Finite Group Databasebeta

← #14758360

Subgroups — #14758360

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×#10622320C211yesmaximal, characteristic
3D11×#382C211yesmaximal, characteristic
4#13069590C211yesmaximal, characteristic, complemented
5#13069589C211yesmaximal, characteristic, complemented
6#13069588C211yesmaximal, characteristic, complemented
7#13069579C214yesmaximal, complemented
8#13068334C214yesmaximal
9C11×#1993C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C2×Q8×Dic11—21no—
13C22×#4313C2212yes—
14#10623259—24no—
15#10623259C418yescomplemented
16C2×#66950—21no—
17C2×#66945C2212yes—
18C2×C4⋊C4×D11C2212yes—
19C2×#66943C2212yes—
20C2×#66940—21no—
21C2×C42×D11C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C11×#382C2211yescharacteristic
25C2×C8×Dic11C2212yes—
26#10622590C2212yes—
27#10622549C2211yescharacteristic
28C2×#66867C2211yescharacteristic
29#10622320—24no—
30D11×#95—21no—
31D11×#95—21no—
32#10622263—21no—
33#10622263—21no—
34C11×#340C2214yes—
35#10622189C2214yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C22×C4×D11—22no—
40C22×C4×D11D411yescharacteristic
41C22×C4×D11D411yescharacteristic
42C22×C4×D11C2311yescharacteristic
43C22×Dic22—21no—
44C22×C8×C11C2312yes—
45C11×C4⋊Q8—22no—
46C11×C4⋊Q8C2×C414yescomplemented
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11C2311yescharacteristic
51#66999—28no—
52Q8×Dic11—28no—
53C2×(C2×D11)⋊C4—22no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11C2312yes—
57C2×C4⋊Dic11C2312yes—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—22no—
60C2×C4×Dic11—22no—
61C2×C4×Dic11D411yescharacteristic
62C2×C4×Dic11D411yescharacteristic
63C2×C4×Dic11C2311yescharacteristic
64C22×C11⋊C8C2312yes—
65C2×#4313—24no—
66C2×#4313—24no—
67C2×#4313Q818yescomplemented
68#66950—28no—
69#66945—24no—
70#66945C2×C418yes—
71C4⋊C4×D11—28no—
72#66943—24no—
73#66943C2×C418yescomplemented
74#66940—28no—
75C42×D11C2×C414yes—
76C42×D11D414yes—
77#66922—22no—
78#66922C2×C414yescomplemented
79C11×#97—22no—
80C11×#95—21no—
81C11×#95—21no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C8×Dic11—24no—
87#66867—22no—
88#21323—111nomaximal, Sylow
89C23×D11C2×D411yescharacteristic
90C2×Q8×C11—24no—
91C2×Q8×C11—44no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—22no—
98C22×Dic11—22no—
99C22×Dic11C2×D411yescharacteristic
100C22×Dic11C2×D411yescharacteristic
101C22×Dic11C2×D411yescharacteristic
102C2×C4×D11—42no—
103C2×C4×D11—42no—
104C2×C4×D11—44no—
105C2×C4×D11—44no—
106C2×C4×D11—44no—
107C2×C4×D11C22⋊C414yes—
108C2×C4×D11C22⋊C414yes—
109C2×C4×D11C22×C412yes—
110C2×C4×D11C2×D412yes—
111C2×C4×D11C2×Q814yes—
112C2×C4×D11#4114yes—
113C2×Dic22—24no—
114C2×Dic22—44no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11C2×Q814yes—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4C22×C414yes—
122C42×C11C22×C412yes—
123C42×C11C2×D412yes—
124(C2×D11)⋊C4—28no—
125C4⋊Dic11—28no—
126C4⋊Dic11—24no—
127C4⋊Dic11—22no—
128C4⋊Dic11—24no—
129C4⋊Dic11C22×C414yes—
130Dic11⋊C4—28no—
131Dic11⋊C4—44no—
132C4×Dic11—28no—
133C4×Dic11C22⋊C414yes—
