Group #34190802 — subgroups

Subgroups — #34190802

Order 20224.

574 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 139 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×#19098770	C₂	1	2	yes	maximal
2	#23764336	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098309	C₂	1	2	yes	maximal
4	#23761235	C₂	1	1	yes	maximal, characteristic
5	C₂×#500×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11929614	—	2	2	no	—
7	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
8	#19098770	—	2	4	no	—
9	#19098770	—	2	4	no	—
10	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
12	C₂×#14579085	—	2	2	no	—
13	#19098317	—	2	2	no	—
14	#19098309	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
16	#500×C₇₉	—	2	4	no	—
17	C₂×#107×C₇₉	—	2	2	no	—
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×Dic₁₅₈	D₄	1	1	yes	characteristic
20	C₂×#11929614	—	2	8	no	—
21	C₂×#11929614	—	4	4	no	—
22	C₂×#11929614	—	4	4	no	—
23	C₂²×C₇₉⋊C₈	—	2	2	no	—
24	C₂²×C₇₉⋊C₈	—	2	1	no	—
25	C₄×Dic₁₅₈	—	2	2	no	—
26	C₄×Dic₁₅₈	—	2	2	no	—
27	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
28	C₂×Dic₇₉⋊C₄	—	2	1	no	—
29	C₂×C₄×Dic₇₉	—	2	1	no	—
30	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	—
33	#14579085	—	2	8	no	—
34	C₂²×Q₈×C₇₉	—	2	2	no	—
35	C₂²×C₈×C₇₉	D₄	1	2	yes	—
36	C₄⋊Q₈×C₇₉	—	2	2	no	—
37	C₄⋊Q₈×C₇₉	—	2	2	no	—
38	C₄⋊Q₈×C₇₉	—	2	2	no	—
39	C₄⋊Q₈×C₇₉	D₄	1	4	yes	—
40	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
41	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
42	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
43	#107×C₇₉	—	2	8	no	—
44	C₄×C₈×C₇₉	—	2	2	no	—
45	C₂×Dic₁₅₈	—	2	2	no	—
46	C₂×Dic₁₅₈	—	2	1	no	—
47	C₂×Dic₁₅₈	—	2	2	no	—
48	C₂×Dic₁₅₈	D₈	1	2	yes	—
49	C₂²×Dic₇₉	—	2	1	no	—
50	C₂²×Dic₇₉	—	2	1	no	—
51	#11929614	—	4	16	no	—
52	C₂×C₇₉⋊C₈	—	2	4	no	—
53	C₂×C₇₉⋊C₈	—	4	1	no	—
54	C₂×C₇₉⋊C₈	—	4	2	no	—
55	C₂×C₇₉⋊C₈	—	4	2	no	—
56	C₂×C₇₉⋊C₈	—	4	2	no	—
57	C₄⋊Dic₇₉	—	2	2	no	—
58	Dic₇₉⋊C₄	—	4	2	no	—
59	C₄×Dic₇₉	—	4	1	no	—
60	C₄×Dic₇₉	—	4	1	no	—
61	C₂×Q₈×C₇₉	—	2	4	no	—
62	C₂×Q₈×C₇₉	—	4	2	no	—
63	C₂×Q₈×C₇₉	—	4	2	no	—
64	C₂×Q₈×C₇₉	—	4	2	no	—
65	C₂×Q₈×C₇₉	—	4	2	no	—
66	C₂×Q₈×C₇₉	—	4	2	no	—
67	C₂²×C₄×C₇₉	—	4	2	no	—
68	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
71	C₂×C₈×C₇₉	—	2	2	no	—
72	C₂×C₈×C₇₉	—	2	2	no	—
73	C₂×C₈×C₇₉	Q₁₆	1	4	yes	complemented
74	C₄⋊C₄×C₇₉	—	2	4	no	—
75	C₄⋊C₄×C₇₉	—	2	4	no	—
76	C₄⋊C₄×C₇₉	—	4	2	no	—
77	C₄⋊C₄×C₇₉	—	4	2	no	—
78	C₄²×C₇₉	C₂×D₄	1	2	yes	—
79	C₄²×C₇₉	C₂×D₄	1	2	yes	—
80	C₂³×C₇₉	#121	1	1	yes	characteristic
81	Q₈×C₇₉	—	4	4	no	—
