Finite Group Databasebeta

← #13074809

Subgroups — #13074809

Order 1408.

408 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#399C211yesmaximal, characteristic
2#10622598C211yesmaximal, characteristic, complemented
3#10622597C211yesmaximal, characteristic, complemented
4#10622596C211yesmaximal, characteristic, complemented
5#10622593C211yesmaximal, characteristic, complemented
6#10622591C211yesmaximal, characteristic, complemented
7#10622585C211yesmaximal, characteristic, complemented
8#10622562C211yesmaximal, characteristic
9#10622561C211yesmaximal, characteristic
10#10622561C211yesmaximal, characteristic
11#10622556C211yesmaximal, characteristic
12#10622555C211yesmaximal, characteristic
13C22⋊C4×Dic11C211yesmaximal, characteristic
14#10622270C211yesmaximal, characteristic, complemented
15#10622265C211yesmaximal, characteristic, complemented
16C23×Dic11C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×C4×Dic11C2211yescharacteristic
38C2×C4×Dic11C2211yescharacteristic
39C11×#95C2211yescharacteristic
40C11⋊#95C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C24×C11C2311yescharacteristic
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×Dic11—41no—
59C22×Dic11—41no—
60C22×Dic11Q814yes—
61C22×Dic11C2311yescharacteristic
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C11×C4⋊C4—22no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C22⋊C4—22no—
73C11×C22⋊C4—41no—
74C11×C22⋊C4—41no—
75C22⋊Dic11—22no—
76C22⋊Dic11—41no—
77C22⋊Dic11—41no—
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81Dic11⋊C4—22no—
82Dic11⋊C4—22no—
83Dic11⋊C4—22no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89C4×Dic11—41no—
90C4×Dic11—41no—
91#2667—111nomaximal, Sylow
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11C2×Q812yes—
99C23×C11C2411yescharacteristic
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11#4112yes—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—44no—
140C2×Dic11C2×Q812yes—
141C2×Dic11C2×Q812yes—
142C2×Dic11#4112yes—
143#399—111no—
144#399D1111yescharacteristic
145#398—111no—
146#398—111no—
147#398—111no—
148#398—111no—
149#396—111no—
150#396—111no—
151#389—111no—
152#389—111no—
153#387—111no—
154#387—111no—
155#381—111no—
156#380—111no—
157C4×C22⋊C4—111no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11C22×Q811yescharacteristic
166C22×C11C2×#4111yescharacteristic
167C22×C11C2×#4111yescharacteristic
168C22×C11H(5,𝔽2)11yescharacteristic
169C22×C11H(5,𝔽2)11yescharacteristic
170C22×C11H(5,𝔽2)11yescharacteristic
171C22×C112−1+411yescharacteristic
172C4×C11—22no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—41no—
178Dic11—22no—
179Dic11—22no—
180Dic11—22no—
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184Dic11—41no—
185Dic11—41no—
186C23×C4—111no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4—111no—
192C2×C4⋊C4—111no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4C2×D1111yescharacteristic
199C2×C4⋊C4C2×D1111yescharacteristic
200C2×C4⋊C4C2×D1111yescharacteristic
201C2×C22⋊C4—111no—
202C2×C22⋊C4—111no—
203C2×C22⋊C4—111no—
204C2×C22⋊C4C2×D1111yescharacteristic
205C2×C22⋊C4C2×D1111yescharacteristic
206C2×C22⋊C4C2×D1111yescharacteristic
207C2×C42—111no—
208C2×C42—111no—
209#95—111no—
210#95—111no—
211#95—111no—
212#95—111no—
213#95—111no—
214#95—111no—
215#95—111no—
216#95—111no—
217#95—111no—
218#95—111no—
219#95—111no—
220#95C2×D1111yescharacteristic
221C2×C11—42no—
222C2×C11#53311yescharacteristic
223C2×C11#53911yescharacteristic
224C2×C11#53911yescharacteristic
225C2×C11#54011yescharacteristic
226C2×C11#54011yescharacteristic
227C2×C11#54311yescharacteristic
228C2×C11#54411yescharacteristic
229C24C22×D1111yescharacteristic
230C22×C4—111no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4—114no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—111no—
239C22×C4—441no—
240C22×C4—441no—
241C22×C4C22×D1111yescharacteristic
242C22×C4C22×D1111yescharacteristic
243C22×C4C22×D1111yescharacteristic
244C22×C4C22×D1111yescharacteristic
245C22×C4C22×D1111yescharacteristic
246C22×C4C22×D1111yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—222no—
251C4⋊C4—222no—
252C4⋊C4—222no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C22⋊C4—22no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—222no—
265C22⋊C4—441no—
266C22⋊C4—441no—
267C42—441no—
268C42—441no—
269C11#266711yescharacteristic, complemented, Sylow
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23Q8×D1112yes—
277C23C23×D1111yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—112no—
296C2×C4—112no—
297C2×C4—112no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—444no—
320C2×C4#434112yes—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22C2×#434111yescharacteristic
329C22#6703711yescharacteristic
330C22#6703711yescharacteristic
331C22C2×Q8×D1111yescharacteristic
332C22#41×D1111yescharacteristic
333C22#6704211yescharacteristic
334C22#6704311yescharacteristic
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—222no—
342C4—222no—
343C4—222no—
344C4—441no—
345C4—441no—
346C4—441no—
347C4—441no—
348C4—441no—
349C2—42no—
350C2#1062315311yescharacteristic
351C2#1062315411yescharacteristic
352C2#1062316511yescharacteristic
353C2#1062319111yescharacteristic
354C2#1062319411yescharacteristic
355C2#1062319611yescharacteristic
356C2#1062325011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#399C2
prime radicalC24×C11C23
hypercenter#399D11
hypocenterC11#2667
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #10622598C2semidirect
3. #10622597C2semidirect
4. #10622596C2semidirect
5. #10622593C2semidirect
6. #10622591C2semidirect
7. #10622585C2semidirect
14. #10622270C2semidirect
15. #10622265C2semidirect
269. C11#2667semidirect

Maximal subgroups

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

subgroupindex
C11×#3992
#106225982
#106225972
#106225962
#106225932
#106225912
#106225852
#106225622
#106225612
#106225562
#106225552
C22⋊C4×Dic112
#106222702
#106222652
#266711