Finite Group Databasebeta

← #14764071

Subgroups — #14764071

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622723C211yesmaximal, characteristic
2#13071205C212yesmaximal
3#13068818C212yesmaximal, complemented
4#13068814C212yesmaximal, complemented
5#13068807C212yesmaximal, complemented
6#13068805C212yesmaximal, complemented
7#13068647C212yesmaximal, complemented
8#13068645C211yesmaximal, characteristic, complemented
9C11×#1807C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×#4318C2211yescharacteristic
13C2×#66945C2212yes—
14C2×C4⋊C4×D11C2212yes—
15C2×C11×#106C2212yes—
16C11×#380C2212yes—
17#10622825C2212yes—
18#10622723C418yescomplemented
19C2×(C2×D11)⋊C8C2212yes—
20C2×(C2×D11)⋊C8C2212yes—
21C2×#66882C2212yes—
22#10622600C2212yes—
23#10622600C2212yes—
24C2×#66872C2212yes—
25C2×#66871C2212yes—
26#10622570—22no—
27#10622569—22no—
28#10622278—22no—
29#10622259—22no—
30C11×#340C2211yescharacteristic
31C11×#340C2211yescharacteristic
32#10622189C2211yescharacteristic
33#10622189C2211yescharacteristic
34#10622167C2212yes—
35#10622167C2212yes—
36C23×C4×C11C2311yescharacteristic
37C22×C22⋊D11D412yes—
38C2×#4339—42no—
39C2×#4339—42no—
40C2×#4339C2×C414yes—
41C2×#4339Q814yes—
42C22×D44D411yescharacteristic
43C22×C4×D11—22no—
44C22×C4×D11C2312yes—
45C22×Dic22D411yescharacteristic
46C22×C8×C11—42no—
47C22×C8×C11C2×C414yescomplemented
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C22⋊C4—22no—
53C2×C22⋊Dic11—22no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11C2312yes—
58C2×C4⋊Dic11C2312yes—
59C2×Dic11⋊C4—22no—
60C2×C4×Dic11—22no—
61C2×#4318—42no—
62C2×#4318C2×C414yescomplemented
63C22×C11⋊C8C2312yes—
64#66945—42no—
65#66945—42no—
66C4⋊C4×D11—42no—
67C4⋊C4×D11—42no—
68C11×#106—42no—
69C11×#95—22no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73(C2×D11)⋊C8C2×C418yescomplemented
74(C2×D11)⋊C8C2×C418yescomplemented
75#66882—42no—
76#66872—42no—
77#66871—42no—
78#21945—111nomaximal, Sylow
79C24×C11C2×D411yescharacteristic
80C23×D11C2×D412yes—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×Q812yes—
88C22×C4×C11C2411yescharacteristic
89C2×C22⋊D11—42no—
90C2×C22⋊D11—42no—
91C2×C22⋊D11C4⋊C418yes—
92C22×Dic11—22no—
93C22×Dic11—22no—
94C22×Dic11C2×D412yes—
95#4339—44no—
96#4339—44no—
97#4339—48no—
98C2×D44—42no—
99C2×D44C4⋊C414yes—
100C2×C4×D11—22no—
101C2×C4×D11—22no—
102C2×C4×D11—22no—
103C2×C4×D11—22no—
104C2×C4×D11—44no—
105C2×C4×D11—82no—
106C2×C4×D11—82no—
107C2×C4×D11C22×C414yes—
108C2×C4×D11C2×Q814yes—
109C2×Dic22—42no—
110C2×Dic22C4⋊C414yes—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—44no—
114C2×C8×C11C22×C412yes—
115C2×C8×C11C22×C412yes—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C22⋊C4—82no—
121C22⋊Dic11—82no—
122(C2×D11)⋊C4—44no—
123(C2×D11)⋊C4—82no—
124(C2×D11)⋊C4—82no—
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129Dic11⋊C4—44no—
130C4×Dic11—44no—
131#4318—44no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8C22×C414yes—
135C2×#408—111no—
136#2311—112no—
137#1854—112no—
138#1854—112no—
139#1853—112no—
140#1852—112no—
