Finite Group Databasebeta

← #14655624

Subgroups — #14655624

Order 2816.

556 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 113 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#13079554C211yesmaximal, characteristic
2C2×#10622701C211yesmaximal, characteristic
3#13069456C211yesmaximal, characteristic
4#13067297C211yesmaximal, characteristic, complemented
5#13067071C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#3165C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66927C2211yescharacteristic
11C11×#501—22no—
12C11×#500—21no—
13C11×#498—21no—
14C11×#428—22no—
15C4×C11×M16C2211yescharacteristic
16C2×#66887—22no—
17#10622701—21no—
18#10622701—22no—
19#10622701—22no—
20#10622698—21no—
21#10622659—22no—
22#10622640—22no—
23C2×#66873—22no—
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27#10622184—22no—
28Q8⋊(C11⋊C8)—22no—
29C22×Q8×C11—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44D412yes—
33C2×C11×M16D412yes—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D412yes—
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4325—24no—
50C2×#4318—21no—
51C22×C11⋊C8—21no—
52#66927—21no—
53#66927—21no—
54#66927—21no—
55#66927—21no—
56C11×#107—24no—
57C11×#106—24no—
58C11×#97—21no—
59C4×C8×C11—21no—
60C22⋊(C11⋊C8)—21no—
61#66887—44no—
62#66873—28no—
63#66873—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)D412yes—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10161—111nomaximal, Sylow
71C23×D11—22no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—41no—
76C2×Q8×C11—82no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×D44—22no—
82C2×D44—22no—
83C2×D44—44no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—42no—
89C2×D44—42no—
90C2×D44—82no—
91C11×M16—22no—
92C11×M16SD1614yescomplemented
93C2×C8×C11—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—41no—
105C42×C11—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110#4325—84no—
111#4318—42no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—41no—
116#3208—111no—
117#3165D1111yescharacteristic, complemented
118C2×#486—111no—
119#1965—111no—
120#1548—111no—
121#1493—111no—
122#1278—111no—
123C23×C11#12111yescharacteristic
124C22×D11—42no—
125C22×D11—44no—
126C22×D11—82no—
127C22×D11—82no—
128Q8×C11—42no—
129Q8×C11—42no—
130Q8×C11—82no—
131Q8×C11—82no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—82no—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12711yescharacteristic
144C2×C4×C11C2×SD1612yes—
145C2×C4×C11#13712yes—
146D44—44no—
147D44—44no—
148D44—82no—
149D44—82no—
150D44—82no—
151D44—81no—
152D44—81no—
153C8×C11—24no—
154C11⋊C8—42no—
155C11⋊C8—42no—
156C11⋊C8—81no—
157#533C2×D1111yescharacteristic
158C2×C4⋊Q8C2×D1111yescharacteristic
159C2×#127—111no—
160#501—22no—
161#500—21no—
162#498—21no—
163#492—221no—
164#486—222no—
165#486—222no—
166#486—221no—
167#460—222no—
168#450—222no—
169#431—111no—
170#428—22no—
171#423—111no—
172C2×#102—222no—
173C2×#100—222no—
174C4×M16C2×D1111yescharacteristic
175C2×C4×C8—111no—
176#333—222no—
177Q8⋊C8—222no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11#39211yescharacteristic
181C22×C11#46112yes—
182C2×D11—82no—
183C2×D11—82no—
184C2×D11—82no—
185C2×D11—164no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—81no—
189C4×C11—82no—
190C4×C11—81no—
191C4×C11#44812yes—
192C4×C11#45512yes—
193C4×C11#47212yes—
194C4×C11#49211yescharacteristic
195C4×C11#49711yescharacteristic
196C22×Q8—21no—
197C22×D4—112no—
198C22×D4—221no—
199C22×D4—221no—
200C2×SD16—224no—
201C2×M16—221no—
202C2×M16C22⋊D1112yes—
203C22×C8—221no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8C22⋊D1112yes—
208C4⋊Q8C22⋊D1111yescharacteristic
209C4⋊Q8C22⋊D1111yescharacteristic
210#127—221no—
211#127—221no—
212#127—221no—
213#127—221no—
214#125—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219#117—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C42C22×D1111yescharacteristic
223#107—24no—
224#106—24no—
225C4⋊C8—112no—
226C4⋊C8—221no—
227C4⋊C8—221no—
228#102—228no—
229#102—224no—
230#100—444no—
231C22⋊C8—221no—
232#97—21no—
233C4×C8—21no—
234C4×C8—112no—
235C4×C8—221no—
236C4×C8—221no—
237C2×C11—22no—
238C2×C11#200411yescharacteristic
239C2×C11#201311yescharacteristic
240C2×C11#201811yescharacteristic
241D11—162no—
242C24—222no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—82no—
248C2×D4—222no—
249C2×D4—222no—
250C2×D4—444no—
251C2×D4—441no—
252C2×D4—441no—
253C2×D4—441no—
254C2×D4—442no—
255C2×D4—442no—
256C2×D4—441no—
257C2×D4—882no—
258C22×C4—41no—
259C22×C4D4×D1111yescharacteristic
260C22×C4#434111yescharacteristic
261C22×C4C2×C22⋊D1111yescharacteristic
262SD16—884no—
263M16—22no—
264M16—442no—
265M16#432514yescomplemented
266C2×C8—22no—
267C2×C8—222no—
268C2×C8—222no—
269C2×C8—442no—
270C2×C8—441no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C22⋊C4—41no—
282C42—41no—
283C42D4×D1111yescharacteristic
284C42D4×D1111yescharacteristic
285C42C2×C22⋊D1111yescharacteristic
286C42C2×C22⋊D1111yescharacteristic
287C11#1016111yescharacteristic, complemented, Sylow
288C23—442no—
289C23—444no—
290C23—882no—
291C23—882no—
292C23#6699111yescharacteristic
293Q8—42no—
294Q8—42no—
295Q8—82no—
296Q8—82no—
297D4—444no—
298D4—444no—
299D4—882no—
300D4—882no—
301D4—882no—
302D4—881no—
303D4—881no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—82no—
310C2×C4#6699011yescharacteristic
311C2×C4#6699011yescharacteristic
312C2×C4#6699211yescharacteristic
313C2×C4#6699211yescharacteristic
314C2×C4#6699311yescharacteristic
315C2×C4C2×#432512yes—
316C2×C4#6699512yes—
317C2×C4#6700611yescharacteristic
318C8—24no—
319C8—442no—
320C8—442no—
321C8—881no—
322C22—21no—
323C22—21no—
324C22—882no—
325C22—882no—
326C22—882no—
327C22—1764no—
328C22#1062269612yes—
329C22#1062283611yescharacteristic
330C4—21no—
331C4—21no—
332C4—81no—
333C4—82no—
334C4—81no—
335C4#1062269811yescharacteristic
336C4#1062269911yescharacteristic
337C4#1062281212yes—
338C4#1062281512yes—
339C4#1062284012yes—
340C2—22no—
341C2—1762no—
342C2#1306964211yescharacteristic
343C2#1306969911yescharacteristic
344C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3165C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#3165D11
hypocenterC11#10161
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
4. #13067297C2semidirect
5. #13067071C2semidirect
6. #13066454C2semidirect
7. C11×#3165C2semidirect
92. C11×M16SD16semidirect
117. #3165D11semidirect
265. M16#4325semidirect
287. C11#10161semidirect

Maximal subgroups

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

subgroupindex
#130795542
C2×#106227012
#130694562
#130672972
#130670712
#130664542
C11×#31652
#1016111