Finite Group Databasebeta

← #14653564

Subgroups — #14653564

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622306C211yesmaximal, characteristic
2#13069576C211yesmaximal, characteristic, complemented
3#13069576C211yesmaximal, characteristic, complemented
4#13069421C211yesmaximal, characteristic
5#13069421C211yesmaximal, characteristic
6C2×#10622092C211yesmaximal, characteristic, complemented
7C11×#1834C211yesmaximal, characteristic, complemented
8C22×#4314—22no—
9C2×#66927C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C11×#384C2211yescharacteristic
13C11×#384C2211yescharacteristic
14C2×#66873—22no—
15C2×#66873—22no—
16C2×C4×C11⋊C8C2211yescharacteristic
17C2×C4×C11⋊C8C2211yescharacteristic
18#10622306—22no—
19#10622306C414yescomplemented
20C11×#340—22no—
21#10622167—22no—
22#10622167—22no—
23#10622092—22no—
24C22×D44—21no—
25C22×D44—21no—
26C22×D44—21no—
27C22×Dic22—21no—
28C22×C8×C11D412yes—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C22×C11⋊C8D412yes—
39C22×C11⋊C8D412yes—
40C2×#4314—28no—
41C2×#4314—44no—
42C2×#4314—44no—
43#66927—21no—
44#66927—21no—
45#66927—21no—
46#66927C2×C412yes—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922C2×C412yes—
51C4×C8×C11C2×C412yes—
52C4×C8×C11D412yes—
53#66873—44no—
54#66873—44no—
55C4×C11⋊C8—21no—
56C4×C11⋊C8—21no—
57C4×C11⋊C8—21no—
58C4×C11⋊C8—21no—
59#9829—111nomaximal, Sylow
60C23×D11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—41no—
67C2×D44—22no—
68C2×D44—22no—
69C2×D44—22no—
70C2×D44—41no—
71C2×D44—41no—
72C2×D44—41no—
73C2×D44—42no—
74C2×D44—42no—
75C2×D44—42no—
76C2×D44—42no—
77C2×D44—42no—
78C2×D44—42no—
79C2×Dic22—22no—
80C2×Dic22—41no—
81C2×Dic22—42no—
82C2×Dic22—42no—
83C2×C8×C11—22no—
84C2×C8×C11—22no—
85C2×C8×C11C22⋊C414yes—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4—42no—
92C42×C11C22×C411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11#4111yescharacteristic
95C42×C11#4111yescharacteristic
96C4⋊Dic11—22no—
97C4⋊Dic11—22no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8SD1614yescomplemented
106#4314—416no—
107C2×#492—111no—
108#1990—111no—
109#1990—111no—
110#1957—111no—
111#1957—111no—
112#1834D1111yescharacteristic, complemented
113C2×#322—111no—
114C23×C11#12711yescharacteristic
115C22×D11—42no—
116C22×D11—81no—
117C22×D11—81no—
118C22×D11—81no—
119C22×D11—81no—
120C22×D11—81no—
121C22×D11—81no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11C2×C22⋊C411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11C2×SD1612yes—
135C2×C4×C11#13512yes—
136C2×C4×C11AGL(1,ℤ/8)12yes—
137C2×C4×C11AGL(1,ℤ/8)12yes—
138C2×C4×C11AGL(1,ℤ/8)12yes—
139C2×C4×C11#13712yes—
140C2×Dic11—42no—
141C2×Dic11—81no—
142C2×Dic11—81no—
143D44—44no—
144D44—44no—
145D44—44no—
146D44—82no—
147D44—82no—
148D44—82no—
149Dic22—44no—
150Dic22—82no—
151C8×C11—24no—
152C11⋊C8—24no—
153C11⋊C8—42no—
154C22×SD16—222no—
155C2×C4⋊Q8—111no—
156C2×#127—111no—
157#492—114no—
158#492—222no—
159C2×#102—222no—
160C2×#102—222no—
161C2×C4×C8—111no—
162C2×C4×C8—111no—
163C2×C4×C8C2×D1111yescharacteristic
164#384C2×D1111yescharacteristic
165#384C2×D1111yescharacteristic
166#340—22no—
167#340—222no—
168#340—222no—
169#322—222no—
170C22×C11#39011yescharacteristic
171C22×C11#49211yescharacteristic
172C22×C11#49511yescharacteristic
173C22×C11#49611yescharacteristic
174C22×C11#49611yescharacteristic
175C22×C11#49611yescharacteristic
176C22×C11#49711yescharacteristic
177C2×D11—82no—
178C2×D11—82no—
179C2×D11—82no—
180C2×D11—161no—
181C2×D11—161no—
182C2×D11—161no—
183C2×D11—161no—
184C4×C11—161no—
185C4×C11—161no—
186C4×C11#41812yes—
187C4×C11C4×SD1612yes—
188C4×C11#44012yes—
189C4×C11#46512yes—
190C4×C11#46812yes—
191C4×C11#49012yes—
192Dic11—82no—
193C22×Q8—221no—
194C22×D4—221no—
