Group #34186134 — subgroups

Subgroups — #34186134

Order 20224.

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

normal subgroups only

This group has 454 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	#23772485	C₂	1	1	yes	maximal, characteristic
2	#23763396	C₂	1	1	yes	maximal, characteristic
3	#23761829	C₂	1	2	yes	maximal
4	#23761258	C₂	1	2	yes	maximal
5	C₇₉×#2581	C₂	1	1	yes	maximal, characteristic
6	#19098694	—	2	4	no	—
7	#19098620	—	2	2	no	—
8	#19098616	C₂²	1	2	yes	—
9	#19098587	C₂²	1	2	yes	—
10	C₂×#14579080	—	2	1	no	—
11	#19098332	—	2	1	no	—
12	Q₈⋊(C₇₉⋊C₈)	—	2	4	no	—
13	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
15	#400×C₇₉	C₄	1	2	yes	—
16	#395×C₇₉	C₄	1	2	yes	—
17	#391×C₇₉	—	2	1	no	—
18	#389×C₇₉	—	2	1	no	—
19	#387×C₇₉	—	2	2	no	—
20	#382×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#11929608	—	2	2	no	—
22	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
23	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
24	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
25	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
26	#14579080	—	4	2	no	—
27	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
28	#14579072	—	2	4	no	—
29	C₄×C₇₉⋊C₈	D₄	1	4	yes	—
30	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
32	C₄×Q₈×C₇₉	—	2	2	no	—
33	C₄×Q₈×C₇₉	—	2	2	no	—
34	C₄×Q₈×C₇₉	—	2	2	no	—
35	C₄×Q₈×C₇₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
41	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₇₉	—	2	1	no	—
43	C₂×C₄²×C₇₉	D₄	1	2	yes	—
44	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
45	#95×C₇₉	—	2	2	no	—
46	#95×C₇₉	—	2	2	no	—
47	#95×C₇₉	—	2	2	no	—
48	#95×C₇₉	—	2	1	no	—
49	#95×C₇₉	C₂×C₄	1	2	yes	—
50	#11929608	—	4	2	no	—
51	#11929608	—	4	2	no	—
52	C₂×C₇₉⋊C₈	—	2	4	no	—
53	C₂×C₇₉⋊C₈	—	4	2	no	—
54	C₂×Q₈×C₇₉	—	2	2	no	—
55	C₂×Q₈×C₇₉	—	2	1	no	—
56	C₂×Q₈×C₇₉	—	2	1	no	—
57	C₂×Q₈×C₇₉	—	2	2	no	—
58	C₂×Q₈×C₇₉	—	2	2	no	—
59	C₂×Q₈×C₇₉	—	4	2	no	—
60	C₂²×C₄×C₇₉	—	2	1	no	—
61	C₂²×C₄×C₇₉	—	2	2	no	—
62	C₂²×C₄×C₇₉	—	2	1	no	—
63	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₇₉	C₂²⋊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×D₄	1	1	yes	characteristic
68	C₄⋊C₄×C₇₉	—	2	4	no	—
69	C₄⋊C₄×C₇₉	—	2	2	no	—
70	C₄⋊C₄×C₇₉	—	2	2	no	—
71	C₄⋊C₄×C₇₉	—	4	4	no	—
72	C₄⋊C₄×C₇₉	—	4	1	no	—
73	C₄⋊C₄×C₇₉	—	4	1	no	—
74	C₄⋊C₄×C₇₉	—	4	1	no	—
75	C₄⋊C₄×C₇₉	—	4	1	no	—
76	C₄²×C₇₉	—	2	2	no	—
77	C₄²×C₇₉	—	2	2	no	—
78	C₄²×C₇₉	—	4	2	no	—
79	C₄²×C₇₉	C₂×D₄	1	2	yes	—
80	C₄²×C₇₉	#41	1	2	yes	—
