Group #39939090 — subgroups

Subgroups — C₁₀₃×#33815 #39939090

Order 26368.

490 conjugacy classes of subgroups; only the 214 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 214 normal subgroups are shown.

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

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×#3170	C₂	1	2	yes	maximal
2	C₁₀₃×#2227	C₂	1	4	yes	maximal, complemented
3	C₁₀₃×#2216	C₂	1	4	yes	maximal
4	C₁₀₃×#2209	C₂	1	4	yes	maximal, complemented
5	C₂×C₄⋊C₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic
6	#533×C₁₀₃	—	2	2	no	—
7	C₂×Q₃₂×C₁₀₃	C₂²	1	4	yes	—
8	C₂²×C₁₆×C₁₀₃	C₂²	1	2	yes	—
9	#500×C₁₀₃	C₂²	1	2	yes	—
10	#494×C₁₀₃	C₂²	1	2	yes	—
11	#487×C₁₀₃	—	2	2	no	—
12	#467×C₁₀₃	—	2	2	no	—
13	#467×C₁₀₃	C₂²	1	4	yes	—
14	C₄×Q₁₆×C₁₀₃	—	2	2	no	—
15	C₄×Q₁₆×C₁₀₃	C₂²	1	4	yes	—
16	C₂×C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
17	#366×C₁₀₃	C₂²	1	4	yes	—
18	C₄⋊C₁₆×C₁₀₃	C₂²	1	4	yes	—
19	#358×C₁₀₃	C₂²	1	8	yes	—
20	C₂×Q₁₆×C₁₀₃	—	2	2	no	—
21	C₂×Q₁₆×C₁₀₃	C₂³	1	4	yes	—
22	C₂²×C₈×C₁₀₃	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
24	C₄⋊Q₈×C₁₀₃	—	2	2	no	—
25	C₄⋊Q₈×C₁₀₃	—	2	2	no	—
26	#125×C₁₀₃	—	4	2	no	—
27	C₂²⋊Q₈×C₁₀₃	—	2	4	no	—
28	C₂²⋊Q₈×C₁₀₃	—	4	2	no	—
29	C₄×Q₈×C₁₀₃	—	2	4	no	—
30	C₄×Q₈×C₁₀₃	—	4	2	no	—
31	#117×C₁₀₃	—	4	2	no	—
32	C₂×C₄²×C₁₀₃	D₄	1	1	yes	characteristic
33	Q₃₂×C₁₀₃	—	4	4	no	—
34	C₂×C₁₆×C₁₀₃	—	4	2	no	—
35	C₂×C₁₆×C₁₀₃	C₂³	1	4	yes	—
36	#107×C₁₀₃	—	2	2	no	—
37	#107×C₁₀₃	C₂³	1	4	yes	—
38	#103×C₁₀₃	—	2	4	no	—
39	#103×C₁₀₃	—	2	4	no	—
40	C₄×C₈×C₁₀₃	D₄	1	2	yes	—
41	C₄×C₈×C₁₀₃	C₂³	1	2	yes	—
42	C₂×Q₈×C₁₀₃	—	2	4	no	—
43	C₂×Q₈×C₁₀₃	—	4	2	no	—
44	C₂²×C₄×C₁₀₃	D₈	1	1	yes	characteristic
45	C₂²×C₄×C₁₀₃	D₈	1	1	yes	characteristic
46	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
47	Q₁₆×C₁₀₃	—	2	4	no	—
48	Q₁₆×C₁₀₃	—	2	4	no	—
49	Q₁₆×C₁₀₃	—	4	4	no	—
50	C₂×C₈×C₁₀₃	—	2	1	no	—
51	C₂×C₈×C₁₀₃	—	2	1	no	—
52	C₂×C₈×C₁₀₃	—	4	1	no	—
53	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
54	C₂×C₈×C₁₀₃	C₂×D₄	1	2	yes	—
55	C₂×C₈×C₁₀₃	C₂⁴	1	1	yes	characteristic
56	C₄⋊C₄×C₁₀₃	—	2	4	no	—
57	C₄⋊C₄×C₁₀₃	—	4	2	no	—
58	C₄⋊C₄×C₁₀₃	—	4	2	no	—
59	C₄⋊C₄×C₁₀₃	—	4	4	no	—
