Group #34188145 — subgroups

Subgroups — #34188145

Order 20224.

554 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 131 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	#23773979	C₂	1	1	yes	maximal, characteristic
2	#23764227	C₂	1	2	yes	maximal, complemented
3	C₄×C₈×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#23761850	C₂	1	2	yes	maximal, complemented
5	C₇₉×#1567	C₂	1	1	yes	maximal, characteristic, complemented
6	#19099113	C₂²	1	2	yes	—
7	#19098968	C₄	1	1	yes	characteristic, complemented
8	#19098940	C₄	1	1	yes	characteristic, complemented
9	#19098910	C₄	1	2	yes	complemented
10	#19098799	—	2	2	no	—
11	C₄×D₆₃₂	—	2	2	no	—
12	C₂×#14579087	—	2	4	no	—
13	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₈×Dic₇₉	—	2	2	no	—
15	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
16	#19098290	—	2	4	no	—
17	#423×C₇₉	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	#335×C₇₉	—	2	2	no	—
20	C₂×#11929624	—	2	2	no	—
21	C₂×D₆₃₂	—	2	2	no	—
22	C₂²×C₇₉⋊C₈	—	2	1	no	—
23	#14579161	C₂×C₄	1	2	yes	—
24	#14579158	C₂×C₄	1	2	yes	—
25	#14579149	—	2	2	no	—
26	#14579135	—	2	2	no	—
27	#14579135	—	2	2	no	—
28	C₄×D₃₁₆	—	2	2	no	—
29	C₄×D₃₁₆	—	2	2	no	—
30	C₂×C₄×Dic₇₉	—	2	1	no	—
31	C₂×C₄×Dic₇₉	—	2	1	no	—
32	C₂×C₄×Dic₇₉	D₄	1	2	yes	—
33	#14579095	—	2	2	no	—
34	#14579087	—	4	8	no	—
35	#14579083	—	2	4	no	—
36	C₄×C₇₉⋊C₈	—	2	1	no	—
37	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
38	C₈×Dic₇₉	—	2	8	no	—
39	C₂×M₁₆×C₇₉	—	2	2	no	—
40	C₂²×C₈×C₇₉	D₄	1	2	yes	—
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	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₇₉	D₄	1	2	yes	—
47	#11929624	—	4	4	no	—
48	#11929624	—	4	4	no	—
49	C₂×Dic₁₅₈	—	2	2	no	—
50	C₂×D₃₁₆	—	2	2	no	—
51	C₂×D₃₁₆	—	2	2	no	—
52	C₂×D₃₁₆	—	2	2	no	—
53	C₂×C₂²⋊D₇₉	—	4	2	no	—
54	C₂²×Dic₇₉	—	2	2	no	—
55	C₂×C₄×D₇₉	—	4	2	no	—
56	D₆₃₂	—	4	4	no	—
57	C₂×C₇₉⋊C₈	—	2	4	no	—
58	C₂×C₇₉⋊C₈	—	2	2	no	—
59	C₄⋊Dic₇₉	—	2	2	no	—
60	C₄⋊Dic₇₉	—	2	2	no	—
61	(C₂×D₇₉)⋊C₄	—	4	2	no	—
62	(C₂×D₇₉)⋊C₄	—	4	2	no	—
63	C₄×Dic₇₉	—	2	4	no	—
64	C₄×Dic₇₉	—	2	4	no	—
65	C₄×Dic₇₉	—	2	2	no	—
66	C₄×Dic₇₉	D₈	1	4	yes	complemented
67	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
70	M₁₆×C₇₉	—	4	4	no	—
71	C₂×C₈×C₇₉	—	2	4	no	—
72	C₂×C₈×C₇₉	—	4	2	no	—
73	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
74	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
75	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₇₉	#41	1	1	yes	characteristic
79	C₂³×C₇₉	#121	1	1	yes	characteristic
