Group #39915896 — subgroups

Subgroups — C₁₀₃×#10621 #39915896

Order 26368.

402 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 134 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×#1954	C₂	1	1	yes	maximal, characteristic
2	C₁₀₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₃×#1802	C₂	1	2	yes	maximal
4	C₁₀₃×#1296	C₂	1	2	yes	maximal, complemented
5	C₁₀₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	2	yes	—
9	C₂×#102×C₁₀₃	—	2	2	no	—
10	C₂×C₂²⋊C₈×C₁₀₃	—	2	2	no	—
11	C₂×C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
12	#384×C₁₀₃	C₂²	1	2	yes	—
13	#340×C₁₀₃	—	2	2	no	—
14	#340×C₁₀₃	—	2	2	no	—
15	C₂²×D₄×C₁₀₃	D₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₀₃	—	2	1	no	—
17	C₂²×C₈×C₁₀₃	—	2	1	no	—
18	C₂²×C₈×C₁₀₃	—	2	2	no	—
19	C₂²×C₈×C₁₀₃	D₄	1	2	yes	—
20	C₄×D₄×C₁₀₃	—	2	2	no	—
21	C₄×D₄×C₁₀₃	—	2	2	no	—
22	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₀₃	D₄	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
27	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
28	C₄⋊C₈×C₁₀₃	—	2	2	no	—
29	C₄⋊C₈×C₁₀₃	—	2	2	no	—
30	C₄⋊C₈×C₁₀₃	—	2	2	no	—
31	#102×C₁₀₃	—	4	4	no	—
32	C₂²⋊C₈×C₁₀₃	—	4	4	no	—
33	C₄×C₈×C₁₀₃	—	2	2	no	—
34	C₂⁴×C₁₀₃	—	2	1	no	—
35	C₂×D₄×C₁₀₃	—	2	2	no	—
36	C₂×D₄×C₁₀₃	—	2	1	no	—
37	C₂×D₄×C₁₀₃	—	2	2	no	—
38	C₂×D₄×C₁₀₃	D₈	1	2	yes	—
39	C₂²×C₄×C₁₀₃	—	2	1	no	—
40	C₂²×C₄×C₁₀₃	—	4	1	no	—
41	C₂²×C₄×C₁₀₃	—	4	1	no	—
42	C₂²×C₄×C₁₀₃	—	4	2	no	—
43	C₂²×C₄×C₁₀₃	—	4	2	no	—
44	C₂²×C₄×C₁₀₃	—	4	2	no	—
45	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₀₃	#41	1	1	yes	characteristic
48	C₂×C₈×C₁₀₃	—	2	2	no	—
49	C₂×C₈×C₁₀₃	—	2	2	no	—
50	C₂×C₈×C₁₀₃	—	2	2	no	—
51	C₂×C₈×C₁₀₃	—	4	2	no	—
52	C₂×C₈×C₁₀₃	—	4	1	no	—
53	C₂×C₈×C₁₀₃	—	4	2	no	—
54	C₂×C₈×C₁₀₃	—	4	2	no	—
55	C₂×C₈×C₁₀₃	—	4	2	no	—
56	C₄⋊C₄×C₁₀₃	—	2	2	no	—
57	C₄⋊C₄×C₁₀₃	—	4	2	no	—
58	C₄⋊C₄×C₁₀₃	—	4	2	no	—
59	C₄⋊C₄×C₁₀₃	—	4	2	no	—
60	C₄⋊C₄×C₁₀₃	—	4	2	no	—
61	C₄⋊C₄×C₁₀₃	—	8	2	no	—
62	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
63	C₄²×C₁₀₃	#41	1	2	yes	—
64	C₄²×C₁₀₃	#41	1	2	yes	—
65	C₂³×C₁₀₃	—	2	2	no	—
66	C₂³×C₁₀₃	—	4	1	no	—
67	C₂³×C₁₀₃	—	4	2	no	—
68	C₂³×C₁₀₃	—	4	1	no	—
69	C₂³×C₁₀₃	—	4	2	no	—
70	C₂³×C₁₀₃	#121	1	1	yes	characteristic
71	D₄×C₁₀₃	—	2	4	no	—
72	D₄×C₁₀₃	—	4	2	no	—
73	C₂×C₄×C₁₀₃	—	2	2	no	—
74	C₂×C₄×C₁₀₃	—	4	1	no	—
75	C₂×C₄×C₁₀₃	—	4	2	no	—
