Group #34187169 — subgroups

Subgroups — #34187169

Order 20224.

482 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 147 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×C₄×Dic₃₁₆	C₂	1	1	yes	maximal, characteristic
2	#23764335	C₂	1	2	yes	maximal
3	C₂×#19098293	C₂	1	2	yes	maximal
4	C₂×#19098285	C₂	1	1	yes	maximal, characteristic
5	C₂×#334×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₁₆	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₁₅₈	C₂²	1	2	yes	—
8	C₄×Dic₃₁₆	—	2	2	no	—
9	C₄×Dic₃₁₆	—	2	2	no	—
10	C₂×#14579095	C₄	1	1	yes	characteristic
11	C₂×#14579086	C₄	1	2	yes	—
12	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
14	#19098317	—	2	4	no	—
15	#19098293	—	2	4	no	—
16	#19098285	—	2	2	no	—
17	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	#334×C₇₉	—	2	2	no	—
20	C₂²×Dic₁₅₈	C₂×C₄	1	2	yes	—
21	C₂×Dic₃₁₆	—	2	2	no	—
22	C₂×Dic₃₁₆	—	2	4	no	—
23	C₂²×C₇₉⋊C₈	—	2	1	no	—
24	C₂²×C₇₉⋊C₈	D₄	1	2	yes	—
25	C₄×Dic₁₅₈	—	2	2	no	—
26	C₄×Dic₁₅₈	—	2	2	no	—
27	C₄×Dic₁₅₈	—	2	2	no	—
28	C₄×Dic₁₅₈	—	2	2	no	—
29	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
30	C₂×Dic₇₉⋊C₄	—	2	2	no	—
31	C₂×C₄×Dic₇₉	—	2	2	no	—
32	#14579095	—	2	2	no	—
33	#14579086	—	2	4	no	—
34	C₄×C₇₉⋊C₈	—	2	1	no	—
35	C₄×C₇₉⋊C₈	—	2	1	no	—
36	C₄×C₇₉⋊C₈	—	2	1	no	—
37	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
38	C₂²×C₈×C₇₉	—	2	2	no	—
39	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₇₉	—	2	2	no	—
43	C₄⋊C₈×C₇₉	—	2	2	no	—
44	C₄×C₈×C₇₉	D₄	1	2	yes	—
45	C₄×C₈×C₇₉	D₄	1	2	yes	—
46	C₂×Dic₁₅₈	—	2	2	no	—
47	C₂×Dic₁₅₈	—	2	2	no	—
48	C₂×Dic₁₅₈	—	2	2	no	—
49	C₂×Dic₁₅₈	—	2	2	no	—
50	C₂×Dic₁₅₈	—	2	2	no	—
51	C₂×Dic₁₅₈	M₁₆	1	4	yes	—
52	C₂²×Dic₇₉	—	2	2	no	—
53	C₂²×Dic₇₉	—	2	2	no	—
54	Dic₃₁₆	—	2	8	no	—
55	C₂×C₇₉⋊C₈	—	2	4	no	—
56	C₂×C₇₉⋊C₈	—	2	2	no	—
57	C₂×C₇₉⋊C₈	—	2	2	no	—
58	C₂×C₇₉⋊C₈	—	2	4	no	—
59	C₄⋊Dic₇₉	—	2	2	no	—
60	C₄⋊Dic₇₉	—	2	2	no	—
61	Dic₇₉⋊C₄	—	4	2	no	—
62	Dic₇₉⋊C₄	—	4	2	no	—
63	C₄×Dic₇₉	—	4	2	no	—
64	C₄×Dic₇₉	—	4	2	no	—
65	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
68	C₂×C₈×C₇₉	—	2	2	no	—
69	C₂×C₈×C₇₉	—	2	2	no	—
70	C₂×C₈×C₇₉	—	4	2	no	—
71	C₂×C₈×C₇₉	—	4	4	no	—
72	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
74	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₇₉	#41	1	1	yes	characteristic
78	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
79	C₂×C₄×C₇₉	—	2	2	no	—
80	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
82	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
83	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
84	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
85	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
86	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
87	C₂×C₄×C₇₉	#131	1	2	yes	—
88	C₂×C₄×C₇₉	#137	1	4	yes	—
89	C₂×Dic₇₉	—	2	4	no	—
90	C₂×Dic₇₉	—	4	2	no	—
91	C₂×Dic₇₉	—	4	2	no	—
92	C₂×Dic₇₉	—	4	2	no	—
93	C₂×Dic₇₉	—	4	4	no	—
94	Dic₁₅₈	—	2	4	no	—
95	Dic₁₅₈	—	2	4	no	—
96	Dic₁₅₈	—	4	2	no	—
97	Dic₁₅₈	—	4	2	no	—
98	C₈×C₇₉	—	2	2	no	—
99	C₈×C₇₉	—	2	2	no	—
100	C₈×C₇₉	—	8	2	no	—
101	C₇₉⋊C₈	—	2	4	no	—
102	C₇₉⋊C₈	—	4	2	no	—
103	C₂²×C₇₉	#390	1	1	yes	characteristic
104	C₂²×C₇₉	#435	1	2	yes	—
105	C₂²×C₇₉	#441	1	2	yes	—
106	C₂²×C₇₉	#443	1	2	yes	—
107	C₄×C₇₉	—	2	1	no	—
108	C₄×C₇₉	—	2	1	no	—
109	C₄×C₇₉	#407	1	1	yes	characteristic
110	C₄×C₇₉	#408	1	1	yes	characteristic
111	C₄×C₇₉	#435	1	2	yes	—
112	C₄×C₇₉	#470	1	2	yes	—
113	C₄×C₇₉	#497	1	2	yes	—
114	Dic₇₉	—	4	4	no	—
115	Dic₇₉	—	8	2	no	—
116	#9664	—	79	1	no	maximal, Sylow
117	C₂×C₇₉	#1587	1	4	yes	—
118	C₂×C₇₉	#1955	1	1	yes	characteristic
119	C₂×C₇₉	#1971	1	1	yes	characteristic
120	C₂×C₇₉	#1974	1	1	yes	characteristic
