Subgroups — C₂×C₄×#14556637 #33992587

Order 18688.

12378 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556637	C₂	1	1	yes	maximal, characteristic
2	C₄×#14556637	C₂	1	32	yes	maximal, direct product factor
3	C₂×#17989070	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#17989069	C₂	1	2	yes	maximal, complemented
5	C₂×#17989067	C₂	1	3	yes	maximal, complemented
6	C₂×#17989061	C₂	1	3	yes	maximal, complemented
7	C₂×#17989059	C₂	1	6	yes	maximal, complemented
8	C₂×C₄×#11924029	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×#11924028	C₂	1	3	yes	maximal, complemented
10	C₂²×C₄×D₂₉₂	C₂	1	3	yes	maximal, complemented
11	C₂×C₄×D₄×D₇₃	C₂	1	6	yes	maximal, complemented
12	C₂×C₄×#41×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#14556637	C₄	1	32	yes	direct product factor
14	C₂×#14556637	C₂²	1	16	yes	—
15	C₂²×#11924029	C₂²	1	2	yes	—
16	C₂²×#11924028	C₂²	1	3	yes	—
17	C₂³×D₂₉₂	C₂²	1	3	yes	—
18	C₂²×D₄×D₇₃	C₂²	1	6	yes	—
19	C₂³×C₄×D₇₃	C₂²	1	6	yes	complemented
20	#17989070	C₂²	1	16	yes	complemented
21	#17989069	C₂²	1	32	yes	complemented
22	#17989067	C₂²	1	48	yes	complemented
23	#17989061	C₂²	1	48	yes	complemented
24	#17989059	C₂²	1	96	yes	complemented
25	C₄×#11924029	C₂²	1	32	yes	complemented
26	C₄×#11924028	C₂²	1	48	yes	complemented
27	C₂×Q₈×Dic₇₃	C₂²	1	2	yes	complemented
28	C₂×C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×Dic₁₄₆	C₂²	1	3	yes	complemented
30	C₂×C₄×D₂₉₂	C₂²	1	6	yes	complemented
31	C₂×C₄×D₂₉₂	C₂²	1	3	yes	complemented
32	C₂×C₄×D₂₉₂	C₂²	1	6	yes	complemented
33	C₂×C₄×D₂₉₂	C₂²	1	6	yes	complemented
34	C₂×C₄×D₂₉₂	C₂²	1	3	yes	complemented
35	C₂×C₄×D₂₉₂	C₂²	1	48	yes	complemented
36	C₂×D₄×Dic₇₃	C₂²	1	6	yes	complemented
37	C₂×#14556553	C₂²	1	6	yes	complemented
38	C₂×#14556553	C₂²	1	6	yes	complemented
39	C₂×C₄×C₂²⋊D₇₃	C₂²	1	6	yes	complemented
40	C₂×C₄×C₂²⋊D₇₃	C₂²	1	6	yes	complemented
41	C₂×#14556551	C₂²	1	12	yes	complemented
42	C₄×D₄×D₇₃	C₂²	1	96	yes	complemented
43	C₂×#14556550	C₂²	1	3	yes	complemented
44	C₂×#14556549	C₂²	1	6	yes	complemented
45	C₂×#14556548	C₂²	1	6	yes	complemented
46	C₂²×C₄⋊Dic₇₃	C₂²	1	3	yes	complemented
47	C₂×C₄⋊C₄×D₇₃	C₂²	1	6	yes	complemented
48	C₂²×#11924005	C₂²	1	6	yes	complemented
49	C₂×C₂²⋊C₄×D₇₃	C₂²	1	12	yes	complemented
50	C₂×C₄²×D₇₃	C₂²	1	6	yes	complemented
51	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
52	C₄×#41×C₇₃	C₂²	1	16	yes	complemented
53	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₄×C₇₃	C₂²	1	3	yes	complemented
56	C₂×C₄×D₄×C₇₃	C₂²	1	3	yes	complemented
57	C₂×#117×C₇₃	C₂²	1	3	yes	complemented
58	C₂²×C₄²×C₇₃	C₂²	1	3	yes	complemented
59	C₂⁴×D₇₃	C₂³	1	6	yes	—
60	#14556637	C₂×C₄	1	256	yes	direct product factor
61	C₂×#11924029	C₂×C₄	1	32	yes	complemented
62	C₂×#11924029	C₂³	1	16	yes	—
63	C₂×#11924028	C₂×C₄	1	48	yes	complemented
64	C₂×#11924028	C₂³	1	24	yes	—
65	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
66	C₂²×D₂₉₂	C₂×C₄	1	48	yes	complemented
