Group #34185869 — subgroups

Subgroups — #34185869

Order 20224.

504 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 111 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	#23772467	C₂	1	1	yes	maximal, characteristic
2	#23762135	C₂	1	1	yes	maximal, characteristic
3	#23762085	C₂	1	2	yes	maximal, complemented
4	#23761290	C₂	1	2	yes	maximal, complemented
5	C₇₉×#3152	C₂	1	1	yes	maximal, characteristic
6	#19098641	—	2	2	no	—
7	D₄×C₇₉⋊C₈	—	2	2	no	—
8	#19098616	C₂²	1	2	yes	—
9	#19098587	C₂²	1	2	yes	—
10	#19098530	—	2	2	no	—
11	#19098312	—	2	1	no	—
12	#19098309	—	2	2	no	—
13	#19098309	—	2	2	no	—
14	#19098307	—	2	1	no	—
15	C₂×#137×C₇₉	—	2	2	no	—
16	#532×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
18	#497×C₇₉	C₄	1	4	yes	—
19	#494×C₇₉	—	2	1	no	—
20	#492×C₇₉	—	2	1	no	—
21	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×#11929608	—	2	2	no	—
23	C₂×#11929608	—	2	2	no	—
24	C₂²×C₇₉⋊C₈	—	2	2	no	—
25	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
26	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
27	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
28	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
29	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
30	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
31	C₄×C₇₉⋊C₈	—	2	2	no	—
32	C₂×#41×C₇₉	D₄	1	2	yes	—
33	C₂²×Q₈×C₇₉	—	2	1	no	—
34	#137×C₇₉	—	4	4	no	—
35	#137×C₇₉	—	4	4	no	—
36	C₂×Q₁₆×C₇₉	—	2	4	no	—
37	C₂×SD₁₆×C₇₉	—	2	4	no	—
38	C₂×M₁₆×C₇₉	—	2	1	no	—
39	C₄⋊Q₈×C₇₉	—	2	2	no	—
40	C₄⋊Q₈×C₇₉	—	2	1	no	—
41	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
42	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
43	#127×C₇₉	D₄	1	1	yes	characteristic
44	#124×C₇₉	C₂×C₄	1	2	yes	—
45	#121×C₇₉	—	2	2	no	—
46	C₄×D₄×C₇₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
48	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
49	#97×C₇₉	C₂×C₄	1	2	yes	—
50	C₄×C₈×C₇₉	—	2	1	no	—
51	#11929608	—	8	2	no	—
52	#11929608	—	8	2	no	—
53	C₂×C₇₉⋊C₈	—	2	2	no	—
54	C₂×C₇₉⋊C₈	—	2	2	no	—
55	C₂×C₇₉⋊C₈	—	4	2	no	—
56	C₂×C₇₉⋊C₈	—	8	2	no	—
57	#41×C₇₉	—	4	2	no	—
58	#41×C₇₉	—	4	2	no	—
59	C₂×Q₈×C₇₉	—	2	2	no	—
60	C₂×Q₈×C₇₉	—	4	2	no	—
61	C₂×Q₈×C₇₉	—	4	2	no	—
62	C₂×Q₈×C₇₉	—	4	1	no	—
63	C₂×Q₈×C₇₉	C₂²⋊C₄	1	2	yes	—
64	C₂×D₄×C₇₉	—	2	2	no	—
65	C₂×D₄×C₇₉	—	2	2	no	—
66	C₂×D₄×C₇₉	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₇₉	—	2	2	no	—
68	C₂²×C₄×C₇₉	—	4	1	no	—
69	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₇₉	#41	1	2	yes	—
71	Q₁₆×C₇₉	—	4	8	no	—
72	SD₁₆×C₇₉	—	4	8	no	—
73	M₁₆×C₇₉	—	2	2	no	—
74	M₁₆×C₇₉	—	2	2	no	—
75	C₂×C₈×C₇₉	—	2	2	no	—
76	C₄⋊C₄×C₇₉	—	2	2	no	—
77	C₄⋊C₄×C₇₉	—	2	4	no	—
78	C₄⋊C₄×C₇₉	—	4	2	no	—
79	C₂²⋊C₄×C₇₉	—	2	4	no	—
80	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
81	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₇₉	C₂×D₄	1	2	yes	—
83	C₂³×C₇₉	—	2	2	no	—
84	C₂³×C₇₉	#123	1	1	yes	characteristic
85	Q₈×C₇₉	—	4	2	no	—
86	Q₈×C₇₉	—	4	4	no	—
87	Q₈×C₇₉	—	8	1	no	—
88	Q₈×C₇₉	—	8	1	no	—
89	D₄×C₇₉	—	4	2	no	—
90	D₄×C₇₉	—	4	2	no	—
91	D₄×C₇₉	—	4	2	no	—
92	D₄×C₇₉	—	8	2	no	—
93	C₂×C₄×C₇₉	—	2	1	no	—
94	C₂×C₄×C₇₉	—	2	1	no	—
95	C₂×C₄×C₇₉	—	2	2	no	—
96	C₂×C₄×C₇₉	—	2	2	no	—
97	C₂×C₄×C₇₉	—	2	2	no	—
98	C₂×C₄×C₇₉	—	4	2	no	—
99	C₂×C₄×C₇₉	—	4	2	no	—
100	C₂×C₄×C₇₉	—	4	2	no	—
101	C₂×C₄×C₇₉	—	8	2	no	—
102	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
104	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
105	C₂×C₄×C₇₉	#121	1	2	yes	—
106	C₈×C₇₉	—	2	4	no	—
107	C₇₉⋊C₈	—	4	2	no	—
108	C₇₉⋊C₈	—	4	2	no	—
109	C₇₉⋊C₈	—	8	2	no	—
110	C₂²×C₇₉	—	2	1	no	—
111	C₂²×C₇₉	—	2	2	no	—
112	C₂²×C₇₉	—	4	2	no	—
113	C₂²×C₇₉	—	4	4	no	—
114	C₂²×C₇₉	#386	1	1	yes	characteristic
115	C₄×C₇₉	—	2	1	no	—
