Group #31819049 — subgroups

Subgroups — #31819049

Order 17792.

350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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	#22581663	C₂	1	1	yes	maximal, characteristic, complemented
2	#22581307	C₂	1	2	yes	maximal, complemented
3	#22581303	C₂	1	1	yes	maximal, characteristic, complemented
4	#22581260	C₂	1	2	yes	maximal, complemented
5	#22581243	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581165	C₂	1	2	yes	maximal
7	#22581155	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₁₃₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#14555772	C₂	1	2	yes	maximal, complemented
10	C₄×#14555770	C₂	1	1	yes	maximal, characteristic
11	#556×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14555772	C₂²	1	2	yes	—
13	C₂×#14555770	C₂²	1	1	yes	characteristic
14	#17984842	C₂²	1	1	yes	characteristic
15	#17984834	C₂²	1	2	yes	—
16	#17984820	—	2	2	no	—
17	#17984818	—	2	1	no	—
18	C₄×D₅₅₆	C₂²	1	1	yes	characteristic
19	C₄×D₅₅₆	C₂²	1	2	yes	—
20	C₄⋊C₄×D₁₃₉	—	2	1	no	—
21	#17984775	C₂²	1	1	yes	characteristic
22	#17984773	C₂²	1	2	yes	—
23	C₄⋊(C₁₃₉⋊C₈)	C₂²	1	2	yes	—
24	C₄⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic
25	#17984766	C₂²	1	2	yes	—
26	#17984766	C₂²	1	2	yes	—
27	#17984766	C₂²	1	2	yes	—
28	#17984763	C₂²	1	1	yes	characteristic
29	#17984763	C₂²	1	2	yes	—
30	#17984762	C₂²	1	1	yes	characteristic
31	C₄×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×C₁₃₉⋊C₈	C₂²	1	2	yes	—
33	C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	#126×C₁₃₉	—	2	2	no	—
35	#124×C₁₃₉	C₂²	1	2	yes	—
36	C₂²⋊Q₈×C₁₃₉	—	2	1	no	—
37	C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
38	C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	#117×C₁₃₉	—	2	1	no	—
41	C₂×Dic₂₇₈	—	2	1	no	—
42	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
43	C₂×C₄×D₁₃₉	—	2	1	no	—
44	C₂×C₄×D₁₃₉	—	2	2	no	—
45	#14555772	—	2	4	no	—
46	#14555770	—	2	2	no	—
47	C₂×C₁₃₉⋊C₈	C₂³	1	2	yes	—
48	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
49	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
50	C₄⋊Dic₁₃₉	—	2	1	no	—
51	C₄⋊Dic₁₃₉	C₂³	1	2	yes	—
52	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
53	Dic₁₃₉⋊C₄	—	2	2	no	—
54	Dic₁₃₉⋊C₄	—	2	2	no	—
55	(C₂×D₁₃₉)⋊C₄	—	2	2	no	—
56	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
57	C₂×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
58	C₂×Q₈×C₁₃₉	C₂³	1	2	yes	—
59	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₁₃₉	—	2	1	no	—
61	C₄⋊C₄×C₁₃₉	—	2	1	no	—
62	C₄⋊C₄×C₁₃₉	—	2	2	no	—
