Finite Group Databasebeta

← #13117913

Subgroups — #13117913

Order 1664.

548 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88150C211yesmaximal, characteristic
2C13×#387C211yesmaximal, characteristic, complemented
3#11718650C211yesmaximal, characteristic
4C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
5#11718635C211yesmaximal, characteristic, complemented
6C4×#6103C211yesmaximal, characteristic
7C4×#6101C211yesmaximal, characteristic, complemented
8#11718329C211yesmaximal, characteristic
9#11718327C211yesmaximal, characteristic
10#11718327C211yesmaximal, characteristic
11D13×#95C211yesmaximal, characteristic
12#11718316C211yesmaximal, characteristic, complemented
13#11718313C211yesmaximal, characteristic, complemented
14#11718313C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×C4×D13C2211yescharacteristic
17C22×C4×D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C42×C13C2211yescharacteristic
23C2×#6103C2211yescharacteristic
24C2×#6103C2211yescharacteristic
25C2×#6103C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×C4×Dic13C2211yescharacteristic
33C2×C4×Dic13C2211yescharacteristic
34C2×C4×Dic13C2211yescharacteristic
35C2×C4×Dic13C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37#88150C418yescomplemented
38C13×#95C2211yescharacteristic
39C13×#95C2211yescharacteristic
40C13×#95C2211yescharacteristic
41C13×#95C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52C23×D13C2311yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×Dic13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C2×C4×D13—22no—
68C2×C4×D13—22no—
69C2×C4×D13—22no—
70C2×C4×D13—22no—
71C2×C4×D13—41no—
72C2×C4×D13—41no—
73C2×C4×D13—41no—
74C2×C4×D13—41no—
75C2×C4×D13C2×C414yes—
76C2×Dic26—41no—
77C2×Dic26—41no—
78C2×Dic26C2×C414yescomplemented
79C13×C4⋊C4—41no—
80C13×C4⋊C4C2×C414yescomplemented
81C42×C13—41no—
82#6103—22no—
83#6103C2×C414yes—
84#6103C2×C414yes—
85#6103Q814yescomplemented
86C4⋊Dic13—22no—
87#6101—22no—
88#6101—41no—
89#6101C2×C414yescomplemented
90#6101C2×C414yescomplemented
91C4×Dic13—22no—
92C4×Dic13—22no—
93C4×Dic13—41no—
94C4×Dic13—41no—
95C4×Dic13—41no—
96#2368—131nomaximal, Sylow
97C23×C13C2411yescharacteristic
98C22×D13—21no—
99C22×D13—21no—
100C22×D13—21no—
101C22×D13—21no—
102C22×D13C22×C412yes—
103C22×D13C2×Q812yes—
104C22×D13#4112yes—
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×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13C22×C412yes—
123C2×C4×C13C22×C412yes—
124C2×C4×C13C22×C412yes—
125C2×C4×C13C2×Q812yes—
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—21no—
140C2×Dic13—21no—
141C2×Dic13C22×C412yes—
142C2×Dic13C22×C412yes—
143C2×Dic13C22×C412yes—
144C2×Dic13C2×Q812yes—
145C2×Dic13#4112yes—
146C2×Dic13#4112yes—
147C4×D13—44no—
148C4×D13—44no—
149C4×D13—44no—
150Dic26—44no—
151C2×C22⋊Q8—131no—
152#391—131no—
153#391—131no—
154#387—131no—
155#387—131no—
156#387—131no—
157#387D1311yescharacteristic, complemented
158#385—131no—
159#385—131no—
160C4×C4⋊C4—131no—
161C4×C4⋊C4—131no—
162C4×C22⋊C4—131no—
163C4×C22⋊C4—131no—
164C4×C22⋊C4—131no—
165C2×#95—131no—
166C22×C13C23×C411yescharacteristic
167C22×C13C22×Q811yescharacteristic
168C22×C13C2×#4111yescharacteristic
169C22×C13C2×#4111yescharacteristic
170C22×C13C2×#4111yescharacteristic
171C22×C13H(5,𝔽2)11yescharacteristic
172C22×C13H(5,𝔽2)11yescharacteristic
173C2×D13—22no—
174C2×D13—22no—
175C2×D13—22no—
176C2×D13—22no—
177C2×D13—22no—
178C2×D13—22no—
179C2×D13C4×Q814yes—
180C4×C13—22no—
181C4×C13—22no—
182C4×C13—22no—
183C4×C13—22no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—41no—
187Dic13—22no—
188Dic13—22no—
189Dic13—22no—
190Dic13—22no—
191Dic13—22no—
192Dic13—22no—
193Dic13—41no—
194C22×Q8—131no—
195C23×C4—131no—
196C23×C4—131no—
