Finite Group Databasebeta

← #13078167

Subgroups — #13078167

Order 1408.

472 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66968C211yesmaximal, characteristic, complemented
2C2×#66965C211yesmaximal, characteristic
3#10623206C211yesmaximal, characteristic, complemented
4#10623077C211yesmaximal, characteristic, complemented
5C11×#463C211yesmaximal, characteristic, complemented
6#10622775C211yesmaximal, characteristic, complemented
7#10622766C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622632C211yesmaximal, characteristic, complemented
10#10622462C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12D11×#103C211yesmaximal, characteristic, complemented
13#10622406C211yesmaximal, characteristic, complemented
14#10622384C211yesmaximal, characteristic, complemented
15#10622380C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×#4341C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C2×C11×D8C2211yescharacteristic
21C11×#124C2211yescharacteristic
22C4×D4×C11C2211yescharacteristic
23#66997C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25#66989C2211yescharacteristic
26D4×Dic11C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28C2×#4324C2211yescharacteristic
29C2×#4324C2211yescharacteristic
30C4×C22⋊D11—21no—
31C2×Dic11⋊C4—21no—
32#66968—24no—
33#66965—24no—
34C2×Dic44C2211yescharacteristic
35C2×Dic44C2211yescharacteristic
36C2×#4313C2211yescharacteristic
37C2×C8×D11C2211yescharacteristic
38C4⋊C4×D11C2211yescharacteristic
39#66940C2211yescharacteristic
40#66936—21no—
41#66936—21no—
42(C22⋊D11)⋊C4—21no—
43#66931—21no—
44#66931—21no—
45#66930—21no—
46#66925C2211yescharacteristic
47#66922C2211yescharacteristic
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×D4×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70Q8×D11—22no—
71Q8×D11—22no—
72#4341—22no—
73#4341—22no—
74#4341—22no—
75#4341D414yes—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×Dic22—21no—
80C2×Dic22C2311yescharacteristic
81C2×Dic22C2311yescharacteristic
82C2×Dic22C2311yescharacteristic
83C11×SD16—22no—
84C11×D8—22no—
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C22⋊C4—21no—
89C11×C22⋊C4—21no—
90C11×C22⋊C4—21no—
91C42×C11C2311yescharacteristic
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94C22⋊Dic11—21no—
95#4326—22no—
96#4324—22no—
97#4324—22no—
98#4324—22no—
99(C2×D11)⋊C4D411yescharacteristic
100(C2×D11)⋊C4D411yescharacteristic
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11C2311yescharacteristic
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109Dic11⋊C4D411yescharacteristic
110Dic11⋊C4D411yescharacteristic
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#3046—111nomaximal, Sylow
121C23×C11—21no—
122C23×C11—21no—
123C22×D11C2×D411yescharacteristic
124Q8×C11—21no—
125Q8×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—21no—
129D4×C11C2×D412yes—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—81no—
133C2×C4×C11C2×D411yescharacteristic
134C2×C4×C11C2×D411yescharacteristic
135C2×C4×C11C2411yescharacteristic
136C22⋊D11—24no—
137C22⋊D11—42no—
138C2×Dic11—21no—
139C2×Dic11—24no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—42no—
144C2×Dic11—81no—
145C2×Dic11C2×D411yescharacteristic
146C2×Dic11C2×D411yescharacteristic
147C2×Dic11C2×D411yescharacteristic
148C4×D11—42no—
149C4×D11—81no—
150C4×D11C2×D412yes—
151C4×D11#4112yes—
152Dic22—21no—
153Dic22—21no—
154Dic22—21no—
155Dic22—21no—
156Dic22—21no—
157Dic22—42no—
158Dic22C2×D412yes—
159C8×C11—21no—
160C8×C11—21no—
161C11⋊C8—21no—
162C11⋊C8—21no—
163C2×#137—111no—
164C2×#135—111no—
165#536—111no—
166#520—111no—
167#464—111no—
168#464—111no—
169#463—111no—
170#463D1111yescharacteristic, complemented
171#462—111no—
172#462—111no—
173#461—111no—
174#461—111no—
175#424—111no—
176#417—111no—
177C2×#103—111no—
178C22×C11—22no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11C22×D411yescharacteristic
185C2×D11—21no—
186C2×D11—21no—
187C2×D11#12112yes—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11C22×D411yescharacteristic
