Finite Group Databasebeta

← #13069613

Subgroups — #13069613

Order 1408.

496 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C2×#66991C211yesmaximal, characteristic, complemented
2C22×#4323C211yesmaximal, characteristic, complemented
3C2×#66948C211yesmaximal, characteristic, complemented
4C2×C11×#102C211yesmaximal, characteristic, complemented
5C2×#66885C211yesmaximal, characteristic, complemented
6C2×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C22×C22⋊D11—21no—
10C22×D44—21no—
11C22×D44C2211yescharacteristic
12C22×C4×D11C2211yescharacteristic
13C22×C8×C11C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C22⋊Dic11—21no—
16#66991—22no—
17#66991—22no—
18C2×#4323—22no—
19C2×#4323—22no—
20C2×#4323—22no—
21C2×(C2×D11)⋊C4—21no—
22C2×C4⋊Dic11C2211yescharacteristic
23C22×C11⋊C8C2211yescharacteristic
24#66948—22no—
25#66948—22no—
26C11×#102—22no—
27#66885—22no—
28(C2×D11)⋊C8—22no—
29C24×C11—21no—
30C23×D11—21no—
31C23×D11D411yescharacteristic
32C2×D4×C11—21no—
33C2×D4×C11—21no—
34C2×D4×C11—21no—
35C2×D4×C11—21no—
36C2×D4×C11—21no—
37C2×D4×C11D412yescomplemented
38C22×C4×C11—21no—
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—24no—
41C2×C22⋊D11—42no—
42C2×C22⋊D11—42no—
43C22×Dic11—21no—
44C22×Dic11D411yescharacteristic
45C2×D44—24no—
46C2×D44—21no—
47C2×D44—21no—
48C2×D44—21no—
49C2×D44—21no—
50C2×D44—21no—
51C2×D44—42no—
52C2×D44—42no—
53C2×D44D412yescomplemented
54C2×C4×D11—21no—
55C2×C4×D11—21no—
56C2×C4×D11—21no—
57C2×C4×D11—21no—
58C2×C4×D11—21no—
59C2×C4×D11—21no—
60C2×C8×C11—21no—
61C2×C8×C11—21no—
62C2×C8×C11—21no—
63C11×C4⋊C4—21no—
64C11×C4⋊C4D412yescomplemented
65C22⋊Dic11—24no—
66#4323—28no—
67(C2×D11)⋊C4—24no—
68C4⋊Dic11—21no—
69C4⋊Dic11D412yescomplemented
70C2×C11⋊C8—21no—
71C2×C11⋊C8—21no—
72C2×C11⋊C8D412yescomplemented
73#1999—111nomaximal, Sylow
74C23×C11—22no—
75C23×C11—41no—
76C23×C11—41no—
77C23×C11—41no—
78C23×C11—41no—
79C23×C11—41no—
80C23×C11—41no—
81C23×C11C2×D411yescharacteristic
82C22×D11—21no—
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—21no—
86C22×D11—21no—
87C22×D11—21no—
88C22×D11—22no—
89C22×D11—41no—
90C22×D11—41no—
91C22×D11—41no—
92C22×D11—41no—
93C22×D11—41no—
94C22×D11—41no—
95C22×D11D812yescomplemented
96D4×C11—22no—
97D4×C11—22no—
98D4×C11—41no—
99D4×C11—41no—
100C2×C4×C11—22no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11C2×D411yescharacteristic
104C2×C4×C11C2×D411yescharacteristic
105C2×C4×C11C2×D411yescharacteristic
106C2×C4×C11C2×D411yescharacteristic
107C2×C4×C11C2×D411yescharacteristic
108C2×C4×C11#4111yescharacteristic
109C22⋊D11—48no—
110C2×Dic11—22no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116D44—22no—
117D44—22no—
118D44—48no—
119D44—41no—
120D44—41no—
121C4×D11—41no—
122C4×D11—41no—
123C4×D11—41no—
124C4×D11—41no—
125C8×C11—41no—
126C11⋊C8—22no—
127C22×D8—111no—
128C2×#121—111no—
129C2×#121—111no—
130C2×#102—111no—
131C2×#102D1111yescharacteristic, complemented
132C2×C22⋊C8—111no—
133#340—111no—
134C22×C11—42no—
135C22×C11—42no—
136C22×C11—42no—
137C22×C11—81no—
138C22×C11—81no—
139C22×C11—81no—
140C22×C11—81no—
141C22×C11#12011yescharacteristic
142C22×C11#12011yescharacteristic
143C22×C11#12111yescharacteristic
144C22×C11C2×D811yescharacteristic
145C22×C11#13511yescharacteristic
146C22×C11AGL(1,ℤ/8)11yescharacteristic
147C22×C11AGL(1,ℤ/8)11yescharacteristic
148C2×D11—22no—
149C2×D11—22no—
150C2×D11—22no—
151C2×D11—41no—
152C2×D11—41no—
153C2×D11—41no—
154C2×D11—41no—
155C2×D11—42no—
156C2×D11—42no—
157C2×D11—42no—
158C2×D11—81no—
159C2×D11—81no—
160C2×D11—81no—
161C2×D11—81no—
162C4×C11—42no—
163C4×C11#12011yescharacteristic
164C4×C11#12111yescharacteristic
165C4×C11#12111yescharacteristic
166C4×C11#12711yescharacteristic
167Dic11—41no—
168Dic11—42no—
169C22×D4—111no—
170C22×D4—221no—
171C22×D4—221no—
172C22×D4C2×D1111yescharacteristic
173C23×C4—111no—
174C2×D8—222no—
