Group #18087352 — subgroups

Subgroups — #18087352

Order 4864.

294 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 85 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	#14564456	C₂	1	1	yes	maximal, characteristic
2	#14563775	C₂	1	1	yes	maximal, characteristic
3	#14562307	C₂	1	1	yes	maximal, characteristic
4	#14561495	C₂	1	1	yes	maximal, characteristic
5	#14561494	C₂	1	1	yes	maximal, characteristic
6	#14561479	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×#10597292	—	2	1	no	—
11	C₂×#10597292	—	2	1	no	—
12	C₂×#10597260	C₂²	1	1	yes	characteristic
13	#11926410	C₂²	1	1	yes	characteristic
14	#11926308	—	2	1	no	—
15	#11926308	—	2	1	no	—
16	#11926290	—	2	2	no	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₉×#431	C₂²	1	1	yes	characteristic
19	C₁₉×#423	C₂²	1	1	yes	characteristic
20	C₁₉×#332	—	2	2	no	—
21	C₂²×Q₈×C₁₉	—	2	1	no	—
22	C₂×M₁₆×C₁₉	—	2	1	no	—
23	C₁₉×C₄⋊Q₈	—	2	1	no	—
24	C₁₉×C₄⋊Q₈	—	2	1	no	—
25	C₁₉×C₄⋊Q₈	—	2	1	no	—
26	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×#64520	—	2	1	no	—
32	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
33	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
34	C₁₉×C₄⋊C₈	—	2	1	no	—
35	C₁₉×C₄⋊C₈	—	2	1	no	—
36	C₁₉×C₄⋊C₈	—	2	1	no	—
37	C₁₉×C₂²⋊C₈	—	2	1	no	—
38	C₄×C₈×C₁₉	—	2	1	no	—
39	#10597292	—	4	2	no	—
40	#10597292	—	4	2	no	—
41	C₁₉⋊#95	—	2	1	no	—
42	C₁₉⋊#95	—	2	1	no	—
43	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
47	#10597260	—	2	1	no	—
48	#10597260	—	2	1	no	—
49	C₄×C₁₉⋊C₈	—	2	1	no	—
50	C₂×Q₈×C₁₉	—	2	2	no	—
51	C₂×Q₈×C₁₉	—	4	1	no	—
52	C₂×Q₈×C₁₉	—	4	1	no	—
53	C₂×Q₈×C₁₉	—	4	1	no	—
54	C₂×Q₈×C₁₉	—	4	1	no	—
55	C₂×Q₈×C₁₉	—	4	1	no	—
56	C₂²×C₄×C₁₉	—	4	1	no	—
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
60	C₂²×Dic₁₉	—	4	1	no	—
61	M₁₆×C₁₉	—	4	1	no	—
62	M₁₆×C₁₉	—	4	1	no	—
63	C₂×C₈×C₁₉	—	4	1	no	—
64	C₂×C₈×C₁₉	—	4	1	no	—
65	C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₄⋊C₄×C₁₉	—	4	1	no	—
68	C₄⋊C₄×C₁₉	—	4	1	no	—
69	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₉	#41	1	1	yes	characteristic
71	C₄²×C₁₉	#41	1	1	yes	characteristic
72	C₄²×C₁₉	#41	1	1	yes	characteristic
73	C₄⋊Dic₁₉	—	4	1	no	—
74	C₄⋊Dic₁₉	—	4	1	no	—
75	#64520	—	4	1	no	—
76	#64520	—	4	1	no	—
77	C₂×C₁₉⋊C₈	—	2	1	no	—
78	C₂×C₁₉⋊C₈	—	2	1	no	—
79	C₂×C₁₉⋊C₈	—	2	1	no	—
80	C₂×C₁₉⋊C₈	—	2	1	no	—
81	C₂×C₁₉⋊C₈	—	2	1	no	—
82	C₂×C₁₉⋊C₈	—	2	1	no	—
83	C₂×C₁₉⋊C₈	—	4	1	no	—
84	C₂×C₁₉⋊C₈	—	4	1	no	—
85	#10635	—	19	1	no	maximal, Sylow
86	C₂³×C₁₉	#124	1	1	yes	characteristic
