Subgroups — C₂×#22623724 #33994456

Order 18688.

11534 conjugacy classes of subgroups.

The subgroup lattice has 480 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	#22623724	C₂	1	32	yes	maximal, direct product factor
4	C₂×#17989249	C₂	1	4	yes	maximal, complemented
5	C₂×#17989232	C₂	1	12	yes	maximal, complemented
6	C₂×#17989163	C₂	1	3	yes	maximal, complemented
7	C₂×#17989156	C₂	1	3	yes	maximal, complemented
8	C₂×#17989137	C₂	1	3	yes	maximal, complemented
9	C₂²×#14556579	C₂	1	3	yes	maximal, complemented
10	C₂×C₄×#41×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#14556638	—	2	16	no	—
12	C₂×#14556638	C₂²	1	16	yes	complemented
13	C₂×#14556637	—	2	16	no	—
14	C₂×#14556637	C₂²	1	16	yes	complemented
15	C₂²×#11924029	C₂²	1	2	yes	—
16	C₂²×#11924028	C₂²	1	3	yes	—
17	C₂²×#11924028	C₂²	1	3	yes	complemented
18	C₂²×#11924027	C₂²	1	6	yes	complemented
19	C₂³×Dic₁₄₆	C₂²	1	3	yes	complemented
20	C₂²×Q₈×D₇₃	C₂²	1	2	yes	complemented
21	C₂³×D₂₉₂	C₂²	1	3	yes	—
22	C₂²×D₄×D₇₃	C₂²	1	6	yes	—
23	#17989249	C₂²	1	64	yes	complemented
24	#17989232	C₂²	1	192	yes	complemented
25	#17989163	C₂²	1	48	yes	complemented
26	#17989156	C₂²	1	48	yes	complemented
27	#17989137	C₂²	1	48	yes	complemented
28	C₂×#14556591	C₂²	1	3	yes	complemented
29	C₂×#14556588	C₂²	1	3	yes	complemented
30	C₂×#14556579	C₂²	1	6	yes	complemented
31	C₂×#14556579	C₂²	1	12	yes	complemented
32	C₂×#14556579	C₂²	1	3	yes	complemented
33	C₂×#14556579	C₂²	1	1	yes	characteristic, complemented
34	C₂×#14556579	C₂²	1	48	yes	complemented
35	C₂×#14556575	C₂²	1	12	yes	complemented
36	C₂×#14556571	C₂²	1	12	yes	complemented
37	C₂×#14556566	C₂²	1	12	yes	complemented
38	C₂×#14556565	C₂²	1	12	yes	complemented
39	C₂×#14556561	C₂²	1	12	yes	complemented
40	C₂×C₄×D₂₉₂	C₂²	1	12	yes	complemented
41	C₂²×#11924005	C₂²	1	12	yes	complemented
42	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
43	C₄×#41×C₇₃	C₂²	1	16	yes	complemented
44	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₇₃	C₂²	1	6	yes	complemented
46	C₂×#117×C₇₃	C₂²	1	3	yes	complemented
47	C₂²×C₄²×C₇₃	C₂²	1	3	yes	complemented
48	C₂⁴×D₇₃	C₂³	1	6	yes	—
49	#14556638	—	2	128	no	—
50	#14556637	—	2	128	no	—
51	C₂×#11924029	—	2	16	no	—
