Finite Group Databasebeta

← #13069739

Subgroups — #13069739

Order 1408.

638 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 75 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×C11×#120C211yesmaximal, characteristic, complemented
2C2×#67006C211yesmaximal, characteristic, complemented
3#10623335C211yesmaximal, characteristic, complemented
4#10622860C211yesmaximal, characteristic, complemented
5C2×#66898C211yesmaximal, characteristic, complemented
6C2×#66870C211yesmaximal, characteristic, complemented
7#10622165C211yesmaximal, characteristic, complemented
8C25×C11C2211yescharacteristic
9C22×D4×C11—21no—
10C22×D4×C11C2211yescharacteristic
11C22×C22⋊D11—21no—
12C22×C22⋊D11C2211yescharacteristic
13C11×#120—22no—
14C11×#120—22no—
15C2×C11×C22⋊C4—21no—
16C2×C11×C22⋊C4C2211yescharacteristic
17#67006—21no—
18#67006—22no—
19#67006—22no—
20C2×C22⋊Dic11—21no—
21C2×C22⋊Dic11—22no—
22C2×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25#66992—22no—
26#66990—21no—
27#66988—21no—
28#66982—21no—
29#66898—22no—
30#66870—22no—
31C24×C11—21no—
32C24×C11—21no—
33C24×C11—21no—
34C24×C11—21no—
35C24×C11—21no—
36C24×C11—21no—
37C24×C11—44no—
38C24×C11D412yescomplemented
39C24×C11D411yescharacteristic, complemented
40C24×C11C2311yescharacteristic
41C23×D11D411yescharacteristic, complemented
42C2×D4×C11—24no—
43C2×D4×C11—21no—
44C2×D4×C11—21no—
45C2×D4×C11—21no—
46C2×D4×C11—21no—
47C2×D4×C11—21no—
48C2×D4×C11—21no—
49C2×D4×C11—44no—
50C22×C4×C11—21no—
51C22×C4×C11D411yescharacteristic, complemented
52C2×C22⋊D11—24no—
53C2×C22⋊D11—22no—
54C2×C22⋊D11—21no—
55C2×C22⋊D11—21no—
56C2×C22⋊D11—21no—
57C2×C22⋊D11—21no—
58C2×C22⋊D11—21no—
59C2×C22⋊D11—21no—
60C2×C22⋊D11—44no—
61C22×Dic11—21no—
62C22×Dic11—21no—
63C22×Dic11D411yescharacteristic, complemented
64C22×Dic11D412yescomplemented
65C11×C22⋊C4—24no—
66C11×C22⋊C4—21no—
67C11×C22⋊C4D412yescomplemented
68C22⋊Dic11—22no—
69C22⋊Dic11—24no—
70C22⋊Dic11—21no—
71C22⋊Dic11—21no—
72C22⋊Dic11—21no—
73C22⋊Dic11—21no—
74C22⋊Dic11—21no—
75C22⋊Dic11—44no—
76C22⋊Dic11D412yescomplemented
77(C2×D11)⋊C4—22no—
78Dic11⋊C4—22no—
79#2021—111nomaximal, Sylow
80C23×C11—24no—
81C23×C11—24no—
82C23×C11—24no—
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—22no—
86C23×C11—21no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—44no—
90C23×C11—42no—
91C23×C11—42no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11—44no—
95C23×C11—44no—
96C23×C11—44no—
97C23×C11—42no—
98C23×C11—41no—
99C23×C11—41no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11C2×D411yescharacteristic
103C23×C11C2×D411yescharacteristic
104C23×C11C2×D411yescharacteristic
105C23×C11C2×D411yescharacteristic
106C23×C11C2×D411yescharacteristic
107C23×C11C2×D411yescharacteristic
108C23×C11#4111yescharacteristic
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—42no—
113D4×C11—48no—
114D4×C11—41no—
115D4×C11—41no—
116D4×C11—41no—
117D4×C11—41no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—21no—
122C2×C4×C11—42no—
123C22⋊D11—48no—
124C22⋊D11—41no—
125C22⋊D11—41no—
126C22⋊D11—41no—
127C22⋊D11—41no—
128C22⋊D11—82no—
129C2×Dic11—21no—
130C2×Dic11—22no—
131C2×Dic11—21no—
132C2×Dic11—22no—
133C2×Dic11—21no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—41no—
138#534—111no—
139C2×#120—111no—
140C2×#120D1111yescharacteristic, complemented
141C2×#99—111no—
142C2×#99—111no—
143#379—111no—
144#342—111no—
145C22×C11—22no—
146C22×C11—22no—
147C22×C11—22no—
148C22×C11—24no—
149C22×C11—24no—
150C22×C11—24no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—42no—
156C22×C11—44no—
157C22×C11—42no—
158C22×C11—44no—
159C22×C11—42no—
160C22×C11—44no—
161C22×C11—42no—
162C22×C11—42no—
163C22×C11—44no—
164C22×C11—41no—
165C22×C11—42no—
166C22×C11—81no—
167C22×C11#12011yescharacteristic
168C22×C11#12011yescharacteristic
169C22×C11#12011yescharacteristic
170C22×C11#12111yescharacteristic
171C22×C11#12111yescharacteristic
172C22×C11#12111yescharacteristic
173C22×C11#12711yescharacteristic
174C2×D11—42no—
175C2×D11—41no—
176C2×D11—42no—
177C2×D11—81no—
178C4×C11—42no—
179C4×C11—41no—
180Dic11—42no—
