#2992—111no—
119#1843—111no—
120#1573—111no—
121#1500D1111yescharacteristic
122#1483—111no—
123#1300—111no—
124#1283—111no—
125C23×C11—21no—
126C23×C11C4×D411yescharacteristic
127Q8×C11—41no—
128D4×C11—41no—
129D4×C11—41no—
130D4×C11—41no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11C2×C4⋊C411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11C22⋊Q811yescharacteristic
151C2×C4×C11C22⋊Q811yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C8×C11—41no—
154C8×C11—41no—
155C11⋊C8—42no—
156C11⋊C8—41no—
157C11⋊C8—41no—
158C11⋊C8—41no—
159C11⋊C8—41no—
160C11⋊C8—81no—
161#529C2×D1111yescharacteristic
162#446—221no—
163#435—221no—
164#435—221no—
165C8×D4—221no—
166#433—221no—
167#432—111no—
168#431C2×D1111yescharacteristic
169#424—221no—
170C2×C4⋊C8—111no—
171C2×C4⋊C8—111no—
172C2×C4⋊C8—221no—
173C2×C4⋊C8—221no—
174C4×M16—111no—
175#376C2×D1111yescharacteristic
176#335—221no—
177#334—221no—
178#328Dic1111yescharacteristic
179#328Dic1111yescharacteristic
180#327Dic1111yescharacteristic
181#327Dic1111yescharacteristic
182Q8⋊C8—221no—
183D4⋊C8—221no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11#38511yescharacteristic
190C22×C11#44311yescharacteristic
191C22×C11#44411yescharacteristic
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—42no—
198C4×C11—42no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11#45311yescharacteristic
203C4×C11#45611yescharacteristic
204C2×M16—221no—
205C2×M16—221no—
206C22×C8—111no—
207C22×C8—111no—
208C22×C8—221no—
209C22×C8—221no—
210#126—21no—
211#125Dic2211yescharacteristic
212#124Dic2211yescharacteristic
213#123—21no—
214C22⋊Q8C2×Dic1111yescharacteristic
215#121C2×Dic1111yescharacteristic
216C4×Q8D4411yescharacteristic
217C4×D4—21no—
218C4×D4D4411yescharacteristic
219#117—21no—
220C2×C42—21no—
221C2×C42C22×D1111yescharacteristic
222C4⋊C8—21no—
223C4⋊C8—111no—
224C4⋊C8—111no—
225C4⋊C8—221no—
226C4⋊C8—221no—
227C4⋊C8—221no—
228C4⋊C8—221no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231C4⋊C8—442no—
232C4⋊C8—442no—
233C22⋊C8—221no—
234C22⋊C8—221no—
235C22⋊C8—221no—
236C22⋊C8C2×Dic1111yescharacteristic
237C22⋊C8C2×Dic1111yescharacteristic
238#97—221no—
239#97—221no—
240#97—221no—
241C4×C8—21no—
242C4×C8—221no—
243C4×C8—221no—
244#95—21no—
245#95C2×Dic1111yescharacteristic
246#95C2×Dic1111yescharacteristic
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—81no—
250C2×C11#185911yescharacteristic
251C2×C11#186611yescharacteristic
252C2×C11#186811yescharacteristic
253C2×Q8C4⋊Dic1111yescharacteristic
254C2×D4—21no—
255C2×D4C4⋊Dic1111yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4D4×D1111yescharacteristic
260C22×C4#434111yescharacteristic
261C22×C4C22×Dic1111yescharacteristic
262M16—222no—
263M16—441no—
264M16—881no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—221no—
268C2×C8—221no—
269C2×C8—221no—
270C2×C8—221no—
271C2×C8—441no—
272C2×C8—441no—
273C2×C8—441no—
274C2×C8—441no—
275C2×C8—441no—
276C2×C8—441no—
277C2×C8—881no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4C4⋊Dic1111yescharacteristic
283C4⋊C4C4⋊Dic1111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C42—22no—
290C42—22no—
291C42—21no—
292C42C2×Dic2211yescharacteristic
293C42C2×D4411yescharacteristic
294C42D4×D1111yescharacteristic
295C42#434111yescharacteristic
296C11#887611yescharacteristic, complemented, Sylow
297C23—21no—
298C23D4×Dic1111yescharacteristic
299Q8—41no—
300D4—41no—
301D4—41no—
302D4—41no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4#6693111yescharacteristic
320C2×C4#6693111yescharacteristic
321C2×C4#6693511yescharacteristic
322C2×C4#6693911yescharacteristic
323C2×C4C2×C4⋊Dic1111yescharacteristic
324C2×C4D4×Dic1111yescharacteristic
325C8—41no—
326C8—41no—
327C8—442no—
328C8—441no—
329C8—441no—
330C8—441no—
331C8—441no—
332C8—881no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22#1062256311yescharacteristic
339C22#1062280911yescharacteristic
340C22#1062281011yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4#1062243511yescharacteristic
352C4#1062243911yescharacteristic
353C2—21no—
354C2—21no—
355C2—81no—
356C2#1306884411yescharacteristic
357C2#1306889311yescharacteristic
358C2#1306890411yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1500C2
socleC22×C11#385
prime radicalC11×#121C2×C4
cosocleC2×C42×C11C23
hypercenter#1500D11
hypocenterC11#8876
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1500

Complements

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

NH ≅ G/Ntype
2. #13068770C2semidirect
3. #13067401C2semidirect
5. #13066509C2semidirect
6. #13066465C2semidirect
296. C11#8876semidirect

Maximal subgroups

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

subgroupindex
#130777552
#130687702
#130674012
#130670292
#130665092
#130664652
C11×#15002
#887611