Finite Group Databasebeta

← #14647900

Subgroups — #14647900

Order 2816.

360 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077755C211yesmaximal, characteristic
2#13068736C211yesmaximal, 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)C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C4×#4318C2211yescharacteristic
21C11×#328C411yescharacteristic
22C11×#328C411yescharacteristic
23C11×#327C411yescharacteristic
24C11×#327C411yescharacteristic
25Q8⋊(C11⋊C8)—21no—
26D4⋊(C11⋊C8)—21no—
27#10622162—21no—
28#10622162—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)D411yescharacteristic
66C4⋊(C11⋊C8)D411yescharacteristic
67#66867—21no—
68#66867—21no—
69#66867—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#8877—111nomaximal, Sylow
73C2×Q8×C11C4⋊C411yescharacteristic
74C2×D4×C11—21no—
75C2×D4×C11C4⋊C411yescharacteristic
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4C4⋊C411yescharacteristic
89C11×C4⋊C4C4⋊C411yescharacteristic
90C11×C22⋊C4—21no—
91C11×C22⋊C4—21no—
92C11×C22⋊C4—21no—
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C42×C11—21no—
96C42×C11—41no—
97C42×C11—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×Q811yescharacteristic
101C42×C11#4111yescharacteristic
102#4318—22no—
103#4318—41no—
104#4318—81no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—42no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—81no—
115#2992—111no—
116#1832—111no—
117#1573—111no—
118#1500D1111yescharacteristic
119#1483—111no—
120#1300—111no—
121#1283—111no—
122C23×C11—21no—
123C23×C11C4×D411yescharacteristic
124Q8×C11—41no—
125D4×C11—41no—
126D4×C11—41no—
127D4×C11—41no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11C2×C4⋊C411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11C22⋊Q811yescharacteristic
148C2×C4×C11C22⋊Q811yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C8×C11—41no—
151C8×C11—41no—
152C11⋊C8—42no—
153C11⋊C8—41no—
154C11⋊C8—41no—
155C11⋊C8—41no—
156C11⋊C8—41no—
157C11⋊C8—81no—
158#529C2×D1111yescharacteristic
159#446—221no—
160#435—221no—
161#435—221no—
162C8×D4—221no—
163#433—221no—
164#432—111no—
165#431C2×D1111yescharacteristic
166#424—221no—
167C2×C4⋊C8—111no—
168C2×C4⋊C8—111no—
169C4×M16—111no—
170#376C2×D1111yescharacteristic
171#336—221no—
172#336—221no—
173#335—221no—
174#334—221no—
175#328Dic1111yescharacteristic
176#328Dic1111yescharacteristic
177#327Dic1111yescharacteristic
178#327Dic1111yescharacteristic
179Q8⋊C8—221no—
180D4⋊C8—221no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11#38511yescharacteristic
187C22×C11#44311yescharacteristic
188C22×C11#44411yescharacteristic
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11#45411yescharacteristic
200C4×C11#45511yescharacteristic
201C2×M16—221no—
202C2×M16—221no—
203C22×C8—111no—
204C22×C8—111no—
205C22×C8—221no—
206C22×C8—221no—
207#126—21no—
208#125Dic2211yescharacteristic
209#124Dic2211yescharacteristic
210#123—21no—
211C22⋊Q8C2×Dic1111yescharacteristic
212#121C2×Dic1111yescharacteristic
213C4×Q8D4411yescharacteristic
214C4×D4—21no—
215C4×D4D4411yescharacteristic
216#117—21no—
217C2×C42—21no—
218C2×C42C22×D1111yescharacteristic
219C4⋊C8—21no—
220C4⋊C8—111no—
221C4⋊C8—111no—
222C4⋊C8—221no—
223C4⋊C8—221no—
224C4⋊C8—221no—
225C4⋊C8—221no—
226C4⋊C8—221no—
227C4⋊C8—221no—
228C22⋊C8—221no—
229C22⋊C8—221no—
230C22⋊C8—221no—
231C22⋊C8C2×Dic1111yescharacteristic
232C22⋊C8C2×Dic1111yescharacteristic
233#97—221no—
234#97—221no—
235#97—221no—
236C4×C8—21no—
237C4×C8—221no—
238C4×C8—221no—
239#95—21no—
240#95C2×Dic1111yescharacteristic
241#95C2×Dic1111yescharacteristic
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—81no—
245C2×C11#186011yescharacteristic
246C2×C11#186611yescharacteristic
247C2×C11#186811yescharacteristic
248C2×Q8C4⋊Dic1111yescharacteristic
249C2×D4—21no—
250C2×D4C4⋊Dic1111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4D4×D1111yescharacteristic
255C22×C4#434111yescharacteristic
256C22×C4C22×Dic1111yescharacteristic
257M16—222no—
258M16—441no—
259M16—881no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—221no—
263C2×C8—221no—
264C2×C8—221no—
265C2×C8—221no—
266C2×C8—441no—
267C2×C8—441no—
268C2×C8—441no—
269C2×C8—442no—
270C2×C8—441no—
271C2×C8—881no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4C4⋊Dic1111yescharacteristic
277C4⋊C4C4⋊Dic1111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C42—21no—
284C42—41no—
285C42—41no—
286C42C2×Dic2211yescharacteristic
287C42C2×D4411yescharacteristic
288C42D4×D1111yescharacteristic
289C42#434111yescharacteristic
290C11#887711yescharacteristic, complemented, Sylow
291C23—21no—
292C23D4×Dic1111yescharacteristic
293Q8—41no—
294D4—41no—
295D4—41no—
296D4—41no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4#6693111yescharacteristic
314C2×C4#6693111yescharacteristic
315C2×C4#6693511yescharacteristic
316C2×C4#6693911yescharacteristic
317C2×C4C2×C4⋊Dic1111yescharacteristic
318C2×C4D4×Dic1111yescharacteristic
319C8—41no—
320C8—41no—
321C8—442no—
322C8—441no—
323C8—441no—
324C8—441no—
325C8—441no—
326C8—881no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22#1062256311yescharacteristic
333C22#1062280911yescharacteristic
334C22#1062281011yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4#1062243811yescharacteristic
346C4#1062244011yescharacteristic
347C2—21no—
348C2—21no—
349C2—81no—
350C2#1306885111yescharacteristic
351C2#1306889311yescharacteristic
352C2#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#8877
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. #13068736C2semidirect
3. #13067401C2semidirect
5. #13066509C2semidirect
6. #13066465C2semidirect
290. C11#8877semidirect

Maximal subgroups

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

subgroupindex
#130777552
#130687362
#130674012
#130670292
#130665092
#130664652
C11×#15002
#887711