Finite Group Databasebeta

← #14655701

Subgroups — #14655701

Order 2816.

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

normal subgroups only

This group has 562 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#13079741C211yesmaximal, characteristic
2C2×#10622692C211yesmaximal, characteristic, complemented
3#13069605C211yesmaximal, characteristic, complemented
4#13067288C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic
6#13066454C211yesmaximal, characteristic, complemented
7C11×#3152C211yesmaximal, characteristic
8C2×C11×#137—22no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#497—22no—
13C11×#494—21no—
14C11×#492—21no—
15C4×C11×M16C2211yescharacteristic
16#10622692—22no—
17#10622692—21no—
18#10622692—22no—
19#10622683—21no—
20#10622647—22no—
21#10622621—22no—
22C2×#66872—22no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26#10622192—22no—
27#10622185—22no—
28D4⋊(C11⋊C8)—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×Dic22—21no—
32C11×#137—44no—
33C11×#137—44no—
34C2×C11×Q16—24no—
35C2×C11×SD16—24no—
36C2×C11×M16D412yes—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D412yes—
42C11×#127D411yescharacteristic
43C11×#124—21no—
44C11×#121—21no—
45C11×#121—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11D412yes—
53C2×#4318—21no—
54C22×C11⋊C8—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59C11×#97—21no—
60C4×C8×C11—21no—
61#66896—24no—
62C22⋊(C11⋊C8)—21no—
63#66872—28no—
64#66872—24no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yes—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8D412yes—
71#10172—111nomaximal, Sylow
72C11×#41—42no—
73C11×#41—42no—
74C2×Q8×C11—21no—
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—42no—
78C2×Q8×C11—42no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×Dic11—22no—
89C2×Dic22—41no—
90C2×Dic22—41no—
91C2×Dic22—82no—
92C11×Q16—48no—
93C11×SD16—48no—
94C11×M16—22no—
95C11×M16SD1614yes—
96C2×C8×C11—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113#4318—42no—
114C2×C11⋊C8—24no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—41no—
118#3227—111no—
119C2×#498—111no—
120#3152D1111yescharacteristic
121#1997—111no—
122#1546—111no—
123#1492—111no—
124#1278—111no—
125C23×C11—41no—
126C23×C11#12111yescharacteristic
127Q8×C11—44no—
128Q8×C11—42no—
129Q8×C11—81no—
130Q8×C11—81no—
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—42no—
134D4×C11—82no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—82no—
140C2×C4×C11—81no—
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×SD1612yes—
149C2×C4×C11AGL(1,ℤ/8)12yes—
150C2×Dic11—42no—
151C2×Dic11—82no—
152Dic22—82no—
153Dic22—82no—
154C8×C11—24no—
155C11⋊C8—24no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158C2×#137—22no—
159#532C2×D1111yescharacteristic
160C2×C4⋊Q8—111no—
161C2×C4⋊Q8C2×D1111yescharacteristic
162#498—222no—
163#498—222no—
164#498—221no—
165#497—22no—
166#494—21no—
167#492—21no—
168#486—221no—
169#481—222no—
170#476—222no—
171#431—111no—
172C2×#106—222no—
173#423—111no—
174C4×M16C2×D1111yescharacteristic
175C2×C4×C8—111no—
176#343—222no—
177#332—222no—
178D4⋊C8—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11#39211yescharacteristic
185C22×C11#46012yes—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—81no—
189C4×C11—82no—
190C4×C11#45012yes—
191C4×C11#45612yes—
192C4×C11#47112yes—
193C4×C11#49211yescharacteristic
194C4×C11#49611yescharacteristic
195Dic11—82no—
196C2×#41—21no—
197C22×Q8—21no—
198C22×Q8—221no—
199#137—44no—
200#137—44no—
201C2×Q16—24no—
202C2×SD16—24no—
203C2×M16—221no—
204C2×M16C22⋊D1112yes—
205C22×C8—221no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211C4⋊Q8—221no—
212C4⋊Q8—221no—
213C4⋊Q8C22⋊D1112yes—
214C4⋊Q8C22⋊D1111yescharacteristic
215#127C22⋊D1111yescharacteristic
216#124—21no—
217#121—21no—
218#121—21no—
219C4×D4—21no—
220C4×D4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—112no—
224C2×C4⋊C4—221no—
225C2×C42C22×D1111yescharacteristic
226#106—228no—
227#106—224no—
228C4⋊C8—112no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231#102—224no—
232C22⋊C8—221no—
233#97—21no—
234C4×C8—21no—
235C4×C8—112no—
236C4×C8—221no—
237C4×C8—221no—
238C2×C11—22no—
239C2×C11—161no—
240C2×C11#200511yescharacteristic
241C2×C11#201411yescharacteristic
242C2×C11#201911yescharacteristic
243#41—42no—
244#41—42no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—441no—
251C2×Q8—441no—
252C2×Q8—882no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—222no—
260C22×C4D4×D1111yescharacteristic
261C22×C4#434111yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263Q16—48no—
264SD16—48no—
265M16—22no—
266M16—442no—
267M16#432414yes—
268C2×C8—22no—
269C2×C8—224no—
270C2×C8—222no—
271C2×C8—222no—
272C2×C8—441no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—222no—
280C4⋊C4—222no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C42D4×D1111yescharacteristic
286C42D4×D1111yescharacteristic
287C42C2×C22⋊D1111yescharacteristic
288C42C2×C22⋊D1111yescharacteristic
289C11#1017211yescharacteristic, complemented, Sylow
290C23—41no—
291C23#6699111yescharacteristic
292Q8—44no—
293Q8—42no—
294Q8—81no—
295Q8—81no—
296Q8—882no—
297Q8—882no—
298D4—42no—
299D4—42no—
300D4—42no—
301D4—82no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—82no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—442no—
310C2×C4—882no—
311C2×C4#6698512yes—
312C2×C4C2×#432412yes—
313C2×C4#6699011yescharacteristic
314C2×C4#6699011yescharacteristic
315C2×C4#6699211yescharacteristic
316C2×C4#6699211yescharacteristic
317C2×C4#6699311yescharacteristic
318C2×C4#6700611yescharacteristic
319C8—24no—
320C8—224no—
321C8—442no—
322C8—881no—
323C22—21no—
324C22—21no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22#1062268812yes—
329C22#1062283611yescharacteristic
330C4—21no—
331C4—21no—
332C4—81no—
333C4—82no—
334C4—882no—
335C4#1062268711yescharacteristic
336C4#1062268911yescharacteristic
337C4#1062281612yes—
338C4#1062281812yes—
339C4#1062283112yes—
340C2—22no—
341C2—161no—
342C2#1306964911yescharacteristic
343C2#1306970411yescharacteristic
344C2#1306972711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3152C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3152D11
hypocenterC11#10172
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3152

Complements

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

NH ≅ G/Ntype
2. C2×#10622692C2semidirect
3. #13069605C2semidirect
4. #13067288C2semidirect
6. #13066454C2semidirect
289. C11#10172semidirect

Maximal subgroups

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

subgroupindex
#130797412
C2×#106226922
#130696052
#130672882
#130670672
#130664542
C11×#31522
#1017211