Finite Group Databasebeta

← #14655782

Subgroups — #14655782

Order 2816.

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

normal subgroups only

This group has 476 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#13079566C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic
3C2×#10622634C211yesmaximal, characteristic
4#13067300C211yesmaximal, characteristic
5#13067020C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic
7C11×#1461C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622838—21no—
14C2×#66899—21no—
15#10622635—22no—
16#10622634—22no—
17#10622634—21no—
18#10622634—22no—
19#10622633—21no—
20#10622577—21no—
21C2×#66871—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622462—22no—
25#10622352—22no—
26#10622312—21no—
27#10622294—21no—
28C11×#324—22no—
29#10622120—22no—
30#10622094—22no—
31C22×Q8×C11D411yescharacteristic
32C22×Dic22—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C42×C11—21no—
40C2×C42×C11C2311yescharacteristic
41#66979—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44#66977—21no—
45#66977—21no—
46C2×#4318—21no—
47C22×C11⋊C8—21no—
48C2×Dic44—24no—
49#66923—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922D412yes—
54#66922D411yescharacteristic
55#66922D411yescharacteristic
56C4×Dic22—21no—
57C4×Dic22—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8D412yes—
62C4×C8×C11—21no—
63C4×C8×C11—21no—
64#66899—24no—
65#66899—22no—
66#66899—22no—
67#66880—24no—
68#66872—22no—
69#66871—24no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4⋊(C11⋊C8)D412yes—
75#10183—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11Q1612yescomplemented
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×Dic11—41no—
88C2×Dic22—22no—
89C2×Dic22—21no—
90C2×Dic22—21no—
91C2×Dic22—41no—
92C2×Dic22—82no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C42×C11—41no—
100C42×C11—41no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C22⋊Dic11—41no—
106C4⋊Dic11—22no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—22no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114Dic11⋊C4—41no—
115Dic11⋊C4—41no—
116C4×Dic11—41no—
117#4318—41no—
118#4318—41no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123Dic44—84no—
124#3209—111no—
125#3078—111no—
126C2×#477—111no—
127#1549—111no—
128#1481—111no—
129#1461D1111yescharacteristic
130#1301—111no—
131C23×C11#12111yescharacteristic
132Q8×C11—22no—
133Q8×C11—22no—
134Q8×C11—41no—
135Q8×C11—41no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—81no—
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12711yescharacteristic
149C2×C4×C11C2×Q1611yescharacteristic
150C2×C4×C11#13511yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×C4×C11#13711yescharacteristic
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—42no—
156C2×Dic11—82no—
157Dic22—42no—
158Dic22—44no—
159Dic22—42no—
160Dic22—82no—
161C8×C11—42no—
162C8×C11—81no—
163C11⋊C8—42no—
164C11⋊C8—42no—
165#533—111no—
166C2×C4⋊Q8—111no—
167C2×C4×Q8C2×D1111yescharacteristic
168#494—221no—
169#487—221no—
170#479—222no—
171#477—222no—
172#477—222no—
173#477—221no—
174#475—221no—
175#462—222no—
176#451—222no—
177#431C2×D1111yescharacteristic
178#431C2×D1111yescharacteristic
179#428—221no—
180C2×#107—221no—
181#423—111no—
182C2×C4⋊C8—111no—
183#419—221no—
184C2×#103—221no—
185#332—222no—
186Q8⋊C8—222no—
187#324—22no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11#39211yescharacteristic
191C22×C11#46711yescharacteristic
192C22×C11#47011yescharacteristic
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—42no—
197C4×C11—81no—
198C4×C11#45111yescharacteristic
199C4×C11#45111yescharacteristic
200C4×C11#45211yescharacteristic
201C4×C11#45211yescharacteristic
202C4×C11#47312yes—
203Dic11—82no—
204Dic11—81no—
205Dic11—81no—
206C22×Q8—221no—
207C22×Q8D4411yescharacteristic
208C2×Q16—224no—
209C2×M16—221no—
210C22×C8—221no—
211C4⋊Q8—112no—
212C4⋊Q8—111no—
213C4⋊Q8—111no—
214C4⋊Q8—221no—
215C4⋊Q8—221no—
216C4⋊Q8—221no—
217#125—221no—
218C22⋊Q8—221no—
219C22⋊Q8—221no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—221no—
225C4×Q8—221no—
226#117—221no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4D4411yescharacteristic
231C2×C42—21no—
232C2×C42C22×D1111yescharacteristic
233#107—224no—
234#107—222no—
235#106—222no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—112no—
239C4⋊C8—112no—
240C4⋊C8—221no—
241C4⋊C8—221no—
242#103—224no—
243#103—224no—
244#103—222no—
245#103—222no—
246C22⋊C8—21no—
247C22⋊C8C22⋊D1112yes—
248C4×C8—21no—
249C4×C8—21no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11#200111yescharacteristic
253C2×C11#200811yescharacteristic
254C2×C11#202011yescharacteristic
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—221no—
261C2×Q8—222no—
262C2×Q8—221no—
263C2×Q8—441no—
264C2×Q8—882no—
265C2×Q8Dic4412yescomplemented
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—441no—
269C22×C4C2×D4411yescharacteristic
270C22×C4#433911yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272Q16—884no—
273M16—441no—
274M16—441no—
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—222no—
278C2×C8—222no—
279C2×C8—441no—
280C2×C8—441no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—221no—
286C4⋊C4—222no—
287C4⋊C4—221no—
288C4⋊C4—222no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C22⋊C4—441no—
296C42—41no—
297C42—41no—
298C42—441no—
299C42D4×D1111yescharacteristic
300C42D4×D1111yescharacteristic
301C42D4×D1111yescharacteristic
302C42D4×D1111yescharacteristic
303C11#1018311yescharacteristic, complemented, Sylow
304C23#6698311yescharacteristic
305Q8—22no—
306Q8—22no—
307Q8—41no—
308Q8—41no—
309Q8—442no—
310Q8—444no—
311Q8—442no—
312Q8—882no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—442no—
323C2×C4—882no—
324C2×C4#6693511yescharacteristic
325C2×C4#6693511yescharacteristic
326C2×C4#6693711yescharacteristic
327C2×C4#6693711yescharacteristic
328C2×C4#6695711yescharacteristic
329C2×C4C2×Dic4411yescharacteristic
330C2×C4#6696211yescharacteristic
331C2×C4#6696211yescharacteristic
332C2×C4#6699011yescharacteristic
333C2×C4#6699311yescharacteristic
334C8—42no—
335C8—81no—
336C8—442no—
337C8—442no—
338C22—21no—
339C22—21no—
340C22#1062257311yescharacteristic
341C22#1062272911yescharacteristic
342C22#1062275011yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—81no—
348C4—882no—
349C4—881no—
350C4—881no—
351C4#1062234611yescharacteristic
352C4#1062234611yescharacteristic
353C4#1062235211yescharacteristic
354C4#1062235211yescharacteristic
355C4#1062236812yes—
356C2—21no—
357C2—21no—
358C2#1306962611yescharacteristic
359C2#1306966811yescharacteristic
360C2#1306973611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1461C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1461D11
hypocenterC11#10183
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
81. C2×Q8×C11Q16semidirect
265. C2×Q8Dic44semidirect
303. C11#10183semidirect

Maximal subgroups

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

subgroupindex
#130795662
#130784212
C2×#106226342
#130673002
#130670202
#130665122
C11×#14612
#1018311