Finite Group Databasebeta

← #13118537

Subgroups — #13118537

Order 1664.

608 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88178C211yesmaximal, characteristic
2C22×#6101C211yesmaximal, characteristic
3C2×#88142C211yesmaximal, characteristic, complemented
4C2×#88132C211yesmaximal, characteristic
5C13×#385C211yesmaximal, characteristic
6#11718645C211yesmaximal, characteristic, complemented
7#11718640C211yesmaximal, characteristic, complemented
8#11718637C211yesmaximal, characteristic, complemented
9#11718611C211yesmaximal, characteristic
10#11718603C211yesmaximal, characteristic
11C22⋊C4×Dic13C211yesmaximal, characteristic
12#11718318C211yesmaximal, characteristic, complemented
13#11718317C211yesmaximal, characteristic, complemented
14#11718308C211yesmaximal, characteristic, complemented
15#11718308C211yesmaximal, 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×#6101—24no—
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×#6101C2211yescharacteristic
42C2×#6101C2211yescharacteristic
43C2×C4×Dic13C2211yescharacteristic
44C2×C4×Dic13C2211yescharacteristic
45#88142—24no—
46#88132—24no—
47C13×#95C2211yescharacteristic
48C13×#95C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54#88071C2211yescharacteristic
55C24×C13C2311yescharacteristic
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—41no—
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—22no—
69C22×Dic13—41no—
70C22×Dic13Q814yescomplemented
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C2×Dic26—22no—
80C2×Dic26—22no—
81C2×Dic26—22no—
82C2×Dic26—22no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—41no—
87C13×C22⋊C4—22no—
88C13×C22⋊C4Q814yescomplemented
89C22⋊Dic13—22no—
90C22⋊Dic13D414yes—
91C4⋊Dic13—22no—
92C4⋊Dic13—22no—
93C4⋊Dic13—22no—
94C4⋊Dic13—41no—
95#6101—22no—
96#6101—22no—
97#6101—22no—
98#6101—22no—
99#6101—22no—
100#6101—22no—
101#6101—22no—
102#6101—22no—
103#6101—22no—
104#6101D414yes—
105C4×Dic13—22no—
106C4×Dic13—22no—
107#2440—131nomaximal, Sylow
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13C2×D412yes—
113C23×C13C2×Q812yes—
114C23×C13C2×Q812yes—
115C23×C13C2411yescharacteristic
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—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—44no—
132C2×C4×C13C2×D412yes—
133C2×C4×C13C2×Q812yes—
134C2×C4×C13C2×Q812yes—
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—28no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—44no—
154C2×Dic13C2×D412yes—
155C2×Dic13C2×D412yes—
156C2×Dic13C2×D412yes—
157C2×Dic13C2×D412yes—
158C2×Dic13C2×Q812yes—
159C2×Dic13C2×Q812yes—
160C2×Dic13#4112yes—
161Dic26—44no—
162Dic26—44no—
163C2×C4⋊Q8—131no—
164C2×C22⋊Q8—131no—
165C2×C22⋊Q8—131no—
166C22×C4⋊C4—131no—
167#398—131no—
168#398—131no—
169#395—131no—
170#395—131no—
171#389—131no—
172#389—131no—
173#385—131no—
174#385D1311yescharacteristic
175#384—131no—
176#380—131no—
177C4×C22⋊C4—131no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—22no—
183C22×C13—22no—
184C22×C13C4⋊Q814yescomplemented
185C22×C13C22×D411yescharacteristic
186C22×C13C22×D411yescharacteristic
187C22×C13C22×Q811yescharacteristic
188C22×C13C22×Q811yescharacteristic
189C22×C13C2×#4111yescharacteristic
190C22×C13H(5,𝔽2)11yescharacteristic
191C22×C132−1+411yescharacteristic
192C4×C13—22no—
193C4×C13—22no—
194C4×C13—22no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—41no—
198Dic13—22no—
199Dic13—22no—
200Dic13—22no—
201Dic13—22no—
202Dic13—41no—
203Dic13—41no—
204Dic13—41no—
205Dic13C22⋊Q814yescomplemented
206C22×Q8—131no—
207C22×Q8—131no—
208C23×C4—131no—
209C23×C4—131no—
210C23×C4C2×D1311yescharacteristic
211C4⋊Q8—264no—
212C22⋊Q8—264no—
213C22⋊Q8—264no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—131no—
219C2×C4⋊C4—131no—
220C2×C4⋊C4—131no—
221C2×C4⋊C4—131no—
