Subgroups — #32991821

Order 18688.

898 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988611	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988355	C₂	1	4	yes	maximal
4	C₂×#423×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11924012	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₇₃	C₂²	1	2	yes	—
7	C₂²×C₄×Dic₇₃	C₄	1	2	yes	—
8	#17988611	—	2	2	no	—
9	#17988611	C₄	1	4	yes	complemented
10	C₂×C₄⋊#10596831	—	2	1	no	—
11	C₂×C₄⋊#10596831	—	2	1	no	—
12	C₄×C₄⋊Dic₇₃	—	2	1	no	—
13	C₄×C₄⋊Dic₇₃	—	2	1	no	—
14	C₄×C₄⋊Dic₇₃	—	2	1	no	—
15	C₄×C₄⋊Dic₇₃	—	2	1	no	—
16	C₂×#14556498	C₄	1	2	yes	—
17	#17988355	—	2	8	no	—
18	C₂²×M₁₆×C₇₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
20	#423×C₇₃	—	2	2	no	—
21	#423×C₇₃	C₄	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₇₃	—	2	1	no	—
23	C₂×C₄⋊C₈×C₇₃	—	2	1	no	—
24	C₂³×Dic₇₃	C₂×C₄	1	4	yes	—
25	C₂×#11924012	—	2	2	no	—
26	C₂×#11924012	—	2	4	no	—
27	C₂×#11924012	—	2	4	no	—
28	C₂×#11924012	C₂×C₄	1	4	yes	—
29	C₂²×#10596831	—	2	2	no	—
30	C₂×C₄⋊Dic₇₃	—	2	2	no	—
31	C₂×C₄⋊Dic₇₃	—	2	2	no	—
32	C₂×C₄⋊Dic₇₃	—	2	2	no	—
33	C₂×C₄⋊Dic₇₃	—	2	2	no	—
34	C₂×C₄⋊Dic₇₃	D₄	1	4	yes	—
35	C₂×C₄⋊Dic₇₃	Q₈	1	4	yes	—
36	C₂×C₄×Dic₇₃	—	2	2	no	—
37	C₂×C₄×Dic₇₃	—	2	2	no	—
38	C₂×C₄×Dic₇₃	—	4	4	no	—
39	C₄⋊#10596831	—	2	4	no	—
40	C₄⋊#10596831	—	2	4	no	—
41	#14556498	—	2	2	no	—
42	#14556498	—	2	2	no	—
43	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₇₃	—	2	2	no	—
47	C₂×M₁₆×C₇₃	—	2	4	no	—
48	C₂×M₁₆×C₇₃	—	2	4	no	—
49	C₂×M₁₆×C₇₃	C₂×C₄	1	4	yes	—
50	C₂²×C₈×C₇₃	—	2	2	no	—
51	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₇₃	D₄	1	2	yes	—
54	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₇₃	Q₈	1	2	yes	—
59	C₄⋊C₈×C₇₃	—	2	4	no	—
60	C₄⋊C₈×C₇₃	—	2	4	no	—
61	C₂²×Dic₇₃	—	2	4	no	—
62	C₂²×Dic₇₃	—	2	4	no	—
63	C₂²×Dic₇₃	—	4	4	no	—
64	C₂²×Dic₇₃	—	4	4	no	—
65	C₂²×Dic₇₃	C₄⋊C₄	1	8	yes	—
66	#11924012	—	2	8	no	—
67	#11924012	—	4	2	no	—
68	#11924012	—	4	2	no	—
69	C₂×#10596831	—	2	4	no	—
70	C₂×#10596831	—	4	4	no	—
71	C₄⋊Dic₇₃	—	2	4	no	—
72	C₄⋊Dic₇₃	—	2	4	no	—
73	C₄⋊Dic₇₃	—	2	4	no	—
74	C₄⋊Dic₇₃	—	2	4	no	—
75	C₄×Dic₇₃	—	4	4	no	—
76	C₄×Dic₇₃	—	4	4	no	—
77	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₇₃	—	2	2	no	—
79	C₂²×C₄×C₇₃	—	2	2	no	—
80	C₂²×C₄×C₇₃	—	4	2	no	—
81	C₂²×C₄×C₇₃	C₄²	1	2	yes	—
82	C₂²×C₄×C₇₃	C₄²	1	2	yes	—
83	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
