Finite Group Databasebeta

← #13117864

Subgroups — #13117864

Order 1664.

576 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
2C2×#88126C211yesmaximal, characteristic
3C2×C4×Dic26C211yesmaximal, characteristic, complemented
4C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
5#11718651C211yesmaximal, characteristic
6#11718642C211yesmaximal, characteristic, complemented
7#11718633C211yesmaximal, characteristic, complemented
8#11718601C211yesmaximal, characteristic
9#11718601C211yesmaximal, characteristic
10#11718594C211yesmaximal, characteristic, complemented
11C4×#6101C211yesmaximal, characteristic, complemented
12#11718331C211yesmaximal, characteristic
13#11718327C211yesmaximal, characteristic
14#11718310C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×C4×D13C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C42×C13C2211yescharacteristic
21C2×C42×C13C2211yescharacteristic
22C2×C42×C13C2211yescharacteristic
23C2×#6103C2211yescharacteristic
24C2×#6103C2211yescharacteristic
25C2×#6103C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×C4⋊Dic13C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41#88150C418yescomplemented
42#88126—24no—
43C4×Dic26—24no—
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×D13C2×C414yes—
72C2×Dic26—22no—
73C2×Dic26—22no—
74C2×Dic26C2×C414yes—
75C13×C4⋊C4—22no—
76C13×C4⋊C4C2×C414yes—
77C42×C13—22no—
78C42×C13—22no—
79C42×C13—22no—
80#6103—22no—
81#6103—22no—
82#6103—22no—
83#6103—22no—
84#6103C2×C414yes—
85#6103C2×C414yes—
86C4⋊Dic13—22no—
87#6101—22no—
88#6101—22no—
89#6101—22no—
90#6101C2×C414yes—
91#6101C2×C414yes—
92#6101D414yes—
93C4×Dic13—22no—
94C4×Dic13—22no—
95C4×Dic13—22no—
96C4×Dic13—22no—
97C4×Dic13—22no—
98#2362—131nomaximal, Sylow
99C23×C13C2411yescharacteristic
100C22×D13—21no—
101C22×D13—21no—
102C22×D13—21no—
103C22×D13—21no—
104C22×D13—21no—
105C22×D13—21no—
106C22×D13C22×C412yes—
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×D412yes—
126C2×C4×C13#4112yes—
127C2×C4×C13#4112yes—
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×Dic13C2×D412yes—
148C2×Dic13#4112yes—
149C4×D13—28no—
150Dic26—28no—
151C2×C22⋊Q8—131no—
152C2×C4×Q8—131no—
153C2×#117—131no—
154#391—131no—
155#389—131no—
156#388—131no—
157#388—131no—
158#388—131no—
159#388—131no—
160#387—131no—
161#387—131no—
162C4×C4⋊C4—131no—
163C4×C4⋊C4—131no—
164C4×C4⋊C4D1311yescharacteristic, complemented
165C4×C22⋊C4—131no—
166C22×C13C23×C411yescharacteristic
167C22×C13C22×D411yescharacteristic
168C22×C13C2×#4111yescharacteristic
169C22×C13C2×#4111yescharacteristic
170C22×C13C2×#4111yescharacteristic
171C22×C132−1+411yescharacteristic
172C22×C132−1+411yescharacteristic
173C2×D13—22no—
174C2×D13—22no—
175C2×D13—22no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—41no—
179C2×D13—41no—
180C4×C13—22no—
181C4×C13—22no—
182C4×C13—22no—
183C4×C13—22no—
184C4×C13—22no—
185C4×C13—22no—
186C4×C13—41no—
187Dic13—22no—
188Dic13—22no—
189Dic13—22no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193Dic13C4×D414yes—
194C22×Q8—131no—
195C23×C4—131no—
196C22⋊Q8—138no—
197C4×Q8—264no—
198#117—264no—
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×C22⋊C4—131no—
209C2×C22⋊C4—131no—
210C2×C22⋊C4—131no—
211C2×C22⋊C4—131no—
212C2×C22⋊C4—131no—
213C2×C22⋊C4—131no—
