Subgroups — C₄×#22627711 #49175353

Order 37504.

572 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22627711	C₂	1	2	yes	maximal
2	#34037094	C₂	1	2	yes	maximal, complemented
3	#34037093	C₂	1	4	yes	maximal, complemented
4	C₄×#17989812	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#17989811	C₂	1	2	yes	maximal, complemented
6	C₄×D₂₉₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×#14556880	C₂	1	2	yes	maximal, complemented
8	C₄×#17989801	C₂	1	1	yes	maximal, characteristic
9	#22627711	C₄	1	16	yes	direct product factor
10	C₂×#17989812	C₂²	1	2	yes	—
11	C₂×#17989811	C₂²	1	4	yes	—
12	C₂×D₂₉₃⋊C₈	C₂²	1	2	yes	—
13	C₂²×#14556880	C₂²	1	4	yes	—
14	#22627679	C₂²	1	4	yes	—
15	#22627679	C₂²	1	2	yes	—
16	C₄×#14556880	C₂²	1	1	yes	characteristic
17	C₄×#14556880	C₂²	1	2	yes	—
18	C₄×#14556880	C₂²	1	4	yes	—
19	C₄×#14556880	C₂²	1	1	yes	characteristic
20	C₄×#14556880	C₂²	1	2	yes	—
21	C₂×#17989801	C₂²	1	1	yes	characteristic
22	C₄×Dic₅₈₆	C₄	1	1	yes	characteristic
23	#22627589	C₄	1	1	yes	characteristic
24	D₄×Dic₂₉₃	C₄	1	1	yes	characteristic
25	C₄×C₂²⋊D₂₉₃	C₄	1	2	yes	—
26	#22627584	C₄	1	2	yes	—
27	#22627582	C₂²	1	1	yes	characteristic
28	#22627580	C₂²	1	2	yes	—
29	C₂×C₄×Dic₂₉₃	C₂²	1	2	yes	—
30	C₄²×D₂₉₃	C₂²	1	1	yes	characteristic
31	C₄×D₄×C₂₉₃	C₄	1	1	yes	characteristic
32	#17989812	C₂×C₄	1	8	yes	complemented
33	#17989811	C₂×C₄	1	16	yes	complemented
34	D₂₉₃⋊C₈	C₂×C₄	1	8	yes	complemented
35	C₂×#14556880	C₂×C₄	1	16	yes	complemented
36	C₂×#14556880	C₂³	1	2	yes	—
37	C₂×#14556880	C₂³	1	4	yes	—
38	C₂×#14556880	C₂³	1	2	yes	—
39	#17989801	C₂×C₄	1	8	yes	—
40	C₂×Dic₅₈₆	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊D₂₉₃	C₂×C₄	1	2	yes	—
42	C₂²×Dic₂₉₃	C₂×C₄	1	2	yes	—
43	C₂²×Dic₂₉₃	C₂³	1	2	yes	—
44	C₂×C₄×D₂₉₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₂₉₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×D₂₉₃	C₂³	1	1	yes	characteristic
47	C₄⋊Dic₂₉₃	C₂×C₄	1	1	yes	characteristic
48	#17989781	C₂×C₄	1	2	yes	—
49	#17989781	C₂×C₄	1	2	yes	—
50	C₂²⋊Dic₂₉₃	C₂×C₄	1	2	yes	—
51	#17989779	C₂×C₄	1	2	yes	—
52	C₄×Dic₂₉₃	C₂×C₄	1	2	yes	—
53	C₄×Dic₂₉₃	C₂×C₄	1	2	yes	—
54	C₄×Dic₂₉₃	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₂₉₃	C₂³	1	1	yes	characteristic
56	C₄×Dic₂₉₃	C₂³	1	1	yes	characteristic
57	C₄×Dic₂₉₃	C₂³	1	2	yes	—
58	C₂×D₄×C₂₉₃	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₂₉₃	C₂×C₄	1	2	yes	—
60	C₄⋊C₄×C₂₉₃	C₂×C₄	1	1	yes	characteristic
61	C₂²⋊C₄×C₂₉₃	C₂×C₄	1	2	yes	—
62	C₄²×C₂₉₃	C₂×C₄	1	1	yes	characteristic
63	#14556880	C₂²×C₄	1	4	yes	—
64	#14556880	C₂²×C₄	1	8	yes	—
65	#14556880	C₂²×C₄	1	4	yes	—
