Subgroups — C₄×#127×D₇₃ #33244494

Order 18688.

5694 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#127×D₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄×D₇₃	C₂	1	6	yes	maximal, complemented
3	#127×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#14556588	C₂	1	1	yes	maximal, characteristic, complemented
5	#22612495	C₂	1	6	yes	maximal, complemented
6	C₄×#14556587	C₂	1	6	yes	maximal, complemented
7	#22612493	C₂	1	1	yes	maximal, characteristic, complemented
8	#390×D₇₃	C₂	1	6	yes	maximal, complemented
9	#384×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄³×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₄×D₇₃	C₂²	1	6	yes	—
13	C₂³×C₄×D₇₃	C₂²	1	4	yes	—
14	C₂×#14556588	C₂²	1	1	yes	characteristic
15	C₂×#14556587	C₂²	1	6	yes	—
16	#127×D₇₃	C₄	1	16	yes	direct product factor
17	C₂×C₄×D₂₉₂	C₂²	1	6	yes	complemented
18	C₂×D₄×Dic₇₃	C₂²	1	6	yes	complemented
19	C₂×#14556553	C₂²	1	6	yes	complemented
20	C₂×C₄×C₂²⋊D₇₃	C₂²	1	12	yes	complemented
21	C₂×#14556551	C₂²	1	12	yes	complemented
22	C₄×D₄×D₇₃	—	2	48	no	—
23	C₂×C₄⋊C₄×D₇₃	C₂²	1	6	yes	—
24	C₂×C₂²⋊C₄×D₇₃	C₂²	1	12	yes	—
25	C₂×C₄²×D₇₃	C₂²	1	3	yes	—
26	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄²×D₇₃	C₂²	1	3	yes	—
28	#17988490	C₂²	1	6	yes	complemented
29	#17988489	C₂²	1	6	yes	complemented
30	#17988488	C₂²	1	6	yes	complemented
31	#17988487	C₂²	1	24	yes	complemented
32	#17988457	C₂²	1	1	yes	characteristic, complemented
33	#17988456	C₂²	1	6	yes	complemented
34	C₄²×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
35	C₄²×Dic₇₃	C₂²	1	3	yes	complemented
36	C₄²×Dic₇₃	C₂²	1	3	yes	complemented
37	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₇₃	C₂²	1	6	yes	complemented
39	#390×C₇₃	C₂²	1	6	yes	complemented
40	#384×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	C₄³×C₇₃	C₂²	1	1	yes	characteristic, complemented
42	C₂⁴×D₇₃	C₂³	1	4	yes	—
43	C₂²×D₂₉₂	C₂³	1	6	yes	—
44	C₂²×C₂²⋊D₇₃	C₂³	1	12	yes	—
45	C₂×D₄×D₇₃	—	2	24	no	—
46	C₂×D₄×D₇₃	—	2	24	no	—
47	C₂×D₄×D₇₃	C₂×C₄	1	48	yes	complemented
48	C₂³×Dic₇₃	C₂³	1	4	yes	—
49	C₂²×C₄×D₇₃	—	2	48	no	—
50	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
51	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
