Finite Group Databasebeta

← #14753991

Subgroups — #14753991

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×Dic11C211yesmaximal, characteristic
2#13071019C211yesmaximal, characteristic
3C2×#10622590C211yesmaximal, characteristic
4#13068748C214yesmaximal, complemented
5#13068745C214yesmaximal, complemented
6#13068337C211yesmaximal, characteristic
7#13068336C211yesmaximal, characteristic
8#13068335C211yesmaximal, characteristic
9C11×#1736C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4×Dic11C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C2×C11⋊#95—22no—
18M16×Dic11C418yescomplemented
19C2×#66879C2212yes—
20C2×C8×Dic11C2212yes—
21#10622590—22no—
22#10622590C2212yes—
23#10622590C2212yes—
24#10622590C2212yes—
25#10622589C2212yes—
26#10622555—22no—
27C4×Dic11⋊C4—22no—
28C11×#340C2214yes—
29#10622189C2214yes—
30#10622167C2214yes—
31#10622167C2214yes—
32C23×C4×C11—21no—
33C23×C4×C11C2311yescharacteristic
34C23×Dic11—21no—
35C23×Dic11D412yes—
36C2×C11×M16—22no—
37C2×C11×M16—22no—
38C2×C11×M16C2×C414yes—
39C22×C8×C11C2312yes—
40C11×#117—22no—
41C11×#117—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4C2312yes—
46C2×C11×C4⋊C4C2312yes—
47C2×C11×C22⋊C4—21no—
48C2×C42×C11—21no—
49C2×C22⋊Dic11—21no—
50#66979—22no—
51#66979—22no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11C2312yes—
56C2×C4⋊Dic11C2312yes—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—22no—
59C2×C4×Dic11—21no—
60C2×C4×Dic11C2×C414yes—
61C2×C4×Dic11D412yes—
62C2×C4×Dic11Q814yes—
63C2×C4×Dic11C2311yescharacteristic
64C2×C4×Dic11C2311yescharacteristic
65C2×#4318—22no—
66C2×#4318—22no—
67C2×#4318C2×C414yes—
68C22×C11⋊C8C2312yes—
69C11⋊#95—24no—
70C11⋊#95—24no—
71C11⋊#95—24no—
72#66879C2×C418yescomplemented
73C8×Dic11C2×C418yescomplemented
74#20765—111nomaximal, Sylow
75C24×C11C2×D411yescharacteristic
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—44no—
79C22×C4×C11—42no—
80C22×C4×C11C22×C412yes—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×Q812yes—
83C22×C4×C11#4112yes—
84C22×C4×C11#4112yes—
85C22×C4×C11#4112yes—
86C22×C4×C11#4112yes—
87C22×C4×C11C2411yescharacteristic
88C22×Dic11—22no—
89C22×Dic11—22no—
90C22×Dic11—42no—
91C22×Dic11—42no—
92C22×Dic11—44no—
93C22×Dic11—42no—
94C22×Dic11C4⋊C418yes—
95C22×Dic11C2×D412yes—
96C22×Dic11C2×D412yes—
97C11×M16—28no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11C22×C414yes—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—42no—
106C11×C22⋊C4—42no—
107C42×C11—42no—
108C22⋊Dic11—42no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11—42no—
114Dic11⋊C4—44no—
115Dic11⋊C4—44no—
116C4×Dic11—42no—
117C4×Dic11C4⋊C418yes—
118C4×Dic11C22×C412yes—
119C4×Dic11C22×C412yes—
120C4×Dic11C2×Q812yes—
121C4×Dic11C2×Q812yes—
122#4318—28no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8C22×C414yes—
126C2×C4×M16—111no—
127#2285—111no—
128C2×#382—111no—
129#1836—114no—
130#1835—114no—
131#1736—111no—
132#1736—111no—
133#1736—111no—
134#1736D1111yescharacteristic
135C23×C11—22no—
136C23×C11—22no—
137C23×C11C2×C4⋊C412yes—
138C23×C11#12412yes—
139C23×C11#12412yes—
140C23×C11C22×D411yescharacteristic
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—44no—
146C2×C4×C11—84no—
147C2×C4×C11C2×C4⋊C412yes—
148C2×C4×C11#11714yes—
149C2×C4×C11#11714yes—
150C2×C4×C11#12412yes—
151C2×C4×C11#12412yes—
152C2×C4×C11#12514yes—
153C2×C4×C11#12514yes—
154C2×C4×C11C23×C411yescharacteristic
155C2×C4×C11C22×Q811yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C2×C4×C11C2×#4111yescharacteristic
159C2×C4×C11C2×#4111yescharacteristic
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—48no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—44no—
170C2×Dic11—84no—
171C2×Dic11C2×C4⋊C414yes—
172C2×Dic11C2×C4⋊C414yes—
173C8×C11—24no—
174C11⋊C8—24no—
175C22×M16—111no—
176C22×M16C2×D1111yescharacteristic
177C2×#117—111no—
178C2×#117C2×D1111yescharacteristic
179C22×C4⋊C4—111no—
180C22×C4⋊C4C2×D1111yescharacteristic
181C22×C42—111no—
182C4×M16—118no—
183C2×#97—112no—
184C2×C4×C8—112no—
185#384—112no—
186#382—112no—
187#382—112no—
188#382—112no—
189#382—222no—
190#380—222no—
191C4×C4⋊C4—222no—
192C2×#95—222no—
193#340—114no—
194#340—114no—
195#340—114no—
196#340C2×D1114yes—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—24no—
