Group #32942208 — subgroups

Subgroups — C₇₃×#32804 #32942208

Order 18688.

768 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2658	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#2644	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2043	C₂	1	3	yes	maximal, complemented
4	C₇₃×#2042	C₂	1	3	yes	maximal, complemented
5	C₇₃×#2013	C₂	1	3	yes	maximal, complemented
6	C₇₃×#2012	C₂	1	3	yes	maximal
7	C₇₃×#1840	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₇₃	C₂²	1	3	yes	—
9	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Q₈×C₇₃	C₂²	1	3	yes	—
11	C₂×#124×C₇₃	C₂²	1	3	yes	—
12	C₂×#103×C₇₃	C₂²	1	3	yes	—
13	C₂×#103×C₇₃	C₂²	1	3	yes	—
14	C₂×#103×C₇₃	C₂²	1	3	yes	—
15	C₂×#102×C₇₃	C₂²	1	3	yes	—
16	#399×C₇₃	—	2	1	no	—
17	#399×C₇₃	—	2	3	no	—
18	#397×C₇₃	—	2	3	no	—
19	#396×C₇₃	—	2	1	no	—
20	#390×C₇₃	C₂²	1	3	yes	—
21	#389×C₇₃	C₂²	1	3	yes	—
22	#376×C₇₃	C₂²	1	1	yes	characteristic
23	#336×C₇₃	C₂²	1	3	yes	—
24	#336×C₇₃	C₂²	1	3	yes	—
25	C₂²×Q₈×C₇₃	C₂³	1	3	yes	—
26	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
27	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
28	C₂×SD₁₆×C₇₃	—	4	3	no	—
29	C₂×SD₁₆×C₇₃	—	4	3	no	—
30	C₂×SD₁₆×C₇₃	—	4	3	no	—
31	C₂×D₈×C₇₃	—	4	3	no	—
32	C₂²×C₈×C₇₃	C₂³	1	3	yes	—
33	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
34	C₄⋊Q₈×C₇₃	—	4	3	no	—
35	C₄⋊Q₈×C₇₃	—	4	3	no	—
36	#124×C₇₃	—	4	3	no	—
37	#124×C₇₃	—	4	3	no	—
38	C₂×C₄⋊C₄×C₇₃	—	2	3	no	—
39	C₂×C₄⋊C₄×C₇₃	—	2	3	no	—
40	C₂×C₄⋊C₄×C₇₃	—	2	3	no	—
41	C₂×C₄⋊C₄×C₇₃	C₂³	1	3	yes	—
42	C₂×C₂²⋊C₄×C₇₃	—	2	3	no	—
43	C₂×C₂²⋊C₄×C₇₃	—	2	3	no	—
44	C₂×C₂²⋊C₄×C₇₃	—	2	3	no	—
45	C₂×C₂²⋊C₄×C₇₃	—	2	3	no	—
46	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
47	#103×C₇₃	—	4	3	no	—
48	#103×C₇₃	—	4	3	no	—
49	#103×C₇₃	—	4	3	no	—
50	#102×C₇₃	—	4	3	no	—
51	#95×C₇₃	—	2	3	no	—
52	#95×C₇₃	D₄	1	1	yes	characteristic
53	#95×C₇₃	D₄	1	3	yes	—
54	C₂⁴×C₇₃	—	2	1	no	—
55	C₂⁴×C₇₃	—	2	1	no	—
56	C₂×Q₈×C₇₃	—	2	3	no	—
57	C₂×Q₈×C₇₃	—	2	3	no	—
58	C₂×Q₈×C₇₃	—	2	3	no	—
59	C₂×Q₈×C₇₃	—	2	3	no	—
60	C₂×Q₈×C₇₃	—	2	3	no	—
61	C₂×Q₈×C₇₃	—	2	3	no	—
62	C₂×D₄×C₇₃	—	2	3	no	—
63	C₂×D₄×C₇₃	—	2	3	no	—
64	C₂×D₄×C₇₃	—	2	3	no	—
65	C₂×D₄×C₇₃	—	2	3	no	—
66	C₂²×C₄×C₇₃	—	2	3	no	—
67	C₂²×C₄×C₇₃	—	2	3	no	—
68	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
69	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
70	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
71	SD₁₆×C₇₃	—	4	12	no	—
72	D₈×C₇₃	—	4	4	no	—
73	C₂×C₈×C₇₃	—	2	3	no	—
74	C₂×C₈×C₇₃	—	2	3	no	—
75	C₂×C₈×C₇₃	—	2	3	no	—
76	C₂×C₈×C₇₃	—	2	3	no	—
77	C₄⋊C₄×C₇₃	—	2	3	no	—
78	C₄⋊C₄×C₇₃	—	2	3	no	—
79	C₄⋊C₄×C₇₃	—	4	6	no	—
80	C₄⋊C₄×C₇₃	—	4	6	no	—
