Finite Group Databasebeta

← #13072096

Subgroups — #13072096

Order 1408.

560 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66947C211yesmaximal, characteristic
2C2×#66946C211yesmaximal, characteristic
3C11×#400C211yesmaximal, characteristic, complemented
4#10622593C211yesmaximal, characteristic, complemented
5#10622591C211yesmaximal, characteristic, complemented
6#10622288C211yesmaximal, characteristic, complemented
7#10622288C211yesmaximal, characteristic, complemented
8#10622281C211yesmaximal, characteristic, complemented
9#10622281C211yesmaximal, characteristic, complemented
10#10622280C211yesmaximal, characteristic, complemented
11#10622278C211yesmaximal, characteristic
12#10622277C211yesmaximal, characteristic, complemented
13#10622277C211yesmaximal, characteristic, complemented
14D11×#95C211yesmaximal, characteristic, complemented
15#10622266C211yesmaximal, characteristic, complemented
16C22×D44C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C22×C4×D11C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×C4×Dic11C2211yescharacteristic
37#66947—24no—
38#66946—24no—
39C11×#95C2211yescharacteristic
40C11×#95C2211yescharacteristic
41C11×#95C2211yescharacteristic
42C11×#95C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C23×D11C2311yescharacteristic
54C23×D11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C2×D44—22no—
69C2×D44—22no—
70C2×D44D414yes—
71C2×C4×D11—22no—
72C2×C4×D11—22no—
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—22no—
80C2×C4×D11—41no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85(C2×D11)⋊C4—22no—
86(C2×D11)⋊C4—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—41no—
93C4⋊Dic11—22no—
94Dic11⋊C4—22no—
95Dic11⋊C4—22no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98C4×Dic11—22no—
99#2419—111nomaximal, Sylow
100C23×C11C2411yescharacteristic
101C22×D11—21no—
102C22×D11—21no—
103C22×D11—21no—
104C22×D11—21no—
105C22×D11—21no—
106C22×D11—21no—
107C22×D11—21no—
108C22×D11—21no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11C2×D412yes—
112C22×D11C2×D412yes—
113C22×D11#4112yes—
114C22×D11#4112yes—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
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×C11—21no—
135C2×C4×C11C2×D412yes—
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#4112yes—
153C2×Dic11#4112yes—
154D44—28no—
155C4×D11—44no—
156C4×D11—44no—
157C4×D11—44no—
158C4×D11—44no—
159C2×#123—111no—
160C2×C4×D4—111no—
161#400D1111yescharacteristic, complemented
162#398—111no—
163#397—111no—
164#397—111no—
165#387—111no—
166#387—111no—
167#386—111no—
168#385—111no—
169#385—111no—
170#381—111no—
171#381—111no—
172#380—111no—
173C2×#95—111no—
174C22×C11C22×D411yescharacteristic
175C22×C11C2×#4111yescharacteristic
176C22×C11C2×#4111yescharacteristic
177C22×C11C2×#4111yescharacteristic
178C22×C11C2×#4111yescharacteristic
179C22×C11H(5,𝔽2)11yescharacteristic
180C22×C112−1+411yescharacteristic
181C2×D11—22no—
182C2×D11—22no—
183C2×D11—22no—
184C2×D11—22no—
185C2×D11—22no—
186C2×D11—22no—
187C2×D11—22no—
188C2×D11—22no—
189C2×D11—22no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11#12314yes—
195C4×C11—22no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11—41no—
202Dic11—22no—
203Dic11—22no—
204Dic11—41no—
205Dic11—41no—
206Dic11—41no—
207Dic11—41no—
208C22×D4—111no—
209C23×C4—111no—
210C23×C4—111no—
211C23×C4—111no—
212C23×C4—111no—
213#123—224no—
214C4×D4—224no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4C2×D1111yescharacteristic
