Group #18075764 — subgroups

Subgroups — #18075764

Order 4864.

418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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	#14572348	C₂	1	1	yes	maximal, characteristic
2	#14563766	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562196	C₂	1	2	yes	maximal
4	#14561494	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597347	—	2	1	no	—
7	#11927094	C₂²	1	1	yes	characteristic
8	#11926623	—	2	1	no	—
9	#11926623	C₄	1	2	yes	complemented
10	C₈×D₇₆	—	2	1	no	—
11	C₈×D₇₆	C₄	1	2	yes	complemented
12	#11926568	C₂²	1	1	yes	characteristic
13	#11926510	—	2	1	no	—
14	#11926410	C₂²	1	2	yes	—
15	#11926307	—	2	1	no	—
16	#11926307	—	2	1	no	—
17	#11926279	—	2	4	no	—
18	C₁₉×#431	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#335	—	2	1	no	—
21	C₁₉×#334	—	2	1	no	—
22	C₂×#64541	—	2	1	no	—
23	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	#10597376	—	2	1	no	—
27	#10597376	D₄	1	2	yes	—
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₂×#64520	—	2	1	no	—
30	#10597347	—	4	4	no	—
31	C₂×#64515	—	2	2	no	—
32	C₂×C₈×D₁₉	—	2	2	no	—
33	#10597321	—	2	1	no	—
34	#10597320	Q₈	1	1	yes	characteristic
35	C₄×D₇₆	—	2	1	no	—
36	C₄×D₇₆	C₂×C₄	1	2	yes	—
37	#10597315	Q₈	1	1	yes	characteristic
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₁₉×C₂²⋊C₈	—	2	2	no	—
40	C₄×C₈×C₁₉	—	2	2	no	—
41	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
45	C₁₉⋊#95	—	2	2	no	—
46	C₁₉⋊#95	—	2	2	no	—
47	(C₂×D₁₉)⋊C₈	—	2	2	no	—
48	(C₂×D₁₉)⋊C₈	—	2	2	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
50	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂×C₂²⋊D₁₉	—	2	2	no	—
55	C₂²×Dic₁₉	—	4	2	no	—
56	#64541	—	4	2	no	—
57	#64541	—	4	2	no	—
58	C₂×D₇₆	—	2	1	no	—
59	C₂×D₇₆	—	2	1	no	—
60	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
61	C₂×C₄×D₁₉	—	2	2	no	—
62	C₂×Dic₃₈	—	2	1	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
73	C₄²×C₁₉	#41	1	1	yes	characteristic
74	(C₂×D₁₉)⋊C₄	—	2	2	no	—
75	(C₂×D₁₉)⋊C₄	—	2	2	no	—
76	C₄⋊Dic₁₉	—	2	1	no	—
77	C₄⋊Dic₁₉	—	4	2	no	—
78	C₄⋊Dic₁₉	—	4	2	no	—
79	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
80	#64520	—	4	2	no	—
81	C₂×C₁₉⋊C₈	—	2	2	no	—
82	#64515	—	4	4	no	—
83	C₈×D₁₉	—	4	4	no	—
84	#8678	—	19	1	no	maximal, Sylow
85	C₂³×C₁₉	#121	1	1	yes	characteristic
86	C₂²×D₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	4	1	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#135	1	2	yes	—
96	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
97	C₂²⋊D₁₉	—	4	4	no	—
98	C₂×Dic₁₉	—	2	2	no	—
99	C₂×Dic₁₉	—	8	2	no	—
100	C₂×Dic₁₉	—	8	2	no	—
101	C₂×Dic₁₉	—	8	2	no	—
102	D₇₆	—	4	2	no	—
103	D₇₆	—	4	2	no	—
104	D₇₆	—	4	2	no	—
105	C₄×D₁₉	—	4	2	no	—
106	C₄×D₁₉	—	4	2	no	—
107	Dic₃₈	—	4	2	no	—
108	C₈×C₁₉	—	2	1	no	—
109	C₈×C₁₉	—	2	1	no	—
110	C₈×C₁₉	—	2	1	no	—
111	C₈×C₁₉	—	2	1	no	—
112	C₈×C₁₉	—	8	2	no	—
113	C₁₉⋊C₈	—	4	2	no	—
114	#2931	—	19	1	no	—
115	#1835	—	19	1	no	—
116	#1564	D₁₉	1	1	yes	characteristic, complemented
117	#1517	—	19	2	no	—
118	#1286	—	19	2	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	#380	1	1	yes	characteristic
122	C₂²×C₁₉	#463	1	2	yes	—
123	C₂×D₁₉	—	4	2	no	—
124	C₂×D₁₉	—	4	2	no	—
125	C₂×D₁₉	—	4	2	no	—
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	#416	1	1	yes	characteristic
131	C₄×C₁₉	#418	1	1	yes	characteristic
132	C₄×C₁₉	#478	1	2	yes	—
133	Dic₁₉	—	4	2	no	—
134	Dic₁₉	—	16	2	no	—
135	C₂×#131	—	38	1	no	—
136	#532	—	19	1	no	—
137	#436	—	19	2	no	—
138	#436	—	38	1	no	—
139	C₈×D₄	—	19	2	no	—
140	C₈×D₄	—	38	1	no	—
141	#431	C₂×D₁₉	1	2	yes	—
142	#423	—	19	1	no	—
143	#408	—	38	1	no	—
144	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
145	#382	—	19	2	no	—