81	C₄⋊C₄×C₇₃	—	8	3	no	—
82	C₂²⋊C₄×C₇₃	—	4	6	no	—
83	C₂²⋊C₄×C₇₃	—	4	6	no	—
84	C₂²⋊C₄×C₇₃	—	8	3	no	—
85	C₂²⋊C₄×C₇₃	—	8	3	no	—
86	C₄²×C₇₃	—	2	3	no	—
87	C₄²×C₇₃	—	2	3	no	—
88	C₂³×C₇₃	—	4	3	no	—
89	C₂³×C₇₃	—	4	3	no	—
90	C₂³×C₇₃	—	4	3	no	—
91	C₂³×C₇₃	—	4	3	no	—
92	C₂³×C₇₃	—	4	1	no	—
93	C₂³×C₇₃	—	4	1	no	—
94	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
95	Q₈×C₇₃	—	4	3	no	—
96	Q₈×C₇₃	—	4	3	no	—
97	Q₈×C₇₃	—	4	3	no	—
98	Q₈×C₇₃	—	4	3	no	—
99	D₄×C₇₃	—	4	1	no	—
100	D₄×C₇₃	—	4	1	no	—
101	D₄×C₇₃	—	4	3	no	—
102	D₄×C₇₃	—	4	3	no	—
103	C₂×C₄×C₇₃	—	2	3	no	—
104	C₂×C₄×C₇₃	—	2	3	no	—
105	C₂×C₄×C₇₃	—	2	3	no	—
106	C₂×C₄×C₇₃	—	2	3	no	—
107	C₂×C₄×C₇₃	—	2	3	no	—
108	C₂×C₄×C₇₃	—	2	3	no	—
109	C₂×C₄×C₇₃	—	4	3	no	—
110	C₂×C₄×C₇₃	—	4	3	no	—
111	C₂×C₄×C₇₃	—	4	3	no	—
112	C₂×C₄×C₇₃	—	4	3	no	—
113	C₂×C₄×C₇₃	—	4	3	no	—
114	C₂×C₄×C₇₃	—	4	3	no	—
115	C₂×C₄×C₇₃	H(5,𝔽₂)	1	3	yes	—
116	C₂×C₄×C₇₃	H(5,𝔽₂)	1	3	yes	—
117	C₈×C₇₃	—	4	1	no	—
118	C₈×C₇₃	—	4	3	no	—
119	C₂²×C₇₃	—	8	1	no	—
120	C₂²×C₇₃	—	8	1	no	—
121	C₂²×C₇₃	—	8	3	no	—
122	C₂²×C₇₃	—	8	3	no	—
123	C₂²×C₇₃	—	8	3	no	—
124	C₂²×C₇₃	—	8	3	no	—
125	C₂²×C₇₃	#535	1	3	yes	—
126	C₂²×C₇₃	#577	1	3	yes	—
127	C₂²×C₇₃	#578	1	1	yes	characteristic
128	C₄×C₇₃	—	4	3	no	—
129	C₄×C₇₃	—	4	3	no	—
130	C₄×C₇₃	—	8	3	no	—
131	C₄×C₇₃	—	8	3	no	—
132	C₄×C₇₃	#560	1	1	yes	characteristic
133	C₄×C₇₃	#560	1	3	yes	—
134	#32804	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂×C₇₃	—	16	1	no	—
136	C₂×C₇₃	—	16	1	no	—
137	C₂×C₇₃	#2818	1	1	yes	characteristic
138	C₂×C₇₃	#3221	1	3	yes	—
139	C₂×C₇₃	#3225	1	3	yes	—
140	#2658	C₂×C₇₃	1	1	yes	characteristic, complemented
141	#2644	C₂×C₇₃	1	1	yes	characteristic, complemented
142	#2043	C₂×C₇₃	1	3	yes	complemented
143	#2042	C₂×C₇₃	1	3	yes	complemented
144	#2013	C₂×C₇₃	1	3	yes	complemented
145	#2012	C₂×C₇₃	1	3	yes	—
146	#1840	C₂×C₇₃	1	1	yes	characteristic, complemented
147	C₇₃	#32804	1	1	yes	characteristic, direct product factor, Sylow
148	C₂²×SD₁₆	C₂²×C₇₃	1	3	yes	—
149	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
150	C₂×C₄⋊Q₈	C₂²×C₇₃	1	3	yes	—
151	C₂×#124	C₂²×C₇₃	1	3	yes	—
152	C₂×#103	C₂²×C₇₃	1	3	yes	—
153	C₂×#103	C₂²×C₇₃	1	3	yes	—
154	C₂×#103	C₂²×C₇₃	1	3	yes	—
155	C₂×#102	C₂²×C₇₃	1	3	yes	—
156	#399	—	2	1	no	—
157	#399	—	2	3	no	—
158	#397	—	2	3	no	—
159	#396	—	2	1	no	—
160	#390	C₂²×C₇₃	1	3	yes	—
161	#389	C₂²×C₇₃	1	3	yes	—
162	#376	C₂²×C₇₃	1	1	yes	characteristic
163	#336	C₂²×C₇₃	1	3	yes	—
164	#336	C₂²×C₇₃	1	3	yes	—
165	C₂²×Q₈	C₂³×C₇₃	1	3	yes	—
166	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
167	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
168	C₂×SD₁₆	—	4	3	no	—
169	C₂×SD₁₆	—	4	3	no	—