60	C₄⋊C₄×C₁₀₃	—	4	4	no	—
61	C₄⋊C₄×C₁₀₃	—	4	2	no	—
62	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
63	C₄²×C₁₀₃	—	4	4	no	—
64	C₄²×C₁₀₃	D₈	1	2	yes	—
65	C₄²×C₁₀₃	C₂×D₄	1	2	yes	—
66	C₁₆×C₁₀₃	—	2	4	no	—
67	C₂³×C₁₀₃	C₂×D₈	1	1	yes	characteristic
68	Q₈×C₁₀₃	—	4	4	no	—
69	Q₈×C₁₀₃	—	4	4	no	—
70	Q₈×C₁₀₃	—	8	4	no	—
71	C₂×C₄×C₁₀₃	—	2	1	no	—
72	C₂×C₄×C₁₀₃	—	2	1	no	—
73	C₂×C₄×C₁₀₃	—	4	1	no	—
74	C₂×C₄×C₁₀₃	—	4	4	no	—
75	C₂×C₄×C₁₀₃	—	4	4	no	—
76	C₂×C₄×C₁₀₃	Q₃₂	1	4	yes	complemented
77	C₂×C₄×C₁₀₃	C₂×D₈	1	1	yes	characteristic
78	C₂×C₄×C₁₀₃	C₂×D₈	1	2	yes	—
79	C₂×C₄×C₁₀₃	C₂×D₈	1	2	yes	—
80	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
81	C₈×C₁₀₃	—	2	1	no	—
82	C₈×C₁₀₃	—	2	2	no	—
83	C₈×C₁₀₃	H(5,𝔽₂)	1	1	yes	characteristic
84	C₈×C₁₀₃	2₋¹⁺⁴	1	1	yes	characteristic
85	C₂²×C₁₀₃	—	2	1	no	—
86	C₂²×C₁₀₃	—	2	1	no	—
87	C₂²×C₁₀₃	C₂×Q₃₂	1	2	yes	—
88	C₂²×C₁₀₃	C₂²×D₈	1	1	yes	characteristic
89	C₄×C₁₀₃	—	2	2	no	—
90	C₄×C₁₀₃	—	2	1	no	—
91	C₄×C₁₀₃	—	8	4	no	—
92	C₄×C₁₀₃	—	8	4	no	—
93	C₄×C₁₀₃	C₂×Q₃₂	1	4	yes	—
94	C₄×C₁₀₃	#537	1	1	yes	characteristic
95	C₄×C₁₀₃	#575	1	1	yes	characteristic
96	#33815	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂×C₁₀₃	—	2	2	no	—
98	C₂×C₁₀₃	#3245	1	1	yes	characteristic
99	C₂×C₁₀₃	C₂²×Q₃₂	1	1	yes	characteristic
100	C₂×C₁₀₃	#3414	1	1	yes	characteristic
101	#3170	C₂×C₁₀₃	1	2	yes	—
102	#2227	C₂×C₁₀₃	1	4	yes	complemented
103	#2216	C₂×C₁₀₃	1	4	yes	—
104	#2209	C₂×C₁₀₃	1	4	yes	complemented
105	C₂×C₄⋊C₁₆	C₂×C₁₀₃	1	1	yes	characteristic
106	C₁₀₃	#33815	1	1	yes	characteristic, direct product factor, Sylow
107	#533	—	2	2	no	—
108	C₂×Q₃₂	C₂²×C₁₀₃	1	4	yes	—
109	C₂²×C₁₆	C₂²×C₁₀₃	1	2	yes	—
110	#500	C₂²×C₁₀₃	1	2	yes	—
111	#494	C₂²×C₁₀₃	1	2	yes	—
112	#487	—	2	2	no	—
113	#467	—	2	2	no	—
114	#467	C₂²×C₁₀₃	1	4	yes	—
115	C₄×Q₁₆	—	2	2	no	—
116	C₄×Q₁₆	C₂²×C₁₀₃	1	4	yes	—
117	C₂×C₄×C₈	C₂²×C₁₀₃	1	1	yes	characteristic
118	#366	C₂²×C₁₀₃	1	4	yes	—
119	C₄⋊C₁₆	C₂²×C₁₀₃	1	4	yes	—
120	#358	C₂²×C₁₀₃	1	8	yes	—
121	C₂×Q₁₆	—	2	2	no	—
122	C₂×Q₁₆	C₂³×C₁₀₃	1	4	yes	—
123	C₂²×C₈	D₄×C₁₀₃	1	1	yes	characteristic
124	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
125	C₄⋊Q₈	—	2	2	no	—
