Finite Group Databasebeta

← #13126997

Subgroups — #13126997

Order 1664.

414 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#11719268C211yesmaximal, characteristic, complemented
2#11719259C211yesmaximal, characteristic, complemented
3C13×#442C211yesmaximal, characteristic, complemented
4#11718819C211yesmaximal, characteristic, complemented
5#11718817C211yesmaximal, characteristic, complemented
6#11718677C211yesmaximal, characteristic, complemented
7#11718668C211yesmaximal, characteristic, complemented
8#11718528C211yesmaximal, characteristic, complemented
9#11718527C211yesmaximal, characteristic, complemented
10#11718441C211yesmaximal, characteristic, complemented
11#11718436C211yesmaximal, characteristic, complemented
12#11718433C211yesmaximal, characteristic, complemented
13#11718431C211yesmaximal, characteristic, complemented
14#11718375C211yesmaximal, characteristic, complemented
15#11718367C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C2×C13×D8C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic, complemented
21#88192C2211yescharacteristic
22#88192C2211yescharacteristic, complemented
23C2×#6105C2211yescharacteristic, complemented
24C2×#6104C2211yescharacteristic
25#88184—21no—
26#88184—21no—
27C2×#6103—21no—
28#88180—21no—
29C2×#6094C2211yescharacteristic
30C2×C8×D13C2211yescharacteristic, complemented
31#88151C2211yescharacteristic
32#88149C2211yescharacteristic
33#88146C2211yescharacteristic
34#88146C2211yescharacteristic, complemented
35#88140—21no—
36#88139—21no—
37#88139—21no—
38#88136—21no—
39#88129C2211yescharacteristic
40C4×D52C2211yescharacteristic
41#88123C2211yescharacteristic, complemented
42C13×#106C2211yescharacteristic, complemented
43C13×#102C2211yescharacteristic
44C13×#102C2211yescharacteristic, complemented
45C13×#97C2211yescharacteristic, complemented
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88060C2211yescharacteristic
51#88060C2211yescharacteristic, complemented
52#88056C2211yescharacteristic, complemented
53#88056C2211yescharacteristic, complemented
54#88050C2211yescharacteristic, complemented
55#88049C2211yescharacteristic
56#88047C2211yescharacteristic, complemented
57#88047C2211yescharacteristic, complemented
58C4⋊#1055C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×D4×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C22×Dic13—21no—
69#6129—22no—
70#6129—41no—
71D4×D13—22no—
72D4×D13—41no—
73C2×D52—21no—
74C2×D52D411yescharacteristic
75C2×D52C2311yescharacteristic
76C2×C4×D13C2311yescharacteristic
77C2×C4×D13C2311yescharacteristic
78C2×Dic26—21no—
79C2×Dic26C2311yescharacteristic
80C13×D8—22no—
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C22⋊C4—21no—
86C13×C22⋊C4—21no—
87C42×C13C2311yescharacteristic
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90#6105—41no—
91#6104—41no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98#6103D411yescharacteristic
99#6103D411yescharacteristic
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13D411yescharacteristic
103C4⋊Dic13C2311yescharacteristic
104C4⋊Dic13C2311yescharacteristic
105C4×Dic13—21no—
106C4×Dic13—21no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109#6094—41no—
110C8×D13—41no—
111#3319—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C22×D13—21no—
115C22×D13—42no—
116C22×D13—42no—
117C22×D13—81no—
118C22×D13C2×D411yescharacteristic
119C22×D13C2×D411yescharacteristic
120D4×C13—21no—
121D4×C13—21no—
122D4×C13—21no—
123D4×C13#4112yes—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—42no—
127C2×C4×C13—81no—
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2411yescharacteristic
131C22⋊D13—42no—
132C22⋊D13—42no—
133C22⋊D13—81no—
134C22⋊D13—81no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—42no—
139C2×Dic13C2×D411yescharacteristic
140C2×Dic13C2×D411yescharacteristic
141D52—21no—
142D52—21no—
143D52—41no—
144D52—81no—
145C4×D13—21no—
146C4×D13—21no—
147C4×D13—21no—
148C4×D13—21no—
149Dic26—21no—
150Dic26—21no—
151Dic26—81no—
152C8×C13—21no—
153C8×C13—21no—
154#1055—21no—
155#1055—21no—
156#555—131no—
157#546—131no—
158#489—131no—
159#485—131no—
160#482—131no—
161#474—131no—
162#468—131no—
163#466—131no—
164#463—131no—
165#449—131no—
166#447—131no—
167#442D1311yescharacteristic, complemented
168#435—131no—
169#418—131no—
170#416—131no—
171C22×C13—22no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13C22×D411yescharacteristic
178C2×D13—21no—
179C2×D13—21no—
180C2×D13—21no—
181C2×D13—21no—
182C2×D13—21no—
183C2×D13—21no—
184C2×D13—41no—
185C2×D13—41no—
186C2×D13—41no—
187C2×D13—84no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13C2×#4111yescharacteristic
