Finite Group Databasebeta

← #16822616

Subgroups — #16822616

Order 3712.

496 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271062C211yesmaximal, characteristic, complemented
2#14271056C211yesmaximal, characteristic
3#14271056C211yesmaximal, characteristic
4#14271056C211yesmaximal, characteristic
5#14271049C211yesmaximal, characteristic, complemented
6#14271049C211yesmaximal, characteristic, complemented
7#14271049C211yesmaximal, characteristic, complemented
8#14271038C211yesmaximal, characteristic
9C4⋊C4×Dic29C211yesmaximal, characteristic, complemented
10C4⋊C4×Dic29C211yesmaximal, characteristic, complemented
11C4×C4⋊Dic29C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic29C211yesmaximal, characteristic
13C22⋊C4×Dic29C211yesmaximal, characteristic
14#14271009C211yesmaximal, characteristic, complemented
15C2×C29×#126C211yesmaximal, characteristic
16C23×Dic29C2211yescharacteristic
17C29×#126C418yescomplemented
18C2×C4⋊C4×C29C2211yescharacteristic
19C2×C4⋊C4×C29C2211yescharacteristic
20C2×C4⋊C4×C29C2211yescharacteristic
21C2×C22⋊C4×C29C2211yescharacteristic
22C2×C22⋊C4×C29C2211yescharacteristic
23C2×C22⋊C4×C29C2211yescharacteristic
24C2×C42×C29C2211yescharacteristic
25C2×C22⋊Dic29C2211yescharacteristic
26C2×C22⋊Dic29C2211yescharacteristic
27C2×C22⋊Dic29C2211yescharacteristic
28C2×C4⋊Dic29C2211yescharacteristic
29C2×C4⋊Dic29C2211yescharacteristic
30C2×C4⋊Dic29C2211yescharacteristic
31C2×C4⋊Dic29C2211yescharacteristic
32C2×C4⋊Dic29C2211yescharacteristic
33C2×C4×Dic29C2211yescharacteristic
34C2×C4×Dic29C2211yescharacteristic
35C2×C4×Dic29C2211yescharacteristic
36C2×C4×Dic29C2211yescharacteristic
37C2×C4×Dic29C2211yescharacteristic
38C2×C4×Dic29C2211yescharacteristic
39C2×C4×Dic29C2211yescharacteristic
40#11745179C2211yescharacteristic
41#11745179C2211yescharacteristic
42#11745179C2211yescharacteristic
43#11745179C2211yescharacteristic
44#11745179C2211yescharacteristic
45#11745179C2211yescharacteristic
46#11745179C2211yescharacteristic
47#11745179C2211yescharacteristic
48#11745179C2211yescharacteristic
49#11745179C2211yescharacteristic
50#11745179C2211yescharacteristic
51#11745179C2211yescharacteristic
52C24×C29C2311yescharacteristic
53C22×C4×C29C2311yescharacteristic
54C22×C4×C29C2311yescharacteristic
55C22×C4×C29C2311yescharacteristic
56C22×C4×C29C2311yescharacteristic
57C22×C4×C29C2311yescharacteristic
58C22×C4×C29C2311yescharacteristic
59C22×Dic29—22no—
60C22×Dic29—22no—
61C22×Dic29—41no—
62C22×Dic29C2311yescharacteristic
63C22×Dic29C2311yescharacteristic
64C22×Dic29C2311yescharacteristic
65C22×Dic29C2311yescharacteristic
66C22×Dic29C2311yescharacteristic
67C22×Dic29C2311yescharacteristic
68C22×Dic29C2311yescharacteristic
69C22×Dic29C2311yescharacteristic
70C4⋊C4×C29C2×C414yescomplemented
71C4⋊C4×C29C2×C414yescomplemented
72C4⋊C4×C29C2×C414yescomplemented
73C22⋊C4×C29C2×C414yes—
74C22⋊C4×C29C2×C414yes—
75C22⋊C4×C29C2×C414yes—
76C42×C29C2×C414yescomplemented
77C22⋊Dic29—22no—
78C22⋊Dic29—22no—
79C22⋊Dic29—41no—
80C4⋊Dic29—22no—
81C4⋊Dic29—22no—
82C4⋊Dic29—22no—