52	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
53	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
54	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
55	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
56	#14556588	C₂×C₄	1	8	yes	complemented
57	#14556587	C₂×C₄	1	48	yes	complemented
58	C₄×D₂₉₂	—	2	24	no	—
59	D₄×Dic₇₃	—	2	24	no	—
60	#14556553	—	2	24	no	—
61	C₄×C₂²⋊D₇₃	—	2	48	no	—
62	#14556551	—	2	48	no	—
63	C₂×C₄⋊Dic₇₃	C₂³	1	6	yes	—
64	C₂×#11924007	C₂³	1	12	yes	—
65	C₄⋊C₄×D₇₃	—	2	24	no	—
66	C₂×C₂²⋊Dic₇₃	C₂³	1	12	yes	—
67	C₂×#11924005	C₂³	1	12	yes	—
68	C₂×#11924005	C₂³	1	12	yes	—
69	C₂²⋊C₄×D₇₃	—	2	48	no	—
70	C₂×C₄×Dic₇₃	C₂³	1	6	yes	—
71	C₂×C₄×Dic₇₃	C₂³	1	3	yes	—
72	C₂×C₄×Dic₇₃	C₂³	1	3	yes	—
73	C₂×C₄×Dic₇₃	C₂³	1	3	yes	—
74	C₂×C₄×Dic₇₃	C₂³	1	3	yes	—
75	C₂×C₄×Dic₇₃	C₂³	1	3	yes	—
76	C₄²×D₇₃	—	2	12	no	—
77	C₄²×D₇₃	C₂×C₄	1	8	yes	complemented
78	C₄²×D₇₃	D₄	1	24	yes	complemented
79	C₂²×D₄×C₇₃	C₂³	1	6	yes	—
80	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
81	#127×C₇₃	C₂×C₄	1	8	yes	complemented
82	C₄×D₄×C₇₃	—	2	24	no	—
83	C₂×C₄⋊C₄×C₇₃	C₂³	1	6	yes	—
84	C₂×C₂²⋊C₄×C₇₃	C₂³	1	12	yes	—
85	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
86	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
88	C₂³×D₇₃	—	2	24	no	—
89	C₂³×D₇₃	—	2	24	no	—
90	C₂³×D₇₃	C₂²×C₄	1	16	yes	—
91	C₂³×D₇₃	C₂⁴	1	4	yes	—
92	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
93	C₂×D₂₉₂	—	2	12	no	—
94	C₂×D₂₉₂	—	2	12	no	—
95	C₂×D₂₉₂	C₂²×C₄	1	24	yes	complemented
96	C₂×C₂²⋊D₇₃	—	2	24	no	—
97	C₂×C₂²⋊D₇₃	—	2	24	no	—
98	C₂×C₂²⋊D₇₃	C₂²×C₄	1	48	yes	complemented
99	D₄×D₇₃	—	2	192	no	—
100	C₂²×Dic₇₃	—	2	24	no	—
101	C₂²×Dic₇₃	C₂⁴	1	4	yes	—
102	C₂²×Dic₇₃	C₂⁴	1	3	yes	—
103	C₂²×Dic₇₃	C₂⁴	1	3	yes	—
104	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
105	C₂×C₄×D₇₃	—	2	12	no	—
106	C₂×C₄×D₇₃	—	2	24	no	—
107	C₂×C₄×D₇₃	—	2	24	no	—
108	C₂×C₄×D₇₃	—	2	24	no	—
109	C₂×C₄×D₇₃	—	4	64	no	—
110	C₂×C₄×D₇₃	C₂²×C₄	1	12	yes	—
111	C₂×C₄×D₇₃	C₂×D₄	1	12	yes	—
112	C₂×C₄×D₇₃	C₂×D₄	1	12	yes	—
113	C₂×C₄×D₇₃	C₂×D₄	1	12	yes	—
114	C₂×C₄×D₇₃	#41	1	12	yes	—
115	C₄⋊Dic₇₃	—	2	12	no	—
116	#11924007	—	2	24	no	—
117	C₂²⋊Dic₇₃	—	2	24	no	—
