Group #34197607 — subgroups

Subgroups — #34197607

Order 20224.

330 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 97 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×#19098687	C₂	1	1	yes	maximal, characteristic
2	#23765200	C₂	1	2	yes	maximal
3	#23761340	C₂	1	1	yes	maximal, characteristic
4	#23761339	C₂	1	2	yes	maximal
5	C₇₉×#1322	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₅₈	C₄	1	1	yes	characteristic
7	#19098687	—	2	2	no	—
8	#19098687	—	2	2	no	—
9	C₂×Dic₇₉⋊C₈	C₄	1	1	yes	characteristic
10	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₇₉⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₇₉	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
14	Dic₇₉⋊C₁₆	—	2	2	no	—
15	C₂²⋊(C₇₉⋊C₁₆)	C₂²	1	2	yes	—
16	#19098338	—	2	2	no	—
17	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²⋊C₁₆×C₇₉	C₂²	1	2	yes	—
19	C₂²×Dic₁₅₈	C₈	1	1	yes	characteristic
20	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₁₅₈	—	2	2	no	—
23	C₄×Dic₁₅₈	—	2	2	no	—
24	C₂×C₄⋊Dic₇₉	C₈	1	1	yes	characteristic
25	C₂×Dic₇₉⋊C₄	C₈	1	1	yes	characteristic
26	C₂×Dic₇₉⋊C₄	C₈	1	1	yes	characteristic
27	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₇₉⋊C₁₆	—	2	2	no	—
30	Dic₇₉⋊C₈	—	2	2	no	—
31	Dic₇₉⋊C₈	—	2	2	no	—
32	C₄×C₇₉⋊C₈	—	2	1	no	—
33	C₄×C₇₉⋊C₈	—	2	1	no	—
34	C₈×Dic₇₉	—	2	1	no	—
35	C₈×Dic₇₉	—	2	1	no	—
36	C₈×Dic₇₉	D₄	1	2	yes	—
37	C₈×Dic₇₉	D₄	1	2	yes	—
38	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
40	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₁₆×C₇₉	—	2	2	no	—
42	C₄⋊C₈×C₇₉	—	2	2	no	—
43	C₂×Dic₁₅₈	—	2	2	no	—
44	C₂×Dic₁₅₈	—	2	2	no	—
45	C₂×Dic₁₅₈	—	2	2	no	—
46	C₂²×Dic₇₉	C₂×C₈	1	1	yes	characteristic
47	C₂²×Dic₇₉	C₂×C₈	1	1	yes	characteristic
48	C₂²×Dic₇₉	C₂×C₈	1	1	yes	characteristic
49	C₂²×Dic₇₉	C₂×C₈	1	1	yes	characteristic
50	C₂×C₇₉⋊C₈	—	2	2	no	—
51	C₂×C₇₉⋊C₈	—	2	1	no	—
52	C₂×C₇₉⋊C₈	—	4	1	no	—
53	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
55	C₄⋊Dic₇₉	—	2	2	no	—
56	Dic₇₉⋊C₄	—	2	2	no	—
57	Dic₇₉⋊C₄	—	2	2	no	—
58	C₄×Dic₇₉	—	2	1	no	—
59	C₄×Dic₇₉	—	2	1	no	—
60	C₄×Dic₇₉	C₂²⋊C₄	1	2	yes	—
61	C₄×Dic₇₉	M₁₆	1	2	yes	—
62	C₇₉⋊C₁₆	—	4	2	no	—
63	C₂²×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
64	C₂²×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
65	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₈×C₇₉	—	2	1	no	—
