Subgroups — C₄×#17989061 #33244221

Order 18688.

4186 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989061	C₂	1	2	yes	maximal
2	C₂²×C₄×D₂₉₂	C₂	1	1	yes	maximal, characteristic
3	#22612293	C₂	1	4	yes	maximal, complemented
4	#22612291	C₂	1	4	yes	maximal, complemented
5	#22612287	C₂	1	2	yes	maximal, complemented
6	#22612283	C₂	1	4	yes	maximal, complemented
7	C₄²×D₂₉₂	C₂	1	4	yes	maximal, complemented
8	C₄×#14556553	C₂	1	4	yes	maximal, complemented
9	C₄×#14556550	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₂²⋊C₄×D₇₃	C₂	1	4	yes	maximal, complemented
11	C₄×#117×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₂₉₂	C₂²	1	1	yes	characteristic
13	C₂³×C₄×D₇₃	C₂²	1	2	yes	—
14	#17989061	C₄	1	32	yes	direct product factor
15	C₂×C₄×D₂₉₂	C₄	1	16	yes	complemented
16	C₂×C₄×D₂₉₂	C₂²	1	2	yes	—
17	C₂×C₄×D₂₉₂	C₂²	1	2	yes	—
18	C₂×C₄×D₂₉₂	C₂²	1	8	yes	—
19	C₂×C₄×D₂₉₂	C₂²	1	2	yes	—
20	C₂×C₄×D₂₉₂	C₂²	1	2	yes	—
21	C₂×#14556553	C₂²	1	8	yes	—
22	C₂×#14556550	C₂²	1	2	yes	—
23	C₂²×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
24	C₂²×#11924005	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₄×D₇₃	C₂²	1	8	yes	—
26	C₂×C₄²×D₇₃	C₂²	1	8	yes	complemented
27	C₄⋊C₄×Dic₇₃	C₂²	1	8	yes	complemented
28	C₄×C₄⋊Dic₇₃	C₂²	1	2	yes	complemented
29	C₄×C₄⋊Dic₇₃	C₂²	1	2	yes	complemented
30	C₄×C₄⋊Dic₇₃	C₂²	1	8	yes	complemented
31	C₂²⋊C₄×Dic₇₃	C₂²	1	8	yes	—
32	C₄×#11924005	C₂²	1	8	yes	complemented
33	C₄×#11924005	C₂²	1	16	yes	complemented
34	C₄×C₂²⋊Dic₇₃	C₂²	1	2	yes	—
35	C₄×C₂²⋊Dic₇₃	C₂²	1	2	yes	—
36	#17988434	C₂²	1	8	yes	complemented
37	#17988434	C₂²	1	16	yes	complemented
38	#17988433	C₂²	1	2	yes	complemented
39	#95×D₇₃	C₂²	1	8	yes	complemented
40	C₄²×Dic₇₃	C₂²	1	2	yes	complemented
41	C₂×#117×C₇₃	C₂²	1	2	yes	—
42	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	complemented
44	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	complemented
45	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
46	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
47	#376×C₇₃	C₂²	1	2	yes	complemented
48	C₄³×C₇₃	C₂²	1	2	yes	complemented
49	C₂⁴×D₇₃	C₂³	1	2	yes	—
50	C₂²×D₂₉₂	C₂×C₄	1	8	yes	—
51	C₂²×D₂₉₂	C₂×C₄	1	16	yes	—
52	C₂²×D₂₉₂	C₂³	1	2	yes	—
53	C₂²×D₂₉₂	C₂³	1	2	yes	—
54	C₂³×Dic₇₃	C₂³	1	2	yes	—
55	C₂²×C₄×D₇₃	—	4	8	no	—
56	C₂²×C₄×D₇₃	C₂×C₄	1	16	yes	complemented
57	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
58	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