52	C₂×#11924029	C₂³	1	16	yes	—
53	C₂×#11924028	—	2	24	no	—
54	C₂×#11924028	—	2	24	no	—
55	C₂×#11924028	C₂³	1	24	yes	—
56	C₂×#11924028	C₂³	1	24	yes	complemented
57	C₂×#11924027	—	2	48	no	—
58	C₂×#11924027	C₂³	1	48	yes	complemented
59	C₂²×Dic₁₄₆	—	2	24	no	—
60	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
61	C₂²×Dic₁₄₆	C₂³	1	3	yes	—
62	C₂²×Dic₁₄₆	C₂³	1	6	yes	—
63	C₂²×Dic₁₄₆	C₂³	1	24	yes	complemented
64	C₂×Q₈×D₇₃	—	2	16	no	—
65	C₂×Q₈×D₇₃	C₂³	1	16	yes	complemented
66	C₂²×D₂₉₂	—	2	24	no	—
67	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
68	C₂²×D₂₉₂	C₂³	1	3	yes	—
69	C₂²×D₂₉₂	C₂³	1	6	yes	—
70	C₂²×D₂₉₂	C₂³	1	24	yes	—
71	C₂²×D₂₉₂	C₂³	1	12	yes	—
72	C₂²×C₂²⋊D₇₃	C₂³	1	6	yes	—
73	C₂²×C₂²⋊D₇₃	C₂³	1	6	yes	—
74	C₂×D₄×D₇₃	—	2	48	no	—
75	C₂×D₄×D₇₃	C₂³	1	48	yes	—
76	C₂³×Dic₇₃	C₂³	1	6	yes	—
77	C₂²×C₄×D₇₃	C₂³	1	6	yes	—
78	C₂²×C₄×D₇₃	C₂³	1	6	yes	—
79	#14556591	C₂³	1	24	yes	complemented
80	#14556588	C₂³	1	24	yes	complemented
81	#14556579	C₂³	1	8	yes	complemented
82	#14556579	C₂³	1	24	yes	complemented
83	#14556579	C₂³	1	48	yes	complemented
84	#14556579	C₂³	1	96	yes	complemented
85	#14556575	C₂³	1	96	yes	complemented
86	#14556571	C₂³	1	96	yes	complemented
87	#14556566	C₂³	1	96	yes	complemented
88	#14556565	C₂³	1	96	yes	complemented
89	#14556561	C₂³	1	96	yes	complemented
90	C₄×D₂₉₂	C₂³	1	96	yes	complemented
91	C₂×C₄⋊Dic₇₃	C₂³	1	12	yes	—
92	C₂×#11924005	C₂³	1	12	yes	—
93	C₂×#11924005	C₂³	1	24	yes	—
94	C₂×#11924005	C₂³	1	4	yes	—
95	C₂×#11924005	C₂³	1	96	yes	complemented
96	C₂×#41×C₇₃	D₄	1	16	yes	complemented
97	C₂×#41×C₇₃	C₂³	1	8	yes	—
98	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₇₃	C₂³	1	3	yes	—
100	C₂³×C₄×C₇₃	C₂³	1	6	yes	—
101	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
102	C₄×Q₈×C₇₃	C₂³	1	16	yes	complemented
103	C₄×D₄×C₇₃	C₂³	1	48	yes	complemented
104	#117×C₇₃	C₂³	1	24	yes	complemented
105	C₂×C₄⋊C₄×C₇₃	C₂³	1	6	yes	—
106	C₂×C₂²⋊C₄×C₇₃	C₂³	1	6	yes	—
107	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
108	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₇₃	C₂³	1	6	yes	—
110	C₂×C₄²×C₇₃	C₂³	1	24	yes	complemented
111	C₂³×D₇₃	—	2	24	no	—
112	C₂³×D₇₃	—	4	24	no	—
113	C₂³×D₇₃	C₂⁴	1	6	yes	—
114	C₂³×D₇₃	C₂⁴	1	2	yes	—
