Group #34190877 — subgroups

Subgroups — #34190877

Order 20224.

574 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 139 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×#19098943	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098848	C₂	1	2	yes	maximal
3	C₂×#19098310	C₂	1	2	yes	maximal
4	#23761235	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#1984	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₁₆	—	2	2	no	—
7	C₂×#14579161	C₂²	1	2	yes	—
8	#19098943	—	2	4	no	—
9	#19098848	—	2	4	no	—
10	#19098848	—	2	4	no	—
11	C₂×#14579092	—	2	2	no	—
12	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
13	C₂×#14579085	—	2	2	no	—
14	#19098310	—	2	4	no	—
15	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
18	#336×C₇₉	—	2	2	no	—
19	C₂²×Dic₁₅₈	—	2	2	no	—
20	C₂×Dic₃₁₆	—	2	8	no	—
21	C₂×Dic₃₁₆	—	4	4	no	—
22	C₂×Dic₃₁₆	—	4	4	no	—
23	C₂²×C₇₉⋊C₈	—	2	2	no	—
24	#14579161	—	2	2	no	—
25	#14579161	—	2	2	no	—
26	#14579161	—	2	2	no	—
27	#14579161	D₄	1	4	yes	—
28	C₂×C₄⋊Dic₇₉	—	2	2	no	—
29	C₂×C₄⋊Dic₇₉	—	2	2	no	—
30	#14579092	—	2	8	no	—
31	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	—
33	#14579085	—	2	8	no	—
34	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₇₉	—	2	1	no	—
36	C₂²×C₈×C₇₉	D₄	1	2	yes	—
37	C₄×Q₈×C₇₉	—	2	2	no	—
38	C₄×Q₈×C₇₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₇₉	—	2	1	no	—
42	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₇₉	—	2	2	no	—
44	C₄×C₈×C₇₉	—	2	2	no	—
45	C₂×Dic₁₅₈	—	2	4	no	—
46	C₂×Dic₁₅₈	—	4	2	no	—
47	C₂×Dic₁₅₈	—	4	4	no	—
48	C₂×Dic₁₅₈	—	4	4	no	—
49	C₂²×Dic₇₉	—	4	2	no	—
50	Dic₃₁₆	—	4	16	no	—
51	C₂×C₇₉⋊C₈	—	2	4	no	—
52	C₂×C₇₉⋊C₈	—	4	2	no	—
53	C₂×C₇₉⋊C₈	—	4	2	no	—
54	C₄⋊Dic₇₉	—	2	4	no	—
55	C₄⋊Dic₇₉	—	2	4	no	—
56	C₄⋊Dic₇₉	—	4	2	no	—
57	C₄⋊Dic₇₉	—	4	2	no	—
58	C₂×Q₈×C₇₉	—	2	1	no	—
59	C₂×Q₈×C₇₉	—	2	2	no	—
60	C₂×Q₈×C₇₉	—	2	2	no	—
61	C₂×Q₈×C₇₉	Q₁₆	1	2	yes	complemented
62	C₂²×C₄×C₇₉	—	2	1	no	—
63	C₂²×C₄×C₇₉	—	2	1	no	—
64	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
67	C₂×C₈×C₇₉	—	2	2	no	—
68	C₂×C₈×C₇₉	—	2	2	no	—
69	C₂×C₈×C₇₉	—	4	1	no	—
70	C₂×C₈×C₇₉	—	4	2	no	—
71	C₂×C₈×C₇₉	SD₁₆	1	4	yes	—
72	C₄⋊C₄×C₇₉	—	2	2	no	—
73	C₄⋊C₄×C₇₉	—	4	2	no	—
74	C₄²×C₇₉	—	4	1	no	—
75	C₄²×C₇₉	—	4	1	no	—
76	C₄²×C₇₉	C₂×D₄	1	2	yes	—
77	C₄²×C₇₉	C₂×D₄	1	2	yes	—
78	C₂³×C₇₉	#121	1	1	yes	characteristic
79	Q₈×C₇₉	—	2	4	no	—
80	Q₈×C₇₉	—	4	2	no	—
81	C₂×C₄×C₇₉	—	2	2	no	—
82	C₂×C₄×C₇₉	—	2	2	no	—
83	C₂×C₄×C₇₉	—	4	1	no	—
84	C₂×C₄×C₇₉	—	4	1	no	—
85	C₂×C₄×C₇₉	—	4	1	no	—
86	C₂×C₄×C₇₉	—	4	2	no	—
87	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
88	C₂×C₄×C₇₉	#120	1	2	yes	—
89	C₂×C₄×C₇₉	#121	1	2	yes	—
90	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
91	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
92	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
93	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
94	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
95	C₂×C₄×C₇₉	#137	1	2	yes	—
96	C₂×Dic₇₉	—	4	4	no	—
97	C₂×Dic₇₉	—	8	4	no	—
98	Dic₁₅₈	—	4	8	no	—
99	Dic₁₅₈	—	8	2	no	—
100	Dic₁₅₈	—	8	2	no	—
101	C₈×C₇₉	—	2	4	no	—
102	C₈×C₇₉	—	8	1	no	—
103	C₇₉⋊C₈	—	4	4	no	—
104	C₂²×C₇₉	#392	1	1	yes	characteristic
105	C₂²×C₇₉	#460	1	2	yes	—
106	C₂²×C₇₉	#467	1	1	yes	characteristic
107	C₂²×C₇₉	#470	1	1	yes	characteristic
108	C₂²×C₇₉	#473	1	2	yes	—
109	C₄×C₇₉	—	2	2	no	—
110	C₄×C₇₉	—	4	2	no	—
111	C₄×C₇₉	—	8	1	no	—
112	C₄×C₇₉	#450	1	2	yes	—
113	C₄×C₇₉	#451	1	2	yes	—
114	C₄×C₇₉	#452	1	2	yes	—
115	C₄×C₇₉	#492	1	1	yes	characteristic
116	C₄×C₇₉	#496	1	1	yes	characteristic
117	Dic₇₉	—	8	4	no	—
118	#10276	—	79	1	no	maximal, Sylow
119	C₂×C₇₉	#1670	1	2	yes	—
120	C₂×C₇₉	#1690	1	2	yes	—
