Subgroups — C₂²×#17989394 #33999799

Order 18688.

11118 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556638	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14556637	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#17989394	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#14556623	C₂	1	2	yes	maximal, complemented
5	C₂²×#14556621	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#14556616	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#14556615	C₂	1	2	yes	maximal, complemented
8	C₂²×#14556612	C₂	1	2	yes	maximal, complemented
9	C₂³×#11924017	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×D₇₃	C₂	1	2	yes	maximal, complemented
11	C₂²×#14556597	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#135×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#14556638	—	2	12	no	—
14	C₂×#14556638	C₂²	1	24	yes	complemented
15	C₂×#14556637	—	2	12	no	—
16	C₂×#14556637	C₂²	1	24	yes	complemented
17	C₂²×#11924029	C₂²	1	2	yes	—
18	C₂²×#11924028	—	2	1	no	—
19	C₂²×#11924028	—	2	1	no	—
20	C₂²×#11924028	C₂²	1	1	yes	characteristic
21	C₂²×#11924027	—	2	2	no	—
22	C₂²×#11924027	C₂²	1	2	yes	complemented
23	C₂³×Dic₁₄₆	—	2	1	no	—
24	C₂³×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
25	C₂²×Q₈×D₇₃	C₂²	1	2	yes	complemented
26	C₂³×D₂₉₂	—	2	1	no	—
27	C₂³×D₂₉₂	C₂²	1	1	yes	characteristic
28	C₂²×D₄×D₇₃	—	2	2	no	—
29	C₂²×D₄×D₇₃	C₂²	1	2	yes	—
30	#17989394	C₂²	1	256	yes	direct product factor
31	C₂×#14556623	C₂²	1	48	yes	complemented
32	C₂×#14556621	C₂²	1	24	yes	complemented
33	C₂×#14556616	C₂²	1	24	yes	complemented
34	C₂×#14556615	C₂²	1	48	yes	complemented
35	C₂×#14556612	C₂²	1	48	yes	complemented
36	C₂²×#11924018	C₂²	1	2	yes	complemented
37	C₂²×#11924017	C₂²	1	2	yes	complemented
38	C₂²×#11924017	C₂²	1	2	yes	complemented
39	C₂²×#11924017	C₂²	1	24	yes	complemented
40	C₂²×#11924016	C₂²	1	2	yes	complemented
41	C₂²×#11924015	C₂²	1	2	yes	complemented
42	C₂×SD₁₆×D₇₃	C₂²	1	48	yes	complemented
43	C₂²×#11924013	C₂²	1	2	yes	complemented
44	C₂×#14556597	C₂²	1	24	yes	complemented
45	C₂²×#11924012	C₂²	1	1	yes	characteristic, complemented
46	C₂²×#11924011	C₂²	1	2	yes	complemented
47	C₂²×C₈×D₇₃	C₂²	1	2	yes	complemented
48	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
49	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×#135×C₇₃	C₂²	1	24	yes	complemented
51	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
52	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
53	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
54	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
55	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
56	C₂⁴×D₇₃	—	2	2	no	—
57	C₂⁴×D₇₃	—	2	1	no	—
58	#14556638	—	2	96	no	—
59	#14556638	C₂³	1	64	yes	complemented
60	#14556637	—	2	96	no	—
61	#14556637	C₂³	1	64	yes	complemented
62	C₂×#11924029	—	2	12	no	—
63	C₂×#11924029	C₂³	1	24	yes	—
64	C₂×#11924028	—	2	24	no	—
