Group #32917039 — subgroups

Subgroups — C₇₃×#7635 #32917039

Order 18688.

520 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 146 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	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#1767	C₂	1	2	yes	maximal, complemented
3	C₇₃×#1272	C₂	1	2	yes	maximal, complemented
4	C₇₃×#1270	C₂	1	2	yes	maximal
5	C₂×#124×C₇₃	C₄	1	1	yes	characteristic
6	C₂×C₄×Q₈×C₇₃	C₄	1	1	yes	characteristic
7	C₂×C₄×D₄×C₇₃	C₄	1	1	yes	characteristic
8	C₂×C₄⋊C₈×C₇₃	—	2	2	no	—
9	C₂×#97×C₇₃	—	2	2	no	—
10	#391×C₇₃	C₂²	1	1	yes	characteristic
11	#390×C₇₃	C₂²	1	1	yes	characteristic
12	#388×C₇₃	—	2	2	no	—
13	#382×C₇₃	C₄	1	1	yes	characteristic
14	C₄×C₂²⋊C₄×C₇₃	—	2	2	no	—
15	C₄³×C₇₃	C₂²	1	1	yes	characteristic
16	#336×C₇₃	C₂²	1	4	yes	—
17	C₂²×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂³×C₄×C₇₃	—	2	1	no	—
20	C₂²×C₈×C₇₃	—	2	4	no	—
21	#124×C₇₃	—	2	2	no	—
22	#124×C₇₃	—	2	2	no	—
23	C₄×Q₈×C₇₃	—	4	2	no	—
24	C₄×D₄×C₇₃	—	4	2	no	—
25	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
26	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
29	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
30	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
31	C₂×C₄²×C₇₃	—	2	1	no	—
32	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₇₃	D₄	1	2	yes	—
35	C₂×C₄²×C₇₃	D₄	1	2	yes	—
36	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
37	C₄⋊C₈×C₇₃	—	2	8	no	—
38	#97×C₇₃	—	4	4	no	—
39	#95×C₇₃	—	2	2	no	—
40	#95×C₇₃	—	2	2	no	—
41	C₂⁴×C₇₃	—	2	1	no	—
42	C₂×Q₈×C₇₃	—	2	1	no	—
43	C₂×Q₈×C₇₃	—	4	1	no	—
44	C₂×Q₈×C₇₃	—	4	1	no	—
45	C₂×Q₈×C₇₃	M₁₆	1	2	yes	—
46	C₂×D₄×C₇₃	—	2	1	no	—
47	C₂×D₄×C₇₃	—	4	1	no	—
48	C₂×D₄×C₇₃	—	4	1	no	—
49	C₂×D₄×C₇₃	M₁₆	1	2	yes	—
50	C₂²×C₄×C₇₃	—	2	1	no	—
51	C₂²×C₄×C₇₃	—	2	1	no	—
52	C₂²×C₄×C₇₃	—	2	1	no	—
53	C₂²×C₄×C₇₃	—	4	2	no	—
54	C₂²×C₄×C₇₃	—	4	4	no	—
55	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
60	C₂×C₈×C₇₃	—	2	8	no	—
61	C₂×C₈×C₇₃	—	4	4	no	—
62	C₂×C₈×C₇₃	—	4	4	no	—
63	C₄⋊C₄×C₇₃	—	4	1	no	—
64	C₄⋊C₄×C₇₃	—	4	1	no	—
65	C₄⋊C₄×C₇₃	—	4	2	no	—
66	C₂²⋊C₄×C₇₃	—	2	8	no	—
67	C₂²⋊C₄×C₇₃	—	4	2	no	—
68	C₂²⋊C₄×C₇₃	—	4	2	no	—
69	C₂²⋊C₄×C₇₃	—	4	2	no	—
70	C₄²×C₇₃	—	2	2	no	—
71	C₄²×C₇₃	—	2	4	no	—
72	C₄²×C₇₃	—	2	1	no	—
73	C₄²×C₇₃	—	2	1	no	—
74	C₄²×C₇₃	—	2	2	no	—
75	C₄²×C₇₃	—	2	2	no	—
76	C₄²×C₇₃	—	4	1	no	—
77	C₄²×C₇₃	—	4	2	no	—
78	C₂³×C₇₃	—	2	2	no	—
79	C₂³×C₇₃	—	4	1	no	—
80	C₂³×C₇₃	—	4	1	no	—
81	C₂³×C₇₃	—	4	2	no	—
82	C₂³×C₇₃	—	4	2	no	—
83	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	Q₈×C₇₃	—	4	2	no	—
85	Q₈×C₇₃	—	4	2	no	—
86	D₄×C₇₃	—	4	2	no	—
87	D₄×C₇₃	—	4	2	no	—
88	C₂×C₄×C₇₃	—	2	2	no	—
89	C₂×C₄×C₇₃	—	2	1	no	—
