Finite Group Databasebeta

← #13072311

Subgroups — #13072311

Order 1408.

608 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66999C211yesmaximal, characteristic
2C2×#66997C211yesmaximal, characteristic, complemented
3C2×#66949C211yesmaximal, characteristic
4C2×C4⋊C4×D11C211yesmaximal, characteristic
5C11×#395C211yesmaximal, characteristic, complemented
6#10622602C211yesmaximal, characteristic
7#10622597C211yesmaximal, characteristic, complemented
8#10622589C211yesmaximal, characteristic, complemented
9#10622585C211yesmaximal, characteristic, complemented
10#10622281C211yesmaximal, characteristic
11#10622280C211yesmaximal, characteristic
12#10622279C211yesmaximal, characteristic
13#10622270C211yesmaximal, characteristic, complemented
14#10622269C211yesmaximal, characteristic, complemented
15#10622260C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C22×C4×D11C2211yescharacteristic
20C22×Dic22C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24#66999—24no—
25#66997—24no—
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42C2×Dic11⋊C4C2211yescharacteristic
43C2×C4×Dic11C2211yescharacteristic
44C2×C4×Dic11C2211yescharacteristic
45#66949—24no—
46C4⋊C4×D11—24no—
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C23×D11C2311yescharacteristic
56C2×Q8×C11—22no—
57C2×Q8×C11—22no—
58C2×Q8×C11—41no—
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C2×C4×D11—22no—
74C2×C4×D11—22no—
75C2×C4×D11—22no—
76C2×C4×D11—22no—
77C2×C4×D11—22no—
78C2×C4×D11—22no—
79C2×C4×D11—41no—
80C2×C4×D11—41no—
81C2×C4×D11Q814yescomplemented
82C2×Dic22—22no—
83C2×Dic22—22no—
84C2×Dic22—41no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—41no—
88(C2×D11)⋊C4—22no—
89(C2×D11)⋊C4—22no—
90(C2×D11)⋊C4D414yes—
91(C2×D11)⋊C4Q814yescomplemented
92C4⋊Dic11—22no—
93C4⋊Dic11—22no—
94C4⋊Dic11—41no—
95Dic11⋊C4—22no—
96Dic11⋊C4—22no—
97Dic11⋊C4—22no—
98Dic11⋊C4—22no—
99Dic11⋊C4—22no—
100Dic11⋊C4—22no—
101Dic11⋊C4—22no—
102Dic11⋊C4—22no—
103Dic11⋊C4—22no—
104Dic11⋊C4D414yes—
105C4×Dic11—22no—
106C4×Dic11—22no—
107#2440—111nomaximal, Sylow
108C23×C11C2411yescharacteristic
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—21no—
113C22×D11C2×D412yes—
114C22×D11C2×Q812yes—
115C22×D11C2×Q812yes—
116Q8×C11—44no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11C2×D412yes—
135C2×C4×C11C2×D412yes—
136C2×C4×C11C2×Q812yes—
137C2×C4×C11C2×Q812yes—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11C2×D412yes—
154C2×Dic11C2×D412yes—
155C2×Dic11C2×D412yes—
156C2×Dic11C2×Q812yes—
157C2×Dic11C2×Q812yes—
158C2×Dic11#4112yes—
159C4×D11—28no—
160C4×D11—44no—
161C4×D11—44no—
162Dic22—44no—
163C2×C4⋊Q8—111no—
164C2×C22⋊Q8—111no—
165C2×C22⋊Q8—111no—
166C22×C4⋊C4—111no—
167#398—111no—
168#398—111no—
169#395—111no—
170#395D1111yescharacteristic, complemented
171#389—111no—
172#389—111no—
173#385—111no—
174#385—111no—
175#384—111no—
176#380—111no—
177C4×C22⋊C4—111no—
178C22×C11C22×D411yescharacteristic
179C22×C11C22×D411yescharacteristic
180C22×C11C22×Q811yescharacteristic
181C22×C11C22×Q811yescharacteristic
182C22×C11C2×#4111yescharacteristic
183C22×C11H(5,𝔽2)11yescharacteristic
184C22×C112−1+411yescharacteristic
185C2×D11—22no—
186C2×D11—22no—
187C2×D11—22no—
188C2×D11—22no—
189C2×D11—22no—
190C2×D11—22no—
191C2×D11C4⋊Q814yescomplemented
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—22no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199Dic11—22no—
200Dic11—22no—
201Dic11—22no—
202Dic11—41no—
203Dic11—41no—
204Dic11—41no—
205Dic11C22⋊Q814yescomplemented
206C22×Q8—111no—
207C22×Q8C2×D1111yescharacteristic
208C23×C4—111no—
209C23×C4—111no—
210C23×C4—111no—
211C4⋊Q8—224no—
212C22⋊Q8—224no—