65	C₂×#11924028	—	2	24	no	—
66	C₂×#11924028	D₄	1	12	yes	—
67	C₂×#11924028	C₂³	1	12	yes	—
68	C₂×#11924027	—	2	48	no	—
69	C₂×#11924027	—	2	12	no	—
70	C₂×#11924027	C₂³	1	24	yes	complemented
71	C₂²×Dic₁₄₆	—	2	24	no	—
72	C₂²×Dic₁₄₆	—	2	2	no	—
73	C₂²×Dic₁₄₆	—	2	1	no	—
74	C₂²×Dic₁₄₆	—	2	6	no	—
75	C₂²×Dic₁₄₆	D₄	1	1	yes	characteristic
76	C₂²×Dic₁₄₆	C₂³	1	2	yes	—
77	C₂²×Dic₁₄₆	C₂³	1	12	yes	complemented
78	C₂×Q₈×D₇₃	—	2	12	no	—
79	C₂×Q₈×D₇₃	C₂³	1	24	yes	complemented
80	C₂²×D₂₉₂	—	2	2	no	—
81	C₂²×D₂₉₂	—	2	24	no	—
82	C₂²×D₂₉₂	—	2	1	no	—
83	C₂²×D₂₉₂	—	2	6	no	—
84	C₂²×D₂₉₂	D₄	1	1	yes	characteristic
85	C₂²×D₂₉₂	C₂³	1	2	yes	—
86	C₂²×D₂₉₂	C₂³	1	12	yes	—
87	C₂²×C₂²⋊D₇₃	—	2	2	no	—
88	C₂²×C₂²⋊D₇₃	—	2	2	no	—
89	C₂²×C₂²⋊D₇₃	D₄	1	2	yes	—
90	C₂×D₄×D₇₃	—	2	48	no	—
91	C₂×D₄×D₇₃	—	2	12	no	—
92	C₂×D₄×D₇₃	C₂³	1	24	yes	—
93	C₂³×Dic₇₃	—	2	2	no	—
94	C₂³×Dic₇₃	—	2	1	no	—
95	C₂²×C₄×D₇₃	—	2	2	no	—
96	C₂²×C₄×D₇₃	—	2	2	no	—
97	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
98	#14556623	C₂³	1	128	yes	complemented
99	#14556621	C₂³	1	64	yes	complemented
100	#14556616	C₂³	1	64	yes	complemented
101	#14556615	C₂³	1	128	yes	complemented
102	#14556612	C₂³	1	128	yes	complemented
103	C₂×#11924018	C₂³	1	24	yes	complemented
104	C₂×#11924017	C₂³	1	24	yes	complemented
105	C₂×#11924017	C₂³	1	24	yes	complemented
106	C₂×#11924017	C₂³	1	64	yes	complemented
107	C₂×#11924016	C₂³	1	24	yes	complemented
108	C₂×#11924015	C₂³	1	24	yes	complemented
109	SD₁₆×D₇₃	C₂³	1	128	yes	complemented
110	C₂×#11924013	C₂³	1	24	yes	complemented
111	#14556597	C₂³	1	64	yes	complemented
112	C₂×#11924012	C₂³	1	12	yes	complemented
113	C₂×#11924011	C₂³	1	24	yes	complemented
114	C₂²×#10596831	C₂³	1	2	yes	—
115	C₂×C₈×D₇₃	C₂³	1	24	yes	complemented
116	C₂×#41×C₇₃	—	2	6	no	—
117	C₂×#41×C₇₃	—	2	6	no	—
118	C₂×#41×C₇₃	C₂³	1	12	yes	—
119	C₂×#41×C₇₃	C₂³	1	12	yes	complemented
120	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₇₃	—	2	1	no	—
123	C₂²×D₄×C₇₃	—	2	1	no	—
124	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₇₃	—	2	1	no	—
127	C₂³×C₄×C₇₃	—	2	1	no	—
128	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
129	#135×C₇₃	C₂³	1	64	yes	complemented
130	C₂×Q₁₆×C₇₃	C₂³	1	12	yes	complemented
131	C₂×SD₁₆×C₇₃	C₂³	1	12	yes	complemented
132	C₂×SD₁₆×C₇₃	C₂³	1	12	yes	complemented
133	C₂×D₈×C₇₃	C₂³	1	12	yes	complemented
134	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
136	C₂²×C₈×C₇₃	C₂³	1	12	yes	complemented
137	C₂³×D₇₃	—	2	2	no	—
138	C₂³×D₇₃	—	2	12	no	—
139	C₂³×D₇₃	—	2	24	no	—
140	C₂³×D₇₃	—	8	8	no	—
141	C₂³×D₇₃	—	8	4	no	—
142	C₂³×D₇₃	C₂×D₄	1	2	yes	—
143	#11924029	—	2	48	no	—
144	#11924029	C₂⁴	1	32	yes	—
145	#11924028	—	2	64	no	—
146	#11924028	—	2	64	no	—
147	#11924028	C₂×D₄	1	48	yes	—
148	#11924028	C₂⁴	1	16	yes	—
149	#11924027	—	2	128	no	—
150	#11924027	—	2	48	no	—
151	#11924027	C₂⁴	1	32	yes	complemented
152	C₂×Dic₁₄₆	—	2	6	no	—
153	C₂×Dic₁₄₆	—	2	12	no	—