116	C₄×C₇₉	—	2	2	no	—
117	C₄×C₇₉	—	4	2	no	—
118	C₄×C₇₉	—	8	2	no	—
119	C₄×C₇₉	#453	1	1	yes	characteristic
120	C₄×C₇₉	#453	1	1	yes	characteristic
121	C₄×C₇₉	#471	1	2	yes	—
122	C₄×C₇₉	#473	1	2	yes	—
123	#9435	—	79	1	no	maximal, Sylow
124	C₂×C₇₉	—	4	1	no	—
125	C₂×C₇₉	—	8	2	no	—
126	C₂×C₇₉	#1887	1	1	yes	characteristic
127	C₂×C₇₉	#1908	1	2	yes	—
128	#3152	D₇₉	1	1	yes	characteristic
129	#2979	—	79	1	no	—
130	#1560	—	79	1	no	—
131	#1549	—	79	2	no	—
132	#1299	—	79	2	no	—
133	C₇₉	#9435	1	1	yes	characteristic, complemented, Sylow
134	C₂×#137	—	2	2	no	—
135	#532	C₂×D₇₉	1	1	yes	characteristic
136	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
137	#497	Dic₇₉	1	4	yes	—
138	#494	—	2	1	no	—
139	#492	—	2	1	no	—
140	#436	—	158	2	no	—
141	C₈×D₄	—	158	2	no	—
142	#431	—	79	2	no	—
143	#423	—	79	2	no	—
144	#408	—	158	2	no	—
145	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
146	#333	—	158	1	no	—
147	#332	—	158	2	no	—
148	#332	—	158	2	no	—
149	#331	—	158	1	no	—
150	C₂×#41	C₂²⋊D₇₉	1	2	yes	—
151	C₂²×Q₈	—	2	1	no	—
152	#137	—	4	4	no	—
153	#137	—	4	4	no	—
154	C₂×Q₁₆	—	2	4	no	—
155	C₂×SD₁₆	—	2	4	no	—
156	C₂×M₁₆	—	2	1	no	—
157	C₂×M₁₆	—	158	2	no	—
158	C₂×M₁₆	—	158	2	no	—
159	C₂²×C₈	—	158	2	no	—
160	C₄⋊Q₈	—	2	2	no	—
161	C₄⋊Q₈	—	2	1	no	—
162	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
163	C₄⋊Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
164	#127	C₂²⋊D₇₉	1	1	yes	characteristic
165	#124	C₂×Dic₇₉	1	2	yes	—
166	#121	—	2	2	no	—
167	C₄×D₄	—	2	2	no	—
168	C₂×C₄⋊C₄	—	2	2	no	—
169	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
170	C₄⋊C₈	—	79	2	no	—
171	C₄⋊C₈	—	79	2	no	—
172	C₄⋊C₈	—	158	2	no	—
173	C₄⋊C₈	—	158	2	no	—
174	C₂²⋊C₈	—	158	4	no	—
175	C₂²⋊C₈	—	158	2	no	—
176	#97	C₂×Dic₇₉	1	2	yes	—
177	C₄×C₈	—	2	1	no	—
178	C₄×C₈	—	158	2	no	—
179	#41	—	4	2	no	—
180	#41	—	4	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	C₂²⋊Dic₇₉	1	2	yes	—
186	C₂×D₄	—	2	2	no	—
187	C₂×D₄	—	2	2	no	—
188	C₂×D₄	C₂²⋊Dic₇₉	1	2	yes	—
189	C₂²×C₄	—	2	2	no	—
190	C₂²×C₄	—	4	1	no	—
191	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
192	C₂²×C₄	#11929623	1	2	yes	—
193	Q₁₆	—	4	8	no	—
194	SD₁₆	—	4	8	no	—
195	M₁₆	—	2	2	no	—
196	M₁₆	—	2	2	no	—
197	M₁₆	—	632	2	no	—
198	M₁₆	—	632	2	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	316	2	no	—
201	C₂×C₈	—	632	2	no	—
202	C₂×C₈	—	158	2	no	—
203	C₂×C₈	—	158	2	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	2	4	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	2	4	no	—
208	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
209	C₄²	D₄×D₇₉	1	2	yes	—
210	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
211	C₂³	—	2	2	no	—
212	C₂³	#14579142	1	1	yes	characteristic
213	Q₈	—	4	2	no	—
214	Q₈	—	4	4	no	—
215	Q₈	—	8	1	no	—
216	Q₈	—	8	1	no	—
217	D₄	—	4	2	no	—
218	D₄	—	4	2	no	—
219	D₄	—	4	2	no	—
220	D₄	—	8	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	8	2	no	—
230	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
231	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
232	C₂×C₄	#14579129	1	1	yes	characteristic
233	C₂×C₄	#14579133	1	2	yes	—
234	C₈	—	2	4	no	—
235	C₈	—	316	2	no	—
236	C₈	—	316	2	no	—
237	C₈	—	632	2	no	—
238	C₂²	—	2	1	no	—
239	C₂²	—	2	2	no	—
240	C₂²	—	4	2	no	—
241	C₂²	—	4	4	no	—
242	C₂²	#19098443	1	1	yes	characteristic
243	C₄	—	2	1	no	—
244	C₄	—	2	2	no	—
245	C₄	—	4	2	no	—
246	C₄	—	8	2	no	—
247	C₄	#19098730	1	1	yes	characteristic
248	C₄	#19098730	1	1	yes	characteristic
249	C₄	#19098828	1	2	yes	—
250	C₄	#19098836	1	2	yes	—
251	C₂	—	4	1	no	—
252	C₂	—	8	2	no	—
253	C₂	#23763799	1	1	yes	characteristic
254	C₂	#23763917	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#23772467

