Group #18075336 — subgroups

Subgroups — #18075336

Order 4864.

516 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 161 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	#14566202	C₂	1	1	yes	maximal, characteristic
2	#14563786	C₂	1	2	yes	maximal
3	C₂×#11926292	C₂	1	2	yes	maximal
4	#14561518	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597333	C₄	1	2	yes	—
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×Dic₁₉⋊C₈	—	2	2	no	—
10	C₂×Dic₁₉⋊C₈	—	2	2	no	—
11	#11926449	C₄	1	2	yes	—
12	#11926440	—	2	2	no	—
13	C₄⋊C₄×Dic₁₉	—	2	2	no	—
14	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
15	#11926292	—	2	4	no	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₁₉×#384	C₂²	1	1	yes	characteristic
18	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
19	C₂²×C₈×C₁₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₉	—	2	2	no	—
24	C₂×Dic₁₉⋊C₄	—	2	2	no	—
25	C₂×C₄×Dic₁₉	—	2	2	no	—
26	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
29	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
30	C₂²×C₁₉⋊C₈	—	2	2	no	—
31	#10597333	—	4	4	no	—
32	#10597315	—	2	2	no	—
33	#10597315	D₄	1	2	yes	—
34	#10597315	Q₈	1	2	yes	—
35	C₁₉×C₄⋊C₈	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉⋊#95	—	2	4	no	—
38	Dic₁₉⋊C₈	—	4	4	no	—
39	Dic₁₉⋊C₈	—	4	4	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₂²×C₄×C₁₉	—	2	2	no	—
43	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂²×Dic₁₉	—	2	2	no	—
46	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
48	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×Dic₃₈	—	2	2	no	—
50	C₂×Dic₃₈	—	4	2	no	—
51	C₂×Dic₃₈	—	4	2	no	—
52	C₂×Dic₃₈	C₄⋊C₄	1	4	yes	—
53	C₂×C₈×C₁₉	—	4	2	no	—
54	C₂×C₈×C₁₉	—	4	2	no	—
55	C₂×C₈×C₁₉	—	4	2	no	—
56	C₄⋊C₄×C₁₉	—	4	2	no	—
57	C₄⋊C₄×C₁₉	—	4	2	no	—
58	C₄⋊C₄×C₁₉	—	4	2	no	—
59	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
61	C₄²×C₁₉	#41	1	2	yes	—
62	C₄⋊Dic₁₉	—	2	4	no	—
63	C₄⋊Dic₁₉	—	2	4	no	—
64	Dic₁₉⋊C₄	—	4	4	no	—
65	C₄×Dic₁₉	—	2	2	no	—
66	C₄×Dic₁₉	—	2	2	no	—
67	C₄×Dic₁₉	—	2	2	no	—
68	C₄×Dic₁₉	—	4	1	no	—
69	C₄×Dic₁₉	—	4	4	no	—
70	C₄×Dic₁₉	SD₁₆	1	4	yes	—
71	C₄×Dic₁₉	Q₁₆	1	4	yes	—
72	C₂×C₁₉⋊C₈	—	4	2	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	#8587	—	19	1	no	maximal, Sylow
76	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	4	2	no	—
80	C₂×C₄×C₁₉	—	4	4	no	—