67	C₂²×D₂₉₂	C₂³	1	6	yes	—
68	C₂²×D₂₉₂	C₂³	1	3	yes	—
69	C₂²×D₂₉₂	C₂³	1	24	yes	—
70	C₂²×C₂²⋊D₇₃	C₂³	1	6	yes	—
71	C₂×D₄×D₇₃	C₂×C₄	1	96	yes	complemented
72	C₂×D₄×D₇₃	C₂³	1	48	yes	—
73	C₂³×Dic₇₃	C₂³	1	6	yes	—
74	C₂²×C₄×D₇₃	—	4	24	no	—
75	C₂²×C₄×D₇₃	C₂³	1	6	yes	—
76	C₂²×C₄×D₇₃	C₂³	1	12	yes	—
77	C₂²×C₄×D₇₃	C₂³	1	6	yes	—
78	C₂²×C₄×D₇₃	C₂³	1	6	yes	—
79	C₂²×C₄×D₇₃	C₂³	1	48	yes	complemented
80	Q₈×Dic₇₃	C₂³	1	16	yes	complemented
81	C₄×Dic₁₄₆	C₂³	1	8	yes	complemented
82	C₄×Dic₁₄₆	C₂³	1	24	yes	complemented
83	C₄×D₂₉₂	C₂³	1	48	yes	complemented
84	C₄×D₂₉₂	C₂³	1	24	yes	complemented
85	C₄×D₂₉₂	C₂³	1	48	yes	complemented
86	C₄×D₂₉₂	C₂³	1	48	yes	complemented
87	C₄×D₂₉₂	C₂³	1	24	yes	complemented
88	D₄×Dic₇₃	C₂³	1	48	yes	complemented
89	#14556553	C₂³	1	48	yes	complemented
90	#14556553	C₂³	1	48	yes	complemented
91	C₄×C₂²⋊D₇₃	C₂³	1	48	yes	complemented
92	C₄×C₂²⋊D₇₃	C₂³	1	48	yes	complemented
93	#14556551	C₂³	1	96	yes	complemented
94	#14556550	C₂³	1	24	yes	complemented
95	#14556549	C₂³	1	48	yes	complemented
96	#14556548	C₂³	1	48	yes	complemented
97	C₂×C₄⋊Dic₇₃	C₂³	1	6	yes	—
98	C₂×C₄⋊Dic₇₃	C₂³	1	3	yes	—
99	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊Dic₇₃	C₂³	1	24	yes	complemented
101	C₂×#11924007	C₂³	1	6	yes	—
102	C₂×#11924007	C₂³	1	2	yes	—
103	C₄⋊C₄×D₇₃	C₂³	1	48	yes	complemented
104	C₂×C₂²⋊Dic₇₃	C₂³	1	6	yes	—
105	C₂×#11924005	C₂³	1	6	yes	—
106	C₂×#11924005	C₂³	1	12	yes	—
107	C₂×#11924005	C₂³	1	6	yes	—
108	C₂×#11924005	C₂³	1	48	yes	complemented
109	C₂²⋊C₄×D₇₃	C₂³	1	96	yes	complemented
110	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
111	C₂×C₄×Dic₇₃	C₂³	1	6	yes	—
112	C₂×C₄×Dic₇₃	C₂³	1	6	yes	—
113	C₄²×D₇₃	C₂³	1	48	yes	complemented
114	C₂×#41×C₇₃	C₂×C₄	1	16	yes	complemented
115	C₂×#41×C₇₃	C₂³	1	8	yes	—
116	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₇₃	C₂³	1	3	yes	—
118	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
119	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
120	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
121	C₄×Q₈×C₇₃	C₂³	1	8	yes	complemented
122	C₄×Q₈×C₇₃	C₂³	1	8	yes	complemented
123	C₄×D₄×C₇₃	C₂³	1	24	yes	complemented
124	C₄×D₄×C₇₃	C₂³	1	24	yes	complemented
125	#117×C₇₃	C₂³	1	24	yes	complemented
126	C₂×C₄⋊C₄×C₇₃	C₂³	1	3	yes	—
127	C₂×C₄⋊C₄×C₇₃	C₂³	1	3	yes	—
128	C₂×C₂²⋊C₄×C₇₃	C₂³	1	6	yes	—
129	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
131	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
132	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
133	C₂×C₄²×C₇₃	C₂³	1	24	yes	complemented
134	C₂³×D₇₃	—	4	12	no	—
135	C₂³×D₇₃	—	4	12	no	—
136	C₂³×D₇₃	C₂²×C₄	1	48	yes	complemented
137	C₂³×D₇₃	C₂⁴	1	6	yes	—
138	C₂³×D₇₃	C₂⁴	1	24	yes	—
139	#11924029	C₂²×C₄	1	128	yes	complemented
140	#11924028	C₂²×C₄	1	192	yes	complemented
141	C₂×Dic₁₄₆	C₂²×C₄	1	8	yes	complemented
142	C₂×Dic₁₄₆	C₂⁴	1	4	yes	—
143	C₂×D₂₉₂	C₂²×C₄	1	48	yes	complemented
144	C₂×D₂₉₂	C₂²×C₄	1	24	yes	complemented
