Finite Group Databasebeta

← #17997311

Subgroups — #17997311

Order 4736.

516 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924535C211yesmaximal, characteristic
2C2×C4×Dic74C211yesmaximal, characteristic
3C2×#11924501C211yesmaximal, characteristic
4#14557437C211yesmaximal, characteristic
5#14557437C211yesmaximal, characteristic
6#14557420C211yesmaximal, characteristic
7#14557419C211yesmaximal, characteristic
8#14557418C211yesmaximal, characteristic
9#14557417C211yesmaximal, characteristic
10#14557416C211yesmaximal, characteristic
11#14557415C211yesmaximal, characteristic
12#14557414C211yesmaximal, characteristic
13#14557397C211yesmaximal, characteristic
14#14557378C211yesmaximal, characteristic
15C37×#387C211yesmaximal, characteristic
16C22×Dic74C2211yescharacteristic
17C22×Dic74C2211yescharacteristic
18#11924535C418yescomplemented
19C4×Dic74—24no—
20#11924501—24no—
21C2×C4⋊Dic37C2211yescharacteristic
22C2×C4⋊Dic37C2211yescharacteristic
23C2×#10596936C2211yescharacteristic
24C2×#10596936C2211yescharacteristic
25C2×#10596936C2211yescharacteristic
26C2×#10596936C2211yescharacteristic
27C2×#10596936C2211yescharacteristic
28C2×#10596936C2211yescharacteristic
29C2×C4×Dic37C2211yescharacteristic
30C2×C4×Dic37C2211yescharacteristic
31C2×C4×Dic37C2211yescharacteristic
32C2×C4×Dic37C2211yescharacteristic
33C2×C4×Dic37C2211yescharacteristic
34C2×C4×Dic37C2211yescharacteristic
35#11924443C2211yescharacteristic
36#11924443C2211yescharacteristic
37#11924443C2211yescharacteristic
38#11924443C2211yescharacteristic
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
50#95×C37C2211yescharacteristic
51#95×C37C2211yescharacteristic
52#95×C37C2211yescharacteristic
53#95×C37C2211yescharacteristic
54C22×C4×C37C2311yescharacteristic
55C22×C4×C37C2311yescharacteristic
56C22×C4×C37C2311yescharacteristic
57C22×C4×C37C2311yescharacteristic
58C22×C4×C37C2311yescharacteristic
59C22×C4×C37C2311yescharacteristic
60C22×C4×C37C2311yescharacteristic
61C22×Dic37C2311yescharacteristic
62C22×Dic37C2311yescharacteristic
63C22×Dic37C2311yescharacteristic
64C22×Dic37C2311yescharacteristic
65C22×Dic37C2311yescharacteristic
66C22×Dic37C2311yescharacteristic
67C22×Dic37C2311yescharacteristic
68C22×Dic37C2311yescharacteristic
69C2×Dic74—22no—
70C2×Dic74—22no—
71C2×Dic74—22no—
72C2×Dic74—22no—
73C2×Dic74C2×C414yes—
74C2×Dic74C2×C414yes—
75C4⋊C4×C37—22no—
76C4⋊C4×C37C2×C414yes—
77C42×C37—22no—
78C4⋊Dic37—22no—
79C4⋊Dic37C2×C414yes—
80#10596936—22no—
81#10596936—22no—
82#10596936—22no—
83#10596936—22no—
84#10596936C2×C414yes—
85#10596936C2×C414yes—
86C4×Dic37—22no—
87C4×Dic37—22no—
88C4×Dic37—22no—
89C4×Dic37—22no—
90C4×Dic37C2×C414yes—
91C4×Dic37D414yes—
92C23×C37C2411yescharacteristic
93C2×C4×C37—21no—
94C2×C4×C37—21no—
95C2×C4×C37—21no—
96C2×C4×C37—21no—
97C2×C4×C37—21no—
98C2×C4×C37—21no—
99C2×C4×C37—21no—
100C2×C4×C37—21no—
101C2×C4×C37—21no—
102C2×C4×C37—21no—
103C2×C4×C37—21no—
104C2×C4×C37—21no—
105C2×C4×C37—21no—
106C2×C4×C37—21no—
107C2×C4×C37—21no—
108C2×C4×C37—21no—
109C2×C4×C37—21no—
110C2×C4×C37C22×C412yes—
111C2×C4×C37C22×C412yes—
112C2×C4×C37C22×C412yes—
113C2×C4×C37C2×D412yes—
114C2×Dic37—21no—
115C2×Dic37—21no—
116C2×Dic37—21no—
117C2×Dic37—21no—
118C2×Dic37—21no—
119C2×Dic37—21no—
120C2×Dic37—21no—
121C2×Dic37—21no—
122C2×Dic37—21no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37—21no—
126C2×Dic37—21no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37C22×C412yes—
132C2×Dic37C22×C412yes—
133C2×Dic37C22×C412yes—
134C2×Dic37C22×C412yes—
135C2×Dic37C2×D412yes—
136C2×Dic37C2×D412yes—
137C2×Dic37#4112yes—
138Dic74—28no—
139Dic74—28no—
140C22×C37C23×C411yescharacteristic
141C22×C37C22×D411yescharacteristic
142C22×C37C2×#4111yescharacteristic
143C22×C372−1+411yescharacteristic
144C22×C372−1+411yescharacteristic
145C22×C372−1+411yescharacteristic
146C22×C372−1+411yescharacteristic
147C4×C37—22no—
148C4×C37—22no—
149C4×C37—22no—
150C4×C37—22no—
