Finite Group Databasebeta

← #14771491

Subgroups — #14771491

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622493C211yesmaximal, characteristic
2#13071505C212yesmaximal
3#13069354C211yesmaximal, characteristic, complemented
4#13069352C211yesmaximal, characteristic, complemented
5#13069201C212yesmaximal, complemented
6#13069199C212yesmaximal, complemented
7#13068710C212yesmaximal
8#13068638C211yesmaximal, characteristic
9#13068515C211yesmaximal, characteristic, complemented
10#13068393C211yesmaximal, characteristic
11C11×#1776C211yesmaximal, characteristic, complemented
12C22×C8×D11C2211yescharacteristic
13C2×#66945C2212yes—
14C2×C11×#107C2211yescharacteristic
15C2×C11×#106C2211yescharacteristic
16C2×C11×#97C2211yescharacteristic
17C4×C11×C4⋊C4C2212yes—
18C2×(C2×D11)⋊C8C2211yescharacteristic
19C2×#66882C2211yescharacteristic
20C2×#66881C2211yescharacteristic
21C2×#66879C2211yescharacteristic
22#10622600C2212yes—
23C4⋊C4×Dic11C2212yes—
24#10622586C2212yes—
25C2×#66872C2212yes—
26#10622553—22no—
27C4×(C2×D11)⋊C4C2211yescharacteristic
28C4×Dic11⋊C4—22no—
29#10622541C2212yes—
30#10622493C418yescomplemented
31#10622282—22no—
32#10622264—22no—
33C11×#340C2212yes—
34#10622189C2212yes—
35#10622188C2211yescharacteristic
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622162C2211yescharacteristic
40C22×C4×D11C2311yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C2×C11×C4⋊C4C2312yes—
44C2×C11×C4⋊C4C2312yes—
45C2×C42×C11—22no—
46C2×C42×C11C2311yescharacteristic
47C2×(C2×D11)⋊C4—22no—
48C2×(C2×D11)⋊C4—22no—
49C2×(C2×D11)⋊C4D412yes—
50C2×C4⋊Dic11C2312yes—
51C2×C4⋊Dic11C2312yes—
52C2×Dic11⋊C4—22no—
53C2×Dic11⋊C4—22no—
54C2×C4×Dic11—22no—
55C2×C4×Dic11—22no—
56C2×C4×Dic11C2311yescharacteristic
57C22×C11⋊C8C2311yescharacteristic
58C22×C11⋊C8C2311yescharacteristic
59C2×C8×D11—22no—
60C2×C8×D11—22no—
61C2×C8×D11C2×C414yes—
62#66945—24no—
63#66945C2×C418yes—
64C11×#107C2×C414yes—
65C11×#106—22no—
66C11×#97—22no—
67C11×#95—22no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95D412yes—
73(C2×D11)⋊C8—22no—
74#66882C2×C414yes—
75#66881—22no—
76#66879—22no—
77#66872C2×C418yes—
78#22620—111nomaximal, Sylow
79C23×D11C2×D411yescharacteristic
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2411yescharacteristic
84C22×Dic11—22no—
85C22×Dic11—22no—
86C22×Dic11C2×D412yes—
87C22×Dic11C2×D411yescharacteristic
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11C22×C412yes—
93C2×C4×D11#4112yes—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—21no—
97C2×C8×C11C22×C412yes—
98C2×C8×C11#4112yes—
99C2×C8×C11#4112yes—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4C22×C414yes—
104C42×C11—21no—
105C42×C11—21no—
106C42×C11—82no—
107(C2×D11)⋊C4—28no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—82no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11C22×C414yes—
114Dic11⋊C4—44no—
115Dic11⋊C4—44no—
116C4×Dic11—28no—
117C4×Dic11—21no—
118C4×Dic11—21no—
119C4×Dic11—82no—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—21no—
122C2×C11⋊C8—21no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—21no—
125C2×C11⋊C8C22×C412yes—
126C8×D11—28no—
127C2×#427—111no—
128#2347—112no—
129#1943—111no—
130#1943—111no—
131#1920—112no—
132#1920—112no—
133#1825—112no—
134#1807—111no—
135#1776—111no—
136#1776D1111yescharacteristic, complemented
137#1752—111no—
138C23×C11C22×D411yescharacteristic
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—22no—
142C22×D11—22no—
143C22×D11C4×D412yes—
144C2×C4×C11—24no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11C23×C411yescharacteristic
154C2×C4×C11C2×#4111yescharacteristic
155C2×C4×C11C2×#4111yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C2×C4×C112−1+411yescharacteristic
158C2×C4×C112−1+411yescharacteristic
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—24no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11C4×D412yes—
171C4×D11—22no—
172C4×D11—22no—
173C4×D11—22no—
174C4×D11—22no—
175C8×C11—41no—
176C8×C11#11714yes—
177C11⋊C8—22no—
178C11⋊C8—41no—
179C23×C8—111no—
180C2×#117—112no—
181#427—118no—
182C2×#107—111no—
183C2×#107C2×D1111yescharacteristic
184C2×#106—112no—
185C2×#106—111no—
186C2×#106C2×D1111yescharacteristic
187C2×C22⋊C8—111no—
188C2×#97—111no—
189C2×#97C2×D1111yescharacteristic
190#389—112no—
191#389—112no—
192#388—222no—
193#388—222no—
194#383—222no—