154	C₂×Dic₁₄₆	—	2	24	no	—
155	C₂×Dic₁₄₆	—	2	24	no	—
156	C₂×Dic₁₄₆	—	2	64	no	—
157	C₂×Dic₁₄₆	C₂×D₄	1	12	yes	—
158	C₂×Dic₁₄₆	C₂⁴	1	12	yes	—
159	C₂×Dic₁₄₆	C₂⁴	1	16	yes	complemented
160	Q₈×D₇₃	—	2	48	no	—
161	Q₈×D₇₃	C₂⁴	1	32	yes	complemented
162	C₂×D₂₉₂	—	2	24	no	—
163	C₂×D₂₉₂	—	2	6	no	—
164	C₂×D₂₉₂	—	2	12	no	—
165	C₂×D₂₉₂	—	2	24	no	—
166	C₂×D₂₉₂	—	2	64	no	—
167	C₂×D₂₉₂	C₂×D₄	1	12	yes	—
168	C₂×D₂₉₂	C₂⁴	1	12	yes	—
169	C₂×D₂₉₂	C₂⁴	1	16	yes	—
170	C₂×C₂²⋊D₇₃	—	2	24	no	—
171	C₂×C₂²⋊D₇₃	—	2	24	no	—
172	C₂×C₂²⋊D₇₃	C₂×D₄	1	24	yes	—
173	D₄×D₇₃	—	2	128	no	—
174	D₄×D₇₃	—	2	48	no	—
175	D₄×D₇₃	C₂⁴	1	32	yes	—
176	C₂²×Dic₇₃	—	2	2	no	—
177	C₂²×Dic₇₃	—	2	12	no	—
178	C₂²×Dic₇₃	—	2	24	no	—
179	C₂²×Dic₇₃	C₂×D₄	1	2	yes	—
180	C₂×C₄×D₇₃	—	2	24	no	—
181	C₂×C₄×D₇₃	—	2	24	no	—
182	C₂×C₄×D₇₃	C₂×D₄	1	12	yes	—
183	C₂×C₄×D₇₃	C₂⁴	1	12	yes	—
184	#11924018	C₂⁴	1	32	yes	complemented
185	#11924017	C₂⁴	1	32	yes	complemented
186	#11924017	C₂⁴	1	32	yes	complemented
187	#11924016	C₂⁴	1	32	yes	complemented
188	#11924015	C₂⁴	1	32	yes	complemented
189	#11924013	C₂⁴	1	32	yes	complemented
190	#11924012	C₂⁴	1	16	yes	complemented
191	#11924011	C₂⁴	1	32	yes	complemented
192	C₂×#10596831	C₂⁴	1	12	yes	—
193	C₈×D₇₃	C₂⁴	1	32	yes	complemented
194	C₂⁴×C₇₃	—	2	1	no	—
195	C₂⁴×C₇₃	—	2	1	no	—
196	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
197	#41×C₇₃	—	2	24	no	—
198	#41×C₇₃	—	2	24	no	—
199	#41×C₇₃	C₂⁴	1	16	yes	—
200	#41×C₇₃	C₂⁴	1	16	yes	complemented
201	C₂×Q₈×C₇₃	—	2	3	no	—
202	C₂×Q₈×C₇₃	—	2	3	no	—
203	C₂×Q₈×C₇₃	C₂⁴	1	6	yes	—
204	C₂×Q₈×C₇₃	C₂⁴	1	6	yes	—
205	C₂×D₄×C₇₃	—	2	12	no	—
206	C₂×D₄×C₇₃	—	2	12	no	—
207	C₂×D₄×C₇₃	—	2	3	no	—
208	C₂×D₄×C₇₃	—	2	3	no	—
209	C₂×D₄×C₇₃	C₂⁴	1	6	yes	—
210	C₂×D₄×C₇₃	C₂⁴	1	6	yes	—
211	C₂²×C₄×C₇₃	—	2	1	no	—
212	C₂²×C₄×C₇₃	—	2	1	no	—
213	C₂²×C₄×C₇₃	—	2	12	no	—
214	C₂²×C₄×C₇₃	—	2	12	no	—
215	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₇₃	C₂×D₄	1	6	yes	—
217	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₇₃	C₂⁴	1	6	yes	—
219	Q₁₆×C₇₃	C₂⁴	1	16	yes	complemented
220	SD₁₆×C₇₃	C₂⁴	1	16	yes	complemented
221	SD₁₆×C₇₃	C₂⁴	1	16	yes	complemented
222	D₈×C₇₃	C₂⁴	1	16	yes	complemented
223	C₂×C₈×C₇₃	C₂⁴	1	6	yes	—
224	C₂×C₈×C₇₃	C₂⁴	1	6	yes	—
225	C₂×C₈×C₇₃	C₂⁴	1	16	yes	complemented
226	C₂³×C₇₃	—	2	4	no	—
227	C₂³×C₇₃	—	2	6	no	—
228	C₂³×C₇₃	—	2	6	no	—
229	C₂³×C₇₃	—	4	4	no	—
230	C₂³×C₇₃	—	4	4	no	—
231	C₂³×C₇₃	C₂²×D₄	1	6	yes	—
232	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
233	C₂²×D₇₃	—	2	8	no	—
234	C₂²×D₇₃	—	2	12	no	—
235	C₂²×D₇₃	—	2	16	no	—
236	C₂²×D₇₃	—	2	32	no	—
237	C₂²×D₇₃	—	4	8	no	—
238	C₂²×D₇₃	—	8	48	no	—
239	C₂²×D₇₃	—	8	24	no	—
240	C₂²×D₇₃	C₂²×D₄	1	12	yes	—
241	Q₈×C₇₃	—	2	6	no	—
242	Q₈×C₇₃	—	2	6	no	—
243	Q₈×C₇₃	C₂⁵	1	4	yes	—
244	Q₈×C₇₃	C₂⁵	1	4	yes	—
245	D₄×C₇₃	—	2	16	no	—
246	D₄×C₇₃	—	2	16	no	—
247	D₄×C₇₃	—	2	6	no	—
248	D₄×C₇₃	—	2	6	no	—
249	D₄×C₇₃	C₂⁵	1	4	yes	—
250	D₄×C₇₃	C₂⁵	1	4	yes	—