121	C₂×C₇₉	#2001	1	1	yes	characteristic
122	C₂×C₇₉	#2014	1	1	yes	characteristic
123	C₂×C₇₉	#2020	1	1	yes	characteristic
124	C₂×#494	—	79	1	no	—
125	C₂×#475	—	79	2	no	—
126	#1984	D₇₉	1	1	yes	characteristic
127	C₂×#332	—	79	2	no	—
128	#1277	—	79	1	no	—
129	C₇₉	#10276	1	1	yes	characteristic, complemented, Sylow
130	C₂²×Q₁₆	—	158	2	no	—
131	C₂×C₄⋊Q₈	—	79	2	no	—
132	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
133	#494	—	158	4	no	—
134	#475	—	158	4	no	—
135	#475	—	158	4	no	—
136	C₂×#106	—	158	2	no	—
137	C₂×C₄⋊C₈	—	79	2	no	—
138	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
139	C₂×#103	—	158	2	no	—
140	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
141	#336	—	2	2	no	—
142	#332	—	158	4	no	—
143	C₂²×Q₈	—	158	2	no	—
144	C₂²×Q₈	D₃₁₆	1	1	yes	characteristic
145	C₂×Q₁₆	—	316	4	no	—
146	C₂×Q₁₆	—	316	4	no	—
147	C₂×Q₁₆	—	158	8	no	—
148	C₂²×C₈	—	2	1	no	—
149	C₂²×C₈	—	158	2	no	—
150	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
151	C₄⋊Q₈	—	79	4	no	—
152	C₄⋊Q₈	—	158	2	no	—
153	C₄⋊Q₈	—	158	2	no	—
154	C₄⋊Q₈	—	158	2	no	—
155	C₄×Q₈	—	2	2	no	—
156	C₄×Q₈	—	2	2	no	—
157	C₂×C₄⋊C₄	—	2	1	no	—
158	C₂×C₄⋊C₄	—	158	2	no	—
159	C₂×C₄⋊C₄	—	158	2	no	—
160	C₂×C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
161	C₂×C₄²	—	2	1	no	—
162	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
163	#106	—	158	8	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	79	4	no	—
166	C₄⋊C₈	—	158	2	no	—
167	#103	—	158	8	no	—
168	C₄×C₈	—	2	2	no	—
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	2	2	no	—
172	C₂×Q₈	—	316	2	no	—
173	C₂×Q₈	—	316	4	no	—
174	C₂×Q₈	—	316	4	no	—
175	C₂×Q₈	—	158	4	no	—
176	C₂×Q₈	Dic₃₁₆	1	2	yes	complemented
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	—	316	2	no	—
180	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
181	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
182	C₂²×C₄	#11929624	1	1	yes	characteristic
183	Q₁₆	—	316	16	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	—	4	1	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	316	2	no	—
189	C₂×C₈	—	316	2	no	—
190	C₂×C₈	—	158	4	no	—
191	C₂×C₈	#11929611	1	4	yes	—
192	C₄⋊C₄	—	2	2	no	—
193	C₄⋊C₄	—	4	2	no	—
194	C₄⋊C₄	—	316	2	no	—
195	C₄⋊C₄	—	316	2	no	—
196	C₄⋊C₄	—	158	4	no	—
197	C₄⋊C₄	—	158	4	no	—
198	C₄²	—	4	1	no	—
199	C₄²	—	4	1	no	—
200	C₄²	D₄×D₇₉	1	2	yes	—
201	C₄²	D₄×D₇₉	1	2	yes	—
202	C₂³	#14579135	1	1	yes	characteristic
203	Q₈	—	2	4	no	—
204	Q₈	—	4	2	no	—
205	Q₈	—	316	8	no	—
206	Q₈	—	632	2	no	—
207	Q₈	—	632	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	316	4	no	—
215	C₂×C₄	—	632	4	no	—
216	C₂×C₄	#14579129	1	1	yes	characteristic
217	C₂×C₄	#14579131	1	2	yes	—
218	C₂×C₄	#14579134	1	2	yes	—
219	C₂×C₄	#14579157	1	1	yes	characteristic
220	C₂×C₄	C₂×#11929611	1	2	yes	—
221	C₂×C₄	C₂×Dic₃₁₆	1	1	yes	characteristic
222	C₂×C₄	#14579183	1	1	yes	characteristic
223	C₂×C₄	#14579186	1	2	yes	—
224	C₂×C₄	#14579194	1	2	yes	—
225	C₈	—	2	4	no	—
226	C₈	—	8	1	no	—
227	C₈	—	316	4	no	—
228	C₂²	#19098472	1	1	yes	characteristic
229	C₂²	#19098763	1	2	yes	—
230	C₂²	#19098804	1	1	yes	characteristic
231	C₂²	#19098821	1	1	yes	characteristic
232	C₂²	#19098838	1	2	yes	—
233	C₄	—	2	2	no	—
234	C₄	—	4	2	no	—
235	C₄	—	8	1	no	—
236	C₄	—	632	4	no	—
237	C₄	#19098713	1	2	yes	—
238	C₄	#19098721	1	2	yes	—
239	C₄	#19098727	1	2	yes	—
240	C₄	#19098937	1	1	yes	characteristic
241	C₄	#19098953	1	1	yes	characteristic
242	C₂	#23762770	1	2	yes	—
243	C₂	#23762894	1	2	yes	—
244	C₂	#23764410	1	1	yes	characteristic
245	C₂	#23764487	1	1	yes	characteristic
246	C₂	#23764521	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098943

