Group #34207626 — subgroups

Subgroups — #34207626

Order 20224.

462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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×#19098943	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098368	C₂	1	2	yes	maximal
3	C₂×#19098368	C₂	1	2	yes	maximal
4	#23764133	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#1374	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₁₆	—	2	1	no	—
7	C₂²×Dic₃₁₆	C₂²	1	2	yes	—
8	C₂×#14579161	—	2	1	no	—
9	#19098943	—	2	4	no	—
10	C₂×#14579095	C₂²	1	1	yes	characteristic
11	C₂×#14579095	C₂²	1	1	yes	characteristic
12	#19098461	—	2	1	no	—
13	#19098368	—	2	4	no	—
14	#19098368	—	2	4	no	—
15	#19098326	—	2	1	no	—
16	C₂²×C₁₆×C₇₉	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×Dic₁₅₈	—	2	2	no	—
19	C₂×Dic₃₁₆	—	2	2	no	—
20	C₂×Dic₃₁₆	—	2	2	no	—
21	C₂×Dic₃₁₆	—	2	2	no	—
22	C₂×Dic₃₁₆	—	2	2	no	—
23	C₂×Dic₃₁₆	—	2	4	no	—
24	C₂×Dic₃₁₆	—	2	2	no	—
25	C₂×Dic₃₁₆	—	4	2	no	—
26	C₂×Dic₃₁₆	—	4	2	no	—
27	C₂×Dic₃₁₆	D₄	1	4	yes	—
28	#14579161	—	2	4	no	—
29	#14579161	—	4	2	no	—
30	C₂×C₄⋊Dic₇₉	—	2	1	no	—
31	C₂×C₄⋊Dic₇₉	—	2	1	no	—
32	C₂×C₄⋊Dic₇₉	—	4	1	no	—
33	C₂×C₄⋊Dic₇₉	—	4	1	no	—
34	C₂×Dic₇₉⋊C₄	—	4	1	no	—
35	#14579095	—	2	1	no	—
36	#14579095	—	2	2	no	—
37	#14579095	D₄	1	2	yes	—
38	C₇₉⋊#95	—	4	1	no	—
39	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
41	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
42	C₂×C₁₆×C₇₉	—	2	2	no	—
43	C₂×C₁₆×C₇₉	—	2	2	no	—
44	C₂×C₁₆×C₇₉	—	2	2	no	—
45	C₄×C₈×C₇₉	—	2	2	no	—
46	C₂×Dic₁₅₈	—	2	4	no	—
47	C₂×Dic₁₅₈	—	4	2	no	—
48	C₂×Dic₁₅₈	—	4	2	no	—
49	C₂×Dic₁₅₈	—	4	2	no	—
50	C₂×Dic₁₅₈	—	4	2	no	—
51	C₂×Dic₁₅₈	—	4	2	no	—
52	C₂²×Dic₇₉	—	4	2	no	—
53	C₂²×Dic₇₉	—	4	1	no	—
54	C₂²×Dic₇₉	—	4	1	no	—
55	Dic₃₁₆	—	2	4	no	—
56	Dic₃₁₆	—	2	4	no	—
57	Dic₃₁₆	—	4	8	no	—
58	Dic₃₁₆	—	4	2	no	—
59	Dic₃₁₆	—	4	2	no	—
60	C₄⋊Dic₇₉	—	2	2	no	—
61	C₄⋊Dic₇₉	—	4	4	no	—
62	C₄⋊Dic₇₉	—	4	4	no	—
63	C₄⋊Dic₇₉	—	4	1	no	—
64	C₄⋊Dic₇₉	—	4	1	no	—
65	C₄⋊Dic₇₉	—	4	1	no	—
66	Dic₇₉⋊C₄	—	8	2	no	—
67	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
