Finite Group Databasebeta

← #13071955

Subgroups — #13071955

Order 1408.

908 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#41C211yesmaximal, characteristic, complemented
2C2×#66999C211yesmaximal, characteristic, complemented
3C2×#66991C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
5#10622843C211yesmaximal, characteristic, complemented
6#10622836C212yesmaximal, complemented
7#10622835C212yesmaximal, complemented
8#10622834C211yesmaximal, characteristic, complemented
9#10622826C212yesmaximal, complemented
10#10622825C211yesmaximal, characteristic, complemented
11#10622823C212yesmaximal, complemented
12C2×C11×#41—24no—
13C2×C11×#41—24no—
14C2×C11×#41—24no—
15C22×Q8×C11C2211yescharacteristic
16C22×D4×C11C2212yes—
17C22×D4×C11C2211yescharacteristic
18C23×C4×C11C2212yes—
19C23×C4×C11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2212yes—
22C22×C4×D11C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2212yes—
25C2×C22⋊Dic11C2212yes—
26C2×C22⋊Dic11C2212yes—
27C2×C22⋊Dic11C2212yes—
28#66999—24no—
29#66991—24no—
30C4×C22⋊D11—24no—
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2212yes—
33C2×C4⋊Dic11C2211yescharacteristic
34C2×C4⋊Dic11C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2212yes—
37C2×C4×Dic11C2211yescharacteristic
38C11⋊#95C2212yes—
39C11⋊#95C2212yes—
40C11⋊#95C2212yes—
41C24×C11C2312yes—
42C24×C11C2311yescharacteristic
43C23×D11C2311yescharacteristic
44C11×#41—232no—
45C2×Q8×C11—22no—
46C2×Q8×C11—22no—
47C2×Q8×C11D414yescomplemented
48C2×D4×C11—24no—
49C2×D4×C11—24no—
50C2×D4×C11—24no—
51C2×D4×C11—22no—
52C2×D4×C11—22no—
53C2×D4×C11D414yescomplemented
54C22×C4×C11—24no—
55C22×C4×C11—24no—
56C22×C4×C11—24no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11D414yescomplemented
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2312yes—
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—22no—
64C2×C22⋊D11—22no—
65C2×C22⋊D11—24no—
66C2×C22⋊D11—22no—
67C2×C22⋊D11—24no—
68C2×C22⋊D11—42no—
69C22×Dic11C2312yes—
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2312yes—
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C2×C4×D11—22no—
75C2×C4×D11—22no—
76C2×C4×D11—22no—
77C22⋊Dic11—24no—
78C22⋊Dic11—22no—
79C22⋊Dic11—24no—
80C22⋊Dic11—42no—
81C22⋊Dic11—42no—
82(C2×D11)⋊C4—22no—
83(C2×D11)⋊C4—24no—
84C4⋊Dic11—22no—
85C4⋊Dic11—22no—
86Dic11⋊C4—22no—
87Dic11⋊C4—24no—
88C4×Dic11—22no—
89#2407—111nomaximal, Sylow
90C23×C11—22no—
91C23×C11—21no—
92C23×C11—22no—
93C23×C11—21no—
94C23×C11—22no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—22no—
98C23×C11—21no—
99C23×C11—22no—
100C23×C11—21no—
101C23×C11—22no—
102C23×C11C2×D414yes—
103C23×C11C2×D412yes—
104C23×C11C2411yescharacteristic
105C22×D11—21no—
106C22×D11—21no—
107C22×D11—21no—
108C22×D11—21no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11#4112yescomplemented
112Q8×C11—28no—
113D4×C11—216no—
114D4×C11—28no—
115C2×C4×C11—216no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—28no—
121C2×C4×C11C2×D412yes—
122C2×C4×C11C2×D414yes—
123C2×C4×C11C2×D412yes—
124C2×C4×C11C2×D412yes—
125C2×C4×C11C2×D412yes—
126C22⋊D11—28no—
127C22⋊D11—48no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—22no—
133C2×Dic11—21no—
134C2×Dic11—22no—
135C2×Dic11—21no—
136C2×Dic11—22no—
137C2×Dic11—22no—
138C2×Dic11—21no—
139C2×Dic11—22no—
140C2×Dic11—22no—
141C2×Dic11—21no—
142C2×Dic11#4112yescomplemented
143C4×D11—44no—
144C22×#41D1111yescharacteristic, complemented
145C2×C22⋊Q8—111no—
146C2×#121—111no—
147C2×C4×D4—111no—
148#394—112no—
149#392—112no—
150#391—111no—
151#390—111no—
152#386—112no—
153#385—112no—
154#380—111no—
155C22×C11—24no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—24no—
160C22×C11—24no—
161C22×C11—42no—
162C22×C11—42no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—42no—
167C22×C11—42no—
168C22×C11—41no—
169C22×C11C22×D411yescharacteristic
170C22×C11C22×D411yescharacteristic
171C22×C11C22×D411yescharacteristic
172C22×C11C2×#4111yescharacteristic
173C22×C11C2×#4111yescharacteristic
174C22×C11H(5,𝔽2)11yescharacteristic
175C22×C112−1+411yescharacteristic
176C2×D11—22no—
177C2×D11—22no—
178C2×D11—22no—
179C2×D11—41no—
180C2×D11—41no—
181C2×D11—41no—
182C2×D11—41no—
183C4×C11—22no—
184C4×C11—24no—
185C4×C11#12014yes—
186Dic11—22no—
187Dic11—41no—
188Dic11—41no—
189Dic11—42no—
190Dic11—42no—
191C2×#41—24no—
192C2×#41—24no—
193C2×#41—24no—
194C22×Q8C2×D1111yescharacteristic
