Subgroups — C₂×#22623732 #33993883

Order 18688.

7738 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623732	C₂	1	32	yes	maximal, direct product factor
2	C₂×#17989298	C₂	1	2	yes	maximal, complemented
3	C₂×#17989297	C₂	1	4	yes	maximal, complemented
4	C₂×#17989297	C₂	1	2	yes	maximal, complemented
5	C₂×#17989293	C₂	1	4	yes	maximal, complemented
6	C₂×Q₈×D₂₉₂	C₂	1	2	yes	maximal, complemented
7	C₂×#17989252	C₂	1	2	yes	maximal, complemented
8	C₂×#17989215	C₂	1	2	yes	maximal, complemented
9	C₂×#17989212	C₂	1	4	yes	maximal, complemented
10	C₂×#17989144	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂²⋊Q₈×D₇₃	C₂	1	4	yes	maximal, complemented
12	C₂×#17989061	C₂	1	2	yes	maximal
13	C₂²×C₄×D₂₉₂	C₂	1	1	yes	maximal, characteristic
14	C₂×#533×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×Q₈×D₇₃	C₂²	1	4	yes	complemented
16	C₂³×D₂₉₂	C₂²	1	1	yes	characteristic
17	C₂³×C₄×D₇₃	C₂²	1	2	yes	—
18	#17989298	C₂²	1	32	yes	complemented
19	#17989297	C₂²	1	32	yes	complemented
20	#17989297	C₂²	1	64	yes	complemented
21	#17989293	C₂²	1	64	yes	complemented
22	Q₈×D₂₉₂	C₂²	1	32	yes	complemented
23	#17989252	C₂²	1	32	yes	complemented
24	#17989215	C₂²	1	32	yes	complemented
25	#17989212	C₂²	1	64	yes	complemented
26	#17989144	C₂²	1	16	yes	complemented
27	C₂×#14556591	C₂²	1	4	yes	complemented
28	C₂×#14556591	C₂²	1	1	yes	characteristic, complemented
29	C₂×#14556591	C₂²	1	1	yes	characteristic, complemented
30	C₂×#14556590	C₂²	1	4	yes	complemented
31	C₂×#14556583	C₂²	1	4	yes	complemented
32	C₂×#14556583	C₂²	1	2	yes	complemented
33	C₂×#14556582	C₂²	1	4	yes	complemented
34	C₂×#14556571	C₂²	1	8	yes	complemented
35	C₂×#14556571	C₂²	1	4	yes	complemented
36	C₂×#14556570	C₂²	1	2	yes	—
37	C₂×#14556570	C₂²	1	2	yes	—
38	C₂×#14556569	C₂²	1	8	yes	complemented
39	C₂×#14556569	C₂²	1	8	yes	complemented
40	C₂×#14556569	C₂²	1	8	yes	complemented
41	C₂×#14556568	C₂²	1	8	yes	—
42	C₂×#14556567	C₂²	1	8	yes	complemented
43	C₂×#14556567	C₂²	1	4	yes	complemented
44	C₂²⋊Q₈×D₇₃	C₂²	1	64	yes	complemented
45	#17989061	C₂²	1	32	yes	—
46	C₂×C₄×Dic₁₄₆	C₂²	1	2	yes	complemented
47	C₂×C₄×Dic₁₄₆	C₂²	1	2	yes	complemented
48	C₂×C₄×D₂₉₂	C₂²	1	2	yes	—
49	C₂×C₄×D₂₉₂	C₂²	1	2	yes	—
50	C₂×C₄×D₂₉₂	C₂²	1	2	yes	—
51	C₂×C₄×D₂₉₂	C₂²	1	2	yes	—
52	C₂×C₄×D₂₉₂	C₂²	1	16	yes	—
53	C₂×C₄×D₂₉₂	C₂²	1	4	yes	—
54	C₂×C₄×D₂₉₂	C₂²	1	4	yes	—
55	C₂×#14556553	C₂²	1	4	yes	—
56	C₂×#14556553	C₂²	1	4	yes	—
57	C₂×#14556550	C₂²	1	2	yes	—
58	C₂²×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
59	C₂×C₄⋊C₄×D₇₃	C₂²	1	8	yes	complemented
60	C₂×C₄⋊C₄×D₇₃	C₂²	1	4	yes	complemented
61	C₂²×#11924005	C₂²	1	2	yes	—
62	C₂×C₂²⋊C₄×D₇₃	C₂²	1	8	yes	—
63	#533×C₇₃	C₂²	1	16	yes	complemented
64	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×#125×C₇₃	C₂²	1	2	yes	complemented
67	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
68	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
69	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	complemented
70	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	complemented
71	C₂×#117×C₇₃	C₂²	1	2	yes	—
72	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
