Finite Group Databasebeta

← #14724326

Subgroups — #14724326

Order 2816.

666 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079176C211yesmaximal, characteristic
2#13077551C211yesmaximal, characteristic, complemented
3#13077327C211yesmaximal, characteristic
4#13067521C214yesmaximal, complemented
5#13067431C214yesmaximal, complemented
6#13067374C211yesmaximal, characteristic, complemented
7#13067068C211yesmaximal, characteristic
8C2×#10622092C211yesmaximal, characteristic, complemented
9C11×#1493C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×#66960—21no—
12#10623008C2211yescharacteristic
13C11×#423C2211yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15#10622742—21no—
16#10622701C411yescharacteristic
17#10622698C411yescharacteristic
18#10622694C411yescharacteristic
19#10622692C411yescharacteristic
20#10622661C414yes—
21C4×#4325C2214yes—
22#10622637—21no—
23#10622637C2212yes—
24Q8×C11⋊C8—21no—
25Q8×C11⋊C8C2212yes—
26#10622612—21no—
27#10622610—21no—
28#10622537C2211yescharacteristic
29C2×C4×C11⋊C8C2211yescharacteristic
30C2×C4×C11⋊C8C2211yescharacteristic
31#10622451—21no—
32#10622451C2212yes—
33#10622447—21no—
34#10622447C2212yes—
35C11×Q8⋊C8C2214yes—
36#10622117C2214yes—
37#10622097C2214yes—
38#10622092C2212yes—
39#10622092C2212yes—
40C2×#4339—21no—
41C2×C11×M16—21no—
42C22×C8×C11—21no—
43C11×C4⋊Q8C2×C411yescharacteristic
44C11×C4⋊Q8C2×C411yescharacteristic
45C11×#125—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8C2×C412yes—
48C4×Q8×C11—21no—
49C4×Q8×C11C2312yes—
50C11×#117—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4325C2×C414yes—
53#66983—21no—
54#66983C2×C412yes—
55C2×#4318—21no—
56C22×C11⋊C8C2×C412yes—
57C22×C11⋊C8D411yescharacteristic
58C22×C11⋊C8D411yescharacteristic
59#66960—44no—
60C2×#4313—22no—
61C2×C8×D11—22no—
62#66928—21no—
63#66927C2×C411yescharacteristic
64C4×D44—21no—
65C4×D44C2312yes—
66#66922C2×C411yescharacteristic
67C11×C4⋊C8—21no—
68C11×C4⋊C8C2312yes—
69C4×C8×C11—21no—
70C4×C8×C11C2312yes—
71#66899C2×C414yes—
72(C2×D11)⋊C8—22no—
73(C2×D11)⋊C8—22no—
74#66873C2×C414yes—
75#66872C2×C414yes—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—22no—
78C4⋊(C11⋊C8)—22no—
79C4⋊(C11⋊C8)C2312yes—
80#66867—22no—
81C4×C11⋊C8—22no—
82C4×C11⋊C8C2×C411yescharacteristic
83C4×C11⋊C8C2×C411yescharacteristic
84C4×C11⋊C8D411yescharacteristic
85C4×C11⋊C8D411yescharacteristic
86C4×C11⋊C8C2312yes—
87C4×C11⋊C8C2311yescharacteristic
88C4×C11⋊C8C2311yescharacteristic
89#17960—111nomaximal, Sylow
90C2×Q8×C11—21no—
91C2×Q8×C11C22×C412yes—
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C2×C22⋊D11—22no—
96#4339—42no—
97#4339—42no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44C22×C412yes—
101C2×C4×D11—22no—
102C2×Dic22—21no—
103C11×M16—42no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—42no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4C22×C412yes—
113C11×C22⋊C4—22no—
114C42×C11—22no—
115C42×C11C22×C411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C42×C11C2411yescharacteristic
119#4325—28no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122C4⋊Dic11—21no—
123C4⋊Dic11C22×C412yes—
124#4318—42no—
125C2×C11⋊C8—24no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8C22×C412yes—
130C2×C11⋊C8C22×C412yes—
131C2×C11⋊C8C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133C2×C11⋊C8C2×D411yescharacteristic
134C2×C11⋊C8C2×D411yescharacteristic
135#4313—44no—
136C8×D11—44no—
137#3167—111no—
138#2960—111no—
139#2931—111no—
140#1592—114no—
141SD16⋊C8—114no—
142#1567—111no—
143#1493D1111yescharacteristic, complemented
144#1492—111no—
145C2×#322—111no—
146C23×C11C4×D411yescharacteristic
147C22×D11—22no—
148Q8×C11—24no—
149Q8×C11—42no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)12yes—
158C2×C4×C11#13712yes—
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C2×#4111yescharacteristic
162C22⋊D11—44no—
163C2×Dic11—22no—
164D44—24no—
165D44—42no—
166D44—42no—
167C4×D11—42no—
168C4×D11—42no—
169Dic22—42no—
170C8×C11—42no—
171C8×C11—42no—
172C11⋊C8—22no—
173C11⋊C8—21no—
174C11⋊C8—21no—
175C11⋊C8—21no—
176C11⋊C8—21no—
177C11⋊C8—42no—
178C11⋊C8#13114yescomplemented
179C2×#131—221no—
180#533C2×D1111yescharacteristic
181#532—111no—
182#498—111no—
183#492—111no—
184#487—111no—
185#486—111no—
186#465—114no—
187#446—112no—
188#446—221no—
189C8×Q8—112no—
190C8×Q8—221no—
191C4×SD16—114no—