251	C₂×C₄×C₇₃	—	2	6	no	—
252	C₂×C₄×C₇₃	—	2	6	no	—
253	C₂×C₄×C₇₃	—	2	16	no	—
254	C₂×C₄×C₇₃	—	2	16	no	—
255	C₂×C₄×C₇₃	C₂²×D₄	1	6	yes	—
256	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
257	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
258	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
259	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
260	C₂²⋊D₇₃	—	2	32	no	—
261	C₂²⋊D₇₃	—	2	32	no	—
262	C₂²⋊D₇₃	C₂²×D₄	1	32	yes	—
263	C₂×Dic₇₃	—	2	12	no	—
264	C₂×Dic₇₃	—	2	16	no	—
265	C₂×Dic₇₃	—	2	32	no	—
266	C₂×Dic₇₃	C₂²×D₄	1	12	yes	—
267	D₂₉₂	—	2	32	no	—
268	D₂₉₂	—	2	12	no	—
269	D₂₉₂	—	2	16	no	—
270	D₂₉₂	C₂²×D₄	1	16	yes	—
271	D₂₉₂	C₂⁵	1	8	yes	—
272	C₄×D₇₃	—	2	32	no	—
273	C₄×D₇₃	—	2	32	no	—
274	C₄×D₇₃	C₂²×D₄	1	24	yes	—
275	C₄×D₇₃	C₂⁵	1	8	yes	—
276	Dic₁₄₆	—	2	12	no	—
277	Dic₁₄₆	—	2	16	no	—
278	Dic₁₄₆	—	2	32	no	—
279	Dic₁₄₆	C₂²×D₄	1	16	yes	—
280	Dic₁₄₆	C₂⁵	1	8	yes	—
281	C₈×C₇₃	C₂⁵	1	4	yes	—
282	C₈×C₇₃	C₂⁵	1	4	yes	—
283	#10596831	C₂⁵	1	8	yes	—
284	C₂²×C₇₃	—	2	12	no	—
285	C₂²×C₇₃	—	2	4	no	—
286	C₂²×C₇₃	—	2	4	no	—
287	C₂²×C₇₃	—	4	12	no	—
288	C₂²×C₇₃	—	4	12	no	—
289	C₂²×C₇₃	#577	1	4	yes	complemented
290	C₂²×C₇₃	C₂³×D₄	1	4	yes	—
291	C₂²×C₇₃	C₂³×D₄	1	3	yes	—
292	C₂×D₇₃	—	2	24	no	—
293	C₂×D₇₃	—	2	8	no	—
294	C₂×D₇₃	—	4	24	no	—
295	C₂×D₇₃	—	8	32	no	—
296	C₂×D₇₃	—	8	16	no	—
297	C₂×D₇₃	C₂³×D₄	1	8	yes	—
298	C₄×C₇₃	—	2	4	no	—
299	C₄×C₇₃	—	2	4	no	—
300	C₄×C₇₃	C₂³×D₄	1	4	yes	—
301	C₄×C₇₃	C₂³×D₄	1	3	yes	—
302	C₄×C₇₃	C₂⁶	1	1	yes	characteristic
303	Dic₇₃	—	2	8	no	—
304	Dic₇₃	C₂³×D₄	1	8	yes	—
305	C₂²×#577	—	73	1	no	maximal, Sylow
306	C₂×C₇₃	—	2	4	no	—
307	C₂×C₇₃	—	4	4	no	—
308	C₂×C₇₃	—	4	4	no	—
309	C₂×C₇₃	C₂×#577	1	6	yes	complemented
310	C₂×C₇₃	C₂⁴×D₄	1	1	yes	characteristic
311	D₇₃	—	2	8	no	—
312	D₇₃	—	4	8	no	—
313	C₂²×2₋¹⁺⁴	—	73	1	no	—
314	C₂²×H(5,𝔽₂)	—	73	1	no	—
315	C₂×#577	—	73	48	no	—
316	C₂²×#137	—	73	1	no	—
317	C₂²×#137	—	73	2	no	—
318	C₂²×AGL(1,ℤ/8)	—	73	1	no	—
319	C₂²×AGL(1,ℤ/8)	—	73	2	no	—
320	C₂²×#135	—	73	2	no	—
321	C₂²×#135	D₇₃	1	1	yes	characteristic, complemented
322	C₂³×SD₁₆	—	73	2	no	—
323	C₂³×SD₁₆	—	73	1	no	—
324	C₂²×#131	—	73	1	no	—
325	C₇₃	C₂²×#577	1	1	yes	characteristic, complemented, Sylow
326	C₂×2₋¹⁺⁴	—	73	24	no	—
327	C₂×2₋¹⁺⁴	—	146	12	no	—
328	C₂×H(5,𝔽₂)	—	73	24	no	—
329	C₂×H(5,𝔽₂)	—	146	12	no	—
330	C₂²×#41	—	73	1	no	—
331	C₂²×#41	—	73	2	no	—
332	C₂²×#41	—	73	2	no	—
333	C₂²×#41	—	146	1	no	—
334	C₂²×#41	—	146	1	no	—
335	C₂²×#41	—	146	2	no	—
336	C₂²×#41	C₂×D₇₃	1	1	yes	characteristic
337	C₂²×#41	C₂×D₇₃	1	1	yes	characteristic, complemented
338	C₂³×Q₈	—	73	2	no	—
339	C₂³×Q₈	—	73	1	no	—
340	C₂³×Q₈	—	146	1	no	—
341	C₂³×D₄	—	73	2	no	—
342	C₂³×D₄	—	73	1	no	—
343	C₂³×D₄	—	146	1	no	—
344	C₂³×D₄	—	146	2	no	—
345	#577	—	73	256	no	—
346	C₂×#137	—	73	24	no	—
347	C₂×#137	—	73	48	no	—
348	C₂×AGL(1,ℤ/8)	—	73	24	no	—
349	C₂×AGL(1,ℤ/8)	—	73	48	no	—
350	C₂×#135	—	73	48	no	—