170	C₂×SD₁₆	—	4	3	no	—
171	C₂×D₈	—	4	3	no	—
172	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
173	C₂²×C₈	C₂³×C₇₃	1	3	yes	—
174	C₄⋊Q₈	—	4	3	no	—
175	C₄⋊Q₈	—	4	3	no	—
176	#124	—	4	3	no	—
177	#124	—	4	3	no	—
178	C₂×C₄⋊C₄	—	2	3	no	—
179	C₂×C₄⋊C₄	—	2	3	no	—
180	C₂×C₄⋊C₄	—	2	3	no	—
181	C₂×C₄⋊C₄	C₂³×C₇₃	1	3	yes	—
182	C₂×C₂²⋊C₄	—	2	3	no	—
183	C₂×C₂²⋊C₄	—	2	3	no	—
184	C₂×C₂²⋊C₄	—	2	3	no	—
185	C₂×C₂²⋊C₄	—	2	3	no	—
186	C₂×C₄²	C₂³×C₇₃	1	3	yes	—
187	#103	—	4	3	no	—
188	#103	—	4	3	no	—
189	#103	—	4	3	no	—
190	#102	—	4	3	no	—
191	#95	—	2	3	no	—
192	#95	D₄×C₇₃	1	1	yes	characteristic
193	#95	D₄×C₇₃	1	3	yes	—
194	C₂⁴	—	2	1	no	—
195	C₂⁴	—	2	1	no	—
196	C₂×Q₈	—	2	3	no	—
197	C₂×Q₈	—	2	3	no	—
198	C₂×Q₈	—	2	3	no	—
199	C₂×Q₈	—	2	3	no	—
200	C₂×Q₈	—	2	3	no	—
201	C₂×Q₈	—	2	3	no	—
202	C₂×D₄	—	2	3	no	—
203	C₂×D₄	—	2	3	no	—
204	C₂×D₄	—	2	3	no	—
205	C₂×D₄	—	2	3	no	—
206	C₂²×C₄	—	2	3	no	—
207	C₂²×C₄	—	2	3	no	—
208	C₂²×C₄	C₂×D₄×C₇₃	1	3	yes	—
209	C₂²×C₄	C₂×D₄×C₇₃	1	3	yes	—
210	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
211	SD₁₆	—	4	12	no	—
212	D₈	—	4	4	no	—
213	C₂×C₈	—	2	3	no	—
214	C₂×C₈	—	2	3	no	—
215	C₂×C₈	—	2	3	no	—
216	C₂×C₈	—	2	3	no	—
217	C₄⋊C₄	—	2	3	no	—
218	C₄⋊C₄	—	2	3	no	—
219	C₄⋊C₄	—	4	6	no	—
220	C₄⋊C₄	—	4	6	no	—
221	C₄⋊C₄	—	8	3	no	—
222	C₂²⋊C₄	—	4	6	no	—
223	C₂²⋊C₄	—	4	6	no	—
224	C₂²⋊C₄	—	8	3	no	—
225	C₂²⋊C₄	—	8	3	no	—
226	C₄²	—	2	3	no	—
227	C₄²	—	2	3	no	—
228	C₂³	—	4	3	no	—
229	C₂³	—	4	3	no	—
230	C₂³	—	4	3	no	—
231	C₂³	—	4	3	no	—
232	C₂³	—	4	1	no	—
233	C₂³	—	4	1	no	—
234	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
235	Q₈	—	4	3	no	—
236	Q₈	—	4	3	no	—
237	Q₈	—	4	3	no	—
238	Q₈	—	4	3	no	—
239	D₄	—	4	1	no	—
240	D₄	—	4	1	no	—
241	D₄	—	4	3	no	—
242	D₄	—	4	3	no	—
243	C₂×C₄	—	2	3	no	—
244	C₂×C₄	—	2	3	no	—
245	C₂×C₄	—	2	3	no	—
246	C₂×C₄	—	2	3	no	—
247	C₂×C₄	—	2	3	no	—
248	C₂×C₄	—	2	3	no	—
249	C₂×C₄	—	4	3	no	—
250	C₂×C₄	—	4	3	no	—
251	C₂×C₄	—	4	3	no	—
252	C₂×C₄	—	4	3	no	—
253	C₂×C₄	—	4	3	no	—
254	C₂×C₄	—	4	3	no	—
255	C₂×C₄	H(5,𝔽₂)×C₇₃	1	3	yes	—
256	C₂×C₄	H(5,𝔽₂)×C₇₃	1	3	yes	—
257	C₈	—	4	1	no	—
258	C₈	—	4	3	no	—
259	C₂²	—	8	3	no	—
260	C₂²	—	8	3	no	—
261	C₂²	—	8	3	no	—
262	C₂²	—	8	3	no	—
263	C₂²	—	8	1	no	—
264	C₂²	—	8	1	no	—
265	C₂²	#535×C₇₃	1	3	yes	—
266	C₂²	#577×C₇₃	1	3	yes	—
267	C₂²	#578×C₇₃	1	1	yes	characteristic
268	C₄	—	4	3	no	—
269	C₄	—	4	3	no	—
270	C₄	—	8	3	no	—
271	C₄	—	8	3	no	—
272	C₄	#560×C₇₃	1	1	yes	characteristic
273	C₄	#560×C₇₃	1	3	yes	—
274	C₂	—	16	1	no	—
275	C₂	—	16	1	no	—
276	C₂	C₇₃×#2818	1	1	yes	characteristic
277	C₂	C₇₃×#3221	1	3	yes	—
278	C₂	C₇₃×#3225	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₃×#2658