67	C₂×C₈×C₇₉	—	4	1	no	—
68	C₂×C₈×C₇₉	—	4	1	no	—
69	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
70	C₄²×C₇₉	—	2	1	no	—
71	C₄²×C₇₉	—	2	1	no	—
72	C₁₆×C₇₉	—	4	2	no	—
73	C₂³×C₇₉	C₂²×C₈	1	1	yes	characteristic
74	C₂×C₄×C₇₉	—	2	1	no	—
75	C₂×C₄×C₇₉	—	2	1	no	—
76	C₂×C₄×C₇₉	—	2	1	no	—
77	C₂×C₄×C₇₉	—	2	1	no	—
78	C₂×C₄×C₇₉	—	2	1	no	—
79	C₂×C₄×C₇₉	—	4	1	no	—
80	C₂×C₄×C₇₉	M₃₂	1	2	yes	—
81	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
83	C₂×Dic₇₉	—	2	1	no	—
84	C₂×Dic₇₉	—	2	1	no	—
85	C₂×Dic₇₉	—	2	1	no	—
86	C₂×Dic₇₉	—	2	1	no	—
87	C₂×Dic₇₉	—	2	1	no	—
88	C₂×Dic₇₉	—	4	1	no	—
89	C₂×Dic₇₉	—	4	1	no	—
90	C₂×Dic₇₉	C₂²⋊C₈	1	2	yes	—
91	C₂×Dic₇₉	C₂²⋊C₈	1	2	yes	—
92	C₂×Dic₇₉	M₃₂	1	2	yes	—
93	Dic₁₅₈	—	2	8	no	—
94	C₈×C₇₉	—	2	2	no	—
95	C₈×C₇₉	—	4	1	no	—
96	C₇₉⋊C₈	—	2	1	no	—
97	C₇₉⋊C₈	—	4	1	no	—
98	C₇₉⋊C₈	#101	1	2	yes	—
99	C₂²×C₇₉	—	2	1	no	—
100	C₂²×C₇₉	—	2	1	no	—
101	C₂²×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
102	C₂²×C₇₉	C₂×M₃₂	1	1	yes	characteristic
103	C₂²×C₇₉	C₂×M₃₂	1	1	yes	characteristic
104	C₄×C₇₉	—	2	2	no	—
105	C₄×C₇₉	—	2	1	no	—
106	C₄×C₇₉	—	4	1	no	—
107	C₄×C₇₉	#410	1	1	yes	characteristic
108	C₄×C₇₉	C₂×#101	1	1	yes	characteristic
109	Dic₇₉	—	2	2	no	—
110	Dic₇₉	—	2	2	no	—
111	Dic₇₉	—	2	2	no	—
112	Dic₇₉	—	4	1	no	—
113	#11494	—	79	1	no	maximal, Sylow
114	C₂×C₇₉	—	2	1	no	—
115	C₂×C₇₉	—	2	1	no	—
116	C₂×C₇₉	#1461	1	1	yes	characteristic
117	C₂×C₇₉	#2112	1	1	yes	characteristic
118	C₂×C₇₉	#2115	1	1	yes	characteristic
119	C₂×C₈×Q₈	—	79	1	no	—
120	#2163	—	79	2	no	—
121	#1322	—	79	1	no	—
122	#1322	—	79	2	no	—
123	#1322	D₇₉	1	1	yes	characteristic
124	C₇₉	#11494	1	1	yes	characteristic, complemented, Sylow
125	C₂×C₄×Q₈	—	79	1	no	—
126	C₈×Q₈	—	158	2	no	—
127	C₈×Q₈	—	158	2	no	—
128	C₂×C₄⋊C₈	—	79	1	no	—
129	C₂×C₄⋊C₈	—	79	1	no	—
130	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
131	C₂×C₄×C₈	—	79	1	no	—
132	C₂×C₄×C₈	—	79	1	no	—
133	C₂×C₄×C₈	—	79	1	no	—
134	C₄⋊C₁₆	—	158	2	no	—
135	C₂²⋊C₁₆	—	79	2	no	—
136	C₂²⋊C₁₆	C₂×D₇₉	1	2	yes	—
137	#346	—	158	2	no	—
138	C₂²×Q₈	—	79	1	no	—
139	C₂²×C₈	—	79	1	no	—
140	C₂²×C₈	—	79	1	no	—
141	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
142	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
143	C₄×Q₈	—	158	2	no	—
144	C₄×Q₈	—	158	2	no	—
145	C₂×C₄⋊C₄	—	79	1	no	—
