Subgroups — C₂×#22624765 #34002141

Order 18688.

974 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11924036	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊#64408	C₂	1	1	yes	maximal, characteristic
3	#22624765	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11924036	—	2	1	no	—
6	C₂²×C₄⋊#64408	C₄	1	2	yes	—
7	C₂²×C₄×#64408	—	2	1	no	—
8	C₄×#11924036	—	2	1	no	—
9	C₄×#11924036	—	2	1	no	—
10	C₄×#11924036	C₄	1	2	yes	complemented
11	C₄×#11924036	C₂²	1	2	yes	—
12	C₂×C₄×#10596833	—	2	1	no	—
13	C₂×C₄×#10596833	C₄	1	2	yes	complemented
14	C₄×C₄⋊#64408	—	2	1	no	—
15	C₄×C₄⋊#64408	—	2	1	no	—
16	C₄×C₄⋊#64408	C₄	1	2	yes	—
17	C₄×C₄⋊#64408	C₂²	1	2	yes	—
18	C₂×(C₂×#64408)⋊C₄	—	2	1	no	—
19	C₂²×C₈×D₇₃	—	2	1	no	—
20	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#10596831	C₄	1	1	yes	characteristic, complemented
22	C₂×#14556520	—	2	1	no	—
23	C₄⋊C₈×D₇₃	—	2	1	no	—
24	C₄⋊C₈×D₇₃	—	2	1	no	—
25	C₄⋊C₈×D₇₃	C₄	1	2	yes	complemented
26	C₄⋊C₈×D₇₃	C₂²	1	2	yes	—
27	C₂×C₄⋊C₈×C₇₃	C₄	1	1	yes	characteristic, complemented
28	C₂³×#64408	—	2	2	no	—
29	C₂×#11924036	—	2	8	no	—
30	C₂×#11924036	—	2	2	no	—
31	C₂×#11924036	—	2	2	no	—
32	C₂²×#10596833	—	2	2	no	—
33	C₂×C₄⋊#64408	—	2	2	no	—
34	C₂×C₄⋊#64408	—	2	4	no	—
35	C₂×C₄⋊#64408	C₈	1	8	yes	complemented
36	C₂×C₄⋊#64408	C₂×C₄	1	4	yes	—
37	C₂×C₄×#64408	—	2	2	no	—
38	C₂×C₄×#64408	—	2	2	no	—
39	C₂×C₄×#64408	—	4	2	no	—
40	C₂×C₄×#64408	—	4	2	no	—
41	C₄×#10596833	—	2	2	no	—
42	C₄×#10596833	—	2	2	no	—
43	C₄×#10596833	—	2	2	no	—
44	C₄×#10596833	C₂×C₄	1	4	yes	complemented
45	(C₂×#64408)⋊C₄	—	2	2	no	—
46	(C₂×#64408)⋊C₄	—	2	2	no	—
47	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
50	C₂²×#10596831	—	2	1	no	—
51	C₂×C₈×D₇₃	—	2	2	no	—
52	C₂×C₈×D₇₃	—	2	2	no	—
53	C₂×C₈×D₇₃	—	4	2	no	—
54	C₂×C₈×D₇₃	—	4	2	no	—
55	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
57	C₂×C₄×Dic₇₃	Q₈	1	1	yes	characteristic
58	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₇₃	D₄	1	1	yes	characteristic
62	C₄²×D₇₃	D₄	1	1	yes	characteristic
63	C₄²×D₇₃	D₄	1	1	yes	characteristic
64	C₄²×D₇₃	Q₈	1	1	yes	characteristic
65	C₄²×D₇₃	C₂³	1	1	yes	characteristic
66	C₄⋊#10596831	—	2	1	no	—
67	C₄⋊#10596831	C₂×C₄	1	2	yes	complemented
68	#14556520	—	2	2	no	—
69	#14556520	—	2	2	no	—