181Dic11—41no—
182Dic11—42no—
183Dic11—81no—
184C25C2×D1111yescharacteristic
185C22×D4—21no—
186C22×D4—111no—
187C22×D4—221no—
188C22×D4C2×D1111yescharacteristic
189#123—221no—
190#123—221no—
191#121—222no—
192#120—22no—
193#120—22no—
194#120—222no—
195#120—221no—
196#120—222no—
197#120—221no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—111no—
200C2×C22⋊C4—111no—
201C2×C22⋊C4—111no—
202C2×C22⋊C4—221no—
203C2×C22⋊C4—222no—
204C2×C22⋊C4C2×D1111yescharacteristic
205#99—222no—
206#99—222no—
207C2×C11—21no—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11—21no—
211C2×C11—21no—
212C2×C11—21no—
213C2×C11—44no—
214C2×C11—81no—
215C2×C11#39211yescharacteristic
216C2×C11B(4,𝔽2)12yes—
217D11—81no—
218C24—21no—
219C24—21no—
220C24—21no—
221C24—21no—
222C24—21no—
223C24—21no—
224C24—44no—
225C24—111no—
226C24C22⋊D1112yescomplemented
227C24C22⋊D1111yescharacteristic, complemented
228C24C22×D1111yescharacteristic
229C2×D4—24no—
230C2×D4—21no—
231C2×D4—21no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—44no—
237C2×D4—224no—
238C2×D4—221no—
239C2×D4—221no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4—222no—
245C2×D4—444no—
246C22×C4—21no—
247C22×C4—111no—
248C22×C4—112no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4C22⋊D1111yescharacteristic, complemented
252C4⋊C4—222no—
253C22⋊C4—24no—
254C22⋊C4—21no—
255C22⋊C4—112no—
256C22⋊C4—222no—
257C22⋊C4—224no—
258C22⋊C4—222no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—444no—
265C22⋊C4C22⋊D1112yescomplemented
266C11#202111yescharacteristic, complemented, Sylow
267C23—24no—
268C23—24no—
269C23—24no—
270C23—22no—
271C23—22no—
272C23—22no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—42no—
277C23—44no—
278C23—42no—
279C23—42no—
280C23—42no—
281C23—44no—
282C23—44no—
283C23—44no—
284C23—42no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—221no—
290C23—221no—
291C23—221no—
292C23—442no—
293C23D4×D1111yescharacteristic
294C23D4×D1111yescharacteristic
295C23D4×D1111yescharacteristic
296C23#434111yescharacteristic
297C23C2×C22⋊D1111yescharacteristic
298C23C2×C22⋊D1111yescharacteristic
299C23C2×C22⋊D1111yescharacteristic
300D4—48no—
301D4—41no—
302D4—41no—
303D4—41no—
304D4—41no—
305D4—448no—
306D4—441no—
307D4—441no—
308D4—441no—
309D4—441no—
310D4—882no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—222no—
317C2×C4—221no—
318C2×C4—222no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4—441no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—24no—
329C22—24no—
330C22—24no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—42no—
336C22—42no—
337C22—44no—
338C22—42no—
339C22—44no—
340C22—44no—
341C22—42no—
342C22—42no—
343C22—44no—
344C22—41no—
345C22—42no—
346C22—81no—
347C22—442no—
348C22—441no—
349C22—442no—
350C22—881no—
351C22#6699011yescharacteristic
352C22#6699011yescharacteristic
353C22#6699111yescharacteristic
354C22#6699211yescharacteristic
355C22#6699211yescharacteristic
356C22#6699311yescharacteristic
357C22#6700611yescharacteristic
358C4—42no—
359C4—41no—
360C4—442no—
361C4—441no—
362C4—442no—
363C4—881no—
364C2—21no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—44no—
371C2—81no—
372C2—881no—
373C2#1062264512yes—
374C2#1062283611yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC24×C11C23
FrattiniC24C22×D11
FittingC2×C11×#120C2
socleC22×C11#120
hypercenterC2×#120D11
hypocenterC11#2021
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×C11×#120C2semidirect
2. C2×#67006C2semidirect
3. #10623335C2semidirect
4. #10622860C2semidirect
5. C2×#66898C2semidirect
6. C2×#66870C2semidirect
7. #10622165C2semidirect
38. C24×C11D4semidirect
39. C24×C11D4semidirect
41. C23×D11D4semidirect
51. C22×C4×C11D4semidirect
63. C22×Dic11D4semidirect
64. C22×Dic11D4semidirect
67. C11×C22⋊C4D4semidirect
76. C22⋊Dic11D4semidirect
140. C2×#120D11semidirect
226. C24C22⋊D11semidirect
227. C24C22⋊D11semidirect
251. C22×C4C22⋊D11semidirect
265. C22⋊C4C22⋊D11semidirect
266. C11#2021semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1202
C2×#670062
#106233352
#106228602
C2×#668982
C2×#668702
#106221652
#202111