213C22⋊Q8—224no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—224no—
228C2×C4⋊C4C2×D1111yescharacteristic
229C2×C4⋊C4C2×D1111yescharacteristic
230C2×C4⋊C4C2×D1111yescharacteristic
231C2×C22⋊C4—111no—
232C2×C22⋊C4—111no—
233C2×C22⋊C4—111no—
234C2×C22⋊C4—111no—
235C2×C42—111no—
236C2×C42—111no—
237#95—111no—
238#95—111no—
239#95—111no—
240#95—111no—
241#95—111no—
242#95C2×D1111yescharacteristic
243#95C2×D1111yescharacteristic
244#95C2×D1111yescharacteristic
245C2×C11C2×C22⋊Q811yescharacteristic
246C2×C11C2×C4⋊Q811yescharacteristic
247C2×C11#54411yescharacteristic
248C2×C11D4211yescharacteristic
249C2×C11#54711yescharacteristic
250C2×C11D4×Q811yescharacteristic
251C2×C11#55411yescharacteristic
252D11—24no—
253C24—111no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—222no—
258C2×Q8—222no—
259C2×Q8—441no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—111no—
263C22×C4—111no—
264C22×C4—114no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—222no—
269C22×C4—222no—
270C22×C4—222no—
271C22×C4—222no—
272C22×C4—222no—
273C22×C4—222no—
274C22×C4—441no—
275C22×C4—441no—
276C22×C4C22×D1111yescharacteristic
277C22×C4C22×D1111yescharacteristic
278C22×C4C22×D1111yescharacteristic
279C22×C4C22×D1111yescharacteristic
280C22×C4C22×D1111yescharacteristic
281C22×C4C22×D1111yescharacteristic
282C22×C4C22×D1111yescharacteristic
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—114no—
287C4⋊C4—222no—
288C4⋊C4—222no—
289C4⋊C4—222no—
290C4⋊C4—222no—
291C4⋊C4—222no—
292C4⋊C4—222no—
293C4⋊C4—222no—
294C4⋊C4—222no—
295C4⋊C4—222no—
296C4⋊C4—222no—
297C4⋊C4—222no—
298C4⋊C4—441no—
299C22⋊C4—114no—
300C22⋊C4—114no—
301C22⋊C4—222no—
302C22⋊C4—222no—
303C42—222no—
304C42—222no—
305C11#244011yescharacteristic, complemented, Sylow
306C23—112no—
307C23—112no—
308C23—112no—
309C23—221no—
310C23—221no—
311C23—221no—
312C23—221no—
313C23C23×D1111yescharacteristic
314Q8—44no—
315Q8—444no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—112no—
334C2×C4—112no—
335C2×C4—112no—
336C2×C4—112no—
337C2×C4—112no—
338C2×C4—112no—
339C2×C4—228no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—444no—
356C2×C4—444no—
357C2×C4D4×D1112yes—
358C2×C4D4×D1112yes—
359C2×C4Q8×D1112yes—
360C2×C4Q8×D1112yes—
361C22—114no—
362C22—222no—
363C22—222no—
364C22—222no—
365C22—222no—
366C22—222no—
367C22—222no—
368C22C2×D4×D1111yescharacteristic
369C22C2×D4×D1111yescharacteristic
370C22#6703711yescharacteristic
371C22C2×Q8×D1111yescharacteristic
372C22C2×Q8×D1111yescharacteristic
373C22#6704011yescharacteristic
374C22#41×D1111yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—114no—
383C4—222no—
384C4—222no—
385C4—222no—
386C4—441no—
387C4—441no—
388C4—441no—
389C2—224no—
390C2#1062312111yescharacteristic
391C2D11×C22⋊Q811yescharacteristic
392C2#1062316211yescharacteristic
393C2#1062316711yescharacteristic
394C2D11×C4⋊Q811yescharacteristic
395C2#1062325811yescharacteristic
396C2#1062326011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#395C2
prime radicalC23×D11C23
hypercenter#395D11
hypocenterC11#2440
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#66997C2semidirect
5. C11×#395C2semidirect
7. #10622597C2semidirect
8. #10622589C2semidirect
9. #10622585C2semidirect
13. #10622270C2semidirect
14. #10622269C2semidirect
15. #10622260C2semidirect
81. C2×C4×D11Q8semidirect
91. (C2×D11)⋊C4Q8semidirect
170. #395D11semidirect
191. C2×D11C4⋊Q8semidirect
205. Dic11C22⋊Q8semidirect
305. C11#2440semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×#669972
C2×#669492
C2×C4⋊C4×D112
C11×#3952
#106226022
#106225972
#106225892
#106225852
#106222812
#106222802
#106222792
#106222702
#106222692
#106222602
#244011