59	C₂²×C₄×D₇₃	C₂³	1	16	yes	—
60	C₄×D₂₉₂	C₂×C₄	1	16	yes	complemented
61	C₄×D₂₉₂	C₂×C₄	1	16	yes	complemented
62	C₄×D₂₉₂	C₂×C₄	1	16	yes	complemented
63	C₄×D₂₉₂	C₂×C₄	1	16	yes	complemented
64	C₄×D₂₉₂	C₂×C₄	1	64	yes	complemented
65	#14556553	C₂×C₄	1	64	yes	complemented
66	#14556550	C₂×C₄	1	16	yes	complemented
67	C₂×C₄⋊Dic₇₃	C₂×C₄	1	8	yes	complemented
68	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
69	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
70	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
71	C₂×C₂²⋊Dic₇₃	C₂³	1	4	yes	—
72	C₂×#11924005	C₂×C₄	1	16	yes	complemented
73	C₂×#11924005	C₂³	1	4	yes	—
74	C₂×#11924005	C₂³	1	4	yes	—
75	C₂×#11924005	C₂³	1	16	yes	—
76	C₂²⋊C₄×D₇₃	C₂×C₄	1	64	yes	complemented
77	C₂×C₄×Dic₇₃	C₂³	1	4	yes	—
78	C₂×C₄×Dic₇₃	C₂³	1	4	yes	—
79	C₂×C₄×Dic₇₃	C₂³	1	16	yes	—
80	C₂×C₄×Dic₇₃	C₂³	1	4	yes	—
81	C₄²×D₇₃	—	4	16	no	—
82	#14556498	C₂³	1	4	yes	—
83	#14556498	C₂³	1	16	yes	—
84	#14556498	C₂³	1	4	yes	—
85	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
88	#117×C₇₃	C₂×C₄	1	16	yes	complemented
89	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
91	C₂×C₄²×C₇₃	C₂×C₄	1	8	yes	complemented
92	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
93	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
94	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
99	#95×C₇₃	C₂³	1	4	yes	—
100	#95×C₇₃	C₂³	1	4	yes	—
101	C₂³×D₇₃	—	4	4	no	—
102	C₂³×D₇₃	—	4	4	no	—
103	C₂³×D₇₃	C₂²×C₄	1	16	yes	—
104	C₂³×D₇₃	C₂²×C₄	1	8	yes	—
105	C₂³×D₇₃	C₂⁴	1	4	yes	—
106	C₂×D₂₉₂	C₄²	1	64	yes	complemented
107	C₂×D₂₉₂	C₂²×C₄	1	16	yes	—
108	C₂×D₂₉₂	C₂²×C₄	1	8	yes	—
109	C₂×D₂₉₂	C₂²×C₄	1	8	yes	—
110	C₂×D₂₉₂	C₂²×C₄	1	16	yes	—
111	C₂²×Dic₇₃	—	4	4	no	—
112	C₂²×Dic₇₃	C₂²×C₄	1	8	yes	—
113	C₂²×Dic₇₃	C₂⁴	1	8	yes	—
114	C₂²×Dic₇₃	C₂⁴	1	4	yes	—
115	C₂×C₄×D₇₃	—	2	16	no	—
116	C₂×C₄×D₇₃	—	4	32	no	—
117	C₂×C₄×D₇₃	—	4	16	no	—
118	C₂×C₄×D₇₃	—	4	8	no	—
119	C₂×C₄×D₇₃	—	4	16	no	—
120	C₂×C₄×D₇₃	C₂²×C₄	1	16	yes	—
121	C₂×C₄×D₇₃	C₂²×C₄	1	16	yes	—
122	C₂×C₄×D₇₃	C₂²×C₄	1	64	yes	complemented
123	C₄⋊Dic₇₃	C₂²×C₄	1	8	yes	—
124	C₄⋊Dic₇₃	C₂²×C₄	1	8	yes	—
125	C₄⋊Dic₇₃	C₂²×C₄	1	16	yes	complemented
126	C₂²⋊Dic₇₃	C₂²×C₄	1	16	yes	—
127	#11924005	C₂²×C₄	1	16	yes	—
128	#11924005	C₂²×C₄	1	16	yes	—
129	#11924005	C₂²×C₄	1	64	yes	complemented
130	C₄×Dic₇₃	—	2	8	no	—
131	C₄×Dic₇₃	—	4	16	no	—
132	C₄×Dic₇₃	—	4	4	no	—
133	C₄×Dic₇₃	C₂²×C₄	1	16	yes	complemented
