Finite Group Databasebeta

← #13120574

Subgroups — #13120574

Order 1664.

824 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#120C211yesmaximal, characteristic, complemented
2C2×#88207C211yesmaximal, characteristic, complemented
3C22×C22⋊Dic13C211yesmaximal, characteristic, complemented
4C2×#88193C211yesmaximal, characteristic, complemented
5#11718884C212yesmaximal, complemented
6#11718883C212yesmaximal, complemented
7#11718881C211yesmaximal, characteristic, complemented
8#11718620C212yesmaximal, complemented
9#11718619C211yesmaximal, characteristic, complemented
10#11718613C212yesmaximal, complemented
11#11718603C211yesmaximal, characteristic, complemented
12C25×C13C2211yescharacteristic
13C22×D4×C13C2211yescharacteristic
14C22×D4×C13C2212yes—
15C22×C22⋊D13C2211yescharacteristic
16C22×C22⋊D13C2212yes—
17C22×C22⋊D13C2211yescharacteristic, complemented
18C23×Dic13C2211yescharacteristic
19C23×Dic13C2211yescharacteristic
20C13×#120—24no—
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2212yes—
23#88207—24no—
24C2×C22⋊Dic13—24no—
25C2×C22⋊Dic13C2212yes—
26C2×C22⋊Dic13C2212yes—
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2212yes—
29C2×C22⋊Dic13C2211yescharacteristic, complemented
30C2×C22⋊Dic13C2212yescomplemented
31#88193—24no—
32C2×#6103C2211yescharacteristic, complemented
33C2×#6103C2212yescomplemented
34C2×#6101C2211yescharacteristic, complemented
35C2×#6101C2212yescomplemented
36#88071C2212yescomplemented
37#88071C2212yescomplemented
38#88071C2212yescomplemented
39C24×C13—22no—
40C24×C13—22no—
41C24×C13—42no—
42C24×C13—42no—
43C24×C13D414yescomplemented
44C24×C13C2311yescharacteristic
45C24×C13C2312yes—
46C24×C13C2311yescharacteristic
47C23×D13C2311yescharacteristic
48C2×D4×C13—22no—
49C2×D4×C13—24no—
50C2×D4×C13—22no—
51C2×D4×C13—22no—
52C2×D4×C13—42no—
53C2×D4×C13—42no—
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2312yes—
56C2×C22⋊D13—22no—
57C2×C22⋊D13—24no—
58C2×C22⋊D13—22no—
59C2×C22⋊D13—22no—
60C2×C22⋊D13—22no—
61C2×C22⋊D13—42no—
62C2×C22⋊D13—42no—
63C2×C22⋊D13—42no—
64C22×Dic13—22no—
65C22×Dic13—42no—
66C22×Dic13—42no—
67C22×Dic13D414yescomplemented
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2312yes—
70C22×Dic13C2312yes—
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C13×C22⋊C4—24no—
74C13×C22⋊C4—22no—
75C22⋊Dic13—24no—
76C22⋊Dic13—22no—
77C22⋊Dic13—22no—
78C22⋊Dic13—24no—
79C22⋊Dic13—24no—
80C22⋊Dic13—42no—
81#6103—22no—
82#6103—42no—
83#6101—22no—
84#6101—42no—
85#2617—131nomaximal, Sylow
86C23×C13—22no—
87C23×C13—22no—
88C23×C13—28no—
89C23×C13—22no—
90C23×C13—22no—
91C23×C13—22no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—48no—
101C23×C13—44no—
102C23×C13—44no—
103C23×C13—48no—
104C23×C13C2×D414yes—
105C23×C13C2×D412yes—
106C23×C13C2×D412yes—
107C23×C13#4112yes—
108C23×C13C2411yescharacteristic
109C22×D13—21no—
110C22×D13—21no—
111C22×D13—21no—
112C22×D13—22no—
113C22×D13—22no—
114D4×C13—48no—
115D4×C13—44no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—22no—
119C2×C4×C13—21no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C22⋊D13—44no—
123C22⋊D13—48no—
124C22⋊D13—44no—
125C2×Dic13—22no—
126C2×Dic13—22no—
127C2×Dic13—21no—
128C2×Dic13—22no—
129C2×Dic13—21no—
130C2×Dic13—22no—
131C2×Dic13—21no—
132C2×Dic13—22no—
133C2×Dic13—22no—
134C2×Dic13—22no—
135C2×Dic13—22no—
136C2×Dic13—44no—
137C2×Dic13—44no—
138C2×Dic13C2×D412yes—
139C2×Dic13C2×D412yes—
140C2×#121—131no—
141C2×#120—131no—
142C2×#120D1311yescharacteristic, complemented
143C22×C22⋊C4—131no—
144#397—132no—
145#394—132no—
146#394—132no—
147#392—132no—
148#386—131no—
149#386—131no—
150#380—131no—
151C22×C13—22no—
152C22×C13—24no—
153C22×C13—22no—
154C22×C13—24no—
155C22×C13—24no—
156C22×C13—24no—
157C22×C13—24no—
158C22×C13—416no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—42no—
162C22×C13—42no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—42no—
166C22×C13—41no—
167C22×C13—42no—
168C22×C13#12114yes—
169C22×C13C22×D411yescharacteristic
170C22×C13C22×D411yescharacteristic
171C22×C13C2×#4111yescharacteristic
172C22×C13H(5,𝔽2)12yes—
173C22×C13H(5,𝔽2)12yes—
174C2×D13—41no—
175C2×D13—42no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—42no—
179C4×C13—41no—
180C4×C13—42no—