145	C₂×D₂₉₂	C₂²×C₄	1	192	yes	complemented
146	C₂×D₂₉₂	C₂⁴	1	24	yes	—
147	C₂×D₂₉₂	C₂⁴	1	12	yes	—
148	C₂×C₂²⋊D₇₃	C₂²×C₄	1	48	yes	complemented
149	C₂×C₂²⋊D₇₃	C₂⁴	1	24	yes	—
150	D₄×D₇₃	C₂²×C₄	1	384	yes	complemented
151	C₂²×Dic₇₃	—	4	12	no	—
152	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
153	C₂²×Dic₇₃	C₂⁴	1	6	yes	—
154	C₂²×Dic₇₃	C₂⁴	1	24	yes	—
155	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
156	C₂×C₄×D₇₃	—	2	24	no	—
157	C₂×C₄×D₇₃	—	4	96	no	—
158	C₂×C₄×D₇₃	—	4	24	no	—
159	C₂×C₄×D₇₃	—	4	12	no	—
160	C₂×C₄×D₇₃	C₂²×C₄	1	48	yes	complemented
161	C₂×C₄×D₇₃	C₂⁴	1	24	yes	—
162	C₂×C₄×D₇₃	C₂⁴	1	24	yes	—
163	C₂×C₄×D₇₃	C₂⁴	1	48	yes	—
164	C₂×C₄×D₇₃	C₂⁴	1	24	yes	—
165	C₄⋊Dic₇₃	C₂⁴	1	24	yes	—
166	C₄⋊Dic₇₃	C₂⁴	1	12	yes	—
167	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
168	#11924007	C₂⁴	1	24	yes	—
169	#11924007	C₂⁴	1	8	yes	—
170	C₂²⋊Dic₇₃	C₂⁴	1	24	yes	—
171	#11924005	C₂⁴	1	24	yes	—
172	#11924005	C₂⁴	1	48	yes	—
173	#11924005	C₂⁴	1	24	yes	—
174	C₄×Dic₇₃	C₂⁴	1	8	yes	—
175	C₄×Dic₇₃	C₂⁴	1	24	yes	—
176	C₄×Dic₇₃	C₂⁴	1	24	yes	—
177	C₂⁴×C₇₃	C₂⁴	1	3	yes	—
178	#41×C₇₃	C₂²×C₄	1	64	yes	complemented
179	C₂×Q₈×C₇₃	C₂²×C₄	1	8	yes	complemented
180	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
181	C₂×D₄×C₇₃	C₂²×C₄	1	24	yes	complemented
182	C₂×D₄×C₇₃	C₂⁴	1	12	yes	—
183	C₂²×C₄×C₇₃	—	2	12	no	—
184	C₂²×C₄×C₇₃	—	4	6	no	—
185	C₂²×C₄×C₇₃	C₂²×C₄	1	24	yes	complemented
186	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
188	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
189	C₂²×C₄×C₇₃	C₂⁴	1	12	yes	—
190	C₂²×C₄×C₇₃	C₂⁴	1	12	yes	—
191	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
193	C₂²×C₄×C₇₃	C₂⁴	1	12	yes	—
194	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
195	C₄⋊C₄×C₇₃	C₂⁴	1	12	yes	—
196	C₄⋊C₄×C₇₃	C₂⁴	1	12	yes	—
197	C₂²⋊C₄×C₇₃	C₂⁴	1	24	yes	—
198	C₄²×C₇₃	C₂⁴	1	4	yes	—
199	C₄²×C₇₃	C₂⁴	1	12	yes	—
200	C₄²×C₇₃	C₂⁴	1	12	yes	—
201	C₄²×C₇₃	C₂⁴	1	12	yes	—
202	C₂³×C₇₃	—	2	6	no	—
203	C₂³×C₇₃	—	2	6	no	—
204	C₂³×C₇₃	C₂³×C₄	1	12	yes	—
205	C₂³×C₇₃	C₂⁵	1	6	yes	—
206	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
207	C₂²×D₇₃	—	2	12	no	—
208	C₂²×D₇₃	—	2	12	no	—
209	C₂²×D₇₃	—	4	24	no	—
210	C₂²×D₇₃	—	4	96	no	—
211	C₂²×D₇₃	—	4	24	no	—
212	C₂²×D₇₃	C₂³×C₄	1	24	yes	—
213	C₂²×D₇₃	C₂³×C₄	1	96	yes	complemented
214	C₂²×D₇₃	C₂⁵	1	12	yes	—
215	Q₈×C₇₃	C₂³×C₄	1	16	yes	complemented
216	D₄×C₇₃	C₂³×C₄	1	48	yes	complemented
217	C₂×C₄×C₇₃	—	2	6	no	—
218	C₂×C₄×C₇₃	—	2	2	no	—
219	C₂×C₄×C₇₃	—	2	6	no	—
220	C₂×C₄×C₇₃	—	2	24	no	—
221	C₂×C₄×C₇₃	—	4	12	no	—
222	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
223	C₂×C₄×C₇₃	C₂³×C₄	1	12	yes	—
224	C₂×C₄×C₇₃	C₂³×C₄	1	48	yes	complemented
225	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	complemented
226	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
227	C₂×C₄×C₇₃	C₂⁵	1	6	yes	—
228	C₂×C₄×C₇₃	C₂⁵	1	6	yes	—
229	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
230	C₂×C₄×C₇₃	C₂⁵	1	6	yes	—