134	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
135	C₂²×C₄×C₇₃	—	2	4	no	—
136	C₂²×C₄×C₇₃	—	4	2	no	—
137	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
139	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₇₃	C₂²×C₄	1	8	yes	—
141	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₇₃	C₂⁴	1	8	yes	—
144	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
148	C₄⋊C₄×C₇₃	C₂²×C₄	1	16	yes	complemented
149	C₂²⋊C₄×C₇₃	C₂²×C₄	1	16	yes	—
150	C₄²×C₇₃	—	2	8	no	—
151	C₄²×C₇₃	—	4	4	no	—
152	C₄²×C₇₃	C₂²×C₄	1	4	yes	—
153	C₄²×C₇₃	C₂²×C₄	1	4	yes	—
154	C₄²×C₇₃	C₂²×C₄	1	4	yes	—
155	C₄²×C₇₃	C₂²×C₄	1	4	yes	—
156	C₄²×C₇₃	C₂²×C₄	1	16	yes	complemented
157	C₂³×C₇₃	—	2	2	no	—
158	C₂³×C₇₃	—	2	2	no	—
159	C₂³×C₇₃	C₂³×C₄	1	4	yes	—
160	C₂³×C₇₃	C₂³×C₄	1	2	yes	—
161	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
162	C₂²×D₇₃	—	2	8	no	—
163	C₂²×D₇₃	—	2	8	no	—
164	C₂²×D₇₃	—	4	8	no	—
165	C₂²×D₇₃	—	4	8	no	—
166	C₂²×D₇₃	—	4	32	no	—
167	C₂²×D₇₃	C₂×C₄²	1	32	yes	complemented
168	C₂²×D₇₃	C₂³×C₄	1	8	yes	—
169	C₂²×D₇₃	C₂³×C₄	1	16	yes	—
170	C₂×C₄×C₇₃	—	2	8	no	—
171	C₂×C₄×C₇₃	—	2	2	no	—
172	C₂×C₄×C₇₃	—	2	2	no	—
173	C₂×C₄×C₇₃	—	2	8	no	—
174	C₂×C₄×C₇₃	—	2	2	no	—
175	C₂×C₄×C₇₃	—	2	8	no	—
176	C₂×C₄×C₇₃	—	4	4	no	—
177	C₂×C₄×C₇₃	C₂×C₄²	1	16	yes	complemented
178	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
179	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
180	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
181	C₂×C₄×C₇₃	C₂³×C₄	1	16	yes	—
182	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
183	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
184	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
185	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
186	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
187	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	—
188	C₂×Dic₇₃	—	2	8	no	—
189	C₂×Dic₇₃	—	2	8	no	—
190	C₂×Dic₇₃	—	2	8	no	—
191	C₂×Dic₇₃	—	4	8	no	—
192	C₂×Dic₇₃	C₂³×C₄	1	16	yes	—
193	C₂×Dic₇₃	C₂³×C₄	1	8	yes	—
194	D₂₉₂	C₂×C₄²	1	32	yes	complemented
195	D₂₉₂	C₂×C₄²	1	32	yes	complemented
196	C₄×D₇₃	—	2	32	no	—
197	C₄×D₇₃	—	4	16	no	—
198	C₄×D₇₃	—	4	64	no	—
199	C₂²×C₇₃	—	2	2	no	—
200	C₂²×C₇₃	—	2	2	no	—
201	C₂²×C₇₃	—	2	8	no	—
202	C₂²×C₇₃	C₂²×C₄²	1	4	yes	—
203	C₂²×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
204	C₂²×C₇₃	C₂⁴×C₄	1	2	yes	—
205	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
206	C₂²×C₇₃	#585	1	2	yes	—
