Subgroups — C₄×#17989656 #34030526

Order 18688.

3698 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989656	C₂	1	2	yes	maximal
2	#22626371	C₂	1	2	yes	maximal, complemented
3	#22626370	C₂	1	6	yes	maximal, complemented
4	#22626368	C₂	1	6	yes	maximal, complemented
5	C₄×Q₈×#64408	C₂	1	2	yes	maximal, complemented
6	C₄×D₄×#64408	C₂	1	6	yes	maximal, complemented
7	C₄×#14556670	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×C₄⋊#64408	C₂	1	3	yes	maximal, complemented
9	C₄×#41×D₇₃	C₂	1	1	yes	maximal, characteristic
10	#17989656	C₄	1	32	yes	direct product factor
11	C₂×Q₈×#64408	C₂²	1	4	yes	—
12	C₂×D₄×#64408	C₂²	1	12	yes	—
13	C₂×#14556670	C₂²	1	6	yes	—
14	C₂²×C₄⋊#64408	C₂²	1	6	yes	—
15	C₂²×C₄×#64408	C₂²	1	6	yes	—
16	C₄⋊C₄×#64408	C₂²	1	12	yes	—
17	C₄⋊C₄×#64408	C₂²	1	12	yes	—
18	C₄×C₄⋊#64408	C₂²	1	3	yes	—
19	C₄×C₄⋊#64408	C₂²	1	6	yes	—
20	C₄×C₄⋊#64408	C₂²	1	6	yes	—
21	C₄×C₄⋊#64408	C₂²	1	6	yes	—
22	C₄×C₄⋊#64408	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊#64408	C₂²	1	6	yes	—
24	C₂²⋊C₄×#64408	C₂²	1	24	yes	—
25	C₄×C₂²⋊#64408	C₂²	1	6	yes	—
26	C₄×C₂²⋊#64408	C₂²	1	6	yes	—
27	#17989523	C₂²	1	6	yes	—
28	C₂×(C₂×#64408)⋊C₄	C₂²	1	6	yes	—
29	C₄²×#64408	C₂²	1	6	yes	—
30	C₂×#41×D₇₃	C₂²	1	1	yes	characteristic
31	#41×Dic₇₃	C₄	1	1	yes	characteristic, complemented
32	C₄×#11924029	C₄	1	1	yes	characteristic, complemented
33	C₄×#11924029	C₄	1	1	yes	characteristic, complemented
34	C₄×#11924028	C₄	1	3	yes	complemented
35	#17989055	C₄	1	3	yes	complemented
36	C₄×#11924027	C₄	1	3	yes	complemented
37	C₄×#11924027	C₄	1	3	yes	complemented
38	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
39	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
40	C₄×D₄×D₇₃	C₂²	1	3	yes	—
41	C₄×D₄×D₇₃	C₂²	1	3	yes	—
42	#117×D₇₃	C₂²	1	3	yes	—
43	C₂×C₄²×D₇₃	C₂²	1	3	yes	—
44	C₄×#41×C₇₃	C₄	1	1	yes	characteristic, complemented
45	C₂³×#64408	C₂³	1	12	yes	—
46	Q₈×#64408	C₂×C₄	1	32	yes	complemented
47	D₄×#64408	C₂×C₄	1	96	yes	complemented
48	#14556670	C₂×C₄	1	48	yes	complemented
49	C₂×C₄⋊#64408	C₂×C₄	1	48	yes	complemented
50	C₂×C₄⋊#64408	C₂³	1	6	yes	—
51	C₂×C₄⋊#64408	C₂³	1	12	yes	—
52	C₂×C₄⋊#64408	C₂³	1	2	yes	—
53	C₂×C₂²⋊#64408	C₂³	1	12	yes	—
54	C₂×C₄×#64408	—	4	12	no	—
55	C₂×C₄×#64408	C₂³	1	6	yes	—
56	C₂×C₄×#64408	C₂³	1	2	yes	—
57	C₂×C₄×#64408	C₂³	1	12	yes	—
58	C₂×C₄×#64408	C₂³	1	12	yes	—
59	C₂×C₄×#64408	C₂³	1	12	yes	—
60	(C₂×#64408)⋊C₄	C₂³	1	6	yes	—
61	(C₂×#64408)⋊C₄	C₂³	1	12	yes	—
62	(C₂×#64408)⋊C₄	C₂³	1	2	yes	—
63	(C₂×#64408)⋊C₄	C₂³	1	12	yes	—
64	C₂×#11924029	C₂×C₄	1	1	yes	characteristic
65	C₂×#11924028	C₂×C₄	1	3	yes	—
