Finite Group Databasebeta

← #16832560

Subgroups — #16832560

Order 3712.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271898C211yesmaximal, characteristic, complemented
2#14271886C211yesmaximal, characteristic, complemented
3#14271557C211yesmaximal, characteristic, complemented
4#14271552C211yesmaximal, characteristic
5#14271547C211yesmaximal, characteristic, complemented
6#14271386C211yesmaximal, characteristic, complemented
7#14271386C211yesmaximal, characteristic, complemented
8#14271379C211yesmaximal, characteristic, complemented
9#14271379C211yesmaximal, characteristic, complemented
10#14271369C211yesmaximal, characteristic, complemented
11#14271364C211yesmaximal, characteristic, complemented
12#14271276C211yesmaximal, characteristic, complemented
13#14271271C211yesmaximal, characteristic, complemented
14C4×#90773C211yesmaximal, characteristic, complemented
15C29×#446C211yesmaximal, characteristic, complemented
16C4×Q8×C29C2211yescharacteristic
17#11745309—21no—
18#11745308—21no—
19C2×Dic116C2211yescharacteristic
20C2×Dic116C2211yescharacteristic
21C2×D232C2211yescharacteristic
22C2×D232C2211yescharacteristic
23C2×#90773C2211yescharacteristic
24C2×#90773C2211yescharacteristic
25C2×#90773C2211yescharacteristic
26C2×#90773C2211yescharacteristic
27C2×#90773C2211yescharacteristic
28#11745260—21no—
29#11745260—21no—
30#11745256—21no—
31#11745256—21no—
32#11745255—21no—
33#11745254—21no—
34#11745237C2211yescharacteristic
35#11745237C2211yescharacteristic
36#11745237C2211yescharacteristic
37#11745237C2211yescharacteristic
38#11745236C2211yescharacteristic
39C4×D116C2211yescharacteristic
40C4×D116C2211yescharacteristic
41C4×D116C2211yescharacteristic
42#11745231C2211yescharacteristic
43C4×Dic58C2211yescharacteristic
44C4×Dic58C2211yescharacteristic
45C4×Dic58C2211yescharacteristic
46C29×C4⋊C8C2211yescharacteristic
47C29×C4⋊C8C2211yescharacteristic
48C29×C4⋊C8C2211yescharacteristic
49C29×#97C2211yescharacteristic
50C29×#97C2211yescharacteristic
51C4×C8×C29C2211yescharacteristic
52#11745169C2211yescharacteristic
53#11745169C2211yescharacteristic
54#11745169C2211yescharacteristic
55#11745165C2211yescharacteristic
56#11745164C2211yescharacteristic
57#11745164C2211yescharacteristic
58#11745164C2211yescharacteristic
59C2×Q8×C29D411yescharacteristic
60C2×D116—21no—
61C2×D116—21no—
62C2×D116C2311yescharacteristic
63C2×D116C2311yescharacteristic
64C2×D116C2311yescharacteristic
65C2×C4×D29—21no—
66C2×C4×D29—21no—
67C2×C4×D29—21no—
68C2×Dic58C2311yescharacteristic
69C2×Dic58C2311yescharacteristic
70C2×Dic58C2311yescharacteristic
71C2×C8×C29C2311yescharacteristic
72C2×C8×C29C2311yescharacteristic
73C2×C8×C29C2311yescharacteristic
74C2×C8×C29C2311yescharacteristic
75C4⋊C4×C29D411yescharacteristic
76C4⋊C4×C29D411yescharacteristic
77C4⋊C4×C29D411yescharacteristic
78C42×C29C2311yescharacteristic
79C42×C29C2311yescharacteristic
80C42×C29C2311yescharacteristic