90	C₂×C₄×C₇₃	—	2	1	no	—
91	C₂×C₄×C₇₃	—	2	2	no	—
92	C₂×C₄×C₇₃	—	2	2	no	—
93	C₂×C₄×C₇₃	—	2	2	no	—
94	C₂×C₄×C₇₃	—	2	1	no	—
95	C₂×C₄×C₇₃	—	2	2	no	—
96	C₂×C₄×C₇₃	—	2	2	no	—
97	C₂×C₄×C₇₃	—	2	2	no	—
98	C₂×C₄×C₇₃	—	4	1	no	—
99	C₂×C₄×C₇₃	—	4	1	no	—
100	C₂×C₄×C₇₃	—	4	1	no	—
101	C₂×C₄×C₇₃	—	4	1	no	—
102	C₂×C₄×C₇₃	—	4	2	no	—
103	C₂×C₄×C₇₃	—	4	2	no	—
104	C₂×C₄×C₇₃	—	8	4	no	—
105	C₂×C₄×C₇₃	#100	1	2	yes	—
106	C₂×C₄×C₇₃	#104	1	4	yes	—
107	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
108	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
109	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
110	C₂×C₄×C₇₃	#137	1	2	yes	—
111	C₈×C₇₃	—	4	8	no	—
112	C₂²×C₇₃	—	4	2	no	—
113	C₂²×C₇₃	—	4	4	no	—
114	C₂²×C₇₃	—	8	1	no	—
115	C₂²×C₇₃	—	8	2	no	—
116	C₂²×C₇₃	—	8	1	no	—
117	C₂²×C₇₃	#407	1	1	yes	characteristic
118	C₂²×C₇₃	#410	1	1	yes	characteristic
119	C₂²×C₇₃	C₂×#100	1	1	yes	characteristic
120	C₂²×C₇₃	#417	1	2	yes	—
121	C₂²×C₇₃	C₂×#104	1	2	yes	—
122	C₄×C₇₃	—	2	1	no	—
123	C₄×C₇₃	—	2	1	no	—
124	C₄×C₇₃	—	2	2	no	—
125	C₄×C₇₃	—	2	2	no	—
126	C₄×C₇₃	—	4	1	no	—
127	C₄×C₇₃	—	4	2	no	—
128	C₄×C₇₃	—	4	2	no	—
129	C₄×C₇₃	—	8	1	no	—
130	C₄×C₇₃	—	8	1	no	—
131	C₄×C₇₃	#329	1	4	yes	—
132	#7635	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂×C₇₃	—	8	2	no	—
134	C₂×C₇₃	#1466	1	1	yes	characteristic
135	C₂×C₇₃	#1489	1	2	yes	—
136	C₂×C₇₃	#1509	1	2	yes	—
137	C₂×C₇₃	C₂×#329	1	1	yes	characteristic
138	C₂×C₇₃	#1560	1	1	yes	characteristic
139	C₄×#124	C₂×C₇₃	1	1	yes	characteristic
140	#1767	C₂×C₇₃	1	2	yes	complemented
141	#1272	C₂×C₇₃	1	2	yes	complemented
142	#1270	C₂×C₇₃	1	2	yes	—
143	C₇₃	#7635	1	1	yes	characteristic, direct product factor, Sylow
144	C₂×#124	C₄×C₇₃	1	1	yes	characteristic
145	C₂×C₄×Q₈	C₄×C₇₃	1	1	yes	characteristic
146	C₂×C₄×D₄	C₄×C₇₃	1	1	yes	characteristic
147	C₂×C₄⋊C₈	—	2	2	no	—
148	C₂×#97	—	2	2	no	—
149	#391	C₂²×C₇₃	1	1	yes	characteristic
150	#390	C₂²×C₇₃	1	1	yes	characteristic
151	#388	—	2	2	no	—
152	#382	C₄×C₇₃	1	1	yes	characteristic
153	C₄×C₂²⋊C₄	—	2	2	no	—
154	C₄³	C₂²×C₇₃	1	1	yes	characteristic
155	#336	C₂²×C₇₃	1	4	yes	—
156	C₂²×Q₈	C₂×C₄×C₇₃	1	1	yes	characteristic
157	C₂²×D₄	C₂×C₄×C₇₃	1	1	yes	characteristic
158	C₂³×C₄	—	2	1	no	—
159	C₂²×C₈	—	2	4	no	—
160	#124	—	2	2	no	—
161	#124	—	2	2	no	—
162	C₄×Q₈	—	4	2	no	—
163	C₄×D₄	—	4	2	no	—
164	C₂×C₄⋊C₄	—	2	1	no	—
165	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
166	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
167	C₂×C₂²⋊C₄	—	2	2	no	—
168	C₂×C₂²⋊C₄	—	2	1	no	—
169	C₂×C₂²⋊C₄	—	2	2	no	—
170	C₂×C₄²	—	2	1	no	—
171	C₂×C₄²	C₂×C₄×C₇₃	1	1	yes	characteristic
172	C₂×C₄²	C₂×C₄×C₇₃	1	1	yes	characteristic