88	C₂²×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
89	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₇₃	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₇₃	#41	1	2	yes	—
98	C₂²×C₄×C₇₃	#41	1	2	yes	—
99	M₁₆×C₇₃	—	2	8	no	—
100	M₁₆×C₇₃	—	4	2	no	—
101	M₁₆×C₇₃	—	4	2	no	—
102	C₂×C₈×C₇₃	—	2	4	no	—
103	C₂×C₈×C₇₃	—	4	4	no	—
104	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
105	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
106	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
107	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
108	C₄²×C₇₃	C₄⋊C₄	1	2	yes	—
109	C₄²×C₇₃	C₄⋊C₄	1	2	yes	—
110	C₄²×C₇₃	C₄⋊C₄	1	2	yes	—
111	C₄²×C₇₃	C₄⋊C₄	1	2	yes	—
112	C₂³×C₇₃	—	2	1	no	—
113	C₂³×C₇₃	—	2	1	no	—
114	C₂³×C₇₃	—	2	2	no	—
115	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
116	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂³×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
118	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂³×C₇₃	#117	1	2	yes	—
120	C₂×C₄×C₇₃	—	2	1	no	—
121	C₂×C₄×C₇₃	—	2	1	no	—
122	C₂×C₄×C₇₃	—	2	2	no	—
123	C₂×C₄×C₇₃	—	2	2	no	—
124	C₂×C₄×C₇₃	—	2	4	no	—
125	C₂×C₄×C₇₃	—	2	4	no	—
126	C₂×C₄×C₇₃	—	4	2	no	—
127	C₂×C₄×C₇₃	—	4	2	no	—
128	C₂×C₄×C₇₃	#95	1	2	yes	—
129	C₂×C₄×C₇₃	#95	1	2	yes	—
130	C₂×C₄×C₇₃	#95	1	2	yes	—
131	C₂×C₄×C₇₃	#95	1	2	yes	—
132	C₂×C₄×C₇₃	#100	1	2	yes	—
133	C₂×C₄×C₇₃	#101	1	2	yes	—
134	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
139	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
140	C₂×C₄×C₇₃	C₄×Q₈	1	2	yes	—
141	C₂×C₄×C₇₃	C₄×Q₈	1	2	yes	—
142	C₂×C₄×C₇₃	#121	1	2	yes	—
143	C₂×C₄×C₇₃	#121	1	2	yes	—
144	C₂×C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
145	C₂×C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
146	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
147	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
148	C₂×C₄×C₇₃	#125	1	2	yes	—
149	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
150	C₂×C₄×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₇₃	C₄⋊Q₈	1	2	yes	—
152	C₂×Dic₇₃	—	2	8	no	—
153	C₂×Dic₇₃	—	4	8	no	—
154	C₂×Dic₇₃	—	4	4	no	—
155	C₂×Dic₇₃	—	4	4	no	—
156	C₂×Dic₇₃	—	4	8	no	—
157	C₈×C₇₃	—	4	4	no	—
158	#10596831	—	4	4	no	—
159	C₂²×C₇₃	—	2	2	no	—
160	C₂²×C₇₃	—	2	2	no	—
161	C₂²×C₇₃	—	2	2	no	—
162	C₂²×C₇₃	—	2	2	no	—
163	C₂²×C₇₃	—	2	1	no	—