141#1809—112no—
142#1808—111no—
143#1807D1111yescharacteristic, complemented
144C23×C11—22no—
145C23×C11—21no—
146C23×C11—22no—
147C23×C11—21no—
148C23×C11C2×C4⋊C412yes—
149C23×C11C22×D411yescharacteristic
150C22×D11—22no—
151C22×D11—22no—
152C22×D11—22no—
153C22×D11—22no—
154C22×D11—22no—
155C22×D11—22no—
156C22×D11C2×C4⋊C414yes—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—24no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11C2×C4⋊C412yes—
168C2×C4×C11C23×C411yescharacteristic
169C2×C4×C11C22×Q811yescharacteristic
170C2×C4×C11H(5,𝔽2)12yes—
171C2×C4×C11H(5,𝔽2)12yes—
172C22⋊D11—48no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11C2×C4⋊C414yes—
182D44—44no—
183C4×D11—24no—
184C4×D11—24no—
185C4×D11—24no—
186C4×D11—24no—
187C4×D11—88no—
188Dic22—44no—
189C8×C11—22no—
190C8×C11—22no—
191C11⋊C8—24no—
192C22×#41—111no—
193C22×M16—111no—
194C23×C8C2×D1111yescharacteristic
195C2×#117—112no—
196C22×C4⋊C4—112no—
197C2×#107—112no—
198C2×#107—112no—
199C2×#106—112no—
200C2×#106C2×D1112yes—
201#408—118no—
202C2×C22⋊C8—112no—
203C2×C22⋊C8—112no—
204#391—222no—
205#390—222no—
206#386—222no—
207#386—222no—
208#380—112no—
209#380—112no—
210#380—112no—
211#380C2×D1112yes—
212#340—111no—
213#340—111no—
214#340—112no—
215#340—112no—
216#340C2×D1111yescharacteristic
217#340C2×D1111yescharacteristic
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—42no—
222C22×C11—42no—
223C22×C11C22×C4⋊C411yescharacteristic
224C22×C11#53412yes—
225C22×C11#57611yescharacteristic
226C22×C11#57712yes—
227C22×C11#57811yescharacteristic
228C2×D11—24no—
229C2×D11—24no—
230C2×D11—24no—
231C2×D11—42no—
232C2×D11—42no—
233C2×D11—42no—
234C2×D11—42no—
235C4×C11—22no—
236C4×C11—82no—
237C4×C11—82no—
238C4×C11#51811yescharacteristic
239C4×C11#51811yescharacteristic
240C4×C11#54312yes—
241Dic11—24no—
242Dic11—82no—
243Dic11—82no—
244C2×#41—114no—
245C2×#41—114no—
246C2×#41—442no—
247C2×#41—442no—
248C22×Q8—111no—
249C22×D4—112no—
250C22×D4—111no—
251C23×C4—112no—
252C23×C4—222no—
253C23×C4C22×D1111yescharacteristic
254C2×M16—114no—
255C2×M16—442no—
256C22×C8—42no—
257C22×C8—112no—
258C22×C8C4×D1114yescomplemented
259C22×C8C22×D1111yescharacteristic
260C22×C8C22×D1111yescharacteristic
261#117—442no—
262#117—442no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—112no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4—442no—
267C2×C4⋊C4—442no—
268C2×C4⋊C4C22×D1112yes—
269C2×C4⋊C4C22×D1112yes—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—222no—
272C2×C22⋊C4—222no—
273C2×C22⋊C4—222no—
274C2×C22⋊C4—222no—
275C2×C42—222no—
276#107—442no—
277#107—442no—
278#106—42no—
279#106—442no—
280C22⋊C8—118no—
281C22⋊C8—118no—
282#95—22no—
283#95—222no—
284#95—222no—
285#95—222no—
286C2×C11—42no—
287C2×C11#231511yescharacteristic
288C2×C11#291211yescharacteristic
289C2×C11#291311yescharacteristic
290C2×C11#319812yes—
291C2×C11#320112yes—
292D11—44no—
293C24—112no—
294C24D4×D1111yescharacteristic
295#41—444no—
296#41—444no—
297#41—448no—
298C2×Q8—114no—
299C2×Q8—442no—
300C2×D4—118no—
301C2×D4—114no—
