Subgroups — C₂×#22618807 #33950139

Order 18688.

2806 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989070	C₂	1	2	yes	maximal, complemented
2	#22618807	C₂	1	16	yes	maximal, direct product factor
3	C₂×#17988688	C₂	1	4	yes	maximal, complemented
4	C₂×Q₁₆×Dic₇₃	C₂	1	2	yes	maximal, complemented
5	C₂×D₈×Dic₇₃	C₂	1	2	yes	maximal, complemented
6	C₂²×#14556525	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#17988588	C₂	1	2	yes	maximal, complemented
8	C₂×#17988542	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#135×C₇₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×#11924012	C₂²	1	1	yes	characteristic
11	#17989070	—	2	8	no	—
12	#17989070	C₂²	1	16	yes	complemented
13	C₂×Q₈×Dic₇₃	C₂²	1	4	yes	—
14	C₂×D₄×Dic₇₃	—	2	4	no	—
15	C₂×D₄×Dic₇₃	C₂²	1	4	yes	—
16	C₂×#14556550	—	2	2	no	—
17	C₂×#14556550	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊Dic₇₃	—	2	2	no	—
19	C₂²×C₄⋊Dic₇₃	C₂²	1	2	yes	—
20	#17988688	C₂²	1	32	yes	complemented
21	Q₁₆×Dic₇₃	C₂²	1	16	yes	complemented
22	D₈×Dic₇₃	C₂²	1	16	yes	complemented
23	C₂×#14556525	C₂²	1	2	yes	—
24	C₂×#14556525	C₂²	1	2	yes	—
25	C₂×#14556525	C₂²	1	8	yes	complemented
26	#17988588	C₂²	1	16	yes	complemented
27	C₂×#14556515	C₂²	1	4	yes	—
28	C₂×#14556512	C₂²	1	4	yes	—
29	#17988542	C₂²	1	8	yes	complemented
30	C₂×#14556501	C₂²	1	2	yes	—
31	C₂×C₈×Dic₇₃	C₂²	1	2	yes	—
32	C₂²×#41×C₇₃	C₂²	1	2	yes	—
33	C₂×#135×C₇₃	C₄	1	16	yes	complemented
34	C₂×#135×C₇₃	C₂²	1	8	yes	—
35	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
36	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
37	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
38	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₂³×Dic₇₃	—	2	4	no	—
40	C₂³×Dic₇₃	—	2	2	no	—
41	C₂×#11924012	—	2	4	no	—
42	C₂×#11924012	C₂³	1	4	yes	—
43	C₂²×#10596831	C₂³	1	2	yes	—
44	Q₈×Dic₇₃	—	2	8	no	—
45	Q₈×Dic₇₃	C₂³	1	16	yes	—
46	D₄×Dic₇₃	—	2	32	no	—
47	D₄×Dic₇₃	—	2	8	no	—
48	D₄×Dic₇₃	C₂³	1	16	yes	—
49	#14556550	—	2	16	no	—
50	#14556550	D₄	1	4	yes	—
51	#14556550	C₂³	1	4	yes	—
52	C₂×C₄⋊Dic₇₃	—	2	4	no	—
53	C₂×C₄⋊Dic₇₃	—	2	16	no	—
54	C₂×C₄⋊Dic₇₃	—	2	2	no	—
55	C₂×C₄⋊Dic₇₃	—	2	4	no	—
56	C₂×C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
57	C₂×C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
58	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
59	C₂×C₄⋊Dic₇₃	C₂³	1	8	yes	—
60	C₂×C₂²⋊Dic₇₃	—	2	4	no	—
61	C₂×C₂²⋊Dic₇₃	D₄	1	2	yes	—
62	C₂×C₄×Dic₇₃	—	2	4	no	—
63	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
64	#14556525	C₂³	1	8	yes	—