164	C₂²×C₇₃	—	2	1	no	—
165	C₂²×C₇₃	—	2	1	no	—
166	C₂²×C₇₃	—	2	1	no	—
167	C₂²×C₇₃	C₂×#95	1	1	yes	characteristic
168	C₂²×C₇₃	C₄×C₄⋊C₄	1	2	yes	—
169	C₂²×C₇₃	#380	1	2	yes	—
170	C₂²×C₇₃	#382	1	1	yes	characteristic
171	C₂²×C₇₃	#384	1	1	yes	characteristic
172	C₂²×C₇₃	C₂×#100	1	1	yes	characteristic
173	C₂²×C₇₃	C₂×#101	1	1	yes	characteristic
174	C₂²×C₇₃	#413	1	2	yes	—
175	C₄×C₇₃	—	2	2	no	—
176	C₄×C₇₃	—	2	2	no	—
177	C₄×C₇₃	—	2	2	no	—
178	C₄×C₇₃	#343	1	4	yes	complemented
179	C₄×C₇₃	#389	1	2	yes	—
180	C₄×C₇₃	#389	1	2	yes	—
181	C₄×C₇₃	#390	1	1	yes	characteristic
182	C₄×C₇₃	#390	1	1	yes	characteristic
183	C₄×C₇₃	#391	1	1	yes	characteristic
184	C₄×C₇₃	#391	1	1	yes	characteristic
185	Dic₇₃	—	4	8	no	—
186	#10847	—	73	1	no	maximal, Sylow
187	C₂×C₇₃	—	2	2	no	—
188	C₂×C₇₃	—	2	1	no	—
189	C₂×C₇₃	—	2	1	no	—
190	C₂×C₇₃	C₄⋊#95	1	1	yes	characteristic
191	C₂×C₇₃	C₂×#343	1	1	yes	characteristic
192	C₂×C₇₃	#1742	1	1	yes	characteristic
193	C₂×C₇₃	#1800	1	2	yes	—
194	C₂×C₇₃	#1801	1	2	yes	—
195	C₂×#423	—	73	1	no	—
196	C₂×#423	D₇₃	1	1	yes	characteristic
197	C₂×C₄×C₄⋊C₄	—	73	1	no	—
198	C₂×#343	—	73	4	no	—
199	C₇₃	#10847	1	1	yes	characteristic, complemented, Sylow
200	C₂²×M₁₆	—	73	2	no	—
201	C₂²×M₁₆	C₂×D₇₃	1	2	yes	—
202	C₂²×C₄⋊C₄	—	73	2	no	—
203	C₂²×C₄²	—	73	2	no	—
204	C₂²×C₄²	C₂×D₇₃	1	1	yes	characteristic
205	#423	—	2	2	no	—
206	#423	—	73	4	no	—
207	#423	—	146	2	no	—
208	#423	Dic₇₃	1	4	yes	complemented
209	C₂×C₄⋊C₈	—	2	1	no	—
210	C₂×C₄⋊C₈	—	2	1	no	—
211	C₂×C₄⋊C₈	—	146	1	no	—
212	C₂×C₄⋊C₈	—	146	1	no	—
213	C₄×C₄⋊C₄	—	146	1	no	—
214	C₄×C₄⋊C₄	—	146	1	no	—
215	C₄×C₄⋊C₄	—	146	1	no	—
216	C₄×C₄⋊C₄	—	146	1	no	—
217	C₂×#95	—	73	2	no	—
218	#343	—	146	8	no	—
219	C₂³×C₄	—	73	4	no	—
220	C₂³×C₄	C₄×D₇₃	1	1	yes	characteristic
221	C₂³×C₄	C₄×D₇₃	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	4	no	—
225	C₂×M₁₆	—	2	4	no	—
226	C₂×M₁₆	—	73	4	no	—
227	C₂×M₁₆	—	146	4	no	—
228	C₂×M₁₆	—	146	4	no	—
229	C₂×M₁₆	—	146	2	no	—
230	C₂×M₁₆	C₂×Dic₇₃	1	4	yes	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	146	2	no	—
233	C₂×C₄⋊C₄	—	73	4	no	—
234	C₂×C₄⋊C₄	—	73	4	no	—
235	C₂×C₄⋊C₄	—	146	2	no	—
236	C₂×C₄⋊C₄	—	146	2	no	—
237	C₂×C₄⋊C₄	—	146	2	no	—
238	C₂×C₄⋊C₄	—	146	2	no	—
239	C₂×C₄²	—	292	4	no	—
240	C₂×C₄²	—	146	2	no	—
241	C₂×C₄²	—	146	2	no	—
242	C₂×C₄²	Dic₁₄₆	1	2	yes	—
243	C₂×C₄²	C₄×D₇₃	1	2	yes	—
244	C₂×C₄²	D₂₉₂	1	1	yes	characteristic
