Finite Group Databasebeta

← #14650127

Subgroups — #14650127

Order 2816.

406 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622635C211yesmaximal, characteristic
2#13077705C211yesmaximal, characteristic
3#13067217C211yesmaximal, characteristic
4#13066973C211yesmaximal, characteristic
5#13066485C211yesmaximal, characteristic
6#13066467C211yesmaximal, characteristic
7C11×#1491C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C2×#66899C411yescharacteristic
13C2×#66899C411yescharacteristic
14#10622637—21no—
15#10622637—22no—
16Q8×C11⋊C8—21no—
17#10622635—21no—
18#10622635—21no—
19#10622635—21no—
20#10622635—21no—
21C2×#66872C411yescharacteristic
22C2×#66871C411yescharacteristic
23#10622539—21no—
24#10622539C2211yescharacteristic
25#10622538—21no—
26#10622538C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C11×Q8⋊C8—21no—
29C11×Q8⋊C8—21no—
30#10622107—21no—
31#10622107—21no—
32#10622103—22no—
33C22×Q8×C11C2×C411yescharacteristic
34C2×C11×M16—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11D411yescharacteristic
38C4×Q8×C11D411yescharacteristic
39C4×Q8×C11D411yescharacteristic
40C4×Q8×C11D411yescharacteristic
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C42×C11—21no—
44C2×C42×C11C2311yescharacteristic
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C22×C11⋊C8C2×C411yescharacteristic
50C22×C11⋊C8C2×C411yescharacteristic
51#66923—21no—
52#66923—21no—
53#66923—21no—
54#66923—21no—
55C11×C4⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×#97—21no—
58C11×#97—21no—
59C4×C8×C11—21no—
60#66899—21no—
61#66899—21no—
62#66899—21no—
63#66899—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)D411yescharacteristic
66C22⋊(C11⋊C8)D411yescharacteristic
67#66872—21no—
68#66872—21no—
69#66871—21no—
70#66871—21no—
71C4⋊(C11⋊C8)—22no—
72C4⋊(C11⋊C8)—22no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77#66867—22no—
78#66867D412yes—
79C4×C11⋊C8—22no—
80C4×C11⋊C8—21no—
81#9246—111nomaximal, Sylow
82C2×Q8×C11—21no—
83C2×Q8×C11—22no—
84C2×Q8×C11—41no—
85C2×Q8×C11C22⋊C411yescharacteristic
86C2×Q8×C11C22⋊C411yescharacteristic
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×Dic11—21no—
93C22×Dic11—21no—
94C11×M16—22no—
95C11×M16—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4C22⋊C411yescharacteristic
104C11×C4⋊C4C22⋊C411yescharacteristic
105C42×C11—21no—
106C42×C11—21no—
107C42×C11—21no—
108C42×C11—21no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121C2×C11⋊C8—21no—
122C2×C11⋊C8—21no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—21no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×#479—111no—
129#2984—111no—
130#1528—111no—
131#1491D1111yescharacteristic
132#1470—111no—
133#1290—111no—
134#1283—111no—
135C23×C11C4×D411yescharacteristic
136Q8×C11—21no—
137Q8×C11—21no—
138Q8×C11—21no—
139Q8×C11—42no—
140Q8×C11#10112yes—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11C2×C22⋊C411yescharacteristic
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12311yescharacteristic
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—81no—
164C8×C11—42no—
165C8×C11—81no—
166C11⋊C8—41no—
167C11⋊C8—41no—
168C11⋊C8—42no—
169C11⋊C8—41no—
170C11⋊C8—41no—
171C2×#125—111no—
172C2×C4×Q8C2×D1111yescharacteristic
173#479—221no—
174#479—221no—
175#479—221no—
176#479—221no—
177#446—222no—
178#446—221no—
179C8×Q8—221no—
180#432—111no—
181#432—221no—
182#432C2×D1111yescharacteristic
183#431—111no—
184#431—221no—
185C2×#107—111no—
186C2×#106—111no—
187C2×C4⋊C8—111no—
188C2×#103—111no—
189C2×#103—111no—
190C4×M16C2×D1111yescharacteristic
191#330—222no—
