Finite Group Databasebeta

← #14783697

Subgroups — #14783697

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071098C211yesmaximal, characteristic
2C2×#10622589C211yesmaximal, characteristic
3#13070181C214yesmaximal, complemented
4#13070176C214yesmaximal, complemented
5#13068337C211yesmaximal, characteristic
6#13068336C211yesmaximal, characteristic
7#13068335C211yesmaximal, characteristic
8#13068309C211yesmaximal, characteristic
9C11×#1736C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×Dic11⋊C4—22no—
16C22×C4×Dic11C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18#10622589—22no—
19#10622589C2212yes—
20#10622589C2212yes—
21#10622586C2212yes—
22#10622586C2212yes—
23#10622559—22no—
24C4×Dic11⋊C4—22no—
25C11×#340C2214yes—
26#10622189C2214yes—
27#10622188C2212yes—
28#10622188C2212yes—
29#10622167C2214yes—
30#10622167C2214yes—
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C23×Dic11—21no—
34C23×Dic11D412yes—
35C2×C11×M16—22no—
36C2×C11×M16—22no—
37C2×C11×M16—22no—
38C22×C8×C11C2312yes—
39C11×#117—22no—
40C11×#117—22no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C4⋊C4C2312yes—
46C2×C11×C22⋊C4—21no—
47C2×C42×C11—21no—
48C2×C22⋊Dic11—21no—
49#66979—22no—
50#66979Q814yes—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11C2312yes—
55C2×C4⋊Dic11C2312yes—
56C2×Dic11⋊C4—22no—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—24no—
59C2×Dic11⋊C4—24no—
60C2×Dic11⋊C4—48no—
61C2×C4×Dic11—21no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11D412yes—
65C2×C4×Dic11C2311yescharacteristic
66C2×C4×Dic11C2311yescharacteristic
67C2×#4318—22no—
68C2×#4318—22no—
69C2×#4318—22no—
70C22×C11⋊C8C2312yes—
71C11⋊#95—22no—
72C11⋊#95—22no—
73#23745—111nomaximal, Sylow
74C24×C11C2×D411yescharacteristic
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—44no—
78C22×C4×C11—42no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×Q812yes—
81C22×C4×C11#4112yes—
82C22×C4×C11#4112yes—
83C22×C4×C11#4112yes—
84C22×C4×C11#4112yes—
85C22×C4×C11#4112yes—
86C22×C4×C11C2411yescharacteristic
87C22×Dic11—24no—
88C22×Dic11—24no—
89C22×Dic11—24no—
90C22×Dic11—22no—
91C22×Dic11—22no—
92C22×Dic11—44no—
93C22×Dic11—42no—
94C22×Dic11C2×D412yes—
95C22×Dic11C2×D412yes—
96C11×M16—44no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—42no—
105C11×C22⋊C4—42no—
106C42×C11—42no—
107C22⋊Dic11—24no—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—42no—
112C4⋊Dic11C2×Q814yes—
113Dic11⋊C4—48no—
114Dic11⋊C4—44no—
115Dic11⋊C4—48no—
116Dic11⋊C4—44no—
117C4×Dic11—24no—
118C4×Dic11—24no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121C4×Dic11—21no—
122C4×Dic11—21no—
123#4318—44no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127#2296—111no—
128C2×#384—111no—
129#2100—114no—
130#2099—114no—
131#1736—111no—
132#1736—111no—
133#1736—111no—
134#1736D1111yescharacteristic
135#1728—111no—
136C23×C11—22no—
137C23×C11—22no—
138C23×C11C22⋊Q812yes—
139C23×C11#12312yes—
140C23×C11#12412yes—
141C23×C11C22×D411yescharacteristic
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—44no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—84no—
148C2×C4×C11C22⋊Q812yes—
149C2×C4×C11#12312yes—
150C2×C4×C11#12412yes—
151C2×C4×C11#12514yes—
152C2×C4×C11#12514yes—
153C2×C4×C11#12614yes—
154C2×C4×C11#12614yes—
155C2×C4×C11C22×Q811yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C2×C4×C11C2×#4111yescharacteristic
159C2×C4×C11C2×#4111yescharacteristic
160C2×C4×C11C2×#4111yescharacteristic
161C2×Dic11—216no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—24no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—44no—
171C2×Dic11—84no—
172C2×Dic11AGL(1,ℤ/8)14yes—
173C2×Dic11#13714yes—
174C8×C11—42no—
175C11⋊C8—42no—
176C22×M16—111no—
177C22×M16C2×D1111yescharacteristic
178C2×#117—111no—
179C2×#117C2×D1111yescharacteristic
180C22×C4⋊C4—111no—
181C22×C4⋊C4—222no—
182C22×C4⋊C4C2×D1111yescharacteristic
183C22×C42—111no—
184#389—112no—
185#389—112no—
186#385—222no—
187#384—112no—
188#384—112no—
189#384—222no—
190C4×C4⋊C4—222no—
191#340—114no—
192#340—114no—
193#340—114no—
194#340C2×D1114yes—
195#336—112no—
196#336—112no—
197C22×C11—24no—
198C22×C11—24no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11#40014yes—