245	C₂×C₄²	D₂₉₂	1	1	yes	characteristic
246	C₂×C₄²	C₂×Dic₇₃	1	2	yes	—
247	C₂×C₄²	C₂²⋊D₇₃	1	2	yes	—
248	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
249	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
250	C₄⋊C₈	—	2	4	no	—
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	146	4	no	—
253	C₄⋊C₈	—	146	4	no	—
254	#95	—	146	2	no	—
255	#95	—	146	2	no	—
256	C₂⁴	C₂×C₄×D₇₃	1	1	yes	characteristic
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	292	4	no	—
261	C₂²×C₄	—	292	4	no	—
262	C₂²×C₄	—	73	8	no	—
263	C₂²×C₄	—	146	4	no	—
264	C₂²×C₄	—	146	4	no	—
265	C₂²×C₄	C₄×Dic₇₃	1	2	yes	—
266	C₂²×C₄	C₄×Dic₇₃	1	2	yes	—
267	C₂²×C₄	#11924005	1	1	yes	characteristic
268	C₂²×C₄	#11924005	1	1	yes	characteristic
269	C₂²×C₄	#11924005	1	1	yes	characteristic
270	C₂²×C₄	#11924005	1	1	yes	characteristic
271	C₂²×C₄	#11924007	1	2	yes	—
272	C₂²×C₄	#11924007	1	2	yes	—
273	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
274	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
275	C₂²×C₄	D₄×D₇₃	1	2	yes	—
276	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
279	C₂²×C₄	Q₈×D₇₃	1	2	yes	—
280	C₂²×C₄	C₂×Dic₁₄₆	1	1	yes	characteristic
281	C₂²×C₄	#11924027	1	2	yes	—
282	C₂²×C₄	#11924029	1	2	yes	—
283	M₁₆	—	2	8	no	—
284	M₁₆	—	4	2	no	—
285	M₁₆	—	4	2	no	—
286	M₁₆	—	292	2	no	—
287	M₁₆	—	292	2	no	—
288	M₁₆	—	146	8	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	4	4	no	—
291	C₂×C₈	—	292	4	no	—
292	C₂×C₈	—	146	4	no	—
293	C₄⋊C₄	—	146	4	no	—
294	C₄⋊C₄	—	146	4	no	—
295	C₄⋊C₄	—	146	4	no	—
296	C₄⋊C₄	—	146	4	no	—
297	C₄²	—	292	4	no	—
298	C₄²	—	292	4	no	—
299	C₄²	#11924005	1	2	yes	—
300	C₄²	#11924005	1	2	yes	—
301	C₄²	C₂²⋊Dic₇₃	1	2	yes	—
302	C₄²	C₂²⋊Dic₇₃	1	2	yes	—
303	C₄²	#11924007	1	2	yes	—
304	C₄²	#11924007	1	2	yes	—
305	C₄²	C₄⋊Dic₇₃	1	2	yes	—
306	C₄²	C₄⋊Dic₇₃	1	2	yes	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	2	no	—
310	C₂³	C₂×C₄×Dic₇₃	1	1	yes	characteristic
311	C₂³	C₂×#11924005	1	1	yes	characteristic
312	C₂³	C₄⋊C₄×D₇₃	1	2	yes	—
313	C₂³	C₂×#11924007	1	1	yes	characteristic
314	C₂³	#14556549	1	2	yes	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	292	8	no	—
324	C₂×C₄	—	292	4	no	—
325	C₂×C₄	—	292	4	no	—
326	C₂×C₄	—	292	8	no	—
327	C₂×C₄	—	146	8	no	—
328	C₂×C₄	#14556498	1	2	yes	—
329	C₂×C₄	#14556498	1	2	yes	—
330	C₂×C₄	#14556498	1	2	yes	—
331	C₂×C₄	#14556498	1	2	yes	—