70	C₂²×C₈×C₇₃	—	2	1	no	—
71	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
72	C₄⋊C₈×C₇₃	—	2	1	no	—
73	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	complemented
74	C₂²×#64408	—	2	8	no	—
75	C₂²×#64408	—	2	4	no	—
76	C₂²×#64408	—	4	4	no	—
77	C₂²×#64408	—	4	4	no	—
78	#11924036	—	2	8	no	—
79	#11924036	—	2	8	no	—
80	C₂×#10596833	—	2	8	no	—
81	C₂×#10596833	—	2	4	no	—
82	C₄⋊#64408	—	2	8	no	—
83	C₄⋊#64408	—	2	4	no	—
84	C₄⋊#64408	C₂×C₈	1	8	yes	complemented
85	C₄×#64408	—	4	4	no	—
86	C₄×#64408	—	4	2	no	—
87	C₄×#64408	—	4	2	no	—
88	C₂³×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₇₃	—	2	4	no	—
93	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
94	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₇₃	C₂×C₈	1	4	yes	—
103	C₂×C₄×D₇₃	M₁₆	1	4	yes	—
104	C₂×C₄×D₇₃	D₈	1	2	yes	—
105	C₂×C₄×D₇₃	SD₁₆	1	2	yes	—
106	C₂×C₄×D₇₃	SD₁₆	1	2	yes	—
107	C₂×C₄×D₇₃	Q₁₆	1	2	yes	—
108	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
111	C₂×#10596831	—	2	2	no	—
112	C₂×#10596831	—	4	2	no	—
113	C₈×D₇₃	—	4	4	no	—
114	C₈×D₇₃	—	4	2	no	—
115	C₈×D₇₃	—	4	2	no	—
116	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
117	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₈×C₇₃	—	2	2	no	—
132	C₂×C₈×C₇₃	—	4	2	no	—
133	C₄²×C₇₃	C₄²	1	1	yes	characteristic
134	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
135	C₄²×C₇₃	C₄⋊C₄	1	1	yes	characteristic
136	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
137	C₂³×C₇₃	#95	1	1	yes	characteristic
138	C₂²×D₇₃	#95	1	1	yes	characteristic
139	C₂²×D₇₃	C₂²⋊C₈	1	4	yes	—
140	C₂²×D₇₃	#102	1	2	yes	—
141	C₂²×D₇₃	#103	1	2	yes	—
142	C₂²×D₇₃	#104	1	4	yes	—
143	C₂²×D₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×#64408	—	2	8	no	—
145	C₂×#64408	—	4	16	no	—
146	C₂×#64408	—	4	4	no	—
147	C₂×#64408	—	4	4	no	—
148	C₂×C₄×C₇₃	—	2	2	no	—
149	C₂×C₄×C₇₃	#95	1	1	yes	characteristic
150	C₂×C₄×C₇₃	#95	1	1	yes	characteristic
151	C₂×C₄×C₇₃	#95	1	1	yes	characteristic
152	C₂×C₄×C₇₃	C₄×C₈	1	2	yes	—
153	C₂×C₄×C₇₃	#97	1	2	yes	—
154	C₂×C₄×C₇₃	#102	1	2	yes	—
155	C₂×C₄×C₇₃	#103	1	2	yes	—
156	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×Dic₇₃	—	2	2	no	—
160	C₂×Dic₇₃	#95	1	1	yes	characteristic
161	C₂×Dic₇₃	#95	1	1	yes	characteristic
162	C₂×Dic₇₃	#95	1	1	yes	characteristic
