Finite Group Databasebeta

← #13119849

Subgroups — #13119849

Order 1664.

544 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88178C211yesmaximal, characteristic
2C2×#88132C211yesmaximal, characteristic
3C13×#385C211yesmaximal, characteristic
4C2×#88071C211yesmaximal, characteristic
5#11718646C211yesmaximal, characteristic, complemented
6#11718645C211yesmaximal, characteristic, complemented
7#11718640C211yesmaximal, characteristic, complemented
8#11718634C211yesmaximal, characteristic, complemented
9#11718611C211yesmaximal, characteristic
10#11718603C211yesmaximal, characteristic
11C22⋊C4×Dic13C211yesmaximal, characteristic
12#11718318C211yesmaximal, characteristic, complemented
13#11718317C211yesmaximal, characteristic, complemented
14#11718307C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C23×C4×C13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C23×Dic13C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C22×Dic26C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×C4⋊Dic13C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31#88178—24no—
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40#88132—24no—
41C13×#95C2211yescharacteristic
42C13×#95C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C24×C13C2311yescharacteristic
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—41no—
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×Dic13—22no—
64C22×Dic13—22no—
65C22×Dic13—41no—
66C22×Dic13—41no—
67C22×Dic13—41no—
68C22×Dic13Q814yescomplemented
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C2×Dic26—22no—
78C2×Dic26—22no—
79C2×Dic26—22no—
80C2×Dic26—22no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—41no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4Q814yescomplemented
87C22⋊Dic13—22no—
88C22⋊Dic13D414yes—
89C4⋊Dic13—22no—
90C4⋊Dic13—22no—
91C4⋊Dic13—22no—
92C4⋊Dic13—41no—
93#6101—22no—
94#6101—22no—
95#6101—22no—
96#6101—22no—
97#6101—41no—
98#6101—41no—
99C4×Dic13—41no—
100C4×Dic13—41no—
101#2549—131nomaximal, Sylow
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13C2×D412yes—
107C23×C13C2×Q812yes—
108C23×C13C2×Q812yes—
109C23×C13C2411yescharacteristic
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×C13—44no—
126C2×C4×C13C2×Q812yes—
127C2×C4×C13C2×Q812yes—
128C2×C4×C13#4112yes—
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×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—44no—
149C2×Dic13—44no—
150C2×Dic13C2×D412yes—
151C2×Dic13C2×D412yes—
152C2×Dic13C2×Q812yes—
153C2×Dic13C2×Q812yes—
154C2×Dic13#4112yes—
155Dic26—44no—
156Dic26—44no—
157C2×C22⋊Q8—131no—
158C2×C22⋊Q8—131no—
159#398—131no—
160#398—131no—
161#395—131no—
162#395—131no—
163#391—131no—
164#391—131no—
165#389—131no—
166#389—131no—
167#385—131no—
168#385D1311yescharacteristic
169#380—131no—
170C4×C22⋊C4—131no—
171C2×#95—131no—
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—22no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13C4⋊Q814yes—
179C22×C13C22×D411yescharacteristic
180C22×C13C22×Q811yescharacteristic
181C22×C13C22×Q811yescharacteristic
182C22×C13C2×#4111yescharacteristic
183C22×C13C2×#4111yescharacteristic
184C22×C13H(5,𝔽2)11yescharacteristic
185C22×C13H(5,𝔽2)11yescharacteristic
186C4×C13—22no—
187C4×C13—22no—
188C4×C13—22no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192Dic13—22no—
193Dic13—22no—
194Dic13—22no—
195Dic13—22no—
196Dic13—22no—
197Dic13—41no—
198Dic13—41no—
199Dic13—41no—
200C22×Q8—131no—
201C22×Q8—131no—
202C23×C4—131no—
203C23×C4—131no—
204C23×C4C2×D1311yescharacteristic
205C22⋊Q8—264no—
