Group #34182141 — subgroups

Subgroups — #34182141

Order 20224.

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

normal subgroups only

This group has 454 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	#23764195	C₂	1	1	yes	maximal, characteristic
2	C₄×#14579078	C₂	1	1	yes	maximal, characteristic
3	#23762153	C₂	1	2	yes	maximal, complemented
4	#23761236	C₂	1	2	yes	maximal, complemented
5	C₇₉×#2975	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
7	C₂×#14579078	C₄	1	2	yes	—
8	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
9	C₄×#11929608	C₂²	1	2	yes	—
10	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
11	#19098332	C₄	1	1	yes	characteristic
12	#19098332	C₄	1	1	yes	characteristic
13	#19098315	—	2	2	no	—
14	#19098313	—	2	2	no	—
15	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
16	#436×C₇₉	—	2	2	no	—
17	#436×C₇₉	—	2	2	no	—
18	#431×C₇₉	C₂²	1	2	yes	—
19	#407×C₇₉	—	2	2	no	—
20	C₂×#11929608	C₂×C₄	1	2	yes	—
21	C₂×#11929608	C₂×C₄	1	2	yes	—
22	C₂²×C₇₉⋊C₈	—	2	1	no	—
23	C₂²×C₇₉⋊C₈	—	2	1	no	—
24	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
25	#14579078	—	2	4	no	—
26	C₂²⋊(C₇₉⋊C₈)	—	4	4	no	—
27	#14579072	—	2	2	no	—
28	C₄×C₇₉⋊C₈	—	2	2	no	—
29	C₄×C₇₉⋊C₈	—	2	2	no	—
30	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₇₉	D₄	1	2	yes	—
32	C₂×M₁₆×C₇₉	—	2	2	no	—
33	C₂×M₁₆×C₇₉	—	2	2	no	—
34	C₄×D₄×C₇₉	—	2	2	no	—
35	C₄×D₄×C₇₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₇₉	Q₈	1	2	yes	—
38	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
39	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
40	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
41	C₂²⋊C₈×C₇₉	—	2	4	no	—
42	C₂²⋊C₈×C₇₉	—	2	2	no	—
43	C₄×C₈×C₇₉	—	2	2	no	—
44	#11929608	—	2	2	no	—
45	#11929608	—	2	2	no	—
46	#11929608	—	2	2	no	—
47	#11929608	M₁₆	1	4	yes	complemented
48	C₂×C₇₉⋊C₈	—	2	2	no	—
49	C₂×C₇₉⋊C₈	—	2	2	no	—
50	C₂×C₇₉⋊C₈	—	2	2	no	—
51	C₂×C₇₉⋊C₈	—	4	1	no	—
52	C₂×C₇₉⋊C₈	—	4	2	no	—
53	C₂×C₇₉⋊C₈	—	4	1	no	—
54	C₂×C₇₉⋊C₈	—	4	1	no	—
55	C₂⁴×C₇₉	C₄⋊C₄	1	2	yes	—
56	C₂×D₄×C₇₉	—	2	2	no	—
57	C₂×D₄×C₇₉	—	2	2	no	—
58	C₂×D₄×C₇₉	—	2	1	no	—
59	C₂×D₄×C₇₉	—	2	1	no	—
60	C₂²×C₄×C₇₉	—	2	2	no	—
61	C₂²×C₄×C₇₉	—	2	2	no	—
62	C₂²×C₄×C₇₉	—	4	2	no	—
63	C₂²×C₄×C₇₉	—	4	2	no	—
64	C₂²×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
65	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
68	M₁₆×C₇₉	—	8	2	no	—
69	M₁₆×C₇₉	—	8	2	no	—
70	C₂×C₈×C₇₉	—	2	2	no	—
71	C₂×C₈×C₇₉	—	2	2	no	—
72	C₄⋊C₄×C₇₉	—	2	2	no	—
73	C₂²⋊C₄×C₇₉	—	2	4	no	—
74	C₄²×C₇₉	C₂×D₄	1	2	yes	—
75	C₄²×C₇₉	#41	1	2	yes	—
