Finite Group Databasebeta

← C2×#14558572 #18011347

Subgroups — C2×#14558572 #18011347

Order 4736.

544 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 170 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, complemented
2C2×D4×#3866C211yesmaximal, characteristic
3#14558572C218yesmaximal, direct product factor
4C2×#11924605C211yesmaximal, characteristic, complemented
5C2×#11924599C211yesmaximal, characteristic, complemented
6C2×#11924598C211yesmaximal, characteristic
7C2×#11924590C211yesmaximal, characteristic, complemented
8C2×SD16×D37C211yesmaximal, characteristic
9C23×#3866—21no—
10C2×D37⋊C8C2211yescharacteristic
11Q8×#3866—22no—
12Q8×#3866C2214yescomplemented
13D4×#3866—22no—
14D4×#3866C2214yes—
15C2×C4⋊#3866—21no—
16C2×C4⋊#3866C2211yescharacteristic
17C2×C4⋊#3866C2211yescharacteristic
18C2×C22⋊#3866—21no—
19C2×C4×#3866—21no—
20C2×C4×#3866C2211yescharacteristic
21#11924605C2214yescomplemented
22#11924599C2214yescomplemented
23#11924598C2214yes—
24#11924590C2214yescomplemented
25C2×Q8×D37C2211yescharacteristic
26C2×D4×D37C2211yescharacteristic
27C2×#10596930C411yescharacteristic, complemented
28C2×#10596940C411yescharacteristic, complemented
29C2×#10596941C411yescharacteristic, complemented
30SD16×D37C414yescomplemented
31SD16×D37C2214yes—
32C2×C8×D37C2211yescharacteristic
33C2×SD16×C37C411yescharacteristic, complemented
34C23×D37—21no—
35C22×#3866—21no—
36C22×#3866—21no—
37C22×#3866—24no—
38C22×#3866—44no—
39C22×#3866D411yescharacteristic
40C22×#3866D411yescharacteristic
41C2×Q8×C37C2×C411yescharacteristic, complemented
42C2×D4×C37C2×C411yescharacteristic
43C2×C22⋊D37—21no—
44Q8×D37—21no—
45Q8×D37—21no—
46Q8×D37C2×C412yescomplemented
47Q8×D37C2312yes—
48D4×D37—21no—
49D4×D37—21no—
50D4×D37C2×C412yes—
51D4×D37C2312yes—
52C2×D148C2×C411yescharacteristic
53C2×C4×D37—21no—
54C2×C4×D37C2311yescharacteristic
55C2×Dic74—21no—
56C2×Dic74C2×C411yescharacteristic, complemented
57C22⋊#3866—24no—
58C2×#64438—21no—
59C4⋊#3866—24no—
60C4⋊#3866—21no—
61C4⋊#3866—21no—
62C4⋊#3866C2312yes—
63C4⋊#3866C2312yes—
64C4×#3866—24no—
65C4×#3866D412yes—
66C4×#3866C2312yes—
67D37⋊C8—21no—
68D37⋊C8C2312yes—
69SD16×C37C2×C414yescomplemented
70C2×C8×C37C2×C411yescharacteristic, complemented
71#10596941C2×C414yescomplemented
72#10596940C2×C414yescomplemented
73C2×#64436C2×C411yescharacteristic, complemented
74#10596930C2×C414yescomplemented
75C8×D37C2×C412yescomplemented
76C8×D37C2312yes—
77C23×C37—21no—
78C22×D37—21no—
79C22×D37—22no—
80C22×D37—22no—
81C22×D37—42no—
82C22×D37—42no—
83C22×D37C2×D411yescharacteristic
84C2×#3866—22no—
85C2×#3866—22no—
86C2×#3866—22no—
87C2×#3866—22no—
88C2×#3866—48no—
89C2×#3866—42no—