87	Q₈×C₁₉	—	4	2	no	—
88	Q₈×C₁₉	—	4	2	no	—
89	Q₈×C₁₉	—	8	1	no	—
90	Q₈×C₁₉	—	8	1	no	—
91	C₂×C₄×C₁₉	—	4	1	no	—
92	C₂×C₄×C₁₉	—	4	1	no	—
93	C₂×C₄×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	—	8	1	no	—
95	C₂×C₄×C₁₉	—	8	1	no	—
96	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
104	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
105	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
106	C₂×Dic₁₉	—	8	1	no	—
107	C₂×Dic₁₉	—	8	1	no	—
108	C₂×Dic₁₉	—	8	1	no	—
109	C₈×C₁₉	—	8	1	no	—
110	C₈×C₁₉	—	8	1	no	—
111	C₁₉⋊C₈	—	4	1	no	—
112	C₁₉⋊C₈	—	4	1	no	—
113	C₁₉⋊C₈	—	8	1	no	—
114	C₁₉⋊C₈	—	8	1	no	—
115	#1960	—	19	1	no	—
116	#1838	—	19	1	no	—
117	#1546	—	19	1	no	—
118	#1546	D₁₉	1	1	yes	characteristic
119	#1286	—	19	1	no	—
120	#1286	—	19	1	no	—
121	#1281	—	19	1	no	—
122	C₂²×C₁₉	—	2	1	no	—
123	C₂²×C₁₉	—	2	1	no	—
124	C₂²×C₁₉	#397	1	1	yes	characteristic
125	C₂²×C₁₉	#488	1	1	yes	characteristic
126	C₂²×C₁₉	#490	1	1	yes	characteristic
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	8	2	no	—
132	C₄×C₁₉	#463	1	1	yes	characteristic
133	C₄×C₁₉	#463	1	1	yes	characteristic
134	C₄×C₁₉	#482	1	1	yes	characteristic
135	C₄×C₁₉	#482	1	1	yes	characteristic
136	Dic₁₉	—	16	1	no	—
137	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
138	#431	—	19	1	no	—
139	#431	C₂×D₁₉	1	1	yes	characteristic
140	#423	—	19	1	no	—
141	#423	C₂×D₁₉	1	1	yes	characteristic
142	C₂×#103	—	38	1	no	—
143	C₂×#103	—	38	1	no	—
144	C₂×#97	—	19	1	no	—
145	#382	—	19	1	no	—
146	#341	—	38	1	no	—
147	#341	—	38	1	no	—
148	#332	—	2	2	no	—
149	#332	—	38	2	no	—
150	C₂×C₁₉	—	2	1	no	—
151	C₂×C₁₉	—	2	1	no	—
152	C₂×C₁₉	#2073	1	1	yes	characteristic
153	C₂×C₁₉	#2082	1	1	yes	characteristic
154	C₂×C₁₉	#2082	1	1	yes	characteristic
155	C₂²×Q₈	—	2	1	no	—
156	C₂×M₁₆	—	2	1	no	—
157	C₂×M₁₆	—	38	1	no	—
158	C₂²×C₈	—	19	1	no	—
159	C₂²×C₈	—	19	1	no	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	—	2	1	no	—
162	C₄⋊Q₈	—	2	1	no	—
163	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
164	C₂×C₄⋊C₄	—	2	1	no	—
165	C₂×C₄⋊C₄	—	2	1	no	—
166	C₂×C₄⋊C₄	—	38	1	no	—
167	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
168	C₄⋊C₈	—	2	1	no	—
169	C₄⋊C₈	—	2	1	no	—
170	C₄⋊C₈	—	2	1	no	—
171	C₄⋊C₈	—	38	1	no	—
172	C₄⋊C₈	—	38	1	no	—
173	C₄⋊C₈	—	38	1	no	—
174	#103	—	76	2	no	—
175	#103	—	76	2	no	—
176	C₂²⋊C₈	—	2	1	no	—
177	C₂²⋊C₈	—	38	1	no	—
178	#97	—	38	1	no	—
179	#97	—	38	1	no	—
180	C₄×C₈	—	2	1	no	—
181	C₄×C₈	—	38	1	no	—
182	#95	—	38	1	no	—