173	C₂×C₄²	D₄×C₇₃	1	2	yes	—
174	C₂×C₄²	D₄×C₇₃	1	2	yes	—
175	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
176	C₄⋊C₈	—	2	8	no	—
177	#97	—	4	4	no	—
178	#95	—	2	2	no	—
179	#95	—	2	2	no	—
180	C₂⁴	—	2	1	no	—
181	C₂×Q₈	—	2	1	no	—
182	C₂×Q₈	—	4	1	no	—
183	C₂×Q₈	—	4	1	no	—
184	C₂×Q₈	M₁₆×C₇₃	1	2	yes	—
185	C₂×D₄	—	2	1	no	—
186	C₂×D₄	—	4	1	no	—
187	C₂×D₄	—	4	1	no	—
188	C₂×D₄	M₁₆×C₇₃	1	2	yes	—
189	C₂²×C₄	—	2	1	no	—
190	C₂²×C₄	—	2	1	no	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	—	4	2	no	—
193	C₂²×C₄	—	4	4	no	—
194	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
195	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
196	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
197	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
198	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
199	C₂×C₈	—	2	8	no	—
200	C₂×C₈	—	4	4	no	—
201	C₂×C₈	—	4	4	no	—
202	C₄⋊C₄	—	4	1	no	—
203	C₄⋊C₄	—	4	1	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₂²⋊C₄	—	2	8	no	—
206	C₂²⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	4	2	no	—
208	C₂²⋊C₄	—	4	2	no	—
209	C₄²	—	2	2	no	—
210	C₄²	—	2	4	no	—
211	C₄²	—	2	1	no	—
212	C₄²	—	2	1	no	—
213	C₄²	—	2	2	no	—
214	C₄²	—	2	2	no	—
215	C₄²	—	4	1	no	—
216	C₄²	—	4	2	no	—
217	C₂³	—	2	2	no	—
218	C₂³	—	4	1	no	—
219	C₂³	—	4	1	no	—
220	C₂³	—	4	2	no	—
221	C₂³	—	4	2	no	—
222	C₂³	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
223	Q₈	—	4	2	no	—
224	Q₈	—	4	2	no	—
225	D₄	—	4	2	no	—
226	D₄	—	4	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	4	1	no	—
238	C₂×C₄	—	4	1	no	—
239	C₂×C₄	—	4	1	no	—
240	C₂×C₄	—	4	1	no	—
241	C₂×C₄	—	4	2	no	—
242	C₂×C₄	—	4	2	no	—
243	C₂×C₄	—	8	4	no	—
244	C₂×C₄	#100×C₇₃	1	2	yes	—
245	C₂×C₄	#104×C₇₃	1	4	yes	—
246	C₂×C₄	C₂×M₁₆×C₇₃	1	1	yes	characteristic
247	C₂×C₄	C₂×M₁₆×C₇₃	1	1	yes	characteristic
248	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
249	C₂×C₄	#137×C₇₃	1	2	yes	—
250	C₈	—	4	8	no	—
251	C₂²	—	4	2	no	—
252	C₂²	—	4	4	no	—
253	C₂²	—	8	2	no	—
254	C₂²	—	8	1	no	—
255	C₂²	—	8	1	no	—
256	C₂²	#407×C₇₃	1	1	yes	characteristic
257	C₂²	#410×C₇₃	1	1	yes	characteristic
258	C₂²	C₂×#100×C₇₃	1	1	yes	characteristic
259	C₂²	#417×C₇₃	1	2	yes	—
260	C₂²	C₂×#104×C₇₃	1	2	yes	—
261	C₄	—	2	1	no	—
262	C₄	—	2	1	no	—
263	C₄	—	2	2	no	—
264	C₄	—	2	2	no	—
265	C₄	—	4	2	no	—
266	C₄	—	4	2	no	—
267	C₄	—	4	1	no	—
268	C₄	—	8	1	no	—
269	C₄	—	8	1	no	—
270	C₄	#329×C₇₃	1	4	yes	—
271	C₂	—	8	2	no	—
272	C₂	C₇₃×#1466	1	1	yes	characteristic
273	C₂	C₇₃×#1489	1	2	yes	—
274	C₂	C₇₃×#1509	1	2	yes	—
275	C₂	C₂×#329×C₇₃	1	1	yes	characteristic
276	C₂	C₇₃×#1560	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#124×C₇₃