68	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
69	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₇₉	—	2	1	no	—
71	C₂×C₈×C₇₉	—	2	1	no	—
72	C₂×C₈×C₇₉	SD₁₆	1	2	yes	—
73	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
74	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
76	C₂×C₈×C₇₉	#41	1	2	yes	—
77	C₄²×C₇₉	—	2	1	no	—
78	C₄²×C₇₉	—	2	1	no	—
79	C₁₆×C₇₉	—	4	2	no	—
80	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
81	C₂×C₄×C₇₉	—	2	1	no	—
82	C₂×C₄×C₇₉	—	2	1	no	—
83	C₂×C₄×C₇₉	—	2	1	no	—
84	C₂×C₄×C₇₉	—	2	1	no	—
85	C₂×C₄×C₇₉	SD₃₂	1	2	yes	—
86	C₂×C₄×C₇₉	Q₃₂	1	2	yes	—
87	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
88	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
89	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
90	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
91	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
92	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
93	C₂×Dic₇₉	—	4	4	no	—
94	C₂×Dic₇₉	—	4	2	no	—
95	C₂×Dic₇₉	—	8	2	no	—
96	C₂×Dic₇₉	—	8	2	no	—
97	C₂×Dic₇₉	—	8	1	no	—
98	C₂×Dic₇₉	—	8	1	no	—
99	C₂×Dic₇₉	—	8	1	no	—
100	C₂×Dic₇₉	—	8	1	no	—
101	C₂×Dic₇₉	—	8	1	no	—
102	Dic₁₅₈	—	4	4	no	—
103	Dic₁₅₈	—	4	4	no	—
104	Dic₁₅₈	—	8	2	no	—
105	Dic₁₅₈	—	8	2	no	—
106	C₈×C₇₉	—	2	2	no	—
107	C₈×C₇₉	#121	1	2	yes	—
108	C₈×C₇₉	#123	1	2	yes	—
109	C₂²×C₇₉	#447	1	1	yes	characteristic
110	C₂²×C₇₉	#459	1	1	yes	characteristic
111	C₂²×C₇₉	#486	1	1	yes	characteristic
112	C₂²×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
113	C₂²×C₇₉	C₂×Q₃₂	1	1	yes	characteristic
114	C₂²×C₇₉	#510	1	1	yes	characteristic
115	C₂²×C₇₉	#510	1	1	yes	characteristic
116	C₄×C₇₉	—	2	2	no	—
117	C₄×C₇₉	—	2	2	no	—
118	C₄×C₇₉	#394	1	1	yes	characteristic
119	C₄×C₇₉	#450	1	1	yes	characteristic
120	C₄×C₇₉	#460	1	1	yes	characteristic
121	C₄×C₇₉	#490	1	1	yes	characteristic
122	Dic₇₉	—	8	2	no	—
123	Dic₇₉	—	8	4	no	—
124	Dic₇₉	—	16	1	no	—
125	#13409	—	79	1	no	maximal, Sylow
126	C₂×C₇₉	#2041	1	1	yes	characteristic
127	C₂×C₇₉	#2185	1	1	yes	characteristic
