Finite Group Databasebeta

← #14655163

Subgroups — #14655163

Order 2816.

480 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 83 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#13079802C211yesmaximal, characteristic
2#13079009C211yesmaximal, characteristic
3#13074564C211yesmaximal, characteristic, complemented
4#13067332C211yesmaximal, characteristic, complemented
5#13067219C211yesmaximal, characteristic, complemented
6#13066509C211yesmaximal, characteristic, complemented
7C11×#1505C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#376C2211yescharacteristic
13#10622845—22no—
14#10622694—21no—
15#10622693—21no—
16#10622684—21no—
17#10622683—21no—
18#10622668—22no—
19#10622647—21no—
20#10622646—21no—
21#10622622—22no—
22#10622542—21no—
23#10622542—21no—
24#10622539C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26#10622272—22no—
27#10622272—22no—
28C11×#327—22no—
29#10622124—22no—
30#10622103—22no—
31C2×C11×#41—21no—
32C22×Dic22—21no—
33C11×C4⋊Q8D411yescharacteristic
34C11×#127D411yescharacteristic
35C11×#124—21no—
36C11×#121—21no—
37C11×#121—21no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11D412yes—
44C2×C4⋊Dic11D411yescharacteristic
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×#4318—21no—
49#66923—21no—
50#66923—21no—
51#66923—21no—
52#66923—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57C11×C4⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#97—21no—
60C11×#95—21no—
61C11×#95D412yes—
62#66899—24no—
63#66896—24no—
64#66896—22no—
65#66896—22no—
66C11⋊#95—24no—
67C11⋊#95—24no—
68C22⋊(C11⋊C8)—21no—
69#66872—22no—
70#66871—22no—
71C4⋊(C11⋊C8)D412yes—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10095—111nomaximal, Sylow
76C11×#41—44no—
77C2×Q8×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—41no—
82C22×C4×C11—22no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—22no—
90C2×Dic22—44no—
91C2×Dic22—41no—
92C2×Dic22—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11—42no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—22no—
106C4⋊Dic11—22no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115#4318—42no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118#3234—111no—
119#3141—111no—
120#2642—111no—
121#1556—111no—
122#1528—111no—
123#1505D1111yescharacteristic
124#1300—111no—
125C23×C11—41no—
126C23×C11#12011yescharacteristic
127Q8×C11—42no—
128D4×C11—42no—
129D4×C11—42no—
130D4×C11—81no—
131D4×C11—82no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—82no—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12711yescharacteristic
146C2×Dic11—44no—
147C2×Dic11—42no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152Dic22—82no—
153Dic22—82no—
154C8×C11—81no—
155C11⋊C8—42no—
156C11⋊C8—42no—
157#532C2×D1111yescharacteristic
158C2×C4⋊Q8—111no—
159C2×#125—111no—
160#501—221no—
161#490—221no—
162#489—222no—
163#487—221no—
164#486—221no—
165#481—221no—
166#480—221no—
167#478—222no—
168#432—111no—
169#432C2×D1111yescharacteristic
170#417—222no—
171C4×M16—111no—
172#400—222no—
173#400—222no—
174#391—221no—
175#391—221no—
176#376C2×D1111yescharacteristic
177#332—222no—
178#330—222no—
179#327—22no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11#39211yescharacteristic
186C22×C11#45412yes—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—82no—
193C4×C11—81no—
194C4×C11#45412yes—
195Dic11—82no—
196Dic11—81no—
197Dic11—81no—
198C2×#41—21no—
199C22×Q8—221no—
200C2×M16—221no—
201C4⋊Q8—221no—
202C4⋊Q8—221no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205C4⋊Q8D4411yescharacteristic
206#127D4411yescharacteristic
207#125—221no—
208#125—221no—
209#125—221no—
210#125—221no—
211#124—21no—
212#121—21no—
213#121—21no—
214C4×D4—21no—
215C4×D4—21no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—112no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C42—21no—
223C2×C42C22×D1111yescharacteristic
224#107—222no—
225#106—222no—
226C4⋊C8—21no—
227C4⋊C8—112no—
228#103—224no—
229#102—224no—
230#102—222no—
231#102—222no—
232C22⋊C8—21no—
233C22⋊C8—221no—
234#97—21no—
235#97—112no—
236#97—221no—
237C4×C8—221no—
238#95—21no—
239#95—224no—
240#95—224no—
241#95C22⋊D1112yes—
242C2×C11—22no—
243C2×C11—161no—
244C2×C11#200311yescharacteristic
245C2×C11#200311yescharacteristic
246C2×C11#200911yescharacteristic
247#41—44no—
248C2×Q8—21no—
249C2×Q8—444no—
250C2×Q8—441no—
251C2×Q8—441no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C22×C4—22no—
257C22×C4—41no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—222no—
261C22×C4D4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264M16—442no—
265C2×C8—41no—
266C2×C8—222no—
267C2×C8—222no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—222no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—222no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C42—42no—
285C42C2×D4411yescharacteristic
286C42#433911yescharacteristic
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C11#1009511yescharacteristic, complemented, Sylow
290C23—41no—
291C23#6699011yescharacteristic
292Q8—42no—
293Q8—882no—
294Q8—882no—
295D4—42no—
296D4—42no—
297D4—81no—
298D4—82no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4—444no—
308C2×C4—442no—
309C2×C4—442no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—442no—
313C2×C4#6693511yescharacteristic
314C2×C4#6693511yescharacteristic
315C2×C4#6693711yescharacteristic
316C2×C4#6693711yescharacteristic
317C2×C4#6698311yescharacteristic
318C2×C4#6699311yescharacteristic
319C8—81no—
320C8—442no—
321C8—442no—
322C22—21no—
323C22—21no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22#1062257311yescharacteristic
328C22#1062281412yes—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—82no—
335C4—81no—
336C4—882no—
337C4—881no—
338C4—881no—
339C4#1062244012yes—
340C2—22no—
341C2—161no—
342C2#1306963711yescharacteristic
343C2#1306963911yescharacteristic
344C2#1306967511yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1505C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1505D11
hypocenterC11#10095
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1505

Complements

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

NH ≅ G/Ntype
3. #13074564C2semidirect
4. #13067332C2semidirect
5. #13067219C2semidirect
6. #13066509C2semidirect
289. C11#10095semidirect

Maximal subgroups

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

subgroupindex
#130798022
#130790092
#130745642
#130673322
#130672192
#130665092
C11×#15052
#1009511