Group #33001916 — subgroups

Subgroups — #33001916

Order 18688.

454 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 135 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	C₂×#17988544	C₂	1	1	yes	maximal, characteristic
2	#22611686	C₂	1	2	yes	maximal, complemented
3	C₂×#17988368	C₂	1	2	yes	maximal
4	#22608015	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#11924011	C₂²	1	1	yes	characteristic
7	C₂²×C₈×D₇₃	C₄	1	1	yes	characteristic
8	C₂×#14556548	C₄	1	1	yes	characteristic
9	C₂×#14556531	C₂²	1	2	yes	—
10	#17988544	—	2	4	no	—
11	C₂×#14556501	C₄	1	1	yes	characteristic
12	C₂×C₄×#10596831	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
14	#17988405	—	2	4	no	—
15	#17988368	—	2	4	no	—
16	C₂×M₃₂×C₇₃	C₂²	1	2	yes	—
17	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×#11924011	—	2	2	no	—
20	C₂×#11924011	—	2	2	no	—
21	C₂×#11924011	D₄	1	2	yes	—
22	C₂×#11924011	Q₈	1	2	yes	—
23	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
24	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×D₇₃	—	2	2	no	—
26	C₂×C₈×D₇₃	—	2	2	no	—
27	C₂×C₈×D₇₃	—	2	2	no	—
28	#14556548	—	2	2	no	—
29	#14556548	—	2	2	no	—
30	C₂×#11924007	C₈	1	2	yes	—
31	C₂×#11924005	C₈	1	2	yes	—
32	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
33	#14556531	—	2	2	no	—
34	#14556531	—	2	2	no	—
35	C₂×#11924003	—	2	2	no	—
36	#14556501	—	2	2	no	—
37	C₄×#10596831	—	2	2	no	—
38	C₈×Dic₇₃	D₄	1	4	yes	—
39	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
41	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
42	M₃₂×C₇₃	—	2	2	no	—
43	M₃₂×C₇₃	—	2	2	no	—
44	C₂×C₁₆×C₇₃	—	2	2	no	—
45	#97×C₇₃	—	2	2	no	—
46	C₂³×D₇₃	C₂×C₈	1	1	yes	characteristic
47	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
48	C₂²×Dic₇₃	C₂×C₈	1	2	yes	—
49	C₂×C₄×D₇₃	—	2	1	no	—
50	C₂×C₄×D₇₃	—	2	1	no	—
51	C₂×C₄×D₇₃	—	2	1	no	—
52	C₂×C₄×D₇₃	—	2	1	no	—
53	C₂×C₄×D₇₃	C₄⋊C₄	1	2	yes	—
54	C₂×C₄×D₇₃	M₁₆	1	2	yes	—
55	#11924011	—	2	4	no	—
56	#11924011	—	2	4	no	—
57	C₂×#10596831	—	2	1	no	—
58	C₂×#10596831	—	2	1	no	—
59	C₂×#10596831	—	2	1	no	—
60	C₂×#10596831	—	2	1	no	—
61	C₂×#10596831	C₂²⋊C₄	1	2	yes	—
62	C₂×#10596831	C₄⋊C₄	1	2	yes	—
63	C₈×D₇₃	—	2	8	no	—
64	#11924007	—	2	4	no	—
65	#11924005	—	2	4	no	—
66	C₄×Dic₇₃	C₂²⋊C₄	1	2	yes	—
67	C₄×Dic₇₃	M₁₆	1	2	yes	—
68	#11924003	—	4	2	no	—
69	C₂²×C₄×C₇₃	C₂×C₈	1	2	yes	—
70	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₇₃	—	2	1	no	—
72	C₂×C₈×C₇₃	—	2	1	no	—
73	C₂×C₈×C₇₃	M₁₆	1	2	yes	—
74	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
76	C₂×C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