73	C₂⁴×D₇₃	C₂³	1	2	yes	—
74	C₂²×Dic₁₄₆	C₂³	1	2	yes	—
75	C₂²×Dic₁₄₆	C₂³	1	8	yes	—
76	C₂²×Dic₁₄₆	C₂³	1	2	yes	—
77	C₂×Q₈×D₇₃	—	4	16	no	—
78	C₂×Q₈×D₇₃	C₂³	1	32	yes	complemented
79	C₂²×D₂₉₂	Q₈	1	16	yes	complemented
80	C₂²×D₂₉₂	C₂³	1	2	yes	—
81	C₂²×D₂₉₂	C₂³	1	2	yes	—
82	C₂²×D₂₉₂	C₂³	1	8	yes	—
83	C₂³×Dic₇₃	C₂³	1	2	yes	—
84	C₂²×C₄×D₇₃	—	4	8	no	—
85	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
86	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
87	C₂²×C₄×D₇₃	C₂³	1	16	yes	—
88	C₂²×C₄×D₇₃	C₂³	1	8	yes	—
89	C₂²×C₄×D₇₃	C₂³	1	8	yes	—
90	#14556591	C₂³	1	8	yes	complemented
91	#14556591	C₂³	1	8	yes	complemented
92	#14556591	C₂³	1	32	yes	complemented
93	#14556590	C₂³	1	32	yes	complemented
94	#14556583	C₂³	1	16	yes	complemented
95	#14556583	C₂³	1	32	yes	complemented
96	#14556582	C₂³	1	32	yes	complemented
97	#14556571	C₂³	1	64	yes	complemented
98	#14556571	C₂³	1	32	yes	complemented
99	#14556570	C₂³	1	16	yes	—
100	#14556570	C₂³	1	16	yes	—
101	#14556569	C₂³	1	64	yes	complemented
102	#14556569	C₂³	1	64	yes	complemented
103	#14556569	C₂³	1	64	yes	complemented
104	#14556568	C₂³	1	64	yes	—
105	#14556567	C₂³	1	64	yes	complemented
106	#14556567	C₂³	1	32	yes	complemented
107	C₄×Dic₁₄₆	C₂³	1	16	yes	complemented
108	C₄×Dic₁₄₆	C₂³	1	16	yes	complemented
109	C₄×D₂₉₂	C₂³	1	16	yes	—
110	C₄×D₂₉₂	C₂³	1	16	yes	—
111	C₄×D₂₉₂	C₂³	1	32	yes	—
112	C₄×D₂₉₂	C₂³	1	16	yes	—
113	C₄×D₂₉₂	C₂³	1	16	yes	—
114	C₄×D₂₉₂	C₂³	1	32	yes	—
115	#14556553	C₂³	1	32	yes	—
116	#14556553	C₂³	1	32	yes	—
117	#14556550	C₂³	1	16	yes	—
118	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
119	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
120	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
121	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
122	C₂×C₄⋊Dic₇₃	C₂³	1	8	yes	—
123	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
124	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
125	C₂×C₄⋊Dic₇₃	C₂³	1	8	yes	—
126	C₂×#11924007	C₂³	1	8	yes	—
127	C₂×#11924007	C₂³	1	4	yes	—
128	C₂×#11924007	C₂³	1	8	yes	—
129	C₂×#11924007	C₂³	1	4	yes	—
130	C₄⋊C₄×D₇₃	C₂³	1	64	yes	complemented
131	C₄⋊C₄×D₇₃	C₂³	1	32	yes	complemented
132	C₂×C₂²⋊Dic₇₃	C₂³	1	4	yes	—
133	C₂×#11924005	C₂³	1	16	yes	—
134	C₂×#11924005	C₂³	1	8	yes	—
135	C₂×#11924005	C₂³	1	8	yes	—
136	C₂×#11924005	C₂³	1	4	yes	—
137	C₂×#11924005	C₂³	1	4	yes	—
138	C₂²⋊C₄×D₇₃	C₂³	1	64	yes	—
139	C₂×C₄×Dic₇₃	C₂³	1	4	yes	—
140	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
141	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
145	C₄⋊Q₈×C₇₃	C₂³	1	8	yes	complemented
146	C₄⋊Q₈×C₇₃	C₂³	1	8	yes	complemented
147	#125×C₇₃	C₂³	1	16	yes	complemented
148	C₂²⋊Q₈×C₇₃	C₂³	1	16	yes	—
149	C₂²⋊Q₈×C₇₃	C₂³	1	16	yes	—
150	C₄×Q₈×C₇₃	C₂³	1	16	yes	complemented
151	C₄×Q₈×C₇₃	C₂³	1	16	yes	complemented
152	#117×C₇₃	C₂³	1	16	yes	—
153	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
156	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
157	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
160	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
162	C₂×C₄²×C₇₃	C₂³	1	8	yes	—
