Finite Group Databasebeta

← #14650475

Subgroups — #14650475

Order 2816.

594 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079554C211yesmaximal, characteristic
2#13071341C211yesmaximal, characteristic
3#13067285C211yesmaximal, characteristic
4#13067180C211yesmaximal, characteristic, complemented
5#13066476C211yesmaximal, characteristic, complemented
6#13066445C211yesmaximal, characteristic, complemented
7C11×#1995C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×#66927C2211yescharacteristic
10C2×C4×D44—21no—
11C11×#423C2211yescharacteristic
12C11×#376C2211yescharacteristic
13#10622701C412yescomplemented
14#10622698C412yescomplemented
15#10622659—22no—
16#10622640—22no—
17#10622552—21no—
18#10622549C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622538C2211yescharacteristic
21#10622278—22no—
22#10622278—22no—
23C11×#339—21no—
24C11×#339—21no—
25#10622176—22no—
26#10622123—22no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44D412yes—
30C22×C4×D11—22no—
31C2×C11×M16—21no—
32C11×C4⋊Q8C2×C411yescharacteristic, complemented
33C11×C4⋊Q8C2×C411yescharacteristic, complemented
34C11×#125—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C11×#117—21no—
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11C2311yescharacteristic
43C2×#4325—24no—
44C2×(C2×D11)⋊C4—22no—
45C2×(C2×D11)⋊C4—22no—
46C2×(C2×D11)⋊C4—22no—
47C2×C4⋊Dic11—21no—
48#66927—21no—
49#66927—21no—
50#66927C2×C412yes—
51#66927D412yes—
52C4×D44—42no—
53C4×D44—42no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11⋊#95—21no—
59C11⋊#95D412yes—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66873—24no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4×C11⋊C8—21no—
66C4×C11⋊C8C2×C412yescomplemented
67#9295—111nomaximal, Sylow
68C23×D11—22no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—22no—
77C2×D44—22no—
78C2×D44—22no—
79C2×D44—22no—
80C2×D44—22no—
81C2×D44—22no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—82no—
87C2×D44—82no—
88C2×D44C22⋊C414yes—
89C2×C4×D11—44no—
90C2×C4×D11—82no—
91C2×C4×D11—82no—
92C11×M16—41no—
93C11×M16—41no—
94C2×C8×C11—41no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11—21no—
103C42×C11—21no—
104C42×C11—21no—
105C42×C11—41no—
106C42×C11SD1612yescomplemented
107C42×C11C22×C411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11#4111yescharacteristic
110C42×C11#4111yescharacteristic
111#4325—84no—
112(C2×D11)⋊C4—44no—
113(C2×D11)⋊C4—82no—
114(C2×D11)⋊C4—82no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—41no—
119#3208—111no—
120#2328—111no—
121#1995D1111yescharacteristic, complemented
122#1545—111no—
123#1518—111no—
124#1286—111no—
125#1274—111no—
126C23×C11#12011yescharacteristic
127C22×D11—24no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—42no—
131C22×D11—42no—
132C22×D11—42no—
133C22×D11—42no—
134Q8×C11—42no—
135Q8×C11—81no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
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×C11C2×C22⋊C411yescharacteristic
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159D44—44no—
160D44—42no—
161D44—42no—
162D44—42no—
163D44—42no—
164D44—82no—
165D44—82no—
166D44—82no—
167C4×D11—88no—
168C8×C11—81no—
169C11⋊C8—42no—
170C11⋊C8—81no—
171#533C2×D1111yescharacteristic
172C2×#127—111no—
173C2×C4×D4—221no—
174#492—112no—
175#486—112no—
176#460—222no—
177#450—222no—
178#431—111no—
179#431—111no—
180#423C2×D1111yescharacteristic
181#390—221no—
182#386—222no—
183#386—222no—
184#382—111no—
185#376C2×D1111yescharacteristic
186#339—21no—
187#339—21no—
188#331—222no—
189#328—222no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11#38611yescharacteristic
193C22×C11#45011yescharacteristic
194C22×C11#45211yescharacteristic
195C2×D11—44no—
196C2×D11—44no—
197C2×D11—44no—
198C2×D11—82no—
199C2×D11—82no—
200C2×D11—82no—
201C2×D11—82no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—42no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11C4×SD1611yescharacteristic
211C4×C11#44011yescharacteristic