81	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#121	1	2	yes	—
84	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
86	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
87	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
88	C₂×C₄×C₁₉	#137	1	2	yes	—
89	C₂×Dic₁₉	—	2	2	no	—
90	C₂×Dic₁₉	—	2	2	no	—
91	C₂×Dic₁₉	—	2	4	no	—
92	C₂×Dic₁₉	—	2	1	no	—
93	C₂×Dic₁₉	—	2	2	no	—
94	C₂×Dic₁₉	—	4	2	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	C₂×Dic₁₉	#100	1	2	yes	—
97	C₂×Dic₁₉	#103	1	4	yes	—
98	C₂×Dic₁₉	#103	1	4	yes	—
99	Dic₃₈	—	4	4	no	—
100	Dic₃₈	—	4	4	no	—
101	C₈×C₁₉	—	8	2	no	—
102	C₁₉⋊C₈	—	8	2	no	—
103	C₄×C₄⋊Q₈	—	19	1	no	—
104	#1842	—	19	2	no	—
105	C₂×#333	—	19	2	no	—
106	#1296	—	19	1	no	—
107	#1296	D₁₉	1	1	yes	characteristic
108	C₂²×C₁₉	#380	1	1	yes	characteristic
109	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
110	C₂²×C₁₉	#413	1	1	yes	characteristic
111	C₂²×C₁₉	C₂×#103	1	2	yes	—
112	C₂²×C₁₉	#417	1	2	yes	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	8	2	no	—
116	C₄×C₁₉	#460	1	2	yes	—
117	C₄×C₁₉	#462	1	2	yes	—
118	C₄×C₁₉	#475	1	2	yes	—
119	C₄×C₁₉	#477	1	2	yes	—
120	Dic₁₉	—	2	4	no	—
121	Dic₁₉	—	4	4	no	—
122	Dic₁₉	—	4	1	no	—
123	Dic₁₉	#333	1	4	yes	complemented
124	C₂×C₄⋊Q₈	—	19	1	no	—
125	C₂×C₄×Q₈	—	19	2	no	—
126	C₂×C₄⋊C₈	—	19	2	no	—
127	C₂×C₄⋊C₈	—	38	2	no	—
128	C₂×C₄⋊C₈	—	38	2	no	—
129	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
130	#391	—	19	2	no	—
131	#389	—	38	2	no	—
132	#384	C₂×D₁₉	1	1	yes	characteristic
133	C₄×C₄⋊C₄	—	38	2	no	—
134	C₄³	—	19	1	no	—
135	#333	—	38	4	no	—
136	C₂×C₁₉	C₂×#333	1	1	yes	characteristic
137	C₂×C₁₉	#1550	1	2	yes	—
138	C₂×C₁₉	#1560	1	1	yes	characteristic
139	C₂×C₁₉	#1800	1	1	yes	characteristic
140	C₂×C₁₉	#1803	1	2	yes	—
141	C₂²×Q₈	—	19	2	no	—
142	C₂²×C₈	—	2	2	no	—
143	C₂²×C₈	—	38	2	no	—
144	C₄⋊Q₈	—	19	2	no	—
145	C₄⋊Q₈	—	19	2	no	—
146	C₄⋊Q₈	—	38	2	no	—
147	C₄×Q₈	—	76	4	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	38	2	no	—
150	C₂×C₄⋊C₄	—	38	2	no	—
151	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
152	C₂×C₄²	—	19	2	no	—
153	C₂×C₄²	—	19	1	no	—
154	C₂×C₄²	—	19	2	no	—
155	C₂×C₄²	—	19	1	no	—
156	C₂×C₄²	—	38	2	no	—
157	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	2	2	no	—
160	C₄⋊C₈	—	38	2	no	—
161	C₄⋊C₈	—	38	2	no	—
162	C₄⋊C₈	—	76	4	no	—
163	C₄⋊C₈	—	76	4	no	—
164	#95	—	38	4	no	—
