Finite Group Databasebeta

← #14656333

Subgroups — #14656333

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic
2C2×#10622704C211yesmaximal, characteristic, complemented
3C2×#10622461C211yesmaximal, characteristic
4#13069551C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#333C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4314—21no—
10C2×#66927C2211yescharacteristic
11C2×C4×Dic22C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×#66885—21no—
15#10622704—22no—
16#10622704—22no—
17#10622701—22no—
18#10622701—22no—
19C2×#66874—21no—
20C2×#66873—22no—
21C2×#66871—21no—
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622461—22no—
25#10622461—22no—
26C11×#333—22no—
27#10622188—22no—
28#10622123—22no—
29C22×Q8×C11—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44—21no—
33C22×Dic22D411yescharacteristic
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D412yes—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C42×C11C2311yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8D412yes—
48C2×#4314—24no—
49C2×#4314—42no—
50C2×#4314—42no—
51#66927—21no—
52#66927—21no—
53#66927—21no—
54#66927D412yes—
55C4×Dic22—21no—
56C4×Dic22—21no—
57C4×Dic22—21no—
58C4×Dic22—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63#66885—24no—
64#66874—24no—
65#66873—28no—
66#66871—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#10269—111nomaximal, Sylow
72C23×D11—41no—
73C2×Q8×C11—22no—
74C2×Q8×C11—41no—
75C2×Q8×C11—82no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—21no—
82C2×D44—22no—
83C2×D44—22no—
84C2×D44—22no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44—42no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—42no—
94C2×D44—82no—
95C2×Dic22—21no—
96C2×Dic22—21no—
97C2×Dic22—21no—
98C2×Dic22—21no—
99C2×Dic22—21no—
100C2×Dic22SD1612yes—
101C2×C8×C11—22no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—42no—
105C2×C8×C11—41no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116Dic11⋊C4—41no—
117Dic11⋊C4—41no—
118C4×Dic11—41no—
119C4×Dic11—41no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126#4314—48no—
127C2×#486—111no—
128C2×#477—111no—
129C2×#460—111no—
130#1984—111no—
131C2×#333D1111yescharacteristic, complemented
132C2×#331—111no—
133#1277—111no—
134C23×C11#12111yescharacteristic
135C22×D11—42no—
136C22×D11—82no—
137C22×D11—81no—
138C22×D11—81no—
139C22×D11—82no—
140Q8×C11—82no—
141Q8×C11—82no—
142C2×C4×C11—22no—
143C2×C4×C11—42no—
144C2×C4×C11—82no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12711yescharacteristic
151C2×C4×C11C2×SD1611yescharacteristic
152C2×C4×C11#13512yes—
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C2×C4×C11#13712yes—
157C2×Dic11—22no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—42no—
162D44—42no—
163D44—42no—
164D44—44no—
165D44—82no—
166D44—82no—
167D44—81no—
168D44—81no—
169D44—81no—
170D44—81no—
171Dic22—22no—
172Dic22—22no—
173Dic22—41no—
174Dic22—41no—
175C8×C11—42no—
176C8×C11—81no—
177C11⋊C8—42no—
178C11⋊C8—42no—
179C22×SD16—221no—
180C2×C4⋊Q8C2×D1111yescharacteristic
181C2×#127—111no—
182C2×C4×Q8—111no—
183#486—222no—
184#486—222no—
185#477—222no—
186#477—222no—
187#460—222no—
188#460—222no—
189C2×#107—221no—
190C2×C4⋊C8—111no—
191C2×C4⋊C8C2×D1111yescharacteristic
192C2×C4⋊C8C2×D1111yescharacteristic
193C2×#103—221no—
194C2×#102—222no—
195C2×#102—221no—
196C2×C4×C8—111no—
197#336—222no—
198#333—22no—
199#331—222no—
200C22×C11#39211yescharacteristic
201C22×C11#46412yes—
202C22×C11#46511yescharacteristic
203C22×C11#46811yescharacteristic
204C22×C11#47212yes—
205C2×D11—82no—
206C2×D11—82no—
207C2×D11—82no—
208C2×D11—162no—
209C2×D11—162no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—82no—
213C4×C11#44811yescharacteristic
214C4×C11#44911yescharacteristic
215C4×C11#45011yescharacteristic
216C4×C11#45211yescharacteristic
217C4×C11#45212yes—
218C4×C11#49511yescharacteristic
219C4×C11#49711yescharacteristic