82	Q₈×C₇₉	—	4	4	no	—
83	Q₈×C₇₉	—	8	2	no	—
84	Q₈×C₇₉	—	8	2	no	—
85	C₂×C₄×C₇₉	—	2	2	no	—
86	C₂×C₄×C₇₉	—	4	4	no	—
87	C₂×C₄×C₇₉	—	8	2	no	—
88	C₂×C₄×C₇₉	—	8	2	no	—
89	C₂×C₄×C₇₉	#120	1	2	yes	—
90	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
91	C₂×C₄×C₇₉	#121	1	2	yes	—
92	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
93	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
94	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
95	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
96	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
97	C₂×C₄×C₇₉	#137	1	2	yes	—
98	C₂×Dic₇₉	—	2	2	no	—
99	C₂×Dic₇₉	—	4	1	no	—
100	C₂×Dic₇₉	—	4	1	no	—
101	C₂×Dic₇₉	—	4	1	no	—
102	C₂×Dic₇₉	—	4	2	no	—
103	Dic₁₅₈	—	2	4	no	—
104	Dic₁₅₈	—	4	2	no	—
105	C₈×C₇₉	—	2	4	no	—
106	C₇₉⋊C₈	—	4	4	no	—
107	C₇₉⋊C₈	—	8	1	no	—
108	C₂²×C₇₉	#392	1	1	yes	characteristic
109	C₂²×C₇₉	#462	1	2	yes	—
110	C₂²×C₇₉	#466	1	1	yes	characteristic
111	C₂²×C₇₉	#469	1	1	yes	characteristic
112	C₂²×C₇₉	#473	1	2	yes	—
113	C₄×C₇₉	—	2	2	no	—
114	C₄×C₇₉	—	8	4	no	—
115	C₄×C₇₉	#447	1	2	yes	—
116	C₄×C₇₉	#449	1	2	yes	—
117	C₄×C₇₉	#451	1	2	yes	—
118	C₄×C₇₉	#494	1	1	yes	characteristic
119	C₄×C₇₉	#497	1	1	yes	characteristic
120	Dic₇₉	—	4	2	no	—
121	Dic₇₉	—	8	1	no	—
122	#10265	—	79	1	no	maximal, Sylow
123	C₂×C₇₉	#1674	1	2	yes	—
124	C₂×C₇₉	#1694	1	2	yes	—
125	C₂×C₇₉	#1999	1	1	yes	characteristic
126	C₂×C₇₉	#2016	1	1	yes	characteristic
127	C₂×C₇₉	#2020	1	1	yes	characteristic
128	C₂×#500	D₇₉	1	1	yes	characteristic
129	C₂×#462	—	79	2	no	—
130	#1984	—	79	1	no	—
131	C₂×#332	—	79	2	no	—
132	#1277	—	79	1	no	—
133	C₇₉	#10265	1	1	yes	characteristic, complemented, Sylow
134	C₂²×Q₁₆	—	158	2	no	—
135	C₂×C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
136	C₂×C₄×Q₈	—	79	1	no	—
137	#500	—	2	4	no	—
138	#462	—	158	4	no	—
139	#462	—	158	4	no	—
140	C₂×#107	—	2	2	no	—
141	C₂×C₄⋊C₈	—	79	2	no	—
142	C₂×C₄⋊C₈	—	79	1	no	—
143	C₂×#103	—	158	2	no	—
144	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
145	#336	—	158	2	no	—
146	#332	—	158	4	no	—
147	C₂²×Q₈	—	2	2	no	—
148	C₂²×Q₈	—	79	1	no	—
149	C₂×Q₁₆	—	316	4	no	—
150	C₂×Q₁₆	—	316	4	no	—
151	C₂×Q₁₆	—	158	8	no	—
152	C₂²×C₈	—	158	1	no	—
153	C₂²×C₈	—	158	2	no	—
154	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
155	C₄⋊Q₈	—	2	2	no	—
156	C₄⋊Q₈	—	2	2	no	—
157	C₄⋊Q₈	—	2	2	no	—
158	C₄⋊Q₈	C₂²⋊D₇₉	1	4	yes	—
159	C₄×Q₈	—	158	2	no	—
160	C₄×Q₈	—	158	2	no	—
161	C₂×C₄⋊C₄	—	2	2	no	—
162	C₂×C₄⋊C₄	—	2	2	no	—
163	C₂×C₄⋊C₄	—	79	1	no	—
164	C₂×C₄⋊C₄	—	158	1	no	—
165	C₂×C₄²	—	158	1	no	—
