Subgroups — C₂×C₁₀₃×#2072 #39928900

Order 26368.

1150 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#103×C₁₀₃	C₂	1	2	yes	maximal
2	C₂×#391×C₁₀₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#384×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₁₀₃×#2072	C₂	1	8	yes	maximal, direct product factor
5	C₂×#340×C₁₀₃	C₂	1	2	yes	maximal
6	C₂×#336×C₁₀₃	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₀₃	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₀₃	—	2	1	no	—
10	C₂²×C₄⋊C₄×C₁₀₃	—	2	1	no	—
11	C₂²×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
13	C₂²×C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂×#103×C₁₀₃	—	2	8	no	—
15	C₂×#103×C₁₀₃	C₂²	1	8	yes	—
16	#391×C₁₀₃	—	2	2	no	—
17	#391×C₁₀₃	C₂²	1	4	yes	—
18	#384×C₁₀₃	—	2	2	no	—
19	#384×C₁₀₃	C₂²	1	4	yes	—
20	C₂×#95×C₁₀₃	—	2	1	no	—
21	C₂×#95×C₁₀₃	—	2	1	no	—
22	#340×C₁₀₃	C₂²	1	8	yes	—
23	#336×C₁₀₃	C₂²	1	4	yes	—
24	C₂²×Q₈×C₁₀₃	—	2	1	no	—
25	C₂²×Q₈×C₁₀₃	—	2	2	no	—
26	C₂²×Q₈×C₁₀₃	—	2	4	no	—
27	C₂²×Q₈×C₁₀₃	—	2	4	no	—
28	C₂²×Q₈×C₁₀₃	D₄	1	4	yes	—
29	C₂²×Q₈×C₁₀₃	C₂³	1	2	yes	—
30	C₂³×C₄×C₁₀₃	—	2	1	no	—
31	C₂³×C₄×C₁₀₃	—	2	1	no	—
32	C₂³×C₄×C₁₀₃	—	2	2	no	—
33	C₂³×C₄×C₁₀₃	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₀₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₀₃	—	2	4	no	—
37	C₂²×C₈×C₁₀₃	—	2	4	no	—
38	C₂²×C₈×C₁₀₃	—	2	4	no	—
39	C₂²×C₈×C₁₀₃	C₂³	1	4	yes	—
40	C₂×C₄⋊C₄×C₁₀₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₀₃	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₀₃	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₀₃	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₀₃	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₀₃	—	4	4	no	—
48	C₂×C₄⋊C₄×C₁₀₃	—	4	4	no	—
49	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	4	yes	—
50	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₀₃	—	2	4	no	—
52	C₂×C₄²×C₁₀₃	D₄	1	2	yes	—
53	C₂×C₄²×C₁₀₃	C₂³	1	2	yes	—
54	#103×C₁₀₃	—	2	16	no	—
55	#95×C₁₀₃	—	2	4	no	—
56	#95×C₁₀₃	—	2	4	no	—
57	C₂⁴×C₁₀₃	C₂×D₄	1	1	yes	characteristic
58	C₂×Q₈×C₁₀₃	—	2	4	no	—
59	C₂×Q₈×C₁₀₃	—	2	2	no	—
60	C₂×Q₈×C₁₀₃	—	2	16	no	—
61	C₂×Q₈×C₁₀₃	—	2	4	no	—
62	C₂×Q₈×C₁₀₃	—	2	4	no	—
63	C₂×Q₈×C₁₀₃	—	4	2	no	—