192Q8⋊C8—21no—
193Q8⋊C8—21no—
194#324—221no—
195#324—221no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11#38611yescharacteristic
199C22×C11#44311yescharacteristic
200C22×C11#44411yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—22no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11C2×#10111yescharacteristic
211C4×C11#41311yescharacteristic
212Dic11—81no—
213Dic11—81no—
214C22×Q8C4×D1111yescharacteristic
215C2×M16—21no—
216C22×C8—111no—
217C22×C8—111no—
218#125—221no—
219#125—221no—
220#125—221no—
221#125—221no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8D4411yescharacteristic
225C4×Q8D4411yescharacteristic
226C4×Q8C22⋊D1111yescharacteristic
227C4×Q8C22⋊D1111yescharacteristic
228C2×C4⋊C4—21no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4C4×D1111yescharacteristic
234C2×C42—21no—
235C2×C42C22×D1111yescharacteristic
236#107—221no—
237#107—221no—
238#106—221no—
239#106—221no—
240C4⋊C8—21no—
241C4⋊C8—222no—
242C4⋊C8—222no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246C4⋊C8—221no—
247#103—221no—
248#103—221no—
249#103—221no—
250#103—221no—
251C22⋊C8—21no—
252C22⋊C8—111no—
253C22⋊C8—111no—
254C22⋊C8—221no—
255#97—21no—
256#97—21no—
257#97—112no—
258#97—222no—
259C4×C8—21no—
260C4×C8—222no—
261C4×C8—221no—
262C2×C11—21no—
263C2×C11—21no—
264C2×C11#187611yescharacteristic
265C2×C11#190111yescharacteristic
266C2×C11#190511yescharacteristic
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8(C2×D11)⋊C411yescharacteristic
271C2×Q8(C2×D11)⋊C411yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4C2×C4×D1111yescharacteristic
277C22×C4D4×D1111yescharacteristic
278C22×C4#434111yescharacteristic
279M16—22no—
280M16—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—221no—
284C2×C8—222no—
285C2×C8—221no—
286C2×C8—221no—
287C2×C8—221no—
288C2×C8—441no—
289C2×C8—441no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—441no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C4⋊C4(C2×D11)⋊C411yescharacteristic
304C4⋊C4(C2×D11)⋊C411yescharacteristic
305C42—21no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42C2×D4411yescharacteristic
310C42D4×D1111yescharacteristic
311C42#434111yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C11#924611yescharacteristic, complemented, Sylow
314C23(C22⋊D11)⋊C411yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—42no—
319Q8#6688812yes—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—881no—
337C2×C4(C22⋊D11)⋊C411yescharacteristic
338C2×C4#6693511yescharacteristic
339C2×C4#6693911yescharacteristic
340C2×C4C2×(C2×D11)⋊C411yescharacteristic
341C2×C4#6699211yescharacteristic
342C2×C4#6699211yescharacteristic
343C8—42no—
344C8—81no—
345C8—441no—
346C8—442no—
347C8—441no—
348C8—441no—
349C8—441no—
350C22—21no—
351C22—21no—
352C22#1062243611yescharacteristic
353C22#1062243711yescharacteristic
354C22#1062257111yescharacteristic
355C4—21no—
356C4—22no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—881no—
365C4—881no—
366C4#1062274511yescharacteristic
367C4C2×#6688811yescharacteristic
368C2—21no—
369C2—21no—
370C2#1306894111yescharacteristic
371C2#1306908211yescharacteristic
372C2#1306910811yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1491C2
socleC22×C11#386
prime radicalC23×C11C4×D4
cosocleC2×C42×C11C23
hypercenter#1491D11
hypocenterC11#9246
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
313. C11#9246semidirect

Maximal subgroups

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

subgroupindex
C2×#106226352
#130777052
#130672172
#130669732
#130664852
#130664672
C11×#14912
#924611