166	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
167	#107	—	2	8	no	—
168	C₄⋊C₈	—	79	4	no	—
169	C₄⋊C₈	—	158	2	no	—
170	C₄⋊C₈	—	158	2	no	—
171	#103	—	158	8	no	—
172	C₄×C₈	—	2	2	no	—
173	C₂×Q₈	—	2	4	no	—
174	C₂×Q₈	—	4	2	no	—
175	C₂×Q₈	—	4	2	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	—	4	2	no	—
178	C₂×Q₈	—	4	2	no	—
179	C₂×Q₈	—	79	2	no	—
180	C₂×Q₈	—	158	2	no	—
181	C₂×Q₈	—	158	2	no	—
182	C₂×Q₈	—	158	1	no	—
183	C₂²×C₄	—	4	2	no	—
184	C₂²×C₄	—	158	1	no	—
185	C₂²×C₄	—	158	1	no	—
186	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
187	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
188	C₂²×C₄	#11929623	1	1	yes	characteristic
189	Q₁₆	—	316	16	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	316	2	no	—
193	C₂×C₈	—	316	2	no	—
194	C₂×C₈	—	316	1	no	—
195	C₂×C₈	—	316	2	no	—
196	C₂×C₈	—	158	4	no	—
197	C₂×C₈	#11929614	1	4	yes	complemented
198	C₄⋊C₄	—	2	4	no	—
199	C₄⋊C₄	—	2	4	no	—
200	C₄⋊C₄	—	4	2	no	—
201	C₄⋊C₄	—	4	2	no	—
202	C₄⋊C₄	—	316	2	no	—
203	C₄⋊C₄	—	158	2	no	—
204	C₄²	—	316	1	no	—
205	C₄²	—	316	1	no	—
206	C₄²	D₄×D₇₉	1	2	yes	—
207	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
208	C₂³	#14579132	1	1	yes	characteristic
209	Q₈	—	4	4	no	—
210	Q₈	—	4	4	no	—
211	Q₈	—	8	2	no	—
212	Q₈	—	8	2	no	—
213	Q₈	—	316	2	no	—
214	Q₈	—	158	4	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	4	no	—
217	C₂×C₄	—	8	2	no	—
218	C₂×C₄	—	8	2	no	—
219	C₂×C₄	—	316	1	no	—
220	C₂×C₄	—	316	1	no	—
221	C₂×C₄	—	316	1	no	—
222	C₂×C₄	—	316	2	no	—
223	C₂×C₄	—	158	2	no	—
224	C₂×C₄	#14579129	1	2	yes	—
225	C₂×C₄	#14579130	1	1	yes	characteristic
226	C₂×C₄	#14579133	1	2	yes	—
227	C₂×C₄	#14579157	1	1	yes	characteristic
228	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
229	C₂×C₄	C₂×#11929614	1	2	yes	—
230	C₂×C₄	#14579180	1	1	yes	characteristic
231	C₂×C₄	#14579185	1	2	yes	—
232	C₂×C₄	#14579192	1	2	yes	—
233	C₈	—	2	4	no	—
234	C₈	—	316	4	no	—
235	C₈	—	632	1	no	—
236	C₂²	#19098471	1	1	yes	characteristic
237	C₂²	#19098770	1	2	yes	—
238	C₂²	#19098796	1	1	yes	characteristic
239	C₂²	#19098813	1	1	yes	characteristic
240	C₂²	#19098835	1	2	yes	—
241	C₄	—	2	2	no	—
242	C₄	—	8	4	no	—
243	C₄	—	316	2	no	—
244	C₄	—	632	1	no	—
245	C₄	#19098695	1	2	yes	—
246	C₄	#19098705	1	2	yes	—
247	C₄	#19098719	1	2	yes	—
248	C₄	#19098942	1	1	yes	characteristic
249	C₄	#19098955	1	1	yes	characteristic
250	C₂	#23762791	1	2	yes	—
251	C₂	#23762915	1	2	yes	—
252	C₂	#23764395	1	1	yes	characteristic
253	C₂	#23764500	1	1	yes	characteristic
254	C₂	#23764519	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098770

