Subgroups — C₄⋊C₄×#11924011 #33083972

Order 18688.

1242 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988609	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#11924011	C₂	1	2	yes	maximal
3	C₂×C₄×#11924011	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄⋊C₄×D₇₃	C₂	1	1	yes	maximal, characteristic
5	#22609805	C₂	1	2	yes	maximal, complemented
6	#22609802	C₂	1	2	yes	maximal, complemented
7	#22609801	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609798	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₄×#10596831	C₂	1	1	yes	maximal, characteristic, complemented
10	#22609623	C₂	1	2	yes	maximal
11	C₈×C₄⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11924011	C₂²	1	2	yes	—
13	C₂²×#11924011	C₂²	1	1	yes	characteristic
14	C₂²×#11924011	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×D₇₃	C₄	1	2	yes	—
16	C₂×C₄²×D₇₃	C₂²	1	2	yes	—
17	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
18	#17988609	C₄	1	8	yes	complemented
19	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
20	C₂×#14556520	C₂²	1	2	yes	—
21	C₄×#11924011	—	2	8	no	—
22	C₄×#11924011	C₄	1	8	yes	complemented
23	C₂×#14556501	C₂²	1	2	yes	—
24	C₂×#14556501	C₂²	1	2	yes	—
25	C₂×#14556501	C₂²	1	1	yes	characteristic
26	C₂×#14556501	C₂²	1	1	yes	characteristic
27	C₂×C₄×#10596831	C₂²	1	2	yes	—
28	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
29	C₄⋊C₄×Dic₇₃	C₄	1	2	yes	—
30	C₄×#11924007	C₂²	1	2	yes	—
31	C₄×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
32	#17988438	C₄	1	2	yes	—
33	#95×D₇₃	C₄	1	2	yes	—
34	#17988342	C₂²	1	2	yes	—
35	#17988341	C₂²	1	2	yes	—
36	#17988341	C₂²	1	2	yes	—
37	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
41	#336×C₇₃	C₂²	1	2	yes	—
42	C₂²×C₄×D₇₃	C₂×C₄	1	4	yes	—
43	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
46	C₂×#11924011	—	2	4	no	—
47	C₂×#11924011	—	2	2	no	—
48	C₂×#11924011	—	2	2	no	—
49	C₂×#11924011	—	2	4	no	—
50	C₂×#11924011	C₂×C₄	1	8	yes	—
51	C₂×#11924011	C₂×C₄	1	4	yes	—
52	C₂×#11924011	C₂×C₄	1	4	yes	—
53	C₂×#11924011	D₄	1	4	yes	—
54	C₂×#11924011	Q₈	1	4	yes	—
55	C₂²×#10596831	C₂³	1	2	yes	—
56	C₂²×#10596831	C₂³	1	1	yes	characteristic
57	C₂²×#10596831	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
59	C₂×#11924007	C₂×C₄	1	4	yes	—
60	C₄⋊C₄×D₇₃	—	2	8	no	—
61	C₂×C₄×Dic₇₃	C₂×C₄	1	4	yes	—
62	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
65	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
66	C₄²×D₇₃	—	2	4	no	—
67	C₄²×D₇₃	—	2	4	no	—
68	C₄²×D₇₃	C₂×C₄	1	4	yes	—
69	C₄²×D₇₃	C₂×C₄	1	4	yes	—
70	C₄⋊#10596831	C₂×C₄	1	4	yes	complemented
71	#14556520	C₂×C₄	1	8	yes	complemented
72	#14556501	—	2	4	no	—
73	#14556501	—	2	4	no	—
74	#14556501	C₂×C₄	1	4	yes	complemented
75	#14556501	C₂×C₄	1	4	yes	complemented
76	C₄×#10596831	—	2	4	no	—
77	C₄×#10596831	C₂×C₄	1	4	yes	complemented
78	#14556498	C₂×C₄	1	2	yes	—
79	#14556498	C₂×C₄	1	4	yes	—