C₂

yes

maximal, characteristic, complemented

C₇₃×#2644

C₂

yes

maximal, characteristic, complemented

C₇₃×#2043

C₂

yes

maximal, complemented

C₇₃×#2042

C₂

yes

maximal, complemented

C₇₃×#2013

C₂

yes

maximal, complemented

C₇₃×#2012

C₂

yes

maximal

C₇₃×#1840

C₂

yes

maximal, characteristic, complemented

C₂²×SD₁₆×C₇₃

C₂²

yes

—

C₂²×D₈×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊Q₈×C₇₃

C₂²

yes

—

C₂×#124×C₇₃

C₂²

yes

—

C₂×#103×C₇₃

C₂²

yes

—

C₂×#103×C₇₃

C₂²

yes

—

C₂×#103×C₇₃

C₂²

yes

—

C₂×#102×C₇₃

C₂²

yes

—

#399×C₇₃

—

#399×C₇₃

—

#397×C₇₃

—

#396×C₇₃

—

#390×C₇₃

C₂²

yes

—

#389×C₇₃

C₂²

yes

—

#376×C₇₃

C₂²

yes

characteristic

#336×C₇₃

C₂²

yes

—

#336×C₇₃

C₂²

yes

—

C₂²×Q₈×C₇₃

C₂³

yes

—

C₂²×D₄×C₇₃

C₂³

yes

characteristic

C₂²×D₄×C₇₃

C₂³

yes

characteristic

C₂×SD₁₆×C₇₃

—

C₂×SD₁₆×C₇₃

—

C₂×SD₁₆×C₇₃

—

C₂×D₈×C₇₃

—

C₂²×C₈×C₇₃

C₂³

yes

—

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

—

#124×C₇₃

—

#124×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

C₂³

yes

—

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₄²×C₇₃

C₂³

yes

—

#103×C₇₃

—

#103×C₇₃

—

#103×C₇₃

—

#102×C₇₃

—

#95×C₇₃

—

#95×C₇₃

D₄

yes

characteristic

#95×C₇₃

D₄

yes

—

C₂⁴×C₇₃

—

C₂⁴×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂⁴

yes

characteristic

SD₁₆×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂²×D₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