126	C₄⋊Q₈	—	2	2	no	—
127	#125	—	4	2	no	—
128	C₂²⋊Q₈	—	2	4	no	—
129	C₂²⋊Q₈	—	4	2	no	—
130	C₄×Q₈	—	2	4	no	—
131	C₄×Q₈	—	4	2	no	—
132	#117	—	4	2	no	—
133	C₂×C₄²	D₄×C₁₀₃	1	1	yes	characteristic
134	Q₃₂	—	4	4	no	—
135	C₂×C₁₆	—	4	2	no	—
136	C₂×C₁₆	C₂³×C₁₀₃	1	4	yes	—
137	#107	—	2	2	no	—
138	#107	C₂³×C₁₀₃	1	4	yes	—
139	#103	—	2	4	no	—
140	#103	—	2	4	no	—
141	C₄×C₈	D₄×C₁₀₃	1	2	yes	—
142	C₄×C₈	C₂³×C₁₀₃	1	2	yes	—
143	C₂×Q₈	—	2	4	no	—
144	C₂×Q₈	—	4	2	no	—
145	C₂²×C₄	D₈×C₁₀₃	1	1	yes	characteristic
146	C₂²×C₄	D₈×C₁₀₃	1	1	yes	characteristic
147	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
148	Q₁₆	—	2	4	no	—
149	Q₁₆	—	2	4	no	—
150	Q₁₆	—	4	4	no	—
151	C₂×C₈	—	2	1	no	—
152	C₂×C₈	—	2	1	no	—
153	C₂×C₈	—	4	1	no	—
154	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
155	C₂×C₈	C₂×D₄×C₁₀₃	1	2	yes	—
156	C₂×C₈	C₂⁴×C₁₀₃	1	1	yes	characteristic
157	C₄⋊C₄	—	2	4	no	—
158	C₄⋊C₄	—	4	2	no	—
159	C₄⋊C₄	—	4	2	no	—
160	C₄⋊C₄	—	4	4	no	—
161	C₄⋊C₄	—	4	4	no	—
162	C₄⋊C₄	—	4	2	no	—
163	C₂²⋊C₄	—	4	4	no	—
164	C₄²	—	4	4	no	—
165	C₄²	D₈×C₁₀₃	1	2	yes	—
166	C₄²	C₂×D₄×C₁₀₃	1	2	yes	—
167	C₁₆	—	2	4	no	—
168	C₂³	C₂×D₈×C₁₀₃	1	1	yes	characteristic
169	Q₈	—	4	4	no	—
170	Q₈	—	4	4	no	—
171	Q₈	—	8	4	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	1	no	—
174	C₂×C₄	—	4	1	no	—
175	C₂×C₄	—	4	4	no	—
176	C₂×C₄	—	4	4	no	—
177	C₂×C₄	Q₃₂×C₁₀₃	1	4	yes	complemented
178	C₂×C₄	C₂×D₈×C₁₀₃	1	1	yes	characteristic
179	C₂×C₄	C₂×D₈×C₁₀₃	1	2	yes	—
180	C₂×C₄	C₂×D₈×C₁₀₃	1	2	yes	—
181	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
182	C₈	—	2	1	no	—
183	C₈	—	2	2	no	—
184	C₈	H(5,𝔽₂)×C₁₀₃	1	1	yes	characteristic
185	C₈	2₋¹⁺⁴×C₁₀₃	1	1	yes	characteristic
186	C₂²	—	2	1	no	—
187	C₂²	—	2	1	no	—
188	C₂²	C₂×Q₃₂×C₁₀₃	1	2	yes	—
189	C₂²	C₂²×D₈×C₁₀₃	1	1	yes	characteristic
190	C₄	—	2	1	no	—
191	C₄	—	2	2	no	—
192	C₄	—	8	4	no	—
193	C₄	—	8	4	no	—
194	C₄	C₂×Q₃₂×C₁₀₃	1	4	yes	—
195	C₄	#537×C₁₀₃	1	1	yes	characteristic
196	C₄	#575×C₁₀₃	1	1	yes	characteristic
197	C₂	—	2	2	no	—
198	C₂	C₁₀₃×#3245	1	1	yes	characteristic
199	C₂	C₂²×Q₃₂×C₁₀₃	1	1	yes	characteristic
200	C₂	C₁₀₃×#3414	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₀₃×#3170

