Finite Group Databasebeta

← #14657473

Subgroups — #14657473

Order 2816.

428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 99 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#13078088C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic, complemented
3#13067372C211yesmaximal, characteristic, complemented
4#13067291C211yesmaximal, characteristic
5#13067068C211yesmaximal, characteristic
6#13066491C211yesmaximal, characteristic, complemented
7C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66995—21no—
10#10623008C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×#66900—21no—
14#10622644—21no—
15#10622641—22no—
16#10622640—21no—
17#10622579—21no—
18#10622537C2211yescharacteristic
19#10622537C2211yescharacteristic
20#10622537C2211yescharacteristic
21C11×Q8⋊C8—21no—
22C11×Q8⋊C8—21no—
23#10622168—21no—
24#10622124—21no—
25#10622123—21no—
26#10622097—21no—
27#10622097—21no—
28#10622095—22no—
29C22×Q8×C11D411yescharacteristic
30C2×#4339—21no—
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C42×C11—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4326—22no—
42#66995—42no—
43#66995—42no—
44C2×#4325—22no—
45#66983—21no—
46#66983—21no—
47C2×#4318—21no—
48C2×#4318—21no—
49C2×#4318—21no—
50#66928—21no—
51#66927D411yescharacteristic
52C4×D44—21no—
53C4×D44—21no—
54#66922D411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C4×C8×C11—21no—
58C4×C8×C11D411yescharacteristic
59C4×C8×C11D411yescharacteristic
60#66900—42no—
61#66874—22no—
62#66873—22no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69#10459—111nomaximal, Sylow
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11SD1612yes—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×C22⋊D11—41no—
82#4339—41no—
83#4339—41no—
84#4339—41no—
85#4339—41no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×C4×D11—41no—
90C2×Dic22—21no—
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—42no—
94C2×C8×C11—41no—
95C2×C8×C11—81no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C42×C11—41no—
101C42×C11—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106#4326—44no—
107#4325—44no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112#4318—41no—
113#4318—41no—
114#4318—41no—
115#4318—41no—
116#4318—41no—
117#4318—41no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121#3037—111no—
122#1801—111no—
123#1566—111no—
124#1547—111no—
125#1492—111no—
126C2×Q8⋊C8D1111yescharacteristic, complemented
127#1292—111no—
128C23×C11#12311yescharacteristic
129C22×D11—41no—
130Q8×C11—22no—
131Q8×C11—22no—
132Q8×C11—41no—
133Q8×C11—41no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—81no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11#12411yescharacteristic
148C2×C4×C11C2×SD1611yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C22⋊D11—81no—
153C22⋊D11—81no—
154C2×Dic11—41no—
155D44—41no—
156D44—41no—
157D44—41no—
158D44—41no—
159D44—81no—
160C4×D11—81no—
161C4×D11—81no—
162Dic22—41no—
163Dic22—41no—
164C8×C11—22no—
165C8×C11—41no—
166C8×C11—81no—
167C11⋊C8—42no—
168C11⋊C8—81no—
169C11⋊C8—81no—
170C2×#137—221no—
171#532—111no—
172C2×C4×Q8C2×D1111yescharacteristic
173#464—222no—
174#462—221no—
175#460—221no—
176#423—111no—
177#423—111no—
178#423—111no—
179C2×C4⋊C8C2×D1111yescharacteristic
180#417—221no—
181C2×#101—221no—
182C2×C4×C8C2×D1111yescharacteristic
183#343—221no—
184#334—222no—
185#332—221no—
186#331—221no—
187Q8⋊C8—21no—
188Q8⋊C8—21no—
189D4⋊C8—221no—
190D4⋊C8—221no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11#39411yescharacteristic
194C22×C11#48111yescharacteristic
195C22×C11#48211yescharacteristic
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—42no—
203C4×C11—81no—
204C4×C11#44911yescharacteristic
205C4×C11#45011yescharacteristic