163	C₂×Dic₇₃	C₄⋊C₈	1	4	yes	—
164	C₂×Dic₇₃	#106	1	2	yes	—
165	C₂×Dic₇₃	#107	1	2	yes	—
166	C₂×Dic₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₄×D₇₃	—	2	2	no	—
170	C₄×D₇₃	—	2	2	no	—
171	C₄×D₇₃	—	2	2	no	—
172	C₄×D₇₃	—	2	2	no	—
173	C₄×D₇₃	C₄×C₈	1	2	yes	—
174	C₄×D₇₃	#97	1	2	yes	—
175	C₄×D₇₃	C₂²⋊C₈	1	4	yes	—
176	C₄×D₇₃	#102	1	2	yes	—
177	C₄×D₇₃	#102	1	2	yes	—
178	C₄×D₇₃	#103	1	2	yes	—
179	C₄×D₇₃	#103	1	2	yes	—
180	C₄×D₇₃	C₄⋊C₈	1	4	yes	—
181	C₄×D₇₃	#106	1	2	yes	—
182	C₄×D₇₃	#107	1	2	yes	—
183	C₄×D₇₃	C₂²×C₈	1	2	yes	—
184	C₄×D₇₃	C₂×M₁₆	1	2	yes	—
185	C₄×D₇₃	C₂×D₈	1	1	yes	characteristic
186	C₄×D₇₃	C₂×SD₁₆	1	1	yes	characteristic
187	C₄×D₇₃	C₂×SD₁₆	1	1	yes	characteristic
188	C₄×D₇₃	C₂×Q₁₆	1	1	yes	characteristic
189	#10596833	—	2	8	no	—
190	C₈×C₇₃	—	4	2	no	—
191	#10596831	—	4	2	no	—
192	C₂²×C₇₃	#336	1	2	yes	—
193	C₂²×C₇₃	#339	1	2	yes	—
194	C₂²×C₇₃	#340	1	2	yes	—
195	C₂²×C₇₃	C₂×#95	1	1	yes	characteristic
196	C₂×D₇₃	D₄⋊C₈	1	8	yes	—
197	C₂×D₇₃	Q₈⋊C₈	1	8	yes	—
198	C₂×D₇₃	#336	1	2	yes	—
199	C₂×D₇₃	#339	1	2	yes	—
200	C₂×D₇₃	#340	1	2	yes	—
201	C₂×D₇₃	C₂×C₂²⋊C₈	1	2	yes	—
202	C₂×D₇₃	C₂×#102	1	1	yes	characteristic
203	C₂×D₇₃	C₂×#103	1	1	yes	characteristic
204	C₂×D₇₃	C₂×#104	1	2	yes	—
205	#64408	—	4	8	no	—
206	C₄×C₇₃	—	2	1	no	—
207	C₄×C₇₃	—	2	1	no	—
208	C₄×C₇₃	#336	1	2	yes	—
209	C₄×C₇₃	#340	1	2	yes	—
210	C₄×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
211	C₄×C₇₃	C₂×#97	1	1	yes	characteristic
212	C₄×C₇₃	C₂×#102	1	1	yes	characteristic
213	C₄×C₇₃	C₂×#103	1	1	yes	characteristic
214	Dic₇₃	—	2	1	no	—
215	Dic₇₃	—	2	1	no	—
216	Dic₇₃	#336	1	2	yes	—
217	Dic₇₃	#340	1	2	yes	—
218	Dic₇₃	C₂×C₄⋊C₈	1	2	yes	—
219	Dic₇₃	C₂×#106	1	1	yes	characteristic
220	Dic₇₃	C₂×#107	1	1	yes	characteristic
221	C₂×#1279	—	73	1	no	maximal, Sylow
222	C₂×C₇₃	#1279	1	4	yes	complemented
223	C₂×C₇₃	C₂×#336	1	1	yes	characteristic
224	C₂×C₇₃	C₂×#339	1	1	yes	characteristic
225	C₂×C₇₃	C₂×#340	1	1	yes	characteristic
226	D₇₃	#1279	1	4	yes	complemented
227	D₇₃	C₂×D₄⋊C₈	1	2	yes	—
228	D₇₃	C₂×Q₈⋊C₈	1	2	yes	—
229	C₂²×C₄⋊C₈	—	73	1	no	—
230	C₂²×C₄×C₈	—	73	1	no	—
231	C₂×C₄×C₄⋊C₄	—	73	1	no	—
232	#1279	—	73	4	no	—
233	C₇₃	C₂×#1279	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₈	—	146	1	no	—
235	C₂³×C₈	—	146	1	no	—