64	C₂×Q₈×C₁₀₃	—	4	2	no	—
65	C₂×Q₈×C₁₀₃	—	4	8	no	—
66	C₂×Q₈×C₁₀₃	C₂×D₄	1	4	yes	—
67	C₂²×C₄×C₁₀₃	—	2	2	no	—
68	C₂²×C₄×C₁₀₃	—	2	2	no	—
69	C₂²×C₄×C₁₀₃	—	2	2	no	—
70	C₂²×C₄×C₁₀₃	—	2	2	no	—
71	C₂²×C₄×C₁₀₃	—	2	4	no	—
72	C₂²×C₄×C₁₀₃	—	2	2	no	—
73	C₂²×C₄×C₁₀₃	—	2	2	no	—
74	C₂²×C₄×C₁₀₃	—	2	4	no	—
75	C₂²×C₄×C₁₀₃	—	4	2	no	—
76	C₂²×C₄×C₁₀₃	—	4	2	no	—
77	C₂²×C₄×C₁₀₃	—	4	4	no	—
78	C₂²×C₄×C₁₀₃	—	4	2	no	—
79	C₂²×C₄×C₁₀₃	—	4	4	no	—
80	C₂²×C₄×C₁₀₃	—	4	4	no	—
81	C₂²×C₄×C₁₀₃	—	4	2	no	—
82	C₂²×C₄×C₁₀₃	—	4	2	no	—
83	C₂²×C₄×C₁₀₃	SD₁₆	1	4	yes	—
84	C₂²×C₄×C₁₀₃	Q₁₆	1	4	yes	—
85	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₀₃	#41	1	2	yes	—
90	C₂²×C₄×C₁₀₃	#41	1	4	yes	—
91	C₂²×C₄×C₁₀₃	#41	1	4	yes	—
92	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
93	C₂×C₈×C₁₀₃	—	2	4	no	—
94	C₂×C₈×C₁₀₃	—	2	4	no	—
95	C₂×C₈×C₁₀₃	—	2	4	no	—
96	C₂×C₈×C₁₀₃	—	4	8	no	—
97	C₄⋊C₄×C₁₀₃	—	2	4	no	—
98	C₄⋊C₄×C₁₀₃	—	2	4	no	—
99	C₄⋊C₄×C₁₀₃	—	2	4	no	—
100	C₄⋊C₄×C₁₀₃	—	4	8	no	—
101	C₄⋊C₄×C₁₀₃	—	4	4	no	—
102	C₄⋊C₄×C₁₀₃	—	4	2	no	—
103	C₄⋊C₄×C₁₀₃	—	4	8	no	—
104	C₄²×C₁₀₃	—	2	4	no	—
105	C₄²×C₁₀₃	—	2	4	no	—
106	C₂³×C₁₀₃	#121	1	2	yes	—
107	C₂³×C₁₀₃	#123	1	2	yes	—
108	C₂³×C₁₀₃	#124	1	2	yes	—
109	C₂³×C₁₀₃	C₂×SD₁₆	1	2	yes	—
110	C₂³×C₁₀₃	C₂×Q₁₆	1	2	yes	—
111	C₂³×C₁₀₃	AGL(1,ℤ/8)	1	2	yes	—
112	C₂³×C₁₀₃	#137	1	2	yes	—
113	C₂³×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
114	Q₈×C₁₀₃	—	2	8	no	—
115	Q₈×C₁₀₃	—	4	4	no	—
116	Q₈×C₁₀₃	—	4	8	no	—
117	C₂×C₄×C₁₀₃	—	2	2	no	—
118	C₂×C₄×C₁₀₃	—	2	2	no	—
119	C₂×C₄×C₁₀₃	—	2	2	no	—
120	C₂×C₄×C₁₀₃	—	2	2	no	—
121	C₂×C₄×C₁₀₃	—	2	8	no	—
122	C₂×C₄×C₁₀₃	—	2	8	no	—
123	C₂×C₄×C₁₀₃	—	2	4	no	—
124	C₂×C₄×C₁₀₃	—	4	2	no	—
125	C₂×C₄×C₁₀₃	—	4	2	no	—
126	C₂×C₄×C₁₀₃	—	4	8	no	—
127	C₂×C₄×C₁₀₃	—	4	4	no	—
128	C₂×C₄×C₁₀₃	—	4	2	no	—
129	C₂×C₄×C₁₀₃	—	4	4	no	—
130	C₂×C₄×C₁₀₃	—	4	4	no	—
131	C₂×C₄×C₁₀₃	—	4	2	no	—
132	C₂×C₄×C₁₀₃	—	4	2	no	—
133	C₂×C₄×C₁₀₃	—	8	8	no	—
134	C₂×C₄×C₁₀₃	—	8	4	no	—
135	C₂×C₄×C₁₀₃	#121	1	2	yes	—
136	C₂×C₄×C₁₀₃	#123	1	8	yes	—
137	C₂×C₄×C₁₀₃	#123	1	2	yes	—
138	C₂×C₄×C₁₀₃	#124	1	2	yes	—
139	C₂×C₄×C₁₀₃	#126	1	8	yes	—
140	C₂×C₄×C₁₀₃	C₂×SD₁₆	1	4	yes	—
141	C₂×C₄×C₁₀₃	C₂×Q₁₆	1	4	yes	—
142	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₀₃	C₂×#41	1	2	yes	—
