Finite Group Databasebeta

← #13071056

Subgroups — #13071056

Order 1408.

696 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic11C211yesmaximal, characteristic
2C22×C4×Dic11C211yesmaximal, characteristic, complemented
3C2×#66930C211yesmaximal, characteristic, complemented
4C11×#386C211yesmaximal, characteristic
5#10622833C211yesmaximal, characteristic
6#10622823C211yesmaximal, characteristic, complemented
7#10622559C211yesmaximal, characteristic, complemented
8#10622558C211yesmaximal, characteristic, complemented
9#10622557C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
12#10622267C211yesmaximal, characteristic, complemented
13#10622266C211yesmaximal, characteristic, complemented
14#10622262C211yesmaximal, characteristic, complemented
15#10622261C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C23×Dic11C2211yescharacteristic
19C23×Dic11C2211yescharacteristic
20C23×Dic11C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29D4×Dic11C418yescomplemented
30C2×C4⋊Dic11C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×C4×Dic11—24no—
36C2×C4×Dic11C2211yescharacteristic
37C2×C4×Dic11C2211yescharacteristic
38C2×C4×Dic11C2211yescharacteristic
39C2×C4×Dic11C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41C2×C4×Dic11C2211yescharacteristic
42C2×C4×Dic11C2211yescharacteristic
43#66930—24no—
44C11×#95C2211yescharacteristic
45C11×#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C24×C11C2311yescharacteristic
55C24×C11C2311yescharacteristic
56C2×D4×C11—22no—
57C2×D4×C11—22no—
58C2×D4×C11C2×C414yes—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×Dic11—22no—
68C22×Dic11—22no—
69C22×Dic11—22no—
70C22×Dic11—22no—
71C22×Dic11—22no—
72C22×Dic11—22no—
73C22×Dic11—22no—
74C22×Dic11C2×C414yes—
75C22×Dic11C2×C414yescomplemented
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C22×Dic11C2311yescharacteristic
84C11×C22⋊C4—22no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—22no—
87C22⋊Dic11—22no—
88C22⋊Dic11—22no—
89C22⋊Dic11—22no—
90C22⋊Dic11C2×C414yes—
91C22⋊Dic11C2×C414yescomplemented
92C4⋊Dic11C2×C414yescomplemented
93Dic11⋊C4—22no—
94Dic11⋊C4—22no—
95Dic11⋊C4—22no—
96Dic11⋊C4—22no—
97C4×Dic11—22no—
98C4×Dic11—22no—
99C4×Dic11—22no—
100C4×Dic11—22no—
101C4×Dic11—22no—
102C4×Dic11C2×C414yescomplemented
103C4×Dic11D414yescomplemented
104#2290—111nomaximal, Sylow
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11C22×C412yes—
116C23×C11C22×C412yes—
117C23×C11#4112yes—
118C23×C11#4112yes—
119C23×C11C2411yescharacteristic
120D4×C11—28no—
121C2×C4×C11—28no—
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×C11C22×C412yes—
135C2×C4×C11C2×D412yes—
136C2×C4×C11#4112yes—
137C2×Dic11—28no—
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—28no—
149C2×Dic11—28no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11C22×C412yes—
157C2×Dic11C22×C412yes—
158C2×Dic11C22×C412yes—
159C2×Dic11C22×C412yes—
160C2×Dic11C2×D412yes—
161C2×Dic11C2×D412yes—
162C2×Dic11#4112yes—
163C2×Dic11#4112yes—
164C2×C4×D4—111no—
165C2×#117—111no—
166C22×C42—111no—
167#388—111no—
168#388—111no—
169#387—111no—
170#387—111no—
171#386—111no—
172#386D1111yescharacteristic
173#385—111no—
174#385—111no—
175C4×C4⋊C4—111no—
176C4×C22⋊C4—111no—
177C4×C22⋊C4—111no—
178#376—111no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11—22no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11#11714yescomplemented
193C22×C11C23×C411yescharacteristic
194C22×C11C22×D411yescharacteristic
195C22×C11C2×#4111yescharacteristic
196C22×C11C2×#4111yescharacteristic
197C22×C11C2×#4111yescharacteristic
198C22×C11C2×#4111yescharacteristic
199C22×C11C2×#4111yescharacteristic
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—41no—
204C4×C11—41no—
205Dic11—22no—
206Dic11—22no—
207Dic11—22no—
208Dic11—22no—
209Dic11—22no—
210Dic11—41no—
211Dic11—41no—
212Dic11C4×D414yes—
213C22×D4C2×D1111yescharacteristic
214C23×C4—111no—
215C23×C4—111no—
216C23×C4—111no—
217C23×C4C2×D1111yescharacteristic
