Subgroups — #32991934

Order 18688.

714 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556527	C₂	1	1	yes	maximal, characteristic
2	C₂²×#14556527	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988357	C₂	1	2	yes	maximal
4	#22609657	C₂	1	2	yes	maximal
5	C₂×#405×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11924012	C₂²	1	2	yes	—
7	C₂²×#11924012	C₂²	1	2	yes	—
8	C₂×#14556527	—	2	2	no	—
9	C₂×#14556527	—	2	2	no	—
10	C₂×#14556527	—	2	1	no	—
11	C₂×#14556527	—	2	1	no	—
12	C₂×#14556527	—	2	2	no	—
13	C₂×#14556527	C₄	1	4	yes	complemented
14	C₂×#14556527	C₄	1	4	yes	complemented
15	#17988357	—	2	4	no	—
16	#17988351	—	2	4	no	—
17	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
20	#405×C₇₃	—	2	2	no	—
21	#405×C₇₃	C₄	1	4	yes	—
22	C₂×#97×C₇₃	—	2	1	no	—
23	C₂×C₄×C₈×C₇₃	—	2	1	no	—
24	C₂×#11924012	—	2	2	no	—
25	C₂×#11924012	—	2	2	no	—
26	C₂×#11924012	—	2	2	no	—
27	C₂×#11924012	—	2	2	no	—
28	C₂×#11924012	—	2	2	no	—
29	C₂×#11924012	—	2	2	no	—
30	C₂×#11924012	—	2	2	no	—
31	C₂×#11924012	—	2	2	no	—
32	C₂×#11924012	—	2	2	no	—
33	C₂×#11924012	—	2	2	no	—
34	C₂×#11924012	C₂×C₄	1	4	yes	—
35	C₂×#11924012	C₂×C₄	1	4	yes	—
36	C₂²×#10596831	—	2	2	no	—
37	C₂²×#10596831	—	2	2	no	—
38	#14556527	—	2	4	no	—
39	#14556527	—	2	4	no	—
40	#14556527	—	2	8	no	—
41	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₇₃	—	2	1	no	—
43	C₂×M₁₆×C₇₃	—	2	1	no	—
44	C₂×M₁₆×C₇₃	—	2	1	no	—
45	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
46	C₂×M₁₆×C₇₃	D₄	1	2	yes	—
47	C₂×M₁₆×C₇₃	Q₈	1	2	yes	—
48	C₂²×C₈×C₇₃	—	2	1	no	—
49	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
50	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
52	C₂²×C₈×C₇₃	D₄	1	2	yes	—
53	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₇₃	D₄	1	2	yes	—
56	C₂²×C₈×C₇₃	Q₈	1	2	yes	—
57	#117×C₇₃	—	2	1	no	—
58	#117×C₇₃	—	2	1	no	—
59	#117×C₇₃	C₂×C₄	1	2	yes	—
60	#117×C₇₃	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₇₃	Q₈	1	2	yes	—
63	C₂×C₄²×C₇₃	—	2	1	no	—
64	#97×C₇₃	—	2	4	no	—
65	C₄×C₈×C₇₃	—	2	4	no	—
66	#11924012	—	2	4	no	—
67	#11924012	—	2	4	no	—
68	#11924012	—	2	4	no	—
69	#11924012	—	2	4	no	—
70	#11924012	—	4	2	no	—
71	#11924012	—	4	2	no	—
72	#11924012	—	4	2	no	—
73	#11924012	—	4	2	no	—
74	C₂×#10596831	—	2	4	no	—
75	C₂×#10596831	—	2	4	no	—
76	C₂×#10596831	—	4	2	no	—
77	C₂×#10596831	—	4	2	no	—
78	C₂×#10596831	—	4	2	no	—
79	C₂×#10596831	—	4	2	no	—
80	C₂⁴×C₇₃	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₇₃	—	2	2	no	—
82	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
93	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
94	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
95	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
96	M₁₆×C₇₃	—	2	2	no	—
97	M₁₆×C₇₃	—	2	2	no	—
98	M₁₆×C₇₃	—	2	2	no	—
99	M₁₆×C₇₃	C₄⋊C₄	1	4	yes	—
100	C₂×C₈×C₇₃	—	2	2	no	—
101	C₂×C₈×C₇₃	—	2	2	no	—
102	C₂×C₈×C₇₃	—	2	2	no	—
103	C₂×C₈×C₇₃	C₄²	1	4	yes	—
104	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
105	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
106	C₂×C₈×C₇₃	C₂²⋊C₄	1	4	yes	—
107	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
