Finite Group Databasebeta

← #18010589

Subgroups — #18010589

Order 4736.

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

normal subgroups only

This group has 402 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×D4×#3866C211yesmaximal, characteristic
2C2×#11924599C211yesmaximal, characteristic, complemented
3C2×#11924598C211yesmaximal, characteristic
4(C2×#3866)⋊Q8C211yesmaximal, characteristic, complemented
5#14558407C211yesmaximal, characteristic, complemented
6(C2×#3866)⋊C8C211yesmaximal, characteristic, complemented
7C2×SD16×D37C211yesmaximal, characteristic
8C23×#3866—21no—
9C2×D37⋊C8C2211yescharacteristic
10D4×#3866—22no—
11D4×#3866—22no—
12C2×C4⋊#3866C2211yescharacteristic
13C2×C4⋊#3866C2211yescharacteristic
14C2×C22⋊#3866—21no—
15C2×C4×#3866C2211yescharacteristic
16#11924599—22no—
17#11924598—22no—
18(C2×#3866)⋊C4—21no—
19(C2×#3866)⋊C4—21no—
20C2×Q8×D37C2211yescharacteristic
21C2×D4×D37C2211yescharacteristic
22C2×#10596930C411yescharacteristic, complemented
23C2×#10596940C411yescharacteristic, complemented
24C2×#10596941C411yescharacteristic, complemented
25SD16×D37—22no—
26SD16×D37—22no—
27C2×C8×D37C2211yescharacteristic
28C2×SD16×C37C411yescharacteristic, complemented
29C23×D37—21no—
30C22×#3866—24no—
31C22×#3866—21no—
32C22×#3866—21no—
33C22×#3866—42no—
34C22×#3866—42no—
35C22×#3866D411yescharacteristic
36C22×#3866D411yescharacteristic
37C2×Q8×C37C2×C411yescharacteristic, complemented
38C2×D4×C37C2×C411yescharacteristic
39C2×C22⋊D37—21no—
40Q8×D37—21no—
41Q8×D37—21no—
42Q8×D37—21no—
43Q8×D37—21no—
44D4×D37—21no—
45D4×D37—21no—
46D4×D37D412yes—
47D4×D37D412yes—
48C2×D148C2×C411yescharacteristic
49C2×C4×D37—21no—
50C2×C4×D37C2311yescharacteristic
51C2×Dic74—21no—
52C2×Dic74C2×C411yescharacteristic, complemented
53C22⋊#3866—24no—
54C2×#64438—21no—
55C4⋊#3866—21no—
56C4⋊#3866—21no—
57C4⋊#3866—21no—
58C4⋊#3866D412yes—
59C4×#3866—21no—
60C4×#3866—21no—
61D37⋊C8—21no—
62D37⋊C8—21no—
63SD16×C37—22no—
64C2×C8×C37C2×C411yescharacteristic, complemented
65#10596941—22no—
66#10596940—22no—
67C2×#64436C2×C411yescharacteristic, complemented
68#10596930—22no—
69C8×D37—21no—
70C8×D37—21no—
71C23×C37—21no—
72C22×D37—21no—
73C22×D37—22no—
74C22×D37—22no—
75C22×D37—41no—
76C22×D37—41no—
77C22×D37—41no—
78C22×D37—41no—
79C22×D37C2×D411yescharacteristic
80C2×#3866—21no—
81C2×#3866—21no—
82C2×#3866—21no—
83C2×#3866—22no—
84C2×#3866—21no—
85C2×#3866—21no—
86C2×#3866—48no—
87C2×#3866—41no—
88C2×#3866—41no—
89C2×#3866—41no—
90C2×#3866—41no—
91C2×#3866—41no—
92C2×#3866SD1612yescomplemented
93Q8×C37—21no—
94Q8×C37—21no—
95D4×C37—21no—
96D4×C37C22⋊C412yes—
97C2×C4×C37—21no—
98C2×C4×C37C22×C411yescharacteristic
99C22⋊D37—22no—
100C22⋊D37—22no—
101C2×Dic37—21no—
102C2×Dic37#4111yescharacteristic
103D148—21no—
104D148C22⋊C412yes—
105C4×D37—41no—
106C4×D37—41no—
107C4×D37C2×D411yescharacteristic
108C4×D37C2×D411yescharacteristic
109C4×D37C2×D411yescharacteristic
110C4×D37#4111yescharacteristic
111Dic74—21no—
112Dic74—21no—
113Dic74—41no—
114Dic74—41no—
115#64438—41no—
116C8×C37—21no—
117#64436—21no—
118C22×C37—22no—
119C22×C37—41no—
120C22×C37—41no—
121C22×C37C4×D411yescharacteristic
122C2×D37—22no—
123C2×D37—41no—
124C2×D37—41no—
125C2×D37—42no—
126C2×D37—42no—
127C2×D37—42no—
128C2×D37—42no—
129C2×D37#12011yescharacteristic
130C2×D37#12111yescharacteristic
131C2×D37C2×SD1611yescharacteristic
132C2×D37#13511yescharacteristic
133C2×D37AGL(1,ℤ/8)11yescharacteristic
134C2×D37#13711yescharacteristic
135#3866—22no—
136#3866—42no—
137#3866—41no—
138#3866—81no—
139C4×C37—41no—
140C4×C37C2×C22⋊C411yescharacteristic
141C4×C37C4×D411yescharacteristic
142Dic37—41no—
143Dic37#12111yescharacteristic
144Dic37#12311yescharacteristic
145#1877—371nomaximal, Sylow
146C2×C37—42no—
147C2×C37#38611yescharacteristic
