Finite Group Databasebeta

← #14771451

Subgroups — #14771451

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071493C211yesmaximal, characteristic
2#13071485C211yesmaximal, characteristic
3#13069360C212yesmaximal, complemented
4#13069203C212yesmaximal, complemented
5#13069196C212yesmaximal, complemented
6#13068706C211yesmaximal, characteristic
7#13068702C211yesmaximal, characteristic
8#13068645C211yesmaximal, characteristic
9#13068516C212yesmaximal, complemented
10#13068392C211yesmaximal, characteristic
11C22×C11×#106C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979—21no—
16C2×C11×#106C418yescomplemented
17C2×C11×#106C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21#10622825—21no—
22#10622825C2211yescharacteristic
23#10622825C2211yescharacteristic
24#10622824—21no—
25C4×C22⋊Dic11—21no—
26C4×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×#66882C2212yes—
29C2×#66879C2212yes—
30#10622598C2212yes—
31#10622598C2212yes—
32#10622594—22no—
33#10622594—22no—
34C4⋊C4×Dic11C2212yes—
35C4⋊C4×Dic11C2212yes—
36#10622189C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11—21no—
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C22×C8×C11—24no—
46C22×C8×C11C2×C414yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C11×C4⋊C4C2×C414yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11D411yescharacteristic
62C2×C22⋊Dic11D411yescharacteristic
63#66979—44no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2312yes—
68C2×C4×Dic11—22no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11C2312yes—
71C22×C11⋊C8C2312yes—
72C11×#106C2×C414yes—
73C11×#106C2×C414yes—
74C11×#106C2×C414yes—
75C11×#106C2×C414yes—
76C11⋊#95—21no—
77C11⋊#95—21no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95D412yes—
83C22⋊(C11⋊C8)—22no—
84#66882—24no—
85#66879—24no—
86#22615—111nomaximal, Sylow
87C24×C11C2×D411yescharacteristic
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—24no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—24no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—82no—
99C22×C4×C11C22×C412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4112yes—
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11C2×D412yes—
106C22×Dic11C2×D412yes—
107C2×C8×C11—28no—
108C2×C8×C11—22no—
109C2×C8×C11C22×C412yes—
110C2×C8×C11C22×C412yes—
111C2×C8×C11#4114yes—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4C22×C412yes—
119C11×C4⋊C4C22×C412yes—
120C11×C4⋊C4C22×C412yes—
121C11×C4⋊C4C22×C412yes—
122C22⋊Dic11—22no—
123C22⋊Dic11—22no—
124C22⋊Dic11—42no—
125C22⋊Dic11—42no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—44no—
131C4⋊Dic11—82no—
132C4×Dic11—22no—
133C4×Dic11—22no—
134C4×Dic11—44no—
135C4×Dic11—82no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C22×#106D1111yescharacteristic
140#2345—111no—
141#2344—111no—
142#1944—112no—
143#1920—112no—
144#1919—112no—
145#1824—111no—
146#1823—111no—
147#1808—111no—
148#1776—112no—
149#1752—111no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11C4×D412yes—
153C23×C11AGL(1,ℤ/8)12yes—
154C23×C11#13712yes—
155C23×C11C22×D411yescharacteristic
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—48no—
171C2×C4×C11—84no—
172C2×C4×C11C4×D412yes—
173C2×C4×C11C23×C411yescharacteristic
174C2×C4×C11C2×#4112yes—
175C2×C4×C11C2×#4111yescharacteristic
176C2×C4×C112−1+412yes—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C8×C11—22no—
190C8×C11#11714yescomplemented
191C11⋊C8—42no—
192C23×C8C2×D1111yescharacteristic
193C2×#117—221no—
194C22×C4⋊C4C2×D1111yescharacteristic
195C22×C4⋊C4C2×D1111yescharacteristic
196C2×#107—112no—
197C2×#106Dic1118yescomplemented
198C2×#106C2×D1111yescharacteristic
199C2×#106C2×D1111yescharacteristic
200C2×#106C2×D1111yescharacteristic
201C2×#106C2×D1111yescharacteristic
202C2×C22⋊C8—111no—
203C2×#97—112no—
204#389—112no—
205#389—112no—
206#387—222no—
207#387—222no—
208#381—221no—
209#380—111no—
210#380—111no—
211#380—221no—
212C4×C4⋊C4—112no—
213C4×C4⋊C4—112no—
214C4×C22⋊C4—111no—
215C4×C22⋊C4—221no—
216#340—112no—
217#340—112no—
218#340—112no—
219#340—112no—
220#340—112no—
221#336—112no—
222C22×C11—24no—
223C22×C11—24no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11#44014yes—
