Finite Group Databasebeta

← #14655619

Subgroups — #14655619

Order 2816.

578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079009C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3#13069457C211yesmaximal, characteristic, complemented
4#13067296C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#3205C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#493—21no—
12C11×#486—21no—
13C11×#459—22no—
14C11×#447—22no—
15C11×#431C2211yescharacteristic
16#10622845—22no—
17C2×#66897—22no—
18C2×#66896—22no—
19#10622694—21no—
20#10622683—21no—
21#10622683—22no—
22#10622683—22no—
23#10622668—22no—
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27D4⋊(C11⋊C8)—22no—
28#10622119—22no—
29C2×C11×#41—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D412yes—
33C22×Dic22—21no—
34C2×C11×D8—24no—
35C11×C4⋊Q8D411yescharacteristic
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C42×C11C2311yescharacteristic
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×#4318—21no—
50C2×#4318D412yes—
51C22×C11⋊C8—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922D412yes—
56C11×C4⋊C8D412yes—
57C11×#102—24no—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66899—24no—
61#66897—44no—
62#66896—28no—
63#66896—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10160—111nomaximal, Sylow
71C24×C11—22no—
72C11×#41—42no—
73C11×#41—42no—
74C2×Q8×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—44no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—42no—
87C2×D4×C11—42no—
88C2×D4×C11—82no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×Dic11—41no—
94C2×Dic22—22no—
95C2×Dic22—41no—
96C2×Dic22—82no—
97C11×D8—84no—
98C2×C8×C11—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111#4318—22no—
112#4318—22no—
113#4318—42no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—42no—
117C2×C11⋊C8—41no—
118#3205D1111yescharacteristic
119#3141—111no—
120C2×#486—111no—
121#1965—111no—
122#1548—111no—
123#1492—111no—
124#1278—111no—
125C23×C11—41no—
126C23×C11—42no—
127C23×C11—44no—
128C23×C11—82no—
129C23×C11—82no—
130C23×C11#12111yescharacteristic
131Q8×C11—42no—
132D4×C11—44no—
133D4×C11—42no—
134D4×C11—42no—
135D4×C11—44no—
136D4×C11—42no—
137D4×C11—82no—
138D4×C11—82no—
139D4×C11—82no—
140D4×C11—82no—
141D4×C11—81no—
142D4×C11—81no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—41no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12711yescharacteristic
154C2×C4×C11#13512yes—
155C2×C4×C11AGL(1,ℤ/8)12yes—
156C2×Dic11—42no—
157C2×Dic11—82no—
158Dic22—82no—
159Dic22—82no—
160C8×C11—42no—
161C11⋊C8—42no—
162C11⋊C8—42no—
163C11⋊C8—81no—
164#532C2×D1111yescharacteristic
165C2×C4⋊Q8—111no—
166C2×#127C2×D1111yescharacteristic
167#493—21no—
168#489—222no—
169#487—221no—
170#486—21no—
171#486—222no—
172#486—222no—
173#486—221no—
174#459—22no—
175#447—22no—
176#431C2×D1111yescharacteristic
177#423—111no—
178#417—222no—
179C2×#102—222no—
180C2×#100—222no—
181C4×M16—111no—
182C2×C4×C8—111no—
183#333—222no—
184D4⋊C8—222no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—82no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—82no—
191C22×C11—81no—
192C22×C11—82no—
193C22×C11—164no—
194C22×C11#39211yescharacteristic
195C22×C11#46312yes—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—81no—
199C4×C11#44912yes—
200C4×C11#45512yes—
201C4×C11#47212yes—
202C4×C11#49511yescharacteristic
203C4×C11#49611yescharacteristic
204Dic11—82no—
205C2×#41—21no—
