Group #33240409 — subgroups

Subgroups — C₂×#22612023 #33240409

Order 18688.

702 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 195 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	C₂²×Dic₅₈₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988829	C₂	1	2	yes	maximal
4	#22612023	C₂	1	8	yes	maximal, direct product factor
5	C₂×#17988390	C₂	1	2	yes	maximal, complemented
6	C₂×#366×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Dic₂₉₂	C₂²	1	2	yes	—
8	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
9	C₂×#14556571	—	2	2	no	—
10	C₂×Dic₅₈₄	—	2	4	no	—
11	C₂×Dic₅₈₄	C₂²	1	4	yes	complemented
12	C₂²×#11924003	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×D₇₃	—	2	4	no	—
14	C₂×C₁₆×D₇₃	C₂²	1	4	yes	—
15	#17988829	—	2	4	no	—
16	#17988829	C₂²	1	8	yes	—
17	C₂×#14556514	—	2	2	no	—
18	#17988390	C₂²	1	8	yes	complemented
19	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#107×C₇₃	C₂²	1	2	yes	—
21	#366×C₇₃	C₂²	1	4	yes	complemented
22	C₂²×Dic₁₄₆	—	2	2	no	—
23	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
24	C₂×Dic₂₉₂	—	2	4	no	—
25	C₂×Dic₂₉₂	—	2	2	no	—
26	C₂×Dic₂₉₂	—	2	4	no	—
27	C₂×Dic₂₉₂	C₂³	1	4	yes	—
28	C₂²×#10596831	D₄	1	1	yes	characteristic
29	C₂×C₈×D₇₃	—	2	2	no	—
30	C₂×C₈×D₇₃	—	2	2	no	—
31	C₂×C₈×D₇₃	D₄	1	2	yes	—
32	C₂×C₈×D₇₃	C₂³	1	2	yes	—
33	#14556571	—	2	8	no	—
34	#14556571	—	4	4	no	—
35	C₂×C₄⋊Dic₇₃	—	4	2	no	—
36	C₂×#11924005	—	4	2	no	—
37	Dic₅₈₄	—	2	8	no	—
38	C₂×#11924003	—	2	2	no	—
39	C₂×#11924003	C₂³	1	2	yes	—
40	C₁₆×D₇₃	—	2	8	no	—
41	#14556514	—	2	8	no	—
42	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
44	C₂×C₁₆×C₇₃	D₄	1	4	yes	—
45	C₂×C₁₆×C₇₃	C₂³	1	2	yes	—
46	#107×C₇₃	—	2	2	no	—
47	#107×C₇₃	C₂³	1	4	yes	—
48	C₂³×D₇₃	D₈	1	1	yes	characteristic
49	C₂×Dic₁₄₆	—	2	4	no	—
50	C₂×Dic₁₄₆	—	4	4	no	—
51	C₂×Dic₁₄₆	—	4	4	no	—
52	C₂×Dic₁₄₆	—	4	2	no	—
53	C₂²×Dic₇₃	—	4	2	no	—
54	C₂²×Dic₇₃	D₈	1	1	yes	characteristic
55	C₂×C₄×D₇₃	—	2	2	no	—
56	C₂×C₄×D₇₃	—	2	2	no	—
57	C₂×C₄×D₇₃	D₈	1	2	yes	—
58	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
59	Dic₂₉₂	—	2	4	no	—
60	Dic₂₉₂	—	2	4	no	—
61	Dic₂₉₂	—	4	4	no	—
62	C₂×#10596831	—	2	2	no	—
63	C₂×#10596831	C₂×D₄	1	2	yes	—
64	C₈×D₇₃	—	2	4	no	—
65	C₈×D₇₃	—	2	2	no	—
66	C₈×D₇₃	—	2	2	no	—
67	C₄⋊Dic₇₃	—	4	8	no	—
68	#11924005	—	4	8	no	—
69	#11924003	—	2	2	no	—
70	C₂²×C₄×C₇₃	—	4	2	no	—
71	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
74	C₂×C₈×C₇₃	#41	1	2	yes	—
75	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
76	C₄⋊C₄×C₇₃	—	2	4	no	—
