Subgroups — C₁₀₃×#21311 #39926586

Order 26368.

1194 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic
3	C₄×#117×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₁₀₃×#1989	C₂	1	4	yes	maximal, complemented
5	C₁₀₃×#1988	C₂	1	2	yes	maximal, complemented
6	C₁₀₃×#1987	C₂	1	2	yes	maximal, complemented
7	C₁₀₃×#1735	C₂	1	4	yes	maximal
8	C₂³×C₈×C₁₀₃	C₂²	1	2	yes	—
9	#533×C₁₀₃	—	2	4	no	—
10	#533×C₁₀₃	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₀₃	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₁₀₃	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₁₀₃	—	2	1	no	—
16	C₂×C₄×Q₈×C₁₀₃	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₀₃	—	2	1	no	—
18	C₂×#117×C₁₀₃	C₂²	1	2	yes	—
19	C₂×#117×C₁₀₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₀₃	—	2	4	no	—
22	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	2	yes	—
24	C₄×C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
26	C₄×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
27	C₄×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
28	#376×C₁₀₃	—	2	1	no	—
29	C₄³×C₁₀₃	—	2	1	no	—
30	#340×C₁₀₃	C₂²	1	8	yes	—
31	#340×C₁₀₃	C₂²	1	8	yes	—
32	C₂²×Q₈×C₁₀₃	—	2	1	no	—
33	C₂²×Q₈×C₁₀₃	—	2	1	no	—
34	C₂³×C₄×C₁₀₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₀₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₀₃	—	2	4	no	—
38	C₂²×C₈×C₁₀₃	—	2	8	no	—
39	C₂²×C₈×C₁₀₃	C₂³	1	4	yes	—
40	C₄⋊Q₈×C₁₀₃	—	2	2	no	—
41	C₄⋊Q₈×C₁₀₃	—	2	2	no	—
42	C₄⋊Q₈×C₁₀₃	C₂×C₄	1	4	yes	—
43	C₄⋊Q₈×C₁₀₃	C₂×C₄	1	4	yes	—
44	#125×C₁₀₃	—	2	4	no	—
45	#125×C₁₀₃	C₂×C₄	1	8	yes	—
46	C₂²⋊Q₈×C₁₀₃	—	2	8	no	—
47	C₂²⋊Q₈×C₁₀₃	—	2	8	no	—
48	C₄×Q₈×C₁₀₃	—	2	8	no	—
49	C₄×Q₈×C₁₀₃	—	2	8	no	—
50	#117×C₁₀₃	—	2	4	no	—
51	#117×C₁₀₃	—	2	4	no	—
52	#117×C₁₀₃	C₂×C₄	1	8	yes	—
53	#117×C₁₀₃	Q₈	1	8	yes	complemented
54	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	4	yes	—
61	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
63	C₂×C₄²×C₁₀₃	—	2	2	no	—
64	C₂×C₄²×C₁₀₃	—	2	2	no	—
65	C₂×C₄²×C₁₀₃	—	2	2	no	—
66	C₂×C₄²×C₁₀₃	—	2	2	no	—
67	C₂×C₄²×C₁₀₃	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₁₀₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₀₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₀₃	D₄	1	4	yes	—
71	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₁₀₃	—	2	4	no	—
74	C₄⋊C₈×C₁₀₃	—	2	4	no	—
75	#95×C₁₀₃	—	2	2	no	—
76	#95×C₁₀₃	—	2	2	no	—
77	C₂⁴×C₁₀₃	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₁₀₃	—	2	4	no	—
79	C₂×Q₈×C₁₀₃	—	2	4	no	—
80	C₂×Q₈×C₁₀₃	—	4	4	no	—
81	C₂×Q₈×C₁₀₃	—	4	4	no	—
82	C₂²×C₄×C₁₀₃	—	2	4	no	—
83	C₂²×C₄×C₁₀₃	—	2	4	no	—
84	C₂²×C₄×C₁₀₃	—	2	2	no	—
85	C₂²×C₄×C₁₀₃	—	2	2	no	—
86	C₂²×C₄×C₁₀₃	—	4	2	no	—
87	C₂²×C₄×C₁₀₃	C₂²⋊C₄	1	4	yes	—
88	C₂²×C₄×C₁₀₃	C₂²⋊C₄	1	4	yes	—
89	C₂²×C₄×C₁₀₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₀₃	C₂×Q₈	1	4	yes	—