81	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	Q₈×C₇₉	—	2	4	no	—
83	Q₈×C₇₉	—	4	2	no	—
84	Q₈×C₇₉	—	4	2	no	—
85	Q₈×C₇₉	—	4	2	no	—
86	C₂×C₄×C₇₉	—	2	2	no	—
87	C₂×C₄×C₇₉	—	2	2	no	—
88	C₂×C₄×C₇₉	—	2	2	no	—
89	C₂×C₄×C₇₉	—	2	2	no	—
90	C₂×C₄×C₇₉	—	2	2	no	—
91	C₂×C₄×C₇₉	—	4	1	no	—
92	C₂×C₄×C₇₉	—	4	1	no	—
93	C₂×C₄×C₇₉	—	4	1	no	—
94	C₂×C₄×C₇₉	—	4	1	no	—
95	C₂×C₄×C₇₉	—	4	2	no	—
96	C₂×C₄×C₇₉	—	4	2	no	—
97	C₂×C₄×C₇₉	—	4	2	no	—
98	C₂×C₄×C₇₉	—	4	2	no	—
99	C₂×C₄×C₇₉	—	4	1	no	—
100	C₂×C₄×C₇₉	—	4	2	no	—
101	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
102	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
103	C₂×C₄×C₇₉	#121	1	2	yes	—
104	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
105	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
106	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
107	C₂×C₄×C₇₉	#137	1	2	yes	—
108	C₇₉⋊C₈	—	4	4	no	—
109	C₇₉⋊C₈	—	8	2	no	—
110	C₂²×C₇₉	—	2	1	no	—
111	C₂²×C₇₉	—	2	1	no	—
112	C₂²×C₇₉	#386	1	1	yes	characteristic
113	C₂²×C₇₉	#417	1	1	yes	characteristic
114	C₂²×C₇₉	#419	1	1	yes	characteristic
115	C₄×C₇₉	—	2	2	no	—
116	C₄×C₇₉	—	2	1	no	—
117	C₄×C₇₉	—	2	1	no	—
118	C₄×C₇₉	—	4	2	no	—
119	C₄×C₇₉	—	4	2	no	—
120	C₄×C₇₉	—	4	2	no	—
121	C₄×C₇₉	—	8	2	no	—
122	C₄×C₇₉	—	8	1	no	—
123	C₄×C₇₉	#468	1	2	yes	—
124	C₄×C₇₉	#470	1	2	yes	—
125	#9488	—	79	1	no	maximal, Sylow
126	C₂×C₇₉	—	2	1	no	—
127	C₂×C₇₉	—	2	1	no	—
128	C₂×C₇₉	#1891	1	1	yes	characteristic
129	C₂×C₇₉	#1894	1	1	yes	characteristic
130	C₂×C₇₉	#1912	1	1	yes	characteristic
131	#2983	—	79	1	no	—
132	#2581	D₇₉	1	1	yes	characteristic
133	#1801	—	79	1	no	—
134	#1487	—	79	2	no	—
135	#1286	—	79	2	no	—
136	C₇₉	#9488	1	1	yes	characteristic, complemented, Sylow
137	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
138	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
139	#446	—	158	4	no	—
140	#432	—	158	2	no	—
141	#431	—	79	2	no	—
142	#423	—	79	2	no	—
143	C₂×#101	—	158	1	no	—
144	#400	Dic₇₉	1	2	yes	—
145	#395	Dic₇₉	1	2	yes	—
146	#391	—	2	1	no	—
147	#389	—	2	1	no	—
148	#387	—	2	2	no	—
149	#382	C₂×D₇₉	1	1	yes	characteristic
150	#343	—	158	1	no	—
151	Q₈⋊C₈	—	158	4	no	—
152	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
153	C₂²×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
154	C₂×M₁₆	—	158	2	no	—
155	C₄×Q₈	—	2	2	no	—
156	C₄×Q₈	—	2	2	no	—
157	C₄×Q₈	—	2	2	no	—
158	C₄×Q₈	—	2	2	no	—
159	C₂×C₄⋊C₄	—	2	2	no	—
160	C₂×C₄⋊C₄	—	2	1	no	—
161	C₂×C₄⋊C₄	—	2	1	no	—
162	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
163	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