76	C₂³×C₇₉	—	2	2	no	—
77	C₂³×C₇₉	—	2	2	no	—
78	C₂³×C₇₉	—	2	2	no	—
79	C₂³×C₇₉	—	4	2	no	—
80	C₂³×C₇₉	—	4	2	no	—
81	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
82	D₄×C₇₉	—	4	2	no	—
83	D₄×C₇₉	—	4	2	no	—
84	C₂×C₄×C₇₉	—	2	1	no	—
85	C₂×C₄×C₇₉	—	2	1	no	—
86	C₂×C₄×C₇₉	—	2	2	no	—
87	C₂×C₄×C₇₉	—	4	1	no	—
88	C₂×C₄×C₇₉	—	4	2	no	—
89	C₂×C₄×C₇₉	—	4	2	no	—
90	C₂×C₄×C₇₉	—	4	2	no	—
91	C₂×C₄×C₇₉	—	8	2	no	—
92	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
93	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
94	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
95	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
96	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
97	C₂×C₄×C₇₉	#131	1	1	yes	characteristic
98	C₂×C₄×C₇₉	#131	1	1	yes	characteristic
99	C₈×C₇₉	—	4	2	no	—
100	C₈×C₇₉	—	4	2	no	—
101	C₇₉⋊C₈	—	2	4	no	—
102	C₇₉⋊C₈	—	4	2	no	—
103	C₇₉⋊C₈	—	4	2	no	—
104	C₇₉⋊C₈	—	8	1	no	—
105	C₂²×C₇₉	—	2	1	no	—
106	C₂²×C₇₉	—	2	1	no	—
107	C₂²×C₇₉	—	4	4	no	—
108	C₂²×C₇₉	—	4	2	no	—
109	C₂²×C₇₉	—	4	2	no	—
110	C₂²×C₇₉	—	4	2	no	—
111	C₂²×C₇₉	—	8	2	no	—
112	C₂²×C₇₉	#385	1	1	yes	characteristic
113	C₂²×C₇₉	#423	1	1	yes	characteristic
114	C₂²×C₇₉	#424	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	#435	1	2	yes	—
119	C₄×C₇₉	#436	1	2	yes	—
120	C₄×C₇₉	#453	1	1	yes	characteristic
121	C₄×C₇₉	#455	1	1	yes	characteristic
122	#8837	—	79	1	no	maximal, Sylow
123	C₂×C₇₉	—	2	1	no	—
124	C₂×C₇₉	—	2	1	no	—
125	C₂×C₇₉	—	8	2	no	—
126	C₂×C₇₉	#1851	1	1	yes	characteristic
127	C₂×C₇₉	#1856	1	1	yes	characteristic
128	C₂×C₇₉	#1858	1	1	yes	characteristic
129	#2975	D₇₉	1	1	yes	characteristic
130	#1954	—	79	1	no	—
131	C₄×#100	—	79	1	no	—
132	#1565	—	79	2	no	—
133	#1278	—	79	2	no	—
134	C₇₉	#8837	1	1	yes	characteristic, complemented, Sylow
135	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
136	#436	—	2	2	no	—
137	#436	—	2	2	no	—
138	#431	C₂×D₇₉	1	2	yes	—
139	C₂×C₄⋊C₈	—	79	1	no	—
140	C₂×#100	—	79	2	no	—
141	#407	—	2	2	no	—
142	C₂×C₂²⋊C₈	—	158	2	no	—
143	C₄×M₁₆	—	79	2	no	—
144	C₂×C₄×C₈	—	79	1	no	—
145	#343	—	79	1	no	—
146	#343	—	79	1	no	—
147	#335	—	158	2	no	—
148	#334	—	158	2	no	—
149	C₂²×D₄	C₄×D₇₉	1	1	yes	characteristic
150	C₂³×C₄	C₂²⋊D₇₉	1	2	yes	—
151	C₂×M₁₆	—	2	2	no	—
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	—	79	2	no	—
154	C₂×M₁₆	—	79	2	no	—
155	C₂²×C₈	—	158	1	no	—
156	C₂²×C₈	—	158	1	no	—
157	C₄×D₄	—	2	2	no	—
158	C₄×D₄	—	2	2	no	—
159	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
160	C₂×C₂²⋊C₄	Dic₁₅₈	1	2	yes	—
161	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