66	C₂×#11924027	C₂×C₄	1	3	yes	—
67	#41×D₇₃	C₂×C₄	1	16	yes	—
68	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
69	C₂×D₄×D₇₃	C₂³	1	3	yes	—
70	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
71	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
72	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
73	Q₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic, complemented
74	Q₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic, complemented
75	C₄×Dic₁₄₆	C₂×C₄	1	3	yes	complemented
76	C₄×Dic₁₄₆	C₂×C₄	1	3	yes	complemented
77	#14556556	C₂×C₄	1	3	yes	complemented
78	#14556556	C₂×C₄	1	3	yes	complemented
79	C₄×D₂₉₂	C₂×C₄	1	3	yes	complemented
80	C₄×D₂₉₂	C₂×C₄	1	3	yes	complemented
81	D₄×Dic₇₃	C₂×C₄	1	3	yes	complemented
82	D₄×Dic₇₃	C₂×C₄	1	3	yes	complemented
83	#14556553	C₂×C₄	1	3	yes	complemented
84	#14556553	C₂×C₄	1	3	yes	complemented
85	C₄×C₂²⋊D₇₃	C₂×C₄	1	6	yes	complemented
86	C₄×C₂²⋊D₇₃	C₂×C₄	1	6	yes	complemented
87	#14556551	C₂×C₄	1	6	yes	complemented
88	#14556551	C₂×C₄	1	6	yes	complemented
89	#14556550	C₂×C₄	1	3	yes	complemented
90	#14556549	C₂×C₄	1	3	yes	complemented
91	#14556549	C₂×C₄	1	3	yes	complemented
92	#14556548	C₂×C₄	1	6	yes	complemented
93	#14556547	C₂×C₄	1	6	yes	complemented
94	C₄⋊C₄×D₇₃	C₂³	1	3	yes	—
95	C₄⋊C₄×D₇₃	C₂³	1	3	yes	—
96	C₂²⋊C₄×D₇₃	C₂³	1	6	yes	—
97	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	complemented
98	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	complemented
99	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	complemented
100	C₄²×D₇₃	C₂×C₄	1	3	yes	complemented
101	C₄²×D₇₃	C₂×C₄	1	3	yes	complemented
102	C₄²×D₇₃	C₂×C₄	1	3	yes	complemented
103	C₄²×D₇₃	C₂×C₄	1	3	yes	complemented
104	C₄²×D₇₃	C₂³	1	3	yes	—
105	C₄²×D₇₃	C₂³	1	3	yes	—
106	C₄²×D₇₃	C₂³	1	1	yes	characteristic
107	C₄²×D₇₃	C₂³	1	3	yes	—
108	C₂×#41×C₇₃	C₂×C₄	1	1	yes	characteristic
109	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
110	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
111	C₄×D₄×C₇₃	C₂×C₄	1	3	yes	complemented
112	C₄×D₄×C₇₃	C₂×C₄	1	3	yes	complemented
113	#117×C₇₃	C₂×C₄	1	3	yes	complemented
114	C₂×C₄²×C₇₃	C₂×C₄	1	3	yes	complemented
115	C₂²×#64408	—	4	12	no	—
116	C₂²×#64408	—	4	12	no	—
117	C₂²×#64408	C₂²×C₄	1	48	yes	—
118	C₂²×#64408	C₂⁴	1	12	yes	—
119	C₂²×#64408	C₂⁴	1	4	yes	—
120	C₄⋊#64408	C₂²×C₄	1	48	yes	—
121	C₄⋊#64408	C₂²×C₄	1	24	yes	—
122	C₄⋊#64408	C₂²×C₄	1	8	yes	—
123	C₂²⋊#64408	C₂²×C₄	1	48	yes	—
124	C₄×#64408	—	2	12	no	—
125	C₄×#64408	—	2	4	no	—
126	C₄×#64408	—	4	12	no	—
127	C₄×#64408	—	4	12	no	—
128	C₄×#64408	C₂²×C₄	1	48	yes	—
