Group #32917201 — subgroups

Subgroups — C₇₃×#7797 #32917201

Order 18688.

478 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2683	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#2093	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2083	C₂	1	2	yes	maximal, complemented
4	C₇₃×#1271	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1270	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂²⋊Q₈×C₇₃	—	2	2	no	—
7	C₂×#107×C₇₃	—	2	2	no	—
8	C₂×#107×C₇₃	—	2	1	no	—
9	C₂×#102×C₇₃	—	2	1	no	—
10	#396×C₇₃	—	2	2	no	—
11	#395×C₇₃	—	2	1	no	—
12	#390×C₇₃	C₂²	1	1	yes	characteristic
13	#389×C₇₃	C₂²	1	2	yes	—
14	#386×C₇₃	—	2	1	no	—
15	#384×C₇₃	C₂²	1	1	yes	characteristic
16	#340×C₇₃	—	2	2	no	—
17	#336×C₇₃	C₂²	1	2	yes	—
18	#336×C₇₃	C₂²	1	1	yes	characteristic
19	C₂²×Q₈×C₇₃	—	2	1	no	—
20	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₇₃	—	2	1	no	—
22	C₂²×C₈×C₇₃	—	2	1	no	—
23	C₂²×C₈×C₇₃	—	2	2	no	—
24	C₂²⋊Q₈×C₇₃	—	4	4	no	—
25	C₂²⋊Q₈×C₇₃	—	4	4	no	—
26	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
27	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
28	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
29	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
30	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
31	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
34	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
35	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
36	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
37	#107×C₇₃	—	4	2	no	—
38	#107×C₇₃	—	4	4	no	—
39	#102×C₇₃	—	4	2	no	—
40	#95×C₇₃	—	2	1	no	—
41	#95×C₇₃	—	2	2	no	—
42	C₂⁴×C₇₃	—	2	1	no	—
43	C₂×Q₈×C₇₃	—	4	4	no	—
44	C₂×Q₈×C₇₃	—	8	1	no	—
45	C₂×D₄×C₇₃	—	2	1	no	—
46	C₂×D₄×C₇₃	—	4	1	no	—
47	C₂×D₄×C₇₃	—	4	1	no	—
48	C₂×D₄×C₇₃	Q₁₆	1	2	yes	—
49	C₂²×C₄×C₇₃	—	2	2	no	—
50	C₂²×C₄×C₇₃	—	2	2	no	—
51	C₂²×C₄×C₇₃	—	2	1	no	—
52	C₂²×C₄×C₇₃	—	4	4	no	—
53	C₂²×C₄×C₇₃	—	4	1	no	—
54	C₂²×C₄×C₇₃	—	8	1	no	—
55	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
56	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₇₃	—	2	2	no	—
58	C₂×C₈×C₇₃	—	2	4	no	—
59	C₂×C₈×C₇₃	—	4	2	no	—
60	C₂×C₈×C₇₃	—	4	1	no	—
61	C₂×C₈×C₇₃	—	4	2	no	—
62	C₂×C₈×C₇₃	—	4	1	no	—
63	C₄⋊C₄×C₇₃	—	2	2	no	—
64	C₄⋊C₄×C₇₃	—	4	1	no	—
65	C₄⋊C₄×C₇₃	—	4	2	no	—
66	C₄⋊C₄×C₇₃	—	4	4	no	—
67	C₄⋊C₄×C₇₃	—	4	1	no	—
68	C₄⋊C₄×C₇₃	—	4	1	no	—
69	C₄⋊C₄×C₇₃	—	4	2	no	—
70	C₄⋊C₄×C₇₃	—	4	2	no	—
71	C₄⋊C₄×C₇₃	—	4	2	no	—
72	C₄⋊C₄×C₇₃	—	4	2	no	—
73	C₄⋊C₄×C₇₃	D₈	1	4	yes	—
74	C₂²⋊C₄×C₇₃	—	4	4	no	—
75	C₂²⋊C₄×C₇₃	—	4	2	no	—
76	C₂²⋊C₄×C₇₃	—	4	2	no	—
