Finite Group Databasebeta

← #13117702

Subgroups — #13117702

Order 1664.

604 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88146C211yesmaximal, characteristic
2C2×C4⋊C4×D13C211yesmaximal, characteristic
3C2×#88126C211yesmaximal, characteristic
4C13×#387C211yesmaximal, characteristic, complemented
5#11718642C211yesmaximal, characteristic, complemented
6#11718633C211yesmaximal, characteristic, complemented
7C4×#6101C211yesmaximal, characteristic, complemented
8#11718328C211yesmaximal, characteristic
9#11718327C211yesmaximal, characteristic
10#11718325C211yesmaximal, characteristic
11#11718325C211yesmaximal, characteristic
12#11718315C211yesmaximal, characteristic, complemented
13#11718314C211yesmaximal, characteristic, complemented
14#11718310C211yesmaximal, characteristic, complemented
15#11718308C211yesmaximal, characteristic, complemented
16C22×C4×D13C2211yescharacteristic
17C22×C4×D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C42×C13C2211yescharacteristic
22C2×#6103C2211yescharacteristic
23C2×#6103C2211yescharacteristic
24C2×#6103C2211yescharacteristic
25C2×#6103C2211yescharacteristic
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
37C2×C4×Dic13C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39#88146—24no—
40C4⋊C4×D13C418yescomplemented
41#88126—24no—
42C13×#95C2211yescharacteristic
43C13×#95C2211yescharacteristic
44C13×#95C2211yescharacteristic
45C13×#95C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54C23×D13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C2×C4×D13—22no—
70C2×C4×D13—22no—
71C2×C4×D13—22no—
72C2×C4×D13—22no—
73C2×C4×D13—22no—
74C2×C4×D13—22no—
75C2×C4×D13C2×C414yes—
76C2×C4×D13C2×C414yes—
77C2×C4×D13C2×C414yes—
78C13×C4⋊C4—22no—
79C13×C4⋊C4C2×C414yes—
80C42×C13—22no—
81#6103—22no—
82#6103—22no—
83#6103—22no—
84#6103D414yes—
85C4⋊Dic13—22no—
86C4⋊Dic13C2×C414yes—
87#6101—22no—
88#6101—22no—
89#6101—22no—
90#6101—22no—
91#6101C2×C414yes—
92#6101C2×C414yes—
93C4×Dic13—22no—
94C4×Dic13—22no—
95C4×Dic13—22no—
96C4×Dic13—22no—
97C4×Dic13—22no—
98#2344—131nomaximal, Sylow
99C23×C13C2411yescharacteristic
100C22×D13—21no—
101C22×D13—21no—
102C22×D13—21no—
103C22×D13—21no—
104C22×D13C22×C412yes—
105C22×D13C2×D412yes—
106C22×D13#4112yes—
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×C13C22×C412yes—
125C2×C4×C13C22×C412yes—
126C2×C4×C13C22×C412yes—
127C2×C4×C13C2×D412yes—
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×Dic13—21no—
143C2×Dic13C22×C412yes—
144C2×Dic13C22×C412yes—
145C2×Dic13C22×C412yes—
146C2×Dic13C2×D412yes—
147C2×Dic13#4112yes—
148C2×Dic13#4112yes—
149C4×D13—28no—
150C4×D13—28no—
151C4×D13—28no—
152C2×#117—131no—
153C2×#117—131no—
154C22×C4⋊C4—131no—
155#389—131no—
156#389—131no—
157#387—131no—
158#387—131no—
159#387—131no—
160#387D1311yescharacteristic, complemented
161#381—131no—
162#381—131no—
163#380—131no—
164C4×C4⋊C4—131no—
165C4×C4⋊C4—131no—
166C4×C22⋊C4—131no—
167C22×C13C23×C411yescharacteristic
168C22×C13C22×D411yescharacteristic
169C22×C13C2×#4111yescharacteristic
170C22×C13C2×#4111yescharacteristic
171C22×C13C2×#4111yescharacteristic
172C22×C132−1+411yescharacteristic
173C22×C132−1+411yescharacteristic
174C2×D13—22no—
175C2×D13—22no—
176C2×D13—22no—
177C2×D13—22no—
178C2×D13—22no—
179C2×D13—22no—
180C2×D13C4×D414yes—
181C4×C13—22no—
182C4×C13—22no—
183C4×C13—22no—
184C4×C13—22no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188Dic13—22no—
189Dic13—22no—
190Dic13—22no—
191Dic13—41no—
192Dic13—41no—
193Dic13—41no—
194Dic13#11714yescomplemented
195C23×C4—131no—
196C23×C4—131no—
197C23×C4—131no—
198#117—264no—