115	C₂³×D₇₃	C₂⁴	1	24	yes	—
116	#11924029	—	2	64	no	—
117	#11924028	—	2	96	no	—
118	#11924028	—	2	96	no	—
119	#11924027	—	2	192	no	—
120	C₂×Dic₁₄₆	—	2	24	no	—
121	C₂×Dic₁₄₆	—	2	12	no	—
122	C₂×Dic₁₄₆	—	2	96	no	—
123	C₂×Dic₁₄₆	—	2	4	no	—
124	C₂×Dic₁₄₆	C₂⁴	1	24	yes	—
125	C₂×Dic₁₄₆	C₂⁴	1	12	yes	—
126	C₂×Dic₁₄₆	C₂⁴	1	4	yes	—
127	Q₈×D₇₃	—	2	64	no	—
128	C₂×D₂₉₂	—	2	24	no	—
129	C₂×D₂₉₂	—	2	12	no	—
130	C₂×D₂₉₂	—	2	96	no	—
131	C₂×D₂₉₂	—	2	4	no	—
132	C₂×D₂₉₂	—	4	24	no	—
133	C₂×D₂₉₂	C₂⁴	1	24	yes	—
134	C₂×D₂₉₂	C₂⁴	1	12	yes	—
135	C₂×D₂₉₂	C₂⁴	1	4	yes	—
136	C₂×D₂₉₂	C₂⁴	1	48	yes	—
137	C₂×C₂²⋊D₇₃	—	2	24	no	—
138	C₂×C₂²⋊D₇₃	—	2	24	no	—
139	C₂×C₂²⋊D₇₃	C₂⁴	1	24	yes	—
140	C₂×C₂²⋊D₇₃	C₂⁴	1	24	yes	—
141	D₄×D₇₃	—	2	192	no	—
142	C₂²×Dic₇₃	—	2	24	no	—
143	C₂²×Dic₇₃	C₂⁴	1	6	yes	—
144	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
145	C₂²×Dic₇₃	C₂⁴	1	24	yes	—
146	C₂×C₄×D₇₃	—	2	24	no	—
147	C₂×C₄×D₇₃	—	2	24	no	—
148	C₂×C₄×D₇₃	C₂⁴	1	24	yes	—
149	C₂×C₄×D₇₃	C₂⁴	1	24	yes	—
150	C₄⋊Dic₇₃	C₂⁴	1	48	yes	—
151	#11924005	C₂⁴	1	48	yes	—
152	#11924005	C₂⁴	1	96	yes	—
153	#11924005	C₂⁴	1	16	yes	—
154	C₂⁴×C₇₃	C₂⁴	1	3	yes	—
155	#41×C₇₃	C₂×D₄	1	64	yes	complemented
156	C₂×Q₈×C₇₃	C₂×D₄	1	8	yes	—
157	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
158	C₂×D₄×C₇₃	C₂×D₄	1	24	yes	—
159	C₂×D₄×C₇₃	C₂⁴	1	12	yes	—
160	C₂²×C₄×C₇₃	—	4	12	no	—
161	C₂²×C₄×C₇₃	C₂×D₄	1	24	yes	—
162	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₇₃	C₂⁴	1	6	yes	—
164	C₂²×C₄×C₇₃	C₂⁴	1	24	yes	—
165	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
167	C₂²×C₄×C₇₃	C₂⁴	1	12	yes	—
168	C₄⋊C₄×C₇₃	C₂⁴	1	24	yes	—
169	C₂²⋊C₄×C₇₃	C₂⁴	1	24	yes	—
170	C₄²×C₇₃	C₂⁴	1	4	yes	—
171	C₄²×C₇₃	C₂⁴	1	12	yes	—
172	C₄²×C₇₃	C₂⁴	1	24	yes	—
173	C₂³×C₇₃	—	2	12	no	—
174	C₂³×C₇₃	C₂²×D₄	1	12	yes	—
175	C₂³×C₇₃	C₂⁵	1	6	yes	—
176	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
177	C₂²×D₇₃	—	2	4	no	—
178	C₂²×D₇₃	—	2	12	no	—
179	C₂²×D₇₃	—	2	8	no	—
180	C₂²×D₇₃	—	2	24	no	—
181	C₂²×D₇₃	—	2	48	no	—
182	C₂²×D₇₃	—	4	48	no	—
183	C₂²×D₇₃	—	8	48	no	—
184	C₂²×D₇₃	C₂⁵	1	12	yes	—
185	C₂²×D₇₃	C₂⁵	1	4	yes	—
186	Q₈×C₇₃	C₂²×D₄	1	16	yes	—
187	D₄×C₇₃	C₂²×D₄	1	48	yes	—
188	C₂×C₄×C₇₃	—	2	4	no	—
189	C₂×C₄×C₇₃	—	2	12	no	—
190	C₂×C₄×C₇₃	—	4	24	no	—