207	C₂×D₇₃	—	2	8	no	—
208	C₂×D₇₃	—	2	8	no	—
209	C₂×D₇₃	—	2	32	no	—
210	C₂×D₇₃	—	4	32	no	—
211	C₂×D₇₃	C₂²×C₄²	1	16	yes	—
212	C₄×C₇₃	—	2	2	no	—
213	C₄×C₇₃	—	2	2	no	—
214	C₄×C₇₃	—	2	2	no	—
215	C₄×C₇₃	—	2	16	no	—
216	C₄×C₇₃	C₂²×C₄²	1	4	yes	—
217	C₄×C₇₃	C₂²×C₄²	1	4	yes	—
218	C₄×C₇₃	#518	1	4	yes	complemented
219	Dic₇₃	—	2	8	no	—
220	Dic₇₃	—	2	16	no	—
221	C₄×#518	—	73	1	no	maximal, Sylow
222	C₂×C₇₃	—	2	4	no	—
223	C₂×C₇₃	C₂³×C₄²	1	1	yes	characteristic
224	C₂×C₇₃	C₂×#518	1	1	yes	characteristic
225	C₂×C₇₃	#3428	1	1	yes	characteristic
226	C₂×C₇₃	C₄×H(5,𝔽₂)	1	4	yes	—
227	D₇₃	—	2	16	no	—
228	C₂×#518	—	73	2	no	—
229	C₂²×C₄×D₄	—	73	1	no	—
230	#2275	—	73	4	no	—
231	#2275	—	73	4	no	—
232	#2274	—	73	2	no	—
233	#2273	—	73	4	no	—
234	C₄²×D₄	—	73	4	no	—
235	C₄²×D₄	—	73	4	no	—
236	C₄×#117	—	73	1	no	—
237	C₄×#117	D₇₃	1	1	yes	characteristic, complemented
238	C₂×C₄×C₂²⋊C₄	—	73	4	no	—
239	C₇₃	C₄×#518	1	1	yes	characteristic, complemented, Sylow
240	C₂³×D₄	—	73	1	no	—
241	C₂⁴×C₄	—	73	2	no	—
242	#518	—	73	32	no	—
243	C₂×C₄×D₄	—	73	8	no	—
244	C₂×C₄×D₄	—	73	16	no	—
245	C₂×C₄×D₄	—	73	2	no	—
246	C₂×C₄×D₄	—	73	2	no	—
247	C₂×C₄×D₄	—	73	2	no	—
248	C₂×C₄×D₄	—	73	2	no	—
249	C₂×C₄×D₄	—	73	8	no	—
250	C₂×#117	—	73	2	no	—
251	C₂×#117	C₂×D₇₃	1	2	yes	—
252	C₂²×C₄⋊C₄	—	73	1	no	—
253	C₂²×C₂²⋊C₄	—	73	2	no	—
254	C₂²×C₂²⋊C₄	—	73	8	no	—
255	C₂²×C₄²	—	73	8	no	—
256	C₂²×C₄²	C₂×D₇₃	1	1	yes	characteristic
257	C₄×C₄⋊C₄	—	73	8	no	—
258	C₄×C₄⋊C₄	—	73	2	no	—
259	C₄×C₄⋊C₄	—	73	2	no	—
260	C₄×C₄⋊C₄	—	73	8	no	—
261	C₄×C₄⋊C₄	C₂×D₇₃	1	2	yes	complemented
262	C₄×C₄⋊C₄	C₂×D₇₃	1	2	yes	complemented
263	C₄×C₂²⋊C₄	—	73	2	no	—
264	C₄×C₂²⋊C₄	—	73	2	no	—
265	C₄×C₂²⋊C₄	—	73	8	no	—
266	C₄×C₂²⋊C₄	—	73	8	no	—
267	C₄×C₂²⋊C₄	—	73	16	no	—
268	C₄×C₂²⋊C₄	—	73	8	no	—
269	C₄×C₂²⋊C₄	—	73	16	no	—
270	C₄×C₂²⋊C₄	C₂×D₇₃	1	2	yes	—
271	C₄×C₂²⋊C₄	C₂×D₇₃	1	2	yes	—
272	#376	—	73	2	no	—
273	#376	C₂×D₇₃	1	2	yes	complemented
274	C₂×#95	—	73	8	no	—
275	C₄³	—	73	2	no	—
276	C₄³	C₂×D₇₃	1	2	yes	complemented
277	C₂⁵	—	73	2	no	—
278	C₂²×D₄	—	73	8	no	—
279	C₂²×D₄	—	73	16	no	—
280	C₂²×D₄	—	73	2	no	—
281	C₂²×D₄	—	73	2	no	—
282	C₂³×C₄	—	292	8	no	—
283	C₂³×C₄	—	73	2	no	—
284	C₂³×C₄	—	73	16	no	—
285	C₂³×C₄	—	73	16	no	—
286	C₂³×C₄	—	73	4	no	—
287	C₂³×C₄	—	73	4	no	—
288	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
289	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
290	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