C₂

yes

maximal

#23764336

C₂

yes

maximal, characteristic

C₂×#19098309

C₂

yes

maximal

#23761235

C₂

yes

maximal, characteristic

C₂×#500×C₇₉

C₂

yes

maximal, characteristic

C₂²×#11929614

—

C₂×C₄×Dic₁₅₈

C₂²

yes

characteristic

#19098770

—

#19098770

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

C₂×#14579085

—

#19098317

—

#19098309

—

C₂×C₄⋊Q₈×C₇₉

C₂²

yes

—

#500×C₇₉

—

C₂×#107×C₇₉

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂²×Dic₁₅₈

D₄

yes

—

—

—

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₂×C₄⋊Dic₇₉

D₄

yes

characteristic

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

#14579085

—

C₂²×Q₈×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

D₄

yes

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#107×C₇₉

—

C₄×C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

D₈

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

#11929614

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

Q₁₆

yes

complemented

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

#121

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

#120

yes

—

C₂×C₄×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

#121

yes

—

C₂×C₄×C₇₉

#127

yes

characteristic

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₁₆

yes

—

C₂×C₄×C₇₉

#135

yes

characteristic

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

100

C₂×Dic₇₉

—

101

C₂×Dic₇₉

—

102

C₂×Dic₇₉

—

103

Dic₁₅₈

—

104

Dic₁₅₈

—

105

C₈×C₇₉

—

106

C₇₉⋊C₈

—

107

C₇₉⋊C₈

—

108

C₂²×C₇₉

#392

yes

characteristic

109

C₂²×C₇₉

#462

yes

—

110

C₂²×C₇₉

#466

yes

characteristic

111

C₂²×C₇₉

#469

yes

characteristic

112

C₂²×C₇₉

#473

yes

—

113

C₄×C₇₉

—

114

C₄×C₇₉

—

115

C₄×C₇₉

#447

yes

—

116

C₄×C₇₉

#449

yes

—

117

C₄×C₇₉

#451

yes

—

118

C₄×C₇₉

#494

yes

characteristic

119

C₄×C₇₉

#497

yes

characteristic

120

Dic₇₉

—

121

Dic₇₉

—

122

#10265

—

maximal, Sylow

123

C₂×C₇₉

#1674

yes

—

124

C₂×C₇₉

#1694

yes

—

125

C₂×C₇₉

#1999

yes

characteristic

126

C₂×C₇₉

#2016

yes

characteristic

127

C₂×C₇₉

#2020

yes

characteristic

128

C₂×#500

D₇₉

yes

characteristic

129

C₂×#462

—

130

#1984

—

131

C₂×#332

—

132

#1277

—

133

C₇₉

#10265

yes

characteristic, complemented, Sylow

134

C₂²×Q₁₆

—

158

—

135

C₂×C₄⋊Q₈

C₂×D₇₉

yes

—

136

C₂×C₄×Q₈

—

137

#500

—

138

#462

—

158

—

139

#462

—

158

—

140

C₂×#107

—

141

C₂×C₄⋊C₈

—

142

C₂×C₄⋊C₈

—

143

C₂×#103

—

158

—

144

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

145

#336

—

158

—

146

#332

—

158

—

147

C₂²×Q₈

—

148

C₂²×Q₈

—

149

C₂×Q₁₆

—

316

—

150

C₂×Q₁₆

—

316

—

151

C₂×Q₁₆

—

158

—

152

C₂²×C₈

—

158

—

153

C₂²×C₈

—

158

—

154

C₂²×C₈

C₂²⋊D₇₉

yes

—

155

C₄⋊Q₈

—

156

C₄⋊Q₈

—

157

C₄⋊Q₈

—

158

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

159

C₄×Q₈

—

158

—

160

C₄×Q₈

—

158

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

—

158

—

165

C₂×C₄²

—

158

