Group #34181409 — subgroups

Subgroups — #34181409

Order 20224.

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

normal subgroups only

This group has 378 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	C₂×C₈×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic
2	#23763538	C₂	1	1	yes	maximal, characteristic
3	#23761830	C₂	1	2	yes	maximal
4	#23761296	C₂	1	2	yes	maximal
5	C₇₉×#1564	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
7	C₈×Dic₁₅₈	—	2	1	no	—
8	C₈×Dic₁₅₈	—	2	1	no	—
9	C₈×Dic₁₅₈	C₄	1	2	yes	—
10	C₈×Dic₁₅₈	C₄	1	2	yes	—
11	#19098587	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₇₉⋊C₈	—	2	1	no	—
14	C₂×C₈×Dic₇₉	—	2	1	no	—
15	#19098328	—	2	1	no	—
16	#19098328	—	2	1	no	—
17	#19098295	—	2	4	no	—
18	#431×C₇₉	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
20	#335×C₇₉	—	2	1	no	—
21	#334×C₇₉	—	2	1	no	—
22	C₂²×Dic₁₅₈	Q₈	1	1	yes	characteristic
23	C₂×#11929608	—	2	2	no	—
24	C₂²×C₇₉⋊C₈	—	2	1	no	—
25	C₄×Dic₁₅₈	—	2	1	no	—
26	C₄×Dic₁₅₈	—	2	1	no	—
27	C₄×Dic₁₅₈	C₂×C₄	1	2	yes	—
28	C₄×Dic₁₅₈	D₄	1	2	yes	—
29	C₂×C₄⋊Dic₇₉	Q₈	1	1	yes	characteristic
30	C₂×Dic₇₉⋊C₄	—	2	1	no	—
31	C₂×C₄×Dic₇₉	—	2	1	no	—
32	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
33	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
34	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
35	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
36	Dic₇₉⋊C₈	—	2	2	no	—
37	Dic₇₉⋊C₈	—	2	2	no	—
38	C₈×Dic₇₉	—	2	2	no	—
39	C₈×Dic₇₉	—	2	2	no	—
40	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₇₉	—	2	2	no	—
44	C₂²⋊C₈×C₇₉	—	2	2	no	—
45	C₄×C₈×C₇₉	—	2	2	no	—
46	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
50	C₂×Dic₁₅₈	—	2	4	no	—
51	C₂×Dic₁₅₈	—	2	1	no	—
52	C₂×Dic₁₅₈	C₄⋊C₄	1	2	yes	—
53	C₂²×Dic₇₉	—	2	1	no	—
54	C₂²×Dic₇₉	—	2	1	no	—
55	#11929608	—	4	2	no	—
56	#11929608	—	4	2	no	—
57	C₂×C₇₉⋊C₈	—	2	2	no	—
58	C₂×C₇₉⋊C₈	—	4	2	no	—
59	C₂×C₇₉⋊C₈	—	4	2	no	—
60	C₄⋊Dic₇₉	—	2	1	no	—
61	C₄⋊Dic₇₉	C₄⋊C₄	1	2	yes	—
62	Dic₇₉⋊C₄	—	2	2	no	—
63	Dic₇₉⋊C₄	—	2	2	no	—
64	C₄×Dic₇₉	—	2	2	no	—
65	C₄×Dic₇₉	—	2	2	no	—
66	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
69	C₂×C₈×C₇₉	—	2	2	no	—
70	C₂×C₈×C₇₉	—	2	2	no	—
71	C₂×C₈×C₇₉	—	4	2	no	—
72	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₇₉	#41	1	1	yes	characteristic
80	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₇₉	—	2	2	no	—
82	C₂×C₄×C₇₉	—	4	1	no	—
83	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
86	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
88	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₇₉	#135	1	2	yes	—
90	C₂×C₄×C₇₉	#137	1	2	yes	—
91	C₂×Dic₇₉	—	2	4	no	—
92	C₂×Dic₇₉	—	2	2	no	—
93	C₂×Dic₇₉	—	2	2	no	—
94	C₂×Dic₇₉	—	4	2	no	—
95	Dic₁₅₈	—	2	4	no	—
96	Dic₁₅₈	—	2	2	no	—
97	Dic₁₅₈	#108	1	4	yes	—
98	C₈×C₇₉	—	2	1	no	—
99	C₈×C₇₉	—	2	1	no	—
100	C₈×C₇₉	—	2	1	no	—
101	C₈×C₇₉	—	2	1	no	—
102	C₈×C₇₉	—	8	2	no	—
103	C₇₉⋊C₈	—	4	2	no	—
104	C₇₉⋊C₈	—	8	2	no	—
105	C₂²×C₇₉	—	2	1	no	—
106	C₂²×C₇₉	—	2	1	no	—
107	C₂²×C₇₉	#380	1	1	yes	characteristic
108	C₂²×C₇₉	#479	1	2	yes	—
109	C₄×C₇₉	—	2	1	no	—
110	C₄×C₇₉	—	2	1	no	—
111	C₄×C₇₉	—	2	1	no	—
112	C₄×C₇₉	#416	1	1	yes	characteristic
113	C₄×C₇₉	#419	1	1	yes	characteristic
114	C₄×C₇₉	C₂×#108	1	2	yes	—
115	C₄×C₇₉	#464	1	2	yes	—
116	Dic₇₉	—	2	4	no	—
117	Dic₇₉	—	4	2	no	—
118	#8661	—	79	1	no	maximal, Sylow
119	C₂×C₇₉	—	2	2	no	—
120	C₂×C₇₉	#1805	1	1	yes	characteristic
121	C₂×C₇₉	#1810	1	1	yes	characteristic
122	C₂×C₇₉	#1814	1	1	yes	characteristic
123	C₂×C₈×Q₈	—	79	1	no	—
124	#1837	—	79	1	no	—
125	#1564	D₇₉	1	1	yes	characteristic
126	#1487	—	79	2	no	—
127	#1301	—	79	2	no	—
