Group #34007646 — subgroups

Subgroups — #34007646

Order 18688.

486 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 148 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	#22626100	C₂	1	2	yes	maximal
2	C₂×#17989448	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊#10596833	C₂	1	2	yes	maximal
4	C₂×#17989428	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊#10596833	C₂²	1	2	yes	—
7	C₂×C₄×#10596833	C₂²	1	1	yes	characteristic
8	C₂×C₄×#10596833	C₂²	1	1	yes	characteristic
9	#17989453	—	2	4	no	—
10	#17989448	—	2	2	no	—
11	Q₈⋊#10596833	—	2	4	no	—
12	#17989428	—	2	2	no	—
13	C₂×Q₈×Dic₇₃	C₂²	1	2	yes	—
14	Q₁₆×Dic₇₃	—	2	2	no	—
15	Q₁₆×Dic₇₃	—	2	2	no	—
16	C₂×#14556525	C₄	1	1	yes	characteristic
17	C₂×#14556515	C₄	1	2	yes	—
18	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₇₃	C₄	1	1	yes	characteristic
20	C₂²×#10596833	—	2	2	no	—
21	C₂²×#10596833	—	2	1	no	—
22	C₂²×#10596833	D₄	1	2	yes	—
23	C₄⋊#10596833	—	2	2	no	—
24	C₄⋊#10596833	—	2	2	no	—
25	C₄×#10596833	—	2	1	no	—
26	C₄×#10596833	—	2	1	no	—
27	C₄×#10596833	—	2	1	no	—
28	C₄×#10596833	D₄	1	2	yes	—
29	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
30	Q₈×Dic₇₃	—	2	2	no	—
31	Q₈×Dic₇₃	—	2	2	no	—
32	Q₈×Dic₇₃	—	2	2	no	—
33	Q₈×Dic₇₃	—	2	2	no	—
34	C₂×C₄⋊Dic₇₃	—	2	2	no	—
35	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
36	C₂×C₄×Dic₇₃	—	2	2	no	—
37	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
38	#14556525	—	2	2	no	—
39	#14556515	—	2	4	no	—
40	C₈×Dic₇₃	D₄	1	2	yes	—
41	C₈×Dic₇₃	D₄	1	2	yes	—
42	C₂²×Q₈×C₇₃	C₂×C₄	1	2	yes	—
43	C₂×Q₁₆×C₇₃	—	2	2	no	—
44	C₂×Q₁₆×C₇₃	—	2	2	no	—
45	C₂×Q₁₆×C₇₃	C₈	1	4	yes	complemented
46	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
47	C₂×#10596833	—	2	2	no	—
48	C₂×#10596833	—	2	2	no	—
49	C₂×#10596833	—	2	4	no	—
50	C₂×#10596833	—	4	2	no	—
51	C₂×#10596833	—	4	2	no	—
52	C₂×#10596833	—	4	4	no	—
53	C₂²×Dic₇₃	—	2	2	no	—
54	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×Dic₇₃	#41	1	1	yes	characteristic
56	C₂×#10596831	—	2	1	no	—
57	C₂×#10596831	—	2	1	no	—
58	C₂×#10596831	C₂²⋊C₄	1	2	yes	—
59	C₄⋊Dic₇₃	—	2	2	no	—
60	C₄⋊Dic₇₃	—	2	2	no	—
61	C₄⋊Dic₇₃	—	4	2	no	—
62	C₄⋊Dic₇₃	—	4	2	no	—
63	C₄×Dic₇₃	—	4	2	no	—
64	C₄×Dic₇₃	—	4	2	no	—
65	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
66	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
67	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
68	C₄×Dic₇₃	#41	1	1	yes	characteristic
69	C₂×Q₈×C₇₃	—	2	2	no	—
70	C₂×Q₈×C₇₃	—	2	2	no	—
71	C₂×Q₈×C₇₃	—	2	2	no	—
72	C₂×Q₈×C₇₃	—	2	2	no	—
73	C₂×Q₈×C₇₃	—	2	2	no	—
74	C₂×Q₈×C₇₃	C₂×C₈	1	4	yes	—
75	C₂²×C₄×C₇₃	—	2	2	no	—
76	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
