Group #18081267 — subgroups

Subgroups — #18081267

Order 4864.

306 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 109 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	#14563772	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#14562411	C₂	1	1	yes	maximal, characteristic
4	#14562406	C₂	1	1	yes	maximal, characteristic
5	#14562381	C₂	1	1	yes	maximal, characteristic
6	#14561538	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1303	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926308	—	2	1	no	—
14	#11926308	—	2	1	no	—
15	#11926299	—	2	1	no	—
16	#11926296	—	2	2	no	—
17	#11926296	C₄	1	2	yes	complemented
18	#11926295	—	2	2	no	—
19	#11926294	C₄	1	2	yes	complemented
20	C₁₉×#431	C₂²	1	1	yes	characteristic
21	C₁₉×#423	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×M₁₆×C₁₉	—	2	1	no	—
24	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₂×C₄²×C₁₉	—	2	1	no	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×#64520	—	2	1	no	—
28	C₂²×C₁₉⋊C₈	—	2	1	no	—
29	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
30	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
31	C₁₉×C₄⋊C₈	—	2	1	no	—
32	C₁₉×C₄⋊C₈	—	2	1	no	—
33	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
34	C₁₉×C₂²⋊C₈	—	2	1	no	—
35	C₄×C₈×C₁₉	—	2	1	no	—
36	C₁₉×#95	Q₈	1	2	yes	—
37	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
41	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
42	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
43	C₄×C₁₉⋊C₈	—	2	1	no	—
44	C₄×C₁₉⋊C₈	—	4	2	no	—
45	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
46	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
47	C₄×C₁₉⋊C₈	Q₈	1	1	yes	characteristic
48	C₄×C₁₉⋊C₈	Q₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
53	M₁₆×C₁₉	—	4	1	no	—
54	M₁₆×C₁₉	—	4	1	no	—
55	C₂×C₈×C₁₉	—	2	2	no	—
56	C₂×C₈×C₁₉	—	4	1	no	—
57	C₄⋊C₄×C₁₉	—	2	4	no	—
58	C₄²×C₁₉	—	4	1	no	—
59	C₄²×C₁₉	—	4	1	no	—
60	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
63	C₄²×C₁₉	#41	1	1	yes	characteristic
64	#64520	—	4	1	no	—
65	#64520	—	4	1	no	—
66	C₂×C₁₉⋊C₈	—	2	1	no	—
67	C₂×C₁₉⋊C₈	—	2	1	no	—
68	C₂×C₁₉⋊C₈	—	2	1	no	—
69	C₂×C₁₉⋊C₈	—	2	1	no	—
70	C₂×C₁₉⋊C₈	—	2	2	no	—
71	C₂×C₁₉⋊C₈	—	2	2	no	—
72	C₂×C₁₉⋊C₈	—	4	1	no	—
73	C₂×C₁₉⋊C₈	—	4	1	no	—
74	C₂×C₁₉⋊C₈	—	4	1	no	—
75	C₂×C₁₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
76	C₂×C₁₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₁₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₁₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
79	#9629	—	19	1	no	maximal, Sylow
80	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	4	no	—
83	C₂×C₄×C₁₉	—	4	1	no	—
84	C₂×C₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
94	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
96	C₈×C₁₉	—	4	2	no	—
97	C₈×C₁₉	—	8	1	no	—
98	C₁₉⋊C₈	—	2	1	no	—
99	C₁₉⋊C₈	—	2	1	no	—
100	C₁₉⋊C₈	—	2	1	no	—
101	C₁₉⋊C₈	—	2	1	no	—
102	C₁₉⋊C₈	—	4	2	no	—
103	C₁₉⋊C₈	—	4	2	no	—
104	C₁₉⋊C₈	—	8	1	no	—
105	#1837	—	19	1	no	—
106	C₈×C₄⋊C₄	—	19	1	no	—
107	#1571	—	19	1	no	—
108	#1570	—	19	1	no	—
109	#1564	—	19	1	no	—
110	#1303	—	19	1	no	—
111	#1303	D₁₉	1	1	yes	characteristic
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	—	2	1	no	—