212C4×C11#46111yescharacteristic
213C4×C11#46311yescharacteristic
214Dic11—82no—
215C22×D4—112no—
216C22×D4—221no—
217C22×D4—221no—
218C23×C4—222no—
219C2×SD16—224no—
220C2×M16—21no—
221C4⋊Q8C4×D1111yescharacteristic, complemented
222C4⋊Q8C4×D1111yescharacteristic, complemented
223#127—112no—
224#127—112no—
225#127—221no—
226#127—221no—
227#125—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×D4—442no—
233C4×D4—442no—
234#117—21no—
235C2×C4⋊C4—221no—
236C2×C22⋊C4—222no—
237C2×C22⋊C4—222no—
238C2×C22⋊C4—222no—
239C2×C42C22⋊D1111yescharacteristic
240C2×C42C22⋊D1111yescharacteristic
241C2×C42C22×D1111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246#102—224no—
247C22⋊C8—221no—
248C22⋊C8—221no—
249C4×C8—112no—
250C4×C8—221no—
251#95—21no—
252#95—21no—
253#95—112no—
254#95—221no—
255C2×C11—21no—
256C2×C11—21no—
257C2×C11#187711yescharacteristic
258C2×C11#190411yescharacteristic
259C2×C11#191111yescharacteristic
260D11—84no—
261C24—222no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×D4—114no—
265C2×D4—222no—
266C2×D4—222no—
267C2×D4—222no—
268C2×D4—222no—
269C2×D4—222no—
270C2×D4—441no—
271C2×D4—441no—
272C2×D4—441no—
273C2×D4—441no—
274C2×D4—882no—
275C2×D4—882no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—222no—
279C22×C4—444no—
280C22×C4—882no—
281C22×C4—882no—
282C22×C4D4×D1111yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285SD16—884no—
286M16—41no—
287M16—41no—
288C2×C8—41no—
289C2×C8—222no—
290C2×C8—441no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C22⋊C4—41no—
300C22⋊C4—444no—
301C22⋊C4—882no—
302C22⋊C4—882no—
303C42—21no—
304C42—21no—
305C42—21no—
306C42—41no—
307C42#432512yescomplemented
308C42C2×C4×D1111yescharacteristic
309C42#433911yescharacteristic
310C42D4×D1111yescharacteristic
311C42#434111yescharacteristic
312C11#929511yescharacteristic, complemented, Sylow
313C23—224no—
314C23—442no—
315C23—442no—
316C23—442no—
317C23—442no—
318C23—442no—
319C23—442no—
320C23#6699011yescharacteristic
321Q8—42no—
322Q8—81no—
323D4—444no—
324D4—442no—
325D4—442no—
326D4—442no—
327D4—442no—
328D4—882no—
329D4—882no—
330D4—882no—
331C2×C4—22no—
332C2×C4—41no—
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—442no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—888no—
345C2×C4C22⋊C4×D1111yescharacteristic
346C2×C4(C22⋊D11)⋊C411yescharacteristic
347C2×C4#6693611yescharacteristic
348C2×C4#6693711yescharacteristic
349C2×C4C4×C22⋊D1111yescharacteristic
350C2×C4#6699111yescharacteristic
351C2×C4C2×#432511yescharacteristic
352C2×C4#6699511yescharacteristic
353C2×C4#6700211yescharacteristic
354C2×C4#6700311yescharacteristic
355C8—81no—
356C8—442no—
357C8—881no—
358C22—21no—
359C22—21no—
360C22—444no—
361C22—444no—
362C22—444no—
363C22—882no—
364C22—882no—
365C22—882no—
366C22—882no—
367C22#1062256911yescharacteristic
368C22#1062265911yescharacteristic
369C22#1062266011yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—882no—
379C4C4×#432511yescharacteristic
380C4#1062263911yescharacteristic
381C4#1062267011yescharacteristic
382C4#1062269611yescharacteristic
383C2—21no—
384C2—21no—
385C2—884no—
386C2#1306895311yescharacteristic
387C2#1306910011yescharacteristic
388C2#1306914511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1995C2
socleC22×C11#386
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1995D11
hypocenterC11#9295
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
4. #13067180C2semidirect
5. #13066476C2semidirect
6. #13066445C2semidirect
7. C11×#1995C2semidirect
13. #10622701C4semidirect
14. #10622698C4semidirect
32. C11×C4⋊Q8C2×C4semidirect
33. C11×C4⋊Q8C2×C4semidirect
66. C4×C11⋊C8C2×C4semidirect
106. C42×C11SD16semidirect
121. #1995D11semidirect
221. C4⋊Q8C4×D11semidirect
222. C4⋊Q8C4×D11semidirect
307. C42#4325semidirect
312. C11#9295semidirect

Maximal subgroups

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

subgroupindex
#130795542
#130713412
#130672852
#130671802
#130664762
#130664452
C11×#19952
#929511