80	C₂²×D₇₉	—	4	2	no	—
81	C₂×C₄×C₇₉	—	2	2	no	—
82	C₂×C₄×C₇₉	—	2	2	no	—
83	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
88	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
89	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
90	C₂×C₄×C₇₉	#135	1	2	yes	—
91	C₂²⋊D₇₉	—	8	4	no	—
92	C₂×Dic₇₉	—	2	4	no	—
93	C₂×Dic₇₉	—	2	4	no	—
94	C₂×Dic₇₉	—	2	4	no	—
95	C₂×Dic₇₉	—	4	2	no	—
96	D₃₁₆	—	4	4	no	—
97	D₃₁₆	—	4	4	no	—
98	D₃₁₆	—	4	4	no	—
99	C₄×D₇₉	—	8	2	no	—
100	C₄×D₇₉	—	8	2	no	—
101	Dic₁₅₈	—	4	4	no	—
102	C₈×C₇₉	—	2	2	no	—
103	C₈×C₇₉	—	8	2	no	—
104	C₈×C₇₉	#104	1	4	yes	complemented
105	C₇₉⋊C₈	—	2	4	no	—
106	C₂²×C₇₉	—	2	1	no	—
107	C₂²×C₇₉	—	2	1	no	—
108	C₂²×C₇₉	#390	1	1	yes	characteristic
109	C₂²×C₇₉	#466	1	2	yes	—
110	C₂×D₇₉	—	8	2	no	—
111	C₂×D₇₉	—	8	2	no	—
112	C₂×D₇₉	—	8	2	no	—
113	C₄×C₇₉	—	2	1	no	—
114	C₄×C₇₉	—	2	1	no	—
115	C₄×C₇₉	C₂×#104	1	2	yes	—
116	C₄×C₇₉	C₄×D₈	1	2	yes	—
117	C₄×C₇₉	#443	1	2	yes	—
118	C₄×C₇₉	#493	1	1	yes	characteristic
119	C₄×C₇₉	#495	1	1	yes	characteristic
120	Dic₇₉	—	2	8	no	—
121	Dic₇₉	—	8	2	no	—
122	#9844	—	79	1	no	maximal, Sylow
123	C₂×C₇₉	—	2	2	no	—
124	C₂×C₇₉	#1962	1	1	yes	characteristic
125	C₂×C₇₉	#1970	1	1	yes	characteristic
126	C₂×C₇₉	#1974	1	1	yes	characteristic
127	D₇₉	—	16	2	no	—
128	#3169	—	79	1	no	—
129	#1962	—	79	2	no	—
130	C₄²×C₈	—	79	1	no	—
131	#1567	D₇₉	1	1	yes	characteristic, complemented
132	#1492	—	79	2	no	—
133	C₇₉	#9844	1	1	yes	characteristic, complemented, Sylow
134	#532	—	79	2	no	—
135	#500	—	79	1	no	—
136	#493	—	79	1	no	—
137	#486	—	79	2	no	—
138	#466	—	158	2	no	—
139	C₄×D₈	—	158	2	no	—
140	#423	C₂×D₇₉	1	2	yes	—
141	C₂×#104	—	158	4	no	—
142	C₂×C₄×C₈	—	79	1	no	—
143	C₂×C₄×C₈	—	158	2	no	—
144	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
145	C₄³	—	79	1	no	—
146	#335	—	2	2	no	—
147	D₄⋊C₈	—	158	4	no	—
148	C₂×#41	—	158	2	no	—
149	C₂×D₈	—	158	2	no	—
150	C₂×M₁₆	—	2	2	no	—
151	C₂²×C₈	—	158	1	no	—
152	C₂²×C₈	D₃₁₆	1	2	yes	—
153	C₄⋊Q₈	—	79	2	no	—
154	#127	—	79	2	no	—
155	#124	—	158	2	no	—
156	#121	—	158	2	no	—
157	#121	—	158	2	no	—
158	C₄×D₄	—	158	2	no	—
159	C₄×D₄	—	158	2	no	—
160	C₂×C₄²	—	79	2	no	—
161	C₂×C₄²	—	158	1	no	—
162	C₂×C₄²	—	158	1	no	—
163	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
164	#107	—	158	2	no	—
165	C₄⋊C₈	—	2	2	no	—
166	C₄⋊C₈	—	2	2	no	—
167	#104	—	316	8	no	—
168	#102	—	158	4	no	—
169	C₄×C₈	—	79	2	no	—
170	C₄×C₈	—	158	8	no	—
171	C₄×C₈	—	158	1	no	—
172	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
173	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