97	C₂²×C₄×C₁₀₃	#41	1	4	yes	—
98	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₀₃	—	2	4	no	—
100	C₂×C₈×C₁₀₃	—	2	8	no	—
101	C₂×C₈×C₁₀₃	—	4	8	no	—
102	C₄⋊C₄×C₁₀₃	—	2	8	no	—
103	C₄⋊C₄×C₁₀₃	—	2	8	no	—
104	C₄⋊C₄×C₁₀₃	—	2	4	no	—
105	C₄⋊C₄×C₁₀₃	—	2	4	no	—
106	C₄⋊C₄×C₁₀₃	—	2	2	no	—
107	C₄⋊C₄×C₁₀₃	—	2	2	no	—
108	C₄⋊C₄×C₁₀₃	—	2	4	no	—
109	C₄⋊C₄×C₁₀₃	C₂²×C₄	1	4	yes	—
110	C₄⋊C₄×C₁₀₃	C₂²×C₄	1	4	yes	—
111	C₄⋊C₄×C₁₀₃	C₂×Q₈	1	8	yes	—
112	C₂²⋊C₄×C₁₀₃	—	2	8	no	—
113	C₂²⋊C₄×C₁₀₃	—	2	8	no	—
114	C₄²×C₁₀₃	—	2	8	no	—
115	C₄²×C₁₀₃	—	2	8	no	—
116	C₄²×C₁₀₃	—	4	4	no	—
117	C₄²×C₁₀₃	—	4	4	no	—
118	C₄²×C₁₀₃	C₂²⋊C₄	1	4	yes	—
119	C₄²×C₁₀₃	C₂²⋊C₄	1	4	yes	—
120	C₄²×C₁₀₃	C₂²×C₄	1	2	yes	—
121	C₄²×C₁₀₃	C₂²×C₄	1	2	yes	—
122	C₄²×C₁₀₃	C₂×D₄	1	2	yes	—
123	C₄²×C₁₀₃	C₂×D₄	1	2	yes	—
124	C₂³×C₁₀₃	—	2	2	no	—
125	C₂³×C₁₀₃	—	2	2	no	—
126	C₂³×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
127	C₂³×C₁₀₃	C₂²⋊Q₈	1	4	yes	—
128	C₂³×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₁₀₃	—	4	8	no	—
130	Q₈×C₁₀₃	—	4	8	no	—
131	C₂×C₄×C₁₀₃	—	2	2	no	—
132	C₂×C₄×C₁₀₃	—	2	2	no	—
133	C₂×C₄×C₁₀₃	—	2	2	no	—
134	C₂×C₄×C₁₀₃	—	2	8	no	—
135	C₂×C₄×C₁₀₃	—	2	4	no	—
136	C₂×C₄×C₁₀₃	—	2	4	no	—
137	C₂×C₄×C₁₀₃	—	2	8	no	—
138	C₂×C₄×C₁₀₃	—	4	4	no	—
139	C₂×C₄×C₁₀₃	—	4	4	no	—
140	C₂×C₄×C₁₀₃	—	4	4	no	—
141	C₂×C₄×C₁₀₃	—	4	4	no	—
142	C₂×C₄×C₁₀₃	—	4	4	no	—
143	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
146	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₁₀₃	C₄×Q₈	1	8	yes	—
149	C₂×C₄×C₁₀₃	C₂²⋊Q₈	1	4	yes	—
150	C₂×C₄×C₁₀₃	#124	1	4	yes	—
151	C₂×C₄×C₁₀₃	C₄⋊Q₈	1	4	yes	—
152	C₂×C₄×C₁₀₃	#135	1	4	yes	—
153	C₂×C₄×C₁₀₃	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₀₃	C₂²×Q₈	1	2	yes	—
156	C₂×C₄×C₁₀₃	C₂×#41	1	2	yes	—
157	C₈×C₁₀₃	—	4	4	no	—
158	C₂²×C₁₀₃	—	2	8	no	—
159	C₂²×C₁₀₃	—	2	2	no	—
160	C₂²×C₁₀₃	—	2	2	no	—
161	C₂²×C₁₀₃	#391	1	4	yes	—
162	C₂²×C₁₀₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₁₀₃	C₂×C₂²⋊Q₈	1	2	yes	—
164	C₂²×C₁₀₃	C₂×#135	1	2	yes	—
165	C₂²×C₁₀₃	#575	1	2	yes	—
166	C₄×C₁₀₃	—	2	2	no	—
167	C₄×C₁₀₃	—	2	2	no	—
168	C₄×C₁₀₃	—	2	2	no	—
169	C₄×C₁₀₃	—	4	8	no	—
170	C₄×C₁₀₃	—	4	4	no	—
171	C₄×C₁₀₃	—	4	4	no	—
172	C₄×C₁₀₃	#391	1	4	yes	—
173	C₄×C₁₀₃	#416	1	4	yes	—
174	C₄×C₁₀₃	C₂×C₄×Q₈	1	2	yes	—
175	C₄×C₁₀₃	C₂×#124	1	1	yes	characteristic
176	C₄×C₁₀₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
177	#21311	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₁₀₃	—	2	4	no	—
179	C₂×C₁₀₃	C₂×#391	1	1	yes	characteristic
180	C₂×C₁₀₃	C₂×#416	1	1	yes	characteristic
181	C₂×C₁₀₃	#2896	1	1	yes	characteristic
182	C₂×C₁₀₃	#3076	1	4	yes	—
183	C₂×#533	C₂×C₁₀₃	1	1	yes	characteristic
184	C₂²×C₄⋊C₈	C₂×C₁₀₃	1	1	yes	characteristic
185	C₄×#117	C₂×C₁₀₃	1	1	yes	characteristic
186	#1989	C₂×C₁₀₃	1	4	yes	complemented