77	C₄⋊C₄×C₇₃	—	4	2	no	—
78	C₁₆×C₇₃	C₂×D₄	1	4	yes	—
79	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
80	C₂²×D₇₃	—	2	2	no	—
81	C₂²×D₇₃	—	2	2	no	—
82	C₂²×D₇₃	Q₃₂	1	4	yes	complemented
83	C₂²×D₇₃	C₂×D₈	1	2	yes	—
84	C₂×C₄×C₇₃	—	4	4	no	—
85	C₂×C₄×C₇₃	—	8	4	no	—
86	C₂×C₄×C₇₃	#121	1	2	yes	—
87	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
88	C₂×C₄×C₇₃	#135	1	2	yes	—
89	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
90	C₂×Dic₇₃	—	2	2	no	—
91	C₂×Dic₇₃	—	4	4	no	—
92	C₂×Dic₇₃	—	8	4	no	—
93	C₂×Dic₇₃	C₂×D₈	1	2	yes	—
94	C₄×D₇₃	—	2	2	no	—
95	C₄×D₇₃	—	2	2	no	—
96	C₄×D₇₃	—	2	4	no	—
97	Dic₁₄₆	—	4	4	no	—
98	Dic₁₄₆	—	4	4	no	—
99	Dic₁₄₆	—	8	4	no	—
100	C₈×C₇₃	#121	1	2	yes	—
101	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
102	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
103	#10596831	—	2	2	no	—
104	C₂²×C₇₃	#466	1	2	yes	—
105	C₂²×C₇₃	C₂×Q₃₂	1	2	yes	—
106	C₂²×C₇₃	#508	1	2	yes	—
107	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
108	C₂×D₇₃	—	2	2	no	—
109	C₂×D₇₃	—	2	8	no	—
110	C₂×D₇₃	—	2	2	no	—
111	C₂×D₇₃	C₂×Q₃₂	1	4	yes	complemented
112	C₄×C₇₃	—	8	4	no	—
113	C₄×C₇₃	#466	1	2	yes	—
114	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
115	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
116	Dic₇₃	—	2	2	no	—
117	Dic₇₃	—	8	4	no	—
118	C₂×#2216	—	73	1	no	maximal, Sylow
119	C₂×C₇₃	#2216	1	4	yes	complemented
120	C₂×C₇₃	C₂×#466	1	1	yes	characteristic
121	C₂×C₇₃	C₂²×Q₃₂	1	1	yes	characteristic
122	C₂×C₇₃	C₂×#508	1	1	yes	characteristic
123	D₇₃	—	2	4	no	—
124	C₂²×Q₃₂	—	73	1	no	—
125	C₂³×C₁₆	—	73	1	no	—
126	C₂×#467	—	73	2	no	—
127	#2216	—	73	8	no	—
128	C₂×#366	D₇₃	1	1	yes	characteristic, complemented
129	C₂×#358	—	73	2	no	—
130	C₇₃	C₂×#2216	1	1	yes	characteristic, complemented, Sylow
131	C₂²×Q₁₆	—	73	2	no	—
132	C₂³×C₈	—	73	1	no	—
133	C₂×C₂²⋊Q₈	—	146	2	no	—
134	C₂×Q₃₂	—	73	4	no	—
135	C₂×Q₃₂	—	146	4	no	—
136	C₂²×C₁₆	—	73	1	no	—
137	C₂²×C₁₆	—	73	4	no	—
138	C₂²×C₁₆	—	146	4	no	—
139	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
140	#467	—	73	8	no	—
141	#467	—	146	4	no	—
142	C₂×#107	C₂×D₇₃	1	2	yes	—
143	C₂×#103	—	146	2	no	—
144	#366	C₂×D₇₃	1	4	yes	complemented
145	#358	—	73	8	no	—
146	C₂²×Q₈	—	146	2	no	—
147	C₂³×C₄	—	73	1	no	—
148	C₂×Q₁₆	—	73	4	no	—
149	C₂×Q₁₆	—	146	2	no	—
150	C₂×Q₁₆	—	146	4	no	—
151	C₂×Q₁₆	—	146	4	no	—
152	C₂²×C₈	—	73	1	no	—
153	C₂²×C₈	—	73	2	no	—
154	C₂²×C₈	—	73	2	no	—
155	C₂²×C₈	—	146	2	no	—
156	C₂²×C₈	—	146	2	no	—
157	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
158	C₂²⋊Q₈	—	292	4	no	—
