Finite Group Databasebeta

← #16831447

Subgroups — #16831447

Order 3712.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271809C211yesmaximal, characteristic, complemented
2#14271525C211yesmaximal, characteristic, complemented
3#14271493C211yesmaximal, characteristic, complemented
4#14271481C211yesmaximal, characteristic, complemented
5#14271450C211yesmaximal, characteristic, complemented
6#14271414C211yesmaximal, characteristic, complemented
7#14271390C211yesmaximal, characteristic, complemented
8#14271378C211yesmaximal, characteristic, complemented
9#14271306C211yesmaximal, characteristic, complemented
10#14271296C211yesmaximal, characteristic, complemented
11#14271273C211yesmaximal, characteristic, complemented
12#14271235C211yesmaximal, characteristic, complemented
13#14271162C211yesmaximal, characteristic, complemented
14C2×#11745157C211yesmaximal, characteristic, complemented
15C29×#547C211yesmaximal, characteristic, complemented
16C2×#41×C29—21no—
17C2×#90805C2211yescharacteristic
18C22×D116C2211yescharacteristic
19C29×C4⋊Q8C2211yescharacteristic, complemented
20C29×#123—21no—
21C29×#123—21no—
22C29×C22⋊Q8—21no—
23C29×#121C2211yescharacteristic
24C29×#121C2211yescharacteristic, complemented
25C4×D4×C29C2211yescharacteristic
26C4×D4×C29C2211yescharacteristic, complemented
27C2×C4⋊C4×C29C2211yescharacteristic
28C2×C4⋊C4×C29C2211yescharacteristic, complemented
29#11745299—21no—
30C2×#90783C2211yescharacteristic, complemented
31C2×#90782C2211yescharacteristic
32C2×#90782C2211yescharacteristic
33#11745292C2211yescharacteristic
34#11745286C2211yescharacteristic
35C2×#90777C2211yescharacteristic, complemented
36C22×#6597C2211yescharacteristic
37#11745256—21no—
38#11745246—21no—
39C22⋊C4×D29—21no—
40#11745237C2211yescharacteristic
41C4×D116C2211yescharacteristic
42#11745180C2211yescharacteristic, complemented
43C22⋊#6597C2211yescharacteristic
44C22⋊#6597C2211yescharacteristic, complemented
45#11745158C2211yescharacteristic, complemented
46#11745158C2211yescharacteristic, complemented
47#11745158C2211yescharacteristic, complemented
48#11745157C2211yescharacteristic
49#11745157C2211yescharacteristic
50#11745157C2211yescharacteristic
51#11745157C2211yescharacteristic
52#11745157C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745156C2211yescharacteristic, complemented
55#11745156C2211yescharacteristic, complemented
56#11745156C2211yescharacteristic, complemented
57C4⋊#6597C2211yescharacteristic, complemented
58#11745151C2211yescharacteristic, complemented
59C23×D29—21no—
60#41×C29—44no—
61C2×Q8×C29—21no—
62C2×D4×C29—21no—
63C2×D4×C29—21no—
64C2×D4×C29D411yescharacteristic
65C2×D4×C29C2311yescharacteristic
66C22×C4×C29—21no—
67C22×C4×C29—21no—
68C22×C4×C29—21no—
69C22×C4×C29C2311yescharacteristic
70C22×C4×C29C2311yescharacteristic
71C2×C22⋊D29—21no—
72C2×C22⋊D29—21no—
73#90805—22no—
74#90805—41no—
75C2×D116—22no—
76C2×D116—21no—
77C2×D116—41no—
78C2×D116C2311yescharacteristic
79C2×D116C2311yescharacteristic
80C2×C4×D29—21no—
81C2×C4×D29—21no—
82C2×Dic58C2311yescharacteristic
83C4⋊C4×C29—21no—
84C4⋊C4×C29—21no—
85C4⋊C4×C29—21no—
86C4⋊C4×C29D411yescharacteristic
87C4⋊C4×C29C2311yescharacteristic
88C4⋊C4×C29C2311yescharacteristic
89C4⋊C4×C29C2311yescharacteristic
90C22⋊C4×C29—21no—
91C22⋊C4×C29—21no—
92C22⋊C4×C29—21no—