63	C₄⋊C₄×C₁₃₉	—	2	1	no	—
64	C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
65	C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
66	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
68	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
69	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
70	C₄²×C₁₃₉	—	2	2	no	—
71	C₄²×C₁₃₉	C₂³	1	2	yes	—
72	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂²×D₁₃₉	—	2	1	no	—
74	Dic₂₇₈	—	8	1	no	—
75	D₅₅₆	—	2	1	no	—
76	D₅₅₆	#41	1	2	yes	—
77	C₂×Dic₁₃₉	—	2	1	no	—
78	C₂×Dic₁₃₉	—	2	2	no	—
79	C₄×D₁₃₉	—	4	2	no	—
80	C₄×D₁₃₉	—	8	2	no	—
81	C₁₃₉⋊C₈	—	2	1	no	—
82	C₁₃₉⋊C₈	—	2	2	no	—
83	C₁₃₉⋊C₈	—	2	1	no	—
84	C₂³×C₁₃₉	—	2	1	no	—
85	Q₈×C₁₃₉	—	2	2	no	—
86	Q₈×C₁₃₉	—	2	2	no	—
87	Q₈×C₁₃₉	—	2	2	no	—
88	D₄×C₁₃₉	—	2	1	no	—
89	D₄×C₁₃₉	—	2	1	no	—
90	C₂×C₄×C₁₃₉	—	2	1	no	—
91	C₂×C₄×C₁₃₉	—	2	2	no	—
92	C₂×C₄×C₁₃₉	—	4	2	no	—
93	C₂×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
94	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
96	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
98	C₂²×C₁₃₉	—	4	1	no	—
99	C₂²×C₁₃₉	—	4	1	no	—
100	C₂²×C₁₃₉	—	4	1	no	—
101	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
102	C₂×D₁₃₉	—	2	2	no	—
103	C₂×D₁₃₉	—	4	1	no	—
104	C₂×D₁₃₉	—	4	1	no	—
105	C₄×C₁₃₉	—	2	2	no	—
106	C₄×C₁₃₉	—	2	2	no	—
107	C₄×C₁₃₉	—	2	1	no	—
108	C₄×C₁₃₉	—	4	2	no	—
109	C₄×C₁₃₉	—	4	1	no	—
110	C₄×C₁₃₉	#135	1	2	yes	—
111	C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
112	C₄×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
113	Dic₁₃₉	—	4	1	no	—
114	Dic₁₃₉	—	4	2	no	—
115	C₂×C₁₃₉	—	8	1	no	—
116	C₂×C₁₃₉	#548	1	1	yes	characteristic
117	C₂×C₁₃₉	C₂×#135	1	1	yes	characteristic
118	C₂×C₁₃₉	#577	1	1	yes	characteristic
119	D₁₃₉	—	4	2	no	—
120	C₁₃₉	#3360	1	1	yes	characteristic, complemented, Sylow
121	#3360	—	139	1	no	maximal, Sylow
122	#556	D₁₃₉	1	1	yes	characteristic, complemented
123	#554	—	139	1	no	—
124	#488	—	139	2	no	—
125	#487	—	139	1	no	—
126	#479	—	139	2	no	—
127	#476	—	139	1	no	—
128	#463	—	139	2	no	—
129	#461	—	139	1	no	—
130	C₈×Q₈	—	139	1	no	—
131	C₄×SD₁₆	—	139	2	no	—
132	C₄×D₈	—	139	1	no	—
133	C₂×SD₁₆	—	139	2	no	—
134	C₂×D₈	—	139	1	no	—
135	C₄⋊Q₈	—	139	1	no	—
136	C₄⋊Q₈	C₂×D₁₃₉	1	1	yes	characteristic
137	#126	—	2	2	no	—
138	#125	—	139	2	no	—
139	#124	C₂×D₁₃₉	1	2	yes	—
140	C₂²⋊Q₈	—	2	1	no	—
141	C₂²⋊Q₈	—	278	1	no	—
142	C₂²⋊Q₈	—	278	2	no	—
143	C₄×Q₈	C₂×D₁₃₉	1	2	yes	—
144	C₄×Q₈	C₂×D₁₃₉	1	1	yes	characteristic
145	C₄×D₄	—	139	1	no	—
146	C₄×D₄	—	139	2	no	—
147	C₄×D₄	C₂×D₁₃₉	1	1	yes	characteristic
