Finite Group Databasebeta

← #13125052

Subgroups — #13125052

Order 1664.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719228C211yesmaximal, characteristic
2#11719223C211yesmaximal, characteristic, complemented
3C13×#433C211yesmaximal, characteristic, complemented
4#11718510C211yesmaximal, characteristic, complemented
5#11718508C211yesmaximal, characteristic, complemented
6#11718502C211yesmaximal, characteristic, complemented
7#11718490C211yesmaximal, characteristic, complemented
8#11718394C211yesmaximal, characteristic
9#11718394C211yesmaximal, characteristic
10#11718383C211yesmaximal, characteristic, complemented
11#11718382C211yesmaximal, characteristic, complemented
12#11718377C211yesmaximal, characteristic, complemented
13#11718371C211yesmaximal, characteristic, complemented
14C4×Dic52C211yesmaximal, characteristic, complemented
15C4×#6095C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C13×#117C2211yescharacteristic
18C2×C4⋊Dic13C2211yescharacteristic
19#88178C2211yescharacteristic
20#88178C2211yescharacteristic
21C2×Dic52C2211yescharacteristic
22C2×Dic52C2211yescharacteristic
23C2×#6095C2211yescharacteristic
24C2×#6095C2211yescharacteristic
25#88146—21no—
26C4⋊C4×D13—21no—
27#88143—21no—
28#88143—21no—
29#88135—21no—
30#88135—21no—
31#88133—21no—
32#88133—21no—
33C4×D52C2211yescharacteristic
34C4×D52C2211yescharacteristic
35#88124C2211yescharacteristic
36#88123C2211yescharacteristic
37C4×Dic26C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41C13×C4⋊C8C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×C22⋊C8C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45C13×#97C2211yescharacteristic
46C4×C8×C13C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88058C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C2×C22⋊D13—21no—
61C22×Dic13—21no—
62#6127—22no—
63#6127—22no—
64C2×D52C2311yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×Dic26C2311yescharacteristic
69C2×Dic26C2311yescharacteristic
70C2×Dic26C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C13×C4⋊C4D411yescharacteristic
76C13×C4⋊C4D411yescharacteristic
77C13×C22⋊C4D411yescharacteristic
78C13×C22⋊C4D411yescharacteristic
79C42×C13C2311yescharacteristic
80C42×C13C2311yescharacteristic
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83#6103—21no—
84#6103—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104Dic52—22no—
105Dic52—22no—
106#6095—22no—
107#6095—22no—
108#3120—131nomaximal, Sylow
109C23×C13C2×D411yescharacteristic
110C22×D13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C22⋊D13—24no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—81no—
128D52—21no—
129D52#4112yes—
130C4×D13—24no—
131C4×D13—81no—
132C4×D13—81no—
133Dic26—21no—
134Dic26—21no—
135Dic26—21no—
136Dic26—21no—
137Dic26—21no—
138Dic26#4112yes—
139C8×C13—21no—
140C8×C13—21no—
141C8×C13—21no—
142C8×C13—21no—
143#541—131no—
144#520—131no—
145#484—131no—
146#483—131no—
147#479—131no—
148#478—131no—
149#462—131no—
150#461—131no—
151#452—131no—
152#452—131no—
153#441—131no—
154#440—131no—
155C4×Q16—131no—
156C4×SD16—131no—
157#433D1311yescharacteristic, complemented
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13C22×D411yescharacteristic
162C2×D13—22no—
163C2×D13—41no—
164C2×D13—41no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13C2×#4111yescharacteristic
171C4×C13C2×#4111yescharacteristic
172Dic13—22no—
173Dic13—41no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179C2×#41—131no—