151C4×C37—41no—
152C4×C37—41no—
153C4×C37—41no—
154Dic37—22no—
155Dic37—22no—
156Dic37—22no—
157Dic37—22no—
158Dic37—41no—
159Dic37—41no—
160Dic37—41no—
161Dic37C4×D414yes—
162#2327—371nomaximal, Sylow
163C2×C37C2×C4×D411yescharacteristic
164C2×C37#51911yescharacteristic
165C2×C37#51911yescharacteristic
166C2×C37#53611yescharacteristic
167C2×C37#53611yescharacteristic
168C2×C37#54111yescharacteristic
169C2×C37#54111yescharacteristic
170C2×C4⋊Q8—371no—
171C2×C4×Q8—371no—
172C2×C4×Q8—371no—
173#391—371no—
174#391—371no—
175#387—371no—
176#387—371no—
177#387—371no—
178#387—371no—
179#387—371no—
180#387—371no—
181#387—371no—
182#387D3711yescharacteristic
183#382—371no—
184#376—371no—
185C37#232711yescharacteristic, complemented, Sylow
186C22×Q8—371no—
187C22×Q8—371no—
188C4⋊Q8—378no—
189C4×Q8—744no—
190C4×Q8—744no—
191C2×C4⋊C4—371no—
192C2×C4⋊C4—371no—
193C2×C4⋊C4—371no—
194C2×C4⋊C4—371no—
195C2×C4⋊C4—371no—
196C2×C4⋊C4—371no—
197C2×C4⋊C4—371no—
198C2×C4⋊C4—371no—
199C2×C4⋊C4C2×D3711yescharacteristic
200C2×C4⋊C4C2×D3711yescharacteristic
201C2×C42—371no—
202C2×C42—371no—
203C2×C42—371no—
204C2×C42—371no—
205C2×C42—371no—
206C2×C42—371no—
207C2×C42C2×D3711yescharacteristic
208#95—371no—
209#95—371no—
210#95—371no—
211#95—371no—
212#95—371no—
213#95—371no—
214#95—371no—
215#95—371no—
216#95—371no—
217#95—371no—
218#95—371no—
219#95—371no—
220#95C2×D3711yescharacteristic
221#95C2×D3711yescharacteristic
222#95C2×D3711yescharacteristic
223#95C2×D3711yescharacteristic
224C2×Q8—374no—
225C2×Q8—374no—
226C2×Q8—742no—
227C2×Q8—742no—
228C2×Q8—742no—
229C2×Q8—742no—
230C22×C4—371no—
231C22×C4—371no—
232C22×C4—371no—
233C22×C4—371no—
234C22×C4—371no—
235C22×C4—371no—
236C22×C4—371no—
237C22×C4—371no—
238C22×C4C22×D3711yescharacteristic
239C22×C4C22×D3711yescharacteristic
240C22×C4C22×D3711yescharacteristic
241C22×C4C22×D3711yescharacteristic
242C22×C4C22×D3711yescharacteristic
243C22×C4C22×D3711yescharacteristic
244C22×C4C22×D3711yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—374no—
247C4⋊C4—374no—
248C4⋊C4—374no—
249C4⋊C4—742no—
250C4⋊C4—742no—
251C4⋊C4—742no—
252C4⋊C4—742no—
253C4⋊C4—742no—
254C4⋊C4C4×D3714yes—
255C42—22no—
256C42—374no—
257C42—374no—
258C42—742no—
259C42—742no—
260C42—742no—
261C42—742no—
262C23C23×D3711yescharacteristic
263Q8—748no—
264Q8—748no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—372no—
283C2×C4—372no—
284C2×C4—372no—
285C2×C4—372no—
286C2×C4—372no—
287C2×C4—372no—
288C2×C4—372no—
289C2×C4—741no—
290C2×C4—741no—
291C2×C4—741no—
292C2×C4—741no—
293C2×C4—741no—
294C2×C4—741no—
295C2×C4—741no—
296C2×C4—741no—
297C2×C4—741no—
298C2×C4—741no—
299C2×C4—741no—
300C2×C4—741no—
301C2×C4—741no—
302C2×C4—741no—
303C2×C4—741no—
304C2×C4—741no—
305C2×C4—741no—
306C2×C4C2×C4×D3712yes—
307C2×C4C2×C4×D3712yes—
308C2×C4C2×C4×D3712yes—
309C2×C4D4×D3712yes—
310C22C22×C4×D3711yescharacteristic
311C22C2×D4×D3711yescharacteristic
312C22#41×D3711yescharacteristic
313C22#1192458311yescharacteristic
314C22#1192458311yescharacteristic
315C22#1192458311yescharacteristic
316C22#1192458411yescharacteristic
317C4—22no—
318C4—22no—
319C4—22no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—374no—
325C4—742no—
326C4—742no—
327C4—742no—
328C4—742no—
329C4—1481no—
330C4—1481no—
331C4—1481no—
332C2C4×D4×D3711yescharacteristic
333C2#1455800911yescharacteristic
334C2#1455801011yescharacteristic
335C2#1455810511yescharacteristic
336C2#1455810611yescharacteristic
337C2#1455814011yescharacteristic
338C2#1455814211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#387C2
socle, prime radical, cosocleC23×C37C24
hypercenter#387D37
hypocenterC37#2327
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
18. #11924535C4semidirect
185. C37#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#119245352
C2×C4×Dic742
C2×#119245012
#145574372
#145574202
#145574192
#145574182
#145574172
#145574162
#145574152
#145574142
#145573972
#145573782
C37×#3872
#232737