231	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
232	C₂²⋊D₇₃	C₂³×C₄	1	96	yes	complemented
233	C₂×Dic₇₃	—	2	12	no	—
234	C₂×Dic₇₃	—	2	4	no	—
235	C₂×Dic₇₃	—	4	24	no	—
236	C₂×Dic₇₃	C₂³×C₄	1	8	yes	—
237	C₂×Dic₇₃	C₂⁵	1	4	yes	—
238	C₂×Dic₇₃	C₂⁵	1	12	yes	—
239	C₂×Dic₇₃	C₂⁵	1	4	yes	—
240	D₂₉₂	C₂³×C₄	1	96	yes	complemented
241	D₂₉₂	C₂³×C₄	1	48	yes	complemented
242	C₄×D₇₃	—	2	48	no	—
243	C₄×D₇₃	—	4	48	no	—
244	C₄×D₇₃	—	4	24	no	—
245	C₄×D₇₃	C₂³×C₄	1	96	yes	complemented
246	Dic₁₄₆	C₂³×C₄	1	16	yes	complemented
247	C₂²×C₇₃	—	2	6	no	—
248	C₂²×C₇₃	—	2	6	no	—
249	C₂²×C₇₃	—	2	24	no	—
250	C₂²×C₇₃	C₂⁴×C₄	1	12	yes	—
251	C₂²×C₇₃	C₂⁴×C₄	1	2	yes	—
252	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
253	C₂²×C₇₃	#585	1	2	yes	—
254	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
255	C₂×D₇₃	—	2	12	no	—
256	C₂×D₇₃	—	2	12	no	—
257	C₂×D₇₃	—	2	48	no	—
258	C₂×D₇₃	—	4	96	no	—
259	C₂×D₇₃	C₂⁴×C₄	1	24	yes	—
260	C₄×C₇₃	—	2	6	no	—
261	C₄×C₇₃	—	2	6	no	—
262	C₄×C₇₃	—	2	2	no	—
263	C₄×C₇₃	C₂⁴×C₄	1	4	yes	—
264	C₄×C₇₃	C₂⁴×C₄	1	12	yes	—
265	C₄×C₇₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
266	Dic₇₃	—	2	12	no	—
267	Dic₇₃	—	2	4	no	—
268	Dic₇₃	C₂⁴×C₄	1	8	yes	—
269	C₂×C₄×H(5,𝔽₂)	—	73	1	no	maximal, Sylow
270	C₂×C₇₃	—	2	12	no	—
271	C₂×C₇₃	C₄×H(5,𝔽₂)	1	4	yes	complemented
272	C₂×C₇₃	C₂⁵×C₄	1	1	yes	characteristic
273	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
274	C₂×C₇₃	C₂×#585	1	1	yes	characteristic
275	D₇₃	—	2	24	no	—
276	C₂²×H(5,𝔽₂)	—	73	1	no	—
277	C₄×H(5,𝔽₂)	—	73	32	no	—
278	C₂×#520	—	73	1	no	—
279	C₂×#520	—	73	2	no	—
280	C₂×#520	—	73	3	no	—
281	C₂×#518	—	73	6	no	—
282	C₂×#518	—	73	3	no	—
283	C₂×C₄×#41	—	73	3	no	—
284	C₂×C₄×#41	—	73	2	no	—
285	C₂×C₄×#41	D₇₃	1	1	yes	characteristic, complemented
286	C₂²×C₄×D₄	—	73	3	no	—
287	C₂²×C₄×D₄	—	73	6	no	—
288	C₇₃	C₂×C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
289	C₂×H(5,𝔽₂)	—	73	32	no	—
290	C₂×H(5,𝔽₂)	—	73	16	no	—
291	C₂²×#41	—	73	2	no	—
292	C₂²×#41	—	73	3	no	—
293	C₂²×#41	C₂×D₇₃	1	1	yes	characteristic
294	C₂³×D₄	—	73	6	no	—
295	C₂³×D₄	—	73	3	no	—
296	C₂⁴×C₄	—	73	6	no	—
297	#520	—	73	16	no	—
298	#520	—	73	32	no	—
299	#520	—	73	48	no	—
300	#518	—	73	96	no	—
301	#518	—	73	48	no	—
302	C₄×#41	—	73	32	no	—
303	C₄×#41	—	73	48	no	—
304	C₄×#41	C₂×D₇₃	1	16	yes	complemented
305	C₂×C₄×Q₈	—	73	2	no	—
306	C₂×C₄×Q₈	—	73	1	no	—
307	C₂×C₄×Q₈	—	73	3	no	—
308	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
309	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
310	C₂×C₄×D₄	—	73	6	no	—
311	C₂×C₄×D₄	—	73	6	no	—
312	C₂×C₄×D₄	—	73	6	no	—
313	C₂×C₄×D₄	—	73	96	no	—
314	C₂×C₄×D₄	—	73	6	no	—
315	C₂×C₄×D₄	—	73	6	no	—
316	C₂×C₄×D₄	—	73	12	no	—
317	C₂×C₄×D₄	—	73	3	no	—
318	C₂×C₄×D₄	—	73	6	no	—
319	C₂×C₄×D₄	—	73	6	no	—
320	C₂×C₄×D₄	—	73	6	no	—
321	C₂×C₄×D₄	—	73	3	no	—
322	C₂×C₄×D₄	—	73	48	no	—
323	C₂×C₄×D₄	C₂×D₇₃	1	3	yes	complemented
324	C₂×C₄×D₄	C₂×D₇₃	1	3	yes	complemented
325	C₂×#117	—	73	3	no	—