80	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
81	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
85	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₇₃	C₂×C₄	1	4	yes	complemented
87	C₄×C₈×C₇₃	—	2	4	no	—
88	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	complemented
89	#95×C₇₃	C₂×C₄	1	2	yes	—
90	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×Dic₇₃	C₂²×C₄	1	4	yes	—
92	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₄×D₇₃	—	2	4	no	—
96	C₂×C₄×D₇₃	—	2	8	no	—
97	C₂×C₄×D₇₃	—	2	8	no	—
98	C₂×C₄×D₇₃	—	4	2	no	—
99	C₂×C₄×D₇₃	—	4	4	no	—
100	C₂×C₄×D₇₃	C₄²	1	4	yes	—
101	C₂×C₄×D₇₃	C₄²	1	4	yes	—
102	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
103	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
105	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
106	C₂×C₄×D₇₃	#41	1	2	yes	—
107	C₂×C₄×D₇₃	#41	1	2	yes	—
108	#11924011	—	2	8	no	—
109	#11924011	—	2	16	no	—
110	#11924011	C₄⋊C₄	1	16	yes	direct product factor
111	C₂×#10596831	—	2	2	no	—
112	C₂×#10596831	—	2	1	no	—
113	C₂×#10596831	—	2	1	no	—
114	C₂×#10596831	—	2	2	no	—
115	C₂×#10596831	C₂²×C₄	1	2	yes	—
116	C₂×#10596831	C₂²×C₄	1	4	yes	—
117	C₂×#10596831	C₂²×C₄	1	2	yes	—
118	C₂×#10596831	C₂×D₄	1	2	yes	—
119	C₂×#10596831	C₂×Q₈	1	2	yes	—
120	C₄⋊Dic₇₃	—	2	4	no	—
121	#11924007	—	2	8	no	—
122	C₄×Dic₇₃	—	2	2	no	—
123	C₄×Dic₇₃	—	2	2	no	—
124	C₄×Dic₇₃	—	2	8	no	—
125	C₄×Dic₇₃	C₄²	1	4	yes	—
126	C₄×Dic₇₃	C₄²	1	4	yes	—
127	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
128	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
133	C₂×C₈×C₇₃	—	2	2	no	—
134	C₂×C₈×C₇₃	—	2	1	no	—
135	C₂×C₈×C₇₃	—	2	1	no	—
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
139	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₇₃	C₂×Q₈	1	2	yes	—
142	C₄⋊C₄×C₇₃	M₁₆	1	8	yes	complemented
143	C₄²×C₇₃	—	2	2	no	—
144	C₄²×C₇₃	—	2	2	no	—
145	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
146	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
147	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
148	C₂²×D₇₃	—	2	2	no	—
149	C₂²×D₇₃	—	2	2	no	—
150	C₂²×D₇₃	C₂×C₄²	1	2	yes	—
151	C₂²×D₇₃	C₄×D₄	1	2	yes	—
152	C₂²×D₇₃	C₄×Q₈	1	2	yes	—
153	C₂×C₄×C₇₃	—	2	4	no	—
154	C₂×C₄×C₇₃	—	2	2	no	—
155	C₂×C₄×C₇₃	—	2	4	no	—
156	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
157	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
158	C₂×C₄×C₇₃	C₂×M₁₆	1	8	yes	—
159	C₂×C₄×C₇₃	C₂×M₁₆	1	4	yes	—
160	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
166	C₂×Dic₇₃	—	2	2	no	—
167	C₂×Dic₇₃	—	2	2	no	—
168	C₂×Dic₇₃	—	2	4	no	—
169	C₂×Dic₇₃	—	2	4	no	—
170	C₂×Dic₇₃	—	2	4	no	—
171	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
172	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
173	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
174	C₂×Dic₇₃	C₄×D₄	1	2	yes	—
175	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
176	C₄×D₇₃	—	2	8	no	—
