Finite Group Databasebeta

← #16831064

Subgroups — #16831064

Order 3712.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745280C211yesmaximal, characteristic, complemented
2C2×Q16×D29C211yesmaximal, characteristic, complemented
3Q8×D116C211yesmaximal, characteristic, complemented
4#14271825C211yesmaximal, characteristic
5#14271557C211yesmaximal, characteristic, complemented
6#14271422C211yesmaximal, characteristic, complemented
7#14271393C211yesmaximal, characteristic, complemented
8#14271385C211yesmaximal, characteristic, complemented
9#14271373C211yesmaximal, characteristic, complemented
10#14271328C211yesmaximal, characteristic, complemented
11#14271320C211yesmaximal, characteristic, complemented
12#14271320C211yesmaximal, characteristic, complemented
13#14271303C211yesmaximal, characteristic, complemented
14#14271236C211yesmaximal, characteristic, complemented
15C29×#441C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×Q8×D29C2211yescharacteristic
18C2×Q8×D29C2211yescharacteristic
19C2×Q8×D29C2211yescharacteristic
20C2×Q16×C29C2211yescharacteristic
21C4×Q8×C29C2211yescharacteristic
22C4×Q8×C29C2211yescharacteristic
23C2×#90785C2211yescharacteristic
24C2×#90785C2211yescharacteristic
25C2×#90785C2211yescharacteristic
26C2×#90784C2211yescharacteristic
27#11745280—24no—
28Q16×D29—24no—
29C2×Dic116C2211yescharacteristic
30C2×Dic116C2211yescharacteristic
31C2×#90773C2211yescharacteristic
32C2×#90773C2211yescharacteristic
33C2×#90772C2211yescharacteristic
34C2×C8×D29C2211yescharacteristic
35#11745259—21no—
36#11745259—21no—
37#11745259—21no—
38#11745259C2211yescharacteristic
39#11745259C2211yescharacteristic
40#11745259C2211yescharacteristic
41#11745257—21no—
42#11745257C2211yescharacteristic
43#11745237—21no—
44#11745237C2211yescharacteristic
45C4×D116—21no—
46C4×D116—21no—
47C4×D116C2211yescharacteristic
48#11745231—21no—
49#11745231C2211yescharacteristic
50C29×#106C2211yescharacteristic
51C29×#103C2211yescharacteristic
52C29×#103C2211yescharacteristic
53C29×#97C2211yescharacteristic
54#11745168C2211yescharacteristic
55#11745168C2211yescharacteristic
56#11745158C2211yescharacteristic
57#11745158C2211yescharacteristic
58#11745158C2211yescharacteristic
59#11745157C2211yescharacteristic
60C4⋊#6597C2211yescharacteristic
61C2×Q8×C29C2311yescharacteristic
62C2×Q8×C29C2311yescharacteristic
63#90809—22no—
64#90809—41no—
65Q8×D29—22no—
66Q8×D29—22no—
67Q8×D29—22no—
68Q8×D29—41no—
69Q8×D29—41no—
70Q8×D29—41no—
71C2×D116—21no—
72C2×D116—21no—
73C2×D116D411yescharacteristic
74C2×D116C2311yescharacteristic
75C2×C4×D29—21no—
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C4×D29—21no—
79C2×C4×D29C2311yescharacteristic
80C2×C4×D29C2311yescharacteristic
81C2×Dic58—21no—
82C2×Dic58—21no—
83C2×Dic58—21no—
84C2×Dic58C2311yescharacteristic
85C2×Dic58C2311yescharacteristic
86C2×Dic58C2311yescharacteristic
87Q16×C29D414yescomplemented
88C2×C8×C29C2311yescharacteristic
89C2×C8×C29C2311yescharacteristic
90C4⋊C4×C29—21no—
91C4⋊C4×C29—21no—
92C4⋊C4×C29C2311yescharacteristic
93C4⋊C4×C29C2311yescharacteristic
94C42×C29—21no—
95C42×C29—21no—
96C42×C29C2311yescharacteristic
97#90785—22no—
98#90785—22no—
99#90785—22no—