93C22⋊C4×C29D411yescharacteristic
94C22⋊C4×C29D411yescharacteristic
95C42×C29C2311yescharacteristic
96C22⋊Dic29—21no—
97#90783—41no—
98#90782—22no—
99#90782—41no—
100#90781—21no—
101#90781—21no—
102#90781—21no—
103#90781—21no—
104C4⋊Dic29C2311yescharacteristic
105#90779—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—
116C22×D29—21no—
117C22×D29—42no—
118C22×D29—42no—
119C22×D29—81no—
120Q8×C29—42no—
121D4×C29—22no—
122D4×C29—21no—
123D4×C29—21no—
124D4×C29—42no—
125D4×C29—42no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—42no—
134C2×C4×C29—42no—
135C2×C4×C29—42no—
136C2×C4×C29C2×D411yescharacteristic
137C2×C4×C29C2×D411yescharacteristic
138C2×C4×C29C2×D411yescharacteristic
139C2×C4×C29C2×D411yescharacteristic
140C2×C4×C29C2411yescharacteristic
141C22⋊D29—42no—
142C22⋊D29—81no—
143C2×Dic29—21no—
144C2×Dic29—21no—
145D116—21no—
146D116—21no—
147D116—21no—
148D116—42no—
149D116#4112yescomplemented
150C4×D29—42no—
151C4×D29—81no—
152Dic58—21no—
153Dic58—21no—
154#6597—21no—
155#6597—21no—
156#6597—21no—
157#6597—21no—
158#3306—291nomaximal, Sylow
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29—21no—
163C22×C29—21no—
164C22×C29—41no—
165C22×C29—41no—
166C22×C29—41no—
167C22×C29AGL(1,ℤ/8)12yes—
168C22×C29C22×D411yescharacteristic
169C2×D29—22no—
170C2×D29—41no—
171C2×D29—41no—
172C2×D29—41no—
173C2×D29—41no—
174C2×D29—41no—
175C2×D29—84no—
176C4×C29—21no—
177C4×C29—21no—
178C4×C29—21no—
179C4×C29—21no—
180C4×C29—41no—
181C4×C29—41no—
182C4×C29—41no—
183C4×C29C2×#4111yescharacteristic
184C4×C29H(5,𝔽2)11yescharacteristic
185Dic29—41no—
186Dic29—41no—
187#547D2911yescharacteristic, complemented
188#546—291no—
189#489—291no—
190#483—291no—
191#481—291no—
192#476—291no—
193#469—291no—
194#465—291no—
195#463—291no—
196#449—291no—
197#447—291no—
198#442—291no—
199#435—291no—
200#417—291no—
201C2×#102—291no—
202C2×C29—22no—
203C2×C29—41no—
204C2×C29—81no—
205C2×C29#54611yescharacteristic
206C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
207C2×C29#57711yescharacteristic
208D29—42no—
209D29—81no—
210C2×#41—21no—
211C2×#41—291no—
212C22×D4—291no—
213C2×SD16—291no—
214C2×D8—291no—
215C2×D8—291no—
216C2×M16—291no—
217C22×C8—291no—
218C4⋊Q8C2×D2911yescharacteristic, complemented
219#124—291no—
220#123—21no—
221#123—21no—
222#123—581no—
223C22⋊Q8—21no—
224C22⋊Q8—291no—
225#121—291no—
226#121—581no—
227#121C2×D2911yescharacteristic
228#121C2×D2911yescharacteristic, complemented
229#120—581no—
230C4×D4—291no—
231C4×D4C2×D2911yescharacteristic
232C4×D4C2×D2911yescharacteristic, complemented
233C2×C4⋊C4C2×D2911yescharacteristic
234C2×C4⋊C4C2×D2911yescharacteristic, complemented
235C2×C22⋊C4—581no—
236#106—291no—
237#106—291no—
238#106—291no—
239C4⋊C8—291no—
240#103—291no—
241#103—291no—
242#103—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246#102—291no—
247#102—291no—
248#102—291no—
249#102—291no—
250C22⋊C8—291no—
251C22⋊C8—291no—
252#97—291no—
253C29#330611yescharacteristic, complemented, Sylow
254C24—581no—
255#41—44no—
256#41—582no—
257#41—1161no—
258C2×Q8—21no—
259C2×Q8—291no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—291no—
263C2×D4—291no—
264C2×D4—582no—
265C2×D4—581no—
266C2×D4—581no—
267C2×D4—581no—
268C2×D4—1161no—
269C2×D4C22⋊D2911yescharacteristic
270C2×D4C22×D2911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—581no—
