Finite Group Databasebeta

← #14655557

Subgroups — #14655557

Order 2816.

544 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079760C211yesmaximal, characteristic, complemented
2#13078991C211yesmaximal, characteristic
3C2×#10622701C211yesmaximal, characteristic
4#13067285C211yesmaximal, characteristic
5#13067070C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#1966C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66927C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×#101—22no—
13C4×C11×M16C2211yescharacteristic
14#10622744—22no—
15#10622707—22no—
16#10622706—21no—
17#10622701—22no—
18#10622701—22no—
19#10622692—21no—
20#10622584—22no—
21C2×#66873—22no—
22#10622538C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622326—22no—
25#10622307—21no—
26#10622307—21no—
27#10622123—22no—
28#10622122—22no—
29C22×Q8×C11—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44—21no—
33C2×C11×M16—21no—
34C2×C11×M16D412yes—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4D412yes—
41C2×C42×C11C2311yescharacteristic
42#66979—21no—
43#66977—21no—
44#66977—21no—
45C22×C11⋊C8—21no—
46#66927—21no—
47#66927—21no—
48#66927—21no—
49#66927D412yes—
50#66923—21no—
51#66922D411yescharacteristic
52#66922D411yescharacteristic
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×#101—44no—
58C11×#97—21no—
59C4×C8×C11—21no—
60C22⋊(C11⋊C8)—21no—
61#66885—24no—
62#66885—24no—
63#66874—24no—
64#66873—28no—
65#66872—24no—
66C4⋊(C11⋊C8)D412yes—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10151—111nomaximal, Sylow
71C23×D11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—42no—
75C2×Q8×C11—42no—
76C22×C4×C11—22no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×D44—22no—
81C2×D44—22no—
82C2×D44—22no—
83C2×D44—44no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—42no—
88C2×D44—42no—
89C2×D44—82no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C11×M16—22no—
93C11×M16—22no—
94C11×M16—42no—
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C22⋊Dic11—41no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110Dic11⋊C4—41no—
111Dic11⋊C4—41no—
112C4×Dic11—41no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—42no—
116#3229—111no—
117#3138—111no—
118C2×#486—111no—
119#1966D1111yescharacteristic, complemented
120#1545—111no—
121#1493—111no—
122#1278—111no—
123C23×C11#12111yescharacteristic
124C22×D11—42no—
125C22×D11—82no—
126C22×D11—82no—
127C22×D11—82no—
128Q8×C11—82no—
129Q8×C11—81no—
130Q8×C11—81no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—42no—
134C2×C4×C11—44no—
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12711yescharacteristic
141C2×C4×C11#13512yes—
142C2×C4×C11AGL(1,ℤ/8)12yes—
143C2×Dic11—41no—
144C2×Dic11—41no—
145D44—44no—
146D44—44no—
147D44—82no—
148D44—82no—
149D44—82no—
150D44—81no—
151D44—81no—
152Dic22—42no—
153Dic22—42no—
154C8×C11—42no—
155C8×C11—81no—
156C11⋊C8—42no—
157C11⋊C8—42no—
158#533—111no—
159C2×C4⋊Q8C2×D1111yescharacteristic
160C2×#127—111no—
161#498—221no—
162#490—222no—
163#487—221no—
164#486—221no—
165#486—221no—
166#486—222no—
167#486—222no—
168#483—222no—
169#475—222no—
170#431—111no—
171#423C2×D1111yescharacteristic
172#418—222no—
173C2×#102—222no—
174C2×#101—22no—
175C4×M16C2×D1111yescharacteristic
176C2×C4×C8—111no—
177#331—222no—
178Q8⋊C8—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11#39211yescharacteristic
182C22×C11#46312yes—
183C2×D11—82no—
184C2×D11—82no—
185C2×D11—82no—