291	C₄×D₄	—	73	64	no	—
292	C₄×D₄	—	73	16	no	—
293	C₄×D₄	—	73	16	no	—
294	C₄×D₄	—	73	16	no	—
295	C₄×D₄	—	73	16	no	—
296	C₄×D₄	—	73	64	no	—
297	#117	—	73	16	no	—
298	#117	C₄×D₇₃	1	16	yes	complemented
299	C₂×C₄⋊C₄	—	73	8	no	—
300	C₂×C₄⋊C₄	—	73	2	no	—
301	C₂×C₄⋊C₄	—	73	2	no	—
302	C₂×C₄⋊C₄	—	73	4	no	—
303	C₂×C₄⋊C₄	C₂²×D₇₃	1	4	yes	—
304	C₂×C₂²⋊C₄	—	73	4	no	—
305	C₂×C₂²⋊C₄	—	73	16	no	—
306	C₂×C₂²⋊C₄	—	73	4	no	—
307	C₂×C₂²⋊C₄	—	73	4	no	—
308	C₂×C₂²⋊C₄	—	73	16	no	—
309	C₂×C₂²⋊C₄	—	73	64	no	—
310	C₂×C₂²⋊C₄	C₂²×D₇₃	1	4	yes	—
311	C₂×C₄²	—	292	16	no	—
312	C₂×C₄²	—	73	4	no	—
313	C₂×C₄²	—	73	16	no	—
314	C₂×C₄²	—	73	4	no	—
315	C₂×C₄²	—	73	4	no	—
316	C₂×C₄²	C₄×D₇₃	1	8	yes	complemented
317	C₂×C₄²	C₂²×D₇₃	1	4	yes	—
318	C₂×C₄²	C₂²×D₇₃	1	4	yes	—
319	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
320	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
321	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
322	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
323	C₂×C₄²	C₂²×D₇₃	1	4	yes	—
324	#95	—	73	4	no	—
325	#95	—	73	16	no	—
326	#95	—	73	4	no	—
327	#95	C₂²×D₇₃	1	4	yes	—
328	#95	C₂²×D₇₃	1	4	yes	—
329	C₂⁴	—	292	4	no	—
330	C₂⁴	—	292	4	no	—
331	C₂⁴	—	73	16	no	—
332	C₂⁴	—	73	8	no	—
333	C₂⁴	—	73	4	no	—
334	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
335	C₂×D₄	—	73	64	no	—
336	C₂×D₄	—	73	16	no	—
337	C₂×D₄	—	73	8	no	—
338	C₂×D₄	—	73	8	no	—
339	C₂×D₄	—	73	16	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	292	16	no	—
343	C₂²×C₄	—	292	8	no	—
344	C₂²×C₄	—	292	16	no	—
345	C₂²×C₄	—	292	32	no	—
346	C₂²×C₄	—	292	4	no	—
347	C₂²×C₄	—	73	8	no	—
348	C₂²×C₄	—	73	16	no	—
349	C₂²×C₄	—	73	64	no	—
350	C₂²×C₄	—	73	8	no	—
351	C₂²×C₄	—	73	4	no	—
352	C₂²×C₄	—	73	16	no	—
353	C₂²×C₄	—	146	16	no	—
354	C₂²×C₄	C₂×C₄×D₇₃	1	4	yes	—
355	C₂²×C₄	C₂×C₄×D₇₃	1	4	yes	—
356	C₂²×C₄	C₂×C₄×D₇₃	1	4	yes	—
357	C₂²×C₄	C₂×C₄×D₇₃	1	8	yes	—
358	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
359	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
360	C₂²×C₄	C₂³×D₇₃	1	8	yes	—
361	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
362	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
363	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
364	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
365	C₄⋊C₄	—	73	8	no	—
366	C₄⋊C₄	—	73	8	no	—
367	C₄⋊C₄	—	73	16	no	—
368	C₄⋊C₄	C₂×C₄×D₇₃	1	16	yes	complemented
369	C₂²⋊C₄	—	73	16	no	—
370	C₂²⋊C₄	—	73	16	no	—
