Finite Group Databasebeta

← #14655714

Subgroups — #14655714

Order 2816.

578 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079737C211yesmaximal, characteristic
2#13079073C211yesmaximal, characteristic
3#13069461C211yesmaximal, characteristic, complemented
4#13067288C211yesmaximal, characteristic, complemented
5#13067068C211yesmaximal, characteristic
6#13066453C211yesmaximal, characteristic, complemented
7C2×C11×#500C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66995—22no—
11#10623008C2211yescharacteristic
12C11×#500—22no—
13C11×#500—22no—
14C2×C11×#107—22no—
15C2×C4×C8×C11C2211yescharacteristic
16C2×#66900—22no—
17#10622705—21no—
18#10622701—21no—
19#10622700—22no—
20#10622699—22no—
21#10622698—21no—
22#10622691—21no—
23#10622580—22no—
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26C4×#4318C2211yescharacteristic
27#10622185—22no—
28#10622097—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C2×#4339—21no—
32C22×C8×C11—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D412yes—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D412yes—
45C2×C42×C11C2311yescharacteristic
46C2×#4326—24no—
47#66995—44no—
48#66995—44no—
49C2×#4325—24no—
50#66983—21no—
51#66983—21no—
52C2×#4318—21no—
53C2×#4318D412yes—
54#66928—21no—
55#66927D411yescharacteristic
56C4×D44—21no—
57C4×D44—21no—
58#66922D411yescharacteristic
59C11×#107—28no—
60C4×C8×C11—21no—
61C4×C8×C11D412yes—
62#66900—44no—
63C22⋊(C11⋊C8)—21no—
64#66873—24no—
65#66871—24no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69#66867—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10174—111nomaximal, Sylow
73C2×Q8×C11—22no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—42no—
78C2×Q8×C11—42no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C22×C4×C11—22no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C2×C22⋊D11—41no—
87#4339—42no—
88#4339—42no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×C4×D11—41no—
93C2×Dic22—21no—
94C2×C8×C11—24no—
95C2×C8×C11—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108#4326—48no—
109#4325—48no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114#4318—22no—
115#4318—42no—
116#4318D814yes—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120#3226—111no—
121C2×#500D1111yescharacteristic, complemented
122#3152—111no—
123#1966—111no—
124#1546—111no—
125#1492—111no—
126#1278—111no—
127C23×C11#12111yescharacteristic
128C22×D11—41no—
129Q8×C11—44no—
130Q8×C11—82no—
131Q8×C11—81no—
132Q8×C11—81no—
133Q8×C11—81no—
134Q8×C11—81no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—44no—
140C2×C4×C11—82no—
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12711yescharacteristic
147C2×C4×C11C2×D812yes—
148C2×C4×C11AGL(1,ℤ/8)12yes—
149C22⋊D11—82no—
150C2×Dic11—41no—
151D44—42no—
152D44—42no—
153D44—42no—
154C4×D11—81no—
155C4×D11—81no—
156Dic22—42no—
157C8×C11—24no—
158C11⋊C8—24no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161C2×#137—222no—
162#532—111no—
163C2×C4⋊Q8C2×D1111yescharacteristic
164C2×C4⋊Q8C2×D1111yescharacteristic
165#500—22no—
166#500—22no—
167#500—221no—
168#497—222no—
169#494—221no—
170#492—221no—
171#486—221no—
172#480—222no—
173#474—222no—
174#431—111no—
175C2×#107—22no—
176#423—111no—
177C2×#101—222no—
178C4×M16—111no—
179C2×C4×C8C2×D1111yescharacteristic
180#332—222no—
181D4⋊C8—222no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11#39211yescharacteristic
185C22×C11#45912yes—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—82no—
192C4×C11—82no—
193C4×C11#44712yes—
194C4×C11#45612yes—
195C4×C11#47312yes—
196C4×C11#49311yescharacteristic
197C4×C11#49611yescharacteristic
198Dic11—81no—
199C2×#41—221no—
200C22×Q8—21no—
201C22×Q8—21no—
202#137—444no—
203#137—444no—
204C2×Q16—224no—
205C2×SD16—224no—
206C2×M16—112no—
207C2×M16—221no—
208C22×C8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—111no—
217C4⋊Q8C22⋊D1112yes—
218#127—111no—
219#124—221no—
220#121—221no—
221#121—221no—
222C4×D4—221no—
223C4×D4—221no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C22⋊D1112yes—
228C2×C42C22×D1111yescharacteristic
229#107—28no—
230#107—224no—
231C4⋊C8—112no—
232C4⋊C8—221no—
233C4⋊C8—221no—
234#102—224no—
235#101—444no—
236C22⋊C8—221no—
237#97—221no—
238C4×C8—21no—
239C4×C8—221no—
240C4×C8—221no—
241C4×C8C22⋊D1112yes—
242C2×C11—22no—
243C2×C11#200511yescharacteristic
244C2×C11#201111yescharacteristic
245C2×C11#202011yescharacteristic
246D11—161no—
247#41—442no—
248#41—442no—
249C2×Q8—22no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—441no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4—441no—
265C22×C4D4×D1111yescharacteristic
266C22×C4#434111yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268Q16—448no—
269SD16—448no—
270M16—114no—
271M16—222no—
272M16—442no—
273C2×C8—24no—
274C2×C8—22no—
275C2×C8—222no—
276C2×C8—222no—
277C2×C8—441no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C22⋊C4—441no—
289C22⋊C4—441no—
290C42D4×D1111yescharacteristic
291C42D4×D1111yescharacteristic
292C42C2×C22⋊D1111yescharacteristic
293C42C2×C22⋊D1111yescharacteristic
294C11#1017411yescharacteristic, complemented, Sylow
295C23—441no—
296C23#6699211yescharacteristic
297Q8—44no—
298Q8—81no—
299Q8—81no—
300Q8—81no—
301Q8—81no—
302Q8—82no—
303Q8—442no—
304D4—442no—
305D4—442no—
306D4—442no—
307D4—882no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—44no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—82no—
314C2×C4—441no—
315C2×C4—881no—
316C2×C4—881no—
317C2×C4D8×D1112yes—
318C2×C4#6696412yes—
319C2×C4#6699011yescharacteristic
320C2×C4#6699011yescharacteristic
321C2×C4#6699111yescharacteristic
322C2×C4#6699211yescharacteristic
323C2×C4#6699311yescharacteristic
324C2×C4#6700611yescharacteristic
325C8—24no—
326C8—224no—
327C8—442no—
328C8—881no—
329C22—21no—
330C22—21no—
331C22—881no—
332C22—881no—
333C22—881no—
334C22#1062276312yes—
335C22#1062283611yescharacteristic
336C4—21no—
337C4—21no—
338C4—82no—
339C4—82no—
340C4—881no—
341C4#1062270812yes—
342C4#1062276411yescharacteristic
343C4#1062276711yescharacteristic
344C4#1062276912yes—
345C4#1062280512yes—
346C2—22no—
347C2—1761no—
348C2#1306965211yescharacteristic
349C2#1306968511yescharacteristic
350C2#1306973511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#500C2
socleC22×C11#392
prime radical#10623008C22
hypercenterC2×#500D11
hypocenterC11#10174
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
3. #13069461C2semidirect
4. #13067288C2semidirect
6. #13066453C2semidirect
7. C2×C11×#500C2semidirect
121. C2×#500D11semidirect
294. C11#10174semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130790732
#130694612
#130672882
#130670682
#130664532
C2×C11×#5002
#1017411