Finite Group Databasebeta

← #13073591

Subgroups — #13073591

Order 1408.

576 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×#66941C211yesmaximal, characteristic, complemented
2C2×#66940C211yesmaximal, characteristic, complemented
3C2×#66938C211yesmaximal, characteristic
4C2×#66938C211yesmaximal, characteristic
5C11×#396C211yesmaximal, characteristic, complemented
6#10622607C211yesmaximal, characteristic, complemented
7#10622607C211yesmaximal, characteristic, complemented
8#10622603C211yesmaximal, characteristic, complemented
9C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
10#10622570C211yesmaximal, characteristic
11#10622564C211yesmaximal, characteristic, complemented
12#10622561C211yesmaximal, characteristic, complemented
13#10622558C211yesmaximal, characteristic, complemented
14#10622282C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C22×C22⋊D11C2211yescharacteristic
17C22×Dic22C2211yescharacteristic
18C22×Dic22C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×C4⋊Dic11C2211yescharacteristic
35C2×C4⋊Dic11C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41C2×C4×Dic11C2211yescharacteristic
42C2×C4×Dic11C2211yescharacteristic
43C2×C4×Dic11C2211yescharacteristic
44C2×C4×Dic11C2211yescharacteristic
45#66941—24no—
46#66940—24no—
47#66938—24no—
48#66938—24no—
49C11×#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C24×C11C2311yescharacteristic
56C23×D11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—22no—
64C2×C22⋊D11—22no—
65C2×C22⋊D11—22no—
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C2×Dic22—22no—
74C2×Dic22—22no—
75C2×Dic22—22no—
76C2×Dic22—22no—
77C2×Dic22—22no—
78C2×Dic22D414yes—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C22⋊C4—22no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—22no—
85C22⋊Dic11—22no—
86C22⋊Dic11—22no—
87C22⋊Dic11—22no—
88(C2×D11)⋊C4—22no—
89(C2×D11)⋊C4—22no—
90(C2×D11)⋊C4—22no—
91(C2×D11)⋊C4—22no—
92(C2×D11)⋊C4—22no—
93(C2×D11)⋊C4—22no—
94C4⋊Dic11—22no—
95C4⋊Dic11—22no—
96Dic11⋊C4—22no—
97Dic11⋊C4—22no—
98Dic11⋊C4—22no—
99Dic11⋊C4—22no—
100C4×Dic11—22no—
101C4×Dic11—22no—
102C4×Dic11—22no—
103C4×Dic11—22no—
104C4×Dic11D414yes—
105#2545—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11C2411yescharacteristic
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—21no—
120C22×D11—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×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11C2×D412yes—
137C2×C4×C11C2×D412yes—
138C2×C4×C11#4112yes—
139C22⋊D11—44no—
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×Dic11C2×D412yes—
156C2×Dic11C2×D412yes—
157C2×Dic11C2×D412yes—
158C2×Dic11C2×D412yes—
159C2×Dic11#4112yes—
160C2×Dic11#4112yes—
161Dic22—28no—
162Dic22—44no—
163C2×C4⋊Q8—111no—
164C2×#124—111no—
165C2×#124—111no—
166C2×C4×Q8—111no—
167#396—111no—
168#396—111no—
169#396—111no—
170#396D1111yescharacteristic, complemented
171#391—111no—
172#390—111no—
173#388—111no—
174#388—111no—
175#388—111no—
176#388—111no—
177C4×C4⋊C4—111no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11C22×D411yescharacteristic
186C22×C11C22×D411yescharacteristic
187C22×C11C2×#4111yescharacteristic
188C22×C11C2×#4111yescharacteristic
189C22×C11C2×#4111yescharacteristic
190C22×C112−1+411yescharacteristic
191C22×C112−1+411yescharacteristic
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—41no—
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—41no—
205Dic11—22no—
206Dic11—22no—
207Dic11—22no—
208Dic11—41no—
209Dic11—41no—
210Dic11—41no—
211Dic11#12114yes—
212C22×Q8—111no—
213C22×Q8—111no—
214C22×D4—111no—
215C4⋊Q8—224no—
216#124—224no—
217#124—224no—
218C4×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⋊C4C2×D1111yescharacteristic