100#90784—22no—
101#90781—21no—
102#90781—21no—
103#90781—21no—
104#90781—21no—
105#90781—21no—
106#90781—21no—
107#90781D411yescharacteristic
108#90781D411yescharacteristic
109C4⋊Dic29—21no—
110C4⋊Dic29—21no—
111C4⋊Dic29—21no—
112C4⋊Dic29—21no—
113C4⋊Dic29—21no—
114C4⋊Dic29D411yescharacteristic
115C2×#6597C2311yescharacteristic
116C2×#6597C2311yescharacteristic
117Dic116—22no—
118Dic116—41no—
119#90773—22no—
120#90773—41no—
121#90772—22no—
122C8×D29—22no—
123C22×D29—21no—
124C22×D29C2×D411yescharacteristic
125C22×D29C2×D411yescharacteristic
126Q8×C29—21no—
127Q8×C29—21no—
128Q8×C29C2×D412yes—
129Q8×C29C2×D412yes—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29C2×D411yescharacteristic
135C2×C4×C29C2×D411yescharacteristic
136C2×C4×C29C2411yescharacteristic
137C2×Dic29—21no—
138C2×Dic29—21no—
139C2×Dic29—21no—
140C2×Dic29C2×D411yescharacteristic
141C2×Dic29C2×D411yescharacteristic
142D116—22no—
143D116—21no—
144D116—21no—
145D116—42no—
146D116—42no—
147C4×D29—21no—
148C4×D29—21no—
149C4×D29—21no—
150C4×D29—21no—
151C4×D29—42no—
152C4×D29—42no—
153C4×D29—42no—
154C4×D29—42no—
155Dic58—21no—
156Dic58—21no—
157Dic58—21no—
158Dic58—21no—
159Dic58—21no—
160Dic58—21no—
161Dic58—42no—
162Dic58—42no—
163Dic58—42no—
164C8×C29—21no—
165C8×C29C2×D412yes—
166#6597—21no—
167#6597—21no—
168#3270—291nomaximal, Sylow
169C22×C29C22×D411yescharacteristic
170C2×D29—21no—
171C2×D29—21no—
172C2×D29—21no—
173C2×D29—21no—
174C2×D29—21no—
175C2×D29—41no—
176C2×D29—41no—
177C2×D29—41no—
178C2×D29#13712yescomplemented
179C4×C29—22no—
180C4×C29—22no—
181C4×C29—21no—
182C4×C29—21no—
183C4×C29—41no—
184C4×C29—41no—
185C4×C29C22×D411yescharacteristic
186C4×C29H(5,𝔽2)11yescharacteristic
187Dic29—21no—
188Dic29—21no—
189Dic29—41no—
190Dic29—41no—
191Dic29—41no—
192C2×#137—291no—
193C22×Q16—291no—
194D4×Q8—291no—
195#548—291no—
196#497—291no—
197#470—291no—
198#465—291no—
199#464—291no—
200#462—291no—
201#452—291no—
202#451—291no—
203#451—291no—
204#448—291no—
205#441D2911yescharacteristic, complemented
206#435—291no—
207C2×C29D4211yescharacteristic
208C2×C29C2×#13711yescharacteristic
209C2×C29#57811yescharacteristic
210D29—22no—
211D29—41no—
212D29—81no—
213C2×#41—291no—
214C22×Q8—291no—
215C22×Q8—291no—
216C22×Q8—291no—
217#137—584no—
218C2×Q16—291no—
219C2×Q16—291no—
220C2×Q16—291no—
221C2×Q16—291no—
222C2×Q16—291no—
223C2×Q16—584no—
224C2×Q16C2×D2911yescharacteristic
225C2×SD16—291no—
226C2×SD16—291no—
227C2×SD16—291no—
228C2×M16—291no—
229C22×C8—291no—
230C4⋊Q8—291no—
231C4⋊Q8—581no—
232#124—291no—
233#124—581no—
234C22⋊Q8—291no—
235C22⋊Q8—291no—
236C22⋊Q8—291no—
237C22⋊Q8—581no—
238C22⋊Q8—581no—
239C22⋊Q8—581no—
240#121—291no—
241#121—581no—
242C4×Q8C2×D2911yescharacteristic
243C4×Q8C2×D2911yescharacteristic
244C4×D4—291no—
245C4×D4—581no—
246C4×D4—581no—
247#106C2×D2911yescharacteristic
248C4⋊C8—291no—
249#103—291no—
250#103—291no—
251#103—291no—
252#103C2×D2911yescharacteristic
253#103C2×D2911yescharacteristic
254#102—291no—
255C22⋊C8—291no—
256C22⋊C8—291no—
257#97C2×D2911yescharacteristic
258C29#327011yescharacteristic, complemented, Sylow
259#41—582no—
260#41—1161no—
261C2×Q8—291no—
262C2×Q8—291no—
263C2×Q8—291no—
264C2×Q8—581no—
