Finite Group Databasebeta

← #14655896

Subgroups — #14655896

Order 2816.

550 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079923C211yesmaximal, characteristic
2#13079012C211yesmaximal, characteristic, complemented
3#13069540C211yesmaximal, characteristic, complemented
4#13069536C211yesmaximal, characteristic, complemented
5#13067112C211yesmaximal, characteristic, complemented
6#13066465C211yesmaximal, characteristic, complemented
7C11×#3227C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#498—21no—
12C11×#486—21no—
13C11×#481—22no—
14C11×#476—22no—
15C11×#431C2211yescharacteristic
16C2×#66901—22no—
17C2×#66899—22no—
18#10622706—21no—
19#10622702—22no—
20#10622701—21no—
21#10622700—21no—
22#10622685—21no—
23#10622651—22no—
24#10622628—21no—
25#10622620—21no—
26#10622579—22no—
27C4×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30#10622108—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C2×#4339—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D412yes—
39C11×#127D411yescharacteristic
40C11×#124—21no—
41C11×#121—21no—
42C11×#121—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4323—22no—
49#66983—21no—
50#66983—21no—
51C2×C4⋊Dic11—21no—
52C2×C4×Dic11—21no—
53C2×#4318D412yes—
54C22×C11⋊C8D412yes—
55#66928—21no—
56#66927D411yescharacteristic
57C4×D44—21no—
58C4×D44—21no—
59#66922D411yescharacteristic
60C11×#106—24no—
61C11×C4⋊C8—21no—
62C11×#102—24no—
63C11×C22⋊C8D412yes—
64C4×C8×C11—21no—
65#66901—44no—
66#66899—44no—
67#66896—22no—
68C11⋊#95—21no—
69#66874—24no—
70#66873—24no—
71#66873—22no—
72#66871—22no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75#66867—21no—
76C4×C11⋊C8—21no—
77#10200—111nomaximal, Sylow
78C11×#41—42no—
79C11×#41—42no—
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—42no—
83C2×Q8×C11—42no—
84C2×Q8×C11—41no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—41no—
95C22×Dic11—41no—
96#4339—42no—
97#4339—42no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×C4×D11—41no—
102C2×Dic22—21no—
103C2×C8×C11—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116#4323—82no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119C4⋊Dic11—22no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—41no—
123C4×Dic11—42no—
124#4318—22no—
125#4318—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—42no—
129#3245—111no—
130#3227D1111yescharacteristic, complemented
131#3141—111no—
132#1981—111no—
133#1980—111no—
134#1502—111no—
135#1283—111no—
136C23×C11—41no—
137C23×C11#12711yescharacteristic
138C22×D11—41no—
139Q8×C11—44no—
140Q8×C11—42no—
141Q8×C11—81no—
142Q8×C11—81no—
143D4×C11—42no—
144D4×C11—41no—
145D4×C11—41no—
146D4×C11—42no—
147D4×C11—81no—
148D4×C11—81no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—82no—
155C2×C4×C11—82no—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#13512yes—
163C2×C4×C11AGL(1,ℤ/8)12yes—
164C22⋊D11—81no—
165C22⋊D11—81no—
166C2×Dic11—42no—
167C2×Dic11—41no—
168C2×Dic11—81no—
169C2×Dic11—81no—
170D44—42no—
171D44—41no—
172D44—41no—
173D44—81no—
174C4×D11—82no—
175Dic22—42no—
176C8×C11—42no—
177C11⋊C8—42no—
178C11⋊C8—42no—
179#532—111no—
180#532C2×D1111yescharacteristic
181C2×C4⋊Q8C2×D1111yescharacteristic
182#498—21no—
183#489—222no—
184#487—221no—
185#486—21no—
186#486—221no—
187#481—22no—
188#476—22no—
189#474—221no—
190#474—221no—
191#466—222no—
192#459—221no—
193#459—221no—
194#431C2×D1111yescharacteristic
195C2×C4⋊C8—111no—
196C2×#104—222no—
197#417—222no—
198C2×#103—222no—
199C4×M16—111no—
200C4×C4⋊C4—111no—
201#327—222no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11#39211yescharacteristic
208C22×C11#49511yescharacteristic
209C22×C11#49611yescharacteristic
210C2×D11—81no—
211C2×D11—81no—
212C2×D11—81no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—82no—