236	C₂²×C₄⋊C₄	—	73	2	no	—
237	C₂²×C₄²	—	73	1	no	—
238	C₂²×C₄²	—	146	1	no	—
239	C₂×C₄⋊C₈	—	73	1	no	—
240	C₂×C₄⋊C₈	—	73	2	no	—
241	C₂×C₄⋊C₈	—	73	2	no	—
242	C₂×C₄⋊C₈	—	146	1	no	—
243	C₂×C₄⋊C₈	—	146	1	no	—
244	C₂×C₄⋊C₈	—	146	1	no	—
245	C₂×C₄⋊C₈	#64408	1	1	yes	characteristic, complemented
246	C₂×C₄×C₈	—	73	2	no	—
247	C₂×C₄×C₈	—	73	2	no	—
248	C₂×C₄×C₈	—	73	2	no	—
249	C₂×C₄×C₈	—	146	1	no	—
250	C₂×C₄×C₈	—	146	1	no	—
251	C₂×C₄×C₈	—	146	1	no	—
252	C₄×C₄⋊C₄	—	73	2	no	—
253	C₄×C₄⋊C₄	—	73	2	no	—
254	C₄×C₄⋊C₄	—	146	1	no	—
255	C₄×C₄⋊C₄	—	146	1	no	—
256	C₂×#95	—	146	1	no	—
257	C₂³×C₄	—	73	1	no	—
258	C₂³×C₄	—	73	1	no	—
259	C₂³×C₄	—	73	1	no	—
260	C₂³×C₄	—	146	2	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	292	2	no	—
263	C₂²×C₈	—	292	2	no	—
264	C₂²×C₈	—	146	2	no	—
265	C₂²×C₈	—	146	2	no	—
266	C₂²×C₈	—	146	1	no	—
267	C₂²×C₈	—	146	2	no	—
268	C₂²×C₈	—	146	2	no	—
269	C₂²×C₈	—	146	2	no	—
270	C₂²×C₈	—	146	8	no	—
271	C₂×C₄⋊C₄	—	73	4	no	—
272	C₂×C₄⋊C₄	—	73	8	no	—
273	C₂×C₄⋊C₄	—	146	2	no	—
274	C₂×C₄⋊C₄	—	146	4	no	—
275	C₂×C₄²	—	292	2	no	—
276	C₂×C₄²	—	292	2	no	—
277	C₂×C₄²	—	73	1	no	—
278	C₂×C₄²	—	73	1	no	—
279	C₂×C₄²	—	73	1	no	—
280	C₂×C₄²	—	73	1	no	—
281	C₂×C₄²	—	73	1	no	—
282	C₂×C₄²	—	73	1	no	—
283	C₂×C₄²	—	73	1	no	—
284	C₂×C₄²	—	73	1	no	—
285	C₂×C₄²	—	73	1	no	—
286	C₂×C₄²	—	73	1	no	—
287	C₂×C₄²	—	73	1	no	—
288	C₂×C₄²	—	146	2	no	—
289	C₂×C₄²	—	146	2	no	—
290	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	73	2	no	—
293	C₄⋊C₈	—	146	2	no	—
294	C₄⋊C₈	—	146	2	no	—
295	C₄⋊C₈	—	146	1	no	—
296	C₄⋊C₈	C₂×#64408	1	2	yes	complemented
297	C₄×C₈	—	73	4	no	—
298	C₄×C₈	—	146	2	no	—
299	C₄×C₈	—	146	2	no	—
300	C₄×C₈	—	146	2	no	—
301	#95	—	146	2	no	—
302	#95	—	146	2	no	—
303	C₂⁴	—	73	1	no	—
304	C₂²×C₄	—	292	4	no	—
305	C₂²×C₄	—	292	4	no	—
306	C₂²×C₄	—	73	1	no	—
307	C₂²×C₄	—	73	1	no	—
308	C₂²×C₄	—	73	1	no	—
309	C₂²×C₄	—	73	1	no	—
310	C₂²×C₄	—	73	1	no	—
311	C₂²×C₄	—	73	1	no	—
312	C₂²×C₄	—	73	4	no	—
313	C₂²×C₄	—	73	4	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	1	no	—
321	C₂²×C₄	—	73	1	no	—
322	C₂²×C₄	—	73	1	no	—
323	C₂²×C₄	—	73	1	no	—
324	C₂²×C₄	—	73	1	no	—
325	C₂²×C₄	—	73	1	no	—
326	C₂²×C₄	—	73	1	no	—
327	C₂²×C₄	—	146	4	no	—
328	C₂²×C₄	—	146	4	no	—
329	C₂²×C₄	—	146	8	no	—