C₂

yes

maximal, characteristic

C₂×#19098848

C₂

yes

maximal

C₂×#19098310

C₂

yes

maximal

#23761235

C₂

yes

maximal, characteristic

C₇₉×#1984

C₂

yes

maximal, characteristic

C₂²×Dic₃₁₆

—

C₂×#14579161

C₂²

yes

—

—

—

—

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

C₂×#14579085

—

#19098310

—

C₂×C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#336×C₇₉

—

C₂²×Dic₁₅₈

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂²×C₇₉⋊C₈

—

—

—

—

D₄

yes

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

#14579092

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

#14579085

—

C₂²×Q₈×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄×C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

Dic₃₁₆

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

Q₁₆

yes

complemented

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

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

SD₁₆

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

#121

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

#120

yes

—

C₂×C₄×C₇₉

#121

yes

—

C₂×C₄×C₇₉

#127

yes

characteristic

C₂×C₄×C₇₉

C₂×SD₁₆

yes

—

C₂×C₄×C₇₉

C₂×Q₁₆

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

100

Dic₁₅₈

—

101

C₈×C₇₉

—

102

C₈×C₇₉

—

103

C₇₉⋊C₈

—

104

C₂²×C₇₉

#392

yes

characteristic

105

C₂²×C₇₉

#460

yes

—

106

C₂²×C₇₉

#467

yes

characteristic

107

C₂²×C₇₉

#470

yes

characteristic

108

C₂²×C₇₉

#473

yes

—

109

C₄×C₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

#450

yes

—

113

C₄×C₇₉

#451

yes

—

114

C₄×C₇₉

#452

yes

—

115

C₄×C₇₉

#492

yes

characteristic

116

C₄×C₇₉

#496

yes

characteristic

117

Dic₇₉

—

118

#10276

—

maximal, Sylow

119

C₂×C₇₉

#1670

yes

—

120

C₂×C₇₉

#1690

yes

—

121

C₂×C₇₉

#2001

yes

characteristic

122

C₂×C₇₉

#2014

yes

characteristic

123

C₂×C₇₉

#2020

yes

characteristic

124

C₂×#494

—

125

C₂×#475

—

126

#1984

D₇₉

yes

characteristic

127

C₂×#332

—

128

#1277

—

129

C₇₉

#10276

yes

characteristic, complemented, Sylow

130

C₂²×Q₁₆

—

158

—

131

C₂×C₄⋊Q₈

—

132

C₂×C₄×Q₈

C₂×D₇₉

yes

characteristic

133

#494

—

158

—

134

#475

—

158

—

135

#475

—

158

—

136

C₂×#106

—

158

—

137

C₂×C₄⋊C₈

—

138

C₂×C₄⋊C₈

C₂×D₇₉

yes

characteristic

139

C₂×#103

—

158

—

140

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

141

#336

—

142

#332

—

158

—

143

C₂²×Q₈

—

158

—

144

C₂²×Q₈

D₃₁₆

yes

characteristic

145

C₂×Q₁₆

—

316

—

146

C₂×Q₁₆

—

316

—

147

C₂×Q₁₆

—

158

—

148

C₂²×C₈

—

149

C₂²×C₈

—

158

—

150

C₂²×C₈

C₂²⋊D₇₉

yes

—

151

C₄⋊Q₈

—

152

C₄⋊Q₈

—

158

—

153

C₄⋊Q₈

—

158

—

154

C₄⋊Q₈

—

158

—

155

C₄×Q₈

—

156

C₄×Q₈

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

158

—

159

C₂×C₄⋊C₄

—

158

—

160

C₂×C₄⋊C₄

D₃₁₆

yes

characteristic

161

C₂×C₄²

—

162

C₂×C₄²

C₂²×D₇₉