371	C₂²⋊C₄	—	73	16	no	—
372	C₂²⋊C₄	—	73	64	no	—
373	C₂²⋊C₄	C₂×C₄×D₇₃	1	16	yes	—
374	C₄²	—	2	8	no	—
375	C₄²	—	4	4	no	—
376	C₄²	—	292	16	no	—
377	C₄²	—	292	4	no	—
378	C₄²	—	73	16	no	—
379	C₄²	—	146	8	no	—
380	C₄²	C₂×C₄×D₇₃	1	4	yes	—
381	C₄²	C₂×C₄×D₇₃	1	4	yes	—
382	C₄²	C₂×C₄×D₇₃	1	4	yes	—
383	C₄²	C₂×C₄×D₇₃	1	4	yes	—
384	C₄²	C₂×C₄×D₇₃	1	16	yes	complemented
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	292	8	no	—
388	C₂³	—	292	8	no	—
389	C₂³	—	292	32	no	—
390	C₂³	—	73	32	no	—
391	C₂³	—	73	8	no	—
392	C₂³	—	73	16	no	—
393	C₂³	—	146	8	no	—
394	C₂³	—	146	8	no	—
395	C₂³	C₂²×C₄×D₇₃	1	4	yes	—
396	C₂³	C₂²×C₄×D₇₃	1	2	yes	—
397	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
398	D₄	—	73	32	no	—
399	D₄	—	73	32	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	292	16	no	—
408	C₂×C₄	—	292	64	no	—
409	C₂×C₄	—	292	8	no	—
410	C₂×C₄	—	73	16	no	—
411	C₂×C₄	—	73	8	no	—
412	C₂×C₄	—	146	8	no	—
413	C₂×C₄	—	146	8	no	—
414	C₂×C₄	—	146	8	no	—
415	C₂×C₄	—	146	32	no	—
416	C₂×C₄	C₄²×D₇₃	1	16	yes	complemented
417	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
418	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
419	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
420	C₂×C₄	C₂²×C₄×D₇₃	1	16	yes	—
421	C₂×C₄	C₂²×C₄×D₇₃	1	4	yes	—
422	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
423	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
424	C₂×C₄	C₂²×C₄×D₇₃	1	4	yes	—
425	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
426	C₂×C₄	#14556637	1	4	yes	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	8	no	—
430	C₂²	—	292	32	no	—
431	C₂²	—	73	16	no	—
432	C₂²	—	146	8	no	—
433	C₂²	—	146	8	no	—
434	C₂²	—	146	32	no	—
435	C₂²	C₂×C₄²×D₇₃	1	4	yes	—
436	C₂²	C₂³×C₄×D₇₃	1	1	yes	characteristic
437	C₂²	C₂³×C₄×D₇₃	1	2	yes	—
438	C₂²	C₂×#14556637	1	2	yes	—
439	C₂²	#17989423	1	2	yes	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	16	no	—
444	C₄	—	146	8	no	—
445	C₄	—	146	16	no	—
446	C₄	C₂×C₄²×D₇₃	1	4	yes	—
447	C₄	C₂×C₄²×D₇₃	1	4	yes	—
448	C₄	#17989061	1	4	yes	direct product factor
449	C₂	—	2	4	no	—
450	C₂	—	146	16	no	—
451	C₂	C₂²×C₄²×D₇₃	1	1	yes	characteristic
452	C₂	C₂×#17989061	1	1	yes	characteristic
453	C₂	#22623132	1	1	yes	characteristic
454	C₂	C₄×#14556637	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇₃
commutator	C₂×C₇₃	C₂³×C₄²
Frattini	C₂³	C₂⁴×D₇₃
Fitting	C₄×#117×C₇₃	C₂
socle, cosocle	C₂³×C₇₃	C₂⁵
prime radical	C₂³×D₂₉₂	C₂²