330	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
331	C₂²×C₄	C₂²⋊#64408	1	1	yes	characteristic
332	C₂²×C₄	C₄⋊#64408	1	1	yes	characteristic
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	—	292	2	no	—
336	C₂×C₈	—	292	4	no	—
337	C₂×C₈	—	292	2	no	—
338	C₂×C₈	—	292	2	no	—
339	C₂×C₈	—	146	2	no	—
340	C₂×C₈	—	146	4	no	—
341	C₂×C₈	—	146	8	no	—
342	C₂×C₈	—	146	8	no	—
343	C₂×C₈	—	146	8	no	—
344	C₄⋊C₄	—	73	8	no	—
345	C₄⋊C₄	—	146	8	no	—
346	C₄⋊C₄	—	146	4	no	—
347	C₄²	—	292	4	no	—
348	C₄²	—	292	2	no	—
349	C₄²	—	292	2	no	—
350	C₄²	—	73	1	no	—
351	C₄²	—	73	1	no	—
352	C₄²	—	73	1	no	—
353	C₄²	—	73	1	no	—
354	C₄²	—	73	1	no	—
355	C₄²	—	73	1	no	—
356	C₄²	—	73	1	no	—
357	C₄²	—	73	1	no	—
358	C₄²	—	73	1	no	—
359	C₄²	—	73	1	no	—
360	C₄²	—	73	1	no	—
361	C₄²	—	73	1	no	—
362	C₄²	C₄×#64408	1	1	yes	characteristic
363	C₄²	C₂²⋊#64408	1	1	yes	characteristic
364	C₄²	C₄⋊#64408	1	1	yes	characteristic
365	C₄²	C₂²×#64408	1	1	yes	characteristic
366	C₂³	—	73	4	no	—
367	C₂³	—	73	4	no	—
368	C₂³	—	73	2	no	—
369	C₂³	—	73	2	no	—
370	C₂³	—	73	1	no	—
371	C₂³	—	73	1	no	—
372	C₂³	(C₂×#64408)⋊C₄	1	1	yes	characteristic
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	292	4	no	—
375	C₂×C₄	—	292	4	no	—
376	C₂×C₄	—	292	16	no	—
377	C₂×C₄	—	73	4	no	—
378	C₂×C₄	—	73	2	no	—
379	C₂×C₄	—	73	2	no	—
380	C₂×C₄	—	73	1	no	—
381	C₂×C₄	—	73	1	no	—
382	C₂×C₄	—	73	1	no	—
383	C₂×C₄	—	73	1	no	—
384	C₂×C₄	—	73	4	no	—
385	C₂×C₄	—	73	4	no	—
386	C₂×C₄	—	73	2	no	—
387	C₂×C₄	—	73	2	no	—
388	C₂×C₄	—	73	2	no	—
389	C₂×C₄	—	73	2	no	—
390	C₂×C₄	—	73	2	no	—
391	C₂×C₄	—	73	2	no	—
392	C₂×C₄	—	73	2	no	—
393	C₂×C₄	—	73	2	no	—
394	C₂×C₄	—	73	1	no	—
395	C₂×C₄	—	73	2	no	—
396	C₂×C₄	—	73	1	no	—
397	C₂×C₄	—	73	1	no	—
398	C₂×C₄	—	73	2	no	—
399	C₂×C₄	—	73	1	no	—
400	C₂×C₄	—	73	1	no	—
401	C₂×C₄	—	73	1	no	—
402	C₂×C₄	—	146	2	no	—
403	C₂×C₄	—	146	2	no	—
404	C₂×C₄	—	146	2	no	—
405	C₂×C₄	—	146	2	no	—
406	C₂×C₄	—	146	8	no	—
407	C₂×C₄	—	146	2	no	—
408	C₂×C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
409	C₂×C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
410	C₂×C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
411	C₂×C₄	C₈×#64408	1	2	yes	—
412	C₂×C₄	#14556645	1	2	yes	—
413	C₂×C₄	#14556653	1	2	yes	—
414	C₂×C₄	#14556654	1	2	yes	—
