Finite Group Databasebeta

← #14655533

Subgroups — #14655533

Order 2816.

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

normal subgroups only

This group has 614 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, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3#13069605C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#3151C211yesmaximal, characteristic
8C2×C11×AGL(1,ℤ/8)—22no—
9C11×#532C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#496—22no—
13C11×#493—21no—
14C11×#492—21no—
15C4×C11×M16C2211yescharacteristic
16C2×#66896—22no—
17#10622692—21no—
18#10622683—22no—
19#10622683—21no—
20#10622683—22no—
21#10622647—22no—
22#10622621—22no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26#10622192—22no—
27#10622182—22no—
28D4⋊(C11⋊C8)—22no—
29C2×C11×#41—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×Dic22—21no—
34C11×AGL(1,ℤ/8)—44no—
35C11×AGL(1,ℤ/8)—44no—
36C2×C11×SD16—24no—
37C2×C11×D8—24no—
38C2×C11×M16D412yes—
39C11×C4⋊Q8D411yescharacteristic
40C11×#127—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127D411yescharacteristic
44C11×#127D412yes—
45C11×#124—21no—
46C11×#121—21no—
47C11×#121—21no—
48C4×D4×C11—21no—
49C4×D4×C11—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—28no—
62#66896—24no—
63C22⋊(C11⋊C8)—21no—
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#10148—111nomaximal, Sylow
72C24×C11—41no—
73C11×#41—42no—
74C11×#41—42no—
75C2×Q8×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—22no—
78C2×D4×C11—21no—
79C2×D4×C11—22no—
80C2×D4×C11—21no—
81C2×D4×C11—22no—
82C2×D4×C11—44no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C2×D4×C11—82no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—22no—
95C2×Dic22—41no—
96C2×Dic22—41no—
97C2×Dic22—82no—
98C11×SD16—48no—
99C11×D8—48no—
100C11×M16—22no—
101C11×M16SD1614yes—
102C2×C8×C11—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115#4318—42no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—42no—
119C2×C11⋊C8—41no—
120#3227—111no—
121#3151D1111yescharacteristic
122C2×#486—111no—
123#1997—111no—
124#1545—111no—
125#1492—111no—
126#1278—111no—
127C23×C11—41no—
128C23×C11—42no—
129C23×C11—82no—
130C23×C11—82no—
131C23×C11—82no—
132C23×C11#12111yescharacteristic
133Q8×C11—42no—
134D4×C11—44no—
135D4×C11—42no—
136D4×C11—44no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—82no—
140D4×C11—82no—
141D4×C11—82no—
142D4×C11—82no—
143D4×C11—81no—
144D4×C11—81no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12711yescharacteristic
156C2×C4×C11C2×SD1612yes—
157C2×C4×C11AGL(1,ℤ/8)12yes—
158C2×Dic11—42no—
159C2×Dic11—82no—
160Dic22—82no—
161Dic22—82no—
162C8×C11—24no—
163C11⋊C8—42no—
164C11⋊C8—42no—
165C11⋊C8—81no—
166C2×AGL(1,ℤ/8)—22no—
167#532C2×D1111yescharacteristic
168C2×C4⋊Q8—111no—
169C2×#127C2×D1111yescharacteristic
170#498—221no—
171#496—22no—
172#493—21no—
173#492—21no—
174#486—222no—
175#486—222no—
176#486—221no—
177#481—222no—
178#476—222no—
179#431—111no—
180#423—111no—
181C2×#102—222no—
182C4×M16C2×D1111yescharacteristic
183C2×C4×C8—111no—
184#343—222no—
185#331—222no—
186D4⋊C8—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—82no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—82no—
193C22×C11—81no—
194C22×C11—82no—
195C22×C11—164no—
196C22×C11#39211yescharacteristic
197C22×C11#46012yes—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—81no—
201C4×C11#45012yes—
202C4×C11#45412yes—
203C4×C11#47212yes—
204C4×C11#49211yescharacteristic
205C4×C11#49611yescharacteristic
206Dic11—82no—