83C4⋊Dic29—22no—
84C4⋊Dic29—41no—
85C4×Dic29—22no—
86C4×Dic29—22no—
87C4×Dic29—22no—
88C4×Dic29—22no—
89C4×Dic29—41no—
90C4×Dic29—41no—
91C4×Dic29—41no—
92C23×C29—21no—
93C23×C29—21no—
94C23×C29—21no—
95C23×C29—21no—
96C23×C29—21no—
97C23×C29—21no—
98C23×C29C22×C412yes—
99C23×C29C2411yescharacteristic
100C2×C4×C29—21no—
101C2×C4×C29—21no—
102C2×C4×C29—21no—
103C2×C4×C29—21no—
104C2×C4×C29—21no—
105C2×C4×C29—21no—
106C2×C4×C29—21no—
107C2×C4×C29—21no—
108C2×C4×C29—21no—
109C2×C4×C29—21no—
110C2×C4×C29—21no—
111C2×C4×C29—21no—
112C2×C4×C29C22×C412yes—
113C2×C4×C29C22×C412yes—
114C2×C4×C29C22×C412yes—
115C2×C4×C29C22×C412yes—
116C2×C4×C29C22×C412yes—
117C2×C4×C29C22×C412yes—
118C2×Dic29—21no—
119C2×Dic29—21no—
120C2×Dic29—21no—
121C2×Dic29—21no—
122C2×Dic29—21no—
123C2×Dic29—21no—
124C2×Dic29—21no—
125C2×Dic29—21no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—21no—
138C2×Dic29—44no—
139C2×Dic29#4112yes—
140C2×Dic29#4112yes—
141C2×Dic29#4112yes—
142C2×Dic29#4112yes—
143#2373—291nomaximal, Sylow
144C22×C29—22no—
145C22×C29—22no—
146C22×C29—22no—
147C22×C29—41no—
148C22×C29—41no—
149C22×C29—41no—
150C22×C29—41no—
151C22×C29C23×C411yescharacteristic
152C22×C29C2×#4111yescharacteristic
153C22×C29C2×#4111yescharacteristic
154C22×C29C2×#4111yescharacteristic
155C22×C29C2×#4111yescharacteristic
156C22×C29H(5,𝔽2)11yescharacteristic
157C22×C292−1+411yescharacteristic
158C4×C29—22no—
159C4×C29—22no—
160C4×C29—22no—
161C4×C29—22no—
162C4×C29—22no—
163C4×C29—22no—
164Dic29—22no—
165Dic29—22no—
166Dic29—22no—
167Dic29—22no—
168Dic29—41no—
169Dic29—41no—
170Dic29—41no—
171Dic29—41no—
172C2×#126D2911yescharacteristic
173#389—291no—
174#388—291no—
175#388—291no—
176#388—291no—
177#387—291no—
178#387—291no—
179#387—291no—
180#385—291no—
181C4×C4⋊C4—291no—
182C4×C4⋊C4—291no—
183C4×C4⋊C4—291no—
184C4×C22⋊C4—291no—
185C4×C22⋊C4—291no—
186#376—291no—
187C2×C29—42no—
188C2×C29C4×#4111yescharacteristic
189C2×C29C4×#4111yescharacteristic
190C2×C29#52011yescharacteristic
191C2×C29#55111yescharacteristic
192C2×C29#55211yescharacteristic
193C2×C29#55311yescharacteristic
194C2×C29#55611yescharacteristic
195C23×C4—291no—
196#126Dic2918yescomplemented
197C2×C4⋊C4—291no—
198C2×C4⋊C4—291no—
199C2×C4⋊C4—291no—
200C2×C4⋊C4—291no—
201C2×C4⋊C4—291no—
202C2×C4⋊C4C2×D2911yescharacteristic
203C2×C4⋊C4C2×D2911yescharacteristic
204C2×C4⋊C4C2×D2911yescharacteristic
205C2×C22⋊C4—291no—
206C2×C22⋊C4—291no—
207C2×C22⋊C4—291no—
208C2×C22⋊C4C2×D2911yescharacteristic
209C2×C22⋊C4C2×D2911yescharacteristic
210C2×C22⋊C4C2×D2911yescharacteristic
211C2×C42—291no—
212C2×C42—291no—
213C2×C42—291no—
214C2×C42—291no—
215C2×C42—291no—
216C2×C42—291no—
217C2×C42—291no—
218C2×C42C2×D2911yescharacteristic
219#95—291no—
220#95—291no—
221#95—291no—
222#95—291no—
223#95—291no—
224#95—291no—
225#95—291no—
226#95—291no—
227#95—291no—
228#95—291no—
229#95—291no—
230#95—291no—
231C29#237311yescharacteristic, complemented, Sylow
232C24C22×D2911yescharacteristic
233C22×C4—291no—
234C22×C4—291no—
235C22×C4—291no—
236C22×C4—291no—
237C22×C4—291no—
