Finite Group Databasebeta

← #16830905

Subgroups — #16830905

Order 3712.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271784C211yesmaximal, characteristic, complemented
2#14271768C211yesmaximal, characteristic, complemented
3#14271471C211yesmaximal, characteristic, complemented
4#14271464C211yesmaximal, characteristic, complemented
5#14271454C211yesmaximal, characteristic, complemented
6#14271444C211yesmaximal, characteristic, complemented
7#14271416C211yesmaximal, characteristic, complemented
8#14271409C211yesmaximal, characteristic, complemented
9#14271399C211yesmaximal, characteristic, complemented
10#14271392C211yesmaximal, characteristic, complemented
11#14271379C211yesmaximal, characteristic, complemented
12#14271379C211yesmaximal, characteristic, complemented
13#14271364C211yesmaximal, characteristic, complemented
14#14271359C211yesmaximal, characteristic, complemented
15C29×#424C211yesmaximal, characteristic, complemented
16C2×M16×C29C2211yescharacteristic
17C22×C8×C29C2211yescharacteristic
18C29×#117C2211yescharacteristic
19#11745292C2211yescharacteristic
20#11745292C2211yescharacteristic
21#11745292C2211yescharacteristic
22#11745286C2211yescharacteristic
23C2×D232C2211yescharacteristic
24C2×D232C2211yescharacteristic
25C2×#90773C2211yescharacteristic
26C2×#90773C2211yescharacteristic
27#11745260—21no—
28#11745258—21no—
29#11745256—21no—
30#11745256—21no—
31#11745247—21no—
32#11745246—21no—
33#11745246—21no—
34#11745245—21no—
35#11745237C2211yescharacteristic
36#11745236C2211yescharacteristic
37C4×D116C2211yescharacteristic
38C4×D116C2211yescharacteristic
39C4×D116C2211yescharacteristic
40#11745232C2211yescharacteristic
41#11745231C2211yescharacteristic
42C4×Dic58C2211yescharacteristic
43C29×C4⋊C8C2211yescharacteristic
44C29×C4⋊C8C2211yescharacteristic
45C29×C4⋊C8C2211yescharacteristic
46C29×C4⋊C8C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745169C2211yescharacteristic
53#11745166C2211yescharacteristic
54#11745166C2211yescharacteristic
55#11745165C2211yescharacteristic
56#11745165C2211yescharacteristic
57#11745164C2211yescharacteristic
58#11745164C2211yescharacteristic
59C22×C4×C29C2311yescharacteristic
60C2×C22⋊D29—21no—
61C2×C22⋊D29—21no—
62C2×C22⋊D29—21no—
63C2×D116—21no—
64C2×D116—21no—
65C2×D116C2311yescharacteristic
66C2×D116C2311yescharacteristic
67C2×D116C2311yescharacteristic
68C2×C4×D29—21no—
69C2×C4×D29—21no—
70C2×C4×D29—21no—
71C2×Dic58—21no—
72C2×Dic58C2311yescharacteristic
73M16×C29—41no—
74C2×C8×C29—41no—
75C2×C8×C29C2311yescharacteristic
76C2×C8×C29C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C4⋊C4×C29D411yescharacteristic
80C4⋊C4×C29D411yescharacteristic
81C22⋊C4×C29D411yescharacteristic
82C22⋊C4×C29D411yescharacteristic
83C42×C29C2311yescharacteristic
84C42×C29C2311yescharacteristic
85C22⋊Dic29—21no—
86#90781—21no—
87#90781—21no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94C4⋊Dic29—21no—
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99#90779—21no—
100#90779—21no—
101#90779—21no—
102#90779—21no—
103C4×Dic29—21no—
104D232—41no—
105D232—41no—
106#90773—41no—
107#90773—41no—
108C23×C29C2×D411yescharacteristic
109C22×D29—21no—
110C22×D29—21no—
111C22×D29—21no—
112C2×C4×C29—21no—
113C2×C4×C29—21no—
114C2×C4×C29C2×D411yescharacteristic
115C2×C4×C29C2×D411yescharacteristic
116C2×C4×C29C2×D411yescharacteristic
117C2×C4×C29C2×D411yescharacteristic
118C2×C4×C29C2×D411yescharacteristic
119C2×C4×C29C2411yescharacteristic
120C22⋊D29—81no—
121C22⋊D29—81no—
122C22⋊D29—81no—
123C2×Dic29—21no—
124C2×Dic29—21no—
125C2×Dic29—21no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128D116—21no—
129D116—21no—
130D116—21no—
131D116—21no—
132D116—21no—
133D116—21no—
134D116—81no—
135D116—81no—
136C4×D29—81no—
137C4×D29—81no—
138C4×D29—81no—
139Dic58—21no—
140Dic58—21no—
141Dic58—81no—
142C8×C29—21no—
143C8×C29—21no—
144C8×C29—21no—
145C8×C29—21no—
146#3257—291nomaximal, Sylow
147C22×C29—21no—
148C22×C29—21no—
149C22×C29—21no—
150C22×C29C22×D411yescharacteristic
151C2×D29—41no—
152C2×D29—41no—
153C2×D29—41no—
154C2×D29—41no—
155C2×D29—41no—
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
160C4×C29—21no—
161C4×C29—21no—
162C4×C29—21no—
163C4×C29—21no—
164C4×C29—21no—
165C4×C29H(5,𝔽2)11yescharacteristic