175C2×D8—222no—
176C2×D8—222no—
177C22×C8—111no—
178C22×C8C2×D1111yescharacteristic
179#121—222no—
180#121—222no—
181#121—222no—
182#121—222no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4C2×D1111yescharacteristic
185C2×C22⋊C4—221no—
186C2×C22⋊C4—221no—
187#102—22no—
188#102—222no—
189C22⋊C8—222no—
190C2×C11—82no—
191C2×C11#39211yescharacteristic
192C2×C11#44711yescharacteristic
193C2×C11#44711yescharacteristic
194C2×C11#44911yescharacteristic
195C2×C11#44911yescharacteristic
196C2×C11#46611yescharacteristic
197C2×C11#46911yescharacteristic
198D11—42no—
199D11—82no—
200C24—21no—
201C24—111no—
202C24—221no—
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—21no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—112no—
209C2×D4—224no—
210C2×D4—224no—
211C2×D4—221no—
212C2×D4—221no—
213C2×D4—221no—
214C2×D4—221no—
215C2×D4—221no—
216C2×D4—442no—
217C2×D4—442no—
218C2×D4—442no—
219C2×D4—442no—
220C2×D4D4412yescomplemented
221C22×C4—21no—
222C22×C4—111no—
223C22×C4—221no—
224C22×C4—221no—
225C22×C4—221no—
226C22×C4—221no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4C22×D1111yescharacteristic
231D8—228no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—112no—
236C2×C8—221no—
237C2×C8—221no—
238C4⋊C4—21no—
239C4⋊C4—112no—
240C4⋊C4—221no—
241C4⋊C4C22⋊D1112yescomplemented
242C22⋊C4—224no—
243C22⋊C4—224no—
244C11#199911yescharacteristic, complemented, Sylow
245C23—22no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23—112no—
253C23—221no—
254C23—221no—
255C23—221no—
256C23—221no—
257C23—221no—
258C23—221no—
259C23—222no—
260C23—441no—
261C23—441no—
262C23—441no—
263C23—441no—
264C23—441no—
265C23—441no—
266C23D4×D1111yescharacteristic
267D4—22no—
268D4—22no—
269D4—41no—
270D4—41no—
271D4—222no—
272D4—222no—
273D4—448no—
274D4—448no—
275D4—441no—
276D4—441no—
277C2×C4—22no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—221no—
281C2×C4—222no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4C2×D4411yescharacteristic
291C2×C4#433911yescharacteristic
292C2×C4D4×D1111yescharacteristic
293C2×C4D4×D1111yescharacteristic
294C2×C4D4×D1111yescharacteristic
295C2×C4C2×C22⋊D1111yescharacteristic
296C8—41no—
297C8—222no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—81no—
302C22—81no—
303C22—81no—
304C22—81no—
305C22—222no—
306C22—222no—
307C22—222no—
308C22—441no—
309C22—441no—
310C22—441no—
311C22—441no—
312C22—442no—
313C22—442no—
314C22—442no—
315C22—881no—
316C22—881no—
317C22—881no—
318C22—881no—
319C22#6693511yescharacteristic
320C22#6693711yescharacteristic
321C22D8×D1111yescharacteristic
322C22#6696411yescharacteristic
323C22#6696711yescharacteristic
324C22#6696911yescharacteristic
325C22#6699011yescharacteristic
326C4—42no—
327C4—441no—
328C4—442no—
329C4#6693511yescharacteristic
330C4#6693711yescharacteristic
331C4#6698311yescharacteristic
332C4#6699311yescharacteristic
333C2—82no—
334C2—442no—
335C2—882no—
336C2#1062238611yescharacteristic
337C2#1062238811yescharacteristic
338C2#1062239411yescharacteristic
339C2#1062239511yescharacteristic
340C2#1062257311yescharacteristic
341C2#1062276911yescharacteristic
342C2#1062278511yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#102C2
socleC23×C11C2×D4
hypercenterC2×#102D11
hypocenterC11#1999
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#66991C2semidirect
2. C22×#4323C2semidirect
3. C2×#66948C2semidirect
4. C2×C11×#102C2semidirect
5. C2×#66885C2semidirect
6. C2×(C2×D11)⋊C8C2semidirect
7. #10622167C2semidirect
37. C2×D4×C11D4semidirect
53. C2×D44D4semidirect
64. C11×C4⋊C4D4semidirect
69. C4⋊Dic11D4semidirect
72. C2×C11⋊C8D4semidirect
95. C22×D11D8semidirect
131. C2×#102D11semidirect
220. C2×D4D44semidirect
241. C4⋊C4C22⋊D11semidirect
244. C11#1999semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
C22×#43232
C2×#669482
C2×C11×#1022
C2×#668852
C2×(C2×D11)⋊C82
#106221672
#199911