148	#117	—	2	1	no	—
149	C₂×C₄⋊C₄	—	278	1	no	—
150	#107	—	139	1	no	—
151	#106	—	139	2	no	—
152	C₄⋊C₈	—	139	1	no	—
153	C₄⋊C₈	—	139	2	no	—
154	#103	—	139	2	no	—
155	#103	—	139	2	no	—
156	#103	—	139	2	no	—
157	#102	—	139	1	no	—
158	#102	—	139	2	no	—
159	#102	—	139	1	no	—
160	C₄×C₈	—	139	1	no	—
161	C₄×C₈	—	139	2	no	—
162	C₂×Q₈	—	278	1	no	—
163	C₂×Q₈	C₂²⋊D₁₃₉	1	1	yes	characteristic
164	C₂×Q₈	C₂²×D₁₃₉	1	2	yes	—
165	C₂×D₄	—	139	1	no	—
166	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
167	C₂²×C₄	—	2	1	no	—
168	C₂²×C₄	—	278	1	no	—
169	C₂²×C₄	—	278	2	no	—
170	SD₁₆	—	278	4	no	—
171	D₈	—	278	2	no	—
172	C₂×C₈	—	139	1	no	—
173	C₂×C₈	—	139	2	no	—
174	C₂×C₈	—	139	1	no	—
175	C₄⋊C₄	—	2	1	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	1	no	—
178	C₄⋊C₄	—	278	2	no	—
179	C₄⋊C₄	—	278	1	no	—
180	C₄⋊C₄	—	278	2	no	—
181	C₄⋊C₄	—	139	2	no	—
182	C₄⋊C₄	—	139	1	no	—
183	C₄⋊C₄	C₂²⋊D₁₃₉	1	1	yes	characteristic
184	C₄⋊C₄	C₂²⋊D₁₃₉	1	2	yes	—
185	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
186	C₂²⋊C₄	—	2	2	no	—
187	C₂²⋊C₄	—	2	1	no	—
188	C₂²⋊C₄	—	2	2	no	—
189	C₂²⋊C₄	—	278	1	no	—
190	C₂²⋊C₄	—	278	2	no	—
191	C₄²	—	2	2	no	—
192	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
193	C₄²	C₂²×D₁₃₉	1	2	yes	—
194	C₂³	—	2	1	no	—
195	C₂³	—	278	1	no	—
196	Q₈	—	2	2	no	—
197	Q₈	—	2	2	no	—
198	Q₈	—	2	2	no	—
199	Q₈	—	1112	1	no	—
200	D₄	—	2	1	no	—
201	D₄	—	2	1	no	—
202	D₄	—	278	1	no	—
203	D₄	—	139	2	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	278	1	no	—
208	C₂×C₄	—	278	2	no	—
209	C₂×C₄	—	556	2	no	—
210	C₂×C₄	—	1112	2	no	—
211	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	2	yes	—
212	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	2	yes	—
213	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
214	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
215	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
216	C₈	—	278	1	no	—
217	C₈	—	278	2	no	—
218	C₈	—	278	1	no	—
219	C₂²	—	4	1	no	—
220	C₂²	—	4	1	no	—
221	C₂²	—	4	1	no	—
222	C₂²	—	278	2	no	—
223	C₂²	—	556	1	no	—
224	C₂²	—	556	1	no	—
225	C₂²	C₂²×C₂²⋊D₁₃₉	1	1	yes	characteristic
226	C₄	—	2	2	no	—
227	C₄	—	2	1	no	—
228	C₄	—	2	2	no	—
229	C₄	—	4	2	no	—
230	C₄	—	4	1	no	—
231	C₄	—	556	2	no	—
232	C₄	—	556	1	no	—
233	C₄	#17984862	1	2	yes	—
234	C₄	#41×D₁₃₉	1	1	yes	characteristic
235	C₄	#17984889	1	1	yes	characteristic
236	C₂	—	8	1	no	—
237	C₂	—	556	2	no	—
238	C₂	#22581610	1	1	yes	characteristic
239	C₂	C₂×#17984862	1	1	yes	characteristic
240	C₂	#22581761	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22581663

