Group #34186995 — subgroups

Subgroups — #34186995

Order 20224.

306 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 109 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	#23763537	C₂	1	1	yes	maximal, characteristic
2	#23763265	C₂	1	1	yes	maximal, characteristic
3	#23762170	C₂	1	1	yes	maximal, characteristic
4	#23762146	C₂	1	1	yes	maximal, characteristic
5	#23761302	C₂	1	1	yes	maximal, characteristic
6	#23761301	C₂	1	1	yes	maximal, characteristic
7	C₇₉×#1571	C₂	1	1	yes	maximal, characteristic
8	#19098616	C₂²	1	1	yes	characteristic
9	#19098587	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₈×Dic₇₉	—	2	1	no	—
12	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
13	#19098327	—	2	1	no	—
14	#19098327	—	2	1	no	—
15	#19098317	—	2	1	no	—
16	#19098315	C₄	1	2	yes	complemented
17	#19098313	—	2	2	no	—
18	#19098313	C₄	1	2	yes	complemented
19	#431×C₇₉	C₂²	1	1	yes	characteristic
20	#423×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
22	#335×C₇₉	—	2	2	no	—
23	C₂×#11929608	—	2	1	no	—
24	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
25	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
26	C₂×C₄⋊Dic₇₉	—	2	1	no	—
27	C₂×C₄×Dic₇₉	—	2	1	no	—
28	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
29	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
30	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
31	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
32	C₄×C₇₉⋊C₈	—	2	1	no	—
33	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
34	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
35	C₄×C₇₉⋊C₈	Q₈	1	1	yes	characteristic
36	C₄×C₇₉⋊C₈	Q₈	1	1	yes	characteristic
37	C₈×Dic₇₉	—	4	2	no	—
38	C₇₉⋊#95	Q₈	1	2	yes	—
39	C₂×M₁₆×C₇₉	—	2	1	no	—
40	C₂²×C₈×C₇₉	—	2	1	no	—
41	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₇₉	—	2	1	no	—
43	C₄⋊C₈×C₇₉	—	2	1	no	—
44	C₄⋊C₈×C₇₉	—	2	1	no	—
45	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
46	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
47	C₂²⋊C₈×C₇₉	—	2	1	no	—
48	C₄×C₈×C₇₉	—	2	1	no	—
49	C₂²×Dic₇₉	—	2	2	no	—
50	#11929608	—	4	1	no	—
51	#11929608	—	4	1	no	—
52	C₂×C₇₉⋊C₈	—	2	2	no	—
53	C₂×C₇₉⋊C₈	—	2	1	no	—
54	C₂×C₇₉⋊C₈	—	2	1	no	—
55	C₂×C₇₉⋊C₈	—	2	1	no	—
56	C₂×C₇₉⋊C₈	—	2	1	no	—
57	C₂×C₇₉⋊C₈	—	4	1	no	—
58	C₂×C₇₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₇₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₇₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₇₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
62	C₄⋊Dic₇₉	—	2	4	no	—
63	C₄×Dic₇₉	—	4	1	no	—
64	C₄×Dic₇₉	—	4	1	no	—
65	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
67	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