351	C₂×#135	C₂×D₇₃	1	24	yes	complemented
352	C₂²×Q₁₆	—	73	2	no	—
353	C₂²×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
354	C₂²×SD₁₆	—	73	2	no	—
355	C₂²×SD₁₆	—	73	2	no	—
356	C₂²×SD₁₆	—	73	48	no	—
357	C₂²×SD₁₆	—	73	2	no	—
358	C₂²×SD₁₆	—	73	2	no	—
359	C₂²×SD₁₆	—	73	24	no	—
360	C₂²×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
361	C₂²×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
362	C₂²×D₈	—	73	2	no	—
363	C₂²×D₈	C₂×D₇₃	1	1	yes	characteristic, complemented
364	C₂×#131	—	73	24	no	—
365	C₂²×M₁₆	—	73	1	no	—
366	C₂²×M₁₆	—	73	2	no	—
367	C₂³×C₈	—	73	2	no	—
368	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
369	C₂⁵	—	146	2	no	—
370	C₂⁵	—	146	1	no	—
371	2₋¹⁺⁴	—	73	64	no	—
372	2₋¹⁺⁴	—	146	96	no	—
373	H(5,𝔽₂)	—	73	64	no	—
374	H(5,𝔽₂)	—	146	96	no	—
375	C₂×#41	—	2	6	no	—
376	C₂×#41	—	2	6	no	—
377	C₂×#41	—	73	12	no	—
378	C₂×#41	—	73	12	no	—
379	C₂×#41	—	73	24	no	—
380	C₂×#41	—	73	24	no	—
381	C₂×#41	—	146	24	no	—
382	C₂×#41	—	146	24	no	—
383	C₂×#41	—	146	12	no	—
384	C₂×#41	—	146	12	no	—
385	C₂×#41	—	146	48	no	—
386	C₂×#41	C₂²×D₇₃	1	12	yes	—
387	C₂×#41	C₂²×D₇₃	1	12	yes	complemented
388	C₂²×Q₈	—	73	1	no	—
389	C₂²×Q₈	—	73	24	no	—
390	C₂²×Q₈	—	73	2	no	—
391	C₂²×Q₈	—	73	12	no	—
392	C₂²×Q₈	—	146	2	no	—
393	C₂²×Q₈	—	146	24	no	—
394	C₂²×Q₈	—	146	12	no	—
395	C₂²×Q₈	—	146	1	no	—
396	C₂²×Q₈	—	146	6	no	—
397	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
398	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
399	C₂²×D₄	—	2	1	no	—
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	—	73	2	no	—
402	C₂²×D₄	—	73	24	no	—
403	C₂²×D₄	—	73	1	no	—
404	C₂²×D₄	—	73	2	no	—
405	C₂²×D₄	—	73	12	no	—
406	C₂²×D₄	—	146	24	no	—
407	C₂²×D₄	—	146	2	no	—
408	C₂²×D₄	—	146	12	no	—
409	C₂²×D₄	—	146	2	no	—
410	C₂²×D₄	—	146	48	no	—
411	C₂²×D₄	—	146	2	no	—
412	C₂²×D₄	—	146	1	no	—
413	C₂²×D₄	—	146	6	no	—
414	C₂²×D₄	C₂²×D₇₃	1	1	yes	characteristic
415	C₂²×D₄	C₂²×D₇₃	1	1	yes	characteristic
416	C₂³×C₄	—	2	1	no	—
417	C₂³×C₄	—	2	1	no	—
418	C₂³×C₄	—	73	2	no	—
419	C₂³×C₄	—	146	2	no	—
420	C₂³×C₄	—	146	2	no	—
421	C₂³×C₄	—	146	2	no	—
422	C₂³×C₄	—	146	1	no	—
423	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
424	#137	—	73	64	no	—
425	#137	—	73	128	no	—
426	AGL(1,ℤ/8)	—	73	64	no	—
427	AGL(1,ℤ/8)	—	73	128	no	—
428	#135	—	73	128	no	—
429	#135	C₂²×D₇₃	1	64	yes	complemented
430	C₂×Q₁₆	—	73	24	no	—
431	C₂×Q₁₆	C₂²×D₇₃	1	12	yes	complemented
432	C₂×SD₁₆	—	73	24	no	—
433	C₂×SD₁₆	—	73	24	no	—
434	C₂×SD₁₆	—	73	128	no	—
435	C₂×SD₁₆	—	73	24	no	—
436	C₂×SD₁₆	—	73	24	no	—
437	C₂×SD₁₆	—	73	64	no	—
438	C₂×SD₁₆	C₂²×D₇₃	1	12	yes	complemented
439	C₂×SD₁₆	C₂²×D₇₃	1	12	yes	complemented
440	C₂×D₈	—	73	24	no	—
441	C₂×D₈	C₂²×D₇₃	1	12	yes	complemented
442	#131	—	73	64	no	—
443	C₂×M₁₆	—	73	12	no	—
444	C₂×M₁₆	—	73	24	no	—
445	C₂²×C₈	—	73	2	no	—
446	C₂²×C₈	—	73	24	no	—
447	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
