Group #34187746 — subgroups

Subgroups — #34187746

Order 20224.

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

normal subgroups only

This group has 406 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	C₂×#19098914	C₂	1	1	yes	maximal, characteristic
2	#23762086	C₂	1	1	yes	maximal, characteristic
3	#23762082	C₂	1	1	yes	maximal, characteristic
4	#23762073	C₂	1	1	yes	maximal, characteristic
5	#23762073	C₂	1	1	yes	maximal, characteristic
6	#23761692	C₂	1	1	yes	maximal, characteristic
7	C₇₉×#1848	C₂	1	1	yes	maximal, characteristic
8	C₂×#14579161	C₂²	1	1	yes	characteristic
9	C₂×#14579161	C₂²	1	1	yes	characteristic
10	#19098914	—	2	2	no	—
11	#19098914	C₄	1	4	yes	—
12	#19098616	C₂²	1	1	yes	characteristic
13	#19098616	C₂²	1	1	yes	characteristic
14	C₂×#14579086	—	2	2	no	—
15	#19098311	—	2	2	no	—
16	#19098310	—	2	2	no	—
17	#19098310	—	2	2	no	—
18	#19098308	—	2	2	no	—
19	#19098285	—	2	2	no	—
20	C₂×#108×C₇₉	—	2	2	no	—
21	#423×C₇₉	C₂²	1	1	yes	characteristic
22	#423×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
24	C₂²×Dic₁₅₈	—	2	1	no	—
25	C₂²×Dic₁₅₈	—	2	1	no	—
26	#14579161	—	2	1	no	—
27	#14579161	—	2	1	no	—
28	#14579161	—	2	1	no	—
29	#14579161	—	2	1	no	—
30	#14579161	—	2	1	no	—
31	#14579161	—	2	1	no	—
32	#14579161	C₂×C₄	1	2	yes	—
33	#14579161	C₂×C₄	1	2	yes	—
34	C₂×C₄⋊Dic₇₉	—	2	1	no	—
35	C₂×C₄⋊Dic₇₉	—	2	1	no	—
36	C₂×C₄⋊Dic₇₉	—	2	1	no	—
37	C₂×C₄⋊Dic₇₉	—	2	1	no	—
38	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
39	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
40	#14579086	—	2	8	no	—
41	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
42	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
43	C₄×C₇₉⋊C₈	—	2	1	no	—
44	C₄×C₇₉⋊C₈	—	2	1	no	—
45	C₂×M₁₆×C₇₉	—	2	1	no	—
46	C₂×M₁₆×C₇₉	—	2	1	no	—
47	C₂²×C₈×C₇₉	D₄	1	2	yes	—
48	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
49	#108×C₇₉	—	4	4	no	—
50	C₄⋊C₈×C₇₉	—	2	1	no	—
51	C₄⋊C₈×C₇₉	—	2	1	no	—
52	C₄⋊C₈×C₇₉	—	2	1	no	—
53	C₄⋊C₈×C₇₉	—	2	1	no	—
54	C₄×C₈×C₇₉	C₂×C₄	1	2	yes	—
55	C₄×C₈×C₇₉	D₄	1	2	yes	—
56	C₂×Dic₁₅₈	—	2	2	no	—
57	C₂×Dic₁₅₈	—	2	2	no	—
58	C₂×Dic₁₅₈	—	4	1	no	—
59	C₂×Dic₁₅₈	—	4	1	no	—
60	C₂×Dic₁₅₈	—	4	2	no	—
61	C₂×Dic₁₅₈	—	4	2	no	—
62	C₂×Dic₁₅₈	—	8	2	no	—
63	C₂²×Dic₇₉	—	4	1	no	—
64	C₂²×Dic₇₉	—	4	1	no	—
65	C₂×C₇₉⋊C₈	—	2	2	no	—
66	C₂×C₇₉⋊C₈	—	2	2	no	—
67	C₄⋊Dic₇₉	—	2	2	no	—
68	C₄⋊Dic₇₉	—	2	2	no	—
69	C₄⋊Dic₇₉	—	2	2	no	—
70	C₄⋊Dic₇₉	—	2	2	no	—
71	C₄⋊Dic₇₉	—	4	1	no	—
72	C₄⋊Dic₇₉	—	4	1	no	—
73	C₄⋊Dic₇₉	—	4	1	no	—
74	C₄⋊Dic₇₉	—	4	1	no	—
75	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
77	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
78	M₁₆×C₇₉	—	4	2	no	—
79	M₁₆×C₇₉	—	4	2	no	—