174	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
175	#41	—	316	4	no	—
176	#41	—	316	4	no	—
177	C₂×Q₈	—	158	2	no	—
178	C₂×D₄	—	316	2	no	—
179	C₂×D₄	—	158	2	no	—
180	C₂×D₄	—	158	2	no	—
181	C₂×D₄	—	158	2	no	—
182	C₂²×C₄	—	316	2	no	—
183	C₂²×C₄	—	158	2	no	—
184	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
185	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
186	C₂²×C₄	#11929625	1	1	yes	characteristic
187	D₈	—	316	4	no	—
188	M₁₆	—	4	4	no	—
189	C₂×C₈	—	2	4	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	158	4	no	—
192	C₂×C₈	—	158	2	no	—
193	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
194	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
195	C₄⋊C₄	—	158	2	no	—
196	C₄⋊C₄	—	158	2	no	—
197	C₂²⋊C₄	—	316	2	no	—
198	C₂²⋊C₄	—	316	2	no	—
199	C₄²	—	79	4	no	—
200	C₄²	—	158	4	no	—
201	C₄²	—	158	4	no	—
202	C₄²	—	158	2	no	—
203	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
204	C₄²	D₄×D₇₉	1	1	yes	characteristic
205	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
206	C₄²	#11929625	1	1	yes	characteristic
207	C₂³	—	316	2	no	—
208	C₂³	#14579136	1	1	yes	characteristic
209	Q₈	—	316	4	no	—
210	D₄	—	316	4	no	—
211	D₄	—	316	4	no	—
212	D₄	—	316	4	no	—
213	D₄	—	632	4	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	316	2	no	—
217	C₂×C₄	—	632	2	no	—
218	C₂×C₄	—	632	2	no	—
219	C₂×C₄	—	158	4	no	—
220	C₂×C₄	—	158	4	no	—
221	C₂×C₄	—	158	4	no	—
222	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
223	C₂×C₄	#14579123	1	1	yes	characteristic
224	C₂×C₄	#14579123	1	1	yes	characteristic
225	C₂×C₄	#14579136	1	1	yes	characteristic
226	C₂×C₄	#14579150	1	1	yes	characteristic
227	C₂×C₄	#14579157	1	1	yes	characteristic
228	C₂×C₄	D₈×D₇₉	1	2	yes	—
229	C₂×C₄	#14579184	1	2	yes	—
230	C₈	—	2	2	no	—
231	C₈	—	8	2	no	—
232	C₈	—	158	4	no	—
233	C₈	#14579087	1	4	yes	complemented
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	632	2	no	—
237	C₂²	—	632	2	no	—
238	C₂²	—	632	2	no	—
239	C₂²	#19098464	1	1	yes	characteristic
240	C₂²	#19098800	1	2	yes	—
241	C₄	—	2	1	no	—
242	C₄	—	2	1	no	—
243	C₄	—	632	2	no	—
244	C₄	—	158	8	no	—
245	C₄	C₂×#14579087	1	2	yes	—
246	C₄	#19098645	1	2	yes	—
247	C₄	#19098679	1	2	yes	—
248	C₄	#19098938	1	1	yes	characteristic
249	C₄	#19098948	1	1	yes	characteristic
250	C₂	—	2	2	no	—
251	C₂	—	1264	2	no	—
252	C₂	#23764227	1	1	yes	characteristic
253	C₂	#23764264	1	1	yes	characteristic
254	C₂	#23764286	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23773979

