Finite Group Databasebeta

← #14783707

Subgroups — #14783707

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622541C211yesmaximal, characteristic
2#13070183C214yesmaximal, complemented
3#13070178C212yesmaximal, complemented
4#13070173C212yesmaximal, complemented
5#13068337C212yesmaximal
6#13068337C212yesmaximal
7#13068310C211yesmaximal, characteristic
8C11×#2285C211yesmaximal, characteristic
9C2×C11×#117C2212yes—
10C22×C42×C11C2211yescharacteristic
11C22×C4⋊Dic11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×Dic11⋊C4—21no—
14C22×#4318C2212yes—
15C11×#384C2211yescharacteristic
16C11×#384C2211yescharacteristic
17C11×#382C2212yes—
18C11×#380—21no—
19C11×#380—21no—
20C4×C11×C4⋊C4—21no—
21C4×C11×C4⋊C4—21no—
22C2×C11⋊#95—21no—
23#10622541—21no—
24#10622541—21no—
25#10622541C2212yes—
26#10622541C2212yes—
27#10622167C2214yes—
28#10622167C2214yes—
29#10622167C2214yes—
30#10622167C2214yes—
31#10622162C2212yes—
32#10622162C2212yes—
33C23×C4×C11D411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×Dic11—21no—
37C23×Dic11—21no—
38C11×#117—28no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4C2312yes—
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C22⋊C4—22no—
46C2×C42×C11—24no—
47C2×C42×C11—22no—
48C2×C42×C11D411yescharacteristic
49C2×C42×C11D411yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11—24no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11Q814yes—
57C2×C4⋊Dic11C2312yes—
58C2×C4⋊Dic11C2312yes—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—44no—
62C2×#4318—24no—
63C2×#4318—24no—
64C2×#4318—24no—
65C22×C11⋊C8C2314yes—
66C11×#95—22no—
67C11×#95—22no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70#23747—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×Q812yes—
86C22×C4×C11#4112yes—
87C22×C4×C11#4114yes—
88C22×C4×C11#4114yes—
89C22×C4×C11C2411yescharacteristic
90C22×Dic11—24no—
91C22×Dic11—22no—
92C22×Dic11—22no—
93C22×Dic11—42no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C22×Dic11—42no—
97C22×Dic11—42no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—42no—
104C11×C22⋊C4—44no—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11—22no—
108C42×C11—22no—
109C42×C11—44no—
110C4⋊Dic11—24no—
111C4⋊Dic11—22no—
112C4⋊Dic11—24no—
113C4⋊Dic11—42no—
114C4⋊Dic11C2×Q814yes—
115Dic11⋊C4—44no—
116Dic11⋊C4—44no—
117#4318—48no—
118C2×C11⋊C8—24no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—24no—
121C2×#389—111no—
122#2285D1111yescharacteristic
123#2101—114no—
124#2100—112no—
125#2099—112no—
126#1736—112no—
127#1736—112no—
128#1728—111no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11C22⋊Q812yes—
134C23×C11#12312yes—
135C23×C11#12412yes—
136C23×C11C22×D411yescharacteristic
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
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—44no—
148C2×C4×C11—44no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11C22⋊Q812yes—
156C2×C4×C11#12312yes—
157C2×C4×C11#12412yes—
158C2×C4×C11#12518yes—
159C2×C4×C11#12618yes—
160C2×C4×C11AGL(1,ℤ/8)12yes—
161C2×C4×C11#13712yes—
162C2×C4×C11C22×Q811yescharacteristic
163C2×C4×C11C2×#4112yes—
164C2×C4×C11C2×#4112yes—
165C2×C4×C11C2×#4111yescharacteristic
166C2×Dic11—24no—
167C2×Dic11—48no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—84no—
174C11⋊C8—44no—
175C22×M16—112no—
176C2×#117C2×D1112yes—
177C22×C4⋊C4—111no—
178C22×C4⋊C4—111no—
179C22×C4⋊C4—221no—
180C22×C42C2×D1111yescharacteristic
181#389—112no—
182#389—112no—
183#389—221no—
184#389—221no—
185#384C2×D1111yescharacteristic
186#384C2×D1111yescharacteristic
187#382C2×D1112yes—
188#380—21no—
189#380—21no—
190C4×C4⋊C4—21no—
191C4×C4⋊C4—21no—
192C2×#95—221no—
193#340—114no—
194#340—114no—
195#340—114no—
196#340—114no—
197#336—112no—
198#336—112no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11#40014yes—
206C22×C11C2×C22⋊Q811yescharacteristic
207C22×C11C2×#12311yescharacteristic
208C22×C11C2×#12411yescharacteristic
209C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
210C22×C11C2×#13711yescharacteristic
