Finite Group Databasebeta

← #13078591

Subgroups — #13078591

Order 1408.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623139C211yesmaximal, characteristic
2#10623054C211yesmaximal, characteristic, complemented
3C11×#482C211yesmaximal, characteristic, complemented
4#10622646C211yesmaximal, characteristic, complemented
5#10622609C211yesmaximal, characteristic, complemented
6#10622497C211yesmaximal, characteristic, complemented
7D11×#107C211yesmaximal, characteristic, complemented
8#10622480C211yesmaximal, characteristic, complemented
9#10622474C211yesmaximal, characteristic, complemented
10#10622397C211yesmaximal, characteristic, complemented
11#10622387C211yesmaximal, characteristic, complemented
12#10622385C211yesmaximal, characteristic, complemented
13#10622384C211yesmaximal, characteristic, complemented
14#10622340C211yesmaximal, characteristic, complemented
15#10622335C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C11×#121C2211yescharacteristic
19C11×#117C2211yescharacteristic
20#66992—21no—
21#66991—21no—
22#66991C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24#66977C2211yescharacteristic
25C2×#4313C2211yescharacteristic
26C2×C8×D11C2211yescharacteristic
27#66950C2211yescharacteristic
28#66945C2211yescharacteristic
29#66945C2211yescharacteristic
30C4⋊C4×D11C2211yescharacteristic
31C4⋊C4×D11C2211yescharacteristic
32C4⋊C4×D11C2211yescharacteristic
33#66937—21no—
34(C22⋊D11)⋊C4—21no—
35(C22⋊D11)⋊C4—21no—
36#66931—21no—
37C4×D44—21no—
38C4×Dic22—21no—
39C11×#107C2211yescharacteristic
40C11×#106C2211yescharacteristic
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×C22⋊C8C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46C22⋊(C11⋊C8)C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66880C2211yescharacteristic
52#66880C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11D411yescharacteristic
65C2×C22⋊D11D411yescharacteristic
66C22×Dic11—21no—
67C22×Dic11—21no—
68#4341—22no—
69#4341—22no—
70#4339—22no—
71#4339—22no—
72C2×D44D411yescharacteristic
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11C2311yescharacteristic
77C2×C4×D11C2311yescharacteristic
78C2×Dic22D411yescharacteristic
79C2×Dic22C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C42×C11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4313—22no—
107C8×D11—22no—
108#3098—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111C22×D11C2×D411yescharacteristic
112C22×D11C2×D411yescharacteristic
113D4×C11—21no—
114D4×C11—21no—
115D4×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C22⋊D11—22no—
124C22⋊D11—22no—
125C22⋊D11—42no—
126C22⋊D11—81no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—42no—
132C2×Dic11—81no—
133C2×Dic11C2×D411yescharacteristic
134C2×Dic11C2×D411yescharacteristic
135D44—22no—
136C4×D11—21no—
137C4×D11—21no—
138C4×D11—81no—
139C4×D11—81no—
140C4×D11—81no—
141C4×D11#4112yes—
142C4×D11#4112yes—
143Dic22—22no—
144Dic22—21no—
145Dic22—21no—
146C8×C11—21no—
147C8×C11—21no—
148C11⋊C8—21no—
149C11⋊C8—21no—
150#537—111no—
151#520—111no—
152#485—111no—
153#485—111no—
154#484—111no—
155#484—111no—
156#482—111no—
157#482D1111yescharacteristic, complemented
158#480—111no—
159#480—111no—
160#428—111no—
161C2×#107—111no—
162#417—111no—
163#416—111no—
164#408—111no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11C22×D411yescharacteristic
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—21no—
175C2×D11—21no—
176C2×D11—21no—
177C2×D11#12312yes—
178C4×C11—21no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11C2×#4111yescharacteristic
183C4×C11C2×#4111yescharacteristic
184Dic11—21no—
185Dic11—41no—
186Dic11—41no—
187Dic11—41no—
188Dic11—41no—
