Group #34185680 — subgroups

Subgroups — #34185680

Order 20224.

486 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 123 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	#23772485	C₂	1	1	yes	maximal, characteristic
2	#23763396	C₂	1	1	yes	maximal, characteristic
3	#23762072	C₂	1	2	yes	maximal
4	#23761303	C₂	1	2	yes	maximal
5	C₇₉×#2546	C₂	1	1	yes	maximal, characteristic
6	#19098694	—	2	4	no	—
7	#19098620	—	2	2	no	—
8	#19098616	C₂²	1	2	yes	—
9	#19098587	C₂²	1	2	yes	—
10	C₂×#14579080	—	2	1	no	—
11	#19098332	—	2	1	no	—
12	#19098309	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₇₉	—	2	1	no	—
14	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	#398×C₇₉	C₄	1	4	yes	—
17	#391×C₇₉	—	2	1	no	—
18	#389×C₇₉	—	2	2	no	—
19	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×#11929608	—	2	2	no	—
21	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
22	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
23	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
24	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	—
25	#14579080	—	4	2	no	—
26	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
27	#14579072	—	2	4	no	—
28	C₄×C₇₉⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₇₉	—	2	1	no	—
30	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
31	C₄⋊Q₈×C₇₉	—	2	2	no	—
32	C₄⋊Q₈×C₇₉	—	2	2	no	—
33	C₄⋊Q₈×C₇₉	—	4	4	no	—
34	C₄×Q₈×C₇₉	—	2	2	no	—
35	C₄×Q₈×C₇₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
38	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
41	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₇₉	—	2	1	no	—
43	C₂×C₄²×C₇₉	D₄	1	2	yes	—
44	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
45	#95×C₇₉	—	2	4	no	—
46	#95×C₇₉	C₂×C₄	1	2	yes	—
47	#11929608	—	4	2	no	—
48	#11929608	—	4	2	no	—
49	C₂×C₇₉⋊C₈	—	2	4	no	—
50	C₂×C₇₉⋊C₈	—	4	2	no	—
51	C₂×Q₈×C₇₉	—	2	2	no	—
52	C₂×Q₈×C₇₉	—	2	2	no	—
53	C₂×Q₈×C₇₉	—	2	1	no	—
54	C₂×Q₈×C₇₉	—	2	1	no	—
55	C₂×Q₈×C₇₉	—	4	2	no	—
56	C₂×Q₈×C₇₉	—	4	2	no	—
57	C₂×Q₈×C₇₉	—	4	1	no	—
58	C₂×Q₈×C₇₉	—	4	1	no	—
59	C₂²×C₄×C₇₉	—	2	2	no	—
60	C₂²×C₄×C₇₉	—	2	2	no	—
61	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
66	C₄⋊C₄×C₇₉	—	2	4	no	—
67	C₄⋊C₄×C₇₉	—	2	4	no	—
68	C₄⋊C₄×C₇₉	—	2	2	no	—
69	C₄⋊C₄×C₇₉	—	2	4	no	—
70	C₄⋊C₄×C₇₉	—	4	8	no	—
71	C₄⋊C₄×C₇₉	—	4	1	no	—
72	C₄⋊C₄×C₇₉	—	4	1	no	—
73	C₄²×C₇₉	—	2	2	no	—
74	C₄²×C₇₉	—	2	2	no	—
75	C₄²×C₇₉	—	4	2	no	—
