Finite Group Databasebeta

← #14652822

Subgroups — #14652822

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076974C211yesmaximal, characteristic
2#13068732C211yesmaximal, characteristic, complemented
3C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
4C2×#10622185C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6C2×#10622123C211yesmaximal, characteristic
7C2×C11×#332C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#67000—21no—
10C2×#67000—21no—
11C2×#66927C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C8×Dic11—21no—
15#10622601—22no—
16#10622601C414yes—
17C42×Dic11C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#332—22no—
21#10622188—21no—
22#10622188—22no—
23#10622185—22no—
24#10622123—22no—
25#10622123—22no—
26C22×Q8×C11—21no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44C2×C412yes—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C412yes—
38C2×C42×C11C2311yescharacteristic
39#67000—42no—
40#67000—42no—
41#67000—42no—
42#67000—42no—
43C2×(C2×D11)⋊C4—24no—
44C2×(C2×D11)⋊C4—24no—
45C2×C4×Dic11C2×C412yes—
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D412yes—
48C2×C4×Dic11D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51#66927—21no—
52#66927—21no—
53#66927—21no—
54#66927—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C8×Dic11—42no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)D412yes—
64#9696—111nomaximal, Sylow
65C23×D11—22no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C22×C4×C11—22no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11C22⋊C412yes—
77C22×Dic11C22⋊C412yes—
78C2×D44—22no—
79C2×D44—22no—
80C2×D44—44no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—42no—
88C2×D44—42no—
89C2×D44—41no—
90C2×D44—41no—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—42no—
95C2×C8×C11—41no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103C42×C11#4111yescharacteristic
104(C2×D11)⋊C4—48no—
105(C2×D11)⋊C4—48no—
106C4×Dic11—22no—
107C4×Dic11—22no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—42no—
111C4×Dic11D812yes—
112C4×Dic11SD1612yes—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—42no—
117C2×C11⋊C8—41no—
118#2858—111no—
119#1831—111no—
120C4×C4⋊C8—111no—
121C2×#332—111no—
122C2×#332D1111yescharacteristic, complemented
123C2×#331—111no—
124C2×#331—111no—
125C23×C11C2×C22⋊C411yescharacteristic
126C22×D11—42no—
127C22×D11—44no—
128C22×D11—42no—
129C22×D11—44no—
130C22×D11—42no—
131Q8×C11—81no—
132Q8×C11—81no—
133Q8×C11—81no—
134Q8×C11—81no—
135C2×C4×C11—22no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12411yescharacteristic
144C2×C4×C11#12711yescharacteristic
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C2×SD1611yescharacteristic
147C2×C4×C11#13512yes—
148C2×C4×C11#13512yes—
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×Dic11—22no—
152C2×Dic11—22no—
153C2×Dic11—22no—
154C2×Dic11—22no—
155C2×Dic11—22no—
156C2×Dic11#10214yes—
157D44—82no—
158D44—82no—
159D44—81no—
160D44—81no—
161D44—81no—
162D44—81no—
163D44—82no—
164D44—81no—
165D44—81no—
166C8×C11—42no—
167C8×C11—81no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C2×C4⋊Q8C2×D1111yescharacteristic
171C2×#127—111no—
172C2×#124—221no—
173C2×#124—221no—
174C2×C4⋊C8—111no—
175C2×C4⋊C8—111no—
176C2×C4⋊C8C2×D1111yescharacteristic
177C2×C4⋊C8C2×D1111yescharacteristic
178C2×C4×C8—221no—
179#390—114no—
180#390—222no—
181C43—111no—
182#336—222no—
183#336—221no—
184#332—22no—
185#332—222no—
186#331—222no—
187#331—222no—
188C22×C11#39011yescharacteristic
189C22×C11#41312yes—
190C22×C11C2×#10211yescharacteristic
191C22×C11#41612yes—
192C22×C11#41811yescharacteristic
193C2×D11—84no—
194C2×D11—84no—
195C2×D11—82no—
196C2×D11—82no—
197C2×D11—82no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—82no—
201C4×C11#45911yescharacteristic
202C4×C11#45911yescharacteristic
