Finite Group Databasebeta

← #13078163

Subgroups — #13078163

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×#66972C211yesmaximal, characteristic
2C2×#66971C211yesmaximal, characteristic, complemented
3#10623255C211yesmaximal, characteristic, complemented
4#10623105C211yesmaximal, characteristic, complemented
5C11×#462C211yesmaximal, characteristic, complemented
6#10622798C211yesmaximal, characteristic, complemented
7#10622795C211yesmaximal, characteristic, complemented
8#10622696C211yesmaximal, characteristic, complemented
9#10622641C211yesmaximal, characteristic, complemented
10#10622457C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622432C211yesmaximal, characteristic, complemented
13#10622431C211yesmaximal, characteristic, complemented
14#10622416C211yesmaximal, characteristic, complemented
15D11×#103C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic
20C2×C11×Q16C2211yescharacteristic
21C11×C4⋊Q8C2211yescharacteristic
22C4×Q8×C11C2211yescharacteristic
23#67000C2211yescharacteristic
24Q8×Dic11C2211yescharacteristic
25#66997C2211yescharacteristic
26C2×#4326C2211yescharacteristic
27C2×#4325C2211yescharacteristic
28C2×#4325C2211yescharacteristic
29C2×#4325C2211yescharacteristic
30#66972—24no—
31#66971—24no—
32C2×D88C2211yescharacteristic
33C2×#4314C2211yescharacteristic
34C2×#4313C2211yescharacteristic
35C2×C8×D11C2211yescharacteristic
36#66949—21no—
37#66949—21no—
38#66947—21no—
39#66947—21no—
40#66946—21no—
41#66946C2211yescharacteristic
42C4⋊C4×D11—21no—
43C4⋊C4×D11C2211yescharacteristic
44#66928C2211yescharacteristic
45C4×D44—21no—
46C4×D44C2211yescharacteristic
47#66925—21no—
48#66925C2211yescharacteristic
49C11×C4⋊C8C2211yescharacteristic
50C11×#103C2211yescharacteristic
51C11×#103C2211yescharacteristic
52#66899C2211yescharacteristic
53#66899C2211yescharacteristic
54#66885C2211yescharacteristic
55#66880C2211yescharacteristic
56Dic11⋊C8C2211yescharacteristic
57Dic11⋊C8C2211yescharacteristic
58#66874C2211yescharacteristic
59#66873C2211yescharacteristic
60C4⋊(C11⋊C8)C2211yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C2×Q8×C11C2311yescharacteristic
64#4343—22no—
65#4343—22no—
66#4343—22no—
67#4343D414yes—
68Q8×D11—22no—
69Q8×D11—22no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44C2311yescharacteristic
73C2×D44C2311yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11C2311yescharacteristic
81C2×Dic22—21no—
82C2×Dic22C2311yescharacteristic
83C11×Q16—22no—
84C11×Q16—22no—
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4C2311yescharacteristic
91C42×C11—21no—
92C42×C11C2311yescharacteristic
93#4326—22no—
94#4325—22no—
95#4325—22no—
96#4325—22no—
97(C2×D11)⋊C4—21no—
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)⋊C4D411yescharacteristic
104(C2×D11)⋊C4D411yescharacteristic
105C4⋊Dic11—21no—
106C4⋊Dic11C2311yescharacteristic
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109Dic11⋊C4—21no—
110Dic11⋊C4D411yescharacteristic
111Dic11⋊C4D411yescharacteristic
112C4×Dic11—21no—
113C4×Dic11C2311yescharacteristic
114C2×C11⋊C8C2311yescharacteristic
115C2×C11⋊C8C2311yescharacteristic
116D88—22no—
117#4314—22no—
118#4313—22no—
119C8×D11—22no—
120#3046—111nomaximal, Sylow
121C22×D11—21no—
122C22×D11—21no—
123C22×D11C2×D411yescharacteristic
124Q8×C11—21no—
125Q8×C11—21no—
126Q8×C11—21no—
127Q8×C11—21no—
128Q8×C11—21no—
129Q8×C11C2×D412yes—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11C2×D411yescharacteristic
135C2×C4×C11C2×D411yescharacteristic
136C2×C4×C11C2411yescharacteristic
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142D44—24no—
143D44—21no—
144D44—21no—
145D44—21no—
146D44—42no—
147D44C2×D412yes—
148C4×D11—24no—
149C4×D11—42no—
150C4×D11—42no—
151C4×D11—81no—
152C4×D11—81no—
153C4×D11—81no—
154C4×D11C2×D412yes—
155C4×D11#4112yes—
156Dic22—21no—
157Dic22—21no—
158Dic22—42no—
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#463—111no—
171#462—111no—
172#462D1111yescharacteristic, complemented
173#461—111no—
174#461—111no—
175#424—111no—
176#417—111no—