159	C₂²⋊Q₈	—	146	8	no	—
160	C₂×C₄⋊C₄	—	2	2	no	—
161	C₂×C₄⋊C₄	—	292	2	no	—
162	C₂×C₂²⋊C₄	—	292	2	no	—
163	Q₃₂	—	146	8	no	—
164	C₂×C₁₆	—	73	2	no	—
165	C₂×C₁₆	—	146	2	no	—
166	C₂×C₁₆	—	146	8	no	—
167	C₂×C₁₆	D₂₉₂	1	4	yes	—
168	C₂×C₁₆	C₂²×D₇₃	1	2	yes	—
169	#107	—	2	2	no	—
170	#107	C₂²×D₇₃	1	4	yes	—
171	#103	—	146	8	no	—
172	C₂⁴	—	73	1	no	—
173	C₂×Q₈	—	292	2	no	—
174	C₂×Q₈	—	292	4	no	—
175	C₂×Q₈	—	292	4	no	—
176	C₂×Q₈	—	146	4	no	—
177	C₂²×C₄	—	4	2	no	—
178	C₂²×C₄	—	292	2	no	—
179	C₂²×C₄	—	73	1	no	—
180	C₂²×C₄	—	73	2	no	—
181	C₂²×C₄	—	73	2	no	—
182	C₂²×C₄	—	146	2	no	—
183	C₂²×C₄	—	146	2	no	—
184	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
185	Q₁₆	—	292	4	no	—
186	Q₁₆	—	146	4	no	—
187	Q₁₆	—	146	4	no	—
188	C₂×C₈	—	73	2	no	—
189	C₂×C₈	—	146	2	no	—
190	C₂×C₈	—	146	4	no	—
191	C₂×C₈	—	146	2	no	—
192	C₂×C₈	—	146	2	no	—
193	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
194	C₂×C₈	C₂×D₂₉₂	1	2	yes	—
195	C₂×C₈	#11924029	1	2	yes	—
196	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
197	C₄⋊C₄	—	2	4	no	—
198	C₄⋊C₄	—	4	2	no	—
199	C₄⋊C₄	—	292	8	no	—
200	C₂²⋊C₄	—	292	8	no	—
201	C₁₆	—	146	2	no	—
202	C₁₆	C₂×D₂₉₂	1	4	yes	—
203	C₂³	—	73	4	no	—
204	C₂³	—	73	2	no	—
205	C₂³	—	146	2	no	—
206	C₂³	—	146	2	no	—
207	C₂³	D₈×D₇₃	1	1	yes	characteristic
208	Q₈	—	292	4	no	—
209	Q₈	—	292	4	no	—
210	Q₈	—	584	4	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	8	4	no	—
213	C₂×C₄	—	292	4	no	—
214	C₂×C₄	—	584	4	no	—
215	C₂×C₄	—	73	2	no	—
216	C₂×C₄	—	146	2	no	—
217	C₂×C₄	—	146	4	no	—
218	C₂×C₄	—	146	2	no	—
219	C₂×C₄	—	146	2	no	—
220	C₂×C₄	#14556566	1	2	yes	—
221	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
222	C₂×C₄	#14556614	1	2	yes	—
223	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
224	C₈	—	146	2	no	—
225	C₈	#14556566	1	2	yes	—
226	C₈	C₂²×D₂₉₂	1	1	yes	characteristic
227	C₈	C₂×#11924029	1	1	yes	characteristic
228	C₂²	—	73	4	no	—
229	C₂²	—	146	8	no	—
230	C₂²	—	146	2	no	—
231	C₂²	—	146	2	no	—
232	C₂²	#17988824	1	2	yes	—
233	C₂²	Q₃₂×D₇₃	1	2	yes	—
234	C₂²	#17989016	1	2	yes	—
235	C₂²	C₂×D₈×D₇₃	1	1	yes	characteristic
236	C₄	—	8	4	no	—
237	C₄	—	584	4	no	—
238	C₄	—	146	2	no	—
239	C₄	#17988824	1	2	yes	—
240	C₄	C₂×#14556566	1	1	yes	characteristic
241	C₄	C₂×#14556614	1	1	yes	characteristic
242	C₂	—	146	4	no	—
243	C₂	#22612023	1	4	yes	direct product factor
244	C₂	C₂×#17988824	1	1	yes	characteristic
245	C₂	C₂×Q₃₂×D₇₃	1	1	yes	characteristic
246	C₂	C₂×#17989016	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₅₈₄