118	#11924005	—	2	24	no	—
119	#11924005	—	2	24	no	—
120	C₄×Dic₇₃	—	2	6	no	—
121	C₄×Dic₇₃	—	2	12	no	—
122	C₄×Dic₇₃	C₂²×C₄	1	12	yes	complemented
123	C₄×Dic₇₃	C₂×D₄	1	12	yes	complemented
124	C₄×Dic₇₃	C₂×D₄	1	12	yes	complemented
125	C₄×Dic₇₃	C₂×D₄	1	12	yes	complemented
126	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
127	C₂×D₄×C₇₃	—	2	12	no	—
128	C₂×D₄×C₇₃	—	2	12	no	—
129	C₂×D₄×C₇₃	C₂²×C₄	1	24	yes	complemented
130	C₂²×C₄×C₇₃	—	2	24	no	—
131	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
133	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
134	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
135	C₄⋊C₄×C₇₃	—	2	12	no	—
136	C₂²⋊C₄×C₇₃	—	2	24	no	—
137	C₄²×C₇₃	—	2	6	no	—
138	C₄²×C₇₃	C₂²×C₄	1	4	yes	complemented
139	C₄²×C₇₃	C₂×D₄	1	12	yes	complemented
140	C₂³×C₇₃	—	2	12	no	—
141	C₂³×C₇₃	—	2	12	no	—
142	C₂³×C₇₃	C₂³×C₄	1	8	yes	—
143	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
144	C₂²×D₇₃	—	2	12	no	—
145	C₂²×D₇₃	—	2	12	no	—
146	C₂²×D₇₃	—	2	96	no	—
147	C₂²×D₇₃	—	4	16	no	—
148	C₂²×D₇₃	—	4	48	no	—
149	C₂²×D₇₃	C₂³×C₄	1	8	yes	—
150	C₂²×D₇₃	C₂³×C₄	1	2	yes	—
151	C₂²×D₇₃	C₂²×D₄	1	6	yes	—
152	C₂²×D₇₃	C₂×#41	1	6	yes	—
153	D₄×C₇₃	—	2	48	no	—
154	C₂×C₄×C₇₃	—	2	6	no	—
155	C₂×C₄×C₇₃	—	2	12	no	—
156	C₂×C₄×C₇₃	—	4	16	no	—
157	C₂×C₄×C₇₃	C₂³×C₄	1	6	yes	—
158	C₂×C₄×C₇₃	C₂²×D₄	1	6	yes	—
159	C₂×C₄×C₇₃	C₂²×D₄	1	6	yes	—
160	C₂×C₄×C₇₃	C₂²×D₄	1	6	yes	—
161	C₂×C₄×C₇₃	C₂×#41	1	6	yes	—
162	C₂²⋊D₇₃	—	2	96	no	—
163	C₂×Dic₇₃	—	2	6	no	—
164	C₂×Dic₇₃	—	2	12	no	—
165	C₂×Dic₇₃	—	4	16	no	—
166	C₂×Dic₇₃	C₂³×C₄	1	6	yes	—
167	C₂×Dic₇₃	C₂²×D₄	1	6	yes	—
168	C₂×Dic₇₃	C₂²×D₄	1	6	yes	—
169	C₂×Dic₇₃	C₂²×D₄	1	6	yes	—
170	C₂×Dic₇₃	C₂×#41	1	6	yes	—
171	D₂₉₂	—	2	48	no	—
172	C₄×D₇₃	—	2	24	no	—
173	C₄×D₇₃	—	4	16	no	—
174	C₄×D₇₃	—	4	16	no	—
175	C₄×D₇₃	—	4	16	no	—
176	C₄×D₇₃	C₄×D₄	1	48	yes	complemented
177	C₄×D₇₃	#127	1	16	yes	direct product factor
178	C₂²×C₇₃	—	2	24	no	—
179	C₂²×C₇₃	—	4	4	no	—
180	C₂²×C₇₃	—	4	12	no	—
181	C₂²×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
182	C₂²×C₇₃	C₂³×D₄	1	3	yes	—
183	C₂²×C₇₃	C₂²×#41	1	3	yes	—
184	C₂×D₇₃	—	2	24	no	—
185	C₂×D₇₃	—	4	4	no	—
186	C₂×D₇₃	—	4	12	no	—
187	C₂×D₇₃	—	4	64	no	—
