Group #34183229 — subgroups

Subgroups — #34183229

Order 20224.

502 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 103 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	#23772471	C₂	1	1	yes	maximal, characteristic, complemented
2	#23762062	C₂	1	1	yes	maximal, characteristic, complemented
3	#23761869	C₂	1	2	yes	maximal, complemented
4	#23761299	C₂	1	2	yes	maximal, complemented
5	C₇₉×#3150	C₂	1	1	yes	maximal, characteristic
6	#19098635	—	2	4	no	—
7	#19098620	C₂²	1	2	yes	—
8	#19098616	C₂²	1	2	yes	—
9	#19098530	—	2	2	no	—
10	#19098312	—	2	1	no	—
11	#19098307	—	2	1	no	—
12	D₄⋊(C₇₉⋊C₈)	—	2	4	no	—
13	C₂×#135×C₇₉	—	2	2	no	—
14	#532×C₇₉	C₂²	1	1	yes	characteristic
15	#532×C₇₉	C₂²	1	1	yes	characteristic
16	#497×C₇₉	—	2	1	no	—
17	#497×C₇₉	C₄	1	2	yes	—
18	#496×C₇₉	—	2	1	no	—
19	#496×C₇₉	C₄	1	2	yes	—
20	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#11929608	—	2	2	no	—
22	C₂²×C₇₉⋊C₈	—	2	2	no	—
23	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
24	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	—
25	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
26	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
27	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
28	#14579072	—	2	2	no	—
29	C₄×C₇₉⋊C₈	—	2	2	no	—
30	C₂×#41×C₇₉	—	2	1	no	—
31	C₂×#41×C₇₉	D₄	1	2	yes	—
32	#135×C₇₉	—	4	4	no	—
33	#135×C₇₉	—	4	4	no	—
34	C₂×Q₁₆×C₇₉	—	2	2	no	—
35	C₂×SD₁₆×C₇₉	—	2	2	no	—
36	C₂×SD₁₆×C₇₉	—	2	2	no	—
37	C₂×D₈×C₇₉	—	2	2	no	—
38	C₂²×C₈×C₇₉	—	2	1	no	—
39	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
40	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
41	#127×C₇₉	C₂×C₄	1	1	yes	characteristic
42	#127×C₇₉	D₄	1	1	yes	characteristic
43	#124×C₇₉	—	2	1	no	—
44	#124×C₇₉	C₂×C₄	1	2	yes	—
45	#121×C₇₉	—	2	2	no	—
46	#121×C₇₉	—	2	2	no	—
47	C₄×D₄×C₇₉	—	2	2	no	—
48	C₄×D₄×C₇₉	—	2	2	no	—
49	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
50	#97×C₇₉	—	2	1	no	—
51	#97×C₇₉	C₂×C₄	1	2	yes	—
52	#11929608	—	8	2	no	—
53	C₂×C₇₉⋊C₈	—	2	4	no	—
54	C₂×C₇₉⋊C₈	—	4	2	no	—
55	C₂×C₇₉⋊C₈	—	8	2	no	—
56	#41×C₇₉	—	4	2	no	—
57	#41×C₇₉	—	4	2	no	—
58	#41×C₇₉	—	4	2	no	—
59	#41×C₇₉	—	4	2	no	—
60	C₂×Q₈×C₇₉	—	2	1	no	—
61	C₂×Q₈×C₇₉	C₂²⋊C₄	1	2	yes	—
62	C₂×D₄×C₇₉	—	2	2	no	—
63	C₂×D₄×C₇₉	—	2	1	no	—
64	C₂×D₄×C₇₉	—	2	2	no	—
65	C₂×D₄×C₇₉	—	2	2	no	—
66	C₂×D₄×C₇₉	—	4	1	no	—
67	C₂×D₄×C₇₉	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₇₉	—	2	2	no	—
69	C₂²×C₄×C₇₉	—	4	1	no	—
70	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₇₉	#41	1	2	yes	—