192#436—112no—
193#436—221no—
194C8×D4—112no—
195C8×D4—221no—
196#424—221no—
197#423—111no—
198#423C2×D1111yescharacteristic
199#408—221no—
200#405—221no—
201C2×C4×C8—111no—
202C2×C4×C8—111no—
203C2×C4×C8C2×D1111yescharacteristic
204#335—114no—
205Q8⋊C8C2×D1114yes—
206D4⋊C8—114no—
207#322—112no—
208#322—112no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11#44012yes—
212C22×C11C2×C4×D411yescharacteristic
213C2×D11—42no—
214C2×D11—42no—
215C2×D11—42no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—42no—
219C4×C11—42no—
220C4×C11#44012yes—
221C4×C11#44412yes—
222C4×C11C2×#13112yes—
223C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
224C4×C11C2×#13711yescharacteristic
225Dic11—42no—
226C2×#41—221no—
227C2×SD16—114no—
228#131—444no—
229C2×M16—21no—
230C2×M16—222no—
231C2×M16—221no—
232C22×C8—21no—
233C22×C8—112no—
234C22×C8—111no—
235C22×C8—111no—
236C22×C8—222no—
237C4⋊Q8—111no—
238C4⋊Q8C4×D1111yescharacteristic
239C4⋊Q8C4×D1111yescharacteristic
240#127—111no—
241#125—21no—
242#124—221no—
243C22⋊Q8—21no—
244C22⋊Q8C4×D1112yes—
245#121—112no—
246#121—221no—
247C4×Q8—21no—
248C4×Q8C22×D1112yes—
249C4×D4—112no—
250C4×D4—221no—
251#117—21no—
252C2×C42C22×D1111yescharacteristic
253#106—114no—
254C4⋊C8—21no—
255C4⋊C8—112no—
256C4⋊C8—222no—
257C4⋊C8—222no—
258C4⋊C8—221no—
259C4⋊C8C22×D1112yes—
260#103—114no—
261#102—114no—
262C22⋊C8—222no—
263C22⋊C8—222no—
264#97—222no—
265C4×C8—21no—
266C4×C8—111no—
267C4×C8—111no—
268C4×C8—111no—
269C4×C8—111no—
270C4×C8—112no—
271C4×C8—111no—
272C4×C8—111no—
273C4×C8—222no—
274C4×C8C22×D1112yes—
275C2×C11—22no—
276C2×C11#293111yescharacteristic
277C2×C11C2×#44011yescharacteristic
278C2×C11C2×#44411yescharacteristic
279D11—82no—
280#41—442no—
281#41—442no—
282C2×Q8—21no—
283C2×Q8—221no—
284C2×Q8C2×C4×D1112yes—
285C2×D4—112no—
286C2×D4—222no—
287C2×D4—221no—
288C2×D4—221no—
289C22×C4—222no—
290C22×C4C2×C4×D1111yescharacteristic
291C22×C4D4×D1111yescharacteristic
292C22×C4#434111yescharacteristic
293SD16—228no—
294M16—42no—
295M16—444no—
296M16—442no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—42no—
300C2×C8—112no—
301C2×C8—112no—
302C2×C8—111no—
303C2×C8—111no—
304C2×C8—111no—
305C2×C8—111no—
306C2×C8—224no—
307C2×C8—222no—
308C2×C8—222no—
309C2×C8—222no—
310C2×C8—444no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—112no—
317C4⋊C4—221no—
318C4⋊C4C2×C4×D1112yes—
319C22⋊C4—22no—
320C22⋊C4—222no—
321C22⋊C4—222no—
322C42—22no—
323C42C2×C4×D1111yescharacteristic
324C42D4×D1111yescharacteristic
325C42#434111yescharacteristic
326C42C23×D1111yescharacteristic
327C11#1796011yescharacteristic, complemented, Sylow
328C23—222no—
329C23(C22⋊D11)⋊C411yescharacteristic
330Q8—24no—
331Q8—42no—
332Q8—442no—
333D4—224no—
334D4—444no—
335D4—442no—
336D4—442no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—222no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4(C22⋊D11)⋊C411yescharacteristic
345C2×C4(C22⋊D11)⋊C411yescharacteristic
346C2×C4(C22⋊D11)⋊C411yescharacteristic
347C2×C4#6696712yes—
348C2×C4#6697112yes—
349C2×C4C22×C4×D1111yescharacteristic
350C2×C4C2×D4×D1111yescharacteristic
351C2×C4C2×#434111yescharacteristic
352C8—42no—
353C8—42no—
354C8—114no—
355C8—222no—
356C8—221no—
357C8—221no—
358C8—221no—
359C8—221no—
360C8—442no—
361C22—21no—
362C22—21no—
363C22—442no—
364C22—442no—
365C22—442no—
366C22#1062243012yes—
367C22C2×(C22⋊D11)⋊C411yescharacteristic
368C4—21no—
369C4—21no—
370C4—42no—
371C4—42no—
372C4—442no—
373C4#1062243012yes—
374C4#1062243612yes—
375C4D11×#13112yes—
376C4C2×#6696711yescharacteristic
377C4C2×#6697111yescharacteristic
378C2—22no—
379C2—882no—
380C2#1307732411yescharacteristic
381C2C2×#1062243011yescharacteristic
382C2C2×#1062243611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1493C2
socleC22×C11C2×C4×D4
prime radical#10623008C22
cosocleC42×C11C24
hypercenter#1493D11
hypocenterC11#17960
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
2. #13077551C2semidirect
4. #13067521C2semidirect
5. #13067431C2semidirect
6. #13067374C2semidirect
8. C2×#10622092C2semidirect
9. C11×#1493C2semidirect
143. #1493D11semidirect
178. C11⋊C8#131semidirect
327. C11#17960semidirect

Maximal subgroups

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

subgroupindex
#130791762
#130775512
#130773272
#130675212
#130674312
#130673742
#130670682
C2×#106220922
C11×#14932
#1796011