195#380—112no—
196C4×C4⋊C4—112no—
197C4×C4⋊C4—222no—
198C4×C4⋊C4C2×D1112yes—
199C4×C22⋊C4—111no—
200#340—112no—
201#340—112no—
202#340—112no—
203#340—112no—
204#340C2×D1112yes—
205#336—111no—
206#336—111no—
207C22×C11C2×C4×D411yescharacteristic
208C22×C11#54711yescharacteristic
209C22×C11#54711yescharacteristic
210C22×C11#57512yes—
211C22×C11#57712yes—
212C2×D11—22no—
213C2×D11—22no—
214C2×D11—22no—
215C2×D11—42no—
216C2×D11—42no—
217C4×C11—42no—
218C4×C11—44no—
219C4×C11—82no—
220C4×C11C2×#11711yescharacteristic
221C4×C11#51911yescharacteristic
222C4×C11#55211yescharacteristic
223C4×C11#55211yescharacteristic
224Dic11—22no—
225Dic11—42no—
226Dic11—44no—
227Dic11—82no—
228C23×C4—111no—
229C22×C8—111no—
230C22×C8—114no—
231C22×C8—111no—
232C22×C8—222no—
233C22×C8—222no—
234C22×C8C22×D1111yescharacteristic
235C22×C8C22×D1111yescharacteristic
236#117—118no—
237#117—224no—
238C2×C4⋊C4—112no—
239C2×C4⋊C4—112no—
240C2×C4⋊C4—222no—
241C2×C4⋊C4—222no—
242C2×C4⋊C4C22×D1112yes—
243C2×C4⋊C4C22×D1112yes—
244C2×C22⋊C4—112no—
245C2×C22⋊C4—222no—
246C2×C22⋊C4—222no—
247C2×C42—22no—
248C2×C42—111no—
249C2×C42—222no—
250C2×C42—222no—
251C2×C42C22×D1111yescharacteristic
252#107—114no—
253#107C4×D1114yes—
254#106—22no—
255#106—118no—
256#106—222no—
257C22⋊C8—222no—
258#97—22no—
259#97—222no—
260#95—22no—
261#95—112no—
262#95—222no—
263#95—222no—
264#95—222no—
265#95—222no—
266C2×C11#234411yescharacteristic
267C2×C11#294311yescharacteristic
268C2×C11#295211yescharacteristic
269C2×C11#335012yes—
270C2×C11#335012yes—
271D11—42no—
272C24—111no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—111no—
276C22×C4—112no—
277C22×C4—112no—
278C22×C4—112no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—222no—
284C22×C4—222no—
285C22×C4D4×D1112yes—
286C22×C4C23×D1111yescharacteristic
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—112no—
291C2×C8—221no—
292C2×C8—221no—
293C2×C8—228no—
294C2×C8—221no—
295C2×C8—221no—
296C2×C8—221no—
297C2×C8C2×C4×D1112yes—
298C2×C8#433912yes—
299C2×C8#433912yes—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—114no—
304C4⋊C4—222no—
305C4⋊C4—222no—
306C4⋊C4—222no—
307C4⋊C4—444no—
308C4⋊C4—444no—
309C4⋊C4C2×C4×D1114yes—
310C22⋊C4—228no—
311C22⋊C4—442no—
312C22⋊C4—882no—
313C42—21no—
314C42—21no—
315C42—82no—
316C42—228no—
317C42—221no—
318C42—221no—
319C42—882no—
320C11#2262011yescharacteristic, complemented, Sylow
321C23—112no—
322C23—221no—
323C23—222no—
324C23—222no—
325C23—221no—
326C23C2×D4×D1111yescharacteristic
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—24no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—112no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—222no—
340C2×C4—222no—
341C2×C4—222no—
342C2×C4—222no—
343C2×C4—222no—
344C2×C4—222no—
345C2×C4—224no—
346C2×C4—222no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4C22×C4×D1111yescharacteristic
353C2×C4C2×#433911yescharacteristic
354C2×C4C2×#433911yescharacteristic
355C2×C4#6704011yescharacteristic
356C2×C4#41×D1111yescharacteristic
357C2×C4#6704311yescharacteristic
358C8—41no—
359C8—222no—
360C8—441no—
361C8#6692514yes—
362C22—222no—
363C22—222no—
364C22—222no—
365C22—442no—
366C22—442no—
367C22#1062303811yescharacteristic
368C22C4×D4×D1111yescharacteristic
369C22#1062308211yescharacteristic
370C22#1062330612yes—
371C22#1062330812yes—
372C4—42no—
373C4—44no—
374C4—82no—
375C4—222no—
376C4—442no—
377C4—444no—
378C4—882no—
379C4C2×#6692511yescharacteristic
380C4#1062306011yescharacteristic
381C4#1062310311yescharacteristic
382C4#1062311211yescharacteristic
383C2—442no—
384C2#1307148111yescharacteristic
385C2#1307741511yescharacteristic
386C2#1307749811yescharacteristic
387C2#1308116212yes—
388C2#1308116612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1776C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1776D11
hypocenterC11#22620
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
3. #13069354C2semidirect
4. #13069352C2semidirect
5. #13069201C2semidirect
6. #13069199C2semidirect
9. #13068515C2semidirect
11. C11×#1776C2semidirect
30. #10622493C4semidirect
136. #1776D11semidirect
320. C11#22620semidirect

Maximal subgroups

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

subgroupindex
C2×#106224932
#130715052
#130693542
#130693522
#130692012
#130691992
#130687102
#130686382
#130685152
#130683932
C11×#17762
#2262011