144	C₂×C₄×C₁₀₃	C₂×#41	1	2	yes	—
145	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
146	C₈×C₁₀₃	—	4	4	no	—
147	C₂²×C₁₀₃	#397	1	4	yes	—
148	C₂²×C₁₀₃	#460	1	4	yes	—
149	C₂²×C₁₀₃	#462	1	4	yes	—
150	C₂²×C₁₀₃	#483	1	4	yes	—
151	C₂²×C₁₀₃	#484	1	4	yes	—
152	C₂²×C₁₀₃	#487	1	4	yes	—
153	C₂²×C₁₀₃	#489	1	4	yes	—
154	C₂²×C₁₀₃	C₂×#121	1	1	yes	characteristic
155	C₂²×C₁₀₃	C₂×#123	1	1	yes	characteristic
156	C₂²×C₁₀₃	C₂×#124	1	1	yes	characteristic
157	C₂²×C₁₀₃	C₂²×SD₁₆	1	1	yes	characteristic
158	C₂²×C₁₀₃	C₂²×Q₁₆	1	1	yes	characteristic
159	C₂²×C₁₀₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂²×C₁₀₃	C₂×#137	1	1	yes	characteristic
161	C₄×C₁₀₃	—	2	4	no	—
162	C₄×C₁₀₃	—	2	4	no	—
163	C₄×C₁₀₃	—	4	4	no	—
164	C₄×C₁₀₃	—	8	2	no	—
165	C₄×C₁₀₃	—	8	4	no	—
166	C₄×C₁₀₃	#397	1	4	yes	—
167	C₄×C₁₀₃	C₂×#123	1	2	yes	—
168	C₄×C₁₀₃	C₂×#126	1	2	yes	—
169	C₂×#2072	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂×C₁₀₃	#2072	1	8	yes	direct product factor
171	C₂×C₁₀₃	C₂×#397	1	1	yes	characteristic
172	C₂×C₁₀₃	C₂×#460	1	1	yes	characteristic
173	C₂×C₁₀₃	C₂×#462	1	1	yes	characteristic
174	C₂×C₁₀₃	C₂×#483	1	1	yes	characteristic
175	C₂×C₁₀₃	C₂×#484	1	1	yes	characteristic
176	C₂×C₁₀₃	C₂×#487	1	1	yes	characteristic
177	C₂×C₁₀₃	C₂×#489	1	1	yes	characteristic
178	C₂²×#103	C₂×C₁₀₃	1	2	yes	—
179	C₂×#391	C₂×C₁₀₃	1	1	yes	characteristic
180	C₂×#384	C₂×C₁₀₃	1	1	yes	characteristic
181	#2072	C₂×C₁₀₃	1	8	yes	direct product factor
182	C₂×#340	C₂×C₁₀₃	1	2	yes	—
183	C₂×#336	C₂×C₁₀₃	1	1	yes	characteristic
184	C₁₀₃	C₂×#2072	1	1	yes	characteristic, direct product factor, Sylow
185	C₂³×Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
186	C₂³×C₈	C₂²×C₁₀₃	1	2	yes	—
187	C₂²×C₄⋊C₄	—	2	1	no	—
188	C₂²×C₄⋊C₄	—	2	1	no	—
189	C₂²×C₄⋊C₄	C₂²×C₁₀₃	1	2	yes	—
190	C₂²×C₄⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
191	C₂²×C₄²	C₂²×C₁₀₃	1	1	yes	characteristic
192	C₂×#103	—	2	8	no	—
193	C₂×#103	C₂²×C₁₀₃	1	8	yes	—
194	#391	—	2	2	no	—
195	#391	C₂²×C₁₀₃	1	4	yes	—
196	#384	—	2	2	no	—
197	#384	C₂²×C₁₀₃	1	4	yes	—
198	C₂×#95	—	2	1	no	—
199	C₂×#95	—	2	1	no	—
200	#340	C₂²×C₁₀₃	1	8	yes	—
201	#336	C₂²×C₁₀₃	1	4	yes	—
202	C₂²×Q₈	—	2	1	no	—