68	M₁₆×C₇₉	—	4	1	no	—
69	M₁₆×C₇₉	—	4	1	no	—
70	C₂×C₈×C₇₉	—	2	2	no	—
71	C₂×C₈×C₇₉	—	2	2	no	—
72	C₂×C₈×C₇₉	—	4	1	no	—
73	C₂×C₈×C₇₉	—	4	1	no	—
74	C₂×C₈×C₇₉	—	4	1	no	—
75	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
78	C₄²×C₇₉	#41	1	1	yes	characteristic
79	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
80	C₂×C₄×C₇₉	—	2	2	no	—
81	C₂×C₄×C₇₉	—	4	1	no	—
82	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₇₉	C₄×Q₈	1	1	yes	characteristic
85	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
86	C₂×C₄×C₇₉	#125	1	1	yes	characteristic
87	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
88	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
89	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
90	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
91	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
92	C₂×Dic₇₉	—	2	4	no	—
93	C₂×Dic₇₉	—	4	2	no	—
94	C₂×Dic₇₉	—	4	2	no	—
95	C₈×C₇₉	—	4	2	no	—
96	C₈×C₇₉	—	4	2	no	—
97	C₈×C₇₉	—	8	1	no	—
98	C₇₉⋊C₈	—	2	1	no	—
99	C₇₉⋊C₈	—	2	1	no	—
100	C₇₉⋊C₈	—	2	1	no	—
101	C₇₉⋊C₈	—	2	1	no	—
102	C₇₉⋊C₈	—	4	2	no	—
103	C₇₉⋊C₈	—	8	1	no	—
104	C₂²×C₇₉	—	2	1	no	—
105	C₂²×C₇₉	—	2	1	no	—
106	C₂²×C₇₉	#389	1	1	yes	characteristic
107	C₂²×C₇₉	#478	1	1	yes	characteristic
108	C₂²×C₇₉	#479	1	1	yes	characteristic
109	C₄×C₇₉	—	2	1	no	—
110	C₄×C₇₉	—	2	1	no	—
111	C₄×C₇₉	—	2	1	no	—
112	C₄×C₇₉	#427	1	1	yes	characteristic
113	C₄×C₇₉	#428	1	1	yes	characteristic
114	C₄×C₇₉	#443	1	2	yes	—
115	C₄×C₇₉	#463	1	1	yes	characteristic
116	C₄×C₇₉	#464	1	1	yes	characteristic
117	Dic₇₉	—	4	4	no	—
118	#9629	—	79	1	no	maximal, Sylow
119	C₂×C₇₉	—	2	1	no	—
120	C₂×C₇₉	—	2	1	no	—
121	C₂×C₇₉	#1945	1	1	yes	characteristic
122	C₂×C₇₉	#1949	1	1	yes	characteristic
123	C₂×C₇₉	#1953	1	1	yes	characteristic
124	#1837	—	79	1	no	—
125	C₈×C₄⋊C₄	—	79	1	no	—
126	#1571	D₇₉	1	1	yes	characteristic
127	#1570	—	79	1	no	—
128	#1564	—	79	1	no	—
129	#1303	—	79	1	no	—
130	#1303	—	79	1	no	—
131	C₇₉	#9629	1	1	yes	characteristic, complemented, Sylow
132	#431	—	79	1	no	—
133	#431	C₂×D₇₉	1	1	yes	characteristic
134	#423	—	79	1	no	—
135	#423	C₂×D₇₉	1	1	yes	characteristic
136	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
137	C₂×C₄×C₈	—	79	1	no	—
138	C₂×C₄×C₈	—	158	1	no	—
139	C₄×C₄⋊C₄	—	79	1	no	—
140	#341	—	158	1	no	—
141	#341	—	158	1	no	—
142	#336	—	158	1	no	—
143	#335	—	2	2	no	—
144	#335	—	79	2	no	—
145	#334	—	79	2	no	—
146	#334	—	158	2	no	—
147	C₂×M₁₆	—	2	1	no	—
148	C₂×M₁₆	—	158	1	no	—
149	C₂²×C₈	—	2	1	no	—
150	C₂²×C₈	—	79	1	no	—
151	C₂²×C₈	—	79	1	no	—
152	C₂×C₄⋊C₄	—	158	1	no	—
153	C₂×C₄²	—	158	1	no	—
154	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
155	C₄⋊C₈	—	2	1	no	—
