Finite Group Databasebeta

← #14653163

Subgroups — #14653163

Order 2816.

370 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079126C211yesmaximal, characteristic
2#13068746C211yesmaximal, characteristic
3#13067181C211yesmaximal, characteristic
4#13067180C211yesmaximal, characteristic
5#13067179C211yesmaximal, characteristic
6#13066909C211yesmaximal, characteristic
7C11×#1518C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622692C411yescharacteristic, complemented
13#10622692C411yescharacteristic, complemented
14#10622691C411yescharacteristic, complemented
15#10622691C411yescharacteristic, complemented
16#10622677—21no—
17#10622677—21no—
18#10622611—21no—
19#10622611—21no—
20#10622549C2211yescharacteristic
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×#328—22no—
24#10622176—22no—
25#10622167—21no—
26#10622167—21no—
27#10622105—22no—
28#10622093—21no—
29#10622092—21no—
30#10622090—22no—
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#125—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C11×#117—21no—
39C2×C11×C4⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41#66979—21no—
42C2×C4⋊Dic11—21no—
43#66977—21no—
44#66977—21no—
45C22×C11⋊C8D411yescharacteristic
46C22×C11⋊C8D411yescharacteristic
47#66923—21no—
48#66922C2×C411yescharacteristic
49#66922C2×C411yescharacteristic
50C4×Dic22—21no—
51C4×Dic22—21no—
52C11×C4⋊C8—21no—
53C11×C22⋊C8D412yes—
54C4×C8×C11—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C22⋊(C11⋊C8)D412yes—
60#66872—21no—
61#66872—21no—
62#66872—21no—
63#66872—21no—
64#66871—21no—
65#66871—21no—
66#66871—21no—
67#66871—21no—
68C4⋊(C11⋊C8)—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8C2×C411yescharacteristic
71C4×C11⋊C8C2×C411yescharacteristic
72C4×C11⋊C8D411yescharacteristic
73C4×C11⋊C8D411yescharacteristic
74#9759—111nomaximal, Sylow
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—41no—
82C2×Dic22—21no—
83C2×Dic22—21no—
84C2×C8×C11—22no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C22⋊C4—41no—
94C42×C11—41no—
95C42×C11C22×C411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11#4111yescharacteristic
98C42×C11#4111yescharacteristic
99C22⋊Dic11—41no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108C4×Dic11—41no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8C22⋊C411yescharacteristic
115C2×C11⋊C8C22⋊C411yescharacteristic
116C2×C11⋊C8C22⋊C411yescharacteristic
117C2×C11⋊C8C22⋊C411yescharacteristic
118#3160—111no—
119#1835—111no—
120#1518—111no—
121#1518—111no—
122#1518—111no—
123#1518D1111yescharacteristic
124#1452—111no—
125C23×C11#12711yescharacteristic
126Q8×C11—81no—
127Q8×C11—81no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11C2×C22⋊C411yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12411yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C2×C4×C11#13711yescharacteristic
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—81no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150Dic22—81no—
151Dic22—81no—
152C8×C11—42no—
153C11⋊C8—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156C11⋊C8—21no—
157C11⋊C8—42no—
158#533—111no—
159#533C2×D1111yescharacteristic
160#500—111no—
161#500—111no—
162#499—221no—
163#499—221no—
164#498—111no—
165#498—111no—
166#431—111no—
167#431C2×D1111yescharacteristic
168#427—221no—
169#427—221no—
170C2×C4×C8—111no—
171#382—111no—
172#382C2×D1111yescharacteristic
173#340—221no—
174#340—221no—
175#328—22no—
176#328—222no—
177#328—222no—
178#328—222no—
179#322—221no—
180#322—221no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11#39011yescharacteristic