76	C₂×C₄×C₁₀₃	—	8	2	no	—
77	C₂×C₄×C₁₀₃	—	8	1	no	—
78	C₂×C₄×C₁₀₃	—	8	1	no	—
79	C₂×C₄×C₁₀₃	—	8	2	no	—
80	C₂×C₄×C₁₀₃	—	8	2	no	—
81	C₂×C₄×C₁₀₃	—	8	2	no	—
82	C₂×C₄×C₁₀₃	#123	1	2	yes	—
83	C₂×C₄×C₁₀₃	#123	1	1	yes	characteristic
84	C₂×C₄×C₁₀₃	#124	1	1	yes	characteristic
85	C₂×C₄×C₁₀₃	#126	1	2	yes	—
86	C₂×C₄×C₁₀₃	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₁₀₃	#135	1	2	yes	—
88	C₂×C₄×C₁₀₃	#135	1	1	yes	characteristic
89	C₂×C₄×C₁₀₃	AGL(1,ℤ/8)	1	2	yes	—
90	C₂×C₄×C₁₀₃	#137	1	2	yes	—
91	C₈×C₁₀₃	—	4	2	no	—
92	C₈×C₁₀₃	—	8	2	no	—
93	C₈×C₁₀₃	—	8	1	no	—
94	C₂²×C₁₀₃	—	4	2	no	—
95	C₂²×C₁₀₃	—	4	4	no	—
96	C₂²×C₁₀₃	—	8	1	no	—
97	C₂²×C₁₀₃	—	8	1	no	—
98	C₂²×C₁₀₃	—	8	2	no	—
99	C₂²×C₁₀₃	#397	1	1	yes	characteristic
100	C₂²×C₁₀₃	#463	1	2	yes	—
101	C₂²×C₁₀₃	#466	1	1	yes	characteristic
102	C₂²×C₁₀₃	#470	1	1	yes	characteristic
103	C₂²×C₁₀₃	#471	1	2	yes	—
104	C₄×C₁₀₃	—	2	2	no	—
105	C₄×C₁₀₃	—	8	1	no	—
106	C₄×C₁₀₃	—	16	2	no	—
107	C₄×C₁₀₃	#480	1	2	yes	—
108	C₄×C₁₀₃	#482	1	2	yes	—
109	C₄×C₁₀₃	#485	1	2	yes	—
110	C₄×C₁₀₃	#488	1	1	yes	characteristic
111	C₄×C₁₀₃	#490	1	1	yes	characteristic
112	#10621	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂×C₁₀₃	—	8	2	no	—
114	C₂×C₁₀₃	#1681	1	2	yes	—
115	C₂×C₁₀₃	#1703	1	2	yes	—
116	C₂×C₁₀₃	#2073	1	1	yes	characteristic
117	C₂×C₁₀₃	#2075	1	1	yes	characteristic
118	C₂×C₁₀₃	#2079	1	1	yes	characteristic
119	#1954	C₂×C₁₀₃	1	1	yes	characteristic
120	#1834	C₂×C₁₀₃	1	1	yes	characteristic, complemented
121	#1802	C₂×C₁₀₃	1	2	yes	—
122	#1296	C₂×C₁₀₃	1	2	yes	complemented
123	#1277	C₂×C₁₀₃	1	1	yes	characteristic, complemented
124	C₁₀₃	#10621	1	1	yes	characteristic, direct product factor, Sylow
125	C₂×C₄×D₄	C₂²×C₁₀₃	1	1	yes	characteristic
126	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	2	yes	—
127	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	1	yes	characteristic
128	C₂×#102	—	2	2	no	—
129	C₂×C₂²⋊C₈	—	2	2	no	—
130	C₂×C₄×C₈	C₂²×C₁₀₃	1	1	yes	characteristic
131	#384	C₂²×C₁₀₃	1	2	yes	—
132	#340	—	2	2	no	—
133	#340	—	2	2	no	—
134	C₂²×D₄	D₄×C₁₀₃	1	1	yes	characteristic
135	C₂³×C₄	—	2	1	no	—
136	C₂²×C₈	—	2	2	no	—
137	C₂²×C₈	—	2	1	no	—
138	C₂²×C₈	D₄×C₁₀₃	1	2	yes	—
139	C₄×D₄	—	2	2	no	—
140	C₄×D₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	D₄×C₁₀₃	1	1	yes	characteristic
145	C₂×C₂²⋊C₄	—	2	1	no	—