80	C₂×C₈×C₇₉	—	2	2	no	—
81	C₂×C₈×C₇₉	—	2	2	no	—
82	C₂×C₈×C₇₉	—	4	1	no	—
83	C₂×C₈×C₇₉	—	4	1	no	—
84	C₂×C₈×C₇₉	C₂²⋊C₄	1	4	yes	—
85	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
86	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
87	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
88	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
89	C₂³×C₇₉	#124	1	1	yes	characteristic
90	C₂×C₄×C₇₉	—	2	2	no	—
91	C₂×C₄×C₇₉	—	2	2	no	—
92	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
95	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
96	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
97	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
98	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
99	C₂×C₄×C₇₉	#137	1	2	yes	—
100	C₂×Dic₇₉	—	4	2	no	—
101	C₂×Dic₇₉	—	4	2	no	—
102	C₂×Dic₇₉	—	8	2	no	—
103	C₂×Dic₇₉	—	8	2	no	—
104	Dic₁₅₈	—	4	4	no	—
105	Dic₁₅₈	—	8	2	no	—
106	Dic₁₅₈	—	8	1	no	—
107	Dic₁₅₈	—	8	1	no	—
108	Dic₁₅₈	—	8	2	no	—
109	C₈×C₇₉	—	2	4	no	—
110	C₈×C₇₉	—	8	1	no	—
111	C₈×C₇₉	—	8	1	no	—
112	C₇₉⋊C₈	—	4	2	no	—
113	C₇₉⋊C₈	—	4	2	no	—
114	C₂²×C₇₉	—	2	1	no	—
115	C₂²×C₇₉	—	2	1	no	—
116	C₂²×C₇₉	#390	1	1	yes	characteristic
117	C₂²×C₇₉	#489	1	2	yes	—
118	C₄×C₇₉	—	2	1	no	—
119	C₄×C₇₉	—	2	1	no	—
120	C₄×C₇₉	#417	1	2	yes	—
121	C₄×C₇₉	#471	1	2	yes	—
122	C₄×C₇₉	#473	1	2	yes	—
123	C₄×C₇₉	#496	1	1	yes	characteristic
124	C₄×C₇₉	#497	1	1	yes	characteristic
125	Dic₇₉	—	8	2	no	—
126	Dic₇₉	—	8	2	no	—
127	#9775	—	79	1	no	maximal, Sylow
128	C₂×C₇₉	—	2	2	no	—
129	C₂×C₇₉	#1959	1	1	yes	characteristic
130	C₂×C₇₉	#1977	1	1	yes	characteristic
131	C₂×C₇₉	#1979	1	1	yes	characteristic
132	C₂×#487	—	79	1	no	—
133	#1848	D₇₉	1	1	yes	characteristic
134	#1549	—	79	1	no	—
135	#1548	—	79	1	no	—
136	#1546	—	79	1	no	—
137	#1546	—	79	1	no	—
138	#1452	—	79	1	no	—
139	C₇₉	#9775	1	1	yes	characteristic, complemented, Sylow
140	C₂×C₄⋊Q₈	—	79	1	no	—
141	C₂×C₄⋊Q₈	—	79	1	no	—
142	#487	—	79	4	no	—
143	#487	—	158	2	no	—
144	#431	—	79	1	no	—
145	#431	—	79	1	no	—
146	C₂×#108	—	2	2	no	—
147	#423	C₂×D₇₉	1	1	yes	characteristic
148	#423	C₂×D₇₉	1	1	yes	characteristic
149	C₂×#103	—	158	2	no	—
150	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
151	#333	—	158	2	no	—
152	#332	—	158	2	no	—
153	#332	—	158	2	no	—
154	#332	—	158	2	no	—
155	#322	—	158	2	no	—
156	C₂²×Q₈	—	158	1	no	—
157	C₂²×Q₈	—	158	1	no	—
158	C₂×M₁₆	—	2	1	no	—
159	C₂×M₁₆	—	2	1	no	—
160	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
161	C₄⋊Q₈	—	79	2	no	—
162	C₄⋊Q₈	—	79	2	no	—
163	C₄⋊Q₈	—	158	1	no	—
164	C₄⋊Q₈	—	158	1	no	—
165	C₄⋊Q₈	—	158	1	no	—
166	C₄⋊Q₈	—	158	1	no	—
167	C₄⋊Q₈	—	158	1	no	—
168	C₄⋊Q₈	—	158	1	no	—
169	C₂×C₄⋊C₄	—	158	1	no	—
