Finite Group Databasebeta

← #17997624

Subgroups — #17997624

Order 4736.

576 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924514C211yesmaximal, characteristic
2C2×C4×Dic74C211yesmaximal, characteristic, complemented
3C2×#11924493C211yesmaximal, characteristic
4#14557437C211yesmaximal, characteristic, complemented
5#14557428C211yesmaximal, characteristic, complemented
6#14557425C211yesmaximal, characteristic
7#14557424C211yesmaximal, characteristic
8#14557424C211yesmaximal, characteristic
9#14557423C211yesmaximal, characteristic
10#14557419C211yesmaximal, characteristic, complemented
11#14557417C211yesmaximal, characteristic, complemented
12C4×#10596936C211yesmaximal, characteristic, complemented
13#14557384C211yesmaximal, characteristic, complemented
14#14557380C211yesmaximal, characteristic
15C4×C4⋊C4×C37C211yesmaximal, characteristic, complemented
16C22×Dic74C2211yescharacteristic
17C22×C4×D37C2211yescharacteristic
18#11924514C418yescomplemented
19C4×Dic74—24no—
20#11924493—24no—
21C2×C4⋊Dic37C2211yescharacteristic
22C2×#10596936C2211yescharacteristic
23C2×#10596936C2211yescharacteristic
24C2×#10596936C2211yescharacteristic
25C2×#10596936C2211yescharacteristic
26C2×#10596936C2211yescharacteristic
27C2×#10596936C2211yescharacteristic
28C2×#10596938C2211yescharacteristic
29C2×#10596938C2211yescharacteristic
30C2×#10596938C2211yescharacteristic
31C2×#10596938C2211yescharacteristic
32C2×#10596938C2211yescharacteristic
33C2×#10596938C2211yescharacteristic
34C2×C4×Dic37C2211yescharacteristic
35C2×C4×Dic37C2211yescharacteristic
36C2×C4×Dic37C2211yescharacteristic
37C2×C4×Dic37C2211yescharacteristic
38C2×C4×Dic37C2211yescharacteristic
39#11924443C2211yescharacteristic
40#11924443C2211yescharacteristic
41#11924443C2211yescharacteristic
42#11924443C2211yescharacteristic
43#11924443C2211yescharacteristic
44#11924443C2211yescharacteristic
45#11924443C2211yescharacteristic
46#11924443C2211yescharacteristic
47C2×C4⋊C4×C37C2211yescharacteristic
48C2×C4⋊C4×C37C2211yescharacteristic
49C2×C42×C37C2211yescharacteristic
50C2×C42×C37C2211yescharacteristic
51C2×C42×C37C2211yescharacteristic
52#95×C37C2211yescharacteristic
53#95×C37C2211yescharacteristic
54C23×D37C2311yescharacteristic
55C22×C4×C37C2311yescharacteristic
56C22×C4×C37C2311yescharacteristic
57C22×C4×C37C2311yescharacteristic
58C22×C4×C37C2311yescharacteristic
59C22×C4×C37C2311yescharacteristic
60C22×C4×C37C2311yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C22×Dic37C2311yescharacteristic
63C22×Dic37C2311yescharacteristic
64C22×Dic37C2311yescharacteristic
65C22×Dic37C2311yescharacteristic
66C22×Dic37C2311yescharacteristic
67C22×Dic37C2311yescharacteristic
68C22×Dic37C2311yescharacteristic
69C2×C4×D37—22no—
70C2×C4×D37—22no—
71C2×C4×D37C2×C414yes—
72C2×Dic74—22no—
73C2×Dic74—22no—
74C2×Dic74C2×C414yes—
75C4⋊C4×C37—22no—
76C4⋊C4×C37C2×C414yes—
77C42×C37—22no—
78C42×C37—22no—
79C42×C37—22no—
80#10596938—22no—
81#10596938—22no—
82#10596938—22no—
83#10596938—22no—