206C4×C11#46511yescharacteristic
207C4×C11#46911yescharacteristic
208C4×C11#47111yescharacteristic
209C4×C11#47311yescharacteristic
210Dic11—81no—
211C2×#41—221no—
212C22×Q8D4411yescharacteristic
213#137—442no—
214#137—442no—
215C2×Q16—222no—
216C2×SD16—222no—
217C2×M16—221no—
218C2×M16—221no—
219C2×M16—221no—
220C22×C8—21no—
221C22×C8—21no—
222C4⋊Q8—111no—
223#127—111no—
224#124—221no—
225#121—221no—
226#121—221no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×D4—221no—
232C4×D4—221no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4D4411yescharacteristic
235C2×C42—21no—
236C2×C42C22×D1111yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—112no—
240C4⋊C8—221no—
241C4⋊C8—221no—
242C4⋊C8—221no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245#103—222no—
246#102—222no—
247#101—442no—
248C4×C8—21no—
249C4×C8C22⋊D1111yescharacteristic
250C4×C8C22⋊D1111yescharacteristic
251C2×C11—21no—
252C2×C11—21no—
253C2×C11#203411yescharacteristic
254C2×C11#205011yescharacteristic
255C2×C11#205211yescharacteristic
256D11—161no—
257#41—441no—
258#41—441no—
259#41—441no—
260#41—441no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—221no—
267C2×Q8#431412yes—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—441no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—441no—
275C22×C4C2×D4411yescharacteristic
276C22×C4#434111yescharacteristic
277C22×C4#434111yescharacteristic
278Q16—444no—
279SD16—444no—
280M16—441no—
281M16—441no—
282M16—441no—
283M16—441no—
284M16—441no—
285M16—441no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—42no—
289C2×C8—41no—
290C2×C8—81no—
291C2×C8—222no—
292C2×C8—441no—
293C2×C8—441no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C42—41no—
303C42—41no—
304C42#433911yescharacteristic
305C42D4×D1111yescharacteristic
306C42D4×D1111yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C11#1045911yescharacteristic, complemented, Sylow
309C23—441no—
310C23#6693911yescharacteristic
311Q8—22no—
312Q8—22no—
313Q8—41no—
314Q8—41no—
315Q8—441no—
316Q8—441no—
317D4—441no—
318D4—441no—
319D4—441no—
320D4—441no—
321D4—881no—
322D4—881no—
323D4—881no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—441no—
333C2×C4—881no—
334C2×C4—881no—
335C2×C4#6693511yescharacteristic
336C2×C4#6693611yescharacteristic
337C2×C4#6693811yescharacteristic
338C2×C4C2×#431411yescharacteristic
339C2×C4#6695711yescharacteristic
340C2×C4#6696111yescharacteristic
341C2×C4#6696111yescharacteristic
342C2×C4#6698311yescharacteristic
343C2×C4#6699111yescharacteristic
344C2×C4#6699211yescharacteristic
345C8—22no—
346C8—41no—
347C8—81no—
348C8—442no—
349C8—881no—
350C8—881no—
351C22—21no—
352C22—21no—
353C22—881no—
354C22—881no—
355C22—881no—
356C22#1062234811yescharacteristic
357C22#1062235011yescharacteristic
358C22#1062257411yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—42no—
363C4—81no—
364C4—881no—
365C4#1062234411yescharacteristic
366C4#1062234711yescharacteristic
367C4#1062272711yescharacteristic
368C4#1062274811yescharacteristic
369C4#1062279011yescharacteristic
370C4#1062280511yescharacteristic
371C2—21no—
372C2—21no—
373C2—1761no—
374C2#1306980611yescharacteristic
375C2#1306990211yescharacteristic
376C2#1306991611yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×Q8⋊C8C2
socleC22×C11#394
prime radical#10623008C22
hypercenterC2×Q8⋊C8D11
hypocenterC11#10459
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #13068612C2semidirect
3. #13067372C2semidirect
6. #13066491C2semidirect
7. C2×C11×Q8⋊C8C2semidirect
126. C2×Q8⋊C8D11semidirect
308. C11#10459semidirect

Maximal subgroups

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

subgroupindex
#130780882
#130686122
#130673722
#130672912
#130670682
#130664912
C2×C11×Q8⋊C82
#1045911