191	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
192	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
193	C₂×C₄×C₇₃	C₂²×D₄	1	48	yes	—
194	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
195	C₂×C₄×C₇₃	C₂⁵	1	12	yes	—
196	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
197	C₂×C₄×C₇₃	C₂⁵	1	6	yes	—
198	C₂²⋊D₇₃	—	2	48	no	—
199	C₂²⋊D₇₃	—	2	48	no	—
200	C₂×Dic₇₃	—	2	4	no	—
201	C₂×Dic₇₃	—	2	12	no	—
202	C₂×Dic₇₃	—	2	48	no	—
203	C₂×Dic₇₃	C₂⁵	1	12	yes	—
204	C₂×Dic₇₃	C₂⁵	1	4	yes	—
205	D₂₉₂	—	2	48	no	—
206	D₂₉₂	—	2	24	no	—
207	D₂₉₂	—	2	8	no	—
208	D₂₉₂	—	4	48	no	—
209	C₄×D₇₃	—	2	48	no	—
210	C₄×D₇₃	—	2	48	no	—
211	Dic₁₄₆	—	2	48	no	—
212	Dic₁₄₆	—	2	24	no	—
213	Dic₁₄₆	—	2	8	no	—
214	C₂²×C₇₃	—	2	12	no	—
215	C₂²×C₇₃	—	2	24	no	—
216	C₂²×C₇₃	C₂³×D₄	1	12	yes	—
217	C₂²×C₇₃	C₂³×D₄	1	2	yes	—
218	C₂²×C₇₃	#585	1	4	yes	—
219	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
220	C₂×D₇₃	—	2	4	no	—
221	C₂×D₇₃	—	2	12	no	—
222	C₂×D₇₃	—	2	8	no	—
223	C₂×D₇₃	—	2	24	no	—
224	C₂×D₇₃	—	4	8	no	—
225	C₂×D₇₃	—	4	24	no	—
226	C₂×D₇₃	—	8	48	no	—
227	C₄×C₇₃	—	2	12	no	—
228	C₄×C₇₃	—	2	4	no	—
229	C₄×C₇₃	C₂³×D₄	1	4	yes	—
230	C₄×C₇₃	C₂³×D₄	1	12	yes	—
231	Dic₇₃	—	2	12	no	—
232	Dic₇₃	—	2	4	no	—
233	C₂×#3500	—	73	1	no	maximal, Sylow
234	C₂×C₇₃	—	2	12	no	—
235	C₂×C₇₃	#3500	1	4	yes	complemented
236	C₂×C₇₃	C₂⁴×D₄	1	1	yes	characteristic
237	C₂×C₇₃	C₂×#585	1	2	yes	—
238	D₇₃	—	4	4	no	—
239	D₇₃	—	4	12	no	—
240	C₂²×2₋¹⁺⁴	—	73	1	no	—
241	C₂²×H(5,𝔽₂)	—	73	1	no	—
242	#3500	—	73	32	no	—
243	C₂×#548	—	73	4	no	—
244	C₂×#546	—	73	12	no	—
245	C₂×#536	—	73	3	no	—
246	C₂×#535	—	73	3	no	—
247	C₂×#532	—	73	3	no	—
248	C₂²×#124	—	73	3	no	—
249	C₂×C₄×#41	D₇₃	1	1	yes	characteristic, complemented
250	C₇₃	C₂×#3500	1	1	yes	characteristic, complemented, Sylow
251	C₂×2₋¹⁺⁴	—	73	16	no	—
252	C₂×2₋¹⁺⁴	—	146	16	no	—
253	C₂×H(5,𝔽₂)	—	73	16	no	—
254	C₂×H(5,𝔽₂)	—	146	16	no	—
255	C₂²×#41	—	73	2	no	—
256	C₂²×#41	—	73	6	no	—
257	C₂²×#41	—	73	3	no	—
258	C₂²×#41	—	73	3	no	—
259	C₂²×#41	C₂×D₇₃	1	1	yes	characteristic
260	C₂³×Q₈	—	73	2	no	—
261	C₂³×Q₈	—	73	3	no	—
262	C₂³×D₄	—	73	6	no	—
263	C₂³×D₄	—	73	3	no	—
264	#548	—	73	64	no	—
265	#546	—	73	192	no	—
266	#536	—	73	48	no	—
