Finite Group Databasebeta

← #13080903

Subgroups — #13080903

Order 1408.

386 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D11C211yesmaximal, characteristic, complemented
2#10623147C211yesmaximal, characteristic
3C11×#448C211yesmaximal, characteristic, complemented
4#10622838C211yesmaximal, characteristic, complemented
5#10622787C211yesmaximal, characteristic, complemented
6#10622783C211yesmaximal, characteristic, complemented
7#10622775C211yesmaximal, characteristic, complemented
8SD16×Dic11C211yesmaximal, characteristic, complemented
9#10622655C211yesmaximal, characteristic, complemented
10#10622428C211yesmaximal, characteristic, complemented
11#10622415C211yesmaximal, characteristic, complemented
12#10622407C211yesmaximal, characteristic, complemented
13#10622405C211yesmaximal, characteristic, complemented
14#10622342C211yesmaximal, characteristic, complemented
15#10622336C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C11×#121C2211yescharacteristic
21#66999—21no—
22#66999C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24#66997—21no—
25#66997C2211yescharacteristic
26#66992—21no—
27#66991C2211yescharacteristic
28#66989—21no—
29D4×Dic11C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31C4×C22⋊D11—21no—
32C4×C22⋊D11C2211yescharacteristic
33#66979C2211yescharacteristic
34#66977—21no—
35#66977C2211yescharacteristic
36C2×#4318C2211yescharacteristic
37C2×#4313C2211yescharacteristic
38#66945C2211yescharacteristic
39#66941C2211yescharacteristic
40#66938—21no—
41#66930—21no—
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66882C2211yescharacteristic
52#66881C2211yescharacteristic
53#66880C2211yescharacteristic
54#66880C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56C8×Dic11C2211yescharacteristic
57#66874C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11—22no—
61C2×Q8×C11—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×Q8×C11C2311yescharacteristic
64C2×D4×C11—21no—
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—21no—
69C2×C22⋊D11D411yescharacteristic
70C22×Dic11—21no—
71Q8×D11—22no—
72Q8×D11—41no—
73C2×C4×D11—21no—
74C2×C4×D11C2311yescharacteristic
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22C2311yescharacteristic
78C11×SD16—22no—
79C11×SD16—41no—
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11D411yescharacteristic
89#4324—41no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4D411yescharacteristic
93C4⋊Dic11—21no—
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4D411yescharacteristic
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107#4318—41no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111#3329—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11C2×D411yescharacteristic
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—42no—
119Q8×C11#4112yes—
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—81no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—42no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—22no—
132C22⋊D11—81no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—42no—
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141C4×D11—21no—
142C4×D11—21no—
143C4×D11—42no—
144Dic22—21no—
145Dic22—21no—
146Dic22—42no—
147Dic22—81no—
148C8×C11—21no—
149C8×C11—21no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152#555—111no—
153D4×Q8—111no—
154#487—111no—
155#485—111no—
156#485—111no—
157#477—111no—
158#468—111no—
159#468—111no—
160#461—111no—
161#448—111no—
162#448D1111yescharacteristic, complemented
163C4×SD16—111no—
164#436—111no—
165#419—111no—
166#419—111no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11C22×D411yescharacteristic
174C2×D11—21no—
175C2×D11—21no—
176C2×D11—21no—
177C4×C11—21no—
178C4×C11—22no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11C2×#4111yescharacteristic