65	#14556525	C₂³	1	8	yes	—
66	#14556515	C₂³	1	16	yes	—
67	#14556512	C₂³	1	16	yes	—
68	#14556501	C₂³	1	8	yes	—
69	C₈×Dic₇₃	C₂³	1	8	yes	—
70	C₂×#41×C₇₃	—	2	4	no	—
71	C₂×#41×C₇₃	—	2	8	no	—
72	C₂×#41×C₇₃	C₂×C₄	1	16	yes	complemented
73	C₂×#41×C₇₃	C₂³	1	8	yes	—
74	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
75	C₂²×D₄×C₇₃	—	2	2	no	—
76	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₇₃	—	2	2	no	—
78	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
79	#135×C₇₃	C₂×C₄	1	64	yes	complemented
80	C₂×Q₁₆×C₇₃	C₂×C₄	1	8	yes	complemented
81	C₂×Q₁₆×C₇₃	C₂³	1	4	yes	—
82	C₂×SD₁₆×C₇₃	C₂×C₄	1	16	yes	complemented
83	C₂×SD₁₆×C₇₃	C₂³	1	8	yes	—
84	C₂×D₈×C₇₃	C₂×C₄	1	8	yes	complemented
85	C₂×D₈×C₇₃	C₂³	1	4	yes	—
86	C₂²×C₈×C₇₃	C₂×C₄	1	8	yes	complemented
87	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
90	C₂²×Dic₇₃	—	2	4	no	—
91	C₂²×Dic₇₃	—	2	8	no	—
92	C₂²×Dic₇₃	—	2	16	no	—
93	C₂²×Dic₇₃	—	8	8	no	—
94	C₂²×Dic₇₃	—	8	4	no	—
95	C₂²×Dic₇₃	C₂×D₄	1	2	yes	—
96	C₂²×Dic₇₃	C₂×D₄	1	2	yes	—
97	#11924012	—	2	8	no	—
98	C₂×#10596831	—	2	4	no	—
99	C₂×#10596831	C₂⁴	1	4	yes	—
100	C₄⋊Dic₇₃	—	2	8	no	—
101	C₄⋊Dic₇₃	—	2	4	no	—
102	C₄⋊Dic₇₃	—	2	16	no	—
103	C₄⋊Dic₇₃	C₂×D₄	1	4	yes	—
104	C₄⋊Dic₇₃	C₂×D₄	1	4	yes	—
105	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
106	C₂²⋊Dic₇₃	—	2	16	no	—
107	C₂²⋊Dic₇₃	C₂×D₄	1	8	yes	—
108	C₄×Dic₇₃	—	2	16	no	—
109	C₄×Dic₇₃	C₂×D₄	1	4	yes	—
110	C₄×Dic₇₃	C₂⁴	1	4	yes	—
111	C₂⁴×C₇₃	—	2	2	no	—
112	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
113	#41×C₇₃	—	2	32	no	—
114	#41×C₇₃	—	2	16	no	—
115	#41×C₇₃	C₂²×C₄	1	32	yes	complemented
116	C₂×Q₈×C₇₃	—	2	2	no	—
117	C₂×Q₈×C₇₃	—	2	4	no	—
118	C₂×Q₈×C₇₃	C₂²×C₄	1	8	yes	—
119	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
120	C₂×D₄×C₇₃	—	2	16	no	—
121	C₂×D₄×C₇₃	—	2	8	no	—
122	C₂×D₄×C₇₃	—	2	2	no	—
123	C₂×D₄×C₇₃	—	2	4	no	—
124	C₂×D₄×C₇₃	C₂²×C₄	1	8	yes	—
125	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₇₃	—	2	2	no	—
127	C₂²×C₄×C₇₃	—	2	16	no	—
128	C₂²×C₄×C₇₃	—	2	8	no	—
129	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₇₃	#41	1	4	yes	—
133	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
135	Q₁₆×C₇₃	C₂²×C₄	1	16	yes	complemented
136	SD₁₆×C₇₃	C₂²×C₄	1	32	yes	complemented
137	D₈×C₇₃	C₂²×C₄	1	16	yes	complemented
138	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
139	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
140	C₂×C₈×C₇₃	C₂²×C₄	1	16	yes	complemented
141	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
