Finite Group Databasebeta

← #14649641

Subgroups — #14649641

Order 2816.

478 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078425C211yesmaximal, characteristic
2#13077181C211yesmaximal, 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
9C2×#66954—21no—
10C4×#4339C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13#10622715—21no—
14#10622707C412yes—
15#10622704—21no—
16#10622700C412yes—
17#10622697—21no—
18#10622579—21no—
19#10622577—21no—
20#10622538C2211yescharacteristic
21#10622537C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622452—22no—
24#10622450—21no—
25D11×C4⋊C8—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—
47#66954—42no—
48#66954—42no—
49C2×#4313—22no—
50C2×C8×D11—22no—
51C4×D44C2×C411yescharacteristic
52C4×D44D411yescharacteristic
53#66925—21no—
54C42×D11—21no—
55C4×Dic22C2×C411yescharacteristic
56C4×Dic22D411yescharacteristic
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D411yescharacteristic
61C11×C4⋊C8D411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63Dic11⋊C8—22no—
64Dic11⋊C8—22no—
65#66874—22no—
66#66873—22no—
67#66872—22no—
68#66871—22no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)C2×C412yes—
73C4⋊(C11⋊C8)D412yes—
74C4×C11⋊C8—21no—
75#9169—111nomaximal, Sylow
76C2×Q8×C11—22no—
77C2×Q8×C11—41no—
78C2×Q8×C11—82no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C2×C22⋊D11—21no—
84#4339—21no—
85#4339—21no—
86#4339SD1612yes—
87#4339Q1612yes—
88C2×D44C22⋊C411yescharacteristic
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×Dic22C22⋊C411yescharacteristic
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—81no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C42×C11C22×C411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C22⋊Dic11—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—21no—
110C4⋊Dic11C22⋊C411yescharacteristic
111C4⋊Dic11C22⋊C411yescharacteristic
112Dic11⋊C4—21no—
113Dic11⋊C4—21no—
114C4×Dic11—21no—
115C4×Dic11—21no—
116C4×Dic11—21no—
117#4318—41no—
118#4318—41no—
119#4318—41no—
120#4318—41no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—41no—
124#4313—44no—
125C8×D11—44no—
126#3079—111no—
127#2906—111no—
128#1549—111no—
129C2×#333D1111yescharacteristic, complemented
130#1477—111no—
131#1301—111no—
132#1292—111no—
133C23×C11#12311yescharacteristic
134C22×D11—21no—
135Q8×C11—82no—
136Q8×C11—82no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—82no—
142C2×C4×C11C2×C22⋊C411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11C2×SD1611yescharacteristic
149C2×C4×C11C2×Q1611yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C22⋊D11—22no—
153C22⋊D11—22no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157D44—21no—
158D44#10312yes—
159C4×D11—22no—
160C4×D11—22no—
161C4×D11—41no—
162C4×D11—41no—
163C4×D11—81no—
164Dic22—21no—
165Dic22#10312yes—
166C8×C11—41no—
167C8×C11—41no—
168C8×C11—81no—
169C11⋊C8—42no—
170C11⋊C8—42no—
171C11⋊C8—81no—
172C2×#131—221no—
173C2×C4⋊Q8C2×D1111yescharacteristic
174C4×#41—111no—
175#477—221no—
176#476—221no—
177#475—112no—
178#474—112no—
179#431—111no—
180#428—221no—
181#424—222no—
182#424—221no—
183#423—111no—
184#423—111no—
185#423—221no—
186C2×C4⋊C8—221no—
187C2×C4⋊C8C2×D1111yescharacteristic
188C2×C4⋊C8C2×D1111yescharacteristic
189#417—221no—
190#333—21no—
191#333—21no—
192#332—222no—
193Q8⋊C8—221no—
194D4⋊C8—221no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11#38611yescharacteristic
198C22×C11#48311yescharacteristic
199C22×C11#48411yescharacteristic
200C2×D11—22no—
201C2×D11—41no—
202C2×D11—41no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—82no—
207C4×C11C2×#10311yescharacteristic
208C4×C11#41711yescharacteristic
