Finite Group Databasebeta

← #14655571

Subgroups — #14655571

Order 2816.

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

normal subgroups only

This group has 620 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#13079557C211yesmaximal, characteristic
2#13079162C211yesmaximal, characteristic, complemented
3C2×#10622689C211yesmaximal, characteristic
4#13067302C211yesmaximal, characteristic, complemented
5#13067070C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#1965C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9C22×#4324—22no—
10#10623001C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×#100—22no—
14C4×C11×M16C2211yescharacteristic
15#10622831—22no—
16#10622734—22no—
17#10622689—21no—
18#10622689—22no—
19#10622689—22no—
20#10622688—22no—
21#10622683—21no—
22#10622538C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622315—22no—
25#10622295—21no—
26#10622293—21no—
27#10622124—22no—
28#10622122—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11D412yes—
32C22×Dic22—21no—
33C2×C11×M16—21no—
34C2×C11×M16D412yes—
35C11×#127—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C2×C42×C11C2311yescharacteristic
40C2×#4324—28no—
41C2×#4324—24no—
42C2×#4324—48no—
43#66979—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46#66977—21no—
47#66977—21no—
48C22×C11⋊C8—21no—
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×#100—44no—
61C11×#97—21no—
62C4×C8×C11—21no—
63#66896—24no—
64C22⋊(C11⋊C8)—21no—
65#66882—24no—
66#66881—24no—
67C4⋊(C11⋊C8)D412yes—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8D412yes—
71#10153—111nomaximal, Sylow
72C24×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—22no—
75C2×D4×C11—44no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—42no—
81C2×D4×C11—42no—
82C2×D4×C11—82no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—41no—
87C2×Dic22—21no—
88C2×Dic22—22no—
89C2×Dic22—21no—
90C2×Dic22—44no—
91C2×Dic22—41no—
92C11×M16—22no—
93C11×M16—42no—
94C11×M16SD1614yescomplemented
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C22⋊Dic11—41no—
102#4324—416no—
103#4324—84no—
104C4⋊Dic11—21no—
105C4⋊Dic11—22no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—22no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114C4×Dic11—41no—
115C2×C11⋊C8—24no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118#3208—111no—
119#3165—111no—
120C2×#492—111no—
121#1965D1111yescharacteristic
122#1549—111no—
123#1493—111no—
124#1278—111no—
125C23×C11—42no—
126C23×C11—44no—
127C23×C11—82no—
128C23×C11—82no—
129C23×C11#12111yescharacteristic
130D4×C11—44no—
131D4×C11—44no—
132D4×C11—82no—
133D4×C11—82no—
134D4×C11—82no—
135D4×C11—81no—
136D4×C11—81no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12711yescharacteristic
145C2×C4×C11C2×SD1612yes—
146C2×C4×C11#13712yes—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150C2×Dic11—82no—
151Dic22—44no—
152Dic22—42no—
153Dic22—42no—
154Dic22—82no—
155C8×C11—24no—
156C8×C11—81no—
157C11⋊C8—24no—
158C11⋊C8—42no—
159C22×SD16—222no—
160#533—111no—
161C2×C4⋊Q8—111no—
162C2×#127C2×D1111yescharacteristic
163#501—222no—
164#500—221no—
165#498—221no—
166#492—222no—
167#492—222no—
168#492—221no—
169#486—221no—
170#460—222no—
171#450—222no—
172#431—111no—
173#428—222no—
174#423C2×D1111yescharacteristic
175C2×#100—22no—
176C4×M16C2×D1111yescharacteristic
177C2×C4×C8—111no—
178#332—222no—
179Q8⋊C8—222no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11—82no—
185C22×C11—164no—
186C22×C11#39211yescharacteristic
187C22×C11#46112yes—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11#44812yes—