129	C₂³×D₇₃	C₂⁴	1	3	yes	—
130	#11924029	C₄²	1	8	yes	complemented
131	#11924028	C₄²	1	24	yes	complemented
132	#11924027	C₄²	1	24	yes	complemented
133	C₂×Dic₁₄₆	C₂²×C₄	1	3	yes	—
134	Q₈×D₇₃	C₂²×C₄	1	8	yes	—
135	C₂×D₂₉₂	C₂²×C₄	1	3	yes	—
136	C₂×C₂²⋊D₇₃	C₂²×C₄	1	6	yes	—
137	D₄×D₇₃	C₂²×C₄	1	24	yes	—
138	C₂²×Dic₇₃	C₂²×C₄	1	3	yes	—
139	C₂²×Dic₇₃	C₂²×C₄	1	3	yes	—
140	C₂²×Dic₇₃	C₂²×C₄	1	3	yes	—
141	C₂×C₄×D₇₃	—	2	6	no	—
142	C₂×C₄×D₇₃	—	2	6	no	—
143	C₂×C₄×D₇₃	—	4	6	no	—
144	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
145	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
146	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
147	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
148	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
149	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
150	C₂×C₄×D₇₃	C₂²×C₄	1	24	yes	—
151	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×D₇₃	C₂⁴	1	3	yes	—
153	C₂×C₄×D₇₃	C₂⁴	1	3	yes	—
154	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×D₇₃	C₂⁴	1	3	yes	—
156	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
157	C₄⋊Dic₇₃	C₂²×C₄	1	3	yes	—
158	C₄⋊Dic₇₃	C₂²×C₄	1	3	yes	—
159	#11924007	C₂²×C₄	1	6	yes	—
160	#11924007	C₂²×C₄	1	6	yes	—
161	C₂²⋊Dic₇₃	C₂²×C₄	1	6	yes	—
162	#11924005	C₂²×C₄	1	6	yes	—
163	#11924005	C₂²×C₄	1	6	yes	—
164	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
165	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
166	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
167	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
168	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
169	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
170	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
171	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
172	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
173	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
174	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
175	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
176	#41×C₇₃	C₄²	1	8	yes	complemented
177	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
178	C₂×D₄×C₇₃	C₂²×C₄	1	3	yes	—
179	C₂²×C₄×C₇₃	C₂²×C₄	1	3	yes	—
180	C₂²×C₄×C₇₃	C₂²×C₄	1	3	yes	—
181	C₂²×C₄×C₇₃	C₂²×C₄	1	3	yes	—
182	C₄⋊C₄×C₇₃	C₂²×C₄	1	3	yes	—
183	C₄⋊C₄×C₇₃	C₂²×C₄	1	3	yes	—
184	C₂²⋊C₄×C₇₃	C₂²×C₄	1	6	yes	—
185	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₇₃	C₂²×C₄	1	3	yes	—
187	C₄²×C₇₃	C₂²×C₄	1	3	yes	—
188	C₄²×C₇₃	C₂²×C₄	1	3	yes	—
189	C₂³×C₇₃	C₂³×C₄	1	3	yes	—
190	C₂²×D₇₃	—	2	3	no	—