90C2×#3866—42no—
91C2×#3866C2×D412yes—
92C2×#3866C2×D412yes—
93Q8×C37—21no—
94Q8×C37C22×C412yescomplemented
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—22no—
106C4×D37—22no—
107C4×D37C22×C411yescharacteristic
108C4×D37C2×D411yescharacteristic
109C4×D37#4111yescharacteristic
110C4×D37C2411yescharacteristic
111Dic74—21no—
112Dic74—22no—
113Dic74—22no—
114Dic74C22×C412yescomplemented
115#64438—22no—
116C8×C37C22×C412yescomplemented
117#64436C22×C412yescomplemented
118C22×C37—22no—
119C22×C37—42no—
120C22×C37C4×D411yescharacteristic
121C2×D37—22no—
122C2×D37—42no—
123C2×D37—42no—
124C2×D37—42no—
125C2×D37—44no—
126C2×D37C4×D411yescharacteristic
127C2×D37AGL(1,ℤ/8)12yes—
128C2×D37#13712yes—
129C2×D37C22×D411yescharacteristic
130#3866—22no—
131#3866—22no—
132#3866—42no—
133#3866—42no—
134C4×C37—22no—
135C4×C37C4×D411yescharacteristic
136C4×C37C23×C411yescharacteristic
137Dic37—22no—
138Dic37C4×D411yescharacteristic
139Dic37C2×#4111yescharacteristic
140C2×#440—371nomaximal, Sylow
141C2×C37—42no—
142C2×C37#44012yescomplemented
143C2×C37C2×C4×D411yescharacteristic
144D37—42no—
145D37#44012yescomplemented
146D37C2×AGL(1,ℤ/8)11yescharacteristic
147D37C2×#13711yescharacteristic
148C22×SD16—371no—
149C2×C4×Q8—371no—
150C2×C4×D4—371no—
151#440—378no—
152C2×#107—371no—
153C2×#103—371no—
154C2×#102—371no—
155C2×#97—371no—
156C37C2×#44011yescharacteristic, complemented, Sylow
157C22×Q8—371no—
158C22×D4—371no—
159C23×C4—741no—
160C2×SD16—371no—
161C2×SD16—371no—
162C2×SD16—374no—
163C2×SD16—374no—
164C2×SD16—371no—
165C2×SD16#386611yescharacteristic, complemented
166C22×C8—371no—
167C22×C8—371no—
168C4×Q8—374no—
169C4×Q8—742no—
170C4×D4—374no—
171C4×D4—742no—
172C2×C4⋊C4—371no—
173C2×C4⋊C4—371no—
174C2×C4⋊C4—741no—
175C2×C22⋊C4—741no—
176C2×C42—371no—
177C2×C42—741no—
178#107—374no—
179#103—374no—
180#102—374no—
181#97—374no—
182C24—741no—
183C2×Q8—372no—
184C2×Q8—372no—
185C2×Q8—371no—
186C2×Q8—741no—
187C2×Q8—741no—
188C2×Q8—741no—
189C2×Q8C2×#386611yescharacteristic, complemented
190C2×D4—372no—
191C2×D4—372no—
192C2×D4—371no—
193C2×D4—741no—
194C2×D4—741no—
195C2×D4—741no—
196C2×D4C2×#386611yescharacteristic
197C22×C4—371no—
198C22×C4—371no—
199C22×C4—371no—
200C22×C4—741no—
201C22×C4—744no—
202C22×C4—741no—
203C22×C4—741no—
204C22×C4—1484no—
205SD16—374no—
206SD16—374no—
207SD16—374no—
208SD16C2×#386614yescomplemented
209C2×C8—371no—
210C2×C8—372no—
211C2×C8—372no—
212C2×C8—372no—
213C2×C8—741no—
214C2×C8—741no—
215C2×C8C2×#386611yescharacteristic, complemented
216C4⋊C4—372no—
217C4⋊C4—372no—
218C4⋊C4—741no—
219C4⋊C4—741no—
220C4⋊C4—744no—
221C22⋊C4—744no—
222C42—372no—
223C42—372no—
224C42—744no—
