Group #34187433 — subgroups

Subgroups — #34187433

Order 20224.

422 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 119 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	#23773986	C₂	1	1	yes	maximal, characteristic
2	#23764343	C₂	1	2	yes	maximal
3	#23761898	C₂	1	2	yes	maximal
4	#23761689	C₂	1	1	yes	maximal, characteristic
5	C₄×#106×C₇₉	C₂	1	1	yes	maximal, characteristic
6	#19099120	C₂²	1	2	yes	—
7	#19098968	C₄	1	1	yes	characteristic, complemented
8	#19098943	C₄	1	1	yes	characteristic, complemented
9	#19098914	C₄	1	2	yes	complemented
10	#19098804	—	2	1	no	—
11	#19098804	—	2	1	no	—
12	C₄×Dic₃₁₆	—	2	1	no	—
13	C₄×Dic₃₁₆	—	2	1	no	—
14	#19098616	C₂²	1	1	yes	characteristic
15	C₄×#11929608	C₂²	1	1	yes	characteristic
16	#19098323	—	2	4	no	—
17	#19098299	—	2	4	no	—
18	#19098285	—	2	1	no	—
19	#19098284	—	2	1	no	—
20	C₂×#106×C₇₉	—	2	1	no	—
21	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
23	#340×C₇₉	—	2	1	no	—
24	C₂×Dic₃₁₆	—	2	1	no	—
25	C₂×Dic₃₁₆	—	2	1	no	—
26	C₂×#11929608	D₄	1	2	yes	—
27	#14579161	C₂×C₄	1	2	yes	—
28	#14579161	C₂×C₄	1	2	yes	—
29	#14579153	—	2	2	no	—
30	#14579140	—	2	2	no	—
31	#14579140	—	2	2	no	—
32	C₄×Dic₁₅₈	—	2	2	no	—
33	C₄×Dic₁₅₈	—	2	2	no	—
34	#14579120	—	2	2	no	—
35	#14579095	—	2	1	no	—
36	#14579095	—	2	1	no	—
37	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
38	#14579086	—	2	2	no	—
39	#14579086	—	2	2	no	—
40	C₂²⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
41	#14579072	—	2	1	no	—
42	C₄×C₇₉⋊C₈	—	2	1	no	—
43	C₄×C₇₉⋊C₈	—	2	1	no	—
44	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
47	C₂×C₄²×C₇₉	—	2	2	no	—
48	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
49	#106×C₇₉	—	2	4	no	—
50	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
51	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
52	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
53	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
54	#95×C₇₉	—	2	2	no	—
55	C₂×Dic₁₅₈	—	2	2	no	—
56	C₂×Dic₁₅₈	—	2	2	no	—
57	Dic₃₁₆	—	4	2	no	—
58	Dic₃₁₆	—	4	2	no	—
59	#11929608	—	2	4	no	—
60	C₂×C₇₉⋊C₈	—	2	2	no	—
61	C₂×C₇₉⋊C₈	—	2	2	no	—
62	C₄⋊Dic₇₉	—	2	2	no	—
63	C₄⋊Dic₇₉	—	2	2	no	—
64	C₄⋊Dic₇₉	—	2	2	no	—
65	C₄⋊Dic₇₉	—	2	2	no	—
66	Dic₇₉⋊C₄	—	4	2	no	—
67	Dic₇₉⋊C₄	—	4	2	no	—
68	C₂²⋊Dic₇₉	—	4	2	no	—
69	C₄×Dic₇₉	—	4	2	no	—
70	C₂²×C₄×C₇₉	—	4	2	no	—
71	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
74	C₂×C₈×C₇₉	—	2	2	no	—
75	C₂×C₈×C₇₉	—	4	1	no	—
76	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₄⋊C₄×C₇₉	—	2	4	no	—
81	C₄⋊C₄×C₇₉	—	4	2	no	—
82	C₄²×C₇₉	—	4	4	no	—
83	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
84	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
