Finite Group Databasebeta

← #13125134

Subgroups — #13125134

Order 1664.

358 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719436C211yesmaximal, characteristic
2#11719277C211yesmaximal, characteristic
3C13×#462C211yesmaximal, characteristic, complemented
4#11718847C211yesmaximal, characteristic
5#11718847C211yesmaximal, characteristic
6#11718845C211yesmaximal, characteristic, complemented
7Q16×Dic13C211yesmaximal, characteristic, complemented
8#11718751C211yesmaximal, characteristic, complemented
9#11718683C211yesmaximal, characteristic, complemented
10#11718501C211yesmaximal, characteristic
11#11718490C211yesmaximal, characteristic, complemented
12#11718476C211yesmaximal, characteristic
13#11718475C211yesmaximal, characteristic
14#11718451C211yesmaximal, characteristic, complemented
15#11718450C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×C13×Q16C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic
19C13×C4⋊Q8C2211yescharacteristic
20C4×Q8×C13C2211yescharacteristic
21#88200C2211yescharacteristic
22#88200C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24Q8×Dic13C2211yescharacteristic
25Q8×Dic13C2211yescharacteristic
26C2×#6107C2211yescharacteristic
27C2×#6107C2211yescharacteristic
28#88152—21no—
29#88152—21no—
30#88146—21no—
31#88146C2211yescharacteristic
32#88143—21no—
33#88143—21no—
34#88141—21no—
35#88141C2211yescharacteristic
36#88126—21no—
37#88126C2211yescharacteristic
38#88124C2211yescharacteristic
39C4×Dic26—21no—
40C4×Dic26C2211yescharacteristic
41C13×C4⋊C8C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88060C2211yescharacteristic
49#88060C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88055C2211yescharacteristic
55C8×Dic13C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62Q8×D13—22no—
63Q8×D13—22no—
64C2×C4×D13—21no—
65C2×C4×D13C2311yescharacteristic
66C2×Dic26—21no—
67C2×Dic26C2311yescharacteristic
68C13×Q16—22no—
69C13×Q16—22no—
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4C2311yescharacteristic
76C42×C13—21no—
77C42×C13C2311yescharacteristic
78#6107—22no—
79#6107—22no—
80#6103—21no—
81#6103—21no—
82#6103—21no—
83#6103D411yescharacteristic
84#6103D411yescharacteristic
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98#6101D411yescharacteristic
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3127—131nomaximal, Sylow
109C22×D13C2×D411yescharacteristic
110Q8×C13—21no—
111Q8×C13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114Q8×C13—21no—
115Q8×C13#4112yes—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130C4×D13—24no—
131C4×D13—21no—
132C4×D13—21no—
133Dic26—24no—
134Dic26—21no—
135Dic26#4112yes—
136C8×C13—21no—
137C8×C13—21no—
138#1055—21no—
139#1055—21no—
140#541—131no—
141#519—131no—
142#485—131no—
143#485—131no—
144#479—131no—
145#479—131no—
146#462—131no—
147#462D1311yescharacteristic, complemented
148#451—131no—
149#451—131no—
150#441—131no—
151#441—131no—
152C4×Q16—131no—
153C4×Q16—131no—
154#433—131no—
155C22×C13C22×D411yescharacteristic
156C2×D13—21no—
157C2×D13—21no—
158C2×D13—21no—
159C4×C13—22no—
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13C2×#4111yescharacteristic
166C4×C13C2×#4111yescharacteristic
167Dic13—21no—
168Dic13—22no—
169Dic13—21no—
170Dic13—21no—
171Dic13—41no—
172Dic13—41no—
173Dic13—41no—
174C22×Q8—131no—
175C2×Q16—131no—
176C2×Q16—131no—
177C2×Q16C2×D1311yescharacteristic
178C2×Q16C2×D1311yescharacteristic
179C4⋊Q8C2×D1311yescharacteristic
180#126—261no—
181#126—261no—
182#125—131no—
183#125—261no—
184#125—261no—
185C22⋊Q8—131no—
186C22⋊Q8—131no—
187C4×Q8—131no—
188C4×Q8—131no—
189C4×Q8—131no—
190C4×Q8—131no—
191C4×Q8—131no—
192C4×Q8—261no—
193C4×Q8—261no—
194C4×Q8C2×D1311yescharacteristic
195#117—131no—
196#117—131no—
197#117—261no—
198#117—261no—
199#107—131no—
200#107—131no—
201#106—131no—
202#106—131no—
203C4⋊C8—131no—
204C4⋊C8C2×D1311yescharacteristic
205#103—131no—
206#103—131no—
207#103—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103C2×D1311yescharacteristic
212#103C2×D1311yescharacteristic
213C22⋊C8—131no—
214C22⋊C8—131no—
215#97—131no—
216C4×C8—131no—
217C2×C13#52511yescharacteristic
218C2×C13#57811yescharacteristic
219C2×C13#57811yescharacteristic
220D13—41no—
221C2×Q8—131no—
222C2×Q8—261no—
223C2×Q8—262no—
224C2×Q8—262no—
225C2×Q8C22×D1311yescharacteristic
226C2×Q8C22×D1311yescharacteristic
227C2×Q8C22×D1311yescharacteristic
228C22×C4—131no—
229C22×C4—261no—
230Q16—22no—
231Q16—22no—
232Q16—262no—
233Q16—262no—
234C2×C8—131no—
235C2×C8—131no—
236C2×C8C22×D1311yescharacteristic
237C2×C8C22×D1311yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—131no—
242C4⋊C4—131no—
243C4⋊C4—131no—
244C4⋊C4—131no—
245C4⋊C4—131no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4C22×D1311yescharacteristic
256C22⋊C4—131no—
257C22⋊C4—131no—
258C22⋊C4—261no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C42—21no—
262C42—131no—
263C42—261no—
264C42—261no—
265C42—261no—
266C42—261no—
267C42—261no—
268C42—261no—
269C42C22×D1311yescharacteristic
270C13#312711yescharacteristic, complemented, Sylow
271C23—131no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—21no—
277Q8—132no—
278Q8—264no—
279Q8—261no—
280Q8#612912yes—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—131no—
286C2×C4—131no—
287C2×C4—131no—
288C2×C4—264no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4D4×D1311yescharacteristic
296C2×C4D4×D1311yescharacteristic
297C2×C4C23×D1311yescharacteristic
298C8—21no—
299C8—21no—
300C8—261no—
301C8—261no—
302C22—261no—
303C22—261no—
304C22—261no—
305C22C2×D4×D1311yescharacteristic
306C4—21no—
307C4—21no—
308C4—22no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—261no—
313C4—261no—
314C4—261no—
315C4—262no—
316C4—521no—
317C4—521no—
318C4—521no—
319C4C2×#612911yescharacteristic
320C4#41×D1311yescharacteristic
321C2—521no—
322C2#1171931111yescharacteristic
323C2#1171947111yescharacteristic
324C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#462C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#462D13
hypocenterC13#3127
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. C13×#462C2semidirect
6. #11718845C2semidirect
7. Q16×Dic13C2semidirect
8. #11718751C2semidirect
9. #11718683C2semidirect
11. #11718490C2semidirect
14. #11718451C2semidirect
15. #11718450C2semidirect
147. #462D13semidirect
270. C13#3127semidirect

Maximal subgroups

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

subgroupindex
#117194362
#117192772
C13×#4622
#117188472
#117188452
Q16×Dic132
#117187512
#117186832
#117185012
#117184902
#117184762
#117184752
#117184512
#117184502
#312713