183	#95	—	38	1	no	—
184	C₁₉	#10635	1	1	yes	characteristic, complemented, Sylow
185	C₂×Q₈	—	2	2	no	—
186	C₂×Q₈	—	4	1	no	—
187	C₂×Q₈	—	4	1	no	—
188	C₂×Q₈	—	4	1	no	—
189	C₂×Q₈	—	4	1	no	—
190	C₂×Q₈	—	4	1	no	—
191	C₂²×C₄	—	4	1	no	—
192	C₂²×C₄	—	76	1	no	—
193	C₂²×C₄	#64541	1	1	yes	characteristic
194	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
195	C₂²×C₄	#64543	1	1	yes	characteristic
196	M₁₆	—	4	1	no	—
197	M₁₆	—	4	1	no	—
198	M₁₆	—	76	1	no	—
199	M₁₆	—	76	1	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	4	1	no	—
202	C₂×C₈	—	38	1	no	—
203	C₂×C₈	—	38	1	no	—
204	C₂×C₈	—	38	1	no	—
205	C₂×C₈	—	38	1	no	—
206	C₂×C₈	—	38	1	no	—
207	C₂×C₈	—	38	1	no	—
208	C₂×C₈	—	76	1	no	—
209	C₂×C₈	—	76	1	no	—
210	C₄⋊C₄	—	2	2	no	—
211	C₄⋊C₄	—	2	2	no	—
212	C₄⋊C₄	—	4	1	no	—
213	C₄⋊C₄	—	4	1	no	—
214	C₄⋊C₄	—	76	1	no	—
215	C₄⋊C₄	—	76	1	no	—
216	C₄²	#64541	1	1	yes	characteristic
217	C₄²	#64543	1	1	yes	characteristic
218	C₄²	#64543	1	1	yes	characteristic
219	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
220	C₂³	#10597331	1	1	yes	characteristic
221	Q₈	—	4	2	no	—
222	Q₈	—	4	2	no	—
223	Q₈	—	8	1	no	—
224	Q₈	—	8	1	no	—
225	C₂×C₄	—	4	1	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	8	1	no	—
229	C₂×C₄	—	8	1	no	—
230	C₂×C₄	—	152	1	no	—
231	C₂×C₄	—	152	1	no	—
232	C₂×C₄	—	152	1	no	—
233	C₂×C₄	#10597325	1	1	yes	characteristic
234	C₂×C₄	#10597325	1	1	yes	characteristic
235	C₂×C₄	#10597329	1	1	yes	characteristic
236	C₂×C₄	#10597357	1	1	yes	characteristic
237	C₂×C₄	#10597358	1	1	yes	characteristic
238	C₂×C₄	#10597360	1	1	yes	characteristic
239	C₂×C₄	#10597362	1	1	yes	characteristic
240	C₂×C₄	#10597375	1	1	yes	characteristic
241	C₂×C₄	#10597381	1	1	yes	characteristic
242	C₂×C₄	#10597385	1	1	yes	characteristic
243	C₈	—	8	1	no	—
244	C₈	—	8	1	no	—
245	C₈	—	76	1	no	—
246	C₈	—	76	1	no	—
247	C₈	—	152	1	no	—
248	C₈	—	152	1	no	—
249	C₂²	—	2	1	no	—
250	C₂²	—	2	1	no	—
251	C₂²	#11926472	1	1	yes	characteristic
252	C₂²	#11926897	1	1	yes	characteristic
253	C₂²	#11926907	1	1	yes	characteristic
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	8	2	no	—
259	C₄	—	304	1	no	—
260	C₄	#11926757	1	1	yes	characteristic
261	C₄	#11926761	1	1	yes	characteristic
262	C₄	#11926866	1	1	yes	characteristic
263	C₄	#11926867	1	1	yes	characteristic
264	C₂	—	2	1	no	—
265	C₂	—	2	1	no	—
266	C₂	#14565051	1	1	yes	characteristic
267	C₂	#14565102	1	1	yes	characteristic
268	C₂	#14565103	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564456

