Finite Group Databasebeta

← #13118356

Subgroups — #13118356

Order 1664.

500 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88150C211yesmaximal, characteristic
2C2×#88141C211yesmaximal, characteristic, complemented
3C13×#398C211yesmaximal, characteristic, complemented
4#11718653C211yesmaximal, characteristic
5#11718653C211yesmaximal, characteristic
6#11718651C211yesmaximal, characteristic
7#11718639C211yesmaximal, characteristic, complemented
8#11718637C211yesmaximal, characteristic, complemented
9#11718633C211yesmaximal, characteristic, complemented
10#11718331C211yesmaximal, characteristic
11#11718328C211yesmaximal, characteristic
12#11718327C211yesmaximal, characteristic
13#11718318C211yesmaximal, characteristic, complemented
14#11718313C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×C4×D13C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×#6103C2211yescharacteristic
23C2×#6103C2211yescharacteristic
24C2×#6103C2211yescharacteristic
25C2×#6103C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41#88150—24no—
42#88141—24no—
43C13×#95C2211yescharacteristic
44C13×#95C2211yescharacteristic
45C13×#95C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C23×D13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C2×C4×D13—22no—
69C2×C4×D13—22no—
70C2×C4×D13—22no—
71C2×Dic26—22no—
72C2×Dic26—22no—
73C2×Dic26D414yes—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78#6103—22no—
79#6103—22no—
80#6103—22no—
81#6103—41no—
82#6103—41no—
83#6103Q814yescomplemented
84C4⋊Dic13—41no—
85#6101—22no—
86#6101—22no—
87#6101—22no—
88#6101—22no—
89#6101—22no—
90#6101—22no—
91#6101—22no—
92#6101—41no—
93C4×Dic13—22no—
94C4×Dic13—22no—
95C4×Dic13—22no—
96C4×Dic13—22no—
97#2423—131nomaximal, Sylow
98C23×C13C2411yescharacteristic
99C22×D13—21no—
100C22×D13—21no—
101C22×D13—21no—
102C22×D13—21no—
103C22×D13—21no—
104C22×D13—21no—
105C22×D13C2×Q812yes—
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×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13C2×D412yes—
126C2×C4×C13C2×Q812yes—
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—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13C2×D412yes—
143C2×Dic13C2×D412yes—
144C2×Dic13C2×Q812yes—
145C2×Dic13#4112yes—
146C2×Dic13#4112yes—
147C2×Dic13#4112yes—
148C4×D13—44no—
149Dic26—28no—
150C2×C22⋊Q8—131no—
151C2×C4×Q8—131no—
152#399—131no—
153#399—131no—
154#398—131no—
155#398D1311yescharacteristic, complemented
156#391—131no—
157#389—131no—
158#388—131no—
159#388—131no—
160#387—131no—
161#387—131no—
162#384—131no—
163#380—131no—
164C4×C22⋊C4—131no—
165C22×C13C22×D411yescharacteristic
166C22×C13C22×Q811yescharacteristic
167C22×C13C2×#4111yescharacteristic
168C22×C13C2×#4111yescharacteristic
169C22×C13C2×#4111yescharacteristic
170C22×C13H(5,𝔽2)11yescharacteristic
171C22×C132−1+411yescharacteristic
172C2×D13—22no—
173C2×D13—22no—
174C2×D13—22no—
175C2×D13—41no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—41no—
179C4×C13—22no—
180C4×C13—22no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186Dic13—22no—
187Dic13—22no—
188Dic13—22no—
189Dic13—41no—
190Dic13—41no—
191Dic13—41no—
192Dic13#12314yes—
193C22×Q8—131no—
194C23×C4—131no—
195C22⋊Q8—264no—
196C4×Q8—264no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4C2×D1311yescharacteristic