220Dic11—42no—
221Dic11—81no—
222C22×Q8—21no—
223C22×Q8—111no—
224C22×D4—221no—
225C22×D4—221no—
226C22×D4—221no—
227C2×SD16—224no—
228C2×SD16—442no—
229C2×SD16—442no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—112no—
233C22×C8—221no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8D4412yes—
238#127—112no—
239#127—221no—
240#127—221no—
241#127—221no—
242C4×Q8—221no—
243C4×Q8—221no—
244C4×Q8—221no—
245C4×Q8—221no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—111no—
249C2×C4⋊C4—221no—
250C2×C42—221no—
251C2×C42C22×D1111yescharacteristic
252#107—224no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—112no—
257C4⋊C8—221no—
258C4⋊C8C22⋊D1112yes—
259#103—224no—
260#102—228no—
261#102—224no—
262C4×C8—221no—
263C4×C8—221no—
264C2×C11#167812yes—
265C2×C11#169812yes—
266C2×C11#200011yescharacteristic
267C2×C11#201511yescharacteristic
268C2×C11#201811yescharacteristic
269D11—162no—
270C24—441no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—82no—
274C2×Q8—112no—
275C2×Q8—221no—
276C2×Q8—221no—
277C2×Q8—221no—
278C2×Q8—221no—
279C2×Q8—221no—
280C2×D4—222no—
281C2×D4—222no—
282C2×D4—222no—
283C2×D4—441no—
284C2×D4—441no—
285C2×D4—441no—
286C2×D4—442no—
287C2×D4—441no—
288C2×D4—442no—
289C2×D4—441no—
290C2×D4—441no—
291C2×D4—441no—
292C2×D4—882no—
293C22×C4—41no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4#433911yescharacteristic
297C22×C4D4×D1111yescharacteristic
298C22×C4D4×D1111yescharacteristic
299SD16—448no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—42no—
304C2×C8—41no—
305C2×C8—222no—
306C2×C8—222no—
307C2×C8—222no—
308C2×C8—222no—
309C2×C8—441no—
310C2×C8—441no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C42—441no—
320C42—441no—
321C42C2×D4411yescharacteristic
322C42D4×D1111yescharacteristic
323C42D4×D1111yescharacteristic
324C42C2×C22⋊D1111yescharacteristic
325C11#1026911yescharacteristic, complemented, Sylow
326C23—442no—
327C23—882no—
328C23—882no—
329C23—881no—
330C23—881no—
331C23#6693711yescharacteristic
332Q8—82no—
333Q8—82no—
334Q8—222no—
335Q8—222no—
336Q8—441no—
337Q8—441no—
338D4—442no—
339D4—442no—
340D4—444no—
341D4—882no—
342D4—882no—
343D4—881no—
344D4—881no—
345D4—881no—
346D4—881no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—82no—
350C2×C4—222no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—442no—
355C2×C4#6693511yescharacteristic
356C2×C4#6693511yescharacteristic
357C2×C4#6693711yescharacteristic
358C2×C4SD16×D1111yescharacteristic
359C2×C4#6696711yescharacteristic
360C2×C4#6696912yes—
361C2×C4#6697111yescharacteristic
362C2×C4#6697112yes—
363C2×C4#6697211yescharacteristic
364C2×C4#6698311yescharacteristic
365C2×C4#6699011yescharacteristic
366C2×C4#6699311yescharacteristic
367C8—42no—
368C8—81no—
369C8—442no—
370C8—442no—
371C22—882no—
372C22—882no—
373C22—882no—
374C22—1762no—
375C22—1762no—
376C22#1062236212yes—
377C22#1062241112yes—
378C22#1062242011yescharacteristic
379C22#1062242511yescharacteristic
380C22#1062257311yescharacteristic
381C4—21no—
382C4—21no—
383C4—82no—
384C4—442no—
385C4—881no—
386C4#1062241911yescharacteristic
387C4#1062242312yes—
388C4#1062242411yescharacteristic
389C4#1062278111yescharacteristic
390C4#1062278211yescharacteristic
391C4#1062280011yescharacteristic
392C4#1062280311yescharacteristic
393C2—1762no—
394C2#1306803512yes—
395C2#1306815912yes—
396C2#1306961811yescharacteristic
397C2#1306971111yescharacteristic
398C2#1306972411yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#333C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenterC2×#333D11
hypocenterC11#10269
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
2. C2×#10622704C2semidirect
4. #13069551C2semidirect
6. #13066450C2semidirect
7. C2×C11×#333C2semidirect
131. C2×#333D11semidirect
325. C11#10269semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106227042
C2×#106224612
#130695512
C2×#106221232
#130664502
C2×C11×#3332
#1026911