Subgroups — C₁₀₃×#19957 #39925232

Order 26368.

584 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₃×#3357	C₂	1	2	yes	maximal, complemented
3	C₁₀₃×#3341	C₂	1	1	yes	maximal, characteristic
4	C₁₀₃×#1713	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₃×#1695	C₂	1	2	yes	maximal, complemented
6	C₁₀₃×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₃×#1675	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₃×#1634	C₂	1	2	yes	maximal, complemented
9	C₁₀₃×#1632	C₂	1	2	yes	maximal, complemented
10	C₁₀₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#555×C₁₀₃	C₂²	1	2	yes	—
13	#554×C₁₀₃	C₂²	1	2	yes	—
14	#500×C₁₀₃	C₂²	1	1	yes	characteristic
15	#500×C₁₀₃	C₂²	1	1	yes	characteristic
16	#500×C₁₀₃	C₂²	1	2	yes	—
17	#499×C₁₀₃	—	2	1	no	—
18	#494×C₁₀₃	C₂²	1	2	yes	—
19	#485×C₁₀₃	—	2	2	no	—
20	#482×C₁₀₃	—	2	2	no	—
21	#480×C₁₀₃	—	2	2	no	—
22	#478×C₁₀₃	—	2	2	no	—
23	#477×C₁₀₃	C₂²	1	2	yes	—
24	#476×C₁₀₃	C₂²	1	2	yes	—
25	#476×C₁₀₃	C₂²	1	2	yes	—
26	#476×C₁₀₃	C₂²	1	2	yes	—
27	#468×C₁₀₃	—	2	2	no	—
28	#466×C₁₀₃	—	2	1	no	—
29	C₈×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
30	C₄×SD₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
31	C₄×D₈×C₁₀₃	—	2	1	no	—
32	C₄×D₈×C₁₀₃	C₂²	1	1	yes	characteristic
33	#436×C₁₀₃	C₂²	1	2	yes	—
34	C₈×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
35	#428×C₁₀₃	—	2	2	no	—
36	#427×C₁₀₃	—	2	1	no	—
37	#335×C₁₀₃	C₂²	1	1	yes	characteristic
38	#334×C₁₀₃	C₂²	1	1	yes	characteristic
39	#333×C₁₀₃	C₂²	1	2	yes	—
40	#333×C₁₀₃	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₁₀₃	C₂²	1	1	yes	characteristic
42	D₄⋊C₈×C₁₀₃	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₁₀₃	C₂²	1	2	yes	—
44	C₈²×C₁₀₃	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₁₀₃	—	4	2	no	—
46	C₂×SD₁₆×C₁₀₃	D₄	1	1	yes	characteristic
47	C₂×D₈×C₁₀₃	D₄	1	1	yes	characteristic
48	C₂×M₁₆×C₁₀₃	—	2	2	no	—
49	C₂²×C₈×C₁₀₃	—	2	1	no	—
50	C₄⋊Q₈×C₁₀₃	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₁₀₃	C₂³	1	2	yes	—
52	#125×C₁₀₃	—	2	2	no	—
53	#124×C₁₀₃	—	4	2	no	—
54	C₂²⋊Q₈×C₁₀₃	—	2	2	no	—
55	C₂²⋊Q₈×C₁₀₃	—	4	2	no	—
56	#121×C₁₀₃	—	2	2	no	—
57	#121×C₁₀₃	—	2	2	no	—
58	C₄×Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
59	C₄×D₄×C₁₀₃	—	2	2	no	—
60	C₄×D₄×C₁₀₃	C₂³	1	1	yes	characteristic
61	C₄×D₄×C₁₀₃	C₂³	1	2	yes	—
