Finite Group Databasebeta

← #16831477

Subgroups — #16831477

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#14271822C211yesmaximal, characteristic, complemented
2#14271525C211yesmaximal, characteristic, complemented
3#14271498C211yesmaximal, characteristic, complemented
4#14271476C211yesmaximal, characteristic, complemented
5#14271455C211yesmaximal, characteristic, complemented
6#14271407C211yesmaximal, characteristic, complemented
7#14271397C211yesmaximal, characteristic, complemented
8#14271378C211yesmaximal, characteristic, complemented
9#14271306C211yesmaximal, characteristic, complemented
10#14271301C211yesmaximal, characteristic, complemented
11#14271263C211yesmaximal, characteristic, complemented
12#14271235C211yesmaximal, characteristic, complemented
13#14271162C211yesmaximal, characteristic, complemented
14C2×#11745158C211yesmaximal, characteristic, complemented
15C29×#547C211yesmaximal, characteristic, complemented
16C2×#41×C29—21no—
17C2×#90805C2211yescharacteristic
18C22×Dic58C2211yescharacteristic
19C29×C4⋊Q8C2211yescharacteristic
20C29×#123—21no—
21C29×#123—21no—
22C29×C22⋊Q8—21no—
23C29×#121C2211yescharacteristic
24C29×#121C2211yescharacteristic
25C4×D4×C29C2211yescharacteristic
26C4×D4×C29C2211yescharacteristic
27C2×C4⋊C4×C29C2211yescharacteristic
28C2×C4⋊C4×C29C2211yescharacteristic
29#11745301—21no—
30C2×#90783C2211yescharacteristic
31C2×#90783C2211yescharacteristic
32C2×#90782C2211yescharacteristic
33#11745292C2211yescharacteristic
34#11745286C2211yescharacteristic
35C2×#90777C2211yescharacteristic
36C22×#6597C2211yescharacteristic
37#11745258—21no—
38#11745247—21no—
39#11745243—21no—
40#11745237C2211yescharacteristic
41C4×Dic58C2211yescharacteristic
42#11745180C2211yescharacteristic
43C22⋊#6597C2211yescharacteristic
44C22⋊#6597C2211yescharacteristic
45#11745158C2211yescharacteristic
46#11745158C2211yescharacteristic
47#11745158C2211yescharacteristic
48#11745158C2211yescharacteristic
49#11745158C2211yescharacteristic
50#11745158C2211yescharacteristic
51#11745157C2211yescharacteristic
52#11745157C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745155C2211yescharacteristic
55#11745155C2211yescharacteristic
56#11745155C2211yescharacteristic
57C4⋊#6597C2211yescharacteristic
58#11745151C2211yescharacteristic
59#41×C29—44no—
60C2×Q8×C29—21no—
61C2×D4×C29—21no—
62C2×D4×C29—21no—
63C2×D4×C29D411yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C22×C4×C29—21no—
66C22×C4×C29—21no—
67C22×C4×C29—21no—
68C22×C4×C29C2311yescharacteristic
69C22×C4×C29C2311yescharacteristic
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C22×Dic29—21no—
73#90805—22no—
74#90805—41no—
75C2×D116C2311yescharacteristic
76C2×C4×D29—21no—
77C2×Dic58—22no—
78C2×Dic58—21no—
79C2×Dic58—41no—
80C2×Dic58C2311yescharacteristic
81C2×Dic58C2311yescharacteristic
82C4⋊C4×C29—21no—
83C4⋊C4×C29—21no—
84C4⋊C4×C29—21no—
85C4⋊C4×C29D411yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C4⋊C4×C29C2311yescharacteristic
88C4⋊C4×C29C2311yescharacteristic
89C22⋊C4×C29—21no—
90C22⋊C4×C29—21no—
91C22⋊C4×C29—21no—
92C22⋊C4×C29D411yescharacteristic
93C22⋊C4×C29D411yescharacteristic
94C42×C29C2311yescharacteristic
95C22⋊Dic29—21no—
96#90783—22no—
97#90783—41no—
98#90782—41no—
99#90781—21no—
100#90781—21no—
101#90781—21no—
102C4⋊Dic29C2311yescharacteristic
103#90779—21no—
104#90779—21no—
105C4×Dic29—21no—
106#90777—41no—
107C2×#6597—41no—
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C2×#6597C2311yescharacteristic
112C23×C29—21no—
113C23×C29C2×D411yescharacteristic
114C23×C29C2×D411yescharacteristic
115C22×D29—21no—
116Q8×C29—42no—
117D4×C29—22no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—42no—
121D4×C29—42no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—21no—
129C2×C4×C29—42no—
130C2×C4×C29—42no—
131C2×C4×C29—42no—
132C2×C4×C29C2×D411yescharacteristic
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2×D411yescharacteristic
135C2×C4×C29C2×D411yescharacteristic
136C2×C4×C29C2411yescharacteristic
137C22⋊D29—42no—
138C22⋊D29—42no—
139C2×Dic29—21no—
140C2×Dic29—21no—
141C2×Dic29—21no—
142C2×Dic29—42no—
143D116—21no—
144D116—21no—
145C4×D29—42no—
146Dic58—21no—
147Dic58—21no—
148Dic58—21no—
149Dic58—42no—
150Dic58#4112yescomplemented
151#6597—21no—
152#6597—21no—
153#6597—21no—
154#6597—21no—
