Finite Group Databasebeta

← #13079296

Subgroups — #13079296

Order 1408.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623250C211yesmaximal, characteristic, complemented
2#10623213C211yesmaximal, characteristic, complemented
3C11×#496C211yesmaximal, characteristic, complemented
4#10622787C211yesmaximal, characteristic, complemented
5#10622784C211yesmaximal, characteristic, complemented
6#10622777C211yesmaximal, characteristic, complemented
7SD16×Dic11C211yesmaximal, characteristic, complemented
8#10622772C211yesmaximal, characteristic, complemented
9#10622770C211yesmaximal, characteristic, complemented
10#10622765C211yesmaximal, characteristic, complemented
11D8×Dic11C211yesmaximal, characteristic, complemented
12#10622683C211yesmaximal, characteristic, complemented
13#10622669C211yesmaximal, characteristic, complemented
14#10622321C211yesmaximal, characteristic, complemented
15#10622315C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C2×C11×D8C2211yescharacteristic
19C2×C11×D8C2211yescharacteristic
20C11×#127C2211yescharacteristic
21C11×#124C2211yescharacteristic
22#66999C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24#66992—21no—
25#66992—21no—
26#66991C2211yescharacteristic
27#66991C2211yescharacteristic
28#66991C2211yescharacteristic
29#66988—21no—
30#66988—21no—
31D4×Dic11C2211yescharacteristic
32D4×Dic11C2211yescharacteristic
33D4×Dic11C2211yescharacteristic
34C2×#4313C2211yescharacteristic
35C2×C8×D11C2211yescharacteristic
36#66939—21no—
37#66938—21no—
38#66932—21no—
39#66931—21no—
40#66925C2211yescharacteristic
41#66923C2211yescharacteristic
42#66922C2211yescharacteristic
43C11×#97C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50#66896C2211yescharacteristic
51#66896C2211yescharacteristic
52#66882C2211yescharacteristic
53#66882C2211yescharacteristic
54#66881C2211yescharacteristic
55#66881C2211yescharacteristic
56#66879C2211yescharacteristic
57C8×Dic11C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C2×C4×D11C2311yescharacteristic
72C2×Dic22—21no—
73C11×SD16—22no—
74C11×SD16—22no—
75C11×D8—22no—
76C11×D8—22no—
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C22⋊C4—21no—
80C11×C22⋊C4—21no—
81C42×C11C2311yescharacteristic
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4D411yescharacteristic
90(C2×D11)⋊C4D411yescharacteristic
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4D411yescharacteristic
101Dic11⋊C4D411yescharacteristic
102C4×Dic11—21no—
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4313—22no—
107C8×D11—22no—
108#3179—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C22×D11C2×D411yescharacteristic
113Q8×C11—21no—
114Q8×C11—21no—
115D4×C11—21no—
116D4×C11—21no—
117D4×C11—21no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11—21no—
121D4×C11—81no—
122D4×C11—81no—
123C2×C4×C11—21no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C22⋊D11—81no—
128C22⋊D11—81no—
129C22⋊D11—81no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140C4×D11—21no—
141C4×D11—21no—
142Dic22—81no—
143C8×C11#4112yes—
144C8×C11#4112yes—
145C11⋊C8—21no—
146C11⋊C8—21no—
147#542—111no—
148#540—111no—
149#501—111no—
150#496D1111yescharacteristic, complemented
151#488—111no—
152#486—111no—
153#469—111no—
154#468—111no—
155#466—111no—
156#465—111no—
157#442—111no—
158#440—111no—
159C4×SD16—111no—
160C4×D8—111no—
161#405—111no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11C22×D411yescharacteristic
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—41no—
178C4×C11C2×#4111yescharacteristic
179C4×C11C2×#4111yescharacteristic
180Dic11—21no—
181Dic11—21no—