265C2×Q8—581no—
266C2×Q8—581no—
267C2×Q8—582no—
268C2×Q8—582no—
269C2×Q8—582no—
270C2×Q8—1161no—
271C2×Q8—1161no—
272C2×Q8—1161no—
273C2×Q8C22×D2911yescharacteristic
274C2×Q8C22×D2911yescharacteristic
275C2×D4—291no—
276C2×D4—291no—
277C2×D4—581no—
278C2×D4—581no—
279C22×C4—291no—
280C22×C4—291no—
281C22×C4—581no—
282C22×C4—581no—
283C22×C4—581no—
284C22×C4—581no—
285Q16—582no—
286Q16—582no—
287Q16—582no—
288Q16—582no—
289Q16—1161no—
290Q16D11614yescomplemented
291SD16—582no—
292SD16—582no—
293SD16—1161no—
294M16—582no—
295C2×C8—291no—
296C2×C8—291no—
297C2×C8—582no—
298C2×C8C22×D2911yescharacteristic
299C2×C8C22×D2911yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—291no—
303C4⋊C4—581no—
304C4⋊C4—581no—
305C4⋊C4—581no—
306C4⋊C4—581no—
307C4⋊C4—581no—
308C4⋊C4C22×D2911yescharacteristic
309C4⋊C4C22×D2911yescharacteristic
310C22⋊C4—291no—
311C22⋊C4—291no—
312C22⋊C4—581no—
313C22⋊C4—581no—
314C22⋊C4—581no—
315C22⋊C4—581no—
316C22⋊C4—581no—
317C22⋊C4—581no—
318C42—21no—
319C42—21no—
320C42C22×D2911yescharacteristic
321C23—291no—
322C23—291no—
323C23—581no—
324Q8—21no—
325Q8—21no—
326Q8—581no—
327Q8—581no—
328Q8—581no—
329Q8—581no—
330Q8—581no—
331Q8—581no—
332Q8—1162no—
333Q8—1162no—
334Q8—1162no—
335Q8C2×D11612yes—
336Q8C2×D11612yes—
337D4—582no—
338D4—581no—
339D4—581no—
340D4—1162no—
341D4—1162no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—291no—
347C2×C4—291no—
348C2×C4—581no—
349C2×C4—581no—
350C2×C4—581no—
351C2×C4—581no—
352C2×C4—581no—
353C2×C4—581no—
354C2×C4—581no—
355C2×C4—1162no—
356C2×C4—1162no—
357C2×C4—1162no—
358C2×C4—1162no—
359C2×C4D4×D2911yescharacteristic
360C2×C4D4×D2911yescharacteristic
361C2×C4C23×D2911yescharacteristic
362C8—21no—
363C8—581no—
364C8—581no—
365C8C2×D11612yes—
366C22—292no—
367C22—581no—
368C22—581no—
369C22—581no—
370C22—581no—
371C22—581no—
372C22—1161no—
373C22—1161no—
374C22—1161no—
375C22C2×D4×D2911yescharacteristic
376C4—22no—
377C4—22no—
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—581no—
383C4—581no—
384C4—1161no—
385C4—1161no—
386C4—1161no—
387C4C22×D11611yescharacteristic
388C4#1174536411yescharacteristic
389C2—582no—
390C2—1161no—
391C2—2321no—
392C2D4×D11611yescharacteristic
393C2#137×D2911yescharacteristic
394C2#1427197911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#441C2
socleC22×C29C22×D4
prime radical#14271825C2
hypercenter#441D29
hypocenterC29#3270
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. C2×#11745280C2semidirect
2. C2×Q16×D29C2semidirect
3. Q8×D116C2semidirect
5. #14271557C2semidirect
6. #14271422C2semidirect
7. #14271393C2semidirect
8. #14271385C2semidirect
9. #14271373C2semidirect
10. #14271328C2semidirect
11. #14271320C2semidirect
12. #14271320C2semidirect
13. #14271303C2semidirect
14. #14271236C2semidirect
15. C29×#441C2semidirect
87. Q16×C29D4semidirect
178. C2×D29#137semidirect
205. #441D29semidirect
258. C29#3270semidirect
290. Q16D116semidirect

Maximal subgroups

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

subgroupindex
C2×#117452802
C2×Q16×D292
Q8×D1162
#142718252
#142715572
#142714222
#142713932
#142713852
#142713732
#142713282
#142713202
#142713032
#142712362
C29×#4412
#327029