191	C₂²×D₇₃	—	2	3	no	—
192	C₂²×D₇₃	—	2	6	no	—
193	C₂²×D₇₃	C₂³×C₄	1	12	yes	—
194	C₂²×D₇₃	C₂³×C₄	1	3	yes	—
195	C₂²×D₇₃	C₂⁵	1	1	yes	characteristic
196	C₂×#64408	—	2	12	no	—
197	C₂×#64408	—	2	4	no	—
198	C₂×#64408	—	2	4	no	—
199	C₂×#64408	—	2	12	no	—
200	C₂×#64408	—	4	48	no	—
201	C₂×#64408	C₂³×C₄	1	8	yes	—
202	C₂×#64408	C₂³×C₄	1	24	yes	—
203	Q₈×C₇₃	C₂×C₄²	1	4	yes	complemented
204	D₄×C₇₃	C₂×C₄²	1	12	yes	complemented
205	C₂×C₄×C₇₃	—	2	6	no	—
206	C₂×C₄×C₇₃	—	4	3	no	—
207	C₂×C₄×C₇₃	C₂×C₄²	1	12	yes	complemented
208	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₇₃	C₂³×C₄	1	3	yes	—
210	C₂×C₄×C₇₃	C₂³×C₄	1	3	yes	—
211	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₇₃	C₂³×C₄	1	3	yes	—
213	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
214	C₂²⋊D₇₃	C₂×C₄²	1	24	yes	complemented
215	C₂×Dic₇₃	—	2	6	no	—
216	C₂×Dic₇₃	—	4	3	no	—
217	C₂×Dic₇₃	C₂×C₄²	1	12	yes	complemented
218	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
219	C₂×Dic₇₃	C₂³×C₄	1	3	yes	—
220	C₂×Dic₇₃	C₂³×C₄	1	3	yes	—
221	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
222	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
223	C₂×Dic₇₃	C₂³×C₄	1	3	yes	—
224	D₂₉₂	C₂×C₄²	1	12	yes	complemented
225	C₄×D₇₃	—	2	3	no	—
226	C₄×D₇₃	—	2	3	no	—
227	C₄×D₇₃	—	2	2	no	—
228	C₄×D₇₃	—	2	6	no	—
229	C₄×D₇₃	—	2	6	no	—
230	C₄×D₇₃	—	2	6	no	—
231	C₄×D₇₃	—	4	3	no	—
232	C₄×D₇₃	—	4	3	no	—
233	C₄×D₇₃	C₂×C₄²	1	12	yes	complemented
234	C₄×D₇₃	C₂×C₄²	1	12	yes	complemented
235	C₄×D₇₃	C₂³×C₄	1	4	yes	—
236	C₄×D₇₃	C₂³×C₄	1	12	yes	—
237	C₄×D₇₃	H(5,𝔽₂)	1	2	yes	—
238	C₄×D₇₃	2₋¹⁺⁴	1	2	yes	—
239	Dic₁₄₆	C₂×C₄²	1	12	yes	complemented
240	C₂²×C₇₃	—	2	3	no	—
241	C₂²×C₇₃	—	2	3	no	—
242	C₂²×C₇₃	C₂²×C₄²	1	6	yes	—
243	C₂²×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
244	C₂×D₇₃	—	2	3	no	—
245	C₂×D₇₃	—	2	3	no	—
246	C₂×D₇₃	—	2	12	no	—
247	C₂×D₇₃	—	2	12	no	—
248	C₂×D₇₃	C₂²×C₄²	1	6	yes	—
249	C₂×D₇₃	C₂⁴×C₄	1	2	yes	—
250	C₂×D₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
251	C₂×D₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
252	C₂×D₇₃	#585	1	2	yes	—
253	#64408	—	2	24	no	—
254	#64408	—	2	8	no	—
255	C₄×C₇₃	—	2	3	no	—
256	C₄×C₇₃	—	2	1	no	—
257	C₄×C₇₃	—	2	3	no	—
258	C₄×C₇₃	C₂²×C₄²	1	6	yes	—
259	C₄×C₇₃	C₂²×C₄²	1	2	yes	—
260	C₄×C₇₃	#520	1	2	yes	complemented
261	Dic₇₃	—	2	3	no	—
262	Dic₇₃	—	2	1	no	—
263	Dic₇₃	—	2	3	no	—
264	Dic₇₃	C₂²×C₄²	1	6	yes	—
265	Dic₇₃	C₂²×C₄²	1	2	yes	—
266	Dic₇₃	#520	1	2	yes	complemented
267	C₄×#520	—	73	1	no	maximal, Sylow
268	C₂×C₇₃	—	2	6	no	—
269	C₂×C₇₃	C₂³×C₄²	1	1	yes	characteristic
270	C₂×C₇₃	C₂×#520	1	1	yes	characteristic
