Finite Group Databasebeta

← #14655899

Subgroups — #14655899

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#13079741C211yesmaximal, characteristic, complemented
2#13079009C211yesmaximal, characteristic, complemented
3#13069538C211yesmaximal, characteristic, complemented
4#13069536C211yesmaximal, characteristic, complemented
5#13067111C211yesmaximal, characteristic, complemented
6#13066466C211yesmaximal, characteristic, complemented
7C11×#3245C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C11×#532C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#474—21no—
12C11×#474—21no—
13C11×#466—22no—
14C11×#459—21no—
15C11×#459—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×#66901—22no—
18#10622845—22no—
19C2×#66880—22no—
20#10622694—21no—
21#10622692—21no—
22#10622683—21no—
23#10622683—21no—
24#10622668—22no—
25#10622647—22no—
26#10622621—22no—
27C4×C4⋊Dic11C2211yescharacteristic
28#10622538C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30#10622175—22no—
31C2×C11×#41—21no—
32C2×C11×#41—21no—
33C22×Dic22—21no—
34C2×C11×D8—22no—
35C22×C8×C11D412yes—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×#127D411yescharacteristic
39C11×#127D411yescharacteristic
40C11×#124—21no—
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C11×#121—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4×Dic11—21no—
55C2×#4318D412yes—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922D412yes—
60C11×#107—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×#102—22no—
64C11×#102—22no—
65#66901—44no—
66#66899—24no—
67#66896—24no—
68#66896—24no—
69C11⋊#95—21no—
70C22⋊(C11⋊C8)D412yes—
71#66880—44no—
72#66872—24no—
73C4⋊(C11⋊C8)—21no—
74#66867—21no—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10200—111nomaximal, Sylow
78C11×#41—42no—
79C11×#41—42no—
80C11×#41—42no—
81C11×#41—42no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×Dic11—41no—
98C22×Dic11—41no—
99C2×Dic22—22no—
100C2×Dic22—42no—
101C2×Dic22—42no—
102C2×Dic22—41no—
103C11×D8—82no—
104C2×C8×C11—22no—
105C2×C8×C11—42no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4×Dic11—42no—
125#4318—22no—
126#4318—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129#3245D1111yescharacteristic
130#3227—111no—
131#3141—111no—
132#1981—111no—
133#1980—111no—
134#1502—111no—
135#1283—111no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11#12711yescharacteristic
139Q8×C11—42no—
140Q8×C11—42no—
141D4×C11—42no—
142D4×C11—42no—
143D4×C11—41no—
144D4×C11—41no—
145D4×C11—41no—
146D4×C11—41no—
147D4×C11—42no—
148D4×C11—81no—
149D4×C11—81no—
150D4×C11—81no—
151D4×C11—81no—
152D4×C11—81no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#13512yes—
167C2×C4×C11AGL(1,ℤ/8)12yes—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—82no—
171C2×Dic11—81no—
172C2×Dic11—81no—
173Dic22—44no—
174Dic22—81no—
175Dic22—81no—
176C8×C11—42no—
177C11⋊C8—42no—
178C11⋊C8—42no—
179#532C2×D1111yescharacteristic
180#532C2×D1111yescharacteristic
181C2×C4⋊Q8—111no—
182#498—221no—
183#489—222no—
184#487—221no—
185#486—221no—
186#486—221no—
187#481—222no—
188#476—222no—
189#474—21no—
190#474—21no—
191#466—22no—
192#459—21no—
193#459—21no—
194#431—111no—
195C2×C4⋊C8C2×D1111yescharacteristic
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—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11#39211yescharacteristic
211C22×C11#49511yescharacteristic
212C22×C11#49611yescharacteristic
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—81no—
217C4×C11—81no—
218C4×C11#44912yes—
219C4×C11#45311yescharacteristic
220C4×C11#45411yescharacteristic
221C4×C11#46312yes—
222Dic11—82no—
223Dic11—82no—
224C2×#41—21no—
225C2×#41—21no—
226C22×Q8—221no—
227C2×D8—22no—
228C2×M16—112no—
229C22×C8C22⋊D1112yes—
230C4⋊Q8—112no—
231C4⋊Q8—221no—
232C4⋊Q8—221no—
233C4⋊Q8—221no—
234C4⋊Q8C22⋊D1111yescharacteristic
235C4⋊Q8C22⋊D1111yescharacteristic
236#127C22⋊D1111yescharacteristic
237#127C22⋊D1111yescharacteristic
238#124—21no—
239#124—21no—
240#121—21no—
241#121—21no—
242#121—21no—
243#121—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247C4×D4—21no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4—221no—
251C2×C42—221no—
252C2×C42C22×D1111yescharacteristic
253#107—22no—
254#106—224no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—221no—
258#104—444no—
259#103—224no—
260#103—444no—
261#102—22no—
262#102—22no—
263#102—224no—
264#102—224no—
265C22⋊C8—112no—
266#97—221no—
267C4×C8—221no—
268C4×C8—221no—
269#95—221no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—161no—
273C2×C11—161no—
274C2×C11#200611yescharacteristic
275C2×C11#200911yescharacteristic
276C2×C11#201211yescharacteristic
277#41—42no—
278#41—42no—
279#41—42no—
280#41—42no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—222no—
284C2×Q8—442no—
285C2×Q8—442no—
286C2×Q8—441no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—41no—
294C2×D4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—441no—
298C22×C4—441no—
299C22×C4D4×D1111yescharacteristic
300C22×C4D4×D1111yescharacteristic
301C22×C4C2×C22⋊D1111yescharacteristic
302D8—82no—
303M16—222no—
304M16—222no—
305C2×C8—22no—
306C2×C8—42no—
307C2×C8—222no—
308C2×C8—222no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—222no—
314C4⋊C4—222no—
315C4⋊C4—222no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C42—442no—
324C42D4×D1111yescharacteristic
325C42#434111yescharacteristic
326C42C2×C22⋊D1111yescharacteristic
327C42C2×C22⋊D1111yescharacteristic
328C11#1020011yescharacteristic, complemented, Sylow
329C23—41no—
330C23—41no—
331C23#6699311yescharacteristic
332Q8—42no—
333Q8—42no—
334Q8—444no—
335Q8—881no—
336Q8—881no—
337D4—42no—
338D4—42no—
339D4—42no—
340D4—41no—
341D4—41no—
342D4—41no—
343D4—41no—
344D4—81no—
345D4—81no—
346D4—81no—
347D4—81no—
348D4—81no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—882no—
359C2×C4—881no—
360C2×C4—881no—
361C2×C4#6696412yes—
362C2×C4#6696512yes—
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—81no—
378C22—81no—
379C22—81no—
380C22#1062276711yescharacteristic
381C22#1062276811yescharacteristic
382C22#1062283611yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—81no—
387C4—81no—
388C4—882no—
389C4—882no—
390C4#1062276612yes—
391C4#1062277112yes—
392C4#1062285411yescharacteristic
393C4#1062285811yescharacteristic
394C2—21no—
395C2—21no—
396C2—161no—
397C2—161no—
398C2#1306965811yescharacteristic
399C2#1306967311yescharacteristic
400C2#1306969111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3245C2
socleC22×C11#392
hypercenter#3245D11
hypocenterC11#10200
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #13079741C2semidirect
2. #13079009C2semidirect
3. #13069538C2semidirect
4. #13069536C2semidirect
5. #13067111C2semidirect
6. #13066466C2semidirect
328. C11#10200semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130790092
#130695382
#130695362
#130671112
#130664662
C11×#32452
#1020011