Finite Group Databasebeta

← #14853508

Subgroups — #14853508

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
1C4×#66927C211yesmaximal, characteristic
2#13070179C212yesmaximal, complemented
3#13069850C212yesmaximal
4#13069312C214yesmaximal, complemented
5#13068613C212yesmaximal, complemented
6#13068613C212yesmaximal, complemented
7#13068469C211yesmaximal, characteristic, complemented
8C11×#2859C211yesmaximal, characteristic, complemented
9C2×C11×#125—21no—
10C2×#66927C2211yescharacteristic
11C2×C4×D44—21no—
12C2×C4×D44—21no—
13C2×C4×D44C2212yes—
14C11×#389—21no—
15C11×#389—21no—
16C11×#389C2212yes—
17C11×#389C2212yes—
18C11×#384C2211yescharacteristic
19C11×#384C2211yescharacteristic
20C11×#382—21no—
21C43×C11C2211yescharacteristic
22C2×#66873C2214yes—
23C2×#66873C2214yes—
24#10622552—21no—
25#10622552—21no—
26#10622552C2212yes—
27#10622548C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2212yes—
29C2×#66867C2212yes—
30#10622167C2214yes—
31#10622167C2214yes—
32#10622162C2212yes—
33C22×D44—21no—
34C22×D44—21no—
35C22×D44C2312yes—
36C22×C4×D11—22no—
37C11×#125—44no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C4⋊C4C2312yes—
46C2×C42×C11D411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C2×C42×C11D411yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×(C2×D11)⋊C4—22no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11C2312yes—
59C22×C11⋊C8C2314yes—
60#66927—24no—
61C4×D44—24no—
62C4×D44—24no—
63C4×D44—44no—
64C4×D44—44no—
65C11×#95—22no—
66C11×#95—22no—
67#66873—28no—
68#66873—44no—
69C4⋊(C11⋊C8)—24no—
70#66867—42no—
71#29130—111nomaximal, Sylow
72C23×D11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2411yescharacteristic
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—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—44no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—42no—
106C11×C4⋊C4—44no—
107C42×C11—22no—
108C42×C11—22no—
109C42×C11—22no—
110C42×C11—22no—
111C42×C11—22no—
112C42×C11—21no—
113C42×C11—21no—
114C42×C11#4114yes—
115(C2×D11)⋊C4—44no—
116(C2×D11)⋊C4—44no—
117(C2×D11)⋊C4—44no—
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C4⋊Dic11—42no—
121C4⋊Dic11—42no—
122C2×C11⋊C8—24no—
123C2×C11⋊C8—24no—
124C2×C11⋊C8—24no—
125#2859D1111yescharacteristic, complemented
126C4×#127—111no—
127#2100—112no—
128#2041—112no—
129#1936—114no—
130#1802—112no—
131#1802—112no—
132#1767—111no—
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—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11#12412yes—
160C2×C4×C11#12412yes—
161C2×C4×C11AGL(1,ℤ/8)12yes—
162C2×C4×C11AGL(1,ℤ/8)12yes—
163C2×C4×C11AGL(1,ℤ/8)12yes—
164C2×C4×C11#13712yes—
165C2×C4×C11C2×#4112yes—
166C2×C4×C11C2×#4112yes—
167C2×C4×C11H(5,𝔽2)11yescharacteristic
168C2×C4×C112−1+411yescharacteristic
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172D44—24no—
173D44—24no—
174D44—48no—
175D44—48no—
176D44—42no—
177D44—42no—
178C4×D11—88no—
179C11⋊C8—44no—
180C2×#127—111no—
181C2×#125—21no—
182C2×C4×D4—112no—
183C2×C4×D4—221no—
184C2×C4×D4—221no—
185C2×C4⋊C8—112no—
186C2×#102—114no—
187C2×#102—114no—
188C2×#97—112no—
189#390—112no—
190#390—221no—
191#390—221no—
192#389—21no—
193#389—21no—
194#389C2×D1112yes—
195#389C2×D1112yes—
196#384—111no—
197#384C2×D1111yescharacteristic
198#384C2×D1111yescharacteristic
199#382—21no—
200C43C2×D1111yescharacteristic
201#340—114no—
202#340—114no—
203#336—112no—
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—82no—
224C4×C11—82no—
225C4×C11#49014yes—
226C4×C11#55212yes—
227C4×C11#55312yes—