271	C₂×C₇₃	#3428	1	1	yes	characteristic
272	D₇₃	—	2	6	no	—
273	D₇₃	C₄×H(5,𝔽₂)	1	2	yes	—
274	D₇₃	C₄×2₋¹⁺⁴	1	2	yes	—
275	C₂×#520	—	73	2	no	—
276	C₂×C₄×#41	—	73	1	no	—
277	#2276	—	73	2	no	—
278	#2275	—	73	6	no	—
279	#2274	—	73	6	no	—
280	C₄²×Q₈	—	73	2	no	—
281	C₄²×D₄	—	73	6	no	—
282	C₄×#117	—	73	3	no	—
283	C₂×C₄×C₄⋊C₄	—	73	3	no	—
284	C₇₃	C₄×#520	1	1	yes	characteristic, complemented, Sylow
285	C₂²×#41	—	73	1	no	—
286	#520	—	73	32	no	—
287	C₄×#41	—	73	1	no	—
288	C₄×#41	—	73	1	no	—
289	C₄×#41	—	73	1	no	—
290	C₄×#41	—	73	3	no	—
291	C₄×#41	—	73	3	no	—
292	C₄×#41	—	73	3	no	—
293	C₄×#41	—	73	3	no	—
294	C₄×#41	#64408	1	1	yes	characteristic, complemented
295	C₂×C₄×Q₈	—	73	4	no	—
296	C₂×C₄×Q₈	—	73	1	no	—
297	C₂×C₄×Q₈	—	73	1	no	—
298	C₂×C₄×D₄	—	73	12	no	—
299	C₂×C₄×D₄	—	73	3	no	—
300	C₂×C₄×D₄	—	73	3	no	—
301	C₂×#117	—	73	6	no	—
302	C₂×#117	—	73	3	no	—
303	C₂²×C₄⋊C₄	—	73	6	no	—
304	C₂²×C₄²	—	73	6	no	—
305	C₂²×C₄²	—	73	3	no	—
306	C₄×C₄⋊C₄	—	73	3	no	—
307	C₄×C₄⋊C₄	—	73	6	no	—
308	C₄×C₄⋊C₄	—	73	6	no	—
309	C₄×C₄⋊C₄	—	73	6	no	—
310	C₄×C₄⋊C₄	—	73	1	no	—
311	C₄×C₄⋊C₄	—	73	6	no	—
312	C₄×C₄⋊C₄	—	73	12	no	—
313	C₄×C₄⋊C₄	—	73	12	no	—
314	C₄×C₂²⋊C₄	—	73	6	no	—
315	C₄×C₂²⋊C₄	—	73	6	no	—
316	C₄×C₂²⋊C₄	—	73	24	no	—
317	#376	—	73	6	no	—
318	C₂×#95	—	73	6	no	—
319	C₄³	—	73	6	no	—
320	C₂×#41	—	73	16	no	—
321	C₂×#41	—	73	1	no	—
322	C₂×#41	—	73	3	no	—
323	C₂×#41	—	73	3	no	—
324	C₂×#41	C₂×#64408	1	1	yes	characteristic
325	C₂²×Q₈	—	73	1	no	—
326	C₂²×D₄	—	73	3	no	—
327	C₂³×C₄	—	73	12	no	—
328	C₂³×C₄	—	73	3	no	—
329	C₂³×C₄	—	73	3	no	—
330	C₂³×C₄	—	73	3	no	—
331	C₄×Q₈	—	73	32	no	—
332	C₄×Q₈	—	73	1	no	—
333	C₄×Q₈	—	73	1	no	—
334	C₄×Q₈	—	73	3	no	—
335	C₄×Q₈	—	73	3	no	—
336	C₄×Q₈	—	73	3	no	—
337	C₄×Q₈	—	73	3	no	—
338	C₄×Q₈	C₂×#64408	1	1	yes	characteristic, complemented
339	C₄×Q₈	C₂×#64408	1	1	yes	characteristic, complemented
340	C₄×D₄	—	73	96	no	—
341	C₄×D₄	—	73	3	no	—
342	C₄×D₄	—	73	3	no	—
343	C₄×D₄	—	73	6	no	—
344	C₄×D₄	—	73	6	no	—
345	C₄×D₄	—	73	3	no	—
346	C₄×D₄	—	73	3	no	—
347	C₄×D₄	—	73	6	no	—
348	C₄×D₄	—	73	6	no	—
349	C₄×D₄	—	73	3	no	—
350	C₄×D₄	—	73	3	no	—
351	C₄×D₄	C₂×#64408	1	3	yes	complemented
352	C₄×D₄	C₂×#64408	1	3	yes	complemented
353	#117	—	73	48	no	—
354	#117	—	73	3	no	—
355	#117	—	73	3	no	—
356	#117	—	73	3	no	—
357	#117	—	73	6	no	—
358	#117	—	73	6	no	—
359	#117	C₂×#64408	1	3	yes	complemented
360	C₂×C₄⋊C₄	—	73	6	no	—
361	C₂×C₄⋊C₄	—	73	12	no	—
362	C₂×C₄⋊C₄	—	73	48	no	—
363	C₂×C₄⋊C₄	—	73	2	no	—
364	C₂×C₄⋊C₄	—	73	3	no	—
365	C₂×C₄⋊C₄	—	73	3	no	—
366	C₂×C₂²⋊C₄	—	73	12	no	—
367	C₂×C₂²⋊C₄	—	73	6	no	—