62	#117×C₁₀₃	—	2	2	no	—
63	#117×C₁₀₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
65	#107×C₁₀₃	—	2	1	no	—
66	#107×C₁₀₃	—	2	2	no	—
67	#107×C₁₀₃	—	2	1	no	—
68	#107×C₁₀₃	—	2	1	no	—
69	#107×C₁₀₃	—	2	2	no	—
70	#107×C₁₀₃	—	2	1	no	—
71	#107×C₁₀₃	—	2	2	no	—
72	#107×C₁₀₃	D₄	1	1	yes	characteristic
73	#106×C₁₀₃	—	2	2	no	—
74	#106×C₁₀₃	—	2	2	no	—
75	#106×C₁₀₃	—	2	2	no	—
76	#106×C₁₀₃	D₄	1	1	yes	characteristic
77	C₄⋊C₈×C₁₀₃	—	2	1	no	—
78	C₄⋊C₈×C₁₀₃	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₁₀₃	C₂³	1	2	yes	—
80	C₄⋊C₈×C₁₀₃	C₂³	1	1	yes	characteristic
81	#103×C₁₀₃	—	2	2	no	—
82	#103×C₁₀₃	D₄	1	1	yes	characteristic
83	#102×C₁₀₃	—	2	2	no	—
84	#102×C₁₀₃	—	2	2	no	—
85	#102×C₁₀₃	—	2	2	no	—
86	#102×C₁₀₃	D₄	1	2	yes	—
87	#102×C₁₀₃	D₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₁₀₃	—	2	1	no	—
89	C₂²⋊C₈×C₁₀₃	—	2	2	no	—
90	C₄×C₈×C₁₀₃	—	2	1	no	—
91	C₄×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₁₀₃	—	2	2	no	—
95	C₂×Q₈×C₁₀₃	—	2	2	no	—
96	C₂×Q₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₁₀₃	—	4	2	no	—
98	C₂×D₄×C₁₀₃	C₂×D₄	1	2	yes	—
99	C₂×D₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₀₃	—	2	2	no	—
101	C₂²×C₄×C₁₀₃	—	2	1	no	—
102	C₂²×C₄×C₁₀₃	—	4	2	no	—
103	Q₁₆×C₁₀₃	—	8	4	no	—
104	SD₁₆×C₁₀₃	—	2	2	no	—
105	D₈×C₁₀₃	—	2	2	no	—
106	M₁₆×C₁₀₃	—	4	4	no	—
107	C₂×C₈×C₁₀₃	—	2	1	no	—
108	C₂×C₈×C₁₀₃	—	2	1	no	—
109	C₂×C₈×C₁₀₃	—	2	1	no	—
110	C₂×C₈×C₁₀₃	—	2	2	no	—
111	C₂×C₈×C₁₀₃	—	4	2	no	—
112	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
116	C₄⋊C₄×C₁₀₃	—	2	1	no	—
117	C₄⋊C₄×C₁₀₃	—	2	2	no	—
118	C₄⋊C₄×C₁₀₃	—	2	2	no	—
119	C₄⋊C₄×C₁₀₃	—	2	2	no	—
120	C₄⋊C₄×C₁₀₃	—	2	2	no	—
121	C₄⋊C₄×C₁₀₃	—	4	2	no	—
122	C₄⋊C₄×C₁₀₃	—	4	2	no	—
123	C₄⋊C₄×C₁₀₃	C₂×D₄	1	2	yes	—
124	C₄⋊C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
126	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
127	C₂²⋊C₄×C₁₀₃	—	2	1	no	—
128	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
129	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
130	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
131	C₄²×C₁₀₃	—	2	1	no	—
132	C₄²×C₁₀₃	—	4	2	no	—
133	C₄²×C₁₀₃	C₂⁴	1	1	yes	characteristic
134	C₂³×C₁₀₃	—	2	2	no	—
135	C₂³×C₁₀₃	—	2	1	no	—
136	Q₈×C₁₀₃	—	2	1	no	—
137	Q₈×C₁₀₃	—	2	1	no	—
138	Q₈×C₁₀₃	—	8	2	no	—
139	Q₈×C₁₀₃	—	8	2	no	—
140	D₄×C₁₀₃	—	2	1	no	—