C₂

yes

maximal, characteristic

#14563775

C₂

yes

maximal, characteristic

#14562307

C₂

yes

maximal, characteristic

#14561495

C₂

yes

maximal, characteristic

#14561494

C₂

yes

maximal, characteristic

#14561479

C₂

yes

maximal, characteristic

C₁₉×#1546

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

characteristic

#11926568

C₂²

yes

—

—

C₂²

yes

characteristic

#11926410

C₂²

yes

—

—

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#332

—

C₂²×Q₈×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

#10597292

—

#10597292

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

100

C₂×C₄×C₁₉

#126

yes

characteristic

101

C₂×C₄×C₁₉

#126

yes

characteristic

102

C₂×C₄×C₁₉

#135

yes

characteristic

103

C₂×C₄×C₁₉

#135

yes

characteristic

104

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

105

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

106

C₂×Dic₁₉

—

107

C₂×Dic₁₉

—

108

C₂×Dic₁₉

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

C₁₉⋊C₈

—

112

C₁₉⋊C₈

—

113

C₁₉⋊C₈

—

114

C₁₉⋊C₈

—

115

#1960

—

116

#1838

—

117

#1546

—

118

#1546

D₁₉

yes

characteristic

119

#1286

—

120

#1286

—

121

#1281

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

#397

yes

characteristic

125

C₂²×C₁₉

#488

yes

characteristic

126

C₂²×C₁₉

#490

yes

characteristic

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

#463

yes

characteristic

133

C₄×C₁₉

#463

yes

characteristic

134

C₄×C₁₉

#482

yes

characteristic

135

C₄×C₁₉

#482

yes

characteristic

136

Dic₁₉

—

137

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

138

#431

—

139

#431

C₂×D₁₉

yes

characteristic

140

#423

—

141

#423

C₂×D₁₉

yes

characteristic

142

C₂×#103

—

143

C₂×#103

—

144

C₂×#97

—

145

#382

—

146

#341

—

147

#341

—

148

#332

—

149

#332

—

150

C₂×C₁₉

—

151

C₂×C₁₉

—

152

C₂×C₁₉

#2073

yes

characteristic

153

C₂×C₁₉

#2082

yes

characteristic

154

C₂×C₁₉

#2082

yes

characteristic

155

C₂²×Q₈

—

156

C₂×M₁₆

—

157

C₂×M₁₆

—

158

C₂²×C₈

—

159

C₂²×C₈

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄²

C₂²×D₁₉

yes

characteristic

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

#103

—

175

#103

—

176

C₂²⋊C₈

—

177

C₂²⋊C₈

—

178

#97

—

179

#97

—

180

C₄×C₈

—

181

C₄×C₈

—

182

#95

—

183

#95

—

184

C₁₉

#10635

yes

characteristic, complemented, Sylow

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

#64541

yes

characteristic

194

C₂²×C₄

D₄×D₁₉

yes

characteristic

195

C₂²×C₄

#64543

yes

characteristic

196

M₁₆

—

197

M₁₆

—

198

M₁₆

—

199

M₁₆

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₄²

#64541

yes

characteristic

217

C₄²

#64543

yes

characteristic

218

C₄²

#64543

yes

characteristic

219

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

220

C₂³

#10597331

yes

characteristic

221

Q₈

—

222

Q₈

—

223

Q₈

—

224

Q₈

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

152

—

231

C₂×C₄

—

152

—

232

C₂×C₄

—

152

—

233

C₂×C₄

#10597325

yes

characteristic

234

C₂×C₄

#10597325

yes

characteristic

235

C₂×C₄

#10597329

yes

characteristic

236

C₂×C₄

#10597357

yes

characteristic

237

C₂×C₄

#10597358

yes

characteristic

238

C₂×C₄

#10597360

yes

characteristic

239

C₂×C₄

#10597362

yes

characteristic

240

C₂×C₄

#10597375

yes

characteristic

241

C₂×C₄

#10597381

yes

characteristic

242

C₂×C₄

#10597385

yes

characteristic

243

C₈

—

244

C₈

—

245

C₈

—

246

C₈

—

247

C₈

—

152

—

248

C₈

—

152

—

249

C₂²

—

250

C₂²

—

251

C₂²

#11926472

yes

characteristic

252

C₂²

#11926897

yes

characteristic

253

C₂²

#11926907

yes

characteristic

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

304

—

260

C₄

#11926757

yes

characteristic

261

C₄

#11926761

yes

characteristic

262

C₄

#11926866

yes

characteristic

263

C₄

#11926867

yes

characteristic

264

C₂

—

265

C₂

—

266

C₂

#14565051

yes

characteristic

267

C₂

#14565102

yes

characteristic

268

C₂

#14565103

yes

characteristic

	subgroup	G/H
center	C₂²	#11926472
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1546	C₂
socle	C₂²×C₁₉	#397
prime radical	C₂³×C₁₉	#124
hypercenter	#1546	D₁₉
hypocenter	C₁₉	#10635
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1546

subgroup

G/H

center

C₂²

#11926472

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1546

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1546

N	H ≅ G/N	type
184. C₁₉	#10635	semidirect

H ≅ G/N

type

184. C₁₉

#10635

semidirect

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

subgroup	index
#14564456	2
#14563775	2
#14562307	2
#14561495	2
#14561494	2
#14561479	2
C₁₉×#1546	2
#10635	19

subgroup

index

C₁₉×#1546

Subgroups — #18087352

Conjugacy classes of subgroups

Complements

Maximal subgroups