128	C₇₉	#8661	1	1	yes	characteristic, complemented, Sylow
129	C₂×C₄×Q₈	—	79	1	no	—
130	C₈×Q₈	—	79	2	no	—
131	C₈×Q₈	—	79	2	no	—
132	C₈×Q₈	—	158	1	no	—
133	C₈×Q₈	—	158	1	no	—
134	#431	C₂×D₇₉	1	2	yes	—
135	#423	—	79	2	no	—
136	C₂×C₄⋊C₈	—	79	1	no	—
137	C₂×C₄⋊C₈	—	158	1	no	—
138	C₂×C₄×C₈	—	158	1	no	—
139	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
140	#341	—	158	1	no	—
141	#341	—	158	1	no	—
142	#335	—	2	1	no	—
143	#334	—	2	1	no	—
144	Q₈⋊C₈	—	158	4	no	—
145	C₂²×Q₈	—	79	1	no	—
146	C₂×M₁₆	—	158	2	no	—
147	C₂²×C₈	—	158	1	no	—
148	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
149	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
150	C₄×Q₈	—	79	2	no	—
151	C₄×Q₈	—	79	2	no	—
152	C₄×Q₈	—	158	1	no	—
153	C₄×Q₈	—	158	1	no	—
154	C₂×C₄⋊C₄	—	79	1	no	—
155	C₂×C₄⋊C₄	—	158	1	no	—
156	C₂×C₄²	—	158	1	no	—
157	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	79	2	no	—
160	C₄⋊C₈	—	158	2	no	—
161	C₄⋊C₈	—	158	2	no	—
162	C₄⋊C₈	—	158	2	no	—
163	C₄⋊C₈	—	158	1	no	—
164	C₄⋊C₈	—	158	2	no	—
165	C₂²⋊C₈	—	2	2	no	—
166	C₄×C₈	—	2	2	no	—
167	C₄×C₈	—	158	2	no	—
168	C₄×C₈	—	158	2	no	—
169	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
170	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
171	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
172	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
173	C₂×Q₈	—	79	2	no	—
174	C₂×Q₈	—	158	4	no	—
175	C₂×Q₈	—	158	1	no	—
176	C₂²×C₄	—	158	1	no	—
177	C₂²×C₄	—	158	1	no	—
178	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
179	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
180	C₂²×C₄	#11929623	1	1	yes	characteristic
181	M₁₆	—	316	2	no	—
182	M₁₆	—	316	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	316	2	no	—
187	C₂×C₈	—	316	2	no	—
188	C₂×C₈	—	158	2	no	—
189	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
190	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
191	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
192	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
193	C₄⋊C₄	—	79	2	no	—
194	C₄⋊C₄	—	158	2	no	—
195	C₄⋊C₄	—	158	2	no	—
196	C₄⋊C₄	—	158	1	no	—
197	C₄²	—	158	2	no	—
198	C₄²	—	158	2	no	—
199	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
200	C₄²	D₄×D₇₉	1	1	yes	characteristic
201	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
202	C₄²	#11929625	1	1	yes	characteristic
203	C₂³	#14579141	1	1	yes	characteristic
204	Q₈	—	79	4	no	—
205	Q₈	—	158	4	no	—
206	Q₈	—	158	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	316	2	no	—
210	C₂×C₄	—	158	2	no	—
211	C₂×C₄	—	158	4	no	—
212	C₂×C₄	—	158	2	no	—
213	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
214	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
215	C₂×C₄	#14579119	1	1	yes	characteristic
216	C₂×C₄	#14579132	1	1	yes	characteristic
217	C₂×C₄	#14579136	1	1	yes	characteristic
218	C₂×C₄	#14579137	1	1	yes	characteristic
219	C₂×C₄	#14579183	1	2	yes	—
220	C₂×C₄	#14579194	1	2	yes	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	2	1	no	—
224	C₈	—	2	1	no	—
225	C₈	—	8	2	no	—
226	C₈	—	316	2	no	—
227	C₈	—	632	2	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	#19098420	1	1	yes	characteristic
231	C₂²	#19098871	1	2	yes	—
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	316	2	no	—
236	C₄	—	158	4	no	—
237	C₄	#19098560	1	1	yes	characteristic
238	C₄	#19098573	1	1	yes	characteristic
239	C₄	#108×D₇₉	1	2	yes	—
240	C₄	#19098786	1	2	yes	—
241	C₂	—	2	2	no	—
242	C₂	#23763416	1	1	yes	characteristic
243	C₂	#23763435	1	1	yes	characteristic
244	C₂	#23763451	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₁₅₈