162	C₄⋊C₈	—	158	2	no	—
163	C₄⋊C₈	C₂²⋊D₇₉	1	2	yes	—
164	C₄⋊C₈	C₂²⋊D₇₉	1	2	yes	—
165	#100	—	158	4	no	—
166	C₂²⋊C₈	—	2	4	no	—
167	C₂²⋊C₈	—	2	2	no	—
168	C₂²⋊C₈	—	316	4	no	—
169	#97	—	158	2	no	—
170	C₄×C₈	—	2	2	no	—
171	C₄×C₈	—	158	2	no	—
172	C₄×C₈	—	158	2	no	—
173	C₂⁴	Dic₇₉⋊C₄	1	2	yes	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	—	2	2	no	—
176	C₂×D₄	—	2	1	no	—
177	C₂×D₄	—	2	1	no	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	—	4	2	no	—
181	C₂²×C₄	—	4	2	no	—
182	C₂²×C₄	Dic₇₉⋊C₄	1	2	yes	—
183	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
184	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
185	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
186	M₁₆	—	8	2	no	—
187	M₁₆	—	8	2	no	—
188	M₁₆	—	79	4	no	—
189	M₁₆	—	158	2	no	—
190	M₁₆	—	158	2	no	—
191	M₁₆	—	158	2	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	316	1	no	—
195	C₂×C₈	—	316	1	no	—
196	C₂×C₈	—	316	2	no	—
197	C₂×C₈	—	316	1	no	—
198	C₂×C₈	—	158	2	no	—
199	C₂×C₈	—	158	2	no	—
200	C₂×C₈	—	158	2	no	—
201	C₄⋊C₄	—	2	2	no	—
202	C₂²⋊C₄	—	2	4	no	—
203	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
204	C₄²	#11929624	1	2	yes	—
205	C₂³	—	2	2	no	—
206	C₂³	—	2	2	no	—
207	C₂³	—	2	2	no	—
208	C₂³	—	4	2	no	—
209	C₂³	—	4	2	no	—
210	C₂³	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
211	D₄	—	4	2	no	—
212	D₄	—	4	2	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	1	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	8	2	no	—
221	C₂×C₄	C₄×C₂²⋊D₇₉	1	2	yes	—
222	C₂×C₄	#14579130	1	1	yes	characteristic
223	C₂×C₄	#14579140	1	2	yes	—
224	C₂×C₄	#14579144	1	1	yes	characteristic
225	C₂×C₄	M₁₆×D₇₉	1	2	yes	—
226	C₂×C₄	#14579169	1	1	yes	characteristic
227	C₂×C₄	#14579169	1	1	yes	characteristic
228	C₈	—	4	2	no	—
229	C₈	—	4	2	no	—
230	C₈	—	316	2	no	—
231	C₈	—	316	2	no	—
232	C₈	—	632	1	no	—
233	C₈	—	158	4	no	—
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	4	4	no	—
237	C₂²	—	4	2	no	—
238	C₂²	—	4	2	no	—
239	C₂²	—	4	2	no	—
240	C₂²	—	8	2	no	—
241	C₂²	#19098436	1	1	yes	characteristic
242	C₂²	#19098586	1	1	yes	characteristic
243	C₂²	#19098591	1	1	yes	characteristic
244	C₄	—	2	1	no	—
245	C₄	—	2	2	no	—
246	C₄	—	4	2	no	—
247	C₄	#19098632	1	2	yes	—
248	C₄	#19098639	1	2	yes	—
249	C₄	#19098731	1	1	yes	characteristic
250	C₄	#19098741	1	1	yes	characteristic
251	C₂	—	2	1	no	—
252	C₂	—	2	1	no	—
253	C₂	—	8	2	no	—
254	C₂	#23763583	1	1	yes	characteristic
255	C₂	#23763610	1	1	yes	characteristic
256	C₂	#23763620	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23764195

