Finite Group Databasebeta

← #18010590

Subgroups — #18010590

Order 4736.

338 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C2×Q8×#3866C211yesmaximal, characteristic
2C2×#11924599C211yesmaximal, characteristic
3C2×#11924599C211yesmaximal, characteristic
4(C2×#3866)⋊Q8C211yesmaximal, characteristic
5#14558407C211yesmaximal, characteristic
6(C2×#3866)⋊C8C211yesmaximal, characteristic
7C2×Q16×D37C211yesmaximal, characteristic
8C2×D37⋊C8C2211yescharacteristic
9Q8×#3866—22no—
10Q8×#3866—22no—
11C2×C4⋊#3866—21no—
12C2×C4⋊#3866C2211yescharacteristic
13C2×C4⋊#3866C2211yescharacteristic
14C2×C4×#3866—21no—
15C2×C4×#3866C2211yescharacteristic
16#11924599—22no—
17#11924599—22no—
18(C2×#3866)⋊C4—21no—
19(C2×#3866)⋊C4—21no—
20C2×Q8×D37C2211yescharacteristic
21C2×Q8×D37C2211yescharacteristic
22C2×Dic148C411yescharacteristic, complemented
23C2×#10596942C411yescharacteristic, complemented
24C2×#10596942C411yescharacteristic, complemented
25Q16×D37—22no—
26Q16×D37—22no—
27C2×C8×D37C2211yescharacteristic
28C2×Q16×C37C411yescharacteristic, complemented
29C22×#3866—21no—
30C22×#3866—21no—
31C22×#3866D411yescharacteristic
32C22×#3866D411yescharacteristic
33C2×Q8×C37C2×C411yescharacteristic
34C2×Q8×C37C2×C411yescharacteristic
35Q8×D37—21no—
36Q8×D37—21no—
37Q8×D37—21no—
38Q8×D37—21no—
39Q8×D37—21no—
40Q8×D37—21no—
41Q8×D37D412yes—
42Q8×D37D412yes—
43C2×C4×D37—21no—
44C2×C4×D37—21no—
45C2×C4×D37C2311yescharacteristic
46C2×Dic74—21no—
47C2×Dic74—21no—
48C2×Dic74C2×C411yescharacteristic
49C2×Dic74C2×C411yescharacteristic
50C2×#64438—21no—
51C4⋊#3866—24no—
52C4⋊#3866—21no—
53C4⋊#3866—21no—
54C4⋊#3866—21no—
55C4⋊#3866D412yes—
56C4×#3866—24no—
57C4×#3866—21no—
58C4×#3866—21no—
59D37⋊C8—21no—
60D37⋊C8—21no—
61Q16×C37—22no—
62C2×C8×C37C2×C411yescharacteristic
63#10596942—22no—
64#10596942—22no—
65C2×#64436C2×C411yescharacteristic
66Dic148—22no—
67C8×D37—21no—
68C8×D37—21no—
69C22×D37C2×D411yescharacteristic
70C2×#3866—21no—
71C2×#3866—21no—
72C2×#3866—21no—
73C2×#3866—22no—
74C2×#3866—21no—
75C2×#3866—21no—
76C2×#3866—41no—
77C2×#3866—41no—
78C2×#3866—41no—
79C2×#3866—41no—
80C2×#3866—41no—
81C2×#3866Q1612yescomplemented
82Q8×C37—21no—
83Q8×C37—21no—
84Q8×C37—21no—
85Q8×C37C22⋊C412yes—
86C2×C4×C37—21no—
87C2×C4×C37—21no—
88C2×C4×C37C22×C411yescharacteristic
89C2×Dic37—21no—
90C2×Dic37—21no—
91C2×Dic37#4111yescharacteristic
92C4×D37—22no—
93C4×D37—22no—
94C4×D37—41no—
95C4×D37—41no—
96C4×D37C2×D411yescharacteristic
97C4×D37C2×D411yescharacteristic
98C4×D37C2×D411yescharacteristic
99C4×D37#4111yescharacteristic
100Dic74—21no—
101Dic74—22no—
102Dic74—22no—
103Dic74—21no—
104Dic74—21no—
105Dic74—41no—
106Dic74—41no—
107Dic74C22⋊C412yes—
108#64438—41no—
109C8×C37—21no—
110#64436—21no—
111C22×C37C4×D411yescharacteristic
112C2×D37#12011yescharacteristic
113C2×D37#12111yescharacteristic
114C2×D37C2×Q1611yescharacteristic
115C2×D37#13511yescharacteristic
116C2×D37#13711yescharacteristic
117C2×D37#13711yescharacteristic
118#3866—22no—
119#3866—41no—
120#3866—42no—
121#3866—81no—
122C4×C37—22no—
123C4×C37—41no—
124C4×C37C2×C22⋊C411yescharacteristic
125C4×C37C4×D411yescharacteristic
126Dic37—22no—
127Dic37—41no—
128Dic37#12111yescharacteristic
129Dic37#12311yescharacteristic