85	C₄²×C₇₉	#41	1	1	yes	characteristic
86	C₄²×C₇₉	#41	1	1	yes	characteristic
87	C₂³×C₇₉	#127	1	1	yes	characteristic
88	C₂×C₄×C₇₉	—	2	1	no	—
89	C₂×C₄×C₇₉	—	2	1	no	—
90	C₂×C₄×C₇₉	—	4	1	no	—
91	C₂×C₄×C₇₉	—	4	4	no	—
92	C₂×C₄×C₇₉	—	8	2	no	—
93	C₂×C₄×C₇₉	—	8	2	no	—
94	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
96	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
97	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
98	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
99	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
100	C₂×C₄×C₇₉	#137	1	4	yes	—
101	C₂×Dic₇₉	—	4	2	no	—
102	C₂×Dic₇₉	—	4	2	no	—
103	Dic₁₅₈	—	4	2	no	—
104	Dic₁₅₈	—	4	2	no	—
105	Dic₁₅₈	—	8	2	no	—
106	C₈×C₇₉	—	2	1	no	—
107	C₈×C₇₉	—	2	1	no	—
108	C₈×C₇₉	—	2	1	no	—
109	C₈×C₇₉	#104	1	2	yes	—
110	C₇₉⋊C₈	—	4	2	no	—
111	C₇₉⋊C₈	—	4	2	no	—
112	C₂²×C₇₉	—	2	1	no	—
113	C₂²×C₇₉	—	2	1	no	—
114	C₂²×C₇₉	#390	1	1	yes	characteristic
115	C₂²×C₇₉	#497	1	2	yes	—
116	C₄×C₇₉	—	2	1	no	—
117	C₄×C₇₉	—	2	1	no	—
118	C₄×C₇₉	—	2	1	no	—
119	C₄×C₇₉	—	8	4	no	—
120	C₄×C₇₉	C₂×#104	1	1	yes	characteristic
121	C₄×C₇₉	#421	1	1	yes	characteristic
122	C₄×C₇₉	#441	1	2	yes	—
123	C₄×C₇₉	#470	1	2	yes	—
124	Dic₇₉	—	8	2	no	—
125	Dic₇₉	—	8	2	no	—
126	#9720	—	79	1	no	maximal, Sylow
127	C₂×C₇₉	—	2	2	no	—
128	C₂×C₇₉	#1971	1	1	yes	characteristic
129	C₂×C₇₉	#1976	1	1	yes	characteristic
130	C₂×C₇₉	#1980	1	1	yes	characteristic
131	#3170	—	79	1	no	—
132	#1986	—	79	2	no	—
133	C₄×#106	D₇₉	1	1	yes	characteristic
134	#1503	—	79	2	no	—
135	#1451	—	79	1	no	—
136	C₇₉	#9720	1	1	yes	characteristic, complemented, Sylow
137	#533	—	79	2	no	—
138	#500	—	79	1	no	—
139	#494	—	79	1	no	—
140	#487	—	79	2	no	—
141	#467	—	158	1	no	—
142	#467	—	158	1	no	—
143	C₄×Q₁₆	—	158	1	no	—
144	C₄×Q₁₆	—	158	1	no	—
145	#431	—	79	1	no	—
146	C₂×#106	—	2	1	no	—
147	C₄×M₁₆	—	79	1	no	—
148	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
149	C₄×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
150	#340	—	2	1	no	—
151	#339	—	158	4	no	—
152	#328	—	158	4	no	—
153	#322	—	158	1	no	—
154	#322	—	158	1	no	—
155	C₂×Q₁₆	—	158	1	no	—
156	C₂×Q₁₆	—	158	1	no	—
157	C₂×M₁₆	—	79	2	no	—
158	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
159	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
160	C₄⋊Q₈	—	79	2	no	—
161	C₄⋊Q₈	—	79	2	no	—
162	#125	—	158	2	no	—
163	C₂²⋊Q₈	—	158	2	no	—
164	C₂²⋊Q₈	—	158	2	no	—
165	C₄×Q₈	—	158	2	no	—
166	C₄×Q₈	—	158	2	no	—
167	#117	—	158	2	no	—
168	C₂×C₄⋊C₄	—	2	2	no	—
169	C₂×C₄²	—	2	2	no	—
170	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
171	#107	—	158	1	no	—
172	#107	—	158	1	no	—
173	#106	—	2	4	no	—
174	C₄⋊C₈	—	158	1	no	—
175	#103	—	158	2	no	—
176	#103	—	158	2	no	—