191C4×C11#45312yes—
192C4×C11#47112yes—
193C4×C11#49211yescharacteristic
194C4×C11#49711yescharacteristic
195Dic11—82no—
196Dic11—81no—
197Dic11—81no—
198C22×Q8—221no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4D4412yes—
202C2×SD16—228no—
203C2×SD16—224no—
204C2×SD16—448no—
205C2×M16—21no—
206C2×M16C22⋊D1112yes—
207C22×C8—221no—
208C4⋊Q8—112no—
209C4⋊Q8—111no—
210C4⋊Q8—111no—
211C4⋊Q8—221no—
212C4⋊Q8—221no—
213C4⋊Q8—221no—
214#127—21no—
215#127—21no—
216#127—21no—
217#127—21no—
218#125—221no—
219C22⋊Q8—221no—
220C22⋊Q8—221no—
221C4×Q8—221no—
222C4×Q8—221no—
223#117—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C42C22×D1111yescharacteristic
227#107—224no—
228#106—224no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—112no—
232#102—224no—
233#100—44no—
234C22⋊C8—221no—
235#97—21no—
236C4×C8—21no—
237C4×C8—112no—
238C4×C8—221no—
239C4×C8—221no—
240C2×C11—22no—
241C2×C11—162no—
242C2×C11#200211yescharacteristic
243C2×C11#201311yescharacteristic
244C2×C11#201911yescharacteristic
245C24—22no—
246C2×Q8—221no—
247C2×Q8—222no—
248C2×Q8—221no—
249C2×Q8—444no—
250C2×Q8—441no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—44no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—42no—
260C2×D4—82no—
261C22×C4—441no—
262C22×C4C2×D4411yescharacteristic
263C22×C4#433911yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265SD16—4416no—
266SD16—884no—
267M16—22no—
268M16—42no—
269M16#432414yescomplemented
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—224no—
273C2×C8—222no—
274C2×C8—222no—
275C4⋊C4—221no—
276C4⋊C4—222no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—222no—
280C4⋊C4—221no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C22⋊C4—441no—
286C42—441no—
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C42D4×D1111yescharacteristic
290C42D4×D1111yescharacteristic
291C11#1015311yescharacteristic, complemented, Sylow
292C23—42no—
293C23—44no—
294C23—82no—
295C23—82no—
296C23#6698311yescharacteristic
297Q8—444no—
298Q8—442no—
299Q8—442no—
300Q8—882no—
301D4—44no—
302D4—44no—
303D4—82no—
304D4—82no—
305D4—82no—
306D4—81no—
307D4—81no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—442no—
313C2×C4—882no—
314C2×C4#6693511yescharacteristic
315C2×C4#6693511yescharacteristic
316C2×C4#6693711yescharacteristic
317C2×C4#6693711yescharacteristic
318C2×C4C2×#432412yes—
319C2×C4#6699011yescharacteristic
320C2×C4#6699311yescharacteristic
321C2×C4#6700412yes—
322C8—24no—
323C8—81no—
324C8—224no—
325C8—442no—
326C22—21no—
327C22—21no—
328C22—82no—
329C22—82no—
330C22—82no—
331C22—164no—
332C22#1062257311yescharacteristic
333C22#1062263212yes—
334C4—21no—
335C4—21no—
336C4—882no—
337C4—881no—
338C4—881no—
339C4#1062236012yes—
340C4#1062236112yes—
341C4#1062265312yes—
342C4#1062267311yescharacteristic
343C4#1062268911yescharacteristic
344C2—22no—
345C2—162no—
346C2#1306963311yescharacteristic
347C2#1306969811yescharacteristic
348C2#1306973211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1965C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenter#1965D11
hypocenterC11#10153
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1965

Complements

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

NH ≅ G/Ntype
2. #13079162C2semidirect
4. #13067302C2semidirect
5. #13067070C2semidirect
6. #13066454C2semidirect
94. C11×M16SD16semidirect
269. M16#4324semidirect
291. C11#10153semidirect

Maximal subgroups

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

subgroupindex
#130795572
#130791622
C2×#106226892
#130673022
#130670702
#130664542
C11×#19652
#1015311