Subgroups — C₁₀₃×#21364 #39926639

Order 26368.

894 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#432×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₁₀₃×#2285	C₂	1	1	yes	maximal, characteristic
3	C₄×#117×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₁₀₃×#1948	C₂	1	2	yes	maximal, complemented
5	C₁₀₃×#1947	C₂	1	2	yes	maximal, complemented
6	C₁₀₃×#1854	C₂	1	4	yes	maximal
7	C₁₀₃×#1776	C₂	1	4	yes	maximal, complemented
8	C₂×#117×C₁₀₃	—	2	1	no	—
9	C₂×#117×C₁₀₃	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
11	#432×C₁₀₃	C₄	1	8	yes	complemented
12	C₂×#107×C₁₀₃	C₂²	1	4	yes	—
13	C₂×#106×C₁₀₃	C₂²	1	4	yes	—
14	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₈×C₁₀₃	C₂²	1	2	yes	—
16	C₂×#97×C₁₀₃	C₂²	1	2	yes	—
17	#384×C₁₀₃	C₂²	1	2	yes	—
18	#382×C₁₀₃	—	2	1	no	—
19	#380×C₁₀₃	—	2	1	no	—
20	#380×C₁₀₃	C₂²	1	2	yes	—
21	C₄×C₄⋊C₄×C₁₀₃	—	2	1	no	—
22	C₄×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
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	4	yes	—
31	#340×C₁₀₃	C₂²	1	4	yes	—
32	C₂³×C₄×C₁₀₃	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₀₃	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₁₀₃	C₂³	1	4	yes	—
36	#117×C₁₀₃	—	2	4	no	—
37	#117×C₁₀₃	—	2	4	no	—
38	#117×C₁₀₃	—	4	4	no	—
39	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	4	yes	—
42	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
43	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
44	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
45	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
46	C₂×C₄²×C₁₀₃	—	2	2	no	—
47	C₂×C₄²×C₁₀₃	—	2	2	no	—
48	C₂×C₄²×C₁₀₃	—	2	1	no	—
49	C₂×C₄²×C₁₀₃	—	2	1	no	—
50	C₂×C₄²×C₁₀₃	—	2	2	no	—
51	C₂×C₄²×C₁₀₃	C₂×C₄	1	4	yes	—
52	C₂×C₄²×C₁₀₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₀₃	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₀₃	Q₈	1	4	yes	—
55	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
57	#107×C₁₀₃	—	2	8	no	—
58	#106×C₁₀₃	—	2	8	no	—
59	C₄⋊C₈×C₁₀₃	C₂×C₄	1	8	yes	—
60	C₂²⋊C₈×C₁₀₃	C₂×C₄	1	8	yes	—
61	#97×C₁₀₃	C₂×C₄	1	8	yes	—
62	#95×C₁₀₃	—	2	2	no	—
63	#95×C₁₀₃	—	2	1	no	—
64	#95×C₁₀₃	—	2	1	no	—
65	#95×C₁₀₃	—	2	2	no	—
66	#95×C₁₀₃	—	2	2	no	—
67	C₂⁴×C₁₀₃	C₂×D₄	1	1	yes	characteristic
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	2	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	C₄⋊C₄	1	4	yes	—
77	C₂²×C₄×C₁₀₃	C₄⋊C₄	1	4	yes	—
78	C₂²×C₄×C₁₀₃	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₀₃	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
86	C₂×C₈×C₁₀₃	—	2	4	no	—
87	C₂×C₈×C₁₀₃	—	2	4	no	—
88	C₂×C₈×C₁₀₃	C₂²×C₄	1	8	yes	—
89	C₄⋊C₄×C₁₀₃	—	2	2	no	—
90	C₄⋊C₄×C₁₀₃	—	2	2	no	—
91	C₄⋊C₄×C₁₀₃	—	2	4	no	—
92	C₄⋊C₄×C₁₀₃	—	2	4	no	—