C₂

yes

maximal, characteristic

#23762135

C₂

yes

maximal, characteristic

#23762085

C₂

yes

maximal, complemented

#23761290

C₂

yes

maximal, complemented

C₇₉×#3152

C₂

yes

maximal, characteristic

#19098641

—

D₄×C₇₉⋊C₈

—

#19098616

C₂²

yes

—

#19098587

C₂²

yes

—

—

—

—

—

—

C₂×#137×C₇₉

—

#532×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

#497×C₇₉

C₄

yes

—

#494×C₇₉

—

#492×C₇₉

—

C₄×M₁₆×C₇₉

C₂²

yes

characteristic

C₂×#11929608

—

C₂×#11929608

—

C₂²×C₇₉⋊C₈

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

C₄×C₇₉⋊C₈

—

C₂×#41×C₇₉

D₄

yes

—

C₂²×Q₈×C₇₉

—

#137×C₇₉

—

#137×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×SD₁₆×C₇₉

—

C₂×M₁₆×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

C₂×C₄

yes

—

C₄⋊Q₈×C₇₉

D₄

yes

characteristic

#127×C₇₉

D₄

yes

characteristic

#124×C₇₉

C₂×C₄

yes

—

#121×C₇₉

—

C₄×D₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#97×C₇₉

C₂×C₄

yes

—

C₄×C₈×C₇₉

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

#41×C₇₉

—

#41×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

C₂²⋊C₄

yes

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

—

Q₁₆×C₇₉

—

SD₁₆×C₇₉

—

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

#123

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

100

C₂×C₄×C₇₉

—

101

C₂×C₄×C₇₉

—

102

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

103

C₂×C₄×C₇₉

C₄×D₄

yes

—

104

C₂×C₄×C₇₉

#120

yes

characteristic

105

C₂×C₄×C₇₉

#121

yes

—

106

C₈×C₇₉

—

107

C₇₉⋊C₈

—

108

C₇₉⋊C₈

—

109

C₇₉⋊C₈

—

110

C₂²×C₇₉

—

111

C₂²×C₇₉

—

112

C₂²×C₇₉

—

113

C₂²×C₇₉

—

114

C₂²×C₇₉

#386

yes

characteristic

115

C₄×C₇₉

—

116

C₄×C₇₉

—

117

C₄×C₇₉

—

118

C₄×C₇₉

—

119

C₄×C₇₉

#453

yes

characteristic

120

C₄×C₇₉

#453

yes

characteristic

121

C₄×C₇₉

#471

yes

—

122

C₄×C₇₉

#473

yes

—

123

#9435

—

maximal, Sylow

124

C₂×C₇₉

—

125

C₂×C₇₉

—

126

C₂×C₇₉

#1887

yes

characteristic

127

C₂×C₇₉

#1908

yes

—

128

#3152

D₇₉

yes

characteristic

129

#2979

—

130

#1560

—

131

#1549

—

132

#1299

—

133

C₇₉

#9435

yes

characteristic, complemented, Sylow

134

C₂×#137

—

135

#532

C₂×D₇₉

yes

characteristic

136

C₂×C₄⋊Q₈

C₂×D₇₉

yes

characteristic

137

#497

Dic₇₉

yes

—

138

#494

—

139

#492

—

140

#436

—

158

—

141

C₈×D₄

—

158

—

142

#431

—

143

#423

—

144

#408

—

158

—

145

C₄×M₁₆

C₂×D₇₉

yes

characteristic

146

#333

—

158

—

147

#332

—

158

—

148

#332

—

158

—

149

#331

—

158

—

150

C₂×#41

C₂²⋊D₇₉

yes

—

151

C₂²×Q₈

—

152

#137

—

153

#137

—

154

C₂×Q₁₆

—

155

C₂×SD₁₆

—

156

C₂×M₁₆

—

157

C₂×M₁₆

—

158

—

158

C₂×M₁₆

—

158

—

159

C₂²×C₈

—

158

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

C₂×Dic₇₉