177	C₂²⋊C₈	—	79	2	no	—
178	#97	—	158	1	no	—
179	C₄×C₈	—	158	1	no	—
180	C₄×C₈	—	158	1	no	—
181	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
182	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
183	C₄×C₈	D₃₁₆	1	1	yes	characteristic
184	C₄×C₈	D₃₁₆	1	1	yes	characteristic
185	#95	—	2	2	no	—
186	C₂×Q₈	—	158	2	no	—
187	C₂×Q₈	—	158	2	no	—
188	C₂²×C₄	—	4	2	no	—
189	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
190	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
191	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
192	Q₁₆	—	316	2	no	—
193	Q₁₆	—	316	2	no	—
194	M₁₆	—	158	4	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	—	158	2	no	—
198	C₂×C₈	—	158	2	no	—
199	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
200	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
201	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
202	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
203	C₄⋊C₄	—	2	4	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	316	2	no	—
206	C₄⋊C₄	—	316	2	no	—
207	C₄⋊C₄	—	158	2	no	—
208	C₄⋊C₄	—	158	2	no	—
209	C₄⋊C₄	—	158	2	no	—
210	C₄⋊C₄	—	158	2	no	—
211	C₂²⋊C₄	—	316	2	no	—
212	C₄²	—	4	4	no	—
213	C₄²	—	316	2	no	—
214	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
215	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
216	C₄²	#11929625	1	1	yes	characteristic
217	C₄²	#11929625	1	1	yes	characteristic
218	C₂³	#14579157	1	1	yes	characteristic
219	Q₈	—	316	2	no	—
220	Q₈	—	316	2	no	—
221	Q₈	—	632	2	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	4	4	no	—
226	C₂×C₄	—	8	2	no	—
227	C₂×C₄	—	8	2	no	—
228	C₂×C₄	—	316	2	no	—
229	C₂×C₄	—	316	2	no	—
230	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
231	C₂×C₄	#14579123	1	1	yes	characteristic
232	C₂×C₄	#14579123	1	1	yes	characteristic
233	C₂×C₄	#14579136	1	1	yes	characteristic
234	C₂×C₄	#14579136	1	1	yes	characteristic
235	C₂×C₄	#14579150	1	1	yes	characteristic
236	C₂×C₄	#14579190	1	4	yes	—
237	C₈	—	2	1	no	—
238	C₈	—	2	1	no	—
239	C₈	—	2	1	no	—
240	C₈	—	316	2	no	—
241	C₈	—	316	2	no	—
242	C₈	#14579089	1	2	yes	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	1	no	—
245	C₂²	#19098464	1	1	yes	characteristic
246	C₂²	#19098954	1	2	yes	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	2	1	no	—
250	C₄	—	8	4	no	—
251	C₄	—	632	2	no	—
252	C₄	—	632	2	no	—
253	C₄	C₂×#14579089	1	1	yes	characteristic
254	C₄	#19098581	1	1	yes	characteristic
255	C₄	#19098669	1	2	yes	—
256	C₄	#19098822	1	2	yes	—
257	C₂	—	2	2	no	—
258	C₂	#23764269	1	1	yes	characteristic
259	C₂	#23764296	1	1	yes	characteristic
260	C₂	#23764318	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23773986