182Dic11—21no—
183Dic11—41no—
184Dic11—41no—
185Dic11—41no—
186Dic11—41no—
187C2×SD16C2×D1111yescharacteristic
188C2×SD16C2×D1111yescharacteristic
189C2×D8C2×D1111yescharacteristic
190C2×D8C2×D1111yescharacteristic
191C2×M16—111no—
192C22×C8—111no—
193C4⋊Q8—111no—
194#127C2×D1111yescharacteristic
195#126—221no—
196#125—111no—
197#124—221no—
198#124C2×D1111yescharacteristic
199#123—221no—
200#123—221no—
201#123—221no—
202C22⋊Q8—111no—
203C22⋊Q8—221no—
204#121—111no—
205#121—111no—
206#121—111no—
207#121—221no—
208#121—221no—
209C4×Q8—111no—
210C4×D4—111no—
211C4×D4—111no—
212C4×D4—111no—
213#117—111no—
214#107—111no—
215#107—111no—
216#106—111no—
217#106—111no—
218#103—111no—
219#103—111no—
220#102—111no—
221#102—111no—
222#102—111no—
223#102—111no—
224#102—111no—
225#102—111no—
226#97—111no—
227#97C2×D1111yescharacteristic
228C4×C8—111no—
229C4×C8—111no—
230C2×C11—81no—
231C2×C11—81no—
232C2×C11—81no—
233C2×C11#53211yescharacteristic
234C2×C11#57611yescharacteristic
235C2×C11#57711yescharacteristic
236D11—41no—
237C2×Q8—221no—
238C2×Q8C22×D1111yescharacteristic
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4C22×D1111yescharacteristic
245C2×D4C22×D1111yescharacteristic
246C2×D4C22×D1111yescharacteristic
247C22×C4—111no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—221no—
251SD16—22no—
252SD16—22no—
253D8—22no—
254D8—22no—
255M16—222no—
256C2×C8—111no—
257C2×C8—111no—
258C2×C8—222no—
259C2×C8C22×D1111yescharacteristic
260C2×C8C22×D1111yescharacteristic
261C4⋊C4—111no—
262C4⋊C4—111no—
263C4⋊C4—111no—
264C4⋊C4—111no—
265C4⋊C4—111no—
266C4⋊C4—111no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—111no—
275C22⋊C4—111no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C42—111no—
284C42—221no—
285C42C22×D1111yescharacteristic
286C11#317911yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—111no—
291Q8—21no—
292Q8—21no—
293Q8—881no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—881no—
303D4—881no—
304D4—881no—
305C2×C4—21no—
306C2×C4—111no—
307C2×C4—111no—
308C2×C4—111no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—881no—
316C2×C4—881no—
317C2×C4—881no—
318C2×C4D4×D1111yescharacteristic
319C2×C4D4×D1111yescharacteristic
320C2×C4C23×D1111yescharacteristic
321C8—221no—
322C8—221no—
323C8#434112yes—
324C8#434112yes—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—221no—
335C22—221no—
336C22—221no—
337C22C2×D4×D1111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—221no—
342C4—221no—
343C4—221no—
344C4—441no—
345C4—441no—
346C4—441no—
347C4—441no—
348C4C2×#434111yescharacteristic
349C4C2×#434111yescharacteristic
350C2—81no—
351C2—81no—
352C2—81no—
353C2—441no—
354C2#1062324711yescharacteristic
355C2#1062330511yescharacteristic
356C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#496C2
socleC22×C11C22×D4
hypercenter#496D11
hypocenterC11#3179
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #10623250C2semidirect
2. #10623213C2semidirect
3. C11×#496C2semidirect
4. #10622787C2semidirect
5. #10622784C2semidirect
6. #10622777C2semidirect
7. SD16×Dic11C2semidirect
8. #10622772C2semidirect
9. #10622770C2semidirect
10. #10622765C2semidirect
11. D8×Dic11C2semidirect
12. #10622683C2semidirect
13. #10622669C2semidirect
14. #10622321C2semidirect
15. #10622315C2semidirect
150. #496D11semidirect
286. C11#3179semidirect

Maximal subgroups

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

subgroupindex
#106232502
#106232132
C11×#4962
#106227872
#106227842
#106227772
SD16×Dic112
#106227722
#106227702
#106227652
D8×Dic112
#106226832
#106226692
#106223212
#106223152
#317911