203	C₂²×Q₈	—	2	2	no	—
204	C₂²×Q₈	—	2	4	no	—
205	C₂²×Q₈	—	2	4	no	—
206	C₂²×Q₈	D₄×C₁₀₃	1	4	yes	—
207	C₂²×Q₈	C₂³×C₁₀₃	1	2	yes	—
208	C₂³×C₄	—	2	1	no	—
209	C₂³×C₄	—	2	2	no	—
210	C₂³×C₄	—	2	1	no	—
211	C₂³×C₄	D₄×C₁₀₃	1	1	yes	characteristic
212	C₂³×C₄	D₄×C₁₀₃	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₁₀₃	1	1	yes	characteristic
214	C₂²×C₈	—	2	4	no	—
215	C₂²×C₈	—	2	4	no	—
216	C₂²×C₈	—	2	4	no	—
217	C₂²×C₈	C₂³×C₁₀₃	1	4	yes	—
218	C₂×C₄⋊C₄	—	2	4	no	—
219	C₂×C₄⋊C₄	—	2	4	no	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	2	4	no	—
222	C₂×C₄⋊C₄	—	2	4	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	1	no	—
225	C₂×C₄⋊C₄	—	4	4	no	—
226	C₂×C₄⋊C₄	—	4	4	no	—
227	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
228	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	4	yes	—
229	C₂×C₄²	—	2	4	no	—
230	C₂×C₄²	D₄×C₁₀₃	1	2	yes	—
231	C₂×C₄²	C₂³×C₁₀₃	1	2	yes	—
232	#103	—	2	16	no	—
233	#95	—	2	4	no	—
234	#95	—	2	4	no	—
235	C₂⁴	C₂×D₄×C₁₀₃	1	1	yes	characteristic
236	C₂×Q₈	—	2	4	no	—
237	C₂×Q₈	—	2	2	no	—
238	C₂×Q₈	—	2	16	no	—
239	C₂×Q₈	—	2	4	no	—
240	C₂×Q₈	—	2	4	no	—
241	C₂×Q₈	—	4	2	no	—
242	C₂×Q₈	—	4	2	no	—
243	C₂×Q₈	—	4	8	no	—
244	C₂×Q₈	C₂×D₄×C₁₀₃	1	4	yes	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	—	4	4	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	—	4	4	no	—
258	C₂²×C₄	—	4	4	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	SD₁₆×C₁₀₃	1	4	yes	—
262	C₂²×C₄	Q₁₆×C₁₀₃	1	4	yes	—
263	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
265	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
267	C₂²×C₄	#41×C₁₀₃	1	2	yes	—
268	C₂²×C₄	#41×C₁₀₃	1	4	yes	—
269	C₂²×C₄	#41×C₁₀₃	1	4	yes	—
270	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	4	8	no	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	4	8	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	—	4	2	no	—
281	C₄⋊C₄	—	4	8	no	—
282	C₄²	—	2	4	no	—
283	C₄²	—	2	4	no	—
284	C₂³	#121×C₁₀₃	1	2	yes	—
285	C₂³	#123×C₁₀₃	1	2	yes	—
286	C₂³	#124×C₁₀₃	1	2	yes	—
287	C₂³	C₂×SD₁₆×C₁₀₃	1	2	yes	—
288	C₂³	C₂×Q₁₆×C₁₀₃	1	2	yes	—
289	C₂³	AGL(1,ℤ/8)×C₁₀₃	1	2	yes	—
290	C₂³	#137×C₁₀₃	1	2	yes	—
291	C₂³	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