146	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	2	2	no	—
149	C₄⋊C₈	—	2	2	no	—
150	#102	—	4	4	no	—
151	C₂²⋊C₈	—	4	4	no	—
152	C₄×C₈	—	2	2	no	—
153	C₂⁴	—	2	1	no	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	—	2	1	no	—
156	C₂×D₄	—	2	2	no	—
157	C₂×D₄	D₈×C₁₀₃	1	2	yes	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	4	1	no	—
160	C₂²×C₄	—	4	1	no	—
161	C₂²×C₄	—	4	2	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	—	4	2	no	—
164	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
165	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
166	C₂²×C₄	#41×C₁₀₃	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	4	1	no	—
172	C₂×C₈	—	4	2	no	—
173	C₂×C₈	—	4	2	no	—
174	C₂×C₈	—	4	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	8	2	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	#41×C₁₀₃	1	2	yes	—
183	C₄²	#41×C₁₀₃	1	2	yes	—
184	C₂³	—	2	2	no	—
185	C₂³	—	4	1	no	—
186	C₂³	—	4	2	no	—
187	C₂³	—	4	1	no	—
188	C₂³	—	4	2	no	—
189	C₂³	#121×C₁₀₃	1	1	yes	characteristic
190	D₄	—	2	4	no	—
191	D₄	—	4	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	—	8	1	no	—
197	C₂×C₄	—	8	1	no	—
198	C₂×C₄	—	8	2	no	—
199	C₂×C₄	—	8	2	no	—
200	C₂×C₄	—	8	2	no	—
201	C₂×C₄	#123×C₁₀₃	1	2	yes	—
202	C₂×C₄	#123×C₁₀₃	1	1	yes	characteristic
203	C₂×C₄	#124×C₁₀₃	1	1	yes	characteristic
204	C₂×C₄	#126×C₁₀₃	1	2	yes	—
205	C₂×C₄	C₂×D₈×C₁₀₃	1	1	yes	characteristic
206	C₂×C₄	#135×C₁₀₃	1	2	yes	—
207	C₂×C₄	#135×C₁₀₃	1	1	yes	characteristic
208	C₂×C₄	AGL(1,ℤ/8)×C₁₀₃	1	2	yes	—
209	C₂×C₄	#137×C₁₀₃	1	2	yes	—
210	C₈	—	4	2	no	—
211	C₈	—	8	2	no	—
212	C₈	—	8	1	no	—
213	C₂²	—	4	4	no	—
214	C₂²	—	4	2	no	—
215	C₂²	—	8	2	no	—
216	C₂²	—	8	1	no	—
217	C₂²	—	8	1	no	—
218	C₂²	#397×C₁₀₃	1	1	yes	characteristic
219	C₂²	#463×C₁₀₃	1	2	yes	—
220	C₂²	#466×C₁₀₃	1	1	yes	characteristic
221	C₂²	#470×C₁₀₃	1	1	yes	characteristic
222	C₂²	#471×C₁₀₃	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	8	1	no	—
225	C₄	—	16	2	no	—
226	C₄	#480×C₁₀₃	1	2	yes	—
227	C₄	#482×C₁₀₃	1	2	yes	—
228	C₄	#485×C₁₀₃	1	2	yes	—
229	C₄	#488×C₁₀₃	1	1	yes	characteristic
230	C₄	#490×C₁₀₃	1	1	yes	characteristic
231	C₂	—	8	2	no	—
232	C₂	C₁₀₃×#1681	1	2	yes	—
233	C₂	C₁₀₃×#1703	1	2	yes	—
234	C₂	C₁₀₃×#2073	1	1	yes	characteristic
235	C₂	C₁₀₃×#2075	1	1	yes	characteristic
236	C₂	C₁₀₃×#2079	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₀₃×#1954