146	#340	—	38	1	no	—
147	#340	—	38	1	no	—
148	#335	—	2	1	no	—
149	#334	—	2	1	no	—
150	#327	—	38	4	no	—
151	C₂×C₁₉	—	2	2	no	—
152	C₂×C₁₉	#1804	1	1	yes	characteristic
153	C₂×C₁₉	#1812	1	1	yes	characteristic
154	C₂×C₁₉	#1814	1	1	yes	characteristic
155	D₁₉	—	8	2	no	—
156	C₂×#41	—	38	1	no	—
157	#131	—	76	4	no	—
158	C₂×M₁₆	—	38	1	no	—
159	C₂×M₁₆	—	38	2	no	—
160	C₂²×C₈	—	38	2	no	—
161	C₂²×C₈	D₇₆	1	1	yes	characteristic
162	C₂²×C₈	D₇₆	1	1	yes	characteristic
163	C₄⋊Q₈	—	19	1	no	—
164	#127	—	19	1	no	—
165	#124	—	38	1	no	—
166	#121	—	19	2	no	—
167	#121	—	38	1	no	—
168	C₄×D₄	—	19	2	no	—
169	C₄×D₄	—	38	1	no	—
170	C₂×C₄⋊C₄	—	38	2	no	—
171	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
172	C₄⋊C₈	—	2	2	no	—
173	C₄⋊C₈	—	19	2	no	—
174	C₄⋊C₈	—	38	1	no	—
175	C₂²⋊C₈	—	2	2	no	—
176	C₂²⋊C₈	—	38	2	no	—
177	C₂²⋊C₈	—	38	2	no	—
178	C₄×C₈	—	2	2	no	—
179	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
180	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
181	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
182	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
183	#95	—	38	2	no	—
184	#95	—	38	2	no	—
185	C₁₉	#8678	1	1	yes	characteristic, complemented, Sylow
186	#41	—	76	2	no	—
187	#41	—	76	2	no	—
188	C₂×Q₈	—	38	1	no	—
189	C₂×D₄	—	19	2	no	—
190	C₂×D₄	—	38	2	no	—
191	C₂×D₄	—	38	1	no	—
192	C₂×D₄	—	38	1	no	—
193	C₂²×C₄	—	38	2	no	—
194	C₂²×C₄	—	76	2	no	—
195	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
196	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
197	C₂²×C₄	#64545	1	1	yes	characteristic
198	M₁₆	—	76	4	no	—
199	M₁₆	—	76	2	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	4	2	no	—
203	C₂×C₈	—	38	2	no	—
204	C₂×C₈	—	76	4	no	—
205	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
206	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
207	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
208	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
209	C₄⋊C₄	—	19	2	no	—
210	C₄⋊C₄	—	38	1	no	—
211	C₄⋊C₄	—	76	2	no	—
212	C₄⋊C₄	—	76	2	no	—
213	C₂²⋊C₄	—	38	2	no	—
214	C₂²⋊C₄	—	38	2	no	—
215	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
216	C₄²	#64543	1	1	yes	characteristic
217	C₄²	Q₈×D₁₉	1	1	yes	characteristic
218	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
219	C₂³	—	38	2	no	—
220	C₂³	#10597341	1	1	yes	characteristic
221	Q₈	—	76	2	no	—
222	D₄	—	76	2	no	—
223	D₄	—	76	2	no	—
224	D₄	—	76	4	no	—
225	D₄	—	76	2	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	—	38	2	no	—
229	C₂×C₄	—	76	2	no	—
230	C₂×C₄	—	76	2	no	—
231	C₂×C₄	—	152	2	no	—
232	C₂×C₄	—	152	2	no	—
233	C₂×C₄	—	152	2	no	—
234	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
235	C₂×C₄	#10597338	1	1	yes	characteristic
236	C₂×C₄	#10597343	1	1	yes	characteristic
237	C₂×C₄	#10597350	1	2	yes	—
238	C₂×C₄	#10597354	1	2	yes	—
239	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
240	C₂×C₄	#10597384	1	1	yes	characteristic
241	C₂×C₄	#10597392	1	1	yes	characteristic
242	C₈	—	2	1	no	—
243	C₈	—	2	1	no	—
244	C₈	—	2	1	no	—
245	C₈	—	2	1	no	—
246	C₈	—	8	2	no	—
247	C₈	—	76	2	no	—
248	C₂²	—	2	1	no	—
249	C₂²	—	2	1	no	—
250	C₂²	—	76	2	no	—
251	C₂²	—	76	2	no	—
252	C₂²	—	76	2	no	—
253	C₂²	#11926401	1	1	yes	characteristic
254	C₂²	#11926760	1	2	yes	—
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	2	1	no	—
259	C₄	—	304	2	no	—
260	C₄	—	76	2	no	—
261	C₄	#11926541	1	1	yes	characteristic
262	C₄	#11926550	1	1	yes	characteristic
263	C₄	#11926845	1	2	yes	—
264	C₂	—	2	2	no	—
265	C₂	—	152	2	no	—
266	C₂	#14563646	1	1	yes	characteristic
267	C₂	#14563678	1	1	yes	characteristic
268	C₂	#14563690	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572348