189Dic11#12312yes—
190C2×#41—111no—
191C2×#41—111no—
192C2×M16—111no—
193C22×C8—111no—
194C22⋊Q8—111no—
195C22⋊Q8—111no—
196C22⋊Q8—221no—
197#121—111no—
198#121—221no—
199#121—221no—
200#121—221no—
201#121C2×D1111yescharacteristic
202C4×Q8—221no—
203C4×D4—221no—
204C4×D4—221no—
205C4×D4—221no—
206#117—111no—
207#117—111no—
208#117C2×D1111yescharacteristic
209C2×C4⋊C4—111no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213#107—111no—
214#107—111no—
215#107—111no—
216#107—111no—
217#107—111no—
218#107C2×D1111yescharacteristic
219#106—111no—
220#106C2×D1111yescharacteristic
221#103—111no—
222#103—111no—
223#103—111no—
224#103—111no—
225#102—111no—
226#102—111no—
227#102C2×D1111yescharacteristic
228#102C2×D1111yescharacteristic
229C22⋊C8—111no—
230C22⋊C8—111no—
231C22⋊C8—111no—
232C22⋊C8C2×D1111yescharacteristic
233C2×C11—41no—
234C2×C11—81no—
235C2×C11C2×#12311yescharacteristic
236C2×C11#57611yescharacteristic
237C2×C11#57811yescharacteristic
238D11—22no—
239D11—41no—
240#41—222no—
241#41—222no—
242#41—222no—
243#41—222no—
244C2×Q8—111no—
245C2×Q8—111no—
246C2×D4—21no—
247C2×D4—111no—
248C2×D4—111no—
249C2×D4—111no—
250C2×D4—221no—
251C2×D4—221no—
252C2×D4C22×D1111yescharacteristic
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4C22×D1111yescharacteristic
261M16—222no—
262C2×C8—111no—
263C2×C8—111no—
264C2×C8—222no—
265C2×C8C22×D1111yescharacteristic
266C2×C8C22×D1111yescharacteristic
267C4⋊C4—111no—
268C4⋊C4—111no—
269C4⋊C4—111no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4C22×D1111yescharacteristic
277C4⋊C4C22×D1111yescharacteristic
278C4⋊C4C22×D1111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C42—21no—
287C42—221no—
288C42—221no—
289C11#309811yescharacteristic, complemented, Sylow
290C23—21no—
291C23—111no—
292C23—111no—
293C23D4×D1111yescharacteristic
294Q8—222no—
295Q8—221no—
296Q8—221no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—222no—
301D4—222no—
302D4—222no—
303D4—442no—
304D4—881no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—111no—
311C2×C4—112no—
312C2×C4—112no—
313C2×C4—111no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—442no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4—881no—
324C2×C4—881no—
325C2×C4D4×D1111yescharacteristic
326C2×C4C23×D1111yescharacteristic
327C8—21no—
328C8—21no—
329C8—221no—
330C8—221no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—112no—
338C22—221no—
339C22—221no—
340C22—221no—
341C22—221no—
342C22—221no—
343C22C2×D4×D1111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—112no—
349C4—221no—
350C4—441no—
351C4—441no—
352C4—441no—
353C4—441no—
354C4#41×D1111yescharacteristic
355C4#41×D1111yescharacteristic
356C2—41no—
357C2—81no—
358C2—222no—
359C2—441no—
360C2D11×#12311yescharacteristic
361C2#1062330211yescharacteristic
362C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#482C2
socleC22×C11C22×D4
prime radical#10623139C2
hypercenter#482D11
hypocenterC11#3098
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #10623054C2semidirect
3. C11×#482C2semidirect
4. #10622646C2semidirect
5. #10622609C2semidirect
6. #10622497C2semidirect
7. D11×#107C2semidirect
8. #10622480C2semidirect
9. #10622474C2semidirect
10. #10622397C2semidirect
11. #10622387C2semidirect
12. #10622385C2semidirect
13. #10622384C2semidirect
14. #10622340C2semidirect
15. #10622335C2semidirect
157. #482D11semidirect
289. C11#3098semidirect

Maximal subgroups

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

subgroupindex
#106231392
#106230542
C11×#4822
#106226462
#106226092
#106224972
D11×#1072
#106224802
#106224742
#106223972
#106223872
#106223852
#106223842
#106223402
#106223352
#309811