128	C₂×C₇₉	#2188	1	1	yes	characteristic
129	C₂×C₇₉	#2208	1	1	yes	characteristic
130	C₂×C₇₉	#2209	1	1	yes	characteristic
131	C₂×C₇₉	#2241	1	1	yes	characteristic
132	C₂×C₇₉	#2245	1	1	yes	characteristic
133	C₂×#494	—	79	1	no	—
134	C₂×#358	—	79	2	no	—
135	C₂×#358	—	79	2	no	—
136	#1942	—	79	1	no	—
137	#1374	D₇₉	1	1	yes	characteristic
138	C₇₉	#13409	1	1	yes	characteristic, complemented, Sylow
139	C₂²×Q₁₆	—	79	2	no	—
140	C₂²×Q₁₆	—	158	1	no	—
141	C₂×C₄⋊Q₈	—	158	1	no	—
142	C₂²×C₁₆	C₂×D₇₉	1	2	yes	—
143	#494	—	158	4	no	—
144	C₂×#107	—	79	1	no	—
145	C₂×#107	—	79	1	no	—
146	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
147	#389	—	158	1	no	—
148	#358	—	158	4	no	—
149	#358	—	158	4	no	—
150	#340	—	158	1	no	—
151	C₂²×Q₈	—	158	2	no	—
152	C₂×Q₁₆	—	316	2	no	—
153	C₂×Q₁₆	—	316	2	no	—
154	C₂×Q₁₆	—	79	4	no	—
155	C₂×Q₁₆	—	158	4	no	—
156	C₂×Q₁₆	—	158	2	no	—
157	C₂×Q₁₆	—	158	2	no	—
158	C₂×Q₁₆	—	158	2	no	—
159	C₂×Q₁₆	—	158	2	no	—
160	C₂×Q₁₆	—	158	2	no	—
161	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
162	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
163	C₄⋊Q₈	—	316	2	no	—
164	C₄⋊Q₈	—	158	4	no	—
165	C₂×C₄⋊C₄	—	316	1	no	—
166	C₂×C₄⋊C₄	—	316	1	no	—
167	C₂×C₄⋊C₄	—	316	1	no	—
168	C₂×C₄⋊C₄	—	158	1	no	—
169	C₂×C₄⋊C₄	—	158	1	no	—
170	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
171	C₂×C₁₆	—	2	2	no	—
172	C₂×C₁₆	—	2	2	no	—
173	C₂×C₁₆	—	2	2	no	—
174	#107	—	79	2	no	—
175	#107	—	158	2	no	—
176	#107	—	158	1	no	—
177	C₄×C₈	—	2	2	no	—
178	#95	—	316	1	no	—
179	C₂×Q₈	—	316	2	no	—
180	C₂×Q₈	—	316	2	no	—
181	C₂×Q₈	—	316	2	no	—
182	C₂×Q₈	—	316	2	no	—
183	C₂×Q₈	—	316	2	no	—
184	C₂×Q₈	—	158	4	no	—
185	C₂²×C₄	—	316	1	no	—
186	C₂²×C₄	—	316	2	no	—
187	C₂²×C₄	—	316	1	no	—
188	C₂²×C₄	D₆₃₂	1	1	yes	characteristic
189	C₂²×C₄	D₆₃₂	1	1	yes	characteristic
190	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
191	Q₁₆	—	316	8	no	—
192	Q₁₆	—	316	2	no	—
193	Q₁₆	—	316	2	no	—
194	Q₁₆	—	158	4	no	—
195	Q₁₆	—	158	4	no	—
196	C₂×C₈	—	2	1	no	—
197	C₂×C₈	—	2	1	no	—
198	C₂×C₈	#11929613	1	2	yes	—