146	C₂×C₄⋊C₄	—	79	1	no	—
147	C₂×C₄⋊C₄	—	79	1	no	—
148	C₂×C₄²	—	79	1	no	—
149	C₂×C₄²	—	79	1	no	—
150	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
151	C₂×C₁₆	—	2	2	no	—
152	C₂×C₁₆	—	158	2	no	—
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	—	158	2	no	—
155	C₄⋊C₈	—	158	2	no	—
156	C₄×C₈	—	79	2	no	—
157	C₄×C₈	—	79	2	no	—
158	C₄×C₈	—	158	1	no	—
159	C₄×C₈	—	158	1	no	—
160	C₄×C₈	—	158	1	no	—
161	C₄×C₈	—	158	1	no	—
162	C₂×Q₈	—	158	2	no	—
163	C₂×Q₈	—	158	2	no	—
164	C₂×Q₈	—	158	2	no	—
165	C₂²×C₄	—	79	1	no	—
166	C₂²×C₄	—	79	1	no	—
167	C₂²×C₄	—	79	1	no	—
168	C₂²×C₄	—	79	1	no	—
169	C₂²×C₄	C₈×D₇₉	1	1	yes	characteristic
170	C₂²×C₄	C₈×D₇₉	1	1	yes	characteristic
171	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	4	1	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	316	1	no	—
176	C₂×C₈	—	79	1	no	—
177	C₂×C₈	—	79	1	no	—
178	C₂×C₈	—	158	1	no	—
179	C₂×C₈	—	158	2	no	—
180	C₂×C₈	D₄×D₇₉	1	2	yes	—
181	C₄⋊C₄	—	158	2	no	—
182	C₄⋊C₄	—	158	2	no	—
183	C₄⋊C₄	—	158	2	no	—
184	C₄²	—	2	1	no	—
185	C₄²	—	2	1	no	—
186	C₄²	—	79	2	no	—
187	C₄²	—	79	2	no	—
188	C₄²	—	158	1	no	—
189	C₄²	—	158	1	no	—
190	C₁₆	—	4	2	no	—
191	C₁₆	—	316	2	no	—
192	C₂³	C₂×C₈×D₇₉	1	1	yes	characteristic
193	Q₈	—	158	8	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	316	1	no	—
201	C₂×C₄	—	316	1	no	—
202	C₂×C₄	—	79	2	no	—
203	C₂×C₄	—	79	2	no	—
204	C₂×C₄	—	79	2	no	—
205	C₂×C₄	—	158	1	no	—
206	C₂×C₄	—	158	1	no	—
207	C₂×C₄	—	158	1	no	—
208	C₂×C₄	—	158	1	no	—
209	C₂×C₄	—	158	1	no	—
210	C₂×C₄	#14579100	1	2	yes	—
211	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
212	C₂×C₄	M₁₆×D₇₉	1	1	yes	characteristic
213	C₈	—	2	2	no	—
214	C₈	—	4	1	no	—
215	C₈	—	316	1	no	—
216	C₈	—	79	2	no	—
217	C₈	—	158	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	C₂²⋊C₈×D₇₉	1	1	yes	characteristic
221	C₂²	M₃₂×D₇₉	1	1	yes	characteristic
222	C₂²	C₂×#14579100	1	1	yes	characteristic
223	C₄	—	2	2	no	—
224	C₄	—	2	1	no	—
225	C₄	—	4	1	no	—
226	C₄	—	316	1	no	—
227	C₄	—	158	2	no	—
228	C₄	—	158	2	no	—
229	C₄	—	158	2	no	—
230	C₄	#19098535	1	1	yes	characteristic
231	C₄	#101×D₇₉	1	1	yes	characteristic
232	C₂	—	2	1	no	—
233	C₂	—	2	1	no	—
234	C₂	#23761722	1	1	yes	characteristic
235	C₂	#23765009	1	1	yes	characteristic
236	C₂	#23765019	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098687