448	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
449	C₂²×C₈	C₂²×D₇₃	1	12	yes	complemented
450	C₂⁴	—	2	1	no	—
451	C₂⁴	—	2	1	no	—
452	C₂⁴	—	584	4	no	—
453	C₂⁴	—	584	8	no	—
454	C₂⁴	—	73	2	no	—
455	C₂⁴	—	146	24	no	—
456	C₂⁴	—	146	2	no	—
457	C₂⁴	—	146	12	no	—
458	C₂⁴	D₄×D₇₃	1	1	yes	characteristic
459	#41	—	2	24	no	—
460	#41	—	2	24	no	—
461	#41	—	73	48	no	—
462	#41	—	73	16	no	—
463	#41	—	73	32	no	—
464	#41	—	73	32	no	—
465	#41	—	146	64	no	—
466	#41	—	146	64	no	—
467	#41	—	146	48	no	—
468	#41	—	146	48	no	—
469	#41	—	146	128	no	—
470	#41	C₂³×D₇₃	1	16	yes	—
471	#41	C₂³×D₇₃	1	16	yes	complemented
472	C₂×Q₈	—	2	3	no	—
473	C₂×Q₈	—	2	3	no	—
474	C₂×Q₈	—	73	12	no	—
475	C₂×Q₈	—	73	32	no	—
476	C₂×Q₈	—	73	12	no	—
477	C₂×Q₈	—	73	16	no	—
478	C₂×Q₈	—	146	24	no	—
479	C₂×Q₈	—	146	64	no	—
480	C₂×Q₈	—	146	48	no	—
481	C₂×Q₈	—	146	12	no	—
482	C₂×Q₈	—	146	6	no	—
483	C₂×Q₈	—	146	24	no	—
484	C₂×Q₈	C₂³×D₇₃	1	6	yes	—
485	C₂×Q₈	C₂³×D₇₃	1	6	yes	—
486	C₂×D₄	—	2	12	no	—
487	C₂×D₄	—	2	12	no	—
488	C₂×D₄	—	2	3	no	—
489	C₂×D₄	—	2	3	no	—
490	C₂×D₄	—	73	24	no	—
491	C₂×D₄	—	73	32	no	—
492	C₂×D₄	—	73	12	no	—
493	C₂×D₄	—	73	12	no	—
494	C₂×D₄	—	73	16	no	—
495	C₂×D₄	—	146	64	no	—
496	C₂×D₄	—	146	24	no	—
497	C₂×D₄	—	146	48	no	—
498	C₂×D₄	—	146	24	no	—
499	C₂×D₄	—	146	128	no	—
500	C₂×D₄	—	146	24	no	—
501	C₂×D₄	—	146	12	no	—
502	C₂×D₄	—	146	6	no	—
503	C₂×D₄	—	146	24	no	—
504	C₂×D₄	C₂³×D₇₃	1	6	yes	—
505	C₂×D₄	C₂³×D₇₃	1	6	yes	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	12	no	—
509	C₂²×C₄	—	2	12	no	—
510	C₂²×C₄	—	73	2	no	—
511	C₂²×C₄	—	73	12	no	—
512	C₂²×C₄	—	73	12	no	—
513	C₂²×C₄	—	146	24	no	—
514	C₂²×C₄	—	146	24	no	—
515	C₂²×C₄	—	146	24	no	—
516	C₂²×C₄	—	146	12	no	—
517	C₂²×C₄	—	146	2	no	—
518	C₂²×C₄	D₄×D₇₃	1	6	yes	—
519	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
520	C₂²×C₄	C₂³×D₇₃	1	6	yes	—
521	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
522	Q₁₆	—	73	32	no	—
523	Q₁₆	C₂³×D₇₃	1	16	yes	complemented
524	SD₁₆	—	73	32	no	—
525	SD₁₆	—	73	32	no	—
526	SD₁₆	—	73	32	no	—
527	SD₁₆	—	73	32	no	—
528	SD₁₆	C₂³×D₇₃	1	16	yes	complemented
529	SD₁₆	C₂³×D₇₃	1	16	yes	complemented
530	D₈	—	73	32	no	—
531	D₈	C₂³×D₇₃	1	16	yes	complemented
532	M₁₆	—	73	16	no	—
533	M₁₆	—	73	32	no	—
534	C₂×C₈	—	73	12	no	—
535	C₂×C₈	—	73	32	no	—
536	C₂×C₈	C₂³×D₇₃	1	6	yes	—
537	C₂×C₈	C₂³×D₇₃	1	6	yes	—
538	C₂×C₈	C₂³×D₇₃	1	16	yes	complemented
539	C₂³	—	2	4	no	—
540	C₂³	—	2	6	no	—
541	C₂³	—	2	6	no	—
542	C₂³	—	4	4	no	—
543	C₂³	—	4	4	no	—
544	C₂³	—	292	8	no	—
545	C₂³	—	584	24	no	—
546	C₂³	—	584	48	no	—
547	C₂³	—	73	12	no	—
548	C₂³	—	146	32	no	—
549	C₂³	—	146	12	no	—
550	C₂³	—	146	16	no	—
551	C₂³	—	146	8	no	—
552	C₂³	C₂×D₄×D₇₃	1	6	yes	—
553	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
554	Q₈	—	2	6	no	—
555	Q₈	—	2	6	no	—
556	Q₈	—	73	16	no	—
557	Q₈	—	73	8	no	—
558	Q₈	—	146	32	no	—
559	Q₈	—	146	16	no	—
560	Q₈	—	146	12	no	—
561	Q₈	C₂⁴×D₇₃	1	4	yes	—