177C2×#103—111no—
178C22×C11C22×D411yescharacteristic
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—22no—
182C2×D11—41no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11#12112yes—
188C4×C11—22no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11C22×D411yescharacteristic
195C4×C11C2×#4111yescharacteristic
196Dic11—21no—
197Dic11—21no—
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×Q16C2×D1111yescharacteristic
208C2×Q16C2×D1111yescharacteristic
209C2×SD16—111no—
210C2×SD16—111no—
211C2×SD16—111no—
212C2×SD16—111no—
213C2×D8—111no—
214C2×M16—111no—
215C22×C8—111no—
216C4⋊Q8—111no—
217C4⋊Q8C2×D1111yescharacteristic
218#124—111no—
219#124—111no—
220#123—221no—
221#123—221no—
222C22⋊Q8—221no—
223C22⋊Q8—221no—
224C4×Q8—111no—
225C4×Q8C2×D1111yescharacteristic
226C4×D4—111no—
227C4×D4—111no—
228C4×D4—221no—
229C4×D4—221no—
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#103C2×D1111yescharacteristic
243#103C2×D1111yescharacteristic
244#102—111no—
245#102—111no—
246C2×C11C2×#12111yescharacteristic
247C2×C11#57711yescharacteristic
248C2×C11#57811yescharacteristic
249D11—22no—
250D11—42no—
251D11—81no—
252#41—114no—
253#41—222no—
254#41—222no—
255#41—222no—
256C2×Q8—111no—
257C2×Q8—221no—
258C2×Q8—222no—
259C2×Q8—222no—
260C2×Q8C22×D1111yescharacteristic
261C2×Q8C22×D1111yescharacteristic
262C2×Q8C22×D1111yescharacteristic
263C2×D4—111no—
264C2×D4—111no—
265C2×D4—221no—
266C2×D4—221no—
267C22×C4—111no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274Q16—22no—
275Q16—22no—
276Q16—222no—
277SD16—222no—
278SD16—222no—
279SD16—222no—
280SD16—222no—
281D8—222no—
282M16—222no—
283C2×C8—111no—
284C2×C8—111no—
285C2×C8—222no—
286C2×C8C22×D1111yescharacteristic
287C2×C8C22×D1111yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—111no—
292C4⋊C4—111no—
293C4⋊C4—111no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4C22×D1111yescharacteristic
299C22⋊C4—111no—
300C22⋊C4—111no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C42—21no—
308C42—111no—
309C42—221no—
310C42C22×D1111yescharacteristic
311C11#304611yescharacteristic, complemented, Sylow
312C23—111no—
313C23—221no—
314C23—221no—
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—221no—
321Q8—221no—
322Q8—442no—
323Q8D4×D1112yes—
324D4—112no—
325D4—224no—
326D4—221no—
327D4—221no—
328D4—221no—
329D4—442no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—111no—
335C2×C4—112no—
336C2×C4—112no—
337C2×C4—111no—
338C2×C4—111no—
339C2×C4—224no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4—881no—
347C2×C4D4×D1111yescharacteristic
348C2×C4D4×D1111yescharacteristic
349C2×C4C23×D1111yescharacteristic
350C8—21no—
351C8—21no—
352C8—221no—
353C8—221no—
354C22—112no—
355C22—221no—
356C22—221no—
357C22—222no—
358C22—441no—
359C22—441no—
360C22—441no—
361C22—441no—
362C22—441no—
363C22C2×D4×D1111yescharacteristic
364C4—21no—
365C4—21no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—112no—
371C4—221no—
372C4—221no—
373C4—441no—
374C4—441no—
375C4C2×D4×D1111yescharacteristic
376C4#41×D1111yescharacteristic
377C2—222no—
378C2—442no—
379C2—881no—
380C2D11×#12111yescharacteristic
381C2#1062329711yescharacteristic
382C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#462C2
socleC22×C11C22×D4
prime radicalC2×#66972C2
hypercenter#462D11
hypocenterC11#3046
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. C2×#66971C2semidirect
3. #10623255C2semidirect
4. #10623105C2semidirect
5. C11×#462C2semidirect
6. #10622798C2semidirect
7. #10622795C2semidirect
8. #10622696C2semidirect
9. #10622641C2semidirect
10. #10622457C2semidirect
11. #10622452C2semidirect
12. #10622432C2semidirect
13. #10622431C2semidirect
14. #10622416C2semidirect
15. D11×#103C2semidirect
172. #462D11semidirect
311. C11#3046semidirect

Maximal subgroups

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

subgroupindex
C2×#669722
C2×#669712
#106232552
#106231052
C11×#4622
#106227982
#106227952
#106226962
#106226412
#106224572
#106224522
#106224322
#106224312
#106224162
D11×#1032
#304611