Finite Group Databasebeta

← #13076185

Subgroups — #13076185

Order 1408.

386 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#383C211yesmaximal, characteristic, complemented
2#10622553C211yesmaximal, characteristic
3#10622541C211yesmaximal, characteristic, complemented
4#10622289C211yesmaximal, characteristic
5#10622287C211yesmaximal, characteristic
6#10622287C211yesmaximal, characteristic
7#10622286C211yesmaximal, characteristic
8#10622283C211yesmaximal, characteristic
9#10622282C211yesmaximal, characteristic
10#10622273C211yesmaximal, characteristic, complemented
11#10622269C211yesmaximal, characteristic, complemented
12#10622267C211yesmaximal, characteristic, complemented
13#10622265C211yesmaximal, characteristic, complemented
14#10622263C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C22×Dic22C2211yescharacteristic
17C2×C42×C11C2211yescharacteristic
18C2×(C2×D11)⋊C4C2211yescharacteristic
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×C4×Dic11C2211yescharacteristic
34C2×C4×Dic11C2211yescharacteristic
35C11×#95C2211yescharacteristic
36C11×#95C2211yescharacteristic
37C11×#95C2211yescharacteristic
38C11×#95C2211yescharacteristic
39C11×#95C2211yescharacteristic
40C11×#95C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C23×D11C2311yescharacteristic
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×Dic11C2311yescharacteristic
60C22×Dic11C2311yescharacteristic
61C22×Dic11C2311yescharacteristic
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C2×Dic22—22no—
67C2×Dic22—41no—
68C2×Dic22—41no—
69C42×C11—22no—
70(C2×D11)⋊C4—22no—
71(C2×D11)⋊C4—22no—
72(C2×D11)⋊C4—22no—
73(C2×D11)⋊C4—41no—
74(C2×D11)⋊C4—41no—
75(C2×D11)⋊C4—41no—
76(C2×D11)⋊C4—41no—
77C4⋊Dic11—22no—
78C4⋊Dic11—22no—
79C4⋊Dic11—41no—
80Dic11⋊C4—22no—
81Dic11⋊C4—41no—
82Dic11⋊C4—41no—
83Dic11⋊C4—41no—
84Dic11⋊C4—41no—
85C4×Dic11—22no—
86C4×Dic11—41no—
87#2775—111nomaximal, Sylow
88C23×C11C2411yescharacteristic
89C22×D11—21no—
90C22×D11—21no—
91C22×D11—21no—
92C22×D11—21no—
93C22×D11—21no—
94C22×D11—21no—
95C22×D11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
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#4112yes—
117C2×Dic11—21no—
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#4112yes—
137C2×Dic11#4112yes—
138Dic22—44no—
139#400—111no—
140#397—111no—
141#397—111no—
142#396—111no—
143#395—111no—
144#393—111no—
145#391—111no—
146#389—111no—
147#388—111no—
148#388—111no—
149#388—111no—
150#387—111no—
151#387—111no—
152#383D1111yescharacteristic, complemented
153#382—111no—
154C22×C11C2×#4111yescharacteristic
155C22×C11C2×#4111yescharacteristic
156C22×C11C2×#4111yescharacteristic
157C22×C11H(5,𝔽2)11yescharacteristic
158C22×C11H(5,𝔽2)11yescharacteristic
159C22×C112−1+411yescharacteristic
160C22×C112−1+411yescharacteristic
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C2×D11—41no—
165C2×D11—41no—
166C2×D11—41no—
167C2×D11—41no—
168C4×C11—22no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175Dic11—22no—
176Dic11—22no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C22×Q8—111no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4—111no—
185C2×C4⋊C4—111no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—111no—
191C2×C22⋊C4—111no—
192C2×C22⋊C4—111no—
193C2×C22⋊C4—111no—
194C2×C22⋊C4—111no—
195C2×C22⋊C4—111no—
196C2×C22⋊C4—111no—
197C2×C22⋊C4—111no—
198C2×C42—111no—
199C2×C42—111no—
200C2×C42C2×D1111yescharacteristic
201#95—111no—
202#95—111no—
203#95—111no—
204#95—111no—
205#95—111no—
206#95—111no—
207#95—111no—
208#95—111no—
209#95—111no—
210#95—111no—
211#95C2×D1111yescharacteristic
212#95C2×D1111yescharacteristic
213#95C2×D1111yescharacteristic
214#95C2×D1111yescharacteristic
215#95C2×D1111yescharacteristic
216#95C2×D1111yescharacteristic
217C2×C11#53811yescharacteristic
218C2×C11#53911yescharacteristic
219C2×C11#54211yescharacteristic
220C2×C11#55211yescharacteristic
221C2×C11#55511yescharacteristic
222C2×C11#55611yescharacteristic
223C2×C11#56311yescharacteristic
224D11—81no—
225C24—111no—
226C2×Q8—222no—
227C2×Q8—441no—
228C2×Q8—441no—
229C22×C4—111no—
230C22×C4—111no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4C22×D1111yescharacteristic
237C22×C4C22×D1111yescharacteristic
238C22×C4C22×D1111yescharacteristic
239C22×C4C22×D1111yescharacteristic
240C22×C4C22×D1111yescharacteristic
241C22×C4C22×D1111yescharacteristic
242C22×C4C22×D1111yescharacteristic
243C4⋊C4—222no—
244C4⋊C4—222no—
245C4⋊C4—222no—
246C4⋊C4—441no—
247C4⋊C4—441no—
248C4⋊C4—441no—
249C4⋊C4—441no—
250C4⋊C4—441no—
251C22⋊C4—222no—
252C22⋊C4—222no—
253C22⋊C4—222no—
254C22⋊C4—441no—
255C22⋊C4—441no—
256C22⋊C4—441no—
257C22⋊C4—441no—
258C42—22no—
259C42—222no—
260C42—441no—
261C11#277511yescharacteristic, complemented, Sylow
262C23—221no—
263C23—221no—
264C23—221no—
265C23—221no—
266C23—221no—
267C23—221no—
268C23—221no—
269C23C23×D1111yescharacteristic
270Q8—444no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
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—112no—
292C2×C4—112no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
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#433912yes—
313C22—441no—
314C22—441no—
315C22—441no—
316C22—441no—
317C22—441no—
318C22—441no—
319C22—441no—
320C22C2×#433911yescharacteristic
321C22#41×D1111yescharacteristic
322C22#41×D1111yescharacteristic
323C22#6704211yescharacteristic
324C22#6704211yescharacteristic
325C22#6704311yescharacteristic
326C22#6704311yescharacteristic
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—222no—
335C4—222no—
336C4—441no—
337C4—441no—
338C4—441no—
339C4—441no—
340C4—441no—
341C2—881no—
342C2#1062306211yescharacteristic
343C2#1062306311yescharacteristic
344C2#1062306511yescharacteristic
345C2#1062323311yescharacteristic
346C2#1062323511yescharacteristic
347C2#1062323811yescharacteristic
348C2#1062324311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#383C2
prime radicalC23×D11C23
hypercenter#383D11
hypocenterC11#2775
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
1. C11×#383C2semidirect
3. #10622541C2semidirect
10. #10622273C2semidirect
11. #10622269C2semidirect
12. #10622267C2semidirect
13. #10622265C2semidirect
14. #10622263C2semidirect
15. #10622259C2semidirect
152. #383D11semidirect
261. C11#2775semidirect

Maximal subgroups

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

subgroupindex
C11×#3832
#106225532
#106225412
#106222892
#106222872
#106222862
#106222832
#106222822
#106222732
#106222692
#106222672
#106222652
#106222632
#106222592
#277511