228Dic11—82no—
229C22×D4—112no—
230C22×D4—221no—
231C22×D4—221no—
232C23×C4—222no—
233C22×C8—114no—
234#127—224no—
235#125—44no—
236C4×D4—224no—
237C4×D4—224no—
238C4×D4—444no—
239C4×D4—444no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—112no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4C22×D1112yes—
250C2×C4⋊C4C22×D1112yes—
251C2×C22⋊C4—222no—
252C2×C22⋊C4—222no—
253C2×C22⋊C4—222no—
254C2×C42C22⋊D1111yescharacteristic
255C2×C42C22⋊D1111yescharacteristic
256C2×C42C22⋊D1111yescharacteristic
257C2×C42C22⋊D1111yescharacteristic
258C2×C42C22×D1111yescharacteristic
259C2×C42C22×D1111yescharacteristic
260C2×C42C22×D1111yescharacteristic
261C4⋊C8—224no—
262#102—228no—
263#102—444no—
264#97—442no—
265#95—22no—
266#95—22no—
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—22no—
289C22×C4—22no—
290C22×C4—222no—
291C22×C4—444no—
292C22×C4—444no—
293C22×C4—444no—
294C22×C4C2×C22⋊D1111yescharacteristic
295C22×C4C2×C22⋊D1111yescharacteristic
296C22×C4C2×C22⋊D1111yescharacteristic
297C22×C4C2×C22⋊D1111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299C22×C4C2×C22⋊D1111yescharacteristic
300C22×C4C23×D1111yescharacteristic
301C2×C8—224no—
302C2×C8—224no—
303C2×C8—224no—
304C4⋊C4—24no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C4⋊C4—44no—
310C4⋊C4—44no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—222no—
314C4⋊C4—222no—
315C4⋊C4—442no—
316C4⋊C4—442no—
317C22⋊C4—444no—
318C22⋊C4—444no—
319C22⋊C4—444no—
320C42—22no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—22no—
325C42—21no—
326C42—21no—
327C42#434314yes—
328C11#2913011yescharacteristic, complemented, Sylow
329C23—224no—
330C23—442no—
331C23—442no—
332C23—442no—
333C23—442no—
334C23—442no—
335C23—442no—
336C23C22×C22⋊D1111yescharacteristic
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—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—888no—
365C2×C4#6698512yes—
366C2×C4#6699512yes—
367C2×C4#6700012yes—
368C2×C4#6700012yes—
369C2×C4#6700212yes—
370C2×C4#6700212yes—
371C2×C4C2×#434312yes—
372C2×C4#41×D1112yes—
373C2×C4#6704211yescharacteristic
374C2×C4#6704311yescharacteristic
375C8—444no—
376C22—444no—
377C22—444no—
378C22—444no—
379C22—882no—
380C22—882no—
381C22—882no—
382C22—882no—
383C22C2×#6698511yescharacteristic
384C22C2×#6699511yescharacteristic
385C22C2×#6700011yescharacteristic
386C22C2×#6700211yescharacteristic
387C22C2×#6700211yescharacteristic
388C22#1062335911yescharacteristic
389C22#1062336411yescharacteristic
390C4—22no—
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—82no—
396C4—82no—
397C4—882no—
398C4#1062268014yes—
399C4#1062322512yes—
400C4#1062322612yes—
401C2—884no—
402C2#1307378311yescharacteristic
403C2#1307870311yescharacteristic
404C2#1307871111yescharacteristic
405C2C2×#1062268011yescharacteristic
406C2#1307901211yescharacteristic
407C2#1307999411yescharacteristic
408C2#1307999911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2859C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#2859D11
hypocenterC11#29130
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2859

Complements

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

NH ≅ G/Ntype
2. #13070179C2semidirect
4. #13069312C2semidirect
5. #13068613C2semidirect
6. #13068613C2semidirect
7. #13068469C2semidirect
8. C11×#2859C2semidirect
125. #2859D11semidirect
328. C11#29130semidirect

Maximal subgroups

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

subgroupindex
C4×#669272
#130701792
#130698502
#130693122
#130686132
#130684692
C11×#28592
#2913011