D₄×C₇₃

—

100

D₄×C₇₃

—

101

D₄×C₇₃

—

102

D₄×C₇₃

—

103

C₂×C₄×C₇₃

—

104

C₂×C₄×C₇₃

—

105

C₂×C₄×C₇₃

—

106

C₂×C₄×C₇₃

—

107

C₂×C₄×C₇₃

—

108

C₂×C₄×C₇₃

—

109

C₂×C₄×C₇₃

—

110

C₂×C₄×C₇₃

—

111

C₂×C₄×C₇₃

—

112

C₂×C₄×C₇₃

—

113

C₂×C₄×C₇₃

—

114

C₂×C₄×C₇₃

—

115

C₂×C₄×C₇₃

H(5,𝔽₂)

yes

—

116

C₂×C₄×C₇₃

H(5,𝔽₂)

yes

—

117

C₈×C₇₃

—

118

C₈×C₇₃

—

119

C₂²×C₇₃

—

120

C₂²×C₇₃

—

121

C₂²×C₇₃

—

122

C₂²×C₇₃

—

123

C₂²×C₇₃

—

124

C₂²×C₇₃

—

125

C₂²×C₇₃

#535

yes

—

126

C₂²×C₇₃

#577

yes

—

127

C₂²×C₇₃

#578

yes

characteristic

128

C₄×C₇₃

—

129

C₄×C₇₃

—

130

C₄×C₇₃

—

131

C₄×C₇₃

—

132

C₄×C₇₃

#560

yes

characteristic

133

C₄×C₇₃

#560

yes

—

134

#32804

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

135

C₂×C₇₃

—

136

C₂×C₇₃

—

137

C₂×C₇₃

#2818

yes

characteristic

138

C₂×C₇₃

#3221

yes

—

139

C₂×C₇₃

#3225

yes

—

140

#2658

C₂×C₇₃

yes

characteristic, complemented

141

#2644

C₂×C₇₃

yes

characteristic, complemented

142

#2043

C₂×C₇₃

yes

complemented

143

#2042

C₂×C₇₃

yes

complemented

144

#2013

C₂×C₇₃

yes

complemented

145

#2012

C₂×C₇₃

yes

—

146

#1840

C₂×C₇₃

yes

characteristic, complemented

147

C₇₃

#32804

yes

characteristic, direct product factor, Sylow

148

C₂²×SD₁₆

C₂²×C₇₃

yes

—

149

C₂²×D₈

C₂²×C₇₃

yes

characteristic

150

C₂×C₄⋊Q₈

C₂²×C₇₃

yes

—

151

C₂×#124

C₂²×C₇₃

yes

—

152

C₂×#103

C₂²×C₇₃

yes

—

153

C₂×#103

C₂²×C₇₃

yes

—

154

C₂×#103

C₂²×C₇₃

yes

—

155

C₂×#102

C₂²×C₇₃

yes

—

156

#399

—

157

#399

—

158

#397

—

159

#396

—

160

#390

C₂²×C₇₃

yes

—

161

#389

C₂²×C₇₃

yes

—

162

#376

C₂²×C₇₃

yes

characteristic

163

#336

C₂²×C₇₃

yes

—

164

#336

C₂²×C₇₃

yes

—

165

C₂²×Q₈

C₂³×C₇₃

yes

—

166

C₂²×D₄

C₂³×C₇₃

yes

characteristic

167

C₂²×D₄

C₂³×C₇₃

yes

characteristic

168

C₂×SD₁₆

—

169

C₂×SD₁₆

—

170

C₂×SD₁₆

—

171

C₂×D₈

—

172

C₂²×C₈

C₂³×C₇₃

yes

characteristic

173

C₂²×C₈

C₂³×C₇₃

yes

—

174

C₄⋊Q₈

—

175

C₄⋊Q₈

—

176

#124

—

177

#124

—

178

C₂×C₄⋊C₄

—

179

C₂×C₄⋊C₄

—

180

C₂×C₄⋊C₄

—

181

C₂×C₄⋊C₄

C₂³×C₇₃

yes

—

182

C₂×C₂²⋊C₄

—

183

C₂×C₂²⋊C₄

—

184

C₂×C₂²⋊C₄

—

185

C₂×C₂²⋊C₄

—

186

C₂×C₄²

C₂³×C₇₃

yes

—

187

#103

—

188

#103

—

189

#103

—

190

#102

—

191

#95

—

192

#95

D₄×C₇₃

yes

characteristic

193

#95

D₄×C₇₃

yes

—

194

C₂⁴

—

195

C₂⁴

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×Q₈

—

199

C₂×Q₈

—

200

C₂×Q₈

—

201

C₂×Q₈

—

202

C₂×D₄

—

203

C₂×D₄

—

204

C₂×D₄

—

205

C₂×D₄

—

206

C₂²×C₄

—

207

C₂²×C₄

—

208

C₂²×C₄

C₂×D₄×C₇₃

yes

—

209

