Finite Group Databasebeta

← #14655675

Subgroups — #14655675

Order 2816.

642 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079076C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3#13069457C211yesmaximal, characteristic, complemented
4#13067287C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#3205C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×#67004—22no—
11C2×#66922C2211yescharacteristic
12C11×#493—21no—
13C11×#486—21no—
14C11×#459—22no—
15C11×#447—22no—
16C11×#431C2211yescharacteristic
17C2×#66897—22no—
18C2×#66896—22no—
19#10622705—21no—
20#10622689—21no—
21#10622683—22no—
22#10622683—22no—
23#10622673—22no—
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27D4⋊(C11⋊C8)—22no—
28#10622124—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
47#67004—44no—
48#67004—44no—
49C2×#4326—24no—
50C2×#4324—24no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×#4318—21no—
54C2×#4318D412yes—
55C22×C11⋊C8—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922D412yes—
60C11×C4⋊C8D412yes—
61C11×#102—24no—
62C11×C22⋊C8—21no—
63C4×C8×C11—21no—
64#66897—44no—
65#66896—28no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68#66867—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8D412yes—
72#10168—111nomaximal, Sylow
73C24×C11—22no—
74C11×#41—42no—
75C11×#41—42no—
76C2×Q8×C11—21no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—44no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—42no—
89C2×D4×C11—42no—
90C2×D4×C11—82no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—41no—
96C2×Dic22—22no—
97C2×Dic22—41no—
98C2×Dic22—42no—
99C2×Dic22—42no—
100C11×D8—84no—
101C2×C8×C11—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110#4326—48no—
111#4324—48no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116#4318—22no—
117#4318—42no—
118#4318D814yescomplemented
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—42no—
122C2×C11⋊C8—41no—
123#3205D1111yescharacteristic
124#3152—111no—
125C2×#486—111no—
126#1965—111no—
127#1546—111no—
128#1492—111no—
129#1278—111no—
130C23×C11—41no—
131C23×C11—42no—
132C23×C11—44no—
133C23×C11—82no—
134C23×C11—82no—
135C23×C11#12111yescharacteristic
136Q8×C11—42no—
137D4×C11—44no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—44no—
141D4×C11—42no—
142D4×C11—82no—
143D4×C11—82no—
144D4×C11—82no—
145D4×C11—82no—
146D4×C11—81no—
147D4×C11—81no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C2×C4×C11C2×D812yes—
160C2×C4×C11AGL(1,ℤ/8)12yes—
161C2×Dic11—42no—
162C2×Dic11—82no—
163Dic22—44no—
164Dic22—81no—
165Dic22—81no—
166C8×C11—42no—
167C11⋊C8—24no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C2×#137—222no—
171#532C2×D1111yescharacteristic
172C2×C4⋊Q8—111no—
173C2×#127C2×D1111yescharacteristic
174#497—222no—
175#494—221no—
176#493—21no—
177#492—221no—
178#486—21no—
179#486—222no—
180#486—222no—
181#459—22no—
182#447—22no—
183#431C2×D1111yescharacteristic
184#423—111no—
185C2×#102—222no—
186C2×#100—222no—
187C4×M16—111no—
188C2×C4×C8—111no—
189#332—222no—
190D4⋊C8—222no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—82no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—82no—
197C22×C11—81no—
198C22×C11—82no—
199C22×C11—164no—
200C22×C11#39211yescharacteristic
201C22×C11#45912yes—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11#44712yes—
206C4×C11#45512yes—
207C4×C11#47112yes—
208C4×C11#49311yescharacteristic
209C4×C11#49611yescharacteristic
210Dic11—82no—
211C2×#41—21no—