163	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
166	C₂³×D₇₃	—	4	4	no	—
167	C₂³×D₇₃	—	4	4	no	—
168	C₂³×D₇₃	C₂×Q₈	1	16	yes	complemented
169	C₂³×D₇₃	C₂⁴	1	4	yes	—
170	C₂³×D₇₃	C₂⁴	1	8	yes	—
171	C₂×Dic₁₄₆	—	2	8	no	—
172	C₂×Dic₁₄₆	—	4	16	no	—
173	C₂×Dic₁₄₆	—	4	4	no	—
174	C₂×Dic₁₄₆	C₂⁴	1	8	yes	—
175	C₂×Dic₁₄₆	C₂⁴	1	8	yes	—
176	C₂×Dic₁₄₆	C₂⁴	1	32	yes	—
177	Q₈×D₇₃	—	4	64	no	—
178	C₂×D₂₉₂	C₂×Q₈	1	16	yes	complemented
179	C₂×D₂₉₂	C₂×Q₈	1	16	yes	complemented
180	C₂×D₂₉₂	C₂×Q₈	1	64	yes	complemented
181	C₂×D₂₉₂	C₂⁴	1	8	yes	—
182	C₂×D₂₉₂	C₂⁴	1	8	yes	—
183	C₂²×Dic₇₃	—	4	4	no	—
184	C₂²×Dic₇₃	C₂⁴	1	4	yes	—
185	C₂²×Dic₇₃	C₂⁴	1	4	yes	—
186	C₂²×Dic₇₃	C₂⁴	1	4	yes	—
187	C₂²×Dic₇₃	C₂⁴	1	8	yes	—
188	C₂×C₄×D₇₃	—	2	16	no	—
189	C₂×C₄×D₇₃	—	4	32	no	—
190	C₂×C₄×D₇₃	—	4	8	no	—
191	C₂×C₄×D₇₃	—	4	16	no	—
192	C₂×C₄×D₇₃	—	4	16	no	—
193	C₂×C₄×D₇₃	C₂⁴	1	16	yes	—
194	C₂×C₄×D₇₃	C₂⁴	1	32	yes	—
195	C₂×C₄×D₇₃	C₂⁴	1	32	yes	—
196	C₂×C₄×D₇₃	C₂⁴	1	16	yes	—
197	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
198	C₄⋊Dic₇₃	C₂⁴	1	32	yes	—
199	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
200	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
201	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
202	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
203	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
204	#11924007	C₂⁴	1	16	yes	—
205	#11924007	C₂⁴	1	32	yes	—
206	#11924007	C₂⁴	1	32	yes	—
207	#11924007	C₂⁴	1	16	yes	—
208	C₂²⋊Dic₇₃	C₂⁴	1	16	yes	—
209	#11924005	C₂⁴	1	32	yes	—
210	#11924005	C₂⁴	1	32	yes	—
211	#11924005	C₂⁴	1	16	yes	—
212	#11924005	C₂⁴	1	16	yes	—
213	C₄×Dic₇₃	C₂⁴	1	16	yes	—
214	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
215	C₂×Q₈×C₇₃	—	2	8	no	—
216	C₂×Q₈×C₇₃	—	4	4	no	—
217	C₂×Q₈×C₇₃	C₂⁴	1	8	yes	—
218	C₂×Q₈×C₇₃	C₂⁴	1	8	yes	—
219	C₂²×C₄×C₇₃	—	2	4	no	—
220	C₂²×C₄×C₇₃	—	4	2	no	—
221	C₂²×C₄×C₇₃	C₂×Q₈	1	8	yes	complemented
222	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
226	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
228	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
229	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
232	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
233	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
234	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
235	C₄⋊C₄×C₇₃	C₂⁴	1	16	yes	—
236	C₄⋊C₄×C₇₃	C₂⁴	1	16	yes	—
237	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
238	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
239	C₂²⋊C₄×C₇₃	C₂⁴	1	16	yes	—
240	C₄²×C₇₃	C₂⁴	1	4	yes	—
241	C₄²×C₇₃	C₂⁴	1	4	yes	—
242	C₄²×C₇₃	C₂⁴	1	4	yes	—
243	C₄²×C₇₃	C₂⁴	1	4	yes	—
244	C₄²×C₇₃	C₂⁴	1	16	yes	—
245	C₂³×C₇₃	—	2	2	no	—
246	C₂³×C₇₃	—	2	2	no	—
247	C₂³×C₇₃	C₂²×Q₈	1	4	yes	—
248	C₂³×C₇₃	C₂⁵	1	2	yes	—
249	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
250	C₂²×D₇₃	—	2	8	no	—
251	C₂²×D₇₃	—	2	8	no	—
252	C₂²×D₇₃	—	4	8	no	—
253	C₂²×D₇₃	—	4	32	no	—
254	C₂²×D₇₃	—	4	8	no	—
255	C₂²×D₇₃	C₂²×Q₈	1	16	yes	—
256	C₂²×D₇₃	C₂²×Q₈	1	32	yes	complemented
257	C₂²×D₇₃	C₂⁵	1	8	yes	—
258	Q₈×C₇₃	—	2	16	no	—
259	Q₈×C₇₃	—	4	8	no	—