155#3308—291nomaximal, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29AGL(1,ℤ/8)12yes—
165C22×C29C22×D411yescharacteristic
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—41no—
169C4×C29—21no—
170C4×C29—21no—
171C4×C29—21no—
172C4×C29—21no—
173C4×C29—41no—
174C4×C29—41no—
175C4×C29—41no—
176C4×C29C2×#4111yescharacteristic
177C4×C29H(5,𝔽2)11yescharacteristic
178Dic29—22no—
179Dic29—41no—
180Dic29—41no—
181#548—291no—
182#547D2911yescharacteristic, complemented
183#489—291no—
184#484—291no—
185#480—291no—
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—41no—
198C2×C29—81no—
199C2×C29#54611yescharacteristic
200C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
201C2×C29#57811yescharacteristic
202D29—81no—
203C2×#41—21no—
204C2×#41—291no—
205C22×Q8—291no—
206C2×SD16—291no—
207C2×SD16—291no—
208C2×D8—291no—
209C2×M16—291no—
210C22×C8—291no—
211C4⋊Q8C2×D2911yescharacteristic
212#124—291no—
213#124—581no—
214#123—21no—
215#123—21no—
216C22⋊Q8—21no—
217C22⋊Q8—291no—
218C22⋊Q8—581no—
219#121—291no—
220#121—581no—
221#121C2×D2911yescharacteristic
222#121C2×D2911yescharacteristic
223C4×Q8—291no—
224C4×D4—581no—
225C4×D4C2×D2911yescharacteristic
226C4×D4C2×D2911yescharacteristic
227C2×C4⋊C4C2×D2911yescharacteristic
228C2×C4⋊C4C2×D2911yescharacteristic
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#103—291no—
239#102—291no—
240#102—291no—
241#102—291no—
242#102—291no—
243C22⋊C8—291no—
244C22⋊C8—291no—
245#97—291no—
246C29#330811yescharacteristic, complemented, Sylow
247#41—44no—
248#41—582no—
249#41—1161no—
250C2×Q8—21no—
251C2×Q8—291no—
252C2×Q8—291no—
253C2×Q8—582no—
254C2×Q8—581no—
255C2×Q8—1161no—
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—21no—
265C22×C4—21no—
266C22×C4—581no—
267C22×C4—581no—
268C22×C4C22×D2911yescharacteristic
269C22×C4C22×D2911yescharacteristic
270SD16—582no—
271SD16—1161no—
272D8—1161no—
273M16—1161no—
274C2×C8—291no—
275C2×C8—291no—
276C2×C8—291no—
277C2×C8—291no—
278C2×C8—1161no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—291no—
283C4⋊C4—581no—
284C4⋊C4—581no—
285C4⋊C4C22⋊D2911yescharacteristic
286C4⋊C4C22×D2911yescharacteristic
287C4⋊C4C22×D2911yescharacteristic
288C4⋊C4C22×D2911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4C22⋊D2911yescharacteristic
297C22⋊C4C22⋊D2911yescharacteristic
298C42—581no—
299C42C22×D2911yescharacteristic
300C23—21no—
301C23—581no—
302C23C2×C22⋊D2911yescharacteristic
303C23C2×C22⋊D2911yescharacteristic
304Q8—42no—
305Q8—292no—
306Q8—581no—
307Q8—581no—
308Q8—581no—
309Q8—1162no—
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—581no—
316D4—581no—
317D4—1162no—
318D4—1162no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—581no—
330C2×C4—581no—
331C2×C4—581no—
332C2×C4—1162no—
333C2×C4—1162no—
334C2×C4C2×C22⋊D2911yescharacteristic
335C2×C4C2×C22⋊D2911yescharacteristic
336C2×C4C2×C22⋊D2911yescharacteristic
337C2×C4C2×C22⋊D2911yescharacteristic
338C2×C4C23×D2911yescharacteristic
339C8—581no—
340C8—581no—
341C8—581no—
342C8—581no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—1161no—
352C22—1161no—
353C22—1161no—
354C22#1174529412yes—
355C22C22×C22⋊D2911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—582no—
364C4—1161no—
365C4—1161no—
366C4#41×D2911yescharacteristic
367C4#1174536411yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—2321no—
372C2#1427180111yescharacteristic
373C2C2×#1174529411yescharacteristic
374C2#1427197811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#547C2
socleC22×C29C22×D4
hypercenter#547D29
hypocenterC29#3308
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14271822C2semidirect
2. #14271525C2semidirect
3. #14271498C2semidirect
4. #14271476C2semidirect
5. #14271455C2semidirect
6. #14271407C2semidirect
7. #14271397C2semidirect
8. #14271378C2semidirect
9. #14271306C2semidirect
10. #14271301C2semidirect
11. #14271263C2semidirect
12. #14271235C2semidirect
13. #14271162C2semidirect
14. C2×#11745158C2semidirect
15. C29×#547C2semidirect
150. Dic58#41semidirect
182. #547D29semidirect
246. C29#3308semidirect

Maximal subgroups

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

subgroupindex
#142718222
#142715252
#142714982
#142714762
#142714552
#142714072
#142713972
#142713782
#142713062
#142713012
#142712632
#142712352
#142711622
C2×#117451582
C29×#5472
#330829