182C4×C11H(5,𝔽2)11yescharacteristic
183Dic11—21no—
184Dic11—21no—
185Dic11—41no—
186Dic11—41no—
187Dic11—41no—
188Dic11—41no—
189Dic11#13712yes—
190C22×Q8—111no—
191C22×Q8C2×D1111yescharacteristic
192C2×SD16—111no—
193C2×SD16C2×D1111yescharacteristic
194C2×SD16C2×D1111yescharacteristic
195C2×M16—111no—
196C2×M16—111no—
197C4⋊Q8—111no—
198C4⋊Q8—111no—
199C4⋊Q8—221no—
200#124—221no—
201#124—221no—
202C22⋊Q8—111no—
203C22⋊Q8—111no—
204C22⋊Q8—221no—
205C22⋊Q8—221no—
206#121—111no—
207#121—221no—
208#121C2×D1111yescharacteristic
209C4×Q8—111no—
210C4×D4—111no—
211C4×D4—111no—
212C4×D4—221no—
213#117—111no—
214#117—111no—
215#117—221no—
216#107—111no—
217#107—111no—
218#106—111no—
219C4⋊C8—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103—111no—
224#103—111no—
225#103—111no—
226#103—111no—
227#103C2×D1111yescharacteristic
228#103C2×D1111yescharacteristic
229#102—111no—
230C22⋊C8—111no—
231C22⋊C8C2×D1111yescharacteristic
232C4×C8—111no—
233C2×C11—41no—
234C2×C11—81no—
235C2×C11#54611yescharacteristic
236C2×C11C2×#13711yescharacteristic
237C2×C11#57711yescharacteristic
238D11—41no—
239C2×Q8—21no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8—111no—
243C2×Q8—221no—
244C2×Q8—221no—
245C2×Q8—222no—
246C2×Q8—441no—
247C2×Q8C22×D1111yescharacteristic
248C2×Q8C22×D1111yescharacteristic
249C2×D4—21no—
250C2×D4—111no—
251C2×D4—221no—
252C2×D4C22×D1111yescharacteristic
253C22×C4—21no—
254C22×C4—111no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4C22×D1111yescharacteristic
258SD16—22no—
259SD16—41no—
260SD16—441no—
261M16—441no—
262M16—441no—
263C2×C8—111no—
264C2×C8—111no—
265C2×C8C22×D1111yescharacteristic
266C2×C8C22×D1111yescharacteristic
267C4⋊C4—111no—
268C4⋊C4—111no—
269C4⋊C4—111no—
270C4⋊C4—111no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4C22×D1111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—111no—
280C22⋊C4—111no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C42—111no—
288C42—221no—
289C42—221no—
290C42—221no—
291C11#332911yescharacteristic, complemented, Sylow
292C23—21no—
293C23—111no—
294C23D4×D1111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—221no—
300Q8—221no—
301Q8—442no—
302Q8—881no—
303Q8#434112yes—
304D4—21no—
305D4—21no—
306D4—81no—
307D4—222no—
308D4—881no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—111no—
316C2×C4—111no—
317C2×C4—111no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4D4×D1111yescharacteristic
327C2×C4C23×D1111yescharacteristic
328C8—21no—
329C8—21no—
330C8—221no—
331C8—221no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—221no—
339C22—221no—
340C22—221no—
341C22C2×D4×D1111yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—112no—
347C4—221no—
348C4—221no—
349C4—441no—
350C4—441no—
351C4—441no—
352C4—441no—
353C4C2×#434111yescharacteristic
354C4#6703711yescharacteristic
355C2—41no—
356C2—81no—
357C2—441no—
358C2#1062312211yescharacteristic
359C2#1062329311yescharacteristic
360C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#448C2
socleC22×C11C22×D4
prime radical#10623147C2
hypercenter#448D11
hypocenterC11#3329
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. Q8×C22⋊D11C2semidirect
3. C11×#448C2semidirect
4. #10622838C2semidirect
5. #10622787C2semidirect
6. #10622783C2semidirect
7. #10622775C2semidirect
8. SD16×Dic11C2semidirect
9. #10622655C2semidirect
10. #10622428C2semidirect
11. #10622415C2semidirect
12. #10622407C2semidirect
13. #10622405C2semidirect
14. #10622342C2semidirect
15. #10622336C2semidirect
162. #448D11semidirect
291. C11#3329semidirect

Maximal subgroups

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

subgroupindex
Q8×C22⋊D112
#106231472
C11×#4482
#106228382
#106227872
#106227832
#106227752
SD16×Dic112
#106226552
#106224282
#106224152
#106224072
#106224052
#106223422
#106223362
#332911