Finite Group Databasebeta

← #18010593

Subgroups — #18010593

Order 4736.

310 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558612C211yesmaximal, characteristic, complemented
2#14558532C211yesmaximal, characteristic, complemented
3#14558523C211yesmaximal, characteristic, complemented
4#14558508C211yesmaximal, characteristic, complemented
5#14558416C211yesmaximal, characteristic, complemented
6#14558408C211yesmaximal, characteristic, complemented
7#14558332C211yesmaximal, characteristic
8#11924624—21no—
9#11924623—21no—
10#11924623—22no—
11C2×#10596953—21no—
12C2×#10596953C2211yescharacteristic
13D37⋊M16—21no—
14D37⋊M16C2211yescharacteristic
15C2×D37⋊C8C2211yescharacteristic
16#11924615C2211yescharacteristic
17#11924601—21no—
18#11924601—21no—
19#11924599—21no—
20#11924598—21no—
21#11924593—22no—
22C2×#10596966C2211yescharacteristic
23#41×D37C2211yescharacteristic
24#11924568—21no—
25#11924567C411yescharacteristic, complemented
26#11924564C411yescharacteristic, complemented
27#11924563—21no—
28#11924561C411yescharacteristic, complemented
29#11924559—21no—
30#11924557—21no—
31M16×D37C2211yescharacteristic
32#137×C37C411yescharacteristic, complemented
33#41×C37C2×C411yescharacteristic
34C2×Q8×C37C2×C411yescharacteristic
35#10596966—21no—
36#10596966—21no—
37#10596966—21no—
38#10596966—21no—
39#10596966D411yescharacteristic
40Q8×D37D411yescharacteristic
41#10596964—21no—
42#10596964D411yescharacteristic
43D4×D37—21no—
44D4×D37D411yescharacteristic
45#10596962—21no—
46#10596962C2×C411yescharacteristic
47C2×D148—21no—
48C2×D148C2×C411yescharacteristic
49C2×C4×D37—21no—
50C2×C4×D37—21no—
51C2×C4×D37C2311yescharacteristic
52C22⋊#3866—21no—
53#10596957—22no—
54#10596957—21no—
55C2×#64438—22no—
56C2×#64438—21no—
57C2×#64438D412yes—
58C4⋊#3866—21no—
59C4×#3866—21no—
60#10596953—22no—
61#10596953—21no—
62#10596953—21no—
63#10596953D411yescharacteristic
64#10596953D411yescharacteristic
65D37⋊C8—22no—
66D37⋊C8—21no—
67D37⋊C8—21no—
68D37⋊C8—21no—
69Q16×C37—21no—
70SD16×C37—21no—
71M16×C37C2×C411yescharacteristic
72#10596942—21no—
73#10596941—21no—
74#10596941—21no—
75#10596939—21no—
76#10596934C2×C411yescharacteristic
77D296—21no—
78#10596930—21no—
79#10596929—21no—
80C8×D37—21no—
81C22×D37—21no—
82C22×D37—21no—
83C22×D37#4111yescharacteristic
84C2×#3866—41no—
85Q8×C37—21no—
86Q8×C37—21no—
87Q8×C37C22⋊C411yescharacteristic
88D4×C37—21no—
89D4×C37C22⋊C411yescharacteristic
90C2×C4×C37—21no—
91C2×C4×C37—21no—
92C2×C4×C37C22×C411yescharacteristic
93C22⋊D37—21no—
94C22⋊D37—21no—
95C22⋊D37—21no—
96C2×Dic37—21no—
97C2×Dic37C2×D411yescharacteristic
98D148—21no—
99D148—21no—
100D148—21no—
101D148—41no—
102D148—41no—
103D148C22⋊C411yescharacteristic
104C4×D37—21no—
105C4×D37—21no—
106C4×D37—21no—
107C4×D37—41no—
108C4×D37—41no—
109C4×D37C2×D411yescharacteristic
110C4×D37C2×D411yescharacteristic
111C4×D37C2×D411yescharacteristic
112C4×D37#4111yescharacteristic
113Dic74—21no—
114Dic74C22⋊C411yescharacteristic
115#64438—21no—
116#64438—22no—
117#64438—21no—
118#64438—41no—
119C8×C37—21no—
120#64436—21no—
121C22×C37—21no—
122C22×C37C4×D411yescharacteristic
123C2×D37—21no—
124C2×D37—41no—
125C2×D37—42no—
126C2×D37—41no—
127C2×D37—81no—
128C2×D37#12111yescharacteristic
129C2×D37#12311yescharacteristic
130#3866—81no—
131C4×C37—21no—
132C4×C37—41no—
133C4×C37C2×C22⋊C411yescharacteristic