217C4×C11—81no—
218C4×C11#44912yes—
219C4×C11#45311yescharacteristic
220C4×C11#45411yescharacteristic
221C4×C11#46312yes—
222Dic11—82no—
223Dic11—81no—
224C2×#41—21no—
225C2×#41—221no—
226C22×Q8—21no—
227C2×D8—222no—
228C2×M16—112no—
229C22×C8—112no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—111no—
234C4⋊Q8C22⋊D1112yes—
235C4⋊Q8C22⋊D1111yescharacteristic
236#127—111no—
237#127C22⋊D1111yescharacteristic
238#124—21no—
239#124—221no—
240#121—21no—
241#121—21no—
242#121—221no—
243#121—221no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—221no—
247C4×D4—221no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—221no—
251C2×C42—221no—
252C2×C42C22×D1111yescharacteristic
253#107—222no—
254#106—24no—
255C4⋊C8—21no—
256C4⋊C8—221no—
257C4⋊C8—221no—
258#104—444no—
259#103—224no—
260#103—444no—
261#102—24no—
262#102—224no—
263#102—222no—
264#102—222no—
265C22⋊C8C22⋊D1112yes—
266#97—221no—
267C4×C8—21no—
268C4×C8—221no—
269#95—221no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—161no—
273C2×C11#200611yescharacteristic
274C2×C11#200911yescharacteristic
275C2×C11#201211yescharacteristic
276D11—161no—
277#41—42no—
278#41—42no—
279#41—442no—
280#41—442no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×Q8—41no—
286C2×Q8—221no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—221no—
294C2×D4—441no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—441no—
298C22×C4—441no—
299C22×C4D4×D1111yescharacteristic
300C22×C4D4×D1111yescharacteristic
301C22×C4C2×C22⋊D1111yescharacteristic
302D8—882no—
303M16—222no—
304M16—222no—
305C2×C8—22no—
306C2×C8—222no—
307C2×C8—222no—
308C2×C8—442no—
309C4⋊C4—22no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—222no—
316C4⋊C4—221no—
317C4⋊C4—221no—
318C4⋊C4—441no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—441no—
322C22⋊C4—441no—
323C42—442no—
324C42D4×D1111yescharacteristic
325C42#434111yescharacteristic
326C42C2×C22⋊D1111yescharacteristic
327C42C2×C22⋊D1111yescharacteristic
328C11#1020011yescharacteristic, complemented, Sylow
329C23—41no—
330C23—441no—
331C23#6699311yescharacteristic
332Q8—44no—
333Q8—42no—
334Q8—81no—
335Q8—81no—
336Q8—442no—
337D4—42no—
338D4—42no—
339D4—41no—
340D4—41no—
341D4—81no—
342D4—81no—
343D4—442no—
344D4—441no—
345D4—441no—
346D4—881no—
347D4—881no—
348D4—881no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—442no—
357C2×C4—441no—
358C2×C4—881no—
359C2×C4—881no—
360C2×C4—882no—
361C2×C4#6696712yes—
362C2×C4#6696912yes—
363C2×C4#6699011yescharacteristic
364C2×C4#6699011yescharacteristic
365C2×C4#6699111yescharacteristic
366C2×C4#6699211yescharacteristic
367C2×C4#6699211yescharacteristic
368C2×C4#6700611yescharacteristic
369C8—42no—
370C8—442no—
371C8—442no—
372C22—21no—
373C22—21no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—881no—
378C22—881no—
379C22—881no—
380C22#1062278111yescharacteristic
381C22#1062278911yescharacteristic
382C22#1062283611yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—82no—
387C4—81no—
388C4—882no—
389C4—881no—
390C4#1062277812yes—
391C4#1062278512yes—
392C4#1062281111yescharacteristic
393C4#1062281411yescharacteristic
394C2—21no—
395C2—21no—
396C2—161no—
397C2—1761no—
398C2#1306965611yescharacteristic
399C2#1306967611yescharacteristic
400C2#1306969011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3227C2
socleC22×C11#392
prime radical#13079923C2
hypercenter#3227D11
hypocenterC11#10200
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. #13079012C2semidirect
3. #13069540C2semidirect
4. #13069536C2semidirect
5. #13067112C2semidirect
6. #13066465C2semidirect
7. C11×#3227C2semidirect
130. #3227D11semidirect
328. C11#10200semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130790122
#130695402
#130695362
#130671122
#130664652
C11×#32272
#1020011