206C22⋊Q8—264no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4C2×D1311yescharacteristic
218C2×C4⋊C4C2×D1311yescharacteristic
219C2×C22⋊C4—131no—
220C2×C22⋊C4—131no—
221C2×C22⋊C4C2×D1311yescharacteristic
222C2×C22⋊C4C2×D1311yescharacteristic
223C2×C42—131no—
224C2×C42—131no—
225#95—131no—
226#95—131no—
227#95—131no—
228#95—131no—
229#95—131no—
230#95—131no—
231#95—131no—
232#95—131no—
233#95—131no—
234#95—131no—
235#95C2×D1311yescharacteristic
236#95C2×D1311yescharacteristic
237C2×C13—24no—
238C2×C13C2×C4⋊Q811yescharacteristic
239C2×C13#53311yescharacteristic
240C2×C13#54311yescharacteristic
241C2×C13#54611yescharacteristic
242C2×C13#54611yescharacteristic
243C2×C13#55411yescharacteristic
244C2×C13#55411yescharacteristic
245C24C22×D1311yescharacteristic
246C2×Q8—262no—
247C2×Q8—262no—
248C2×Q8—262no—
249C2×Q8—262no—
250C2×Q8—521no—
251C2×Q8—521no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—41no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—134no—
261C22×C4—131no—
262C22×C4—131no—
263C22×C4—131no—
264C22×C4—262no—
265C22×C4—262no—
266C22×C4—521no—
267C22×C4—521no—
268C22×C4—521no—
269C22×C4C22×D1311yescharacteristic
270C22×C4C22×D1311yescharacteristic
271C22×C4C22×D1311yescharacteristic
272C22×C4C22×D1311yescharacteristic
273C22×C4C22×D1311yescharacteristic
274C22×C4C22×D1311yescharacteristic
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—262no—
278C4⋊C4—262no—
279C4⋊C4—262no—
280C4⋊C4—262no—
281C4⋊C4—262no—
282C4⋊C4—262no—
283C4⋊C4—262no—
284C4⋊C4—521no—
285C4⋊C4—521no—
286C4⋊C4—521no—
287C22⋊C4—22no—
288C22⋊C4—134no—
289C22⋊C4—262no—
290C22⋊C4Dic2614yescomplemented
291C42—521no—
292C42—521no—
293C13#254911yescharacteristic, complemented, Sylow
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23C2×Dic2612yes—
299C23D4×D1312yes—
300C23Q8×D1312yes—
301C23C23×D1311yescharacteristic
302Q8—524no—
303Q8—524no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—44no—
320C2×C4—132no—
321C2×C4—132no—
322C2×C4—132no—
323C2×C4—132no—
324C2×C4—132no—
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×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—524no—
345C2×C4—524no—
346C2×C4C2×Dic2612yes—
347C2×C4C2×Dic2612yes—
348C2×C4#612912yes—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22#8814214yes—
356C22C22×Dic2611yescharacteristic
357C22C2×D4×D1311yescharacteristic
358C22C2×#612911yescharacteristic
359C22#8825111yescharacteristic
360C22C2×Q8×D1311yescharacteristic
361C22#41×D1311yescharacteristic
362C22#8825611yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—262no—
370C4—262no—
371C4—262no—
372C4—262no—
373C4—262no—
374C4—521no—
375C4—521no—
376C4—521no—
377C2—24no—
378C2C2×#8814211yescharacteristic
379C2#1171924411yescharacteristic
380C2#1171924811yescharacteristic
381C2#1171929611yescharacteristic
382C2#1171932711yescharacteristic
383C2#1171933911yescharacteristic
384C2#1171935911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#385C2
prime radicalC24×C13C23
hypercenter#385D13
hypocenterC13#2549
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
5. #11718646C2semidirect
6. #11718645C2semidirect
7. #11718640C2semidirect
8. #11718634C2semidirect
12. #11718318C2semidirect
13. #11718317C2semidirect
14. #11718307C2semidirect
15. #11718307C2semidirect
68. C22×Dic13Q8semidirect
86. C13×C22⋊C4Q8semidirect
290. C22⋊C4Dic26semidirect
293. C13#2549semidirect

Maximal subgroups

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

subgroupindex
C2×#881782
C2×#881322
C13×#3852
C2×#880712
#117186462
#117186452
#117186402
#117186342
#117186112
#117186032
C22⋊C4×Dic132
#117183182
#117183172
#117183072
#254913