222C2×C4⋊C4—131no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4—131no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4—131no—
228C2×C4⋊C4—264no—
229C2×C4⋊C4C2×D1311yescharacteristic
230C2×C4⋊C4C2×D1311yescharacteristic
231C2×C22⋊C4—131no—
232C2×C22⋊C4—131no—
233C2×C22⋊C4C2×D1311yescharacteristic
234C2×C22⋊C4C2×D1311yescharacteristic
235C2×C42—131no—
236C2×C42—131no—
237#95—131no—
238#95—131no—
239#95—131no—
240#95—131no—
241#95—131no—
242#95—131no—
243#95C2×D1311yescharacteristic
244#95C2×D1311yescharacteristic
245C2×C13—24no—
246C2×C13C2×C22⋊Q811yescharacteristic
247C2×C13C2×C4⋊Q811yescharacteristic
248C2×C13#54411yescharacteristic
249C2×C13D4211yescharacteristic
250C2×C13#54711yescharacteristic
251C2×C13D4×Q811yescharacteristic
252C2×C13#55411yescharacteristic
253C24C22×D1311yescharacteristic
254C2×Q8—262no—
255C2×Q8—262no—
256C2×Q8—262no—
257C2×Q8—262no—
258C2×Q8—521no—
259C2×Q8—521no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4—131no—
264C22×C4—134no—
265C22×C4—131no—
266C22×C4—131no—
267C22×C4—131no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—131no—
271C22×C4—131no—
272C22×C4—262no—
273C22×C4—262no—
274C22×C4—262no—
275C22×C4—262no—
276C22×C4—521no—
277C22×C4C22×D1311yescharacteristic
278C22×C4C22×D1311yescharacteristic
279C22×C4C22×D1311yescharacteristic
280C22×C4C22×D1311yescharacteristic
281C22×C4C22×D1311yescharacteristic
282C22×C4C22×D1311yescharacteristic
283C4⋊C4—22no—
284C4⋊C4—41no—
285C4⋊C4—134no—
286C4⋊C4—262no—
287C4⋊C4—262no—
288C4⋊C4—262no—
289C4⋊C4—262no—
290C4⋊C4—262no—
291C4⋊C4—262no—
292C4⋊C4—262no—
293C4⋊C4—262no—
294C4⋊C4—262no—
295C4⋊C4—262no—
296C4⋊C4—262no—
297C4⋊C4—262no—
298C4⋊C4—521no—
299C22⋊C4—22no—
300C22⋊C4—134no—
301C22⋊C4—262no—
302C22⋊C4Dic2614yescomplemented
303C42—262no—
304C42—262no—
305C13#244011yescharacteristic, complemented, Sylow
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23C2×Dic2612yes—
311C23D4×D1312yes—
312C23Q8×D1312yes—
313C23C23×D1311yescharacteristic
314Q8—524no—
315Q8—524no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—44no—
332C2×C4—132no—
333C2×C4—132no—
334C2×C4—132no—
335C2×C4—132no—
336C2×C4—132no—
337C2×C4—132no—
338C2×C4—132no—
339C2×C4—268no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—524no—
358C2×C4C2×Dic2612yes—
359C2×C4C2×Dic2612yes—
360C2×C4D4×D1312yes—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22#8814214yescomplemented
368C22C22×Dic2611yescharacteristic
369C22C2×D4×D1311yescharacteristic
370C22C2×D4×D1311yescharacteristic
371C22#8825111yescharacteristic
372C22C2×Q8×D1311yescharacteristic
373C22#41×D1311yescharacteristic
374C22#8825711yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—134no—
382C4—262no—
383C4—262no—
384C4—262no—
385C4—262no—
386C4—521no—
387C4—521no—
388C4—521no—
389C2—24no—
390C2C2×#8814211yescharacteristic
391C2D4×Dic2611yescharacteristic
392C2#1171924411yescharacteristic
393C2#1171929511yescharacteristic
394C2#1171932811yescharacteristic
395C2D13×C22⋊Q811yescharacteristic
396C2#1171936011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#385C2
prime radicalC24×C13C23
hypercenter#385D13
hypocenterC13#2440
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. C2×#88142C2semidirect
6. #11718645C2semidirect
7. #11718640C2semidirect
8. #11718637C2semidirect
12. #11718318C2semidirect
13. #11718317C2semidirect
14. #11718308C2semidirect
15. #11718308C2semidirect
70. C22×Dic13Q8semidirect
88. C13×C22⋊C4Q8semidirect
184. C22×C13C4⋊Q8semidirect
205. Dic13C22⋊Q8semidirect
302. C22⋊C4Dic26semidirect
305. C13#2440semidirect
367. C22#88142semidirect

Maximal subgroups

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

subgroupindex
C2×#881782
C22×#61012
C2×#881422
C2×#881322
C13×#3852
#117186452
#117186402
#117186372
#117186112
#117186032
C22⋊C4×Dic132
#117183182
#117183172
#117183082
#244013