77	Q₁₆×C₇₃	—	2	8	no	—
78	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
79	C₂×C₈×C₇₃	C₂×C₈	1	2	yes	—
80	C₂×C₈×C₇₃	M₁₆	1	2	yes	—
81	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
82	Q₈×C₇₃	—	2	4	no	—
83	Q₈×C₇₃	—	2	4	no	—
84	Q₈×C₇₃	—	4	2	no	—
85	Q₈×C₇₃	—	4	2	no	—
86	C₂×C₄×C₇₃	—	2	4	no	—
87	C₂×C₄×C₇₃	—	4	2	no	—
88	C₂×C₄×C₇₃	—	4	2	no	—
89	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
91	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
92	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
93	C₂×C₄×C₇₃	#131	1	1	yes	characteristic
94	C₂×C₄×C₇₃	#131	1	1	yes	characteristic
95	C₂×Dic₇₃	—	2	2	no	—
96	C₂×Dic₇₃	—	4	2	no	—
97	C₂×Dic₇₃	—	4	4	no	—
98	C₂×Dic₇₃	#121	1	1	yes	characteristic
99	C₂×Dic₇₃	#121	1	1	yes	characteristic
100	C₂×Dic₇₃	#124	1	1	yes	characteristic
101	C₂×Dic₇₃	#127	1	1	yes	characteristic
102	C₂×Dic₇₃	#137	1	4	yes	—
103	#10596833	—	4	2	no	—
104	#10596833	—	4	2	no	—
105	#10596833	—	8	2	no	—
106	C₈×C₇₃	C₂²⋊C₈	1	4	yes	—
107	#10596831	—	2	2	no	—
108	C₂²×C₇₃	#390	1	1	yes	characteristic
109	C₂²×C₇₃	C₈×D₄	1	1	yes	characteristic
110	C₂²×C₇₃	#436	1	1	yes	characteristic
111	C₂²×C₇₃	#441	1	2	yes	—
112	C₂²×C₇₃	#444	1	2	yes	—
113	C₄×C₇₃	—	4	4	no	—
114	C₄×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
115	C₄×C₇₃	#408	1	1	yes	characteristic
116	C₄×C₇₃	C₈×D₄	1	1	yes	characteristic
117	C₄×C₇₃	#436	1	1	yes	characteristic
118	Dic₇₃	—	2	1	no	—
119	Dic₇₃	—	2	1	no	—
120	Dic₇₃	—	8	2	no	—
121	Dic₇₃	#470	1	2	yes	—
122	Dic₇₃	#497	1	2	yes	—
123	#9658	—	73	1	no	maximal, Sylow
124	C₂×C₇₃	#1579	1	2	yes	—
125	C₂×C₇₃	#1593	1	2	yes	—
126	C₂×C₇₃	#1954	1	1	yes	characteristic
127	C₂×C₇₃	#1971	1	1	yes	characteristic
128	C₂×C₇₃	#1975	1	1	yes	characteristic
129	C₂×C₄×Q₁₆	—	73	1	no	—
130	#1984	—	73	2	no	—
131	C₂×#334	—	73	1	no	—
132	C₂×Q₈⋊C₈	—	73	2	no	—
133	C₂×#322	—	73	1	no	—
134	C₇₃	#9658	1	1	yes	characteristic, complemented, Sylow
135	C₂²×Q₁₆	#64408	1	1	yes	characteristic
136	C₂×C₄×Q₈	—	73	2	no	—
137	C₄×Q₁₆	—	146	2	no	—
138	C₄×Q₁₆	—	146	2	no	—
139	C₂×#107	—	73	1	no	—
140	C₂×C₄⋊C₈	—	73	2	no	—
141	C₂×#103	—	73	2	no	—
142	C₂×C₄×C₈	—	73	1	no	—
143	C₂×C₄×C₈	—	73	1	no	—
144	C₂×C₄×C₈	—	73	1	no	—
145	#336	—	146	4	no	—
146	#334	—	146	2	no	—
147	Q₈⋊C₈	—	146	4	no	—
148	#322	—	146	2	no	—
149	C₂²×Q₈	C₂×#64408	1	2	yes	—
150	C₂×Q₁₆	—	2	2	no	—
151	C₂×Q₁₆	—	2	2	no	—
152	C₂×Q₁₆	#10596833	1	4	yes	complemented
153	C₂²×C₈	—	73	1	no	—
154	C₂²×C₈	—	73	2	no	—
155	C₂²×C₈	—	146	2	no	—
156	C₂²×C₈	—	146	1	no	—
157	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
158	C₄×Q₈	—	146	2	no	—
159	C₄×Q₈	—	146	2	no	—
160	C₄×Q₈	—	146	2	no	—
161	C₄×Q₈	—	146	2	no	—
