Finite Group Databasebeta

← #13080183

Subgroups — #13080183

Order 1408.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66968C211yesmaximal, characteristic, complemented
2C22×Dic44C211yesmaximal, characteristic, complemented
3#10623163C211yesmaximal, characteristic, complemented
4#10623129C211yesmaximal, characteristic
5C11×#465C211yesmaximal, characteristic, complemented
6#10622780C211yesmaximal, characteristic, complemented
7#10622724C211yesmaximal, characteristic, complemented
8#10622663C211yesmaximal, characteristic, complemented
9#10622653C211yesmaximal, characteristic, complemented
10#10622481C211yesmaximal, characteristic, complemented
11#10622466C211yesmaximal, characteristic, complemented
12#10622421C211yesmaximal, characteristic, complemented
13#10622406C211yesmaximal, characteristic, complemented
14#10622396C211yesmaximal, characteristic, complemented
15#10622380C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C22×Dic22C2211yescharacteristic
19C22×Dic22C2211yescharacteristic
20C2×C11×SD16C2211yescharacteristic
21C22×C8×C11C2211yescharacteristic
22C11×C22⋊Q8C2211yescharacteristic
23C11×#121C2211yescharacteristic
24#66997C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26C2×#4326C2211yescharacteristic
27#66992—21no—
28#66989C2211yescharacteristic
29D4×Dic11—21no—
30C2×#4324C2211yescharacteristic
31C2×#4324C2211yescharacteristic
32C4×C22⋊D11C2211yescharacteristic
33#66968—24no—
34C2×Dic44—24no—
35C2×Dic44C2211yescharacteristic
36C2×Dic44C2211yescharacteristic
37C2×Dic44C2211yescharacteristic
38C2×Dic44C2211yescharacteristic
39C2×#4313C2211yescharacteristic
40#66950C2211yescharacteristic
41#66950C2211yescharacteristic
42#66949—21no—
43#66941—21no—
44#66940C2211yescharacteristic
45#66940C2211yescharacteristic
46#66938—21no—
47(C22⋊D11)⋊C4—21no—
48#66931—21no—
49#66931—21no—
50C11×#106C2211yescharacteristic
51C11×#103C2211yescharacteristic
52C11×#102C2211yescharacteristic
53C22⋊(C11⋊C8)C2211yescharacteristic
54(C2×D11)⋊C8C2211yescharacteristic
55#66879C2211yescharacteristic
56Dic11⋊C8C2211yescharacteristic
57#66874C2211yescharacteristic
58#66874C2211yescharacteristic
59#66874C2211yescharacteristic
60#66874C2211yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C2×C22⋊D11—21no—
66C2×C22⋊D11D411yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70Q8×D11—22no—
71Q8×D11—41no—
72#4341—22no—
73#4341—41no—
74C2×C4×D11—21no—
75C2×C4×D11C2311yescharacteristic
76C2×Dic22—22no—
77C2×Dic22—22no—
78C2×Dic22—21no—
79C2×Dic22—21no—
80C2×Dic22—21no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C2×Dic22C2311yescharacteristic
84C2×Dic22C2311yescharacteristic
85C2×Dic22C2311yescharacteristic
86C2×Dic22C2311yescharacteristic
87C11×SD16—22no—
88C2×C8×C11—22no—
89C2×C8×C11C2311yescharacteristic
90C2×C8×C11C2311yescharacteristic
91C11×C4⋊C4—21no—
92C11×C4⋊C4C2311yescharacteristic
93C11×C4⋊C4C2311yescharacteristic
94C11×C22⋊C4—21no—
95C11×C22⋊C4—21no—
96C22⋊Dic11—21no—
97C22⋊Dic11—21no—
98C22⋊Dic11D411yescharacteristic
99#4326—22no—
100#4326—41no—
101#4324—22no—
102#4324—41no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4D411yescharacteristic
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108Dic11⋊C4—21no—
109Dic11⋊C4—21no—
110Dic11⋊C4—21no—
111Dic11⋊C4—21no—
112Dic11⋊C4D411yescharacteristic
113C4×Dic11—21no—
114C4×Dic11—21no—
115C4×Dic11C2311yescharacteristic
116C2×C11⋊C8C2311yescharacteristic
117C2×C11⋊C8C2311yescharacteristic
118Dic44—22no—
119Dic44—22no—
120Dic44—22no—
121Dic44D414yescomplemented
122#4313—22no—
123#3270—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11C2×D411yescharacteristic
126C22×D11C2×D411yescharacteristic
127Q8×C11—21no—
128Q8×C11—21no—
129D4×C11—21no—
130D4×C11—21no—
131D4×C11—42no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2411yescharacteristic
139C22⋊D11—22no—
140C22⋊D11—42no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11C2×D411yescharacteristic
149C2×Dic11C2×D411yescharacteristic
150C2×Dic11C2×D411yescharacteristic
151C4×D11—21no—
152C4×D11—21no—
153C4×D11—42no—
154Dic22—21no—
155Dic22—21no—
156Dic22—21no—
157Dic22—21no—
158Dic22—21no—
159Dic22—21no—
160Dic22—42no—
161Dic22—42no—
162Dic22—42no—
163Dic22C2×D412yes—
164Dic22C2×D412yes—
165C8×C11—21no—
166C8×C11C2×D412yes—
167C11⋊C8—21no—
168C11⋊C8—21no—
169C2×#137—111no—
170C22×Q16—111no—
171D4×Q8—111no—
172#548—111no—
173#497—111no—
174#470—111no—
175#465D1111yescharacteristic, complemented
176#464—111no—
177#462—111no—
178#452—111no—
179#451—111no—
180#451—111no—
181#448—111no—