77	C₂²⋊C₄×C₇₃	—	8	1	no	—
78	C₄²×C₇₃	—	4	1	no	—
79	C₂³×C₇₃	—	2	2	no	—
80	C₂³×C₇₃	—	4	2	no	—
81	C₂³×C₇₃	—	4	1	no	—
82	C₂³×C₇₃	—	4	2	no	—
83	C₂³×C₇₃	—	4	1	no	—
84	C₂³×C₇₃	#120	1	1	yes	characteristic
85	Q₈×C₇₃	—	8	4	no	—
86	D₄×C₇₃	—	4	2	no	—
87	D₄×C₇₃	—	8	1	no	—
88	C₂×C₄×C₇₃	—	2	1	no	—
89	C₂×C₄×C₇₃	—	2	2	no	—
90	C₂×C₄×C₇₃	—	2	2	no	—
91	C₂×C₄×C₇₃	—	2	1	no	—
92	C₂×C₄×C₇₃	—	2	4	no	—
93	C₂×C₄×C₇₃	—	4	2	no	—
94	C₂×C₄×C₇₃	—	4	2	no	—
95	C₂×C₄×C₇₃	—	4	2	no	—
96	C₂×C₄×C₇₃	—	4	2	no	—
97	C₂×C₄×C₇₃	—	4	1	no	—
98	C₂×C₄×C₇₃	—	4	2	no	—
99	C₂×C₄×C₇₃	—	4	2	no	—
100	C₂×C₄×C₇₃	—	8	4	no	—
101	C₂×C₄×C₇₃	—	8	2	no	—
102	C₂×C₄×C₇₃	—	8	1	no	—
103	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
104	C₂×C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
105	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
106	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
107	C₈×C₇₃	—	4	4	no	—
108	C₈×C₇₃	—	4	2	no	—
109	C₂²×C₇₃	—	4	2	no	—
110	C₂²×C₇₃	—	4	4	no	—
111	C₂²×C₇₃	—	8	2	no	—
112	C₂²×C₇₃	—	8	1	no	—
113	C₂²×C₇₃	—	8	1	no	—
114	C₂²×C₇₃	#447	1	2	yes	—
115	C₂²×C₇₃	#451	1	1	yes	characteristic
116	C₂²×C₇₃	#453	1	1	yes	characteristic
117	C₂²×C₇₃	#456	1	2	yes	—
118	C₂²×C₇₃	#458	1	1	yes	characteristic
119	C₄×C₇₃	—	2	2	no	—
120	C₄×C₇₃	—	2	2	no	—
121	C₄×C₇₃	—	2	1	no	—
122	C₄×C₇₃	—	2	1	no	—
123	C₄×C₇₃	—	4	4	no	—
124	C₄×C₇₃	—	8	2	no	—
125	C₄×C₇₃	—	8	1	no	—
126	C₄×C₇₃	—	16	1	no	—
127	#7797	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂×C₇₃	—	8	2	no	—
129	C₂×C₇₃	#1610	1	2	yes	—
130	C₂×C₇₃	#1614	1	1	yes	characteristic
131	C₂×C₇₃	#1619	1	1	yes	characteristic
132	C₂×C₇₃	#1649	1	2	yes	—
133	C₂×C₇₃	#1660	1	1	yes	characteristic
134	#2683	C₂×C₇₃	1	1	yes	characteristic
135	#2093	C₂×C₇₃	1	1	yes	characteristic
136	#2083	C₂×C₇₃	1	2	yes	complemented
137	#1271	C₂×C₇₃	1	2	yes	complemented
138	#1270	C₂×C₇₃	1	1	yes	characteristic
139	C₇₃	#7797	1	1	yes	characteristic, direct product factor, Sylow
140	C₂×C₂²⋊Q₈	—	2	2	no	—
141	C₂×#107	—	2	2	no	—
142	C₂×#107	—	2	1	no	—
143	C₂×#102	—	2	1	no	—
144	#396	—	2	2	no	—
145	#395	—	2	1	no	—
146	#390	C₂²×C₇₃	1	1	yes	characteristic
147	#389	C₂²×C₇₃	1	2	yes	—
148	#386	—	2	1	no	—
149	#384	C₂²×C₇₃	1	1	yes	characteristic
150	#340	—	2	2	no	—
151	#336	C₂²×C₇₃	1	2	yes	—
152	#336	C₂²×C₇₃	1	1	yes	characteristic
153	C₂²×Q₈	—	2	1	no	—
154	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
155	C₂³×C₄	—	2	1	no	—
156	C₂²×C₈	—	2	2	no	—
157	C₂²×C₈	—	2	1	no	—
158	C₂²⋊Q₈	—	4	4	no	—
159	C₂²⋊Q₈	—	4	4	no	—
160	C₂×C₄⋊C₄	—	2	2	no	—
161	C₂×C₄⋊C₄	—	2	2	no	—
162	C₂×C₄⋊C₄	—	2	2	no	—
163	C₂×C₄⋊C₄	—	2	1	no	—