C₂

yes

maximal, characteristic

#23763538

C₂

yes

maximal, characteristic

#23761830

C₂

yes

maximal

#23761296

C₂

yes

maximal

C₇₉×#1564

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₅₈

C₂²

yes

characteristic

C₈×Dic₁₅₈

—

C₈×Dic₁₅₈

—

C₈×Dic₁₅₈

C₄

yes

—

C₈×Dic₁₅₈

C₄

yes

—

#19098587

C₂²

yes

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₂×Dic₇₉⋊C₈

—

C₂×C₈×Dic₇₉

—

#19098328

—

#19098328

—

#19098295

—

#431×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#335×C₇₉

—

#334×C₇₉

—

C₂²×Dic₁₅₈

Q₈

yes

characteristic

C₂×#11929608

—

C₂²×C₇₉⋊C₈

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

C₂×C₄

yes

—

C₄×Dic₁₅₈

D₄

yes

—

C₂×C₄⋊Dic₇₉

Q₈

yes

characteristic

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

C₂×C₄

yes

—

Dic₇₉⋊C₈

—

Dic₇₉⋊C₈

—

C₈×Dic₇₉

—

C₈×Dic₇₉

—

C₂²×C₈×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₂²⋊C₈×C₇₉

—

C₄×C₈×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

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

C₄⋊C₄

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₄⋊C₄

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

C₂×C₈×C₇₉

—

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

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

#41

yes

characteristic

C₂³×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

#135

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

#108

yes

—

C₈×C₇₉

—

C₈×C₇₉

—

100

C₈×C₇₉

—

101

C₈×C₇₉

—

102

C₈×C₇₉

—

103

C₇₉⋊C₈

—

104

C₇₉⋊C₈

—

105

C₂²×C₇₉

—

106

C₂²×C₇₉

—

107

C₂²×C₇₉

#380

yes

characteristic

108

C₂²×C₇₉

#479

yes

—

109

C₄×C₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

#416

yes

characteristic

113

C₄×C₇₉

#419

yes

characteristic

114

C₄×C₇₉

C₂×#108

yes

—

115

C₄×C₇₉

#464

yes

—

116

Dic₇₉

—

117

Dic₇₉

—

118

#8661

—

maximal, Sylow

119

C₂×C₇₉

—

120

C₂×C₇₉

#1805

yes

characteristic

121

C₂×C₇₉

#1810

yes

characteristic

122

C₂×C₇₉

#1814

yes

characteristic

123

C₂×C₈×Q₈

—

124

#1837

—

125

#1564

D₇₉

yes

characteristic

126

#1487

—

127

#1301

—

128

C₇₉

#8661

yes

characteristic, complemented, Sylow

129

C₂×C₄×Q₈

—

130

C₈×Q₈

—

131

C₈×Q₈

—

132

C₈×Q₈

—

158

—

133

C₈×Q₈

—

158

—

134

#431

C₂×D₇₉

yes

—

135

#423

—

136

C₂×C₄⋊C₈

—

137

C₂×C₄⋊C₈

—

158

—

138

C₂×C₄×C₈

—

158

—

139

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

140

#341

—

158

—

141

#341

—

158

—

142

#335

—

143

#334

—

144

Q₈⋊C₈

—

158

—

145

C₂²×Q₈

—

146

C₂×M₁₆

—

158

—

147

C₂²×C₈

—

158

—

148

C₂²×C₈

D₃₁₆

yes

characteristic

149

C₂²×C₈

D₃₁₆

yes

characteristic

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

158

—

153

C₄×Q₈

—

158

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

158

—

156

C₂×C₄²

—

158

—

157

C₂×C₄²

C₂²×D₇₉

yes

characteristic

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

158

—

161

C₄⋊C₈

—

158

—

162

C₄⋊C₈

—

158

—

163

C₄⋊C₈

—

158

—

164

C₄⋊C₈

—

158

—

165

C₂²⋊C₈

—

166