368	C₂×C₄²	—	292	12	no	—
369	C₂×C₄²	—	73	12	no	—
370	C₂×C₄²	—	73	12	no	—
371	C₂×C₄²	—	73	12	no	—
372	C₂×C₄²	—	73	3	no	—
373	C₂×C₄²	—	73	3	no	—
374	C₂×C₄²	—	73	3	no	—
375	C₂×C₄²	—	73	3	no	—
376	C₂×C₄²	—	73	3	no	—
377	C₂×C₄²	—	73	3	no	—
378	C₂×C₄²	—	73	3	no	—
379	C₂×C₄²	—	73	3	no	—
380	C₂×C₄²	—	73	3	no	—
381	C₂×C₄²	—	73	3	no	—
382	C₂×C₄²	—	73	1	no	—
383	C₂×C₄²	—	73	2	no	—
384	C₂×C₄²	—	73	6	no	—
385	C₂×C₄²	C₂×#64408	1	3	yes	complemented
386	#95	—	73	6	no	—
387	#95	—	73	12	no	—
388	#95	—	73	2	no	—
389	#95	—	73	12	no	—
390	C₂⁴	—	73	3	no	—
391	#41	—	73	8	no	—
392	#41	—	73	24	no	—
393	#41	—	73	24	no	—
394	#41	C₄×#64408	1	8	yes	complemented
395	C₂×Q₈	—	73	8	no	—
396	C₂×Q₈	—	73	3	no	—
397	C₂×Q₈	C₂²×#64408	1	1	yes	characteristic
398	C₂×D₄	—	73	6	no	—
399	C₂×D₄	—	73	24	no	—
400	C₂×D₄	—	73	3	no	—
401	C₂×D₄	C₂²×#64408	1	3	yes	—
402	C₂²×C₄	—	292	6	no	—
403	C₂²×C₄	—	292	12	no	—
404	C₂²×C₄	—	292	12	no	—
405	C₂²×C₄	—	73	48	no	—
406	C₂²×C₄	—	73	3	no	—
407	C₂²×C₄	—	73	3	no	—
408	C₂²×C₄	—	73	3	no	—
409	C₂²×C₄	—	73	3	no	—
410	C₂²×C₄	—	73	3	no	—
411	C₂²×C₄	—	73	3	no	—
412	C₂²×C₄	—	73	3	no	—
413	C₂²×C₄	—	73	1	no	—
414	C₂²×C₄	—	73	1	no	—
415	C₂²×C₄	—	73	24	no	—
416	C₂²×C₄	—	73	4	no	—
417	C₂²×C₄	—	73	12	no	—
418	C₂²×C₄	—	73	3	no	—
419	C₂²×C₄	—	73	3	no	—
420	C₂²×C₄	—	73	1	no	—
421	C₂²×C₄	—	73	3	no	—
422	C₂²×C₄	—	73	3	no	—
423	C₂²×C₄	—	73	3	no	—
424	C₂²×C₄	—	146	6	no	—
425	C₂²×C₄	—	146	6	no	—
426	C₂²×C₄	C₂²×#64408	1	3	yes	—
427	C₂²×C₄	C₂²×#64408	1	3	yes	—
428	C₂²×C₄	C₂²×#64408	1	3	yes	—
429	C₄⋊C₄	—	73	24	no	—
430	C₄⋊C₄	—	73	48	no	—
431	C₄⋊C₄	—	73	8	no	—
432	C₄⋊C₄	—	73	6	no	—
433	C₄⋊C₄	—	73	6	no	—
434	C₄⋊C₄	—	73	3	no	—
435	C₄⋊C₄	—	73	3	no	—
436	C₄⋊C₄	C₂²×#64408	1	3	yes	—
437	C₄⋊C₄	C₂²×#64408	1	3	yes	—
438	C₂²⋊C₄	—	73	48	no	—
439	C₂²⋊C₄	—	73	6	no	—
440	C₂²⋊C₄	—	73	6	no	—
441	C₂²⋊C₄	—	73	6	no	—
442	C₂²⋊C₄	C₂²×#64408	1	6	yes	—
443	C₄²	—	292	12	no	—
444	C₄²	—	292	12	no	—
445	C₄²	—	73	48	no	—
446	C₄²	—	73	1	no	—
447	C₄²	—	73	1	no	—
448	C₄²	—	73	3	no	—
449	C₄²	—	73	3	no	—
450	C₄²	—	73	3	no	—
451	C₄²	—	73	3	no	—
452	C₄²	—	73	3	no	—
453	C₄²	—	73	3	no	—
454	C₄²	—	73	3	no	—
455	C₄²	—	73	3	no	—
456	C₄²	—	73	1	no	—
457	C₄²	—	73	3	no	—
458	C₄²	—	146	12	no	—
459	C₄²	—	146	4	no	—
460	C₄²	C₂²×#64408	1	3	yes	—
461	C₄²	C₂²×#64408	1	3	yes	—
462	C₄²	C₂²×#64408	1	1	yes	characteristic
463	C₄²	C₂²×#64408	1	3	yes	—
464	C₂³	—	73	1	no	—
465	C₂³	—	73	12	no	—
466	C₂³	—	73	3	no	—
467	C₂³	—	146	3	no	—
468	C₂³	—	146	6	no	—
469	C₂³	—	146	3	no	—
470	C₂³	C₂³×#64408	1	3	yes	—
471	Q₈	—	73	12	no	—
472	Q₈	C₂×C₄×#64408	1	4	yes	complemented
