Finite Group Databasebeta

← #14908700

Subgroups — #14908700

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079197C211yesmaximal, characteristic, complemented
2C2×D8×Dic11C211yesmaximal, characteristic
3#13070814C211yesmaximal, characteristic, complemented
4#13070811C211yesmaximal, characteristic, complemented
5#13070761C212yesmaximal, complemented
6#13070659C212yesmaximal, complemented
7#13070545C211yesmaximal, characteristic
8#13070471C212yesmaximal, complemented
9SD32×Dic11C212yesmaximal, complemented
10#13070412C211yesmaximal, characteristic, complemented
11C11×#2187C211yesmaximal, characteristic
12C22×C11×D8C2211yescharacteristic
13C2×D4×Dic11—21no—
14#10623153—21no—
15C2×C11×SD32C2212yes—
16C11×#467C2211yescharacteristic
17C2×#66896—21no—
18Q16×Dic11C2211yescharacteristic, complemented
19#10622794C2211yescharacteristic, complemented
20D8×Dic11—21no—
21D8×Dic11—21no—
22D8×Dic11C2212yes—
23D8×Dic11C2212yes—
24C2×#66891C2212yes—
25#10622729C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622664—21no—
29#10622487C2211yescharacteristic, complemented
30#10622486C2211yescharacteristic, complemented
31#10622405—21no—
32#10622403—21no—
33C11×#357C2212yes—
34C11×C22⋊C16C2211yescharacteristic
35#10622202C2212yescomplemented
36#10622200C2212yes—
37C22⋊(C11⋊C16)C2211yescharacteristic
38#10622143C2212yescomplemented
39#10622141C2212yescomplemented
40Dic11⋊C16C2212yescomplemented
41C16×Dic11C2212yescomplemented
42#10622128C2212yescomplemented
43C22×D4×C11—21no—
44C23×Dic11—41no—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×D8—24no—
47C2×C11×D8—21no—
48C2×C11×D8C2312yes—
49C22×C8×C11C2311yescharacteristic
50C11×C22⋊Q8—21no—
51C2×C22⋊Dic11—41no—
52Q8×Dic11—21no—
53#66997—21no—
54C2×#4326—21no—
55D4×Dic11—22no—
56D4×Dic11—22no—
57D4×Dic11—41no—
58D4×Dic11—41no—
59C2×C4⋊Dic11—21no—
60#66977—21no—
61C2×C4×Dic11D411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63C2×Dic44C2311yescharacteristic
64#66942—41no—
65#66941—21no—
66#66940—21no—
67#66940—41no—
68#66931—41no—
69#66930—41no—
70C11×SD32—24no—
71C2×C11×C16C2312yes—
72C11×#107C2311yescharacteristic
73C11×#103—21no—
74#66899—21no—
75#66896—22no—
76#66896—22no—
77#66891—24no—
78#66882—21no—
79#66882C2311yescharacteristic
80#66882C2312yes—
81#66880—21no—
82C8×Dic11D411yescharacteristic
83C8×Dic11D411yescharacteristic
84C8×Dic11C2311yescharacteristic
85C8×Dic11C2311yescharacteristic
86C2×C11⋊C16C2312yes—
87#66874—21no—
88#66871—21no—
89#33661—111nomaximal, Sylow
90C24×C11—41no—
91C2×Q8×C11—21no—
92C2×D4×C11—24no—
93C2×D4×C11—22no—
94C2×D4×C11—42no—
95C2×D4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×Dic11—42no—
98C22×Dic11—42no—
99C22×Dic11—41no—
100C22×Dic11—84no—
101C22×Dic11D811yescharacteristic
102C22×Dic11D811yescharacteristic
103C2×Dic22—21no—
104C2×Dic22—41no—
105C11×Q16—22no—
106C11×D8—24no—
107C11×D8—22no—
108C11×D8#4114yes—
109C2×C8×C11—22no—
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2411yescharacteristic
