Finite Group Databasebeta

← #13078306

Subgroups — #13078306

Order 1408.

472 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66971C211yesmaximal, characteristic, complemented
2C2×#66954C211yesmaximal, characteristic, complemented
3#10623160C211yesmaximal, characteristic
4#10623159C211yesmaximal, characteristic, complemented
5C11×#467C211yesmaximal, characteristic, complemented
6#10622802C211yesmaximal, characteristic, complemented
7#10622727C211yesmaximal, characteristic, complemented
8#10622665C211yesmaximal, characteristic, complemented
9#10622662C211yesmaximal, characteristic, complemented
10#10622499C211yesmaximal, characteristic, complemented
11#10622494C211yesmaximal, characteristic, complemented
12#10622426C211yesmaximal, characteristic, complemented
13#10622420C211yesmaximal, characteristic, complemented
14#10622417C211yesmaximal, characteristic, complemented
15D11×#103C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic
20C22×C8×C11C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22C11×C22⋊Q8C2211yescharacteristic
23#66999C2211yescharacteristic
24#66999C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26C2×#4325C2211yescharacteristic
27#66983C2211yescharacteristic
28#66977C2211yescharacteristic
29C2×#4318C2211yescharacteristic
30#66971—24no—
31C2×#4314C2211yescharacteristic
32#66954—24no—
33C2×#4313C2211yescharacteristic
34C2×#4313C2211yescharacteristic
35C2×C8×D11C2211yescharacteristic
36C2×C8×D11C2211yescharacteristic
37#66950C2211yescharacteristic
38#66949—21no—
39#66948—21no—
40#66948C2211yescharacteristic
41#66947—21no—
42#66945C2211yescharacteristic
43C4⋊C4×D11C2211yescharacteristic
44#66941—21no—
45#66938—21no—
46#66937—21no—
47#66937—21no—
48#66936—21no—
49C11×#107C2211yescharacteristic
50C11×#103C2211yescharacteristic
51C11×#103C2211yescharacteristic
52#66899C2211yescharacteristic
53#66899C2211yescharacteristic
54#66885C2211yescharacteristic
55#66881C2211yescharacteristic
56#66880C2211yescharacteristic
57#66874C2211yescharacteristic
58#66873C2211yescharacteristic
59#66872C2211yescharacteristic
60#66871C2211yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11D411yescharacteristic
66C2×C22⋊D11D411yescharacteristic
67#4343—22no—
68#4343—22no—
69Q8×D11—22no—
70Q8×D11—22no—
71#4339—22no—
72#4339—22no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44D411yescharacteristic
76C2×D44C2311yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11C2311yescharacteristic
81C2×C4×D11C2311yescharacteristic
82C2×Dic22—21no—
83C2×Dic22D411yescharacteristic
84C2×Dic22C2311yescharacteristic
85C11×Q16—22no—
86C2×C8×C11—22no—
87C2×C8×C11C2311yescharacteristic
88C2×C8×C11C2311yescharacteristic
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4C2311yescharacteristic
92C11×C4⋊C4C2311yescharacteristic
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C22⋊Dic11—21no—
96#4326—22no—
97#4325—22no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11C2311yescharacteristic
106C4⋊Dic11C2311yescharacteristic
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109Dic11⋊C4—21no—
110Dic11⋊C4—21no—
111C4×Dic11—21no—
112#4318—22no—
113C2×C11⋊C8C2311yescharacteristic
114C2×C11⋊C8C2311yescharacteristic
115#4314—22no—
116#4313—22no—
117#4313D414yescomplemented
118C8×D11—22no—
119C8×D11—22no—
120#3063—111nomaximal, Sylow
121C23×C11C2×D411yescharacteristic
122C22×D11—21no—
123C22×D11C2×D411yescharacteristic
124C22×D11C2×D411yescharacteristic
125Q8×C11—21no—
126Q8×C11—21no—
127Q8×C11—21no—
128Q8×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×D411yescharacteristic
136C2×C4×C11C2411yescharacteristic
137C22⋊D11—22no—
138C22⋊D11—22no—
139C22⋊D11—81no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11C2×D411yescharacteristic
144C2×Dic11C2×D411yescharacteristic
145D44—22no—
146D44—21no—
147D44—21no—
148D44—42no—
149D44—81no—
150C4×D11—21no—
151C4×D11—21no—
152C4×D11—42no—
153C4×D11—42no—
154C4×D11—81no—
155C4×D11C2×D412yes—
156C4×D11#4112yes—
157Dic22—22no—
158Dic22—21no—
159Dic22—21no—
160Dic22—42no—
161C8×C11—21no—
162C8×C11C2×D412yes—
163C11⋊C8—21no—
164C11⋊C8C2×D412yes—
165C2×#137—111no—
166C2×#131—111no—
167#537—111no—
168#536—111no—
169#470—111no—
170#470—111no—
171#468—111no—
172#468—111no—
173#467—111no—
174#467D1111yescharacteristic, complemented
175#465—111no—
176#465—111no—
177#428—111no—
178#416—111no—