199	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
200	C₂×C₈	D₄×D₇₉	1	2	yes	—
201	C₂×C₈	#11929624	1	2	yes	—
202	C₂×C₈	#11929625	1	1	yes	characteristic
203	C₄⋊C₄	—	316	4	no	—
204	C₄⋊C₄	—	316	4	no	—
205	C₄⋊C₄	—	316	1	no	—
206	C₄⋊C₄	—	316	1	no	—
207	C₄⋊C₄	—	316	1	no	—
208	C₄⋊C₄	—	632	2	no	—
209	C₄⋊C₄	—	158	2	no	—
210	C₄²	—	2	1	no	—
211	C₄²	—	2	1	no	—
212	C₁₆	—	4	2	no	—
213	C₂³	C₂×D₆₃₂	1	1	yes	characteristic
214	Q₈	—	316	4	no	—
215	Q₈	—	316	4	no	—
216	Q₈	—	632	2	no	—
217	Q₈	—	632	2	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	316	4	no	—
223	C₂×C₄	—	316	2	no	—
224	C₂×C₄	—	632	2	no	—
225	C₂×C₄	—	632	1	no	—
226	C₂×C₄	—	632	1	no	—
227	C₂×C₄	—	632	2	no	—
228	C₂×C₄	—	632	1	no	—
229	C₂×C₄	—	632	1	no	—
230	C₂×C₄	—	632	1	no	—
231	C₂×C₄	#14579106	1	2	yes	—
232	C₂×C₄	Dic₆₃₂	1	2	yes	—
233	C₂×C₄	#14579131	1	1	yes	characteristic
234	C₂×C₄	#14579136	1	1	yes	characteristic
235	C₂×C₄	#14579149	1	1	yes	characteristic
236	C₂×C₄	C₂×#11929613	1	1	yes	characteristic
237	C₂×C₄	#14579189	1	1	yes	characteristic
238	C₂×C₄	#14579189	1	1	yes	characteristic
239	C₈	—	2	2	no	—
240	C₈	#14579134	1	2	yes	—
241	C₈	#14579146	1	2	yes	—
242	C₂²	#19098699	1	1	yes	characteristic
243	C₂²	#19098759	1	1	yes	characteristic
244	C₂²	#19098910	1	1	yes	characteristic
245	C₂²	C₂×#14579106	1	1	yes	characteristic
246	C₂²	C₂×Dic₆₃₂	1	1	yes	characteristic
247	C₂²	#19099006	1	1	yes	characteristic
248	C₂²	#19099006	1	1	yes	characteristic
249	C₄	—	2	2	no	—
250	C₄	—	2	2	no	—
251	C₄	—	632	4	no	—
252	C₄	—	632	2	no	—
253	C₄	—	1264	1	no	—
254	C₄	#19098481	1	1	yes	characteristic
255	C₄	#19098716	1	1	yes	characteristic
256	C₄	#19098764	1	1	yes	characteristic
257	C₄	#19098928	1	1	yes	characteristic
258	C₂	#23764635	1	1	yes	characteristic
259	C₂	#23765319	1	1	yes	characteristic
260	C₂	#23765336	1	1	yes	characteristic
261	C₂	#23765446	1	1	yes	characteristic
262	C₂	#23765451	1	1	yes	characteristic
263	C₂	#23765628	1	1	yes	characteristic
264	C₂	#23765646	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098943