188	C₂×D₇₃	C₂×C₄×D₄	1	12	yes	—
189	C₂×D₇₃	C₂×#127	1	4	yes	—
190	C₂×D₇₃	#532	1	12	yes	—
191	C₄×C₇₃	—	2	6	no	—
192	C₄×C₇₃	—	4	4	no	—
193	C₄×C₇₃	C₂×C₄×D₄	1	12	yes	complemented
194	C₄×C₇₃	C₂×#127	1	4	yes	complemented
195	Dic₇₃	—	2	6	no	—
196	Dic₇₃	—	4	4	no	—
197	Dic₇₃	C₂×C₄×D₄	1	12	yes	complemented
198	Dic₇₃	C₂×#127	1	4	yes	complemented
199	C₂×C₄×#127	—	73	1	no	maximal, Sylow
200	C₂×C₇₃	—	4	8	no	—
201	C₂×C₇₃	C₂²×C₄×D₄	1	3	yes	—
202	C₂×C₇₃	C₂²×#127	1	1	yes	characteristic
203	C₂×C₇₃	C₂×#532	1	3	yes	—
204	D₇₃	—	4	8	no	—
205	D₇₃	C₄×#127	1	8	yes	direct product factor
206	C₂²×#127	—	73	1	no	—
207	C₂²×C₄×D₄	—	73	6	no	—
208	C₄×#127	—	73	6	no	—
209	C₄×#127	—	73	1	no	—
210	C₄×#127	—	73	1	no	—
211	C₄×#127	—	73	1	no	—
212	C₄×#127	—	73	6	no	—
213	C₄×#127	D₇₃	1	1	yes	characteristic, direct product factor
214	C₂×#390	—	73	6	no	—
215	C₂×#384	—	73	1	no	—
216	C₂×C₄³	—	73	1	no	—
217	C₇₃	C₂×C₄×#127	1	1	yes	characteristic, complemented, Sylow
218	C₂³×D₄	—	73	6	no	—
219	C₂⁴×C₄	—	73	4	no	—
220	C₂×#127	—	73	6	no	—
221	C₂×#127	—	73	16	no	—
222	C₂×#127	—	73	1	no	—
223	C₂×#127	C₂×D₇₃	1	1	yes	characteristic
224	C₂×C₄×D₄	—	73	6	no	—
225	C₂×C₄×D₄	—	73	12	no	—
226	C₂×C₄×D₄	—	73	6	no	—
227	C₂×C₄×D₄	—	73	12	no	—
228	C₂×C₄×D₄	—	73	6	no	—
229	C₂×C₄×D₄	—	146	48	no	—
230	C₂×C₄×D₄	C₂×D₇₃	1	6	yes	complemented
231	C₂²×C₄⋊C₄	—	73	6	no	—
232	C₂²×C₂²⋊C₄	—	73	12	no	—
233	C₂²×C₄²	—	73	3	no	—
234	C₂²×C₄²	—	73	1	no	—
235	C₂²×C₄²	—	73	3	no	—
236	#390	—	73	6	no	—
237	#390	—	73	6	no	—
238	#390	—	73	24	no	—
239	#390	—	73	6	no	—
240	#390	C₂×D₇₃	1	6	yes	complemented
241	#384	—	73	6	no	—
242	#384	—	73	1	no	—
243	#384	C₂×D₇₃	1	1	yes	characteristic, complemented
244	C₄³	—	73	3	no	—
245	C₄³	—	73	1	no	—
246	C₄³	—	73	3	no	—
247	C₄³	C₂×D₇₃	1	1	yes	characteristic, complemented
248	C₂⁵	—	73	4	no	—
249	C₂²×D₄	—	73	12	no	—
250	C₂²×D₄	—	73	48	no	—
251	C₂²×D₄	—	73	6	no	—
252	C₂²×D₄	—	146	24	no	—
253	C₂²×D₄	—	146	24	no	—
254	C₂²×D₄	C₂²×D₇₃	1	6	yes	—
255	C₂³×C₄	—	73	3	no	—
256	C₂³×C₄	—	73	1	no	—
257	C₂³×C₄	—	73	3	no	—
258	C₂³×C₄	—	73	4	no	—
259	C₂³×C₄	—	73	4	no	—
260	C₂³×C₄	—	73	4	no	—
261	C₂³×C₄	—	73	4	no	—
262	C₂³×C₄	—	146	48	no	—
263	C₂³×C₄	C₂²×D₇₃	1	4	yes	—