207C2×#41—21no—
208C22×Q8—221no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—21no—
212AGL(1,ℤ/8)—44no—
213AGL(1,ℤ/8)—44no—
214C2×SD16—24no—
215C2×D8—24no—
216C2×M16—221no—
217C2×M16C22⋊D1112yes—
218C22×C8—221no—
219C4⋊Q8—221no—
220C4⋊Q8—221no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8C22⋊D1111yescharacteristic
224#127—21no—
225#127—21no—
226#127—21no—
227#127C22⋊D1112yes—
228#127C22⋊D1111yescharacteristic
229#124—21no—
230#121—21no—
231#121—21no—
232C4×D4—21no—
233C4×D4—21no—
234C2×C4⋊C4—112no—
235C2×C4⋊C4—221no—
236C2×C42C22×D1111yescharacteristic
237#106—224no—
238C4⋊C8—112no—
239C4⋊C8—221no—
240C4⋊C8—221no—
241#102—228no—
242#102—224no—
243C22⋊C8—221no—
244#97—21no—
245C4×C8—21no—
246C4×C8—112no—
247C4×C8—221no—
248C4×C8—221no—
249C2×C11—22no—
250C2×C11—161no—
251C2×C11—162no—
252C2×C11#200311yescharacteristic
253C2×C11#201411yescharacteristic
254C2×C11#201811yescharacteristic
255C24—41no—
256#41—42no—
257#41—42no—
258C2×Q8—21no—
259C2×Q8—441no—
260C2×Q8—441no—
261C2×Q8—882no—
262C2×D4—21no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—22no—
266C2×D4—21no—
267C2×D4—22no—
268C2×D4—44no—
269C2×D4—41no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—82no—
276C22×C4—41no—
277C22×C4—222no—
278C22×C4D4×D1111yescharacteristic
279C22×C4#434111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281SD16—48no—
282D8—48no—
283M16—22no—
284M16—442no—
285M16#432414yes—
286C2×C8—22no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—442no—
290C2×C8—441no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—222no—
294C4⋊C4—222no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C42D4×D1111yescharacteristic
300C42D4×D1111yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C11#1014811yescharacteristic, complemented, Sylow
304C23—41no—
305C23—42no—
306C23—82no—
307C23—82no—
308C23—82no—
309C23#6699111yescharacteristic
310Q8—42no—
311Q8—882no—
312Q8—882no—
313D4—44no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—44no—
318D4—82no—
319D4—82no—
320D4—82no—
321D4—82no—
322D4—81no—
323D4—81no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—442no—
330C2×C4—882no—
331C2×C4#6698512yes—
332C2×C4C2×#432412yes—
333C2×C4#6699011yescharacteristic
334C2×C4#6699011yescharacteristic
335C2×C4#6699211yescharacteristic
336C2×C4#6699211yescharacteristic
337C2×C4#6699311yescharacteristic
338C2×C4#6700611yescharacteristic
339C8—24no—
340C8—442no—
341C8—442no—
342C8—881no—
343C22—21no—
344C22—21no—
345C22—82no—
346C22—81no—
347C22—81no—
348C22—82no—
349C22—81no—
350C22—82no—
351C22—164no—
352C22#1062268812yes—
353C22#1062283611yescharacteristic
354C4—21no—
355C4—21no—
356C4—81no—
357C4—882no—
358C4#1062268711yescharacteristic
359C4#1062268911yescharacteristic
360C4#1062281212yes—
361C4#1062281412yes—
362C4#1062283112yes—
363C2—22no—
364C2—162no—
365C2—161no—
366C2#1306963511yescharacteristic
367C2#1306970411yescharacteristic
368C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3151C2
socleC22×C11#392
hypercenter#3151D11
hypocenterC11#10148
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3151

Complements

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

NH ≅ G/Ntype
1. #13079741C2semidirect
2. C2×#10622683C2semidirect
3. #13069605C2semidirect
4. #13067284C2semidirect
5. #13067067C2semidirect
6. #13066454C2semidirect
303. C11#10148semidirect

Maximal subgroups

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

subgroupindex
#130797412
C2×#106226832
#130696052
#130672842
#130670672
#130664542
C11×#31512
#1014811