193C4×C11C2×#4111yescharacteristic
194Dic11—22no—
195Dic11—21no—
196Dic11—21no—
197Dic11—41no—
198Dic11—41no—
199Dic11—41no—
200Dic11#12112yes—
201C2×#41—111no—
202C2×#41—111no—
203C22×Q8—111no—
204#137—224no—
205#135—224no—
206C2×Q16—111no—
207C2×Q16—111no—
208C2×Q16—111no—
209C2×SD16—111no—
210C2×SD16—111no—
211C2×SD16—111no—
212C2×SD16C2×D1111yescharacteristic
213C2×D8C2×D1111yescharacteristic
214C2×M16—111no—
215C22×C8—111no—
216C4⋊Q8—111no—
217C4⋊Q8—111no—
218#124—111no—
219#124C2×D1111yescharacteristic
220#123—221no—
221#123—221no—
222C22⋊Q8—221no—
223C22⋊Q8—221no—
224C4×Q8—111no—
225C4×Q8—111no—
226C4×D4—111no—
227C4×D4—221no—
228C4×D4—221no—
229C4×D4C2×D1111yescharacteristic
230#117—111no—
231#117—221no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—221no—
234C4⋊C8—111no—
235C4⋊C8—111no—
236C4⋊C8—111no—
237C4⋊C8C2×D1111yescharacteristic
238#103—111no—
239#103—111no—
240#103—111no—
241#103—111no—
242#103—111no—
243#103C2×D1111yescharacteristic
244#102—111no—
245#102C2×D1111yescharacteristic
246C2×C11—42no—
247C2×C11—81no—
248C2×C11C2×#12111yescharacteristic
249C2×C11#57711yescharacteristic
250C2×C11#57811yescharacteristic
251D11—22no—
252#41—114no—
253#41—222no—
254#41—222no—
255#41—222no—
256C2×Q8—111no—
257C2×Q8—111no—
258C2×Q8—111no—
259C2×Q8—221no—
260C2×Q8—222no—
261C2×Q8—222no—
262C2×Q8C22×D1111yescharacteristic
263C2×D4—221no—
264C2×D4—221no—
265C2×D4C22×D1111yescharacteristic
266C2×D4C22×D1111yescharacteristic
267C22×C4—21no—
268C22×C4—111no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274Q16—222no—
275Q16—222no—
276Q16—222no—
277SD16—22no—
278SD16—222no—
279SD16—222no—
280SD16—222no—
281D8—22no—
282M16—222no—
283C2×C8—111no—
284C2×C8—111no—
285C2×C8—222no—
286C2×C8C22×D1111yescharacteristic
287C2×C8C22×D1111yescharacteristic
288C4⋊C4—111no—
289C4⋊C4—111no—
290C4⋊C4—111no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4C22×D1111yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—111no—
303C22⋊C4—111no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C42—111no—
308C42—221no—
309C42—221no—
310C42C22×D1111yescharacteristic
311C11#304611yescharacteristic, complemented, Sylow
312C23—21no—
313C23—21no—
314C23—111no—
315Q8—21no—
316Q8—21no—
317Q8—112no—
318Q8—221no—
319Q8—221no—
320Q8—221no—
321Q8—221no—
322Q8—221no—
323Q8—442no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—224no—
328D4—442no—
329D4D4×D1112yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—111no—
334C2×C4—112no—
335C2×C4—112no—
336C2×C4—111no—
337C2×C4—111no—
338C2×C4—224no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—881no—
346C2×C4—881no—
347C2×C4D4×D1111yescharacteristic
348C2×C4D4×D1111yescharacteristic
349C2×C4C23×D1111yescharacteristic
350C8—21no—
351C8—21no—
352C8—221no—
353C8—221no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—112no—
361C22—221no—
362C22—221no—
363C22C2×D4×D1111yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—112no—
369C4—221no—
370C4—221no—
371C4—222no—
372C4—441no—
373C4—441no—
374C4—441no—
375C4C2×D4×D1111yescharacteristic
376C4#41×D1111yescharacteristic
377C2—42no—
378C2—81no—
379C2—222no—
380C2D11×#12111yescharacteristic
381C2#1062330211yescharacteristic
382C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
prime radicalC2×#66965C2
hypercenter#463D11
hypocenterC11#3046
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#66968C2semidirect
3. #10623206C2semidirect
4. #10623077C2semidirect
5. C11×#463C2semidirect
6. #10622775C2semidirect
7. #10622766C2semidirect
8. #10622667C2semidirect
9. #10622632C2semidirect
10. #10622462C2semidirect
11. #10622452C2semidirect
12. D11×#103C2semidirect
13. #10622406C2semidirect
14. #10622384C2semidirect
15. #10622380C2semidirect
170. #463D11semidirect
311. C11#3046semidirect

Maximal subgroups

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

subgroupindex
C2×#669682
C2×#669652
#106232062
#106230772
C11×#4632
#106227752
#106227662
#106226672
#106226322
#106224622
#106224522
D11×#1032
#106224062
#106223842
#106223802
#304611