C₂

yes

maximal, characteristic

C₁₀₃×#1834

C₂

yes

maximal, characteristic, complemented

C₁₀₃×#1802

C₂

yes

maximal

C₁₀₃×#1296

C₂

yes

maximal, complemented

C₁₀₃×#1277

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₄×C₁₀₃

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₁₀₃

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₁₀₃

C₂²

yes

—

C₂×#102×C₁₀₃

—

C₂×C₂²⋊C₈×C₁₀₃

—

C₂×C₄×C₈×C₁₀₃

C₂²

yes

characteristic

#384×C₁₀₃

C₂²

yes

—

#340×C₁₀₃

—

#340×C₁₀₃

—

C₂²×D₄×C₁₀₃

D₄

yes

characteristic

C₂³×C₄×C₁₀₃

—

C₂²×C₈×C₁₀₃

—

C₂²×C₈×C₁₀₃

—

C₂²×C₈×C₁₀₃

D₄

yes

—

C₄×D₄×C₁₀₃

—

C₄×D₄×C₁₀₃

—

C₂×C₄⋊C₄×C₁₀₃

—

C₂×C₄⋊C₄×C₁₀₃

—

C₂×C₄⋊C₄×C₁₀₃

—

C₂×C₄⋊C₄×C₁₀₃

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₀₃

—

C₂×C₄²×C₁₀₃

C₂³

yes

characteristic

C₄⋊C₈×C₁₀₃

—

C₄⋊C₈×C₁₀₃

—

C₄⋊C₈×C₁₀₃

—

#102×C₁₀₃

—

C₂²⋊C₈×C₁₀₃

—

C₄×C₈×C₁₀₃

—

C₂⁴×C₁₀₃

—

C₂×D₄×C₁₀₃

—

C₂×D₄×C₁₀₃

—

C₂×D₄×C₁₀₃

—

C₂×D₄×C₁₀₃

D₈

yes

—

C₂²×C₄×C₁₀₃

—

C₂²×C₄×C₁₀₃

—

C₂²×C₄×C₁₀₃

—

C₂²×C₄×C₁₀₃

—

C₂²×C₄×C₁₀₃

—

C₂²×C₄×C₁₀₃

—

C₂²×C₄×C₁₀₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₀₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₀₃

