Finite Group Databasebeta

← #13075116

Subgroups — #13075116

Order 1408.

536 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66977C211yesmaximal, characteristic, complemented
2C2×#66931C211yesmaximal, characteristic, complemented
3C11×#386C211yesmaximal, characteristic
4#10622834C211yesmaximal, characteristic
5#10622833C211yesmaximal, characteristic
6#10622825C211yesmaximal, characteristic, complemented
7#10622563C211yesmaximal, characteristic, complemented
8#10622562C211yesmaximal, characteristic, complemented
9#10622561C211yesmaximal, characteristic, complemented
10#10622560C211yesmaximal, characteristic, complemented
11#10622560C211yesmaximal, characteristic, complemented
12#10622274C211yesmaximal, characteristic, complemented
13#10622269C211yesmaximal, characteristic, complemented
14#10622268C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C23×Dic11C2211yescharacteristic
19C22×Dic22C2211yescharacteristic
20C22×Dic22C2211yescharacteristic
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
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×C4⋊Dic11C2211yescharacteristic
34C2×C4⋊Dic11C2211yescharacteristic
35C2×C4⋊Dic11C2211yescharacteristic
36#66977—24no—
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C2×C4×Dic11C2211yescharacteristic
42#66931—24no—
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C24×C11C2311yescharacteristic
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11Q814yescomplemented
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—41no—
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×Dic11—22no—
67C22×Dic11—41no—
68C22×Dic11—41no—
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C2×Dic22—22no—
78C2×Dic22—22no—
79C2×Dic22—22no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—22no—
85C11×C22⋊C4—41no—
86C22⋊Dic11—22no—
87C22⋊Dic11—22no—
88C22⋊Dic11—22no—
89C22⋊Dic11—41no—
90C22⋊Dic11—41no—
91C22⋊Dic11—41no—
92C22⋊Dic11—41no—
93C4⋊Dic11—22no—
94C4⋊Dic11—22no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98Dic11⋊C4—22no—
99Dic11⋊C4—22no—
100Dic11⋊C4—41no—
101Dic11⋊C4D414yescomplemented
102C4×Dic11—41no—
103#2692—111nomaximal, Sylow
104C23×C11—21no—
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×C11—21no—
116C23×C11C2×Q812yes—
117C23×C11C2×Q812yes—
118C23×C11C2411yescharacteristic
119D4×C11—44no—
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—44no—
133C2×C4×C11C2×D412yes—
134C2×C4×C11C2×Q812yes—
135C2×C4×C11#4112yes—
136C2×Dic11—21no—
137C2×Dic11—21no—
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×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—44no—
159C2×Dic11C2×D412yes—
160C2×Dic11C2×D412yes—
161Dic22—44no—
162Dic22—44no—
163C2×C22⋊Q8—111no—
164C2×C22⋊Q8—111no—
165#399—111no—
166#398—111no—
167#396—111no—
168#395—111no—
169#393—111no—
170#393—111no—
171#391—111no—
172#390—111no—
173#387—111no—
174#386—111no—
175#386D1111yescharacteristic
176#385—111no—
177#380—111no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11—22no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11C22×D411yescharacteristic
193C22×C11C22×Q811yescharacteristic
194C22×C11C2×#4111yescharacteristic
195C22×C11H(5,𝔽2)11yescharacteristic
196C22×C11H(5,𝔽2)11yescharacteristic
197C22×C11H(5,𝔽2)11yescharacteristic
198C22×C112−1+411yescharacteristic
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—41no—
203C4×C11—41no—
204Dic11—22no—
205Dic11—22no—
206Dic11—41no—
207Dic11—41no—
208Dic11—41no—
209Dic11—41no—
210Dic11—41no—
211Dic11—41no—
212C22×Q8—111no—
213C22×Q8—111no—
214C22×D4C2×D1111yescharacteristic
215C23×C4—111no—
216C23×C4C2×D1111yescharacteristic
217C22⋊Q8—224no—
218C22⋊Q8—224no—
