Finite Group Databasebeta

← #16831481

Subgroups — #16831481

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#14271819C211yesmaximal, characteristic, complemented
2#14271814C211yesmaximal, characteristic, complemented
3#14271521C211yesmaximal, characteristic, complemented
4#14271500C211yesmaximal, characteristic, complemented
5#14271457C211yesmaximal, characteristic, complemented
6#14271410C211yesmaximal, characteristic, complemented
7#14271397C211yesmaximal, characteristic, complemented
8#14271377C211yesmaximal, characteristic, complemented
9#14271309C211yesmaximal, characteristic, complemented
10#14271304C211yesmaximal, characteristic, complemented
11#14271262C211yesmaximal, characteristic, complemented
12#14271231C211yesmaximal, characteristic, complemented
13#14271161C211yesmaximal, characteristic, complemented
14C2×#11745158C211yesmaximal, characteristic, complemented
15C29×#480C211yesmaximal, characteristic, complemented
16C2×#90807C2211yescharacteristic
17C2×#90805—21no—
18C22×Dic58C2211yescharacteristic
19C29×#121C2211yescharacteristic
20C2×C4⋊C4×C29C2211yescharacteristic
21#11745301—21no—
22#11745298C2211yescharacteristic
23D4×Dic29—21no—
24C2×#90782C2211yescharacteristic
25#11745292C2211yescharacteristic
26#11745291—21no—
27C4×C22⋊D29C2211yescharacteristic
28C22×#6597C2211yescharacteristic
29C2×#90773C2211yescharacteristic
30C2×#90773C2211yescharacteristic
31C2×#90772C2211yescharacteristic
32#11745259C2211yescharacteristic
33#11745258—21no—
34#11745257C2211yescharacteristic
35#11745256—21no—
36#11745255C2211yescharacteristic
37C4⋊C4×D29C2211yescharacteristic
38#11745250C2211yescharacteristic
39#11745249C2211yescharacteristic
40#11745247—21no—
41#11745240—21no—
42C29×#107C2211yescharacteristic
43C29×#107C2211yescharacteristic
44C29×#102C2211yescharacteristic
45C29×#102C2211yescharacteristic
46C29×C22⋊C8C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745168C2211yescharacteristic
49#11745164C2211yescharacteristic
50#11745164C2211yescharacteristic
51#11745163C2211yescharacteristic
52#11745162C2211yescharacteristic
53#11745158C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745158C2211yescharacteristic
56#11745158C2211yescharacteristic
57#11745157C2211yescharacteristic
58#11745155C2211yescharacteristic
59C2×D4×C29—21no—
60C2×D4×C29C2311yescharacteristic
61C22×C4×C29—21no—
62C22×C4×C29C2311yescharacteristic
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29D411yescharacteristic
66C22×Dic29—21no—
67C22×Dic29—21no—
68#90807—22no—
69#90807—41no—
70#90805—44no—
71C2×D116—21no—
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29C2311yescharacteristic
76C2×Dic58—22no—
77C2×Dic58—21no—
78C2×Dic58—21no—
79C2×Dic58—41no—
80C2×Dic58C2311yescharacteristic
81C2×Dic58C2311yescharacteristic
82C2×C8×C29C2311yescharacteristic
83C2×C8×C29C2311yescharacteristic
84C4⋊C4×C29—21no—
85C4⋊C4×C29C2311yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C4⋊C4×C29C2311yescharacteristic
88C22⋊C4×C29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29—21no—
91C22⋊Dic29D411yescharacteristic
92#90782—41no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781D411yescharacteristic
98C4⋊Dic29—21no—
99C4⋊Dic29C2311yescharacteristic
100#90779—21no—
101#90779—21no—
102#90779—21no—
103#90779D411yescharacteristic
104C4×Dic29—21no—
105C4×Dic29C2311yescharacteristic
106C2×#6597—41no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109#90773—22no—
110#90773—41no—
111#90772—41no—
112C23×C29—21no—
113C23×C29C2×D411yescharacteristic
114C22×D29—21no—
115C22×D29C2×D411yescharacteristic
116D4×C29—21no—
117D4×C29—21no—
118D4×C29—42no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—42no—
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2411yescharacteristic
127C22⋊D29—22no—
128C22⋊D29—42no—
129C22⋊D29—42no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—42no—
134C2×Dic29—42no—
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138D116—21no—
139D116—21no—
140D116—42no—
141C4×D29—21no—
142C4×D29—21no—
143C4×D29—42no—
144C4×D29—42no—
145Dic58—21no—
146Dic58—21no—
147Dic58—21no—
148Dic58—42no—
149Dic58—42no—
150Dic58#4112yescomplemented
