Finite Group Databasebeta

← #14655886

Subgroups — #14655886

Order 2816.

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

normal subgroups only

This group has 508 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#13079928C211yesmaximal, characteristic
2#13079561C211yesmaximal, characteristic, complemented
3#13079010C211yesmaximal, characteristic
4#13069564C211yesmaximal, characteristic, complemented
5#13067110C211yesmaximal, characteristic
6#13066467C211yesmaximal, characteristic, complemented
7C11×#1986C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9#10623008C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622746—22no—
14#10622706—21no—
15#10622705—21no—
16#10622697—21no—
17#10622696—21no—
18#10622663—22no—
19#10622661—22no—
20#10622644—22no—
21#10622640—21no—
22#10622633—21no—
23#10622538C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25#10622327—22no—
26#10622307—21no—
27#10622294—21no—
28C11×#339—22no—
29#10622167—22no—
30#10622089—22no—
31C2×#4339—21no—
32C22×Dic22—21no—
33C2×C11×M16D412yes—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×#125—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C11×#117—21no—
42C2×C11×C4⋊C4—21no—
43C2×C42×C11—21no—
44C2×C42×C11C2311yescharacteristic
45C2×#4326—24no—
46C2×#4325—22no—
47#66983—21no—
48#66983—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C22×C11⋊C8D412yes—
52#66928—21no—
53#66927D411yescharacteristic
54C4×D44—21no—
55C4×D44—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922D412yes—
60#66922D411yescharacteristic
61C11×#97—21no—
62C4×C8×C11—21no—
63C11×#95—21no—
64#66899—22no—
65C22⋊(C11⋊C8)D412yes—
66#66885—24no—
67#66880—24no—
68#66874—24no—
69#66873—22no—
70#66872—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4×C11⋊C8—21no—
75#10198—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C2×C22⋊D11—41no—
83C22×Dic11—41no—
84#4339—42no—
85#4339—42no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×C4×D11—41no—
90C2×Dic22—22no—
91C2×Dic22—21no—
92C2×Dic22—41no—
93C2×Dic22—82no—
94C11×M16—22no—
95C11×M16—22no—
96C2×C8×C11—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11—41no—
107C42×C11—42no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112#4326—84no—
113#4325—82no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—21no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—42no—
125#3246—111no—
126#3209—111no—
127#3141—111no—
128#1987—111no—
129#1986D1111yescharacteristic, complemented
130#1502—111no—
131#1283—111no—
132C23×C11#12711yescharacteristic
133C22×D11—41no—
134Q8×C11—42no—
135Q8×C11—41no—
136Q8×C11—41no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#13512yes—
152C2×C4×C11#13712yes—
153C22⋊D11—81no—
154C22⋊D11—81no—
155C2×Dic11—42no—
156C2×Dic11—41no—
157C2×Dic11—82no—
158D44—42no—
159D44—41no—
160D44—41no—
161D44—81no—
162C4×D11—82no—
163Dic22—44no—
164Dic22—42no—
165Dic22—82no—
166C8×C11—42no—
167C11⋊C8—42no—
168C11⋊C8—42no—
169#533C2×D1111yescharacteristic
170#532—111no—
171C2×C4⋊Q8—111no—
172#494—221no—
173#489—222no—
174#487—221no—
175#487—221no—
176#486—221no—
177#476—221no—
178#475—221no—
179#465—222no—
180#462—222no—
181#461—221no—
182#460—221no—
183#451—222no—
184#431—111no—
185C2×C4⋊C8—111no—
186#417—222no—
187C4×M16C2×D1111yescharacteristic
188C4×C4⋊C4C2×D1111yescharacteristic
189#340—222no—
190#339—22no—
191#327—222no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11#39211yescharacteristic
195C22×C11#49511yescharacteristic
196C22×C11#49711yescharacteristic
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—82no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11#45212yes—
207C4×C11#45511yescharacteristic
208C4×C11#45611yescharacteristic
209C4×C11#46412yes—
210Dic11—82no—
211Dic11—81no—
212C2×#41—221no—
213C22×Q8—221no—
214C2×Q16—224no—
215C2×SD16—222no—
216C2×M16C22⋊D1112yes—
217C22×C8—112no—
218C4⋊Q8—112no—
219C4⋊Q8—111no—
220C4⋊Q8—221no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8D4411yescharacteristic
224C4⋊Q8D4411yescharacteristic
225#127—111no—
226#125—21no—
227#124—221no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230#121—221no—
231#121—221no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×D4—221no—
235C4×D4—221no—
236#117—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C42—21no—
241C2×C42C22×D1111yescharacteristic
242#106—222no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246#103—224no—
247#103—224no—
248#103—222no—
249#102—222no—
250#102—224no—
251C22⋊C8—112no—
252#97—21no—
253C4×C8—21no—
254C4×C8—221no—
255#95—21no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11#200711yescharacteristic
259C2×C11#200811yescharacteristic
260C2×C11#201511yescharacteristic
261D11—161no—
262#41—442no—
263#41—442no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—222no—
267C2×Q8—221no—
268C2×Q8—441no—
269C2×Q8—882no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—441no—
274C22×C4—41no—
275C22×C4—441no—
276C22×C4—441no—
277C22×C4D4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C22×C4C2×C22⋊D1111yescharacteristic
280Q16—884no—
281SD16—882no—
282M16—22no—
283M16—22no—
284C2×C8—22no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8—442no—
288C4⋊C4—22no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—221no—
297C4⋊C4—222no—
298C4⋊C4—221no—
299C4⋊C4—222no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C22⋊C4—41no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C42—41no—
306C42—42no—
307C42C2×D4411yescharacteristic
308C42#433911yescharacteristic
309C42D4×D1111yescharacteristic
310C42D4×D1111yescharacteristic
311C11#1019811yescharacteristic, complemented, Sylow
312C23—441no—
313C23#6699311yescharacteristic
314Q8—42no—
315Q8—41no—
316Q8—41no—
317Q8—444no—
318Q8—442no—
319Q8—882no—
320D4—442no—
321D4—441no—
322D4—441no—
323D4—881no—
324D4—881no—
325D4—881no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—441no—
335C2×C4—442no—
336C2×C4—882no—
337C2×C4—882no—
338C2×C4#6693511yescharacteristic
339C2×C4#6693511yescharacteristic
340C2×C4#6693711yescharacteristic
341C2×C4#6693711yescharacteristic
342C2×C4#6698311yescharacteristic
343C2×C4#6699011yescharacteristic
344C2×C4#6699512yes—
345C2×C4#6700312yes—
346C8—42no—
347C8—442no—
348C8—442no—
349C22—21no—
350C22—21no—
351C22—881no—
352C22—881no—
353C22—881no—
354C22#1062257311yescharacteristic
355C22#1062267211yescharacteristic
356C22#1062269911yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—82no—
361C4—81no—
362C4—81no—
363C4—882no—
364C4—881no—
365C4#1062243811yescharacteristic
366C4#1062243911yescharacteristic
367C4#1062264112yes—
368C4#1062266012yes—
369C2—21no—
370C2—21no—
371C2—1761no—
372C2#1306966411yescharacteristic
373C2#1306967011yescharacteristic
374C2#1306970911yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1986C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1986D11
hypocenterC11#10198
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. #13079561C2semidirect
4. #13069564C2semidirect
6. #13066467C2semidirect
7. C11×#1986C2semidirect
129. #1986D11semidirect
311. C11#10198semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130795612
#130790102
#130695642
#130671102
#130664672
C11×#19862
#1019811