193C4×C13H(5,𝔽2)11yescharacteristic
194Dic13—21no—
195Dic13—21no—
196Dic13—41no—
197Dic13—41no—
198Dic13—41no—
199C2×#41—131no—
200C22×D4—131no—
201C2×SD16—131no—
202C2×D8—131no—
203C2×D8C2×D1311yescharacteristic
204C2×M16—131no—
205C22×C8—131no—
206C4⋊Q8—131no—
207#124—131no—
208#124—261no—
209#124—261no—
210#123—261no—
211C22⋊Q8—131no—
212#121—131no—
213#121—131no—
214#121—131no—
215#121—261no—
216#121—261no—
217#120—261no—
218C4×D4—131no—
219C4×D4C2×D1311yescharacteristic
220C4×D4C2×D1311yescharacteristic, complemented
221#117—131no—
222#117—131no—
223#117—261no—
224C2×C22⋊C4—261no—
225#107—131no—
226#107—131no—
227#106C2×D1311yescharacteristic, complemented
228C4⋊C8—131no—
229#103—131no—
230#103—131no—
231#103—131no—
232#102—131no—
233#102—131no—
234#102—131no—
235#102—131no—
236#102—131no—
237#102C2×D1311yescharacteristic
238#102C2×D1311yescharacteristic, complemented
239C22⋊C8—131no—
240C22⋊C8—131no—
241#97C2×D1311yescharacteristic, complemented
242C2×C13—42no—
243C2×C13—81no—
244C2×C13#54611yescharacteristic
245C2×C13#57511yescharacteristic
246C2×C13#57611yescharacteristic
247D13—41no—
248D13—41no—
249D13—81no—
250C24—261no—
251#41—262no—
252#41—521no—
253C2×Q8—131no—
254C2×Q8—261no—
255C2×D4—131no—
256C2×D4—131no—
257C2×D4—261no—
258C2×D4—261no—
259C2×D4—262no—
260C2×D4—261no—
261C2×D4—261no—
262C2×D4—261no—
263C2×D4—521no—
264C2×D4C22×D1311yescharacteristic
265C2×D4C22×D1311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—261no—
271SD16—521no—
272D8—22no—
273D8—521no—
274M16—521no—
275C2×C8—131no—
276C2×C8—131no—
277C2×C8—521no—
278C2×C8C22×D1311yescharacteristic
279C2×C8C22×D1311yescharacteristic
280C4⋊C4—131no—
281C4⋊C4—131no—
282C4⋊C4—131no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4C22×D1311yescharacteristic
286C4⋊C4C22×D1311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—131no—
290C22⋊C4—131no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4—261no—
296C22⋊C4—261no—
297C22⋊C4—261no—
298C22⋊C4—261no—
299C42—261no—
300C42—261no—
301C42C22×D1311yescharacteristic
302C13#331911yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—131no—
306C23—131no—
307C23—261no—
308C23—522no—
309C23—522no—
310C23—1041no—
311Q8—261no—
312Q8—261no—
313Q8—1041no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—261no—
318D4—261no—
319D4—521no—
320D4—522no—
321D4—522no—
322D4—1041no—
323D4—1041no—
324D4—1041no—
325D4#612712yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—81no—
330C2×C4—131no—
331C2×C4—131no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—522no—
340C2×C4D4×D1311yescharacteristic
341C2×C4D4×D1311yescharacteristic
342C2×C4C23×D1311yescharacteristic
343C8—21no—
344C8—21no—
345C8—261no—
346C8—261no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—261no—
354C22—261no—
355C22—261no—
356C22—261no—
357C22—261no—
358C22—261no—
359C22—521no—
360C22—521no—
361C22—521no—
362C22—1044no—
363C22C2×D4×D1311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—261no—
369C4—261no—
370C4—521no—
371C4—521no—
372C4—521no—
373C4C2×#612711yescharacteristic
374C4#8825611yescharacteristic
375C2—42no—
376C2—81no—
377C2—521no—
378C2—521no—
379C2—1041no—
380C2#1171925511yescharacteristic
381C2#1171947811yescharacteristic
382C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#442C2
socleC22×C13C22×D4
hypercenter#442D13
hypocenterC13#3319
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #11719268C2semidirect
2. #11719259C2semidirect
3. C13×#442C2semidirect
4. #11718819C2semidirect
5. #11718817C2semidirect
6. #11718677C2semidirect
7. #11718668C2semidirect
8. #11718528C2semidirect
9. #11718527C2semidirect
10. #11718441C2semidirect
11. #11718436C2semidirect
12. #11718433C2semidirect
13. #11718431C2semidirect
14. #11718375C2semidirect
15. #11718367C2semidirect
20. C4×D4×C13C22semidirect
22. #88192C22semidirect
23. C2×#6105C22semidirect
30. C2×C8×D13C22semidirect
34. #88146C22semidirect
41. #88123C22semidirect
42. C13×#106C22semidirect
44. C13×#102C22semidirect
45. C13×#97C22semidirect
51. #88060C22semidirect
52. #88056C22semidirect
53. #88056C22semidirect
54. #88050C22semidirect
56. #88047C22semidirect
57. #88047C22semidirect
58. C4⋊#1055C22semidirect
167. #442D13semidirect
220. C4×D4C2×D13semidirect
227. #106C2×D13semidirect
238. #102C2×D13semidirect
241. #97C2×D13semidirect
302. C13#3319semidirect

Maximal subgroups

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

subgroupindex
#117192682
#117192592
C13×#4422
#117188192
#117188172
#117186772
#117186682
#117185282
#117185272
#117184412
#117184362
#117184332
#117184312
#117183752
#117183672
#331913