93	C₄⋊C₄×C₁₀₃	—	4	4	no	—
94	C₄⋊C₄×C₁₀₃	—	4	4	no	—
95	C₄⋊C₄×C₁₀₃	#41	1	4	yes	—
96	C₄⋊C₄×C₁₀₃	#41	1	4	yes	—
97	C₂²⋊C₄×C₁₀₃	—	2	8	no	—
98	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
99	C₄²×C₁₀₃	—	2	8	no	—
100	C₄²×C₁₀₃	—	4	4	no	—
101	C₄²×C₁₀₃	—	4	4	no	—
102	C₄²×C₁₀₃	—	4	2	no	—
103	C₄²×C₁₀₃	—	4	2	no	—
104	C₄²×C₁₀₃	C₄⋊C₄	1	4	yes	—
105	C₄²×C₁₀₃	C₄⋊C₄	1	4	yes	—
106	C₄²×C₁₀₃	C₂²×C₄	1	2	yes	—
107	C₄²×C₁₀₃	C₂²×C₄	1	2	yes	—
108	C₄²×C₁₀₃	C₂×Q₈	1	2	yes	—
109	C₄²×C₁₀₃	C₂×Q₈	1	2	yes	—
110	C₂³×C₁₀₃	—	2	2	no	—
111	C₂³×C₁₀₃	—	2	1	no	—
112	C₂³×C₁₀₃	—	2	1	no	—
113	C₂³×C₁₀₃	—	2	2	no	—
114	C₂³×C₁₀₃	C₂×C₄⋊C₄	1	2	yes	—
115	C₂³×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
116	C₂×C₄×C₁₀₃	—	2	2	no	—
117	C₂×C₄×C₁₀₃	—	2	1	no	—
118	C₂×C₄×C₁₀₃	—	2	1	no	—
119	C₂×C₄×C₁₀₃	—	2	2	no	—
120	C₂×C₄×C₁₀₃	—	2	2	no	—
121	C₂×C₄×C₁₀₃	—	2	4	no	—
122	C₂×C₄×C₁₀₃	—	2	2	no	—
123	C₂×C₄×C₁₀₃	—	2	2	no	—
124	C₂×C₄×C₁₀₃	—	2	8	no	—
125	C₂×C₄×C₁₀₃	—	2	4	no	—
126	C₂×C₄×C₁₀₃	—	2	4	no	—
127	C₂×C₄×C₁₀₃	—	4	4	no	—
128	C₂×C₄×C₁₀₃	—	4	2	no	—
129	C₂×C₄×C₁₀₃	—	4	2	no	—
130	C₂×C₄×C₁₀₃	—	4	2	no	—
131	C₂×C₄×C₁₀₃	—	4	2	no	—
132	C₂×C₄×C₁₀₃	—	4	4	no	—
133	C₂×C₄×C₁₀₃	—	4	4	no	—
134	C₂×C₄×C₁₀₃	—	4	4	no	—
135	C₂×C₄×C₁₀₃	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×C₄×C₁₀₃	C₂×C₄⋊C₄	1	2	yes	—
137	C₂×C₄×C₁₀₃	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×C₄×C₁₀₃	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₁₀₃	C₂×C₄⋊C₄	1	2	yes	—
140	C₂×C₄×C₁₀₃	AGL(1,ℤ/8)	1	2	yes	—
141	C₂×C₄×C₁₀₃	#137	1	2	yes	—
142	C₂×C₄×C₁₀₃	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₀₃	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₁₀₃	C₂×#41	1	2	yes	—
145	C₂×C₄×C₁₀₃	C₂×#41	1	2	yes	—
146	C₈×C₁₀₃	—	2	8	no	—
147	C₂²×C₁₀₃	—	2	2	no	—
148	C₂²×C₁₀₃	—	2	2	no	—
149	C₂²×C₁₀₃	—	2	2	no	—
150	C₂²×C₁₀₃	—	4	2	no	—
151	C₂²×C₁₀₃	—	4	2	no	—
152	C₂²×C₁₀₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
153	C₂²×C₁₀₃	#525	1	2	yes	—
154	C₂²×C₁₀₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂²×C₁₀₃	C₂×#137	1	1	yes	characteristic
156	C₂²×C₁₀₃	#575	1	2	yes	—
157	C₄×C₁₀₃	—	2	2	no	—
158	C₄×C₁₀₃	—	2	2	no	—
159	C₄×C₁₀₃	—	2	2	no	—
160	C₄×C₁₀₃	—	2	2	no	—
161	C₄×C₁₀₃	—	4	4	no	—
162	C₄×C₁₀₃	—	4	4	no	—
163	C₄×C₁₀₃	—	8	4	no	—
164	C₄×C₁₀₃	#428	1	4	yes	—
165	C₄×C₁₀₃	C₄×#41	1	2	yes	—
166	C₄×C₁₀₃	#533	1	1	yes	characteristic
167	C₄×C₁₀₃	#533	1	1	yes	characteristic
168	#21364	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂×C₁₀₃	—	4	2	no	—
170	C₂×C₁₀₃	#2296	1	1	yes	characteristic
171	C₂×C₁₀₃	C₂×#428	1	1	yes	characteristic
172	C₂×C₁₀₃	#2911	1	1	yes	characteristic
173	C₂×C₁₀₃	#3115	1	2	yes	—
174	C₂×C₁₀₃	#3116	1	2	yes	—
175	C₂×#432	C₂×C₁₀₃	1	1	yes	characteristic