170	C₂×C₄⋊C₄	—	158	1	no	—
171	C₂×C₄⋊C₄	—	158	1	no	—
172	C₂×C₄⋊C₄	—	158	1	no	—
173	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
174	#108	—	4	4	no	—
175	C₄⋊C₈	—	2	1	no	—
176	C₄⋊C₈	—	2	1	no	—
177	C₄⋊C₈	—	2	1	no	—
178	C₄⋊C₈	—	2	1	no	—
179	C₄⋊C₈	—	79	2	no	—
180	C₄⋊C₈	—	79	2	no	—
181	#103	—	158	8	no	—
182	C₂²⋊C₈	—	158	1	no	—
183	C₂²⋊C₈	—	158	1	no	—
184	C₄×C₈	—	158	1	no	—
185	C₄×C₈	—	158	1	no	—
186	C₄×C₈	C₄×D₇₉	1	2	yes	—
187	C₄×C₈	D₃₁₆	1	2	yes	—
188	C₂×Q₈	—	316	1	no	—
189	C₂×Q₈	—	316	1	no	—
190	C₂×Q₈	—	316	2	no	—
191	C₂×Q₈	—	316	2	no	—
192	C₂×Q₈	—	632	2	no	—
193	C₂×Q₈	—	158	2	no	—
194	C₂×Q₈	—	158	2	no	—
195	C₂²×C₄	—	316	1	no	—
196	C₂²×C₄	—	316	1	no	—
197	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
198	C₂²×C₄	#11929625	1	1	yes	characteristic
199	C₂²×C₄	#11929625	1	1	yes	characteristic
200	M₁₆	—	4	2	no	—
201	M₁₆	—	4	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	4	1	no	—
205	C₂×C₈	—	4	1	no	—
206	C₂×C₈	—	158	2	no	—
207	C₂×C₈	—	158	2	no	—
208	C₂×C₈	(C₂×D₇₉)⋊C₄	1	4	yes	—
209	C₄⋊C₄	—	316	1	no	—
210	C₄⋊C₄	—	316	1	no	—
211	C₄⋊C₄	—	316	1	no	—
212	C₄⋊C₄	—	316	1	no	—
213	C₄⋊C₄	—	158	2	no	—
214	C₄⋊C₄	—	158	2	no	—
215	C₄⋊C₄	—	158	2	no	—
216	C₄⋊C₄	—	158	2	no	—
217	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
218	C₄²	D₄×D₇₉	1	1	yes	characteristic
219	C₄²	D₄×D₇₉	1	1	yes	characteristic
220	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
221	C₂³	#14579150	1	1	yes	characteristic
222	Q₈	—	316	4	no	—
223	Q₈	—	632	2	no	—
224	Q₈	—	632	1	no	—
225	Q₈	—	632	1	no	—
226	Q₈	—	632	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	316	2	no	—
230	C₂×C₄	—	316	2	no	—
231	C₂×C₄	—	632	2	no	—
232	C₂×C₄	—	632	2	no	—
233	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
234	C₂×C₄	#14579123	1	1	yes	characteristic
235	C₂×C₄	#14579123	1	1	yes	characteristic
236	C₂×C₄	#14579136	1	1	yes	characteristic
237	C₂×C₄	#14579136	1	1	yes	characteristic
238	C₂×C₄	#14579157	1	1	yes	characteristic
239	C₂×C₄	#14579187	1	2	yes	—
240	C₂×C₄	#14579192	1	2	yes	—
241	C₈	—	2	4	no	—
242	C₈	—	8	1	no	—
243	C₈	—	8	1	no	—
244	C₈	—	316	2	no	—
245	C₈	—	316	2	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	2	1	no	—
248	C₂²	#19098464	1	1	yes	characteristic
249	C₂²	#19098925	1	2	yes	—
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	632	2	no	—
253	C₄	—	632	2	no	—
254	C₄	#19098562	1	2	yes	—
255	C₄	#19098827	1	2	yes	—
256	C₄	#19098839	1	2	yes	—
257	C₄	#19098950	1	1	yes	characteristic
258	C₄	#19098955	1	1	yes	characteristic
259	C₂	—	2	2	no	—
260	C₂	#23764214	1	1	yes	characteristic
261	C₂	#23764301	1	1	yes	characteristic
262	C₂	#23764313	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098914