84#10596938C2×C414yes—
85#10596938C2×C414yes—
86C4⋊Dic37—22no—
87#10596936—22no—
88#10596936—22no—
89#10596936—22no—
90#10596936C2×C414yes—
91#10596936C2×C414yes—
92#10596936D414yes—
93C4×Dic37—22no—
94C4×Dic37—22no—
95C4×Dic37—22no—
96C4×Dic37—22no—
97C4×Dic37—22no—
98C23×C37C2411yescharacteristic
99C22×D37—21no—
100C22×D37—21no—
101C22×D37—21no—
102C22×D37—21no—
103C22×D37—21no—
104C22×D37—21no—
105C22×D37C22×C412yes—
106C2×C4×C37—21no—
107C2×C4×C37—21no—
108C2×C4×C37—21no—
109C2×C4×C37—21no—
110C2×C4×C37—21no—
111C2×C4×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37C22×C412yes—
122C2×C4×C37C22×C412yes—
123C2×C4×C37C22×C412yes—
124C2×C4×C37C2×D412yes—
125C2×C4×C37#4112yes—
126C2×C4×C37#4112yes—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—21no—
140C2×Dic37—21no—
141C2×Dic37—21no—
142C2×Dic37C22×C412yes—
143C2×Dic37C22×C412yes—
144C2×Dic37C22×C412yes—
145C2×Dic37C2×D412yes—
146C2×Dic37C2×D412yes—
147C2×Dic37#4112yes—
148C4×D37—28no—
149Dic74—28no—
150C22×C37C23×C411yescharacteristic
151C22×C37C22×D411yescharacteristic
152C22×C37C2×#4111yescharacteristic
153C22×C37C2×#4111yescharacteristic
154C22×C37C2×#4111yescharacteristic
155C22×C372−1+411yescharacteristic
156C22×C372−1+411yescharacteristic
157C2×D37—22no—
158C2×D37—22no—
159C2×D37—22no—
160C2×D37—41no—
161C2×D37—41no—
162C2×D37—41no—
163C2×D37—41no—
164C4×C37—22no—
165C4×C37—22no—
166C4×C37—22no—
167C4×C37—22no—
168C4×C37—22no—
169C4×C37—22no—
170C4×C37—41no—
171Dic37—22no—
172Dic37—22no—
173Dic37—22no—
174Dic37—41no—
175Dic37—41no—
176Dic37—41no—
177Dic37C4×D414yes—
178#2362—371nomaximal, Sylow
179C2×C37C2×C4×D411yescharacteristic
180C2×C37C4×#4111yescharacteristic
181C2×C37#51911yescharacteristic
182C2×C37#54711yescharacteristic
183C2×C37#54811yescharacteristic
184C2×C37#55211yescharacteristic
185C2×C37#55611yescharacteristic
186D37—42no—
187C2×C22⋊Q8—371no—
188C2×C4×Q8—371no—
189C2×#117—371no—
190#391—371no—
191#389—371no—
192#388—371no—
193#388—371no—
194#388—371no—
195#388—371no—
196#387—371no—
197#387—371no—
198C4×C4⋊C4—371no—
199C4×C4⋊C4—371no—
200C4×C4⋊C4D3711yescharacteristic, complemented
201C4×C22⋊C4—371no—
202C37#236211yescharacteristic, complemented, Sylow
203C22×Q8—371no—
204C23×C4—371no—
205C22⋊Q8—378no—
206C4×Q8—744no—
207#117—744no—
208C2×C4⋊C4—371no—
209C2×C4⋊C4—371no—
210C2×C4⋊C4—371no—
211C2×C4⋊C4—371no—
212C2×C4⋊C4—371no—
213C2×C4⋊C4—371no—
214C2×C4⋊C4—371no—
215C2×C4⋊C4C2×D3711yescharacteristic
216C2×C4⋊C4C2×D3711yescharacteristic
217C2×C22⋊C4—371no—
218C2×C22⋊C4—371no—
219C2×C22⋊C4—371no—
220C2×C22⋊C4—371no—
221C2×C22⋊C4—371no—
222C2×C22⋊C4—371no—
223C2×C42—371no—
224C2×C42—371no—
225C2×C42—371no—
226C2×C42—371no—
227C2×C42—371no—
228C2×C42C2×D3711yescharacteristic
229C2×C42C2×D3711yescharacteristic
230C2×C42C2×D3711yescharacteristic
231#95—371no—
232#95—371no—
233#95—371no—
234#95—371no—
235#95—371no—
236#95—371no—
237#95—371no—
238#95—371no—
239#95C2×D3711yescharacteristic
240#95C2×D3711yescharacteristic
241C24—371no—