C₂

yes

maximal, characteristic

C₂×#19098368

C₂

yes

maximal

C₂×#19098368

C₂

yes

maximal

#23764133

C₂

yes

maximal, characteristic

C₇₉×#1374

C₂

yes

maximal, characteristic

C₂²×Dic₃₁₆

—

C₂²×Dic₃₁₆

C₂²

yes

—

C₂×#14579161

—

#19098943

—

C₂×#14579095

C₂²

yes

characteristic

C₂×#14579095

C₂²

yes

—

—

—

—

C₂²×C₁₆×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂²×Dic₁₅₈

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

D₄

yes

—

#14579161

—

#14579161

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×Dic₇₉⋊C₄

—

#14579095

—

#14579095

—

#14579095

D₄

yes

—

C₇₉⋊#95

—

C₂²×C₈×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

C₂³

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

characteristic

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

—

C₄×C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₂²×C₄×C₇₉

D₈

yes

characteristic

C₂²×C₄×C₇₉

D₈

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

SD₁₆

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

C₂×C₈×C₇₉

yes

C₂×C₈×C₇₉

yes

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₁₆×C₇₉

—

C₂³×C₇₉

C₂×D₈

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

SD₃₂

yes

—

C₂×C₄×C₇₉

Q₃₂

yes

—

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

C₂×SD₁₆

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

100

C₂×Dic₇₉

—

101

C₂×Dic₇₉

—

102

Dic₁₅₈

—

103

Dic₁₅₈

—

104

Dic₁₅₈

—

105

Dic₁₅₈

—

106

C₈×C₇₉

—

107

C₈×C₇₉

#121

yes

—

108

C₈×C₇₉

#123

yes

—

109

C₂²×C₇₉

#447

yes

characteristic

110

C₂²×C₇₉

#459

yes

characteristic

111

C₂²×C₇₉

#486

yes

characteristic

112

C₂²×C₇₉

C₂×SD₃₂

yes

characteristic

113

C₂²×C₇₉

C₂×Q₃₂

yes

characteristic

114

C₂²×C₇₉

#510

yes

characteristic

115

C₂²×C₇₉

#510

yes

characteristic

116

C₄×C₇₉

—

117

C₄×C₇₉

—

118

C₄×C₇₉

#394

yes

characteristic

119

C₄×C₇₉

#450

yes

characteristic

120

C₄×C₇₉

#460

yes

characteristic

121

C₄×C₇₉

#490

yes

characteristic

122

Dic₇₉

—

123

Dic₇₉

—

124

Dic₇₉

—

125

#13409

—

maximal, Sylow

126

C₂×C₇₉

#2041

yes

characteristic

127

C₂×C₇₉

#2185

yes

characteristic

128

C₂×C₇₉

#2188

yes

characteristic

129

C₂×C₇₉

#2208

yes

characteristic

130

C₂×C₇₉

#2209

yes

characteristic

131

C₂×C₇₉

#2241

yes

characteristic

132

C₂×C₇₉

#2245

yes

characteristic

133

C₂×#494

—

134

C₂×#358

—

135

C₂×#358

—

136

#1942

—

137

#1374

D₇₉

yes

characteristic

138

C₇₉

#13409

yes

characteristic, complemented, Sylow

139

C₂²×Q₁₆

—

140

C₂²×Q₁₆

—

158

—

141

C₂×C₄⋊Q₈

—

158

—

142

C₂²×C₁₆

C₂×D₇₉

yes

—

143

#494

—

158

—

144

C₂×#107

—

145

C₂×#107

—

146

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

147

#389

—

158

—

148

#358

—

158

—

149

#358

—

158

—

150

#340

—

158

—

151

C₂²×Q₈

—

158

—

152

C₂×Q₁₆

—

316

—

153

C₂×Q₁₆

—

316

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

158

—

156

C₂×Q₁₆

—

158

—

157

C₂×Q₁₆

—

158

—

158

C₂×Q₁₆

—

158

—

159

C₂×Q₁₆

—

158

—

160

C₂×Q₁₆

—

158

—

161

C₂²×C₈

D₃₁₆

yes

characteristic

162

C₂²×C₈

C₂²×D₇₉

yes

characteristic

163

C₄⋊Q₈

—

316

—

164

C₄⋊Q₈

—

158

—

165

C₂×C₄⋊C₄

—

316

—

166

C₂×C₄⋊C₄

—

316

—

167

C₂×C₄⋊C₄

—

316

—

168

C₂×C₄⋊C₄

—

158

—

169

C₂×C₄⋊C₄

—

158

—

170

C₂×C₄²

D₃₁₆

yes

characteristic

171

C₂×C₁₆

—

172

C₂×C₁₆

—

173

C₂×C₁₆

—