202C22×C11C2×C22⋊Q811yescharacteristic
203C22×C11C2×#12311yescharacteristic
204C22×C11C2×#12411yescharacteristic
205C22×C11C2×AGL(1,ℤ/8)12yes—
206C22×C11C2×#13712yes—
207C4×C11—82no—
208C4×C11—82no—
209C4×C11#40014yes—
210C4×C11C2×#12511yescharacteristic
211C4×C11C2×#12511yescharacteristic
212C4×C11C2×#12611yescharacteristic
213C4×C11C2×#12611yescharacteristic
214Dic11—24no—
215Dic11—24no—
216Dic11—44no—
217Dic11—82no—
218C23×C4—21no—
219C23×C4—112no—
220C23×C4—221no—
221C23×C4C22×D1111yescharacteristic
222C2×M16—22no—
223C2×M16—22no—
224C2×M16—22no—
225C2×M16—222no—
226C2×M16—222no—
227C2×M16—222no—
228C22×C8—112no—
229C22×C8C22×D1112yes—
230#117—22no—
231#117—22no—
232#117—114no—
233#117—222no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—112no—
238C2×C4⋊C4—112no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4—222no—
241C2×C4⋊C4—224no—
242C2×C4⋊C4—224no—
243C2×C4⋊C4—222no—
244C2×C4⋊C4—222no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—448no—
247C2×C4⋊C4C22×D1112yes—
248C2×C4⋊C4C22×D1112yes—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—221no—
251C2×C42—21no—
252C2×C42—112no—
253C2×C42—111no—
254C2×C42—111no—
255C2×C42—222no—
256C2×C42—221no—
257C2×C42—222no—
258#95—222no—
259#95—222no—
260C2×C11—24no—
261C2×C11C2×#40011yescharacteristic
262C2×C11#307912yes—
263C2×C11#309212yes—
264C2×C11#313811yescharacteristic
265C2×C11#313911yescharacteristic
266C24D4×D1111yescharacteristic
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—44no—
270C22×C4—42no—
271C22×C4—112no—
272C22×C4—112no—
273C22×C4—224no—
274C22×C4—224no—
275C22×C4—224no—
276C22×C4—222no—
277C22×C4—222no—
278C22×C4—444no—
279C22×C4—442no—
280C22×C4#433912yes—
281C22×C4#433912yes—
282C22×C4#433912yes—
283C22×C4D4×D1111yescharacteristic
284C22×C4#434112yes—
285C22×C4#434112yes—
286C22×C4Q8×D1112yes—
287C22×C4C23×D1111yescharacteristic
288M16—44no—
289M16—444no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—222no—
294C2×C8—222no—
295C2×C8—222no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—42no—
301C4⋊C4—114no—
302C4⋊C4—222no—
303C4⋊C4—222no—
304C4⋊C4—222no—
305C4⋊C4—448no—
306C4⋊C4—444no—
307C4⋊C4—444no—
308C4⋊C4—448no—
309C4⋊C4—442no—
310C22⋊C4—42no—
311C22⋊C4—224no—
312C42—42no—
313C42—224no—
314C42—224no—
315C42—221no—
316C42—221no—
317C42—221no—
318C42—221no—
319C11#2374511yescharacteristic, complemented, Sylow
320C23—22no—
321C23—22no—
322C23#6693612yes—
323C23#6693812yes—
324C23#6694912yes—
325C23C2×D4×D1111yescharacteristic
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—44no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—84no—
332C2×C4—114no—
333C2×C4—114no—
334C2×C4—2216no—
335C2×C4—222no—
336C2×C4—222no—
337C2×C4—222no—
338C2×C4—222no—
339C2×C4—224no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—444no—
344C2×C4—884no—
345C2×C4#6692914yes—
346C2×C4#6693214yes—
347C2×C4#6693612yes—
348C2×C4#6693812yes—
349C2×C4#6694214yes—
350C2×C4#6694214yes—
351C2×C4#6694912yes—
352C2×C4C2×#433911yescharacteristic
353C2×C4C2×#433911yescharacteristic
354C2×C4C2×#433911yescharacteristic
355C2×C4C2×#434111yescharacteristic
356C2×C4C2×#434111yescharacteristic
357C2×C4C2×Q8×D1111yescharacteristic
358C8—42no—
359C8—442no—
360C22—24no—
361C22—24no—
362C22—22no—
363C22—22no—
364C22#1062227114yes—
365C22C2×#6693611yescharacteristic
366C22C2×#6693811yescharacteristic
367C22C2×#6694911yescharacteristic
368C22D11×AGL(1,ℤ/8)12yes—
369C22D11×#13712yes—
370C4—82no—
371C4—82no—
372C4—224no—
373C4—224no—
374C4—444no—
375C4—882no—
376C4#1062227114yes—
377C4C2×#6692911yescharacteristic
378C4C2×#6693211yescharacteristic
379C4C2×#6694211yescharacteristic
380C4C2×#6694211yescharacteristic
381C2—24no—
382C2C2×#1062227111yescharacteristic
383C2#1307842912yes—
384C2#1307853712yes—
385C2#1307898811yescharacteristic
386C2#1307899411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1736D11
hypocenterC11#23745
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
3. #13070181C2semidirect
4. #13070176C2semidirect
319. C11#23745semidirect

Maximal subgroups

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

subgroupindex
#130710982
C2×#106225892
#130701812
#130701762
#130683372
#130683362
#130683352
#130683092
C11×#17362
#2374511