C₂

yes

maximal, characteristic, complemented

C₂²×C₁₆×D₇₃

C₂

yes

maximal, characteristic

C₂×#17988829

C₂

yes

maximal

#22612023

C₂

yes

maximal, direct product factor

C₂×#17988390

C₂

yes

maximal, complemented

C₂×#366×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₂₉₂

C₂²

yes

—

C₂²×C₈×D₇₃

C₂²

yes

characteristic

C₂×#14556571

—

C₂×Dic₅₈₄

—

C₂×Dic₅₈₄

C₂²

yes

complemented

C₂²×#11924003

C₂²

yes

characteristic

C₂×C₁₆×D₇₃

—

C₂×C₁₆×D₇₃

C₂²

yes

—

#17988829

—

#17988829

C₂²

yes

—

C₂×#14556514

—

#17988390

C₂²

yes

complemented

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×#107×C₇₃

C₂²

yes

—

#366×C₇₃

C₂²

yes

complemented

C₂²×Dic₁₄₆

—

C₂²×C₄×D₇₃

D₄

yes

characteristic

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₂³

yes

—

C₂²×#10596831

D₄

yes

characteristic

C₂×C₈×D₇₃

—

C₂×C₈×D₇₃

—

C₂×C₈×D₇₃

D₄

yes

—

C₂×C₈×D₇₃

C₂³

yes

—

#14556571

—

#14556571

—

C₂×C₄⋊Dic₇₃

—

C₂×#11924005

—

Dic₅₈₄

—

C₂×#11924003

—

C₂×#11924003

C₂³

yes

—

C₁₆×D₇₃

—

#14556514

—

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₇₃

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₂×C₁₆×C₇₃

C₂³

yes

—

#107×C₇₃

—

#107×C₇₃

C₂³

yes

—

C₂³×D₇₃

D₈

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₈

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

D₈

yes

—

C₂×C₄×D₇₃

C₂×D₄

yes

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

C₂×#10596831

—

C₂×#10596831

C₂×D₄

yes

—

C₈×D₇₃

—

C₈×D₇₃

—

C₈×D₇₃

—

C₄⋊Dic₇₃

—

#11924005

—

#11924003

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

#41

yes

—

C₂×C₈×C₇₃

C₂⁴

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₁₆×C₇₃

C₂×D₄

yes

—

C₂³×C₇₃

C₂×D₈

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

Q₃₂

yes

complemented

C₂²×D₇₃

C₂×D₈

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#121

yes

—

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

C₂×C₄×C₇₃

#135

yes

—

C₂×C₄×C₇₃

C₂²×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×D₈

yes

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

100

C₈×C₇₃

#121

yes

—

101

C₈×C₇₃

C₂²×D₄

yes

characteristic

102

C₈×C₇₃

C₂×#41

yes

characteristic

103

#10596831

—

104

C₂²×C₇₃

#466

yes

—

105

C₂²×C₇₃

C₂×Q₃₂

yes

—

106

C₂²×C₇₃

#508

yes

—

107

C₂²×C₇₃

C₂²×D₈

yes

characteristic

108

C₂×D₇₃

—

109

C₂×D₇₃

—

110

C₂×D₇₃

—

111

C₂×D₇₃

C₂×Q₃₂

yes

complemented

112

C₄×C₇₃

—

113

C₄×C₇₃

#466

yes

—

114

C₄×C₇₃

C₂×#121

yes

characteristic

115

C₄×C₇₃

C₂×#135

yes

characteristic

