Finite Group Databasebeta

← #14651449

Subgroups — #14651449

Order 2816.

518 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 95 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#13077644C211yesmaximal, characteristic
2#13073612C211yesmaximal, characteristic
3#13067342C211yesmaximal, characteristic, complemented
4#13066956C211yesmaximal, characteristic
5#13066473C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#1558C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#67000C412yes—
10C2×C4×D44C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#432C2211yescharacteristic
13#10622843C412yes—
14#10622606—21no—
15#10622606—21no—
16#10622600—21no—
17#10622600—21no—
18C4×C4⋊Dic11C2211yescharacteristic
19#10622539C2211yescharacteristic
20#10622539C2211yescharacteristic
21#10622449—22no—
22#10622339—21no—
23D11×C22⋊C8—21no—
24#10622319—22no—
25C11×#333—22no—
26#10622184—22no—
27#10622106—21no—
28#10622106—21no—
29C22×Q8×C11C2×C412yes—
30C22×D44C2×C411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C42×C11C2311yescharacteristic
40#67000—44no—
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4D411yescharacteristic
44C2×(C2×D11)⋊C4D411yescharacteristic
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×C4×Dic11C2×C412yes—
48C2×#4313—22no—
49C2×C8×D11—22no—
50C4×D44—21no—
51C4×D44—21no—
52C4×D44—21no—
53C4×D44—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8D412yes—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×#97—21no—
59C11×#97—21no—
60C11⋊#95—21no—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65(C2×D11)⋊C8—22no—
66(C2×D11)⋊C8—22no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69#66867—21no—
70#66867—21no—
71#9451—111nomaximal, Sylow
72C23×D11C22⋊C411yescharacteristic
73C23×D11C22⋊C411yescharacteristic
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—42no—
77C2×Q8×C11—42no—
78C22×C4×C11—22no—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—22no—
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C2×D44—22no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—41no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—42no—
94C2×C4×D11—42no—
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11#4111yescharacteristic
104C42×C11#4111yescharacteristic
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—44no—
110(C2×D11)⋊C4—44no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—42no—
114C4×Dic11—42no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—41no—
117#4313—82no—
118C8×D11—82no—
119#2973—111no—
120#2547—111no—
121#1558—111no—
122#1558D1111yescharacteristic, complemented
123#1466—111no—
124#1285—111no—
125#1285—111no—
126C23×C11C2×C22⋊C411yescharacteristic
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11#10012yes—
137Q8×C11—82no—
138Q8×C11—82no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12311yescharacteristic
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159D44—42no—
160D44—42no—
161C4×D11—42no—
162C4×D11—42no—
163C4×D11—81no—
164C4×D11—81no—
165C8×C11—42no—
166C8×C11—81no—
167C11⋊C8—42no—
168C11⋊C8—81no—
169C2×C4⋊Q8C2×D1111yescharacteristic
170C2×#124—112no—
171C2×C4×D4—111no—
172#435—222no—
173#435—222no—
174#432—111no—
175#432—111no—
176#432C2×D1111yescharacteristic
177#432C2×D1111yescharacteristic
178#407—221no—
179C2×C22⋊C8—221no—
180#397—221no—
181#397—221no—
182#391—112no—
183#380—221no—
184#380—221no—
185C4×C4⋊C4—111no—
186#333—22no—
187#333—222no—
188#323—221no—
189#323—221no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11#38611yescharacteristic
193C22×C11C2×#10011yescharacteristic
194C22×C11#41311yescharacteristic
195C2×D11—22no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—42no—
199C2×D11—42no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—81no—
204C2×D11—81no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—82no—
211C4×C11#45512yes—
212Dic11—41no—
213Dic11—41no—
214Dic11—82no—
215C22×Q8C4×D1112yes—
216C22×D4—111no—
217C23×C4—111no—
218C23×C4—111no—
219C2×M16—222no—
220C22×C8—222no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225#124—444no—
226C4×D4—221no—
227C4×D4—221no—
228C4×D4—221no—
229C4×D4—221no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—221no—
234C2×C22⋊C4—111no—
235C2×C22⋊C4—111no—
236C2×C22⋊C4—222no—
237C2×C22⋊C4—222no—
238C2×C42—112no—
239C2×C42C22×D1111yescharacteristic
240C4⋊C8—21no—
241C4⋊C8—112no—
242C4⋊C8—221no—
243C4⋊C8C22⋊D1112yes—
244C22⋊C8—21no—
245C22⋊C8—21no—
246C22⋊C8—222no—
247C22⋊C8—222no—
248C22⋊C8—221no—
249C22⋊C8—221no—
250#97—21no—
251#97—21no—
252#97—221no—
253#97—221no—
254#95—222no—
255#95—222no—
256#95—221no—
257C2×C11—21no—
258C2×C11—21no—
259C2×C11#188511yescharacteristic
260C2×C11#190011yescharacteristic
261C2×C11#190911yescharacteristic
262D11—42no—
263D11—81no—
264C24—111no—
265C24—111no—
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×D4—222no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—441no—
274C22×C4—22no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—222no—
282C22×C4—442no—
283C22×C4—442no—
284C22×C4C2×C4×D1111yescharacteristic
285C22×C4D4×D1111yescharacteristic
286C22×C4D4×D1111yescharacteristic
287M16—882no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—222no—
291C2×C8—441no—
292C2×C8—882no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—442no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—444no—
305C22⋊C4—444no—
306C42—442no—
307C42#433911yescharacteristic
308C42D4×D1111yescharacteristic
309C42#434111yescharacteristic
310C42C2×C22⋊D1111yescharacteristic
311C11#945111yescharacteristic, complemented, Sylow
312C23—112no—
313C23—221no—
314C23—221no—
315C23—221no—
316C23—221no—
317C23—221no—
318C23—441no—
319C23—441no—
320C23—441no—
321C23—441no—
322C23C22⋊C4×D1111yescharacteristic
323Q8—82no—
324Q8—82no—
325D4—442no—
326D4—442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4(C22⋊D11)⋊C411yescharacteristic
346C2×C4#6693611yescharacteristic
347C2×C4#6693711yescharacteristic
348C2×C4C4×C22⋊D1111yescharacteristic
349C2×C4#6699011yescharacteristic
350C2×C4#6699111yescharacteristic
351C8—42no—
352C8—81no—
353C8—442no—
354C8—881no—
355C22—21no—
356C22—21no—
357C22—222no—
358C22—442no—
359C22—442no—
360C22—441no—
361C22—441no—
362C22—441no—
363C22—441no—
364C22—441no—
365C22—881no—
366C22—881no—
367C22D11×#10011yescharacteristic
368C22#1062235811yescharacteristic
369C22#1062256911yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—82no—
376C4—441no—
377C4—441no—
378C4—882no—
379C4#1062281512yes—
380C2—21no—
381C2—21no—
382C2—442no—
383C2—881no—
384C2#1306900111yescharacteristic
385C2#1306907611yescharacteristic
386C2#1306913511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1558C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1558D11
hypocenterC11#9451
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

Complements

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

NH ≅ G/Ntype
3. #13067342C2semidirect
5. #13066473C2semidirect
6. #13066471C2semidirect
7. C11×#1558C2semidirect
122. #1558D11semidirect
311. C11#9451semidirect

Maximal subgroups

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

subgroupindex
#130776442
#130736122
#130673422
#130669562
#130664732
#130664712
C11×#15582
#945111