187	#1988	C₂×C₁₀₃	1	2	yes	complemented
188	#1987	C₂×C₁₀₃	1	2	yes	complemented
189	#1735	C₂×C₁₀₃	1	4	yes	—
190	C₁₀₃	#21311	1	1	yes	characteristic, direct product factor, Sylow
191	C₂³×C₈	C₂²×C₁₀₃	1	2	yes	—
192	#533	—	2	4	no	—
193	#533	C₄×C₁₀₃	1	8	yes	complemented
194	C₂×C₄⋊Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
195	C₂×C₄⋊Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
196	C₂×#125	C₂²×C₁₀₃	1	2	yes	—
197	C₂×C₂²⋊Q₈	—	2	1	no	—
198	C₂×C₂²⋊Q₈	—	2	1	no	—
199	C₂×C₄×Q₈	—	2	1	no	—
200	C₂×C₄×Q₈	—	2	1	no	—
201	C₂×#117	C₂²×C₁₀₃	1	2	yes	—
202	C₂×#117	C₂²×C₁₀₃	1	2	yes	—
203	C₂²×C₄²	C₂²×C₁₀₃	1	1	yes	characteristic
204	C₂×C₄⋊C₈	—	2	4	no	—
205	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	2	yes	—
206	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	2	yes	—
207	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	2	yes	—
208	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	2	yes	—
209	C₄×C₂²⋊C₄	—	2	1	no	—
210	C₄×C₂²⋊C₄	—	2	1	no	—
211	#376	—	2	1	no	—
212	C₄³	—	2	1	no	—
213	#340	C₂²×C₁₀₃	1	8	yes	—
214	#340	C₂²×C₁₀₃	1	8	yes	—
215	C₂²×Q₈	—	2	1	no	—
216	C₂²×Q₈	—	2	1	no	—
217	C₂³×C₄	D₄×C₁₀₃	1	1	yes	characteristic
218	C₂³×C₄	D₄×C₁₀₃	1	1	yes	characteristic
219	C₂³×C₄	C₂³×C₁₀₃	1	1	yes	characteristic
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	—	2	8	no	—
222	C₂²×C₈	C₂³×C₁₀₃	1	4	yes	—
223	C₄⋊Q₈	—	2	2	no	—
224	C₄⋊Q₈	—	2	2	no	—
225	C₄⋊Q₈	C₂×C₄×C₁₀₃	1	4	yes	—
226	C₄⋊Q₈	C₂×C₄×C₁₀₃	1	4	yes	—
227	#125	—	2	4	no	—
228	#125	C₂×C₄×C₁₀₃	1	8	yes	—
229	C₂²⋊Q₈	—	2	8	no	—
230	C₂²⋊Q₈	—	2	8	no	—
231	C₄×Q₈	—	2	8	no	—
232	C₄×Q₈	—	2	8	no	—
233	#117	—	2	4	no	—
234	#117	—	2	4	no	—
235	#117	C₂×C₄×C₁₀₃	1	8	yes	—
236	#117	Q₈×C₁₀₃	1	8	yes	complemented
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
243	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	4	yes	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	—	2	2	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	C₂×C₄×C₁₀₃	1	4	yes	—
251	C₂×C₄²	D₄×C₁₀₃	1	1	yes	characteristic
252	C₂×C₄²	D₄×C₁₀₃	1	1	yes	characteristic
253	C₂×C₄²	D₄×C₁₀₃	1	4	yes	—
254	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
256	C₄⋊C₈	—	2	4	no	—
257	C₄⋊C₈	—	2	4	no	—
258	#95	—	2	2	no	—
259	#95	—	2	2	no	—
260	C₂⁴	C₂×D₄×C₁₀₃	1	1	yes	characteristic
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	4	4	no	—
264	C₂×Q₈	—	4	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	C₂²⋊C₄×C₁₀₃	1	4	yes	—
271	C₂²×C₄	C₂²⋊C₄×C₁₀₃	1	4	yes	—
272	C₂²×C₄	C₂²×C₄×C₁₀₃	1	2	yes	—
273	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
279	C₂²×C₄	C₂×Q₈×C₁₀₃	1	4	yes	—
280	C₂²×C₄	#41×C₁₀₃	1	4	yes	—
281	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	8	no	—
284	C₂×C₈	—	4	8	no	—
285	C₄⋊C₄	—	2	8	no	—