415	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
416	C₂×C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
417	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
418	C₈	—	4	2	no	—
419	C₈	—	292	2	no	—
420	C₈	—	146	8	no	—
421	C₂²	—	73	2	no	—
422	C₂²	—	73	2	no	—
423	C₂²	—	73	2	no	—
424	C₂²	—	73	2	no	—
425	C₂²	—	73	1	no	—
426	C₂²	—	73	2	no	—
427	C₂²	—	73	1	no	—
428	C₂²	—	73	8	no	—
429	C₂²	—	73	8	no	—
430	C₂²	#17989452	1	2	yes	—
431	C₂²	#17989459	1	2	yes	—
432	C₂²	#17989460	1	2	yes	—
433	C₂²	C₂×(C₂×#64408)⋊C₄	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	292	8	no	—
437	C₄	—	73	2	no	—
438	C₄	—	73	2	no	—
439	C₄	—	73	2	no	—
440	C₄	—	73	1	no	—
441	C₄	—	73	1	no	—
442	C₄	—	146	1	no	—
443	C₄	—	146	1	no	—
444	C₄	#17989452	1	2	yes	—
445	C₄	#17989460	1	2	yes	—
446	C₄	C₂×C₈×#64408	1	1	yes	characteristic
447	C₄	C₂×#14556645	1	1	yes	characteristic
448	C₄	C₂×#14556653	1	1	yes	characteristic
449	C₄	C₂×#14556654	1	1	yes	characteristic
450	C₂	—	73	2	no	—
451	C₂	—	73	2	no	—
452	C₂	—	73	4	no	—
453	C₂	#22624765	1	4	yes	direct product factor
454	C₂	C₂×#17989452	1	1	yes	characteristic
455	C₂	C₂×#17989459	1	1	yes	characteristic
456	C₂	C₂×#17989460	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊#64408
commutator	C₄×C₇₃	C₂×C₄×C₈
Frattini	C₄²	C₂²×#64408
Fitting	C₂×C₄⋊C₈×C₇₃	C₄
socle	C₂³×C₇₃	#95
prime radical	C₂³×D₇₃	C₂²⋊C₄
cosocle	C₄²×D₇₃	C₂³
hypercenter	C₂×C₄⋊C₈	#64408
hypocenter	C₇₃	C₂×#1279
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #22624765	C₂	direct (N × H)
10. C₄×#11924036	C₄	semidirect
13. C₂×C₄×#10596833	C₄	semidirect
21. C₂×C₄⋊#10596831	C₄	semidirect
25. C₄⋊C₈×D₇₃	C₄	semidirect
27. C₂×C₄⋊C₈×C₇₃	C₄	semidirect
35. C₂×C₄⋊#64408	C₈	semidirect
44. C₄×#10596833	C₂×C₄	semidirect
67. C₄⋊#10596831	C₂×C₄	semidirect
73. C₄⋊C₈×C₇₃	C₂×C₄	semidirect
84. C₄⋊#64408	C₂×C₈	semidirect
222. C₂×C₇₃	#1279	semidirect
226. D₇₃	#1279	semidirect
233. C₇₃	C₂×#1279	semidirect
245. C₂×C₄⋊C₈	#64408	semidirect
296. C₄⋊C₈	C₂×#64408	semidirect
453. C₂	#22624765	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×C₄×#11924036	2
C₂×C₄×C₄⋊#64408	2
#22624765	2
C₂×C₄⋊C₈×D₇₃	2
C₂×#1279	73

Subgroups — C2×#22624765 #34002141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22624765 #34002141