77	C₂×C₈×C₇₃	#41	1	2	yes	—
78	C₄²×C₇₃	—	2	1	no	—
79	C₄²×C₇₃	—	2	1	no	—
80	C₁₆×C₇₃	—	4	2	no	—
81	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
82	C₂²×D₇₃	—	2	1	no	—
83	C₂²×D₇₃	—	2	1	no	—
84	C₂²×D₇₃	—	4	2	no	—
85	C₂²×D₇₃	C₄⋊C₈	1	2	yes	—
86	C₂×C₄×C₇₃	—	2	2	no	—
87	C₂×C₄×C₇₃	—	4	2	no	—
88	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
91	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
92	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
93	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
94	C₂×Dic₇₃	—	2	1	no	—
95	C₂×Dic₇₃	—	2	1	no	—
96	C₂×Dic₇₃	—	4	2	no	—
97	C₂×Dic₇₃	C₂²⋊C₈	1	4	yes	—
98	C₂×Dic₇₃	C₄⋊C₈	1	2	yes	—
99	C₄×D₇₃	—	2	2	no	—
100	C₄×D₇₃	—	2	2	no	—
101	C₄×D₇₃	—	2	2	no	—
102	C₄×D₇₃	—	2	2	no	—
103	C₈×C₇₃	—	2	2	no	—
104	C₈×C₇₃	#121	1	2	yes	—
105	C₈×C₇₃	C₂²⋊Q₈	1	2	yes	—
106	#10596831	—	2	2	no	—
107	#10596831	—	2	2	no	—
108	C₂²×C₇₃	—	2	2	no	—
109	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
110	C₂²×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
111	C₂²×C₇₃	#431	1	1	yes	characteristic
112	C₂×D₇₃	—	2	2	no	—
113	C₂×D₇₃	—	4	2	no	—
114	C₂×D₇₃	—	4	2	no	—
115	C₂×D₇₃	—	4	2	no	—
116	C₄×C₇₃	—	4	2	no	—
117	C₄×C₇₃	#380	1	1	yes	characteristic
118	C₄×C₇₃	#407	1	1	yes	characteristic
119	C₄×C₇₃	#423	1	1	yes	characteristic
120	C₄×C₇₃	#432	1	1	yes	characteristic
121	Dic₇₃	—	2	2	no	—
122	Dic₇₃	—	2	4	no	—
123	#12786	—	73	1	no	maximal, Sylow
124	C₂×C₇₃	—	2	1	no	—
125	C₂×C₇₃	—	2	1	no	—
126	C₂×C₇₃	#1797	1	1	yes	characteristic
127	C₂×C₇₃	#2115	1	2	yes	—
128	D₇₃	—	4	2	no	—
129	C₂×#405	—	73	1	no	—
130	#2150	—	73	2	no	—
131	C₂×#349	—	73	2	no	—
132	#1377	—	73	1	no	—
133	#1377	D₇₃	1	1	yes	characteristic, complemented
134	C₇₃	#12786	1	1	yes	characteristic, complemented, Sylow
135	C₂²×M₁₆	—	73	1	no	—
136	C₂³×C₈	—	73	1	no	—
137	C₂×#117	—	73	1	no	—
138	C₂×M₃₂	—	73	2	no	—
139	C₂×M₃₂	C₂×D₇₃	1	2	yes	—
140	#405	—	146	4	no	—
141	C₂×#97	—	73	1	no	—
142	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
143	C₂×C₄×C₈	—	73	1	no	—
144	C₂×C₄×C₈	—	73	1	no	—
145	C₄⋊C₁₆	—	146	4	no	—
146	#349	—	146	4	no	—
147	C₂³×C₄	—	73	1	no	—
148	C₂×M₁₆	—	73	2	no	—
149	C₂×M₁₆	—	73	2	no	—
150	C₂×M₁₆	—	146	2	no	—
151	C₂×M₁₆	—	146	2	no	—
152	C₂²×C₈	—	73	1	no	—
153	C₂²×C₈	—	73	1	no	—
154	C₂²×C₈	—	146	2	no	—
155	C₂²×C₈	—	146	2	no	—
156	C₂²×C₈	—	146	2	no	—
157	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
158	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
159	#117	—	146	2	no	—
160	#117	—	146	2	no	—
161	C₂×C₄⋊C₄	—	73	2	no	—
162	C₂×C₂²⋊C₄	—	73	2	no	—
163	C₂×C₄²	—	73	1	no	—