81#90781—21no—
82#90781—21no—
83#90781—21no—
84#90781—21no—
85#90781—21no—
86#90781—21no—
87#90781—21no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92C4⋊Dic29—21no—
93C4⋊Dic29—21no—
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99C4×Dic29—21no—
100C4×Dic29—21no—
101C4×Dic29—21no—
102Dic116—22no—
103Dic116—41no—
104D232—22no—
105D232—41no—
106#90773—22no—
107#90773—41no—
108#90773—41no—
109#90773—41no—
110#90773—41no—
111C22×D29—21no—
112C22×D29—21no—
113C22×D29—21no—
114Q8×C29—41no—
115C2×C4×C29C2×D411yescharacteristic
116C2×C4×C29C2×D411yescharacteristic
117C2×C4×C29C2×D411yescharacteristic
118C2×C4×C29C2×D411yescharacteristic
119C2×C4×C29C2×D411yescharacteristic
120C2×C4×C29C2×D411yescharacteristic
121C2×C4×C29C2411yescharacteristic
122C2×Dic29—21no—
123C2×Dic29—21no—
124C2×Dic29—21no—
125C2×Dic29—21no—
126C2×Dic29—21no—
127D116—21no—
128D116—21no—
129D116—21no—
130D116—21no—
131D116—21no—
132D116—21no—
133D116—42no—
134D116—81no—
135C4×D29—42no—
136C4×D29—81no—
137C4×D29—81no—
138Dic58—21no—
139Dic58—21no—
140Dic58—21no—
141Dic58—21no—
142Dic58—21no—
143Dic58—21no—
144C8×C29—21no—
145C8×C29—21no—
146C8×C29—21no—
147C8×C29#4112yes—
148#3401—291nomaximal, Sylow
149C22×C29C22×D411yescharacteristic
150C2×D29—41no—
151C2×D29—41no—
152C2×D29—41no—
153C2×D29—41no—
154C2×D29—41no—
155C2×D29—41no—
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C4×C29—21no—
160C4×C29—21no—
161C4×C29—21no—
162C4×C29—21no—
163C4×C29—21no—
164C4×C29—21no—
165C4×C29C2×#4111yescharacteristic
166C4×C29H(5,𝔽2)11yescharacteristic
167Dic29—41no—
168Dic29—41no—
169Dic29—41no—
170Dic29—41no—
171Dic29—41no—
172#559—291no—
173#556—291no—
174#497—291no—
175#496—291no—
176#495—291no—
177#464—291no—
178#464—291no—
179#463—291no—
180#463—291no—
181#461—291no—
182#460—291no—
183#446D2911yescharacteristic, complemented
184#442—291no—
185#441—291no—
186C4×SD16—291no—
187C2×C29#55011yescharacteristic
188C2×C29#57511yescharacteristic
189C2×C29#57711yescharacteristic
190D29—81no—
191D29—81no—
192D29—81no—
193C2×Q16—291no—
194C2×Q16—291no—
195C2×SD16—291no—
196C2×SD16—291no—
197C2×SD16—291no—
198C2×SD16—291no—
199C2×SD16—291no—
200C2×D8—291no—
201C2×D8—291no—
202C4⋊Q8—291no—
203#127—291no—
204#126—581no—
205#126—581no—
206#124—291no—
207#124—291no—
208#124—291no—
209#124—291no—
210#124—581no—
211#123—581no—
212#123—581no—
213C22⋊Q8—581no—
214C4×Q8—291no—
215C4×Q8—291no—
216C4×Q8—291no—
217C4×Q8C2×D2911yescharacteristic
218C4×D4—291no—
219C4×D4—291no—
220C4×D4—291no—
221C4×D4—581no—
222#117—581no—
223#106—291no—
224C4⋊C8C2×D2911yescharacteristic
225C4⋊C8C2×D2911yescharacteristic
226C4⋊C8C2×D2911yescharacteristic
227#103—291no—
228#103—291no—
229#103—291no—
230#102—291no—
231#102—291no—
232#102—291no—
233#97C2×D2911yescharacteristic
234#97C2×D2911yescharacteristic
235C4×C8C2×D2911yescharacteristic
236C29#340111yescharacteristic, complemented, Sylow
237C2×Q8—291no—
238C2×Q8—291no—