162	C₂×C₄⋊C₄	—	73	2	no	—
163	C₂×C₄⋊C₄	—	146	2	no	—
164	C₂×C₄²	—	73	1	no	—
165	C₂×C₄²	—	146	2	no	—
166	#107	—	146	2	no	—
167	C₄⋊C₈	—	146	2	no	—
168	C₄⋊C₈	—	146	2	no	—
169	#103	—	146	4	no	—
170	C₄×C₈	—	73	2	no	—
171	C₄×C₈	—	73	2	no	—
172	C₄×C₈	—	73	2	no	—
173	C₄×C₈	—	146	1	no	—
174	C₄×C₈	—	146	1	no	—
175	C₄×C₈	—	146	1	no	—
176	C₂×Q₈	—	2	2	no	—
177	C₂×Q₈	—	2	2	no	—
178	C₂×Q₈	—	2	2	no	—
179	C₂×Q₈	—	2	2	no	—
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	C₂×#10596833	1	4	yes	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	—	73	1	no	—
184	C₂²×C₄	—	73	1	no	—
185	C₂²×C₄	—	146	2	no	—
186	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
187	Q₁₆	—	2	8	no	—
188	C₂×C₈	—	292	2	no	—
189	C₂×C₈	—	292	2	no	—
190	C₂×C₈	—	292	4	no	—
191	C₂×C₈	—	73	2	no	—
192	C₂×C₈	—	146	2	no	—
193	C₂×C₈	—	146	2	no	—
194	C₂×C₈	—	146	4	no	—
195	C₂×C₈	—	146	1	no	—
196	C₂×C₈	—	146	1	no	—
197	C₂×C₈	C₂²⋊#64408	1	2	yes	—
198	C₂×C₈	C₂×#10596833	1	2	yes	—
199	C₂×C₈	#11924037	1	2	yes	—
200	C₄⋊C₄	—	292	2	no	—
201	C₄⋊C₄	—	292	2	no	—
202	C₄⋊C₄	—	146	2	no	—
203	C₄⋊C₄	—	146	2	no	—
204	C₄²	—	292	2	no	—
205	C₄²	—	292	2	no	—
206	C₄²	—	73	1	no	—
207	C₄²	—	73	1	no	—
208	C₄²	—	73	1	no	—
209	C₄²	—	73	1	no	—
210	C₂³	D₄×#64408	1	1	yes	characteristic
211	Q₈	—	2	4	no	—
212	Q₈	—	2	4	no	—
213	Q₈	—	4	2	no	—
214	Q₈	—	4	2	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	292	4	no	—
219	C₂×C₄	—	292	2	no	—
220	C₂×C₄	—	73	1	no	—
221	C₂×C₄	—	73	1	no	—
222	C₂×C₄	—	73	4	no	—
223	C₂×C₄	—	73	1	no	—
224	C₂×C₄	—	73	1	no	—
225	C₂×C₄	—	146	2	no	—
226	C₂×C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
227	C₂×C₄	D₄×#64408	1	1	yes	characteristic
228	C₂×C₄	C₂²×#10596833	1	1	yes	characteristic
229	C₂×C₄	C₂×#11924037	1	1	yes	characteristic
230	C₂×C₄	#14556678	1	1	yes	characteristic
231	C₂×C₄	#14556678	1	1	yes	characteristic
232	C₈	—	292	2	no	—
233	C₈	—	292	2	no	—
234	C₈	—	584	2	no	—
235	C₈	—	146	2	no	—
236	C₈	C₂²⋊#10596833	1	4	yes	—
237	C₂²	#17989539	1	1	yes	characteristic
238	C₂²	D₄×#10596833	1	1	yes	characteristic
239	C₂²	#17989622	1	1	yes	characteristic
240	C₂²	#17989627	1	2	yes	—
241	C₂²	#17989633	1	2	yes	—
242	C₄	—	4	4	no	—
243	C₄	—	584	2	no	—
244	C₄	—	73	2	no	—
245	C₄	—	73	2	no	—
246	C₄	—	146	1	no	—
247	C₄	—	146	1	no	—
248	C₄	C₂×C₂²⋊#10596833	1	1	yes	characteristic
249	C₄	#17989561	1	1	yes	characteristic
250	C₄	D₄×#10596833	1	1	yes	characteristic
251	C₄	#17989622	1	1	yes	characteristic
252	C₂	#22625524	1	2	yes	—
253	C₂	#22625578	1	2	yes	—
254	C₂	#22626052	1	1	yes	characteristic
255	C₂	#22626079	1	1	yes	characteristic
256	C₂	#22626085	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22626100

