Finite Group Databasebeta

← #14654741

Subgroups — #14654741

Order 2816.

550 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 97 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#13078964C211yesmaximal, characteristic, complemented
2#13078616C211yesmaximal, characteristic
3#13069415C211yesmaximal, characteristic, complemented
4#13067019C211yesmaximal, characteristic, complemented
5#13067016C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#3101C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#483—21no—
12C11×#476—21no—
13C11×#461—21no—
14C11×#450—21no—
15C4×C11×SD16—22no—
16C11×#431C2211yescharacteristic
17#10622830—21no—
18C2×C22⋊(C11⋊C8)—22no—
19#10622702—21no—
20#10622702—21no—
21#10622682—21no—
22#10622680—21no—
23#10622628—21no—
24C4×#4323—22no—
25#10622620—21no—
26#10622615—22no—
27#10622580—21no—
28#10622538C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×#66867C2211yescharacteristic
31Q8⋊(C11⋊C8)—22no—
32#10622097—22no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C2×#4339—21no—
36C2×C11×SD16—22no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×#125—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C11×#117—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4323—22no—
53#66983—21no—
54#66983—21no—
55C22×C11⋊C8—21no—
56C22×C11⋊C8D412yes—
57#66928—21no—
58#66927D411yescharacteristic
59C4×D44—21no—
60C4×D44—21no—
61#66922D411yescharacteristic
62C11×#106—22no—
63C11×C4⋊C8—21no—
64C11×#103—22no—
65C11×#102—22no—
66C11×C22⋊C8—21no—
67C4×C8×C11D412yes—
68#66896—22no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—44no—
71#66874—22no—
72#66874—22no—
73#66873—22no—
74#66873—22no—
75#66873—22no—
76#66871—22no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80#66867—21no—
81#66867—21no—
82C4×C11⋊C8D412yes—
83#10033—111nomaximal, Sylow
84C24×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—42no—
90C22×C4×C11—21no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C2×C22⋊D11—41no—
99#4339—42no—
100#4339—42no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×C4×D11—41no—
105C2×Dic22—21no—
106C11×SD16—44no—
107C2×C8×C11—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124#4323—44no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—42no—
135#3135—111no—
136#3101D1111yescharacteristic, complemented
137#3100—111no—
138#1955—111no—
139#1481—111no—
140#1480—111no—
141#1275—111no—
142C23×C11—22no—
143C23×C11—41no—
144C23×C11—42no—
145C23×C11—41no—
146C23×C11—42no—
147C23×C11#12111yescharacteristic
148C22×D11—41no—
149Q8×C11—42no—
150Q8×C11—42no—
151D4×C11—22no—
152D4×C11—22no—
153D4×C11—41no—
154D4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—82no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12711yescharacteristic
170C2×C4×C11#13512yes—
171C2×C4×C11AGL(1,ℤ/8)12yes—
172C22⋊D11—82no—
173C2×Dic11—41no—
174D44—42no—
175D44—42no—
176D44—42no—
177C4×D11—81no—
178C4×D11—81no—
179Dic22—42no—
180C8×C11—42no—
181C11⋊C8—42no—
182C11⋊C8—42no—
183C11⋊C8—81no—
184#533C2×D1111yescharacteristic
185#532—111no—
186C2×C4×D4C2×D1111yescharacteristic
187#491—221no—
188#490—221no—
189#489—221no—
190#489—221no—
191#483—21no—
192#480—221no—
193#476—21no—
194#474—221no—
195#461—21no—
196#459—221no—
197#450—21no—
198#447—221no—
199C4×SD16—22no—
200C4×D8—222no—
201#431—111no—
202#431C2×D1111yescharacteristic
203C2×C4⋊C8—111no—
204#416—222no—
205C2×C22⋊C8—222no—
206C2×#97—111no—
207Q8⋊C8—222no—
208D4⋊C8—222no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—44no—
212C22×C11—42no—
213C22×C11—82no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11#39211yescharacteristic
217C22×C11#46312yes—
218C2×D11—81no—
219C2×D11—81no—
220C2×D11—81no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11—81no—
228C4×C11#44912yes—
229C4×C11#49511yescharacteristic
