Finite Group Databasebeta

← #14649648

Subgroups — #14649648

Order 2816.

432 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078425C211yesmaximal, characteristic
2#13077281C211yesmaximal, characteristic
3#13067301C211yesmaximal, characteristic, complemented
4#13067001C211yesmaximal, characteristic
5#13066513C211yesmaximal, characteristic, complemented
6#13066491C211yesmaximal, characteristic, complemented
7C2×C11×#333C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C4×#4339C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12#10622723—21no—
13#10622714—21no—
14#10622707C412yes—
15#10622704—21no—
16#10622700C412yes—
17#10622697—21no—
18#10622579—21no—
19#10622577—21no—
20#10622538C2211yescharacteristic
21#10622537C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622453—22no—
24#10622448—21no—
25#10622446—21no—
26C11×#333—21no—
27C11×#333—21no—
28#10622185—22no—
29#10622122—21no—
30#10622121—21no—
31C22×Q8×C11—21no—
32C2×#4339D411yescharacteristic
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8C2×C412yes—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C4×C22⋊D11—21no—
43C4×C22⋊D11—21no—
44#66979D411yescharacteristic
45C2×#4318—21no—
46C2×#4318—21no—
47C4×D44C2×C411yescharacteristic
48C4×D44D411yescharacteristic
49#66925—21no—
50C42×D11—21no—
51C4×Dic22C2×C411yescharacteristic
52C4×Dic22D411yescharacteristic
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8D411yescharacteristic
57C11×C4⋊C8D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59(C2×D11)⋊C8—22no—
60(C2×D11)⋊C8—22no—
61#66879—22no—
62C8×Dic11—22no—
63#66874—22no—
64#66873—22no—
65#66872—22no—
66#66871—22no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)C2×C412yes—
71C4⋊(C11⋊C8)D412yes—
72C4×C11⋊C8—21no—
73#9170—111nomaximal, Sylow
74C2×Q8×C11—22no—
75C2×Q8×C11—41no—
76C2×Q8×C11—82no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×C22⋊D11—21no—
82#4339—21no—
83#4339—21no—
84#4339—21no—
85#4339—21no—
86C2×D44C22⋊C411yescharacteristic
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×Dic22C22⋊C411yescharacteristic
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—81no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C42×C11C22×C411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C22⋊Dic11—21no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108C4⋊Dic11C22⋊C411yescharacteristic
109C4⋊Dic11C22⋊C411yescharacteristic
110Dic11⋊C4—21no—
111Dic11⋊C4—21no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115#4318—41no—
116#4318—41no—
117#4318—41no—
118#4318—41no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122#3079—111no—
123#2925—111no—
124#1549—111no—
125C2×#333D1111yescharacteristic, complemented
126#1477—111no—
127#1301—111no—
128#1292—111no—
129C23×C11#12311yescharacteristic
130C22×D11—21no—
131Q8×C11—82no—
132Q8×C11—82no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—82no—
138C2×C4×C11C2×C22⋊C411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C22⋊D11—41no—
149C22⋊D11—41no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153D44—21no—
154D44—21no—
155C4×D11—41no—
156C4×D11—41no—
157C4×D11—41no—
158C4×D11—41no—
159C4×D11—81no—
160Dic22—21no—
161Dic22—21no—
162C8×C11—41no—
163C8×C11—41no—
164C8×C11—81no—
165C11⋊C8—42no—
166C11⋊C8—42no—
167C11⋊C8—81no—
168C2×C4⋊Q8C2×D1111yescharacteristic
169C4×#41—111no—
170#477—221no—
171#476—221no—
172#475—112no—
173#474—112no—
174#433—222no—
175#432—221no—
176#431—111no—
177#431—221no—
178#428—221no—
179#423—111no—
180#423—111no—
181C2×C4⋊C8C2×D1111yescharacteristic
182C2×C4⋊C8C2×D1111yescharacteristic
183#417—221no—
184#408—221no—
185#405—221no—
186#333—21no—
187#333—21no—
188#332—222no—
189Q8⋊C8—221no—
190D4⋊C8—221no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11#38611yescharacteristic
194C22×C11#48511yescharacteristic
195C22×C11#48511yescharacteristic
