Finite Group Databasebeta

← #13079521

Subgroups — #13079521

Order 1408.

402 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
1#10623160C211yesmaximal, characteristic, complemented
2#10623139C211yesmaximal, characteristic, complemented
3C11×#465C211yesmaximal, characteristic, complemented
4#10622786C211yesmaximal, characteristic, complemented
5#10622785C211yesmaximal, characteristic, complemented
6#10622727C211yesmaximal, characteristic, complemented
7#10622723C211yesmaximal, characteristic, complemented
8#10622665C211yesmaximal, characteristic, complemented
9#10622652C211yesmaximal, characteristic, complemented
10#10622476C211yesmaximal, characteristic, complemented
11#10622475C211yesmaximal, characteristic, complemented
12#10622423C211yesmaximal, characteristic, complemented
13#10622418C211yesmaximal, characteristic, complemented
14#10622394C211yesmaximal, characteristic, complemented
15#10622390C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C22×C8×C11C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22C11×#121C2211yescharacteristic
23#66999C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25#66992—21no—
26#66991—21no—
27#66991C2211yescharacteristic
28C2×#4323C2211yescharacteristic
29#66983C2211yescharacteristic
30#66977C2211yescharacteristic
31C2×#4318C2211yescharacteristic
32C2×#4314C2211yescharacteristic
33#66950C2211yescharacteristic
34#66949—21no—
35#66948—21no—
36#66948C2211yescharacteristic
37C4⋊C4×D11C2211yescharacteristic
38C4⋊C4×D11C2211yescharacteristic
39#66937—21no—
40#66937—21no—
41#66937—21no—
42#66931—21no—
43C11×#106C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66881C2211yescharacteristic
54#66880C2211yescharacteristic
55#66874C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66872C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11D411yescharacteristic
67C2×C22⋊D11D411yescharacteristic
68C22×Dic11—21no—
69#4343—41no—
70#4343—41no—
71#4341—41no—
72#4341—41no—
73#4339—41no—
74#4339—41no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44D411yescharacteristic
78C2×D44C2311yescharacteristic
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11C2311yescharacteristic
83C2×C4×D11C2311yescharacteristic
84C2×Dic22D411yescharacteristic
85C2×Dic22C2311yescharacteristic
86C11×SD16—41no—
87C2×C8×C11—41no—
88C2×C8×C11C2311yescharacteristic
89C2×C8×C11C2311yescharacteristic
90C11×C4⋊C4—21no—
91C11×C4⋊C4C2311yescharacteristic
92C11×C4⋊C4C2311yescharacteristic
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C22⋊Dic11—21no—
96C22⋊Dic11—21no—
97#4326—41no—
98#4323—41no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11C2311yescharacteristic
105C4⋊Dic11C2311yescharacteristic
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109Dic11⋊C4—21no—
110#4318—41no—
111C2×C11⋊C8C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113#4314—41no—
114#3204—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11C2×D411yescharacteristic
117C22×D11—21no—
118C22×D11C2×D411yescharacteristic
119C22×D11C2×D411yescharacteristic
120Q8×C11—21no—
121Q8×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—81no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C22⋊D11—41no—
133C22⋊D11—41no—
134C22⋊D11—42no—
135C22⋊D11—81no—
136C22⋊D11—81no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—42no—
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143D44—21no—
144D44—21no—
145D44—41no—
146D44—42no—
147D44—81no—
148C4×D11—21no—
149C4×D11—21no—
150C4×D11—21no—
151C4×D11—21no—
152C4×D11—42no—
153C4×D11—81no—
154C4×D11—81no—
155Dic22—21no—
156Dic22—21no—
157Dic22—41no—
158C8×C11—21no—
159C8×C11—21no—
160C11⋊C8—21no—
161C11⋊C8—21no—
162#537—111no—
163#537—111no—
164#483—111no—
165#483—111no—
166#481—111no—
167#481—111no—
168#470—111no—
169#469—111no—
170#465—111no—
171#465D1111yescharacteristic, complemented
172#452—111no—
173#452—111no—
174#449—111no—
175#449—111no—
176#408—111no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11C22×D411yescharacteristic
