Finite Group Databasebeta

← #14645321

Subgroups — #14645321

Order 2816.

1054 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 167 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#13069411C211yesmaximal, characteristic, complemented
2#13068608C211yesmaximal, characteristic, complemented
3#13067293C212yesmaximal, complemented
4#13067067C212yesmaximal, complemented
5C11×#3496C211yesmaximal, characteristic
6C2×C11×H(5,𝔽2)—21no—
7C11×#547—22no—
8C11×#546—24no—
9D42×C11—22no—
10C11×#537—21no—
11C11×#534C414yes—
12C11×#532C2212yes—
13C2×C11×#121—22no—
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66897—21no—
16C2×C22⋊(C11⋊C8)—22no—
17#10622537C2212yescomplemented
18C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
19C2×C4×C11⋊C8C2211yescharacteristic, complemented
20#10622185—22no—
21#10622182—22no—
22D4⋊(C11⋊C8)—24no—
23#10622168—21no—
24C11×H(5,𝔽2)—44no—
25C11×H(5,𝔽2)—42no—
26C11×H(5,𝔽2)—42no—
27C2×C11×#41—24no—
28C2×C11×#41—22no—
29C22×D4×C11—24no—
30C22×D4×C11—24no—
31C22×D4×C11—22no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11D412yes—
34C11×C4⋊Q8D412yes—
35C11×#127D412yes—
36C11×#124—22no—
37C11×#123—28no—
38C11×C22⋊Q8—24no—
39C11×#121—24no—
40C11×#121—24no—
41C11×#121—24no—
42C11×#121—24no—
43C11×#121—22no—
44C11×#121C2×C414yes—
45C11×#120—28no—
46C4×D4×C11—22no—
47C4×D4×C11—22no—
48C4×D4×C11—22no—
49C4×D4×C11D414yes—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—24no—
53C2×C11×C22⋊C4C2×C412yes—
54C2×C42×C11C2311yescharacteristic
55C2×#4318—22no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8—21no—
58#66897—42no—
59C22⋊(C11⋊C8)—44no—
60C4⋊(C11⋊C8)—22no—
61C4⋊(C11⋊C8)—22no—
62C4⋊(C11⋊C8)—22no—
63C4×C11⋊C8—22no—
64#8353—111nomaximal, Sylow
65C24×C11—24no—
66C24×C11C22⋊C412yes—
67C11×#41—48no—
68C11×#41—48no—
69C11×#41—42no—
70C11×#41—42no—
71C11×#41—42no—
72C11×#41—42no—
73C2×Q8×C11—22no—
74C2×D4×C11—28no—
75C2×D4×C11—24no—
76C2×D4×C11—24no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—48no—
82C2×D4×C11—48no—
83C2×D4×C11—48no—
84C2×D4×C11—48no—
85C2×D4×C11—82no—
86C2×D4×C11—82no—
87C2×D4×C11C22⋊C414yes—
88C2×D4×C11D812yes—
89C2×D4×C11SD1612yes—
90C22×C4×C11—24no—
91C22×C4×C11—22no—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C22⋊C412yes—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C11×C4⋊C4—24no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4C22⋊C414yes—
104C11×C22⋊C4—28no—
105C11×C22⋊C4—24no—
106C11×C22⋊C4—24no—
107C11×C22⋊C4—24no—
108C42×C11C2×D412yes—
109C42×C11C2×D412yes—
110#4318—42no—
111#4318—42no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—42no—
118#3496D1111yescharacteristic
119#1954—111no—
120#1800—111no—
121#1547—112no—
122#1492—112no—
123C23×C11—22no—
124C23×C11—22no—
125C23×C11—24no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—48no—
129C23×C11—84no—
130C23×C11—84no—
131C23×C11#10214yes—
132C23×C11C2×C22⋊C411yescharacteristic
133Q8×C11—42no—
134Q8×C11—42no—
135D4×C11—24no—
136D4×C11—24no—
137D4×C11—44no—
138D4×C11—416no—
139D4×C11—44no—
140D4×C11—44no—
141D4×C11—42no—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—42no—
145D4×C11—84no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—41no—
151C2×C4×C11—48no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11C2×C22⋊C412yes—
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12012yes—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11C2×SD1611yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)12yes—
165C11⋊C8—42no—
166C11⋊C8—82no—
167C11⋊C8—81no—
168C2×H(5,𝔽2)—21no—
169#547—22no—
170#546—24no—
171D42—22no—
172#537—21no—
173#534Dic1114yes—
174#532C2×D1112yes—
175C2×#121—22no—
176C2×C4×D4C2×D1111yescharacteristic
177#423—112no—
178C2×C4⋊C8—111no—
179C2×#100—221no—
180C2×C22⋊C8—222no—
181C2×C4×C8—111no—
182#343—221no—
183#332—222no—
184#331—222no—
185D4⋊C8—224no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—24no—
189C22×C11—44no—
190C22×C11—42no—
191C22×C11—42no—
192C22×C11—44no—
193C22×C11—44no—