203C4×C11#46011yescharacteristic
204C4×C11#46011yescharacteristic
205C4×C11#48812yes—
206C4×C11#49511yescharacteristic
207C4×C11#49511yescharacteristic
208Dic11—24no—
209Dic11—42no—
210C22×Q8—21no—
211C22×D4—112no—
212C22×D4—221no—
213C22×D4—221no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—221no—
217C22×C8—221no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222#127—221no—
223#127—221no—
224#127—221no—
225#127—221no—
226#124—442no—
227#124—442no—
228#124—442no—
229#124—442no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C4×D1112yes—
232C2×C22⋊C4—224no—
233C2×C22⋊C4—224no—
234C2×C42—111no—
235C2×C42—111no—
236C2×C42—112no—
237C2×C42—112no—
238C2×C42C22×D1111yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—112no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246C4⋊C8C22⋊D1112yes—
247C4×C8—442no—
248C2×C11#154012yes—
249C2×C11#155312yes—
250C2×C11#195811yescharacteristic
251C2×C11#196711yescharacteristic
252C2×C11#198211yescharacteristic
253D11—162no—
254C24—222no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×D4—222no—
262C2×D4—222no—
263C2×D4—444no—
264C2×D4—441no—
265C2×D4—441no—
266C2×D4—441no—
267C2×D4—441no—
268C2×D4—441no—
269C2×D4—441no—
270C2×D4—442no—
271C2×D4—442no—
272C2×D4—441no—
273C2×D4—441no—
274C22×C4—22no—
275C22×C4—112no—
276C22×C4—112no—
277C22×C4C2×C4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—42no—
284C2×C8—41no—
285C2×C8—222no—
286C2×C8—441no—
287C2×C8—441no—
288C2×C8—442no—
289C2×C8—441no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C22⋊C4—448no—
295C22⋊C4—448no—
296C42—112no—
297C42—112no—
298C42—221no—
299C42—221no—
300C42—222no—
301C42—222no—
302C42—442no—
303C42#433911yescharacteristic
304C42D4×D1111yescharacteristic
305C42#434111yescharacteristic
306C42C2×C22⋊D1111yescharacteristic
307C11#969611yescharacteristic, complemented, Sylow
308C23—442no—
309C23—444no—
310C23—442no—
311C23—442no—
312C23—444no—
313C23C22⋊C4×D1111yescharacteristic
314Q8—81no—
315Q8—81no—
316Q8—81no—
317Q8—81no—
318D4—882no—
319D4—882no—
320D4—881no—
321D4—881no—
322D4—881no—
323D4—881no—
324D4—881no—
325D4—881no—
326D4—882no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—114no—
332C2×C4—222no—
333C2×C4—222no—
334C2×C4—222no—
335C2×C4—222no—
336C2×C4—222no—
337C2×C4(C22⋊D11)⋊C411yescharacteristic
338C2×C4#6693711yescharacteristic
339C2×C4#6693811yescharacteristic
340C2×C4D8×D1111yescharacteristic
341C2×C4#6696411yescharacteristic
342C2×C4SD16×D1111yescharacteristic
343C2×C4#6696711yescharacteristic
344C2×C4#6696912yes—
345C2×C4#6697212yes—
346C2×C4C4×C22⋊D1111yescharacteristic
347C2×C4#6699211yescharacteristic
348C2×C4#6699311yescharacteristic
349C8—42no—
350C8—81no—
351C8—442no—
352C8—881no—
353C22—884no—
354C22—884no—
355C22—882no—
356C22—882no—
357C22—882no—
358C22#1062236412yes—
359C22D11×#10211yescharacteristic
360C22#1062238311yescharacteristic
361C22#1062241712yes—
362C22#1062257011yescharacteristic
363C4—21no—
364C4—21no—
365C4—82no—
366C4—224no—
367C4—442no—
368C4#1062237511yescharacteristic
369C4#1062239911yescharacteristic
370C4#1062241312yes—
371C4#1062276311yescharacteristic
372C4#1062277611yescharacteristic
373C4#1062278111yescharacteristic
374C4#1062280411yescharacteristic
375C2—1762no—
376C2#1306726412yes—
377C2#1306732012yes—
378C2#1306942411yescharacteristic
379C2#1306946411yescharacteristic
380C2#1306954111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenterC2×#332D11
hypocenterC11#9696
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #13068732C2semidirect
3. C4⋊C8×Dic11C2semidirect
4. C2×#10622185C2semidirect
7. C2×C11×#332C2semidirect
122. C2×#332D11semidirect
307. C11#9696semidirect

Maximal subgroups

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

subgroupindex
#130769742
#130687322
C4⋊C8×Dic112
C2×#106221852
C2×#106221232
C2×C11×#3322
#969611