C₂

yes

maximal, characteristic

#23764343

C₂

yes

maximal

#23761898

C₂

yes

maximal

#23761689

C₂

yes

maximal, characteristic

C₄×#106×C₇₉

C₂

yes

maximal, characteristic

#19099120

C₂²

yes

—

#19098968

C₄

yes

characteristic, complemented

#19098943

C₄

yes

characteristic, complemented

#19098914

C₄

yes

complemented

#19098804

—

#19098804

—

C₄×Dic₃₁₆

—

C₄×Dic₃₁₆

—

#19098616

C₂²

yes

characteristic

C₄×#11929608

C₂²

yes

—

—

—

—

C₂×#106×C₇₉

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₇₉

C₂²

yes

—

#340×C₇₉

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×#11929608

D₄

yes

—

#14579161

C₂×C₄

yes

—

#14579161

C₂×C₄

yes

—

#14579153

—

#14579140

—

#14579140

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

#14579120

—

#14579095

—

#14579095

—

C₄⋊(C₇₉⋊C₈)

—

#14579086

—

#14579086

—

C₂²⋊(C₇₉⋊C₈)

D₄

yes

—

#14579072

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

—

C₂²×C₈×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#106×C₇₉

—

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

characteristic

#95×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

C₄²×C₇₉

yes

C₄²×C₇₉

yes

C₂³×C₇₉

yes

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

100

C₂×C₄×C₇₉

#137

yes

—

101

C₂×Dic₇₉

—

102

C₂×Dic₇₉

—

103

Dic₁₅₈

—

104

Dic₁₅₈

—

105

Dic₁₅₈

—

106

C₈×C₇₉

—

107

C₈×C₇₉

—

108

C₈×C₇₉

—

109

C₈×C₇₉

#104

yes

—

110

C₇₉⋊C₈

—

111

C₇₉⋊C₈

—

112

C₂²×C₇₉

—

113

C₂²×C₇₉

—

114

C₂²×C₇₉

#390

yes

characteristic

115

C₂²×C₇₉

#497

yes

—

116

C₄×C₇₉

—

117

C₄×C₇₉

—

118

C₄×C₇₉

—

119

C₄×C₇₉

—

120

C₄×C₇₉

C₂×#104

yes

characteristic

121

C₄×C₇₉

#421

yes

characteristic

122

C₄×C₇₉

#441

yes

—

123

C₄×C₇₉

#470

yes

—

124

Dic₇₉

—

125

Dic₇₉

—

126

#9720

—

maximal, Sylow

127

C₂×C₇₉

—

128

C₂×C₇₉

#1971

yes

characteristic

129

C₂×C₇₉

#1976

yes

characteristic

130

C₂×C₇₉

#1980

yes

characteristic

131

#3170

—

132

#1986

—

133

C₄×#106

D₇₉

yes

characteristic

134

#1503

—

135

#1451

—

136

C₇₉

#9720

yes

characteristic, complemented, Sylow

137

#533

—

138

#500

—

139

#494

—

140

#487

—

141

#467

—

158

—

142

#467

—

158

—

143

C₄×Q₁₆

—

158

—

144

C₄×Q₁₆

—

158

—

145

#431

—

146

C₂×#106

—

147

C₄×M₁₆

—

148

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

149

C₄×C₄⋊C₄

C₂×D₇₉

yes

—

150

#340

—

151

#339

—

158

—

152

#328

—

158

—

153

#322

—

158

—

154

#322

—

158

—

155

C₂×Q₁₆

—

158

—

156

C₂×Q₁₆

—

158

—

157

C₂×M₁₆

—

158

C₂²×C₈

C₂²⋊D₇₉

yes

characteristic

159

C₂²×C₈

C₂²⋊D₇₉

yes

characteristic

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

#125

—

158

—

163

C₂²⋊Q₈

—

158

—

164

C₂²⋊Q₈

—

158

—

165

C₄×Q₈

—

158

—

166

C₄×Q₈

—

158

—

167

#117

—

158

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄²

—

170

C₂×C₄²

C₂²×D₇₉

yes

characteristic

171

#107

—

158

—

172

#107

—

158

—

173

#106

—

174

C₄⋊C₈

—

158

—

175

#103

—

158

—

176

#103

—

158

—

177

C₂²⋊C₈

—

178

#97

—

158

—

179

C₄×C₈

—

158

—

180

C₄×C₈

