Finite Group Databasebeta

← #14655563

Subgroups — #14655563

Order 2816.

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

normal subgroups only

This group has 642 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
1C2×#10622689C211yesmaximal, characteristic, complemented
2#13079009C211yesmaximal, characteristic, complemented
3#13069457C211yesmaximal, characteristic, complemented
4#13067300C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#3205C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C22×#4324—22no—
11C2×#66922C2211yescharacteristic
12C11×#493—21no—
13C11×#486—21no—
14C11×#459—22no—
15C11×#447—22no—
16C11×#431C2211yescharacteristic
17#10622845—22no—
18C2×#66897—22no—
19#10622694—21no—
20#10622689—22no—
21#10622689—22no—
22#10622683—21no—
23#10622668—22no—
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27D4⋊(C11⋊C8)—22no—
28#10622120—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×#4324—28no—
48C2×#4324—48no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×#4318—21no—
52C2×#4318D412yes—
53C22×C11⋊C8—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922D412yes—
58C11×C4⋊C8D412yes—
59C11×#102—24no—
60C11×C22⋊C8—21no—
61C4×C8×C11—21no—
62#66899—24no—
63#66897—44no—
64#66896—24no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67#66867—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8D412yes—
71#10152—111nomaximal, Sylow
72C24×C11—22no—
73C11×#41—42no—
74C11×#41—42no—
75C2×Q8×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—44no—
82C2×D4×C11—41no—
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—41no—
95C2×Dic22—22no—
96C2×Dic22—44no—
97C2×Dic22—41no—
98C11×D8—84no—
99C2×C8×C11—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108#4324—416no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113#4318—22no—
114#4318—22no—
115#4318—42no—
116C2×C11⋊C8—24no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120#3205D1111yescharacteristic
121C2×#492—111no—
122#3141—111no—
123#1965—111no—
124#1549—111no—
125#1492—111no—
126#1278—111no—
127C23×C11—41no—
128C23×C11—42no—
129C23×C11—44no—
130C23×C11—82no—
131C23×C11—82no—
132C23×C11#12111yescharacteristic
133Q8×C11—42no—
134D4×C11—44no—
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—44no—
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×C11#13512yes—
157C2×C4×C11AGL(1,ℤ/8)12yes—
158C2×Dic11—42no—
159C2×Dic11—82no—
160Dic22—44no—
161Dic22—82no—
162C8×C11—42no—
163C11⋊C8—24no—
164C11⋊C8—42no—
165C11⋊C8—81no—
166C22×SD16—222no—
167#532C2×D1111yescharacteristic
168C2×C4⋊Q8—111no—
169C2×#127C2×D1111yescharacteristic
170#493—21no—
171#492—222no—
172#492—222no—
173#489—222no—
174#487—221no—
175#486—21no—
176#486—221no—
177#459—22no—
178#447—22no—
179#431C2×D1111yescharacteristic
180#423—111no—
181#417—222no—
182C2×#100—222no—
183C4×M16—111no—
184C2×C4×C8—111no—
185#332—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#46312yes—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—81no—
201C4×C11#44912yes—
202C4×C11#45312yes—
203C4×C11#47112yes—
204C4×C11#49511yescharacteristic
205C4×C11#49611yescharacteristic
206Dic11—82no—
207C2×#41—21no—
208C22×Q8—221no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4C22⋊D1112yes—
212C2×SD16—228no—
213C2×SD16—448no—
214C2×D8—24no—
215C2×M16—112no—
216C2×M16—221no—
217C22×C8—221no—
218C4⋊Q8—112no—
219C4⋊Q8—221no—
220C4⋊Q8—221no—
221C4⋊Q8—221no—
222C4⋊Q8C22⋊D1111yescharacteristic
223#127—21no—
224#127—21no—
225#127—21no—
226#127—21no—
227#127C22⋊D1111yescharacteristic
228#124—21no—
229#121—21no—
230#121—21no—
231C4×D4—21no—
232C4×D4—21no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C42C22×D1111yescharacteristic
236C4⋊C8—221no—
237C4⋊C8—221no—
238C4⋊C8C22⋊D1112yes—
239#103—224no—
240#102—24no—
241#102—224no—
242#100—444no—
243C22⋊C8—21no—
244#97—221no—
245C4×C8—21no—
246C4×C8—112no—
247C4×C8—221no—
248C4×C8—221no—
249C2×C11—22no—
250C2×C11—161no—
251C2×C11—162no—
252C2×C11#200211yescharacteristic
253C2×C11#201211yescharacteristic
254C2×C11#201911yescharacteristic
255C24—22no—
256#41—42no—
257#41—42no—
258C2×Q8—21no—
259C2×Q8—222no—
260C2×Q8—444no—
261C2×Q8—441no—
262C2×D4—21no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—22no—
266C2×D4—21no—
267C2×D4—44no—
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—82no—
276C22×C4—41no—
277C22×C4—441no—
278C22×C4D4×D1111yescharacteristic
279C22×C4#434111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281SD16—4416no—
282D8—84no—
283M16—222no—
284M16—222no—
285M16—442no—
286C2×C8—22no—
287C2×C8—224no—
288C2×C8—222no—
289C2×C8—222no—
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#1015211yescharacteristic, complemented, Sylow
304C23—41no—
305C23—42no—
306C23—44no—
307C23—82no—
308C23—82no—
309C23#6699211yescharacteristic
310Q8—42no—
311Q8—444no—
312Q8—882no—
313D4—44no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—44no—
318D4—82no—
319D4—82no—
320D4—81no—
321D4—81no—
322D4—82no—
323D4—82no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—442no—
330C2×C4—882no—
331C2×C4#6696412yes—
332C2×C4#6696512yes—
333C2×C4#6699011yescharacteristic
334C2×C4#6699011yescharacteristic
335C2×C4#6699111yescharacteristic
336C2×C4#6699211yescharacteristic
337C2×C4#6699311yescharacteristic
338C2×C4#6700611yescharacteristic
339C8—42no—
340C8—224no—
341C8—442no—
342C8—881no—
343C22—21no—
344C22—21no—
345C22—82no—
346C22—81no—
347C22—81no—
348C22—82no—
349C22—81no—
350C22—82no—
351C22—164no—
352C22#1062276612yes—
353C22#1062283611yescharacteristic
354C4—21no—
355C4—21no—
356C4—81no—
357C4—882no—
358C4#1062276711yescharacteristic
359C4#1062276811yescharacteristic
360C4#1062277112yes—
361C4#1062281312yes—
362C4#1062285412yes—
363C2—22no—
364C2—162no—
365C2—161no—
366C2#1306962911yescharacteristic
367C2#1306969111yescharacteristic
368C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3205C2
socleC22×C11#392
hypercenter#3205D11
hypocenterC11#10152
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. C2×#10622689C2semidirect
2. #13079009C2semidirect
3. #13069457C2semidirect
4. #13067300C2semidirect
5. #13067067C2semidirect
6. #13066452C2semidirect
303. C11#10152semidirect

Maximal subgroups

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

subgroupindex
C2×#106226892
#130790092
#130694572
#130673002
#130670672
#130664522
C11×#32052
#1015211