Finite Group Databasebeta

← #13123678

Subgroups — #13123678

Order 1664.

470 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
1C2×#88172C211yesmaximal, characteristic
2#11719279C211yesmaximal, characteristic
3#11719277C211yesmaximal, characteristic, complemented
4C13×#441C211yesmaximal, characteristic, complemented
5Q16×Dic13C211yesmaximal, characteristic, complemented
6C4×#6107C211yesmaximal, characteristic, complemented
7C4×#6106C211yesmaximal, characteristic, complemented
8#11718522C211yesmaximal, characteristic, complemented
9#11718513C211yesmaximal, characteristic, complemented
10#11718478C211yesmaximal, characteristic, complemented
11#11718465C211yesmaximal, characteristic
12D13×#103C211yesmaximal, characteristic, complemented
13#11718450C211yesmaximal, characteristic, complemented
14#11718371C211yesmaximal, characteristic, complemented
15#11718369C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20C4×Q8×C13C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23C2×#6107C2211yescharacteristic
24C2×#6106C2211yescharacteristic
25#88172C418yescomplemented
26C2×#6095C2211yescharacteristic
27C2×#6094C2211yescharacteristic
28C2×C8×D13C2211yescharacteristic
29#88147—21no—
30#88147C2211yescharacteristic
31#88146—21no—
32#88146C2211yescharacteristic
33C4⋊C4×D13—21no—
34C4⋊C4×D13C2211yescharacteristic
35#88141—21no—
36#88141C2211yescharacteristic
37C4×D52—21no—
38C4×D52C2211yescharacteristic
39#88126—21no—
40#88126—21no—
41#88126C2211yescharacteristic
42C4×Dic26—21no—
43C4×Dic26C2211yescharacteristic
44C13×#106C2211yescharacteristic
45C13×#103C2211yescharacteristic
46C13×#103C2211yescharacteristic
47C13×#97C2211yescharacteristic
48#88075C2211yescharacteristic
49#88075C2211yescharacteristic
50#88061C2211yescharacteristic
51#88058C2211yescharacteristic
52#88056C2211yescharacteristic
53#88055C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88050C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C4×#1055C2211yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62#6131—22no—
63#6131C2×C414yes—
64Q8×D13—22no—
65Q8×D13C2×C414yescomplemented
66C2×D52—21no—
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13C2311yescharacteristic
74C2×Dic26—21no—
75C2×Dic26C2311yescharacteristic
76C13×Q16C2×C414yescomplemented
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C42×C13—21no—
84C42×C13—21no—
85C42×C13C2311yescharacteristic
86#6107C2×C414yescomplemented
87#6106C2×C414yescomplemented
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103D411yescharacteristic
92#6103D411yescharacteristic
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101D411yescharacteristic
101#6101D411yescharacteristic
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6095C2×C414yescomplemented
111#6094C2×C414yescomplemented
112C8×D13—22no—
113#2947—131nomaximal, Sylow
114C22×D13—21no—
115C22×D13C2×D411yescharacteristic
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13C22×C412yes—
119Q8×C13C22×C412yes—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133D52—24no—
134D52—21no—
135D52C22×C412yes—
136C4×D13—24no—
137C4×D13—24no—
138C4×D13—81no—
139C4×D13—81no—
140C4×D13—81no—
141C4×D13C22×C412yes—
142C4×D13#4112yes—
143Dic26—21no—
144Dic26—24no—
145Dic26C22×C412yes—
146C8×C13—21no—
147C8×C13C22×C412yes—
148#1055—21no—
149#1055C22×C412yes—
150C2×#137—131no—
151#520—131no—
152#519—131no—
153#441—131no—
154#441D1311yescharacteristic, complemented
155#440—131no—
156#440—131no—
157C4×Q16—131no—
158C4×Q16—131no—
159C4×SD16—131no—
160C4×SD16—131no—
161#428—131no—
162#416—131no—
163C2×#103—131no—
164#405—131no—
165C22×C13C22×D411yescharacteristic
166C2×D13—21no—
167C2×D13—21no—
168C2×D13—22no—
169C2×D13—41no—
170C2×D13—41no—
171C2×D13C4×D412yes—
172C4×C13—22no—
173C4×C13—22no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13C23×C411yescharacteristic
179C4×C13C2×#4111yescharacteristic
180Dic13—22no—
181Dic13—21no—
182Dic13—21no—
183Dic13—41no—
184Dic13—41no—
185Dic13C4×D412yes—
186C2×#41—131no—
187C22×Q8—131no—
188#137—138no—