473	D₄	—	73	24	no	—
474	D₄	—	73	12	no	—
475	D₄	C₂×C₄×#64408	1	12	yes	complemented
476	C₂×C₄	—	2	6	no	—
477	C₂×C₄	—	4	3	no	—
478	C₂×C₄	—	292	3	no	—
479	C₂×C₄	—	292	3	no	—
480	C₂×C₄	—	292	3	no	—
481	C₂×C₄	—	292	48	no	—
482	C₂×C₄	—	73	12	no	—
483	C₂×C₄	—	73	1	no	—
484	C₂×C₄	—	73	1	no	—
485	C₂×C₄	—	73	3	no	—
486	C₂×C₄	—	73	12	no	—
487	C₂×C₄	—	73	4	no	—
488	C₂×C₄	—	73	12	no	—
489	C₂×C₄	—	73	12	no	—
490	C₂×C₄	—	73	2	no	—
491	C₂×C₄	—	73	2	no	—
492	C₂×C₄	—	73	8	no	—
493	C₂×C₄	—	73	24	no	—
494	C₂×C₄	—	73	1	no	—
495	C₂×C₄	—	73	3	no	—
496	C₂×C₄	—	73	3	no	—
497	C₂×C₄	—	146	6	no	—
498	C₂×C₄	—	146	3	no	—
499	C₂×C₄	—	146	6	no	—
500	C₂×C₄	—	146	2	no	—
501	C₂×C₄	—	146	3	no	—
502	C₂×C₄	—	146	6	no	—
503	C₂×C₄	—	146	4	no	—
504	C₂×C₄	—	146	12	no	—
505	C₂×C₄	—	146	12	no	—
506	C₂×C₄	—	146	4	no	—
507	C₂×C₄	—	146	6	no	—
508	C₂×C₄	C₂×C₄×#64408	1	12	yes	complemented
509	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
510	C₂×C₄	C₂³×#64408	1	3	yes	—
511	C₂×C₄	C₂³×#64408	1	3	yes	—
512	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
513	C₂×C₄	C₂³×#64408	1	3	yes	—
514	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
515	C₂²	—	2	3	no	—
516	C₂²	—	2	3	no	—
517	C₂²	—	73	2	no	—
518	C₂²	—	73	1	no	—
519	C₂²	—	73	1	no	—
520	C₂²	—	73	2	no	—
521	C₂²	—	73	6	no	—
522	C₂²	—	146	12	no	—
523	C₂²	—	146	12	no	—
524	C₂²	—	146	3	no	—
525	C₂²	—	146	3	no	—
526	C₂²	C₂²×C₄×#64408	1	6	yes	—
527	C₂²	C₂⁴×#64408	1	1	yes	characteristic
528	C₄	—	2	3	no	—
529	C₄	—	2	1	no	—
530	C₄	—	2	3	no	—
531	C₄	—	73	2	no	—
532	C₄	—	73	6	no	—
533	C₄	—	73	2	no	—
534	C₄	—	146	24	no	—
535	C₄	—	146	8	no	—
536	C₄	—	146	3	no	—
537	C₄	—	146	1	no	—
538	C₄	—	146	3	no	—
539	C₄	C₂²×C₄×#64408	1	2	yes	—
540	C₄	C₂²×C₄×#64408	1	6	yes	—
541	C₄	#17989656	1	2	yes	direct product factor
542	C₂	—	2	6	no	—
543	C₂	—	73	2	no	—
544	C₂	—	73	2	no	—
545	C₂	—	146	6	no	—
546	C₂	C₂³×C₄×#64408	1	1	yes	characteristic
547	C₂	C₂×#17989656	1	1	yes	characteristic
548	C₂	#22626911	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×#64408
commutator	C₂×C₇₃	C₂³×C₄²
Frattini	C₂²	C₂⁴×#64408
Fitting	C₄×#41×C₇₃	C₄
socle	C₂²×C₇₃	C₂⁴×C₄
prime radical	C₂×#41×D₇₃	C₂²
cosocle	C₂²×D₇₃	C₂⁵
hypercenter	C₄×#41	#64408
hypocenter	C₇₃	C₄×#520
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
2. #22626371	C₂	semidirect
3. #22626370	C₂	semidirect
4. #22626368	C₂	semidirect
5. C₄×Q₈×#64408	C₂	semidirect
6. C₄×D₄×#64408	C₂	semidirect
7. C₄×#14556670	C₂	semidirect
8. C₂×C₄×C₄⋊#64408	C₂	semidirect
10. #17989656	C₄	direct (N × H)
31. #41×Dic₇₃	C₄	semidirect
32. C₄×#11924029	C₄	semidirect