275C22×C4—581no—
276C22×C4C22×D2911yescharacteristic
277C22×C4C22×D2911yescharacteristic
278SD16—1161no—
279D8—582no—
280D8—1161no—
281M16—1161no—
282C2×C8—291no—
283C2×C8—291no—
284C2×C8—291no—
285C2×C8—291no—
286C2×C8—1161no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—291no—
291C4⋊C4—581no—
292C4⋊C4C22⋊D2911yescharacteristic
293C4⋊C4C22×D2911yescharacteristic
294C4⋊C4C22×D2911yescharacteristic
295C4⋊C4C22×D2911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—581no—
300C22⋊C4—581no—
301C22⋊C4—581no—
302C22⋊C4—581no—
303C22⋊C4—581no—
304C22⋊C4C22⋊D2911yescharacteristic
305C22⋊C4C22⋊D2911yescharacteristic
306C42C22×D2911yescharacteristic
307C23—21no—
308C23—581no—
309C23—581no—
310C23—1162no—
311C23—1162no—
312C23—2321no—
313C23C2×C22⋊D2911yescharacteristic
314C23C2×C22⋊D2911yescharacteristic
315Q8—42no—
316Q8—581no—
317Q8—581no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—292no—
324D4—581no—
325D4—581no—
326D4—581no—
327D4—1162no—
328D4—1162no—
329D4—2321no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—581no—
341C2×C4—581no—
342C2×C4—1162no—
343C2×C4—2321no—
344C2×C4C2×C22⋊D2911yescharacteristic
345C2×C4C2×C22⋊D2911yescharacteristic
346C2×C4C2×C22⋊D2911yescharacteristic
347C2×C4C2×C22⋊D2911yescharacteristic
348C2×C4C23×D2911yescharacteristic
349C8—581no—
350C8—581no—
351C8—581no—
352C8—581no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—582no—
362C22—1161no—
363C22—1161no—
364C22—1161no—
365C22—1161no—
366C22—1161no—
367C22—2324no—
368C22#1174529412yes—
369C22C22×C22⋊D2911yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—1161no—
378C4—1161no—
379C4#41×D2911yescharacteristic
380C4#1174536411yescharacteristic
381C2—22no—
382C2—41no—
383C2—81no—
384C2—1162no—
385C2—2321no—
386C2#1427180111yescharacteristic
387C2C2×#1174529411yescharacteristic
388C2#1427197111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#547C2
socleC22×C29C22×D4
hypercenter#547D29
hypocenterC29#3306
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. #14271809C2semidirect
2. #14271525C2semidirect
3. #14271493C2semidirect
4. #14271481C2semidirect
5. #14271450C2semidirect
6. #14271414C2semidirect
7. #14271390C2semidirect
8. #14271378C2semidirect
9. #14271306C2semidirect
10. #14271296C2semidirect
11. #14271273C2semidirect
12. #14271235C2semidirect
13. #14271162C2semidirect
14. C2×#11745157C2semidirect
15. C29×#547C2semidirect
19. C29×C4⋊Q8C22semidirect
24. C29×#121C22semidirect
26. C4×D4×C29C22semidirect
28. C2×C4⋊C4×C29C22semidirect
30. C2×#90783C22semidirect
35. C2×#90777C22semidirect
42. #11745180C22semidirect
44. C22⋊#6597C22semidirect
45. #11745158C22semidirect
46. #11745158C22semidirect
47. #11745158C22semidirect
54. #11745156C22semidirect
55. #11745156C22semidirect
56. #11745156C22semidirect
57. C4⋊#6597C22semidirect
58. #11745151C22semidirect
149. D116#41semidirect
187. #547D29semidirect
218. C4⋊Q8C2×D29semidirect
228. #121C2×D29semidirect
232. C4×D4C2×D29semidirect
234. C2×C4⋊C4C2×D29semidirect
253. C29#3306semidirect

Maximal subgroups

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

subgroupindex
#142718092
#142715252
#142714932
#142714812
#142714502
#142714142
#142713902
#142713782
#142713062
#142712962
#142712732
#142712352
#142711622
C2×#117451572
C29×#5472
#330629