Finite Group Databasebeta

← #16829612

Subgroups — #16829612

Order 3712.

424 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#14271710C211yesmaximal, characteristic
2C4×Q8×D29C211yesmaximal, characteristic, complemented
3#14271478C211yesmaximal, characteristic, complemented
4#14271475C211yesmaximal, characteristic, complemented
5#14271457C211yesmaximal, characteristic, complemented
6#14271456C211yesmaximal, characteristic, complemented
7#14271362C211yesmaximal, characteristic, complemented
8#14271361C211yesmaximal, characteristic, complemented
9#14271303C211yesmaximal, characteristic, complemented
10#14271300C211yesmaximal, characteristic, complemented
11#14271265C211yesmaximal, characteristic, complemented
12#14271263C211yesmaximal, characteristic, complemented
13#14271261C211yesmaximal, characteristic, complemented
14#14271218C211yesmaximal, characteristic, complemented
15C29×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D29C2211yescharacteristic
17C2×#90805—21no—
18C2×SD16×C29C2211yescharacteristic
19C4×Q8×C29C2211yescharacteristic
20C4×D4×C29C2211yescharacteristic
21Q8×Dic29C2211yescharacteristic
22C2×#90784C2211yescharacteristic
23#11745302C2211yescharacteristic
24#11745300C2211yescharacteristic
25C2×#90783C2211yescharacteristic
26C4×C22⋊D29—21no—
27C2×#90773C2211yescharacteristic
28#11745257C2211yescharacteristic
29C4⋊C4×D29—21no—
30C4⋊C4×D29C2211yescharacteristic
31#11745250C2211yescharacteristic
32#11745249—21no—
33#11745249C2211yescharacteristic
34#11745247—21no—
35#11745246—21no—
36C4×D116C2211yescharacteristic
37C42×D29—21no—
38C42×D29C2211yescharacteristic
39C4×Dic58—21no—
40C4×Dic58C2211yescharacteristic
41C29×#107C2211yescharacteristic
42C29×#103C2211yescharacteristic
43C29×#102C2211yescharacteristic
44C29×#97C2211yescharacteristic
45#11745183C2211yescharacteristic
46#11745180C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745168C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745166C2211yescharacteristic
51#11745164C2211yescharacteristic
52#11745162C2211yescharacteristic
53#11745162C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745155C2211yescharacteristic
57#11745155C2211yescharacteristic
58#11745151C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×D4×C29C2311yescharacteristic
61C22×C4×C29—21no—
62C2×C22⋊D29—21no—
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65Q8×D29—22no—
66Q8×D29—22no—
67#90805—44no—
68C2×D116—21no—
69C2×D116C2311yescharacteristic
70C2×C4×D29—21no—
71C2×C4×D29—21no—
72C2×C4×D29—21no—
73C2×C4×D29D411yescharacteristic
74C2×C4×D29D411yescharacteristic
75C2×C4×D29C2311yescharacteristic
76C2×Dic58—21no—
77C2×Dic58—21no—
78C2×Dic58C2311yescharacteristic
79SD16×C29—22no—
80C2×C8×C29C2311yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C4⋊C4×C29—21no—
83C4⋊C4×C29C2311yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C22⋊C4×C29—21no—
86C42×C29—21no—
87C42×C29C2311yescharacteristic
88C22⋊Dic29—21no—
89#90784—22no—
90#90783—22no—
91#90781—21no—
92#90781—21no—
93C4⋊Dic29—21no—
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100C4×Dic29—21no—
101C4×Dic29—21no—
102C4×Dic29—21no—
103C4×Dic29D411yescharacteristic
104C4×Dic29D411yescharacteristic
105C4×Dic29C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108#90773—22no—
109C23×C29—21no—
110C22×D29—21no—
111C22×D29C2×D411yescharacteristic
112Q8×C29—21no—
113Q8×C29#4112yescomplemented
114D4×C29—21no—
115D4×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—42no—
120C2×C4×C29C2×D411yescharacteristic
121C2×C4×C29C2×D411yescharacteristic
122C2×C4×C29C2411yescharacteristic
123C22⋊D29—42no—
124C22⋊D29—42no—
125C22⋊D29—42no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29C2×D411yescharacteristic
130C2×Dic29C2×D411yescharacteristic
131C2×Dic29C2×D411yescharacteristic
132D116—21no—
133D116—21no—
134D116—42no—
135C4×D29—24no—
136C4×D29—22no—
137C4×D29—21no—
138C4×D29—21no—
139C4×D29—22no—
140C4×D29—42no—
141C4×D29—42no—
142Dic58—24no—
143Dic58—21no—
144Dic58—42no—
145Dic58#4112yescomplemented
146C8×C29—21no—
147C8×C29—21no—
148#6597—21no—
149#6597—21no—
150#3112—291nomaximal, Sylow
151C22×C29—41no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29C22×D411yescharacteristic
155C2×D29—21no—
156C2×D29—21no—
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
160C2×D29AGL(1,ℤ/8)12yes—
161C4×C29—22no—
162C4×C29—21no—
163C4×C29—21no—
164C4×C29—41no—
165C4×C29—41no—