177	C₄×D₇₃	—	4	4	no	—
178	C₄×D₇₃	—	4	16	no	—
179	C₄×D₇₃	C₂×C₄⋊C₄	1	4	yes	—
180	C₄×D₇₃	#117	1	4	yes	—
181	C₄×D₇₃	C₄×D₄	1	4	yes	—
182	C₄×D₇₃	C₄×Q₈	1	4	yes	—
183	C₈×C₇₃	—	2	2	no	—
184	C₈×C₇₃	—	2	4	no	—
185	C₈×C₇₃	C₂×C₄⋊C₄	1	4	yes	complemented
186	#10596831	—	2	2	no	—
187	#10596831	—	2	4	no	—
188	#10596831	C₂×C₄⋊C₄	1	4	yes	complemented
189	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
190	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
191	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
192	C₂²×C₇₃	C₂²×M₁₆	1	2	yes	—
193	C₂²×C₇₃	#568	1	2	yes	—
194	C₂×D₇₃	—	2	2	no	—
195	C₂×D₇₃	—	2	2	no	—
196	C₂×D₇₃	—	2	4	no	—
197	C₂×D₇₃	—	2	4	no	—
198	C₂×D₇₃	C₄×C₄⋊C₄	1	4	yes	—
199	C₄×C₇₃	—	2	2	no	—
200	C₄×C₇₃	—	2	8	no	—
201	C₄×C₇₃	C₄×M₁₆	1	4	yes	complemented
202	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
203	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
204	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
205	C₄×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
206	Dic₇₃	—	2	2	no	—
207	Dic₇₃	—	2	2	no	—
208	Dic₇₃	—	4	4	no	—
209	Dic₇₃	C₄×C₄⋊C₄	1	4	yes	—
210	C₄⋊C₄×M₁₆	—	73	1	no	maximal, Sylow
211	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
212	C₂×C₇₃	C₂×C₄×M₁₆	1	1	yes	characteristic
213	C₂×C₇₃	#2873	1	1	yes	characteristic
214	C₂×C₇₃	D₄×M₁₆	1	2	yes	—
215	C₂×C₇₃	Q₈×M₁₆	1	2	yes	—
216	D₇₃	—	2	4	no	—
217	C₂×#423	—	73	1	no	—
218	C₂×C₄×M₁₆	—	73	1	no	—
219	C₂×C₄×M₁₆	—	73	2	no	—
220	C₂×C₄×C₄⋊C₄	—	73	1	no	—
221	#1771	—	73	2	no	—
222	#1771	—	73	2	no	—
223	#1770	—	73	1	no	—
224	#1770	—	73	1	no	—
225	C₈×C₄⋊C₄	—	73	1	no	—
226	C₈×C₄⋊C₄	D₇₃	1	1	yes	characteristic, complemented
227	#1728	—	73	2	no	—
228	C₇₃	C₄⋊C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
229	C₂²×M₁₆	—	73	1	no	—
230	C₂²×M₁₆	—	73	2	no	—
231	C₂²×M₁₆	—	73	1	no	—
232	C₂²×C₄⋊C₄	—	73	2	no	—
233	C₂²×C₄²	—	73	1	no	—
234	C₂²×C₄²	—	73	2	no	—
235	#423	—	73	8	no	—
236	C₂×C₄⋊C₈	—	73	2	no	—
237	C₂×C₄⋊C₈	—	73	1	no	—
238	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
239	C₄×M₁₆	—	73	8	no	—
240	C₄×M₁₆	—	146	8	no	—
241	C₂×#97	—	73	1	no	—
242	C₂×#97	—	73	1	no	—
243	C₂×#97	—	73	2	no	—
244	C₂×#97	—	73	2	no	—
245	C₂×C₄×C₈	—	73	1	no	—
246	C₂×C₄×C₈	—	73	2	no	—
247	C₂×C₄×C₈	C₂×D₇₃	1	2	yes	—
248	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
249	C₄×C₄⋊C₄	—	73	2	no	—
250	C₄×C₄⋊C₄	—	73	1	no	—
251	C₄×C₄⋊C₄	—	73	2	no	—
252	C₄×C₄⋊C₄	—	73	2	no	—
253	C₄×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
254	C₂×#95	—	73	2	no	—
255	#336	—	73	2	no	—
256	#336	—	73	2	no	—
257	#336	—	73	2	no	—
258	#336	C₂×D₇₃	1	2	yes	—
259	C₂³×C₄	—	73	1	no	—
260	C₂³×C₄	—	73	4	no	—
261	C₂³×C₄	—	73	1	no	—
262	C₂³×C₄	—	73	1	no	—
263	C₂×M₁₆	—	73	4	no	—
264	C₂×M₁₆	—	73	4	no	—
265	C₂×M₁₆	—	73	8	no	—
266	C₂×M₁₆	—	73	4	no	—
267	C₂×M₁₆	—	73	4	no	—
268	C₂×M₁₆	—	146	4	no	—
269	C₂×M₁₆	—	146	2	no	—
270	C₂×M₁₆	—	146	4	no	—
271	C₂×M₁₆	—	146	2	no	—