108	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
109	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
110	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
111	C₂×C₈×C₇₃	C₄⋊C₄	1	4	yes	—
112	C₂×C₈×C₇₃	C₄⋊C₄	1	4	yes	—
113	C₄⋊C₄×C₇₃	—	2	2	no	—
114	C₄⋊C₄×C₇₃	—	2	2	no	—
115	C₂²⋊C₄×C₇₃	—	2	2	no	—
116	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	4	yes	—
117	C₄²×C₇₃	—	2	2	no	—
118	C₄²×C₇₃	—	2	2	no	—
119	C₂³×C₇₃	—	4	2	no	—
120	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₇₃	C₄×Q₈	1	1	yes	characteristic
122	C₂³×C₇₃	C₄×Q₈	1	1	yes	characteristic
123	C₂³×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
124	C₂³×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
125	C₂³×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
126	C₂³×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
127	C₂×C₄×C₇₃	—	2	4	no	—
128	C₂×C₄×C₇₃	—	4	4	no	—
129	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
130	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
138	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
139	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
146	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
147	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
148	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
149	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
152	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
153	C₂×C₄×C₇₃	#125	1	1	yes	characteristic
154	C₂×C₄×C₇₃	#125	1	1	yes	characteristic
155	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
156	C₂×C₄×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
157	C₈×C₇₃	—	2	4	no	—
158	C₈×C₇₃	#95	1	4	yes	—
159	C₈×C₇₃	#95	1	4	yes	—
160	#10596831	—	4	4	no	—
161	#10596831	—	4	4	no	—
162	C₂²×C₇₃	—	2	2	no	—
163	C₂²×C₇₃	—	2	2	no	—
164	C₂²×C₇₃	—	2	2	no	—
165	C₂²×C₇₃	—	4	1	no	—
166	C₂²×C₇₃	—	4	1	no	—
167	C₂²×C₇₃	—	4	1	no	—
168	C₂²×C₇₃	—	4	1	no	—
169	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
170	C₂²×C₇₃	#380	1	1	yes	characteristic
171	C₂²×C₇₃	#384	1	1	yes	characteristic
172	C₂²×C₇₃	#389	1	1	yes	characteristic
173	C₂²×C₇₃	#389	1	1	yes	characteristic
174	C₂²×C₇₃	#391	1	1	yes	characteristic
175	C₂²×C₇₃	#391	1	1	yes	characteristic
176	C₄×C₇₃	—	4	4	no	—
177	C₄×C₇₃	C₂×#95	1	1	yes	characteristic
178	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
179	C₄×C₇₃	#380	1	1	yes	characteristic
180	C₄×C₇₃	#382	1	1	yes	characteristic
181	C₄×C₇₃	#389	1	1	yes	characteristic
182	C₄×C₇₃	#389	1	1	yes	characteristic
183	C₄×C₇₃	#390	1	1	yes	characteristic
184	C₄×C₇₃	#390	1	1	yes	characteristic
185	#10873	—	73	1	no	maximal, Sylow
186	C₂×C₇₃	—	2	1	no	—
187	C₂×C₇₃	—	2	1	no	—
188	C₂×C₇₃	—	2	1	no	—
189	C₂×C₇₃	—	2	1	no	—
190	C₂×C₇₃	—	2	1	no	—
191	C₂×C₇₃	—	2	1	no	—
192	C₂×C₇₃	C₄⋊#95	1	1	yes	characteristic
193	C₂×C₇₃	#1953	1	2	yes	—
194	C₂²×#108	—	73	1	no	—
195	C₂²×#108	—	73	1	no	—
196	C₂×#405	D₇₃	1	1	yes	characteristic
197	C₂×#344	—	73	2	no	—
198	#1738	—	73	2	no	—
199	C₇₃	#10873	1	1	yes	characteristic, complemented, Sylow
200	C₂²×M₁₆	—	73	2	no	—