267	#535	—	73	48	no	—
268	#532	—	73	48	no	—
269	C₂×C₄⋊Q₈	—	73	3	no	—
270	C₂×#127	—	73	3	no	—
271	C₂×#124	—	73	3	no	—
272	C₂×#124	—	73	6	no	—
273	C₂×#124	—	73	12	no	—
274	C₂×#124	—	73	1	no	—
275	C₂×#124	—	73	48	no	—
276	C₂×#123	—	73	12	no	—
277	C₂×C₂²⋊Q₈	—	73	12	no	—
278	C₂×#121	—	73	12	no	—
279	C₂×#121	—	73	12	no	—
280	C₂×#120	—	73	12	no	—
281	C₄×#41	C₂×D₇₃	1	16	yes	complemented
282	C₂×C₄×Q₈	C₂×D₇₃	1	2	yes	complemented
283	C₂×C₄×D₄	—	73	12	no	—
284	C₂×C₄×D₄	C₂×D₇₃	1	6	yes	complemented
285	C₂×#117	C₂×D₇₃	1	3	yes	complemented
286	C₂²×C₂²⋊C₄	—	73	12	no	—
287	C₂²×C₄²	C₂×D₇₃	1	3	yes	complemented
288	C₂⁵	—	73	6	no	—
289	2₋¹⁺⁴	—	146	128	no	—
290	H(5,𝔽₂)	—	146	128	no	—
291	C₂×#41	—	73	16	no	—
292	C₂×#41	—	73	48	no	—
293	C₂×#41	—	73	24	no	—
294	C₂×#41	—	73	24	no	—
295	C₂×#41	—	146	16	no	—
296	C₂×#41	—	146	48	no	—
297	C₂×#41	—	146	24	no	—
298	C₂×#41	—	146	24	no	—
299	C₂×#41	D₂₉₂	1	16	yes	complemented
300	C₂×#41	C₂²×D₇₃	1	8	yes	—
301	C₂²×Q₈	—	73	16	no	—
302	C₂²×Q₈	—	73	6	no	—
303	C₂²×Q₈	—	73	3	no	—
304	C₂²×Q₈	—	73	24	no	—
305	C₂²×Q₈	—	73	1	no	—
306	C₂²×Q₈	—	146	16	no	—
307	C₂²×Q₈	—	146	24	no	—
308	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
309	C₂²×D₄	—	73	6	no	—
310	C₂²×D₄	—	73	6	no	—
311	C₂²×D₄	—	73	48	no	—
312	C₂²×D₄	—	73	12	no	—
313	C₂²×D₄	—	73	6	no	—
314	C₂²×D₄	—	73	3	no	—
315	C₂²×D₄	—	73	24	no	—
316	C₂²×D₄	—	73	1	no	—
317	C₂²×D₄	—	146	48	no	—
318	C₂²×D₄	—	146	24	no	—
319	C₂²×D₄	C₂²×D₇₃	1	3	yes	—
320	C₂³×C₄	—	73	6	no	—
321	C₂³×C₄	—	73	6	no	—
322	C₂³×C₄	—	73	6	no	—
323	C₂³×C₄	C₂²×D₇₃	1	6	yes	—
324	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
325	C₄⋊Q₈	—	73	24	no	—
326	#127	—	73	24	no	—
327	#124	—	73	24	no	—
328	#124	—	73	48	no	—
329	#124	—	73	96	no	—
330	#124	—	73	8	no	—
331	#123	—	73	96	no	—
332	C₂²⋊Q₈	—	73	96	no	—
333	#121	—	73	96	no	—
334	#121	—	73	96	no	—
335	#120	—	73	96	no	—
336	C₄×Q₈	C₂²×D₇₃	1	16	yes	complemented
337	C₄×D₄	—	73	96	no	—
338	C₄×D₄	C₂²×D₇₃	1	48	yes	complemented
339	#117	C₂²×D₇₃	1	24	yes	complemented
340	C₂×C₄⋊C₄	—	73	12	no	—
341	C₂×C₄⋊C₄	C₂²×D₇₃	1	6	yes	—
342	C₂×C₂²⋊C₄	—	73	12	no	—
343	C₂×C₂²⋊C₄	—	73	24	no	—
344	C₂×C₂²⋊C₄	—	73	96	no	—
345	C₂×C₂²⋊C₄	—	73	4	no	—
346	C₂×C₂²⋊C₄	C₂²×D₇₃	1	6	yes	—