C₂

yes

maximal, characteristic

C₄×#14579078

C₂

yes

maximal, characteristic

#23762153

C₂

yes

maximal, complemented

#23761236

C₂

yes

maximal, complemented

C₇₉×#2975

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₂×#14579078

C₄

yes

—

C₂×C₂²⋊(C₇₉⋊C₈)

—

C₄×#11929608

C₂²

yes

—

C₂×C₄×C₇₉⋊C₈

C₂²

yes

characteristic

#19098332

C₄

yes

characteristic

#19098332

C₄

yes

characteristic

#19098315

—

#19098313

—

C₂×C₄×D₄×C₇₉

C₂²

yes

characteristic

#436×C₇₉

—

#436×C₇₉

—

#431×C₇₉

C₂²

yes

—

#407×C₇₉

—

C₂×#11929608

C₂×C₄

yes

—

C₂×#11929608

C₂×C₄

yes

—

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₄⋊(C₇₉⋊C₈)

—

#14579078

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

—

C₂²×D₄×C₇₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₇₉

D₄

yes

—

C₂×M₁₆×C₇₉

—

C₂×M₁₆×C₇₉

—

C₄×D₄×C₇₉

—

C₄×D₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₇₉

Q₈

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

D₄

yes

—

C₄⋊C₈×C₇₉

D₄

yes

—

C₂²⋊C₈×C₇₉

—

C₂²⋊C₈×C₇₉

—

C₄×C₈×C₇₉

—

—

—

—

M₁₆

yes

complemented

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂⁴×C₇₉

C₄⋊C₄

yes

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₄⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×Q₈