195C22×D4—221no—
196C22×D4—221no—
197C2×SD16—228no—
198C2×SD16—444no—
199C2×SD16—444no—
200C22×C8—112no—
201C22×C8—112no—
202C22×C8C22⋊D1112yes—
203C4⋊Q8—112no—
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207#127—112no—
208#127—221no—
209#127—221no—
210#127—221no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C42C22×D1111yescharacteristic
220#102—444no—
221#102—444no—
222C4×C8—221no—
223C4×C8—221no—
224C4×C8—221no—
225C4×C8—221no—
226C4×C8C4×D1112yes—
227C4×C8D4412yes—
228C2×C11#171411yescharacteristic
229C2×C11#171511yescharacteristic
230C2×C11#171711yescharacteristic
231C2×C11#171911yescharacteristic
232C2×C11#196111yescharacteristic
233C2×C11#196811yescharacteristic
234C2×C11#197311yescharacteristic
235D11—162no—
236C24—441no—
237C2×Q8—222no—
238C2×Q8—441no—
239C2×Q8—442no—
240C2×Q8—442no—
241C2×D4—222no—
242C2×D4—222no—
243C2×D4—222no—
244C2×D4—441no—
245C2×D4—441no—
246C2×D4—442no—
247C2×D4—442no—
248C2×D4—442no—
249C2×D4—442no—
250C2×D4—441no—
251C2×D4—442no—
252C2×D4—442no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—441no—
256C22×C4D4×D1111yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259SD16—4416no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—114no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8—222no—
266C2×C8—222no—
267C2×C8—222no—
268C2×C8(C2×D11)⋊C414yes—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—222no—
276C4⋊C4—222no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C42C2×C4×D1111yescharacteristic
280C42C2×D4411yescharacteristic
281C42#434311yescharacteristic
282C42#434311yescharacteristic
283C11#982911yescharacteristic, complemented, Sylow
284C23—442no—
285C23—881no—
286C23—881no—
287C23—881no—
288C23—881no—
289C23—881no—
290C23—881no—
291C23#6699311yescharacteristic
292Q8—444no—
293Q8—882no—
294D4—444no—
295D4—444no—
296D4—444no—
297D4—882no—
298D4—882no—
299D4—882no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—442no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4#6694611yescharacteristic
310C2×C4#6694611yescharacteristic
311C2×C4#6694811yescharacteristic
312C2×C4#6694811yescharacteristic
313C2×C4#6696412yes—
314C2×C4SD16×D1112yes—
315C2×C4#6696912yes—
316C2×C4#6697112yes—
317C2×C4C2×(C2×D11)⋊C411yescharacteristic
318C2×C4#6700011yescharacteristic
319C2×C4#6700212yes—
320C2×C4#6700212yes—
321C8—24no—
322C8—224no—
323C8—442no—
324C22—882no—
325C22—882no—
326C22—882no—
327C22—1761no—
328C22—1761no—
329C22—1761no—
330C22—1761no—
331C22#1062260111yescharacteristic
332C22#1062267111yescharacteristic
333C22#1062267111yescharacteristic
334C22#1062276711yescharacteristic
335C22#1062278111yescharacteristic
336C22#1062278811yescharacteristic
337C22#1062280311yescharacteristic
338C4—161no—
339C4—161no—
340C4—882no—
341C4#1062246512yes—
342C4#1062247712yes—
343C4#1062249912yes—
344C4#1062250212yes—
345C4#1062261412yes—
346C4#1062268012yes—
347C2—1762no—
348C2#1306824011yescharacteristic
349C2#1306824611yescharacteristic
350C2#1306825711yescharacteristic
351C2#1306827111yescharacteristic
352C2#1306943911yescharacteristic
353C2#1306946811yescharacteristic
354C2#1306949511yescharacteristic
subgroupG/H
centerC23#66993
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1834C2
socleC23×C11#127
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1834D11
hypocenterC11#9829
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
2. #13069576C2semidirect
3. #13069576C2semidirect
6. C2×#10622092C2semidirect
7. C11×#1834C2semidirect
19. #10622306C4semidirect
105. C2×C11⋊C8SD16semidirect
112. #1834D11semidirect
283. C11#9829semidirect

Maximal subgroups

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

subgroupindex
C2×#106223062
#130695762
#130694212
C2×#106220922
C11×#18342
#982911