—

166

C₂×C₄²

C₂²×D₇₉

yes

characteristic

167

#107

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

158

—

170

C₄⋊C₈

—

158

—

171

#103

—

158

—

172

C₄×C₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

—

158

—

181

C₂×Q₈

—

158

—

182

C₂×Q₈

—

158

—

183

C₂²×C₄

—

184

C₂²×C₄

—

158

—

185

C₂²×C₄

—

158

—

186

C₂²×C₄

D₄×D₇₉

yes

characteristic

187

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

188

C₂²×C₄

#11929623

yes

characteristic

189

Q₁₆

—

316

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

316

—

193

C₂×C₈

—

316

—

194

C₂×C₈

—

316

—

195

C₂×C₈

—

316

—

196

C₂×C₈

—

158

—

197

C₂×C₈

#11929614

yes

complemented

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

316

—

203

C₄⋊C₄

—

158

—

204

C₄²

—

316

—

205

C₄²

—

316

—

206

C₄²

D₄×D₇₉

yes

—

207

C₄²

C₂×C₂²⋊D₇₉

yes

—

208

C₂³

#14579132

yes

characteristic

209

Q₈

—

210

Q₈

—

211

Q₈

—

212

Q₈

—

213

Q₈

—

316

—

214

Q₈

—

158

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

316

—

220

C₂×C₄

—

316

—

221

C₂×C₄

—

316

—

222

C₂×C₄

—

316

—

223

C₂×C₄

—

158

—

224

C₂×C₄

#14579129

yes

—

225

C₂×C₄

#14579130

yes

characteristic

226

C₂×C₄

#14579133

yes

—

227

C₂×C₄

#14579157

yes

characteristic

228

C₂×C₄

D₈×D₇₉

yes

characteristic

229

C₂×C₄

C₂×#11929614

yes

—

230

C₂×C₄

#14579180

yes

characteristic

231

C₂×C₄

#14579185

yes

—

232

C₂×C₄

#14579192

yes

—

233

C₈

—

234

C₈

—

316

—

235

C₈

—

632

—

236

C₂²

#19098471

yes

characteristic

237

C₂²

#19098770

yes

—

238

C₂²

#19098796

yes

characteristic

239

C₂²

#19098813

yes

characteristic

240

C₂²

#19098835

yes

—

241

C₄

—

242

C₄

—

243

C₄

—

316

—

244

C₄

—

632

—

245

C₄

#19098695

yes

—

246

C₄

#19098705

yes

—

247

C₄

#19098719

yes

—

248

C₄

#19098942

yes

characteristic

249

C₄

#19098955

yes

characteristic

250

C₂

#23762791

yes

—

251

C₂

#23762915

yes

—

252

C₂

#23764395

yes

characteristic

253

C₂

#23764500

yes

characteristic

254

C₂

#23764519

yes

characteristic

	subgroup	G/H
center	C₂³	#14579132
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₂×#500×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	#121
hypercenter	C₂×#500	D₇₉
hypocenter	C₇₉	#10265
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

subgroup

G/H

center

C₂³

#14579132

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₂×#500×C₇₉

C₂

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

N	H ≅ G/N	type
73. C₂×C₈×C₇₉	Q₁₆	semidirect
133. C₇₉	#10265	semidirect
197. C₂×C₈	#11929614	semidirect

H ≅ G/N

type

73. C₂×C₈×C₇₉

Q₁₆

semidirect

133. C₇₉

#10265

semidirect

197. C₂×C₈

#11929614

semidirect

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

subgroup	index
C₂×#19098770	2
#23764336	2
C₂×#19098309	2
#23761235	2
C₂×#500×C₇₉	2
#10265	79

subgroup

index

C₂×#500×C₇₉

Subgroups — #34190802

Conjugacy classes of subgroups

Complements

Maximal subgroups