Finite Group Databasebeta

← #13078144

Subgroups — #13078144

Order 1408.

458 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D11C211yesmaximal, characteristic, complemented
2C2×#66968C211yesmaximal, characteristic
3#10623206C211yesmaximal, characteristic
4#10623103C211yesmaximal, characteristic, complemented
5C11×#464C211yesmaximal, characteristic, complemented
6#10622795C211yesmaximal, characteristic, complemented
7#10622779C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622644C211yesmaximal, characteristic, complemented
10#10622462C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622415C211yesmaximal, characteristic, complemented
13#10622406C211yesmaximal, characteristic, complemented
14#10622385C211yesmaximal, characteristic
15#10622380C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×#4341C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic
20C2×C11×SD16C2211yescharacteristic
21C11×#124C2211yescharacteristic
22C4×Q8×C11C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24#66997C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26C2×#4326C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28#66989C2211yescharacteristic
29C2×#4324C2211yescharacteristic
30Q16×D11—24no—
31#66968—24no—
32C2×Dic44C2211yescharacteristic
33C2×Dic44C2211yescharacteristic
34C2×#4313C2211yescharacteristic
35C2×C8×D11C2211yescharacteristic
36#66945—21no—
37#66945C2211yescharacteristic
38#66940—21no—
39#66940C2211yescharacteristic
40#66936—21no—
41#66936—21no—
42#66931—21no—
43#66931—21no—
44#66925—21no—
45#66925C2211yescharacteristic
46#66922C2211yescharacteristic
47C4×Dic22—21no—
48C4×Dic22C2211yescharacteristic
49C11×C4⋊C8C2211yescharacteristic
50C11×#103C2211yescharacteristic
51C11×#102C2211yescharacteristic
52#66899C2211yescharacteristic
53#66896C2211yescharacteristic
54#66880C2211yescharacteristic
55#66880C2211yescharacteristic
56Dic11⋊C8C2211yescharacteristic
57Dic11⋊C8C2211yescharacteristic
58#66874C2211yescharacteristic
59#66874C2211yescharacteristic
60C4⋊(C11⋊C8)C2211yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C22×Dic11—21no—
66Q8×D11—22no—
67Q8×D11—22no—
68Q8×D11—22no—
69Q8×D11D414yes—
70#4341—22no—
71#4341—22no—
72C2×C4×D11—21no—
73C2×C4×D11—21no—
74C2×C4×D11C2311yescharacteristic
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22C2311yescharacteristic
78C2×Dic22C2311yescharacteristic
79C2×Dic22C2311yescharacteristic
80C11×Q16—22no—
81C11×SD16—22no—
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C11×C4⋊C4—21no—
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C42×C11—21no—
89C42×C11C2311yescharacteristic
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92#4326—22no—
93#4326—22no—
94#4326—22no—
95#4324—22no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4D411yescharacteristic
98(C2×D11)⋊C4D411yescharacteristic
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107Dic11⋊C4D411yescharacteristic
108Dic11⋊C4D411yescharacteristic
109C4×Dic11—21no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11C2311yescharacteristic
114C2×C11⋊C8C2311yescharacteristic
115C2×C11⋊C8C2311yescharacteristic
116Dic44—22no—
117Dic44—22no—
118#4313—22no—
119C8×D11—22no—
120#3044—111nomaximal, Sylow
121C23×C11—21no—
122C22×D11C2×D411yescharacteristic
123Q8×C11—21no—
124Q8×C11—21no—
125Q8×C11—21no—
126Q8×C11C2×D412yes—
127D4×C11—21no—
128D4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2×D411yescharacteristic
134C2×C4×C11C2411yescharacteristic
135C22⋊D11—42no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—42no—
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143C2×Dic11C2×D411yescharacteristic
144C4×D11—24no—
145C4×D11—42no—
146C4×D11C2×D412yes—
147C4×D11#4112yes—
148Dic22—21no—
149Dic22—24no—
150Dic22—21no—
151Dic22—21no—
152Dic22—21no—
153Dic22—21no—
154Dic22—42no—
155Dic22C2×D412yes—
156C8×C11—21no—
157C8×C11—21no—
158C11⋊C8—21no—
159C11⋊C8—21no—
160C2×#137—111no—
161C22×Q16—111no—
162#536—111no—
163#519—111no—
164#464—111no—
165#464—111no—
166#464—111no—
167#464D1111yescharacteristic, complemented
168#462—111no—
169#462—111no—
170#462—111no—
171#462—111no—
172#424—111no—
173#419—111no—
