Finite Group Databasebeta

← #13125085

Subgroups — #13125085

Order 1664.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719288C211yesmaximal, characteristic, complemented
2#11719250C211yesmaximal, characteristic
3C4×C13×SD16C211yesmaximal, characteristic, complemented
4#11718830C211yesmaximal, characteristic
5#11718823C211yesmaximal, characteristic, complemented
6#11718687C211yesmaximal, characteristic, complemented
7#11718679C211yesmaximal, characteristic, complemented
8#11718532C211yesmaximal, characteristic, complemented
9#11718528C211yesmaximal, characteristic, complemented
10#11718479C211yesmaximal, characteristic, complemented
11#11718476C211yesmaximal, characteristic, complemented
12#11718437C211yesmaximal, characteristic
13#11718424C211yesmaximal, characteristic, complemented
14C4×#6095C211yesmaximal, characteristic, complemented
15#11718351C211yesmaximal, characteristic, complemented
16C2×D4×D13C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic, complemented
19C4×D4×C13C2211yescharacteristic
20#88200C2211yescharacteristic
21#88198C2211yescharacteristic, complemented
22C2×#6106C2211yescharacteristic
23D4×Dic13C2211yescharacteristic
24C2×#6105C2211yescharacteristic
25C4×C22⋊D13—21no—
26C2×#6103—21no—
27C2×#6095C2211yescharacteristic
28#88152—21no—
29#88151C2211yescharacteristic
30#88147C2211yescharacteristic
31#88146C2211yescharacteristic
32#88144C2211yescharacteristic, complemented
33#88143—21no—
34#88135—21no—
35C22⋊C4×D13—21no—
36#88130—21no—
37C4×D52C2211yescharacteristic
38#88126C2211yescharacteristic
39#88124—21no—
40C4×Dic26C2211yescharacteristic, complemented
41C13×#106C2211yescharacteristic, complemented
42C13×#103C2211yescharacteristic, complemented
43C13×#102C2211yescharacteristic
44C4×C8×C13C2211yescharacteristic, complemented
45#88075C2211yescharacteristic, complemented
46#88072C2211yescharacteristic
47#88061C2211yescharacteristic
48#88060C2211yescharacteristic
49#88060C2211yescharacteristic
50#88057C2211yescharacteristic, complemented
51#88056C2211yescharacteristic, complemented
52#88054C2211yescharacteristic, complemented
53#88054C2211yescharacteristic, complemented
54#88050C2211yescharacteristic, complemented
55#88049C2211yescharacteristic
56#88047C2211yescharacteristic, complemented
57#88047C2211yescharacteristic, complemented
58#88043C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C2×C22⋊D13—21no—
64C22×Dic13—21no—
65D4×D13—22no—
66D4×D13—22no—
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13C2311yescharacteristic
71C2×Dic26C2311yescharacteristic
72C13×SD16—22no—
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C13×C4⋊C4—21no—
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C22⋊C4—21no—
79C42×C13—21no—
80C42×C13C2311yescharacteristic
81C22⋊Dic13—21no—
82#6106—22no—
83#6105—22no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103D411yescharacteristic
90#6103D411yescharacteristic
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101D411yescharacteristic
101#6101D411yescharacteristic
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107#6095—22no—
108#3123—131nomaximal, Sylow
109C23×C13—21no—
110C22×D13—21no—
111C22×D13—24no—
112C22×D13—81no—
113C22×D13—81no—
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117D4×C13—21no—
118D4×C13#4112yes—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—81no—
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2411yescharacteristic
126C22⋊D13—24no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—81no—
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134D52—21no—
135D52#4112yes—
136C4×D13—21no—
137C4×D13—21no—
138C4×D13—81no—
139C4×D13—81no—
140Dic26—21no—
141Dic26—21no—
142C8×C13—21no—
143C8×C13—21no—
144#1055—21no—
145#1055—21no—
146#541—131no—
147#518—131no—
148#485—131no—
149#485—131no—
150#478—131no—
151#478—131no—
152#461—131no—
153#461—131no—
154#450—131no—
155#450—131no—
156#440—131no—
157#440—131no—
158C4×SD16—131no—
159C4×SD16D1311yescharacteristic, complemented
160#433—131no—
161C22×C13—22no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13C22×D411yescharacteristic
165C2×D13—21no—
166C2×D13—22no—
167C2×D13—21no—
168C2×D13—21no—
169C2×D13—41no—
170C2×D13—41no—
171C2×D13—84no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13C2×#4111yescharacteristic
178C4×C13C2×#4111yescharacteristic
179Dic13—21no—
180Dic13—21no—