212C22×Q8—221no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4C22⋊D1112yes—
216#137—444no—
217#137—444no—
218C2×Q16—224no—
219C2×SD16—224no—
220C2×D8—24no—
221C2×M16—112no—
222C2×M16—221no—
223C22×C8—221no—
224C4⋊Q8—112no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228C4⋊Q8C22⋊D1111yescharacteristic
229#127—21no—
230#127—21no—
231#127—21no—
232#127—21no—
233#127C22⋊D1111yescharacteristic
234#124—21no—
235#121—21no—
236#121—21no—
237C4×D4—21no—
238C4×D4—21no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C42C22×D1111yescharacteristic
242C4⋊C8—221no—
243C4⋊C8—221no—
244C4⋊C8C22⋊D1112yes—
245#102—24no—
246#102—228no—
247#100—444no—
248C22⋊C8—21no—
249#97—221no—
250C4×C8—21no—
251C4×C8—112no—
252C4×C8—221no—
253C4×C8—221no—
254C2×C11—22no—
255C2×C11—161no—
256C2×C11—162no—
257C2×C11#200411yescharacteristic
258C2×C11#201111yescharacteristic
259C2×C11#201911yescharacteristic
260C24—22no—
261#41—42no—
262#41—42no—
263C2×Q8—21no—
264C2×Q8—222no—
265C2×Q8—441no—
266C2×Q8—442no—
267C2×Q8—442no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—22no—
272C2×D4—21no—
273C2×D4—44no—
274C2×D4—41no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—82no—
282C22×C4—41no—
283C22×C4—441no—
284C22×C4D4×D1111yescharacteristic
285C22×C4#434111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287Q16—448no—
288SD16—448no—
289D8—84no—
290M16—114no—
291M16—222no—
292M16—442no—
293C2×C8—22no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8—442no—
297C2×C8—441no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—222no—
301C4⋊C4—222no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42D4×D1111yescharacteristic
307C42D4×D1111yescharacteristic
308C42C2×C22⋊D1111yescharacteristic
309C42C2×C22⋊D1111yescharacteristic
310C11#1016811yescharacteristic, complemented, Sylow
311C23—41no—
312C23—42no—
313C23—44no—
314C23—82no—
315C23—82no—
316C23#6699211yescharacteristic
317Q8—42no—
318Q8—444no—
319Q8—881no—
320Q8—881no—
321D4—44no—
322D4—42no—
323D4—42no—
324D4—42no—
325D4—44no—
326D4—82no—
327D4—82no—
328D4—81no—
329D4—81no—
330D4—82no—
331D4—82no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—442no—
338C2×C4—882no—
339C2×C4D8×D1112yes—
340C2×C4#6696412yes—
341C2×C4#6699011yescharacteristic
342C2×C4#6699011yescharacteristic
343C2×C4#6699111yescharacteristic
344C2×C4#6699211yescharacteristic
345C2×C4#6699311yescharacteristic
346C2×C4#6700611yescharacteristic
347C8—42no—
348C8—224no—
349C8—442no—
350C8—881no—
351C22—21no—
352C22—21no—
353C22—82no—
354C22—81no—
355C22—81no—
356C22—82no—
357C22—81no—
358C22—82no—
359C22—164no—
360C22#1062276312yes—
361C22#1062283611yescharacteristic
362C4—21no—
363C4—21no—
364C4—81no—
365C4—882no—
366C4#1062276411yescharacteristic
367C4#1062276711yescharacteristic
368C4#1062276912yes—
369C4#1062281312yes—
370C4#1062285512yes—
371C2—22no—
372C2—162no—
373C2—161no—
374C2#1306964311yescharacteristic
375C2#1306968511yescharacteristic
376C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3205C2
socleC22×C11#392
hypercenter#3205D11
hypocenterC11#10168
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. #13079076C2semidirect
2. C2×#10622683C2semidirect
3. #13069457C2semidirect
4. #13067287C2semidirect
5. #13067067C2semidirect
6. #13066452C2semidirect
118. #4318D8semidirect
310. C11#10168semidirect

Maximal subgroups

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

subgroupindex
#130790762
C2×#106226832
#130694572
#130672872
#130670672
#130664522
C11×#32052
#1016811