164	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
165	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
166	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
167	C₂×C₂²⋊C₄	—	2	2	no	—
168	C₂×C₂²⋊C₄	—	2	2	no	—
169	C₂×C₂²⋊C₄	—	2	1	no	—
170	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
171	#107	—	4	2	no	—
172	#107	—	4	4	no	—
173	#102	—	4	2	no	—
174	#95	—	2	1	no	—
175	#95	—	2	2	no	—
176	C₂⁴	—	2	1	no	—
177	C₂×Q₈	—	4	4	no	—
178	C₂×Q₈	—	8	1	no	—
179	C₂×D₄	—	2	1	no	—
180	C₂×D₄	—	4	1	no	—
181	C₂×D₄	—	4	1	no	—
182	C₂×D₄	Q₁₆×C₇₃	1	2	yes	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	—	4	4	no	—
187	C₂²×C₄	—	4	1	no	—
188	C₂²×C₄	—	8	1	no	—
189	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
190	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	2	4	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	4	1	no	—
195	C₂×C₈	—	4	2	no	—
196	C₂×C₈	—	4	1	no	—
197	C₄⋊C₄	—	2	2	no	—
198	C₄⋊C₄	—	4	1	no	—
199	C₄⋊C₄	—	4	2	no	—
200	C₄⋊C₄	—	4	4	no	—
201	C₄⋊C₄	—	4	1	no	—
202	C₄⋊C₄	—	4	1	no	—
203	C₄⋊C₄	—	4	2	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₄⋊C₄	D₈×C₇₃	1	4	yes	—
208	C₂²⋊C₄	—	4	4	no	—
209	C₂²⋊C₄	—	4	2	no	—
210	C₂²⋊C₄	—	4	2	no	—
211	C₂²⋊C₄	—	8	1	no	—
212	C₄²	—	4	1	no	—
213	C₂³	—	2	2	no	—
214	C₂³	—	4	2	no	—
215	C₂³	—	4	1	no	—
216	C₂³	—	4	2	no	—
217	C₂³	—	4	1	no	—
218	C₂³	#120×C₇₃	1	1	yes	characteristic
219	Q₈	—	8	4	no	—
220	D₄	—	4	2	no	—
221	D₄	—	8	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	4	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	1	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂×C₄	—	8	4	no	—
235	C₂×C₄	—	8	2	no	—
236	C₂×C₄	—	8	1	no	—
237	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
238	C₂×C₄	C₂×Q₁₆×C₇₃	1	1	yes	characteristic
239	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
240	C₂×C₄	#137×C₇₃	1	1	yes	characteristic
241	C₈	—	4	4	no	—
242	C₈	—	4	2	no	—
243	C₂²	—	4	2	no	—
244	C₂²	—	4	4	no	—
245	C₂²	—	8	2	no	—
246	C₂²	—	8	1	no	—
247	C₂²	—	8	1	no	—
248	C₂²	#447×C₇₃	1	2	yes	—
249	C₂²	#451×C₇₃	1	1	yes	characteristic
250	C₂²	#453×C₇₃	1	1	yes	characteristic
251	C₂²	#456×C₇₃	1	2	yes	—
252	C₂²	#458×C₇₃	1	1	yes	characteristic
253	C₄	—	2	2	no	—
254	C₄	—	2	2	no	—
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	4	4	no	—
258	C₄	—	8	2	no	—
259	C₄	—	8	1	no	—
260	C₄	—	16	1	no	—
261	C₂	—	8	2	no	—
262	C₂	C₇₃×#1610	1	2	yes	—
263	C₂	C₇₃×#1614	1	1	yes	characteristic
264	C₂	C₇₃×#1619	1	1	yes	characteristic
265	C₂	C₇₃×#1649	1	2	yes	—
266	C₂	C₇₃×#1660	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₃×#2683