164	C₂×C₄²	C₄×D₇₃	1	1	yes	characteristic
165	M₃₂	—	2	2	no	—
166	M₃₂	—	2	2	no	—
167	M₃₂	—	146	2	no	—
168	M₃₂	—	146	2	no	—
169	C₂×C₁₆	—	2	2	no	—
170	C₂×C₁₆	—	146	2	no	—
171	#97	—	2	2	no	—
172	#97	—	146	2	no	—
173	C₄×C₈	—	73	4	no	—
174	C₄×C₈	—	146	2	no	—
175	C₂⁴	—	73	1	no	—
176	C₂²×C₄	—	73	2	no	—
177	C₂²×C₄	—	73	1	no	—
178	C₂²×C₄	—	73	2	no	—
179	C₂²×C₄	—	73	2	no	—
180	C₂²×C₄	—	146	1	no	—
181	C₂²×C₄	—	146	1	no	—
182	C₂²×C₄	—	146	1	no	—
183	C₂²×C₄	—	146	1	no	—
184	C₂²×C₄	C₈×D₇₃	1	2	yes	—
185	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
186	M₁₆	—	146	4	no	—
187	M₁₆	—	146	4	no	—
188	C₂×C₈	—	2	1	no	—
189	C₂×C₈	—	2	1	no	—
190	C₂×C₈	—	73	2	no	—
191	C₂×C₈	—	73	2	no	—
192	C₂×C₈	—	146	8	no	—
193	C₂×C₈	—	146	1	no	—
194	C₂×C₈	—	146	1	no	—
195	C₂×C₈	—	146	1	no	—
196	C₂×C₈	—	146	1	no	—
197	C₂×C₈	#11924011	1	2	yes	—
198	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
199	C₂×C₈	D₄×D₇₃	1	2	yes	—
200	C₂×C₈	Q₈×D₇₃	1	1	yes	characteristic
201	C₂×C₈	#11924028	1	2	yes	—
202	C₄⋊C₄	—	146	4	no	—
203	C₂²⋊C₄	—	146	4	no	—
204	C₄²	—	2	1	no	—
205	C₄²	—	2	1	no	—
206	C₄²	—	73	2	no	—
207	C₄²	—	73	2	no	—
208	C₁₆	—	4	2	no	—
209	C₁₆	—	292	2	no	—
210	C₂³	—	292	2	no	—
211	C₂³	—	73	2	no	—
212	C₂³	—	146	1	no	—
213	C₂³	—	146	1	no	—
214	C₂³	C₂×C₈×D₇₃	1	1	yes	characteristic
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	292	2	no	—
218	C₂×C₄	—	73	4	no	—
219	C₂×C₄	—	73	2	no	—
220	C₂×C₄	—	146	1	no	—
221	C₂×C₄	—	146	1	no	—
222	C₂×C₄	—	146	2	no	—
223	C₂×C₄	—	146	2	no	—
224	C₂×C₄	—	146	2	no	—
225	C₂×C₄	—	146	2	no	—
226	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
227	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
228	C₂×C₄	#14556548	1	1	yes	characteristic
229	C₂×C₄	M₁₆×D₇₃	1	1	yes	characteristic
230	C₂×C₄	M₁₆×D₇₃	1	1	yes	characteristic
231	C₂×C₄	C₂×#11924011	1	1	yes	characteristic
232	C₈	—	2	2	no	—
233	C₈	—	146	2	no	—
234	C₈	—	146	2	no	—
235	C₈	#14556564	1	2	yes	—
236	C₈	#14556569	1	2	yes	—
237	C₂²	—	2	2	no	—
238	C₂²	—	292	2	no	—
239	C₂²	—	292	2	no	—
240	C₂²	—	292	2	no	—
241	C₂²	—	146	2	no	—
242	C₂²	C₂²⋊C₈×D₇₃	1	1	yes	characteristic
243	C₂²	C₄⋊C₈×D₇₃	1	1	yes	characteristic
244	C₂²	#17988638	1	1	yes	characteristic
245	C₄	—	4	2	no	—
246	C₄	—	146	4	no	—
247	C₄	—	146	2	no	—
248	C₄	#17988446	1	1	yes	characteristic
249	C₄	#17988549	1	1	yes	characteristic
250	C₄	#17988609	1	1	yes	characteristic
251	C₄	#17988642	1	1	yes	characteristic
252	C₂	—	2	1	no	—
253	C₂	—	2	1	no	—
254	C₂	—	292	2	no	—
255	C₂	#22609910	1	1	yes	characteristic
256	C₂	#22611550	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988544