347	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
348	C₂×C₄²	C₂²×D₇₃	1	6	yes	—
349	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
350	C₂×C₄²	C₂²×D₇₃	1	24	yes	complemented
351	C₂⁴	—	292	24	no	—
352	C₂⁴	—	73	24	no	—
353	C₂⁴	—	73	6	no	—
354	C₂⁴	—	73	2	no	—
355	C₂⁴	—	146	24	no	—
356	C₂⁴	C₂³×D₇₃	1	3	yes	—
357	#41	—	146	64	no	—
358	#41	—	146	192	no	—
359	#41	—	146	96	no	—
360	#41	—	146	96	no	—
361	#41	C₂×D₂₉₂	1	64	yes	complemented
362	C₂×Q₈	—	73	24	no	—
363	C₂×Q₈	—	73	12	no	—
364	C₂×Q₈	—	73	4	no	—
365	C₂×Q₈	—	146	64	no	—
366	C₂×Q₈	—	146	24	no	—
367	C₂×Q₈	—	146	12	no	—
368	C₂×Q₈	—	146	96	no	—
369	C₂×Q₈	—	146	4	no	—
370	C₂×Q₈	C₂×D₂₉₂	1	8	yes	—
371	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
372	C₂×D₄	—	292	24	no	—
373	C₂×D₄	—	73	24	no	—
374	C₂×D₄	—	73	24	no	—
375	C₂×D₄	—	73	48	no	—
376	C₂×D₄	—	73	24	no	—
377	C₂×D₄	—	73	12	no	—
378	C₂×D₄	—	73	4	no	—
379	C₂×D₄	—	146	24	no	—
380	C₂×D₄	—	146	24	no	—
381	C₂×D₄	—	146	192	no	—
382	C₂×D₄	—	146	24	no	—
383	C₂×D₄	—	146	12	no	—
384	C₂×D₄	—	146	96	no	—
385	C₂×D₄	—	146	4	no	—
386	C₂×D₄	C₂×D₂₉₂	1	24	yes	—
387	C₂×D₄	C₂³×D₇₃	1	12	yes	—
388	C₂²×C₄	—	4	12	no	—
389	C₂²×C₄	—	73	24	no	—
390	C₂²×C₄	—	73	6	no	—
391	C₂²×C₄	—	73	2	no	—
392	C₂²×C₄	—	73	24	no	—
393	C₂²×C₄	—	73	24	no	—
394	C₂²×C₄	—	146	24	no	—
395	C₂²×C₄	—	146	24	no	—
396	C₂²×C₄	—	146	24	no	—
397	C₂²×C₄	C₂×D₂₉₂	1	24	yes	—
398	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
399	C₂²×C₄	C₂³×D₇₃	1	6	yes	—
400	C₂²×C₄	C₂³×D₇₃	1	24	yes	—
401	C₂²×C₄	C₂³×D₇₃	1	12	yes	—
402	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
403	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
404	C₄⋊C₄	—	73	48	no	—
405	C₄⋊C₄	C₂³×D₇₃	1	24	yes	—
406	C₂²⋊C₄	—	73	48	no	—
407	C₂²⋊C₄	—	73	96	no	—
408	C₂²⋊C₄	—	73	16	no	—
409	C₂²⋊C₄	C₂³×D₇₃	1	24	yes	—
410	C₄²	C₂³×D₇₃	1	4	yes	—
411	C₄²	C₂³×D₇₃	1	12	yes	—
412	C₄²	C₂³×D₇₃	1	24	yes	—
413	C₂³	—	2	12	no	—
414	C₂³	—	292	48	no	—
415	C₂³	—	584	48	no	—
416	C₂³	—	73	12	no	—
417	C₂³	—	73	4	no	—
418	C₂³	—	146	4	no	—
419	C₂³	—	146	12	no	—
420	C₂³	—	146	8	no	—
421	C₂³	—	146	24	no	—
422	C₂³	—	146	48	no	—
423	C₂³	C₂²×D₂₉₂	1	12	yes	—
424	C₂³	C₂⁴×D₇₃	1	6	yes	—
425	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
