Finite Group Databasebeta

← #14771464

Subgroups — #14771464

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622719C211yesmaximal, characteristic
2#13071511C211yesmaximal, characteristic
3#13071503C211yesmaximal, characteristic
4#13069357C212yesmaximal, complemented
5#13069207C212yesmaximal, complemented
6#13069186C212yesmaximal, complemented
7#13068708C211yesmaximal, characteristic
8#13068708C211yesmaximal, characteristic
9#13068515C212yesmaximal, complemented
10#13068392C211yesmaximal, characteristic
11C11×#1808C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×C11×#107C2212yes—
16C11×#380C2211yescharacteristic
17C11×#380C2211yescharacteristic
18C4×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20#10622719C418yescomplemented
21C2×#66882C2211yescharacteristic
22C2×#66882C2211yescharacteristic
23C2×#66881C2211yescharacteristic
24C2×#66881C2211yescharacteristic
25C2×#66879C2212yes—
26C4⋊C4×Dic11C2212yes—
27C4⋊C4×Dic11C2212yes—
28#10622586C2212yes—
29#10622586C2212yes—
30#10622558—22no—
31#10622557—22no—
32#10622264—21no—
33#10622263—21no—
34#10622262—21no—
35#10622261—21no—
36C11×#340C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11C2311yescharacteristic
43C22×C8×C11—24no—
44C22×C8×C11C2×C414yes—
45C22×C8×C11C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11D412yes—
54#66979—22no—
55#66979—22no—
56#66979C2×C414yes—
57#66979C2×C414yes—
58C2×C4⋊Dic11C2311yescharacteristic
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2311yescharacteristic
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11C2312yes—
69C22×C11⋊C8C2312yes—
70C11×#107—24no—
71C11×#95—21no—
72C11×#95—21no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77C11⋊#95D411yescharacteristic
78C11⋊#95D411yescharacteristic
79C22⋊(C11⋊C8)—22no—
80#66882C2×C414yes—
81#66882C2×C414yes—
82#66881C2×C414yes—
83#66881C2×C414yes—
84#66879—24no—
85#22616—111nomaximal, Sylow
86C24×C11C2×D411yescharacteristic
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11C22×C412yes—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4112yes—
94C22×C4×C11C2411yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11C2×D412yes—
100C22×Dic11C2×D412yes—
101C2×C8×C11—28no—
102C2×C8×C11—22no—
103C2×C8×C11C22×C412yes—
104C2×C8×C11C22×C412yes—
105C2×C8×C11#4114yes—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C22⋊C4—81no—
111C11×C22⋊C4—81no—
112C22⋊Dic11—24no—
113C22⋊Dic11—24no—
114C22⋊Dic11—42no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11C22×C412yes—
120C4⋊Dic11C22×C412yes—
121C4⋊Dic11C22×C412yes—
122C4⋊Dic11C22×C412yes—
123Dic11⋊C4—44no—
124Dic11⋊C4—82no—
125C4×Dic11—24no—
126C4×Dic11—24no—
127C4×Dic11—22no—
128C4×Dic11—22no—
129C4×Dic11—44no—
130C4×Dic11—82no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×#427—111no—
135#2347—111no—
136#2346—111no—
137#1944—112no—
138#1921—112no—
139#1918—112no—
140#1825—111no—
141#1825—111no—
142#1808D1111yescharacteristic
143#1776—112no—
144#1752—111no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11C4×D412yes—
150C23×C11C22×D411yescharacteristic
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11C4×D412yes—
162C2×C4×C11C23×C411yescharacteristic
163C2×C4×C11C2×#4112yes—
164C2×C4×C11C2×#4111yescharacteristic
165C2×C4×C112−1+412yes—
166C2×Dic11—22no—
167C2×Dic11—22no—
168C2×Dic11—22no—
169C2×Dic11—22no—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C8×C11—22no—
183C8×C11#11714yes—
184C11⋊C8—42no—
185C23×C8C2×D1111yescharacteristic
186C2×#117—111no—
187C2×#117—111no—
188#427—118no—
189C2×#107—111no—
190C2×#107—111no—
191C2×#107C2×D1112yes—
192C2×#106—111no—
193C2×#106—111no—
194C2×C22⋊C8—111no—
195C2×#97—112no—
196#389—112no—
197#389—112no—
198#388—222no—
199#388—222no—
200#383—221no—
201#382—221no—
202#380C2×D1111yescharacteristic
203#380C2×D1111yescharacteristic
204C4×C4⋊C4—112no—
205C4×C4⋊C4—112no—
206C4×C4⋊C4—221no—
207C4×C22⋊C4—111no—
208#376—221no—
209#340—112no—
210#340—112no—