242C2×Q8—374no—
243C2×Q8—742no—
244C2×Q8—742no—
245C22×C4—371no—
246C22×C4—371no—
247C22×C4—371no—
248C22×C4—371no—
249C22×C4—374no—
250C22×C4—371no—
251C22×C4—371no—
252C22×C4—371no—
253C22×C4—742no—
254C22×C4—742no—
255C22×C4C22×D3711yescharacteristic
256C22×C4C22×D3711yescharacteristic
257C22×C4C22×D3711yescharacteristic
258C22×C4C22×D3711yescharacteristic
259C22×C4C22×D3711yescharacteristic
260C22×C4C22×D3711yescharacteristic
261C22×C4C22×D3711yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—374no—
264C4⋊C4—374no—
265C4⋊C4—374no—
266C4⋊C4—742no—
267C4⋊C4—742no—
268C4⋊C4—742no—
269C4⋊C4—742no—
270C4⋊C4C4×D3714yes—
271C22⋊C4—374no—
272C22⋊C4—374no—
273C22⋊C4—742no—
274C22⋊C4—742no—
275C22⋊C4—742no—
276C22⋊C4—742no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—742no—
281C42—742no—
282C42—742no—
283C42—742no—
284C42—742no—
285C23—372no—
286C23—741no—
287C23—741no—
288C23—741no—
289C23—741no—
290C23—741no—
291C23—741no—
292C23C23×D3711yescharacteristic
293Q8—748no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—372no—
310C2×C4—372no—
311C2×C4—372no—
312C2×C4—372no—
313C2×C4—372no—
314C2×C4—372no—
315C2×C4—748no—
316C2×C4—741no—
317C2×C4—741no—
318C2×C4—741no—
319C2×C4—741no—
320C2×C4—741no—
321C2×C4—741no—
322C2×C4—741no—
323C2×C4—741no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4—741no—
329C2×C4—741no—
330C2×C4—741no—
331C2×C4C2×C4×D3712yes—
332C2×C4C2×C4×D3712yes—
333C2×C4C2×C4×D3712yes—
334C2×C4#1059696212yes—
335C2×C4#1059696212yes—
336C2×C4D4×D3712yes—
337C22—742no—
338C22—742no—
339C22—742no—
340C22—1481no—
341C22—1481no—
342C22—1481no—
343C22—1481no—
344C22C22×C4×D3711yescharacteristic
345C22C2×D4×D3711yescharacteristic
346C22#41×D3711yescharacteristic
347C22C2×#1059696211yescharacteristic
348C22C2×#1059696211yescharacteristic
349C22#1192458311yescharacteristic
350C22#1192458411yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—374no—
359C4—742no—
360C4—742no—
361C4—742no—
362C4—1481no—
363C4—1481no—
364C4—1481no—
365C2—1482no—
366C2C4×D4×D3711yescharacteristic
367C2C4×#1059696211yescharacteristic
368C2#1455800911yescharacteristic
369C2#1455818411yescharacteristic
370C2#1455819211yescharacteristic
371C2#1455821611yescharacteristic
372C2#1455825511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC4×C4⋊C4×C37C2
socle, cosocleC23×C37C24
prime radicalC23×D37C23
hypercenterC4×C4⋊C4D37
hypocenterC37#2362
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic74C2semidirect
4. #14557437C2semidirect
5. #14557428C2semidirect
10. #14557419C2semidirect
11. #14557417C2semidirect
12. C4×#10596936C2semidirect
13. #14557384C2semidirect
15. C4×C4⋊C4×C37C2semidirect
18. #11924514C4semidirect
200. C4×C4⋊C4D37semidirect
202. C37#2362semidirect

Maximal subgroups

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

subgroupindex
C2×#119245142
C2×C4×Dic742
C2×#119244932
#145574372
#145574282
#145574252
#145574242
#145574232
#145574192
#145574172
C4×#105969362
#145573842
#145573802
C4×C4⋊C4×C372
#236237