426	Q₈	—	146	48	no	—
427	Q₈	—	146	24	no	—
428	Q₈	—	146	8	no	—
429	Q₈	C₂²×D₂₉₂	1	16	yes	—
430	D₄	—	292	48	no	—
431	D₄	—	146	48	no	—
432	D₄	—	146	48	no	—
433	D₄	—	146	48	no	—
434	D₄	—	146	24	no	—
435	D₄	—	146	8	no	—
436	D₄	C₂²×D₂₉₂	1	48	yes	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	12	no	—
439	C₂×C₄	—	4	24	no	—
440	C₂×C₄	—	73	12	no	—
441	C₂×C₄	—	73	4	no	—
442	C₂×C₄	—	146	4	no	—
443	C₂×C₄	—	146	12	no	—
444	C₂×C₄	—	146	48	no	—
445	C₂×C₄	—	146	48	no	—
446	C₂×C₄	—	146	48	no	—
447	C₂×C₄	C₂²×D₂₉₂	1	12	yes	—
448	C₂×C₄	C₂²×D₂₉₂	1	4	yes	—
449	C₂×C₄	C₂²×D₂₉₂	1	48	yes	—
450	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
451	C₂×C₄	C₂⁴×D₇₃	1	12	yes	—
452	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
453	C₂×C₄	C₂⁴×D₇₃	1	6	yes	—
454	C₂²	—	2	12	no	—
455	C₂²	—	2	24	no	—
456	C₂²	—	292	24	no	—
457	C₂²	—	292	8	no	—
458	C₂²	—	584	48	no	—
459	C₂²	—	146	4	no	—
460	C₂²	—	146	12	no	—
461	C₂²	—	146	8	no	—
462	C₂²	—	146	24	no	—
463	C₂²	C₂³×D₂₉₂	1	12	yes	—
464	C₂²	C₂³×D₂₉₂	1	2	yes	—
465	C₂²	#17989423	1	4	yes	—
466	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
467	C₄	—	2	4	no	—
468	C₄	—	2	12	no	—
469	C₄	—	146	4	no	—
470	C₄	—	146	12	no	—
471	C₄	C₂³×D₂₉₂	1	12	yes	—
472	C₄	C₂³×D₂₉₂	1	4	yes	—
473	C₂	—	2	12	no	—
474	C₂	—	292	12	no	—
475	C₂	—	292	4	no	—
476	C₂	#22623724	1	4	yes	direct product factor
477	C₂	C₂⁴×D₂₉₂	1	1	yes	characteristic
478	C₂	C₂×#17989423	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₃
commutator, cosocle	C₂²×C₇₃	C₂⁶
Frattini	C₂²	C₂⁵×D₇₃
Fitting	C₂×C₄×#41×C₇₃	C₂
socle	C₂³×C₇₃	C₂⁵
hypercenter	C₂×C₄×#41	D₇₃
hypocenter	C₇₃	C₂×#3500
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×#41

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. #22623724	C₂	direct (N × H)
4. C₂×#17989249	C₂	semidirect
5. C₂×#17989232	C₂	semidirect
6. C₂×#17989163	C₂	semidirect
7. C₂×#17989156	C₂	semidirect
8. C₂×#17989137	C₂	semidirect
9. C₂²×#14556579	C₂	semidirect
10. C₂×C₄×#41×C₇₃	C₂	semidirect
12. C₂×#14556638	C₂²	semidirect
14. C₂×#14556637	C₂²	semidirect
17. C₂²×#11924028	C₂²	semidirect
18. C₂²×#11924027	C₂²	semidirect
19. C₂³×Dic₁₄₆	C₂²	semidirect
20. C₂²×Q₈×D₇₃	C₂²	semidirect
23. #17989249	C₂²	semidirect
