Finite Group Databasebeta

← #13127653

Subgroups — #13127653

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#11719264C211yesmaximal, characteristic
3C13×#474C211yesmaximal, characteristic, complemented
4#11718750C211yesmaximal, characteristic, complemented
5#11718679C211yesmaximal, characteristic, complemented
6#11718551C211yesmaximal, characteristic, complemented
7#11718550C211yesmaximal, characteristic, complemented
8#11718536C211yesmaximal, characteristic, complemented
9#11718534C211yesmaximal, characteristic, complemented
10#11718506C211yesmaximal, characteristic, complemented
11#11718489C211yesmaximal, characteristic, complemented
12#11718428C211yesmaximal, characteristic, complemented
13#11718426C211yesmaximal, characteristic, complemented
14#11718423C211yesmaximal, characteristic
15#11718421C211yesmaximal, characteristic
16C13×C4⋊Q8C2211yescharacteristic
17C4×D4×C13C2211yescharacteristic
18#88198—21no—
19#88198—21no—
20#88194C2211yescharacteristic
21#88190C2211yescharacteristic
22C2×#6105C2211yescharacteristic
23#88183—21no—
24C4×C22⋊D13—21no—
25C2×Dic52C2211yescharacteristic
26C2×#6095C2211yescharacteristic
27#88147C2211yescharacteristic
28#88142—21no—
29#88142C2211yescharacteristic
30#88142C2211yescharacteristic
31#88141—21no—
32#88141C2211yescharacteristic
33#88141C2211yescharacteristic
34#88141C2211yescharacteristic
35#88139—21no—
36#88137—21no—
37#88129C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#102C2211yescharacteristic
45#88072C2211yescharacteristic
46#88061C2211yescharacteristic
47#88056C2211yescharacteristic
48#88055C2211yescharacteristic
49#88054C2211yescharacteristic
50#88054C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C2×D52C2311yescharacteristic
65C2×C4×D13—21no—
66C2×Dic26—21no—
67C2×Dic26—21no—
68C2×Dic26D411yescharacteristic
69C2×Dic26C2311yescharacteristic
70C2×Dic26C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C42×C13C2311yescharacteristic
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81#6105—22no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85C4⋊Dic13D411yescharacteristic
86C4⋊Dic13C2311yescharacteristic
87#6101—21no—
88#6101—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101D411yescharacteristic
94#6101D411yescharacteristic
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13C2311yescharacteristic
100C4×Dic13C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103Dic52—22no—
104#6095—22no—
105#3375—131nomaximal, Sylow
106C23×C13—21no—
107C22×D13—21no—
108Q8×C13—81no—
109D4×C13—21no—
110D4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—81no—
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2411yescharacteristic
118C22⋊D13—42no—
119C22⋊D13—81no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13C2×D411yescharacteristic
124C2×Dic13C2×D411yescharacteristic
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127D52—21no—
128D52—21no—
129C4×D13—81no—
130Dic26—21no—
131Dic26—22no—
132Dic26—21no—
133Dic26—21no—
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#489—131no—
145#486—131no—
146#477—131no—
147#474—131no—
148#474D1311yescharacteristic, complemented
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—131no—
189#124—261no—
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—261no—
200C4×D4C2×D1311yescharacteristic
201#107—131no—
202#107C2×D1311yescharacteristic
203#107C2×D1311yescharacteristic
204C4⋊C8—131no—
205C4⋊C8—131no—
206C4⋊C8C2×D1311yescharacteristic
207#103—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#102—131no—
212#102—131no—
213#102—131no—
214#102—131no—
215#102C2×D1311yescharacteristic
216#102C2×D1311yescharacteristic
217#97—131no—
218#97—131no—
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—131no—
229C2×Q8—261no—
230C2×Q8—261no—
231C2×D4—131no—
232C2×D4—261no—
233C2×D4—261no—
234C2×D4C22×D1311yescharacteristic
235C22×C4—21no—
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—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4C22×D1311yescharacteristic
256C4⋊C4C22×D1311yescharacteristic
257C4⋊C4C22×D1311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—261no—
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—81no—
275Q8—132no—
276Q8—262no—
277Q8—261no—
278Q8—261no—
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—81no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
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#8825411yescharacteristic
327C4#41×D1311yescharacteristic
328C2—81no—
329C2—1041no—
330C2#1171933811yescharacteristic
331C2#1171946211yescharacteristic
332C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radical#88194C22
hypercenter#474D13
hypocenterC13#3375
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719427C2semidirect
3. C13×#474C2semidirect
4. #11718750C2semidirect
5. #11718679C2semidirect
6. #11718551C2semidirect
7. #11718550C2semidirect
8. #11718536C2semidirect
9. #11718534C2semidirect
10. #11718506C2semidirect
11. #11718489C2semidirect
12. #11718428C2semidirect
13. #11718426C2semidirect
148. #474D13semidirect
271. C13#3375semidirect

Maximal subgroups

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

subgroupindex
#117194272
#117192642
C13×#4742
#117187502
#117186792
#117185512
#117185502
#117185362
#117185342
#117185062
#117184892
#117184282
#117184262
#117184232
#117184212
#337513