Finite Group Databasebeta

← #13069865

Subgroups — #13069865

Order 1408.

382 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623335C211yesmaximal, characteristic
2C11×#386C211yesmaximal, characteristic, complemented
3C2×#66898C211yesmaximal, characteristic, complemented
4#10622826C211yesmaximal, characteristic, complemented
5#10622823C211yesmaximal, characteristic, complemented
6C2×#66870C211yesmaximal, characteristic, complemented
7#10622165C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C23×C4×C11C2211yescharacteristic
10C22×C22⋊D11C2211yescharacteristic
11C2×C11×C22⋊C4—21no—
12C2×C11×C22⋊C4C2211yescharacteristic
13#67006—21no—
14C2×C22⋊Dic11C2211yescharacteristic
15C2×C22⋊Dic11C2211yescharacteristic
16C2×C22⋊Dic11C2211yescharacteristic
17#66992—21no—
18#66992—21no—
19#66990—21no—
20#66988—21no—
21#66982—21no—
22C2×(C2×D11)⋊C4—21no—
23C2×Dic11⋊C4—21no—
24C11×#95—21no—
25#66898—22no—
26C11⋊#95—21no—
27C11⋊#95—21no—
28#66870—22no—
29C24×C11D411yescharacteristic
30C24×C11C2311yescharacteristic
31C23×D11D411yescharacteristic
32C2×D4×C11—21no—
33C2×D4×C11—21no—
34C2×D4×C11—21no—
35C2×D4×C11—21no—
36C2×D4×C11—21no—
37C2×D4×C11—21no—
38C22×C4×C11—21no—
39C22×C4×C11—21no—
40C22×C4×C11—21no—
41C22×C4×C11—21no—
42C22×C4×C11—42no—
43C22×C4×C11D411yescharacteristic
44C2×C22⋊D11—21no—
45C2×C22⋊D11—21no—
46C2×C22⋊D11—21no—
47C2×C22⋊D11—21no—
48C2×C22⋊D11—21no—
49C2×C22⋊D11—21no—
50C2×C22⋊D11—21no—
51C2×C22⋊D11—21no—
52C22×Dic11—21no—
53C22×Dic11—21no—
54C22×Dic11D411yescharacteristic
55C22×Dic11D411yescharacteristic
56C22×Dic11D411yescharacteristic
57C11×C22⋊C4—21no—
58C11×C22⋊C4—21no—
59C11×C22⋊C4—42no—
60C22⋊Dic11—21no—
61C22⋊Dic11—21no—
62C22⋊Dic11—21no—
63C22⋊Dic11—21no—
64C22⋊Dic11—21no—
65C22⋊Dic11—21no—
66C22⋊Dic11—21no—
67C22⋊Dic11D412yescomplemented
68(C2×D11)⋊C4—21no—
69(C2×D11)⋊C4—21no—
70(C2×D11)⋊C4—42no—
71Dic11⋊C4—21no—
72Dic11⋊C4—21no—
73Dic11⋊C4—42no—
74#2044—111nomaximal, Sylow
75C23×C11—21no—
76C23×C11—21no—
77C23×C11—21no—
78C23×C11—41no—
79C23×C11—41no—
80C23×C11—41no—
81C23×C11—41no—
82C23×C11C2×D411yescharacteristic
83C23×C11C2×D411yescharacteristic
84C23×C11C2×D411yescharacteristic
85C23×C11C2×D411yescharacteristic
86C23×C11#4111yescharacteristic
87C23×C11#4111yescharacteristic
88C23×C11#4111yescharacteristic
89C22×D11—21no—
90C22×D11—21no—
91C22×D11—21no—
92C22×D11—41no—
93C22×D11—41no—
94D4×C11—41no—
95D4×C11—41no—
96D4×C11—41no—
97D4×C11—41no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C22⋊D11—41no—
112C22⋊D11—41no—
113C22⋊D11—41no—
114C22⋊D11—41no—
115C22⋊D11—81no—
116C22⋊D11—81no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—22no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130#534—111no—
131C2×#99—111no—
132C2×#99—111no—
133#386—111no—
134#386D1111yescharacteristic, complemented
135#385—111no—
136#342—111no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—41no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11—41no—
147C22×C11—42no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11—81no—
152C22×C11#12011yescharacteristic
153C22×C11#12111yescharacteristic
154C22×C11#12111yescharacteristic
155C22×C11#12111yescharacteristic
156C22×C11#12311yescharacteristic
157C22×C11#12311yescharacteristic
158C22×C11#12411yescharacteristic
159C2×D11—42no—
160C2×D11—41no—
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—81no—
164C4×C11—41no—