214C2×C42—131no—
215C2×C42—131no—
216C2×C42—131no—
217C2×C42—131no—
218C2×C42—131no—
219C2×C42C2×D1311yescharacteristic
220C2×C42C2×D1311yescharacteristic
221C2×C42C2×D1311yescharacteristic
222#95—131no—
223#95—131no—
224#95—131no—
225#95—131no—
226#95—131no—
227#95—131no—
228#95—131no—
229#95—131no—
230#95C2×D1311yescharacteristic
231#95C2×D1311yescharacteristic
232C2×C13C2×C4×D411yescharacteristic
233C2×C13C4×#4111yescharacteristic
234C2×C13#51911yescharacteristic
235C2×C13#54711yescharacteristic
236C2×C13#54811yescharacteristic
237C2×C13#55211yescharacteristic
238C2×C13#55611yescharacteristic
239D13—42no—
240C24—131no—
241C2×Q8—134no—
242C2×Q8—262no—
243C2×Q8—262no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—134no—
249C22×C4—131no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—262no—
253C22×C4—262no—
254C22×C4C22×D1311yescharacteristic
255C22×C4C22×D1311yescharacteristic
256C22×C4C22×D1311yescharacteristic
257C22×C4C22×D1311yescharacteristic
258C22×C4C22×D1311yescharacteristic
259C22×C4C22×D1311yescharacteristic
260C22×C4C22×D1311yescharacteristic
261C4⋊C4—22no—
262C4⋊C4—134no—
263C4⋊C4—134no—
264C4⋊C4—134no—
265C4⋊C4—262no—
266C4⋊C4—262no—
267C4⋊C4—262no—
268C4⋊C4—262no—
269C4⋊C4C4×D1314yes—
270C22⋊C4—134no—
271C22⋊C4—134no—
272C22⋊C4—262no—
273C22⋊C4—262no—
274C22⋊C4—262no—
275C22⋊C4—262no—
276C42—22no—
277C42—22no—
278C42—22no—
279C42—262no—
280C42—262no—
281C42—262no—
282C42—262no—
283C42—262no—
284C13#236211yescharacteristic, complemented, Sylow
285C23—132no—
286C23—261no—
287C23—261no—
288C23—261no—
289C23—261no—
290C23—261no—
291C23—261no—
292C23C23×D1311yescharacteristic
293Q8—268no—
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—268no—
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—261no—
331C2×C4C2×C4×D1312yes—
332C2×C4C2×C4×D1312yes—
333C2×C4C2×C4×D1312yes—
334C2×C4#612712yes—
335C2×C4#612712yes—
336C2×C4D4×D1312yes—
337C22—262no—
338C22—262no—
339C22—262no—
340C22—521no—
341C22—521no—
342C22—521no—
343C22—521no—
344C22C22×C4×D1311yescharacteristic
345C22C2×#612711yescharacteristic
346C22C2×#612711yescharacteristic
347C22C2×D4×D1311yescharacteristic
348C22#8825411yescharacteristic
349C22#41×D1311yescharacteristic
350C22#8825711yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—134no—
359C4—262no—
360C4—262no—
361C4—262no—
362C4—521no—
363C4—521no—
364C4—521no—
365C2—522no—
366C2C4×#612711yescharacteristic
367C2#1171921211yescharacteristic
368C2#1171923611yescharacteristic
369C2C4×D4×D1311yescharacteristic
370C2#1171925711yescharacteristic
371C2#1171927311yescharacteristic
372C2#1171927711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC4×C13×C4⋊C4C2
socle, cosocleC23×C13C24
prime radicalC23×D13C23
hypercenterC4×C4⋊C4D13
hypocenterC13#2362
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic26C2semidirect
4. C4×C13×C4⋊C4C2semidirect
6. #11718642C2semidirect
7. #11718633C2semidirect
10. #11718594C2semidirect
11. C4×#6101C2semidirect
14. #11718310C2semidirect
15. #11718307C2semidirect
41. #88150C4semidirect
164. C4×C4⋊C4D13semidirect
284. C13#2362semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C2×#881262
C2×C4×Dic262
C4×C13×C4⋊C42
#117186512
#117186422
#117186332
#117186012
#117185942
C4×#61012
#117183312
#117183272
#117183102
#117183072
#236213