174

#107

—

175

#107

—

158

—

176

#107

—

158

—

177

C₄×C₈

—

178

#95

—

316

—

179

C₂×Q₈

—

316

—

180

C₂×Q₈

—

316

—

181

C₂×Q₈

—

316

—

182

C₂×Q₈

—

316

—

183

C₂×Q₈

—

316

—

184

C₂×Q₈

—

158

—

185

C₂²×C₄

—

316

—

186

C₂²×C₄

—

316

—

187

C₂²×C₄

—

316

—

188

C₂²×C₄

D₆₃₂

yes

characteristic

189

C₂²×C₄

D₆₃₂

yes

characteristic

190

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

191

Q₁₆

—

316

—

192

Q₁₆

—

316

—

193

Q₁₆

—

316

—

194

Q₁₆

—

158

—

195

Q₁₆

—

158

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

#11929613

yes

—

199

C₂×C₈

D₄×D₇₉

yes

characteristic

200

C₂×C₈

D₄×D₇₉

yes

—

201

C₂×C₈

#11929624

yes

—

202

C₂×C₈

#11929625

yes

characteristic

203

C₄⋊C₄

—

316

—

204

C₄⋊C₄

—

316

—

205

C₄⋊C₄

—

316

—

206

C₄⋊C₄

—

316

—

207

C₄⋊C₄

—

316

—

208

C₄⋊C₄

—

632

—

209

C₄⋊C₄

—

158

—

210

C₄²

—

211

C₄²

—

212

C₁₆

—

213

C₂³

C₂×D₆₃₂

yes

characteristic

214

Q₈

—

316

—

215

Q₈

—

316

—

216

Q₈

—

632

—

217

Q₈

—

632

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

316

—

223

C₂×C₄

—

316

—

224

C₂×C₄

—

632

—

225

C₂×C₄

—

632

—

226

C₂×C₄

—

632

—

227

C₂×C₄

—

632

—

228

C₂×C₄

—

632

—

229

C₂×C₄

—

632

—

230

C₂×C₄

—

632

—

231

C₂×C₄

#14579106

yes

—

232

C₂×C₄

Dic₆₃₂

yes

—

233

C₂×C₄

#14579131

yes

characteristic

234

C₂×C₄

#14579136

yes

characteristic

235

C₂×C₄

#14579149

yes

characteristic

236

C₂×C₄

C₂×#11929613

yes

characteristic

237

C₂×C₄

#14579189

yes

characteristic

238

C₂×C₄

#14579189

yes

characteristic

239

C₈

—

240

C₈

#14579134

yes

—

241

C₈

#14579146

yes

—

242

C₂²

#19098699

yes

characteristic

243

C₂²

#19098759

yes

characteristic

244

C₂²

#19098910

yes

characteristic

245

C₂²

C₂×#14579106

yes

characteristic

246

C₂²

C₂×Dic₆₃₂

yes

characteristic

247

C₂²

#19099006

yes

characteristic

248

C₂²

#19099006

yes

characteristic

249

C₄

—

250

C₄

—

251

C₄

—

632

—

252

C₄

—

632

—

253

C₄

—

1264

—

254

C₄

#19098481

yes

characteristic

255

C₄

#19098716

yes

characteristic

256

C₄

#19098764

yes

characteristic

257

C₄

#19098928

yes

characteristic

258

C₂

#23764635

yes

characteristic

259

C₂

#23765319

yes

characteristic

260

C₂

#23765336

yes

characteristic

261

C₂

#23765446

yes

characteristic

262

C₂

#23765451

yes

characteristic

263

C₂

#23765628

yes

characteristic

264

C₂

#23765646

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₆₃₂
commutator, cosocle	C₂²×C₈×C₇₉	C₂³
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₇₉×#1374	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₈
hypercenter	#1374	D₇₉
hypocenter	C₇₉	#13409
LCS	G ▷ C₂²×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

subgroup

G/H

center

C₂³

C₂×D₆₃₂

commutator, cosocle

C₂²×C₈×C₇₉

C₂³

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₇₉×#1374

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₈

D₇₉

C₇₉

G ▷ C₂²×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

N	H ≅ G/N	type
138. C₇₉	#13409	semidirect

H ≅ G/N

type

138. C₇₉

#13409

semidirect

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

subgroup	index
C₂×#19098943	2
C₂×#19098368	2
#23764133	2
C₇₉×#1374	2
#13409	79

subgroup

index

C₇₉×#1374

Subgroups — #34207626

Conjugacy classes of subgroups

Complements

Maximal subgroups