184C22×C11#49711yescharacteristic
185C22×C11#49711yescharacteristic
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—81no—
191C4×C11—81no—
192C4×C11—161no—
193C4×C11#41911yescharacteristic
194C4×C11#41911yescharacteristic
195C4×C11#49111yescharacteristic
196C4×C11#49111yescharacteristic
197Dic11—81no—
198Dic11—81no—
199Dic11—161no—
200C22×C8—111no—
201C22×C8—111no—
202C4⋊Q8—111no—
203C4⋊Q8—111no—
204C4⋊Q8C4×D1111yescharacteristic
205C4⋊Q8C4×D1111yescharacteristic
206#125—21no—
207#125—221no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—221no—
211C22⋊Q8—221no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8—221no—
215C4×Q8—221no—
216#117—21no—
217#117—221no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—221no—
220C2×C42C22×D1111yescharacteristic
221#107—221no—
222#107—221no—
223#107—221no—
224#107—221no—
225#106—221no—
226#106—221no—
227#106—221no—
228#106—221no—
229C4⋊C8—21no—
230C4⋊C8—221no—
231C22⋊C8—112no—
232C22⋊C8C22⋊D1112yes—
233C4×C8—21no—
234C4×C8—111no—
235C4×C8—111no—
236C4×C8—111no—
237C4×C8—111no—
238C4×C8—221no—
239#95—21no—
240#95—21no—
241#95—221no—
242#95—221no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11#196011yescharacteristic
246C2×C11#197611yescharacteristic
247C2×C11#197611yescharacteristic
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—221no—
251C2×Q8—221no—
252C22×C4—41no—
253C22×C4—441no—
254C22×C4D4×D1111yescharacteristic
255C22×C4D4×D1111yescharacteristic
256C22×C4C2×C22⋊D1111yescharacteristic
257C2×C8—22no—
258C2×C8—111no—
259C2×C8—111no—
260C2×C8—111no—
261C2×C8—111no—
262C2×C8—221no—
263C2×C8—221no—
264C2×C8—221no—
265C2×C8—221no—
266C2×C8—222no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C22⋊C4—41no—
284C22⋊C4—441no—
285C42—41no—
286C42—441no—
287C42C2×C4×D1111yescharacteristic
288C42#433911yescharacteristic
289C42D4×D1111yescharacteristic
290C42#434111yescharacteristic
291C11#975911yescharacteristic, complemented, Sylow
292C23#6699311yescharacteristic
293Q8—81no—
294Q8—81no—
295Q8—881no—
296Q8—881no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—881no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4C22⋊C4×D1111yescharacteristic
310C2×C4(C22⋊D11)⋊C411yescharacteristic
311C2×C4#6693711yescharacteristic
312C2×C4#6693811yescharacteristic
313C2×C4#6696811yescharacteristic
314C2×C4#6696811yescharacteristic
315C2×C4#6697111yescharacteristic
316C2×C4#6697111yescharacteristic
317C2×C4C4×C22⋊D1111yescharacteristic
318C2×C4#6699211yescharacteristic
319C8—42no—
320C8—221no—
321C8—221no—
322C8—221no—
323C8—221no—
324C8—442no—
325C22—21no—
326C22—21no—
327C22#1062257011yescharacteristic
328C22#1062278011yescharacteristic
329C22#1062280311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—81no—
335C4—81no—
336C4—161no—
337C4—881no—
338C4—881no—
339C4—1761no—
340C4#1062241011yescharacteristic
341C4#1062241011yescharacteristic
342C4#1062241511yescharacteristic
343C4#1062241511yescharacteristic
344C2—21no—
345C2—21no—
346C2#1306943411yescharacteristic
347C2#1306951111yescharacteristic
348C2#1306951311yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1518C2
socleC22×C11#390
prime radicalC23×C11#127
cosocleC2×C42×C11C23
hypercenter#1518D11
hypocenterC11#9759
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
12. #10622692C4semidirect
13. #10622692C4semidirect
14. #10622691C4semidirect
15. #10622691C4semidirect
291. C11#9759semidirect

Maximal subgroups

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

subgroupindex
#130791262
#130687462
#130671812
#130671802
#130671792
#130669092
C11×#15182
#975911