264	#127	—	73	48	no	—
265	#127	—	73	8	no	—
266	#127	C₄×D₇₃	1	8	yes	direct product factor
267	C₄×D₄	—	2	24	no	—
268	C₄×D₄	—	146	48	no	—
269	C₄×D₄	—	146	24	no	—
270	C₄×D₄	—	146	48	no	—
271	C₄×D₄	—	146	24	no	—
272	C₄×D₄	—	146	24	no	—
273	C₂×C₄⋊C₄	—	73	12	no	—
274	C₂×C₄⋊C₄	—	73	6	no	—
275	C₂×C₄⋊C₄	—	146	24	no	—
276	C₂×C₄⋊C₄	C₂²×D₇₃	1	6	yes	—
277	C₂×C₂²⋊C₄	—	73	12	no	—
278	C₂×C₂²⋊C₄	—	73	12	no	—
279	C₂×C₂²⋊C₄	—	73	12	no	—
280	C₂×C₂²⋊C₄	—	146	48	no	—
281	C₂×C₂²⋊C₄	C₂²×D₇₃	1	12	yes	—
282	C₂×C₄²	—	73	3	no	—
283	C₂×C₄²	—	73	3	no	—
284	C₂×C₄²	—	73	3	no	—
285	C₂×C₄²	—	73	3	no	—
286	C₂×C₄²	—	73	8	no	—
287	C₂×C₄²	—	73	24	no	—
288	C₂×C₄²	—	73	6	no	—
289	C₂×C₄²	—	73	3	no	—
290	C₂×C₄²	—	146	12	no	—
291	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
292	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
293	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
294	C₂⁴	—	73	1	no	—
295	C₂⁴	—	73	16	no	—
296	C₂⁴	—	73	4	no	—
297	C₂⁴	—	146	24	no	—
298	C₂⁴	—	146	24	no	—
299	C₂⁴	C₂³×D₇₃	1	4	yes	—
300	C₂×D₄	—	2	12	no	—
301	C₂×D₄	—	2	12	no	—
302	C₂×D₄	—	73	48	no	—
303	C₂×D₄	—	73	24	no	—
304	C₂×D₄	—	146	192	no	—
305	C₂×D₄	—	146	24	no	—
306	C₂×D₄	—	146	24	no	—
307	C₂×D₄	—	146	12	no	—
308	C₂×D₄	—	146	12	no	—
309	C₂×D₄	C₂×C₄×D₇₃	1	24	yes	complemented
310	C₂²×C₄	—	2	24	no	—
311	C₂²×C₄	—	292	64	no	—
312	C₂²×C₄	—	73	3	no	—
313	C₂²×C₄	—	73	1	no	—
314	C₂²×C₄	—	73	12	no	—
315	C₂²×C₄	—	73	12	no	—
316	C₂²×C₄	—	73	12	no	—
317	C₂²×C₄	—	73	12	no	—
318	C₂²×C₄	—	73	3	no	—
319	C₂²×C₄	—	73	12	no	—
320	C₂²×C₄	—	73	4	no	—
321	C₂²×C₄	—	146	24	no	—
322	C₂²×C₄	—	146	24	no	—
323	C₂²×C₄	—	146	12	no	—
324	C₂²×C₄	—	146	24	no	—
325	C₂²×C₄	—	146	24	no	—
326	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
327	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
328	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
329	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
330	C₄⋊C₄	—	2	12	no	—
331	C₄⋊C₄	—	146	24	no	—
332	C₄⋊C₄	—	146	12	no	—
333	C₂²⋊C₄	—	2	24	no	—
334	C₂²⋊C₄	—	146	24	no	—
335	C₂²⋊C₄	—	146	24	no	—
336	C₂²⋊C₄	—	146	24	no	—
337	C₄²	—	2	6	no	—
338	C₄²	—	73	12	no	—
339	C₄²	—	73	12	no	—
340	C₄²	—	73	12	no	—
341	C₄²	—	73	12	no	—