C₄×C₈

—

167

C₄×C₈

—

158

—

168

C₄×C₈

—

158

—

169

C₄×C₈

C₄×D₇₉

yes

characteristic

170

C₄×C₈

C₄×D₇₉

yes

characteristic

171

C₄×C₈

C₂²⋊D₇₉

yes

characteristic

172

C₄×C₈

C₂²⋊D₇₉

yes

characteristic

173

C₂×Q₈

—

174

C₂×Q₈

—

158

—

175

C₂×Q₈

—

158

—

176

C₂²×C₄

—

158

—

177

C₂²×C₄

—

158

—

178

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

179

C₂²×C₄

Q₈×D₇₉

yes

characteristic

180

C₂²×C₄

#11929623

yes

characteristic

181

M₁₆

—

316

—

182

M₁₆

—

316

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

316

—

187

C₂×C₈

—

316

—

188

C₂×C₈

—

158

—

189

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

190

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

191

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

192

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

193

C₄⋊C₄

—

194

C₄⋊C₄

—

158

—

195

C₄⋊C₄

—

158

—

196

C₄⋊C₄

—

158

—

197

C₄²

—

158

—

198

C₄²

—

158

—

199

C₄²

C₂×C₄×D₇₉

yes

characteristic

200

C₄²

D₄×D₇₉

yes

characteristic

201

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

202

C₄²

#11929625

yes

characteristic

203

C₂³

#14579141

yes

characteristic

204

Q₈

—

205

Q₈

—

158

—

206

Q₈

—

158

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

316

—

210

C₂×C₄

—

158

—

211

C₂×C₄

—

158

—

212

C₂×C₄

—

158

—

213

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

214

C₂×C₄

C₄⋊C₄×D₇₉

yes

characteristic

215

C₂×C₄

#14579119

yes

characteristic

216

C₂×C₄

#14579132

yes

characteristic

217

C₂×C₄

#14579136

yes

characteristic

218

C₂×C₄

#14579137

yes

characteristic

219

C₂×C₄

#14579183

yes

—

220

C₂×C₄

#14579194

yes

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

225

C₈

—

226

C₈

—

316

—

227

C₈

—

632

—

228

C₂²

—

229

C₂²

—

230

C₂²

#19098420

yes

characteristic

231

C₂²

#19098871

yes

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

316

—

236

C₄

—

158

—

237

C₄

#19098560

yes

characteristic

238

C₄

#19098573

yes

characteristic

239

C₄

#108×D₇₉

yes

—

240

C₄

#19098786

yes

—

241

C₂

—

242

C₂

#23763416

yes

characteristic

243

C₂

#23763435

yes

characteristic

244

C₂

#23763451

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579136
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1564	C₂
socle	C₂²×C₇₉	#380
prime radical	C₂³×C₇₉	C₂²⋊Q₈
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1564	D₇₉
hypocenter	C₇₉	#8661
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂×C₄

#14579136

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1564

C₂

socle

C₂²×C₇₉

#380

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 ◁ #1564

N	H ≅ G/N	type
128. C₇₉	#8661	semidirect

H ≅ G/N

type

128. C₇₉

#8661

semidirect

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

subgroup	index
C₂×C₈×Dic₁₅₈	2
#23763538	2
#23761830	2
#23761296	2
C₇₉×#1564	2
#8661	79

subgroup

index

C₂×C₈×Dic₁₅₈

C₇₉×#1564

Subgroups — #34181409

Conjugacy classes of subgroups

Complements

Maximal subgroups