221C2×C4⋊C4C2×D1111yescharacteristic
222C2×C22⋊C4—111no—
223C2×C22⋊C4—111no—
224C2×C22⋊C4—111no—
225C2×C22⋊C4—111no—
226C2×C22⋊C4—111no—
227C2×C22⋊C4—111no—
228C2×C22⋊C4—111no—
229C2×C22⋊C4—111no—
230C2×C42—111no—
231#95—111no—
232#95—111no—
233#95—111no—
234#95—111no—
235#95—111no—
236#95—111no—
237#95—111no—
238#95—111no—
239#95—111no—
240#95C2×D1111yescharacteristic
241#95C2×D1111yescharacteristic
242#95C2×D1111yescharacteristic
243#95C2×D1111yescharacteristic
244#95C2×D1111yescharacteristic
245C2×C11C2×#12311yescharacteristic
246C2×C11#52911yescharacteristic
247C2×C11#53911yescharacteristic
248C2×C11#54611yescharacteristic
249C2×C11#54711yescharacteristic
250C2×C11#55111yescharacteristic
251C2×C11#55211yescharacteristic
252D11—24no—
253D11—42no—
254C24—111no—
255C24—111no—
256C2×D4—114no—
257C2×D4—222no—
258C2×D4—222no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—111no—
263C22×C4—111no—
264C22×C4—111no—
265C22×C4—222no—
266C22×C4—222no—
267C22×C4—222no—
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×C4—441no—
277C22×C4C22×D1111yescharacteristic
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—222no—
287C4⋊C4—222no—
288C4⋊C4—222no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C22⋊C4—222no—
292C22⋊C4—222no—
293C22⋊C4—222no—
294C22⋊C4—222no—
295C22⋊C4—222no—
296C22⋊C4—222no—
297C22⋊C4—222no—
298C22⋊C4—441no—
299C42—222no—
300C11#241911yescharacteristic, complemented, Sylow
301C23—112no—
302C23—112no—
303C23—112no—
304C23—112no—
305C23—221no—
306C23—221no—
307C23—221no—
308C23—221no—
309C23—221no—
310C23—221no—
311C23—221no—
312C23—221no—
313C23—221no—
314C23—221no—
315C23C23×D1111yescharacteristic
316D4—228no—
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—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—112no—
338C2×C4—112no—
339C2×C4—221no—
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×C4—444no—
358C2×C4—444no—
359C2×C4D4×D1112yes—
360C22—114no—
361C22—222no—
362C22—222no—
363C22—222no—
364C22—222no—
365C22—222no—
366C22—222no—
367C22—222no—
368C22—222no—
369C22—222no—
370C22—441no—
371C22—441no—
372C22—441no—
373C22—441no—
374C22C2×D4×D1111yescharacteristic
375C22#6704011yescharacteristic
376C22#41×D1111yescharacteristic
377C22#41×D1111yescharacteristic
378C22#41×D1111yescharacteristic
379C22#41×D1111yescharacteristic
380C22#6704211yescharacteristic
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—222no—
389C4—222no—
390C4—441no—
391C4—441no—
392C4—441no—
393C4—441no—
394C2—224no—
395C2—442no—
396C2#1062316211yescharacteristic
397C2D11×#12311yescharacteristic
398C2#1062320711yescharacteristic
399C2#1062322311yescharacteristic
400C2#1062322411yescharacteristic
401C2#1062323611yescharacteristic
402C2#1062323711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#400C2
prime radicalC22×D44C22
hypercenter#400D11
hypocenterC11#2419
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. C11×#400C2semidirect
4. #10622593C2semidirect
5. #10622591C2semidirect
6. #10622288C2semidirect
7. #10622288C2semidirect
8. #10622281C2semidirect
9. #10622281C2semidirect
10. #10622280C2semidirect
12. #10622277C2semidirect
13. #10622277C2semidirect
14. D11×#95C2semidirect
15. #10622266C2semidirect
161. #400D11semidirect
300. C11#2419semidirect

Maximal subgroups

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

subgroupindex
C2×#669472
C2×#669462
C11×#4002
#106225932
#106225912
#106222882
#106222812
#106222802
#106222782
#106222772
D11×#952
#106222662
#241911