326	C₂×#117	—	73	6	no	—
327	C₂×#117	—	73	6	no	—
328	C₂×#117	C₂×D₇₃	1	3	yes	complemented
329	C₂²×C₄⋊C₄	—	73	3	no	—
330	C₂²×C₄⋊C₄	—	73	6	no	—
331	C₂²×C₂²⋊C₄	—	73	6	no	—
332	C₂²×C₂²⋊C₄	—	73	12	no	—
333	C₂²×C₄²	—	73	6	no	—
334	C₂²×C₄²	C₂×D₇₃	1	3	yes	complemented
335	C₂⁵	—	73	6	no	—
336	H(5,𝔽₂)	—	73	256	no	—
337	C₂×#41	—	73	32	no	—
338	C₂×#41	—	73	16	no	—
339	C₂×#41	—	73	48	no	—
340	C₂×#41	—	73	24	no	—
341	C₂×#41	C₄×D₇₃	1	16	yes	complemented
342	C₂×#41	C₂²×D₇₃	1	8	yes	—
343	C₂²×Q₈	—	73	1	no	—
344	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
345	C₂²×D₄	—	73	6	no	—
346	C₂²×D₄	—	73	96	no	—
347	C₂²×D₄	—	73	48	no	—
348	C₂²×D₄	—	73	48	no	—
349	C₂²×D₄	—	73	6	no	—
350	C₂²×D₄	—	73	3	no	—
351	C₂²×D₄	—	73	24	no	—
352	C₂²×D₄	C₂²×D₇₃	1	3	yes	—
353	C₂³×C₄	—	292	24	no	—
354	C₂³×C₄	—	73	6	no	—
355	C₂³×C₄	—	73	6	no	—
356	C₂³×C₄	—	73	12	no	—
357	C₂³×C₄	—	73	48	no	—
358	C₂³×C₄	—	73	6	no	—
359	C₂³×C₄	—	73	6	no	—
360	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
361	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
362	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
363	C₄×Q₈	—	73	16	no	—
364	C₄×Q₈	—	73	8	no	—
365	C₄×Q₈	—	73	24	no	—
366	C₄×Q₈	C₂²×D₇₃	1	8	yes	complemented
367	C₄×Q₈	C₂²×D₇₃	1	8	yes	complemented
368	C₄×D₄	—	73	48	no	—
369	C₄×D₄	—	73	48	no	—
370	C₄×D₄	—	73	48	no	—
371	C₄×D₄	—	73	48	no	—
372	C₄×D₄	—	73	48	no	—
373	C₄×D₄	—	73	96	no	—
374	C₄×D₄	—	73	48	no	—
375	C₄×D₄	—	73	24	no	—
376	C₄×D₄	—	73	48	no	—
377	C₄×D₄	—	73	48	no	—
378	C₄×D₄	—	73	24	no	—
379	C₄×D₄	C₂²×D₇₃	1	24	yes	complemented
380	C₄×D₄	C₂²×D₇₃	1	24	yes	complemented
381	#117	—	73	24	no	—
382	#117	—	73	48	no	—
383	#117	—	73	48	no	—
384	#117	C₂²×D₇₃	1	24	yes	complemented
385	C₂×C₄⋊C₄	—	73	6	no	—
386	C₂×C₄⋊C₄	—	73	6	no	—
387	C₂×C₄⋊C₄	—	73	3	no	—
388	C₂×C₄⋊C₄	—	73	24	no	—
389	C₂×C₄⋊C₄	—	73	2	no	—
390	C₂×C₄⋊C₄	—	73	1	no	—
391	C₂×C₄⋊C₄	—	73	48	no	—
392	C₂×C₄⋊C₄	C₂²×D₇₃	1	3	yes	—
393	C₂×C₄⋊C₄	C₂²×D₇₃	1	3	yes	—
394	C₂×C₂²⋊C₄	—	73	6	no	—
395	C₂×C₂²⋊C₄	—	73	6	no	—
396	C₂×C₂²⋊C₄	—	73	12	no	—
397	C₂×C₂²⋊C₄	—	73	6	no	—
398	C₂×C₂²⋊C₄	—	73	48	no	—
399	C₂×C₂²⋊C₄	—	73	96	no	—
400	C₂×C₂²⋊C₄	C₂²×D₇₃	1	6	yes	—
401	C₂×C₄²	—	73	6	no	—
402	C₂×C₄²	—	73	6	no	—
403	C₂×C₄²	—	73	2	no	—
404	C₂×C₄²	—	73	48	no	—
405	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
406	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
407	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
408	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
409	C₂×C₄²	C₂²×D₇₃	1	24	yes	complemented
410	C₂⁴	—	292	12	no	—
411	C₂⁴	—	292	12	no	—
412	C₂⁴	—	73	48	no	—
413	C₂⁴	—	73	24	no	—
414	C₂⁴	—	73	6	no	—
415	C₂⁴	C₂³×D₇₃	1	3	yes	—
416	#41	—	73	128	no	—
417	#41	—	73	192	no	—
418	#41	C₂×C₄×D₇₃	1	64	yes	complemented
419	C₂×Q₈	—	73	8	no	—
420	C₂×Q₈	—	73	4	no	—
421	C₂×Q₈	C₂×C₄×D₇₃	1	8	yes	complemented
422	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
423	C₂×D₄	—	73	48	no	—
424	C₂×D₄	—	73	24	no	—