C₂

yes

maximal

C₂×#17989448

C₂

yes

maximal, characteristic

C₂×Q₈⋊#10596833

C₂

yes

maximal

C₂×#17989428

C₂

yes

maximal, characteristic

C₂×Q₁₆×Dic₇₃

C₂

yes

maximal, characteristic

C₂×C₄⋊#10596833

C₂²

yes

—

C₂×C₄×#10596833

C₂²

yes

characteristic

C₂×C₄×#10596833

C₂²

yes

—

—

—

—

C₂×Q₈×Dic₇₃

C₂²

yes

—

Q₁₆×Dic₇₃

—

Q₁₆×Dic₇₃

—

C₂×#14556525

C₄

yes

characteristic

C₂×#14556515

C₄

yes

—

C₂×C₈×Dic₇₃

C₂²

yes

characteristic

C₂²×Q₁₆×C₇₃

C₄

yes

—

—

D₄

yes

—

—

—

—

—

—

D₄

yes

—

C₂²×#10596831

C₂×C₄

yes

characteristic

Q₈×Dic₇₃

—

Q₈×Dic₇₃

—

Q₈×Dic₇₃

—

Q₈×Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

—

C₂×C₄×Dic₇₃

C₂³

yes

characteristic

#14556525

—

#14556515

—

C₈×Dic₇₃

D₄

yes

—

C₈×Dic₇₃

D₄

yes

—

C₂²×Q₈×C₇₃

C₂×C₄

yes

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

C₈

yes

complemented

C₂²×C₈×C₇₃

C₂×C₄

yes

—

—

—

—

—

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

C₂×D₄

yes

C₂²×Dic₇₃

yes

—

—

C₂²⋊C₄

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂×D₄

yes

characteristic

C₄×Dic₇₃

C₂×D₄

yes

characteristic

C₄×Dic₇₃

C₂×D₄

yes

characteristic

C₄×Dic₇₃

#41

yes

characteristic

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

C₂×C₈

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

C₂×C₈

yes

—

C₂×C₈×C₇₃

M₁₆

yes

—

C₂³×C₇₃

C₄×D₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

yes

C₂×Dic₇₃

yes

100

C₂×Dic₇₃

#124

yes

characteristic

101

C₂×Dic₇₃

#127

yes

characteristic

102

C₂×Dic₇₃

#137

yes

—

103

#10596833

—

104

#10596833

—

105

#10596833

—

106

C₈×C₇₃

C₂²⋊C₈

yes

—

107

#10596831

—

108

C₂²×C₇₃

#390

yes

characteristic

109

C₂²×C₇₃

C₈×D₄

yes

characteristic

110

C₂²×C₇₃

#436

yes

characteristic

111

C₂²×C₇₃

#441

yes

—

112

C₂²×C₇₃

#444

yes

—

113

C₄×C₇₃

—

114

C₄×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

115

C₄×C₇₃

#408

yes

characteristic

116

C₄×C₇₃

C₈×D₄

yes

characteristic

117

C₄×C₇₃

#436

yes

characteristic

118

Dic₇₃

—

119

Dic₇₃

—

120

Dic₇₃

—

121

Dic₇₃

#470

yes

—

122

Dic₇₃

#497

yes

—

123

#9658

—

maximal, Sylow

124

C₂×C₇₃

#1579

yes

—

125

C₂×C₇₃

#1593

yes

—

126

C₂×C₇₃

#1954

yes

characteristic

127

C₂×C₇₃

#1971

yes

characteristic

128

C₂×C₇₃

#1975

yes

characteristic

129

C₂×C₄×Q₁₆

—

130

#1984

—

131

C₂×#334

—

132

C₂×Q₈⋊C₈

—

133

C₂×#322

—

134

C₇₃

#9658

yes

characteristic, complemented, Sylow

135

C₂²×Q₁₆

#64408

yes

characteristic

136

C₂×C₄×Q₈

—

137

C₄×Q₁₆

—

146

—

138

C₄×Q₁₆

—

146

—

139

C₂×#107

—

140

C₂×C₄⋊C₈

—

141

C₂×#103

—

142

C₂×C₄×C₈

—

143

C₂×C₄×C₈

—

144

C₂×C₄×C₈

—

145

#336

—

146

—

146

#334

—

146

—

147

Q₈⋊C₈

—

146

—

148

#322

—

146

—

149

C₂²×Q₈

C₂×#64408

yes

—

150

C₂×Q₁₆

—

151

C₂×Q₁₆

—

152

C₂×Q₁₆

#10596833

yes

complemented

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

—

146

—

156

C₂²×C₈

—

146

—

157

C₂²×C₈

C₂×#64408

yes

characteristic

158

C₄×Q₈

—

146

—

159

C₄×Q₈

—

146

—

160

C₄×Q₈

—

146

—

161

C₄×Q₈

—

146