260	C₂×C₄×C₇₃	—	2	2	no	—
261	C₂×C₄×C₇₃	—	2	8	no	—
262	C₂×C₄×C₇₃	—	2	2	no	—
263	C₂×C₄×C₇₃	—	2	2	no	—
264	C₂×C₄×C₇₃	—	2	8	no	—
265	C₂×C₄×C₇₃	—	2	8	no	—
266	C₂×C₄×C₇₃	—	4	4	no	—
267	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
268	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
269	C₂×C₄×C₇₃	C₂²×Q₈	1	16	yes	complemented
270	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	—
271	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
272	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
273	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
274	C₂×C₄×C₇₃	C₂⁵	1	8	yes	—
275	C₂×C₄×C₇₃	C₂⁵	1	8	yes	—
276	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
277	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
278	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
279	C₂×Dic₇₃	—	2	8	no	—
280	C₂×Dic₇₃	—	2	8	no	—
281	C₂×Dic₇₃	—	2	8	no	—
282	C₂×Dic₇₃	—	4	8	no	—
283	C₂×Dic₇₃	C₂⁵	1	8	yes	—
284	C₂×Dic₇₃	C₂⁵	1	8	yes	—
285	C₂×Dic₇₃	C₂⁵	1	8	yes	—
286	D₂₉₂	C₂²×Q₈	1	32	yes	complemented
287	D₂₉₂	C₂²×Q₈	1	32	yes	complemented
288	C₄×D₇₃	—	2	32	no	—
289	C₄×D₇₃	—	4	16	no	—
290	C₄×D₇₃	—	4	32	no	—
291	C₄×D₇₃	—	4	32	no	—
292	Dic₁₄₆	—	2	16	no	—
293	Dic₁₄₆	—	4	32	no	—
294	Dic₁₄₆	—	4	8	no	—
295	C₂²×C₇₃	—	2	2	no	—
296	C₂²×C₇₃	—	2	2	no	—
297	C₂²×C₇₃	—	2	8	no	—
298	C₂²×C₇₃	C₂³×Q₈	1	4	yes	—
299	C₂²×C₇₃	C₂³×Q₈	1	2	yes	—
300	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
301	C₂²×C₇₃	#585	1	2	yes	—
302	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
303	C₂×D₇₃	—	2	8	no	—
304	C₂×D₇₃	—	2	8	no	—
305	C₂×D₇₃	—	2	32	no	—
306	C₂×D₇₃	—	4	32	no	—
307	C₂×D₇₃	C₂³×Q₈	1	16	yes	—
308	C₄×C₇₃	—	2	8	no	—
309	C₄×C₇₃	—	2	2	no	—
310	C₄×C₇₃	—	2	2	no	—
311	C₄×C₇₃	—	2	8	no	—
312	C₄×C₇₃	—	2	2	no	—
313	C₄×C₇₃	C₂³×Q₈	1	4	yes	—
314	C₄×C₇₃	C₂³×Q₈	1	4	yes	—
315	C₄×C₇₃	C₂×H(5,𝔽₂)	1	4	yes	—
316	Dic₇₃	—	2	8	no	—
317	Dic₇₃	—	2	8	no	—
318	Dic₇₃	—	2	8	no	—
319	C₂×#3501	—	73	1	no	maximal, Sylow
320	C₂×C₇₃	—	2	4	no	—
321	C₂×C₇₃	#3501	1	4	yes	complemented
322	C₂×C₇₃	C₂⁴×Q₈	1	1	yes	characteristic
323	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₇₃	C₂×#585	1	1	yes	characteristic
325	D₇₃	—	2	16	no	—
326	#3501	—	73	32	no	—
327	C₂×#554	—	73	2	no	—
328	C₂×#554	—	73	4	no	—
329	C₂×#554	—	73	2	no	—
330	C₂×#554	—	73	4	no	—
331	C₂×D₄×Q₈	—	73	2	no	—
332	C₂×D₄×Q₈	—	73	2	no	—
333	C₂×#544	—	73	2	no	—
334	C₂×#543	—	73	4	no	—
335	C₂×#533	—	73	1	no	—
336	C₂×#533	D₇₃	1	1	yes	characteristic, complemented
337	C₂²×C₂²⋊Q₈	—	73	4	no	—
338	C₂×#518	—	73	2	no	—
339	C₂²×C₄×D₄	—	73	1	no	—
340	C₇₃	C₂×#3501	1	1	yes	characteristic, complemented, Sylow
341	C₂³×Q₈	—	73	4	no	—
342	C₂³×D₄	—	73	1	no	—
343	C₂⁴×C₄	—	73	2	no	—
344	#554	—	73	32	no	—
345	#554	—	73	64	no	—
346	#554	—	73	32	no	—
347	#554	—	73	64	no	—
348	D₄×Q₈	—	73	32	no	—
349	D₄×Q₈	—	73	32	no	—
350	#544	—	73	32	no	—
351	#543	—	73	64	no	—
352	#533	—	73	16	no	—
353	#533	C₂×D₇₃	1	16	yes	complemented
354	C₂×C₄⋊Q₈	—	73	4	no	—
355	C₂×C₄⋊Q₈	—	73	1	no	—
356	C₂×C₄⋊Q₈	—	73	1	no	—
357	C₂×C₄⋊Q₈	—	73	4	no	—
358	C₂×C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