562	Q₈	C₂⁴×D₇₃	1	4	yes	—
563	D₄	—	2	16	no	—
564	D₄	—	2	16	no	—
565	D₄	—	2	6	no	—
566	D₄	—	2	6	no	—
567	D₄	—	73	32	no	—
568	D₄	—	73	16	no	—
569	D₄	—	73	8	no	—
570	D₄	—	146	32	no	—
571	D₄	—	146	32	no	—
572	D₄	—	146	32	no	—
573	D₄	—	146	16	no	—
574	D₄	—	146	12	no	—
575	D₄	C₂⁴×D₇₃	1	4	yes	—
576	D₄	C₂⁴×D₇₃	1	4	yes	—
577	C₂×C₄	—	2	6	no	—
578	C₂×C₄	—	2	6	no	—
579	C₂×C₄	—	2	16	no	—
580	C₂×C₄	—	2	16	no	—
581	C₂×C₄	—	73	12	no	—
582	C₂×C₄	—	73	24	no	—
583	C₂×C₄	—	73	8	no	—
584	C₂×C₄	—	146	32	no	—
585	C₂×C₄	—	146	32	no	—
586	C₂×C₄	—	146	32	no	—
587	C₂×C₄	—	146	12	no	—
588	C₂×C₄	—	146	16	no	—
589	C₂×C₄	C₂×D₄×D₇₃	1	6	yes	—
590	C₂×C₄	C₂×D₄×D₇₃	1	3	yes	—
591	C₂×C₄	C₂×D₄×D₇₃	1	12	yes	—
592	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
593	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
594	C₈	—	73	8	no	—
595	C₈	C₂⁴×D₇₃	1	4	yes	—
596	C₈	C₂⁴×D₇₃	1	4	yes	—
597	C₂²	—	2	12	no	—
598	C₂²	—	2	4	no	—
599	C₂²	—	2	4	no	—
600	C₂²	—	4	12	no	—
601	C₂²	—	4	12	no	—
602	C₂²	—	292	24	no	—
603	C₂²	—	584	16	no	—
604	C₂²	—	584	32	no	—
605	C₂²	—	73	8	no	—
606	C₂²	—	146	8	no	—
607	C₂²	—	146	24	no	—
608	C₂²	#17989394	1	4	yes	direct product factor
609	C₂²	C₂²×D₄×D₇₃	1	4	yes	—
610	C₂²	C₂²×D₄×D₇₃	1	3	yes	—
611	C₄	—	2	4	no	—
612	C₄	—	2	4	no	—
613	C₄	—	73	8	no	—
614	C₄	—	146	8	no	—
615	C₄	C₂²×D₄×D₇₃	1	4	yes	—
616	C₄	C₂²×D₄×D₇₃	1	3	yes	—
617	C₄	C₂⁵×D₇₃	1	1	yes	characteristic
618	C₂	—	2	4	no	—
619	C₂	—	4	4	no	—
620	C₂	—	4	4	no	—
621	C₂	—	292	8	no	—
622	C₂	—	146	8	no	—
623	C₂	C₂×#17989394	1	6	yes	direct product factor
624	C₂	C₂³×D₄×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₇₃
commutator, cosocle	C₄×C₇₃	C₂⁶
Frattini	C₄	C₂⁵×D₇₃
Fitting	C₂²×#135×C₇₃	C₂
socle	C₂³×C₇₃	C₂²×D₄
hypercenter	C₂²×#135	D₇₃
hypocenter	C₇₃	C₂²×#577
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. C₂²×#14556638	C₂	semidirect
2. C₂²×#14556637	C₂	semidirect
3. C₂×#17989394	C₂	direct (N × H)
4. C₂²×#14556623	C₂	semidirect
5. C₂²×#14556621	C₂	semidirect
6. C₂²×#14556616	C₂	semidirect
7. C₂²×#14556615	C₂	semidirect
8. C₂²×#14556612	C₂	semidirect
9. C₂³×#11924017	C₂	semidirect
10. C₂²×SD₁₆×D₇₃	C₂	semidirect
11. C₂²×#14556597	C₂	semidirect
12. C₂²×#135×C₇₃	C₂	semidirect
14. C₂×#14556638	C₂²	semidirect
16. C₂×#14556637	C₂²	semidirect
22. C₂²×#11924027	C₂²	semidirect
24. C₂³×Dic₁₄₆	C₂²	semidirect
25. C₂²×Q₈×D₇₃	C₂²	semidirect
30. #17989394	C₂²	direct (N × H)
31. C₂×#14556623	C₂²	semidirect
32. C₂×#14556621	C₂²	semidirect
33. C₂×#14556616	C₂²	semidirect
34. C₂×#14556615	C₂²	semidirect
35. C₂×#14556612	C₂²	semidirect
36. C₂²×#11924018	C₂²	semidirect
37. C₂²×#11924017	C₂²	semidirect
38. C₂²×#11924017	C₂²	semidirect
39. C₂²×#11924017	C₂²	semidirect
40. C₂²×#11924016	C₂²	semidirect
41. C₂²×#11924015	C₂²	semidirect
42. C₂×SD₁₆×D₇₃	C₂²	semidirect
43. C₂²×#11924013	C₂²	semidirect
44. C₂×#14556597	C₂²	semidirect
45. C₂²×#11924012	C₂²	semidirect