156	C₄⋊C₈	—	2	1	no	—
157	C₄⋊C₈	—	2	1	no	—
158	C₄⋊C₈	—	79	2	no	—
159	C₄⋊C₈	—	158	1	no	—
160	C₄⋊C₈	—	158	1	no	—
161	C₄⋊C₈	C₄×D₇₉	1	2	yes	—
162	C₄⋊C₈	C₂²⋊D₇₉	1	2	yes	—
163	C₂²⋊C₈	—	2	1	no	—
164	C₂²⋊C₈	—	158	1	no	—
165	C₄×C₈	—	2	1	no	—
166	C₄×C₈	—	316	2	no	—
167	C₄×C₈	—	79	1	no	—
168	C₄×C₈	—	79	1	no	—
169	C₄×C₈	—	79	1	no	—
170	C₄×C₈	—	79	1	no	—
171	C₄×C₈	—	158	1	no	—
172	#95	—	79	2	no	—
173	C₂²×C₄	—	158	2	no	—
174	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
175	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
176	C₂²×C₄	#11929624	1	1	yes	characteristic
177	M₁₆	—	4	1	no	—
178	M₁₆	—	4	1	no	—
179	M₁₆	—	316	1	no	—
180	M₁₆	—	316	1	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	4	1	no	—
184	C₂×C₈	—	4	1	no	—
185	C₂×C₈	—	4	1	no	—
186	C₂×C₈	—	316	1	no	—
187	C₂×C₈	—	79	1	no	—
188	C₂×C₈	—	79	1	no	—
189	C₂×C₈	—	79	1	no	—
190	C₂×C₈	—	79	1	no	—
191	C₂×C₈	—	158	2	no	—
192	C₂×C₈	—	158	1	no	—
193	C₂×C₈	—	158	1	no	—
194	C₂×C₈	—	158	1	no	—
195	C₂×C₈	—	158	1	no	—
196	C₄⋊C₄	—	158	4	no	—
197	C₄²	—	316	1	no	—
198	C₄²	—	316	1	no	—
199	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
200	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
201	C₄²	Q₈×D₇₉	1	1	yes	characteristic
202	C₄²	#11929623	1	1	yes	characteristic
203	C₂³	#14579139	1	1	yes	characteristic
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	316	2	no	—
207	C₂×C₄	—	316	2	no	—
208	C₂×C₄	—	158	4	no	—
209	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
210	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
211	C₂×C₄	#14579126	1	1	yes	characteristic
212	C₂×C₄	#14579133	1	1	yes	characteristic
213	C₂×C₄	#14579151	1	1	yes	characteristic
214	C₂×C₄	#14579159	1	1	yes	characteristic
215	C₂×C₄	#14579180	1	1	yes	characteristic
216	C₂×C₄	#14579184	1	1	yes	characteristic
217	C₂×C₄	#14579185	1	1	yes	characteristic
218	C₂×C₄	#14579193	1	1	yes	characteristic
219	C₈	—	4	2	no	—
220	C₈	—	4	2	no	—
221	C₈	—	8	1	no	—
222	C₈	—	316	2	no	—
223	C₈	—	632	1	no	—
224	C₈	—	158	1	no	—
225	C₈	—	158	1	no	—
226	C₈	—	158	1	no	—
227	C₈	—	158	1	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	#19098458	1	1	yes	characteristic
231	C₂²	#19098866	1	1	yes	characteristic
232	C₂²	#19098869	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	2	1	no	—
236	C₄	—	316	4	no	—
237	C₄	#19098600	1	1	yes	characteristic
238	C₄	#19098604	1	1	yes	characteristic
239	C₄	#19098678	1	2	yes	—
240	C₄	#19098776	1	1	yes	characteristic
241	C₄	#19098787	1	1	yes	characteristic
242	C₂	—	2	1	no	—
243	C₂	—	2	1	no	—
244	C₂	#23764145	1	1	yes	characteristic
245	C₂	#23764165	1	1	yes	characteristic
246	C₂	#23764187	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23763537