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

—

146

—

164

C₂×C₄²

—

165

C₂×C₄²

—

146

—

166

#107

—

146

—

167

C₄⋊C₈

—

146

—

168

C₄⋊C₈

—

146

—

169

#103

—

146

—

170

C₄×C₈

—

171

C₄×C₈

—

172

C₄×C₈

—

173

C₄×C₈

—

146

—

174

C₄×C₈

—

146

—

175

C₄×C₈

—

146

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂×Q₈

C₂×#10596833

yes

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

146

—

186

C₂²×C₄

C₂²×#64408

yes

characteristic

187

Q₁₆

—

188

C₂×C₈

—

292

—

189

C₂×C₈

—

292

—

190

C₂×C₈

—

292

—

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

C₂²⋊#64408

yes

—

198

C₂×C₈

C₂×#10596833

yes

—

199

C₂×C₈

#11924037

yes

—

200

C₄⋊C₄

—

292

—

201

C₄⋊C₄

—

292

—

202

C₄⋊C₄

—

146

—

203

C₄⋊C₄

—

146

—

204

C₄²

—

292

—

205

C₄²

—

292

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

210

C₂³

D₄×#64408

yes

characteristic

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

Q₈

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

292

—

219

C₂×C₄

—

292

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

146

—

226

C₂×C₄

C₂×C₂²⋊#64408

yes

characteristic

227

C₂×C₄

D₄×#64408

yes

characteristic

228

C₂×C₄

C₂²×#10596833

yes

characteristic

229

C₂×C₄

C₂×#11924037

yes

characteristic

230

C₂×C₄

#14556678

yes

characteristic

231

C₂×C₄

#14556678

yes

characteristic

232

C₈

—

292

—

233

C₈

—

292

—

234

C₈

—

584

—

235

C₈

—

146

—

236

C₈

C₂²⋊#10596833

yes

—

237

C₂²

#17989539

yes

characteristic

238

C₂²

D₄×#10596833

yes

characteristic

239

C₂²

#17989622

yes

characteristic

240

C₂²

#17989627

yes

—

241

C₂²

#17989633

yes

—

242

C₄

—

243

C₄

—

584

—

244

C₄

—

245

C₄

—

246

C₄

—

146

—

247

C₄

—

146

—

248

C₄

C₂×C₂²⋊#10596833

yes

characteristic

249

C₄

#17989561

yes

characteristic

250

C₄

D₄×#10596833

yes

characteristic

251

C₄

#17989622

yes

characteristic

252

C₂

#22625524

yes

—

253

C₂

#22625578

yes

—

254

C₂

#22626052

yes

characteristic

255

C₂

#22626079

yes

characteristic

256

C₂

#22626085

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×#64408
commutator	C₂×C₄×C₇₃	C₂²×C₈
Frattini	C₂²×C₄	C₂²×#64408
Fitting	C₂²×Q₁₆×C₇₃	C₄
socle, prime radical	C₂³×C₇₃	C₄×D₄
cosocle	C₂×C₄×Dic₇₃	C₂³
hypercenter	C₂²×Q₁₆	#64408
hypocenter	C₇₃	#9658
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂³

D₄×#64408

commutator

C₂×C₄×C₇₃

C₂²×C₈

Frattini

C₂²×C₄

C₂²×#64408

Fitting

C₂²×Q₁₆×C₇₃

C₄

socle, prime radical

C₂³×C₇₃

C₄×D₄

cosocle

C₂×C₄×Dic₇₃

C₂³

C₂²×Q₁₆

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
45. C₂×Q₁₆×C₇₃	C₈	semidirect
134. C₇₃	#9658	semidirect
152. C₂×Q₁₆	#10596833	semidirect

H ≅ G/N

type

45. C₂×Q₁₆×C₇₃

C₈

semidirect

134. C₇₃

#9658

semidirect

152. C₂×Q₁₆

#10596833

semidirect

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

subgroup	index
#22626100	2
C₂×#17989448	2
C₂×Q₈⋊#10596833	2
C₂×#17989428	2
C₂×Q₁₆×Dic₇₃	2
#9658	73

subgroup

index

C₂×Q₁₆×Dic₇₃

Subgroups — #34007646

Conjugacy classes of subgroups

Complements

Maximal subgroups