332	C₂×C₄	#14556507	1	2	yes	—
333	C₂×C₄	#14556509	1	2	yes	—
334	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
335	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
336	C₂×C₄	C₂×#11924007	1	1	yes	characteristic
337	C₂×C₄	C₂×C₄⋊Dic₇₃	1	1	yes	characteristic
338	C₂×C₄	#14556553	1	2	yes	—
339	C₂×C₄	D₄×Dic₇₃	1	2	yes	—
340	C₂×C₄	#14556556	1	2	yes	—
341	C₂×C₄	Q₈×Dic₇₃	1	2	yes	—
342	C₂×C₄	#14556562	1	2	yes	—
343	C₂×C₄	#14556566	1	2	yes	—
344	C₂×C₄	#14556567	1	2	yes	—
345	C₂×C₄	#14556571	1	2	yes	—
346	C₂×C₄	#14556578	1	1	yes	characteristic
347	C₂×C₄	#14556580	1	1	yes	characteristic
348	C₂×C₄	#14556582	1	2	yes	—
349	C₂×C₄	#14556587	1	1	yes	characteristic
350	C₂×C₄	#14556589	1	1	yes	characteristic
351	C₂×C₄	#14556590	1	2	yes	—
352	C₈	—	4	4	no	—
353	C₈	—	292	4	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	C₂×#14556498	1	1	yes	characteristic
363	C₂²	C₄⋊C₄×Dic₇₃	1	2	yes	—
364	C₂²	#17988444	1	2	yes	—
365	C₂²	#17988452	1	1	yes	characteristic
366	C₂²	#17988456	1	1	yes	characteristic
367	C₂²	C₂×#14556507	1	1	yes	characteristic
368	C₂²	C₂×#14556509	1	1	yes	characteristic
369	C₂²	#17988569	1	2	yes	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	292	8	no	—
374	C₄	#17988355	1	4	yes	complemented
375	C₄	#17988483	1	2	yes	—
376	C₄	#17988486	1	2	yes	—
377	C₄	#17988488	1	1	yes	characteristic
378	C₄	#17988490	1	1	yes	characteristic
379	C₄	#17988492	1	1	yes	characteristic
380	C₄	#17988494	1	1	yes	characteristic
381	C₂	—	2	2	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	#22608160	1	1	yes	characteristic
385	C₂	C₂×#17988355	1	1	yes	characteristic
386	C₂	#22609669	1	1	yes	characteristic
387	C₂	#22609920	1	2	yes	—
388	C₂	#22609924	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×#11924005
commutator	C₂³×C₇₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₃
Fitting	C₂×#423×C₇₃	C₂
socle	C₂³×C₇₃	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₇₃	C₂²×C₄
cosocle	C₂³×C₄×C₇₃	C₂³
hypercenter	C₂×#423	D₇₃
hypocenter	C₇₃	#10847
LCS	G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
9. #17988611	C₄	semidirect
21. #423×C₇₃	C₄	semidirect
178. C₄×C₇₃	#343	semidirect
199. C₇₃	#10847	semidirect
208. #423	Dic₇₃	semidirect
374. C₄	#17988355	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988611	2
C₂×C₄×C₄⋊Dic₇₃	2
C₂×#17988355	2
C₂×#423×C₇₃	2
#10847	73