176	#2285	C₂×C₁₀₃	1	1	yes	characteristic
177	C₄×#117	C₂×C₁₀₃	1	1	yes	characteristic
178	#1948	C₂×C₁₀₃	1	2	yes	complemented
179	#1947	C₂×C₁₀₃	1	2	yes	complemented
180	#1854	C₂×C₁₀₃	1	4	yes	—
181	#1776	C₂×C₁₀₃	1	4	yes	complemented
182	C₁₀₃	#21364	1	1	yes	characteristic, direct product factor, Sylow
183	C₂×#117	—	2	1	no	—
184	C₂×#117	C₂²×C₁₀₃	1	2	yes	—
185	C₂²×C₄²	C₂²×C₁₀₃	1	1	yes	characteristic
186	#432	C₄×C₁₀₃	1	8	yes	complemented
187	C₂×#107	C₂²×C₁₀₃	1	4	yes	—
188	C₂×#106	C₂²×C₁₀₃	1	4	yes	—
189	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	2	yes	—
190	C₂×C₂²⋊C₈	C₂²×C₁₀₃	1	2	yes	—
191	C₂×#97	C₂²×C₁₀₃	1	2	yes	—
192	#384	C₂²×C₁₀₃	1	2	yes	—
193	#382	—	2	1	no	—
194	#380	—	2	1	no	—
195	#380	C₂²×C₁₀₃	1	2	yes	—
196	C₄×C₄⋊C₄	—	2	1	no	—
197	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
198	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
199	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	2	yes	—
200	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	2	yes	—
201	C₄×C₂²⋊C₄	—	2	1	no	—
202	C₄×C₂²⋊C₄	—	2	1	no	—
203	#376	—	2	1	no	—
204	C₄³	—	2	1	no	—
205	#340	C₂²×C₁₀₃	1	4	yes	—
206	#340	C₂²×C₁₀₃	1	4	yes	—
207	C₂³×C₄	D₄×C₁₀₃	1	1	yes	characteristic
208	C₂³×C₄	D₄×C₁₀₃	1	1	yes	characteristic
209	C₂³×C₄	C₂³×C₁₀₃	1	1	yes	characteristic
210	C₂²×C₈	C₂³×C₁₀₃	1	4	yes	—
211	#117	—	2	4	no	—
212	#117	—	2	4	no	—
213	#117	—	4	4	no	—
214	C₂×C₄⋊C₄	—	2	2	no	—
215	C₂×C₄⋊C₄	—	2	2	no	—
216	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	4	yes	—
217	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
218	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
219	C₂×C₂²⋊C₄	—	2	2	no	—
220	C₂×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₄²	—	2	2	no	—
222	C₂×C₄²	—	2	2	no	—
223	C₂×C₄²	—	2	2	no	—
224	C₂×C₄²	—	2	1	no	—
225	C₂×C₄²	—	2	1	no	—
226	C₂×C₄²	C₂×C₄×C₁₀₃	1	4	yes	—
227	C₂×C₄²	D₄×C₁₀₃	1	1	yes	characteristic
228	C₂×C₄²	D₄×C₁₀₃	1	1	yes	characteristic
229	C₂×C₄²	Q₈×C₁₀₃	1	4	yes	—
230	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
232	#107	—	2	8	no	—
233	#106	—	2	8	no	—
234	C₄⋊C₈	C₂×C₄×C₁₀₃	1	8	yes	—
235	C₂²⋊C₈	C₂×C₄×C₁₀₃	1	8	yes	—
236	#97	C₂×C₄×C₁₀₃	1	8	yes	—
237	#95	—	2	2	no	—
238	#95	—	2	1	no	—
239	#95	—	2	1	no	—
240	#95	—	2	2	no	—
241	#95	—	2	2	no	—
242	C₂⁴	C₂×D₄×C₁₀₃	1	1	yes	characteristic
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	2	no	—
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	—	4	2	no	—
251	C₂²×C₄	C₄⋊C₄×C₁₀₃	1	4	yes	—
252	C₂²×C₄	C₄⋊C₄×C₁₀₃	1	4	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₀₃	1	2	yes	—
254	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
255	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