76	C₄²×C₇₉	C₂×D₄	1	2	yes	—
77	C₄²×C₇₉	#41	1	2	yes	—
78	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	Q₈×C₇₉	—	4	2	no	—
80	Q₈×C₇₉	—	4	2	no	—
81	Q₈×C₇₉	—	8	2	no	—
82	Q₈×C₇₉	—	8	2	no	—
83	C₂×C₄×C₇₉	—	2	2	no	—
84	C₂×C₄×C₇₉	—	2	4	no	—
85	C₂×C₄×C₇₉	—	2	2	no	—
86	C₂×C₄×C₇₉	—	2	2	no	—
87	C₂×C₄×C₇₉	—	2	2	no	—
88	C₂×C₄×C₇₉	—	2	2	no	—
89	C₂×C₄×C₇₉	—	4	1	no	—
90	C₂×C₄×C₇₉	—	4	2	no	—
91	C₂×C₄×C₇₉	—	4	2	no	—
92	C₂×C₄×C₇₉	—	4	2	no	—
93	C₂×C₄×C₇₉	—	4	2	no	—
94	C₂×C₄×C₇₉	—	4	2	no	—
95	C₂×C₄×C₇₉	—	4	2	no	—
96	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
97	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
98	C₂×C₄×C₇₉	#121	1	2	yes	—
99	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
100	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
101	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
102	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
103	C₇₉⋊C₈	—	4	4	no	—
104	C₇₉⋊C₈	—	8	2	no	—
105	C₂²×C₇₉	—	2	1	no	—
106	C₂²×C₇₉	—	2	1	no	—
107	C₂²×C₇₉	#386	1	1	yes	characteristic
108	C₂²×C₇₉	#417	1	1	yes	characteristic
109	C₂²×C₇₉	#418	1	1	yes	characteristic
110	C₄×C₇₉	—	2	1	no	—
111	C₄×C₇₉	—	2	2	no	—
112	C₄×C₇₉	—	4	4	no	—
113	C₄×C₇₉	—	4	2	no	—
114	C₄×C₇₉	—	4	2	no	—
115	C₄×C₇₉	—	8	2	no	—
116	C₄×C₇₉	#456	1	2	yes	—
117	C₄×C₇₉	#468	1	2	yes	—
118	C₄×C₇₉	#469	1	2	yes	—
119	#9402	—	79	1	no	maximal, Sylow
120	C₂×C₇₉	—	2	1	no	—
121	C₂×C₇₉	—	2	1	no	—
122	C₂×C₇₉	#1886	1	1	yes	characteristic
123	C₂×C₇₉	#1895	1	1	yes	characteristic
124	C₂×C₇₉	#1915	1	1	yes	characteristic
125	#2983	—	79	1	no	—
126	#2546	D₇₉	1	1	yes	characteristic
127	#1801	—	79	1	no	—
128	#1546	—	79	2	no	—
129	#1303	—	79	2	no	—
130	C₇₉	#9402	1	1	yes	characteristic, complemented, Sylow
131	C₂×C₄⋊Q₈	—	2	1	no	—
132	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
133	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
134	#446	—	158	4	no	—
135	#432	—	158	2	no	—
136	#431	—	79	2	no	—
137	#423	—	79	2	no	—
138	C₂×#101	—	158	1	no	—
139	#398	Dic₇₉	1	4	yes	—
140	#391	—	2	1	no	—
141	#389	—	2	2	no	—
142	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
143	#343	—	158	1	no	—
144	#332	—	158	4	no	—
145	C₂²×Q₈	—	2	1	no	—
146	C₂²×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
147	C₂×M₁₆	—	158	2	no	—
148	C₄⋊Q₈	—	2	2	no	—
149	C₄⋊Q₈	—	2	2	no	—
150	C₄⋊Q₈	—	4	4	no	—
151	C₄×Q₈	—	2	2	no	—
152	C₄×Q₈	—	2	2	no	—
153	C₂×C₄⋊C₄	—	2	1	no	—