66	C₂²×D₂₉₃	C₂²×C₄	1	1	yes	characteristic
67	Dic₅₈₆	C₄²	1	4	yes	—
68	C₂²⋊D₂₉₃	C₄²	1	8	yes	—
69	C₂×Dic₂₉₃	—	2	4	no	—
70	C₂×Dic₂₉₃	C₂²×C₄	1	2	yes	—
71	C₂×Dic₂₉₃	C₂²×C₄	1	1	yes	characteristic
72	C₂×Dic₂₉₃	C₂²×C₄	1	2	yes	—
73	C₂×Dic₂₉₃	C₂²×C₄	1	8	yes	—
74	C₂×Dic₂₉₃	C₂²×C₄	1	1	yes	characteristic
75	C₂×Dic₂₉₃	C₂⁴	1	1	yes	characteristic
76	C₄×D₂₉₃	—	2	2	no	—
77	C₄×D₂₉₃	—	2	2	no	—
78	C₄×D₂₉₃	C₂²×C₄	1	4	yes	—
79	C₂³×C₂₉₃	C₂²×C₄	1	2	yes	—
80	D₄×C₂₉₃	C₄²	1	4	yes	—
81	C₂×C₄×C₂₉₃	—	2	4	no	—
82	C₂×C₄×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₄×C₂₉₃	C₂²×C₄	1	2	yes	—
84	C₂×C₄×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₄×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₂₉₃	—	2	2	no	—
87	C₂²×C₂₉₃	—	2	2	no	—
88	C₂²×C₂₉₃	C₂×C₄²	1	4	yes	—
89	C₂²×C₂₉₃	C₂³×C₄	1	1	yes	characteristic
90	C₂×D₂₉₃	—	2	1	no	—
91	C₂×D₂₉₃	—	2	1	no	—
92	C₂×D₂₉₃	C₂×C₄²	1	2	yes	—
93	C₄×C₂₉₃	—	2	2	no	—
94	C₄×C₂₉₃	—	2	1	no	—
95	C₄×C₂₉₃	C₂×C₄²	1	2	yes	—
96	C₄×C₂₉₃	#131	1	2	yes	complemented
97	Dic₂₉₃	—	2	1	no	—
98	Dic₂₉₃	—	2	2	no	—
99	Dic₂₉₃	C₂×C₄²	1	4	yes	—
100	Dic₂₉₃	#131	1	2	yes	complemented
101	Dic₂₉₃	C₂³×C₄	1	2	yes	—
102	C₂×C₂₉₃	—	2	4	no	—
103	C₂×C₂₉₃	C₂²×C₄²	1	1	yes	characteristic
104	C₂×C₂₉₃	C₂×#131	1	1	yes	characteristic
105	C₂×C₂₉₃	C₂×#131	1	1	yes	characteristic
106	D₂₉₃	—	2	2	no	—
107	C₂₉₃	C₄×#131	1	1	yes	characteristic, complemented, Sylow
108	C₄×#131	—	293	1	no	maximal, Sylow
109	C₂×#131	—	293	2	no	—
110	C₄×#41	—	293	1	no	—
111	#405	—	293	4	no	—
112	#405	—	293	2	no	—
113	C₄×M₁₆	—	293	2	no	—
114	C₄×M₁₆	—	293	1	no	—
115	C₂×C₄×C₈	—	293	2	no	—
116	C₂×C₄×C₈	—	293	1	no	—
117	C₂×#41	—	293	1	no	—
118	#131	—	293	16	no	—
119	C₂×M₁₆	—	293	4	no	—
120	C₂×M₁₆	—	293	2	no	—
121	C₂²×C₈	—	293	4	no	—
122	C₂²×C₈	—	293	2	no	—
123	C₄×Q₈	—	293	1	no	—
124	C₄×Q₈	—	293	1	no	—
125	C₄×D₄	—	293	1	no	—
126	C₄×D₄	—	293	2	no	—
127	C₄×D₄	—	293	2	no	—
128	C₄×D₄	#11924078	1	1	yes	characteristic
129	#117	—	293	1	no	—
130	#117	—	293	2	no	—
131	C₂×C₄²	—	293	2	no	—
132	C₂×C₄²	—	293	1	no	—
133	#97	—	293	4	no	—
134	#97	—	293	2	no	—
135	C₄×C₈	—	293	1	no	—
136	C₄×C₈	—	293	2	no	—
137	C₄×C₈	—	293	1	no	—
138	C₄×C₈	—	293	4	no	—
139	C₄×C₈	—	293	2	no	—
140	#41	—	293	8	no	—
141	C₂×Q₈	—	293	1	no	—
142	C₂×D₄	—	293	2	no	—
143	C₂×D₄	C₂×#11924078	1	1	yes	characteristic
144	C₂²×C₄	—	293	2	no	—
145	C₂²×C₄	—	293	1	no	—
146	C₂²×C₄	—	293	2	no	—
147	C₂²×C₄	—	293	1	no	—
148	C₂²×C₄	—	293	1	no	—
149	C₂²×C₄	C₂×#11924078	1	2	yes	—
150	M₁₆	—	293	16	no	—
151	M₁₆	—	293	8	no	—
152	C₂×C₈	—	293	2	no	—
153	C₂×C₈	—	293	4	no	—
154	C₂×C₈	—	293	2	no	—
155	C₂×C₈	—	293	16	no	—
156	C₂×C₈	—	293	8	no	—
157	C₄⋊C₄	—	293	2	no	—