C₂

yes

maximal, characteristic, complemented

#22581307

C₂

yes

maximal, complemented

#22581303

C₂

yes

maximal, characteristic, complemented

#22581260

C₂

yes

maximal, complemented

#22581243

C₂

yes

maximal, characteristic, complemented

#22581165

C₂

yes

maximal

#22581155

C₂

yes

maximal, characteristic, complemented

Q₈×C₁₃₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄×#14555772

C₂

yes

maximal, complemented

C₄×#14555770

C₂

yes

maximal, characteristic

#556×C₁₃₉

C₂

yes

maximal, characteristic, complemented

C₂×#14555772

C₂²

yes

—

C₂×#14555770

C₂²

yes

characteristic

#17984842

C₂²

yes

characteristic

#17984834

C₂²

yes

—

#17984820

—

#17984818

—

C₄×D₅₅₆

C₂²

yes

characteristic

C₄×D₅₅₆

C₂²

yes

—

C₄⋊C₄×D₁₃₉

—

#17984775

C₂²

yes

characteristic

#17984773

C₂²

yes

—

C₄⋊(C₁₃₉⋊C₈)

C₂²

yes

—

C₄⋊(C₁₃₉⋊C₈)

C₂²

yes

characteristic

#17984766

C₂²

yes

—

#17984766

C₂²

yes

—

#17984766

C₂²

yes

—

#17984763

C₂²

yes

characteristic

#17984763

C₂²

yes

—

#17984762

C₂²

yes

characteristic

C₄×C₁₃₉⋊C₈

C₂²

yes

characteristic

C₄×C₁₃₉⋊C₈

C₂²

yes

—

C₄⋊Q₈×C₁₃₉

C₂²

yes

characteristic

#126×C₁₃₉

—

#124×C₁₃₉

C₂²

yes

—

C₂²⋊Q₈×C₁₃₉

—

C₄×Q₈×C₁₃₉

C₂²

yes

—

C₄×Q₈×C₁₃₉

C₂²

yes

characteristic

C₄×D₄×C₁₃₉

C₂²

yes

characteristic

#117×C₁₃₉

—

C₂×Dic₂₇₈

—

C₂×D₅₅₆

C₂³

yes

characteristic

C₂×C₄×D₁₃₉

—

C₂×C₄×D₁₃₉

—

#14555772

—

#14555770

—

C₂×C₁₃₉⋊C₈

C₂³

yes

—

C₂×C₁₃₉⋊C₈

C₂³

yes

characteristic

C₂×C₁₃₉⋊C₈

C₂³

yes

characteristic

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

C₂³

yes

—

C₄⋊Dic₁₃₉

C₂³

yes

characteristic

Dic₁₃₉⋊C₄

—

Dic₁₃₉⋊C₄

—

(C₂×D₁₃₉)⋊C₄

—

(C₂×D₁₃₉)⋊C₄

—

C₂×Q₈×C₁₃₉

D₄

yes

characteristic

C₂×Q₈×C₁₃₉

C₂³

yes

—

C₂×D₄×C₁₃₉

C₂³

yes

characteristic

C₂²×C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

D₄

yes

characteristic

C₄⋊C₄×C₁₃₉

D₄

yes

—

C₄⋊C₄×C₁₃₉

C₂³

yes

characteristic

C₂²⋊C₄×C₁₃₉

—

C₂²⋊C₄×C₁₃₉

—

C₂²⋊C₄×C₁₃₉

—

C₄²×C₁₃₉

—

C₄²×C₁₃₉

C₂³

yes

—

C₄²×C₁₃₉

C₂³

yes

characteristic

C₂²×D₁₃₉

—

Dic₂₇₈

—

D₅₅₆

—

D₅₅₆

#41

yes

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₄×D₁₃₉

—

C₄×D₁₃₉

—

C₁₃₉⋊C₈

—

C₁₃₉⋊C₈

—

C₁₃₉⋊C₈

—

C₂³×C₁₃₉

—

Q₈×C₁₃₉

—

Q₈×C₁₃₉

—

Q₈×C₁₃₉

—

D₄×C₁₃₉

—

D₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂×D₄

yes

—

C₂×C₄×C₁₃₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃₉

C₂×D₄

yes

—