272	C₂²×C₈	—	73	1	no	—
273	C₂²×C₈	—	73	1	no	—
274	C₂²×C₈	—	73	2	no	—
275	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
276	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
277	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
278	C₂×C₄⋊C₄	—	73	4	no	—
279	C₂×C₄⋊C₄	—	73	2	no	—
280	C₂×C₄⋊C₄	—	146	8	no	—
281	C₂×C₄⋊C₄	C₄×D₇₃	1	2	yes	—
282	C₂×C₄²	—	73	1	no	—
283	C₂×C₄²	—	73	1	no	—
284	C₂×C₄²	—	73	1	no	—
285	C₂×C₄²	—	73	4	no	—
286	C₂×C₄²	—	73	4	no	—
287	C₂×C₄²	—	73	4	no	—
288	C₂×C₄²	—	73	2	no	—
289	C₂×C₄²	—	146	4	no	—
290	C₂×C₄²	—	146	4	no	—
291	C₂×C₄²	C₂²×D₇₃	1	2	yes	—
292	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
293	C₄⋊C₈	—	73	8	no	—
294	C₄⋊C₈	—	73	4	no	—
295	C₄⋊C₈	C₄×D₇₃	1	4	yes	complemented
296	#97	—	73	4	no	—
297	#97	—	73	4	no	—
298	#97	—	146	4	no	—
299	#97	—	146	4	no	—
300	C₄×C₈	—	2	4	no	—
301	C₄×C₈	—	73	4	no	—
302	C₄×C₈	—	146	4	no	—
303	C₄×C₈	C₄×D₇₃	1	4	yes	complemented
304	#95	—	73	4	no	—
305	#95	—	73	2	no	—
306	#95	C₄×D₇₃	1	2	yes	—
307	C₂⁴	—	73	1	no	—
308	C₂²×C₄	—	292	4	no	—
309	C₂²×C₄	—	292	2	no	—
310	C₂²×C₄	—	73	4	no	—
311	C₂²×C₄	—	73	1	no	—
312	C₂²×C₄	—	73	2	no	—
313	C₂²×C₄	—	73	2	no	—
314	C₂²×C₄	—	73	2	no	—
315	C₂²×C₄	—	73	2	no	—
316	C₂²×C₄	—	73	2	no	—
317	C₂²×C₄	—	73	2	no	—
318	C₂²×C₄	—	73	1	no	—
319	C₂²×C₄	—	73	1	no	—
320	C₂²×C₄	—	73	4	no	—
321	C₂²×C₄	—	73	4	no	—
322	C₂²×C₄	—	146	8	no	—
323	C₂²×C₄	—	146	8	no	—
324	C₂²×C₄	—	146	4	no	—
325	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₄×D₇₃	1	4	yes	—
327	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
328	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
329	M₁₆	—	73	16	no	—
330	M₁₆	—	146	8	no	—
331	M₁₆	—	146	16	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	73	2	no	—
337	C₂×C₈	—	73	2	no	—
338	C₂×C₈	—	73	2	no	—
339	C₂×C₈	—	73	2	no	—
340	C₂×C₈	—	73	4	no	—
341	C₂×C₈	—	146	2	no	—
342	C₂×C₈	—	146	1	no	—
343	C₂×C₈	—	146	1	no	—
344	C₂×C₈	—	146	2	no	—
345	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
346	C₂×C₈	C₂×C₄×D₇₃	1	4	yes	—
347	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
348	C₂×C₈	D₄×D₇₃	1	2	yes	—
349	C₂×C₈	Q₈×D₇₃	1	2	yes	—
350	C₄⋊C₄	—	146	8	no	—
351	C₄⋊C₄	—	146	4	no	—
352	C₄⋊C₄	#11924011	1	8	yes	direct product factor
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	73	4	no	—
356	C₄²	—	73	4	no	—
357	C₄²	—	73	2	no	—
358	C₄²	—	73	2	no	—
359	C₄²	—	146	8	no	—
360	C₄²	—	146	2	no	—
361	C₄²	—	146	2	no	—
362	C₄²	C₂×C₄×D₇₃	1	2	yes	—
363	C₄²	C₂×C₄×D₇₃	1	2	yes	—
364	C₂³	—	73	2	no	—
365	C₂³	—	73	2	no	—
366	C₂³	—	73	2	no	—
367	C₂³	—	146	2	no	—
368	C₂³	—	146	2	no	—
369	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	292	16	no	—
374	C₂×C₄	—	292	4	no	—
375	C₂×C₄	—	73	2	no	—
376	C₂×C₄	—	73	2	no	—
377	C₂×C₄	—	73	2	no	—
378	C₂×C₄	—	73	4	no	—
379	C₂×C₄	—	73	4	no	—
380	C₂×C₄	—	73	4	no	—
381	C₂×C₄	—	73	4	no	—
382	C₂×C₄	—	73	2	no	—
383	C₂×C₄	—	73	2	no	—