227C22×C11C2×C4×D411yescharacteristic
228C22×C11#54712yes—
229C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
230C22×C11C2×#13711yescharacteristic
231C22×C11#57712yes—
232C4×C11—22no—
233C4×C11—42no—
234C4×C11—42no—
235C4×C11—42no—
236C4×C11—42no—
237C4×C11C2×#11711yescharacteristic
238C4×C11#51911yescharacteristic
239C4×C11#55212yes—
240Dic11—42no—
241Dic11—42no—
242Dic11—82no—
243Dic11—82no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4C22×D1111yescharacteristic
247C22×C8—24no—
248C22×C8—112no—
249C22×C8C2×Dic1114yes—
250C22×C8C22×D1111yescharacteristic
251C22×C8C22×D1111yescharacteristic
252#117—444no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—112no—
258C2×C4⋊C4—112no—
259C2×C4⋊C4—222no—
260C2×C4⋊C4—222no—
261C2×C4⋊C4C2×Dic1114yes—
262C2×C4⋊C4C2×Dic1114yes—
263C2×C4⋊C4C22×D1111yescharacteristic
264C2×C4⋊C4C22×D1111yescharacteristic
265C2×C4⋊C4C22×D1111yescharacteristic
266C2×C4⋊C4C22×D1111yescharacteristic
267C2×C22⋊C4—111no—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—221no—
271C2×C42—112no—
272C2×C42—222no—
273C2×C42—222no—
274#107—224no—
275#106C2×Dic1114yes—
276#106C2×Dic1114yes—
277#106C2×Dic1114yes—
278#106C2×Dic1114yes—
279C22⋊C8—222no—
280#97—224no—
281#95—112no—
282#95—222no—
283#95—222no—
284#95—222no—
285#95—222no—
286#95—221no—
287#95—221no—
288C2×C11—24no—
289C2×C11#234411yescharacteristic
290C2×C11C2×#44011yescharacteristic
291C2×C11#294911yescharacteristic
292C2×C11#334412yes—
293C2×C11#334512yes—
294C24D4×D1111yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—24no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—24no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—82no—
306C22×C4—112no—
307C22×C4—112no—
308C22×C4—222no—
309C22×C4—222no—
310C22×C4D4×D1111yescharacteristic
311C22×C4#434112yes—
312C22×C4C22×Dic1112yes—
313C22×C4C23×D1111yescharacteristic
314C2×C8—22no—
315C2×C8—28no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—222no—
319C2×C8#433914yes—
320C2×C8C22×Dic1112yes—
321C2×C8C22×Dic1112yes—
322C4⋊C4—24no—
323C4⋊C4—24no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—222no—
329C4⋊C4—222no—
330C4⋊C4—222no—
331C4⋊C4—222no—
332C4⋊C4—444no—
333C4⋊C4—882no—
334C4⋊C4C22×Dic1112yes—
335C4⋊C4C22×Dic1112yes—
336C4⋊C4C22×Dic1112yes—
337C4⋊C4C22×Dic1112yes—
338C22⋊C4—222no—
339C22⋊C4—222no—
340C22⋊C4—442no—
341C22⋊C4—442no—
342C42—222no—
343C42—222no—
344C42—444no—
345C42—882no—
346C11#2261511yescharacteristic, complemented, Sylow
347C23—22no—
348C23—22no—
349C23#6696712yes—
350C23#6696812yes—
351C23D4×Dic1112yes—
352C23C2×D4×D1111yescharacteristic
353C2×C4—22no—
354C2×C4—24no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—48no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—84no—
369C2×C4—222no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4D4×Dic1112yes—
382C2×C4C2×#433912yes—
383C2×C4C2×#434111yescharacteristic
384C2×C4#6704012yes—
385C2×C4C23×Dic1111yescharacteristic
386C8—22no—
387C8—442no—
388C8#6697914yescomplemented
389C22—22no—
390C22—22no—
391C22—24no—
392C22—24no—
393C22#1062277714yes—
394C22#1062303812yes—
395C22C2×#6696711yescharacteristic
396C22C2×#6696811yescharacteristic
397C22#1062329312yes—
398C22C2×D4×Dic1111yescharacteristic
399C4—22no—
400C4—42no—
401C4—42no—
402C4—42no—
403C4—42no—
404C4—442no—
405C4—442no—
406C4—882no—
407C4—882no—
408C4#1062304412yes—
409C4C2×#6697911yescharacteristic
410C4#1062334311yescharacteristic
411C2—24no—
412C2#1307148511yescharacteristic
413C2C2×#1062277711yescharacteristic
414C2#1307747611yescharacteristic
415C2#1308106712yes—
416C2#1308108212yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#106C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC22×#106D11
hypocenterC11#22615
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
3. #13069360C2semidirect
4. #13069203C2semidirect
5. #13069196C2semidirect
9. #13068516C2semidirect
16. C2×C11×#106C4semidirect
190. C8×C11#117semidirect
197. C2×#106Dic11semidirect
346. C11#22615semidirect
388. C8#66979semidirect

Maximal subgroups

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

subgroupindex
#130714932
#130714852
#130693602
#130692032
#130691962
#130687062
#130687022
#130686452
#130685162
#130683922
C22×C11×#1062
#2261511