148C2×C37C4×SD1611yescharacteristic
149C2×C37#44011yescharacteristic
150D37—42no—
151D37#45011yescharacteristic
152D37#45211yescharacteristic
153D37#46111yescharacteristic
154D37#46311yescharacteristic
155C22×SD16—371no—
156C2×C4×D4—371no—
157C2×#103—371no—
158C2×#102—371no—
159#391—371no—
160#340—371no—
161#336—371no—
162C37#187711yescharacteristic, complemented, Sylow
163C22×Q8—371no—
164C22×D4—371no—
165C23×C4—741no—
166C2×SD16—371no—
167C2×SD16—371no—
168C2×SD16—371no—
169C2×SD16—742no—
170C2×SD16—742no—
171C2×SD16#386611yescharacteristic, complemented
172C22×C8—371no—
173C22×C8—371no—
174C4×D4—742no—
175C4×D4—742no—
176C2×C4⋊C4—371no—
177C2×C4⋊C4—371no—
178C2×C22⋊C4—741no—
179C2×C42—371no—
180#103—742no—
181#102—742no—
182#95—741no—
183#95—741no—
184C24—741no—
185C2×Q8—371no—
186C2×Q8—741no—
187C2×Q8—741no—
188C2×Q8—741no—
189C2×Q8—741no—
190C2×Q8—741no—
191C2×Q8C2×#386611yescharacteristic, complemented
192C2×D4—372no—
193C2×D4—372no—
194C2×D4—371no—
195C2×D4—741no—
196C2×D4—741no—
197C2×D4—741no—
198C2×D4C2×#386611yescharacteristic
199C22×C4—371no—
200C22×C4—371no—
201C22×C4—371no—
202C22×C4—741no—
203C22×C4—741no—
204C22×C4—744no—
205C22×C4—741no—
206C22×C4—1482no—
207C22×C4—1482no—
208SD16—22no—
209SD16—742no—
210SD16—742no—
211SD16—742no—
212C2×C8—371no—
213C2×C8—741no—
214C2×C8—741no—
215C2×C8—741no—
216C2×C8—741no—
217C2×C8—741no—
218C2×C8C2×#386611yescharacteristic, complemented
219C4⋊C4—372no—
220C4⋊C4—741no—
221C4⋊C4—741no—
222C4⋊C4—741no—
223C22⋊C4—744no—
224C42—741no—
225C42—741no—
226C23—21no—
227C23—371no—
228C23—742no—
229C23—742no—
230C23—741no—
231C23—1481no—
232C23—1481no—
233C23—1481no—
234C23—1481no—
235Q8—21no—
236Q8—21no—
237Q8—741no—
238Q8—741no—
239Q8—1481no—
240Q8—1481no—
241D4—21no—
242D4—372no—
243D4—742no—
244D4—742no—
245D4—741no—
246D4C22⋊#386612yes—
247C2×C4—21no—
248C2×C4—371no—
249C2×C4—371no—
250C2×C4—371no—
251C2×C4—371no—
252C2×C4—371no—
253C2×C4—372no—
254C2×C4—741no—
255C2×C4—741no—
256C2×C4—741no—
257C2×C4—742no—
258C2×C4—741no—
259C2×C4—741no—
260C2×C4—741no—
261C2×C4—1481no—
262C2×C4—1481no—
263C2×C4—1481no—
264C2×C4—1481no—
265C2×C4—1481no—
266C2×C4—1488no—
267C2×C4—1481no—
268C2×C4—1481no—
269C2×C4C22×#386611yescharacteristic
270C8—21no—
271C8—741no—
272C8—1481no—
273C22—22no—
274C22—41no—
275C22—41no—
276C22—371no—
277C22—371no—
278C22—371no—
279C22—371no—
280C22—371no—
281C22—371no—
282C22—742no—
283C22—1482no—
284C22—1482no—
285C22—1482no—
286C22—1482no—
287C22—1481no—
288C22—1481no—
289C22D4×#386611yescharacteristic
290C4—41no—
291C4—371no—
292C4—371no—
293C4—2961no—
294C4—742no—
295C4—1481no—
296C4—1482no—
297C4—1481no—
298C4C2×C22⋊#386611yescharacteristic
299C4D4×#386611yescharacteristic
300C2—42no—
301C2—371no—
302C2—371no—
303C2—371no—
304C2—371no—
305C2—1482no—
306C2#1455848111yescharacteristic
307C2SD16×#386611yescharacteristic
308C2#1455857211yescharacteristic
subgroupG/H
centerC22D4×#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×SD16×C37C4
socleC22×C37C4×D4
prime radicalC2×D4×D37C22
cosocleC2×C4×D37C23
hypercenterC2×SD16#3866
hypocenterC37#1877
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#11924599C2semidirect
4. (C2×#3866)⋊Q8C2semidirect
5. #14558407C2semidirect
6. (C2×#3866)⋊C8C2semidirect
22. C2×#10596930C4semidirect
23. C2×#10596940C4semidirect
24. C2×#10596941C4semidirect
28. C2×SD16×C37C4semidirect
37. C2×Q8×C37C2×C4semidirect
52. C2×Dic74C2×C4semidirect
64. C2×C8×C37C2×C4semidirect
67. C2×#64436C2×C4semidirect
92. C2×#3866SD16semidirect
162. C37#1877semidirect
171. C2×SD16#3866semidirect
191. C2×Q8C2×#3866semidirect
218. C2×C8C2×#3866semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#38662
C2×#119245992
C2×#119245982
(C2×#3866)⋊Q82
#145584072
(C2×#3866)⋊C82
C2×SD16×D372
#187737