Finite Group Databasebeta

← #14908702

Subgroups — #14908702

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×#10622485C211yesmaximal, characteristic
3#13070813C211yesmaximal, characteristic, complemented
4#13070762C212yesmaximal, complemented
5#13070660C212yesmaximal, complemented
6#13070547C211yesmaximal, characteristic
7#13070544C211yesmaximal, characteristic
8#13070467C212yesmaximal, complemented
9#13070465C212yesmaximal, complemented
10#13070412C211yesmaximal, characteristic, complemented
11C11×#2235C211yesmaximal, characteristic, complemented
12C22×D88C2211yescharacteristic
13#10623153—21no—
14C2×#66946—21no—
15C11×#467C2211yescharacteristic
16C2×C11×#107C2211yescharacteristic
17Q16×Dic11C2211yescharacteristic, complemented
18#10622794C2211yescharacteristic, complemented
19C2×#66892C2212yes—
20#10622729C2211yescharacteristic
21C2×C8×Dic11C2211yescharacteristic
22#10622664—21no—
23C2×#66873—21no—
24C2×#66864C2212yes—
25#10622487C2211yescharacteristic, complemented
26#10622486C2211yescharacteristic, complemented
27#10622485—21no—
28#10622485—21no—
29#10622485C2212yes—
30#10622485C2212yes—
31#10622405—21no—
32#10622403—21no—
33C11×#367C2212yescomplemented
34C11×#358C2212yescomplemented
35C11×C22⋊C16C2211yescharacteristic
36C22⋊(C11⋊C16)C2211yescharacteristic
37#10622147C2212yes—
38Dic11⋊C16C2212yescomplemented
39C16×Dic11C2212yescomplemented
40#10622130C2212yescomplemented
41#10622129C2212yes—
42#10622128C2212yescomplemented
43C22×D44—21no—
44C22×C4×D11—41no—
45C2×C11×Q16C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×C22⋊Q8—21no—
48C2×C11×C4⋊C4—21no—
49Q8×Dic11—21no—
50#66997—21no—
51C2×#4326—21no—
52C2×(C2×D11)⋊C4—41no—
53#66977—21no—
54C2×C4×Dic11D411yescharacteristic
55C22×C11⋊C8D411yescharacteristic
56C2×Dic44C2311yescharacteristic
57C2×D88—21no—
58C2×D88—24no—
59C2×D88C2312yes—
60#66946—22no—
61#66946—22no—
62#66946—41no—
63#66946—41no—
64#66942—41no—
65#66941—21no—
66#66940—21no—
67#66940—41no—
68#66931—41no—
69#66930—41no—
70C2×C11×C16C2312yes—
71C11×#107—21no—
72C11×#107C2312yes—
73C11×#107C2311yescharacteristic
74C11×#103—21no—
75#66899—21no—
76#66892—24no—
77#66882C2311yescharacteristic
78#66880—21no—
79C8×Dic11D411yescharacteristic
80C8×Dic11D411yescharacteristic
81C8×Dic11C2311yescharacteristic
82C8×Dic11C2311yescharacteristic
83C2×C11⋊C16C2312yes—
84#66874—21no—
85#66873—22no—
86#66873—22no—
87#66871—21no—
88#66864—24no—
89#33661—111nomaximal, Sylow
90C23×D11—41no—
91C2×Q8×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×Dic11D811yescharacteristic
95C22×Dic11D811yescharacteristic
96C2×D44—24no—
97C2×D44—22no—
98C2×D44—42no—
99C2×D44—41no—
100C2×C4×D11—42no—
101C2×C4×D11—42no—
102C2×C4×D11—84no—
103C2×Dic22—21no—
104C2×Dic22—41no—
105C11×Q16—22no—
106C2×C8×C11—22no—
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2411yescharacteristic
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C22⋊C4—41no—
114C22⋊Dic11—41no—
115#4326—42no—
116(C2×D11)⋊C4—42no—
117(C2×D11)⋊C4—42no—
118C4⋊Dic11—21no—
119C4⋊Dic11—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125C4×Dic11—41no—
126C4×Dic11—41no—
127C4×Dic11D811yescharacteristic
128C4×Dic11D811yescharacteristic
129C4×Dic11C2×D411yescharacteristic
130C4×Dic11C2×D411yescharacteristic
131C2×C11⋊C8—41no—
132C2×C11⋊C8C2×D411yescharacteristic
133C2×C11⋊C8C2×D411yescharacteristic
134Dic44—22no—
135D88—24no—
136D88—22no—
137D88#4114yes—
138C11×C16—22no—
139C11⋊C16—22no—
140#3170—111no—
141C2×C4×D8—111no—
142#2235—111no—
143#2235D1111yescharacteristic, complemented
144#2226—112no—
145#2208—112no—
146#2187—111no—
147#2187—111no—
148C4×SD32—112no—
149C4×SD32—112no—
150#2162—111no—
151C23×C11C2×D811yescharacteristic
152C22×D11—44no—
153C22×D11—42no—
154C22×D11—82no—
155C22×D11—82no—
156Q8×C11—41no—
157Q8×C11—41no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11SD3214yescomplemented
170C2×Dic11C2×D811yescharacteristic
171C2×Dic11C2×D811yescharacteristic
172C2×Dic11C2×D811yescharacteristic
173C2×Dic11C2×D811yescharacteristic
174D44—24no—
175D44—44no—
176D44—42no—
177C4×D11—84no—
178C4×D11—84no—
179Dic22—41no—
180Dic22—41no—