256	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
259	C₂²×C₄	C₂×Q₈×C₁₀₃	1	2	yes	—
260	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	C₂²×C₄×C₁₀₃	1	8	yes	—
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	—	2	2	no	—
266	C₄⋊C₄	—	2	4	no	—
267	C₄⋊C₄	—	2	4	no	—
268	C₄⋊C₄	—	4	4	no	—
269	C₄⋊C₄	—	4	4	no	—
270	C₄⋊C₄	#41×C₁₀₃	1	4	yes	—
271	C₄⋊C₄	#41×C₁₀₃	1	4	yes	—
272	C₂²⋊C₄	—	2	8	no	—
273	C₂²⋊C₄	—	4	4	no	—
274	C₄²	—	2	8	no	—
275	C₄²	—	4	4	no	—
276	C₄²	—	4	4	no	—
277	C₄²	—	4	2	no	—
278	C₄²	—	4	2	no	—
279	C₄²	C₄⋊C₄×C₁₀₃	1	4	yes	—
280	C₄²	C₄⋊C₄×C₁₀₃	1	4	yes	—
281	C₄²	C₂²×C₄×C₁₀₃	1	2	yes	—
282	C₄²	C₂²×C₄×C₁₀₃	1	2	yes	—
283	C₄²	C₂×Q₈×C₁₀₃	1	2	yes	—
284	C₄²	C₂×Q₈×C₁₀₃	1	2	yes	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	1	no	—
287	C₂³	—	2	1	no	—
288	C₂³	—	2	2	no	—
289	C₂³	C₂×C₄⋊C₄×C₁₀₃	1	2	yes	—
290	C₂³	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	C₂×C₄⋊C₄×C₁₀₃	1	2	yes	—
311	C₂×C₄	C₂×C₄⋊C₄×C₁₀₃	1	2	yes	—
312	C₂×C₄	C₂×C₄⋊C₄×C₁₀₃	1	2	yes	—
313	C₂×C₄	C₂×C₄⋊C₄×C₁₀₃	1	2	yes	—
314	C₂×C₄	C₂×C₄⋊C₄×C₁₀₃	1	2	yes	—
315	C₂×C₄	AGL(1,ℤ/8)×C₁₀₃	1	2	yes	—
316	C₂×C₄	#137×C₁₀₃	1	2	yes	—
317	C₂×C₄	C₂³×C₄×C₁₀₃	1	1	yes	characteristic
318	C₂×C₄	C₂²×Q₈×C₁₀₃	1	1	yes	characteristic
319	C₂×C₄	C₂×#41×C₁₀₃	1	2	yes	—
320	C₂×C₄	C₂×#41×C₁₀₃	1	2	yes	—
321	C₈	—	2	8	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	4	2	no	—
326	C₂²	—	4	2	no	—
327	C₂²	C₂²×C₄⋊C₄×C₁₀₃	1	1	yes	characteristic
328	C₂²	#525×C₁₀₃	1	2	yes	—
329	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₃	1	1	yes	characteristic
330	C₂²	C₂×#137×C₁₀₃	1	1	yes	characteristic
331	C₂²	#575×C₁₀₃	1	2	yes	—
332	C₄	—	2	2	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	2	no	—
335	C₄	—	2	2	no	—
336	C₄	—	4	4	no	—
337	C₄	—	4	4	no	—
338	C₄	—	8	4	no	—
339	C₄	#428×C₁₀₃	1	4	yes	—
340	C₄	C₄×#41×C₁₀₃	1	2	yes	—
341	C₄	#533×C₁₀₃	1	1	yes	characteristic
342	C₄	#533×C₁₀₃	1	1	yes	characteristic
343	C₂	—	4	2	no	—
344	C₂	C₁₀₃×#2296	1	1	yes	characteristic
345	C₂	C₂×#428×C₁₀₃	1	1	yes	characteristic
346	C₂	C₁₀₃×#2911	1	1	yes	characteristic
347	C₂	C₁₀₃×#3115	1	2	yes	—
348	C₂	C₁₀₃×#3116	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₁₀₃×#1948	C₂	semidirect
5. C₁₀₃×#1947	C₂	semidirect
7. C₁₀₃×#1776	C₂	semidirect
11. #432×C₁₀₃	C₄	semidirect
168. #21364	C₁₀₃	direct (N × H)
178. #1948	C₂×C₁₀₃	semidirect
179. #1947	C₂×C₁₀₃	semidirect
181. #1776	C₂×C₁₀₃	semidirect
182. C₁₀₃	#21364	direct (N × H)
186. #432	C₄×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#432×C₁₀₃	2
C₁₀₃×#2285	2
C₄×#117×C₁₀₃	2
C₁₀₃×#1948	2
C₁₀₃×#1947	2
C₁₀₃×#1854	2
C₁₀₃×#1776	2
#21364	103

Subgroups — C103×#21364 #39926639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#21364 #39926639