Finite Group Databasebeta

← #13075583

Subgroups — #13075583

Order 1408.

512 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#66999C211yesmaximal, characteristic, complemented
3#10622843C211yesmaximal, characteristic, complemented
4#10622826C211yesmaximal, characteristic
5#10622823C211yesmaximal, characteristic, complemented
6#10622606C211yesmaximal, characteristic, complemented
7#10622603C211yesmaximal, characteristic, complemented
8#10622602C211yesmaximal, characteristic, complemented
9#10622599C211yesmaximal, characteristic, complemented
10#10622597C211yesmaximal, characteristic, complemented
11#10622595C211yesmaximal, characteristic, complemented
12#10622574C211yesmaximal, characteristic
13#10622569C211yesmaximal, characteristic
14#10622566C211yesmaximal, characteristic, complemented
15#10622558C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C4×D11C2211yescharacteristic
20C11×C22⋊Q8—24no—
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29#66999—24no—
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×C4⋊Dic11C2211yescharacteristic
36C2×C4⋊Dic11C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C23×D11C2311yescharacteristic
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×Q8×C11D414yescomplemented
58C22×C4×C11—22no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—22no—
68C2×C22⋊D11—22no—
69C2×C22⋊D11—41no—
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C2×C4×D11—22no—
78C2×C4×D11—41no—
79C2×C4×D11—41no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—22no—
85C22⋊Dic11—22no—
86C22⋊Dic11—22no—
87C22⋊Dic11—41no—
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—
94C4⋊Dic11—41no—
95Dic11⋊C4—22no—
96Dic11⋊C4—22no—
97Dic11⋊C4—41no—
98C4×Dic11—41no—
99#2728—111nomaximal, Sylow
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11#4112yes—
107C23×C11C2411yescharacteristic
108C22×D11—21no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—21no—
113C22×D11—21no—
114C22×D11#4112yes—
115Q8×C11—44no—
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—44no—
132C2×C4×C11C2×D412yes—
133C2×C4×C11C2×D412yes—
134C2×C4×C11C2×D412yes—
135C22⋊D11—44no—
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—
157C4×D11—44no—
158C2×C22⋊Q8—111no—
159C2×C22⋊Q8D1111yescharacteristic, complemented
160#400—111no—
161#400—111no—
162#398—111no—
163#397—111no—
164#397—111no—
165#394—111no—
166#391—111no—
167#388—111no—
168#388—111no—
169#386—111no—
170#386—111no—
171#385—111no—
172#385—111no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11C22×D411yescharacteristic
181C22×C11C2×#4111yescharacteristic
182C22×C11C2×#4111yescharacteristic
183C22×C11H(5,𝔽2)11yescharacteristic
184C22×C11H(5,𝔽2)11yescharacteristic
185C22×C112−1+411yescharacteristic
186C22×C112−1+411yescharacteristic
187C2×D11—22no—
188C2×D11—22no—
189C2×D11—22no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C4×C11—22no—
195C4×C11—22no—
196C4×C11—22no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200Dic11—41no—
201Dic11—41no—
202Dic11—41no—
203Dic11—41no—
204Dic11—41no—
205Dic11—41no—
206Dic11—41no—
207C22×Q8C2×D1111yescharacteristic
208C22×D4—111no—
209C23×C4—111no—
210C23×C4C2×D1111yescharacteristic
211C22⋊Q8—24no—
212C22⋊Q8—224no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4C2×D1111yescharacteristic
219C2×C4⋊C4C2×D1111yescharacteristic
220C2×C4⋊C4C2×D1111yescharacteristic
221C2×C22⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
230C2×C22⋊C4C2×D1111yescharacteristic
231C2×C42—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#95—111no—
241#95—111no—
242#95—111no—
243#95—111no—
244C2×C11—42no—
245C2×C11#53411yescharacteristic
246C2×C11#53911yescharacteristic
247C2×C11#53911yescharacteristic
248C2×C11#54811yescharacteristic
249C2×C11#54811yescharacteristic
250C2×C11#55111yescharacteristic
251C2×C11#56311yescharacteristic
252D11—42no—
253C24—111no—
254C24C22×D1111yescharacteristic
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8C22⋊D1114yescomplemented
258C2×D4—222no—
259C2×D4—222no—
260C2×D4—441no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—111no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—111no—
271C22×C4—222no—
272C22×C4—441no—
273C22×C4—441no—
274C22×C4C22×D1111yescharacteristic
275C22×C4C22×D1111yescharacteristic
276C22×C4C22×D1111yescharacteristic
277C22×C4C22×D1111yescharacteristic
278C22×C4C22×D1111yescharacteristic
279C22×C4C22×D1111yescharacteristic
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—222no—
284C4⋊C4—222no—
285C4⋊C4—222no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—222no—
291C22⋊C4—222no—
292C22⋊C4—222no—
293C22⋊C4—222no—
294C22⋊C4—222no—
295C22⋊C4—222no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C42—441no—
299C11#272811yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—112no—
307C23—221no—
308C23—221no—
309C23—221no—
310C23—221no—
311C23—221no—
312C23—221no—
313C23#434312yes—
314C23C23×D1111yescharacteristic
315Q8—44no—
316D4—444no—
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—44no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
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—444no—
355C2×C4C2×C22⋊D1112yes—
356C2×C4C2×C22⋊D1112yes—
357C2×C4C2×C22⋊D1112yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—222no—
366C22—222no—
367C22—222no—
368C22—441no—
369C22—441no—
370C22—441no—
371C22—441no—
372C22#6703711yescharacteristic
373C22#6703711yescharacteristic
374C22C2×#434311yescharacteristic
375C22#6704011yescharacteristic
376C22#41×D1111yescharacteristic
377C22#6704311yescharacteristic
378C22C22×C22⋊D1111yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—441no—
386C4—441no—
387C4—441no—
388C4—441no—
389C4—441no—
390C4—441no—
391C4—441no—
392C2—42no—
393C2—442no—
394C2#1062316811yescharacteristic
395C2#1062316911yescharacteristic
396C2#1062317611yescharacteristic
397C2#1062317711yescharacteristic
398C2#1062333511yescharacteristic
399C2#1062334811yescharacteristic
400C2#1062336211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC22×C22⋊D11C22
hypercenterC2×C22⋊Q8D11
hypocenterC11#2728
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C11×C22⋊Q8C2semidirect
2. C2×#66999C2semidirect
3. #10622843C2semidirect
5. #10622823C2semidirect
6. #10622606C2semidirect
7. #10622603C2semidirect
8. #10622602C2semidirect
9. #10622599C2semidirect
10. #10622597C2semidirect
11. #10622595C2semidirect
14. #10622566C2semidirect
15. #10622558C2semidirect
57. C2×Q8×C11D4semidirect
159. C2×C22⋊Q8D11semidirect
257. C2×Q8C22⋊D11semidirect
299. C11#2728semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#669992
#106228432
#106228262
#106228232
#106226062
#106226032
#106226022
#106225992
#106225972
#106225952
#106225742
#106225692
#106225662
#106225582
#272811