359	C₂×C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
360	C₂×#125	—	73	4	no	—
361	C₂×#125	—	73	2	no	—
362	C₂×#125	—	73	4	no	—
363	C₂×#125	C₂×D₇₃	1	2	yes	complemented
364	C₂×C₂²⋊Q₈	—	73	4	no	—
365	C₂×C₂²⋊Q₈	—	73	8	no	—
366	C₂×C₂²⋊Q₈	—	73	2	no	—
367	C₂×C₂²⋊Q₈	—	73	2	no	—
368	C₂×C₂²⋊Q₈	—	73	64	no	—
369	C₂×C₂²⋊Q₈	—	73	4	no	—
370	C₂×C₂²⋊Q₈	—	73	8	no	—
371	C₂×C₂²⋊Q₈	—	73	8	no	—
372	C₂×C₂²⋊Q₈	—	73	8	no	—
373	C₂×C₂²⋊Q₈	—	73	8	no	—
374	C₂×C₂²⋊Q₈	—	73	8	no	—
375	C₂×C₂²⋊Q₈	C₂×D₇₃	1	2	yes	—
376	C₂×C₂²⋊Q₈	C₂×D₇₃	1	2	yes	—
377	#518	—	73	32	no	—
378	C₂×C₄×Q₈	—	73	2	no	—
379	C₂×C₄×Q₈	—	73	2	no	—
380	C₂×C₄×Q₈	C₂×D₇₃	1	2	yes	complemented
381	C₂×C₄×Q₈	C₂×D₇₃	1	2	yes	complemented
382	C₂×C₄×D₄	—	73	4	no	—
383	C₂×C₄×D₄	—	73	4	no	—
384	C₂×C₄×D₄	—	73	2	no	—
385	C₂×C₄×D₄	—	73	2	no	—
386	C₂×C₄×D₄	—	73	2	no	—
387	C₂×C₄×D₄	—	73	2	no	—
388	C₂×C₄×D₄	—	73	16	no	—
389	C₂×C₄×D₄	—	73	4	no	—
390	C₂×C₄×D₄	—	73	4	no	—
391	C₂×#117	—	73	2	no	—
392	C₂×#117	C₂×D₇₃	1	2	yes	—
393	C₂²×C₄⋊C₄	—	73	1	no	—
394	C₂²×C₄⋊C₄	—	73	8	no	—
395	C₂²×C₄⋊C₄	—	73	4	no	—
396	C₂²×C₂²⋊C₄	—	73	2	no	—
397	C₂²×C₂²⋊C₄	—	73	8	no	—
398	C₂²×C₄²	C₂×D₇₃	1	1	yes	characteristic
399	C₂⁵	—	73	2	no	—
400	C₂²×Q₈	—	292	16	no	—
401	C₂²×Q₈	—	73	32	no	—
402	C₂²×Q₈	—	73	2	no	—
403	C₂²×Q₈	—	73	8	no	—
404	C₂²×Q₈	—	73	2	no	—
405	C₂²×Q₈	C₂²×D₇₃	1	2	yes	—
406	C₂²×Q₈	C₂²×D₇₃	1	2	yes	—
407	C₂²×D₄	—	73	16	no	—
408	C₂²×D₄	—	73	2	no	—
409	C₂²×D₄	—	73	2	no	—
410	C₂²×D₄	—	73	8	no	—
411	C₂³×C₄	—	292	8	no	—
412	C₂³×C₄	—	73	2	no	—
413	C₂³×C₄	—	73	8	no	—
414	C₂³×C₄	—	73	8	no	—
415	C₂³×C₄	—	73	4	no	—
416	C₂³×C₄	—	73	16	no	—
417	C₂³×C₄	—	73	4	no	—
418	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
419	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
420	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
421	C₄⋊Q₈	—	73	32	no	—
422	C₄⋊Q₈	—	73	8	no	—
423	C₄⋊Q₈	—	73	8	no	—
424	C₄⋊Q₈	—	73	32	no	—
425	C₄⋊Q₈	C₂²×D₇₃	1	8	yes	complemented
426	C₄⋊Q₈	C₂²×D₇₃	1	8	yes	complemented
427	#125	—	73	32	no	—
428	#125	—	73	16	no	—
429	#125	—	73	32	no	—
430	#125	C₂²×D₇₃	1	16	yes	complemented
431	C₂²⋊Q₈	—	73	32	no	—
432	C₂²⋊Q₈	—	73	64	no	—
433	C₂²⋊Q₈	—	73	16	no	—
434	C₂²⋊Q₈	—	73	16	no	—
435	C₂²⋊Q₈	—	73	32	no	—
436	C₂²⋊Q₈	—	73	64	no	—
437	C₂²⋊Q₈	—	73	64	no	—
438	C₂²⋊Q₈	—	73	64	no	—
439	C₂²⋊Q₈	—	73	64	no	—
440	C₂²⋊Q₈	—	73	64	no	—
441	C₂²⋊Q₈	C₂²×D₇₃	1	16	yes	—
442	C₂²⋊Q₈	C₂²×D₇₃	1	16	yes	—
443	C₄×Q₈	—	73	16	no	—
444	C₄×Q₈	—	73	16	no	—
445	C₄×Q₈	C₂²×D₇₃	1	16	yes	complemented
446	C₄×Q₈	C₂²×D₇₃	1	16	yes	complemented
447	C₄×D₄	—	73	32	no	—
448	C₄×D₄	—	73	32	no	—
449	C₄×D₄	—	73	16	no	—
450	C₄×D₄	—	73	16	no	—
451	C₄×D₄	—	73	16	no	—
452	C₄×D₄	—	73	16	no	—
453	C₄×D₄	—	73	32	no	—
454	C₄×D₄	—	73	32	no	—
455	#117	—	73	16	no	—
456	#117	C₂²×D₇₃	1	16	yes	—
457	C₂×C₄⋊C₄	—	73	4	no	—
458	C₂×C₄⋊C₄	—	73	2	no	—
459	C₂×C₄⋊C₄	—	73	2	no	—
460	C₂×C₄⋊C₄	—	73	2	no	—
461	C₂×C₄⋊C₄	—	73	8	no	—
462	C₂×C₄⋊C₄	—	73	8	no	—
463	C₂×C₄⋊C₄	—	73	8	no	—
464	C₂×C₄⋊C₄	—	73	8	no	—
465	C₂×C₄⋊C₄	—	73	2	no	—
466	C₂×C₄⋊C₄	—	73	2	no	—
467	C₂×C₄⋊C₄	—	73	4	no	—
468	C₂×C₄⋊C₄	—	73	2	no	—
469	C₂×C₄⋊C₄	—	73	64	no	—
470	C₂×C₄⋊C₄	—	73	32	no	—
471	C₂×C₄⋊C₄	C₂²×D₇₃	1	4	yes	—