141	D₄×C₁₀₃	—	2	2	no	—
142	D₄×C₁₀₃	—	2	2	no	—
143	D₄×C₁₀₃	—	2	1	no	—
144	D₄×C₁₀₃	—	16	2	no	—
145	C₂×C₄×C₁₀₃	—	2	1	no	—
146	C₂×C₄×C₁₀₃	—	2	1	no	—
147	C₂×C₄×C₁₀₃	—	2	1	no	—
148	C₂×C₄×C₁₀₃	—	2	2	no	—
149	C₂×C₄×C₁₀₃	—	4	2	no	—
150	C₂×C₄×C₁₀₃	—	4	1	no	—
151	C₂×C₄×C₁₀₃	—	4	1	no	—
152	C₂×C₄×C₁₀₃	—	4	2	no	—
153	C₂×C₄×C₁₀₃	—	4	2	no	—
154	C₂×C₄×C₁₀₃	—	4	2	no	—
155	C₂×C₄×C₁₀₃	—	16	2	no	—
156	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₀₃	H(5,𝔽₂)	1	1	yes	characteristic
159	C₈×C₁₀₃	—	2	2	no	—
160	C₈×C₁₀₃	—	2	1	no	—
161	C₈×C₁₀₃	—	2	1	no	—
162	C₈×C₁₀₃	—	4	2	no	—
163	C₈×C₁₀₃	—	4	1	no	—
164	C₈×C₁₀₃	—	4	1	no	—
165	C₈×C₁₀₃	#135	1	2	yes	—
166	C₈×C₁₀₃	#137	1	2	yes	—
167	C₂²×C₁₀₃	—	4	1	no	—
168	C₂²×C₁₀₃	—	4	2	no	—
169	C₂²×C₁₀₃	—	4	2	no	—
170	C₂²×C₁₀₃	—	4	1	no	—
171	C₂²×C₁₀₃	—	4	2	no	—
172	C₂²×C₁₀₃	—	4	1	no	—
173	C₂²×C₁₀₃	D₄²	1	1	yes	characteristic
174	C₄×C₁₀₃	—	2	1	no	—
175	C₄×C₁₀₃	—	4	1	no	—
176	C₄×C₁₀₃	—	4	2	no	—
177	C₄×C₁₀₃	—	4	1	no	—
178	C₄×C₁₀₃	—	4	1	no	—
179	C₄×C₁₀₃	—	8	2	no	—
180	C₄×C₁₀₃	—	8	2	no	—
181	C₄×C₁₀₃	C₂×#135	1	1	yes	characteristic
182	C₄×C₁₀₃	C₂×#137	1	1	yes	characteristic
183	C₄×C₁₀₃	#578	1	1	yes	characteristic
184	C₄×C₁₀₃	#578	1	1	yes	characteristic
185	#19957	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂×C₁₀₃	—	8	1	no	—
187	C₂×C₁₀₃	—	8	2	no	—
188	C₂×C₁₀₃	#3276	1	1	yes	characteristic
189	C₂×C₁₀₃	#3283	1	1	yes	characteristic
190	C₂×C₁₀₃	#3292	1	1	yes	characteristic
191	#3380	C₂×C₁₀₃	1	1	yes	characteristic, complemented
192	#3357	C₂×C₁₀₃	1	2	yes	complemented
193	#3341	C₂×C₁₀₃	1	1	yes	characteristic
194	#1713	C₂×C₁₀₃	1	1	yes	characteristic, complemented
195	#1695	C₂×C₁₀₃	1	2	yes	complemented
196	#1676	C₂×C₁₀₃	1	1	yes	characteristic, complemented
197	#1675	C₂×C₁₀₃	1	1	yes	characteristic, complemented
198	#1634	C₂×C₁₀₃	1	2	yes	complemented
199	#1632	C₂×C₁₀₃	1	2	yes	complemented
200	#1589	C₂×C₁₀₃	1	1	yes	characteristic, complemented
201	C₈×SD₁₆	C₂×C₁₀₃	1	1	yes	characteristic, complemented
202	C₁₀₃	#19957	1	1	yes	characteristic, direct product factor, Sylow
203	#555	C₂²×C₁₀₃	1	2	yes	—
204	#554	C₂²×C₁₀₃	1	2	yes	—
205	#500	C₂²×C₁₀₃	1	1	yes	characteristic
206	#500	C₂²×C₁₀₃	1	2	yes	—
207	#500	C₂²×C₁₀₃	1	1	yes	characteristic
208	#499	—	2	1	no	—
209	#494	C₂²×C₁₀₃	1	2	yes	—
210	#485	—	2	2	no	—
211	#482	—	2	2	no	—
212	#480	—	2	2	no	—