186C2×D11—164no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11#44912yes—
191C4×C11#45412yes—
192C4×C11#47112yes—
193C4×C11#49511yescharacteristic
194C4×C11#49611yescharacteristic
195Dic11—81no—
196Dic11—81no—
197C22×Q8—21no—
198C22×D4—221no—
199C22×D4—221no—
200C22×D4—221no—
201C2×M16—21no—
202C2×M16C22⋊D1112yes—
203C22×C8—221no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—111no—
209C4⋊Q8—111no—
210#127—112no—
211#127—221no—
212#127—221no—
213#127—221no—
214#125—221no—
215C22⋊Q8—221no—
216C22⋊Q8—221no—
217C4×Q8—221no—
218C4×Q8—221no—
219#117—221no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4D4412yes—
222C2×C42C22×D1111yescharacteristic
223#106—224no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—112no—
227#103—224no—
228#102—228no—
229#102—224no—
230#102—224no—
231#101—44no—
232C22⋊C8—221no—
233#97—21no—
234C4×C8—21no—
235C4×C8—112no—
236C4×C8—221no—
237C4×C8—221no—
238C2×C11—22no—
239C2×C11#200311yescharacteristic
240C2×C11#201211yescharacteristic
241C2×C11#201911yescharacteristic
242D11—162no—
243C24—441no—
244C2×Q8—42no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—42no—
248C2×Q8—221no—
249C2×Q8—221no—
250C2×D4—222no—
251C2×D4—222no—
252C2×D4—222no—
253C2×D4—444no—
254C2×D4—441no—
255C2×D4—441no—
256C2×D4—442no—
257C2×D4—441no—
258C2×D4—442no—
259C2×D4—882no—
260C22×C4—22no—
261C22×C4C2×D4411yescharacteristic
262C22×C4#433911yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264M16—22no—
265M16—22no—
266M16—42no—
267C2×C8—22no—
268C2×C8—41no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8—442no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C22⋊C4—441no—
283C42—441no—
284C42D4×D1111yescharacteristic
285C42D4×D1111yescharacteristic
286C42D4×D1111yescharacteristic
287C42D4×D1111yescharacteristic
288C11#1015111yescharacteristic, complemented, Sylow
289C23—442no—
290C23—882no—
291C23—882no—
292C23—882no—
293C23#6698311yescharacteristic
294Q8—82no—
295Q8—81no—
296Q8—81no—
297Q8—442no—
298Q8—442no—
299D4—444no—
300D4—444no—
301D4—882no—
302D4—882no—
303D4—882no—
304D4—881no—
305D4—881no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4#6693511yescharacteristic
313C2×C4#6693511yescharacteristic
314C2×C4#6693711yescharacteristic
315C2×C4#6693711yescharacteristic
316C2×C4#6698512yes—
317C2×C4#6699011yescharacteristic
318C2×C4#6699311yescharacteristic
319C2×C4#6700312yes—
320C8—42no—
321C8—81no—
322C8—442no—
323C8—442no—
324C22—21no—
325C22—21no—
326C22—882no—
327C22—882no—
328C22—882no—
329C22—1764no—
330C22#1062257311yescharacteristic
331C22#1062262912yes—
332C4—21no—
333C4—21no—
334C4—82no—
335C4—881no—
336C4—881no—
337C4#1062236612yes—
338C4#1062236712yes—
339C4#1062265012yes—
340C4#1062267211yescharacteristic
341C4#1062268711yescharacteristic
342C2—22no—
343C2—1762no—
344C2#1306964011yescharacteristic
345C2#1306969211yescharacteristic
346C2#1306972911yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1966C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#1966D11
hypocenterC11#10151
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1966

Complements

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

NH ≅ G/Ntype
1. #13079760C2semidirect
5. #13067070C2semidirect
6. #13066454C2semidirect
7. C11×#1966C2semidirect
119. #1966D11semidirect
288. C11#10151semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130789912
C2×#106227012
#130672852
#130670702
#130664542
C11×#19662
#1015111