225C23—21no—
226C23—371no—
227C23—742no—
228C23—742no—
229C23—741no—
230C23—1482no—
231C23—1482no—
232Q8—21no—
233Q8—372no—
234Q8—742no—
235Q8—742no—
236Q8—741no—
237Q8C22×#386612yescomplemented
238D4—21no—
239D4—372no—
240D4—742no—
241D4—742no—
242D4—741no—
243D4C22×#386612yes—
244C2×C4—21no—
245C2×C4—371no—
246C2×C4—371no—
247C2×C4—371no—
248C2×C4—371no—
249C2×C4—371no—
250C2×C4—372no—
251C2×C4—372no—
252C2×C4—742no—
253C2×C4—742no—
254C2×C4—742no—
255C2×C4—742no—
256C2×C4—741no—
257C2×C4—742no—
258C2×C4—742no—
259C2×C4—1488no—
260C2×C4—1482no—
261C2×C4—1482no—
262C2×C4C22×#386611yescharacteristic
263C8—372no—
264C8—742no—
265C8C22×#386612yescomplemented
266C22—22no—
267C22—42no—
268C22—372no—
269C22—372no—
270C22—371no—
271C22—371no—
272C22—742no—
273C22—1482no—
274C22—1482no—
275C22—1484no—
276C22—1482no—
277C22D4×#386611yescharacteristic
278C4—22no—
279C4—371no—
280C4—371no—
281C4—742no—
282C4—742no—
283C4—742no—
284C4—1482no—
285C4—1482no—
286C4D4×#386611yescharacteristic
287C4C23×#386611yescharacteristic
288C2—42no—
289C2—371no—
290C2—371no—
291C2—372no—
292C2—1482no—
293C2#1455857212yesdirect product factor
294C2C2×D4×#386611yescharacteristic
subgroupG/H
centerC22D4×#3866
commutatorC4×C37C23×C4
FrattiniC4C23×#3866
FittingC2×SD16×C37C4
socleC22×C37C4×D4
prime radicalC2×D4×D37C22
cosocleC4×D37C24
hypercenterC2×SD16#3866
hypocenterC37C2×#440
LCSG ▷ 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
1. C2×Q8×#3866C2semidirect
3. #14558572C2direct (N × H)
4. C2×#11924605C2semidirect
5. C2×#11924599C2semidirect
7. C2×#11924590C2semidirect
12. Q8×#3866C22semidirect
21. #11924605C22semidirect
22. #11924599C22semidirect
24. #11924590C22semidirect
27. C2×#10596930C4semidirect
28. C2×#10596940C4semidirect
29. C2×#10596941C4semidirect
30. SD16×D37C4semidirect
33. C2×SD16×C37C4semidirect
41. C2×Q8×C37C2×C4semidirect
46. Q8×D37C2×C4semidirect
56. C2×Dic74C2×C4semidirect
69. SD16×C37C2×C4semidirect
70. C2×C8×C37C2×C4semidirect
71. #10596941C2×C4semidirect
72. #10596940C2×C4semidirect
73. C2×#64436C2×C4semidirect
74. #10596930C2×C4semidirect
75. C8×D37C2×C4semidirect
94. Q8×C37C22×C4semidirect
114. Dic74C22×C4semidirect
116. C8×C37C22×C4semidirect
117. #64436C22×C4semidirect
142. C2×C37#440semidirect
145. D37#440semidirect
156. C37C2×#440semidirect
165. C2×SD16#3866semidirect
189. C2×Q8C2×#3866semidirect
208. SD16C2×#3866semidirect
215. C2×C8C2×#3866semidirect
237. Q8C22×#3866semidirect
265. C8C22×#3866semidirect
293. C2#14558572direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×#38662
C2×D4×#38662
#145585722
C2×#119246052
C2×#119245992
C2×#119245982
C2×#119245902
C2×SD16×D372
C2×#44037