134C4×Dic11C22⋊C414yes—
135C4×Dic11C22×C412yes—
136C4×Dic11C2×D412yes—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8C2×Q814yes—
140#4313—216no—
141C2×#533—111no—
142C2×C4×M16—111no—
143C2×#382—111no—
144#1993—111no—
145#1993—111no—
146#1993—111no—
147#1993D1111yescharacteristic, complemented
148#1991—114no—
149#1736—114no—
150C23×C11C22×D411yescharacteristic
151C22×D11—22no—
152C22×D11—22no—
153C22×D11C2×C22⋊C412yes—
154C22×D11#12412yes—
155C22×D11C4⋊Q812yes—
156Q8×C11—48no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—44no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11C2×C22⋊C412yes—
165C2×C4×C11C2×C22⋊C412yes—
166C2×C4×C11C23×C411yescharacteristic
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C22×Q812yes—
169C2×C4×C11C2×#4112yes—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—24no—
173C2×Dic11—44no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11C2×C22⋊C412yes—
178C2×Dic11C2×C22⋊C412yes—
179C2×Dic11C2×C22⋊C412yes—
180C2×Dic11#12412yes—
181C2×Dic11C4⋊Q812yes—
182C4×D11—44no—
183C4×D11—44no—
184C4×D11—88no—
185C4×D11C4×Q818yes—
186C4×D11C22⋊Q818yes—
187Dic22—48no—
188C8×C11—24no—
189C11⋊C8—24no—
190C22×M16—112no—
191#533—118no—
192#533—224no—
193C2×C4⋊Q8—111no—
194C2×C4⋊Q8C2×D1111yescharacteristic
195C2×#125—112no—
196C2×C22⋊Q8—221no—
197C2×C22⋊Q8—221no—
198C2×C4×Q8—221no—
199C2×C4×Q8—221no—
200C2×#117—112no—
201C22×C4⋊C4—112no—
202C22×C42—111no—
203C4×M16—224no—
204C2×#97—111no—
205C2×#97C2×D1111yescharacteristic
206C2×C4×C8—112no—
207#382—112no—
208#382—111no—
209#382—221no—
210#382—221no—
211#382C2×D1111yescharacteristic
212C2×#95—221no—
213C2×#95—221no—
214#340—114no—
215#340—114no—
216#340—114no—
217#340C2×D1114yes—
218C22×C11C22×C22⋊C411yescharacteristic
219C22×C11C2×#12411yescharacteristic
220C22×C11C2×C4⋊Q811yescharacteristic
221C22×C11#57512yes—
222C22×C11#57512yes—
223C2×D11—24no—
224C2×D11—22no—
225C2×D11—22no—
226C2×D11—24no—
227C2×D11#39114yes—
228C4×C11—22no—
229C4×C11—22no—
230C4×C11—44no—
231C4×C11—82no—
232C4×C11C2×C4×Q812yes—
233C4×C11C2×C22⋊Q812yes—
234Dic11—22no—
235Dic11—22no—
236Dic11—44no—
237Dic11—82no—
238Dic11#39114yes—
239C22×Q8—21no—
240C22×Q8—221no—
241C23×C4—111no—
242C23×C4—111no—
243C23×C4—111no—
244C23×C4—222no—
245C2×M16—118no—
246C2×M16—224no—
247C2×M16—224no—
248C22×C8—112no—
249C22×C8C22×D1112yes—
250C4⋊Q8—22no—
251C4⋊Q8—114no—
252C4⋊Q8—222no—
253C4⋊Q8C4×D1114yescomplemented
254#125—118no—
255#125—224no—
256C22⋊Q8—228no—
257C22⋊Q8—228no—
258C4×Q8—228no—
259C4×Q8—228no—
260#117—118no—
261#117—224no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—112no—
265C2×C4⋊C4—228no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4—222no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4C22×D1112yes—
271C2×C4⋊C4C22×D1112yes—
272C2×C22⋊C4—222no—
273C2×C42—111no—
274C2×C42—111no—
275C2×C42—111no—
276C2×C42—114no—
277C2×C42—114no—
278C2×C42—222no—
279C2×C42C22×D1111yescharacteristic
280#97—22no—
281#97—222no—
282C4×C8—224no—
283#95—21no—
284#95—21no—
285#95—222no—
286#95—222no—
287#95—221no—
288#95—221no—
289C2×C11C2×#39111yescharacteristic