199#117—264no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—138no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4C2×D1311yescharacteristic
210C2×C4⋊C4C2×D1311yescharacteristic
211C2×C22⋊C4—131no—
212C2×C22⋊C4—131no—
213C2×C22⋊C4—131no—
214C2×C22⋊C4—131no—
215C2×C42—131no—
216C2×C42—131no—
217C2×C42—131no—
218C2×C42—131no—
219C2×C42—131no—
220C2×C42C2×D1311yescharacteristic
221#95—131no—
222#95—131no—
223#95—131no—
224#95—131no—
225#95—131no—
226#95—131no—
227#95—131no—
228#95—131no—
229#95C2×D1311yescharacteristic
230#95C2×D1311yescharacteristic
231#95C2×D1311yescharacteristic
232#95C2×D1311yescharacteristic
233C2×C13C2×#11711yescharacteristic
234C2×C13C2×C4×D411yescharacteristic
235C2×C13#51911yescharacteristic
236C2×C13#54711yescharacteristic
237C2×C13#54711yescharacteristic
238C2×C13#55211yescharacteristic
239C2×C13#55211yescharacteristic
240D13—24no—
241C24—131no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—134no—
247C22×C4—134no—
248C22×C4—134no—
249C22×C4—131no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—262no—
253C22×C4—262no—
254C22×C4—262no—
255C22×C4—262no—
256C22×C4—262no—
257C22×C4—262no—
258C22×C4C22×D1311yescharacteristic
259C22×C4C22×D1311yescharacteristic
260C22×C4C22×D1311yescharacteristic
261C22×C4C22×D1311yescharacteristic
262C22×C4C22×D1311yescharacteristic
263C22×C4C22×D1311yescharacteristic
264C22×C4C22×D1311yescharacteristic
265C4⋊C4—22no—
266C4⋊C4—134no—
267C4⋊C4—134no—
268C4⋊C4—134no—
269C4⋊C4—262no—
270C4⋊C4—262no—
271C4⋊C4—262no—
272C4⋊C4—262no—
273C4⋊C4—262no—
274C4⋊C4C4×D1314yes—
275C22⋊C4—134no—
276C22⋊C4—262no—
277C22⋊C4—262no—
278C22⋊C4—262no—
279C42—22no—
280C42—262no—
281C42—262no—
282C42—262no—
283C42—262no—
284C42—262no—
285C13#234411yescharacteristic, complemented, Sylow
286C23—132no—
287C23—132no—
288C23—132no—
289C23—261no—
290C23—261no—
291C23—261no—
292C23—261no—
293C23C23×D1311yescharacteristic
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—268no—
318C2×C4—268no—
319C2×C4—268no—
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—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4C2×C4×D1312yes—
336C2×C4C2×C4×D1312yes—
337C2×C4C2×C4×D1312yes—
338C2×C4D4×D1312yes—
339C22—134no—
340C22—262no—
341C22—262no—
342C22—262no—
343C22—262no—
344C22—262no—
345C22—262no—
346C22C22×C4×D1311yescharacteristic
347C22C2×D4×D1311yescharacteristic
348C22#8825411yescharacteristic
349C22#41×D1311yescharacteristic
350C22#41×D1311yescharacteristic
351C22#41×D1311yescharacteristic
352C22#8825711yescharacteristic
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—134no—
361C4—262no—
362C4—262no—
363C4—262no—
364C4—521no—
365C4—521no—
366C4—521no—
367C2—264no—
368C2D13×#11711yescharacteristic
369C2C4×D4×D1311yescharacteristic
370C2#1171927711yescharacteristic
371C2#1171933611yescharacteristic
372C2#1171936011yescharacteristic
373C2#1171939811yescharacteristic
374C2#1171941311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#387C2
socle, cosocleC23×C13C24
prime radicalC23×D13C23
hypercenter#387D13
hypocenterC13#2344
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
4. C13×#387C2semidirect
5. #11718642C2semidirect
6. #11718633C2semidirect
7. C4×#6101C2semidirect
12. #11718315C2semidirect
13. #11718314C2semidirect
14. #11718310C2semidirect
15. #11718308C2semidirect
40. C4⋊C4×D13C4semidirect
160. #387D13semidirect
194. Dic13#117semidirect
285. C13#2344semidirect

Maximal subgroups

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

subgroupindex
C2×#881462
C2×C4⋊C4×D132
C2×#881262
C13×#3872
#117186422
#117186332
C4×#61012
#117183282
#117183272
#117183252
#117183152
#117183142
#117183102
#117183082
#234413