116

Dic₇₃

—

117

Dic₇₃

—

118

C₂×#2216

—

maximal, Sylow

119

C₂×C₇₃

#2216

yes

complemented

120

C₂×C₇₃

C₂×#466

yes

characteristic

121

C₂×C₇₃

C₂²×Q₃₂

yes

characteristic

122

C₂×C₇₃

C₂×#508

yes

characteristic

123

D₇₃

—

124

C₂²×Q₃₂

—

125

C₂³×C₁₆

—

126

C₂×#467

—

127

#2216

—

128

C₂×#366

D₇₃

yes

characteristic, complemented

129

C₂×#358

—

130

C₇₃

C₂×#2216

yes

characteristic, complemented, Sylow

131

C₂²×Q₁₆

—

132

C₂³×C₈

—

133

C₂×C₂²⋊Q₈

—

146

—

134

C₂×Q₃₂

—

135

C₂×Q₃₂

—

146

—

136

C₂²×C₁₆

—

137

C₂²×C₁₆

—

138

C₂²×C₁₆

—

146

—

139

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

140

#467

—

141

#467

—

146

—

142

C₂×#107

C₂×D₇₃

yes

—

143

C₂×#103

—

146

—

144

#366

C₂×D₇₃

yes

complemented

145

#358

—

146

C₂²×Q₈

—

146

—

147

C₂³×C₄

—

148

C₂×Q₁₆

—

149

C₂×Q₁₆

—

146

—

150

C₂×Q₁₆

—

146

—

151

C₂×Q₁₆

—

146

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

—

146

—

156

C₂²×C₈

—

146

—

157

C₂²×C₈

C₂²×D₇₃

yes

characteristic

158

C₂²⋊Q₈

—

292

—

159

C₂²⋊Q₈

—

146

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

292

—

162

C₂×C₂²⋊C₄

—

292

—

163

Q₃₂

—

146

—

164

C₂×C₁₆

—

165

C₂×C₁₆

—

146

—

166

C₂×C₁₆

—

146

—

167

C₂×C₁₆

D₂₉₂

yes

—

168

C₂×C₁₆

C₂²×D₇₃

yes

—

169

#107

—

170

#107

C₂²×D₇₃

yes

—

171

#103

—

146

—

172

C₂⁴

—

173

C₂×Q₈

—

292

—

174

C₂×Q₈

—

292

—

175

C₂×Q₈

—

292

—

176

C₂×Q₈

—

146

—

177

C₂²×C₄

—

178

C₂²×C₄

—

292

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

146

—

183

C₂²×C₄

—

146

—

184

C₂²×C₄

D₄×D₇₃

yes

characteristic

185

Q₁₆

—

292

—

186

Q₁₆

—

146

—

187

Q₁₆

—

146

—

188

C₂×C₈

—

189

C₂×C₈

—

146

—

190

C₂×C₈

—

146

—

191

C₂×C₈

—

146

—

192

C₂×C₈

—

146

—

193

C₂×C₈

D₄×D₇₃

yes

characteristic

194

C₂×C₈

C₂×D₂₉₂

yes

—

195

C₂×C₈

#11924029

yes

—

196

C₂×C₈

C₂³×D₇₃

yes

characteristic

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

292

—

200

C₂²⋊C₄

—

292

—

201

C₁₆

—

146

—

202

C₁₆

C₂×D₂₉₂

yes

—

203

C₂³

—

204

C₂³

—

205

C₂³

—

146

—

206

C₂³

—

146

—

207

C₂³

D₈×D₇₃

yes

characteristic

208

Q₈

—

292

—

209

Q₈

—

292

—

210

Q₈

—

584

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

292

—

214

C₂×C₄

—

584

—

215

C₂×C₄

—

216

C₂×C₄

—

146

—

217

C₂×C₄

—

146

—

218

C₂×C₄

—

146

—

219

C₂×C₄

—

146

—

220

C₂×C₄

#14556566

yes

—

221

C₂×C₄

D₈×D₇₃

yes

characteristic

222

C₂×C₄

#14556614

yes

—