174#416—111no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11C22×D411yescharacteristic
179C2×D11—21no—
180C2×D11—21no—
181C2×D11#12112yes—
182C4×C11—22no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11C22×D411yescharacteristic
188C4×C11C2×#4111yescharacteristic
189Dic11—22no—
190Dic11—21no—
191Dic11—21no—
192Dic11—41no—
193Dic11—41no—
194Dic11—41no—
195Dic11#12112yes—
196C2×#41—111no—
197C22×Q8—111no—
198C22×Q8—111no—
199#137—224no—
200C2×Q16—111no—
201C2×Q16—111no—
202C2×Q16—111no—
203C2×Q16—111no—
204C2×Q16—111no—
205C2×Q16—224no—
206C2×Q16C2×D1111yescharacteristic
207C2×SD16—111no—
208C2×SD16C2×D1111yescharacteristic
209C2×M16—111no—
210C22×C8—111no—
211C4⋊Q8—111no—
212C4⋊Q8—111no—
213#124—111no—
214#124C2×D1111yescharacteristic
215#123—221no—
216#123—221no—
217C22⋊Q8—221no—
218C22⋊Q8—221no—
219C4×Q8—111no—
220C4×Q8—111no—
221C4×Q8—111no—
222C4×Q8—221no—
223C4×Q8—221no—
224C4×Q8C2×D1111yescharacteristic
225#117—111no—
226#117—111no—
227#117—221no—
228#117—221no—
229C4⋊C8—111no—
230C4⋊C8—111no—
231C4⋊C8—111no—
232C4⋊C8C2×D1111yescharacteristic
233#103—111no—
234#103—111no—
235#103—111no—
236#103—111no—
237#103—111no—
238#103C2×D1111yescharacteristic
239#102—111no—
240#102C2×D1111yescharacteristic
241C2×C11—81no—
242C2×C11C2×#12111yescharacteristic
243C2×C11#57811yescharacteristic
244C2×C11#57811yescharacteristic
245D11—22no—
246#41—222no—
247#41—222no—
248C2×Q8—114no—
249C2×Q8—111no—
250C2×Q8—111no—
251C2×Q8—111no—
252C2×Q8—221no—
253C2×Q8—221no—
254C2×Q8—222no—
255C2×Q8—222no—
256C2×Q8—222no—
257C2×Q8C22×D1111yescharacteristic
258C2×Q8C22×D1111yescharacteristic
259C2×D4—221no—
260C2×D4C22×D1111yescharacteristic
261C22×C4—111no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265Q16—22no—
266Q16—222no—
267Q16—222no—
268Q16—222no—
269Q16—222no—
270Q16—222no—
271SD16—22no—
272SD16—222no—
273M16—222no—
274C2×C8—111no—
275C2×C8—111no—
276C2×C8—222no—
277C2×C8C22×D1111yescharacteristic
278C2×C8C22×D1111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—111no—
281C4⋊C4—111no—
282C4⋊C4—111no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4C22×D1111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—111no—
294C22⋊C4—111no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C42—21no—
299C42—111no—
300C42—221no—
301C42—221no—
302C42—221no—
303C42—221no—
304C42C22×D1111yescharacteristic
305C11#304411yescharacteristic, complemented, Sylow
306C23—21no—
307C23—111no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—112no—
312Q8—224no—
313Q8—221no—
314Q8—221no—
315Q8—221no—
316Q8—221no—
317Q8—221no—
318Q8—442no—
319Q8D4×D1112yes—
320D4—21no—
321D4—21no—
322D4—442no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—111no—
327C2×C4—112no—
328C2×C4—112no—
329C2×C4—111no—
330C2×C4—111no—
331C2×C4—224no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4D4×D1111yescharacteristic
339C2×C4D4×D1111yescharacteristic
340C2×C4C23×D1111yescharacteristic
341C8—21no—
342C8—21no—
343C8—221no—
344C8—221no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—112no—
349C22—221no—
350C22—221no—
351C22C2×D4×D1111yescharacteristic
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—112no—
358C4—221no—
359C4—221no—
360C4—222no—
361C4—441no—
362C4—441no—
363C4—441no—
364C4C2×D4×D1111yescharacteristic
365C4#41×D1111yescharacteristic
366C2—81no—
367C2—222no—
368C2D11×#12111yescharacteristic
369C2#1062330211yescharacteristic
370C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
prime radicalC2×#4341C22
hypercenter#464D11
hypocenterC11#3044
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D11C2semidirect
4. #10623103C2semidirect
5. C11×#464C2semidirect
6. #10622795C2semidirect
7. #10622779C2semidirect
8. #10622667C2semidirect
9. #10622644C2semidirect
10. #10622462C2semidirect
11. #10622452C2semidirect
12. #10622415C2semidirect
13. #10622406C2semidirect
15. #10622380C2semidirect
167. #464D11semidirect
305. C11#3044semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D112
C2×#669682
#106232062
#106231032
C11×#4642
#106227952
#106227792
#106226672
#106226442
#106224622
#106224522
#106224152
#106224062
#106223852
#106223802
#304411