Finite Group Databasebeta

← #14655704

Subgroups — #14655704

Order 2816.

562 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 111 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#13079744C211yesmaximal, characteristic
2C2×#10622692C211yesmaximal, characteristic, complemented
3#13079075C211yesmaximal, characteristic
4#13067289C211yesmaximal, characteristic, complemented
5#13067066C211yesmaximal, characteristic
6#13066454C211yesmaximal, characteristic, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66962—22no—
10#10623008C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C4×C11×M16C2211yescharacteristic
14#10622701—21no—
15#10622697—22no—
16#10622692—22no—
17#10622692—21no—
18#10622692—22no—
19#10622581—22no—
20C2×#66872—22no—
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622328—22no—
24#10622312—21no—
25#10622306—21no—
26C11×#343—22no—
27#10622121—22no—
28#10622120—22no—
29C22×Q8×C11—21no—
30C2×#4339—21no—
31C22×Dic22—21no—
32C2×C11×M16—21no—
33C2×C11×M16D412yes—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D412yes—
40C2×C42×C11C2311yescharacteristic
41#66983—21no—
42#66983—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C22×C11⋊C8—21no—
46#66962—44no—
47#66962—44no—
48C2×Dic44—24no—
49C2×#4314—24no—
50#66928—21no—
51#66927D411yescharacteristic
52C4×D44—21no—
53C4×D44—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922D412yes—
58#66922D411yescharacteristic
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×#97—21no—
62C4×C8×C11—21no—
63C22⋊(C11⋊C8)—21no—
64#66873—24no—
65#66872—28no—
66#66872—24no—
67C4⋊(C11⋊C8)D412yes—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8D412yes—
71#10172—111nomaximal, Sylow
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—82no—
75C22×C4×C11—22no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C2×C22⋊D11—41no—
80C22×Dic11—41no—
81#4339—42no—
82#4339—42no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×C4×D11—41no—
87C2×Dic22—22no—
88C2×Dic22—21no—
89C2×Dic22—41no—
90C2×Dic22—42no—
91C2×Dic22—42no—
92C11×M16—22no—
93C11×M16—42no—
94C11×M16SD1614yes—
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
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107C4⋊Dic11—22no—
108C4⋊Dic11—21no—
109C4⋊Dic11—22no—
110C4⋊Dic11—21no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116Dic44—48no—
117#4314—48no—
118#3227—111no—
119C2×#498—111no—
120#3152—111no—
121#1997D1111yescharacteristic, complemented
122#1546—111no—
123#1492—111no—
124#1278—111no—
125C23×C11#12111yescharacteristic
126C22×D11—41no—
127Q8×C11—82no—
128Q8×C11—82no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—42no—
132C2×C4×C11—82no—
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12711yescharacteristic
139C2×C4×C11C2×SD1612yes—
140C2×C4×C11AGL(1,ℤ/8)12yes—
141C22⋊D11—82no—
142C2×Dic11—42no—
143C2×Dic11—41no—
144C2×Dic11—82no—
145D44—42no—
146D44—42no—
147D44—42no—
148C4×D11—81no—
149C4×D11—81no—
150Dic22—44no—
151Dic22—42no—
152Dic22—81no—
153Dic22—81no—
154C8×C11—24no—
155C8×C11—81no—
156C11⋊C8—24no—
157C11⋊C8—42no—
158C2×#137—222no—
159#532—111no—
160C2×C4⋊Q8—111no—
161C2×C4⋊Q8C2×D1111yescharacteristic
162#498—222no—
163#498—222no—
164#498—221no—
165#497—222no—
166#494—221no—
167#492—221no—
168#486—221no—
169#481—222no—
170#476—222no—
171#431—111no—
172C2×#106—222no—
173#423C2×D1111yescharacteristic
174C4×M16C2×D1111yescharacteristic
175C2×C4×C8—111no—
176#343—22no—
177#332—222no—
178D4⋊C8—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11#39211yescharacteristic