472	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
473	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
474	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
475	C₂×C₄⋊C₄	C₂²×D₇₃	1	4	yes	—
476	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
477	C₂×C₂²⋊C₄	—	73	4	no	—
478	C₂×C₂²⋊C₄	—	73	8	no	—
479	C₂×C₂²⋊C₄	—	73	8	no	—
480	C₂×C₂²⋊C₄	—	73	4	no	—
481	C₂×C₂²⋊C₄	—	73	4	no	—
482	C₂×C₂²⋊C₄	—	73	16	no	—
483	C₂×C₂²⋊C₄	—	73	64	no	—
484	C₂×C₂²⋊C₄	C₂²×D₇₃	1	4	yes	—
485	C₂×C₄²	—	73	4	no	—
486	C₂×C₄²	C₂²×D₇₃	1	4	yes	—
487	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
488	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
489	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
490	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
491	C₂×C₄²	C₂²×D₇₃	1	8	yes	—
492	C₂⁴	—	292	4	no	—
493	C₂⁴	—	292	4	no	—
494	C₂⁴	—	73	16	no	—
495	C₂⁴	—	73	8	no	—
496	C₂⁴	—	73	4	no	—
497	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
498	C₂×Q₈	—	2	8	no	—
499	C₂×Q₈	—	4	4	no	—
500	C₂×Q₈	—	292	16	no	—
501	C₂×Q₈	—	292	4	no	—
502	C₂×Q₈	—	292	64	no	—
503	C₂×Q₈	—	73	8	no	—
504	C₂×Q₈	—	73	32	no	—
505	C₂×Q₈	—	73	8	no	—
506	C₂×Q₈	—	146	8	no	—
507	C₂×Q₈	C₂³×D₇₃	1	8	yes	—
508	C₂×Q₈	C₂³×D₇₃	1	8	yes	—
509	C₂×D₄	—	73	16	no	—
510	C₂×D₄	—	73	16	no	—
511	C₂×D₄	—	73	64	no	—
512	C₂×D₄	—	73	8	no	—
513	C₂×D₄	—	73	8	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	292	8	no	—
517	C₂²×C₄	—	292	16	no	—
518	C₂²×C₄	—	292	16	no	—
519	C₂²×C₄	—	292	32	no	—
520	C₂²×C₄	—	292	4	no	—
521	C₂²×C₄	—	73	8	no	—
522	C₂²×C₄	—	73	32	no	—
523	C₂²×C₄	—	73	32	no	—
524	C₂²×C₄	—	73	16	no	—
525	C₂²×C₄	—	73	4	no	—
526	C₂²×C₄	—	73	4	no	—
527	C₂²×C₄	—	73	4	no	—
528	C₂²×C₄	—	73	16	no	—
529	C₂²×C₄	—	146	16	no	—
530	C₂²×C₄	Q₈×D₇₃	1	8	yes	complemented
531	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
532	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
533	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
534	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
535	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
536	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
537	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
538	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
539	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
540	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
541	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
542	C₄⋊C₄	—	73	16	no	—
543	C₄⋊C₄	—	73	32	no	—
544	C₄⋊C₄	—	73	32	no	—
545	C₄⋊C₄	—	73	16	no	—
546	C₄⋊C₄	—	73	8	no	—
547	C₄⋊C₄	—	73	8	no	—
548	C₄⋊C₄	—	73	8	no	—
549	C₄⋊C₄	—	73	32	no	—
550	C₄⋊C₄	—	73	8	no	—
551	C₄⋊C₄	—	73	8	no	—
552	C₄⋊C₄	—	73	8	no	—
553	C₄⋊C₄	C₂³×D₇₃	1	16	yes	—
554	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
555	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
556	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
557	C₄⋊C₄	C₂³×D₇₃	1	16	yes	—
558	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
559	C₂²⋊C₄	—	73	16	no	—
560	C₂²⋊C₄	—	73	32	no	—
561	C₂²⋊C₄	—	73	32	no	—
562	C₂²⋊C₄	—	73	16	no	—
563	C₂²⋊C₄	—	73	16	no	—