211#340—112no—
212#340—112no—
213#340C2×D1112yes—
214#336—112no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11C2×C4×D411yescharacteristic
221C22×C11#54712yes—
222C22×C11#57512yes—
223C22×C11#57611yescharacteristic
224C22×C11#57811yescharacteristic
225C4×C11—22no—
226C4×C11—82no—
227C4×C11—82no—
228C4×C11C2×#11711yescharacteristic
229C4×C11#51911yescharacteristic
230C4×C11#55212yes—
231Dic11—42no—
232Dic11—42no—
233Dic11—42no—
234Dic11—42no—
235Dic11—42no—
236Dic11—42no—
237C23×C4C22×D1111yescharacteristic
238C22×C8—24no—
239C22×C8—112no—
240C22×C8C4×D1114yes—
241C22×C8C22×D1111yescharacteristic
242C22×C8C22×D1111yescharacteristic
243#117—114no—
244#117—114no—
245#117—222no—
246#117—222no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—111no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—222no—
252C2×C4⋊C4—222no—
253C2×C4⋊C4C22×D1112yes—
254C2×C4⋊C4C22×D1112yes—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—112no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C42—112no—
261C2×C42—221no—
262C2×C42—221no—
263C2×C42—222no—
264C2×C42—222no—
265#107—24no—
266#107—114no—
267#107—114no—
268#106—114no—
269#106—114no—
270C22⋊C8—222no—
271#97—224no—
272#95—21no—
273#95—21no—
274#95—111no—
275#95—111no—
276#95—222no—
277#95—222no—
278#95—222no—
279#95—222no—
280C2×C11—42no—
281C2×C11#234411yescharacteristic
282C2×C11#294311yescharacteristic
283C2×C11#295111yescharacteristic
284C2×C11#334712yes—
285C2×C11#334912yes—
286C24D4×D1111yescharacteristic
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—112no—
292C22×C4—112no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4C2×C4×D1112yes—
298C22×C4D4×D1111yescharacteristic
299C22×C4#434312yes—
300C22×C4C23×D1111yescharacteristic
301C2×C8—22no—
302C2×C8—28no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8—222no—
306C2×C8C2×C4×D1112yes—
307C2×C8C2×C4×D1112yes—
308C2×C8#434114yes—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—112no—
314C4⋊C4—112no—
315C4⋊C4—112no—
316C4⋊C4—112no—
317C4⋊C4—221no—
318C4⋊C4—221no—
319C4⋊C4—221no—
320C4⋊C4—221no—
321C4⋊C4—444no—
322C4⋊C4—882no—
323C22⋊C4—81no—
324C22⋊C4—81no—
325C22⋊C4—224no—
326C22⋊C4—224no—
327C22⋊C4—442no—
328C42—224no—
329C42—224no—
330C42—222no—
331C42—222no—
332C42—444no—
333C42—882no—
334C11#2261611yescharacteristic, complemented, Sylow
335C23—21no—
336C23—21no—
337C23—22no—
338C23—22no—
339C23#6694612yes—
340C23C2×D4×D1111yescharacteristic
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—222no—
352C2×C4—222no—
353C2×C4—222no—
354C2×C4—222no—
355C2×C4—222no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4#6694612yes—
368C2×C4C22×C4×D1111yescharacteristic
369C2×C4C2×#434112yes—
370C2×C4C2×#434311yescharacteristic
371C2×C4#6704312yes—
372C8—22no—
373C8—442no—
374C8#6693014yes—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—42no—
379C22—42no—
380C22C2×#6694611yescharacteristic
381C22#1062314212yes—
382C22#1062328811yescharacteristic
383C22#1062329711yescharacteristic
384C22#1062329912yes—
385C4—22no—
386C4—82no—
387C4—82no—
388C4—442no—
389C4—442no—
390C4—442no—
391C4—442no—
392C4—442no—
393C4—442no—
394C4C2×#6693011yescharacteristic
395C4#1062304711yescharacteristic
396C4#1062317312yes—
397C2—42no—
398C2#1307148711yescharacteristic
399C2#1307741611yescharacteristic
400C2#1307749011yescharacteristic
401C2#1308112212yes—
402C2#1308115212yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1808C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1808D11
hypocenterC11#22616
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
4. #13069357C2semidirect
5. #13069207C2semidirect
6. #13069186C2semidirect
9. #13068515C2semidirect
20. #10622719C4semidirect
334. C11#22616semidirect

Maximal subgroups

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

subgroupindex
C2×#106227192
#130715112
#130715032
#130693572
#130692072
#130691862
#130687082
#130685152
#130683922
C11×#18082
#2261611