151C8×C29—21no—
152C8×C29—21no—
153#6597—21no—
154#6597—21no—
155#3308—291nomaximal, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—41no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29AGL(1,ℤ/8)12yes—
162C22×C29C22×D411yescharacteristic
163C2×D29—21no—
164C2×D29—21no—
165C2×D29—21no—
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—41no—
169C4×C29—21no—
170C4×C29—41no—
171C4×C29—41no—
172C4×C29—41no—
173C4×C29C2×#4111yescharacteristic
174C4×C29H(5,𝔽2)11yescharacteristic
175Dic29—22no—
176Dic29—21no—
177Dic29—21no—
178Dic29—21no—
179Dic29—41no—
180Dic29—41no—
181#548—291no—
182#547—291no—
183#489—291no—
184#484—291no—
185#480D2911yescharacteristic, complemented
186#477—291no—
187#468—291no—
188#466—291no—
189#463—291no—
190#449—291no—
191#448—291no—
192#440—291no—
193#435—291no—
194#417—291no—
195C2×#103—291no—
196C2×C29—22no—
197C2×C29—81no—
198C2×C29#54611yescharacteristic
199C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
200C2×C29#57811yescharacteristic
201D29—41no—
202D29—81no—
203C2×#41—291no—
204C2×#41—581no—
205C22×Q8—291no—
206C2×SD16—291no—
207C2×SD16—291no—
208C2×D8—291no—
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⋊C4C2×D2911yescharacteristic
229#107—291no—
230#107C2×D2911yescharacteristic
231#107C2×D2911yescharacteristic
232C4⋊C8—291no—
233#103—291no—
234#103—291no—
235#103—291no—
236#103—291no—
237#103—291no—
238#103—291no—
239#102—291no—
240#102—291no—
241#102C2×D2911yescharacteristic
242#102C2×D2911yescharacteristic
243C22⋊C8—291no—
244C22⋊C8C2×D2911yescharacteristic
245#97—291no—
246C29#330811yescharacteristic, complemented, Sylow
247#41—582no—
248#41—1164no—
249#41—1161no—
250C2×Q8—291no—
251C2×Q8—291no—
252C2×Q8—581no—
253C2×Q8—582no—
254C2×Q8—581no—
255C2×Q8—1161no—
256C2×D4—21no—
257C2×D4—291no—
258C2×D4—291no—
259C2×D4—581no—
260C2×D4—581no—
261C2×D4—581no—
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—582no—
271SD16—1161no—
272D8—1161no—
273M16—1161no—
274C2×C8—291no—
275C2×C8—291no—
276C2×C8—1161no—
277C2×C8C22×D2911yescharacteristic
278C2×C8C22×D2911yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—291no—
281C4⋊C4—291no—
282C4⋊C4—581no—
283C4⋊C4—581no—
284C4⋊C4—581no—
285C4⋊C4—581no—
286C4⋊C4C22×D2911yescharacteristic
287C4⋊C4C22×D2911yescharacteristic
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—291no—
302C23—581no—
303C23D4×D2911yescharacteristic
304Q8—292no—
305Q8—581no—
306Q8—581no—
307Q8—581no—
308Q8—1162no—
309Q8—1162no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—582no—
314D4—581no—
315D4—581no—
316D4—1162no—
317D4—1162no—
318D4—1162no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—291no—
326C2×C4—291no—
327C2×C4—291no—
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—41no—
346C22—41no—
347C22—41no—
348C22—581no—
349C22—581no—
350C22—581no—
351C22—1161no—
352C22—1161no—
353C22—1161no—
354C22#1174527312yes—
355C22C2×D4×D2911yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—581no—
361C4—582no—
362C4—581no—
363C4—581no—
364C4—1161no—
365C4—1161no—
366C4#41×D2911yescharacteristic
367C4#1174536411yescharacteristic
368C2—22no—
369C2—81no—
370C2—1161no—
371C2—2321no—
372C2#1427180511yescharacteristic
373C2C2×#1174527311yescharacteristic
374C2#1427197911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#480C2
socleC22×C29C22×D4
hypercenter#480D29
hypocenterC29#3308
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #14271819C2semidirect
2. #14271814C2semidirect
3. #14271521C2semidirect
4. #14271500C2semidirect
5. #14271457C2semidirect
6. #14271410C2semidirect
7. #14271397C2semidirect
8. #14271377C2semidirect
9. #14271309C2semidirect
10. #14271304C2semidirect
11. #14271262C2semidirect
12. #14271231C2semidirect
13. #14271161C2semidirect
14. C2×#11745158C2semidirect
15. C29×#480C2semidirect
150. Dic58#41semidirect
185. #480D29semidirect
246. C29#3308semidirect

Maximal subgroups

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

subgroupindex
#142718192
#142718142
#142715212
#142715002
#142714572
#142714102
#142713972
#142713772
#142713092
#142713042
#142712622
#142712312
#142711612
C2×#117451582
C29×#4802
#330829