C₂

yes

maximal, characteristic

#23763265

C₂

yes

maximal, characteristic

#23762170

C₂

yes

maximal, characteristic

#23762146

C₂

yes

maximal, characteristic

#23761302

C₂

yes

maximal, characteristic

#23761301

C₂

yes

maximal, characteristic

C₇₉×#1571

C₂

yes

maximal, characteristic

#19098616

C₂²

yes

characteristic

#19098587

C₂²

yes

characteristic

C₂×C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×Dic₇₉

—

C₄×C₄⋊Dic₇₉

C₂²

yes

—

—

—

C₄

yes

complemented

#19098313

—

#19098313

C₄

yes

complemented

#431×C₇₉

C₂²

yes

characteristic

#423×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₇₉

C₂²

yes

characteristic

#335×C₇₉

—

C₂×#11929608

—

C₂²×C₇₉⋊C₈

D₄

yes

characteristic

C₂²×C₇₉⋊C₈

D₄

yes

characteristic

C₂×C₄⋊Dic₇₉

—

C₂×C₄×Dic₇₉

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

C₂×C₄

yes

—

C₂²⋊(C₇₉⋊C₈)

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₇₉⋊C₈

Q₈

yes

characteristic

C₄×C₇₉⋊C₈

Q₈

yes

characteristic

C₈×Dic₇₉

—

C₇₉⋊#95

Q₈

yes

—

C₂×M₁₆×C₇₉

—

C₂²×C₈×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

C₂×C₄

yes

—

C₄⋊C₈×C₇₉

D₄

yes

—

C₂²⋊C₈×C₇₉

—

C₄×C₈×C₇₉

—

C₂²×Dic₇₉

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₇₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₇₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₇₉⋊C₈