yes

characteristic

163

#106

—

158

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

158

—

167

#103

—

158

—

168

C₄×C₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

316

—

173

C₂×Q₈

—

316

—

174

C₂×Q₈

—

316

—

175

C₂×Q₈

—

158

—

176

C₂×Q₈

Dic₃₁₆

yes

complemented

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

316

—

180

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

181

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

182

C₂²×C₄

#11929624

yes

characteristic

183

Q₁₆

—

316

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

316

—

189

C₂×C₈

—

316

—

190

C₂×C₈

—

158

—

191

C₂×C₈

#11929611

yes

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

316

—

195

C₄⋊C₄

—

316

—

196

C₄⋊C₄

—

158

—

197

C₄⋊C₄

—

158

—

198

C₄²

—

199

C₄²

—

200

C₄²

D₄×D₇₉

yes

—

201

C₄²

D₄×D₇₉

yes

—

202

C₂³

#14579135

yes

characteristic

203

Q₈

—

204

Q₈

—

205

Q₈

—

316

—

206

Q₈

—

632

—

207

Q₈

—

632

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

316

—

215

C₂×C₄

—

632

—

216

C₂×C₄

#14579129

yes

characteristic

217

C₂×C₄

#14579131

yes

—

218

C₂×C₄

#14579134

yes

—

219

C₂×C₄

#14579157

yes

characteristic

220

C₂×C₄

C₂×#11929611

yes

—

221

C₂×C₄

C₂×Dic₃₁₆

yes

characteristic

222

C₂×C₄

#14579183

yes

characteristic

223

C₂×C₄

#14579186

yes

—

224

C₂×C₄

#14579194

yes

—

225

C₈

—

226

C₈

—

227

C₈

—

316

—

228

C₂²

#19098472

yes

characteristic

229

C₂²

#19098763

yes

—

230

C₂²

#19098804

yes

characteristic

231

C₂²

#19098821

yes

characteristic

232

C₂²

#19098838

yes

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

632

—

237

C₄

#19098713

yes

—

238

C₄

#19098721

yes

—

239

C₄

#19098727

yes

—

240

C₄

#19098937

yes

characteristic

241

C₄

#19098953

yes

characteristic

242

C₂

#23762770

yes

—

243

C₂

#23762894

yes

—

244

C₂

#23764410

yes

characteristic

245

C₂

#23764487

yes

characteristic

246

C₂

#23764521

yes

characteristic

	subgroup	G/H
center	C₂³	#14579135
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1984	C₂
socle, prime radical	C₂³×C₇₉	#121
hypercenter	#1984	D₇₉
hypocenter	C₇₉	#10276
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

subgroup

G/H

center

C₂³

#14579135

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1984

C₂

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

N	H ≅ G/N	type
61. C₂×Q₈×C₇₉	Q₁₆	semidirect
129. C₇₉	#10276	semidirect
176. C₂×Q₈	Dic₃₁₆	semidirect

H ≅ G/N

type

61. C₂×Q₈×C₇₉

Q₁₆

semidirect

129. C₇₉

#10276

semidirect

176. C₂×Q₈

Dic₃₁₆

semidirect

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

subgroup	index
C₂×#19098943	2
C₂×#19098848	2
C₂×#19098310	2
#23761235	2
C₇₉×#1984	2
#10276	79

subgroup

index

C₇₉×#1984

Subgroups — #34190877

Conjugacy classes of subgroups

Complements

Maximal subgroups