Finite Group Databasebeta

← #13073557

Subgroups — #13073557

Order 1408.

948 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 948 conjugacy classes of subgroups — too many to draw. Only its 171 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×#66993C212yesmaximal, complemented
2C2×#66993C211yesmaximal, characteristic, complemented
3C2×#66992C212yesmaximal, complemented
4C2×#66937C212yesmaximal, complemented
5C2×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
6C11×#392C211yesmaximal, characteristic, complemented
7#10622836C211yesmaximal, characteristic, complemented
8#10622573C211yesmaximal, characteristic, complemented
9#10622570C212yesmaximal, complemented
10#10622284C211yesmaximal, characteristic, complemented
11#10622262C211yesmaximal, characteristic, complemented
12C22×D4×C11C2212yes—
13C22×D4×C11C2211yescharacteristic
14C22×C22⋊D11C2212yes—
15C22×C22⋊D11C2212yes—
16C22×C22⋊D11C2212yes—
17C22×C22⋊D11C2212yes—
18C22×C22⋊D11C2211yescharacteristic
19C23×Dic11C2211yescharacteristic
20C22×D44C2212yes—
21C22×D44C2211yescharacteristic
22C22×C4×D11C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2212yes—
25C2×C22⋊Dic11C2212yes—
26#66993—28no—
27#66993—24no—
28#66992—28no—
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2212yes—
31C2×(C2×D11)⋊C4C2212yes—
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2212yes—
34C2×C4×Dic11C2212yes—
35C2×C4×Dic11C2211yescharacteristic
36#66937—28no—
37(C22⋊D11)⋊C4—24no—
38C11×#95C2211yescharacteristic
39C11⋊#95C2211yescharacteristic
40C24×C11C2312yes—
41C24×C11C2311yescharacteristic
42C23×D11C2312yes—
43C23×D11C2311yescharacteristic
44C2×D4×C11—24no—
45C2×D4×C11—24no—
46C2×D4×C11—22no—
47C2×D4×C11—42no—
48C2×D4×C11—42no—
49C22×C4×C11C2311yescharacteristic
50C22×C4×C11C2311yescharacteristic
51C22×C4×C11C2312yes—
52C2×C22⋊D11—22no—
53C2×C22⋊D11—24no—
54C2×C22⋊D11—24no—
55C2×C22⋊D11—24no—
56C2×C22⋊D11—24no—
57C2×C22⋊D11—24no—
58C2×C22⋊D11—24no—
59C2×C22⋊D11—24no—
60C2×C22⋊D11—22no—
61C2×C22⋊D11—24no—
62C2×C22⋊D11—24no—
63C2×C22⋊D11—24no—
64C2×C22⋊D11—42no—
65C2×C22⋊D11—42no—
66C2×C22⋊D11D414yescomplemented
67C22×Dic11—22no—
68C22×Dic11—24no—
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2312yes—
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C2×D44—24no—
74C2×D44—24no—
75C2×D44—22no—
76C2×D44—42no—
77C2×D44—42no—
78C2×C4×D11—22no—
79C2×C4×D11—24no—
80C11×C22⋊C4—22no—
81C11×C22⋊C4—24no—
82C22⋊Dic11—24no—
83(C2×D11)⋊C4—24no—
84(C2×D11)⋊C4—22no—
85(C2×D11)⋊C4—24no—
86Dic11⋊C4—22no—
87Dic11⋊C4D418yescomplemented
88C4×Dic11—24no—
89C4×Dic11D414yescomplemented
90#2541—111nomaximal, Sylow
91C23×C11—21no—
92C23×C11—22no—
93C23×C11—21no—
94C23×C11—22no—
95C23×C11—22no—
96C23×C11—22no—
97C23×C11—22no—
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11—22no—
102C23×C11C2×D412yes—