195C22×D4—111no—
196C22×D4—112no—
197C22×D4C2×D1112yes—
198C22×D4C2×D1111yescharacteristic
199C23×C4—111no—
200C23×C4C2×D1112yes—
201C23×C4C2×D1111yescharacteristic
202C22⋊Q8—224no—
203#121—224no—
204C4×D4—224no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—112no—
209C2×C22⋊C4—111no—
210C2×C22⋊C4—112no—
211C2×C22⋊C4—112no—
212C2×C22⋊C4—111no—
213C2×C22⋊C4—112no—
214C2×C22⋊C4—112no—
215C2×C22⋊C4—112no—
216C2×C42—111no—
217#95—112no—
218#95—112no—
219#95—112no—
220C2×C11—42no—
221C2×C11—44no—
222C2×C11C2×#12011yescharacteristic
223C2×C11#52511yescharacteristic
224C2×C11#53711yescharacteristic
225C2×C11#54611yescharacteristic
226C2×C11#54711yescharacteristic
227C2×C11#54811yescharacteristic
228C2×C11#55011yescharacteristic
229D11—42no—
230C24—111no—
231C24C22×D1112yes—
232C24C22×D1111yescharacteristic
233#41—232no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8C22⋊D1114yescomplemented
237C2×D4—24no—
238C2×D4—24no—
239C2×D4—24no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—222no—
243C2×D4—222no—
244C2×D4—222no—
245C2×D4—224no—
246C2×D4—224no—
247C2×D4—442no—
248C2×D4C22⋊D1114yescomplemented
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—24no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—111no—
255C22×C4—112no—
256C22×C4—111no—
257C22×C4—112no—
258C22×C4—111no—
259C22×C4—222no—
260C22×C4—222no—
261C22×C4—222no—
262C22×C4C22⋊D1114yescomplemented
263C22×C4C22×D1111yescharacteristic
264C22×C4C22×D1112yes—
265C22×C4C22×D1111yescharacteristic
266C4⋊C4—222no—
267C4⋊C4—222no—
268C4⋊C4—224no—
269C4⋊C4—222no—
270C22⋊C4—224no—
271C22⋊C4—222no—
272C22⋊C4—224no—
273C22⋊C4—222no—
274C22⋊C4—224no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C42—222no—
278C11#240711yescharacteristic, complemented, Sylow
279C23—22no—
280C23—21no—
281C23—21no—
282C23—22no—
283C23—21no—
284C23—22no—
285C23—22no—
286C23—21no—
287C23—21no—
288C23—22no—
289C23—22no—
290C23—21no—
291C23—112no—
292C23—221no—
293C23—221no—
294C23—221no—
295C23—221no—
296C23—221no—
297C23—221no—
298C23C2×C22⋊D1114yes—
299C23C2×C22⋊D1112yes—
300C23C23×D1111yescharacteristic
301Q8—28no—
302D4—216no—
303D4—28no—
304D4—228no—
305D4—448no—
306C2×C4—216no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—28no—
312C2×C4—112no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—222no—
316C2×C4—222no—
317C2×C4—221no—
318C2×C4—222no—
319C2×C4—222no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—222no—
324C2×C4—221no—
325C2×C4—222no—
326C2×C4—221no—
327C2×C4—444no—
328C2×C4C2×C22⋊D1112yes—
329C2×C4C2×C22⋊D1114yes—
330C2×C4C2×C22⋊D1112yes—
331C2×C4C2×C22⋊D1112yes—
332C2×C4C2×C22⋊D1112yes—
333C22—24no—
334C22—22no—
335C22—24no—
336C22—22no—
337C22—24no—
338C22—22no—
339C22—41no—
340C22—42no—
341C22—41no—
342C22—42no—
343C22—41no—
344C22—42no—
345C22—42no—
346C22—41no—
347C22—222no—
348C22—222no—
349C22—222no—
350C22—441no—
351C22—441no—
352C22—441no—
353C22—441no—
354C22#41×D1111yescharacteristic
355C22#41×D1111yescharacteristic
356C22#6704211yescharacteristic
357C22#6704311yescharacteristic
358C22C22×C22⋊D1111yescharacteristic
359C22C22×C22⋊D1111yescharacteristic
360C22C22×C22⋊D1111yescharacteristic
361C4—22no—
362C4—24no—
363C4—222no—
364C4—442no—
365C4—441no—
366C4—442no—
367C4—441no—
368C4#6700614yes—
369C2—44no—
370C2—42no—
371C2—442no—
372C2#1062335511yescharacteristic
373C2#1062335911yescharacteristic
374C2#1062336011yescharacteristic
375C2#1062336211yescharacteristic
376C2#1062336411yescharacteristic
377C2#1062336511yescharacteristic
378C2C2×#6700611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC22×C11×#41C2
hypercenterC22×#41D11
hypocenterC11#2407
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×C11×#41C2semidirect
2. C2×#66999C2semidirect
3. C2×#66991C2semidirect
4. C2×C4×C22⋊D11C2semidirect
5. #10622843C2semidirect
6. #10622836C2semidirect
7. #10622835C2semidirect
8. #10622834C2semidirect
9. #10622826C2semidirect
10. #10622825C2semidirect
11. #10622823C2semidirect
47. C2×Q8×C11D4semidirect
53. C2×D4×C11D4semidirect
59. C22×C4×C11D4semidirect
111. C22×D11#41semidirect
142. C2×Dic11#41semidirect
144. C22×#41D11semidirect
236. C2×Q8C22⋊D11semidirect
248. C2×D4C22⋊D11semidirect
262. C22×C4C22⋊D11semidirect
278. C11#2407semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#412
C2×#669992
C2×#669912
C2×C4×C22⋊D112
#106228432
#106228362
#106228352
#106228342
#106228262
#106228252
#106228232
#240711