130#1878—371nomaximal, Sylow
131C2×C37#38611yescharacteristic
132C2×C37C4×Q1611yescharacteristic
133C2×C37#44111yescharacteristic
134D37#45111yescharacteristic
135D37#45211yescharacteristic
136D37#46211yescharacteristic
137D37#46411yescharacteristic
138C22×Q16—371no—
139C2×C4×Q8—371no—
140C2×#103—371no—
141C2×#103—371no—
142#391—371no—
143#340—371no—
144#336—371no—
145C37#187811yescharacteristic, complemented, Sylow
146C22×Q8—371no—
147C22×Q8—371no—
148C2×Q16—371no—
149C2×Q16—371no—
150C2×Q16—371no—
151C2×Q16—742no—
152C2×Q16—742no—
153C2×Q16#386611yescharacteristic, complemented
154C22×C8—371no—
155C22×C8—371no—
156C4×Q8—742no—
157C4×Q8—742no—
158C2×C4⋊C4—371no—
159C2×C4⋊C4—371no—
160C2×C4⋊C4—741no—
161C2×C42—371no—
162C2×C42—741no—
163#103—742no—
164#103—742no—
165#95—741no—
166#95—741no—
167C2×Q8—372no—
168C2×Q8—372no—
169C2×Q8—371no—
170C2×Q8—371no—
171C2×Q8—741no—
172C2×Q8—741no—
173C2×Q8—741no—
174C2×Q8—741no—
175C2×Q8—741no—
176C2×Q8—741no—
177C2×Q8—741no—
178C2×Q8—741no—
179C2×Q8C2×#386611yescharacteristic
180C2×Q8C2×#386611yescharacteristic
181C22×C4—371no—
182C22×C4—371no—
183C22×C4—371no—
184C22×C4—741no—
185C22×C4—741no—
186C22×C4—741no—
187C22×C4—741no—
188Q16—22no—
189Q16—742no—
190Q16—742no—
191Q16—742no—
192C2×C8—371no—
193C2×C8—741no—
194C2×C8—741no—
195C2×C8—741no—
196C2×C8—741no—
197C2×C8—741no—
198C2×C8C2×#386611yescharacteristic
199C4⋊C4—372no—
200C4⋊C4—741no—
201C4⋊C4—741no—
202C4⋊C4—741no—
203C4⋊C4—744no—
204C42—741no—
205C42—741no—
206C42—744no—
207C23—371no—
208Q8—21no—
209Q8—21no—
210Q8—21no—
211Q8—372no—
212Q8—742no—
213Q8—742no—
214Q8—741no—
215Q8—741no—
216Q8—741no—
217Q8—1481no—
218Q8—1481no—
219Q8C22⋊#386612yes—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—371no—
223C2×C4—371no—
224C2×C4—371no—
225C2×C4—371no—
226C2×C4—371no—
227C2×C4—372no—
228C2×C4—742no—
229C2×C4—742no—
230C2×C4—741no—
231C2×C4—741no—
232C2×C4—741no—
233C2×C4—742no—
234C2×C4—741no—
235C2×C4—741no—
236C2×C4—741no—
237C2×C4—741no—
238C2×C4—1481no—
239C2×C4—1481no—
240C2×C4—1481no—
241C2×C4—1481no—
242C2×C4—1481no—
243C2×C4—1481no—
244C2×C4—1481no—
245C2×C4C22×#386611yescharacteristic
246C8—21no—
247C8—741no—
248C8—1481no—
249C22—371no—
250C22—371no—
251C22—371no—
252C22—371no—
253C22—371no—
254C22—371no—
255C22D4×#386611yescharacteristic
256C4—22no—
257C4—41no—
258C4—371no—
259C4—371no—
260C4—2961no—
261C4—742no—
262C4—742no—
263C4—1481no—
264C4—1482no—
265C4—1481no—
266C4C2×C22⋊#386611yescharacteristic
267C4D4×#386611yescharacteristic
268C2—371no—
269C2—371no—
270C2—371no—
271C2—371no—
272C2#1455848111yescharacteristic
273C2Q16×#386611yescharacteristic
274C2#1455857311yescharacteristic
subgroupG/H
centerC22D4×#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×Q16×C37C4
socleC22×C37C4×D4
prime radicalC22×D37C2×D4
cosocleC2×C4×D37C23
hypercenterC2×Q16#3866
hypocenterC37#1878
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
22. C2×Dic148C4semidirect
23. C2×#10596942C4semidirect
24. C2×#10596942C4semidirect
28. C2×Q16×C37C4semidirect
81. C2×#3866Q16semidirect
145. C37#1878semidirect
153. C2×Q16#3866semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#38662
C2×#119245992
(C2×#3866)⋊Q82
#145584072
(C2×#3866)⋊C82
C2×Q16×D372
#187837