72	Q₁₆×C₇₉	—	4	4	no	—
73	SD₁₆×C₇₉	—	4	4	no	—
74	SD₁₆×C₇₉	—	4	4	no	—
75	D₈×C₇₉	—	4	4	no	—
76	C₂×C₈×C₇₉	—	2	4	no	—
77	C₂×C₈×C₇₉	—	2	2	no	—
78	C₄⋊C₄×C₇₉	—	2	2	no	—
79	C₄⋊C₄×C₇₉	—	2	2	no	—
80	C₂²⋊C₄×C₇₉	—	2	4	no	—
81	C₂²⋊C₄×C₇₉	—	4	2	no	—
82	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
83	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
84	C₄²×C₇₉	C₂×D₄	1	2	yes	—
85	C₂³×C₇₉	—	2	2	no	—
86	C₂³×C₇₉	—	4	1	no	—
87	C₂³×C₇₉	#123	1	1	yes	characteristic
88	Q₈×C₇₉	—	4	2	no	—
89	Q₈×C₇₉	—	4	2	no	—
90	D₄×C₇₉	—	4	2	no	—
91	D₄×C₇₉	—	4	2	no	—
92	D₄×C₇₉	—	4	4	no	—
93	D₄×C₇₉	—	8	2	no	—
94	D₄×C₇₉	—	8	2	no	—
95	D₄×C₇₉	—	8	1	no	—
96	D₄×C₇₉	—	8	1	no	—
97	C₂×C₄×C₇₉	—	2	2	no	—
98	C₂×C₄×C₇₉	—	2	2	no	—
99	C₂×C₄×C₇₉	—	4	2	no	—
100	C₂×C₄×C₇₉	—	4	2	no	—
101	C₂×C₄×C₇₉	—	4	2	no	—
102	C₂×C₄×C₇₉	—	4	1	no	—
103	C₂×C₄×C₇₉	—	8	2	no	—
104	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
106	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
107	C₂×C₄×C₇₉	#121	1	2	yes	—
108	C₈×C₇₉	—	2	4	no	—
109	C₇₉⋊C₈	—	4	4	no	—
110	C₇₉⋊C₈	—	8	2	no	—
111	C₂²×C₇₉	—	2	2	no	—
112	C₂²×C₇₉	—	2	1	no	—
113	C₂²×C₇₉	—	4	4	no	—
114	C₂²×C₇₉	—	4	2	no	—
115	C₂²×C₇₉	—	8	2	no	—
116	C₂²×C₇₉	—	8	1	no	—
117	C₂²×C₇₉	#386	1	1	yes	characteristic
118	C₄×C₇₉	—	2	2	no	—
119	C₄×C₇₉	—	2	2	no	—
120	C₄×C₇₉	—	2	1	no	—
121	C₄×C₇₉	—	4	2	no	—
122	C₄×C₇₉	—	8	1	no	—
123	C₄×C₇₉	#453	1	2	yes	—
124	#9007	—	79	1	no	maximal, Sylow
125	C₂×C₇₉	—	4	1	no	—
126	C₂×C₇₉	—	8	2	no	—
127	C₂×C₇₉	—	16	1	no	—
128	C₂×C₇₉	#1881	1	2	yes	—
129	C₂×C₇₉	#1887	1	1	yes	characteristic
130	#3150	D₇₉	1	1	yes	characteristic
131	#2980	—	79	1	no	—
132	#1543	—	79	1	no	—
133	#1496	—	79	2	no	—
134	#1302	—	79	2	no	—
135	C₇₉	#9007	1	1	yes	characteristic, complemented, Sylow
136	C₂×#135	—	2	2	no	—
137	#532	C₂×D₇₉	1	1	yes	characteristic
138	#532	C₂×D₇₉	1	1	yes	characteristic
139	#497	—	2	1	no	—
140	#497	Dic₇₉	1	2	yes	—
141	#496	—	2	1	no	—
142	#496	Dic₇₉	1	2	yes	—
143	#435	—	158	4	no	—
144	#432	—	79	2	no	—
145	#431	—	79	2	no	—
146	#408	—	158	2	no	—
147	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
148	#333	—	158	1	no	—
149	#331	—	158	1	no	—
150	D₄⋊C₈	—	158	4	no	—
151	C₂×#41	—	2	1	no	—
152	C₂×#41	C₂²⋊D₇₉	1	2	yes	—
153	#135	—	4	4	no	—
154	#135	—	4	4	no	—
155	C₂×Q₁₆	—	2	2	no	—
156	C₂×SD₁₆	—	2	2	no	—
157	C₂×SD₁₆	—	2	2	no	—
158	C₂×D₈	—	2	2	no	—
159	C₂×M₁₆	—	158	2	no	—
160	C₂²×C₈	—	2	1	no	—
161	C₂²×C₈	—	158	2	no	—
162	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