hypercenter	C₄×#117	D₇₃
hypocenter	C₇₃	C₄×#518
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
3. #22612293	C₂	semidirect
4. #22612291	C₂	semidirect
5. #22612287	C₂	semidirect
6. #22612283	C₂	semidirect
7. C₄²×D₂₉₂	C₂	semidirect
8. C₄×#14556553	C₂	semidirect
9. C₄×#14556550	C₂	semidirect
10. C₄×C₂²⋊C₄×D₇₃	C₂	semidirect
11. C₄×#117×C₇₃	C₂	semidirect
14. #17989061	C₄	direct (N × H)
15. C₂×C₄×D₂₉₂	C₄	semidirect
26. C₂×C₄²×D₇₃	C₂²	semidirect
27. C₄⋊C₄×Dic₇₃	C₂²	semidirect
28. C₄×C₄⋊Dic₇₃	C₂²	semidirect
29. C₄×C₄⋊Dic₇₃	C₂²	semidirect
30. C₄×C₄⋊Dic₇₃	C₂²	semidirect
32. C₄×#11924005	C₂²	semidirect
33. C₄×#11924005	C₂²	semidirect
36. #17988434	C₂²	semidirect
37. #17988434	C₂²	semidirect
38. #17988433	C₂²	semidirect
39. #95×D₇₃	C₂²	semidirect
40. C₄²×Dic₇₃	C₂²	semidirect
43. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
44. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
47. #376×C₇₃	C₂²	semidirect
48. C₄³×C₇₃	C₂²	semidirect
56. C₂²×C₄×D₇₃	C₂×C₄	semidirect
60. C₄×D₂₉₂	C₂×C₄	semidirect
61. C₄×D₂₉₂	C₂×C₄	semidirect
62. C₄×D₂₉₂	C₂×C₄	semidirect
63. C₄×D₂₉₂	C₂×C₄	semidirect
64. C₄×D₂₉₂	C₂×C₄	semidirect
65. #14556553	C₂×C₄	semidirect
66. #14556550	C₂×C₄	semidirect
67. C₂×C₄⋊Dic₇₃	C₂×C₄	semidirect
72. C₂×#11924005	C₂×C₄	semidirect
76. C₂²⋊C₄×D₇₃	C₂×C₄	semidirect
88. #117×C₇₃	C₂×C₄	semidirect
91. C₂×C₄²×C₇₃	C₂×C₄	semidirect
106. C₂×D₂₉₂	C₄²	semidirect
122. C₂×C₄×D₇₃	C₂²×C₄	semidirect
125. C₄⋊Dic₇₃	C₂²×C₄	semidirect
129. #11924005	C₂²×C₄	semidirect
133. C₄×Dic₇₃	C₂²×C₄	semidirect
148. C₄⋊C₄×C₇₃	C₂²×C₄	semidirect
156. C₄²×C₇₃	C₂²×C₄	semidirect
167. C₂²×D₇₃	C₂×C₄²	semidirect
177. C₂×C₄×C₇₃	C₂×C₄²	semidirect
194. D₂₉₂	C₂×C₄²	semidirect
195. D₂₉₂	C₂×C₄²	semidirect
218. C₄×C₇₃	#518	semidirect
237. C₄×#117	D₇₃	semidirect
239. C₇₃	C₄×#518	semidirect
261. C₄×C₄⋊C₄	C₂×D₇₃	semidirect
262. C₄×C₄⋊C₄	C₂×D₇₃	semidirect
273. #376	C₂×D₇₃	semidirect
276. C₄³	C₂×D₇₃	semidirect
298. #117	C₄×D₇₃	semidirect
316. C₂×C₄²	C₄×D₇₃	semidirect
368. C₄⋊C₄	C₂×C₄×D₇₃	semidirect
384. C₄²	C₂×C₄×D₇₃	semidirect
416. C₂×C₄	C₄²×D₇₃	semidirect
448. C₄	#17989061	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×#17989061	2
C₂²×C₄×D₂₉₂	2
#22612293	2
#22612291	2
#22612287	2
#22612283	2
C₄²×D₂₉₂	2
C₄×#14556553	2
C₄×#14556550	2
C₄×C₂²⋊C₄×D₇₃	2
C₄×#117×C₇₃	2
C₄×#518	73

Subgroups — C4×#17989061 #33244221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#17989061 #33244221