181Dic22—82no—
182C8×C11—21no—
183C8×C11C2×#4112yes—
184C11⋊C8—21no—
185C11⋊C8—21no—
186C22×D8—111no—
187#533—221no—
188C2×C4×D4—221no—
189C2×SD32—112no—
190C2×SD32—112no—
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×#107C2×D1111yescharacteristic
205C2×#102—221no—
206C2×C4×C8—111no—
207#367—112no—
208#367C2×D1112yescomplemented
209C4⋊C16—112no—
210#358—112no—
211#358C2×D1112yescomplemented
212#357—112no—
213#357—112no—
214C22⋊C16—111no—
215C22⋊C16C2×D1111yescharacteristic
216C4×C16—112no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11C2×SD3212yes—
220C22×C11C22×D811yescharacteristic
221C2×D11—44no—
222C2×D11—88no—
223C2×D11—82no—
224C2×D11—82no—
225C4×C11—21no—
226C4×C11—81no—
227C4×C11—82no—
228C4×C11—81no—
229C4×C11#52511yescharacteristic
230C4×C11#57511yescharacteristic
231Dic11—21no—
232Dic11—21no—
233Dic11—81no—
234Dic11—81no—
235Dic11C2×SD3212yes—
236Dic11C2×SD3212yes—
237C22×D4—221no—
238C23×C4—441no—
239C2×Q16—111no—
240C2×Q16—221no—
241C2×Q16C22×D1111yescharacteristic
242C2×D8—112no—
243C2×D8—224no—
244C2×D8—221no—
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—21no—
262C2×C22⋊C4—441no—
263C2×C42—111no—
264SD32—224no—
265SD32—224no—
266C2×C16—112no—
267C2×C16C22×D1112yes—
268#107—21no—
269#107—111no—
270#107—221no—
271#107C22×D1111yescharacteristic
272#107C22×D1112yes—
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#310011yescharacteristic
285C2×C11C22×SD3211yescharacteristic
286C2×C11#341411yescharacteristic
287D11—84no—
288C24—441no—
289C2×Q8—21no—
290C2×Q8—221no—
291C2×Q8—441no—
292C2×D4—224no—
293C2×D4—222no—
294C2×D4—442no—
295C2×D4—441no—
296C22×C4—41no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—442no—
300C22×C4—442no—
301C22×C4—884no—
302C22×C4D4×D1111yescharacteristic
303Q16—22no—
304Q16—222no—
305Q16—442no—
306D8—114no—
307D8—224no—
308D8—222no—
309C2×C8—22no—
310C2×C8—111no—
311C2×C8—111no—
312C2×C8—441no—
313C2×C8D4×D1111yescharacteristic
314C2×C8C23×D1111yescharacteristic
315C4⋊C4—22no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—221no—
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—444no—
340C23—442no—
341C23—882no—
342C23—882no—
343C23D8×D1111yescharacteristic
344Q8—41no—
345Q8—41no—
346Q8—441no—
347Q8—441no—
348Q8—882no—
349D4—224no—
350D4—444no—
351D4—442no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—82no—
358C2×C4—111no—
359C2×C4—111no—
360C2×C4—114no—
361C2×C4—111no—
362C2×C4—111no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—884no—
367C2×C4—884no—
368C2×C4D8×D1111yescharacteristic
369C2×C4C2×D4×D1111yescharacteristic
370C8—21no—
371C8—221no—
372C8—221no—
373C8#41×D1112yes—
374C22—21no—
375C22—21no—
376C22—444no—
377C22—888no—
378C22—882no—
379C22—882no—
380C22D11×SD3212yes—
381C22C2×D8×D1111yescharacteristic
382C4—21no—
383C4—81no—
384C4—82no—
385C4—81no—
386C4—112no—
387C4—112no—
388C4—221no—
389C4—221no—
390C4—881no—
391C4—881no—
392C4#1062318711yescharacteristic
393C4#1062330811yescharacteristic
394C2—22no—
395C2—884no—
396C2#1307861311yescharacteristic
397C2C2×D11×SD3211yescharacteristic
398C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2235C2
socleC22×C11C22×D8
prime radicalC22×D88C22
hypercenter#2235D11
hypocenterC11#33661
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2235

Complements

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

NH ≅ G/Ntype
1. #13079197C2semidirect
3. #13070813C2semidirect
4. #13070762C2semidirect
5. #13070660C2semidirect
8. #13070467C2semidirect
9. #13070465C2semidirect
10. #13070412C2semidirect
11. C11×#2235C2semidirect
17. Q16×Dic11C22semidirect
18. #10622794C22semidirect
25. #10622487C22semidirect
26. #10622486C22semidirect
33. C11×#367C22semidirect
34. C11×#358C22semidirect
38. Dic11⋊C16C22semidirect
39. C16×Dic11C22semidirect
40. #10622130C22semidirect
42. #10622128C22semidirect
143. #2235D11semidirect
169. C2×Dic11SD32semidirect
208. #367C2×D11semidirect
211. #358C2×D11semidirect
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×#106224852
#130708132
#130707622
#130706602
#130705472
#130705442
#130704672
#130704652
#130704122
C11×#22352
#3366111