165C4×C11—42no—
166C4×C11—81no—
167Dic11—42no—
168Dic11—41no—
169Dic11—41no—
170Dic11—41no—
171Dic11—81no—
172C22×D4—111no—
173C22×D4C2×D1111yescharacteristic
174C23×C4C2×D1111yescharacteristic
175#123—221no—
176#123—221no—
177#121—221no—
178#121—221no—
179#120—221no—
180#120—221no—
181C2×C4⋊C4—221no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—111no—
184C2×C22⋊C4—111no—
185C2×C22⋊C4—111no—
186C2×C22⋊C4—221no—
187C2×C22⋊C4C2×D1111yescharacteristic
188#99—222no—
189#99—222no—
190#95—21no—
191#95—221no—
192#95—221no—
193C2×C11—21no—
194C2×C11—21no—
195C2×C11—21no—
196C2×C11—21no—
197C2×C11—21no—
198C2×C11—21no—
199C2×C11—81no—
200C2×C11#39411yescharacteristic
201C2×C11B(4,𝔽2)11yescharacteristic
202C2×C11#45811yescharacteristic
203D11—81no—
204C24—111no—
205C24C22⋊D1111yescharacteristic
206C24C22×D1111yescharacteristic
207C2×D4—21no—
208C2×D4—21no—
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—221no—
214C2×D4—221no—
215C2×D4—221no—
216C2×D4—221no—
217C2×D4—221no—
218C2×D4—221no—
219C2×D4—221no—
220C2×D4—221no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—42no—
226C22×C4—111no—
227C22×C4—111no—
228C22×C4—111no—
229C22×C4—221no—
230C22×C4—221no—
231C22×C4C22⋊D1111yescharacteristic
232C4⋊C4—221no—
233C4⋊C4—221no—
234C4⋊C4—442no—
235C22⋊C4—21no—
236C22⋊C4—21no—
237C22⋊C4—42no—
238C22⋊C4—112no—
239C22⋊C4—221no—
240C22⋊C4—221no—
241C22⋊C4—221no—
242C22⋊C4—221no—
243C22⋊C4—221no—
244C22⋊C4—221no—
245C22⋊C4—221no—
246C22⋊C4—221no—
247C22⋊C4—221no—
248C22⋊C4—442no—
249C11#204411yescharacteristic, complemented, Sylow
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—221no—
258C23—221no—
259C23—221no—
260C23—441no—
261C23—441no—
262C23#433911yescharacteristic
263C23#433911yescharacteristic
264C23D4×D1111yescharacteristic
265C23D4×D1111yescharacteristic
266C23D4×D1111yescharacteristic
267C23#434111yescharacteristic
268C23C2×C22⋊D1111yescharacteristic
269D4—41no—
270D4—41no—
271D4—41no—
272D4—41no—
273D4—441no—
274D4—441no—
275D4—441no—
276D4—441no—
277D4—881no—
278D4—881no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—221no—
293C2×C4—222no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—81no—
320C22—442no—
321C22—441no—
322C22—441no—
323C22—441no—
324C22—881no—
325C22#6693611yescharacteristic
326C22#6693711yescharacteristic
327C22#6693711yescharacteristic
328C22#6693811yescharacteristic
329C22#6698211yescharacteristic
330C22#6699011yescharacteristic
331C22#6699211yescharacteristic
332C4—41no—
333C4—42no—
334C4—81no—
335C4—442no—
336C4—441no—
337C4—441no—
338C4—441no—
339C4—881no—
340C2—21no—
341C2—21no—
342C2—21no—
343C2—21no—
344C2—21no—
345C2—21no—
346C2—81no—
347C2—881no—
348C2#1062257211yescharacteristic
349C2#1062264511yescharacteristic
350C2#1062266611yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC24×C11C23
FrattiniC24C22×D11
FittingC11×#386C2
socleC22×C11#120
prime radical#10623335C2
hypercenter#386D11
hypocenterC11#2044
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C11×#386C2semidirect
3. C2×#66898C2semidirect
4. #10622826C2semidirect
5. #10622823C2semidirect
6. C2×#66870C2semidirect
7. #10622165C2semidirect
67. C22⋊Dic11D4semidirect
134. #386D11semidirect
249. C11#2044semidirect

Maximal subgroups

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

subgroupindex
#106233352
C11×#3862
C2×#668982
#106228262
#106228232
C2×#668702
#106221652
#204411