142	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
143	C₂³×C₇₃	—	2	2	no	—
144	C₂³×C₇₃	—	2	2	no	—
145	C₂³×C₇₃	—	2	8	no	—
146	C₂³×C₇₃	—	2	4	no	—
147	C₂³×C₇₃	—	4	4	no	—
148	C₂³×C₇₃	—	4	4	no	—
149	C₂³×C₇₃	C₄×D₄	1	4	yes	—
150	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
151	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₇₃	—	2	8	no	—
153	Q₈×C₇₃	—	2	4	no	—
154	Q₈×C₇₃	C₂³×C₄	1	8	yes	—
155	D₄×C₇₃	—	2	32	no	—
156	D₄×C₇₃	—	2	8	no	—
157	D₄×C₇₃	—	2	4	no	—
158	D₄×C₇₃	C₂³×C₄	1	8	yes	—
159	C₂×C₄×C₇₃	—	2	8	no	—
160	C₂×C₄×C₇₃	—	2	4	no	—
161	C₂×C₄×C₇₃	—	2	32	no	—
162	C₂×C₄×C₇₃	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₇₃	C₄×D₄	1	8	yes	—
164	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
165	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
166	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
167	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
169	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
170	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
171	C₂×Dic₇₃	—	2	4	no	—
172	C₂×Dic₇₃	—	2	4	no	—
173	C₂×Dic₇₃	—	2	8	no	—
174	C₂×Dic₇₃	—	4	8	no	—
175	C₂×Dic₇₃	—	8	16	no	—
176	C₂×Dic₇₃	—	8	8	no	—
177	C₂×Dic₇₃	C₂²×D₄	1	4	yes	—
178	C₂×Dic₇₃	C₂²×D₄	1	4	yes	—
179	C₈×C₇₃	C₂³×C₄	1	4	yes	—
180	C₈×C₇₃	C₂³×C₄	1	4	yes	—
181	#10596831	—	2	4	no	—
182	C₂²×C₇₃	—	2	8	no	—
183	C₂²×C₇₃	—	2	2	no	—
184	C₂²×C₇₃	—	2	2	no	—
185	C₂²×C₇₃	—	2	8	no	—
186	C₂²×C₇₃	—	4	16	no	—
187	C₂²×C₇₃	—	4	4	no	—
188	C₂²×C₇₃	—	4	4	no	—
189	C₂²×C₇₃	C₂×C₄×D₄	1	4	yes	—
190	C₂²×C₇₃	C₂×C₄×D₄	1	2	yes	—
191	C₂²×C₇₃	#576	1	2	yes	—
192	C₂²×C₇₃	#578	1	2	yes	—
193	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
194	C₄×C₇₃	—	2	8	no	—
195	C₄×C₇₃	C₂×C₄×D₄	1	4	yes	—
196	C₄×C₇₃	C₂×C₄×D₄	1	2	yes	—
197	C₄×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
198	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
199	Dic₇₃	—	2	4	no	—
200	Dic₇₃	—	2	4	no	—
201	Dic₇₃	—	4	8	no	—
202	C₂×#2951	—	73	1	no	maximal, Sylow
203	C₂×C₇₃	—	2	4	no	—
204	C₂×C₇₃	—	4	8	no	—
205	C₂×C₇₃	#2951	1	4	yes	complemented
206	C₂×C₇₃	C₂²×C₄×D₄	1	1	yes	characteristic
207	C₂×C₇₃	C₂×#576	1	1	yes	characteristic
208	C₂×C₇₃	C₂×#578	1	1	yes	characteristic
209	C₂²×#135	D₇₃	1	1	yes	characteristic
210	C₂×#520	—	73	2	no	—
211	#2951	—	73	16	no	—
212	C₂×#440	—	73	4	no	—
213	C₂×C₄×Q₁₆	—	73	2	no	—
214	C₂×C₄×D₈	—	73	2	no	—
215	C₂²×#107	—	73	1	no	—
216	C₂×#417	—	73	2	no	—
217	C₂×#405	—	73	1	no	—
218	C₇₃	C₂×#2951	1	1	yes	characteristic, complemented, Sylow
219	C₂²×#41	C₂×D₇₃	1	2	yes	—