C₂

yes

maximal, characteristic

#23764227

C₂

yes

maximal, complemented

C₄×C₈×Dic₇₉

C₂

yes

maximal, characteristic, complemented

#23761850

C₂

yes

maximal, complemented

C₇₉×#1567

C₂

yes

maximal, characteristic, complemented

#19099113

C₂²

yes

—

#19098968

C₄

yes

characteristic, complemented

#19098940

C₄

yes

characteristic, complemented

#19098910

C₄

yes

complemented

#19098799

—

C₄×D₆₃₂

—

C₂×#14579087

—

C₂×C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×Dic₇₉

—

C₄²×Dic₇₉

C₂²

yes

characteristic

#19098290

—

#423×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#335×C₇₉

—

C₂×#11929624

—

C₂×D₆₃₂

—

C₂²×C₇₉⋊C₈

—

#14579161

C₂×C₄

yes

—

#14579158

C₂×C₄

yes

—

#14579149

—

#14579135

—

#14579135

—

C₄×D₃₁₆

—

C₄×D₃₁₆

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

D₄

yes

—

#14579095

—

#14579087

—

#14579083

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

D₄

yes

—

C₈×Dic₇₉

—

C₂×M₁₆×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

—

#11929624

—

#11929624

—

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×C₂²⋊D₇₉

—

C₂²×Dic₇₉

—

C₂×C₄×D₇₉

—

D₆₃₂

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

D₈

yes

complemented

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

C₄²×C₇₉

yes

C₂³×C₇₉

yes

C₂²×D₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

C₂×D₈

yes

—

C₂×C₄×C₇₉

#135

yes

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

100

C₄×D₇₉

—

101

Dic₁₅₈

—

102

C₈×C₇₉

—

103

C₈×C₇₉

—

104

C₈×C₇₉

#104

yes

complemented

105

C₇₉⋊C₈

—

106

C₂²×C₇₉

—

107

C₂²×C₇₉

—

108

C₂²×C₇₉

#390

yes

characteristic

109

C₂²×C₇₉

#466

yes

—

110

C₂×D₇₉

—

111

C₂×D₇₉

—

112

C₂×D₇₉

—

113

C₄×C₇₉

—

114

C₄×C₇₉

—

115

C₄×C₇₉

C₂×#104

yes

—

116

C₄×C₇₉

C₄×D₈

yes

—

117

C₄×C₇₉

#443

yes

—

118

C₄×C₇₉

#493

yes

characteristic

119

C₄×C₇₉

#495

yes

characteristic

120

Dic₇₉

—

121

Dic₇₉

—

122

#9844

—

maximal, Sylow

123

C₂×C₇₉

—

124

C₂×C₇₉

#1962

yes

characteristic

125

C₂×C₇₉

#1970

yes

characteristic

126

C₂×C₇₉

#1974

yes

characteristic

127

D₇₉

—

128

#3169

—

129

#1962

—

130

C₄²×C₈

—

131

#1567

D₇₉

yes

characteristic, complemented

132

#1492

—

133

C₇₉

#9844

yes

characteristic, complemented, Sylow

134

#532

—

135

#500

—

136

#493

—

137

#486

—

138

#466

—

158

—

139

C₄×D₈

—

158

—

140

#423

C₂×D₇₉

yes

—

141

C₂×#104

—

158

—

142

C₂×C₄×C₈

—

143

C₂×C₄×C₈

—

158

—

144

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

145

C₄³

—

146

#335

—

147

D₄⋊C₈

—

158

—

148

C₂×#41

—

158

—

149

C₂×D₈

—

158

—

150

C₂×M₁₆

—

151

C₂²×C₈

—

158

—

152

C₂²×C₈

D₃₁₆

yes

—

153

C₄⋊Q₈

—

154

#127

—

155

#124

—

158

—

156

#121

—

158

—

157

#121

—

158

—

158

C₄×D₄

—

158

—

159

C₄×D₄

—

158

—

160

C₂×C₄²

—

161

C₂×C₄²

—

158

—

162

C₂×C₄²

—

158

—

163

C₂×C₄²

C₂²×D₇₉

yes

characteristic

164

#107

—

158

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

#104

—

316

—

168

#102

—

158

—

169

C₄×C₈

—

170

C₄×C₈

—

158

—

171

C₄×C₈

—

158

—

172

C₄×C₈

C₄×D₇₉

yes

characteristic

173

C₄×C₈

C₄×D₇₉

yes

characteristic

174

C₄×C₈

C₂²⋊D₇₉

yes

—

175

#41

—

316

—

176

#41

—

316

—

177

C₂×Q₈

—

158

—

178

C₂×D₄

—

316

—

179

C₂×D₄

—

158

—

180

C₂×D₄

—

158

—

181

C₂×D₄

—

158

—

182

C₂²×C₄

—

316

—

183

C₂²×C₄

—

158