163	C₄⋊Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
164	#127	C₂×Dic₇₉	1	1	yes	characteristic
165	#127	C₂²⋊D₇₉	1	1	yes	characteristic
166	#124	—	2	1	no	—
167	#124	C₂×Dic₇₉	1	2	yes	—
168	#121	—	2	2	no	—
169	#121	—	2	2	no	—
170	C₄×D₄	—	2	2	no	—
171	C₄×D₄	—	2	2	no	—
172	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
173	C₄⋊C₈	—	79	4	no	—
174	C₄⋊C₈	—	158	2	no	—
175	C₂²⋊C₈	—	158	2	no	—
176	C₂²⋊C₈	—	158	4	no	—
177	C₂²⋊C₈	—	158	2	no	—
178	#97	—	2	1	no	—
179	#97	—	158	2	no	—
180	#97	C₂×Dic₇₉	1	2	yes	—
181	C₄×C₈	—	158	2	no	—
182	#41	—	4	2	no	—
183	#41	—	4	2	no	—
184	#41	—	4	2	no	—
185	#41	—	4	2	no	—
186	C₂×Q₈	—	2	1	no	—
187	C₂×Q₈	C₂²⋊Dic₇₉	1	2	yes	—
188	C₂×D₄	—	2	2	no	—
189	C₂×D₄	—	2	1	no	—
190	C₂×D₄	—	2	2	no	—
191	C₂×D₄	—	2	2	no	—
192	C₂×D₄	—	4	1	no	—
193	C₂×D₄	C₂²⋊Dic₇₉	1	2	yes	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	—	4	1	no	—
196	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
197	C₂²×C₄	#11929623	1	2	yes	—
198	Q₁₆	—	4	4	no	—
199	SD₁₆	—	4	4	no	—
200	SD₁₆	—	4	4	no	—
201	D₈	—	4	4	no	—
202	M₁₆	—	632	2	no	—
203	C₂×C₈	—	2	4	no	—
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	316	2	no	—
206	C₂×C₈	—	632	2	no	—
207	C₂×C₈	—	158	4	no	—
208	C₄⋊C₄	—	2	2	no	—
209	C₄⋊C₄	—	2	2	no	—
210	C₂²⋊C₄	—	2	4	no	—
211	C₂²⋊C₄	—	4	2	no	—
212	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
213	C₄²	D₄×D₇₉	1	2	yes	—
214	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
215	C₂³	—	2	2	no	—
216	C₂³	—	4	1	no	—
217	C₂³	#14579142	1	1	yes	characteristic
218	Q₈	—	4	2	no	—
219	Q₈	—	4	2	no	—
220	D₄	—	4	2	no	—
221	D₄	—	4	2	no	—
222	D₄	—	4	4	no	—
223	D₄	—	8	2	no	—
224	D₄	—	8	2	no	—
225	D₄	—	8	1	no	—
226	D₄	—	8	1	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	4	1	no	—
233	C₂×C₄	—	8	2	no	—
234	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
235	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
236	C₂×C₄	#14579129	1	1	yes	characteristic
237	C₂×C₄	#14579133	1	2	yes	—
238	C₈	—	2	4	no	—
239	C₈	—	316	4	no	—
240	C₈	—	632	2	no	—
241	C₂²	—	2	2	no	—
242	C₂²	—	2	1	no	—
243	C₂²	—	4	4	no	—
244	C₂²	—	4	2	no	—
245	C₂²	—	8	2	no	—
246	C₂²	—	8	1	no	—
247	C₂²	#19098443	1	1	yes	characteristic
248	C₄	—	2	2	no	—
249	C₄	—	2	2	no	—
250	C₄	—	2	1	no	—
251	C₄	—	4	2	no	—
252	C₄	—	8	1	no	—
253	C₄	#19098730	1	2	yes	—
254	C₂	—	4	1	no	—
255	C₂	—	8	2	no	—
256	C₂	—	16	1	no	—
257	C₂	#23763764	1	2	yes	—
258	C₂	#23763799	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23772471