C₂

yes

maximal

C₁₀₃×#2227

C₂

yes

maximal, complemented

C₁₀₃×#2216

C₂

yes

maximal

C₁₀₃×#2209

C₂

yes

maximal, complemented

C₂×C₄⋊C₁₆×C₁₀₃

C₂

yes

maximal, characteristic

#533×C₁₀₃

—

C₂×Q₃₂×C₁₀₃

C₂²

yes

—

C₂²×C₁₆×C₁₀₃

C₂²

yes

—

#500×C₁₀₃

C₂²

yes

—

#494×C₁₀₃

C₂²

yes

—

#487×C₁₀₃

—

#467×C₁₀₃

—

#467×C₁₀₃

C₂²

yes

—

C₄×Q₁₆×C₁₀₃

—

C₄×Q₁₆×C₁₀₃

C₂²

yes

—

C₂×C₄×C₈×C₁₀₃

C₂²

yes

characteristic

#366×C₁₀₃

C₂²

yes

—

C₄⋊C₁₆×C₁₀₃

C₂²

yes

—

#358×C₁₀₃

C₂²

yes

—

C₂×Q₁₆×C₁₀₃

—

C₂×Q₁₆×C₁₀₃

C₂³

yes

—

C₂²×C₈×C₁₀₃

D₄

yes

characteristic

C₂²×C₈×C₁₀₃

C₂³

yes

characteristic

C₄⋊Q₈×C₁₀₃

—

C₄⋊Q₈×C₁₀₃

—

#125×C₁₀₃

—

C₂²⋊Q₈×C₁₀₃

—

C₂²⋊Q₈×C₁₀₃

—

C₄×Q₈×C₁₀₃

—

C₄×Q₈×C₁₀₃

—

#117×C₁₀₃

—

C₂×C₄²×C₁₀₃

D₄

yes

characteristic

Q₃₂×C₁₀₃

—

C₂×C₁₆×C₁₀₃

—

C₂×C₁₆×C₁₀₃

C₂³

yes

—

#107×C₁₀₃

—

#107×C₁₀₃

C₂³

yes

—

#103×C₁₀₃

—

#103×C₁₀₃

—

C₄×C₈×C₁₀₃

D₄

yes

—

C₄×C₈×C₁₀₃

C₂³

yes

—

C₂×Q₈×C₁₀₃

—

C₂×Q₈×C₁₀₃

—

C₂²×C₄×C₁₀₃

D₈

yes

characteristic

C₂²×C₄×C₁₀₃

D₈

yes

characteristic

C₂²×C₄×C₁₀₃

C₂×D₄

yes

characteristic

Q₁₆×C₁₀₃

—

Q₁₆×C₁₀₃

—

Q₁₆×C₁₀₃

—

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₀₃

C₂×D₄

yes

—

C₂×C₈×C₁₀₃

C₂⁴

yes

characteristic

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₂²⋊C₄×C₁₀₃

—

C₄²×C₁₀₃

—

C₄²×C₁₀₃

D₈

yes

—

C₄²×C₁₀₃

C₂×D₄

yes

—

C₁₆×C₁₀₃

—

C₂³×C₁₀₃

C₂×D₈

yes

characteristic

Q₈×C₁₀₃

—

Q₈×C₁₀₃

—

Q₈×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

Q₃₂

yes

complemented

C₂×C₄×C₁₀₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₀₃

C₂×D₈

yes

—

C₂×C₄×C₁₀₃

C₂×D₈

yes

—

C₂×C₄×C₁₀₃

C₂²×D₄

yes

characteristic

C₈×C₁₀₃

—

C₈×C₁₀₃

—

C₈×C₁₀₃

H(5,𝔽₂)