121	C₂×C₄×Q₁₆	—	79	1	no	—
122	#1984	—	79	2	no	—
123	C₂×#334	D₇₉	1	1	yes	characteristic
124	C₂×Q₈⋊C₈	—	79	2	no	—
125	C₂×#322	—	79	1	no	—
126	C₇₉	#9664	1	1	yes	characteristic, complemented, Sylow
127	C₂²×Q₁₆	—	79	1	no	—
128	C₂×C₄×Q₈	—	79	2	no	—
129	C₄×Q₁₆	—	158	2	no	—
130	C₄×Q₁₆	—	158	2	no	—
131	C₂×#107	—	79	1	no	—
132	C₂×C₄⋊C₈	C₂×D₇₉	1	2	yes	—
133	C₂×#103	—	79	2	no	—
134	C₂×C₄×C₈	—	79	1	no	—
135	C₂×C₄×C₈	—	79	1	no	—
136	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
137	#336	—	158	4	no	—
138	#334	—	2	2	no	—
139	Q₈⋊C₈	—	158	4	no	—
140	#322	—	158	2	no	—
141	C₂²×Q₈	—	79	2	no	—
142	C₂×Q₁₆	—	158	4	no	—
143	C₂×Q₁₆	—	158	2	no	—
144	C₂²×C₈	—	2	2	no	—
145	C₂²×C₈	—	79	2	no	—
146	C₂²×C₈	—	158	1	no	—
147	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
148	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
149	C₄×Q₈	—	158	2	no	—
150	C₄×Q₈	—	158	2	no	—
151	C₄×Q₈	—	158	2	no	—
152	C₄×Q₈	—	158	2	no	—
153	C₂×C₄⋊C₄	—	79	2	no	—
154	C₂×C₄⋊C₄	—	158	2	no	—
155	C₂×C₄²	—	158	2	no	—
156	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
157	#107	—	158	2	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	2	2	no	—
160	#103	—	158	4	no	—
161	C₄×C₈	—	79	2	no	—
162	C₄×C₈	—	158	1	no	—
163	C₄×C₈	—	158	1	no	—
164	C₄×C₈	—	158	1	no	—
165	C₄×C₈	D₃₁₆	1	2	yes	—
166	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
167	C₂×Q₈	—	79	4	no	—
168	C₂×Q₈	—	158	2	no	—
169	C₂×Q₈	—	158	2	no	—
170	C₂×Q₈	—	158	2	no	—
171	C₂×Q₈	—	158	2	no	—
172	C₂×Q₈	—	158	2	no	—
173	C₂²×C₄	—	158	2	no	—
174	C₂²×C₄	—	158	2	no	—
175	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
176	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
177	C₂²×C₄	#11929625	1	1	yes	characteristic
178	Q₁₆	—	158	8	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	4	4	no	—
183	C₂×C₈	—	158	2	no	—
184	C₂×C₈	—	158	4	no	—
185	C₂×C₈	—	158	4	no	—
186	C₂×C₈	—	158	2	no	—
187	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
188	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
189	C₄⋊C₄	—	316	2	no	—
190	C₄⋊C₄	—	316	2	no	—
191	C₄⋊C₄	—	158	2	no	—
192	C₄⋊C₄	—	158	2	no	—
193	C₄²	—	316	2	no	—
194	C₄²	—	316	2	no	—
195	C₄²	D₄×D₇₉	1	1	yes	characteristic
196	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
197	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
198	C₄²	#11929625	1	1	yes	characteristic
199	C₂³	#14579123	1	1	yes	characteristic
200	Q₈	—	316	2	no	—
201	Q₈	—	316	2	no	—
202	Q₈	—	158	4	no	—
203	Q₈	—	158	4	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	316	2	no	—
206	C₂×C₄	—	316	2	no	—
207	C₂×C₄	—	316	4	no	—
208	C₂×C₄	—	316	2	no	—
209	C₂×C₄	—	158	4	no	—
210	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
211	C₂×C₄	#14579123	1	1	yes	characteristic
212	C₂×C₄	#14579136	1	1	yes	characteristic
213	C₂×C₄	#14579136	1	1	yes	characteristic
214	C₂×C₄	#14579150	1	1	yes	characteristic
215	C₂×C₄	#14579157	1	1	yes	characteristic
216	C₂×C₄	M₁₆×D₇₉	1	2	yes	—
217	C₂×C₄	#14579167	1	2	yes	—
218	C₂×C₄	#14579190	1	4	yes	—
219	C₈	—	2	2	no	—
220	C₈	—	2	2	no	—
221	C₈	—	8	2	no	—
222	C₈	—	316	2	no	—
223	C₈	—	158	4	no	—
224	C₂²	#19098464	1	1	yes	characteristic
225	C₂²	#19098633	1	2	yes	—
226	C₂²	#19098669	1	2	yes	—
227	C₂²	#19098679	1	2	yes	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	316	4	no	—
231	C₄	—	632	2	no	—
232	C₄	#19098526	1	1	yes	characteristic
233	C₄	#19098529	1	1	yes	characteristic
234	C₄	#19098633	1	2	yes	—
235	C₄	#19098822	1	2	yes	—
236	C₄	#19098954	1	2	yes	—
237	C₂	#23762270	1	4	yes	—
238	C₂	#23764197	1	1	yes	characteristic
239	C₂	#23764269	1	1	yes	characteristic
240	C₂	#23764286	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₃₁₆