201	C₂²×M₁₆	—	73	2	no	—
202	C₂²×M₁₆	C₂×D₇₃	1	1	yes	characteristic
203	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic
204	C₂×#117	C₂×D₇₃	1	1	yes	characteristic
205	C₂×#108	—	73	4	no	—
206	C₂×#108	—	73	4	no	—
207	C₂×#108	—	146	2	no	—
208	C₂×#108	—	146	2	no	—
209	C₂×#108	—	146	1	no	—
210	C₂×#108	—	146	1	no	—
211	C₂×#108	—	146	2	no	—
212	#405	—	2	2	no	—
213	#405	Dic₇₃	1	4	yes	—
214	C₂×#97	—	2	1	no	—
215	C₂×C₄×C₈	—	2	1	no	—
216	#344	—	146	4	no	—
217	#341	—	146	4	no	—
218	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
219	C₂×M₁₆	—	2	1	no	—
220	C₂×M₁₆	—	2	1	no	—
221	C₂×M₁₆	—	2	1	no	—
222	C₂×M₁₆	—	73	4	no	—
223	C₂×M₁₆	—	73	4	no	—
224	C₂×M₁₆	—	146	2	no	—
225	C₂×M₁₆	—	146	2	no	—
226	C₂×M₁₆	—	146	2	no	—
227	C₂×M₁₆	—	146	2	no	—
228	C₂×M₁₆	—	146	2	no	—
229	C₂×M₁₆	—	146	2	no	—
230	C₂×M₁₆	—	146	2	no	—
231	C₂×M₁₆	—	146	2	no	—
232	C₂×M₁₆	—	146	2	no	—
233	C₂×M₁₆	—	146	2	no	—
234	C₂×M₁₆	Dic₁₄₆	1	2	yes	—
235	C₂×M₁₆	D₂₉₂	1	2	yes	—
236	C₂×M₁₆	C₂×Dic₇₃	1	2	yes	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	146	2	no	—
239	C₂²×C₈	—	146	2	no	—
240	C₂²×C₈	Dic₁₄₆	1	2	yes	—
241	C₂²×C₈	C₄×D₇₃	1	2	yes	—
242	C₂²×C₈	C₄×D₇₃	1	2	yes	—
243	C₂²×C₈	D₂₉₂	1	2	yes	—
244	C₂²×C₈	C₂×Dic₇₃	1	2	yes	—
245	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
246	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
247	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
248	#117	—	2	1	no	—
249	#117	—	2	1	no	—
250	#117	D₂₉₂	1	2	yes	—
251	#117	C₂×Dic₇₃	1	2	yes	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	Dic₁₄₆	1	2	yes	—
254	C₂×C₄²	—	2	1	no	—
255	#108	—	146	4	no	—
256	#108	—	146	4	no	—
257	#108	—	146	8	no	—
258	#97	—	2	4	no	—
259	C₄×C₈	—	2	4	no	—
260	C₂⁴	C₂×Dic₁₄₆	1	1	yes	characteristic
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
264	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
270	C₂²×C₄	C₂×Dic₁₄₆	1	1	yes	characteristic
271	C₂²×C₄	C₂×Dic₁₄₆	1	1	yes	characteristic
272	C₂²×C₄	#11924028	1	1	yes	characteristic
273	C₂²×C₄	#11924028	1	1	yes	characteristic
274	C₂²×C₄	#11924028	1	1	yes	characteristic
275	C₂²×C₄	#11924028	1	1	yes	characteristic
276	M₁₆	—	2	2	no	—
277	M₁₆	—	2	2	no	—
278	M₁₆	—	2	2	no	—
279	M₁₆	—	292	2	no	—
280	M₁₆	—	292	2	no	—
281	M₁₆	—	292	2	no	—
282	M₁₆	—	292	2	no	—
283	M₁₆	—	146	4	no	—
284	M₁₆	—	146	4	no	—
285	M₁₆	—	146	4	no	—
286	M₁₆	—	146	4	no	—
287	M₁₆	C₄⋊Dic₇₃	1	4	yes	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	292	2	no	—
292	C₂×C₈	—	292	2	no	—
293	C₂×C₈	—	292	2	no	—
294	C₂×C₈	—	292	2	no	—
295	C₂×C₈	—	146	4	no	—
296	C₂×C₈	—	146	4	no	—
297	C₂×C₈	C₄×Dic₇₃	1	4	yes	—
298	C₂×C₈	#11924005	1	2	yes	—
299	C₂×C₈	#11924005	1	2	yes	—
300	C₂×C₈	#11924005	1	4	yes	—
301	C₂×C₈	C₂²⋊Dic₇₃	1	2	yes	—
302	C₂×C₈	C₂²⋊Dic₇₃	1	2	yes	—
303	C₂×C₈	#11924007	1	2	yes	—
304	C₂×C₈	#11924007	1	2	yes	—
305	C₂×C₈	#11924007	1	4	yes	—
306	C₂×C₈	C₄⋊Dic₇₃	1	4	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	C₄⋊Dic₇₃	1	4	yes	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	C₂×C₄⋊Dic₇₃	1	1	yes	characteristic
315	C₂³	C₄×Dic₁₄₆	1	1	yes	characteristic