239C2×Q8—291no—
240C2×Q8D11611yescharacteristic
241C2×D4—291no—
242C2×D4—291no—
243C2×D4—291no—
244C2×D4—581no—
245C2×D4—581no—
246C22×C4—581no—
247C22×C4—581no—
248C22×C4—581no—
249Q16—582no—
250Q16—1161no—
251SD16—582no—
252SD16—1161no—
253SD16—1161no—
254SD16—1161no—
255SD16—1161no—
256D8—582no—
257D8—1161no—
258C2×C8C22×D2911yescharacteristic
259C2×C8C22×D2911yescharacteristic
260C2×C8C22×D2911yescharacteristic
261C2×C8C22×D2911yescharacteristic
262C4⋊C4—291no—
263C4⋊C4—291no—
264C4⋊C4—581no—
265C4⋊C4—581no—
266C4⋊C4—581no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4D11611yescharacteristic
270C4⋊C4D11611yescharacteristic
271C4⋊C4D11611yescharacteristic
272C22⋊C4—581no—
273C22⋊C4—581no—
274C22⋊C4—581no—
275C22⋊C4—581no—
276C22⋊C4—581no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C42—581no—
284C42—581no—
285C42—581no—
286C42C22×D2911yescharacteristic
287C42C22×D2911yescharacteristic
288C42C22×D2911yescharacteristic
289C23—581no—
290C23—581no—
291C23—581no—
292Q8—41no—
293Q8—581no—
294Q8—581no—
295Q8—581no—
296Q8—581no—
297Q8—581no—
298Q8—581no—
299D4—581no—
300D4—581no—
301D4—581no—
302D4—581no—
303D4—581no—
304D4—581no—
305D4—1162no—
306D4—2321no—
307C2×C4—581no—
308C2×C4—581no—
309C2×C4—581no—
310C2×C4—581no—
311C2×C4—581no—
312C2×C4—1162no—
313C2×C4—2321no—
314C2×C4—2321no—
315C2×C4C2×D11611yescharacteristic
316C2×C4C2×D11611yescharacteristic
317C2×C4C2×D11611yescharacteristic
318C2×C4C2×D11611yescharacteristic
319C2×C4C2×D11611yescharacteristic
320C2×C4C2×D11611yescharacteristic
321C2×C4C23×D2911yescharacteristic
322C8—21no—
323C8—21no—
324C8—21no—
325C8#9080912yes—
326C22—1161no—
327C22—1161no—
328C22—1161no—
329C22—1161no—
330C22—1161no—
331C22—1161no—
332C22—1161no—
333C22—1161no—
334C22—1161no—
335C22C22×D11611yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—1161no—
343C4—1161no—
344C4—1161no—
345C4—1161no—
346C4—1161no—
347C4C2×#9080911yescharacteristic
348C4#1174536411yescharacteristic
349C2—2321no—
350C2—2321no—
351C2—2321no—
352C2#1427183511yescharacteristic
353C2#1427196311yescharacteristic
354C2#1427197511yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#446C2
socleC22×C29C22×D4
prime radical#14271552C2
hypercenter#446D29
hypocenterC29#3401
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #14271898C2semidirect
2. #14271886C2semidirect
3. #14271557C2semidirect
5. #14271547C2semidirect
6. #14271386C2semidirect
7. #14271386C2semidirect
8. #14271379C2semidirect
9. #14271379C2semidirect
10. #14271369C2semidirect
11. #14271364C2semidirect
12. #14271276C2semidirect
13. #14271271C2semidirect
14. C4×#90773C2semidirect
15. C29×#446C2semidirect
183. #446D29semidirect
236. C29#3401semidirect

Maximal subgroups

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

subgroupindex
#142718982
#142718862
#142715572
#142715522
#142715472
#142713862
#142713792
#142713692
#142713642
#142712762
#142712712
C4×#907732
C29×#4462
#340129