286	C₄⋊C₄	—	2	8	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	C₂²×C₄×C₁₀₃	1	4	yes	—
293	C₄⋊C₄	C₂²×C₄×C₁₀₃	1	4	yes	—
294	C₄⋊C₄	C₂×Q₈×C₁₀₃	1	8	yes	—
295	C₂²⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	2	8	no	—
297	C₄²	—	2	8	no	—
298	C₄²	—	2	8	no	—
299	C₄²	—	4	4	no	—
300	C₄²	—	4	4	no	—
301	C₄²	C₂²⋊C₄×C₁₀₃	1	4	yes	—
302	C₄²	C₂²⋊C₄×C₁₀₃	1	4	yes	—
303	C₄²	C₂²×C₄×C₁₀₃	1	2	yes	—
304	C₄²	C₂²×C₄×C₁₀₃	1	2	yes	—
305	C₄²	C₂×D₄×C₁₀₃	1	2	yes	—
306	C₄²	C₂×D₄×C₁₀₃	1	2	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
310	C₂³	C₂²⋊Q₈×C₁₀₃	1	4	yes	—
311	C₂³	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
312	Q₈	—	4	8	no	—
313	Q₈	—	4	8	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
328	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
329	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
330	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
331	C₂×C₄	C₄×Q₈×C₁₀₃	1	8	yes	—
332	C₂×C₄	C₂²⋊Q₈×C₁₀₃	1	4	yes	—
333	C₂×C₄	#124×C₁₀₃	1	4	yes	—
334	C₂×C₄	C₄⋊Q₈×C₁₀₃	1	4	yes	—
335	C₂×C₄	#135×C₁₀₃	1	4	yes	—
336	C₂×C₄	C₂³×C₄×C₁₀₃	1	1	yes	characteristic
337	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
338	C₂×C₄	C₂²×Q₈×C₁₀₃	1	2	yes	—
339	C₂×C₄	C₂×#41×C₁₀₃	1	2	yes	—
340	C₈	—	4	4	no	—
341	C₂²	—	2	8	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	#391×C₁₀₃	1	4	yes	—
345	C₂²	C₂²×C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
346	C₂²	C₂×C₂²⋊Q₈×C₁₀₃	1	2	yes	—
347	C₂²	C₂×#135×C₁₀₃	1	2	yes	—
348	C₂²	#575×C₁₀₃	1	2	yes	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	4	8	no	—
353	C₄	—	4	4	no	—
354	C₄	—	4	4	no	—
355	C₄	#391×C₁₀₃	1	4	yes	—
356	C₄	#416×C₁₀₃	1	4	yes	—
357	C₄	C₂×C₄×Q₈×C₁₀₃	1	2	yes	—
358	C₄	C₂×#124×C₁₀₃	1	1	yes	characteristic
359	C₄	C₂×C₄⋊Q₈×C₁₀₃	1	1	yes	characteristic
360	C₂	—	2	4	no	—
361	C₂	C₂×#391×C₁₀₃	1	1	yes	characteristic
362	C₂	C₂×#416×C₁₀₃	1	1	yes	characteristic
363	C₂	C₁₀₃×#2896	1	1	yes	characteristic
364	C₂	C₁₀₃×#3076	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₀₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₃
socle	C₂³×C₁₀₃	C₂²×D₄
prime radical	C₂⁴×C₁₀₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₃ ◁ C₂²×C₄²×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₀₃×#1989	C₂	semidirect
5. C₁₀₃×#1988	C₂	semidirect
6. C₁₀₃×#1987	C₂	semidirect
10. #533×C₁₀₃	C₄	semidirect
53. #117×C₁₀₃	Q₈	semidirect
177. #21311	C₁₀₃	direct (N × H)
186. #1989	C₂×C₁₀₃	semidirect
187. #1988	C₂×C₁₀₃	semidirect
188. #1987	C₂×C₁₀₃	semidirect
190. C₁₀₃	#21311	direct (N × H)
193. #533	C₄×C₁₀₃	semidirect
236. #117	Q₈×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₀₃	2
C₂²×C₄⋊C₈×C₁₀₃	2
C₄×#117×C₁₀₃	2
C₁₀₃×#1989	2
C₁₀₃×#1988	2
C₁₀₃×#1987	2
C₁₀₃×#1735	2
#21311	103

Subgroups — C103×#21311 #39926586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#21311 #39926586