Finite Group Databasebeta

← #13117996

Subgroups — #13117996

Order 1664.

464 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88132C211yesmaximal, characteristic
2C13×#388C211yesmaximal, characteristic
3#11718635C211yesmaximal, characteristic, complemented
4#11718633C211yesmaximal, characteristic, complemented
5#11718612C211yesmaximal, characteristic
6#11718605C211yesmaximal, characteristic
7#11718605C211yesmaximal, characteristic
8#11718604C211yesmaximal, characteristic
9#11718603C211yesmaximal, characteristic
10#11718594C211yesmaximal, characteristic, complemented
11#11718589C211yesmaximal, characteristic, complemented
12#11718316C211yesmaximal, characteristic, complemented
13#11718315C211yesmaximal, characteristic, complemented
14#11718313C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C23×Dic13C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C42×C13C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×C4×Dic13C2211yescharacteristic
35C2×C4×Dic13C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37#88132C418yescomplemented
38C13×#95C2211yescharacteristic
39C13×#95C2211yescharacteristic
40#88071C2211yescharacteristic
41#88071C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52C24×C13C2311yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×Dic13—41no—
60C22×Dic13—41no—
61C22×Dic13C2×C414yes—
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C2×Dic26—41no—
71C2×Dic26—41no—
72C2×Dic26C2×C414yes—
73C13×C4⋊C4—41no—
74C13×C22⋊C4—41no—
75C13×C22⋊C4—41no—
76C13×C22⋊C4C2×C414yes—
77C42×C13—41no—
78C22⋊Dic13—41no—
79C22⋊Dic13—41no—
80C22⋊Dic13C2×C414yes—
81C4⋊Dic13—41no—
82C4⋊Dic13C2×C414yes—
83#6101—41no—
84#6101—41no—
85#6101—41no—
86#6101—41no—
87#6101C2×C414yes—
88#6101C2×C414yes—
89C4×Dic13—41no—
90C4×Dic13—41no—
91C4×Dic13—41no—
92#2378—131nomaximal, Sylow
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13C22×C412yes—
100C23×C13C2411yescharacteristic
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13C22×C412yes—
118C2×C4×C13C22×C412yes—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—44no—
140C2×Dic13C22×C412yes—
141C2×Dic13C22×C412yes—
142C2×Dic13C22×C412yes—
143C2×Dic13C22×C412yes—
144Dic26—44no—
145C2×C22⋊Q8—131no—
146#391—131no—
147#391—131no—
148#389—131no—
149#389—131no—
150#388—131no—
151#388—131no—
152#388—131no—
153#388D1311yescharacteristic
154#387—131no—
155#387—131no—
156#387—131no—
157#387—131no—
158#381—131no—
159#380—131no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13—22no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13C23×C411yescharacteristic
168C22×C13H(5,𝔽2)11yescharacteristic
169C22×C13H(5,𝔽2)11yescharacteristic
170C22×C13H(5,𝔽2)11yescharacteristic
171C22×C132−1+411yescharacteristic
172C22×C132−1+411yescharacteristic
173C22×C132−1+411yescharacteristic
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180Dic13—22no—
181Dic13—22no—
182Dic13—22no—
183Dic13—22no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188C22×Q8—131no—
189C23×C4—131no—
190C22⋊Q8—138no—
191C2×C4⋊C4—131no—
192C2×C4⋊C4—131no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4C2×D1311yescharacteristic
200C2×C22⋊C4—131no—
201C2×C22⋊C4—131no—
202C2×C22⋊C4—131no—
203C2×C22⋊C4C2×D1311yescharacteristic
204C2×C22⋊C4C2×D1311yescharacteristic
205C2×C22⋊C4C2×D1311yescharacteristic
206C2×C42—131no—
207C2×C42—131no—
208C2×C42—131no—
209C2×C42C2×D1311yescharacteristic
210#95—131no—
211#95—131no—
212#95—131no—
213#95—131no—
214#95—131no—
215#95—131no—
216#95—131no—
217#95—131no—
218#95—131no—
219#95—131no—
220#95—131no—
221#95—131no—
222#95C2×D1311yescharacteristic
223#95C2×D1311yescharacteristic
224C2×C13—42no—
225C2×C13#51811yescharacteristic
226C2×C13#51911yescharacteristic
227C2×C13#52011yescharacteristic
228C2×C13#56211yescharacteristic
229C2×C13#56211yescharacteristic
230C2×C13#56311yescharacteristic
231C2×C13#56311yescharacteristic
232C24C22×D1311yescharacteristic
233C2×Q8—134no—
234C2×Q8—521no—
235C2×Q8—521no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—134no—
241C22×C4—131no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—521no—
246C22×C4—521no—
247C22×C4C22×D1311yescharacteristic
248C22×C4C22×D1311yescharacteristic
249C22×C4C22×D1311yescharacteristic
250C22×C4C22×D1311yescharacteristic
251C22×C4C22×D1311yescharacteristic
252C22×C4C22×D1311yescharacteristic
253C4⋊C4—41no—
254C4⋊C4—134no—
255C4⋊C4—134no—
256C4⋊C4—134no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—134no—
265C22⋊C4—521no—
266C22⋊C4—521no—
267C22⋊C4C4×D1314yes—
268C42—41no—
269C42—521no—
270C42—521no—
271C42—521no—
272C13#237811yescharacteristic, complemented, Sylow
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23C2×C4×D1312yes—
280C23C23×D1311yescharacteristic
281Q8—524no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—132no—
299C2×C4—132no—
300C2×C4—132no—
301C2×C4—132no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—524no—
323C2×C4C2×C4×D1312yes—
324C2×C4C2×C4×D1312yes—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22C22×C4×D1311yescharacteristic
333C22#8825111yescharacteristic
334C22#8825111yescharacteristic
335C22#8825611yescharacteristic
336C22#8825711yescharacteristic
337C22#8825711yescharacteristic
338C22#8825711yescharacteristic
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—262no—
346C4—262no—
347C4—262no—
348C4—262no—
349C4—521no—
350C4—521no—
351C4—521no—
352C4—521no—
353C2—42no—
354C2#1171922111yescharacteristic
355C2#1171925011yescharacteristic
356C2#1171925111yescharacteristic
357C2#1171932611yescharacteristic
358C2#1171937211yescharacteristic
359C2#1171937711yescharacteristic
360C2#1171941711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#388C2
socle, cosocleC23×C13C24
prime radicalC24×C13C23
hypercenter#388D13
hypocenterC13#2378
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. #11718635C2semidirect
4. #11718633C2semidirect
10. #11718594C2semidirect
11. #11718589C2semidirect
12. #11718316C2semidirect
13. #11718315C2semidirect
14. #11718313C2semidirect
15. #11718307C2semidirect
37. #88132C4semidirect
272. C13#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#881322
C13×#3882
#117186352
#117186332
#117186122
#117186052
#117186042
#117186032
#117185942
#117185892
#117183162
#117183152
#117183132
#117183072
#237813