164	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
165	C₂×C₄²	—	2	1	no	—
166	C₂×C₄²	C₂²⋊D₇₉	1	2	yes	—
167	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
168	C₄⋊C₈	—	158	4	no	—
169	C₄⋊C₈	—	158	2	no	—
170	C₄⋊C₈	—	158	2	no	—
171	C₄⋊C₈	—	158	2	no	—
172	#101	—	316	2	no	—
173	C₂²⋊C₈	—	158	2	no	—
174	#97	—	158	4	no	—
175	C₄×C₈	—	79	4	no	—
176	#95	—	2	2	no	—
177	#95	—	2	2	no	—
178	#95	—	2	2	no	—
179	#95	—	2	1	no	—
180	#95	C₂×Dic₇₉	1	2	yes	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	2	1	no	—
183	C₂×Q₈	—	2	1	no	—
184	C₂×Q₈	—	2	2	no	—
185	C₂×Q₈	—	2	2	no	—
186	C₂×Q₈	—	4	2	no	—
187	C₂²×C₄	—	2	1	no	—
188	C₂²×C₄	—	2	2	no	—
189	C₂²×C₄	—	2	1	no	—
190	C₂²×C₄	C₂²⋊Dic₇₉	1	2	yes	—
191	C₂²×C₄	C₂²⋊Dic₇₉	1	2	yes	—
192	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
193	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
194	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
195	M₁₆	—	316	2	no	—
196	M₁₆	—	316	2	no	—
197	C₂×C₈	—	316	2	no	—
198	C₂×C₈	—	158	4	no	—
199	C₄⋊C₄	—	2	4	no	—
200	C₄⋊C₄	—	2	2	no	—
201	C₄⋊C₄	—	2	2	no	—
202	C₄⋊C₄	—	4	4	no	—
203	C₄⋊C₄	—	4	1	no	—
204	C₄⋊C₄	—	4	1	no	—
205	C₄⋊C₄	—	4	1	no	—
206	C₄⋊C₄	—	4	1	no	—
207	C₄²	—	2	2	no	—
208	C₄²	—	2	2	no	—
209	C₄²	—	4	2	no	—
210	C₄²	D₄×D₇₉	1	2	yes	—
211	C₄²	#11929623	1	2	yes	—
212	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
213	Q₈	—	2	4	no	—
214	Q₈	—	4	2	no	—
215	Q₈	—	4	2	no	—
216	Q₈	—	4	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	4	1	no	—
223	C₂×C₄	—	4	1	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	4	1	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	1	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
233	C₂×C₄	#14579129	1	1	yes	characteristic
234	C₂×C₄	#14579133	1	2	yes	—
235	C₂×C₄	#14579142	1	1	yes	characteristic
236	C₂×C₄	#14579186	1	1	yes	characteristic
237	C₂×C₄	#14579191	1	1	yes	characteristic
238	C₂×C₄	#14579192	1	2	yes	—
239	C₈	—	316	4	no	—
240	C₈	—	632	2	no	—
241	C₂²	—	2	1	no	—
242	C₂²	—	2	1	no	—
243	C₂²	#19098443	1	1	yes	characteristic
244	C₂²	#19098564	1	1	yes	characteristic
245	C₂²	#19098572	1	1	yes	characteristic
246	C₄	—	2	2	no	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	4	2	no	—
250	C₄	—	4	2	no	—
251	C₄	—	4	2	no	—
252	C₄	—	8	2	no	—
253	C₄	—	8	1	no	—
254	C₄	#19098811	1	2	yes	—
255	C₄	#19098819	1	2	yes	—
256	C₂	—	2	1	no	—
257	C₂	—	2	1	no	—
258	C₂	#23763819	1	1	yes	characteristic
259	C₂	#23763834	1	1	yes	characteristic
260	C₂	#23763938	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23772485

