Finite Group Databasebeta

← #13127647

Subgroups — #13127647

Order 1664.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719427C211yesmaximal, characteristic, complemented
2#11719386C211yesmaximal, characteristic
3C13×#489C211yesmaximal, characteristic, complemented
4#11718748C211yesmaximal, characteristic, complemented
5#11718715C211yesmaximal, characteristic, complemented
6#11718459C211yesmaximal, characteristic, complemented
7#11718456C211yesmaximal, characteristic, complemented
8#11718455C211yesmaximal, characteristic, complemented
9#11718451C211yesmaximal, characteristic, complemented
10#11718423C211yesmaximal, characteristic
11#11718421C211yesmaximal, characteristic
12#11718420C211yesmaximal, characteristic, complemented
13#11718418C211yesmaximal, characteristic, complemented
14#11718371C211yesmaximal, characteristic, complemented
15#11718362C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#124C2211yescharacteristic
18#88201C2211yescharacteristic
19Q8×Dic13C2211yescharacteristic
20#88198—21no—
21#88198—21no—
22C2×#6107C2211yescharacteristic
23#88194C2211yescharacteristic
24D4×Dic13C2211yescharacteristic
25C2×#6105C2211yescharacteristic
26C2×#6095C2211yescharacteristic
27#88142—21no—
28#88142C2211yescharacteristic
29#88142C2211yescharacteristic
30#88141—21no—
31#88141C2211yescharacteristic
32#88141C2211yescharacteristic
33#88140—21no—
34#88139—21no—
35#88137—21no—
36#88135—21no—
37C4×D52C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#103C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#97C2211yescharacteristic
45#88075C2211yescharacteristic
46#88072C2211yescharacteristic
47#88061C2211yescharacteristic
48#88058C2211yescharacteristic
49#88056C2211yescharacteristic
50#88055C2211yescharacteristic
51#88054C2211yescharacteristic
52#88054C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54#88049C2211yescharacteristic
55#88049C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C22×Dic13—21no—
65C2×D52C2311yescharacteristic
66C2×C4×D13—21no—
67C2×Dic26—21no—
68C2×Dic26—21no—
69C2×Dic26D411yescharacteristic
70C2×Dic26C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C22⋊C4—21no—
77C13×C22⋊C4—21no—
78C42×C13C2311yescharacteristic
79C22⋊Dic13—21no—
80#6107—22no—
81#6105—22no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13D411yescharacteristic
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101D411yescharacteristic
95#6101D411yescharacteristic
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13C2311yescharacteristic
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104#6095—22no—
105#3375—131nomaximal, Sylow
106C23×C13—21no—
107C22×D13—21no—
108Q8×C13—21no—
109Q8×C13—21no—
110Q8×C13—81no—
111D4×C13—21no—
112D4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C22⋊D13—42no—
120C22⋊D13—81no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—81no—
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129D52—21no—
130D52—21no—
131C4×D13—81no—
132Dic26—21no—
133Dic26—22no—
134Dic26—81no—
135Dic26—81no—
136Dic26#4112yes—
137C8×C13—21no—
138C8×C13—21no—
139#1055—21no—
140#1055—21no—
141#559—131no—
142Q82—131no—
143#489—131no—
144#489D1311yescharacteristic, complemented
145#486—131no—
146#477—131no—
147#474—131no—
148#474—131no—
149#464—131no—
150#464—131no—
151#460—131no—
152#446—131no—
153#440—131no—
154#440—131no—
155C4×Q16—131no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13C22×D411yescharacteristic
160C2×D13—41no—
161C2×D13—41no—
162C2×D13—41no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13C2×#4111yescharacteristic
