Finite Group Databasebeta

← #16831476

Subgroups — #16831476

Order 3712.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271820C211yesmaximal, characteristic, complemented
2#14271813C211yesmaximal, characteristic, complemented
3#14271521C211yesmaximal, characteristic, complemented
4#14271499C211yesmaximal, characteristic, complemented
5#14271475C211yesmaximal, characteristic, complemented
6#14271456C211yesmaximal, characteristic, complemented
7#14271407C211yesmaximal, characteristic, complemented
8#14271396C211yesmaximal, characteristic, complemented
9#14271376C211yesmaximal, characteristic, complemented
10#14271300C211yesmaximal, characteristic, complemented
11#14271264C211yesmaximal, characteristic, complemented
12#14271237C211yesmaximal, characteristic, complemented
13#14271164C211yesmaximal, characteristic, complemented
14#103×D29C211yesmaximal, characteristic, complemented
15C29×#449C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×Q8×D29C2211yescharacteristic
18C2×#90807—21no—
19C2×SD16×C29C2211yescharacteristic
20C2×D8×C29C2211yescharacteristic
21C29×#121C2211yescharacteristic
22Q8×Dic29C2211yescharacteristic
23#11745300—21no—
24#11745300C2211yescharacteristic
25#11745300C2211yescharacteristic
26#11745298—21no—
27#11745298C2211yescharacteristic
28#11745297—21no—
29D4×Dic29C2211yescharacteristic
30C2×#90783C2211yescharacteristic
31C4×C22⋊D29—21no—
32C4×C22⋊D29C2211yescharacteristic
33C2×C4⋊Dic29C2211yescharacteristic
34#11745286—21no—
35#11745286C2211yescharacteristic
36C2×#90777C2211yescharacteristic
37C2×C8×D29C2211yescharacteristic
38C4⋊C4×D29C2211yescharacteristic
39#11745250C2211yescharacteristic
40#11745245—21no—
41#11745240—21no—
42C29×#103C2211yescharacteristic
43C29×#102C2211yescharacteristic
44C29×C22⋊C8C2211yescharacteristic
45#11745183C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745180C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745166C2211yescharacteristic
52#11745166C2211yescharacteristic
53#11745164C2211yescharacteristic
54#11745164C2211yescharacteristic
55#11745163C2211yescharacteristic
56#11745162C2211yescharacteristic
57#11745158C2211yescharacteristic
58#11745155C2211yescharacteristic
59#41×C29—22no—
60#41×C29—41no—
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29—21no—
63C2×D4×C29—21no—
64C2×D4×C29C2311yescharacteristic
65C2×D4×C29C2311yescharacteristic
66C22×C4×C29—21no—
67C22×C4×C29C2311yescharacteristic
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29D411yescharacteristic
71C22×Dic29—21no—
72C22×Dic29—21no—
73Q8×D29—22no—
74Q8×D29—41no—
75#90807—44no—
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C4×D29C2311yescharacteristic
79C2×Dic58—21no—
80C2×Dic58—21no—
81C2×Dic58C2311yescharacteristic
82SD16×C29—22no—
83D8×C29—41no—
84C2×C8×C29C2311yescharacteristic
85C2×C8×C29C2311yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C22⋊C4×C29—21no—
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29—21no—
91C22⋊Dic29—21no—
92C22⋊Dic29—21no—
93C22⋊Dic29—21no—
94C22⋊Dic29D411yescharacteristic
95#90783—41no—
96#90781D411yescharacteristic
97C4⋊Dic29—21no—
98C4⋊Dic29—21no—
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779—21no—
104#90779—21no—
105#90779D411yescharacteristic
106C4×Dic29—21no—
107C4×Dic29C2311yescharacteristic
108#90777—41no—
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C8×D29—41no—
112C23×C29—21no—
113C23×C29—21no—
114C23×C29C2×D411yescharacteristic
115C22×D29C2×D411yescharacteristic
116Q8×C29—21no—
117Q8×C29#4112yescomplemented
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—21no—
121D4×C29—21no—
122D4×C29—42no—
123D4×C29—42no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—42no—
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2411yescharacteristic
131C22⋊D29—22no—
132C22⋊D29—42no—
133C22⋊D29—42no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—21no—
138C2×Dic29—42no—
139C2×Dic29—42no—
140C2×Dic29C2×D411yescharacteristic
141C2×Dic29C2×D411yescharacteristic
142C2×Dic29C2×D411yescharacteristic
143C4×D29—21no—
144C4×D29—21no—
145C4×D29—42no—
146C4×D29—42no—
147Dic58—21no—
148Dic58—21no—
149Dic58—42no—
150Dic58—42no—
151C8×C29—21no—
152C8×C29—21no—
153#6597—21no—
154#6597—21no—
155#3308—291nomaximal, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29C22×D411yescharacteristic
166C2×D29—21no—
167C2×D29—21no—
168C2×D29AGL(1,ℤ/8)12yes—
169C4×C29—22no—
170C4×C29—21no—
171C4×C29—41no—
172C4×C29C2×#4111yescharacteristic