425	C₂×D₄	—	73	384	no	—
426	C₂×D₄	—	73	48	no	—
427	C₂×D₄	—	73	24	no	—
428	C₂×D₄	—	73	192	no	—
429	C₂×D₄	—	73	24	no	—
430	C₂×D₄	—	73	12	no	—
431	C₂×D₄	C₂×C₄×D₇₃	1	24	yes	complemented
432	C₂×D₄	C₂³×D₇₃	1	12	yes	—
433	C₂²×C₄	—	2	12	no	—
434	C₂²×C₄	—	4	6	no	—
435	C₂²×C₄	—	292	24	no	—
436	C₂²×C₄	—	292	12	no	—
437	C₂²×C₄	—	292	96	no	—
438	C₂²×C₄	—	292	12	no	—
439	C₂²×C₄	—	73	24	no	—
440	C₂²×C₄	—	73	24	no	—
441	C₂²×C₄	—	73	48	no	—
442	C₂²×C₄	—	73	2	no	—
443	C₂²×C₄	—	73	48	no	—
444	C₂²×C₄	—	73	24	no	—
445	C₂²×C₄	—	73	2	no	—
446	C₂²×C₄	—	73	6	no	—
447	C₂²×C₄	—	73	24	no	—
448	C₂²×C₄	—	146	24	no	—
449	C₂²×C₄	C₂×C₄×D₇₃	1	24	yes	complemented
450	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
451	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
452	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
453	C₂²×C₄	C₂³×D₇₃	1	12	yes	—
454	C₂²×C₄	C₂³×D₇₃	1	12	yes	—
455	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
456	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
457	C₂²×C₄	C₂³×D₇₃	1	12	yes	—
458	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
459	C₄⋊C₄	—	73	24	no	—
460	C₄⋊C₄	—	73	8	no	—
461	C₄⋊C₄	—	73	24	no	—
462	C₄⋊C₄	—	73	12	no	—
463	C₄⋊C₄	—	73	4	no	—
464	C₄⋊C₄	C₂³×D₇₃	1	12	yes	—
465	C₄⋊C₄	C₂³×D₇₃	1	12	yes	—
466	C₂²⋊C₄	—	73	24	no	—
467	C₂²⋊C₄	—	73	24	no	—
468	C₂²⋊C₄	—	73	48	no	—
469	C₂²⋊C₄	—	73	24	no	—
470	C₂²⋊C₄	C₂³×D₇₃	1	24	yes	—
471	C₄²	—	73	8	no	—
472	C₄²	—	73	24	no	—
473	C₄²	—	73	24	no	—
474	C₄²	C₂³×D₇₃	1	12	yes	—
475	C₄²	C₂³×D₇₃	1	4	yes	—
476	C₄²	C₂³×D₇₃	1	12	yes	—
477	C₄²	C₂³×D₇₃	1	12	yes	—
478	C₂³	—	2	6	no	—
479	C₂³	—	2	6	no	—
480	C₂³	—	292	24	no	—
481	C₂³	—	292	96	no	—
482	C₂³	—	292	24	no	—
483	C₂³	—	73	96	no	—
484	C₂³	—	73	24	no	—
485	C₂³	—	73	12	no	—
486	C₂³	—	146	12	no	—
487	C₂³	—	146	12	no	—
488	C₂³	C₂²×C₄×D₇₃	1	12	yes	—
489	C₂³	C₂⁴×D₇₃	1	6	yes	—
490	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
491	Q₈	—	73	16	no	—
492	Q₈	C₂²×C₄×D₇₃	1	16	yes	complemented
493	D₄	—	73	96	no	—
494	D₄	—	73	96	no	—
495	D₄	—	73	48	no	—
496	D₄	C₂²×C₄×D₇₃	1	48	yes	complemented
497	C₂×C₄	—	2	6	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	6	no	—
500	C₂×C₄	—	2	24	no	—
501	C₂×C₄	—	4	12	no	—
502	C₂×C₄	—	292	48	no	—
503	C₂×C₄	—	292	24	no	—
504	C₂×C₄	—	292	24	no	—
505	C₂×C₄	—	73	8	no	—
506	C₂×C₄	—	73	4	no	—
507	C₂×C₄	—	73	96	no	—
508	C₂×C₄	—	73	4	no	—
509	C₂×C₄	—	73	12	no	—
510	C₂×C₄	—	146	12	no	—
511	C₂×C₄	—	146	4	no	—
512	C₂×C₄	—	146	48	no	—
513	C₂×C₄	C₂²×C₄×D₇₃	1	12	yes	—
514	C₂×C₄	C₂²×C₄×D₇₃	1	4	yes	—
515	C₂×C₄	C₂²×C₄×D₇₃	1	48	yes	complemented
516	C₂×C₄	#14556637	1	4	yes	direct product factor
517	C₂×C₄	C₂⁴×D₇₃	1	6	yes	—
518	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
519	C₂×C₄	C₂⁴×D₇₃	1	6	yes	—
520	C₂×C₄	C₂⁴×D₇₃	1	6	yes	—
521	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
522	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
523	C₂²	—	2	24	no	—
524	C₂²	—	2	6	no	—
525	C₂²	—	2	6	no	—