342	C₄²	—	146	12	no	—
343	C₄²	—	146	6	no	—
344	C₄²	C₂×C₄×D₇₃	1	4	yes	complemented
345	C₄²	D₄×D₇₃	1	12	yes	complemented
346	C₂³	—	2	12	no	—
347	C₂³	—	2	12	no	—
348	C₂³	—	292	16	no	—
349	C₂³	—	292	48	no	—
350	C₂³	—	73	2	no	—
351	C₂³	—	73	6	no	—
352	C₂³	—	73	6	no	—
353	C₂³	—	73	8	no	—
354	C₂³	—	146	96	no	—
355	C₂³	—	146	12	no	—
356	C₂³	—	146	12	no	—
357	C₂³	C₂²×C₄×D₇₃	1	8	yes	—
358	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
359	D₄	—	2	48	no	—
360	D₄	—	146	96	no	—
361	D₄	—	146	48	no	—
362	C₂×C₄	—	2	6	no	—
363	C₂×C₄	—	2	12	no	—
364	C₂×C₄	—	4	16	no	—
365	C₂×C₄	—	292	16	no	—
366	C₂×C₄	—	292	16	no	—
367	C₂×C₄	—	292	16	no	—
368	C₂×C₄	—	292	16	no	—
369	C₂×C₄	—	73	6	no	—
370	C₂×C₄	—	73	6	no	—
371	C₂×C₄	—	73	6	no	—
372	C₂×C₄	—	73	6	no	—
373	C₂×C₄	—	73	16	no	—
374	C₂×C₄	—	73	48	no	—
375	C₂×C₄	—	73	6	no	—
376	C₂×C₄	—	146	24	no	—
377	C₂×C₄	—	146	12	no	—
378	C₂×C₄	—	146	6	no	—
379	C₂×C₄	C₂²×C₄×D₇₃	1	6	yes	—
380	C₂×C₄	C₂×D₄×D₇₃	1	6	yes	—
381	C₂×C₄	C₂×D₄×D₇₃	1	6	yes	—
382	C₂×C₄	C₂×D₄×D₇₃	1	6	yes	—
383	C₂×C₄	#41×D₇₃	1	6	yes	—
384	C₂²	—	2	24	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	4	12	no	—
387	C₂²	—	292	64	no	—
388	C₂²	—	292	4	no	—
389	C₂²	—	292	12	no	—
390	C₂²	—	73	12	no	—
391	C₂²	—	73	4	no	—
392	C₂²	—	73	12	no	—
393	C₂²	—	146	24	no	—
394	C₂²	C₂³×C₄×D₇₃	1	1	yes	characteristic
395	C₂²	C₂²×D₄×D₇₃	1	3	yes	—
396	C₂²	C₂×#41×D₇₃	1	3	yes	—
397	C₄	—	2	6	no	—
398	C₄	—	4	4	no	—
399	C₄	—	292	4	no	—
400	C₄	—	73	12	no	—
401	C₄	—	73	4	no	—
402	C₄	—	146	6	no	—
403	C₄	C₄×D₄×D₇₃	1	12	yes	complemented
404	C₄	#127×D₇₃	1	4	yes	direct product factor
405	C₂	—	4	8	no	—
406	C₂	—	292	8	no	—
407	C₂	—	73	8	no	—
408	C₂	C₂×C₄×D₄×D₇₃	1	3	yes	—
409	C₂	C₂×#127×D₇₃	1	1	yes	characteristic
410	C₂	#532×D₇₃	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇₃
commutator	C₂²×C₇₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₇₃
Fitting	C₄×#127×C₇₃	C₂
socle, cosocle	C₂³×C₇₃	C₂⁵
prime radical	C₂×#127×D₇₃	C₂
hypercenter	C₄×#127	D₇₃
hypocenter	C₇₃	C₂×C₄×#127
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#127

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₄×D₇₃	C₂	semidirect
3. #127×Dic₇₃	C₂	semidirect