209C4×C11#45011yescharacteristic
210C4×C11#45111yescharacteristic
211C4×C11#47111yescharacteristic
212C4×C11#47311yescharacteristic
213Dic11—22no—
214Dic11—41no—
215Dic11—41no—
216C2×#41—111no—
217C22×Q8—21no—
218#131—442no—
219#131—442no—
220C2×M16—222no—
221C2×M16—221no—
222C2×M16—221no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—222no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8C4×D1112yes—
230C4×Q8—111no—
231C4×Q8—111no—
232C4×D4—111no—
233C4×D4—111no—
234C4×D4—221no—
235C4×D4—221no—
236#117—111no—
237#117—221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C42—221no—
241C2×C42C22×D1111yescharacteristic
242#107—222no—
243#106—222no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—112no—
248C4⋊C8—112no—
249C4⋊C8—222no—
250C4⋊C8—222no—
251C4⋊C8—221no—
252C4⋊C8—221no—
253C4⋊C8—221no—
254C4⋊C8C22⋊D1111yescharacteristic
255C4⋊C8C22⋊D1111yescharacteristic
256#103—222no—
257#102—222no—
258C22⋊C8—221no—
259C4×C8—221no—
260C2×C11—21no—
261C2×C11—21no—
262C2×C11#187211yescharacteristic
263C2×C11#190311yescharacteristic
264C2×C11#190811yescharacteristic
265D11—42no—
266#41—112no—
267#41—112no—
268#41—221no—
269#41—221no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—82no—
273C2×Q8—111no—
274C2×D4—111no—
275C2×D4—221no—
276C22×C4—41no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4#433911yescharacteristic
281C22×C4D4×D1111yescharacteristic
282C22×C4#434111yescharacteristic
283M16—444no—
284M16—441no—
285M16—441no—
286M16—441no—
287M16—441no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—81no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8—444no—
297C2×C8—441no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—111no—
303C4⋊C4—111no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C42—221no—
310C42—221no—
311C42—221no—
312C42C2×C4×D1111yescharacteristic
313C42D4×D1111yescharacteristic
314C42D4×D1111yescharacteristic
315C42C2×C22⋊D1111yescharacteristic
316C11#916911yescharacteristic, complemented, Sylow
317C23—221no—
318C23#6693611yescharacteristic
319Q8—82no—
320Q8—82no—
321Q8—112no—
322Q8—221no—
323D4—112no—
324D4—222no—
325D4—222no—
326D4—221no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—82no—
332C2×C4—221no—
333C2×C4—222no—
334C2×C4—222no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—881no—
340C2×C4C22⋊C4×D1111yescharacteristic
341C2×C4(C22⋊D11)⋊C411yescharacteristic
342C2×C4#6693711yescharacteristic
343C2×C4SD16×D1111yescharacteristic
344C2×C4#6696711yescharacteristic
345C2×C4Q16×D1111yescharacteristic
346C2×C4#6697111yescharacteristic
347C2×C4C4×C22⋊D1111yescharacteristic
348C2×C4#6699011yescharacteristic
349C2×C4#6699111yescharacteristic
350C8—41no—
351C8—41no—
352C8—81no—
353C8—442no—
354C8—442no—
355C8—881no—
356C22—21no—
357C22—21no—
358C22—222no—
359C22—441no—
360C22—441no—
361C22#1062241811yescharacteristic
362C22#1062242211yescharacteristic
363C22#1062256911yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—82no—
368C4—222no—
369C4—441no—
370C4—441no—
371C4D11×#10311yescharacteristic
372C4#1062241611yescharacteristic
373C4#1062278211yescharacteristic
374C4#1062279011yescharacteristic
375C4#1062279911yescharacteristic
376C4#1062280511yescharacteristic
377C2—21no—
378C2—21no—
379C2—442no—
380C2#1306892011yescharacteristic
381C2#1306909911yescharacteristic
382C2#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#9169
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
129. C2×#333D11semidirect
316. C11#9169semidirect

Maximal subgroups

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

subgroupindex
#130784252
#130771812
#130673012
#130670012
#130665132
#130664912
C2×C11×#3332
#916911