526	C₂²	—	292	96	no	—
527	C₂²	—	73	24	no	—
528	C₂²	—	146	48	no	—
529	C₂²	—	146	12	no	—
530	C₂²	—	146	12	no	—
531	C₂²	C₂³×C₄×D₇₃	1	12	yes	—
532	C₂²	C₂³×C₄×D₇₃	1	2	yes	—
533	C₂²	C₂×#14556637	1	2	yes	—
534	C₂²	#17989423	1	2	yes	—
535	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
536	C₄	—	2	6	no	—
537	C₄	—	2	2	no	—
538	C₄	—	2	6	no	—
539	C₄	—	73	8	no	—
540	C₄	—	146	12	no	—
541	C₄	—	146	4	no	—
542	C₄	C₂³×C₄×D₇₃	1	12	yes	—
543	C₄	C₂³×C₄×D₇₃	1	4	yes	—
544	C₄	C₂×#14556637	1	4	yes	direct product factor
545	C₂	—	2	12	no	—
546	C₂	—	146	24	no	—
547	C₂	C₄×#14556637	1	4	yes	direct product factor
548	C₂	C₂⁴×C₄×D₇₃	1	1	yes	characteristic
549	C₂	C₂²×#14556637	1	1	yes	characteristic
550	C₂	C₂×#17989423	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇₃
commutator	C₂×C₇₃	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₇₃
Fitting	C₂×C₄×#41×C₇₃	C₂
socle	C₂³×C₇₃	C₂⁵
prime radical	C₂²×#14556637	C₂
cosocle	C₂²×C₇₃	C₂⁶
hypercenter	C₂×C₄×#41	D₇₃
hypocenter	C₇₃	C₂×C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
2. C₄×#14556637	C₂	direct (N × H)
3. C₂×#17989070	C₂	semidirect
4. C₂×#17989069	C₂	semidirect
5. C₂×#17989067	C₂	semidirect
6. C₂×#17989061	C₂	semidirect
7. C₂×#17989059	C₂	semidirect
8. C₂×C₄×#11924029	C₂	semidirect
9. C₂×C₄×#11924028	C₂	semidirect
10. C₂²×C₄×D₂₉₂	C₂	semidirect
11. C₂×C₄×D₄×D₇₃	C₂	semidirect
12. C₂×C₄×#41×C₇₃	C₂	semidirect
13. C₂×#14556637	C₄	direct (N × H)
19. C₂³×C₄×D₇₃	C₂²	semidirect
20. #17989070	C₂²	semidirect
21. #17989069	C₂²	semidirect
22. #17989067	C₂²	semidirect
23. #17989061	C₂²	semidirect
24. #17989059	C₂²	semidirect
25. C₄×#11924029	C₂²	semidirect
26. C₄×#11924028	C₂²	semidirect
27. C₂×Q₈×Dic₇₃	C₂²	semidirect
28. C₂×C₄×Dic₁₄₆	C₂²	semidirect
29. C₂×C₄×Dic₁₄₆	C₂²	semidirect
30. C₂×C₄×D₂₉₂	C₂²	semidirect
31. C₂×C₄×D₂₉₂	C₂²	semidirect
32. C₂×C₄×D₂₉₂	C₂²	semidirect
33. C₂×C₄×D₂₉₂	C₂²	semidirect
34. C₂×C₄×D₂₉₂	C₂²	semidirect
35. C₂×C₄×D₂₉₂	C₂²	semidirect
36. C₂×D₄×Dic₇₃	C₂²	semidirect
37. C₂×#14556553	C₂²	semidirect
38. C₂×#14556553	C₂²	semidirect
39. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
40. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
41. C₂×#14556551	C₂²	semidirect
42. C₄×D₄×D₇₃	C₂²	semidirect
43. C₂×#14556550	C₂²	semidirect
44. C₂×#14556549	C₂²	semidirect
45. C₂×#14556548	C₂²	semidirect
46. C₂²×C₄⋊Dic₇₃	C₂²	semidirect
47. C₂×C₄⋊C₄×D₇₃	C₂²	semidirect
48. C₂²×#11924005	C₂²	semidirect
49. C₂×C₂²⋊C₄×D₇₃	C₂²	semidirect
50. C₂×C₄²×D₇₃	C₂²	semidirect
52. C₄×#41×C₇₃	C₂²	semidirect
53. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
54. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
55. C₂×C₄×D₄×C₇₃	C₂²	semidirect
56. C₂×C₄×D₄×C₇₃	C₂²	semidirect
57. C₂×#117×C₇₃	C₂²	semidirect
58. C₂²×C₄²×C₇₃	C₂²	semidirect
60. #14556637	C₂×C₄	direct (N × H)
61. C₂×#11924029	C₂×C₄	semidirect
63. C₂×#11924028	C₂×C₄	semidirect
66. C₂²×D₂₉₂	C₂×C₄	semidirect
71. C₂×D₄×D₇₃	C₂×C₄	semidirect