24. #17989232	C₂²	semidirect
25. #17989163	C₂²	semidirect
26. #17989156	C₂²	semidirect
27. #17989137	C₂²	semidirect
28. C₂×#14556591	C₂²	semidirect
29. C₂×#14556588	C₂²	semidirect
30. C₂×#14556579	C₂²	semidirect
31. C₂×#14556579	C₂²	semidirect
32. C₂×#14556579	C₂²	semidirect
33. C₂×#14556579	C₂²	semidirect
34. C₂×#14556579	C₂²	semidirect
35. C₂×#14556575	C₂²	semidirect
36. C₂×#14556571	C₂²	semidirect
37. C₂×#14556566	C₂²	semidirect
38. C₂×#14556565	C₂²	semidirect
39. C₂×#14556561	C₂²	semidirect
40. C₂×C₄×D₂₉₂	C₂²	semidirect
41. C₂²×#11924005	C₂²	semidirect
43. C₄×#41×C₇₃	C₂²	semidirect
44. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
45. C₂×C₄×D₄×C₇₃	C₂²	semidirect
46. C₂×#117×C₇₃	C₂²	semidirect
47. C₂²×C₄²×C₇₃	C₂²	semidirect
56. C₂×#11924028	C₂³	semidirect
58. C₂×#11924027	C₂³	semidirect
63. C₂²×Dic₁₄₆	C₂³	semidirect
65. C₂×Q₈×D₇₃	C₂³	semidirect
79. #14556591	C₂³	semidirect
80. #14556588	C₂³	semidirect
81. #14556579	C₂³	semidirect
82. #14556579	C₂³	semidirect
83. #14556579	C₂³	semidirect
84. #14556579	C₂³	semidirect
85. #14556575	C₂³	semidirect
86. #14556571	C₂³	semidirect
87. #14556566	C₂³	semidirect
88. #14556565	C₂³	semidirect
89. #14556561	C₂³	semidirect
90. C₄×D₂₉₂	C₂³	semidirect
95. C₂×#11924005	C₂³	semidirect
96. C₂×#41×C₇₃	D₄	semidirect
102. C₄×Q₈×C₇₃	C₂³	semidirect
103. C₄×D₄×C₇₃	C₂³	semidirect
104. #117×C₇₃	C₂³	semidirect
110. C₂×C₄²×C₇₃	C₂³	semidirect
155. #41×C₇₃	C₂×D₄	semidirect
235. C₂×C₇₃	#3500	semidirect
249. C₂×C₄×#41	D₇₃	semidirect
250. C₇₃	C₂×#3500	semidirect
281. C₄×#41	C₂×D₇₃	semidirect
282. C₂×C₄×Q₈	C₂×D₇₃	semidirect
284. C₂×C₄×D₄	C₂×D₇₃	semidirect
285. C₂×#117	C₂×D₇₃	semidirect
287. C₂²×C₄²	C₂×D₇₃	semidirect
299. C₂×#41	D₂₉₂	semidirect
336. C₄×Q₈	C₂²×D₇₃	semidirect
338. C₄×D₄	C₂²×D₇₃	semidirect
339. #117	C₂²×D₇₃	semidirect
350. C₂×C₄²	C₂²×D₇₃	semidirect
361. #41	C₂×D₂₉₂	semidirect
476. C₂	#22623724	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
#22623724	2
C₂×#17989249	2
C₂×#17989232	2
C₂×#17989163	2
C₂×#17989156	2
C₂×#17989137	2
C₂²×#14556579	2
C₂×C₄×#41×C₇₃	2
C₂×#3500	73

Subgroups — C2×#22623724 #33994456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22623724 #33994456