169C4×C132−1+411yescharacteristic
170Dic13—22no—
171Dic13—21no—
172Dic13—21no—
173Dic13—21no—
174Dic13—41no—
175Dic13—41no—
176Dic13#13712yes—
177C2×Q16—131no—
178C2×SD16—131no—
179C2×SD16—131no—
180C4⋊Q8—131no—
181C4⋊Q8—131no—
182C4⋊Q8—261no—
183C4⋊Q8—261no—
184C4⋊Q8—261no—
185C4⋊Q8C2×D1311yescharacteristic
186#127—131no—
187#124—131no—
188#124—261no—
189#124C2×D1311yescharacteristic
190#123—261no—
191#123—261no—
192C4×Q8—131no—
193C4×Q8—131no—
194C4×Q8—131no—
195C4×Q8—131no—
196C4×Q8—131no—
197C4×Q8—261no—
198C4×D4—131no—
199C4×D4—131no—
200C4×D4—261no—
201#107—131no—
202#107—131no—
203#107—131no—
204C4⋊C8—131no—
205C4⋊C8—131no—
206C4⋊C8—131no—
207#103—131no—
208#103—131no—
209#103C2×D1311yescharacteristic
210#103C2×D1311yescharacteristic
211#102—131no—
212#102—131no—
213#102—131no—
214#102—131no—
215#102C2×D1311yescharacteristic
216#102C2×D1311yescharacteristic
217#97—131no—
218#97C2×D1311yescharacteristic
219C4×C8—131no—
220C2×C13—81no—
221C2×C13#54811yescharacteristic
222C2×C13C2×#13711yescharacteristic
223C2×C13#57611yescharacteristic
224D13—81no—
225C2×Q8—21no—
226C2×Q8—131no—
227C2×Q8—131no—
228C2×Q8—261no—
229C2×Q8—261no—
230C2×Q8C22×D1311yescharacteristic
231C2×D4—131no—
232C2×D4—261no—
233C2×D4—261no—
234C2×D4C22×D1311yescharacteristic
235C22×C4—261no—
236C22×C4—261no—
237Q16—262no—
238SD16—262no—
239SD16—262no—
240C2×C8—131no—
241C2×C8—131no—
242C2×C8C22×D1311yescharacteristic
243C2×C8C22×D1311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—131no—
246C4⋊C4—131no—
247C4⋊C4—131no—
248C4⋊C4—131no—
249C4⋊C4—131no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4C22×D1311yescharacteristic
257C4⋊C4C22×D1311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C42—131no—
265C42—131no—
266C42—261no—
267C42—261no—
268C42—261no—
269C42—261no—
270C42C22×D1311yescharacteristic
271C13#337511yescharacteristic, complemented, Sylow
272C23—21no—
273C23—261no—
274Q8—21no—
275Q8—21no—
276Q8—81no—
277Q8—132no—
278Q8—262no—
279Q8—261no—
280Q8—1041no—
281Q8—1041no—
282D4—21no—
283D4—21no—
284D4—261no—
285D4—261no—
286D4—522no—
287D4—1041no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—1041no—
299C2×C4—1041no—
300C2×C4D4×D1311yescharacteristic
301C2×C4D4×D1311yescharacteristic
302C2×C4C23×D1311yescharacteristic
303C8—21no—
304C8—21no—
305C8—261no—
306C8—261no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—521no—
311C22—521no—
312C22—521no—
313C22C2×D4×D1311yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—132no—
320C4—261no—
321C4—261no—
322C4—261no—
323C4—262no—
324C4—521no—
325C4—521no—
326C4#41×D1311yescharacteristic
327C4#8825711yescharacteristic
328C2—81no—
329C2—1041no—
330C2#1171938211yescharacteristic
331C2#1171947911yescharacteristic
332C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#489C2
socleC22×C13C22×D4
prime radical#88194C22
hypercenter#489D13
hypocenterC13#3375
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #11719427C2semidirect
3. C13×#489C2semidirect
4. #11718748C2semidirect
5. #11718715C2semidirect
6. #11718459C2semidirect
7. #11718456C2semidirect
8. #11718455C2semidirect
9. #11718451C2semidirect
12. #11718420C2semidirect
13. #11718418C2semidirect
14. #11718371C2semidirect
15. #11718362C2semidirect
144. #489D13semidirect
271. C13#3375semidirect

Maximal subgroups

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

subgroupindex
#117194272
#117193862
C13×#4892
#117187482
#117187152
#117184592
#117184562
#117184552
#117184512
#117184232
#117184212
#117184202
#117184182
#117183712
#117183622
#337513