C₂

yes

maximal, characteristic

#23764335

C₂

yes

maximal

C₂×#19098293

C₂

yes

maximal

C₂×#19098285

C₂

yes

maximal, characteristic

C₂×#334×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₃₁₆

C₄

yes

characteristic

C₂×C₄×Dic₁₅₈

C₂²

yes

—

C₄×Dic₃₁₆

—

C₄×Dic₃₁₆

—

C₂×#14579095

C₄

yes

characteristic

C₂×#14579086

C₄

yes

—

C₂×C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₇₉⋊C₈

C₂²

yes

—

—

—

C₂×C₄⋊C₈×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#334×C₇₉

—

C₂²×Dic₁₅₈

C₂×C₄

yes

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

D₄

yes

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₂×C₄⋊Dic₇₉

C₂×C₄

yes

—

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

#14579095

—

#14579086

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

D₄

yes

—

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄×C₈×C₇₉

D₄

yes

—

C₄×C₈×C₇₉

D₄

yes

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

M₁₆

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

Dic₃₁₆

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

#41

yes

characteristic

C₂³×C₇₉

C₄×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

C₂×M₁₆

yes

—

C₂×C₄×C₇₉

#131

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

100

C₈×C₇₉

—

101

C₇₉⋊C₈

—

102

C₇₉⋊C₈

—

103

C₂²×C₇₉

#390

yes

characteristic

104

C₂²×C₇₉

#435

yes

—

105

C₂²×C₇₉

#441

yes

—

106

C₂²×C₇₉

#443

yes

—

107

C₄×C₇₉

—

108

C₄×C₇₉

—

109

C₄×C₇₉

#407

yes

characteristic

110

C₄×C₇₉

#408

yes

characteristic

111

C₄×C₇₉

#435

yes

—

112

C₄×C₇₉

#470

yes

—

113

C₄×C₇₉

#497

yes

—

114

Dic₇₉

—

115

Dic₇₉

—

116

#9664

—

maximal, Sylow

117

C₂×C₇₉

#1587

yes

—

118

C₂×C₇₉

#1955

yes

characteristic

119

C₂×C₇₉

#1971

yes

characteristic

120

C₂×C₇₉

#1974

yes

characteristic

121

C₂×C₄×Q₁₆

—

122

#1984

—

123

C₂×#334

D₇₉

yes

characteristic

124

C₂×Q₈⋊C₈

—

125

C₂×#322

—

126

C₇₉

#9664

yes

characteristic, complemented, Sylow

127

C₂²×Q₁₆

—

128

C₂×C₄×Q₈

—

129

C₄×Q₁₆

—

158

—

130

C₄×Q₁₆

—

158

—

131

C₂×#107

—

132

C₂×C₄⋊C₈

C₂×D₇₉

yes

—

133

C₂×#103

—

134

C₂×C₄×C₈

—

135

C₂×C₄×C₈

—

136

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

137

#336

—

158

—

138

#334

—

139

Q₈⋊C₈

—

158

—

140

#322

—

158

—

141

C₂²×Q₈

—

142

C₂×Q₁₆

—

158

—

143

C₂×Q₁₆

—

158

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₂²×C₈

—

158

—

147

C₂²×C₈

C₄×D₇₉

yes

characteristic

148

C₂²×C₈

C₄×D₇₉

yes

characteristic

149

C₄×Q₈

—

158

—

150

C₄×Q₈

—

158

—

151

C₄×Q₈

—

158

—

152

C₄×Q₈

—

158

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

158

—

155

C₂×C₄²

—

158

—

156

C₂×C₄²

C₂²×D₇₉

yes

characteristic

157

#107

—

158

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

#103

—

158

—

161

C₄×C₈

—

162

C₄×C₈

—

158

—

163

C₄×C₈

—

158

—

164

C₄×C₈

—

158

—

165

C₄×C₈

D₃₁₆

yes

—

166