165	C₁₉	#8587	1	1	yes	characteristic, complemented, Sylow
166	C₂×Q₈	—	19	4	no	—
167	C₂×Q₈	—	38	2	no	—
168	C₂×Q₈	—	76	2	no	—
169	C₂×Q₈	—	76	2	no	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	19	1	no	—
172	C₂²×C₄	—	19	2	no	—
173	C₂²×C₄	—	19	1	no	—
174	C₂²×C₄	—	38	2	no	—
175	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
176	C₂²×C₄	D₄×D₁₉	1	2	yes	—
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	4	2	no	—
179	C₂×C₈	—	4	2	no	—
180	C₂×C₈	—	76	2	no	—
181	C₂×C₈	—	76	2	no	—
182	C₂×C₈	—	76	2	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	38	4	no	—
187	C₄⋊C₄	—	38	4	no	—
188	C₄⋊C₄	—	76	4	no	—
189	C₄²	—	19	4	no	—
190	C₄²	—	19	4	no	—
191	C₄²	—	38	2	no	—
192	C₄²	—	38	2	no	—
193	C₄²	—	38	2	no	—
194	C₄²	—	76	1	no	—
195	C₄²	—	76	4	no	—
196	C₄²	#64541	1	2	yes	—
197	C₄²	D₄×D₁₉	1	1	yes	characteristic
198	C₄²	Q₈×D₁₉	1	1	yes	characteristic
199	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
200	Q₈	—	76	4	no	—
201	Q₈	—	76	4	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	4	4	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	19	4	no	—
207	C₂×C₄	—	19	2	no	—
208	C₂×C₄	—	19	4	no	—
209	C₂×C₄	—	38	2	no	—
210	C₂×C₄	—	38	2	no	—
211	C₂×C₄	—	38	2	no	—
212	C₂×C₄	—	38	4	no	—
213	C₂×C₄	—	38	1	no	—
214	C₂×C₄	—	76	2	no	—
215	C₂×C₄	—	76	2	no	—
216	C₂×C₄	#10597318	1	1	yes	characteristic
217	C₂×C₄	#10597330	1	2	yes	—
218	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
219	C₂×C₄	#10597342	1	2	yes	—
220	C₂×C₄	#10597357	1	2	yes	—
221	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
222	C₂×C₄	#10597361	1	2	yes	—
223	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
224	C₈	—	8	2	no	—
225	C₈	—	152	2	no	—
226	C₂²	#11926403	1	1	yes	characteristic
227	C₂²	#100×D₁₉	1	1	yes	characteristic
228	C₂²	#11926527	1	1	yes	characteristic
229	C₂²	#103×D₁₉	1	2	yes	—
230	C₂²	#11926542	1	2	yes	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	8	2	no	—
234	C₄	—	19	4	no	—
235	C₄	—	38	4	no	—
236	C₄	—	76	4	no	—
237	C₄	—	76	1	no	—
238	C₄	#11926743	1	2	yes	—
239	C₄	#11926753	1	2	yes	—
240	C₄	#11926828	1	2	yes	—
241	C₄	#11926838	1	2	yes	—
242	C₂	D₁₉×#333	1	1	yes	characteristic
243	C₂	#14562324	1	2	yes	—
244	C₂	#14562367	1	1	yes	characteristic
245	C₂	#14563626	1	1	yes	characteristic
246	C₂	#14563639	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14566202