182C22×C11#46012yes—
183C2×D11—81no—
184C2×D11—81no—
185C2×D11—81no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—82no—
189C4×C11#45012yes—
190C4×C11#45612yes—
191C4×C11#47112yes—
192C4×C11#49211yescharacteristic
193C4×C11#49611yescharacteristic
194Dic11—82no—
195Dic11—81no—
196C2×#41—221no—
197C22×Q8—21no—
198C22×Q8—221no—
199#137—444no—
200#137—444no—
201C2×Q16—224no—
202C2×SD16—224no—
203C2×M16—21no—
204C2×M16C22⋊D1112yes—
205C22×C8—221no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—112no—
211C4⋊Q8—111no—
212C4⋊Q8—221no—
213C4⋊Q8—221no—
214C4⋊Q8—221no—
215#127—111no—
216#124—221no—
217#121—221no—
218#121—221no—
219C4×D4—221no—
220C4×D4—221no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4D4412yes—
225C2×C42C22×D1111yescharacteristic
226#106—228no—
227#106—224no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—112no—
231#102—224no—
232C22⋊C8—221no—
233#97—21no—
234C4×C8—21no—
235C4×C8—112no—
236C4×C8—221no—
237C4×C8—221no—
238C2×C11—22no—
239C2×C11#200511yescharacteristic
240C2×C11#201411yescharacteristic
241C2×C11#201911yescharacteristic
242D11—161no—
243#41—442no—
244#41—442no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—82no—
248C2×Q8—221no—
249C2×Q8—222no—
250C2×Q8—441no—
251C2×Q8—442no—
252C2×Q8—442no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—441no—
257C22×C4—22no—
258C22×C4—441no—
259C22×C4—441no—
260C22×C4C2×D4411yescharacteristic
261C22×C4#433911yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263Q16—448no—
264SD16—448no—
265M16—22no—
266M16—42no—
267M16#432514yes—
268C2×C8—22no—
269C2×C8—41no—
270C2×C8—224no—
271C2×C8—222no—
272C2×C8—222no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—222no—
278C4⋊C4—221no—
279C4⋊C4—222no—
280C4⋊C4—221no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C42D4×D1111yescharacteristic
286C42D4×D1111yescharacteristic
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C11#1017211yescharacteristic, complemented, Sylow
290C23—441no—
291C23#6698311yescharacteristic
292Q8—82no—
293Q8—82no—
294Q8—444no—
295Q8—442no—
296Q8—881no—
297Q8—881no—
298D4—442no—
299D4—442no—
300D4—442no—
301D4—882no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—441no—
307C2×C4—442no—
308C2×C4—882no—
309C2×C4—881no—
310C2×C4—881no—
311C2×C4#6693511yescharacteristic
312C2×C4#6693511yescharacteristic
313C2×C4#6693711yescharacteristic
314C2×C4#6693711yescharacteristic
315C2×C4#6699011yescharacteristic
316C2×C4#6699311yescharacteristic
317C2×C4C2×#432512yes—
318C2×C4#6700212yes—
319C8—24no—
320C8—81no—
321C8—224no—
322C8—442no—
323C22—21no—
324C22—21no—
325C22—881no—
326C22—881no—
327C22—881no—
328C22#1062257311yescharacteristic
329C22#1062264012yes—
330C4—21no—
331C4—21no—
332C4—82no—
333C4—881no—
334C4—882no—
335C4#1062236112yes—
336C4#1062236512yes—
337C4#1062265912yes—
338C4#1062267111yescharacteristic
339C4#1062269811yescharacteristic
340C2—22no—
341C2—1761no—
342C2#1306965411yescharacteristic
343C2#1306970311yescharacteristic
344C2#1306973211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1997C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1997D11
hypocenterC11#10172
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
2. C2×#10622692C2semidirect
4. #13067289C2semidirect
6. #13066454C2semidirect
7. C11×#1997C2semidirect
121. #1997D11semidirect
289. C11#10172semidirect

Maximal subgroups

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

subgroupindex
#130797442
C2×#106226922
#130790752
#130672892
#130670662
#130664542
C11×#19972
#1017211