Finite Group Databasebeta

← #13072044

Subgroups — #13072044

Order 1408.

604 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×#66949C211yesmaximal, characteristic, complemented
2C2×#66949C211yesmaximal, characteristic, complemented
3C2×#66946C211yesmaximal, characteristic
4C2×#66925C211yesmaximal, characteristic, complemented
5C11×#389C211yesmaximal, characteristic, complemented
6#10622606C211yesmaximal, characteristic, complemented
7#10622604C211yesmaximal, characteristic
8#10622603C211yesmaximal, characteristic, complemented
9#10622585C211yesmaximal, characteristic, complemented
10#10622585C211yesmaximal, characteristic, complemented
11#10622553C211yesmaximal, characteristic, complemented
12#10622288C211yesmaximal, characteristic, complemented
13#10622285C211yesmaximal, characteristic
14#10622280C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C22×D44C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C22×Dic22C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C42×C11C2211yescharacteristic
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C2×C4×Dic11C2211yescharacteristic
42C2×C4×Dic11C2211yescharacteristic
43#66949—24no—
44#66949—24no—
45#66946—24no—
46#66925—24no—
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C23×D11C2311yescharacteristic
56C23×D11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C2×D44—22no—
71C2×D44—22no—
72C2×D44—22no—
73C2×C4×D11—22no—
74C2×C4×D11—22no—
75C2×C4×D11—22no—
76C2×C4×D11—22no—
77C2×C4×D11—22no—
78C2×C4×D11D414yes—
79C2×Dic22—22no—
80C2×Dic22—22no—
81C2×Dic22—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C42×C11—22no—
87(C2×D11)⋊C4—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—
94(C2×D11)⋊C4—22no—
95(C2×D11)⋊C4—22no—
96(C2×D11)⋊C4—22no—
97Dic11⋊C4—22no—
98Dic11⋊C4—22no—
99Dic11⋊C4—22no—
100Dic11⋊C4—22no—
101Dic11⋊C4—22no—
102Dic11⋊C4D414yescomplemented
103C4×Dic11—22no—
104C4×Dic11—22no—
105#2415—111nomaximal, Sylow
106C23×C11C2411yescharacteristic
107C22×D11—21no—
108C22×D11—21no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—21no—
113C22×D11—21no—
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11C2×D412yes—
120C22×D11#4112yes—
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×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11C2×D412yes—
140C2×C4×C11C2×D412yes—
141C2×C4×C11#4112yes—
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×Dic11C2×D412yes—
157C2×Dic11C2×D412yes—
158C2×Dic11C2×D412yes—
159C2×Dic11#4112yes—
160D44—28no—
161C4×D11—28no—
162C4×D11—44no—
163Dic22—44no—
164C2×C22⋊Q8—111no—
165C2×C22⋊Q8—111no—
166C2×C4×D4—111no—
167C2×#117—111no—
168#397—111no—
169#397—111no—
170#394—111no—
171#394—111no—
172#391—111no—
173#389—111no—
174#389—111no—
175#389D1111yescharacteristic, complemented
176#388—111no—
177#388—111no—
178#380—111no—
179C22×C11C22×D411yescharacteristic
180C22×C11C22×D411yescharacteristic
181C22×C11C2×#4111yescharacteristic
182C22×C11C2×#4111yescharacteristic
183C22×C11C2×#4111yescharacteristic
184C22×C112−1+411yescharacteristic
185C22×C112−1+411yescharacteristic
186C2×D11—22no—
187C2×D11—22no—
188C2×D11—22no—
189C2×D11—22no—
190C2×D11—22no—
191C2×D11—22no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—41no—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—41no—
207Dic11—22no—
208Dic11—41no—
209Dic11—41no—
210Dic11—41no—
211Dic11—41no—
212Dic11#12114yes—
213C22×Q8—111no—
214C22×D4—111no—
215C23×C4—111no—
216C23×C4—111no—
217C22⋊Q8—224no—
218C22⋊Q8—224no—
219C4×D4—224no—
220#117—224no—
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⋊C4C2×D1111yescharacteristic
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×C22⋊C4—111no—
236C2×C22⋊C4—111no—