226C2×C4⋊C4C2×D1111yescharacteristic
227C2×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
236C2×C22⋊C4—111no—
237C2×C22⋊C4C2×D1111yescharacteristic
238C2×C22⋊C4C2×D1111yescharacteristic
239C2×C22⋊C4C2×D1111yescharacteristic
240C2×C42—111no—
241C2×C42—111no—
242C2×C42—111no—
243C2×C42—111no—
244C2×C42—111no—
245#95—111no—
246#95—111no—
247#95—111no—
248#95—111no—
249#95—111no—
250#95C2×D1111yescharacteristic
251C2×C11—81no—
252C2×C11C2×#12111yescharacteristic
253C2×C11#53211yescharacteristic
254C2×C11#53611yescharacteristic
255C2×C11#54811yescharacteristic
256C2×C11#54811yescharacteristic
257C2×C11#55611yescharacteristic
258C2×C11#55611yescharacteristic
259D11—81no—
260C24—111no—
261C24C22×D1111yescharacteristic
262C2×Q8—114no—
263C2×Q8—222no—
264C2×Q8—222no—
265C2×Q8—222no—
266C2×Q8—222no—
267C2×Q8—222no—
268C2×D4—222no—
269C2×D4—222no—
270C2×D4—222no—
271C22×C4—111no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—111no—
278C22×C4C22×D1111yescharacteristic
279C22×C4C22×D1111yescharacteristic
280C22×C4C22×D1111yescharacteristic
281C22×C4C22×D1111yescharacteristic
282C22×C4C22×D1111yescharacteristic
283C22×C4C22×D1111yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—222no—
288C4⋊C4—222no—
289C4⋊C4—222no—
290C4⋊C4—222no—
291C4⋊C4—222no—
292C4⋊C4—222no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—222no—
297C22⋊C4—222no—
298C22⋊C4—222no—
299C22⋊C4—222no—
300C22⋊C4—222no—
301C22⋊C4—222no—
302C22⋊C4—222no—
303C22⋊C4—222no—
304C22⋊C4—222no—
305C42—114no—
306C42—222no—
307C42—222no—
308C42—222no—
309C42—222no—
310C11#254511yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—221no—
319C23—221no—
320C23—221no—
321C23—221no—
322C23—221no—
323C23—221no—
324C23—221no—
325C23C23×D1111yescharacteristic
326Q8—228no—
327Q8—444no—
328D4—444no—
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—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—112no—
345C2×C4—112no—
346C2×C4—112no—
347C2×C4—112no—
348C2×C4—112no—
349C2×C4—112no—
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—221no—
365C2×C4D4×D1112yes—
366C2×C4D4×D1112yes—
367C2×C4#434112yes—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—441no—
376C22—441no—
377C22—441no—
378C22—441no—
379C22—441no—
380C22—441no—
381C22—441no—
382C22C2×D4×D1111yescharacteristic
383C22C2×D4×D1111yescharacteristic
384C22C2×#434111yescharacteristic
385C22#6704011yescharacteristic
386C22#41×D1111yescharacteristic
387C22#41×D1111yescharacteristic
388C22#6704311yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—114no—
396C4—222no—
397C4—222no—
398C4—222no—
399C4—441no—
400C4—441no—
401C4—441no—
402C2—81no—
403C2—881no—
404C2#1062312711yescharacteristic
405C2#1062312911yescharacteristic
406C2D11×#12111yescharacteristic
407C2#1062315911yescharacteristic
408C2#1062316411yescharacteristic
409C2#1062317211yescharacteristic
410C2#1062323311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#396C2
prime radicalC22×C22⋊D11C22
hypercenter#396D11
hypocenterC11#2545
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#66941C2semidirect
2. C2×#66940C2semidirect
5. C11×#396C2semidirect
6. #10622607C2semidirect
7. #10622607C2semidirect
8. #10622603C2semidirect
9. C4⋊C4×Dic11C2semidirect
11. #10622564C2semidirect
12. #10622561C2semidirect
13. #10622558C2semidirect
14. #10622282C2semidirect
15. #10622259C2semidirect
170. #396D11semidirect
310. C11#2545semidirect

Maximal subgroups

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

subgroupindex
C2×#669412
C2×#669402
C2×#669382
C11×#3962
#106226072
#106226032
C4⋊C4×Dic112
#106225702
#106225642
#106225612
#106225582
#106222822
#106222592
#254511