—

158

—

181

C₄×C₈

C₄×D₇₉

yes

characteristic

182

C₄×C₈

C₄×D₇₉

yes

characteristic

183

C₄×C₈

D₃₁₆

yes

characteristic

184

C₄×C₈

D₃₁₆

yes

characteristic

185

#95

—

186

C₂×Q₈

—

158

—

187

C₂×Q₈

—

158

—

188

C₂²×C₄

—

189

C₂²×C₄

D₄×D₇₉

yes

characteristic

190

C₂²×C₄

D₄×D₇₉

yes

characteristic

191

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

192

Q₁₆

—

316

—

193

Q₁₆

—

316

—

194

M₁₆

—

158

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

158

—

198

C₂×C₈

—

158

—

199

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

200

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

201

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

202

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

316

—

206

C₄⋊C₄

—

316

—

207

C₄⋊C₄

—

158

—

208

C₄⋊C₄

—

158

—

209

C₄⋊C₄

—

158

—

210

C₄⋊C₄

—

158

—

211

C₂²⋊C₄

—

316

—

212

C₄²

—

213

C₄²

—

316

—

214

C₄²

C₂×C₄×D₇₉

yes

characteristic

215

C₄²

C₂×D₃₁₆

yes

characteristic

216

C₄²

#11929625

yes

characteristic

217

C₄²

#11929625

yes

characteristic

218

C₂³

#14579157

yes

characteristic

219

Q₈

—

316

—

220

Q₈

—

316

—

221

Q₈

—

632

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

316

—

229

C₂×C₄

—

316

—

230

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

231

C₂×C₄

#14579123

yes

characteristic

232

C₂×C₄

#14579123

yes

characteristic

233

C₂×C₄

#14579136

yes

characteristic

234

C₂×C₄

#14579136

yes

characteristic

235

C₂×C₄

#14579150

yes

characteristic

236

C₂×C₄

#14579190

yes

—

237

C₈

—

238

C₈

—

239

C₈

—

240

C₈

—

316

—

241

C₈

—

316

—

242

C₈

#14579089

yes

—

243

C₂²

—

244

C₂²

—

245

C₂²

#19098464

yes

characteristic

246

C₂²

#19098954

yes

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

632

—

252

C₄

—

632

—

253

C₄

C₂×#14579089

yes

characteristic

254

C₄

#19098581

yes

characteristic

255

C₄

#19098669

yes

—

256

C₄

#19098822

yes

—

257

C₂

—

258

C₂

#23764269

yes

characteristic

259

C₂

#23764296

yes

characteristic

260

C₂

#23764318

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579136
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₄×#106×C₇₉	C₂
socle	C₂²×C₇₉	#390
prime radical	C₂³×C₇₉	#127
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₄×#106	D₇₉
hypocenter	C₇₉	#9720
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#106

subgroup

G/H

center

C₂×C₄

#14579136

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₄×#106×C₇₉

C₂

C₂²×C₇₉

C₂³×C₇₉

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#106

N	H ≅ G/N	type
7. #19098968	C₄	semidirect
8. #19098943	C₄	semidirect
9. #19098914	C₄	semidirect
136. C₇₉	#9720	semidirect

H ≅ G/N

type

7. #19098968

C₄

semidirect

8. #19098943

C₄

semidirect

9. #19098914

C₄

semidirect

136. C₇₉

#9720

semidirect

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

subgroup	index
#23773986	2
#23764343	2
#23761898	2
#23761689	2
C₄×#106×C₇₉	2
#9720	79

subgroup

index

C₄×#106×C₇₉

Subgroups — #34187433

Conjugacy classes of subgroups

Complements

Maximal subgroups