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

#41

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂×C₄⋊C₄

yes

characteristic

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

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄×D₄

yes

—

C₂×C₄×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₉

#123

yes

characteristic

C₂×C₄×C₇₉

C₂×M₁₆

yes

—

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₈×C₇₉

—

100

C₈×C₇₉

—

101

C₇₉⋊C₈

—

102

C₇₉⋊C₈

—

103

C₇₉⋊C₈

—

104

C₇₉⋊C₈

—

105

C₂²×C₇₉

—

106

C₂²×C₇₉

—

107

C₂²×C₇₉

—

108

C₂²×C₇₉

—

109

C₂²×C₇₉

—

110

C₂²×C₇₉

—

111

C₂²×C₇₉

—

112

C₂²×C₇₉

#385

yes

characteristic

113

C₂²×C₇₉

#423

yes

characteristic

114

C₂²×C₇₉

#424

yes

characteristic

115

C₄×C₇₉

—

116

C₄×C₇₉

—

117

C₄×C₇₉

—

118

C₄×C₇₉

#435

yes

—

119

C₄×C₇₉

#436

yes

—

120

C₄×C₇₉

#453

yes

characteristic

121

C₄×C₇₉

yes

122

—

123

C₂×C₇₉

—

124

C₂×C₇₉

—

125

C₂×C₇₉

—

126

C₂×C₇₉

#1851

yes

characteristic

127

C₂×C₇₉

#1856

yes

characteristic

128

C₂×C₇₉

#1858

yes

characteristic

129

#2975

D₇₉

yes

characteristic

130

#1954

—

131

C₄×#100

—

132

#1565

—

133

#1278

—

134

C₇₉

#8837

yes

characteristic, complemented, Sylow

135

C₂×C₄×D₄

C₂×D₇₉

yes

characteristic

136

#436

—

137

#436

—

138

#431

C₂×D₇₉

yes

—

139

C₂×C₄⋊C₈

—

140

C₂×#100

—

141

#407

—

142

C₂×C₂²⋊C₈

—

158

—

143

C₄×M₁₆

—

144

C₂×C₄×C₈

—

145

#343

—

146

#343

—

147

#335

—

158

—

148

#334

—

158

—

149

C₂²×D₄

C₄×D₇₉

yes

characteristic

150

C₂³×C₄

C₂²⋊D₇₉

yes

—

151

C₂×M₁₆

—

152

C₂×M₁₆

—

153

C₂×M₁₆

—

154

C₂×M₁₆

—

155

C₂²×C₈

—

158

—

156

C₂²×C₈

—

158

—

157

C₄×D₄

—

158

C₄×D₄

—

159

C₂×C₄⋊C₄

C₄×D₇₉

yes

characteristic

160

C₂×C₂²⋊C₄

Dic₁₅₈

yes

—

161

C₂×C₄²

C₂²×D₇₉

yes

characteristic

162

C₄⋊C₈

—

158

—

163

C₄⋊C₈

C₂²⋊D₇₉

yes

—

164

C₄⋊C₈

C₂²⋊D₇₉

yes

—

165

#100

—

158

—

166

C₂²⋊C₈

—

167

C₂²⋊C₈

—

168

C₂²⋊C₈

—

316

—

169

#97

—

158

—

170

C₄×C₈

—

171

C₄×C₈

—

158

—

172

C₄×C₈

—

158

—

173

C₂⁴

Dic₇₉⋊C₄

yes

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

Dic₇₉⋊C₄

yes

—

183

C₂²×C₄

C₂×C₄×D₇₉

yes

characteristic

184

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

185

C₂²×C₄

C₂×Dic₁₅₈

yes

characteristic

186

M₁₆

—

187

M₁₆

—

188

M₁₆

—

189

M₁₆

—

158

—

190

M₁₆

—

158

—

191

M₁₆

—

158

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

316

—

195

C₂×C₈

—

316

—

196

C₂×C₈

—

316

—

197

C₂×C₈

—

316

—

198

C₂×C₈

—

158

—

199

C₂×C₈

—

158

—

200

C₂×C₈

—

158

—

201

C₄⋊C₄

—

202

C₂²⋊C₄

—

203

C₄²

C₂×C₂²⋊D₇₉

yes

—

204

C₄²

#11929624

yes

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

C₂×Dic₇₉⋊C₄

yes

characteristic

211

D₄

—

212

D₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

C₄×C₂²⋊D₇₉

yes

—

222

C₂×C₄

#14579130

yes

characteristic

223

C₂×C₄

#14579140

yes

—

224

C₂×C₄

#14579144

yes

characteristic

225

C₂×C₄

M₁₆×D₇₉

yes

—

226

C₂×C₄

#14579169

yes

characteristic

227

C₂×C₄

#14579169

yes

characteristic

228

C₈

—

229

C₈

—

230

C₈

—

316

—

231

C₈

—

316

—

232

C₈

—

632

—

233

C₈

—

158

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

#19098436

yes

characteristic

242

C₂²

#19098586

yes

characteristic

243

C₂²

#19098591

yes

characteristic

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

#19098632

yes

—

248

C₄

#19098639

yes

—

249

C₄

#19098731

yes

characteristic

250

C₄

#19098741

yes

characteristic

251

C₂

—

252

C₂

—

253

C₂

—

254

C₂

#23763583

yes

characteristic

255

C₂

#23763610

yes

characteristic

256

C₂

#23763620

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579130
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#2975	C₂
socle	C₂²×C₇₉	#385
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#2975	D₇₉
hypocenter	C₇₉	#8837
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2975

subgroup

G/H

center

C₂×C₄

#14579130

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#2975

C₂

socle

C₂²×C₇₉

#385

prime radical

C₂²×D₄×C₇₉

C₂×C₄

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2975

N	H ≅ G/N	type
3. #23762153	C₂	semidirect
4. #23761236	C₂	semidirect
47. #11929608	M₁₆	semidirect
134. C₇₉	#8837	semidirect

H ≅ G/N

type

3. #23762153

C₂

semidirect

4. #23761236

C₂

semidirect

47. #11929608

M₁₆

semidirect

134. C₇₉

#8837

semidirect

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

subgroup	index
#23764195	2
C₄×#14579078	2
#23762153	2
#23761236	2
C₇₉×#2975	2
#8837	79

subgroup

index

C₇₉×#2975

Subgroups — #34182141

Conjugacy classes of subgroups

Complements

Maximal subgroups