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C22⋊Dic11—42no—
116C22⋊Dic11—42no—
117C22⋊Dic11—41no—
118#4326—42no—
119C4⋊Dic11—21no—
120C4⋊Dic11—22no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128C4×Dic11—41no—
129C4×Dic11—41no—
130C4×Dic11D811yescharacteristic
131C4×Dic11D811yescharacteristic
132C4×Dic11C2×D411yescharacteristic
133C4×Dic11C2×D411yescharacteristic
134C2×C11⋊C8—41no—
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137Dic44—22no—
138C11×C16—22no—
139C11⋊C16—22no—
140#3170—111no—
141C2×C4×D8—111no—
142#2235—111no—
143#2235—111no—
144#2226—112no—
145#2208—112no—
146#2187—111no—
147#2187D1111yescharacteristic
148C4×SD32—112no—
149C4×SD32—112no—
150#2162—111no—
151C23×C11—44no—
152C23×C11—42no—
153C23×C11—82no—
154C23×C11—82no—
155C23×C11C2×D811yescharacteristic
156Q8×C11—41no—
157Q8×C11—41no—
158D4×C11—24no—
159D4×C11—44no—
160D4×C11—42no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171C2×Dic11—82no—
172C2×Dic11—84no—
173C2×Dic11—84no—
174C2×Dic11SD3214yescomplemented
175C2×Dic11C2×D811yescharacteristic
176C2×Dic11C2×D811yescharacteristic
177C2×Dic11C2×D811yescharacteristic
178C2×Dic11C2×D811yescharacteristic
179Dic22—41no—
180Dic22—41no—
181Dic22—82no—
182C8×C11—21no—
183C8×C11C2×#4112yes—
184C11⋊C8—21no—
185C11⋊C8—21no—
186C22×D8C2×D1111yescharacteristic
187#533—221no—
188C2×C4×D4—221no—
189C2×SD32—112no—
190C2×SD32C2×D1112yes—
191#500—111no—
192#494—111no—
193#487—221no—
194#467—111no—
195#467—221no—
196#467C2×D1111yescharacteristic
197C4×Q16—111no—
198C4×Q16—111no—
199C4×Q16—221no—
200C4×D8—112no—
201C4×D8—112no—
202C4×D8—221no—
203C4×D8—221no—
204C2×#107—111no—
205C2×#102—221no—
206C2×C4×C8—111no—
207#367—112no—
208#367—112no—
209C4⋊C16—112no—
210#358—112no—
211#358—112no—
212#357—112no—
213#357C2×D1112yes—
214C22⋊C16—111no—
215C22⋊C16C2×D1111yescharacteristic
216C4×C16—112no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—44no—
220C22×C11—88no—
221C22×C11—82no—
222C22×C11—82no—
223C22×C11C2×SD3212yes—
224C22×C11C22×D811yescharacteristic
225C4×C11—21no—
226C4×C11—81no—
227C4×C11—81no—
228C4×C11#52511yescharacteristic
229C4×C11#57511yescharacteristic
230Dic11—21no—
231Dic11—21no—
232Dic11—81no—
233Dic11—82no—
234Dic11—81no—
235Dic11C2×SD3212yes—
236Dic11C2×SD3212yes—
237C22×D4—21no—
238C23×C4—441no—
239C2×Q16—111no—
240C2×Q16—221no—
241C2×Q16C22×D1111yescharacteristic
242C2×D8—24no—
243C2×D8—21no—
244C2×D8C22×D1112yes—
245C22×C8—111no—
246C22×C8C22×D1111yescharacteristic
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249#125—441no—
250C22⋊Q8—21no—
251C22⋊Q8—221no—
252C22⋊Q8—441no—
253C4×Q8—221no—
254C4×Q8—221no—
255C4×Q8—441no—
256C4×D4—222no—
257C4×D4—222no—
258C4×D4—441no—
259C4×D4—441no—
260#117—441no—
261C2×C4⋊C4—221no—
262C2×C22⋊C4—441no—
263C2×C42—111no—
264SD32—24no—
265SD32—224no—
266C2×C16—112no—
267C2×C16C22×D1112yes—
268#107—111no—
269#107—112no—
270#107—221no—
271#107—221no—
272#107C22×D1111yescharacteristic
273#103—21no—
274#103—221no—
275#103—221no—
276#103—221no—