166C4×C292−1+411yescharacteristic
167Dic29—41no—
168Dic29—41no—
169Dic29—41no—
170Dic29—41no—
171Dic29—41no—
172#542—291no—
173#540—291no—
174#479—291no—
175#478—291no—
176#476—291no—
177#474—291no—
178#469—291no—
179#468—291no—
180#466—291no—
181#465—291no—
182#463—291no—
183#463—291no—
184#460—291no—
185#459—291no—
186#424D2911yescharacteristic, complemented
187C2×C29—41no—
188C2×C29#53711yescharacteristic
189C2×C29#57611yescharacteristic
190C2×C29#57711yescharacteristic
191D29—81no—
192D29—81no—
193D29—81no—
194C2×SD16—291no—
195C2×SD16—291no—
196C2×D8—291no—
197C2×D8—291no—
198C2×M16C2×D2911yescharacteristic
199C22×C8C2×D2911yescharacteristic
200C4⋊Q8—291no—
201#127—291no—
202#126—581no—
203#125—291no—
204#124—291no—
205#124—581no—
206#123—581no—
207#123—581no—
208#123—581no—
209C22⋊Q8—291no—
210C22⋊Q8—581no—
211#121—291no—
212#121—291no—
213#121—291no—
214#121—581no—
215#121—581no—
216C4×Q8—291no—
217C4×D4—291no—
218C4×D4—291no—
219C4×D4—291no—
220#117C2×D2911yescharacteristic
221#107—291no—
222#107—291no—
223#106—291no—
224#106—291no—
225C4⋊C8C2×D2911yescharacteristic
226C4⋊C8C2×D2911yescharacteristic
227C4⋊C8C2×D2911yescharacteristic
228C4⋊C8C2×D2911yescharacteristic
229#103—291no—
230#103—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234#102—291no—
235#102—291no—
236#102—291no—
237C29#325711yescharacteristic, complemented, Sylow
238C2×Q8—291no—
239C2×Q8—581no—
240C2×D4—291no—
241C2×D4—291no—
242C2×D4—291no—
243C2×D4—581no—
244C2×D4—581no—
245C2×D4—581no—
246C2×D4—581no—
247C2×D4—581no—
248C22×C4—581no—
249C22×C4—581no—
250C22×C4—581no—
251C22×C4C22×D2911yescharacteristic
252SD16—1161no—
253SD16—1161no—
254D8—1161no—
255D8—1161no—
256M16—41no—
257C2×C8—41no—
258C2×C8C22×D2911yescharacteristic
259C2×C8C22×D2911yescharacteristic
260C2×C8C22×D2911yescharacteristic
261C2×C8C22×D2911yescharacteristic
262C4⋊C4—291no—
263C4⋊C4—291no—
264C4⋊C4—291no—
265C4⋊C4—291no—
266C4⋊C4—581no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4D11611yescharacteristic
272C4⋊C4D11611yescharacteristic
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⋊C4D11611yescharacteristic
283C22⋊C4D11611yescharacteristic
284C42—581no—
285C42C22×D2911yescharacteristic
286C42C22×D2911yescharacteristic
287C23—581no—
288C23—581no—
289C23—581no—
290C23C2×D11611yescharacteristic
291Q8—581no—
292Q8—581no—
293Q8—2321no—
294D4—581no—
295D4—581no—
296D4—581no—
297D4—581no—
298D4—581no—
299D4—581no—
300D4—2321no—
301D4—2321no—
302D4—2321no—
303D4—2321no—
304D4—2321no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—581no—
308C2×C4—581no—
309C2×C4—581no—
310C2×C4—581no—
311C2×C4—581no—
312C2×C4—2321no—
313C2×C4—2321no—
314C2×C4—2321no—
315C2×C4C2×D11611yescharacteristic
316C2×C4C2×D11611yescharacteristic
317C2×C4C2×D11611yescharacteristic
318C2×C4C2×D11611yescharacteristic
319C2×C4C2×D11611yescharacteristic
320C2×C4C23×D2911yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—1161no—
329C22—1161no—
330C22—1161no—
331C22—1161no—
332C22—1161no—
333C22—1161no—
334C22—1161no—
335C22—1161no—
336C22—1161no—
337C22C22×D11611yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—1161no—
344C4—1161no—
345C4—1161no—
346C4—1161no—
347C4—1161no—
348C4#1174535911yescharacteristic
349C4#1174536211yescharacteristic
350C2—41no—
351C2—2321no—
352C2—2321no—
353C2—2321no—
354C2#1427174411yescharacteristic
355C2#1427196811yescharacteristic
356C2#1427197511yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#424C2
socleC22×C29C22×D4
hypercenter#424D29
hypocenterC29#3257
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #14271784C2semidirect
2. #14271768C2semidirect
3. #14271471C2semidirect
4. #14271464C2semidirect
5. #14271454C2semidirect
6. #14271444C2semidirect
7. #14271416C2semidirect
8. #14271409C2semidirect
9. #14271399C2semidirect
10. #14271392C2semidirect
11. #14271379C2semidirect
12. #14271379C2semidirect
13. #14271364C2semidirect
14. #14271359C2semidirect
15. C29×#424C2semidirect
186. #424D29semidirect
237. C29#3257semidirect

Maximal subgroups

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

subgroupindex
#142717842
#142717682
#142714712
#142714642
#142714542
#142714442
#142714162
#142714092
#142713992
#142713922
#142713792
#142713642
#142713592
C29×#4242
#325729