Finite Group Databasebeta

← #14853502

Subgroups — #14853502

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076979C211yesmaximal, characteristic, complemented
2C4×#66927C211yesmaximal, characteristic
3#13070180C212yesmaximal, complemented
4#13069851C212yesmaximal
5#13069313C214yesmaximal, complemented
6#13068617C212yesmaximal, complemented
7#13068617C212yesmaximal, complemented
8C11×#1767C211yesmaximal, characteristic, complemented
9C2×#66927C2211yescharacteristic
10C2×C4×D44—21no—
11C2×C4×D44—21no—
12C2×C4×D44C2212yes—
13C2×#66923—21no—
14C2×C11×C4⋊C8C2212yes—
15C2×C11×#97C2212yes—
16C43×C11C2211yescharacteristic
17C2×#66885C2214yes—
18C2×#66885C2214yes—
19#10622552—21no—
20#10622552—21no—
21#10622552C2212yes—
22#10622549—21no—
23#10622548C2211yescharacteristic
24#10622548C2211yescharacteristic
25#10622548C2211yescharacteristic
26#10622541—21no—
27#10622541—21no—
28#10622541C2212yes—
29#10622541C2212yes—
30C11×#336C2212yes—
31#10622189C2214yes—
32#10622189C2214yes—
33C22×D44—21no—
34C22×D44—21no—
35C22×D44C2312yes—
36C22×C4×D11—22no—
37C22×C8×C11C2314yes—
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11C2311yescharacteristic
43C2×C42×C11C2311yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C2×(C2×D11)⋊C4—22no—
46C2×(C2×D11)⋊C4—22no—
47C2×(C2×D11)⋊C4—22no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11C2312yes—
55C2×C4⋊Dic11C2312yes—
56C2×C4⋊Dic11C2312yes—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—22no—
59#66927—24no—
60C4×D44—24no—
61C4×D44—24no—
62C4×D44—44no—
63C4×D44—44no—
64#66923—44no—
65C11×C4⋊C8—24no—
66C11×#97—42no—
67C11⋊#95—22no—
68C11⋊#95—22no—
69#66885—28no—
70#66885—44no—
71#29130—111nomaximal, Sylow
72C23×D11—22no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2411yescharacteristic
80C22×Dic11—22no—
81C22×Dic11—22no—
82C22×Dic11—22no—
83C2×D44—24no—
84C2×D44—24no—
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—22no—
90C2×D44—42no—
91C2×D44—42no—
92C2×D44—42no—
93C2×D44—42no—
94C2×D44#4114yes—
95C2×C4×D11—44no—
96C2×C4×D11—44no—
97C2×C4×D11—44no—
98C2×C8×C11—24no—
99C2×C8×C11—24no—
100C2×C8×C11—24no—
101C42×C11—22no—
102C42×C11—22no—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11—21no—
107C42×C11—21no—
108C42×C11#4114yes—
109(C2×D11)⋊C4—44no—
110(C2×D11)⋊C4—44no—
111(C2×D11)⋊C4—44no—
112C4⋊Dic11—24no—
113C4⋊Dic11—22no—
114C4⋊Dic11—22no—
115C4⋊Dic11—22no—
116C4⋊Dic11—22no—
117C4⋊Dic11—42no—
118C4⋊Dic11—42no—
119C4⋊Dic11—42no—
120C4⋊Dic11—42no—
121C4⋊Dic11—42no—
122C4⋊Dic11—42no—
123Dic11⋊C4—44no—
124Dic11⋊C4—44no—
125#2859—111no—
126C4×#127—111no—
127#2100—112no—
128#2041—112no—
129#1936—114no—
130#1802—112no—
131#1802—112no—
132#1767D1111yescharacteristic, complemented
133C23×C11C22×D411yescharacteristic
134C22×D11—24no—
135C22×D11—42no—
136C22×D11—42no—
137C22×D11—42no—
138C22×D11—42no—
139C22×D11—42no—
140C22×D11—42no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11#12412yes—
154C2×C4×C11#12412yes—
155C2×C4×C11AGL(1,ℤ/8)12yes—
156C2×C4×C11AGL(1,ℤ/8)12yes—
157C2×C4×C11AGL(1,ℤ/8)12yes—
158C2×C4×C11#13712yes—
159C2×C4×C11C2×#4112yes—
160C2×C4×C11C2×#4112yes—
161C2×C4×C11H(5,𝔽2)11yescharacteristic
162C2×C4×C112−1+411yescharacteristic
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172D44—24no—
173D44—24no—
174D44—48no—
175D44—48no—
176D44—42no—
177D44—42no—
178C4×D11—88no—
179C8×C11—44no—
180C2×#127—111no—
181C2×#125—221no—
182C2×C4×D4—112no—
183C2×C4×D4—221no—
184C2×C4×D4—221no—
185C2×C4⋊C8C2×D1112yes—
186C2×#102—114no—
187C2×#102—114no—
188C2×#97C2×D1112yes—
189#390—112no—
190#390—221no—
191#390—221no—
192#389—112no—
193#389—112no—
194#389—221no—
195#389—221no—
196#384—111no—
197#384—111no—
198#384—111no—
199#382—221no—
200C43C2×D1111yescharacteristic
201#340—114no—
202#340—114no—
203#336C2×D1112yes—
204C22×C11#52511yescharacteristic
205C22×C11C2×#12411yescharacteristic
206C22×C11#53711yescharacteristic
207C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
208C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
209C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
210C22×C11C2×#13711yescharacteristic
211C2×D11—44no—
212C2×D11—44no—
213C2×D11—44no—