C₂

yes

maximal, characteristic

C₇₃×#2093

C₂

yes

maximal, characteristic

C₇₃×#2083

C₂

yes

maximal, complemented

C₇₃×#1271

C₂

yes

maximal, complemented

C₇₃×#1270

C₂

yes

maximal, characteristic

C₂×C₂²⋊Q₈×C₇₃

—

C₂×#107×C₇₃

—

C₂×#107×C₇₃

—

C₂×#102×C₇₃

—

#396×C₇₃

—

#395×C₇₃

—

#390×C₇₃

C₂²

yes

characteristic

#389×C₇₃

C₂²

yes

—

#386×C₇₃

—

#384×C₇₃

C₂²

yes

characteristic

#340×C₇₃

—

#336×C₇₃

C₂²

yes

—

#336×C₇₃

C₂²

yes

characteristic

C₂²×Q₈×C₇₃

—

C₂²×D₄×C₇₃

D₄

yes

characteristic

C₂³×C₄×C₇₃

—

C₂²×C₈×C₇₃

—

C₂²×C₈×C₇₃

—

C₂²⋊Q₈×C₇₃

—

C₂²⋊Q₈×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#107×C₇₃

—

#107×C₇₃

—

#102×C₇₃

—

#95×C₇₃

—

#95×C₇₃

—

C₂⁴×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

Q₁₆

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×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