C₂

yes

maximal, characteristic

C₇₃×#1767

C₂

yes

maximal, complemented

C₇₃×#1272

C₂

yes

maximal, complemented

C₇₃×#1270

C₂

yes

maximal

C₂×#124×C₇₃

C₄

yes

characteristic

C₂×C₄×Q₈×C₇₃

C₄

yes

characteristic

C₂×C₄×D₄×C₇₃

C₄

yes

characteristic

C₂×C₄⋊C₈×C₇₃

—

C₂×#97×C₇₃

—

#391×C₇₃

C₂²

yes

characteristic

#390×C₇₃

C₂²

yes

characteristic

#388×C₇₃

—

#382×C₇₃

C₄

yes

characteristic

C₄×C₂²⋊C₄×C₇₃

—

C₄³×C₇₃

C₂²

yes

characteristic

#336×C₇₃

C₂²

yes

—

C₂²×Q₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₄×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₇₃

—

C₂²×C₈×C₇₃

—

#124×C₇₃

—

#124×C₇₃

—

C₄×Q₈×C₇₃

—

C₄×D₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₄²×C₇₃

—

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄⋊C₈×C₇₃

—

#97×C₇₃

—

#95×C₇₃

—

#95×C₇₃

—

C₂⁴×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

M₁₆

yes

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

M₁₆

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×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