C₂

yes

maximal, characteristic

#22611686

C₂

yes

maximal, complemented

C₂×#17988368

C₂

yes

maximal

#22608015

C₂

yes

maximal, characteristic, complemented

C₇₃×#1377

C₂

yes

maximal, characteristic, complemented

C₂²×#11924011

C₂²

yes

characteristic

C₂²×C₈×D₇₃

C₄

yes

characteristic

C₂×#14556548

C₄

yes

characteristic

C₂×#14556531

C₂²

yes

—

#17988544

—

C₂×#14556501

C₄

yes

characteristic

C₂×C₄×#10596831

C₄

yes

characteristic

C₂×C₈×Dic₇₃

C₂²

yes

characteristic

#17988405

—

#17988368

—

C₂×M₃₂×C₇₃

C₂²

yes

—

C₂×#97×C₇₃

C₂²

yes

characteristic

C₂²×C₄×D₇₃

C₂×C₄

yes

—

—

D₄

yes

—

C₂×#11924011

Q₈

yes

—

C₂²×#10596831

C₂×C₄

yes

characteristic

C₂²×#10596831

C₂×C₄

yes

characteristic

C₂×C₈×D₇₃

—

C₂×C₈×D₇₃

—

C₂×C₈×D₇₃

—

#14556548

—

#14556548

—

C₂×#11924007

C₈

yes

—

C₂×#11924005

C₈

yes

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

—

—

—

—

—

C₈×Dic₇₃

D₄

yes

—

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

M₃₂×C₇₃

—

M₃₂×C₇₃

—

C₂×C₁₆×C₇₃

—

#97×C₇₃

—

C₂³×D₇₃

C₂×C₈

yes

characteristic

C₂²×Dic₇₃

C₂×C₈

yes

characteristic

C₂²×Dic₇₃

C₂×C₈

yes

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₄⋊C₄

yes

—

C₂×C₄×D₇₃

M₁₆

yes

—

—

—

—

—

—

—

C₂²⋊C₄

yes

—

C₂×#10596831

C₄⋊C₄

yes

—

C₈×D₇₃

—

#11924007

—

#11924005

—

C₄×Dic₇₃

C₂²⋊C₄

yes

—

C₄×Dic₇₃

M₁₆

yes

—

#11924003

—

C₂²×C₄×C₇₃

C₂×C₈

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

M₁₆

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₇₃

#41

yes

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₁₆×C₇₃

—

C₂³×C₇₃

C₂²×C₈

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

C₄⋊C₈

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

#117

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₈

yes

—

C₂×Dic₇₃

C₄⋊C₈

yes

—

C₄×D₇₃

—

100

C₄×D₇₃

—

101

C₄×D₇₃

—

102

C₄×D₇₃

—

103

C₈×C₇₃

—

104

C₈×C₇₃

#121

yes

—

105

C₈×C₇₃

C₂²⋊Q₈

yes

—

106

#10596831

—

107

#10596831

—

108

C₂²×C₇₃

—

109

C₂²×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

110

C₂²×C₇₃

C₂×C₄⋊C₈

yes

characteristic

111

C₂²×C₇₃

#431

yes

characteristic

112

C₂×D₇₃

—

113

C₂×D₇₃

—

114

C₂×D₇₃

—

115

C₂×D₇₃

—

116

C₄×C₇₃

—

117

C₄×C₇₃

#380

yes

characteristic

118

C₄×C₇₃

#407

yes

characteristic

119

C₄×C₇₃

#423

yes

characteristic

120

C₄×C₇₃

#432

yes

characteristic

121

Dic₇₃

—

122

Dic₇₃

—

123

#12786

—

maximal, Sylow

124

C₂×C₇₃

—

125

C₂×C₇₃

—

126

C₂×C₇₃

#1797

yes

characteristic

127

C₂×C₇₃

#2115

yes

—

128

D₇₃

—

129

C₂×#405

—

130

#2150

—

131

C₂×#349

—

132

#1377

—

133

#1377

D₇₃

yes

characteristic, complemented

134

C₇₃

#12786

yes

characteristic, complemented, Sylow

135

C₂²×M₁₆

—

136

C₂³×C₈

—

137

C₂×#117

—

138

C₂×M₃₂

—

139

C₂×M₃₂

C₂×D₇₃

yes

—

140

#405

—

146

—

141

C₂×#97

—

142

C₂×#97

C₂×D₇₃

yes

characteristic

143

C₂×C₄×C₈

—

144

C₂×C₄×C₈

—

145

C₄⋊C₁₆

—

146

—

146

#349

—

146

—

147

C₂³×C₄

—

148

C₂×M₁₆

—

149

C₂×M₁₆

—

150

C₂×M₁₆

—

146

—

151

C₂×M₁₆

—

146

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

146

—

155

C₂²×C₈

—

146

—

156

C₂²×C₈

—

146

—

157

C₂²×C₈

C₄×D₇₃

yes

characteristic

158

C₂²×C₈

C₂²×D₇₃

yes

characteristic

159

#117

—

146

—

160

#117

—

146

—

161

C₂×C₄⋊C₄

—

162

C₂×C₂²⋊C₄