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—41no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—82no—
203C4×C11#41611yescharacteristic
204C4×C11#41911yescharacteristic
205C4×C11#45211yescharacteristic
206C4×C11#45211yescharacteristic
207C4×C11#47111yescharacteristic
208C4×C11#47311yescharacteristic
209Dic11—41no—
210Dic11—41no—
211Dic11—41no—
212C2×#41—111no—
213C22×Q8—21no—
214C2×M16—221no—
215C2×M16—221no—
216C22×C8—21no—
217C22×C8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8C4×D1112yes—
222C4×Q8—111no—
223C4×Q8—111no—
224C4×D4—111no—
225C4×D4—111no—
226C4×D4—221no—
227C4×D4—221no—
228#117—111no—
229#117—221no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C42—221no—
233C2×C42C22×D1111yescharacteristic
234#107—222no—
235#106—222no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—112no—
240C4⋊C8—112no—
241C4⋊C8—221no—
242C4⋊C8—221no—
243C4⋊C8—221no—
244C4⋊C8C22⋊D1111yescharacteristic
245C4⋊C8C22⋊D1111yescharacteristic
246#103—222no—
247#102—222no—
248C22⋊C8—222no—
249C22⋊C8—222no—
250C22⋊C8—221no—
251#97—222no—
252C4×C8—222no—
253C4×C8—221no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11#187311yescharacteristic
257C2×C11#190311yescharacteristic
258C2×C11#190811yescharacteristic
259D11—81no—
260#41—221no—
261#41—221no—
262#41—221no—
263#41—221no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—82no—
267C2×Q8—111no—
268C2×D4—111no—
269C2×D4—221no—
270C22×C4—41no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4#433911yescharacteristic
275C22×C4D4×D1111yescharacteristic
276C22×C4#434111yescharacteristic
277M16—441no—
278M16—441no—
279M16—441no—
280M16—441no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—81no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—441no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—111no—
295C4⋊C4—111no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C42—221no—
302C42—221no—
303C42—221no—
304C42C2×C4×D1111yescharacteristic
305C42D4×D1111yescharacteristic
306C42D4×D1111yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C11#917011yescharacteristic, complemented, Sylow
309C23—221no—
310C23#6693611yescharacteristic
311Q8—82no—
312Q8—82no—
313Q8—221no—
314Q8—221no—
315D4—221no—
316D4—221no—
317D4—441no—
318D4—441no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—82no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—881no—
332C2×C4C22⋊C4×D1111yescharacteristic
333C2×C4(C22⋊D11)⋊C411yescharacteristic
334C2×C4#6693711yescharacteristic
335C2×C4#6696811yescharacteristic
336C2×C4#6696911yescharacteristic
337C2×C4#6697111yescharacteristic
338C2×C4#6697211yescharacteristic
339C2×C4C4×C22⋊D1111yescharacteristic
340C2×C4#6699011yescharacteristic
341C2×C4#6699111yescharacteristic
342C8—41no—
343C8—41no—
344C8—81no—
345C8—442no—
346C8—442no—
347C8—881no—
348C22—21no—
349C22—21no—
350C22—441no—
351C22—441no—
352C22—441no—
353C22#1062242711yescharacteristic
354C22#1062242811yescharacteristic
355C22#1062256911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—82no—
360C4—441no—
361C4—441no—
362C4—441no—
363C4#1062241511yescharacteristic
364C4#1062241711yescharacteristic
365C4#1062278611yescharacteristic
366C4#1062279011yescharacteristic
367C4#1062280011yescharacteristic
368C4#1062280511yescharacteristic
369C2—21no—
370C2—21no—
371C2—881no—
372C2#1306892511yescharacteristic
373C2#1306909911yescharacteristic
374C2#1306913411yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#333C2
socleC22×C11#386
prime radicalC2×#4339D4
cosocleC2×C42×C11C23
hypercenterC2×#333D11
hypocenterC11#9170
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
3. #13067301C2semidirect
5. #13066513C2semidirect
6. #13066491C2semidirect
7. C2×C11×#333C2semidirect
125. C2×#333D11semidirect
308. C11#9170semidirect

Maximal subgroups

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

subgroupindex
#130784252
#130772812
#130673012
#130670012
#130665132
#130664912
C2×C11×#3332
#917011