C₂

yes

maximal, characteristic

#14563766

C₂

yes

maximal, characteristic, complemented

#14562196

C₂

yes

maximal

#14561494

C₂

yes

maximal, complemented

C₁₉×#1564

C₂

yes

maximal, characteristic, complemented

C₂×#10597347

—

#11927094

C₂²

yes

characteristic

#11926623

—

#11926623

C₄

yes

complemented

C₈×D₇₆

—

C₈×D₇₆

C₄

yes

complemented

#11926568

C₂²

yes

characteristic

#11926510

—

#11926410

C₂²

yes

—

#11926307

—

#11926307

—

#11926279

—

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₂×#64541

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

#10597376

D₄

yes

—

C₂×C₄⋊Dic₁₉

—

C₂×#64520

—

#10597347

—

C₂×#64515

—

C₂×C₈×D₁₉

—

#10597321

—

#10597320

Q₈

yes

characteristic

C₄×D₇₆

—

C₄×D₇₆

C₂×C₄

yes

—

#10597315

Q₈

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉⋊#95

—

C₁₉⋊#95

—

(C₂×D₁₉)⋊C₈

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₄⋊C₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₄⋊C₄

yes

—

#64520

—

C₂×C₁₉⋊C₈

—

#64515

—

C₈×D₁₉

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

D₇₆

—

103

D₇₆

—

104

D₇₆

—

105

C₄×D₁₉

—

106

C₄×D₁₉

—

107

Dic₃₈

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

C₈×C₁₉

—

112

C₈×C₁₉

—

113

C₁₉⋊C₈

—

114

#2931

—

115

#1835

—

116

#1564

D₁₉

yes

characteristic, complemented

117

#1517

—

118

#1286

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

#380

yes

characteristic

122

C₂²×C₁₉

#463

yes

—

123

C₂×D₁₉

—

124

C₂×D₁₉

—

125

C₂×D₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

#416

yes

characteristic

131

C₄×C₁₉

#418

yes

characteristic

132

C₄×C₁₉

#478

yes

—

133

Dic₁₉

—

134

Dic₁₉

—

135

C₂×#131

—

136

#532

—

137

#436

—

138

#436

—

139

C₈×D₄

—

140

C₈×D₄

—

141

#431

C₂×D₁₉

yes

—

142

#423

—

143

#408

—

144

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

145

#382

—

146

#340

—

147

#340

—

148

#335

—

149

#334

—

150

#327

—

151

C₂×C₁₉

—

152

C₂×C₁₉

#1804

yes

characteristic

153

C₂×C₁₉

#1812

yes

characteristic

154

C₂×C₁₉

#1814

yes

characteristic

155

D₁₉

—

156

C₂×#41

—

157

#131

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₂²×C₈

—

161

C₂²×C₈

D₇₆

yes

characteristic

162

C₂²×C₈

D₇₆

yes

characteristic

163

C₄⋊Q₈

—

164

#127

—

165

#124

—

166

#121

—

167

#121

—

168

C₄×D₄

—

169

C₄×D₄

—

170

C₂×C₄⋊C₄

—

171

C₂×C₄²

C₂²×D₁₉

yes

characteristic

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₂²⋊C₈

—

176

C₂²⋊C₈

—

177

C₂²⋊C₈

—

178

C₄×C₈

—

179

C₄×C₈

C₄×D₁₉

yes

characteristic

180

C₄×C₈

C₄×D₁₉

yes

characteristic

181

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

182

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

183

#95

—

184

#95

—

185