182#441—111no—
183#435—111no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11#13712yescomplemented
190C22×C11C22×D411yescharacteristic
191C2×D11—21no—
192C2×D11—21no—
193C2×D11—21no—
194C4×C11—21no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11C22×D411yescharacteristic
199C4×C11H(5,𝔽2)11yescharacteristic
200Dic11—22no—
201Dic11—22no—
202Dic11—21no—
203Dic11—21no—
204Dic11—21no—
205Dic11—41no—
206Dic11—41no—
207C2×#41—111no—
208C22×Q8—111no—
209C22×Q8—111no—
210C22×Q8—111no—
211#137—224no—
212C2×Q16—111no—
213C2×Q16—111no—
214C2×Q16—111no—
215C2×Q16—111no—
216C2×Q16—111no—
217C2×Q16—111no—
218C2×Q16—224no—
219C2×SD16—111no—
220C2×SD16—111no—
221C2×SD16C2×D1111yescharacteristic
222C2×M16—111no—
223C22×C8C2×D1111yescharacteristic
224C4⋊Q8—111no—
225C4⋊Q8—221no—
226#124—111no—
227#124—221no—
228C22⋊Q8—111no—
229C22⋊Q8—111no—
230C22⋊Q8—221no—
231C22⋊Q8—221no—
232C22⋊Q8—221no—
233C22⋊Q8C2×D1111yescharacteristic
234#121—221no—
235#121C2×D1111yescharacteristic
236C4×Q8—111no—
237C4×Q8—111no—
238C4×D4—111no—
239C4×D4—221no—
240C4×D4—221no—
241#106C2×D1111yescharacteristic
242C4⋊C8—111no—
243#103—111no—
244#103—111no—
245#103—111no—
246#103—111no—
247#103C2×D1111yescharacteristic
248#102C2×D1111yescharacteristic
249C22⋊C8—111no—
250C22⋊C8—111no—
251#97—111no—
252C2×C11—22no—
253C2×C11—81no—
254C2×C11D4211yescharacteristic
255C2×C11C2×#13711yescharacteristic
256C2×C11#57811yescharacteristic
257D11—41no—
258#41—222no—
259#41—441no—
260C2×Q8—111no—
261C2×Q8—111no—
262C2×Q8—111no—
263C2×Q8—111no—
264C2×Q8—221no—
265C2×Q8—222no—
266C2×Q8—222no—
267C2×Q8—221no—
268C2×Q8—221no—
269C2×Q8—222no—
270C2×Q8—441no—
271C2×Q8—441no—
272C2×Q8—441no—
273C2×Q8C22×D1111yescharacteristic
274C2×D4—21no—
275C2×D4—111no—
276C2×D4—221no—
277C2×D4C22×D1111yescharacteristic
278C22×C4—111no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4C22×D1111yescharacteristic
284Q16—114no—
285Q16—222no—
286Q16—222no—
287Q16—222no—
288Q16—222no—
289Q16—441no—
290SD16—22no—
291SD16—222no—
292SD16—441no—
293M16—222no—
294C2×C8—22no—
295C2×C8—111no—
296C2×C8—111no—
297C2×C8C22×D1111yescharacteristic
298C2×C8C22×D1111yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—111no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—221no—
307C4⋊C4C22×D1111yescharacteristic
308C4⋊C4C22×D1111yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—111no—
312C22⋊C4—111no—
313C22⋊C4—221no—
314C22⋊C4—221no—
315C22⋊C4—221no—
316C22⋊C4—221no—
317C42—111no—
318C42—221no—
319C42—221no—
320C11#327011yescharacteristic, complemented, Sylow
321C23—21no—
322C23—111no—
323C23D4×D1111yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—112no—
327Q8—112no—
328Q8—221no—
329Q8—221no—
330Q8—221no—
331Q8—221no—
332Q8—221no—
333Q8—221no—
334Q8—442no—
335Q8—442no—
336Q8—442no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—222no—
341D4—442no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—111no—
348C2×C4—111no—
349C2×C4—111no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4D4×D1111yescharacteristic
361C2×C4C23×D1111yescharacteristic
362C8—21no—
363C8—221no—
364C8—221no—
365C8D4×D1112yes—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—221no—
372C22—221no—
373C22—221no—
374C22#6696812yescomplemented
375C22C2×D4×D1111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—221no—
381C4—221no—
382C4—221no—
383C4—222no—
384C4—222no—
385C4—441no—
386C4—441no—
387C4C2×D4×D1111yescharacteristic
388C4#6704211yescharacteristic
389C2—22no—
390C2—81no—
391C2—441no—
392C2#1062314011yescharacteristic
393C2C2×#6696811yescharacteristic
394C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#465C2
socleC22×C11C22×D4
prime radical#10623129C2
hypercenter#465D11
hypocenterC11#3270
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#66968C2semidirect
2. C22×Dic44C2semidirect
3. #10623163C2semidirect
5. C11×#465C2semidirect
6. #10622780C2semidirect
7. #10622724C2semidirect
8. #10622663C2semidirect
9. #10622653C2semidirect
10. #10622481C2semidirect
11. #10622466C2semidirect
12. #10622421C2semidirect
13. #10622406C2semidirect
14. #10622396C2semidirect
15. #10622380C2semidirect
121. Dic44D4semidirect
175. #465D11semidirect
189. C22×C11#137semidirect
320. C11#3270semidirect
374. C22#66968semidirect

Maximal subgroups

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

subgroupindex
C2×#669682
C22×Dic442
#106231632
#106231292
C11×#4652
#106227802
#106227242
#106226632
#106226532
#106224812
#106224662
#106224212
#106224062
#106223962
#106223802
#327011