Finite Group Databasebeta

← #14646293

Subgroups — #14646293

Order 2816.

1102 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 139 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#13067330C212yesmaximal, complemented
2#13067240C212yesmaximal, complemented
3#13066950C212yesmaximal, complemented
4C2×C11×#535C211yesmaximal, characteristic
5C22×C11×#41C411yescharacteristic
6C23×D4×C11C411yescharacteristic
7C11×#535—24no—
8C11×#535—24no—
9C2×C11×#127C411yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C11×#124C411yescharacteristic
12C2×C11×#124C2211yescharacteristic
13C2×C11×#121—22no—
14C2×C11×#120—22no—
15C2×C11×#117C2211yescharacteristic
16#10622539C2214yescomplemented
17#10622182—24no—
18#10622178—24no—
19#10622166—22no—
20#10622163—22no—
21C25×C11—21no—
22C2×C11×#41—22no—
23C2×C11×#41—22no—
24C2×C11×#41—42no—
25C2×C11×#41—42no—
26C22×Q8×C11C2×C411yescharacteristic
27C22×D4×C11—21no—
28C22×D4×C11—22no—
29C22×D4×C11—22no—
30C22×D4×C11—21no—
31C22×D4×C11—22no—
32C22×D4×C11—22no—
33C22×D4×C11—42no—
34C22×D4×C11—42no—
35C22×D4×C11C2×C411yescharacteristic
36C22×D4×C11C2×C411yescharacteristic
37C22×D4×C11C2×C411yescharacteristic
38C23×C4×C11—21no—
39C23×C4×C11C2×C411yescharacteristic
40C11×#127—22no—
41C11×#127—22no—
42C11×#127—22no—
43C11×#127D414yes—
44C11×#124—22no—
45C11×#124—22no—
46C11×#124—22no—
47C11×#124D414yes—
48C11×#121—216no—
49C11×#120—216no—
50C11×#117—22no—
51C11×#117—22no—
52C2×C11×C4⋊C4D412yes—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4D412yes—
56C2×C42×C11C2×C411yescharacteristic
57C2×C42×C11C2311yescharacteristic
58C22⋊(C11⋊C8)—24no—
59C4⋊(C11⋊C8)—24no—
60#66867—24no—
61#8522—111nomaximal, Sylow
62C24×C11—24no—
63C24×C11—21no—
64C24×C11—21no—
65C24×C11—21no—
66C24×C11—42no—
67C24×C11—42no—
68C24×C11—84no—
69C24×C11C22⋊C411yescharacteristic
70C11×#41—48no—
71C11×#41—48no—
72C2×Q8×C11—21no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11C22⋊C412yes—
76C2×D4×C11—24no—
77C2×D4×C11—24no—
78C2×D4×C11—28no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—28no—
83C2×D4×C11—48no—
84C2×D4×C11—48no—
85C2×D4×C11—42no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—42no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—84no—
96C2×D4×C11—84no—
97C2×D4×C11C22⋊C412yes—
98C2×D4×C11C22⋊C412yes—
99C2×D4×C11C22⋊C412yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—24no—
105C22×C4×C11—21no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11C22⋊C411yescharacteristic
109C22×C4×C11C22⋊C412yes—
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C2×D412yes—
112C11×C4⋊C4—24no—
113C11×C22⋊C4—28no—
114C11×C22⋊C4—28no—
115C11×C22⋊C4—24no—
116C42×C11—21no—
117C42×C11—21no—
118C42×C11C2×D412yes—
119C42×C11C2×D412yes—
120C2×C11⋊C8—44no—
121C2×#535D1111yescharacteristic
122#1555—112no—
123#1533—112no—
124#1464—112no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—22no—
128C23×C11—22no—
129C23×C11—22no—
130C23×C11—42no—
131C23×C11—48no—
132C23×C11—44no—
133C23×C11—44no—
134C23×C11—44no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—88no—
142C23×C11—88no—
143C23×C11—88no—
144C23×C11#10012yes—
145C23×C11C2×C22⋊C411yescharacteristic
146Q8×C11—42no—
147Q8×C11—42no—
148D4×C11—42no—
149D4×C11—42no—
150D4×C11—42no—
151D4×C11—48no—
152D4×C11—42no—
153D4×C11—42no—
154D4×C11—42no—
155D4×C11—48no—
156D4×C11—88no—
157D4×C11—88no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—42no—
167C2×C4×C11—48no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11#10012yes—
172C2×C4×C11C2×C22⋊C411yescharacteristic
173C2×C4×C11C2×C22⋊C411yescharacteristic
174C2×C4×C11#12014yes—
175C11⋊C8—84no—
176C22×#41Dic1111yescharacteristic
177C23×D4Dic1111yescharacteristic
178#535—24no—
179#535—24no—
180C2×#127Dic1111yescharacteristic
181C2×#127C2×D1111yescharacteristic
182C2×#124Dic1111yescharacteristic
183C2×#124C2×D1111yescharacteristic
184C2×#121—22no—
185C2×#120—22no—
186C2×#117C2×D1111yescharacteristic
187#432—114no—
188#331—224no—
189#329—224no—
190#324—222no—
191#323—222no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—42no—
195C22×C11—42no—
196C22×C11—42no—
197C22×C11—44no—
198C22×C11—44no—