C₁₉

#8678

yes

characteristic, complemented, Sylow

186

#41

—

187

#41

—

188

C₂×Q₈

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

C₂×D₇₆

yes

characteristic

196

C₂²×C₄

D₄×D₁₉

yes

characteristic

197

C₂²×C₄

#64545

yes

characteristic

198

M₁₆

—

199

M₁₆

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

206

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

207

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

208

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₂²⋊C₄

—

214

C₂²⋊C₄

—

215

C₄²

C₂×C₄×D₁₉

yes

characteristic

216

C₄²

#64543

yes

characteristic

217

C₄²

Q₈×D₁₉

yes

characteristic

218

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

219

C₂³

—

220

C₂³

#10597341

yes

characteristic

221

Q₈

—

222

D₄

—

223

D₄

—

224

D₄

—

225

D₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

152

—

232

C₂×C₄

—

152

—

233

C₂×C₄

—

152

—

234

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

235

C₂×C₄

#10597338

yes

characteristic

236

C₂×C₄

#10597343

yes

characteristic

237

C₂×C₄

#10597350

yes

—

238

C₂×C₄

#10597354

yes

—

239

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

240

C₂×C₄

#10597384

yes

characteristic

241

C₂×C₄

#10597392

yes

characteristic

242

C₈

—

243

C₈

—

244

C₈

—

245

C₈

—

246

C₈

—

247

C₈

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

#11926401

yes

characteristic

254

C₂²

#11926760

yes

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

304

—

260

C₄

—

261

C₄

#11926541

yes

characteristic

262

C₄

#11926550

yes

characteristic

263

C₄

#11926845

yes

—

264

C₂

—

265

C₂

—

152

—

266

C₂

#14563646

yes

characteristic

267

C₂

#14563678

yes

characteristic

268

C₂

#14563690

yes

characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1564	C₂
socle	C₂²×C₁₉	#380
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1564	D₁₉
hypocenter	C₁₉	#8678
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂²

#11926401

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1564

C₂

C₂²×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

N	H ≅ G/N	type
2. #14563766	C₂	semidirect
4. #14561494	C₂	semidirect
5. C₁₉×#1564	C₂	semidirect
9. #11926623	C₄	semidirect
11. C₈×D₇₆	C₄	semidirect
116. #1564	D₁₉	semidirect
185. C₁₉	#8678	semidirect

H ≅ G/N

type

2. #14563766

C₂

semidirect

4. #14561494

C₂

semidirect

5. C₁₉×#1564

C₂

semidirect

9. #11926623

C₄

semidirect

11. C₈×D₇₆

C₄

semidirect

116. #1564

D₁₉

semidirect

185. C₁₉

#8678

semidirect

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

subgroup	index
#14572348	2
#14563766	2
#14562196	2
#14561494	2
C₁₉×#1564	2
#8678	19

subgroup

index

C₁₉×#1564

Subgroups — #18075764

Conjugacy classes of subgroups

Complements

Maximal subgroups