173C4×C29H(5,𝔽2)11yescharacteristic
174Dic29—21no—
175Dic29—21no—
176Dic29—21no—
177Dic29—41no—
178Dic29—41no—
179Dic29—41no—
180Dic29—41no—
181#548—291no—
182#547—291no—
183#489—291no—
184#484—291no—
185#480—291no—
186#477—291no—
187#468—291no—
188#466—291no—
189#463—291no—
190#449D2911yescharacteristic, complemented
191#448—291no—
192#440—291no—
193#435—291no—
194#417—291no—
195C2×#103—291no—
196C2×C29—41no—
197C2×C29—81no—
198C2×C29—81no—
199C2×C29#54611yescharacteristic
200C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
201C2×C29#57811yescharacteristic
202D29—22no—
203C2×#41—581no—
204C2×#41C2×D2911yescharacteristic
205C22×Q8—291no—
206C2×SD16—291no—
207C2×SD16C2×D2911yescharacteristic
208C2×D8C2×D2911yescharacteristic
209C2×M16—291no—
210C22×C8—291no—
211C4⋊Q8—291no—
212#124—291no—
213#124—581no—
214#123—581no—
215#123—581no—
216C22⋊Q8—291no—
217C22⋊Q8—581no—
218C22⋊Q8—581no—
219#121—291no—
220#121—291no—
221#121—581no—
222#121C2×D2911yescharacteristic
223C4×Q8—291no—
224C4×D4—291no—
225C4×D4—291no—
226C4×D4—581no—
227C2×C4⋊C4—291no—
228C2×C4⋊C4—291no—
229#107—291no—
230#107—291no—
231#107—291no—
232C4⋊C8—291no—
233#103—291no—
234#103—291no—
235#103—291no—
236#103—291no—
237#103—291no—
238#103C2×D2911yescharacteristic
239#102—291no—
240#102—291no—
241#102—291no—
242#102C2×D2911yescharacteristic
243C22⋊C8—291no—
244C22⋊C8C2×D2911yescharacteristic
245#97—291no—
246C29#330811yescharacteristic, complemented, Sylow
247#41—22no—
248#41—41no—
249#41—1164no—
250C2×Q8—291no—
251C2×Q8—581no—
252C2×Q8—581no—
253C2×Q8—582no—
254C2×Q8—1161no—
255C2×Q8C22×D2911yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—291no—
259C2×D4—581no—
260C2×D4—581no—
261C2×D4C22×D2911yescharacteristic
262C2×D4C22×D2911yescharacteristic
263C22×C4—21no—
264C22×C4—291no—
265C22×C4—581no—
266C22×C4—581no—
267C22×C4—581no—
268C22×C4—581no—
269C22×C4C22×D2911yescharacteristic
270SD16—22no—
271SD16—1161no—
272D8—41no—
273M16—1161no—
274C2×C8—291no—
275C2×C8—291no—
276C2×C8—1161no—
277C2×C8C22×D2911yescharacteristic
278C2×C8C22×D2911yescharacteristic
279C4⋊C4—291no—
280C4⋊C4—291no—
281C4⋊C4—291no—
282C4⋊C4—291no—
283C4⋊C4—581no—
284C4⋊C4—581no—
285C4⋊C4—581no—
286C4⋊C4—581no—
287C4⋊C4—581no—
288C4⋊C4C22×D2911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—291no—
291C22⋊C4—291no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C22⋊C4—581no—
298C42—291no—
299C42—581no—
300C23—21no—
301C23—21no—
302C23—291no—
303C23D4×D2911yescharacteristic
304Q8—21no—
305Q8—581no—
306Q8—581no—
307Q8—1162no—
308Q8—1162no—
309Q8#9080712yescomplemented
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—42no—
316D4—582no—
317D4—1162no—
318D4—1162no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—291no—
325C2×C4—291no—
326C2×C4—291no—
327C2×C4—581no—
328C2×C4—581no—
329C2×C4—581no—
330C2×C4—581no—
331C2×C4—581no—
332C2×C4—581no—
333C2×C4—1162no—
334C2×C4—1162no—
335C2×C4—1162no—
336C2×C4—1162no—
337C2×C4D4×D2911yescharacteristic
338C2×C4C23×D2911yescharacteristic
339C8—21no—
340C8—21no—
341C8—581no—
342C8—581no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—292no—
353C22—581no—
354C22—581no—
355C22C2×D4×D2911yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—581no—
360C4—581no—
361C4—581no—
362C4—1161no—
363C4—1161no—
364C4—1161no—
365C4—1161no—
366C4C2×#9080711yescharacteristic
367C4#1174535911yescharacteristic
368C2—41no—
369C2—81no—
370C2—81no—
371C2—582no—
372C2#1427180011yescharacteristic
373C2AGL(1,ℤ/8)×D2911yescharacteristic
374C2#1427197711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#449C2
socleC22×C29C22×D4
hypercenter#449D29
hypocenterC29#3308
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14271820C2semidirect
2. #14271813C2semidirect
3. #14271521C2semidirect
4. #14271499C2semidirect
5. #14271475C2semidirect
6. #14271456C2semidirect
7. #14271407C2semidirect
8. #14271396C2semidirect
9. #14271376C2semidirect
10. #14271300C2semidirect
11. #14271264C2semidirect
12. #14271237C2semidirect
13. #14271164C2semidirect
14. #103×D29C2semidirect
15. C29×#449C2semidirect
117. Q8×C29#41semidirect
190. #449D29semidirect
246. C29#3308semidirect
309. Q8#90807semidirect

Maximal subgroups

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

subgroupindex
#142718202
#142718132
#142715212
#142714992
#142714752
#142714562
#142714072
#142713962
#142713762
#142713002
#142712642
#142712372
#142711642
#103×D292
C29×#4492
#330829