154	C₂×C₄⋊C₄	—	2	4	no	—
155	C₂×C₄⋊C₄	—	2	1	no	—
156	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
157	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
158	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
159	C₂×C₄²	—	2	1	no	—
160	C₂×C₄²	C₂²⋊D₇₉	1	2	yes	—
161	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
162	C₄⋊C₈	—	79	4	no	—
163	C₄⋊C₈	—	158	4	no	—
164	C₄⋊C₈	—	158	2	no	—
165	C₄⋊C₈	—	158	2	no	—
166	#101	—	316	2	no	—
167	C₂²⋊C₈	—	158	2	no	—
168	#97	—	158	4	no	—
169	C₄×C₈	—	158	2	no	—
170	#95	—	2	4	no	—
171	#95	C₂×Dic₇₉	1	2	yes	—
172	C₂×Q₈	—	2	2	no	—
173	C₂×Q₈	—	2	1	no	—
174	C₂×Q₈	—	2	2	no	—
175	C₂×Q₈	—	2	1	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	—	4	1	no	—
178	C₂×Q₈	—	4	2	no	—
179	C₂×Q₈	—	4	1	no	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	C₂²⋊Dic₇₉	1	2	yes	—
183	C₂²×C₄	C₂²⋊Dic₇₉	1	2	yes	—
184	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
185	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
187	M₁₆	—	316	2	no	—
188	M₁₆	—	316	2	no	—
189	C₂×C₈	—	316	2	no	—
190	C₂×C₈	—	158	4	no	—
191	C₄⋊C₄	—	2	4	no	—
192	C₄⋊C₄	—	2	4	no	—
193	C₄⋊C₄	—	2	2	no	—
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	4	8	no	—
196	C₄⋊C₄	—	4	1	no	—
197	C₄⋊C₄	—	4	1	no	—
198	C₄²	—	2	2	no	—
199	C₄²	—	2	2	no	—
200	C₄²	—	4	2	no	—
201	C₄²	D₄×D₇₉	1	2	yes	—
202	C₄²	#11929623	1	2	yes	—
203	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
204	Q₈	—	4	2	no	—
205	Q₈	—	4	2	no	—
206	Q₈	—	8	2	no	—
207	Q₈	—	8	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
222	C₂×C₄	#14579129	1	1	yes	characteristic
223	C₂×C₄	#14579133	1	2	yes	—
224	C₂×C₄	#14579142	1	1	yes	characteristic
225	C₂×C₄	#14579186	1	1	yes	characteristic
226	C₂×C₄	#14579187	1	2	yes	—
227	C₂×C₄	#14579191	1	1	yes	characteristic
228	C₈	—	316	4	no	—
229	C₈	—	632	2	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	2	1	no	—
232	C₂²	#19098443	1	1	yes	characteristic
233	C₂²	#19098564	1	1	yes	characteristic
234	C₂²	#19098568	1	1	yes	characteristic
235	C₄	—	2	1	no	—
236	C₄	—	2	2	no	—
237	C₄	—	4	4	no	—
238	C₄	—	4	2	no	—
239	C₄	—	4	2	no	—
240	C₄	—	8	2	no	—
241	C₄	#19098745	1	2	yes	—
242	C₄	#19098807	1	2	yes	—
243	C₄	#19098814	1	2	yes	—
244	C₂	—	2	1	no	—
245	C₂	—	2	1	no	—
246	C₂	#23763794	1	1	yes	characteristic
247	C₂	#23763839	1	1	yes	characteristic
248	C₂	#23763953	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23772485