384	C₂×C₄	—	146	4	no	—
385	C₂×C₄	—	146	4	no	—
386	C₂×C₄	—	146	4	no	—
387	C₂×C₄	—	146	2	no	—
388	C₂×C₄	—	146	2	no	—
389	C₂×C₄	—	146	8	no	—
390	C₂×C₄	C₄²×D₇₃	1	2	yes	—
391	C₂×C₄	C₄²×D₇₃	1	2	yes	—
392	C₂×C₄	C₂×#11924011	1	8	yes	—
393	C₂×C₄	C₂×#11924011	1	4	yes	—
394	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
397	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
398	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
399	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	2	4	no	—
402	C₈	—	73	4	no	—
403	C₈	—	146	2	no	—
404	C₈	—	146	4	no	—
405	C₈	C₄⋊C₄×D₇₃	1	4	yes	complemented
406	C₂²	—	73	4	no	—
407	C₂²	—	146	4	no	—
408	C₂²	—	146	4	no	—
409	C₂²	—	146	2	no	—
410	C₂²	—	146	2	no	—
411	C₂²	C₂×C₄²×D₇₃	1	1	yes	characteristic
412	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
413	C₂²	C₄×Q₈×D₇₃	1	1	yes	characteristic
414	C₂²	C₂²×#11924011	1	2	yes	—
415	C₂²	#17989352	1	2	yes	—
416	C₄	—	2	8	no	—
417	C₄	—	2	2	no	—
418	C₄	—	292	4	no	—
419	C₄	—	73	4	no	—
420	C₄	—	146	2	no	—
421	C₄	—	146	2	no	—
422	C₄	C₄×#11924011	1	4	yes	complemented
423	C₄	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
424	C₄	#117×D₇₃	1	1	yes	characteristic
425	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
426	C₄	C₄×Q₈×D₇₃	1	1	yes	characteristic
427	C₂	—	146	4	no	—
428	C₂	C₄×C₄⋊C₄×D₇₃	1	1	yes	characteristic
429	C₂	C₂×C₄×#11924011	1	1	yes	characteristic
430	C₂	#22618347	1	1	yes	characteristic
431	C₂	D₄×#11924011	1	2	yes	—
432	C₂	Q₈×#11924011	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₃
commutator	C₂²×C₇₃	C₂²×C₄²
Fitting	C₈×C₄⋊C₄×C₇₃	C₂
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₇₃
hypocenter	C₇₃	C₄⋊C₄×M₁₆
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
5. #22609805	C₂	semidirect
6. #22609802	C₂	semidirect
7. #22609801	C₂	semidirect
8. #22609798	C₂	semidirect
9. C₄⋊C₄×#10596831	C₂	semidirect
11. C₈×C₄⋊C₄×C₇₃	C₂	semidirect
18. #17988609	C₄	semidirect
22. C₄×#11924011	C₄	semidirect
70. C₄⋊#10596831	C₂×C₄	semidirect
71. #14556520	C₂×C₄	semidirect
74. #14556501	C₂×C₄	semidirect
75. #14556501	C₂×C₄	semidirect
77. C₄×#10596831	C₂×C₄	semidirect
86. C₄⋊C₈×C₇₃	C₂×C₄	semidirect
88. C₄×C₈×C₇₃	C₂×C₄	semidirect
110. #11924011	C₄⋊C₄	direct (N × H)
142. C₄⋊C₄×C₇₃	M₁₆	semidirect
185. C₈×C₇₃	C₂×C₄⋊C₄	semidirect
188. #10596831	C₂×C₄⋊C₄	semidirect
201. C₄×C₇₃	C₄×M₁₆	semidirect
226. C₈×C₄⋊C₄	D₇₃	semidirect
228. C₇₃	C₄⋊C₄×M₁₆	semidirect
295. C₄⋊C₈	C₄×D₇₃	semidirect
303. C₄×C₈	C₄×D₇₃	semidirect
352. C₄⋊C₄	#11924011	direct (N × H)
405. C₈	C₄⋊C₄×D₇₃	semidirect
422. C₄	C₄×#11924011	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988609	2
C₂×C₄×#11924011	2
C₄×C₄⋊C₄×D₇₃	2
#22609805	2
#22609802	2
#22609801	2
#22609798	2
C₄⋊C₄×#10596831	2
#22609623	2
C₈×C₄⋊C₄×C₇₃	2
C₄⋊C₄×M₁₆	73

Subgroups — C4⋊C4×#11924011 #33083972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₄×#11924011 #33083972