Finite Group Databasebeta

← #16830080

Subgroups — #16830080

Order 3712.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271708C211yesmaximal, characteristic, complemented
2#14271699C211yesmaximal, characteristic, complemented
3#14271571C211yesmaximal, characteristic, complemented
4#14271549C211yesmaximal, characteristic, complemented
5#14271526C211yesmaximal, characteristic, complemented
6#14271524C211yesmaximal, characteristic, complemented
7#14271416C211yesmaximal, characteristic, complemented
8#14271414C211yesmaximal, characteristic, complemented
9#14271411C211yesmaximal, characteristic, complemented
10SD16×Dic29C211yesmaximal, characteristic, complemented
11#14271248C211yesmaximal, characteristic, complemented
12#14271245C211yesmaximal, characteristic, complemented
13#14271243C211yesmaximal, characteristic, complemented
14M16×Dic29C211yesmaximal, characteristic, complemented
15C29×#468C211yesmaximal, characteristic, complemented
16C2×#90807—21no—
17C2×SD16×C29C2211yescharacteristic
18C2×M16×C29C2211yescharacteristic
19C29×C22⋊Q8C2211yescharacteristic
20C29×#121C2211yescharacteristic
21#11745309C2211yescharacteristic
22Q8×Dic29C2211yescharacteristic
23C2×#90784C2211yescharacteristic
24#11745302C2211yescharacteristic
25#11745301—21no—
26D4×Dic29C2211yescharacteristic
27C2×#90782C2211yescharacteristic
28#11745292C2211yescharacteristic
29#11745292C2211yescharacteristic
30C2×C4×Dic29C2211yescharacteristic
31C2×#90777C2211yescharacteristic
32C2×D232C2211yescharacteristic
33#11745260—21no—
34#11745255C2211yescharacteristic
35#11745255C2211yescharacteristic
36#11745254—21no—
37#11745252C2211yescharacteristic
38#11745250C2211yescharacteristic
39#11745248—21no—
40#11745247—21no—
41#11745243—21no—
42#11745243—21no—
43C29×#107C2211yescharacteristic
44C29×#103C2211yescharacteristic
45C29×#102C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745165C2211yescharacteristic
51#11745163C2211yescharacteristic
52#11745163C2211yescharacteristic
53C8×Dic29C2211yescharacteristic
54C8×Dic29C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745156C2211yescharacteristic
58#11745155C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×D4×C29—21no—
61C2×D4×C29C2311yescharacteristic
62C22×C4×C29C2311yescharacteristic
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C22×Dic29—21no—
68C22×Dic29D411yescharacteristic
69C22×Dic29D411yescharacteristic
70#90807—44no—
71C2×D116C2311yescharacteristic
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×Dic58—21no—
76SD16×C29—22no—
77M16×C29—22no—
78C2×C8×C29C2311yescharacteristic
79C2×C8×C29C2311yescharacteristic
80C4⋊C4×C29—21no—
81C4⋊C4×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C22⋊C4×C29—21no—
84C22⋊C4×C29—21no—
85C22⋊Dic29—21no—
86#90784—22no—
87#90782—22no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94C4⋊Dic29—21no—
95C4⋊Dic29—21no—
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98#90779—21no—
99#90779—21no—
100C4×Dic29—21no—
101C4×Dic29D411yescharacteristic
102C4×Dic29D411yescharacteristic
103C4×Dic29C2311yescharacteristic
104C4×Dic29C2311yescharacteristic
105#90777—22no—
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108D232—22no—
109C23×C29—21no—
110C23×C29C2×D411yescharacteristic
111C22×D29—21no—
112C22×D29—21no—
113Q8×C29—21no—
114Q8×C29—21no—
115D4×C29—21no—
116D4×C29—21no—
117D4×C29—42no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2411yescharacteristic
125C22⋊D29—42no—
126C22⋊D29—42no—
127C22⋊D29—42no—
128C22⋊D29—42no—
129C2×Dic29—22no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—41no—
133C2×Dic29—42no—
134C2×Dic29C2×D411yescharacteristic
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138D116—21no—
139D116—21no—
140D116—21no—
141D116—21no—
142C4×D29—42no—
143C4×D29—42no—
144Dic58—42no—
145C8×C29—21no—
146C8×C29#4112yescomplemented
147#6597—21no—
148#6597#4112yescomplemented
149#3171—291nomaximal, Sylow
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—21no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29C22×D411yescharacteristic
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
160C2×D29—41no—
161C2×D29—41no—
162C2×D29—41no—
163C4×C29—21no—
164C4×C29—41no—
165C4×C29—41no—
166C4×C29—41no—
167C4×C29C2×#4111yescharacteristic
168C4×C29C2×#4111yescharacteristic