220	C₂×#135	Dic₇₃	1	16	yes	complemented
221	C₂×#135	C₂×D₇₃	1	8	yes	—
222	C₂²×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
223	C₂²×SD₁₆	C₂×D₇₃	1	2	yes	—
224	C₂²×D₈	C₂×D₇₃	1	1	yes	characteristic
225	C₂²×M₁₆	—	73	1	no	—
226	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic
227	#520	—	73	16	no	—
228	#520	—	146	8	no	—
229	C₂×C₄×Q₈	—	73	4	no	—
230	C₂×C₄×D₄	—	73	4	no	—
231	C₂×C₄×D₄	—	146	4	no	—
232	C₂×#117	—	73	1	no	—
233	C₂×#117	—	146	2	no	—
234	C₂²×C₄⋊C₄	—	73	2	no	—
235	C₂²×C₄⋊C₄	—	146	2	no	—
236	#440	—	73	32	no	—
237	C₄×Q₁₆	—	73	16	no	—
238	C₄×D₈	—	73	16	no	—
239	C₂×#107	—	73	2	no	—
240	C₂×#107	—	73	2	no	—
241	C₂×#107	—	73	8	no	—
242	#417	—	73	16	no	—
243	C₂×#103	—	73	4	no	—
244	C₂×#102	—	73	4	no	—
245	#405	—	73	8	no	—
246	C₂×#97	—	73	2	no	—
247	C₂×C₄×C₈	—	73	2	no	—
248	C₂×#41	—	2	4	no	—
249	C₂×#41	—	2	8	no	—
250	C₂×#41	C₂×Dic₇₃	1	16	yes	complemented
251	C₂×#41	C₂²×D₇₃	1	8	yes	—
252	C₂²×Q₈	C₂²×D₇₃	1	2	yes	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
255	C₂³×C₄	—	2	2	no	—
256	C₂³×C₄	—	146	4	no	—
257	C₂³×C₄	—	146	2	no	—
258	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
259	#135	C₂×Dic₇₃	1	64	yes	complemented
260	C₂×Q₁₆	C₂×Dic₇₃	1	8	yes	complemented
261	C₂×Q₁₆	C₂²×D₇₃	1	4	yes	—
262	C₂×SD₁₆	C₂×Dic₇₃	1	16	yes	complemented
263	C₂×SD₁₆	C₂²×D₇₃	1	8	yes	—
264	C₂×D₈	C₂×Dic₇₃	1	8	yes	complemented
265	C₂×D₈	C₂²×D₇₃	1	4	yes	—
266	C₂×M₁₆	—	73	4	no	—
267	C₂×M₁₆	—	146	4	no	—
268	C₂²×C₈	—	73	2	no	—
269	C₂²×C₈	C₂×Dic₇₃	1	8	yes	complemented
270	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
271	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
272	C₂²×C₈	C₂²×D₇₃	1	4	yes	—
273	C₄×Q₈	—	73	16	no	—
274	C₄×Q₈	—	146	8	no	—
275	C₄×D₄	—	73	16	no	—
276	C₄×D₄	—	146	8	no	—
277	C₄×D₄	—	146	32	no	—
278	#117	—	73	4	no	—
279	#117	—	73	4	no	—
280	#117	—	146	16	no	—
281	C₂×C₄⋊C₄	—	73	1	no	—
282	C₂×C₄⋊C₄	—	73	1	no	—
283	C₂×C₄⋊C₄	—	73	4	no	—
284	C₂×C₄⋊C₄	—	73	8	no	—
285	C₂×C₄⋊C₄	—	146	16	no	—
286	C₂×C₄⋊C₄	—	146	4	no	—
287	C₂×C₄⋊C₄	—	146	2	no	—
288	C₂×C₄⋊C₄	—	146	4	no	—
289	C₂×C₂²⋊C₄	—	73	2	no	—
290	C₂×C₂²⋊C₄	—	146	4	no	—
291	C₂×C₄²	—	73	2	no	—
292	C₂×C₄²	—	146	4	no	—
293	#107	—	73	8	no	—
294	#107	—	73	8	no	—
295	#103	—	73	16	no	—
296	#102	—	73	16	no	—
297	#97	—	73	8	no	—
298	C₄×C₈	—	73	8	no	—
299	C₂⁴	—	2	2	no	—
300	C₂⁴	D₄×D₇₃	1	1	yes	characteristic
301	#41	—	2	32	no	—
302	#41	—	2	16	no	—
303	#41	C₂²×Dic₇₃	1	32	yes	complemented
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	C₂²×Dic₇₃	1	8	yes	—