181Dic13—21no—
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185C22×D4—131no—
186C2×SD16—131no—
187C2×SD16—131no—
188C2×SD16—131no—
189C2×SD16C2×D1311yescharacteristic
190C4⋊Q8—131no—
191#126—261no—
192#126—261no—
193#125—131no—
194#125—261no—
195#125—261no—
196C22⋊Q8—131no—
197C22⋊Q8—131no—
198C4×Q8—131no—
199C4×Q8C2×D1311yescharacteristic, complemented
200C4×D4—131no—
201C4×D4—131no—
202C4×D4—131no—
203C4×D4—261no—
204C4×D4—261no—
205C4×D4C2×D1311yescharacteristic
206#117—131no—
207#117—131no—
208C2×C22⋊C4—261no—
209C2×C22⋊C4—261no—
210#107—131no—
211#107—131no—
212#106—131no—
213#106C2×D1311yescharacteristic, complemented
214C4⋊C8—131no—
215C4⋊C8—131no—
216#103—131no—
217#103—131no—
218#103—131no—
219#103C2×D1311yescharacteristic, complemented
220#102—131no—
221#102—131no—
222#102—131no—
223#102C2×D1311yescharacteristic
224C22⋊C8—131no—
225C22⋊C8—131no—
226#97—131no—
227C4×C8C2×D1311yescharacteristic, complemented
228C2×C13—42no—
229C2×C13#52511yescharacteristic
230C2×C13#57711yescharacteristic
231C2×C13#57711yescharacteristic
232D13—41no—
233D13—42no—
234C24—261no—
235C2×Q8—131no—
236C2×Q8C22×D1311yescharacteristic
237C2×D4—131no—
238C2×D4—261no—
239C2×D4—262no—
240C2×D4—262no—
241C2×D4C22×D1311yescharacteristic
242C22×C4—21no—
243C22×C4—131no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—261no—
247SD16—22no—
248SD16—262no—
249SD16—262no—
250SD16—262no—
251C2×C8—131no—
252C2×C8—131no—
253C2×C8C22×D1311yescharacteristic
254C2×C8C22×D1311yescharacteristic
255C4⋊C4—21no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—131no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4C22×D1311yescharacteristic
268C4⋊C4C22×D1311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—131no—
271C22⋊C4—131no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C22⋊C4—261no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C42—21no—
279C42—131no—
280C42—261no—
281C42—261no—
282C42C22×D1311yescharacteristic
283C13#312311yescharacteristic, complemented, Sylow
284C23—21no—
285C23—131no—
286C23—264no—
287C23—261no—
288C23—1041no—
289C23—1041no—
290Q8—21no—
291Q8—21no—
292Q8—261no—
293Q8—261no—
294D4—21no—
295D4—132no—
296D4—264no—
297D4—261no—
298D4#612712yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—131no—
304C2×C4—131no—
305C2×C4—131no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—1041no—
312C2×C4—1041no—
313C2×C4—1041no—
314C2×C4D4×D1311yescharacteristic
315C2×C4D4×D1311yescharacteristic
316C2×C4C23×D1311yescharacteristic
317C8—21no—
318C8—21no—
319C8—261no—
320C8—261no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—261no—
325C22—261no—
326C22—261no—
327C22—262no—
328C22—521no—
329C22—521no—
330C22—1044no—
331C22C2×D4×D1311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—261no—
338C4—261no—
339C4—261no—
340C4—521no—
341C4—521no—
342C4—521no—
343C4C2×#612711yescharacteristic
344C4#41×D1311yescharacteristic
345C2—42no—
346C2—521no—
347C2—522no—
348C2#1171925211yescharacteristic
349C2#1171946711yescharacteristic
350C2#1171947511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×SD16C2
socleC22×C13C22×D4
prime radicalC2×D4×D13C22
hypercenterC4×SD16D13
hypocenterC13#3123
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #11719288C2semidirect
3. C4×C13×SD16C2semidirect
5. #11718823C2semidirect
6. #11718687C2semidirect
7. #11718679C2semidirect
8. #11718532C2semidirect
9. #11718528C2semidirect
10. #11718479C2semidirect
11. #11718476C2semidirect
13. #11718424C2semidirect
14. C4×#6095C2semidirect
15. #11718351C2semidirect
18. C4×Q8×C13C22semidirect
21. #88198C22semidirect
32. #88144C22semidirect
40. C4×Dic26C22semidirect
41. C13×#106C22semidirect
42. C13×#103C22semidirect
44. C4×C8×C13C22semidirect
45. #88075C22semidirect
50. #88057C22semidirect
51. #88056C22semidirect
52. #88054C22semidirect
53. #88054C22semidirect
54. #88050C22semidirect
56. #88047C22semidirect
57. #88047C22semidirect
58. #88043C22semidirect
159. C4×SD16D13semidirect
199. C4×Q8C2×D13semidirect
213. #106C2×D13semidirect
219. #103C2×D13semidirect
227. C4×C8C2×D13semidirect
283. C13#3123semidirect

Maximal subgroups

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

subgroupindex
#117192882
#117192502
C4×C13×SD162
#117188302
#117188232
#117186872
#117186792
#117185322
#117185282
#117184792
#117184762
#117184372
#117184242
C4×#60952
#117183512
#312313