180C2×Q16—131no—
181C2×Q16—131no—
182C2×SD16—131no—
183C2×SD16—131no—
184C4⋊Q8—131no—
185#126—261no—
186#126—261no—
187#125—131no—
188#125—261no—
189#125—261no—
190C22⋊Q8—131no—
191C22⋊Q8—131no—
192C4×Q8—131no—
193C4×Q8—131no—
194C4×Q8—131no—
195C4×Q8—131no—
196C4×D4—131no—
197C4×D4—131no—
198C4×D4—261no—
199C4×D4—261no—
200#117—261no—
201#117C2×D1311yescharacteristic
202C2×C4⋊C4—131no—
203C2×C4⋊C4—261no—
204#107—131no—
205#107—131no—
206#106—131no—
207#106—131no—
208C4⋊C8C2×D1311yescharacteristic
209C4⋊C8C2×D1311yescharacteristic
210#103—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#103—131no—
215#103—131no—
216#102—131no—
217#102—131no—
218C22⋊C8C2×D1311yescharacteristic
219C22⋊C8C2×D1311yescharacteristic
220#97C2×D1311yescharacteristic
221C4×C8C2×D1311yescharacteristic
222C2×C13—41no—
223C2×C13#52511yescharacteristic
224C2×C13#57711yescharacteristic
225C2×C13#57811yescharacteristic
226D13—42no—
227#41—262no—
228#41—262no—
229C2×Q8—131no—
230C2×Q8—131no—
231C2×Q8—131no—
232C2×D4—131no—
233C2×D4—261no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4C22×D1311yescharacteristic
239Q16—262no—
240Q16—262no—
241SD16—262no—
242SD16—262no—
243C2×C8C22×D1311yescharacteristic
244C2×C8C22×D1311yescharacteristic
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C4⋊C4—131no—
248C4⋊C4—131no—
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4D5211yescharacteristic
263C4⋊C4D5211yescharacteristic
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4D5211yescharacteristic
269C22⋊C4D5211yescharacteristic
270C42—261no—
271C42—261no—
272C42—261no—
273C42—261no—
274C42C22×D1311yescharacteristic
275C42C22×D1311yescharacteristic
276C13#312011yescharacteristic, complemented, Sylow
277C23—261no—
278C23C2×D5211yescharacteristic
279Q8—132no—
280Q8—261no—
281Q8—261no—
282Q8—261no—
283Q8—261no—
284Q8—261no—
285D4—132no—
286D4—264no—
287D4—261no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—264no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—1041no—
299C2×C4—1041no—
300C2×C4—1041no—
301C2×C4C2×D5211yescharacteristic
302C2×C4C2×D5211yescharacteristic
303C2×C4C2×D5211yescharacteristic
304C2×C4C2×D5211yescharacteristic
305C2×C4C2×D5211yescharacteristic
306C2×C4C23×D1311yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—262no—
315C22—521no—
316C22—521no—
317C22C22×D5211yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—262no—
324C4—521no—
325C4—521no—
326C4—521no—
327C4—521no—
328C4—521no—
329C4—521no—
330C4#41×D1311yescharacteristic
331C4#41×D1311yescharacteristic
332C2—41no—
333C2—522no—
334C2#1171922911yescharacteristic
335C2#1171945611yescharacteristic
336C2#1171945811yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#433C2
socleC22×C13C22×D4
prime radicalC2×#6127C22
hypercenter#433D13
hypocenterC13#3120
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #11719223C2semidirect
3. C13×#433C2semidirect
4. #11718510C2semidirect
5. #11718508C2semidirect
6. #11718502C2semidirect
7. #11718490C2semidirect
10. #11718383C2semidirect
11. #11718382C2semidirect
12. #11718377C2semidirect
13. #11718371C2semidirect
14. C4×Dic52C2semidirect
15. C4×#6095C2semidirect
157. #433D13semidirect
276. C13#3120semidirect

Maximal subgroups

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

subgroupindex
#117192282
#117192232
C13×#4332
#117185102
#117185082
#117185022
#117184902
#117183942
#117183832
#117183822
#117183772
#117183712
C4×Dic522
C4×#60952
#312013