179C2×#103—111no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11C22×D411yescharacteristic
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—21no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11#12112yes—
193C4×C11—21no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11C22×D411yescharacteristic
199C4×C11C2×#4111yescharacteristic
200Dic11—21no—
201Dic11—41no—
202Dic11—41no—
203Dic11—41no—
204Dic11#12112yes—
205C2×#41—111no—
206C2×#41—111no—
207C22×Q8—111no—
208#137—224no—
209C2×Q16—111no—
210C2×Q16C2×D1111yescharacteristic
211C2×SD16—111no—
212C2×SD16—111no—
213#131—224no—
214C2×M16—111no—
215C2×M16—111no—
216C2×M16—111no—
217C22×C8—111no—
218C22×C8—111no—
219C22×C8C2×D1111yescharacteristic
220C4⋊Q8—221no—
221#124—221no—
222#123—221no—
223#123—221no—
224C22⋊Q8—111no—
225C22⋊Q8—111no—
226C22⋊Q8—111no—
227C22⋊Q8—111no—
228C22⋊Q8—221no—
229C22⋊Q8C2×D1111yescharacteristic
230C22⋊Q8C2×D1111yescharacteristic
231#121—111no—
232#121—111no—
233#121—221no—
234#121—221no—
235#121—221no—
236#117—111no—
237C2×C4⋊C4—111no—
238#107—111no—
239#107C2×D1111yescharacteristic
240#106—111no—
241#106—111no—
242#103—111no—
243#103—111no—
244#103—111no—
245#103—111no—
246#103C2×D1111yescharacteristic
247#103C2×D1111yescharacteristic
248#102—111no—
249#102—111no—
250C2×C11—41no—
251C2×C11C2×#12111yescharacteristic
252C2×C11#57711yescharacteristic
253C2×C11#57811yescharacteristic
254D11—22no—
255D11—41no—
256D11—81no—
257#41—222no—
258#41—222no—
259#41—222no—
260#41—222no—
261C2×Q8—111no—
262C2×Q8—111no—
263C2×Q8—221no—
264C2×Q8—222no—
265C2×Q8—222no—
266C2×Q8C22×D1111yescharacteristic
267C2×Q8C22×D1111yescharacteristic
268C2×D4—111no—
269C2×D4—111no—
270C2×D4—111no—
271C2×D4—111no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4C22×D1111yescharacteristic
281Q16—22no—
282Q16—222no—
283SD16—222no—
284SD16—222no—
285M16—114no—
286M16—222no—
287M16—222no—
288C2×C8—22no—
289C2×C8—111no—
290C2×C8—111no—
291C2×C8—222no—
292C2×C8—222no—
293C2×C8C22×D1111yescharacteristic
294C2×C8C22×D1111yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—111no—
298C4⋊C4—111no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4C22×D1111yescharacteristic
305C4⋊C4C22×D1111yescharacteristic
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C22⋊C4—221no—
311C22⋊C4—221no—
312C22⋊C4—221no—
313C22⋊C4—221no—
314C22⋊C4—221no—
315C42—221no—
316C11#306311yescharacteristic, complemented, Sylow
317C23—111no—
318C23—111no—
319C23—221no—
320C23D4×D1111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—222no—
326Q8—221no—
327Q8—221no—
328Q8—442no—
329D4—222no—
330D4—222no—
331D4—222no—
332D4—221no—
333D4—221no—
334D4—442no—
335D4—881no—
336D4—881no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—111no—
344C2×C4—112no—
345C2×C4—112no—
346C2×C4—111no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—881no—
355C2×C4D4×D1111yescharacteristic
356C2×C4C23×D1111yescharacteristic
357C8—21no—
358C8—112no—
359C8—221no—
360C8D4×D1112yes—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—112no—
365C22—221no—
366C22—221no—
367C22—221no—
368C22—221no—
369C22—221no—
370C22—441no—
371C22—441no—
372C22—441no—
373C22C2×D4×D1111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—112no—
380C4—221no—
381C4—441no—
382C4—441no—
383C4—441no—
384C4C2×D4×D1111yescharacteristic
385C4#41×D1111yescharacteristic
386C2—41no—
387C2—222no—
388C2—441no—
389C2—881no—
390C2D11×#12111yescharacteristic
391C2#1062329711yescharacteristic
392C2#1062330111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#467C2
socleC22×C11C22×D4
prime radical#10623160C2
hypercenter#467D11
hypocenterC11#3063
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#66971C2semidirect
2. C2×#66954C2semidirect
4. #10623159C2semidirect
5. C11×#467C2semidirect
6. #10622802C2semidirect
7. #10622727C2semidirect
8. #10622665C2semidirect
9. #10622662C2semidirect
10. #10622499C2semidirect
11. #10622494C2semidirect
12. #10622426C2semidirect
13. #10622420C2semidirect
14. #10622417C2semidirect
15. D11×#103C2semidirect
117. #4313D4semidirect
174. #467D11semidirect
316. C11#3063semidirect

Maximal subgroups

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

subgroupindex
C2×#669712
C2×#669542
#106231602
#106231592
C11×#4672
#106228022
#106227272
#106226652
#106226622
#106224992
#106224942
#106224262
#106224202
#106224172
D11×#1032
#306311