103C23×C11C2411yescharacteristic
104C22×D11—21no—
105C22×D11—22no—
106C22×D11—21no—
107C22×D11—22no—
108C22×D11—22no—
109C22×D11—22no—
110C22×D11—22no—
111C22×D11—22no—
112C22×D11—22no—
113C22×D11—22no—
114C22×D11—22no—
115C22×D11C2×D412yes—
116D4×C11—48no—
117D4×C11—44no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—21no—
122C2×C4×C11—22no—
123C2×C4×C11C2×D412yes—
124C2×C4×C11C2×D414yes—
125C22⋊D11—28no—
126C22⋊D11—48no—
127C22⋊D11—48no—
128C22⋊D11—48no—
129C22⋊D11—48no—
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—21no—
133C2×Dic11—22no—
134C2×Dic11—44no—
135C2×Dic11C2×D414yes—
136C2×Dic11C2×D412yes—
137C2×Dic11C2×D412yes—
138C2×Dic11C2×D412yes—
139C2×Dic11C2×D414yes—
140C2×Dic11#4112yes—
141D44—48no—
142D44—44no—
143C4×D11—44no—
144C2×#127—111no—
145C2×#127—112no—
146C2×#121—112no—
147C2×#121—112no—
148C2×C4×D4—111no—
149#392—111no—
150#392—111no—
151#392—111no—
152#392D1111yescharacteristic, complemented
153#390—112no—
154C4×C4⋊C4—111no—
155C22×C11—22no—
156C22×C11—24no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—42no—
160C22×C11—42no—
161C22×C11—42no—
162C22×C11—42no—
163C22×C11—42no—
164C22×C11—42no—
165C22×C11—42no—
166C22×C11—42no—
167C22×C11C22×D411yescharacteristic
168C22×C11C22×D411yescharacteristic
169C22×C11C22×D412yes—
170C22×C11C2×#4111yescharacteristic
171C22×C11H(5,𝔽2)12yes—
172C2×D11—22no—
173C2×D11—24no—
174C2×D11—41no—
175C2×D11—41no—
176C2×D11—42no—
177C2×D11—42no—
178C2×D11—42no—
179C2×D11—42no—
180C2×D11—42no—
181C2×D11—42no—
182C2×D11—42no—
183C2×D11—42no—
184C4×C11—22no—
185C4×C11—24no—
186C4×C11—41no—
187Dic11—24no—
188Dic11—41no—
189Dic11#12114yescomplemented
190Dic11#12714yescomplemented
191C22×D4—111no—
192C22×D4—112no—
193C22×D4—112no—
194C22×D4—112no—
195C22×D4—112no—
196C22×D4—112no—
197C22×D4—111no—
198C22×D4C2×D1112yes—
199C22×D4C2×D1111yescharacteristic
200C23×C4—111no—
201C23×C4—111no—
202#127—224no—
203#127—228no—
204#121—228no—
205#121—228no—
206C4×D4—224no—
207C2×C4⋊C4—112no—
208C2×C4⋊C4—111no—
209C2×C22⋊C4—112no—
210C2×C22⋊C4—111no—
211C2×C22⋊C4—112no—
212C2×C22⋊C4—112no—
213C2×C22⋊C4C2×D1111yescharacteristic
214C2×C22⋊C4C2×D1112yes—
215C2×C42—111no—
216C2×C42—112no—
217#95—111no—
218#95C2×D1111yescharacteristic
219C2×C11—42no—
220C2×C11—82no—
221C2×C11C2×#12111yescharacteristic
222C2×C11C2×#12711yescharacteristic
223C2×C11#53511yescharacteristic
224C2×C11D4212yes—
225C2×C11#55012yes—
226D11—42no—
227D11—82no—
228C24—111no—
229C24—112no—
230C24C22×D1112yes—
231C24C22×D1111yescharacteristic
232C2×D4—24no—
233C2×D4—24no—
234C2×D4—22no—
235C2×D4—42no—
236C2×D4—42no—
237C2×D4—114no—
238C2×D4—224no—
239C2×D4—222no—
240C2×D4—222no—
241C2×D4—224no—
242C2×D4—224no—
243C2×D4—224no—
244C2×D4—224no—
245C2×D4—224no—
246C2×D4—224no—
247C2×D4—224no—
248C2×D4—224no—
249C2×D4—224no—
250C2×D4—224no—