C₂

yes

maximal, characteristic

#23765200

C₂

yes

maximal

#23761340

C₂

yes

maximal, characteristic

#23761339

C₂

yes

maximal

C₇₉×#1322

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₅₈

C₄

yes

characteristic

#19098687

—

#19098687

—

C₂×Dic₇₉⋊C₈

C₄

yes

characteristic

C₂×Dic₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₇₉⋊C₈

C₄

yes

characteristic

C₂×C₈×Dic₇₉

C₄

yes

characteristic

C₂×C₈×Dic₇₉

C₂²

yes

characteristic

Dic₇₉⋊C₁₆

—

C₂²⋊(C₇₉⋊C₁₆)

C₂²

yes

—

#19098338

—

C₂×C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₂²⋊C₁₆×C₇₉

C₂²

yes

—

C₂²×Dic₁₅₈

C₈

yes

characteristic

C₂²×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₂×C₄⋊Dic₇₉

C₈

yes

characteristic

C₂×Dic₇₉⋊C₄

C₈

yes

characteristic

C₂×Dic₇₉⋊C₄

C₈

yes

characteristic

C₂×C₄×Dic₇₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₇₉

C₂×C₄

yes

characteristic

C₂×C₇₉⋊C₁₆

—

Dic₇₉⋊C₈

—

Dic₇₉⋊C₈

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

—

C₈×Dic₇₉

—

C₈×Dic₇₉

—

C₈×Dic₇₉

D₄

yes

—

C₈×Dic₇₉

D₄

yes

—

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₉

C₂³

yes

characteristic

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₉

—

C₄⋊C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

C₂×C₈

yes

characteristic

C₂²×Dic₇₉

C₂×C₈

yes

characteristic

C₂²×Dic₇₉

C₂×C₈

yes

characteristic

C₂²×Dic₇₉

C₂×C₈

yes

characteristic

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₇₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

C₂²⋊C₄

yes

—

C₄×Dic₇₉

M₁₆

yes

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₇₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₁₆×C₇₉