C₂

yes

maximal, characteristic, complemented

#23762062

C₂

yes

maximal, characteristic, complemented

#23761869

C₂

yes

maximal, complemented

#23761299

C₂

yes

maximal, complemented

C₇₉×#3150

C₂

yes

maximal, characteristic

#19098635

—

#19098620

C₂²

yes

—

#19098616

C₂²

yes

—

#19098530

—

#19098312

—

#19098307

—

D₄⋊(C₇₉⋊C₈)

—

C₂×#135×C₇₉

—

#532×C₇₉

C₂²

yes

characteristic

#532×C₇₉

C₂²

yes

characteristic

#497×C₇₉

—

#497×C₇₉

C₄

yes

—

#496×C₇₉

—

#496×C₇₉

C₄

yes

—

C₂×#97×C₇₉

C₂²

yes

characteristic

C₂×#11929608

—

C₂²×C₇₉⋊C₈

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

C₄×C₇₉⋊C₈

—

C₂×#41×C₇₉

—

C₂×#41×C₇₉

D₄

yes

—

#135×C₇₉

—

#135×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×SD₁₆×C₇₉

—

C₂×SD₁₆×C₇₉

—

C₂×D₈×C₇₉

—

C₂²×C₈×C₇₉

—

C₄⋊Q₈×C₇₉

C₂×C₄

yes

characteristic

C₄⋊Q₈×C₇₉

D₄

yes

characteristic

#127×C₇₉

C₂×C₄

yes

characteristic

#127×C₇₉

D₄

yes

characteristic

#124×C₇₉

—

#124×C₇₉

C₂×C₄

yes

—

#121×C₇₉

—

#121×C₇₉

—

C₄×D₄×C₇₉

—

C₄×D₄×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#97×C₇₉

—

#97×C₇₉

C₂×C₄

yes

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

#41×C₇₉

—

#41×C₇₉

—

#41×C₇₉

—

#41×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

C₂²⋊C₄

yes

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

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

—

SD₁₆×C₇₉

—

D₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊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