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

D₈

yes

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

#120

yes

characteristic

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

100

C₂×C₄×C₇₃

—

101

C₂×C₄×C₇₃

—

102

C₂×C₄×C₇₃

—

103

C₂×C₄×C₇₃

C₂×D₈

yes

—

104

C₂×C₄×C₇₃

C₂×Q₁₆

yes

characteristic

105

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

—

106

C₂×C₄×C₇₃

#137

yes

characteristic

107

C₈×C₇₃

—

108

C₈×C₇₃

—

109

C₂²×C₇₃

—

110

C₂²×C₇₃

—

111

C₂²×C₇₃

—

112

C₂²×C₇₃

—

113

C₂²×C₇₃

—

114

C₂²×C₇₃

#447

yes

—

115

C₂²×C₇₃

#451

yes

characteristic

116

C₂²×C₇₃

#453

yes

characteristic

117

C₂²×C₇₃

#456

yes

—

118

C₂²×C₇₃

#458

yes

characteristic

119

C₄×C₇₃

—

120

C₄×C₇₃

—

121

C₄×C₇₃

—

122

C₄×C₇₃

—

123

C₄×C₇₃

—

124

C₄×C₇₃

—

125

C₄×C₇₃

—

126

C₄×C₇₃

—

127

#7797

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

128

C₂×C₇₃

—

129

C₂×C₇₃

#1610

yes

—

130

C₂×C₇₃

#1614

yes

characteristic

131

C₂×C₇₃

#1619

yes

characteristic

132

C₂×C₇₃

#1649

yes

—

133

C₂×C₇₃

#1660

yes

characteristic

134

#2683

C₂×C₇₃

yes

characteristic

135

#2093

C₂×C₇₃

yes

characteristic

136

#2083

C₂×C₇₃

yes

complemented

137

#1271

C₂×C₇₃

yes

complemented

138

#1270

C₂×C₇₃

yes

characteristic

139

C₇₃

#7797

yes

characteristic, direct product factor, Sylow

140

C₂×C₂²⋊Q₈

—

141

C₂×#107

—

142

C₂×#107

—

143

C₂×#102

—

144

#396

—

145

#395

—

146

#390

C₂²×C₇₃

yes

characteristic

147

#389

C₂²×C₇₃

yes

—

148

#386

—

149

#384

C₂²×C₇₃

yes

characteristic

150

#340

—

151

#336

C₂²×C₇₃

yes

—

152

#336

C₂²×C₇₃

yes

characteristic

153

C₂²×Q₈

—

154

C₂²×D₄

D₄×C₇₃

yes

characteristic

155

C₂³×C₄

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

C₂²⋊Q₈

—

159

C₂²⋊Q₈

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

D₄×C₇₃

yes

—

165

C₂×C₄⋊C₄

D₄×C₇₃

yes

—

166

C₂×C₄⋊C₄

D₄×C₇₃

yes

characteristic

167

C₂×C₂²⋊C₄

—

168

C₂×C₂²⋊C₄

—

169

C₂×C₂²⋊C₄

—

170

C₂×C₄²

C₂³×C₇₃

yes

characteristic

171

#107

—

172

#107

—

173

#102

—

174

#95

—

175

#95

—

176

C₂⁴

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

Q₁₆×C₇₃

yes

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

C₂×D₄×C₇₃

yes

—

190

C₂²×C₄

C₂×D₄×C₇₃

yes

characteristic

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

D₈×C₇₃

yes

—

208

C₂²⋊C₄

—

209

C₂²⋊C₄

—

210

C₂²⋊C₄

—

211

C₂²⋊C₄

—

212

C₄²

—

213

C₂³

—

214

C₂³

—

215

C₂³

—

216

C₂³

—

217

C₂³

—

218

C₂³

#120×C₇₃

yes

characteristic

219

Q₈

—

220

D₄

—

221

D₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

C₂×D₈×C₇₃

yes

—

238

C₂×C₄

C₂×Q₁₆×C₇₃

yes

characteristic

239

C₂×C₄

AGL(1,ℤ/8)×C₇₃

yes

—

240

C₂×C₄

#137×C₇₃

yes

characteristic

241

C₈

—

242

C₈

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

#447×C₇₃

yes

—

249

C₂²

#451×C₇₃

yes

characteristic

250

C₂²

#453×C₇₃

yes

characteristic

251

C₂²

#456×C₇₃

yes

—

252

C₂²

#458×C₇₃

yes

characteristic

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₂

—

262

C₂

C₇₃×#1610

yes

—

263

C₂

C₇₃×#1614

yes

characteristic

264

C₂

C₇₃×#1619

yes

characteristic

265

C₂

C₇₃×#1649

yes

—

266

C₂

C₇₃×#1660

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₇₃
prime radical	C₂²×D₄×C₇₃	D₄
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₇₃

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₇₃

prime radical

C₂²×D₄×C₇₃

D₄

LCS

G ▷ C₂×C₄² ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

N	H ≅ G/N	type
3. C₇₃×#2083	C₂	semidirect
4. C₇₃×#1271	C₂	semidirect
127. #7797	C₇₃	direct (N × H)
136. #2083	C₂×C₇₃	semidirect
137. #1271	C₂×C₇₃	semidirect
139. C₇₃	#7797	direct (N × H)

H ≅ G/N

type

3. C₇₃×#2083

C₂

semidirect

4. C₇₃×#1271

C₂

semidirect

127. #7797

C₇₃

direct (N × H)

136. #2083

C₂×C₇₃

semidirect

137. #1271

C₂×C₇₃

semidirect

139. C₇₃

#7797

direct (N × H)

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

subgroup	index
C₇₃×#2683	2
C₇₃×#2093	2
C₇₃×#2083	2
C₇₃×#1271	2
C₇₃×#1270	2
#7797	73

subgroup

index

C₇₃×#2683

C₇₃×#2093

C₇₃×#2083

C₇₃×#1271

C₇₃×#1270

#7797

Subgroups — C₇₃×#7797 #32917201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#7797 #32917201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#7797 #32917201