—

163

C₂×C₄²

—

164

C₂×C₄²

C₄×D₇₃

yes

characteristic

165

M₃₂

—

166

M₃₂

—

167

M₃₂

—

146

—

168

M₃₂

—

146

—

169

C₂×C₁₆

—

170

C₂×C₁₆

—

146

—

171

#97

—

172

#97

—

146

—

173

C₄×C₈

—

174

C₄×C₈

—

146

—

175

C₂⁴

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

146

—

181

C₂²×C₄

—

146

—

182

C₂²×C₄

—

146

—

183

C₂²×C₄

—

146

—

184

C₂²×C₄

C₈×D₇₃

yes

—

185

C₂²×C₄

C₂×C₄×D₇₃

yes

characteristic

186

M₁₆

—

146

—

187

M₁₆

—

146

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

146

—

193

C₂×C₈

—

146

—

194

C₂×C₈

—

146

—

195

C₂×C₈

—

146

—

196

C₂×C₈

—

146

—

197

C₂×C₈

#11924011

yes

—

198

C₂×C₈

D₄×D₇₃

yes

characteristic

199

C₂×C₈

D₄×D₇₃

yes

—

200

C₂×C₈

Q₈×D₇₃

yes

characteristic

201

C₂×C₈

#11924028

yes

—

202

C₄⋊C₄

—

146

—

203

C₂²⋊C₄

—

146

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₁₆

—

209

C₁₆

—

292

—

210

C₂³

—

292

—

211

C₂³

—

212

C₂³

—

146

—

213

C₂³

—

146

—

214

C₂³

C₂×C₈×D₇₃

yes

characteristic

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

292

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

146

—

221

C₂×C₄

—

146

—

222

C₂×C₄

—

146

—

223

C₂×C₄

—

146

—

224

C₂×C₄

—

146

—

225

C₂×C₄

—

146

—

226

C₂×C₄

C₂²⋊C₄×D₇₃

yes

characteristic

227

C₂×C₄

C₄⋊C₄×D₇₃

yes

characteristic

228

C₂×C₄

#14556548

yes

characteristic

229

C₂×C₄

M₁₆×D₇₃

yes

characteristic

230

C₂×C₄

M₁₆×D₇₃

yes

characteristic

231

C₂×C₄

C₂×#11924011

yes

characteristic

232

C₈

—

233

C₈

—

146

—

234

C₈

—

146

—

235

C₈

#14556564

yes

—

236

C₈

#14556569

yes

—

237

C₂²

—

238

C₂²

—

292

—

239

C₂²

—

292

—

240

C₂²

—

292

—

241

C₂²

—

146

—

242

C₂²

C₂²⋊C₈×D₇₃

yes

characteristic

243

C₂²

C₄⋊C₈×D₇₃

yes

characteristic

244

C₂²

#17988638

yes

characteristic

245

C₄

—

246

C₄

—

146

—

247

C₄

—

146

—

248

C₄

#17988446

yes

characteristic

249

C₄

#17988549

yes

characteristic

250

C₄

#17988609

yes

characteristic

251

C₄

#17988642

yes

characteristic

252

C₂

—

253

C₂

—

254

C₂

—

292

—

255

C₂

#22609910

yes

characteristic

256

C₂

#22611550

yes

—

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₇₃
commutator	C₂³×C₇₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₇₃×#1377	C₂
socle	C₂²×C₇₃	C₂×C₂²⋊C₈
prime radical	C₂³×D₇₃	C₂×C₈
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	#1377	D₇₃
hypocenter	C₇₃	#12786
LCS	G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1377

subgroup

G/H

center

C₂×C₄

C₂²⋊C₄×D₇₃

commutator

C₂³×C₇₃

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₇₃×#1377

C₂

socle

C₂²×C₇₃

C₂×C₂²⋊C₈

prime radical

C₂³×D₇₃

C₂×C₈

cosocle

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1377

N	H ≅ G/N	type
2. #22611686	C₂	semidirect
4. #22608015	C₂	semidirect
5. C₇₃×#1377	C₂	semidirect
133. #1377	D₇₃	semidirect
134. C₇₃	#12786	semidirect

H ≅ G/N

type

2. #22611686

C₂

semidirect

4. #22608015

C₂

semidirect

5. C₇₃×#1377

C₂

semidirect

133. #1377

D₇₃

semidirect

134. C₇₃

#12786

semidirect

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

subgroup	index
C₂×#17988544	2
#22611686	2
C₂×#17988368	2
#22608015	2
C₇₃×#1377	2
#12786	73

subgroup

index

C₇₃×#1377

Subgroups — #33001916

Conjugacy classes of subgroups

Complements

Maximal subgroups