218C4×D4—118no—
219#117—224no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C22⋊C4—111no—
226C2×C22⋊C4—111no—
227C2×C22⋊C4—111no—
228C2×C22⋊C4—111no—
229C2×C22⋊C4—111no—
230C2×C22⋊C4C2×D1111yescharacteristic
231C2×C22⋊C4C2×D1111yescharacteristic
232C2×C22⋊C4C2×D1111yescharacteristic
233C2×C42—111no—
234C2×C42—111no—
235C2×C42—111no—
236C2×C42—111no—
237C2×C42—111no—
238C2×C42—111no—
239C2×C42—111no—
240C2×C42—224no—
241#95—111no—
242#95—111no—
243#95—111no—
244#95—111no—
245#95—111no—
246#95—111no—
247#95—111no—
248#95—111no—
249#95C2×D1111yescharacteristic
250#95C2×D1111yescharacteristic
251C2×C11—24no—
252C2×C11—42no—
253C2×C11C2×#11711yescharacteristic
254C2×C11C2×C4×D411yescharacteristic
255C2×C11C4×#4111yescharacteristic
256C2×C11#52511yescharacteristic
257C2×C11#52511yescharacteristic
258C2×C11#52911yescharacteristic
259C2×C11#52911yescharacteristic
260C24C22×D1111yescharacteristic
261C24C22×D1111yescharacteristic
262C2×D4—22no—
263C2×D4—22no—
264C2×D4C4×D1114yes—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—111no—
269C22×C4—114no—
270C22×C4—114no—
271C22×C4—111no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—111no—
278C22×C4—222no—
279C22×C4—222no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4—222no—
283C22×C4—222no—
284C22×C4—222no—
285C22×C4C22×D1111yescharacteristic
286C22×C4C22×D1111yescharacteristic
287C22×C4C22×D1111yescharacteristic
288C22×C4C22×D1111yescharacteristic
289C22×C4C22×D1111yescharacteristic
290C4⋊C4—114no—
291C4⋊C4—222no—
292C4⋊C4—222no—
293C4⋊C4—222no—
294C4⋊C4—222no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—114no—
299C22⋊C4—114no—
300C22⋊C4—222no—
301C22⋊C4—222no—
302C22⋊C4—222no—
303C42—114no—
304C42—114no—
305C42—222no—
306C42—222no—
307C42—222no—
308C42—222no—
309C42—222no—
310C11#229011yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C4×D1112yes—
322C23C2×C4×D1112yes—
323C23#434112yes—
324C23#434112yes—
325C23C23×D1111yescharacteristic
326D4—28no—
327C2×C4—28no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—112no—
341C2×C4—112no—
342C2×C4—112no—
343C2×C4—112no—
344C2×C4—112no—
345C2×C4—112no—
346C2×C4—112no—
347C2×C4—112no—
348C2×C4—228no—
349C2×C4—228no—
350C2×C4—228no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4C2×C4×D1112yes—
368C2×C4D4×D1112yes—
369C2×C4#434112yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22#6693014yescomplemented
384C22C22×C4×D1111yescharacteristic
385C22C2×D4×D1111yescharacteristic
386C22C2×#434111yescharacteristic
387C22C2×#434111yescharacteristic
388C22C2×#434111yescharacteristic
389C22#41×D1111yescharacteristic
390C22#41×D1111yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—114no—
397C4—222no—
398C4—222no—
399C4—222no—
400C4—222no—
401C4—222no—
402C4—441no—
403C4—441no—
404C2—24no—
405C2—42no—
406C2C2×#6693011yescharacteristic
407C2C4×#434111yescharacteristic
408C2C4×D4×D1111yescharacteristic
409C2#1062311711yescharacteristic
410C2#1062313111yescharacteristic
411C2#1062313711yescharacteristic
412C2#1062318011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC11×#386C2
socle, cosocleC23×C11C24
prime radicalC22×D4×C11C22
hypercenter#386D11
hypocenterC11#2290
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic11C2semidirect
3. C2×#66930C2semidirect
6. #10622823C2semidirect
7. #10622559C2semidirect
8. #10622558C2semidirect
9. #10622557C2semidirect
10. C22⋊C4×Dic11C2semidirect
11. C22⋊C4×Dic11C2semidirect
12. #10622267C2semidirect
13. #10622266C2semidirect
14. #10622262C2semidirect
15. #10622261C2semidirect
29. D4×Dic11C4semidirect
75. C22×Dic11C2×C4semidirect
91. C22⋊Dic11C2×C4semidirect
92. C4⋊Dic11C2×C4semidirect
102. C4×Dic11C2×C4semidirect
103. C4×Dic11D4semidirect
192. C22×C11#117semidirect
310. C11#2290semidirect
383. C22#66930semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic112
C22×C4×Dic112
C2×#669302
C11×#3862
#106228332
#106228232
#106225592
#106225582
#106225572
C22⋊C4×Dic112
#106222672
#106222662
#106222622
#106222612
#229011