C₂²×C₄

C₂×D₄×C₇₃

yes

—

210

C₂²×C₄

C₂⁴×C₇₃

yes

characteristic

211

SD₁₆

—

212

D₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₂²⋊C₄

—

223

C₂²⋊C₄

—

224

C₂²⋊C₄

—

225

C₂²⋊C₄

—

226

C₄²

—

227

C₄²

—

228

C₂³

—

229

C₂³

—

230

C₂³

—

231

C₂³

—

232

C₂³

—

233

C₂³

—

234

C₂³

C₂²×D₄×C₇₃

yes

characteristic

235

Q₈

—

236

Q₈

—

237

Q₈

—

238

Q₈

—

239

D₄

—

240

D₄

—

241

D₄

—

242

D₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

252

C₂×C₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

H(5,𝔽₂)×C₇₃

yes

—

256

C₂×C₄

H(5,𝔽₂)×C₇₃

yes

—

257

C₈

—

258

C₈

—

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

#535×C₇₃

yes

—

266

C₂²

#577×C₇₃

yes

—

267

C₂²

#578×C₇₃

yes

characteristic

268

C₄

—

269

C₄

—

270

C₄

—

271

C₄

—

272

C₄

#560×C₇₃

yes

characteristic

273

C₄

#560×C₇₃

yes

—

274

C₂

—

275

C₂

—

276

C₂

C₇₃×#2818

yes

characteristic

277

C₂

C₇₃×#3221

yes

—

278

C₂

C₇₃×#3225

yes

—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×D₈×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ #376×C₇₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₇₃

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₇₃

prime radical

C₂²×D₈×C₇₃

C₂²

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₇₃ ◁ #376×C₇₃ ◁ G

N	H ≅ G/N	type
1. C₇₃×#2658	C₂	semidirect
2. C₇₃×#2644	C₂	semidirect
3. C₇₃×#2043	C₂	semidirect
4. C₇₃×#2042	C₂	semidirect
5. C₇₃×#2013	C₂	semidirect
7. C₇₃×#1840	C₂	semidirect
134. #32804	C₇₃	direct (N × H)
140. #2658	C₂×C₇₃	semidirect
141. #2644	C₂×C₇₃	semidirect
142. #2043	C₂×C₇₃	semidirect
143. #2042	C₂×C₇₃	semidirect
144. #2013	C₂×C₇₃	semidirect
146. #1840	C₂×C₇₃	semidirect
147. C₇₃	#32804	direct (N × H)

H ≅ G/N

type

1. C₇₃×#2658

C₂

semidirect

2. C₇₃×#2644

C₂

semidirect

3. C₇₃×#2043

C₂

semidirect

4. C₇₃×#2042

C₂

semidirect

5. C₇₃×#2013

C₂

semidirect

7. C₇₃×#1840

C₂

semidirect

134. #32804

C₇₃

direct (N × H)

140. #2658

C₂×C₇₃

semidirect

141. #2644

C₂×C₇₃

semidirect

142. #2043

C₂×C₇₃

semidirect

143. #2042

C₂×C₇₃

semidirect

144. #2013

C₂×C₇₃

semidirect

146. #1840

C₂×C₇₃

semidirect

147. C₇₃

#32804

direct (N × H)

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

subgroup	index
C₇₃×#2658	2
C₇₃×#2644	2
C₇₃×#2043	2
C₇₃×#2042	2
C₇₃×#2013	2
C₇₃×#2012	2
C₇₃×#1840	2
#32804	73

subgroup

index

C₇₃×#2658

C₇₃×#2644

C₇₃×#2043

C₇₃×#2042

C₇₃×#2013

C₇₃×#2012

C₇₃×#1840

#32804

Subgroups — C₇₃×#32804 #32942208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#32804 #32942208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#32804 #32942208