181Dic13—22no—
182Dic13—22no—
183Dic13—41no—
184Dic13—42no—
185Dic13—42no—
186C25C2×D1311yescharacteristic
187C22×D4—131no—
188C22×D4—132no—
189C22×D4—131no—
190C22×D4C2×D1311yescharacteristic
191C22×D4C2×D1312yes—
192C23×C4—131no—
193C23×C4—131no—
194#121—264no—
195#120—24no—
196#120—264no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—132no—
199C2×C22⋊C4—132no—
200C2×C22⋊C4—132no—
201C2×C22⋊C4—131no—
202C2×C22⋊C4—132no—
203C2×C22⋊C4—131no—
204C2×C22⋊C4—131no—
205C2×C22⋊C4—132no—
206C2×C22⋊C4—132no—
207C2×C22⋊C4—264no—
208C2×C22⋊C4C2×D1311yescharacteristic
209C2×C22⋊C4C2×D1312yes—
210#95—132no—
211#95—132no—
212#95—132no—
213C2×C13—24no—
214C2×C13—44no—
215C2×C13—81no—
216C2×C13C2×#12111yescharacteristic
217C2×C13#53412yes—
218C2×C13#53411yescharacteristic
219C2×C13#53511yescharacteristic
220C2×C13#53812yes—
221D13—81no—
222C24—22no—
223C24—22no—
224C24—42no—
225C24—42no—
226C24—131no—
227C24C22⋊D1314yescomplemented
228C24C22×D1311yescharacteristic
229C24C22×D1312yes—
230C24C22×D1311yescharacteristic
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—24no—
234C2×D4—22no—
235C2×D4—42no—
236C2×D4—42no—
237C2×D4—262no—
238C2×D4—262no—
239C2×D4—262no—
240C2×D4—264no—
241C2×D4—262no—
242C2×D4—522no—
243C2×D4—522no—
244C2×D4—522no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—134no—
248C22×C4—132no—
249C22×C4—131no—
250C22×C4—132no—
251C22×C4—262no—
252C22×C4—522no—
253C22×C4—522no—
254C22×C4C22×D1311yescharacteristic
255C22×C4C22×D1312yes—
256C4⋊C4—262no—
257C4⋊C4—522no—
258C22⋊C4—24no—
259C22⋊C4—22no—
260C22⋊C4—262no—
261C22⋊C4—264no—
262C22⋊C4—264no—
263C22⋊C4—262no—
264C22⋊C4—264no—
265C22⋊C4—262no—
266C22⋊C4—522no—
267C22⋊C4—522no—
268C13#261711yescharacteristic, complemented, Sylow
269C23—22no—
270C23—22no—
271C23—28no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—21no—
279C23—21no—
280C23—22no—
281C23—22no—
282C23—21no—
283C23—48no—
284C23—44no—
285C23—44no—
286C23—48no—
287C23—261no—
288C23—261no—
289C23—262no—
290C23—262no—
291C23—261no—
292C23D4×D1312yes—
293C23#612912yes—
294C23C2×C22⋊D1314yes—
295C23C2×C22⋊D1312yes—
296C23C23×D1311yescharacteristic
297D4—48no—
298D4—44no—
299D4—524no—
300D4—528no—
301D4—524no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—132no—
309C2×C4—132no—
310C2×C4—262no—
311C2×C4—262no—
312C2×C4—262no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—262no—
316C2×C4—262no—
317C2×C4—262no—
318C2×C4—262no—
319C2×C4—261no—
320C2×C4—262no—
321C2×C4—524no—
322C2×C4—524no—
323C22—24no—
324C22—22no—
325C22—22no—
326C22—24no—
327C22—24no—
328C22—24no—
329C22—24no—
330C22—416no—
331C22—42no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—42no—
337C22—41no—
338C22—41no—
339C22—42no—
340C22—521no—
341C22—522no—
342C22—521no—
343C22—521no—
344C22—522no—
345C22#8819314yes—
346C22C2×D4×D1311yescharacteristic
347C22C2×#612911yescharacteristic
348C22#8825112yes—
349C22#8825112yes—
350C22C22×C22⋊D1311yescharacteristic
351C4—41no—
352C4—42no—
353C4—262no—
354C4—262no—
355C4—521no—
356C4—522no—
357C4—522no—
358C2—24no—
359C2—44no—
360C2—81no—
361C2—1041no—
362C2#1171929411yescharacteristic
363C2#1171929711yescharacteristic
364C2#1171929812yes—
365C2C2×#8819311yescharacteristic
366C2#1171950912yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#120C2
hypercenterC2×#120D13
hypocenterC13#2617
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×C13×#120C2semidirect
2. C2×#88207C2semidirect
3. C22×C22⋊Dic13C2semidirect
4. C2×#88193C2semidirect
5. #11718884C2semidirect
6. #11718883C2semidirect
7. #11718881C2semidirect
8. #11718620C2semidirect
9. #11718619C2semidirect
10. #11718613C2semidirect
11. #11718603C2semidirect
17. C22×C22⋊D13C22semidirect
29. C2×C22⋊Dic13C22semidirect
30. C2×C22⋊Dic13C22semidirect
32. C2×#6103C22semidirect
33. C2×#6103C22semidirect
34. C2×#6101C22semidirect
35. C2×#6101C22semidirect
36. #88071C22semidirect
37. #88071C22semidirect
38. #88071C22semidirect
43. C24×C13D4semidirect
67. C22×Dic13D4semidirect
142. C2×#120D13semidirect
227. C24C22⋊D13semidirect
268. C13#2617semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1202
C2×#882072
C22×C22⋊Dic132
C2×#881932
#117188842
#117188832
#117188812
#117186202
#117186192
#117186132
#117186032
#261713