166C4×C29C2×#4111yescharacteristic
167C4×C29C2×#4111yescharacteristic
168Dic29—21no—
169Dic29—22no—
170Dic29—21no—
171Dic29—41no—
172Dic29—41no—
173Dic29#13712yes—
174#532—291no—
175C2×C4×Q8—291no—
176#480—291no—
177#480—291no—
178#477—291no—
179#477—291no—
180#460—291no—
181#460—291no—
182#448—291no—
183#448—291no—
184#440—291no—
185#440—291no—
186#440—291no—
187#440D2911yescharacteristic, complemented
188#432—291no—
189C2×C29—81no—
190C2×C29#52511yescharacteristic
191C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C29C2×#13711yescharacteristic
193D29—22no—
194D29—81no—
195C2×#41—581no—
196C22×Q8—291no—
197C2×SD16—291no—
198C2×SD16—291no—
199C2×SD16—291no—
200C2×SD16C2×D2911yescharacteristic
201C4⋊Q8—291no—
202#127—291no—
203#124—581no—
204#121—291no—
205#121—291no—
206#121—581no—
207C4×Q8—291no—
208C4×Q8—291no—
209C4×Q8—291no—
210C4×Q8—581no—
211C4×Q8—581no—
212C4×Q8C2×D2911yescharacteristic
213C4×D4—291no—
214C4×D4—581no—
215C4×D4C2×D2911yescharacteristic
216C2×C4⋊C4—291no—
217C2×C4⋊C4—581no—
218C2×C42—291no—
219C2×C42—581no—
220#107—291no—
221#107—291no—
222#107—291no—
223#107C2×D2911yescharacteristic
224C4⋊C8—291no—
225C4⋊C8—291no—
226#103—291no—
227#103—291no—
228#103—291no—
229#103C2×D2911yescharacteristic
230#102—291no—
231#102—291no—
232#102—291no—
233#102C2×D2911yescharacteristic
234C22⋊C8—291no—
235C22⋊C8—291no—
236#97—291no—
237#97C2×D2911yescharacteristic
238C29#311211yescharacteristic, complemented, Sylow
239#41—1164no—
240C2×Q8—291no—
241C2×Q8—581no—
242C2×Q8—581no—
243C2×Q8—582no—
244C2×Q8—582no—
245C2×Q8C22×D2911yescharacteristic
246C2×D4—291no—
247C2×D4—581no—
248C2×D4—581no—
249C2×D4—581no—
250C2×D4—581no—
251C2×D4C22×D2911yescharacteristic
252C22×C4—21no—
253C22×C4—291no—
254C22×C4—291no—
255C22×C4—291no—
256C22×C4—581no—
257C22×C4—581no—
258C22×C4—581no—
259SD16—22no—
260SD16—582no—
261SD16—582no—
262SD16—582no—
263C2×C8—291no—
264C2×C8—291no—
265C2×C8C22×D2911yescharacteristic
266C2×C8C22×D2911yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—291no—
269C4⋊C4—291no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4—581no—
275C4⋊C4C22×D2911yescharacteristic
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C42—21no—
282C42—291no—
283C42—291no—
284C42—291no—
285C42—581no—
286C42—581no—
287C42—581no—
288C42C22×D2911yescharacteristic
289C23—21no—
290C23—291no—
291C23—581no—
292Q8—21no—
293Q8—292no—
294Q8—584no—
295Q8—581no—
296Q8—1162no—
297Q8#9080512yescomplemented
298D4—21no—
299D4—21no—
300D4—581no—
301D4—581no—
302D4—1162no—
303D4—1162no—
304D4—1162no—
305D4—1162no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—291no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—582no—
314C2×C4—582no—
315C2×C4—584no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—581no—
319C2×C4—581no—
320C2×C4—581no—
321C2×C4—1162no—
322C2×C4—1162no—
323C2×C4D4×D2911yescharacteristic
324C2×C4D4×D2911yescharacteristic
325C2×C4C23×D2911yescharacteristic
326C8—21no—
327C8—21no—
328C8—581no—
329C8—581no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—292no—
334C22—581no—
335C22—581no—
336C22—1161no—
337C22—1161no—
338C22—1161no—
339C22C2×D4×D2911yescharacteristic
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—292no—
346C4—581no—
347C4—582no—
348C4—581no—
349C4—1161no—
350C4—1161no—
351C4C2×#9080511yescharacteristic
352C4#41×D2911yescharacteristic
353C2—81no—
354C2—582no—
355C2—2321no—
356C2#1427167211yescharacteristic
357C2AGL(1,ℤ/8)×D2911yescharacteristic
358C2#137×D2911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#440C2
socleC22×C29C22×D4
prime radical#14271710C2
hypercenter#440D29
hypocenterC29#3112
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D29C2semidirect
3. #14271478C2semidirect
4. #14271475C2semidirect
5. #14271457C2semidirect
6. #14271456C2semidirect
7. #14271362C2semidirect
8. #14271361C2semidirect
9. #14271303C2semidirect
10. #14271300C2semidirect
11. #14271265C2semidirect
12. #14271263C2semidirect
13. #14271261C2semidirect
14. #14271218C2semidirect
15. C29×#440C2semidirect
113. Q8×C29#41semidirect
145. Dic58#41semidirect
187. #440D29semidirect
238. C29#3112semidirect
297. Q8#90805semidirect

Maximal subgroups

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

subgroupindex
#142717102
C4×Q8×D292
#142714782
#142714752
#142714572
#142714562
#142713622
#142713612
#142713032
#142713002
#142712652
#142712632
#142712612
#142712182
C29×#4402
#311229