207C2×C4⋊C4C2×D1311yescharacteristic
208C2×C4⋊C4C2×D1311yescharacteristic
209C2×C4⋊C4C2×D1311yescharacteristic
210C2×C22⋊C4—131no—
211C2×C22⋊C4—131no—
212C2×C22⋊C4—131no—
213C2×C22⋊C4—131no—
214C2×C22⋊C4—131no—
215C2×C22⋊C4—131no—
216C2×C42—131no—
217C2×C42—131no—
218C2×C42—131no—
219C2×C42—131no—
220#95—131no—
221#95—131no—
222#95—131no—
223#95—131no—
224#95—131no—
225#95—131no—
226#95—131no—
227#95C2×D1311yescharacteristic
228#95C2×D1311yescharacteristic
229#95C2×D1311yescharacteristic
230C2×C13C2×#12311yescharacteristic
231C2×C13#53311yescharacteristic
232C2×C13#54211yescharacteristic
233C2×C13D4×Q811yescharacteristic
234C2×C13#55011yescharacteristic
235C2×C13#55211yescharacteristic
236C2×C13#55411yescharacteristic
237D13—42no—
238C24—131no—
239C2×Q8—134no—
240C2×Q8—262no—
241C2×Q8—262no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—262no—
250C22×C4—262no—
251C22×C4—262no—
252C22×C4C22×D1311yescharacteristic
253C22×C4C22×D1311yescharacteristic
254C22×C4C22×D1311yescharacteristic
255C22×C4C22×D1311yescharacteristic
256C22×C4C22×D1311yescharacteristic
257C22×C4C22×D1311yescharacteristic
258C22×C4C22×D1311yescharacteristic
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—262no—
264C4⋊C4—262no—
265C4⋊C4—262no—
266C4⋊C4—262no—
267C4⋊C4—262no—
268C4⋊C4—262no—
269C4⋊C4—262no—
270C4⋊C4—521no—
271C4⋊C4—521no—
272C22⋊C4—134no—
273C22⋊C4—262no—
274C22⋊C4—262no—
275C22⋊C4—262no—
276C22⋊C4—521no—
277C22⋊C4—521no—
278C42—262no—
279C42—262no—
280C42—262no—
281C42—262no—
282C13#242311yescharacteristic, complemented, Sylow
283C23—132no—
284C23—261no—
285C23—261no—
286C23—261no—
287C23—261no—
288C23—261no—
289C23—261no—
290C23C23×D1311yescharacteristic
291Q8—268no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—132no—
312C2×C4—132no—
313C2×C4—132no—
314C2×C4—132no—
315C2×C4—132no—
316C2×C4—132no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—524no—
333C2×C4D4×D1312yes—
334C2×C4Q8×D1312yes—
335C22—262no—
336C22—262no—
337C22—262no—
338C22—521no—
339C22—521no—
340C22—521no—
341C22—521no—
342C22C2×D4×D1311yescharacteristic
343C22#8825111yescharacteristic
344C22C2×Q8×D1311yescharacteristic
345C22#8825411yescharacteristic
346C22#41×D1311yescharacteristic
347C22#41×D1311yescharacteristic
348C22#41×D1311yescharacteristic
349C4—22no—
350C4—22no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—134no—
357C4—262no—
358C4—262no—
359C4—262no—
360C4—521no—
361C4—521no—
362C4—521no—
363C2—522no—
364C2#1171930411yescharacteristic
365C2#1171934111yescharacteristic
366C2#1171934511yescharacteristic
367C2D13×#12311yescharacteristic
368C2#1171939311yescharacteristic
369C2#1171939811yescharacteristic
370C2#1171943211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC23×D13C23
hypercenter#398D13
hypocenterC13#2423
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#88141C2semidirect
3. C13×#398C2semidirect
7. #11718639C2semidirect
8. #11718637C2semidirect
9. #11718633C2semidirect
13. #11718318C2semidirect
14. #11718313C2semidirect
15. #11718307C2semidirect
83. #6103Q8semidirect
155. #398D13semidirect
282. C13#2423semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C2×#881412
C13×#3982
#117186532
#117186512
#117186392
#117186372
#117186332
#117183312
#117183282
#117183272
#117183182
#117183132
#117183072
#242313