213	#478	—	2	2	no	—
214	#477	C₂²×C₁₀₃	1	2	yes	—
215	#476	C₂²×C₁₀₃	1	2	yes	—
216	#476	C₂²×C₁₀₃	1	2	yes	—
217	#476	C₂²×C₁₀₃	1	2	yes	—
218	#468	—	2	2	no	—
219	#466	—	2	1	no	—
220	C₈×Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
221	C₄×SD₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
222	C₄×D₈	—	2	1	no	—
223	C₄×D₈	C₂²×C₁₀₃	1	1	yes	characteristic
224	#436	C₂²×C₁₀₃	1	2	yes	—
225	C₈×D₄	C₂²×C₁₀₃	1	1	yes	characteristic
226	#428	—	2	2	no	—
227	#427	—	2	1	no	—
228	#335	C₂²×C₁₀₃	1	1	yes	characteristic
229	#334	C₂²×C₁₀₃	1	1	yes	characteristic
230	#333	C₂²×C₁₀₃	1	2	yes	—
231	#333	C₂²×C₁₀₃	1	2	yes	—
232	Q₈⋊C₈	C₂²×C₁₀₃	1	1	yes	characteristic
233	D₄⋊C₈	C₂²×C₁₀₃	1	1	yes	characteristic
234	D₄⋊C₈	C₂²×C₁₀₃	1	2	yes	—
235	C₈²	C₂²×C₁₀₃	1	1	yes	characteristic
236	C₂×Q₁₆	—	4	2	no	—
237	C₂×SD₁₆	D₄×C₁₀₃	1	1	yes	characteristic
238	C₂×D₈	D₄×C₁₀₃	1	1	yes	characteristic
239	C₂×M₁₆	—	2	2	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₄⋊Q₈	C₂³×C₁₀₃	1	2	yes	—
242	C₄⋊Q₈	C₂³×C₁₀₃	1	2	yes	—
243	#125	—	2	2	no	—
244	#124	—	4	2	no	—
245	C₂²⋊Q₈	—	2	2	no	—
246	C₂²⋊Q₈	—	4	2	no	—
247	#121	—	2	2	no	—
248	#121	—	2	2	no	—
249	C₄×Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	C₂³×C₁₀₃	1	2	yes	—
252	C₄×D₄	C₂³×C₁₀₃	1	1	yes	characteristic
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	#107	—	2	1	no	—
257	#107	—	2	2	no	—
258	#107	—	2	1	no	—
259	#107	—	2	1	no	—
260	#107	—	2	2	no	—
261	#107	—	2	1	no	—
262	#107	—	2	2	no	—
263	#107	D₄×C₁₀₃	1	1	yes	characteristic
264	#106	—	2	2	no	—
265	#106	—	2	2	no	—
266	#106	—	2	2	no	—
267	#106	D₄×C₁₀₃	1	1	yes	characteristic
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	C₂³×C₁₀₃	1	1	yes	characteristic
270	C₄⋊C₈	C₂³×C₁₀₃	1	2	yes	—
271	C₄⋊C₈	C₂³×C₁₀₃	1	1	yes	characteristic
272	#103	—	2	2	no	—
273	#103	D₄×C₁₀₃	1	1	yes	characteristic
274	#102	—	2	2	no	—
275	#102	—	2	2	no	—
276	#102	—	2	2	no	—
277	#102	D₄×C₁₀₃	1	2	yes	—
278	#102	D₄×C₁₀₃	1	1	yes	characteristic
279	C₂²⋊C₈	—	2	1	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	C₂×D₄×C₁₀₃	1	2	yes	—
290	C₂×D₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	4	2	no	—
294	Q₁₆	—	8	4	no	—
295	SD₁₆	—	2	2	no	—
296	D₈	—	2	2	no	—
297	M₁₆	—	4	4	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	C₂×D₄×C₁₀₃	1	2	yes	—