290C2×C11#289611yescharacteristic
291C2×C11#289611yescharacteristic
292C2×C11#314012yes—
293C2×C11#316612yes—
294D11—24no—
295C24—111no—
296C2×Q8—24no—
297C2×Q8—44no—
298C2×Q8—224no—
299C2×Q8—444no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—111no—
303C22×C4—112no—
304C22×C4—112no—
305C22×C4—114no—
306C22×C4—114no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—114no—
310C22×C4—114no—
311C22×C4—222no—
312C22×C4—222no—
313C22×C4—442no—
314C22×C4—442no—
315C22×C4—444no—
316C22×C4—444no—
317C22×C4—444no—
318C22×C4D4×D1111yescharacteristic
319C22×C4D4×D1111yescharacteristic
320C22×C4C23×D1111yescharacteristic
321M16—2216no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—114no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8Q8×D1114yes—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—24no—
331C4⋊C4—114no—
332C4⋊C4—228no—
333C4⋊C4—228no—
334C4⋊C4—224no—
335C4⋊C4—222no—
336C4⋊C4—224no—
337C4⋊C4—444no—
338C4⋊C4C2×C4×D1114yes—
339C22⋊C4—228no—
340C42—114no—
341C42—114no—
342C42—112no—
343C42—112no—
344C42—228no—
345C42C2×C4×D1112yes—
346C42D4×D1112yes—
347C11#2132311yescharacteristic, complemented, Sylow
348C23—112no—
349C23—112no—
350C23—112no—
351C23—222no—
352C23—222no—
353C23C2×D4×D1111yescharacteristic
354Q8—48no—
355Q8—448no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—44no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—112no—
364C2×C4—112no—
365C2×C4—112no—
366C2×C4—118no—
367C2×C4—118no—
368C2×C4—112no—
369C2×C4—112no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—224no—
373C2×C4—444no—
374C2×C4—444no—
375C2×C4—444no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—888no—
380C2×C4C22⋊C4×D1112yes—
381C2×C4C22⋊C4×D1112yes—
382C2×C4C22×C4×D1111yescharacteristic
383C2×C4C2×D4×D1111yescharacteristic
384C2×C4C2×Q8×D1112yes—
385C2×C4#41×D1112yes—
386C8—24no—
387C8—224no—
388C22—114no—
389C22—224no—
390C22—222no—
391C22—222no—
392C22—224no—
393C22C2×C22⋊C4×D1111yescharacteristic
394C22D11×#12411yescharacteristic
395C22D11×C4⋊Q811yescharacteristic
396C22#1062330412yes—
397C22#1062330812yes—
398C4—22no—
399C4—22no—
400C4—44no—
401C4—82no—
402C4—114no—
403C4—222no—
404C4—222no—
405C4—444no—
406C4—882no—
407C4C4×Q8×D1112yes—
408C4D11×C22⋊Q812yes—
409C2—224no—
410C2D11×#39111yescharacteristic
411C2#1307713011yescharacteristic
412C2#1307713411yescharacteristic
413C2#1307900112yes—
414C2#1307916712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1993C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1993D11
hypocenterC11#21323
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
4. #13069590C2semidirect
5. #13069589C2semidirect
6. #13069588C2semidirect
7. #13069579C2semidirect
9. C11×#1993C2semidirect
15. #10623259C4semidirect
46. C11×C4⋊Q8C2×C4semidirect
67. C2×#4313Q8semidirect
73. #66943C2×C4semidirect
78. #66922C2×C4semidirect
147. #1993D11semidirect
253. C4⋊Q8C4×D11semidirect
347. C11#21323semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106223202
D11×#3822
#130695902
#130695892
#130695882
#130695792
#130683342
C11×#19932
#2132311