C₂

yes

maximal, characteristic

#23762086

C₂

yes

maximal, characteristic

#23762082

C₂

yes

maximal, characteristic

#23762073

C₂

yes

maximal, characteristic

#23762073

C₂

yes

maximal, characteristic

#23761692

C₂

yes

maximal, characteristic

C₇₉×#1848

C₂

yes

maximal, characteristic

C₂×#14579161

C₂²

yes

characteristic

C₂×#14579161

C₂²

yes

characteristic

#19098914

—

#19098914

C₄

yes

—

#19098616

C₂²

yes

characteristic

#19098616

C₂²

yes

—

—

—

—

—

—

C₂×#108×C₇₉

—

#423×C₇₉

C₂²

yes

characteristic

#423×C₇₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂²×Dic₁₅₈

—

C₂²×Dic₁₅₈

—

—

—

—

—

—

—

C₂×C₄

yes

—

#14579161

C₂×C₄

yes

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

#14579086

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

—

C₂×M₁₆×C₇₉

—

C₂×M₁₆×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#108×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄×C₈×C₇₉

C₂×C₄

yes

—

C₄×C₈×C₇₉

D₄

yes

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

C₂²×C₄×C₇₉

yes

C₂²×C₄×C₇₉

yes

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₂³×C₇₉

#124

yes

characteristic

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

C₂×C₄×C₇₉

yes

—

C₂×C₄×C₇₉

#137

yes

—

100

C₂×Dic₇₉

—

101

C₂×Dic₇₉

—

102

C₂×Dic₇₉

—

103

C₂×Dic₇₉

—

104

Dic₁₅₈

—

105

Dic₁₅₈

—

106

Dic₁₅₈

—

107

Dic₁₅₈

—

108

Dic₁₅₈

—

109

C₈×C₇₉

—

110

C₈×C₇₉

—

111

C₈×C₇₉

—

112

C₇₉⋊C₈

—

113

C₇₉⋊C₈

—

114

C₂²×C₇₉

—

115

C₂²×C₇₉

—

116

C₂²×C₇₉

#390

yes

characteristic

117

C₂²×C₇₉

#489

yes

—

118

C₄×C₇₉

—

119

C₄×C₇₉

—

120

C₄×C₇₉

#417

yes

—

121

C₄×C₇₉

#471

yes

—

122

C₄×C₇₉

#473

yes

—

123

C₄×C₇₉

#496

yes

characteristic

124

C₄×C₇₉

#497

yes

characteristic

125

Dic₇₉

—

126

Dic₇₉

—

127

#9775

—

maximal, Sylow

128

C₂×C₇₉

—

129

C₂×C₇₉

#1959

yes

characteristic

130

C₂×C₇₉

#1977

yes

characteristic

131

C₂×C₇₉

#1979

yes

characteristic

132

C₂×#487

—

133

#1848

D₇₉

yes

characteristic

134

#1549

—

135

#1548

—

136

#1546

—

137

#1546

—

138

#1452

—

139

C₇₉

#9775

yes

characteristic, complemented, Sylow

140

C₂×C₄⋊Q₈

—

141

C₂×C₄⋊Q₈

—

142

#487

—

143

#487

—

158

—

144

#431

—

145

#431

—

146

C₂×#108

—

147

#423

C₂×D₇₉

yes

characteristic

148

#423

C₂×D₇₉

yes

characteristic

149

C₂×#103

—

158

—

150

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

151

#333

—

158

—

152

#332

—

158

—

153

#332

—

158

—

154

#332

—

158

—

155

#322

—

158

—

156

C₂²×Q₈

—

158

—

157

C₂²×Q₈

—

158

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₂²×C₈

C₂²⋊D₇₉

yes

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

—

158

—

164

C₄⋊Q₈

—

158

—

165

C₄⋊Q₈

—

158

—

166

C₄⋊Q₈

—

158

—

167

C₄⋊Q₈

—

158

—

168

C₄⋊Q₈

—

158

—

169

C₂×C₄⋊C₄

—

158

—

170

C₂×C₄⋊C₄

—

158

—

171

C₂×C₄⋊C₄

—

158

—

172

C₂×C₄⋊C₄

—

158

—

173

C₂×C₄²

C₂²×D₇₉

yes

characteristic

174

#108