277#102—222no—
278#102—222no—
279C4×C8—111no—
280C4×C8—111no—
281C4×C8—111no—
282C4×C8—111no—
283C2×C11—22no—
284C2×C11—84no—
285C2×C11#310011yescharacteristic
286C2×C11C22×SD3211yescharacteristic
287C2×C11#341411yescharacteristic
288C24—41no—
289C2×Q8—21no—
290C2×Q8—221no—
291C2×Q8—441no—
292C2×D4—24no—
293C2×D4—22no—
294C2×D4—42no—
295C2×D4—41no—
296C22×C4—111no—
297C22×C4—111no—
298C22×C4—442no—
299C22×C4—442no—
300C22×C4—441no—
301C22×C4—884no—
302C22×C4D4×D1111yescharacteristic
303Q16—22no—
304Q16—222no—
305Q16—442no—
306D8—24no—
307D8—22no—
308D8#434114yes—
309C2×C8—22no—
310C2×C8—111no—
311C2×C8—111no—
312C2×C8—441no—
313C2×C8D4×D1111yescharacteristic
314C2×C8C23×D1111yescharacteristic
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—222no—
318C4⋊C4—221no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C22⋊C4—41no—
327C22⋊C4—442no—
328C22⋊C4—442no—
329C22⋊C4—441no—
330C42—111no—
331C42—111no—
332C42—111no—
333C42—111no—
334C42—441no—
335C42—441no—
336C16—22no—
337C16—222no—
338C11#3366111yescharacteristic, complemented, Sylow
339C23—44no—
340C23—42no—
341C23—82no—
342C23—82no—
343C23D8×D1111yescharacteristic
344Q8—41no—
345Q8—41no—
346Q8—441no—
347Q8—441no—
348Q8—882no—
349D4—24no—
350D4—44no—
351D4—42no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—111no—
357C2×C4—111no—
358C2×C4—114no—
359C2×C4—111no—
360C2×C4—111no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—442no—
365C2×C4—884no—
366C2×C4—884no—
367C2×C4—882no—
368C2×C4D8×D1111yescharacteristic
369C2×C4C2×D4×D1111yescharacteristic
370C8—21no—
371C8—221no—
372C8—221no—
373C8C2×#434112yes—
374C22—21no—
375C22—21no—
376C22—44no—
377C22—88no—
378C22—82no—
379C22—82no—
380C22D11×SD3212yes—
381C22C2×D8×D1111yescharacteristic
382C4—21no—
383C4—81no—
384C4—81no—
385C4—112no—
386C4—112no—
387C4—221no—
388C4—221no—
389C4—881no—
390C4—882no—
391C4—881no—
392C4#1062311711yescharacteristic
393C4#1062330411yescharacteristic
394C2—22no—
395C2—84no—
396C2#1307861111yescharacteristic
397C2C2×D11×SD3211yescharacteristic
398C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2187C2
socleC22×C11C22×D8
prime radicalC22×C11×D8C22
hypercenter#2187D11
hypocenterC11#33661
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #13079197C2semidirect
3. #13070814C2semidirect
4. #13070811C2semidirect
5. #13070761C2semidirect
6. #13070659C2semidirect
8. #13070471C2semidirect
9. SD32×Dic11C2semidirect
10. #13070412C2semidirect
18. Q16×Dic11C22semidirect
19. #10622794C22semidirect
29. #10622487C22semidirect
30. #10622486C22semidirect
35. #10622202C22semidirect
38. #10622143C22semidirect
39. #10622141C22semidirect
40. Dic11⋊C16C22semidirect
41. C16×Dic11C22semidirect
42. #10622128C22semidirect
174. C2×Dic11SD32semidirect
338. C11#33661semidirect

Maximal subgroups

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

subgroupindex
#130791972
C2×D8×Dic112
#130708142
#130708112
#130707612
#130706592
#130705452
#130704712
SD32×Dic112
#130704122
C11×#21872
#3366111