197C23×C4—131no—
198C22⋊Q8—138no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4C2×D1311yescharacteristic
205C2×C4⋊C4C2×D1311yescharacteristic
206C2×C22⋊C4—131no—
207C2×C22⋊C4—131no—
208C2×C22⋊C4—131no—
209C2×C22⋊C4—131no—
210C2×C42—131no—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42—131no—
214C2×C42—131no—
215C2×C42C2×D1311yescharacteristic
216#95—131no—
217#95—131no—
218#95—131no—
219#95—131no—
220#95—131no—
221#95—131no—
222#95—131no—
223#95—131no—
224#95—131no—
225#95—131no—
226#95C2×D1311yescharacteristic
227#95C2×D1311yescharacteristic
228#95C2×D1311yescharacteristic
229#95C2×D1311yescharacteristic
230C2×C13C2×C4×Q811yescharacteristic
231C2×C13C4×#4111yescharacteristic
232C2×C13#51811yescharacteristic
233C2×C13#55111yescharacteristic
234C2×C13#55111yescharacteristic
235C2×C13#55411yescharacteristic
236C2×C13#55411yescharacteristic
237D13—24no—
238C24—131no—
239C2×Q8—134no—
240C2×Q8—521no—
241C2×Q8—521no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—134no—
249C22×C4—131no—
250C22×C4—262no—
251C22×C4—262no—
252C22×C4—262no—
253C22×C4—262no—
254C22×C4—521no—
255C22×C4—521no—
256C22×C4—521no—
257C22×C4—521no—
258C22×C4C22×D1311yescharacteristic
259C22×C4C22×D1311yescharacteristic
260C22×C4C22×D1311yescharacteristic
261C22×C4C22×D1311yescharacteristic
262C22×C4C22×D1311yescharacteristic
263C22×C4C22×D1311yescharacteristic
264C22×C4C22×D1311yescharacteristic
265C4⋊C4—41no—
266C4⋊C4—134no—
267C4⋊C4—134no—
268C4⋊C4—262no—
269C4⋊C4—262no—
270C4⋊C4—521no—
271C4⋊C4C4×D1314yescomplemented
272C22⋊C4—134no—
273C22⋊C4—134no—
274C22⋊C4—134no—
275C22⋊C4—262no—
276C42—41no—
277C42—262no—
278C42—262no—
279C42—521no—
280C42—521no—
281C42—521no—
282C13#236811yescharacteristic, complemented, Sylow
283C23—132no—
284C23—132no—
285C23—132no—
286C23—261no—
287C23—261no—
288C23—261no—
289C23—261no—
290C23C23×D1311yescharacteristic
291Q8—524no—
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—132no—
310C2×C4—132no—
311C2×C4—132no—
312C2×C4—132no—
313C2×C4—132no—
314C2×C4—132no—
315C2×C4—261no—
316C2×C4—261no—
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—524no—
331C2×C4—524no—
332C2×C4—524no—
333C2×C4C2×C4×D1312yes—
334C2×C4C2×C4×D1312yes—
335C2×C4C2×C4×D1312yes—
336C2×C4Q8×D1312yes—
337C22—134no—
338C22—262no—
339C22—262no—
340C22—262no—
341C22—262no—
342C22—262no—
343C22—262no—
344C22C22×C4×D1311yescharacteristic
345C22#8825111yescharacteristic
346C22C2×Q8×D1311yescharacteristic
347C22#41×D1311yescharacteristic
348C22#41×D1311yescharacteristic
349C22#41×D1311yescharacteristic
350C22#8825611yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—262no—
359C4—262no—
360C4—262no—
361C4—262no—
362C4—262no—
363C4—262no—
364C4—521no—
365C2—264no—
366C2#1171922711yescharacteristic
367C2#1171925011yescharacteristic
368C2C4×Q8×D1311yescharacteristic
369C2#1171934111yescharacteristic
370C2#1171936411yescharacteristic
371C2#1171939511yescharacteristic
372C2#1171941011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#387C2
socle, cosocleC23×C13C24
prime radicalC23×D13C23
hypercenter#387D13
hypocenterC13#2368
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C13×#387C2semidirect
4. C4⋊C4×Dic13C2semidirect
5. #11718635C2semidirect
7. C4×#6101C2semidirect
12. #11718316C2semidirect
13. #11718313C2semidirect
14. #11718313C2semidirect
15. #11718307C2semidirect
37. #88150C4semidirect
78. C2×Dic26C2×C4semidirect
80. C13×C4⋊C4C2×C4semidirect
85. #6103Q8semidirect
89. #6101C2×C4semidirect
90. #6101C2×C4semidirect
157. #387D13semidirect
271. C4⋊C4C4×D13semidirect
282. C13#2368semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C13×#3872
#117186502
C4⋊C4×Dic132
#117186352
C4×#61032
C4×#61012
#117183292
#117183272
D13×#952
#117183162
#117183132
#117183072
#236813