292	Q₈	—	2	8	no	—
293	Q₈	—	4	8	no	—
294	Q₈	—	4	4	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	4	8	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	8	8	no	—
312	C₂×C₄	—	8	4	no	—
313	C₂×C₄	#121×C₁₀₃	1	2	yes	—
314	C₂×C₄	#123×C₁₀₃	1	2	yes	—
315	C₂×C₄	#123×C₁₀₃	1	8	yes	—
316	C₂×C₄	#124×C₁₀₃	1	2	yes	—
317	C₂×C₄	#126×C₁₀₃	1	8	yes	—
318	C₂×C₄	C₂×SD₁₆×C₁₀₃	1	4	yes	—
319	C₂×C₄	C₂×Q₁₆×C₁₀₃	1	4	yes	—
320	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
321	C₂×C₄	C₂×#41×C₁₀₃	1	2	yes	—
322	C₂×C₄	C₂×#41×C₁₀₃	1	2	yes	—
323	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
324	C₈	—	4	4	no	—
325	C₂²	#397×C₁₀₃	1	4	yes	—
326	C₂²	#460×C₁₀₃	1	4	yes	—
327	C₂²	#462×C₁₀₃	1	4	yes	—
328	C₂²	#483×C₁₀₃	1	4	yes	—
329	C₂²	#484×C₁₀₃	1	4	yes	—
330	C₂²	#487×C₁₀₃	1	4	yes	—
331	C₂²	#489×C₁₀₃	1	4	yes	—
332	C₂²	C₂×#121×C₁₀₃	1	1	yes	characteristic
333	C₂²	C₂×#123×C₁₀₃	1	1	yes	characteristic
334	C₂²	C₂×#124×C₁₀₃	1	1	yes	characteristic
335	C₂²	C₂²×SD₁₆×C₁₀₃	1	1	yes	characteristic
336	C₂²	C₂²×Q₁₆×C₁₀₃	1	1	yes	characteristic
337	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₃	1	1	yes	characteristic
338	C₂²	C₂×#137×C₁₀₃	1	1	yes	characteristic
339	C₄	—	2	4	no	—
340	C₄	—	2	4	no	—
341	C₄	—	4	4	no	—
342	C₄	—	8	4	no	—
343	C₄	—	8	2	no	—
344	C₄	#397×C₁₀₃	1	4	yes	—
345	C₄	C₂×#123×C₁₀₃	1	2	yes	—
346	C₄	C₂×#126×C₁₀₃	1	2	yes	—
347	C₂	C₁₀₃×#2072	1	8	yes	direct product factor
348	C₂	C₂×#397×C₁₀₃	1	1	yes	characteristic
349	C₂	C₂×#460×C₁₀₃	1	1	yes	characteristic
350	C₂	C₂×#462×C₁₀₃	1	1	yes	characteristic
351	C₂	C₂×#483×C₁₀₃	1	1	yes	characteristic
352	C₂	C₂×#484×C₁₀₃	1	1	yes	characteristic
353	C₂	C₂×#487×C₁₀₃	1	1	yes	characteristic
354	C₂	C₂×#489×C₁₀₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₀₃×#2072	C₂	direct (N × H)
169. C₂×#2072	C₁₀₃	direct (N × H)
170. C₂×C₁₀₃	#2072	direct (N × H)
181. #2072	C₂×C₁₀₃	direct (N × H)
184. C₁₀₃	C₂×#2072	direct (N × H)
347. C₂	C₁₀₃×#2072	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#103×C₁₀₃	2
C₂×#391×C₁₀₃	2
C₂×#384×C₁₀₃	2
C₁₀₃×#2072	2
C₂×#340×C₁₀₃	2
C₂×#336×C₁₀₃	2
C₂×#2072	103

Subgroups — C2×C103×#2072 #39928900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₃×#2072 #39928900