C₂

yes

maximal, characteristic

#23763396

C₂

yes

maximal, characteristic

#23762072

C₂

yes

maximal

#23761303

C₂

yes

maximal

C₇₉×#2546

C₂

yes

maximal, characteristic

#19098694

—

#19098620

—

#19098616

C₂²

yes

—

#19098587

C₂²

yes

—

C₂×#14579080

—

#19098332

—

#19098309

—

C₂×C₄⋊Q₈×C₇₉

—

C₂×C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

C₂×C₄×Q₈×C₇₉

C₂²

yes

characteristic

#398×C₇₉

C₄

yes

—

#391×C₇₉

—

#389×C₇₉

—

C₄×C₄⋊C₄×C₇₉

C₂²

yes

characteristic

C₂×#11929608

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

#14579080

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

C₄×C₇₉⋊C₈

—

C₂²×Q₈×C₇₉

—

C₂²×Q₈×C₇₉

D₄

yes

characteristic

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#95×C₇₉

—

#95×C₇₉

C₂×C₄

yes

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

#41

yes

—

C₂³×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

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

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄×D₄

yes

—

C₂×C₄×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

#121

yes

—

C₂×C₄×C₇₉

#123

yes

characteristic

100

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

characteristic

101

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

—

102

C₂×C₄×C₇₉

#137

yes

characteristic

103

C₇₉⋊C₈

—

104

C₇₉⋊C₈

—

105

C₂²×C₇₉

—

106

C₂²×C₇₉

—

107

C₂²×C₇₉

#386

yes

characteristic

108

C₂²×C₇₉

#417

yes

characteristic

109

C₂²×C₇₉

#418

yes

characteristic

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

—

113

C₄×C₇₉

—

114

C₄×C₇₉

—

115

C₄×C₇₉

—

116

C₄×C₇₉

#456

yes

—

117

C₄×C₇₉

#468

yes

—

118

C₄×C₇₉

#469

yes

—

119

#9402

—

maximal, Sylow

120

C₂×C₇₉

—

121

C₂×C₇₉

—

122

C₂×C₇₉

#1886

yes

characteristic

123

C₂×C₇₉

#1895

yes

characteristic

124

C₂×C₇₉

#1915

yes

characteristic

125

#2983

—

126

#2546

D₇₉

yes

characteristic

127

#1801

—

128

#1546

—

129

#1303

—

130

C₇₉

#9402

yes

characteristic, complemented, Sylow

131

C₂×C₄⋊Q₈

—

132

C₂×C₄⋊Q₈

C₂×D₇₉

yes

characteristic

133

C₂×C₄×Q₈

C₂×D₇₉

yes

characteristic

134

#446

—

158

—

135

#432

—

158

—

136

#431

—

137

#423

—

138

C₂×#101

—

158

—

139

#398

Dic₇₉

yes

—

140

#391

—

141

#389

—

142

C₄×C₄⋊C₄

C₂×D₇₉

yes

characteristic

143

#343

—

158

—

144

#332

—

158

—

145

C₂²×Q₈

—

146

C₂²×Q₈

C₂²⋊D₇₉

yes

characteristic

147

C₂×M₁₆

—

158

—

148

C₄⋊Q₈

—

149

C₄⋊Q₈

—

150

C₄⋊Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

C₂×Dic₇₉

yes

—

157

C₂×C₄⋊C₄

C₂×Dic₇₉

yes

—

158

C₂×C₄⋊C₄

C₂²⋊D₇₉

yes

characteristic

159

C₂×C₄²

—

160

C₂×C₄²

C₂²⋊D₇₉

yes

—

161

C₂×C₄²

C₂²×D₇₉

yes

characteristic

162

C₄⋊C₈

—

163

C₄⋊C₈

—

158

—

164

C₄⋊C₈

—

158

—

165

C₄⋊C₈

—

158

—

166

#101

—

316

—

167

C₂²⋊C₈

—

158

—

168

#97

—

158

—

169

C₄×C₈

—

158

—

170

#95

—

171

#95

C₂×Dic₇₉

yes

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

C₂²⋊Dic₇₉

yes

—

183

C₂²×C₄

C₂²⋊Dic₇₉

yes

—

184

C₂²×C₄

C₂²×Dic₇₉

yes

characteristic

185

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

186

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

187

M₁₆

—

316

—

188

M₁₆

—

316

—

189

C₂×C₈

—

316

—

190

C₂×C₈

—

158

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

201

C₄²

D₄×D₇₉

yes

—

202

C₄²

#11929623

yes

—

203

C₂³

C₂×C₂²⋊Dic₇₉

yes

characteristic

204

Q₈

—

205

Q₈

—

206

Q₈

—

207

Q₈

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

D₄×Dic₇₉

yes

—

222

C₂×C₄

#14579129

yes

characteristic

223

C₂×C₄

#14579133

yes

—

224

C₂×C₄

#14579142

yes

characteristic

225

C₂×C₄

#14579186

yes

characteristic

226

C₂×C₄

#14579187

yes

—

227

C₂×C₄

#14579191

yes

characteristic

228

C₈

—

316

—

229

C₈

—

632

—

230

C₂²

—

231

C₂²

—

232

C₂²

#19098443

yes

characteristic

233

C₂²

#19098564

yes

characteristic

234

C₂²

#19098568

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

#19098745

yes

—

242

C₄

#19098807

yes

—

243

C₄

#19098814

yes

—

244

C₂

—

245

C₂

—

246

C₂

#23763794

yes

characteristic

247

C₂

#23763839

yes

characteristic

248

C₂

#23763953

yes

characteristic

	subgroup	G/H
center	C₂²	#19098443
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#2546	C₂
socle	C₂²×C₇₉	#386
prime radical	C₂³×C₇₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#2546	D₇₉
hypocenter	C₇₉	#9402
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2546

subgroup

G/H

center

C₂²

#19098443

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#2546

C₂

socle

C₂²×C₇₉

#386

prime radical

C₂³×C₇₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2546

N	H ≅ G/N	type
130. C₇₉	#9402	semidirect

H ≅ G/N

type

130. C₇₉

#9402

semidirect

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

subgroup	index
#23772485	2
#23763396	2
#23762072	2
#23761303	2
C₇₉×#2546	2
#9402	79

subgroup

index

C₇₉×#2546

Subgroups — #34185680

Conjugacy classes of subgroups

Complements

Maximal subgroups