200C22×C11—24no—
201C22×C11#38214yes—
202C22×C11C22×C4⋊C411yescharacteristic
203C22×C11C2×#12411yescharacteristic
204C22×C11C2×#12411yescharacteristic
205C22×C11#57512yes—
206C22×C11#57512yes—
207C4×C11—82no—
208C4×C11—82no—
209C4×C11#38214yes—
210C4×C11C2×#11711yescharacteristic
211C4×C11C2×#11711yescharacteristic
212C4×C11C2×#12511yescharacteristic
213C4×C11C2×#12511yescharacteristic
214Dic11—24no—
215Dic11—24no—
216Dic11—82no—
217Dic11—82no—
218C23×C4—21no—
219C23×C4—112no—
220C23×C4—221no—
221C23×C4C22×D1111yescharacteristic
222C2×M16—22no—
223C2×M16—22no—
224C2×M16—114no—
225C2×M16—222no—
226C2×M16—222no—
227C2×M16C4×D1114yes—
228C22×C8—112no—
229C22×C8C22×D1112yes—
230#117—22no—
231#117—22no—
232#117—222no—
233#117—222no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—112no—
238C2×C4⋊C4—112no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4—222no—
241C2×C4⋊C4—222no—
242C2×C4⋊C4—222no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4C22×D1112yes—
245C2×C4⋊C4C22×D1112yes—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—221no—
248C2×C42—21no—
249C2×C42—114no—
250C2×C42—112no—
251C2×C42—114no—
252C2×C42—111no—
253C2×C42—111no—
254C2×C42—221no—
255#97—118no—
256C4×C8—118no—
257#95—224no—
258#95—224no—
259#95—224no—
260C2×C11—24no—
261C2×C11C2×#38211yescharacteristic
262C2×C11#291112yes—
263C2×C11#314011yescharacteristic
264C2×C11#314011yescharacteristic
265C2×C11#314212yes—
266C24D4×D1111yescharacteristic
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—44no—
270C22×C4—42no—
271C22×C4—112no—
272C22×C4—112no—
273C22×C4—118no—
274C22×C4—222no—
275C22×C4—222no—
276C22×C4—442no—
277C22×C4—442no—
278C22×C4—444no—
279C22×C4—442no—
280C22×C4C2×C4×D1112yes—
281C22×C4#433912yes—
282C22×C4#433912yes—
283C22×C4D4×D1111yescharacteristic
284C22×C4#434112yes—
285C22×C4#434112yes—
286C22×C4Q8×D1112yes—
287C22×C4C23×D1111yescharacteristic
288M16—28no—
289M16—228no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—114no—
293C2×C8—222no—
294C2×C8—222no—
295C2×C8C2×C4×D1114yes—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—42no—
301C4⋊C4—222no—
302C4⋊C4—222no—
303C4⋊C4—222no—
304C4⋊C4—222no—
305C4⋊C4—444no—
306C4⋊C4—444no—
307C4⋊C4—442no—
308C22⋊C4—42no—
309C22⋊C4—442no—
310C42—42no—
311C42—118no—
312C42—112no—
313C42—112no—
314C42—112no—
315C42—112no—
316C42—442no—
317C11#2076511yescharacteristic, complemented, Sylow
318C23—22no—
319C23—22no—
320C23#6693812yes—
321C23#6693812yes—
322C23C4⋊C4×D1112yes—
323C23C2×D4×D1111yescharacteristic
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—44no—
328C2×C4—42no—
329C2×C4—84no—
330C2×C4—114no—
331C2×C4—114no—
332C2×C4—222no—
333C2×C4—222no—
334C2×C4—222no—
335C2×C4—222no—
336C2×C4—448no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—444no—
342C2×C4—884no—
343C2×C4#6692514yes—
344C2×C4#6693014yes—
345C2×C4#6693812yes—
346C2×C4#6693812yes—
347C2×C4#6694214yes—
348C2×C4#6694214yes—
349C2×C4C4⋊C4×D1112yes—
350C2×C4C22×C4×D1111yescharacteristic
351C2×C4C2×#433911yescharacteristic
352C2×C4C2×#433911yescharacteristic
353C2×C4C2×#434111yescharacteristic
354C2×C4C2×#434111yescharacteristic
355C2×C4C2×Q8×D1111yescharacteristic
356C8—24no—
357C8—224no—
358C22—24no—
359C22—22no—
360C22—22no—
361C22—24no—
362C22#1062226314yes—
363C22C2×#6693811yescharacteristic
364C22C2×#6693811yescharacteristic
365C22C2×C4⋊C4×D1111yescharacteristic
366C22#1062330412yes—
367C22#1062330812yes—
368C4—82no—
369C4—82no—
370C4—224no—
371C4—224no—
372C4—882no—
373C4—882no—
374C4#1062226314yes—
375C4C2×#6692511yescharacteristic
376C4C2×#6693011yescharacteristic
377C4C2×#6694211yescharacteristic
378C4C2×#6694211yescharacteristic
379C2—24no—
380C2C2×#1062226311yescharacteristic
381C2#1307720312yes—
382C2#1307900011yescharacteristic
383C2#1307900411yescharacteristic
384C2#1307901412yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#20765
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #13068748C2semidirect
5. #13068745C2semidirect
18. M16×Dic11C4semidirect
72. #66879C2×C4semidirect
73. C8×Dic11C2×C4semidirect
317. C11#20765semidirect

Maximal subgroups

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

subgroupindex
C2×M16×Dic112
#130710192
C2×#106225902
#130687482
#130687452
#130683372
#130683362
#130683352
C11×#17362
#2076511