Finite Group Databasebeta

← #16830085

Subgroups — #16830085

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#14271710C211yesmaximal, characteristic, complemented
2#14271695C211yesmaximal, characteristic, complemented
3#14271571C211yesmaximal, characteristic, complemented
4#14271551C211yesmaximal, characteristic, complemented
5#14271526C211yesmaximal, characteristic, complemented
6#14271521C211yesmaximal, characteristic, complemented
7#14271415C211yesmaximal, characteristic, complemented
8#14271413C211yesmaximal, characteristic, complemented
9#14271410C211yesmaximal, characteristic, complemented
10#14271408C211yesmaximal, characteristic, complemented
11C4×#90773C211yesmaximal, characteristic, complemented
12C4×#90783C211yesmaximal, characteristic, complemented
13C4×#90782C211yesmaximal, characteristic, complemented
14C4×#90772C211yesmaximal, characteristic, complemented
15C4×D8×C29C211yesmaximal, characteristic, complemented
16C2×#90805—21no—
17C2×D8×C29C2211yescharacteristic
18C4×D4×C29C2211yescharacteristic
19C4×D4×C29C2211yescharacteristic
20#11745302C2211yescharacteristic
21#11745300C2211yescharacteristic
22#11745300C2211yescharacteristic
23#11745298C2211yescharacteristic
24C2×#90783C2211yescharacteristic
25C2×#90782C2211yescharacteristic
26C4×C22⋊D29—21no—
27C4×C22⋊D29—21no—
28#11745288—21no—
29C2×#90773C2211yescharacteristic
30C2×#90772C2211yescharacteristic
31C2×#90772C2211yescharacteristic
32#11745259C2211yescharacteristic
33#11745257C2211yescharacteristic
34#11745252C2211yescharacteristic
35#11745250C2211yescharacteristic
36#11745247—21no—
37#11745246—21no—
38#11745245—21no—
39#11745241—21no—
40C4×D116C2211yescharacteristic
41C42×D29C2211yescharacteristic
42C4×Dic58C2211yescharacteristic
43C29×#107C2211yescharacteristic
44C29×#102C2211yescharacteristic
45C29×#102C2211yescharacteristic
46C4×C8×C29C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745165C2211yescharacteristic
51#11745164C2211yescharacteristic
52#11745163C2211yescharacteristic
53#11745163C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745156C2211yescharacteristic
57#11745155C2211yescharacteristic
58C4×#6597C2211yescharacteristic
59C2×D4×C29C2311yescharacteristic
60C2×D4×C29C2311yescharacteristic
61C22×C4×C29—21no—
62C22×C4×C29—21no—
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67#90805—44no—
68C2×D116—21no—
69C2×D116C2311yescharacteristic
70C2×C4×D29—21no—
71C2×C4×D29D411yescharacteristic
72C2×C4×D29D411yescharacteristic
73C2×C4×D29C2311yescharacteristic
74C2×Dic58—21no—
75C2×Dic58C2311yescharacteristic
76D8×C29—22no—
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C4⋊C4×C29C2311yescharacteristic
80C4⋊C4×C29C2311yescharacteristic
81C22⋊C4×C29—21no—
82C22⋊C4×C29—21no—
83C42×C29C2311yescharacteristic
84C22⋊Dic29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88#90783—22no—
89#90782—22no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93C4⋊Dic29—21no—
94C4⋊Dic29—21no—
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97#90779—21no—
98#90779—21no—
99#90779—21no—
100C4×Dic29—21no—
101C4×Dic29D411yescharacteristic
102C4×Dic29D411yescharacteristic
103C4×Dic29C2311yescharacteristic
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106#90773—22no—
107#90772—22no—
108#90772—22no—
109C23×C29—21no—
110C23×C29—21no—
111C22×D29—21no—
112C22×D29C2×D411yescharacteristic
113D4×C29—21no—
114D4×C29—21no—
115D4×C29—21no—
116D4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—42no—
120C2×C4×C29—42no—
121C2×C4×C29C2×D411yescharacteristic
122C2×C4×C29C2×D411yescharacteristic
123C2×C4×C29C2411yescharacteristic
124C22⋊D29—42no—
125C22⋊D29—42no—
126C22⋊D29—42no—
127C22⋊D29—42no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—21no—
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133C2×Dic29C2×D411yescharacteristic
134D116—21no—
135D116—21no—
136D116—42no—
137C4×D29—22no—
138C4×D29—21no—
139C4×D29—21no—
140C4×D29—41no—
141C4×D29—42no—
142Dic58—21no—
143Dic58—21no—
144Dic58—42no—
145C8×C29—21no—
146C8×C29#4112yescomplemented
147#6597—21no—
148#6597#4112yescomplemented
149#3171—291nomaximal, Sylow
150C22×C29—41no—
151C22×C29—41no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29C22×D411yescharacteristic
157C2×D29—21no—
158C2×D29—21no—
159C2×D29—21no—