46. C₂²×#11924011	C₂²	semidirect
47. C₂²×C₈×D₇₃	C₂²	semidirect
49. C₂²×#41×C₇₃	C₂²	semidirect
50. C₂×#135×C₇₃	C₂²	semidirect
51. C₂²×Q₁₆×C₇₃	C₂²	semidirect
52. C₂²×SD₁₆×C₇₃	C₂²	semidirect
53. C₂²×SD₁₆×C₇₃	C₂²	semidirect
54. C₂²×D₈×C₇₃	C₂²	semidirect
55. C₂³×C₈×C₇₃	C₂²	semidirect
59. #14556638	C₂³	semidirect
61. #14556637	C₂³	semidirect
70. C₂×#11924027	C₂³	semidirect
77. C₂²×Dic₁₄₆	C₂³	semidirect
79. C₂×Q₈×D₇₃	C₂³	semidirect
98. #14556623	C₂³	semidirect
99. #14556621	C₂³	semidirect
100. #14556616	C₂³	semidirect
101. #14556615	C₂³	semidirect
102. #14556612	C₂³	semidirect
103. C₂×#11924018	C₂³	semidirect
104. C₂×#11924017	C₂³	semidirect
105. C₂×#11924017	C₂³	semidirect
106. C₂×#11924017	C₂³	semidirect
107. C₂×#11924016	C₂³	semidirect
108. C₂×#11924015	C₂³	semidirect
109. SD₁₆×D₇₃	C₂³	semidirect
110. C₂×#11924013	C₂³	semidirect
111. #14556597	C₂³	semidirect
112. C₂×#11924012	C₂³	semidirect
113. C₂×#11924011	C₂³	semidirect
115. C₂×C₈×D₇₃	C₂³	semidirect
119. C₂×#41×C₇₃	C₂³	semidirect
129. #135×C₇₃	C₂³	semidirect
130. C₂×Q₁₆×C₇₃	C₂³	semidirect
131. C₂×SD₁₆×C₇₃	C₂³	semidirect
132. C₂×SD₁₆×C₇₃	C₂³	semidirect
133. C₂×D₈×C₇₃	C₂³	semidirect
136. C₂²×C₈×C₇₃	C₂³	semidirect
151. #11924027	C₂⁴	semidirect
159. C₂×Dic₁₄₆	C₂⁴	semidirect
161. Q₈×D₇₃	C₂⁴	semidirect
184. #11924018	C₂⁴	semidirect
185. #11924017	C₂⁴	semidirect
186. #11924017	C₂⁴	semidirect
187. #11924016	C₂⁴	semidirect
188. #11924015	C₂⁴	semidirect
189. #11924013	C₂⁴	semidirect
190. #11924012	C₂⁴	semidirect
191. #11924011	C₂⁴	semidirect
193. C₈×D₇₃	C₂⁴	semidirect
200. #41×C₇₃	C₂⁴	semidirect
219. Q₁₆×C₇₃	C₂⁴	semidirect
220. SD₁₆×C₇₃	C₂⁴	semidirect
221. SD₁₆×C₇₃	C₂⁴	semidirect
222. D₈×C₇₃	C₂⁴	semidirect
225. C₂×C₈×C₇₃	C₂⁴	semidirect
289. C₂²×C₇₃	#577	semidirect
309. C₂×C₇₃	C₂×#577	semidirect
321. C₂²×#135	D₇₃	semidirect
325. C₇₃	C₂²×#577	semidirect
337. C₂²×#41	C₂×D₇₃	semidirect
351. C₂×#135	C₂×D₇₃	semidirect
353. C₂²×Q₁₆	C₂×D₇₃	semidirect
360. C₂²×SD₁₆	C₂×D₇₃	semidirect
361. C₂²×SD₁₆	C₂×D₇₃	semidirect
363. C₂²×D₈	C₂×D₇₃	semidirect
368. C₂³×C₈	C₂×D₇₃	semidirect
387. C₂×#41	C₂²×D₇₃	semidirect
429. #135	C₂²×D₇₃	semidirect
431. C₂×Q₁₆	C₂²×D₇₃	semidirect
438. C₂×SD₁₆	C₂²×D₇₃	semidirect
439. C₂×SD₁₆	C₂²×D₇₃	semidirect
441. C₂×D₈	C₂²×D₇₃	semidirect
449. C₂²×C₈	C₂²×D₇₃	semidirect
471. #41	C₂³×D₇₃	semidirect
523. Q₁₆	C₂³×D₇₃	semidirect
528. SD₁₆	C₂³×D₇₃	semidirect
529. SD₁₆	C₂³×D₇₃	semidirect
531. D₈	C₂³×D₇₃	semidirect
538. C₂×C₈	C₂³×D₇₃	semidirect
608. C₂²	#17989394	direct (N × H)
623. C₂	C₂×#17989394	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14556638	2
C₂²×#14556637	2
C₂×#17989394	2
C₂²×#14556623	2
C₂²×#14556621	2
C₂²×#14556616	2
C₂²×#14556615	2
C₂²×#14556612	2
C₂³×#11924017	2
C₂²×SD₁₆×D₇₃	2
C₂²×#14556597	2
C₂²×#135×C₇₃	2
C₂²×#577	73

Subgroups — C22×#17989394 #33999799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#17989394 #33999799