214C2×D11—82no—
215C2×D11—82no—
216C2×D11—82no—
217C2×D11—82no—
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—41no—
222C4×C11—41no—
223C4×C11#49014yes—
224C4×C11#55212yes—
225C4×C11#55312yes—
226Dic11—82no—
227Dic11—82no—
228Dic11—82no—
229C22×D4—112no—
230C22×D4—221no—
231C22×D4—221no—
232C23×C4—222no—
233C22×C8C22×D1114yes—
234#127—224no—
235#125—444no—
236C4×D4—224no—
237C4×D4—224no—
238C4×D4—444no—
239C4×D4—444no—
240C2×C4⋊C4—112no—
241C2×C4⋊C4—112no—
242C2×C4⋊C4—112no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—222no—
248C2×C4⋊C4—222no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4—221no—
251C2×C22⋊C4—222no—
252C2×C22⋊C4—222no—
253C2×C22⋊C4—222no—
254C2×C42D4411yescharacteristic
255C2×C42D4411yescharacteristic
256C2×C42D4411yescharacteristic
257C2×C42D4411yescharacteristic
258C2×C42C22×D1111yescharacteristic
259C2×C42C22×D1111yescharacteristic
260C2×C42C22×D1111yescharacteristic
261C4⋊C8—24no—
262#102—228no—
263#102—444no—
264#97—42no—
265#95—222no—
266#95—222no—
267C2×C11#256211yescharacteristic
268C2×C11#310911yescharacteristic
269C2×C11#311011yescharacteristic
270C2×C11C2×#49011yescharacteristic
271C2×C11#314111yescharacteristic
272C2×C11#325311yescharacteristic
273C2×C11#325411yescharacteristic
274D11—84no—
275C24—222no—
276C2×D4—114no—
277C2×D4—224no—
278C2×D4—224no—
279C2×D4—222no—
280C2×D4—222no—
281C2×D4—222no—
282C2×D4—222no—
283C2×D4—222no—
284C2×D4—442no—
285C2×D4—442no—
286C2×D4—442no—
287C2×D4—442no—
288C22×C4—222no—
289C22×C4—222no—
290C22×C4—222no—
291C22×C4—444no—
292C22×C4—444no—
293C22×C4—444no—
294C22×C4C2×D4411yescharacteristic
295C22×C4C2×D4411yescharacteristic
296C22×C4C2×D4411yescharacteristic
297C22×C4C2×D4411yescharacteristic
298C22×C4C2×D4411yescharacteristic
299C22×C4C2×D4411yescharacteristic
300C22×C4C23×D1111yescharacteristic
301C2×C8—24no—
302C2×C8—24no—
303C2×C8—24no—
304C4⋊C4—222no—
305C4⋊C4—222no—
306C4⋊C4—222no—
307C4⋊C4—222no—
308C4⋊C4—224no—
309C4⋊C4—442no—
310C4⋊C4—442no—
311C4⋊C4—444no—
312C4⋊C4—442no—
313C4⋊C4—442no—
314C4⋊C4—444no—
315C4⋊C4—442no—
316C4⋊C4—442no—
317C22⋊C4—444no—
318C22⋊C4—444no—
319C22⋊C4—444no—
320C42—22no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—21no—
325C42—21no—
326C42—22no—
327C42#433914yes—
328C11#2913011yescharacteristic, complemented, Sylow
329C23—224no—
330C23—442no—
331C23—442no—
332C23—442no—
333C23—442no—
334C23—442no—
335C23—442no—
336C23C22×D4411yescharacteristic
337D4—224no—
338D4—224no—
339D4—448no—
340D4—448no—
341D4—442no—
342D4—442no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—888no—
365C2×C4#6692812yes—
366C2×C4#6692812yes—
367C2×C4#6696112yes—
368C2×C4#6696112yes—
369C2×C4#6696112yes—
370C2×C4#6696212yes—
371C2×C4C2×#433912yes—
372C2×C4#6703711yescharacteristic
373C2×C4#6704011yescharacteristic
374C2×C4#41×D1112yes—
375C8—44no—
376C22—444no—
377C22—444no—
378C22—444no—
379C22—882no—
380C22—882no—
381C22—882no—
382C22—882no—
383C22C2×#6692811yescharacteristic
384C22#1062304111yescharacteristic
385C22#1062305511yescharacteristic
386C22C2×#6696111yescharacteristic
387C22C2×#6696111yescharacteristic
388C22C2×#6696111yescharacteristic
389C22C2×#6696211yescharacteristic
390C4—22no—
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—882no—
396C4—882no—
397C4—882no—
398C4#1062232614yes—
399C4#1062308912yes—
400C4#1062311212yes—
401C2—884no—
402C2#1307377711yescharacteristic
403C2#1307870811yescharacteristic
404C2#1307871611yescharacteristic
405C2C2×#1062232611yescharacteristic
406C2#1307901011yescharacteristic
407C2#1307999711yescharacteristic
408C2#1308000411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1767C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#1767D11
hypocenterC11#29130
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
1. #13076979C2semidirect
3. #13070180C2semidirect
5. #13069313C2semidirect
6. #13068617C2semidirect
7. #13068617C2semidirect
8. C11×#1767C2semidirect
132. #1767D11semidirect
328. C11#29130semidirect

Maximal subgroups

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

subgroupindex
#130769792
C4×#669272
#130701802
#130698512
#130693132
#130686172
C11×#17672
#2913011