158	C₄⋊C₄	—	293	2	no	—
159	C₄⋊C₄	—	293	1	no	—
160	C₄⋊C₄	C₂×#11924078	1	1	yes	characteristic
161	C₂²⋊C₄	—	293	2	no	—
162	C₂²⋊C₄	—	293	2	no	—
163	C₂²⋊C₄	C₂×#11924078	1	2	yes	—
164	C₄²	—	293	2	no	—
165	C₄²	—	293	1	no	—
166	C₄²	—	293	2	no	—
167	C₄²	—	293	1	no	—
168	C₄²	—	293	1	no	—
169	C₄²	—	293	2	no	—
170	C₄²	C₂×#11924078	1	1	yes	characteristic
171	C₂³	—	293	1	no	—
172	C₂³	C₂²×#11924078	1	2	yes	—
173	Q₈	—	293	4	no	—
174	D₄	—	293	8	no	—
175	D₄	C₄×#11924078	1	4	yes	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	293	8	no	—
178	C₂×C₄	—	293	1	no	—
179	C₂×C₄	—	293	1	no	—
180	C₂×C₄	—	293	2	no	—
181	C₂×C₄	—	293	4	no	—
182	C₂×C₄	—	293	1	no	—
183	C₂×C₄	—	293	2	no	—
184	C₂×C₄	—	586	2	no	—
185	C₂×C₄	—	586	4	no	—
186	C₂×C₄	—	586	2	no	—
187	C₂×C₄	C₂²×#11924078	1	2	yes	—
188	C₂×C₄	C₂²×#11924078	1	1	yes	characteristic
189	C₂×C₄	C₂²×#11924078	1	1	yes	characteristic
190	C₂×C₄	C₂²×#11924078	1	1	yes	characteristic
191	C₈	—	293	4	no	—
192	C₈	—	293	8	no	—
193	C₈	—	293	4	no	—
194	C₂²	—	2	2	no	—
195	C₂²	—	2	2	no	—
196	C₂²	—	293	2	no	—
197	C₂²	—	586	1	no	—
198	C₂²	—	586	1	no	—
199	C₂²	C₂×C₄×#11924078	1	4	yes	—
200	C₂²	C₂³×#11924078	1	1	yes	characteristic
201	C₄	—	2	2	no	—
202	C₄	—	2	1	no	—
203	C₄	—	293	2	no	—
204	C₄	—	293	4	no	—
205	C₄	—	293	2	no	—
206	C₄	—	586	1	no	—
207	C₄	—	586	2	no	—
208	C₄	C₂×C₄×#11924078	1	2	yes	—
209	C₄	#22627711	1	2	yes	direct product factor
210	C₂	—	2	4	no	—
211	C₂	—	586	2	no	—
212	C₂	C₂²×C₄×#11924078	1	1	yes	characteristic
213	C₂	C₂×#22627711	1	1	yes	characteristic
214	C₂	D₂₉₃⋊#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#11924078
commutator	C₂×C₂₉₃	C₂²×C₄²
Frattini	C₂²	C₂³×#11924078
Fitting	C₄×D₄×C₂₉₃	C₄
socle	C₂²×C₂₉₃	C₂³×C₄
prime radical	C₂×#17989801	C₂²
cosocle	C₂×Dic₂₉₃	C₂⁴
hypercenter	C₄×D₄	#11924078
hypocenter	C₂₉₃	C₄×#131
LCS	G ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #34037094	C₂	semidirect
3. #34037093	C₂	semidirect
4. C₄×#17989812	C₂	semidirect
5. C₄×#17989811	C₂	semidirect
6. C₄×D₂₉₃⋊C₈	C₂	semidirect
7. C₂×C₄×#14556880	C₂	semidirect
9. #22627711	C₄	direct (N × H)
32. #17989812	C₂×C₄	semidirect
33. #17989811	C₂×C₄	semidirect
34. D₂₉₃⋊C₈	C₂×C₄	semidirect
35. C₂×#14556880	C₂×C₄	semidirect
96. C₄×C₂₉₃	#131	semidirect
100. Dic₂₉₃	#131	semidirect
107. C₂₉₃	C₄×#131	semidirect
209. C₄	#22627711	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#22627711	2
#34037094	2
#34037093	2
C₄×#17989812	2
C₄×#17989811	2
C₄×D₂₉₃⋊C₈	2
C₂×C₄×#14556880	2
C₄×#17989801	2
C₄×#131	293

Subgroups — C4×#22627711 #49175353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#22627711 #49175353