#41

yes

characteristic

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₄⋊C₄×C₁₀₃

—

C₂²⋊C₄×C₁₀₃

—

C₄²×C₁₀₃

#41

yes

—

C₄²×C₁₀₃

#41

yes

—

C₂³×C₁₀₃

—

C₂³×C₁₀₃

—

C₂³×C₁₀₃

—

C₂³×C₁₀₃

—

C₂³×C₁₀₃

—

C₂³×C₁₀₃

#121

yes

characteristic

D₄×C₁₀₃

—

D₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

#123

yes

—

C₂×C₄×C₁₀₃

yes

C₂×C₄×C₁₀₃

yes

C₂×C₄×C₁₀₃

yes

—

C₂×C₄×C₁₀₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₀₃

#135

yes

—

C₂×C₄×C₁₀₃

#135

yes

characteristic

C₂×C₄×C₁₀₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₀₃

#137

yes

—

C₈×C₁₀₃

—

C₈×C₁₀₃

—

C₈×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

#397

yes

characteristic

100

C₂²×C₁₀₃

#463

yes

—

101

C₂²×C₁₀₃

#466

yes

characteristic

102

C₂²×C₁₀₃

#470

yes

characteristic

103

C₂²×C₁₀₃

#471

yes

—

104

C₄×C₁₀₃

—

105

C₄×C₁₀₃

—

106

C₄×C₁₀₃

—

107

C₄×C₁₀₃

#480

yes

—

108

C₄×C₁₀₃

#482

yes

—

109

C₄×C₁₀₃

#485

yes

—

110

C₄×C₁₀₃

#488

yes

characteristic

111

C₄×C₁₀₃

#490

yes

characteristic

112

#10621

C₁₀₃

yes

maximal, characteristic, direct product factor, Sylow

113

C₂×C₁₀₃

—

114

C₂×C₁₀₃

#1681

yes

—

115

C₂×C₁₀₃

#1703

yes

—

116

C₂×C₁₀₃

#2073

yes

characteristic

117

C₂×C₁₀₃

#2075

yes

characteristic

118

C₂×C₁₀₃

#2079

yes

characteristic

119

#1954

C₂×C₁₀₃

yes

characteristic

120

#1834

C₂×C₁₀₃

yes

characteristic, complemented

121

#1802

C₂×C₁₀₃

yes

—

122

#1296

C₂×C₁₀₃

yes

complemented

123

#1277

C₂×C₁₀₃

yes

characteristic, complemented

124

C₁₀₃

#10621

yes

characteristic, direct product factor, Sylow

125

C₂×C₄×D₄

C₂²×C₁₀₃

yes

characteristic

126

C₂×C₄⋊C₈

C₂²×C₁₀₃

yes

—

127

C₂×C₄⋊C₈

C₂²×C₁₀₃

yes

characteristic

128

C₂×#102

—

129

C₂×C₂²⋊C₈

—

130

C₂×C₄×C₈

C₂²×C₁₀₃

yes

characteristic

131

#384

C₂²×C₁₀₃

yes

—

132

#340

—

133

#340

—

134

C₂²×D₄

D₄×C₁₀₃

yes

characteristic

135

C₂³×C₄

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂²×C₈

D₄×C₁₀₃

yes

—

139

C₄×D₄

—

140

C₄×D₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

D₄×C₁₀₃

yes

characteristic

145

C₂×C₂²⋊C₄

—

146

C₂×C₄²

C₂³×C₁₀₃

yes

characteristic

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

#102

—

151

C₂²⋊C₈

—

152

C₄×C₈

—

153

C₂⁴

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

D₈×C₁₀₃

yes

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂×D₄×C₁₀₃

yes

characteristic

165

C₂²×C₄

C₂×D₄×C₁₀₃

yes

characteristic

166

C₂²×C₄

#41×C₁₀₃

yes

characteristic

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₂²⋊C₄

—

182

C₄²

#41×C₁₀₃

yes

—

183

C₄²

#41×C₁₀₃

yes

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

—

189

C₂³

#121×C₁₀₃

yes

characteristic

190

D₄

—

191

D₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

#123×C₁₀₃

yes

—

202

C₂×C₄

#123×C₁₀₃

yes

characteristic

203

C₂×C₄

#124×C₁₀₃

yes

characteristic

204

C₂×C₄

#126×C₁₀₃

yes

—

205

C₂×C₄

C₂×D₈×C₁₀₃

yes

characteristic

206

C₂×C₄

#135×C₁₀₃

yes

—

207

C₂×C₄

#135×C₁₀₃

yes

characteristic

208

C₂×C₄

AGL(1,ℤ/8)×C₁₀₃

yes

—

209

C₂×C₄

#137×C₁₀₃

yes

—

210

C₈

—

211

C₈

—

212

C₈

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

#397×C₁₀₃

yes

characteristic

219

C₂²

#463×C₁₀₃

yes

—

220

C₂²

#466×C₁₀₃

yes

characteristic

221

C₂²

#470×C₁₀₃

yes

characteristic

222

C₂²

#471×C₁₀₃

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

#480×C₁₀₃

yes

—

227

C₄

#482×C₁₀₃

yes

—

228

C₄

#485×C₁₀₃

yes

—

229

C₄

#488×C₁₀₃

yes

characteristic

230

C₄

#490×C₁₀₃

yes

characteristic

231

C₂

—

232

C₂

C₁₀₃×#1681

yes

—

233

C₂

C₁₀₃×#1703

yes

—

234

C₂

C₁₀₃×#2073

yes

characteristic

235

C₂

C₁₀₃×#2075

yes

characteristic

236

C₂

C₁₀₃×#2079

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₃	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₃
prime radical	C₂²×D₄×C₁₀₃	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₀₃

#121

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₀₃

prime radical

C₂²×D₄×C₁₀₃

D₄

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ G

N	H ≅ G/N	type
2. C₁₀₃×#1834	C₂	semidirect
4. C₁₀₃×#1296	C₂	semidirect
5. C₁₀₃×#1277	C₂	semidirect
112. #10621	C₁₀₃	direct (N × H)
120. #1834	C₂×C₁₀₃	semidirect
122. #1296	C₂×C₁₀₃	semidirect
123. #1277	C₂×C₁₀₃	semidirect
124. C₁₀₃	#10621	direct (N × H)

H ≅ G/N

type

2. C₁₀₃×#1834

C₂

semidirect

4. C₁₀₃×#1296

C₂

semidirect

5. C₁₀₃×#1277

C₂

semidirect

112. #10621

C₁₀₃

direct (N × H)

120. #1834

C₂×C₁₀₃

semidirect

122. #1296

C₂×C₁₀₃

semidirect

123. #1277

C₂×C₁₀₃

semidirect

124. C₁₀₃

#10621

direct (N × H)

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

subgroup	index
C₁₀₃×#1954	2
C₁₀₃×#1834	2
C₁₀₃×#1802	2
C₁₀₃×#1296	2
C₁₀₃×#1277	2
#10621	103

subgroup

index

C₁₀₃×#1954

C₁₀₃×#1834

C₁₀₃×#1802

C₁₀₃×#1296

C₁₀₃×#1277

#10621

103

Subgroups — C₁₀₃×#10621 #39915896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C103×#10621 #39915896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#10621 #39915896