Finite Group Databasebeta

← #14663396

Subgroups — #14663396

Order 2816.

444 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 73 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#13073613C211yesmaximal, characteristic
2#13066953C211yesmaximal, characteristic
3#13066933C211yesmaximal, characteristic
4#13066550C211yesmaximal, characteristic, complemented
5#13066549C211yesmaximal, characteristic, complemented
6#13066549C211yesmaximal, characteristic, complemented
7C11×#1319C211yesmaximal, characteristic, complemented
8C2×#67000C411yescharacteristic
9C2×#66997C411yescharacteristic
10C2×#66946C2211yescharacteristic
11C2×#66928C411yescharacteristic
12C11×#391C2211yescharacteristic
13#10622587C2211yescharacteristic
14C4×Dic11⋊C4C411yescharacteristic
15#10622339—21no—
16D11×C22⋊C8—21no—
17#10622288—21no—
18#10622288—21no—
19#10622280—21no—
20#10622280—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622106—21no—
26#10622106—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D44C2×C411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×Dic22C2×C411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34#67000—42no—
35#66997—41no—
36#66997—41no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4D411yescharacteristic
42C2×(C2×D11)⋊C4D411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11C2×C411yescharacteristic
47C2×C4×Dic11C2×C411yescharacteristic
48C2×#4313—41no—
49C2×C8×D11—41no—
50#66946—41no—
51#66946—41no—
52#66928—42no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62(C2×D11)⋊C8—41no—
63(C2×D11)⋊C8—41no—
64#11564—111nomaximal, Sylow
65C23×D11C22⋊C411yescharacteristic
66C23×D11C22⋊C411yescharacteristic
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80C2×D44—22no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—41no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—42no—
89C2×C4×D11—42no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C2×Dic22—41no—
93C2×Dic22—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—41no—
97C42×C11—41no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104Dic11⋊C4—42no—
105Dic11⋊C4—42no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#4313—82no—
114C8×D11—82no—
115#2547—111no—
116#1465—111no—
117#1459—111no—
118#1319—111no—
119#1319—111no—
120#1319—111no—
121#1319D1111yescharacteristic, complemented
122C23×C11C2×C22⋊C411yescharacteristic
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11#10012yes—
133Q8×C11—81no—
134Q8×C11—81no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11#13111yescharacteristic
148C2×C4×C11#13111yescharacteristic
149C2×Dic11—22no—
150C2×Dic11—21no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11#9911yescharacteristic
159C2×Dic11#9911yescharacteristic
160D44—42no—
161D44—42no—
162C4×D11—42no—
163C4×D11—42no—
164C4×D11—81no—
165C4×D11—81no—
166Dic22—81no—
167Dic22—81no—
168C8×C11—81no—
169C8×C11—81no—
170C11⋊C8—81no—
171C11⋊C8—81no—
172C2×C4⋊Q8—111no—
173C2×#124—111no—
174C2×#124—111no—
175C2×C4×D4—111no—
176#407—221no—
177C2×C22⋊C8—221no—
178#397—221no—
179#397—221no—
180#391—111no—
181#391C2×D1111yescharacteristic
182#380—221no—
183#380—221no—
184C4×C4⋊C4—111no—
185#324—111no—
186#324—111no—
187#324C2×D1111yescharacteristic
188#324C2×D1111yescharacteristic
189#323—221no—
190#323—221no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11#40811yescharacteristic
194C22×C11C2×#9911yescharacteristic
195C22×C11C2×#10011yescharacteristic
196C2×D11—22no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—42no—
200C2×D11—42no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—81no—
205C2×D11—81no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—81no—
211C4×C11—81no—
212Dic11—21no—
213Dic11—41no—
214Dic11—81no—
215Dic11—81no—
216Dic11#35412yes—
217C22×Q8—111no—
218C22×Q8C4×D1111yescharacteristic
219C22×D4—111no—
220C23×C4—111no—
221C23×C4—111no—
222C2×M16—441no—
223C22×C8—441no—
224C4⋊Q8—441no—
225C4⋊Q8—441no—
226#124—442no—
227#124—442no—
228C4×D4—441no—
229C4×D4—441no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4C22×D1111yescharacteristic
234C2×C22⋊C4—111no—
235C2×C22⋊C4—111no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C42—111no—
241C2×C42—111no—
242C2×C42C4×D1111yescharacteristic
243C22⋊C8—21no—
244C22⋊C8—21no—
245C22⋊C8—221no—
246C22⋊C8—221no—
247C22⋊C8—441no—
248C22⋊C8—441no—
249#95—21no—
250#95—21no—
251#95—221no—
252#95—221no—
253#95—221no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11#147111yescharacteristic
257C2×C11C2×#35411yescharacteristic
258C2×C11#213511yescharacteristic
259D11—42no—
260D11—81no—
261C24—111no—
262C24—111no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—221no—
268C2×Q8—221no—
269C2×Q8—441no—
270C2×Q8—441no—
271C2×D4—222no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—441no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—111no—
278C22×C4—111no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4C2×C4×D1111yescharacteristic
288C22×C4D4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290M16—882no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—441no—
294C2×C8—441no—
295C2×C8—882no—
296C4⋊C4—41no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4—442no—
300C4⋊C4—442no—
301C22⋊C4—441no—
302C22⋊C4—441no—
303C22⋊C4—442no—
304C22⋊C4—442no—
305C22⋊C4—442no—
306C22⋊C4—442no—
307C42—41no—
308C42—221no—
309C42—221no—
310C42—441no—
311C11#1156411yescharacteristic, 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—81no—
324Q8—81no—
325Q8—881no—
326Q8—881no—
327D4—442no—
328D4—442no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—111no—
342C2×C4—111no—
343C2×C4—222no—
344C2×C4—221no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—881no—
355C2×C4—881no—
356C2×C4#6695411yescharacteristic
357C2×C4#6696011yescharacteristic
358C8—81no—
359C8—81no—
360C8—881no—
361C8—881no—
362C22—21no—
363C22—21no—
364C22—222no—
365C22—442no—
366C22—442no—
367C22—441no—
368C22—441no—
369C22—441no—
370C22—441no—
371C22—441no—
372C22—881no—
373C22—881no—
374C22#1062234011yescharacteristic
375C22D11×#9911yescharacteristic
376C22D11×#10011yescharacteristic
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—81no—
382C4—81no—
383C4—112no—
384C4—221no—
385C4—441no—
386C4—881no—
387C4—881no—
388C2—21no—
389C2—21no—
390C2—442no—
391C2—881no—
392C2#1306697411yescharacteristic
393C2D11×#35411yescharacteristic
394C2#1307030911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1319C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1319D11
hypocenterC11#11564
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
4. #13066550C2semidirect
5. #13066549C2semidirect
6. #13066549C2semidirect
7. C11×#1319C2semidirect
121. #1319D11semidirect
311. C11#11564semidirect

Maximal subgroups

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

subgroupindex
#130736132
#130669532
#130669332
#130665502
#130665492
C11×#13192
#1156411