223

C₂×C₄

C₂×D₄×D₇₃

yes

characteristic

224

C₈

—

146

—

225

C₈

#14556566

yes

—

226

C₈

C₂²×D₂₉₂

yes

characteristic

227

C₈

C₂×#11924029

yes

characteristic

228

C₂²

—

229

C₂²

—

146

—

230

C₂²

—

146

—

231

C₂²

—

146

—

232

C₂²

#17988824

yes

—

233

C₂²

Q₃₂×D₇₃

yes

—

234

C₂²

#17989016

yes

—

235

C₂²

C₂×D₈×D₇₃

yes

characteristic

236

C₄

—

237

C₄

—

584

—

238

C₄

—

146

—

239

C₄

#17988824

yes

—

240

C₄

C₂×#14556566

yes

characteristic

241

C₄

C₂×#14556614

yes

characteristic

242

C₂

—

146

—

243

C₂

#22612023

yes

direct product factor

244

C₂

C₂×#17988824

yes

characteristic

245

C₂

C₂×Q₃₂×D₇₃

yes

characteristic

246

C₂

C₂×#17989016

yes

characteristic

	subgroup	G/H
center	C₂³	D₈×D₇₃
commutator, cosocle	C₂×C₈×C₇₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₂×#366×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₈
prime radical	C₂³×D₇₃	D₈
hypercenter	C₂×#366	D₇₃
hypocenter	C₇₃	C₂×#2216
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

subgroup

G/H

center

C₂³

D₈×D₇₃

commutator, cosocle

C₂×C₈×C₇₃

C₂⁴

Frattini

C₂×C₈

C₂³×D₇₃

Fitting

C₂×#366×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₈

prime radical

C₂³×D₇₃

D₈

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

N	H ≅ G/N	type
1. C₂²×Dic₅₈₄	C₂	semidirect
4. #22612023	C₂	direct (N × H)
5. C₂×#17988390	C₂	semidirect
6. C₂×#366×C₇₃	C₂	semidirect
11. C₂×Dic₅₈₄	C₂²	semidirect
18. #17988390	C₂²	semidirect
21. #366×C₇₃	C₂²	semidirect
82. C₂²×D₇₃	Q₃₂	semidirect
111. C₂×D₇₃	C₂×Q₃₂	semidirect
119. C₂×C₇₃	#2216	semidirect
128. C₂×#366	D₇₃	semidirect
130. C₇₃	C₂×#2216	semidirect
144. #366	C₂×D₇₃	semidirect
243. C₂	#22612023	direct (N × H)

H ≅ G/N

type

1. C₂²×Dic₅₈₄

C₂

semidirect

4. #22612023

C₂

direct (N × H)

5. C₂×#17988390

C₂

semidirect

6. C₂×#366×C₇₃

C₂

semidirect

11. C₂×Dic₅₈₄

C₂²

semidirect

18. #17988390

C₂²

semidirect

21. #366×C₇₃

C₂²

semidirect

82. C₂²×D₇₃

Q₃₂

semidirect

111. C₂×D₇₃

C₂×Q₃₂

semidirect

119. C₂×C₇₃

#2216

semidirect

128. C₂×#366

D₇₃

semidirect

130. C₇₃

C₂×#2216

semidirect

144. #366

C₂×D₇₃

semidirect

243. C₂

#22612023

direct (N × H)

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

subgroup	index
C₂²×Dic₅₈₄	2
C₂²×C₁₆×D₇₃	2
C₂×#17988829	2
#22612023	2
C₂×#17988390	2
C₂×#366×C₇₃	2
C₂×#2216	73

subgroup

index

C₂²×Dic₅₈₄

C₂²×C₁₆×D₇₃

C₂×#366×C₇₃

Subgroups — C₂×#22612023 #33240409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#22612023 #33240409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22612023 #33240409