C₄×C₈

C₂²⋊D₇₉

yes

—

167

C₂×Q₈

—

168

C₂×Q₈

—

158

—

169

C₂×Q₈

—

158

—

170

C₂×Q₈

—

158

—

171

C₂×Q₈

—

158

—

172

C₂×Q₈

—

158

—

173

C₂²×C₄

—

158

—

174

C₂²×C₄

—

158

—

175

C₂²×C₄

C₂×C₄×D₇₉

yes

characteristic

176

C₂²×C₄

D₄×D₇₉

yes

characteristic

177

C₂²×C₄

#11929625

yes

characteristic

178

Q₁₆

—

158

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

158

—

184

C₂×C₈

—

158

—

185

C₂×C₈

—

158

—

186

C₂×C₈

—

158

—

187

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

188

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

189

C₄⋊C₄

—

316

—

190

C₄⋊C₄

—

316

—

191

C₄⋊C₄

—

158

—

192

C₄⋊C₄

—

158

—

193

C₄²

—

316

—

194

C₄²

—

316

—

195

C₄²

D₄×D₇₉

yes

characteristic

196

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

197

C₄²

C₂×D₃₁₆

yes

characteristic

198

C₄²

#11929625

yes

characteristic

199

C₂³

#14579123

yes

characteristic

200

Q₈

—

316

—

201

Q₈

—

316

—

202

Q₈

—

158

—

203

Q₈

—

158

—

204

C₂×C₄

—

205

C₂×C₄

—

316

—

206

C₂×C₄

—

316

—

207

C₂×C₄

—

316

—

208

C₂×C₄

—

316

—

209

C₂×C₄

—

158

—

210

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

211

C₂×C₄

#14579123

yes

characteristic

212

C₂×C₄

#14579136

yes

characteristic

213

C₂×C₄

#14579136

yes

characteristic

214

C₂×C₄

#14579150

yes

characteristic

215

C₂×C₄

#14579157

yes

characteristic

216

C₂×C₄

M₁₆×D₇₉

yes

—

217

C₂×C₄

#14579167

yes

—

218

C₂×C₄

#14579190

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

316

—

223

C₈

—

158

—

224

C₂²

#19098464

yes

characteristic

225

C₂²

#19098633

yes

—

226

C₂²

#19098669

yes

—

227

C₂²

#19098679

yes

—

228

C₄

—

229

C₄

—

230

C₄

—

316

—

231

C₄

—

632

—

232

C₄

#19098526

yes

characteristic

233

C₄

#19098529

yes

characteristic

234

C₄

#19098633

yes

—

235

C₄

#19098822

yes

—

236

C₄

#19098954

yes

—

237

C₂

#23762270

yes

—

238

C₂

#23764197

yes

characteristic

239

C₂

#23764269

yes

characteristic

240

C₂

#23764286

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₇₉
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₂×#334×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₄×D₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₂×#334	D₇₉
hypocenter	C₇₉	#9664
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

subgroup

G/H

center

C₂²×C₄

D₄×D₇₉

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₂×#334×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₄×D₄

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

N	H ≅ G/N	type
126. C₇₉	#9664	semidirect

H ≅ G/N

type

126. C₇₉

#9664

semidirect

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

subgroup	index
C₂×C₄×Dic₃₁₆	2
#23764335	2
C₂×#19098293	2
C₂×#19098285	2
C₂×#334×C₇₉	2
#9664	79

subgroup

index

C₂×C₄×Dic₃₁₆

C₂×#334×C₇₉

Subgroups — #34187169

Conjugacy classes of subgroups

Complements

Maximal subgroups