302C2×D4—442no—
303C2×D4—442no—
304C2×D4—442no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—112no—
310C22×C4—114no—
311C22×C4—114no—
312C22×C4—222no—
313C22×C4—222no—
314C22×C4—222no—
315C22×C4—222no—
316C22×C4—222no—
317C22×C4—222no—
318C22×C4—444no—
319C22×C4—882no—
320C22×C4—882no—
321C22×C4C2×C4×D1112yes—
322C22×C4D4×D1111yescharacteristic
323C22×C4Q8×D1112yes—
324C22×C4C23×D1111yescharacteristic
325M16—444no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—44no—
329C2×C8—114no—
330C2×C8—222no—
331C2×C8—222no—
332C2×C8C2×C4×D1112yes—
333C2×C8C2×C4×D1112yes—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—222no—
339C4⋊C4—222no—
340C4⋊C4—222no—
341C4⋊C4—222no—
342C4⋊C4—444no—
343C22⋊C4—82no—
344C22⋊C4—444no—
345C22⋊C4—882no—
346C22⋊C4—882no—
347C22⋊C4—882no—
348C42—444no—
349C11#2194511yescharacteristic, complemented, Sylow
350C23—22no—
351C23—21no—
352C23—21no—
353C23—22no—
354C23—114no—
355C23—222no—
356C23—222no—
357C23—222no—
358C23—222no—
359C23—222no—
360C23—222no—
361C23C4⋊C4×D1112yes—
362C23C2×D4×D1111yescharacteristic
363Q8—444no—
364D4—444no—
365D4—448no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—114no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—224no—
380C2×C4—224no—
381C2×C4—224no—
382C2×C4—224no—
383C2×C4—442no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—888no—
390C2×C4C4⋊C4×D1112yes—
391C2×C4C22×C4×D1111yescharacteristic
392C2×C4#6703712yes—
393C2×C4C2×Q8×D1111yescharacteristic
394C2×C4#6704212yes—
395C8—22no—
396C8—22no—
397C8—224no—
398C22—22no—
399C22—22no—
400C22—22no—
401C22—42no—
402C22—42no—
403C22—224no—
404C22—224no—
405C22—224no—
406C22—442no—
407C22—442no—
408C22—442no—
409C22—442no—
410C22C2×C4⋊C4×D1111yescharacteristic
411C22#1062313612yes—
412C22#1062329312yes—
413C22#1062330011yescharacteristic
414C22#1062330211yescharacteristic
415C4—22no—
416C4—82no—
417C4—82no—
418C4—224no—
419C4—882no—
420C4—882no—
421C4#1062301711yescharacteristic
422C4#1062305211yescharacteristic
423C4#1062316512yes—
424C2—42no—
425C2—444no—
426C2#1307122911yescharacteristic
427C2#1307720711yescharacteristic
428C2#1307721311yescharacteristic
429C2#1307947112yes—
430C2#1307949112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1807C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1807D11
hypocenterC11#21945
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1807

Complements

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

NH ≅ G/Ntype
3. #13068818C2semidirect
4. #13068814C2semidirect
5. #13068807C2semidirect
6. #13068805C2semidirect
7. #13068647C2semidirect
8. #13068645C2semidirect
9. C11×#1807C2semidirect
18. #10622723C4semidirect
47. C22×C8×C11C2×C4semidirect
62. C2×#4318C2×C4semidirect
73. (C2×D11)⋊C8C2×C4semidirect
74. (C2×D11)⋊C8C2×C4semidirect
143. #1807D11semidirect
258. C22×C8C4×D11semidirect
349. C11#21945semidirect

Maximal subgroups

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

subgroupindex
C2×#106227232
#130712052
#130688182
#130688142
#130688072
#130688052
#130686472
#130686452
C11×#18072
#2194511