199C22×C11—44no—
200C22×C11—42no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11—82no—
204C22×C11—82no—
205C22×C11—82no—
206C22×C11—82no—
207C22×C11—82no—
208C22×C11—82no—
209C22×C11—816no—
210C22×C11#37911yescharacteristic
211C22×C11C2×#10011yescharacteristic
212C22×C11C2×#10011yescharacteristic
213C4×C11—24no—
214C4×C11—22no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—42no—
218C4×C11—42no—
219C25—21no—
220C2×#41—22no—
221C2×#41—22no—
222C2×#41—42no—
223C2×#41—42no—
224C22×Q8C2×Dic1111yescharacteristic
225C22×D4—21no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—21no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—42no—
232C22×D4—42no—
233C22×D4C2×Dic1111yescharacteristic
234C22×D4C2×Dic1111yescharacteristic
235C22×D4C2×Dic1111yescharacteristic
236C23×C4—21no—
237C23×C4C2×Dic1111yescharacteristic
238#127—22no—
239#127—22no—
240#127—22no—
241#127C22⋊D1114yes—
242#124—22no—
243#124—22no—
244#124—22no—
245#124C22⋊D1114yes—
246#121—216no—
247#120—216no—
248#117—22no—
249#117—22no—
250C2×C4⋊C4C22⋊D1112yes—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4C22⋊D1112yes—
254C2×C42C2×Dic1111yescharacteristic
255C2×C42C22×D1111yescharacteristic
256C4⋊C8—224no—
257C22⋊C8—224no—
258#97—224no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—42no—
262C2×C11—82no—
263C2×C11—82no—
264C2×C11—82no—
265C2×C11#178311yescharacteristic
266C2×C11#179512yes—
267C24—24no—
268C24—21no—
269C24—21no—
270C24—21no—
271C24—42no—
272C24—42no—
273C24—84no—
274C24C22⋊Dic1111yescharacteristic
275#41—48no—
276#41—48no—
277C2×Q8—21no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8C22⋊Dic1112yes—
281C2×D4—24no—
282C2×D4—24no—
283C2×D4—28no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—28no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—48no—
295C2×D4—48no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—84no—
301C2×D4—84no—
302C2×D4C22⋊Dic1112yes—
303C2×D4C22⋊Dic1112yes—
304C2×D4C22⋊Dic1112yes—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—24no—
310C22×C4—21no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4C22⋊Dic1111yescharacteristic
314C22×C4C22⋊Dic1112yes—
315C22×C4C22×Dic1111yescharacteristic
316C22×C4C2×C22⋊D1112yes—
317C2×C8—444no—
318C4⋊C4—24no—
319C22⋊C4—28no—
320C22⋊C4—28no—
321C22⋊C4—24no—
322C42—21no—
323C42—21no—
324C42C2×C22⋊D1112yes—
325C42C2×C22⋊D1112yes—
326C11#852211yescharacteristic, complemented, Sylow
327C23—21no—
328C23—21no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—42no—
333C23—48no—
334C23—44no—
335C23—44no—
336C23—44no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—88no—
344C23—88no—
345C23—88no—
346C23#6689712yes—
347C23C2×C22⋊Dic1111yescharacteristic
348Q8—42no—
349Q8—42no—
350D4—42no—
351D4—42no—
352D4—42no—
353D4—48no—
354D4—42no—
355D4—42no—
356D4—42no—
357D4—48no—
358D4—88no—
359D4—88no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—42no—
369C2×C4—48no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4#6689712yes—
374C2×C4C2×C22⋊Dic1111yescharacteristic
375C2×C4C2×C22⋊Dic1111yescharacteristic
376C2×C4#6700614yes—
377C8—884no—
378C22—22no—
379C22—22no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—44no—
384C22—44no—
385C22—44no—
386C22—42no—
387C22—42no—
388C22—42no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—82no—
393C22—82no—
394C22—82no—
395C22—816no—
396C22C2×#6689711yescharacteristic
397C22C2×#6689711yescharacteristic
398C22#1062286011yescharacteristic
399C4—24no—
400C4—22no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—42no—
405C2—21no—
406C2—21no—
407C2—42no—
408C2—82no—
409C2—82no—
410C2—82no—
411C2#1306853711yescharacteristic
412C2#1306858612yes—
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC2×C11×#535C2
socleC22×C11#379
cosocleC2×C42×C11C23
hypercenterC2×#535D11
hypocenterC11#8522
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. #13067330C2semidirect
2. #13067240C2semidirect
3. #13066950C2semidirect
16. #10622539C22semidirect
326. C11#8522semidirect

Maximal subgroups

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

subgroupindex
#130673302
#130672402
#130669502
C2×C11×#5352
#852211