—

184

C₂²×C₄

D₄×D₇₉

yes

characteristic

185

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

186

C₂²×C₄

#11929625

yes

characteristic

187

D₈

—

316

—

188

M₁₆

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

158

—

192

C₂×C₈

—

158

—

193

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

194

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

195

C₄⋊C₄

—

158

—

196

C₄⋊C₄

—

158

—

197

C₂²⋊C₄

—

316

—

198

C₂²⋊C₄

—

316

—

199

C₄²

—

200

C₄²

—

158

—

201

C₄²

—

158

—

202

C₄²

—

158

—

203

C₄²

C₂×C₄×D₇₉

yes

characteristic

204

C₄²

D₄×D₇₉

yes

characteristic

205

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

206

C₄²

#11929625

yes

characteristic

207

C₂³

—

316

—

208

C₂³

#14579136

yes

characteristic

209

Q₈

—

316

—

210

D₄

—

316

—

211

D₄

—

316

—

212

D₄

—

316

—

213

D₄

—

632

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

316

—

217

C₂×C₄

—

632

—

218

C₂×C₄

—

632

—

219

C₂×C₄

—

158

—

220

C₂×C₄

—

158

—

221

C₂×C₄

—

158

—

222

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

223

C₂×C₄

#14579123

yes

characteristic

224

C₂×C₄

#14579123

yes

characteristic

225

C₂×C₄

#14579136

yes

characteristic

226

C₂×C₄

#14579150

yes

characteristic

227

C₂×C₄

#14579157

yes

characteristic

228

C₂×C₄

D₈×D₇₉

yes

—

229

C₂×C₄

#14579184

yes

—

230

C₈

—

231

C₈

—

232

C₈

—

158

—

233

C₈

#14579087

yes

complemented

234

C₂²

—

235

C₂²

—

236

C₂²

—

632

—

237

C₂²

—

632

—

238

C₂²

—

632

—

239

C₂²

#19098464

yes

characteristic

240

C₂²

#19098800

yes

—

241

C₄

—

242

C₄

—

243

C₄

—

632

—

244

C₄

—

158

—

245

C₄

C₂×#14579087

yes

—

246

C₄

#19098645

yes

—

247

C₄

#19098679

yes

—

248

C₄

#19098938

yes

characteristic

249

C₄

#19098948

yes

characteristic

250

C₂

—

251

C₂

—

1264

—

252

C₂

#23764227

yes

characteristic

253

C₂

#23764264

yes

characteristic

254

C₂

#23764286

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579157
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1567	C₂
socle	C₂²×C₇₉	#390
prime radical	#23773979	C₂
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1567	D₇₉
hypocenter	C₇₉	#9844
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

subgroup

G/H

center

C₂×C₄

#14579157

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1567

C₂

C₂²×C₇₉

C₂

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

N	H ≅ G/N	type
2. #23764227	C₂	semidirect
3. C₄×C₈×Dic₇₉	C₂	semidirect
4. #23761850	C₂	semidirect
5. C₇₉×#1567	C₂	semidirect
7. #19098968	C₄	semidirect
8. #19098940	C₄	semidirect
9. #19098910	C₄	semidirect
66. C₄×Dic₇₉	D₈	semidirect
104. C₈×C₇₉	#104	semidirect
131. #1567	D₇₉	semidirect
133. C₇₉	#9844	semidirect
233. C₈	#14579087	semidirect

H ≅ G/N

type

2. #23764227

C₂

semidirect

3. C₄×C₈×Dic₇₉

C₂

semidirect

4. #23761850

C₂

semidirect

5. C₇₉×#1567

C₂

semidirect

7. #19098968

C₄

semidirect

8. #19098940

C₄

semidirect

9. #19098910

C₄

semidirect

66. C₄×Dic₇₉

D₈

semidirect

104. C₈×C₇₉

#104

semidirect

131. #1567

D₇₉

semidirect

133. C₇₉

#9844

semidirect

233. C₈

#14579087

semidirect

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

subgroup	index
#23773979	2
#23764227	2
C₄×C₈×Dic₇₉	2
#23761850	2
C₇₉×#1567	2
#9844	79

subgroup

index

C₄×C₈×Dic₇₉

C₇₉×#1567

Subgroups — #34188145

Conjugacy classes of subgroups

Complements

Maximal subgroups