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₇₃

—

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

—

104

C₂×C₄×C₇₃

—

105

C₂×C₄×C₇₃

#100

yes

—

106

C₂×C₄×C₇₃

#104

yes

—

107

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

108

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

109

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

—

110

C₂×C₄×C₇₃

#137

yes

—

111

C₈×C₇₃

—

112

C₂²×C₇₃

—

113

C₂²×C₇₃

—

114

C₂²×C₇₃

—

115

C₂²×C₇₃

—

116

C₂²×C₇₃

—

117

C₂²×C₇₃

#407

yes

characteristic

118

C₂²×C₇₃

#410

yes

characteristic

119

C₂²×C₇₃

C₂×#100

yes

characteristic

120

C₂²×C₇₃

#417

yes

—

121

C₂²×C₇₃

C₂×#104

yes

—

122

C₄×C₇₃

—

123

C₄×C₇₃

—

124

C₄×C₇₃

—

125

C₄×C₇₃

—

126

C₄×C₇₃

—

127

C₄×C₇₃

—

128

C₄×C₇₃

—

129

C₄×C₇₃

—

130

C₄×C₇₃

—

131

C₄×C₇₃

#329

yes

—

132

#7635

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

133

C₂×C₇₃

—

134

C₂×C₇₃

#1466

yes

characteristic

135

C₂×C₇₃

#1489

yes

—

136

C₂×C₇₃

#1509

yes

—

137

C₂×C₇₃

C₂×#329

yes

characteristic

138

C₂×C₇₃

#1560

yes

characteristic

139

C₄×#124

C₂×C₇₃

yes

characteristic

140

#1767

C₂×C₇₃

yes

complemented

141

#1272

C₂×C₇₃

yes

complemented

142

#1270

C₂×C₇₃

yes

—

143

C₇₃

#7635

yes

characteristic, direct product factor, Sylow

144

C₂×#124

C₄×C₇₃

yes

characteristic

145

C₂×C₄×Q₈

C₄×C₇₃

yes

characteristic

146

C₂×C₄×D₄

C₄×C₇₃

yes

characteristic

147

C₂×C₄⋊C₈

—

148

C₂×#97

—

149

#391

C₂²×C₇₃

yes

characteristic

150

#390

C₂²×C₇₃

yes

characteristic

151

#388

—

152

#382

C₄×C₇₃

yes

characteristic

153

C₄×C₂²⋊C₄

—

154

C₄³

C₂²×C₇₃

yes

characteristic

155

#336

C₂²×C₇₃

yes

—

156

C₂²×Q₈

C₂×C₄×C₇₃

yes

characteristic

157

C₂²×D₄

C₂×C₄×C₇₃

yes

characteristic

158

C₂³×C₄

—

159

C₂²×C₈

—

160

#124

—

161

#124

—

162

C₄×Q₈

—

163

C₄×D₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

C₂×C₄×C₇₃

yes

characteristic

166

C₂×C₄⋊C₄

C₂×C₄×C₇₃

yes

characteristic

167

C₂×C₂²⋊C₄

—

168

C₂×C₂²⋊C₄

—

169

C₂×C₂²⋊C₄

—

170

C₂×C₄²

—

171

C₂×C₄²

C₂×C₄×C₇₃

yes

characteristic

172

C₂×C₄²

C₂×C₄×C₇₃

yes

characteristic

173

C₂×C₄²

D₄×C₇₃

yes

—

174

C₂×C₄²

D₄×C₇₃

yes

—

175

C₂×C₄²

C₂³×C₇₃

yes

characteristic

176

C₄⋊C₈

—

177

#97

—

178

#95

—

179

#95

—

180

C₂⁴

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

M₁₆×C₇₃

yes

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

M₁₆×C₇₃

yes

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

C₂²⋊C₄×C₇₃

yes

—

195

C₂²×C₄

C₂²⋊C₄×C₇₃

yes

characteristic

196

C₂²×C₄

C₂²⋊C₄×C₇₃

yes

characteristic

197

C₂²×C₄

C₂²×C₄×C₇₃

yes

characteristic

198

C₂²×C₄

C₂×D₄×C₇₃

yes

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₂²⋊C₄

—

208

C₂²⋊C₄

—

209

C₄²

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

215

C₄²

—

216

C₄²

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

C₂×C₂²⋊C₄×C₇₃

yes

characteristic

223

Q₈

—

224

Q₈

—

225

D₄

—

226

D₄

—

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

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

#100×C₇₃

yes

—

245

C₂×C₄

#104×C₇₃

yes

—

246

C₂×C₄

C₂×M₁₆×C₇₃

yes

characteristic

247

C₂×C₄

C₂×M₁₆×C₇₃

yes

characteristic

248

C₂×C₄

AGL(1,ℤ/8)×C₇₃

yes

—

249

C₂×C₄

#137×C₇₃

yes

—

250

C₈

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

#407×C₇₃

yes

characteristic

257

C₂²

#410×C₇₃

yes

characteristic

258

C₂²

C₂×#100×C₇₃

yes

characteristic

259

C₂²

#417×C₇₃

yes

—

260

C₂²

C₂×#104×C₇₃

yes

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

—

266

C₄

—

267

C₄

—

268

C₄

—

269

C₄

—

270

C₄

#329×C₇₃

yes

—

271

C₂

—

272

C₂

C₇₃×#1466

yes

characteristic

273

C₂

C₇₃×#1489

yes

—

274

C₂

C₇₃×#1509

yes

—

275

C₂

C₂×#329×C₇₃

yes

characteristic

276

C₂

C₇₃×#1560

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₇₃
Frattini, cosocle	C₂×C₄²	C₂³×C₇₃
prime radical	C₂²×D₄×C₇₃	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄³×C₇₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₇₃

C₂×C₂²⋊C₄

commutator

C₂²×C₄

C₂²×C₄×C₇₃

Frattini, cosocle

C₂×C₄²

C₂³×C₇₃

prime radical

C₂²×D₄×C₇₃

C₂×C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₇₃ ◁ C₄³×C₇₃ ◁ G

N	H ≅ G/N	type
2. C₇₃×#1767	C₂	semidirect
3. C₇₃×#1272	C₂	semidirect
132. #7635	C₇₃	direct (N × H)
140. #1767	C₂×C₇₃	semidirect
141. #1272	C₂×C₇₃	semidirect
143. C₇₃	#7635	direct (N × H)

H ≅ G/N

type

2. C₇₃×#1767

C₂

semidirect

3. C₇₃×#1272

C₂

semidirect

132. #7635

C₇₃

direct (N × H)

140. #1767

C₂×C₇₃

semidirect

141. #1272

C₂×C₇₃

semidirect

143. C₇₃

#7635

direct (N × H)

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

subgroup	index
C₄×#124×C₇₃	2
C₇₃×#1767	2
C₇₃×#1272	2
C₇₃×#1270	2
#7635	73

subgroup

index

C₄×#124×C₇₃

C₇₃×#1767

C₇₃×#1272

C₇₃×#1270

#7635

Subgroups — C₇₃×#7635 #32917039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#7635 #32917039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#7635 #32917039