Finite Group Databasebeta

← #14908435

Subgroups — #14908435

Order 2816.

534 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079128C211yesmaximal, characteristic
2C2×#10622486C211yesmaximal, characteristic
3#13070783C212yesmaximal, complemented
4#13070779C212yesmaximal, complemented
5#13070767C212yesmaximal, complemented
6#13070757C212yesmaximal, complemented
7#13070402C211yesmaximal, characteristic
8#13070371C211yesmaximal, characteristic
9#13070337C211yesmaximal, characteristic
10#13070335C211yesmaximal, characteristic
11C11×#2159C211yesmaximal, characteristic
12C22×Dic44C2211yescharacteristic
13#10623048—21no—
14C2×#66940—21no—
15C2×C11×M32C2211yescharacteristic
16C11×#427C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18#10622719C2211yescharacteristic
19C2×C8×Dic11C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622611—21no—
22C2×#66874—21no—
23#10622491C2211yescharacteristic
24#10622491C2211yescharacteristic
25#10622487C2211yescharacteristic
26#10622487C2211yescharacteristic
27#10622486—21no—
28#10622486—21no—
29#10622486C2212yes—
30#10622486C2212yes—
31#10622471—21no—
32#10622468—21no—
33C11×#367C2212yes—
34C11×#366C2212yes—
35#10622141C2212yes—
36#10622141C2212yes—
37Dic11⋊C16C2212yes—
38Dic11⋊C16C2212yes—
39#10622130C2212yes—
40#10622130C2212yes—
41#10622128C2212yes—
42#10622127C2212yes—
43C22×Dic22—21no—
44C22×C8×C11C2311yescharacteristic
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47#66979—21no—
48C2×Dic11⋊C4—41no—
49C2×C4×Dic11—41no—
50C2×C4×Dic11D411yescharacteristic
51C22×C11⋊C8D411yescharacteristic
52C2×Dic44—21no—
53C2×Dic44—22no—
54C2×Dic44Q814yescomplemented
55C2×Dic44C2312yes—
56#66943—21no—
57#66943—21no—
58#66941—21no—
59#66941—21no—
60#66940—22no—
61#66940—22no—
62#66940—41no—
63#66940—41no—
64#66931—41no—
65#66931—41no—
66C4×Dic22—41no—
67C4×Dic22—41no—
68C11×M32—22no—
69C2×C11×C16C2312yes—
70C11×#107—21no—
71C11×#107C2312yes—
72C11×#107C2311yescharacteristic
73C11×#107C2311yescharacteristic
74C11×#106—21no—
75#66882C2311yescharacteristic
76#66882C2311yescharacteristic
77#66881—21no—
78C8×Dic11D411yescharacteristic
79C8×Dic11D411yescharacteristic
80C8×Dic11C2311yescharacteristic
81C8×Dic11C2311yescharacteristic
82#66876—22no—
83C2×C11⋊C16C2312yes—
84#66874—22no—
85#66874—22no—
86#66872—21no—
87#66872—21no—
88#66871—21no—
89#66871—21no—
90#33628—111nomaximal, Sylow
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×Dic11—41no—
94C22×Dic11D811yescharacteristic
95C22×Dic11D811yescharacteristic
96C2×Dic22—24no—
97C2×Dic22—22no—
98C2×Dic22—41no—
99C2×Dic22—41no—
100C2×Dic22—41no—
101C2×Dic22—42no—
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×Q812yes—
104C2×C8×C11#4112yes—
105C2×C8×C11C2411yescharacteristic
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C22⋊Dic11—41no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—42no—
122Dic11⋊C4—42no—
123C4×Dic11—42no—
124C4×Dic11—42no—
125C4×Dic11—41no—
126C4×Dic11D811yescharacteristic
127C4×Dic11D811yescharacteristic
128C4×Dic11C2×D411yescharacteristic
129C4×Dic11C2×D411yescharacteristic
130C2×C11⋊C8—22no—
131C2×C11⋊C8C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133Dic44—24no—
134Dic44—22no—
135Dic44C2×Q814yes—
136C11×C16—22no—
137C11⋊C16—22no—
138#3160—111no—
139C2×C4×Q16—111no—
140#2229—112no—
141#2229—112no—
142#2227—112no—
143#2225—112no—
144#2159—111no—
145#2159D1111yescharacteristic
146#2150—111no—
147#2141—111no—
148#2141—111no—
149C23×C11C2×D811yescharacteristic
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—82no—
154C2×C4×C11C22⋊Q812yes—
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11#13712yes—
157C2×C4×C11C22×D411yescharacteristic
158C2×Dic11—22no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161C2×Dic11—44no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11C2×D811yescharacteristic
165C2×Dic11C2×D811yescharacteristic
166C2×Dic11C2×D811yescharacteristic
167C2×Dic11C2×D811yescharacteristic
168Dic22—24no—
169Dic22—42no—
170Dic22—44no—
171Dic22—82no—
172Dic22—82no—
173C8×C11C22⋊Q812yes—
174C8×C11C22×Q811yescharacteristic
175C8×C11C2×#4111yescharacteristic
176C11⋊C8—21no—
177C11⋊C8—21no—
178C22×Q16—111no—