316	C₂³	C₄×Dic₁₄₆	1	1	yes	characteristic
317	C₂³	#14556570	1	1	yes	characteristic
318	C₂³	#14556570	1	1	yes	characteristic
319	C₂³	#14556591	1	1	yes	characteristic
320	C₂³	#14556591	1	1	yes	characteristic
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	C₂×C₄×Dic₇₃	1	1	yes	characteristic
324	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
325	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
326	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
327	C₂×C₄	C₂×#11924007	1	1	yes	characteristic
328	C₂×C₄	C₂×#11924007	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄⋊Dic₇₃	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊Dic₇₃	1	1	yes	characteristic
331	C₂×C₄	#14556550	1	1	yes	characteristic
332	C₂×C₄	#14556550	1	1	yes	characteristic
333	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
334	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
335	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
336	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
337	C₂×C₄	C₄×Dic₁₄₆	1	1	yes	characteristic
338	C₂×C₄	C₄×Dic₁₄₆	1	1	yes	characteristic
339	C₂×C₄	#14556565	1	1	yes	characteristic
340	C₂×C₄	#14556565	1	1	yes	characteristic
341	C₂×C₄	#14556565	1	1	yes	characteristic
342	C₂×C₄	#14556565	1	1	yes	characteristic
343	C₂×C₄	#14556570	1	1	yes	characteristic
344	C₂×C₄	#14556570	1	1	yes	characteristic
345	C₂×C₄	#14556579	1	1	yes	characteristic
346	C₂×C₄	#14556579	1	1	yes	characteristic
347	C₂×C₄	#14556583	1	1	yes	characteristic
348	C₂×C₄	#14556583	1	1	yes	characteristic
349	C₂×C₄	#14556588	1	1	yes	characteristic
350	C₂×C₄	#14556591	1	1	yes	characteristic
351	C₈	—	2	4	no	—
352	C₈	—	292	4	no	—
353	C₈	—	292	4	no	—
354	C₈	#14556498	1	4	yes	—
355	C₈	#14556498	1	4	yes	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	C₄×C₄⋊Dic₇₃	1	1	yes	characteristic
364	C₂²	#17988447	1	1	yes	characteristic
365	C₂²	#17988457	1	1	yes	characteristic
366	C₂²	#17988485	1	1	yes	characteristic
367	C₂²	#17988485	1	1	yes	characteristic
368	C₂²	#17988493	1	1	yes	characteristic
369	C₂²	#17988493	1	1	yes	characteristic
370	C₄	—	4	4	no	—
371	C₄	C₂×#14556498	1	1	yes	characteristic
372	C₄	C₄×C₄⋊Dic₇₃	1	1	yes	characteristic
373	C₄	#17988447	1	1	yes	characteristic
374	C₄	#17988453	1	1	yes	characteristic
375	C₄	#17988485	1	1	yes	characteristic
376	C₄	#17988485	1	1	yes	characteristic
377	C₄	#17988489	1	1	yes	characteristic
378	C₄	#17988489	1	1	yes	characteristic
379	C₂	—	2	1	no	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	#22608161	1	1	yes	characteristic
386	C₂	#22610721	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#14556565
commutator	C₂×C₄×C₇₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₃
Fitting	C₂×#405×C₇₃	C₂
socle	C₂²×C₇₃	#389
prime radical	C₂⁴×C₇₃	C₂×Q₈
cosocle	C₂³×C₄×C₇₃	C₂³
hypercenter	C₂×#405	D₇₃
hypocenter	C₇₃	#10873
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
13. C₂×#14556527	C₄	semidirect
14. C₂×#14556527	C₄	semidirect
199. C₇₃	#10873	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14556527	2
C₂×#17988357	2
#22609657	2
C₂×#405×C₇₃	2
#10873	73