238C22×C4—291no—
239C22×C4—291no—
240C22×C4—291no—
241C22×C4—582no—
242C22×C4—582no—
243C22×C4—1161no—
244C22×C4C22×D2911yescharacteristic
245C22×C4C22×D2911yescharacteristic
246C22×C4C22×D2911yescharacteristic
247C22×C4C22×D2911yescharacteristic
248C22×C4C22×D2911yescharacteristic
249C22×C4C22×D2911yescharacteristic
250C4⋊C4—582no—
251C4⋊C4—582no—
252C4⋊C4—582no—
253C4⋊C4—582no—
254C4⋊C4—1161no—
255C4⋊C4C2×Dic2914yescomplemented
256C4⋊C4C2×Dic2914yescomplemented
257C4⋊C4C2×Dic2914yescomplemented
258C22⋊C4—582no—
259C22⋊C4—582no—
260C22⋊C4—1161no—
261C22⋊C4C2×Dic2914yes—
262C22⋊C4C2×Dic2914yes—
263C22⋊C4C2×Dic2914yes—
264C42—582no—
265C42—582no—
266C42—582no—
267C42—582no—
268C42—1161no—
269C42—1161no—
270C42—1161no—
271C42C2×Dic2914yescomplemented
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C22×Dic2912yes—
279C23C23×D2911yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—292no—
293C2×C4—292no—
294C2×C4—292no—
295C2×C4—292no—
296C2×C4—581no—
297C2×C4—581no—
298C2×C4—581no—
299C2×C4—581no—
300C2×C4—581no—
301C2×C4—581no—
302C2×C4—581no—
303C2×C4—581no—
304C2×C4—581no—
305C2×C4—581no—
306C2×C4—581no—
307C2×C4—581no—
308C2×C4—581no—
309C2×C4—581no—
310C2×C4—581no—
311C2×C4—581no—
312C2×C4—581no—
313C2×C4—581no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—1164no—
317C2×C4C22×Dic2912yes—
318C2×C4C22×Dic2912yes—
319C2×C4C22×Dic2912yes—
320C2×C4C22×Dic2912yes—
321C2×C4C22×Dic2912yes—
322C2×C4C22×Dic2912yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22#41×D2911yescharacteristic
331C22#41×D2911yescharacteristic
332C22#41×D2911yescharacteristic
333C22#41×D2911yescharacteristic
334C22#1174536411yescharacteristic
335C22#1174536511yescharacteristic
336C22C23×Dic2911yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—22no—
342C4—22no—
343C4—582no—
344C4—582no—
345C4—582no—
346C4—582no—
347C4—1161no—
348C4—1161no—
349C4—1161no—
350C4—1161no—
351C2—42no—
352C2#41×Dic2911yescharacteristic
353C2#41×Dic2911yescharacteristic
354C2#1427164611yescharacteristic
355C2#1427183811yescharacteristic
356C2#1427184911yescharacteristic
357C2#1427186411yescharacteristic
358C2#1427188011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC2×C29×#126C2
socle, cosocleC23×C29C24
prime radicalC24×C29C23
hypercenterC2×#126D29
hypocenterC29#2373
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #14271062C2semidirect
5. #14271049C2semidirect
6. #14271049C2semidirect
7. #14271049C2semidirect
9. C4⋊C4×Dic29C2semidirect
10. C4⋊C4×Dic29C2semidirect
11. C4×C4⋊Dic29C2semidirect
14. #14271009C2semidirect
17. C29×#126C4semidirect
70. C4⋊C4×C29C2×C4semidirect
71. C4⋊C4×C29C2×C4semidirect
72. C4⋊C4×C29C2×C4semidirect
76. C42×C29C2×C4semidirect
196. #126Dic29semidirect
231. C29#2373semidirect
255. C4⋊C4C2×Dic29semidirect
256. C4⋊C4C2×Dic29semidirect
257. C4⋊C4C2×Dic29semidirect
271. C42C2×Dic29semidirect

Maximal subgroups

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

subgroupindex
#142710622
#142710562
#142710492
#142710382
C4⋊C4×Dic292
C4×C4⋊Dic292
C22⋊C4×Dic292
#142710092
C2×C29×#1262
#237329