C₂

yes

maximal, characteristic

#14563786

C₂

yes

maximal

C₂×#11926292

C₂

yes

maximal

#14561518

C₂

yes

maximal, characteristic

C₁₉×#1296

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×#10597333

C₄

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×Dic₁₉⋊C₈

—

C₂×Dic₁₉⋊C₈

—

#11926449

C₄

yes

—

#11926440

—

C₄⋊C₄×Dic₁₉

—

C₄²×Dic₁₉

C₂²

yes

characteristic

#11926292

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#384

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

D₄

yes

—

C₂×C₄×Dic₁₉

D₄

yes

—

C₂²×C₁₉⋊C₈

—

#10597333

—

#10597315

—

#10597315

D₄

yes

—

#10597315

Q₈

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

Dic₁₉⋊C₈

—

Dic₁₉⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂²⋊C₄

yes

characteristic

C₂²×Dic₁₉

C₂²⋊C₄

yes

—

C₂²×Dic₁₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

SD₁₆

yes

—

C₄×Dic₁₉

Q₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8587

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#100

yes

—

C₂×Dic₁₉

#103

yes

—

C₂×Dic₁₉

#103

yes

—

Dic₃₈

—

100

Dic₃₈

—

101

C₈×C₁₉

—

102

C₁₉⋊C₈

—

103

C₄×C₄⋊Q₈

—

104

#1842

—

105

C₂×#333

—

106

#1296

—

107

#1296

D₁₉

yes

characteristic

108

C₂²×C₁₉

#380

yes

characteristic

109

C₂²×C₁₉

C₂×#100

yes

characteristic

110

C₂²×C₁₉

#413

yes

characteristic

111

C₂²×C₁₉

C₂×#103

yes

—

112

C₂²×C₁₉

#417

yes

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

#460

yes

—

117

C₄×C₁₉

#462

yes

—

118

C₄×C₁₉

#475

yes

—

119

C₄×C₁₉

#477

yes

—

120

Dic₁₉

—

121

Dic₁₉

—

122

Dic₁₉

—

123

Dic₁₉

#333

yes

complemented

124

C₂×C₄⋊Q₈

—

125

C₂×C₄×Q₈

—

126

C₂×C₄⋊C₈

—

127

C₂×C₄⋊C₈

—

128

C₂×C₄⋊C₈

—

129

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

130

#391

—

131

#389

—

132

#384

C₂×D₁₉

yes

characteristic

133

C₄×C₄⋊C₄

—

134

C₄³

—

135

#333

—

136

C₂×C₁₉

C₂×#333

yes

characteristic

137

C₂×C₁₉

#1550

yes

—

138

C₂×C₁₉

#1560

yes

characteristic

139

C₂×C₁₉

#1800

yes

characteristic

140

C₂×C₁₉

#1803

yes

—

141

C₂²×Q₈

—

142

C₂²×C₈

—

143

C₂²×C₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₄×Q₈

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

C₄×D₁₉

yes

—

152

C₂×C₄²

—

153

C₂×C₄²

—

154

C₂×C₄²

—

155

C₂×C₄²

—

156

C₂×C₄²

—

157

C₂×C₄²

C₂²×D₁₉

yes

characteristic

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

#95

—

165

C₁₉

#8587

yes

characteristic, complemented, Sylow

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

176

C₂²×C₄

D₄×D₁₉

yes

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

—

195

C₄²

—

196

C₄²

#64541

yes

—

197

C₄²

D₄×D₁₉

yes

characteristic

198

C₄²

Q₈×D₁₉

yes

characteristic

199

C₂³

C₂²⋊C₄×D₁₉

yes

characteristic

200

Q₈

—

201

Q₈

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

#10597318

yes

characteristic

217

C₂×C₄

#10597330

yes

—

218

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

219

C₂×C₄

#10597342

yes

—

220

C₂×C₄

#10597357

yes

—

221

C₂×C₄

SD₁₆×D₁₉

yes

—

222

C₂×C₄

#10597361

yes

—

223

C₂×C₄

Q₁₆×D₁₉

yes

—

224

C₈

—

225

C₈

—

152

—

226

C₂²

#11926403

yes

characteristic

227

C₂²

#100×D₁₉

yes

characteristic

228

C₂²

#11926527

yes

characteristic

229

C₂²

#103×D₁₉

yes

—

230

C₂²

#11926542

yes

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

#11926743

yes

—

239

C₄

#11926753

yes

—

240

C₄

#11926828

yes

—

241

C₄

#11926838

yes

—

242

C₂

D₁₉×#333

yes

characteristic

243

C₂

#14562324

yes

—

244

C₂

#14562367

yes

characteristic

245

C₂

#14563626

yes

characteristic

246

C₂

#14563639

yes

—

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1296	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1296	D₁₉
hypocenter	C₁₉	#8587
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

subgroup

G/H

center

C₂³

C₂²⋊C₄×D₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1296

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

N	H ≅ G/N	type
123. Dic₁₉	#333	semidirect
165. C₁₉	#8587	semidirect

H ≅ G/N

type

123. Dic₁₉

#333

semidirect

165. C₁₉

#8587

semidirect

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

subgroup	index
#14566202	2
#14563786	2
C₂×#11926292	2
#14561518	2
C₁₉×#1296	2
#8587	19

subgroup

index

C₁₉×#1296

Subgroups — #18075336

Conjugacy classes of subgroups

Complements

Maximal subgroups