315	C₄⋊C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
316	C₄⋊C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	4	2	no	—
324	C₄²	C₂⁴×C₁₀₃	1	1	yes	characteristic
325	C₂³	—	2	2	no	—
326	C₂³	—	2	1	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	2	1	no	—
329	Q₈	—	8	2	no	—
330	Q₈	—	8	2	no	—
331	D₄	—	2	1	no	—
332	D₄	—	2	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	2	1	no	—
335	D₄	—	16	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	16	2	no	—
347	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
349	C₂×C₄	H(5,𝔽₂)×C₁₀₃	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	4	2	no	—
354	C₈	—	4	1	no	—
355	C₈	—	4	1	no	—
356	C₈	#135×C₁₀₃	1	2	yes	—
357	C₈	#137×C₁₀₃	1	2	yes	—
358	C₂²	—	4	1	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	1	no	—
364	C₂²	D₄²×C₁₀₃	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	2	no	—
372	C₄	C₂×#135×C₁₀₃	1	1	yes	characteristic
373	C₄	C₂×#137×C₁₀₃	1	1	yes	characteristic
374	C₄	#578×C₁₀₃	1	1	yes	characteristic
375	C₄	#578×C₁₀₃	1	1	yes	characteristic
376	C₂	—	8	1	no	—
377	C₂	—	8	2	no	—
378	C₂	C₁₀₃×#3276	1	1	yes	characteristic
379	C₂	C₁₀₃×#3283	1	1	yes	characteristic
380	C₂	C₁₀₃×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₃
prime radical	C₁₀₃×#3341	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₄²×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₃×#3380	C₂	semidirect
2. C₁₀₃×#3357	C₂	semidirect
4. C₁₀₃×#1713	C₂	semidirect
5. C₁₀₃×#1695	C₂	semidirect
6. C₁₀₃×#1676	C₂	semidirect
7. C₁₀₃×#1675	C₂	semidirect
8. C₁₀₃×#1634	C₂	semidirect
9. C₁₀₃×#1632	C₂	semidirect
10. C₁₀₃×#1589	C₂	semidirect
11. C₈×SD₁₆×C₁₀₃	C₂	semidirect
185. #19957	C₁₀₃	direct (N × H)
191. #3380	C₂×C₁₀₃	semidirect
192. #3357	C₂×C₁₀₃	semidirect
194. #1713	C₂×C₁₀₃	semidirect
195. #1695	C₂×C₁₀₃	semidirect
196. #1676	C₂×C₁₀₃	semidirect
197. #1675	C₂×C₁₀₃	semidirect
198. #1634	C₂×C₁₀₃	semidirect
199. #1632	C₂×C₁₀₃	semidirect
200. #1589	C₂×C₁₀₃	semidirect
201. C₈×SD₁₆	C₂×C₁₀₃	semidirect
202. C₁₀₃	#19957	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₀₃×#3380	2
C₁₀₃×#3357	2
C₁₀₃×#3341	2
C₁₀₃×#1713	2
C₁₀₃×#1695	2
C₁₀₃×#1676	2
C₁₀₃×#1675	2
C₁₀₃×#1634	2
C₁₀₃×#1632	2
C₁₀₃×#1589	2
C₈×SD₁₆×C₁₀₃	2
#19957	103

Subgroups — C103×#19957 #39925232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#19957 #39925232