160C2×D29—41no—
161C2×D29—41no—
162C2×D29—41no—
163C4×C29—21no—
164C4×C29—41no—
165C4×C29—41no—
166C4×C29AGL(1,ℤ/8)12yes—
167C4×C29C2×#4111yescharacteristic
168C4×C29C2×#4111yescharacteristic
169Dic29—21no—
170Dic29—21no—
171Dic29—21no—
172Dic29—41no—
173Dic29—41no—
174Dic29—41no—
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#468—291no—
185C4×SD16—291no—
186C4×SD16—291no—
187C4×D8—291no—
188C4×D8D2911yescharacteristic, complemented
189C4×M16—291no—
190C2×C29—81no—
191C2×C29—81no—
192C2×C29#53211yescharacteristic
193C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
194C2×C29#57511yescharacteristic
195D29—41no—
196D29—81no—
197C2×#41—581no—
198C2×SD16—291no—
199C2×SD16—291no—
200C2×D8—291no—
201C2×D8C2×D2911yescharacteristic
202C2×M16—291no—
203C2×M16—291no—
204C4⋊Q8—291no—
205#127—291no—
206#126—581no—
207#125—291no—
208#124—291no—
209#124—581no—
210#123—581no—
211C22⋊Q8—291no—
212#121—291no—
213#121—291no—
214#121—291no—
215#121—581no—
216C4×Q8—291no—
217C4×D4—291no—
218C4×D4—581no—
219C4×D4—581no—
220C4×D4C2×D2911yescharacteristic
221C4×D4C2×D2911yescharacteristic
222#117—581no—
223C2×C42—291no—
224#107—291no—
225#107C2×D2911yescharacteristic
226#106—291no—
227#106—291no—
228#103—291no—
229#103—291no—
230#102—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234#102C2×D2911yescharacteristic
235#102C2×D2911yescharacteristic
236#97—291no—
237#97—291no—
238C4×C8—291no—
239C4×C8C2×D2911yescharacteristic
240C29#317111yescharacteristic, complemented, Sylow
241#41—1164no—
242C2×Q8—291no—
243C2×Q8—581no—
244C2×D4—291no—
245C2×D4—581no—
246C2×D4—581no—
247C2×D4—581no—
248C2×D4—581no—
249C2×D4—581no—
250C2×D4C22×D2911yescharacteristic
251C2×D4C22×D2911yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—291no—
255C22×C4—291no—
256C22×C4—291no—
257C22×C4—581no—
258SD16—582no—
259SD16—582no—
260D8—22no—
261D8—582no—
262M16—582no—
263M16—582no—
264C2×C8—291no—
265C2×C8—291no—
266C2×C8C22×D2911yescharacteristic
267C2×C8C22×D2911yescharacteristic
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—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—581no—
290C42C22×D2911yescharacteristic
291C23—21no—
292C23—21no—
293C23—291no—
294C23—581no—
295Q8—581no—
296Q8—581no—
297Q8—1162no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—581no—
303D4—581no—
304D4—1162no—
305D4—1162no—
306D4—1162no—
307D4—1162no—
308D4—1162no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—291no—
314C2×C4—291no—
315C2×C4—291no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—582no—
319C2×C4—581no—
320C2×C4—581no—
321C2×C4—581no—
322C2×C4—1161no—
323C2×C4—1162no—
324C2×C4D4×D2911yescharacteristic
325C2×C4D4×D2911yescharacteristic
326C2×C4C23×D2911yescharacteristic
327C8—21no—
328C8—292no—
329C8—581no—
330C8#9080512yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—581no—
338C22—581no—
339C22—581no—
340C22—1161no—
341C22—1161no—
342C22—1161no—
343C22C2×D4×D2911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—581no—
348C4—581no—
349C4—581no—
350C4—1161no—
351C4—1161no—
352C4—1161no—
353C4#1174527312yes—
354C4C2×#9080511yescharacteristic
355C4#41×D2911yescharacteristic
356C2—81no—
357C2—81no—
358C2—1161no—
359C2—2321no—
360C2#1427171011yescharacteristic
361C2C2×#1174527311yescharacteristic
362C2#1427196011yescharacteristic
subgroupG/H
centerC2×C4D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC4×D8×C29C2
socleC22×C29C22×D4
hypercenterC4×D8D29
hypocenterC29#3171
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #14271710C2semidirect
2. #14271695C2semidirect
3. #14271571C2semidirect
4. #14271551C2semidirect
5. #14271526C2semidirect
6. #14271521C2semidirect
7. #14271415C2semidirect
8. #14271413C2semidirect
9. #14271410C2semidirect
10. #14271408C2semidirect
11. C4×#90773C2semidirect
12. C4×#90783C2semidirect
13. C4×#90782C2semidirect
14. C4×#90772C2semidirect
15. C4×D8×C29C2semidirect
146. C8×C29#41semidirect
148. #6597#41semidirect
188. C4×D8D29semidirect
240. C29#3171semidirect
330. C8#90805semidirect

Maximal subgroups

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

subgroupindex
#142717102
#142716952
#142715712
#142715512
#142715262
#142715212
#142714152
#142714132
#142714102
#142714082
C4×#907732
C4×#907832
C4×#907822
C4×#907722
C4×D8×C292
#317129