4. C₄×#14556588	C₂	semidirect
5. #22612495	C₂	semidirect
6. C₄×#14556587	C₂	semidirect
7. #22612493	C₂	semidirect
8. #390×D₇₃	C₂	semidirect
9. #384×D₇₃	C₂	semidirect
10. C₄³×D₇₃	C₂	semidirect
11. C₄×#127×C₇₃	C₂	semidirect
16. #127×D₇₃	C₄	direct (N × H)
17. C₂×C₄×D₂₉₂	C₂²	semidirect
18. C₂×D₄×Dic₇₃	C₂²	semidirect
19. C₂×#14556553	C₂²	semidirect
20. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
21. C₂×#14556551	C₂²	semidirect
28. #17988490	C₂²	semidirect
29. #17988489	C₂²	semidirect
30. #17988488	C₂²	semidirect
31. #17988487	C₂²	semidirect
32. #17988457	C₂²	semidirect
33. #17988456	C₂²	semidirect
34. C₄²×Dic₇₃	C₂²	semidirect
35. C₄²×Dic₇₃	C₂²	semidirect
36. C₄²×Dic₇₃	C₂²	semidirect
38. C₂×C₄×D₄×C₇₃	C₂²	semidirect
39. #390×C₇₃	C₂²	semidirect
40. #384×C₇₃	C₂²	semidirect
41. C₄³×C₇₃	C₂²	semidirect
47. C₂×D₄×D₇₃	C₂×C₄	semidirect
56. #14556588	C₂×C₄	semidirect
57. #14556587	C₂×C₄	semidirect
77. C₄²×D₇₃	C₂×C₄	semidirect
78. C₄²×D₇₃	D₄	semidirect
81. #127×C₇₃	C₂×C₄	semidirect
95. C₂×D₂₉₂	C₂²×C₄	semidirect
98. C₂×C₂²⋊D₇₃	C₂²×C₄	semidirect
122. C₄×Dic₇₃	C₂²×C₄	semidirect
123. C₄×Dic₇₃	C₂×D₄	semidirect
124. C₄×Dic₇₃	C₂×D₄	semidirect
125. C₄×Dic₇₃	C₂×D₄	semidirect
129. C₂×D₄×C₇₃	C₂²×C₄	semidirect
138. C₄²×C₇₃	C₂²×C₄	semidirect
139. C₄²×C₇₃	C₂×D₄	semidirect
176. C₄×D₇₃	C₄×D₄	semidirect
177. C₄×D₇₃	#127	direct (N × H)
193. C₄×C₇₃	C₂×C₄×D₄	semidirect
194. C₄×C₇₃	C₂×#127	semidirect
197. Dic₇₃	C₂×C₄×D₄	semidirect
198. Dic₇₃	C₂×#127	semidirect
205. D₇₃	C₄×#127	direct (N × H)
213. C₄×#127	D₇₃	direct (N × H)
217. C₇₃	C₂×C₄×#127	semidirect
230. C₂×C₄×D₄	C₂×D₇₃	semidirect
240. #390	C₂×D₇₃	semidirect
243. #384	C₂×D₇₃	semidirect
247. C₄³	C₂×D₇₃	semidirect
266. #127	C₄×D₇₃	direct (N × H)
309. C₂×D₄	C₂×C₄×D₇₃	semidirect
344. C₄²	C₂×C₄×D₇₃	semidirect
345. C₄²	D₄×D₇₃	semidirect
403. C₄	C₄×D₄×D₇₃	semidirect
404. C₄	#127×D₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#127×D₇₃	2
C₂×C₄×D₄×D₇₃	2
#127×Dic₇₃	2
C₄×#14556588	2
#22612495	2
C₄×#14556587	2
#22612493	2
#390×D₇₃	2
#384×D₇₃	2
C₄³×D₇₃	2
C₄×#127×C₇₃	2
C₂×C₄×#127	73

Subgroups — C4×#127×D73 #33244494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#127×D₇₃ #33244494