307	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
308	C₂×D₄	—	2	16	no	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	C₂²×Dic₇₃	1	8	yes	—
313	C₂×D₄	C₂³×D₇₃	1	4	yes	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	16	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	584	4	no	—
318	C₂²×C₄	—	584	8	no	—
319	C₂²×C₄	—	73	2	no	—
320	C₂²×C₄	—	73	2	no	—
321	C₂²×C₄	—	146	4	no	—
322	C₂²×C₄	—	146	16	no	—
323	C₂²×C₄	—	146	8	no	—
324	C₂²×C₄	C₂²×Dic₇₃	1	4	yes	—
325	C₂²×C₄	D₄×D₇₃	1	2	yes	—
326	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
327	C₂²×C₄	#11924027	1	4	yes	—
328	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
329	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
330	Q₁₆	C₂²×Dic₇₃	1	16	yes	complemented
331	SD₁₆	C₂²×Dic₇₃	1	32	yes	complemented
332	D₈	C₂²×Dic₇₃	1	16	yes	complemented
333	M₁₆	—	146	8	no	—
334	C₂×C₈	—	73	4	no	—
335	C₂×C₈	—	146	4	no	—
336	C₂×C₈	C₂²×Dic₇₃	1	4	yes	—
337	C₂×C₈	C₂²×Dic₇₃	1	4	yes	—
338	C₂×C₈	C₂²×Dic₇₃	1	16	yes	complemented
339	C₂×C₈	C₂³×D₇₃	1	2	yes	—
340	C₂×C₈	C₂³×D₇₃	1	2	yes	—
341	C₄⋊C₄	—	73	4	no	—
342	C₄⋊C₄	—	73	4	no	—
343	C₄⋊C₄	—	73	8	no	—
344	C₄⋊C₄	—	146	16	no	—
345	C₄⋊C₄	—	146	8	no	—
346	C₄⋊C₄	—	146	4	no	—
347	C₂²⋊C₄	—	73	8	no	—
348	C₂²⋊C₄	—	146	16	no	—
349	C₄²	—	73	4	no	—
350	C₄²	—	73	4	no	—
351	C₄²	—	146	16	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	4	no	—
358	C₂³	D₄×Dic₇₃	1	4	yes	—
359	C₂³	C₂×D₄×D₇₃	1	2	yes	—
360	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
361	Q₈	—	2	4	no	—
362	Q₈	—	2	8	no	—
363	Q₈	C₂³×Dic₇₃	1	8	yes	—
364	D₄	—	2	32	no	—
365	D₄	—	2	4	no	—
366	D₄	—	2	8	no	—
367	D₄	C₂³×Dic₇₃	1	8	yes	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	32	no	—
371	C₂×C₄	—	292	8	no	—
372	C₂×C₄	—	584	8	no	—
373	C₂×C₄	—	584	16	no	—
374	C₂×C₄	—	73	4	no	—
375	C₂×C₄	—	73	4	no	—
376	C₂×C₄	—	146	8	no	—
377	C₂×C₄	—	146	4	no	—
378	C₂×C₄	—	146	4	no	—
379	C₂×C₄	D₄×Dic₇₃	1	4	yes	—
380	C₂×C₄	D₄×Dic₇₃	1	8	yes	—
381	C₂×C₄	C₂³×Dic₇₃	1	2	yes	—
382	C₂×C₄	C₂³×Dic₇₃	1	4	yes	—
383	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
384	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
385	C₂×C₄	C₂×#11924027	1	2	yes	—
386	C₂×C₄	C₂×#11924027	1	4	yes	—
387	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
388	C₈	—	146	4	no	—
389	C₈	C₂³×Dic₇₃	1	4	yes	—
390	C₈	C₂³×Dic₇₃	1	4	yes	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	8	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	8	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	4	16	no	—
397	C₂²	—	4	4	no	—