33. C₄×#11924029	C₄	semidirect
34. C₄×#11924028	C₄	semidirect
35. #17989055	C₄	semidirect
36. C₄×#11924027	C₄	semidirect
37. C₄×#11924027	C₄	semidirect
44. C₄×#41×C₇₃	C₄	semidirect
46. Q₈×#64408	C₂×C₄	semidirect
47. D₄×#64408	C₂×C₄	semidirect
48. #14556670	C₂×C₄	semidirect
49. C₂×C₄⋊#64408	C₂×C₄	semidirect
73. Q₈×Dic₇₃	C₂×C₄	semidirect
74. Q₈×Dic₇₃	C₂×C₄	semidirect
75. C₄×Dic₁₄₆	C₂×C₄	semidirect
76. C₄×Dic₁₄₆	C₂×C₄	semidirect
77. #14556556	C₂×C₄	semidirect
78. #14556556	C₂×C₄	semidirect
79. C₄×D₂₉₂	C₂×C₄	semidirect
80. C₄×D₂₉₂	C₂×C₄	semidirect
81. D₄×Dic₇₃	C₂×C₄	semidirect
82. D₄×Dic₇₃	C₂×C₄	semidirect
83. #14556553	C₂×C₄	semidirect
84. #14556553	C₂×C₄	semidirect
85. C₄×C₂²⋊D₇₃	C₂×C₄	semidirect
86. C₄×C₂²⋊D₇₃	C₂×C₄	semidirect
87. #14556551	C₂×C₄	semidirect
88. #14556551	C₂×C₄	semidirect
89. #14556550	C₂×C₄	semidirect
90. #14556549	C₂×C₄	semidirect
91. #14556549	C₂×C₄	semidirect
92. #14556548	C₂×C₄	semidirect
93. #14556547	C₂×C₄	semidirect
97. C₂×C₄×Dic₇₃	C₂×C₄	semidirect
98. C₂×C₄×Dic₇₃	C₂×C₄	semidirect
99. C₂×C₄×Dic₇₃	C₂×C₄	semidirect
100. C₄²×D₇₃	C₂×C₄	semidirect
101. C₄²×D₇₃	C₂×C₄	semidirect
102. C₄²×D₇₃	C₂×C₄	semidirect
103. C₄²×D₇₃	C₂×C₄	semidirect
109. C₄×Q₈×C₇₃	C₂×C₄	semidirect
110. C₄×Q₈×C₇₃	C₂×C₄	semidirect
111. C₄×D₄×C₇₃	C₂×C₄	semidirect
112. C₄×D₄×C₇₃	C₂×C₄	semidirect
113. #117×C₇₃	C₂×C₄	semidirect
114. C₂×C₄²×C₇₃	C₂×C₄	semidirect
130. #11924029	C₄²	semidirect
131. #11924028	C₄²	semidirect
132. #11924027	C₄²	semidirect
176. #41×C₇₃	C₄²	semidirect
203. Q₈×C₇₃	C₂×C₄²	semidirect
204. D₄×C₇₃	C₂×C₄²	semidirect
207. C₂×C₄×C₇₃	C₂×C₄²	semidirect
214. C₂²⋊D₇₃	C₂×C₄²	semidirect
217. C₂×Dic₇₃	C₂×C₄²	semidirect
224. D₂₉₂	C₂×C₄²	semidirect
233. C₄×D₇₃	C₂×C₄²	semidirect
234. C₄×D₇₃	C₂×C₄²	semidirect
239. Dic₁₄₆	C₂×C₄²	semidirect
260. C₄×C₇₃	#520	semidirect
266. Dic₇₃	#520	semidirect
284. C₇₃	C₄×#520	semidirect
294. C₄×#41	#64408	semidirect
338. C₄×Q₈	C₂×#64408	semidirect
339. C₄×Q₈	C₂×#64408	semidirect
351. C₄×D₄	C₂×#64408	semidirect
352. C₄×D₄	C₂×#64408	semidirect
359. #117	C₂×#64408	semidirect
385. C₂×C₄²	C₂×#64408	semidirect
394. #41	C₄×#64408	semidirect
472. Q₈	C₂×C₄×#64408	semidirect
475. D₄	C₂×C₄×#64408	semidirect
508. C₂×C₄	C₂×C₄×#64408	semidirect
541. C₄	#17989656	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×#17989656	2
#22626371	2
#22626370	2
#22626368	2
C₄×Q₈×#64408	2
C₄×D₄×#64408	2
C₄×#14556670	2
C₂×C₄×C₄⋊#64408	2
C₄×#41×D₇₃	2
C₄×#520	73

Subgroups — C4×#17989656 #34030526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#17989656 #34030526