251C2×D4—224no—
252C2×D4—222no—
253C2×D4—442no—
254C2×D4—442no—
255C2×D4—442no—
256C2×D4—442no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—112no—
260C22×C4—111no—
261C22×C4—222no—
262C22×C4—224no—
263C22×C4—222no—
264C22×C4—224no—
265C22×C4C22×D1111yescharacteristic
266C22×C4C22×D1111yescharacteristic
267C22×C4C22×D1112yes—
268C4⋊C4—118no—
269C4⋊C4—222no—
270C22⋊C4—22no—
271C22⋊C4—24no—
272C22⋊C4—224no—
273C22⋊C4—224no—
274C22⋊C4—222no—
275C22⋊C4—224no—
276C42—114no—
277C42—224no—
278C11#254111yescharacteristic, complemented, Sylow
279C23—21no—
280C23—22no—
281C23—22no—
282C23—21no—
283C23—22no—
284C23—22no—
285C23—22no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—112no—
291C23—221no—
292C23—222no—
293C23—222no—
294C23—221no—
295C23—222no—
296C23—222no—
297C23—222no—
298C23—222no—
299C23—222no—
300C23—222no—
301C23—222no—
302C23D4×D1112yes—
303C23C23×D1111yescharacteristic
304D4—48no—
305D4—44no—
306D4—228no—
307D4—448no—
308D4—444no—
309D4—448no—
310D4—448no—
311D4—448no—
312D4—448no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—112no—
319C2×C4—112no—
320C2×C4—112no—
321C2×C4—114no—
322C2×C4—112no—
323C2×C4—114no—
324C2×C4—222no—
325C2×C4—222no—
326C2×C4—222no—
327C2×C4—221no—
328C2×C4—444no—
329C2×C4—444no—
330C2×C4D4×D1112yes—
331C2×C4D4×D1114yes—
332C22—24no—
333C22—22no—
334C22—41no—
335C22—41no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—42no—
344C22—224no—
345C22—222no—
346C22—441no—
347C22—441no—
348C22—442no—
349C22—442no—
350C22—442no—
351C22—442no—
352C22—442no—
353C22—442no—
354C22—442no—
355C22—442no—
356C22C2×D4×D1112yes—
357C22C2×D4×D1111yescharacteristic
358C22C2×D4×D1111yescharacteristic
359C22#6703712yes—
360C22#41×D1111yescharacteristic
361C4—24no—
362C4—22no—
363C4—41no—
364C4—114no—
365C4—114no—
366C4—224no—
367C4—441no—
368C2—42no—
369C2—82no—
370C2—442no—
371C2—882no—
372C2#1062312112yes—
373C2#1062312311yescharacteristic
374C2#1062313012yes—
375C2D11×#12111yescharacteristic
376C2D11×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#392C2
hypercenter#392D11
hypocenterC11#2541
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#66993C2semidirect
2. C2×#66993C2semidirect
3. C2×#66992C2semidirect
4. C2×#66937C2semidirect
5. C2×(C22⋊D11)⋊C4C2semidirect
6. C11×#392C2semidirect
7. #10622836C2semidirect
8. #10622573C2semidirect
9. #10622570C2semidirect
10. #10622284C2semidirect
11. #10622262C2semidirect
66. C2×C22⋊D11D4semidirect
87. Dic11⋊C4D4semidirect
89. C4×Dic11D4semidirect
152. #392D11semidirect
189. Dic11#121semidirect
190. Dic11#127semidirect
278. C11#2541semidirect

Maximal subgroups

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

subgroupindex
C2×#669932
C2×#669922
C2×#669372
C2×(C22⋊D11)⋊C42
C11×#3922
#106228362
#106225732
#106225702
#106222842
#106222622
#254111