194C22×C11—44no—
195C22×C11—82no—
196C22×C11—168no—
197C22×C11#37911yescharacteristic
198C22×C11C2×#10211yescharacteristic
199C22×C11#41811yescharacteristic
200C4×C11—21no—
201C4×C11—22no—
202C4×C11—42no—
203C4×C11—44no—
204C4×C11#44712yes—
205C4×C11#45012yes—
206C4×C11#45311yescharacteristic
207C4×C11#45511yescharacteristic
208H(5,𝔽2)—44no—
209H(5,𝔽2)—42no—
210H(5,𝔽2)—42no—
211C2×#41—24no—
212C2×#41—22no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—22no—
216C22×D4C22⋊D1111yescharacteristic
217C23×C4C22⋊D1112yes—
218C2×M16—222no—
219C22×C8—221no—
220C22×C8—221no—
221C4⋊Q8C22⋊D1112yes—
222#127C22⋊D1112yes—
223#124—22no—
224#123—28no—
225C22⋊Q8—24no—
226#121—24no—
227#121—24no—
228#121—24no—
229#121—24no—
230#121—22no—
231#121C2×Dic1114yes—
232#120—28no—
233C4×D4—22no—
234C4×D4—22no—
235C4×D4—22no—
236C4×D4C22⋊D1114yes—
237C2×C4⋊C4—22no—
238C2×C4⋊C4C22⋊D1111yescharacteristic
239C2×C22⋊C4—24no—
240C2×C22⋊C4C2×Dic1112yes—
241C2×C42C22×D1111yescharacteristic
242C4⋊C8—222no—
243C4⋊C8—222no—
244C4⋊C8—222no—
245#100—442no—
246C22⋊C8—444no—
247C4×C8—222no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—44no—
251C2×C11—84no—
252C2×C11#178611yescharacteristic
253C2×C11#179111yescharacteristic
254C2×C11#179211yescharacteristic
255C24—24no—
256C24C22⋊Dic1112yes—
257#41—48no—
258#41—48no—
259#41—42no—
260#41—42no—
261#41—42no—
262#41—42no—
263C2×Q8—22no—
264C2×D4—28no—
265C2×D4—24no—
266C2×D4—24no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—48no—
272C2×D4—48no—
273C2×D4—48no—
274C2×D4—48no—
275C2×D4—82no—
276C2×D4—82no—
277C2×D4#432312yes—
278C2×D4#432412yes—
279C2×D4C22⋊Dic1114yes—
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4C22⋊Dic1112yes—
287C22×C4C22×Dic1111yescharacteristic
288C22×C4C2×C22⋊D1111yescharacteristic
289C22×C4C2×C22⋊D1111yescharacteristic
290M16—442no—
291M16—442no—
292C2×C8—222no—
293C2×C8—441no—
294C2×C8—441no—
295C2×C8—442no—
296C2×C8—441no—
297C2×C8—442no—
298C4⋊C4—24no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4C22⋊Dic1114yes—
302C22⋊C4—28no—
303C22⋊C4—24no—
304C22⋊C4—24no—
305C22⋊C4—24no—
306C42C2×C22⋊D1112yes—
307C42C2×C22⋊D1112yes—
308C11#835311yescharacteristic, complemented, Sylow
309C23—22no—
310C23—22no—
311C23—24no—
312C23—42no—
313C23—42no—
314C23—48no—
315C23—84no—
316C23—84no—
317C23#6689614yes—
318C23C2×C22⋊Dic1111yescharacteristic
319Q8—42no—
320Q8—42no—
321D4—24no—
322D4—24no—
323D4—44no—
324D4—416no—
325D4—44no—
326D4—44no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—84no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—41no—
337C2×C4—48no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—82no—
344C2×C4C2×#432311yescharacteristic
345C2×C4#6698512yes—
346C2×C4C2×#432411yescharacteristic
347C2×C4C2×C22⋊Dic1112yes—
348C2×C4#6700611yescharacteristic
349C2×C4#6700612yes—
350C2×C4#6700611yescharacteristic
351C8—442no—
352C8—882no—
353C8—881no—
354C22—21no—
355C22—21no—
356C22—24no—
357C22—44no—
358C22—42no—
359C22—42no—
360C22—44no—
361C22—44no—
362C22—44no—
363C22—82no—
364C22—168no—
365C22C2×#6689611yescharacteristic
366C22#1062282811yescharacteristic
367C22#1062286011yescharacteristic
368C4—22no—
369C4—21no—
370C4—44no—
371C4—42no—
372C4#1062283012yes—
373C4#1062283112yes—
374C4#1062285411yescharacteristic
375C4#1062285511yescharacteristic
376C2—21no—
377C2—21no—
378C2—44no—
379C2—84no—
380C2#1306854711yescharacteristic
381C2#1306856711yescharacteristic
382C2#1306857011yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3496C2
socleC22×C11#379
cosocleC2×C42×C11C23
hypercenter#3496D11
hypocenterC11#8353
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #13069411C2semidirect
2. #13068608C2semidirect
3. #13067293C2semidirect
4. #13067067C2semidirect
17. #10622537C22semidirect
18. C2×C4⋊(C11⋊C8)C22semidirect
19. C2×C4×C11⋊C8C22semidirect
308. C11#8353semidirect

Maximal subgroups

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

subgroupindex
#130694112
#130686082
#130672932
#130670672
C11×#34962
#835311