—

C₂³×C₇₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

M₃₂

yes

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×M₁₆

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂²⋊C₈

yes

—

C₂×Dic₇₉

C₂²⋊C₈

yes

—

C₂×Dic₇₉

M₃₂

yes

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

#101

yes

—

C₂²×C₇₉

—

100

C₂²×C₇₉

—

101

C₂²×C₇₉

C₂×C₂²⋊C₈

yes

characteristic

102

C₂²×C₇₉

C₂×M₃₂

yes

characteristic

103

C₂²×C₇₉

C₂×M₃₂

yes

characteristic

104

C₄×C₇₉

—

105

C₄×C₇₉

—

106

C₄×C₇₉

—

107

C₄×C₇₉

#410

yes

characteristic

108

C₄×C₇₉

C₂×#101

yes

characteristic

109

Dic₇₉

—

110

Dic₇₉

—

111

Dic₇₉

—

112

Dic₇₉

—

113

#11494

—

maximal, Sylow

114

C₂×C₇₉

—

115

C₂×C₇₉

—

116

C₂×C₇₉

#1461

yes

characteristic

117

C₂×C₇₉

#2112

yes

characteristic

118

C₂×C₇₉

#2115

yes

characteristic

119

C₂×C₈×Q₈

—

120

#2163

—

121

#1322

—

122

#1322

—

123

#1322

D₇₉

yes

characteristic

124

C₇₉

#11494

yes

characteristic, complemented, Sylow

125

C₂×C₄×Q₈

—

126

C₈×Q₈

—

158

—

127

C₈×Q₈

—

158

—

128

C₂×C₄⋊C₈

—

129

C₂×C₄⋊C₈

—

130

C₂×C₄⋊C₈

C₂×D₇₉

yes

characteristic

131

C₂×C₄×C₈

—

132

C₂×C₄×C₈

—

133

C₂×C₄×C₈

—

134

C₄⋊C₁₆

—

158

—

135

C₂²⋊C₁₆

—

136

C₂²⋊C₁₆

C₂×D₇₉

yes

—

137

#346

—

158

—

138

C₂²×Q₈

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₂²×C₈

C₄×D₇₉

yes

characteristic

142

C₂²×C₈

C₂²×D₇₉

yes

characteristic

143

C₄×Q₈

—

158

—

144

C₄×Q₈

—

158

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

C₄×D₇₉

yes

characteristic

151

C₂×C₁₆

—

152

C₂×C₁₆

—

158

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

158

—

155

C₄⋊C₈

—

158

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₄×C₈

—

158

—

159

C₄×C₈

—

158

—

160

C₄×C₈

—

158

—

161

C₄×C₈

—

158

—

162

C₂×Q₈

—

158

—

163

C₂×Q₈

—

158

—

164

C₂×Q₈

—

158

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

C₈×D₇₉

yes

characteristic

170

C₂²×C₄

C₈×D₇₉

yes

characteristic

171

C₂²×C₄

C₂×C₄×D₇₉

yes

characteristic

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

316

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

158

—

179

C₂×C₈

—

158

—

180

C₂×C₈

D₄×D₇₉

yes

—

181

C₄⋊C₄

—

158

—

182

C₄⋊C₄

—

158

—

183

C₄⋊C₄

—

158

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

—

158

—

189

C₄²

—

158

—

190

C₁₆

—

191

C₁₆

—

316

—

192

C₂³

C₂×C₈×D₇₉

yes

characteristic

193

Q₈

—

158

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

316

—

201

C₂×C₄

—

316

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

158

—

206

C₂×C₄

—

158

—

207

C₂×C₄

—

158

—

208

C₂×C₄

—

158

—

209

C₂×C₄

—

158

—

210

C₂×C₄

#14579100

yes

—

211

C₂×C₄

C₂²⋊C₄×D₇₉

yes

characteristic

212

C₂×C₄

M₁₆×D₇₉

yes

characteristic

213

C₈

—

214

C₈

—

215

C₈

—

316

—

216

C₈

—

217

C₈

—

158

—

218

C₂²

—

219

C₂²

—

220

C₂²

C₂²⋊C₈×D₇₉

yes

characteristic

221

C₂²

M₃₂×D₇₉

yes

characteristic

222

C₂²

C₂×#14579100

yes

characteristic

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

316

—

227

C₄

—

158

—

228

C₄

—

158

—

229

C₄

—

158

—

230

C₄

#19098535

yes

characteristic

231

C₄

#101×D₇₉

yes

characteristic

232

C₂

—

233

C₂

—

234

C₂

#23761722

yes

characteristic

235

C₂

#23765009

yes

characteristic

236

C₂

#23765019

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₇₉
commutator, prime radical	C₂³×C₇₉	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₇₉×#1322	C₂
socle	C₂²×C₇₉	C₂×C₂²⋊C₈
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	#1322	D₇₉
hypocenter	C₇₉	#11494
LCS	G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1322

subgroup

G/H

center

C₂×C₄

C₂²⋊C₄×D₇₉

commutator, prime radical

C₂³×C₇₉

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₇₉×#1322

C₂

socle

C₂²×C₇₉

C₂×C₂²⋊C₈

cosocle

C₂²×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1322

N	H ≅ G/N	type
124. C₇₉	#11494	semidirect

H ≅ G/N

type

124. C₇₉

#11494

semidirect

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

subgroup	index
C₂×#19098687	2
#23765200	2
#23761340	2
#23761339	2
C₇₉×#1322	2
#11494	79

subgroup

index

C₇₉×#1322

Subgroups — #34197607

Conjugacy classes of subgroups

Complements

Maximal subgroups