564	C₂²⋊C₄	C₂³×D₇₃	1	16	yes	—
565	C₄²	—	73	16	no	—
566	C₄²	C₂³×D₇₃	1	4	yes	—
567	C₄²	C₂³×D₇₃	1	4	yes	—
568	C₄²	C₂³×D₇₃	1	4	yes	—
569	C₄²	C₂³×D₇₃	1	4	yes	—
570	C₄²	C₂³×D₇₃	1	16	yes	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	292	8	no	—
574	C₂³	—	292	8	no	—
575	C₂³	—	292	32	no	—
576	C₂³	—	73	32	no	—
577	C₂³	—	73	16	no	—
578	C₂³	—	73	8	no	—
579	C₂³	—	146	8	no	—
580	C₂³	—	146	8	no	—
581	C₂³	C₂×Q₈×D₇₃	1	4	yes	—
582	C₂³	C₂⁴×D₇₃	1	2	yes	—
583	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
584	Q₈	—	2	16	no	—
585	Q₈	—	4	8	no	—
586	Q₈	—	292	32	no	—
587	Q₈	—	292	8	no	—
588	Q₈	—	146	16	no	—
589	D₄	—	73	32	no	—
590	D₄	—	73	32	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	8	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	8	no	—
596	C₂×C₄	—	2	8	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	—	292	16	no	—
599	C₂×C₄	—	292	32	no	—
600	C₂×C₄	—	292	32	no	—
601	C₂×C₄	—	292	8	no	—
602	C₂×C₄	—	73	8	no	—
603	C₂×C₄	—	73	8	no	—
604	C₂×C₄	—	73	8	no	—
605	C₂×C₄	—	146	8	no	—
606	C₂×C₄	—	146	8	no	—
607	C₂×C₄	—	146	8	no	—
608	C₂×C₄	—	146	32	no	—
609	C₂×C₄	C₂×Q₈×D₇₃	1	4	yes	—
610	C₂×C₄	C₂×Q₈×D₇₃	1	4	yes	—
611	C₂×C₄	C₂×Q₈×D₇₃	1	16	yes	complemented
612	C₂×C₄	#14556637	1	4	yes	—
613	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
614	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
615	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
616	C₂×C₄	C₂⁴×D₇₃	1	8	yes	—
617	C₂×C₄	C₂⁴×D₇₃	1	8	yes	—
618	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
619	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
620	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	8	no	—
624	C₂²	—	292	32	no	—
625	C₂²	—	73	16	no	—
626	C₂²	—	146	8	no	—
627	C₂²	—	146	8	no	—
628	C₂²	—	146	32	no	—
629	C₂²	C₂²×Q₈×D₇₃	1	4	yes	—
630	C₂²	C₂²×Q₈×D₇₃	1	2	yes	—
631	C₂²	C₂×#14556637	1	2	yes	—
632	C₂²	#17989423	1	2	yes	—
633	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
634	C₄	—	2	2	no	—
635	C₄	—	2	8	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	8	no	—
639	C₄	—	146	8	no	—
640	C₄	—	146	8	no	—
641	C₄	—	146	8	no	—
642	C₄	C₂²×Q₈×D₇₃	1	4	yes	—
643	C₄	C₂²×Q₈×D₇₃	1	4	yes	—
644	C₄	C₂×#14556637	1	4	yes	—
645	C₂	—	2	4	no	—
646	C₂	—	146	16	no	—
647	C₂	#22623732	1	4	yes	direct product factor
648	C₂	C₂³×Q₈×D₇₃	1	1	yes	characteristic
649	C₂	C₂²×#14556637	1	1	yes	characteristic
650	C₂	C₂×#17989423	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₃
commutator, cosocle	C₂²×C₇₃	C₂⁶
Frattini	C₂²	C₂⁵×D₇₃
Fitting	C₂×#533×C₇₃	C₂
socle	C₂³×C₇₃	C₂⁵
prime radical	C₂³×D₂₉₂	C₂²
hypercenter	C₂×#533	D₇₃
hypocenter	C₇₃	C₂×#3501
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. #22623732	C₂	direct (N × H)
2. C₂×#17989298	C₂	semidirect
3. C₂×#17989297	C₂	semidirect
4. C₂×#17989297	C₂	semidirect
5. C₂×#17989293	C₂	semidirect
6. C₂×Q₈×D₂₉₂	C₂	semidirect
7. C₂×#17989252	C₂	semidirect
8. C₂×#17989215	C₂	semidirect
9. C₂×#17989212	C₂	semidirect
10. C₂×#17989144	C₂	semidirect
11. C₂×C₂²⋊Q₈×D₇₃	C₂	semidirect
14. C₂×#533×C₇₃	C₂	semidirect
15. C₂²×Q₈×D₇₃	C₂²	semidirect
18. #17989298	C₂²	semidirect