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C4×C11—21no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11H(5,𝔽2)11yescharacteristic
198C4×C11H(5,𝔽2)11yescharacteristic
199Dic11—21no—
200Dic11—21no—
201Dic11—41no—
202Dic11—41no—
203Dic11—41no—
204C2×#41—111no—
205C2×#41—111no—
206C2×#41—111no—
207C2×Q16—111no—
208C2×SD16—111no—
209C2×SD16C2×D1111yescharacteristic
210C2×D8—111no—
211C2×M16—111no—
212C22×C8C2×D1111yescharacteristic
213C22⋊Q8—111no—
214C22⋊Q8—111no—
215C22⋊Q8—111no—
216C22⋊Q8—221no—
217C22⋊Q8—221no—
218C22⋊Q8C2×D1111yescharacteristic
219#121—111no—
220#121—111no—
221#121—111no—
222#121—221no—
223#121—221no—
224#121—221no—
225#121—221no—
226#121—221no—
227#121—221no—
228#121C2×D1111yescharacteristic
229C2×C4⋊C4—111no—
230C2×C4⋊C4—111no—
231#106—111no—
232#106—111no—
233#106—111no—
234#106C2×D1111yescharacteristic
235#103—111no—
236#103—111no—
237#103—111no—
238#103C2×D1111yescharacteristic
239#102—111no—
240#102—111no—
241#102—111no—
242#102C2×D1111yescharacteristic
243C22⋊C8—111no—
244C22⋊C8—111no—
245C22⋊C8—111no—
246C22⋊C8—111no—
247C2×C11—41no—
248C2×C11—81no—
249C2×C11#53411yescharacteristic
250C2×C11#57711yescharacteristic
251C2×C11#57711yescharacteristic
252D11—41no—
253D11—41no—
254D11—81no—
255#41—441no—
256#41—441no—
257#41—441no—
258#41—441no—
259#41—441no—
260#41—441no—
261C2×Q8—111no—
262C2×Q8—111no—
263C2×Q8C22×D1111yescharacteristic
264C2×D4—21no—
265C2×D4—111no—
266C2×D4—111no—
267C2×D4—111no—
268C2×D4—111no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4C22×D1111yescharacteristic
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4C22×D1111yescharacteristic
282Q16—441no—
283SD16—41no—
284SD16—441no—
285D8—441no—
286M16—441no—
287C2×C8—41no—
288C2×C8—111no—
289C2×C8—111no—
290C2×C8C22×D1111yescharacteristic
291C2×C8C22×D1111yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—111no—
294C4⋊C4—111no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4C22×D1111yescharacteristic
301C4⋊C4C22×D1111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C11#320411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—111no—
313C23—111no—
314C23—221no—
315C23D4×D1111yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—221no—
319Q8—221no—
320Q8—441no—
321D4—21no—
322D4—21no—
323D4—81no—
324D4—221no—
325D4—221no—
326D4—441no—
327D4—442no—
328D4—441no—
329D4—441no—
330D4—442no—
331D4—881no—
332D4—881no—
333D4—881no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—111no—
340C2×C4—111no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—881no—
351C2×C4—881no—
352C2×C4D4×D1111yescharacteristic
353C2×C4C23×D1111yescharacteristic
354C8—21no—
355C8—21no—
356C8—221no—
357C8—221no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—221no—
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—221no—
379C4—221no—
380C4—441no—
381C4—441no—
382C4—441no—
383C4#6703711yescharacteristic
384C4#6704211yescharacteristic
385C2—41no—
386C2—81no—
387C2—441no—
388C2—441no—
389C2—881no—
390C2#1062313611yescharacteristic
391C2#1062329311yescharacteristic
392C2#1062330111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#465C2
socleC22×C11C22×D4
hypercenter#465D11
hypocenterC11#3204
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #10623160C2semidirect
2. #10623139C2semidirect
3. C11×#465C2semidirect
4. #10622786C2semidirect
5. #10622785C2semidirect
6. #10622727C2semidirect
7. #10622723C2semidirect
8. #10622665C2semidirect
9. #10622652C2semidirect
10. #10622476C2semidirect
11. #10622475C2semidirect
12. #10622423C2semidirect
13. #10622418C2semidirect
14. #10622394C2semidirect
15. #10622390C2semidirect
171. #465D11semidirect
310. C11#3204semidirect

Maximal subgroups

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

subgroupindex
#106231602
#106231392
C11×#4652
#106227862
#106227852
#106227272
#106227232
#106226652
#106226522
#106224762
#106224752
#106224232
#106224182
#106223942
#106223902
#320411