Finite Group Databasebeta

← #14655838

Subgroups — #14655838

Order 2816.

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

normal subgroups only

This group has 464 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#13079769C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic
3C2×#10622633C211yesmaximal, characteristic
4#13067296C211yesmaximal, 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—21no—
17#10622633—22no—
18#10622633—21no—
19#10622633—22no—
20#10622577—21no—
21C2×#66872—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622463—22no—
25#10622335—22no—
26#10622295—21no—
27#10622294—21no—
28C11×#324—22no—
29#10622119—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—
48#66923—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52#66922D412yes—
53#66922D411yescharacteristic
54#66922D411yescharacteristic
55C4×Dic22—21no—
56C4×Dic22—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×C22⋊C8D412yes—
61C4×C8×C11—21no—
62C4×C8×C11—21no—
63#66899—24no—
64#66899—22no—
65#66899—22no—
66#66882—24no—
67#66880—24no—
68#66872—24no—
69#66872—22no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4⋊(C11⋊C8)D412yes—
75#10191—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11Q1612yes—
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—21no—
89C2×Dic22—21no—
90C2×Dic22—22no—
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—21no—
107C4⋊Dic11—22no—
108C4⋊Dic11—21no—
109C4⋊Dic11—22no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
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—
123#3230—111no—
124#3078—111no—
125C2×#475—111no—
126#1548—111no—
127#1481—111no—
128#1461D1111yescharacteristic
129#1301—111no—
130C23×C11#12111yescharacteristic
131Q8×C11—22no—
132Q8×C11—22no—
133Q8×C11—41no—
134Q8×C11—41no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—81no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12711yescharacteristic
148C2×C4×C11C2×Q1611yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—42no—
155C2×Dic11—82no—
156Dic22—42no—
157Dic22—42no—
158Dic22—82no—
159Dic22—82no—
160C8×C11—42no—
161C8×C11—81no—
162C11⋊C8—42no—
163C11⋊C8—42no—
164#533—111no—
165C2×C4⋊Q8—111no—
166C2×C4×Q8C2×D1111yescharacteristic
167#500—221no—
168#487—221no—
169#484—222no—
170#479—222no—
171#477—222no—
172#477—221no—
173#475—222no—
174#475—222no—
175#475—221no—
176#431C2×D1111yescharacteristic
177#431C2×D1111yescharacteristic
178#428—221no—
179C2×#106—221no—
180#423—111no—
181C2×C4⋊C8—111no—
182#419—221no—
183C2×#103—221no—
184#333—222no—
185Q8⋊C8—222no—
186#324—22no—
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—42no—
196C4×C11—81no—
197C4×C11#45111yescharacteristic
198C4×C11#45111yescharacteristic
199C4×C11#45211yescharacteristic
200C4×C11#45211yescharacteristic
201C4×C11#47112yes—
202Dic11—81no—
203Dic11—81no—
204Dic11—82no—
205C22×Q8—221no—
206C22×Q8D4411yescharacteristic
207C2×M16—221no—
208C22×C8—221no—
209C4⋊Q8—112no—
210C4⋊Q8—111no—
211C4⋊Q8—111no—
212C4⋊Q8—221no—
213C4⋊Q8—221no—
214C4⋊Q8—221no—
215#125—221no—
216C22⋊Q8—221no—
217C22⋊Q8—221no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—221no—
223C4×Q8—221no—
224#117—221no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4D4411yescharacteristic
229C2×C42—21no—
230C2×C42C22×D1111yescharacteristic
231#107—222no—
232#107—224no—
233#106—224no—
234#106—222no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—112no—
238C4⋊C8—112no—
239C4⋊C8—221no—
240C4⋊C8—221no—
241#103—224no—
242#103—224no—
243#103—222no—
244#103—222no—
245C22⋊C8—21no—
246C22⋊C8C22⋊D1112yes—
247C4×C8—21no—
248C4×C8—21no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11#200111yescharacteristic
252C2×C11#200911yescharacteristic
253C2×C11#201911yescharacteristic
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—221no—
260C2×Q8—222no—
261C2×Q8—221no—
262C2×Q8—441no—
263C2×Q8—882no—
264C2×Q8Dic4412yes—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—441no—
268C22×C4C2×D4411yescharacteristic
269C22×C4#433911yescharacteristic
270C22×C4C2×C22⋊D1111yescharacteristic
271M16—441no—
272M16—441no—
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—222no—
276C2×C8—222no—
277C2×C8—441no—
278C2×C8—441no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—222no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—222no—
288C4⋊C4—221no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C22⋊C4—441no—
294C42—41no—
295C42—41no—
296C42—441no—
297C42D4×D1111yescharacteristic
298C42D4×D1111yescharacteristic
299C42D4×D1111yescharacteristic
300C42D4×D1111yescharacteristic
301C11#1019111yescharacteristic, complemented, Sylow
302C23#6698311yescharacteristic
303Q8—22no—
304Q8—22no—
305Q8—41no—
306Q8—41no—
307Q8—442no—
308Q8—442no—
309Q8—882no—
310Q8—882no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—442no—
321C2×C4—882no—
322C2×C4#6693511yescharacteristic
323C2×C4#6693511yescharacteristic
324C2×C4#6693711yescharacteristic
325C2×C4#6693711yescharacteristic
326C2×C4#6695711yescharacteristic
327C2×C4C2×Dic4411yescharacteristic
328C2×C4#6696211yescharacteristic
329C2×C4#6696211yescharacteristic
330C2×C4#6699011yescharacteristic
331C2×C4#6699311yescharacteristic
332C8—42no—
333C8—81no—
334C8—442no—
335C8—442no—
336C22—21no—
337C22—21no—
338C22#1062257311yescharacteristic
339C22#1062272911yescharacteristic
340C22#1062275011yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—42no—
345C4—81no—
346C4—881no—
347C4—882no—
348C4—881no—
349C4#1062234611yescharacteristic
350C4#1062234611yescharacteristic
351C4#1062235211yescharacteristic
352C4#1062235211yescharacteristic
353C4#1062236712yes—
354C2—21no—
355C2—21no—
356C2#1306962611yescharacteristic
357C2#1306967511yescharacteristic
358C2#1306972911yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1461C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1461D11
hypocenterC11#10191
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
301. C11#10191semidirect

Maximal subgroups

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

subgroupindex
#130797692
#130784212
C2×#106226332
#130672962
#130670202
#130665122
C11×#14612
#1019111