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—111no—
228C2×C22⋊C4—111no—
229C2×C22⋊C4—111no—
230C2×C22⋊C4—111no—
231C2×C22⋊C4—111no—
232C2×C22⋊C4—111no—
233C2×C22⋊C4—111no—
234C2×C22⋊C4—111no—
235C2×C22⋊C4C2×D1111yescharacteristic
236C2×C22⋊C4C2×D1111yescharacteristic
237C2×C22⋊C4C2×D1111yescharacteristic
238C2×C42—111no—
239#95—111no—
240#95—111no—
241#95—111no—
242#95—111no—
243#95—111no—
244#95—111no—
245#95—111no—
246#95—111no—
247#95C2×D1111yescharacteristic
248#95C2×D1111yescharacteristic
249C2×C11—42no—
250C2×C11—42no—
251C2×C11#53511yescharacteristic
252C2×C11#54211yescharacteristic
253C2×C11#54311yescharacteristic
254C2×C11#54611yescharacteristic
255C2×C11D4×Q811yescharacteristic
256C2×C11#55411yescharacteristic
257C2×C11#56211yescharacteristic
258C24C22×D1111yescharacteristic
259C24C22×D1111yescharacteristic
260C2×Q8—222no—
261C2×Q8—222no—
262C2×Q8—222no—
263C2×Q8—441no—
264C2×Q8—441no—
265C2×Q8—441no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4Dic2214yescomplemented
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—41no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—111no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—222no—
281C22×C4—441no—
282C22×C4—441no—
283C22×C4C22×D1111yescharacteristic
284C22×C4C22×D1111yescharacteristic
285C22×C4C22×D1111yescharacteristic
286C22×C4C22×D1111yescharacteristic
287C22×C4C22×D1111yescharacteristic
288C4⋊C4—114no—
289C4⋊C4—222no—
290C4⋊C4—222no—
291C4⋊C4—222no—
292C4⋊C4—222no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—41no—
300C22⋊C4—222no—
301C22⋊C4—222no—
302C22⋊C4—222no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C42—441no—
308C11#269211yescharacteristic, complemented, Sylow
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×Dic2212yes—
322C23C2×Dic2212yes—
323C23C23×D1111yescharacteristic
324Q8—444no—
325Q8—444no—
326D4—44no—
327C2×C4—21no—
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—44no—
340C2×C4—112no—
341C2×C4—112no—
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—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—444no—
365C2×C4C2×Dic2212yes—
366C2×C4D4×D1112yes—
367C2×C4#434112yes—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22C22×Dic2211yescharacteristic
383C22C2×D4×D1111yescharacteristic
384C22C2×#434111yescharacteristic
385C22#6703711yescharacteristic
386C22#6703711yescharacteristic
387C22#6704211yescharacteristic
388C22#6704311yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—222no—
395C4—222no—
396C4—441no—
397C4—441no—
398C4—441no—
399C4—441no—
400C4—441no—
401C4—441no—
402C2—42no—
403C2—42no—
404C2#1062301411yescharacteristic
405C2D4×Dic2211yescharacteristic
406C2#1062307411yescharacteristic
407C2#1062312211yescharacteristic
408C2#1062313411yescharacteristic
409C2#1062313811yescharacteristic
410C2#1062319811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
prime radicalC22×D4×C11C22
hypercenter#386D11
hypocenterC11#2692
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#66977C2semidirect
2. C2×#66931C2semidirect
6. #10622825C2semidirect
7. #10622563C2semidirect
8. #10622562C2semidirect
9. #10622561C2semidirect
10. #10622560C2semidirect
11. #10622560C2semidirect
12. #10622274C2semidirect
13. #10622269C2semidirect
14. #10622268C2semidirect
15. #10622259C2semidirect
57. C2×D4×C11Q8semidirect
101. Dic11⋊C4D4semidirect
268. C2×D4Dic22semidirect
308. C11#2692semidirect

Maximal subgroups

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

subgroupindex
C2×#669772
C2×#669312
C11×#3862
#106228342
#106228332
#106228252
#106225632
#106225622
#106225612
#106225602
#106222742
#106222692
#106222682
#106222592
#269211