211C22×C11#57511yescharacteristic
212C22×C11#57511yescharacteristic
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—41no—
216C4×C11—41no—
217C4×C11—82no—
218C4×C11—82no—
219C4×C11#40014yes—
220C4×C11C2×#12512yes—
221C4×C11C2×#12612yes—
222Dic11—44no—
223Dic11—82no—
224C23×C4—221no—
225C23×C4—221no—
226C23×C4C22⋊D1111yescharacteristic
227C23×C4C22⋊D1111yescharacteristic
228C23×C4C22×D1111yescharacteristic
229C2×M16—224no—
230C2×M16—224no—
231C2×M16—224no—
232C22×C8—114no—
233#117—28no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—114no—
239C2×C4⋊C4—112no—
240C2×C4⋊C4—112no—
241C2×C4⋊C4—222no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—224no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—222no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4—444no—
248C2×C4⋊C4C22×D1112yes—
249C2×C4⋊C4C22×D1112yes—
250C2×C22⋊C4—22no—
251C2×C42—24no—
252C2×C42—22no—
253C2×C42C22⋊D1111yescharacteristic
254C2×C42C22⋊D1111yescharacteristic
255C2×C42C22×D1111yescharacteristic
256C2×C42C22×D1111yescharacteristic
257#95—22no—
258#95—22no—
259#95—222no—
260#95—222no—
261C2×C11—24no—
262C2×C11C2×#40011yescharacteristic
263C2×C11#307711yescharacteristic
264C2×C11#307811yescharacteristic
265C2×C11#309411yescharacteristic
266C2×C11#309511yescharacteristic
267C2×C11#314111yescharacteristic
268C2×C11#314211yescharacteristic
269C24C2×C22⋊D1111yescharacteristic
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—224no—
279C22×C4—222no—
280C22×C4—222no—
281C22×C4—442no—
282C22×C4—442no—
283C22×C4—442no—
284C22×C4—442no—
285C22×C4—442no—
286C22×C4#433914yes—
287C22×C4#434114yes—
288C22×C4Q8×D1112yes—
289C22×C4#434312yes—
290C22×C4C2×C22⋊D1111yescharacteristic
291C22×C4C2×C22⋊D1111yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293C22×C4C2×C22⋊D1111yescharacteristic
294C22×C4C2×C22⋊D1111yescharacteristic
295C22×C4C23×D1111yescharacteristic
296M16—448no—
297C2×C8—224no—
298C2×C8—224no—
299C2×C8—224no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—114no—
307C4⋊C4—224no—
308C4⋊C4—222no—
309C4⋊C4—224no—
310C4⋊C4—444no—
311C4⋊C4—442no—
312C4⋊C4—444no—
313C22⋊C4—44no—
314C42—22no—
315C42—22no—
316C42—22no—
317C42—22no—
318C42—44no—
319C11#2374711yescharacteristic, complemented, Sylow
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23#6698212yes—
325C23#6698912yes—
326C23#6699912yes—
327C23C22×C22⋊D1111yescharacteristic
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—224no—
347C2×C4—448no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4—442no—
353C2×C4—884no—
354C2×C4#6694218yes—
355C2×C4#6695118yes—
356C2×C4#6698212yes—
357C2×C4#6698912yes—
358C2×C4#6699912yes—
359C2×C4#6700212yes—
360C2×C4#6700412yes—
361C2×C4C2×#433912yes—
362C2×C4C2×#434112yes—
363C2×C4C2×Q8×D1111yescharacteristic
364C2×C4C2×#434311yescharacteristic
365C8—444no—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22#1062259514yes—
373C22C2×#6698211yescharacteristic
374C22C2×#6698911yescharacteristic
375C22C2×#6699911yescharacteristic
376C22C2×#6700211yescharacteristic
377C22#1062335311yescharacteristic
378C22#1062335311yescharacteristic
379C22C2×#6700411yescharacteristic
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—82no—
385C4—82no—
386C4—444no—
387C4—882no—
388C4#1062259514yes—
389C4C2×#6694212yes—
390C4C2×#6695112yes—
391C2—24no—
392C2C2×#1062259511yescharacteristic
393C2#1307840911yescharacteristic
394C2#1307841711yescharacteristic
395C2#1307855611yescharacteristic
396C2#1307856411yescharacteristic
397C2#1307900911yescharacteristic
398C2#1307901611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2285C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2285D11
hypocenterC11#23747
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #13070183C2semidirect
3. #13070178C2semidirect
4. #13070173C2semidirect
319. C11#23747semidirect

Maximal subgroups

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

subgroupindex
C2×#106225412
#130701832
#130701782
#130701732
#130683372
#130683102
C11×#22852
#2374711