19. #17989297	C₂²	semidirect
20. #17989297	C₂²	semidirect
21. #17989293	C₂²	semidirect
22. Q₈×D₂₉₂	C₂²	semidirect
23. #17989252	C₂²	semidirect
24. #17989215	C₂²	semidirect
25. #17989212	C₂²	semidirect
26. #17989144	C₂²	semidirect
27. C₂×#14556591	C₂²	semidirect
28. C₂×#14556591	C₂²	semidirect
29. C₂×#14556591	C₂²	semidirect
30. C₂×#14556590	C₂²	semidirect
31. C₂×#14556583	C₂²	semidirect
32. C₂×#14556583	C₂²	semidirect
33. C₂×#14556582	C₂²	semidirect
34. C₂×#14556571	C₂²	semidirect
35. C₂×#14556571	C₂²	semidirect
38. C₂×#14556569	C₂²	semidirect
39. C₂×#14556569	C₂²	semidirect
40. C₂×#14556569	C₂²	semidirect
42. C₂×#14556567	C₂²	semidirect
43. C₂×#14556567	C₂²	semidirect
44. C₂²⋊Q₈×D₇₃	C₂²	semidirect
46. C₂×C₄×Dic₁₄₆	C₂²	semidirect
47. C₂×C₄×Dic₁₄₆	C₂²	semidirect
59. C₂×C₄⋊C₄×D₇₃	C₂²	semidirect
60. C₂×C₄⋊C₄×D₇₃	C₂²	semidirect
63. #533×C₇₃	C₂²	semidirect
64. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
65. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
66. C₂×#125×C₇₃	C₂²	semidirect
69. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
70. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
78. C₂×Q₈×D₇₃	C₂³	semidirect
79. C₂²×D₂₉₂	Q₈	semidirect
90. #14556591	C₂³	semidirect
91. #14556591	C₂³	semidirect
92. #14556591	C₂³	semidirect
93. #14556590	C₂³	semidirect
94. #14556583	C₂³	semidirect
95. #14556583	C₂³	semidirect
96. #14556582	C₂³	semidirect
97. #14556571	C₂³	semidirect
98. #14556571	C₂³	semidirect
101. #14556569	C₂³	semidirect
102. #14556569	C₂³	semidirect
103. #14556569	C₂³	semidirect
105. #14556567	C₂³	semidirect
106. #14556567	C₂³	semidirect
107. C₄×Dic₁₄₆	C₂³	semidirect
108. C₄×Dic₁₄₆	C₂³	semidirect
130. C₄⋊C₄×D₇₃	C₂³	semidirect
131. C₄⋊C₄×D₇₃	C₂³	semidirect
145. C₄⋊Q₈×C₇₃	C₂³	semidirect
146. C₄⋊Q₈×C₇₃	C₂³	semidirect
147. #125×C₇₃	C₂³	semidirect
150. C₄×Q₈×C₇₃	C₂³	semidirect
151. C₄×Q₈×C₇₃	C₂³	semidirect
168. C₂³×D₇₃	C₂×Q₈	semidirect
178. C₂×D₂₉₂	C₂×Q₈	semidirect
179. C₂×D₂₉₂	C₂×Q₈	semidirect
180. C₂×D₂₉₂	C₂×Q₈	semidirect
221. C₂²×C₄×C₇₃	C₂×Q₈	semidirect
256. C₂²×D₇₃	C₂²×Q₈	semidirect
269. C₂×C₄×C₇₃	C₂²×Q₈	semidirect
286. D₂₉₂	C₂²×Q₈	semidirect
287. D₂₉₂	C₂²×Q₈	semidirect
321. C₂×C₇₃	#3501	semidirect
336. C₂×#533	D₇₃	semidirect
340. C₇₃	C₂×#3501	semidirect
353. #533	C₂×D₇₃	semidirect
358. C₂×C₄⋊Q₈	C₂×D₇₃	semidirect
359. C₂×C₄⋊Q₈	C₂×D₇₃	semidirect
363. C₂×#125	C₂×D₇₃	semidirect
380. C₂×C₄×Q₈	C₂×D₇₃	semidirect
381. C₂×C₄×Q₈	C₂×D₇₃	semidirect
425. C₄⋊Q₈	C₂²×D₇₃	semidirect
426. C₄⋊Q₈	C₂²×D₇₃	semidirect
430. #125	C₂²×D₇₃	semidirect
445. C₄×Q₈	C₂²×D₇₃	semidirect
446. C₄×Q₈	C₂²×D₇₃	semidirect
530. C₂²×C₄	Q₈×D₇₃	semidirect
611. C₂×C₄	C₂×Q₈×D₇₃	semidirect
647. C₂	#22623732	direct (N × H)

Maximal subgroups

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

subgroup	index
#22623732	2
C₂×#17989298	2
C₂×#17989297	2
C₂×#17989293	2
C₂×Q₈×D₂₉₂	2
C₂×#17989252	2
C₂×#17989215	2
C₂×#17989212	2
C₂×#17989144	2
C₂×C₂²⋊Q₈×D₇₃	2
C₂×#17989061	2
C₂²×C₄×D₂₉₂	2
C₂×#533×C₇₃	2
C₂×#3501	73

Subgroups — C2×#22623732 #33993883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22623732 #33993883