179#533—221no—
180C2×C4×Q8—221no—
181C2×M32—111no—
182C2×M32C2×D1111yescharacteristic
183#500—111no—
184#500—111no—
185#499—111no—
186#499—111no—
187#499—221no—
188#498—221no—
189C4×Q16—112no—
190C4×Q16—112no—
191C4×Q16—221no—
192C4×Q16—221no—
193#427—111no—
194#427—221no—
195#427C2×D1111yescharacteristic
196C2×#107C2×D1111yescharacteristic
197C2×#103—221no—
198C2×C4×C8—111no—
199#367—112no—
200#367C2×D1112yes—
201#366—112no—
202#366C2×D1112yes—
203C4⋊C16—112no—
204C4⋊C16—112no—
205#358—112no—
206#358—112no—
207#358—112no—
208#358—112no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11#47412yes—
212C22×C11C22×D811yescharacteristic
213C4×C11—81no—
214C4×C11—82no—
215C4×C11—81no—
216C4×C11#47412yes—
217C4×C11C2×C22⋊Q811yescharacteristic
218C4×C11C2×#13711yescharacteristic
219Dic11—21no—
220Dic11—21no—
221Dic11—21no—
222Dic11—44no—
223Dic11—81no—
224Dic11—81no—
225Dic11#51012yes—
226C22×Q8—221no—
227C2×Q16—114no—
228C2×Q16—112no—
229C2×Q16—222no—
230C2×Q16—221no—
231C22×C8—111no—
232C22×C8C22×D1111yescharacteristic
233C4⋊Q8—221no—
234C4⋊Q8—221no—
235#125—221no—
236#125—221no—
237C22⋊Q8—441no—
238C22⋊Q8—441no—
239C4×Q8—222no—
240C4×Q8—222no—
241C4×Q8—441no—
242C4×Q8—441no—
243C4×Q8—441no—
244C4×Q8—441no—
245#117—21no—
246#117—221no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—441no—
249C2×C42—111no—
250C2×C42—441no—
251M32—22no—
252M32—222no—
253C2×C16—112no—
254C2×C16C22×D1112yes—
255#107—21no—
256#107—111no—
257#107—111no—
258#107—221no—
259#107—221no—
260#107C22×D1111yescharacteristic
261#107C22×D1111yescharacteristic
262#107C22×D1112yes—
263#106—21no—
264#106—221no—
265#106—221no—
266#106—221no—
267#103—222no—
268#103—222no—
269C4×C8—111no—
270C4×C8—111no—
271C4×C8—111no—
272C4×C8—111no—
273C2×C11—22no—
274C2×C11C2×#47411yescharacteristic
275C2×C11C2×#51011yescharacteristic
276C2×C11#341411yescharacteristic
277C2×Q8—224no—
278C2×Q8—222no—
279C2×Q8—441no—
280C2×Q8—441no—
281C2×Q8—441no—
282C2×Q8—442no—
283C22×C4—41no—
284C22×C4—111no—
285C22×C4—111no—
286C22×C4—441no—
287C22×C4D4×D1111yescharacteristic
288Q16—114no—
289Q16—224no—
290Q16—222no—
291C2×C8—111no—
292C2×C8—111no—
293C2×C8—222no—
294C2×C8#433912yes—
295C2×C8D4×D1111yescharacteristic
296C2×C8Q8×D1112yes—
297C2×C8C23×D1111yescharacteristic
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—442no—
305C4⋊C4—442no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C4⋊C4—441no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C22⋊C4—41no—
313C22⋊C4—441no—
314C42—41no—
315C42—111no—
316C42—111no—
317C42—111no—
318C42—111no—
319C42—442no—
320C42—442no—
321C42—441no—
322C16—22no—
323C16—222no—
324C11#3362811yescharacteristic, complemented, Sylow
325C23D8×D1111yescharacteristic
326Q8—224no—
327Q8—444no—
328Q8—442no—
329Q8—882no—
330Q8—882no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—111no—
336C2×C4—111no—
337C2×C4—111no—
338C2×C4—111no—
339C2×C4—222no—
340C2×C4—441no—
341C2×C4—444no—
342C2×C4—442no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4#6694912yes—
346C2×C4D8×D1111yescharacteristic
347C2×C4#6697112yes—
348C2×C4C2×D4×D1111yescharacteristic
349C8—221no—
350C8—221no—
351C8#6694912yes—
352C8C2×#433911yescharacteristic
353C8C2×Q8×D1111yescharacteristic
354C22—21no—
355C22—21no—
356C22#1062250312yes—
357C22C2×D8×D1111yescharacteristic
358C4—81no—
359C4—82no—
360C4—81no—
361C4—112no—
362C4—221no—
363C4—221no—
364C4—221no—
365C4—444no—
366C4—881no—
367C4—881no—
368C4#1062250312yes—
369C4C2×#6694911yescharacteristic
370C4C2×#6697111yescharacteristic
371C2—22no—
372C2C2×#1062250311yescharacteristic
373C2D11×#51011yescharacteristic
374C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radicalC23×C11C2×D8
hypercenter#2159D11
hypocenterC11#33628
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
3. #13070783C2semidirect
4. #13070779C2semidirect
5. #13070767C2semidirect
6. #13070757C2semidirect
54. C2×Dic44Q8semidirect
324. C11#33628semidirect

Maximal subgroups

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

subgroupindex
#130791282
C2×#106224862
#130707832
#130707792
#130707672
#130707572
#130704022
#130703712
#130703372
#130703352
C11×#21592
#3362811