yes

characteristic

C₈×C₁₀₃

2₋¹⁺⁴

yes

characteristic

C₂²×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

C₂×Q₃₂

yes

—

C₂²×C₁₀₃

C₂²×D₈

yes

characteristic

C₄×C₁₀₃

—

C₄×C₁₀₃

—

C₄×C₁₀₃

—

C₄×C₁₀₃

—

C₄×C₁₀₃

C₂×Q₃₂

yes

—

C₄×C₁₀₃

yes

C₄×C₁₀₃

yes

C₁₀₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₁₀₃

—

C₂×C₁₀₃

#3245

yes

characteristic

C₂×C₁₀₃

C₂²×Q₃₂

yes

characteristic

100

C₂×C₁₀₃

#3414

yes

characteristic

101

#3170

C₂×C₁₀₃

yes

—

102

#2227

C₂×C₁₀₃

yes

complemented

103

#2216

C₂×C₁₀₃

yes

—

104

#2209

C₂×C₁₀₃

yes

complemented

105

C₂×C₄⋊C₁₆

C₂×C₁₀₃

yes

characteristic

106

C₁₀₃

#33815

yes

characteristic, direct product factor, Sylow

107

#533

—

108

C₂×Q₃₂

C₂²×C₁₀₃

yes

—

109

C₂²×C₁₆

C₂²×C₁₀₃

yes

—

110

#500

C₂²×C₁₀₃

yes

—

111

#494

C₂²×C₁₀₃

yes

—

112

#487

—

113

#467

—

114

#467

C₂²×C₁₀₃

yes

—

115

C₄×Q₁₆

—

116

C₄×Q₁₆

C₂²×C₁₀₃

yes

—

117

C₂×C₄×C₈

C₂²×C₁₀₃

yes

characteristic

118

#366

C₂²×C₁₀₃

yes

—

119

C₄⋊C₁₆

C₂²×C₁₀₃

yes

—

120

#358

C₂²×C₁₀₃

yes

—

121

C₂×Q₁₆

—

122

C₂×Q₁₆

C₂³×C₁₀₃

yes

—

123

C₂²×C₈

D₄×C₁₀₃

yes

characteristic

124

C₂²×C₈

C₂³×C₁₀₃

yes

characteristic

125

C₄⋊Q₈

—

126

C₄⋊Q₈

—

127

#125

—

128

C₂²⋊Q₈

—

129

C₂²⋊Q₈

—

130

C₄×Q₈

—

131

C₄×Q₈

—

132

#117

—

133

C₂×C₄²

D₄×C₁₀₃

yes

characteristic

134

Q₃₂

—

135

C₂×C₁₆

—

136

C₂×C₁₆

C₂³×C₁₀₃

yes

—

137

#107

—

138

#107

C₂³×C₁₀₃

yes

—

139

#103

—

140

#103

—

141

C₄×C₈

D₄×C₁₀₃

yes

—

142

C₄×C₈

C₂³×C₁₀₃

yes

—

143

C₂×Q₈

—

144

C₂×Q₈

—

145

C₂²×C₄

D₈×C₁₀₃

yes

characteristic

146

C₂²×C₄

D₈×C₁₀₃

yes

characteristic

147

C₂²×C₄

C₂×D₄×C₁₀₃

yes

characteristic

148

Q₁₆

—

149

Q₁₆

—

150

Q₁₆

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

C₂×D₄×C₁₀₃

yes

characteristic

155

C₂×C₈

C₂×D₄×C₁₀₃

yes

—

156

C₂×C₈

C₂⁴×C₁₀₃

yes

characteristic

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₂²⋊C₄

—

164

C₄²

—

165

C₄²

D₈×C₁₀₃

yes

—

166

C₄²

C₂×D₄×C₁₀₃

yes

—

167

C₁₆

—

168

C₂³

C₂×D₈×C₁₀₃

yes

