Finite Group Databasebeta

← #14655141

Subgroups — #14655141

Order 2816.

534 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079009C211yesmaximal, characteristic, complemented
2#13074556C211yesmaximal, characteristic, complemented
3#13067332C211yesmaximal, characteristic, complemented
4#13067214C211yesmaximal, characteristic, complemented
5#13067124C211yesmaximal, characteristic, complemented
6#13066508C211yesmaximal, characteristic, complemented
7C11×#3213C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×#124C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#496—21no—
12C11×#489—21no—
13C11×#463—22no—
14C11×#448—21no—
15C11×#447—21no—
16C11×#432C2211yescharacteristic
17#10622845—22no—
18#10622843—21no—
19#10622834—21no—
20#10622694—21no—
21#10622683—21no—
22#10622668—22no—
23#10622566—22no—
24#10622560—22no—
25#10622545C2211yescharacteristic
26#10622539C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622178—22no—
29#10622175—22no—
30#10622124—22no—
31C2×C11×#41—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C22×Dic22—21no—
35C2×C11×SD16—22no—
36C2×C11×D8—22no—
37C11×C4⋊Q8D411yescharacteristic
38C11×#127D411yescharacteristic
39C11×#124—21no—
40C11×#124—21no—
41C11×#124—21no—
42C11×#124—21no—
43C11×#124—21no—
44C11×#121—21no—
45C11×#121—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51C2×C22⋊Dic11—24no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11D412yes—
54C2×C4×Dic11—21no—
55C2×#4318—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60C11×C4⋊C8D412yes—
61C11×#103—22no—
62C11×#102—22no—
63C11×C22⋊C8—21no—
64C11×#97—21no—
65#66899—24no—
66#66896—24no—
67C11⋊#95—24no—
68C11⋊#95—21no—
69C11⋊#95D412yes—
70C22⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10092—111nomaximal, Sylow
76C24×C11—21no—
77C11×#41—44no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—42no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—42no—
88C2×D4×C11—41no—
89C22×C4×C11—21no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×Dic11—22no—
95C22×Dic11—22no—
96C2×Dic22—41no—
97C2×Dic22—41no—
98C2×Dic22—82no—
99C11×SD16—82no—
100C11×D8—82no—
101C2×C8×C11—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114C22⋊Dic11—84no—
115C4⋊Dic11—22no—
116C4⋊Dic11—22no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4×Dic11—42no—
120#4318—42no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—41no—
123#3213D1111yescharacteristic
124#3141—111no—
125#2640—111no—
126#1556—111no—
127#1527—111no—
128#1505—111no—
129#1300—111no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—42no—
135C23×C11#12011yescharacteristic
136Q8×C11—42no—
137Q8×C11—42no—
138Q8×C11—81no—
139D4×C11—42no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—81no—
143D4×C11—81no—
144D4×C11—82no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—82no—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12711yescharacteristic
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—44no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163Dic22—82no—
164Dic22—82no—
165C8×C11—42no—
166C11⋊C8—42no—
167C11⋊C8—81no—
168#532C2×D1111yescharacteristic
169C2×C4⋊Q8—111no—
170C2×#124C2×D1111yescharacteristic
171#496—21no—
172#489—21no—
173#489—222no—
174#487—221no—
175#486—221no—
176#463—22no—
177#448—21no—
178#447—21no—
179#432—111no—
180#432C2×D1111yescharacteristic
181#417—222no—
182C4×M16—111no—
183#397—222no—
184#393—222no—
185#391—221no—
186#390—221no—
187#376—111no—
188#332—222no—
189#329—222no—
190#327—222no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—84no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11#39211yescharacteristic
201C22×C11#45412yes—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11#45512yes—
210Dic11—82no—
211Dic11—82no—
212C2×#41—21no—
213C22×Q8—221no—
214C22×Q8C22⋊D1111yescharacteristic
215C22×D4C22⋊D1111yescharacteristic
216C2×SD16—22no—
217C2×D8—22no—
218C2×M16—221no—
219C4⋊Q8—221no—
220C4⋊Q8—221no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8C22⋊D1111yescharacteristic
224#127C22⋊D1111yescharacteristic
225#124—21no—
226#124—21no—
227#124—21no—
228#124—21no—
229#124—21no—
230#121—21no—
231#121—21no—
232C4×D4—21no—
233C4×D4—21no—
234C2×C4⋊C4—112no—
235C2×C4⋊C4—221no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—224no—
239C2×C42—221no—
240C2×C42C22×D1111yescharacteristic
241C4⋊C8—221no—
242C4⋊C8C22⋊D1112yes—
243#103—22no—
244#103—224no—
245#102—22no—
246#102—224no—
247C22⋊C8—21no—
248C22⋊C8—221no—
249#97—21no—
250#97—112no—
251#97—221no—
252C4×C8—221no—
253#95—112no—
254#95—224no—
255#95—221no—
256C2×C11—22no—
257C2×C11—161no—
258C2×C11—161no—
259C2×C11#200311yescharacteristic
260C2×C11#200411yescharacteristic
261C2×C11#200811yescharacteristic
262C24—21no—
263#41—44no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—42no—
268C2×Q8—441no—
269C2×Q8—441no—
270C2×Q8—882no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—42no—
277C2×D4—41no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4D4×D1111yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285SD16—82no—
286D8—82no—
287M16—442no—
288C2×C8—22no—
289C2×C8—222no—
290C2×C8—441no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—222no—
294C4⋊C4—222no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—884no—
304C42—442no—
305C42D4×D1111yescharacteristic
306C42#434111yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C42C2×C22⋊D1111yescharacteristic
309C11#1009211yescharacteristic, complemented, Sylow
310C23—42no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23—41no—
315C23#6699011yescharacteristic
316Q8—42no—
317Q8—42no—
318Q8—81no—
319Q8—882no—
320Q8—882no—
321D4—42no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—81no—
326D4—82no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—82no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—444no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4#6699011yescharacteristic
340C2×C4#6699111yescharacteristic
341C2×C4#6699211yescharacteristic
342C2×C4#6699211yescharacteristic
343C2×C4#6699311yescharacteristic
344C2×C4#6700611yescharacteristic
345C8—42no—
346C8—442no—
347C8—881no—
348C22—21no—
349C22—21no—
350C22—84no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22#1062281412yes—
358C22#1062283611yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—81no—
366C4—882no—
367C4—882no—
368C4#1062285512yes—
369C2—22no—
370C2—161no—
371C2—161no—
372C2#1306963511yescharacteristic
373C2#1306964311yescharacteristic
374C2#1306966611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3213C2
socleC22×C11#392
hypercenter#3213D11
hypocenterC11#10092
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3213

Complements

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

NH ≅ G/Ntype
1. #13079009C2semidirect
2. #13074556C2semidirect
3. #13067332C2semidirect
4. #13067214C2semidirect
5. #13067124C2semidirect
6. #13066508C2semidirect
309. C11#10092semidirect

Maximal subgroups

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

subgroupindex
#130790092
#130745562
#130673322
#130672142
#130671242
#130665082
C11×#32132
#1009211