C₄⋊C₄

yes

characteristic

C₄⋊Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×Q₈

yes

characteristic

C₄²×C₇₉

#41

yes

characteristic

C₂³×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

characteristic

C₂×C₄×C₇₉

C₄×Q₈

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

C₄⋊Q₈

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

100

C₇₉⋊C₈

—

101

C₇₉⋊C₈

—

102

C₇₉⋊C₈

—

103

C₇₉⋊C₈

—

104

C₂²×C₇₉

—

105

C₂²×C₇₉

—

106

C₂²×C₇₉

#389

yes

characteristic

107

C₂²×C₇₉

#478

yes

characteristic

108

C₂²×C₇₉

#479

yes

characteristic

109

C₄×C₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

#427

yes

characteristic

113

C₄×C₇₉

#428

yes

characteristic

114

C₄×C₇₉

#443

yes

—

115

C₄×C₇₉

#463

yes

characteristic

116

C₄×C₇₉

#464

yes

characteristic

117

Dic₇₉

—

118

#9629

—

maximal, Sylow

119

C₂×C₇₉

—

120

C₂×C₇₉

—

121

C₂×C₇₉

#1945

yes

characteristic

122

C₂×C₇₉

#1949

yes

characteristic

123

C₂×C₇₉

#1953

yes

characteristic

124

#1837

—

125

C₈×C₄⋊C₄

—

126

#1571

D₇₉

yes

characteristic

127

#1570

—

128

#1564

—

129

#1303

—

130

#1303

—

131

C₇₉

#9629

yes

characteristic, complemented, Sylow

132

#431

—

133

#431

C₂×D₇₉

yes

characteristic

134

#423

—

135

#423

C₂×D₇₉

yes

characteristic

136

C₂×C₄⋊C₈

C₂×D₇₉

yes

characteristic

137

C₂×C₄×C₈

—

138

C₂×C₄×C₈

—

158

—

139

C₄×C₄⋊C₄

—

140

#341

—

158

—

141

#341

—

158

—

142

#336

—

158

—

143

#335

—

144

#335

—

145

#334

—

146

#334

—

158

—

147

C₂×M₁₆

—

148

C₂×M₁₆

—

158

—

149

C₂²×C₈

—

150

C₂²×C₈

—

151

C₂²×C₈

—

152

C₂×C₄⋊C₄

—

158

—

153

C₂×C₄²

—

158

—

154

C₂×C₄²

C₂²×D₇₉

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

158

—

160

C₄⋊C₈

—

158

—

161

C₄⋊C₈

C₄×D₇₉

yes

—

162

C₄⋊C₈

C₂²⋊D₇₉

yes

—

163

C₂²⋊C₈

—

164

C₂²⋊C₈

—

158

—

165

C₄×C₈

—

166

C₄×C₈

—

316

—

167

C₄×C₈

—

168

C₄×C₈

—

169

C₄×C₈

—

170

C₄×C₈

—

171

C₄×C₈

—

158

—

172

#95

—

173

C₂²×C₄

—

158

—

174

C₂²×C₄

D₄×D₇₉

yes

characteristic

175

C₂²×C₄

Q₈×D₇₉

yes

characteristic

176

C₂²×C₄

#11929624

yes

characteristic

177

M₁₆

—

178

M₁₆

—

179

M₁₆

—

316

—

180

M₁₆

—

316

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

316

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

158

—

192

C₂×C₈

—

158

—

193

C₂×C₈

—

158

—

194

C₂×C₈

—

158

—

195

C₂×C₈

—

158

—

196

C₄⋊C₄

—

158

—

197

C₄²

—

316

—

198

C₄²

—

316

—

199

C₄²

C₂×C₄×D₇₉

yes

characteristic

200

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

201

C₄²

Q₈×D₇₉

yes

characteristic

202

C₄²

#11929623

yes

characteristic

203

C₂³

#14579139

yes

characteristic

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

316

—

207

C₂×C₄

—

316

—

208

C₂×C₄

—

158

—

209

C₂×C₄

C₄⋊C₄×D₇₉

yes

characteristic

210

C₂×C₄

C₄×C₂²⋊D₇₉

yes

characteristic

211

C₂×C₄

#14579126

yes

characteristic

212

C₂×C₄

#14579133

yes

characteristic

213

C₂×C₄

#14579151

yes

characteristic

214

C₂×C₄

#14579159

yes

characteristic

215

C₂×C₄

#14579180

yes

characteristic

216

C₂×C₄

#14579184

yes

characteristic

217

C₂×C₄

#14579185

yes

characteristic

218

C₂×C₄

#14579193

yes

characteristic

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

316

—

223

C₈

—

632

—

224

C₈

—

158

—

225

C₈

—

158

—

226

C₈

—

158

—

227

C₈

—

158

—

228

C₂²

—

229

C₂²

—

230

C₂²

#19098458

yes

characteristic

231

C₂²

#19098866

yes

characteristic

232

C₂²

#19098869

yes

characteristic

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

316

—

237

C₄

#19098600

yes

characteristic

238

C₄

#19098604

yes

characteristic

239

C₄

#19098678

yes

—

240

C₄

#19098776

yes

characteristic

241

C₄

#19098787

yes

characteristic

242

C₂

—

243

C₂

—

244

C₂

#23764145

yes

characteristic

245

C₂

#23764165

yes

characteristic

246

C₂

#23764187

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579133
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1571	C₂
socle	C₂²×C₇₉	#389
prime radical	C₂³×C₇₉	C₂²⋊Q₈
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1571	D₇₉
hypocenter	C₇₉	#9629
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

subgroup

G/H

center

C₂×C₄

#14579133

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1571

C₂

socle

C₂²×C₇₉

#389

prime radical

C₂³×C₇₉

C₂²⋊Q₈

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

N	H ≅ G/N	type
16. #19098315	C₄	semidirect
18. #19098313	C₄	semidirect
131. C₇₉	#9629	semidirect

H ≅ G/N

type

16. #19098315

C₄

semidirect

18. #19098313

C₄

semidirect

131. C₇₉

#9629

semidirect

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

subgroup	index
#23763537	2
#23763265	2
#23762170	2
#23762146	2
#23761302	2
#23761301	2
C₇₉×#1571	2
#9629	79

subgroup

index

C₇₉×#1571

Subgroups — #34186995

Conjugacy classes of subgroups

Complements

Maximal subgroups