C₂×C₄×C₁₃₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃₉

C₂⁴

yes

characteristic

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

100

C₂²×C₁₃₉

—

101

C₂²×C₁₃₉

C₂²×D₄

yes

characteristic

102

C₂×D₁₃₉

—

103

C₂×D₁₃₉

—

104

C₂×D₁₃₉

—

105

C₄×C₁₃₉

—

106

C₄×C₁₃₉

—

107

C₄×C₁₃₉

—

108

C₄×C₁₃₉

—

109

C₄×C₁₃₉

—

110

C₄×C₁₃₉

#135

yes

—

111

C₄×C₁₃₉

C₂×#41

yes

characteristic

112

C₄×C₁₃₉

2₋¹⁺⁴

yes

characteristic

113

Dic₁₃₉

—

114

Dic₁₃₉

—

115

C₂×C₁₃₉

—

116

C₂×C₁₃₉

#548

yes

characteristic

117

C₂×C₁₃₉

C₂×#135

yes

characteristic

118

C₂×C₁₃₉

#577

yes

characteristic

119

D₁₃₉

—

120

C₁₃₉

#3360

yes

characteristic, complemented, Sylow

121

#3360

—

139

maximal, Sylow

122

#556

D₁₃₉

yes

characteristic, complemented

123

#554

—

139

—

124

#488

—

139

—

125

#487

—

139

—

126

#479

—

139

—

127

#476

—

139

—

128

#463

—

139

—

129

#461

—

139

—

130

C₈×Q₈

—

139

—

131

C₄×SD₁₆

—

139

—

132

C₄×D₈

—

139

—

133

C₂×SD₁₆

—

139

—

134

C₂×D₈

—

139

—

135

C₄⋊Q₈

—

139

—

136

C₄⋊Q₈

C₂×D₁₃₉

yes

characteristic

137

#126

—

138

#125

—

139

—

139

#124

C₂×D₁₃₉

yes

—

140

C₂²⋊Q₈

—

141

C₂²⋊Q₈

—

278

—

142

C₂²⋊Q₈

—

278

—

143

C₄×Q₈

C₂×D₁₃₉

yes

—

144

C₄×Q₈

C₂×D₁₃₉

yes

characteristic

145

C₄×D₄

—

139

—

146

C₄×D₄

—

139

—

147

C₄×D₄

C₂×D₁₃₉

yes

characteristic

148

#117

—

149

C₂×C₄⋊C₄

—

278

—

150

#107

—

139

—

151

#106

—

139

—

152

C₄⋊C₈

—

139

—

153

C₄⋊C₈

—

139

—

154

#103

—

139

—

155

#103

—

139

—

156

#103

—

139

—

157

#102

—

139

—

158

#102

—

139

—

159

#102

—

139

—

160

C₄×C₈

—

139

—

161

C₄×C₈

—

139

—

162

C₂×Q₈

—

278

—

163

C₂×Q₈

C₂²⋊D₁₃₉

yes

characteristic

164

C₂×Q₈

C₂²×D₁₃₉

yes

—

165

C₂×D₄

—

139

—

166

C₂×D₄

C₂²×D₁₃₉

yes

characteristic

167

C₂²×C₄

—

168

C₂²×C₄

—

278

—

169

C₂²×C₄

—

278

—

170

SD₁₆

—

278

—

171

D₈

—

278

—

172

C₂×C₈

—

139

—

173

C₂×C₈

—

139

—

174

C₂×C₈

—

139

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

278

—

179

C₄⋊C₄

—

278

—

180

C₄⋊C₄

—

278

—

181

C₄⋊C₄

—

139

—

182

C₄⋊C₄

—

139

—

183

C₄⋊C₄

C₂²⋊D₁₃₉

yes

characteristic

184

C₄⋊C₄

C₂²⋊D₁₃₉

yes

—

185

C₄⋊C₄

C₂²×D₁₃₉

yes

characteristic

186

C₂²⋊C₄

—

187

C₂²⋊C₄

—

188

C₂²⋊C₄

—

189

C₂²⋊C₄

—

278

—

190

C₂²⋊C₄

—

278

—

191

C₄²

—

192

C₄²

C₂²×D₁₃₉

yes

characteristic

193

C₄²

C₂²×D₁₃₉