—

C₂³×C₇₉

#123

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

100

C₂×C₄×C₇₉

—

101

C₂×C₄×C₇₉

—

102

C₂×C₄×C₇₉

—

103

C₂×C₄×C₇₉

—

104

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

105

C₂×C₄×C₇₉

C₄×D₄

yes

—

106

C₂×C₄×C₇₉

#120

yes

characteristic

107

C₂×C₄×C₇₉

#121

yes

—

108

C₈×C₇₉

—

109

C₇₉⋊C₈

—

110

C₇₉⋊C₈

—

111

C₂²×C₇₉

—

112

C₂²×C₇₉

—

113

C₂²×C₇₉

—

114

C₂²×C₇₉

—

115

C₂²×C₇₉

—

116

C₂²×C₇₉

—

117

C₂²×C₇₉

#386

yes

characteristic

118

C₄×C₇₉

—

119

C₄×C₇₉

—

120

C₄×C₇₉

—

121

C₄×C₇₉

—

122

C₄×C₇₉

—

123

C₄×C₇₉

#453

yes

—

124

#9007

—

maximal, Sylow

125

C₂×C₇₉

—

126

C₂×C₇₉

—

127

C₂×C₇₉

—

128

C₂×C₇₉

#1881

yes

—

129

C₂×C₇₉

#1887

yes

characteristic

130

#3150

D₇₉

yes

characteristic

131

#2980

—

132

#1543

—

133

#1496

—

134

#1302

—

135

C₇₉

#9007

yes

characteristic, complemented, Sylow

136

C₂×#135

—

137

#532

C₂×D₇₉

yes

characteristic

138

#532

C₂×D₇₉

yes

characteristic

139

#497

—

140

#497

Dic₇₉

yes

—

141

#496

—

142

#496

Dic₇₉

yes

—

143

#435

—

158

—

144

#432

—

145

#431

—

146

#408

—

158

—

147

C₂×#97

C₂×D₇₉

yes

characteristic

148

#333

—

158

—

149

#331

—

158

—

150

D₄⋊C₈

—

158

—

151

C₂×#41

—

152

C₂×#41

C₂²⋊D₇₉

yes

—

153

#135

—

154

#135

—

155

C₂×Q₁₆

—

156

C₂×SD₁₆

—

157

C₂×SD₁₆

—

158

C₂×D₈

—

159

C₂×M₁₆

—

158

—

160

C₂²×C₈

—

161

C₂²×C₈

—

158

—

162

C₄⋊Q₈

C₂×Dic₇₉

yes

characteristic

163

C₄⋊Q₈

C₂²⋊D₇₉

yes

characteristic

164

#127

C₂×Dic₇₉

yes

characteristic

165

#127

C₂²⋊D₇₉

yes

characteristic

166

#124

—

167

#124

C₂×Dic₇₉

yes

—

168

#121

—

169

#121

—

170

C₄×D₄

—

171

C₄×D₄

—

172

C₂×C₄²

C₂²×D₇₉

yes

characteristic

173

C₄⋊C₈

—

174

C₄⋊C₈

—

158

—

175

C₂²⋊C₈

—

158

—

176

C₂²⋊C₈

—

158

—

177

C₂²⋊C₈

—

158

—

178

#97

—

179

#97

—

158

—

180

#97

C₂×Dic₇₉

yes

—

181

C₄×C₈

—

158

—

182

#41

—

183

#41

—

184

#41

—

185

#41

—

186

C₂×Q₈

—

187

C₂×Q₈

C₂²⋊Dic₇₉

yes

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

C₂²⋊Dic₇₉

yes

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

197

C₂²×C₄

#11929623

yes

—

198

Q₁₆

—

199

SD₁₆

—

200

SD₁₆

—

201

D₈

—

202

M₁₆

—

632

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

316

—

206

C₂×C₈

—

632

—

207

C₂×C₈

—

158

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₂²⋊C₄

—

211

C₂²⋊C₄

—

212

C₄²

C₂²×Dic₇₉

yes

characteristic

213

C₄²

D₄×D₇₉

yes

—

214

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

215

C₂³

—

216

C₂³

—

217

C₂³

#14579142

yes

characteristic

218

Q₈

—

219

Q₈

—

220

D₄

—

221

D₄

—

222

D₄

—

223

D₄

—

224

D₄

—

225

D₄

—

226

D₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

C₂×C₂²⋊Dic₇₉

yes

characteristic

235

C₂×C₄

D₄×Dic₇₉

yes

—

236

C₂×C₄

#14579129

yes

characteristic

237

C₂×C₄

#14579133

yes

—

238

C₈

—

239

C₈

—

316

—

240

C₈

—

632

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

#19098443

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

#19098730

yes

—

254

C₂

—

255

C₂

—

256

C₂

—

257

C₂

#23763764

yes

—

258

C₂

#23763799

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579129
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting, prime radical	C₇₉×#3150	C₂
socle	C₂²×C₇₉	#386
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#3150	D₇₉
hypocenter	C₇₉	#9007
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3150

subgroup

G/H

center

C₂×C₄

#14579129

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting, prime radical

C₇₉×#3150

C₂

socle

C₂²×C₇₉

#386

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3150

N	H ≅ G/N	type
1. #23772471	C₂	semidirect
2. #23762062	C₂	semidirect
3. #23761869	C₂	semidirect
4. #23761299	C₂	semidirect
135. C₇₉	#9007	semidirect

H ≅ G/N

type

1. #23772471

C₂

semidirect

2. #23762062

C₂

semidirect

3. #23761869

C₂

semidirect

4. #23761299

C₂

semidirect

135. C₇₉

#9007

semidirect

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

subgroup	index
#23772471	2
#23762062	2
#23761869	2
#23761299	2
C₇₉×#3150	2
#9007	79

subgroup

index

C₇₉×#3150

Subgroups — #34183229

Conjugacy classes of subgroups

Complements

Maximal subgroups