230C4×C11#49611yescharacteristic
231Dic11—81no—
232C2×#41—221no—
233C22×D4C22⋊D1111yescharacteristic
234C23×C4—21no—
235C2×SD16—22no—
236C2×D8—222no—
237C22×C8—112no—
238C22×C8—221no—
239C4⋊Q8—111no—
240C4⋊Q8C22⋊D1111yescharacteristic
241C4⋊Q8C22⋊D1111yescharacteristic
242#127—111no—
243#125—21no—
244#124—221no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247#121—221no—
248#121—221no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—221no—
256C4×D4—221no—
257#117—21no—
258C2×C4⋊C4C22⋊D1111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C22×D1111yescharacteristic
261#107—222no—
262#106—22no—
263C4⋊C8—21no—
264C4⋊C8—221no—
265C4⋊C8—221no—
266C4⋊C8—221no—
267#103—22no—
268#103—222no—
269#103—222no—
270#102—22no—
271#102—222no—
272#102—222no—
273#102—222no—
274#102—222no—
275C22⋊C8—21no—
276C22⋊C8—221no—
277C22⋊C8—444no—
278#97—221no—
279#97—221no—
280C4×C8—112no—
281C4×C8C22⋊D1112yes—
282C2×C11—22no—
283C2×C11—82no—
284C2×C11#201011yescharacteristic
285C2×C11#201211yescharacteristic
286C2×C11#201711yescharacteristic
287D11—161no—
288C24—21no—
289#41—442no—
290#41—442no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—221no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—42no—
297C2×D4—221no—
298C2×D4—221no—
299C2×D4—221no—
300C2×D4—441no—
301C22×C4—21no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—441no—
307C22×C4D4×D1111yescharacteristic
308C22×C4#434111yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310SD16—44no—
311D8—444no—
312C2×C8—22no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8—222no—
317C2×C8—442no—
318C2×C8—441no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—221no—
328C4⋊C4—221no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C42—41no—
335C42D4×D1111yescharacteristic
336C42D4×D1111yescharacteristic
337C42C2×C22⋊D1111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C11#1003311yescharacteristic, complemented, Sylow
340C23—22no—
341C23—41no—
342C23—42no—
343C23—42no—
344C23—41no—
345C23—441no—
346C23#6699211yescharacteristic
347Q8—42no—
348Q8—42no—
349Q8—442no—
350D4—22no—
351D4—22no—
352D4—41no—
353D4—41no—
354D4—442no—
355D4—442no—
356D4—442no—
357D4—882no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—81no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—441no—
368C2×C4—881no—
369C2×C4—881no—
370C2×C4#6696712yes—
371C2×C4#6696912yes—
372C2×C4#6699011yescharacteristic
373C2×C4#6699011yescharacteristic
374C2×C4#6699111yescharacteristic
375C2×C4#6699211yescharacteristic
376C2×C4#6699311yescharacteristic
377C2×C4#6700611yescharacteristic
378C8—42no—
379C8—442no—
380C8—442no—
381C8—881no—
382C22—21no—
383C22—21no—
384C22—44no—
385C22—42no—
386C22—82no—
387C22—81no—
388C22—81no—
389C22—881no—
390C22—881no—
391C22—881no—
392C22#1062277812yes—
393C22#1062283611yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—81no—
399C4—81no—
400C4—81no—
401C4—881no—
402C4#1062278111yescharacteristic
403C4#1062278512yes—
404C4#1062278911yescharacteristic
405C2—22no—
406C2—82no—
407C2—1761no—
408C2#1306968111yescharacteristic
409C2#1306969011yescharacteristic
410C2#1306971911yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3101C2
socleC22×C11#392
prime radical#13078616C2
hypercenter#3101D11
hypocenterC11#10033
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3101

Complements

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

NH ≅ G/Ntype
1. #13078964C2semidirect
3. #13069415C2semidirect
4. #13067019C2semidirect
5. #13067016C2semidirect
6. #13066446C2semidirect
7. C11×#3101C2semidirect
136. #3101D11semidirect
339. C11#10033semidirect

Maximal subgroups

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

subgroupindex
#130789642
#130786162
#130694152
#130670192
#130670162
#130664462
C11×#31012
#1003311