C₂

yes

maximal, characteristic

#23763396

C₂

yes

maximal, characteristic

#23761829

C₂

yes

maximal

#23761258

C₂

yes

maximal

C₇₉×#2581

C₂

yes

maximal, characteristic

#19098694

—

#19098620

—

#19098616

C₂²

yes

—

#19098587

C₂²

yes

—

C₂×#14579080

—

#19098332

—

Q₈⋊(C₇₉⋊C₈)

—

C₂×C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₂×C₄×Q₈×C₇₉

C₂²

yes

characteristic

#400×C₇₉

C₄

yes

—

#395×C₇₉

C₄

yes

—

#391×C₇₉

—

#389×C₇₉

—

#387×C₇₉

—

#382×C₇₉

C₂²

yes

characteristic

C₂×#11929608

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

#14579080

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

C₄×C₇₉⋊C₈

D₄

yes

—

C₂²×Q₈×C₇₉

C₂×C₄

yes

characteristic

C₂²×Q₈×C₇₉

D₄

yes

characteristic

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#95×C₇₉

—

#95×C₇₉

—

#95×C₇₉

—

#95×C₇₉

—

#95×C₇₉

C₂×C₄

yes

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

#41

yes

—

C₂³×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×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

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

100

C₂×C₄×C₇₉

—

101

C₂×C₄×C₇₉

C₄×D₄

yes

—

102

C₂×C₄×C₇₉

#120

yes

characteristic

103

C₂×C₄×C₇₉

#121

yes

—

104

C₂×C₄×C₇₉

#123

yes

characteristic

105

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

characteristic

106

C₂×C₄×C₇₉

#137

yes

characteristic

107

C₂×C₄×C₇₉

#137

yes

—

108

C₇₉⋊C₈

—

109

C₇₉⋊C₈

—

110

C₂²×C₇₉

—

111

C₂²×C₇₉

—

112

C₂²×C₇₉

#386

yes

characteristic

113

C₂²×C₇₉

#417

yes

characteristic

114

C₂²×C₇₉

#419

yes

characteristic

115

C₄×C₇₉

—

116

C₄×C₇₉

—

117

C₄×C₇₉

—

118

C₄×C₇₉

—

119

C₄×C₇₉

—

120

C₄×C₇₉

—

121

C₄×C₇₉

—

122

C₄×C₇₉

—

123

C₄×C₇₉

#468

yes

—

124

C₄×C₇₉

#470

yes

—

125

#9488

—

maximal, Sylow

126

C₂×C₇₉

—

127

C₂×C₇₉

—

128

C₂×C₇₉

#1891

yes

characteristic

129

C₂×C₇₉

#1894

yes

characteristic

130

C₂×C₇₉

#1912

yes

characteristic

131

#2983

—

132

#2581

D₇₉

yes

characteristic

133

#1801

—

134

#1487

—

135

#1286

—

136

C₇₉

#9488

yes

characteristic, complemented, Sylow

137

C₂×C₄×Q₈

C₂×D₇₉

yes

characteristic

138

C₂×C₄×Q₈

C₂×D₇₉

yes

characteristic

139

#446

—

158

—

140

#432

—

158

—

141

#431

—

142

#423

—

143

C₂×#101

—

158

—

144

#400

Dic₇₉

yes

—

145

#395

Dic₇₉

yes

—

146

#391

—

147

#389

—

148

#387

—

149

#382

C₂×D₇₉

yes

characteristic

150

#343

—

158

—

151

Q₈⋊C₈

—

158

—

152

C₂²×Q₈

C₂×Dic₇₉

yes

characteristic

153

C₂²×Q₈

C₂²⋊D₇₉

yes

characteristic

154

C₂×M₁₆

—

158

—

155

C₄×Q₈

—

156

C₄×Q₈

—

157

C₄×Q₈

—

158

C₄×Q₈

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

C₂×Dic₇₉

yes

characteristic

163

C₂×C₄⋊C₄

C₂×Dic₇₉

yes

—

164

C₂×C₄⋊C₄

C₂²⋊D₇₉

yes

characteristic

165

C₂×C₄²

—

166

C₂×C₄²

C₂²⋊D₇₉

yes

—

167

C₂×C₄²

C₂²×D₇₉

yes

characteristic

168

C₄⋊C₈

—

158

—

169

C₄⋊C₈

—

158

—

170

C₄⋊C₈

—

158

—

171

C₄⋊C₈

—

158

—

172

#101

—

316

—

173

C₂²⋊C₈

—

158

—

174

#97

—

158

—

175

C₄×C₈

—

176

#95

—

177

#95

—

178

#95

—

179

#95

—

180

#95

C₂×Dic₇₉

yes

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

C₂²⋊Dic₇₉

yes

—

191

C₂²×C₄

C₂²⋊Dic₇₉

yes

—

192

C₂²×C₄

C₂²×Dic₇₉

yes

characteristic

193

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

194

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

195

M₁₆

—

316

—

196

M₁₆

—

316

—

197

C₂×C₈

—

316

—

198

C₂×C₈

—

158

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

210

C₄²

D₄×D₇₉

yes

—

211

C₄²

#11929623

yes

—

212

C₂³

C₂×C₂²⋊Dic₇₉

yes

characteristic

213

Q₈

—

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

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

—

231

C₂×C₄

—

232

C₂×C₄

D₄×Dic₇₉

yes

—

233

C₂×C₄

#14579129

yes

characteristic

234

C₂×C₄

#14579133

yes

—

235

C₂×C₄

#14579142

yes

characteristic

236

C₂×C₄

#14579186

yes

characteristic

237

C₂×C₄

#14579191

yes

characteristic

238

C₂×C₄

#14579192

yes

—

239

C₈

—

316

—

240

C₈

—

632

—

241

C₂²

—

242

C₂²

—

243

C₂²

#19098443

yes

characteristic

244

C₂²

#19098564

yes

characteristic

245

C₂²

#19098572

yes

characteristic

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

#19098811

yes

—

255

C₄

#19098819

yes

—

256

C₂

—

257

C₂

—

258

C₂

#23763819

yes

characteristic

259

C₂

#23763834

yes

characteristic

260

C₂

#23763938

yes

characteristic

	subgroup	G/H
center	C₂²	#19098443
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#2581	C₂
socle	C₂²×C₇₉	#386
prime radical	C₂³×C₇₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#2581	D₇₉
hypocenter	C₇₉	#9488
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2581

subgroup

G/H

center

C₂²

#19098443

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#2581

C₂

socle

C₂²×C₇₉

#386

prime radical

C₂³×C₇₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2581

N	H ≅ G/N	type
136. C₇₉	#9488	semidirect

H ≅ G/N

type

136. C₇₉

#9488

semidirect

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

subgroup	index
#23772485	2
#23763396	2
#23761829	2
#23761258	2
C₇₉×#2581	2
#9488	79

subgroup

index

C₇₉×#2581

Subgroups — #34186134

Conjugacy classes of subgroups

Complements

Maximal subgroups