189C2×Q16—131no—
190C2×Q16C2×D1311yescharacteristic
191C2×SD16—131no—
192C2×SD16—131no—
193C2×M16—131no—
194C22×C8—131no—
195C4×Q8—131no—
196C4×Q8—131no—
197C4×Q8—131no—
198C4×Q8—131no—
199C4×Q8—261no—
200C4×Q8—261no—
201C4×Q8C2×D1311yescharacteristic
202C4×Q8C2×D1311yescharacteristic
203C4×D4—131no—
204C4×D4—131no—
205C4×D4—261no—
206C4×D4—261no—
207#117—131no—
208#117—131no—
209#117—261no—
210#117—261no—
211#117—261no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214#107—131no—
215#107—131no—
216#106—131no—
217#106C2×D1311yescharacteristic
218#103—131no—
219#103—131no—
220#103—131no—
221#103—131no—
222#103C2×D1311yescharacteristic
223#103C2×D1311yescharacteristic
224#102—131no—
225#102—131no—
226#97—131no—
227#97C2×D1311yescharacteristic
228C4×C8—131no—
229C4×C8—131no—
230C2×C13C2×C4×D411yescharacteristic
231C2×C13#57711yescharacteristic
232C2×C13#57811yescharacteristic
233D13—22no—
234D13—42no—
235#41—134no—
236#41—262no—
237C2×Q8—134no—
238C2×Q8—131no—
239C2×Q8—261no—
240C2×Q8—262no—
241C2×Q8C22×D1311yescharacteristic
242C2×Q8C22×D1311yescharacteristic
243C2×D4—131no—
244C2×D4—261no—
245C22×C4—131no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4—261no—
250C22×C4—261no—
251Q16—134no—
252Q16C4×D1314yescomplemented
253SD16—134no—
254SD16—134no—
255M16—134no—
256C2×C8—131no—
257C2×C8—131no—
258C2×C8—262no—
259C2×C8C22×D1311yescharacteristic
260C2×C8C22×D1311yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—131no—
264C4⋊C4—131no—
265C4⋊C4—131no—
266C4⋊C4—131no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4C22×D1311yescharacteristic
273C4⋊C4C22×D1311yescharacteristic
274C22⋊C4—131no—
275C22⋊C4—131no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C42—21no—
280C42—21no—
281C42—131no—
282C42—261no—
283C42—261no—
284C42—261no—
285C42—261no—
286C42—261no—
287C42C22×D1311yescharacteristic
288C13#294711yescharacteristic, complemented, Sylow
289C23—131no—
290C23—261no—
291Q8—21no—
292Q8—21no—
293Q8—132no—
294Q8—264no—
295Q8—261no—
296Q8C2×C4×D1312yes—
297Q8C2×C4×D1312yes—
298D4—132no—
299D4—264no—
300D4—261no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—131no—
306C2×C4—132no—
307C2×C4—132no—
308C2×C4—131no—
309C2×C4—131no—
310C2×C4—264no—
311C2×C4—264no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—1041no—
316C2×C4—1041no—
317C2×C4—1041no—
318C2×C4D4×D1311yescharacteristic
319C2×C4D4×D1311yescharacteristic
320C2×C4C23×D1311yescharacteristic
321C8—21no—
322C8—132no—
323C8—261no—
324C8C2×C4×D1312yes—
325C22—132no—
326C22—261no—
327C22—261no—
328C22—262no—
329C22—521no—
330C22—521no—
331C22C2×D4×D1311yescharacteristic
332C4—21no—
333C4—21no—
334C4—22no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—132no—
339C4—261no—
340C4—261no—
341C4—262no—
342C4—521no—
343C4—521no—
344C4C22×C4×D1311yescharacteristic
345C4#41×D1311yescharacteristic
346C2—262no—
347C2—522no—
348C2C4×D4×D1311yescharacteristic
349C2#1171948311yescharacteristic
350C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutatorC4×C13C23×C4
FrattiniC2×C4C23×D13
FittingC13×#441C2
socleC22×C13C22×D4
prime radicalC2×#6131C22
cosocleC2×C4×C13C24
hypercenter#441D13
hypocenterC13#2947
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. #11719277C2semidirect
4. C13×#441C2semidirect
5. Q16×Dic13C2semidirect
6. C4×#6107C2semidirect
7. C4×#6106C2semidirect
8. #11718522C2semidirect
9. #11718513C2semidirect
10. #11718478C2semidirect
12. D13×#103C2semidirect
13. #11718450C2semidirect
14. #11718371C2semidirect
15. #11718369C2semidirect
25. #88172C4semidirect
65. Q8×D13C2×C4semidirect
76. C13×Q16C2×C4semidirect
86. #6107C2×C4semidirect
87. #6106C2×C4semidirect
110. #6095C2×C4semidirect
111. #6094C2×C4semidirect
154. #441D13semidirect
252. Q16C4×D13semidirect
288. C13#2947semidirect

Maximal subgroups

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

subgroupindex
C2×#881722
#117192792
#117192772
C13×#4412
Q16×Dic132
C4×#61072
C4×#61062
#117185222
#117185132
#117184782
#117184652
D13×#1032
#117184502
#117183712
#117183692
#294713