Finite Group Databasebeta

← #14655835

Subgroups — #14655835

Order 2816.

464 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079767C211yesmaximal, characteristic
2#13078423C211yesmaximal, characteristic
3C2×#10622707C211yesmaximal, characteristic
4#13067020C211yesmaximal, characteristic
5#13066939C211yesmaximal, characteristic
6#13066511C211yesmaximal, characteristic
7C11×#1548C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622734—21no—
14#10622733—21no—
15#10622707—22no—
16#10622707—22no—
17#10622706—21no—
18#10622704—22no—
19#10622691—21no—
20#10622583—22no—
21C2×#66874—21no—
22C2×#66872—21no—
23#10622538C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25#10622464—21no—
26#10622463—21no—
27#10622442—22no—
28C11×#333—22no—
29#10622107—22no—
30#10622094—22no—
31C22×Q8×C11—21no—
32C22×Dic22D411yescharacteristic
33C2×C11×M16—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D412yes—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41#66979—21no—
42C2×C4⋊Dic11D411yescharacteristic
43#66977—21no—
44#66977—21no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C22×C11⋊C8—21no—
48#66923—21no—
49#66922D411yescharacteristic
50#66922D411yescharacteristic
51C4×Dic22—21no—
52C4×Dic22—21no—
53C4×Dic22—21no—
54C4×Dic22—21no—
55C4×Dic22—21no—
56C4×Dic22—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8D412yes—
60C11×C22⋊C8—21no—
61C4×C8×C11—21no—
62C22⋊(C11⋊C8)D412yes—
63#66882—22no—
64#66881—22no—
65#66880—22no—
66#66880—22no—
67#66874—24no—
68#66874—24no—
69#66872—24no—
70#66871—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4×C11⋊C8—21no—
75#10191—111nomaximal, Sylow
76C2×Q8×C11—22no—
77C2×Q8×C11—41no—
78C2×Q8×C11—82no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C2×Dic22Q1612yes—
93C11×M16—41no—
94C11×M16—41no—
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—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115Dic11⋊C4—41no—
116C4×Dic11—41no—
117C4×Dic11—41no—
118C4×Dic11—41no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123#3230—111no—
124#3078—111no—
125C2×#475—111no—
126#1548D1111yescharacteristic
127#1481—111no—
128#1461—111no—
129#1301—111no—
130C23×C11#12111yescharacteristic
131Q8×C11—82no—
132Q8×C11—82no—
133C2×C4×C11—22no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—82no—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12711yescharacteristic
143C2×C4×C11C2×Q1611yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C2×Dic11—22no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—81no—
154Dic22—22no—
155Dic22—22no—
156Dic22—41no—
157Dic22—41no—
158Dic22—42no—
159Dic22—42no—
160C8×C11—42no—
161C8×C11—81no—
162C11⋊C8—42no—
163C11⋊C8—42no—
164#533—111no—
165C2×C4⋊Q8C2×D1111yescharacteristic
166C2×C4×Q8—111no—
167#500—221no—
168#487—221no—
169#484—222no—
170#479—222no—
171#477—221no—
172#477—222no—
173#475—221no—
174#475—222no—
175#475—222no—
176#431—111no—
177#431C2×D1111yescharacteristic
178#428—221no—
179C2×#106—221no—
180#423C2×D1111yescharacteristic
181C2×C4⋊C8—111no—
182#419—221no—
183C2×#103—221no—
184#333—22no—
185Q8⋊C8—222no—
186#324—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11#39211yescharacteristic
190C22×C11#46711yescharacteristic
191C22×C11#47011yescharacteristic
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—82no—
196C4×C11#45111yescharacteristic
197C4×C11#45111yescharacteristic
198C4×C11#45211yescharacteristic
199C4×C11#45211yescharacteristic
200C4×C11#47112yes—
201Dic11—42no—
202Dic11—81no—
203Dic11—81no—
204Dic11—81no—
205C22×Q8—21no—
206C22×Q8—111no—
207C2×M16—21no—
208C22×C8—221no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—111no—
213C4⋊Q8—111no—
214C4⋊Q8D4412yes—
215#125—221no—
216C22⋊Q8—221no—
217C22⋊Q8—221no—
218C4×Q8—221no—
219C4×Q8—221no—
220C4×Q8—221no—
221C4×Q8—221no—
222C4×Q8—221no—
223C4×Q8—221no—
224#117—221no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—221no—
229C2×C42—221no—
230C2×C42C22×D1111yescharacteristic
231#107—224no—
232#107—222no—
233#106—224no—
234#106—222no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—112no—
238C4⋊C8—221no—
239C4⋊C8—221no—
240C4⋊C8C22⋊D1112yes—
241#103—224no—
242#103—224no—
243#103—222no—
244#103—222no—
245C22⋊C8—21no—
246C22⋊C8—112no—
247C4×C8—21no—
248C4×C8—221no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11#200111yescharacteristic
252C2×C11#200911yescharacteristic
253C2×C11#201911yescharacteristic
254C2×Q8—22no—
255C2×Q8—41no—
256C2×Q8—82no—
257C2×Q8—112no—
258C2×Q8—221no—
259C2×Q8—221no—
260C2×Q8—221no—
261C2×Q8—221no—
262C2×Q8—221no—
263C2×Q8—221no—
264C2×Q8—221no—
265C22×C4—41no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4#433911yescharacteristic
269C22×C4D4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271M16—41no—
272M16—41no—
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—222no—
276C2×C8—222no—
277C2×C8—441no—
278C2×C8—441no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C22⋊C4—441no—
294C42—441no—
295C42—441no—
296C42—441no—
297C42C2×D4411yescharacteristic
298C42D4×D1111yescharacteristic
299C42D4×D1111yescharacteristic
300C42C2×C22⋊D1111yescharacteristic
301C11#1019111yescharacteristic, complemented, Sylow
302C23#6693711yescharacteristic
303Q8—82no—
304Q8—82no—
305Q8—222no—
306Q8—222no—
307Q8—442no—
308Q8—441no—
309Q8—441no—
310Q8—442no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—82no—
315C2×C4—222no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—881no—
322C2×C4#6693511yescharacteristic
323C2×C4#6693511yescharacteristic
324C2×C4#6693711yescharacteristic
325C2×C4#6696811yescharacteristic
326C2×C4#6696911yescharacteristic
327C2×C4Q16×D1111yescharacteristic
328C2×C4#6697111yescharacteristic
329C2×C4#6698311yescharacteristic
330C2×C4#6699011yescharacteristic
331C2×C4#6699311yescharacteristic
332C8—42no—
333C8—81no—
334C8—442no—
335C8—442no—
336C22—21no—
337C22—21no—
338C22#1062242611yescharacteristic
339C22#1062242911yescharacteristic
340C22#1062257311yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—82no—
345C4—442no—
346C4—881no—
347C4—881no—
348C4—881no—
349C4#1062236112yes—
350C4#1062242111yescharacteristic
351C4#1062242311yescharacteristic
352C4#1062278611yescharacteristic
353C4#1062279911yescharacteristic
354C2—21no—
355C2—21no—
356C2#1306962511yescharacteristic
357C2#1306967811yescharacteristic
358C2#1306973211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1548C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1548D11
hypocenterC11#10191
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
301. C11#10191semidirect

Maximal subgroups

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

subgroupindex
#130797672
#130784232
C2×#106227072
#130670202
#130669392
#130665112
C11×#15482
#1019111