79. C₂²×C₄×D₇₃	C₂³	semidirect
80. Q₈×Dic₇₃	C₂³	semidirect
81. C₄×Dic₁₄₆	C₂³	semidirect
82. C₄×Dic₁₄₆	C₂³	semidirect
83. C₄×D₂₉₂	C₂³	semidirect
84. C₄×D₂₉₂	C₂³	semidirect
85. C₄×D₂₉₂	C₂³	semidirect
86. C₄×D₂₉₂	C₂³	semidirect
87. C₄×D₂₉₂	C₂³	semidirect
88. D₄×Dic₇₃	C₂³	semidirect
89. #14556553	C₂³	semidirect
90. #14556553	C₂³	semidirect
91. C₄×C₂²⋊D₇₃	C₂³	semidirect
92. C₄×C₂²⋊D₇₃	C₂³	semidirect
93. #14556551	C₂³	semidirect
94. #14556550	C₂³	semidirect
95. #14556549	C₂³	semidirect
96. #14556548	C₂³	semidirect
100. C₂×C₄⋊Dic₇₃	C₂³	semidirect
103. C₄⋊C₄×D₇₃	C₂³	semidirect
108. C₂×#11924005	C₂³	semidirect
109. C₂²⋊C₄×D₇₃	C₂³	semidirect
113. C₄²×D₇₃	C₂³	semidirect
114. C₂×#41×C₇₃	C₂×C₄	semidirect
121. C₄×Q₈×C₇₃	C₂³	semidirect
122. C₄×Q₈×C₇₃	C₂³	semidirect
123. C₄×D₄×C₇₃	C₂³	semidirect
124. C₄×D₄×C₇₃	C₂³	semidirect
125. #117×C₇₃	C₂³	semidirect
133. C₂×C₄²×C₇₃	C₂³	semidirect
136. C₂³×D₇₃	C₂²×C₄	semidirect
139. #11924029	C₂²×C₄	semidirect
140. #11924028	C₂²×C₄	semidirect
141. C₂×Dic₁₄₆	C₂²×C₄	semidirect
143. C₂×D₂₉₂	C₂²×C₄	semidirect
144. C₂×D₂₉₂	C₂²×C₄	semidirect
145. C₂×D₂₉₂	C₂²×C₄	semidirect
148. C₂×C₂²⋊D₇₃	C₂²×C₄	semidirect
150. D₄×D₇₃	C₂²×C₄	semidirect
160. C₂×C₄×D₇₃	C₂²×C₄	semidirect
178. #41×C₇₃	C₂²×C₄	semidirect
179. C₂×Q₈×C₇₃	C₂²×C₄	semidirect
181. C₂×D₄×C₇₃	C₂²×C₄	semidirect
185. C₂²×C₄×C₇₃	C₂²×C₄	semidirect
213. C₂²×D₇₃	C₂³×C₄	semidirect
215. Q₈×C₇₃	C₂³×C₄	semidirect
216. D₄×C₇₃	C₂³×C₄	semidirect
224. C₂×C₄×C₇₃	C₂³×C₄	semidirect
225. C₂×C₄×C₇₃	H(5,𝔽₂)	semidirect
232. C₂²⋊D₇₃	C₂³×C₄	semidirect
240. D₂₉₂	C₂³×C₄	semidirect
241. D₂₉₂	C₂³×C₄	semidirect
245. C₄×D₇₃	C₂³×C₄	semidirect
246. Dic₁₄₆	C₂³×C₄	semidirect
265. C₄×C₇₃	C₂×H(5,𝔽₂)	semidirect
271. C₂×C₇₃	C₄×H(5,𝔽₂)	semidirect
285. C₂×C₄×#41	D₇₃	semidirect
288. C₇₃	C₂×C₄×H(5,𝔽₂)	semidirect
304. C₄×#41	C₂×D₇₃	semidirect
308. C₂×C₄×Q₈	C₂×D₇₃	semidirect
309. C₂×C₄×Q₈	C₂×D₇₃	semidirect
323. C₂×C₄×D₄	C₂×D₇₃	semidirect
324. C₂×C₄×D₄	C₂×D₇₃	semidirect
328. C₂×#117	C₂×D₇₃	semidirect
334. C₂²×C₄²	C₂×D₇₃	semidirect
341. C₂×#41	C₄×D₇₃	semidirect
366. C₄×Q₈	C₂²×D₇₃	semidirect
367. C₄×Q₈	C₂²×D₇₃	semidirect
379. C₄×D₄	C₂²×D₇₃	semidirect
380. C₄×D₄	C₂²×D₇₃	semidirect
384. #117	C₂²×D₇₃	semidirect
409. C₂×C₄²	C₂²×D₇₃	semidirect
418. #41	C₂×C₄×D₇₃	semidirect
421. C₂×Q₈	C₂×C₄×D₇₃	semidirect
431. C₂×D₄	C₂×C₄×D₇₃	semidirect
449. C₂²×C₄	C₂×C₄×D₇₃	semidirect
492. Q₈	C₂²×C₄×D₇₃	semidirect
496. D₄	C₂²×C₄×D₇₃	semidirect
515. C₂×C₄	C₂²×C₄×D₇₃	semidirect
516. C₂×C₄	#14556637	direct (N × H)
544. C₄	C₂×#14556637	direct (N × H)
547. C₂	C₄×#14556637	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×#14556637	2
C₄×#14556637	2
C₂×#17989070	2
C₂×#17989069	2
C₂×#17989067	2
C₂×#17989061	2
C₂×#17989059	2
C₂×C₄×#11924029	2
C₂×C₄×#11924028	2
C₂²×C₄×D₂₉₂	2
C₂×C₄×D₄×D₇₃	2
C₂×C₄×#41×C₇₃	2
C₂×C₄×H(5,𝔽₂)	73

Subgroups — C2×C4×#14556637 #33992587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#14556637 #33992587