yes

—

194

C₂³

—

195

C₂³

—

278

—

196

Q₈

—

197

Q₈

—

198

Q₈

—

199

Q₈

—

1112

—

200

D₄

—

201

D₄

—

202

D₄

—

278

—

203

D₄

—

139

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

278

—

208

C₂×C₄

—

278

—

209

C₂×C₄

—

556

—

210

C₂×C₄

—

1112

—

211

C₂×C₄

C₂×C₂²⋊D₁₃₉

yes

—

212

C₂×C₄

C₂×C₂²⋊D₁₃₉

yes

—

213

C₂×C₄

C₂×C₂²⋊D₁₃₉

yes

characteristic

214

C₂×C₄

C₂×C₂²⋊D₁₃₉

yes

characteristic

215

C₂×C₄

C₂³×D₁₃₉

yes

characteristic

216

C₈

—

278

—

217

C₈

—

278

—

218

C₈

—

278

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

278

—

223

C₂²

—

556

—

224

C₂²

—

556

—

225

C₂²

C₂²×C₂²⋊D₁₃₉

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

556

—

232

C₄

—

556

—

233

C₄

#17984862

yes

—

234

C₄

#41×D₁₃₉

yes

characteristic

235

C₄

#17984889

yes

characteristic

236

C₂

—

237

C₂

—

556

—

238

C₂

#22581610

yes

characteristic

239

C₂

C₂×#17984862

yes

characteristic

240

C₂

#22581761

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	#556×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
prime radical	C₂×#14555770	C₂²
hypercenter	#556	D₁₃₉
hypocenter	C₁₃₉	#3360
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₁₃₉

commutator, cosocle

C₂×C₄×C₁₃₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₃₉

Fitting

#556×C₁₃₉

C₂

socle

C₂²×C₁₃₉

C₂²×D₄

C₂²

D₁₃₉

C₁₃₉

G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

N	H ≅ G/N	type
1. #22581663	C₂	semidirect
2. #22581307	C₂	semidirect
3. #22581303	C₂	semidirect
4. #22581260	C₂	semidirect
5. #22581243	C₂	semidirect
7. #22581155	C₂	semidirect
8. Q₈×C₁₃₉⋊C₈	C₂	semidirect
9. C₄×#14555772	C₂	semidirect
11. #556×C₁₃₉	C₂	semidirect
120. C₁₃₉	#3360	semidirect
122. #556	D₁₃₉	semidirect

H ≅ G/N

type

1. #22581663

C₂

semidirect

2. #22581307

C₂

semidirect

3. #22581303

C₂

semidirect

4. #22581260

C₂

semidirect

5. #22581243

C₂

semidirect

7. #22581155

C₂

semidirect

8. Q₈×C₁₃₉⋊C₈

C₂

semidirect

9. C₄×#14555772

C₂

semidirect

11. #556×C₁₃₉

C₂

semidirect

120. C₁₃₉

#3360

semidirect

122. #556

D₁₃₉

semidirect

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

subgroup	index
#22581663	2
#22581307	2
#22581303	2
#22581260	2
#22581243	2
#22581165	2
#22581155	2
Q₈×C₁₃₉⋊C₈	2
C₄×#14555772	2
C₄×#14555770	2
#556×C₁₃₉	2
#3360	139

subgroup

index

Q₈×C₁₃₉⋊C₈

#556×C₁₃₉

139

Subgroups — #31819049

Conjugacy classes of subgroups

Complements

Maximal subgroups