398	C₂²	C₂×D₄×Dic₇₃	1	4	yes	—
399	C₂²	C₂×D₄×Dic₇₃	1	2	yes	—
400	C₂²	#17989389	1	2	yes	—
401	C₂²	#17989401	1	2	yes	—
402	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
403	C₄	—	2	8	no	—
404	C₄	—	292	8	no	—
405	C₄	—	146	4	no	—
406	C₄	—	146	4	no	—
407	C₄	C₂×D₄×Dic₇₃	1	4	yes	—
408	C₄	C₂×D₄×Dic₇₃	1	2	yes	—
409	C₄	C₂⁴×Dic₇₃	1	1	yes	characteristic
410	C₄	C₂²×#11924027	1	1	yes	characteristic
411	C₂	—	2	4	no	—
412	C₂	—	4	8	no	—
413	C₂	#22618807	1	4	yes	direct product factor
414	C₂	C₂²×D₄×Dic₇₃	1	1	yes	characteristic
415	C₂	C₂×#17989389	1	1	yes	characteristic
416	C₂	C₂×#17989401	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₇₃
commutator	C₄×C₇₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting, prime radical	C₂²×#135×C₇₃	C₂
socle	C₂³×C₇₃	C₂²×D₄
cosocle	C₂×C₄×C₇₃	C₂⁵
hypercenter	C₂²×#135	D₇₃
hypocenter	C₇₃	C₂×#2951
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#17989070	C₂	semidirect
2. #22618807	C₂	direct (N × H)
3. C₂×#17988688	C₂	semidirect
4. C₂×Q₁₆×Dic₇₃	C₂	semidirect
5. C₂×D₈×Dic₇₃	C₂	semidirect
6. C₂²×#14556525	C₂	semidirect
7. C₂×#17988588	C₂	semidirect
8. C₂×#17988542	C₂	semidirect
12. #17989070	C₂²	semidirect
20. #17988688	C₂²	semidirect
21. Q₁₆×Dic₇₃	C₂²	semidirect
22. D₈×Dic₇₃	C₂²	semidirect
25. C₂×#14556525	C₂²	semidirect
26. #17988588	C₂²	semidirect
29. #17988542	C₂²	semidirect
33. C₂×#135×C₇₃	C₄	semidirect
72. C₂×#41×C₇₃	C₂×C₄	semidirect
79. #135×C₇₃	C₂×C₄	semidirect
80. C₂×Q₁₆×C₇₃	C₂×C₄	semidirect
82. C₂×SD₁₆×C₇₃	C₂×C₄	semidirect
84. C₂×D₈×C₇₃	C₂×C₄	semidirect
86. C₂²×C₈×C₇₃	C₂×C₄	semidirect
115. #41×C₇₃	C₂²×C₄	semidirect
135. Q₁₆×C₇₃	C₂²×C₄	semidirect
136. SD₁₆×C₇₃	C₂²×C₄	semidirect
137. D₈×C₇₃	C₂²×C₄	semidirect
140. C₂×C₈×C₇₃	C₂²×C₄	semidirect
205. C₂×C₇₃	#2951	semidirect
218. C₇₃	C₂×#2951	semidirect
220. C₂×#135	Dic₇₃	semidirect
250. C₂×#41	C₂×Dic₇₃	semidirect
259. #135	C₂×Dic₇₃	semidirect
260. C₂×Q₁₆	C₂×Dic₇₃	semidirect
262. C₂×SD₁₆	C₂×Dic₇₃	semidirect
264. C₂×D₈	C₂×Dic₇₃	semidirect
269. C₂²×C₈	C₂×Dic₇₃	semidirect
303. #41	C₂²×Dic₇₃	semidirect
330. Q₁₆	C₂²×Dic₇₃	semidirect
331. SD₁₆	C₂²×Dic₇₃	semidirect
332. D₈	C₂²×Dic₇₃	semidirect
338. C₂×C₈	C₂²×Dic₇₃	semidirect
413. C₂	#22618807	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×#17989070	2
#22618807	2
C₂×#17988688	2
C₂×Q₁₆×Dic₇₃	2
C₂×D₈×Dic₇₃	2
C₂²×#14556525	2
C₂×#17988588	2
C₂×#17988542	2
C₂²×#135×C₇₃	2
C₂×#2951	73

Subgroups — C2×#22618807 #33950139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22618807 #33950139