237C2×C22⋊C4—111no—
238C2×C22⋊C4—111no—
239C2×C22⋊C4—111no—
240C2×C22⋊C4—111no—
241C2×C42—111no—
242C2×C42—111no—
243C2×C42C2×D1111yescharacteristic
244#95—111no—
245#95—111no—
246#95—111no—
247#95—111no—
248#95—111no—
249#95—111no—
250#95C2×D1111yescharacteristic
251#95C2×D1111yescharacteristic
252C2×C11C2×#12111yescharacteristic
253C2×C11#52511yescharacteristic
254C2×C11#53611yescharacteristic
255C2×C11#54711yescharacteristic
256C2×C11#54811yescharacteristic
257C2×C11#55211yescharacteristic
258C2×C11#55611yescharacteristic
259D11—42no—
260D11—42no—
261C24—111no—
262C24—111no—
263C2×Q8—222no—
264C2×Q8—222no—
265C2×Q8—222no—
266C2×D4—222no—
267C2×D4—222no—
268C2×D4—222no—
269C22×C4—111no—
270C22×C4—111no—
271C22×C4—114no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—222no—
277C22×C4—222no—
278C22×C4—222no—
279C22×C4—222no—
280C22×C4—222no—
281C22×C4C22×D1111yescharacteristic
282C22×C4C22×D1111yescharacteristic
283C22×C4C22×D1111yescharacteristic
284C22×C4C22×D1111yescharacteristic
285C22×C4C22×D1111yescharacteristic
286C22×C4C22×D1111yescharacteristic
287C22×C4C22×D1111yescharacteristic
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—114no—
293C4⋊C4—222no—
294C4⋊C4—222no—
295C4⋊C4—222no—
296C4⋊C4—222no—
297C4⋊C4—222no—
298C22⋊C4—222no—
299C22⋊C4—222no—
300C22⋊C4—222no—
301C22⋊C4—222no—
302C22⋊C4—222no—
303C22⋊C4—222no—
304C22⋊C4—222no—
305C22⋊C4—222no—
306C22⋊C4—222no—
307C22⋊C4—222no—
308C42—22no—
309C42—222no—
310C42—222no—
311C11#241511yescharacteristic, complemented, Sylow
312C23—112no—
313C23—112no—
314C23—221no—
315C23—221no—
316C23—221no—
317C23—221no—
318C23—221no—
319C23—221no—
320C23—221no—
321C23—221no—
322C23—221no—
323C23—221no—
324C23—221no—
325C23—221no—
326C23C23×D1111yescharacteristic
327Q8—444no—
328D4—228no—
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—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—112no—
348C2×C4—112no—
349C2×C4—112no—
350C2×C4—112no—
351C2×C4—228no—
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—444no—
367C2×C4#433912yes—
368C2×C4D4×D1112yes—
369C2×C4D4×D1112yes—
370C22—222no—
371C22—222no—
372C22—222no—
373C22—222no—
374C22—222no—
375C22—222no—
376C22—441no—
377C22—441no—
378C22—441no—
379C22—441no—
380C22—441no—
381C22—441no—
382C22—441no—
383C22—441no—
384C22C2×#433911yescharacteristic
385C22C2×D4×D1111yescharacteristic
386C22C2×D4×D1111yescharacteristic
387C22#6704011yescharacteristic
388C22#6704011yescharacteristic
389C22#41×D1111yescharacteristic
390C22#41×D1111yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—114no—
399C4—222no—
400C4—441no—
401C4—441no—
402C4—441no—
403C4—441no—
404C2—442no—
405C2—442no—
406C2#1062303811yescharacteristic
407C2#1062307811yescharacteristic
408C2#1062309911yescharacteristic
409C2D11×#12111yescharacteristic
410C2#1062316411yescharacteristic
411C2#1062322411yescharacteristic
412C2#1062325511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#389C2
prime radicalC22×D44C22
hypercenter#389D11
hypocenterC11#2415
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#66949C2semidirect
2. C2×#66949C2semidirect
4. C2×#66925C2semidirect
5. C11×#389C2semidirect
6. #10622606C2semidirect
8. #10622603C2semidirect
9. #10622585C2semidirect
10. #10622585C2semidirect
11. #10622553C2semidirect
12. #10622288C2semidirect
14. #10622280C2semidirect
15. #10622259C2semidirect
102. Dic11⋊C4D4semidirect
175. #389D11semidirect
311. C11#2415semidirect

Maximal subgroups

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

subgroupindex
C2×#669492
C2×#669462
C2×#669252
C11×#3892
#106226062
#106226042
#106226032
#106225852
#106225532
#106222882
#106222852
#106222802
#106222592
#241511