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

#103

—

158

—

182

C₂²⋊C₈

—

158

—

183

C₂²⋊C₈

—

158

—

184

C₄×C₈

—

158

—

185

C₄×C₈

—

158

—

186

C₄×C₈

C₄×D₇₉

yes

—

187

C₄×C₈

D₃₁₆

yes

—

188

C₂×Q₈

—

316

—

189

C₂×Q₈

—

316

—

190

C₂×Q₈

—

316

—

191

C₂×Q₈

—

316

—

192

C₂×Q₈

—

632

—

193

C₂×Q₈

—

158

—

194

C₂×Q₈

—

158

—

195

C₂²×C₄

—

316

—

196

C₂²×C₄

—

316

—

197

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

198

C₂²×C₄

#11929625

yes

characteristic

199

C₂²×C₄

#11929625

yes

characteristic

200

M₁₆

—

201

M₁₆

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

158

—

207

C₂×C₈

—

158

—

208

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

209

C₄⋊C₄

—

316

—

210

C₄⋊C₄

—

316

—

211

C₄⋊C₄

—

316

—

212

C₄⋊C₄

—

316

—

213

C₄⋊C₄

—

158

—

214

C₄⋊C₄

—

158

—

215

C₄⋊C₄

—

158

—

216

C₄⋊C₄

—

158

—

217

C₄²

C₂×C₄×D₇₉

yes

characteristic

218

C₄²

D₄×D₇₉

yes

characteristic

219

C₄²

D₄×D₇₉

yes

characteristic

220

C₄²

C₂×D₃₁₆

yes

characteristic

221

C₂³

#14579150

yes

characteristic

222

Q₈

—

316

—

223

Q₈

—

632

—

224

Q₈

—

632

—

225

Q₈

—

632

—

226

Q₈

—

632

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

316

—

230

C₂×C₄

—

316

—

231

C₂×C₄

—

632

—

232

C₂×C₄

—

632

—

233

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

234

C₂×C₄

#14579123

yes

characteristic

235

C₂×C₄

#14579123

yes

characteristic

236

C₂×C₄

#14579136

yes

characteristic

237

C₂×C₄

#14579136

yes

characteristic

238

C₂×C₄

#14579157

yes

characteristic

239

C₂×C₄

#14579187

yes

—

240

C₂×C₄

#14579192

yes

—

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

316

—

245

C₈

—

316

—

246

C₂²

—

247

C₂²

—

248

C₂²

#19098464

yes

characteristic

249

C₂²

#19098925

yes

—

250

C₄

—

251

C₄

—

252

C₄

—

632

—

253

C₄

—

632

—

254

C₄

#19098562

yes

—

255

C₄

#19098827

yes

—

256

C₄

#19098839

yes

—

257

C₄

#19098950

yes

characteristic

258

C₄

#19098955

yes

characteristic

259

C₂

—

260

C₂

#23764214

yes

characteristic

261

C₂

#23764301

yes

characteristic

262

C₂

#23764313

yes

characteristic

	subgroup	G/H
center	C₂²	#19098464
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1848	C₂
socle	C₂²×C₇₉	#390
prime radical	C₂³×C₇₉	#124
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1848	D₇₉
hypocenter	C₇₉	#9775
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1848

subgroup

G/H

center

C₂²

#19098464

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1848

C₂

C₂²×C₇₉

C₂³×C₇₉

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1848

N	H ≅ G/N	type
139. C₇₉	#9775	semidirect

H ≅ G/N

type

139. C₇₉

#9775

semidirect

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

subgroup	index
C₂×#19098914	2
#23762086	2
#23762082	2
#23762073	2
#23761692	2
C₇₉×#1848	2
#9775	79

subgroup

index

C₇₉×#1848

Subgroups — #34187746

Conjugacy classes of subgroups

Complements

Maximal subgroups