206C22×Q8—221no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4C22⋊D1112yes—
210C2×D8—24no—
211C2×M16—112no—
212C2×M16—221no—
213C22×C8—221no—
214C4⋊Q8—112no—
215C4⋊Q8—221no—
216C4⋊Q8—221no—
217C4⋊Q8—221no—
218C4⋊Q8C22⋊D1111yescharacteristic
219#127—21no—
220#127—21no—
221#127—21no—
222#127—21no—
223#127C22⋊D1111yescharacteristic
224#124—21no—
225#121—21no—
226#121—21no—
227C4×D4—21no—
228C4×D4—21no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C42C22×D1111yescharacteristic
232C4⋊C8—221no—
233C4⋊C8—221no—
234C4⋊C8C22⋊D1112yes—
235#103—224no—
236#102—24no—
237#102—228no—
238#102—224no—
239#100—444no—
240C22⋊C8—21no—
241#97—221no—
242C4×C8—21no—
243C4×C8—112no—
244C4×C8—221no—
245C4×C8—221no—
246C2×C11—22no—
247C2×C11—161no—
248C2×C11—162no—
249C2×C11#200411yescharacteristic
250C2×C11#201211yescharacteristic
251C2×C11#201811yescharacteristic
252C24—22no—
253#41—42no—
254#41—42no—
255C2×Q8—21no—
256C2×Q8—222no—
257C2×Q8—441no—
258C2×Q8—882no—
259C2×D4—21no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—22no—
263C2×D4—21no—
264C2×D4—44no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—82no—
273C22×C4—41no—
274C22×C4—441no—
275C22×C4D4×D1111yescharacteristic
276C22×C4#434111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278D8—84no—
279M16—222no—
280M16—222no—
281M16—442no—
282C2×C8—22no—
283C2×C8—222no—
284C2×C8—222no—
285C2×C8—442no—
286C2×C8—441no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—222no—
290C4⋊C4—222no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C42D4×D1111yescharacteristic
296C42D4×D1111yescharacteristic
297C42C2×C22⋊D1111yescharacteristic
298C42C2×C22⋊D1111yescharacteristic
299C11#1016011yescharacteristic, complemented, Sylow
300C23—41no—
301C23—42no—
302C23—44no—
303C23—82no—
304C23—82no—
305C23#6699211yescharacteristic
306Q8—42no—
307Q8—882no—
308Q8—882no—
309D4—44no—
310D4—42no—
311D4—42no—
312D4—42no—
313D4—44no—
314D4—82no—
315D4—82no—
316D4—81no—
317D4—81no—
318D4—82no—
319D4—82no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—442no—
326C2×C4—882no—
327C2×C4#6696412yes—
328C2×C4#6696512yes—
329C2×C4#6699011yescharacteristic
330C2×C4#6699011yescharacteristic
331C2×C4#6699111yescharacteristic
332C2×C4#6699211yescharacteristic
333C2×C4#6699311yescharacteristic
334C2×C4#6700611yescharacteristic
335C8—42no—
336C8—442no—
337C8—442no—
338C8—881no—
339C22—21no—
340C22—21no—
341C22—82no—
342C22—81no—
343C22—81no—
344C22—82no—
345C22—81no—
346C22—82no—
347C22—164no—
348C22#1062276612yes—
349C22#1062283611yescharacteristic
350C4—21no—
351C4—21no—
352C4—81no—
353C4—882no—
354C4#1062276711yescharacteristic
355C4#1062276811yescharacteristic
356C4#1062277112yes—
357C4#1062281212yes—
358C4#1062285512yes—
359C2—22no—
360C2—162no—
361C2—161no—
362C2#1306964311yescharacteristic
363C2#1306969111yescharacteristic
364C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3205C2
socleC22×C11#392
hypercenter#3205D11
hypocenterC11#10160
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3205

Complements

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

NH ≅ G/Ntype
1. #13079009C2semidirect
2. C2×#10622683C2semidirect
3. #13069457C2semidirect
4. #13067296C2semidirect
5. #13067067C2semidirect
6. #13066452C2semidirect
299. C11#10160semidirect

Maximal subgroups

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

subgroupindex
#130790092
C2×#106226832
#130694572
#130672962
#130670672
#130664522
C11×#32052
#1016011