yes

—

163

C₄⋊Q₈

C₂²⋊D₇₉

yes

characteristic

164

#127

C₂²⋊D₇₉

yes

characteristic

165

#124

C₂×Dic₇₉

yes

—

166

#121

—

167

C₄×D₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄²

C₂²×D₇₉

yes

characteristic

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

158

—

173

C₄⋊C₈

—

158

—

174

C₂²⋊C₈

—

158

—

175

C₂²⋊C₈

—

158

—

176

#97

C₂×Dic₇₉

yes

—

177

C₄×C₈

—

178

C₄×C₈

—

158

—

179

#41

—

180

#41

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

C₂²⋊Dic₇₉

yes

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

C₂²⋊Dic₇₉

yes

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

192

C₂²×C₄

#11929623

yes

—

193

Q₁₆

—

194

SD₁₆

—

195

M₁₆

—

196

M₁₆

—

197

M₁₆

—

632

—

198

M₁₆

—

632

—

199

C₂×C₈

—

200

C₂×C₈

—

316

—

201

C₂×C₈

—

632

—

202

C₂×C₈

—

158

—

203

C₂×C₈

—

158

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₂²⋊C₄

—

208

C₄²

C₂²×Dic₇₉

yes

characteristic

209

C₄²

D₄×D₇₉

yes

—

210

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

211

C₂³

—

212

C₂³

#14579142

yes

characteristic

213

Q₈

—

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

D₄

—

218

D₄

—

219

D₄

—

220

D₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

C₂×C₂²⋊Dic₇₉

yes

characteristic

231

C₂×C₄

D₄×Dic₇₉

yes

—

232

C₂×C₄

#14579129

yes

characteristic

233

C₂×C₄

#14579133

yes

—

234

C₈

—

235

C₈

—

316

—

236

C₈

—

316

—

237

C₈

—

632

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

#19098443

yes

characteristic

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

#19098730

yes

characteristic

248

C₄

#19098730

yes

characteristic

249

C₄

#19098828

yes

—

250

C₄

#19098836

yes

—

251

C₂

—

252

C₂

—

253

C₂

#23763799

yes

characteristic

254

C₂

#23763917

yes

—

	subgroup	G/H
center	C₂²	#19098443
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#3152	C₂
socle	C₂²×C₇₉	#386
prime radical	#532×C₇₉	C₂²
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#3152	D₇₉
hypocenter	C₇₉	#9435
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3152

subgroup

G/H

center

C₂²

#19098443

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#3152

C₂

socle

C₂²×C₇₉

#386

prime radical

#532×C₇₉

C₂²

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3152

N	H ≅ G/N	type
3. #23762085	C₂	semidirect
4. #23761290	C₂	semidirect
133. C₇₉	#9435	semidirect

H ≅ G/N

type

3. #23762085

C₂

semidirect

4. #23761290

C₂

semidirect

133. C₇₉

#9435

semidirect

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

subgroup	index
#23772467	2
#23762135	2
#23762085	2
#23761290	2
C₇₉×#3152	2
#9435	79

subgroup

index

C₇₉×#3152

Subgroups — #34185869

Conjugacy classes of subgroups

Complements

Maximal subgroups