characteristic

169

Q₈

—

170

Q₈

—

171

Q₈

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

Q₃₂×C₁₀₃

yes

complemented

178

C₂×C₄

C₂×D₈×C₁₀₃

yes

characteristic

179

C₂×C₄

C₂×D₈×C₁₀₃

yes

—

180

C₂×C₄

C₂×D₈×C₁₀₃

yes

—

181

C₂×C₄

C₂²×D₄×C₁₀₃

yes

characteristic

182

C₈

—

183

C₈

—

184

C₈

H(5,𝔽₂)×C₁₀₃

yes

characteristic

185

C₈

2₋¹⁺⁴×C₁₀₃

yes

characteristic

186

C₂²

—

187

C₂²

—

188

C₂²

C₂×Q₃₂×C₁₀₃

yes

—

189

C₂²

C₂²×D₈×C₁₀₃

yes

characteristic

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

C₂×Q₃₂×C₁₀₃

yes

—

195

C₄

#537×C₁₀₃

yes

characteristic

196

C₄

#575×C₁₀₃

yes

characteristic

197

C₂

—

198

C₂

C₁₀₃×#3245

yes

characteristic

199

C₂

C₂²×Q₃₂×C₁₀₃

yes

characteristic

200

C₂

C₁₀₃×#3414

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₀₃
prime radical	C₂³×C₁₀₃	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ C₂×C₄×C₈×C₁₀₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₀₃

C₂²×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂⁴×C₁₀₃

prime radical

C₂³×C₁₀₃

C₂×D₈

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ C₂×C₄×C₈×C₁₀₃ ◁ G

N	H ≅ G/N	type
2. C₁₀₃×#2227	C₂	semidirect
4. C₁₀₃×#2209	C₂	semidirect
76. C₂×C₄×C₁₀₃	Q₃₂	semidirect
96. #33815	C₁₀₃	direct (N × H)
102. #2227	C₂×C₁₀₃	semidirect
104. #2209	C₂×C₁₀₃	semidirect
106. C₁₀₃	#33815	direct (N × H)
177. C₂×C₄	Q₃₂×C₁₀₃	semidirect

H ≅ G/N

type

2. C₁₀₃×#2227

C₂

semidirect

4. C₁₀₃×#2209

C₂

semidirect

76. C₂×C₄×C₁₀₃

Q₃₂

semidirect

96. #33815

C₁₀₃

direct (N × H)

102. #2227

C₂×C₁₀₃

semidirect

104. #2209

C₂×C₁₀₃

semidirect

106. C₁₀₃

#33815

direct (N × H)

177. C₂×C₄

Q₃₂×C₁₀₃

semidirect

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

subgroup	index
C₁₀₃×#3170	2
C₁₀₃×#2227	2
C₁₀₃×#2216	2
C₁₀₃×#2209	2
C₂×C₄⋊C₁₆×C₁₀₃	2
#33815	103

subgroup

index

C₁₀₃×#3170

C₁₀₃×#2227

C₁₀₃×#2216

C₁₀₃×#2209

C₂×C₄⋊C₁₆×C₁₀₃

#33815

103

Subgroups — C₁₀₃×#33815 #39939090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C103×#33815 #39939090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#33815 #39939090