134C4×C37C4×D411yescharacteristic
135Dic37—21no—
136Dic37#12011yescharacteristic
137Dic37#12111yescharacteristic
138#1881—371nomaximal, Sylow
139C2×C37—21no—
140C2×C37—41no—
141C2×C37#38611yescharacteristic
142D37—21no—
143D37—21no—
144D37—41no—
145D37—81no—
146#575—371no—
147#568—371no—
148#421—371no—
149#416—371no—
150#408—371no—
151#344—371no—
152#341—371no—
153C37#188111yescharacteristic, complemented, Sylow
154C2×#41—371no—
155C2×#41—371no—
156#137—371no—
157#137—741no—
158#137#386611yescharacteristic, complemented
159AGL(1,ℤ/8)—371no—
160AGL(1,ℤ/8)—371no—
161AGL(1,ℤ/8)—741no—
162#135—741no—
163#135—741no—
164#131—742no—
165#131—741no—
166#131—741no—
167C2×M16—371no—
168C2×M16—371no—
169C2×M16—371no—
170C2×M16—741no—
171C2×M16—741no—
172C22×C8—371no—
173#117—371no—
174#104—741no—
175#104—741no—
176#103—741no—
177#102—741no—
178C22⋊C8—742no—
179#41—371no—
180#41—371no—
181#41—371no—
182#41—741no—
183#41—741no—
184#41—741no—
185#41—741no—
186#41—741no—
187#41—741no—
188#41C2×#386611yescharacteristic
189C2×Q8—371no—
190C2×Q8C2×#386611yescharacteristic
191C2×D4—371no—
192C2×D4—371no—
193C2×D4—741no—
194C2×D4—741no—
195C22×C4—371no—
196C22×C4—741no—
197C22×C4—741no—
198Q16—21no—
199Q16—741no—
200SD16—21no—
201SD16—741no—
202SD16—741no—
203SD16—741no—
204D8—741no—
205D8—741no—
206M16—371no—
207M16—371no—
208M16—371no—
209M16—741no—
210M16—741no—
211M16—741no—
212M16—741no—
213M16—742no—
214M16—742no—
215M16C2×#386611yescharacteristic
216C2×C8—372no—
217C2×C8—741no—
218C2×C8—741no—
219C2×C8—742no—
220C2×C8—742no—
221C2×C8—741no—
222C2×C8—741no—
223C2×C8—741no—
224C4⋊C4—741no—
225C22⋊C4—741no—
226C42—741no—
227C23—371no—
228C23—741no—
229C23—741no—
230Q8—21no—
231Q8—21no—
232Q8—371no—
233Q8—741no—
234Q8C22⋊#386611yescharacteristic
235D4—21no—
236D4—371no—
237D4—741no—
238D4—741no—
239D4—741no—
240D4—741no—
241D4—741no—
242D4—741no—
243D4—1481no—
244D4—1481no—
245D4C22⋊#386611yescharacteristic
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—371no—
249C2×C4—371no—
250C2×C4—371no—
251C2×C4—371no—
252C2×C4—371no—
253C2×C4—741no—
254C2×C4—741no—
255C2×C4—741no—
256C2×C4—741no—
257C2×C4—1481no—
258C2×C4—1481no—
259C2×C4—1481no—
260C2×C4C22×#386611yescharacteristic
261C8—21no—
262C8—742no—
263C8—741no—
264C8—741no—
265C8—741no—
266C8—1481no—
267C22—21no—
268C22—371no—
269C22—371no—
270C22—2961no—
271C22—741no—
272C22—1482no—
273C22—1481no—
274C22—1481no—
275C22D4×#386611yescharacteristic
276C4—21no—
277C4—41no—
278C4—371no—
279C4—371no—
280C4—2961no—
281C4—741no—
282C4C2×C22⋊#386611yescharacteristic
283C4D4×#386611yescharacteristic
284C2—21no—
285C2—41no—
286C2—2961no—
287C2—741no—
288C2—741no—
289C2—1481no—
290C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#137×C37C4
socleC2×C37#386
prime radical#14558332C2
cosocleC2×C4×D37C23
hypercenter#137#3866
hypocenterC37#1881
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. #14558612C2semidirect
2. #14558532C2semidirect
3. #14558523C2semidirect
4. #14558508C2semidirect
5. #14558416C2semidirect
6. #14558408C2semidirect
25. #11924567C4semidirect
26. #11924564C4semidirect
28. #11924561C4semidirect
32. #137×C37C4semidirect
153. C37#1881semidirect
158. #137#3866semidirect

Maximal subgroups

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

subgroupindex
#145586122
#145585322
#145585232
#145585082
#145584162
#145584082
#145583322
#188137