169Dic29—21no—
170Dic29—21no—
171Dic29—21no—
172Dic29—41no—
173Dic29—41no—
174Dic29AGL(1,ℤ/8)12yes—
175#532—291no—
176#529—291no—
177#501—291no—
178#496—291no—
179#490—291no—
180#489—291no—
181#469—291no—
182#469—291no—
183#468—291no—
184#468D2911yescharacteristic, complemented
185C4×SD16—291no—
186C4×SD16—291no—
187C4×D8—291no—
188C4×D8—291no—
189C4×M16—291no—
190C2×C29—41no—
191C2×C29—81no—
192C2×C29#53211yescharacteristic
193C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
194C2×C29#57511yescharacteristic
195D29—81no—
196D29—81no—
197C2×#41—581no—
198C2×SD16—291no—
199C2×SD16C2×D2911yescharacteristic
200C2×D8—291no—
201C2×D8—291no—
202C2×M16—291no—
203C2×M16C2×D2911yescharacteristic
204C4⋊Q8—291no—
205#127—291no—
206#126—581no—
207#125—291no—
208#124—291no—
209#124—581no—
210#123—581no—
211C22⋊Q8C2×D2911yescharacteristic
212#121—291no—
213#121—291no—
214#121—581no—
215#121C2×D2911yescharacteristic
216C4×Q8—291no—
217C4×D4—291no—
218C4×D4—291no—
219C4×D4—291no—
220C4×D4—581no—
221C4×D4—581no—
222#117—581no—
223C2×C42—291no—
224#107—291no—
225#107C2×D2911yescharacteristic
226#106—291no—
227#106—291no—
228#103—291no—
229#103C2×D2911yescharacteristic
230#102—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234#102—291no—
235#102C2×D2911yescharacteristic
236#97—291no—
237#97—291no—
238C4×C8—291no—
239C4×C8—291no—
240C29#317111yescharacteristic, complemented, Sylow
241#41—1164no—
242C2×Q8—581no—
243C2×Q8C22×D2911yescharacteristic
244C2×D4—21no—
245C2×D4—291no—
246C2×D4—291no—
247C2×D4—581no—
248C2×D4—581no—
249C2×D4—581no—
250C2×D4—581no—
251C2×D4C22×D2911yescharacteristic
252C22×C4—291no—
253C22×C4—291no—
254C22×C4—581no—
255C22×C4—581no—
256C22×C4—581no—
257C22×C4C22×D2911yescharacteristic
258SD16—22no—
259SD16—582no—
260D8—582no—
261D8—582no—
262M16—22no—
263M16—582no—
264C2×C8—291no—
265C2×C8—291no—
266C2×C8C22×D2911yescharacteristic
267C2×C8C22×D2911yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—291no—
270C4⋊C4—291no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4—581no—
275C4⋊C4C22×D2911yescharacteristic
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C42—291no—
287C42—291no—
288C42—291no—
289C42—291no—
290C42—581no—
291C23—21no—
292C23—581no—
293C23—581no—
294C23D4×D2911yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—1162no—
298D4—21no—
299D4—21no—
300D4—42no—
301D4—581no—
302D4—581no—
303D4—581no—
304D4—581no—
305D4—1162no—
306D4—1162no—
307D4—1162no—
308D4—1162no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—291no—
315C2×C4—291no—
316C2×C4—291no—
317C2×C4—291no—
318C2×C4—582no—
319C2×C4—581no—
320C2×C4—581no—
321C2×C4—1162no—
322C2×C4—1162no—
323C2×C4—1162no—
324C2×C4—1161no—
325C2×C4D4×D2911yescharacteristic
326C2×C4C23×D2911yescharacteristic
327C8—21no—
328C8—292no—
329C8—581no—
330C8#9080712yescomplemented
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—1161no—
338C22—1161no—
339C22—1161no—
340C22—1161no—
341C22—1161no—
342C22—1161no—
343C22C2×D4×D2911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—292no—
349C4—581no—
350C4—581no—
351C4—581no—
352C4—1161no—
353C4—1161no—
354C4C2×#9080711yescharacteristic
355C4#41×D2911yescharacteristic
356C2—41no—
357C2—81no—
358C2—2321no—
359C2—2321no—
360C2#1427170811yescharacteristic
361C2AGL(1,ℤ/8)×D2911yescharacteristic
362C2#1427196211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#468C2
socleC22×C29C22×D4
hypercenter#468D29
hypocenterC29#3171
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #14271708C2semidirect
2. #14271699C2semidirect
3. #14271571C2semidirect
4. #14271549C2semidirect
5. #14271526C2semidirect
6. #14271524C2semidirect
7. #14271416C2semidirect
8. #14271414C2semidirect
9. #14271411C2semidirect
10. SD16×Dic29C2semidirect
11. #14271248C2semidirect
12. #14271245C2semidirect
13. #14271243C2semidirect
14. M16×Dic29C2semidirect
15. C29×#468C2semidirect
146. C8×C29#41semidirect
148. #6597#41semidirect
184. #468D29semidirect
240. C29#3171semidirect
330. C8#90807semidirect

Maximal subgroups

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

subgroupindex
#142717082
#142716992
#142715712
#142715492
#142715262
#142715242
#142714162
#142714142
#142714112
SD16×Dic292
#142712482
#142712452
#142712432
M16×Dic292
C29×#4682
#317129