114	C₂²×C₁₉	#389	1	1	yes	characteristic
115	C₂²×C₁₉	#478	1	1	yes	characteristic
116	C₂²×C₁₉	#479	1	1	yes	characteristic
117	C₄×C₁₉	—	2	1	no	—
118	C₄×C₁₉	—	2	1	no	—
119	C₄×C₁₉	—	2	1	no	—
120	C₄×C₁₉	—	4	4	no	—
121	C₄×C₁₉	#427	1	1	yes	characteristic
122	C₄×C₁₉	#428	1	1	yes	characteristic
123	C₄×C₁₉	#443	1	2	yes	—
124	C₄×C₁₉	#463	1	1	yes	characteristic
125	C₄×C₁₉	#464	1	1	yes	characteristic
126	#431	—	19	1	no	—
127	#431	C₂×D₁₉	1	1	yes	characteristic
128	#423	—	19	1	no	—
129	#423	C₂×D₁₉	1	1	yes	characteristic
130	C₂×C₄⋊C₈	—	19	1	no	—
131	C₂×C₄×C₈	—	19	1	no	—
132	C₂×C₄×C₈	—	38	1	no	—
133	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
134	#341	—	38	1	no	—
135	#341	—	38	1	no	—
136	#336	—	38	1	no	—
137	#335	—	19	2	no	—
138	#335	—	38	2	no	—
139	#334	—	19	2	no	—
140	#334	—	38	2	no	—
141	C₂×C₁₉	—	2	1	no	—
142	C₂×C₁₉	—	2	1	no	—
143	C₂×C₁₉	#1945	1	1	yes	characteristic
144	C₂×C₁₉	#1949	1	1	yes	characteristic
145	C₂×C₁₉	#1953	1	1	yes	characteristic
146	C₂×M₁₆	—	2	1	no	—
147	C₂×M₁₆	—	38	1	no	—
148	C₂²×C₈	—	19	1	no	—
149	C₂²×C₈	—	19	1	no	—
150	C₂²×C₈	—	38	1	no	—
151	C₂×C₄⋊C₄	—	2	1	no	—
152	C₂×C₄²	—	2	1	no	—
153	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
154	C₄⋊C₈	—	2	1	no	—
155	C₄⋊C₈	—	2	1	no	—
156	C₄⋊C₈	—	19	2	no	—
157	C₄⋊C₈	—	19	2	no	—
158	C₄⋊C₈	—	38	1	no	—
159	C₄⋊C₈	—	38	1	no	—
160	C₄⋊C₈	—	38	1	no	—
161	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
162	C₂²⋊C₈	—	2	1	no	—
163	C₂²⋊C₈	—	38	1	no	—
164	C₄×C₈	—	2	1	no	—
165	C₄×C₈	—	19	1	no	—
166	C₄×C₈	—	19	1	no	—
167	C₄×C₈	—	19	1	no	—
168	C₄×C₈	—	19	1	no	—
169	C₄×C₈	—	38	1	no	—
170	C₄×C₈	—	76	2	no	—
171	#95	Dic₃₈	1	2	yes	—
172	C₁₉	#9629	1	1	yes	characteristic, complemented, Sylow
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
175	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
176	C₂²×C₄	#64543	1	1	yes	characteristic
177	M₁₆	—	4	1	no	—
178	M₁₆	—	4	1	no	—
179	M₁₆	—	76	1	no	—
180	M₁₆	—	76	1	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	4	1	no	—
183	C₂×C₈	—	19	1	no	—
184	C₂×C₈	—	19	1	no	—
185	C₂×C₈	—	19	1	no	—
186	C₂×C₈	—	19	1	no	—
187	C₂×C₈	—	38	1	no	—
188	C₂×C₈	—	38	1	no	—
189	C₂×C₈	—	38	1	no	—
190	C₂×C₈	—	38	1	no	—
191	C₂×C₈	—	38	2	no	—
192	C₂×C₈	—	38	2	no	—
193	C₂×C₈	—	76	1	no	—
194	C₂×C₈	—	76	1	no	—
195	C₂×C₈	—	76	1	no	—
196	C₄⋊C₄	—	2	4	no	—
197	C₄²	—	4	1	no	—
198	C₄²	—	4	1	no	—
199	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
200	C₄²	#64541	1	1	yes	characteristic
201	C₄²	D₄×D₁₉	1	1	yes	characteristic
202	C₄²	Q₈×D₁₉	1	1	yes	characteristic
203	C₂³	#10597324	1	1	yes	characteristic
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
210	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
211	C₂×C₄	#10597330	1	1	yes	characteristic
212	C₂×C₄	#10597334	1	1	yes	characteristic
213	C₂×C₄	#10597335	1	1	yes	characteristic
214	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
215	C₂×C₄	#10597357	1	1	yes	characteristic
216	C₂×C₄	#10597362	1	1	yes	characteristic
217	C₂×C₄	#10597362	1	1	yes	characteristic
218	C₂×C₄	#10597364	1	1	yes	characteristic
219	C₈	—	4	2	no	—
220	C₈	—	8	1	no	—
221	C₈	—	38	1	no	—
222	C₈	—	38	1	no	—
223	C₈	—	38	1	no	—
224	C₈	—	38	1	no	—
225	C₈	—	76	2	no	—
226	C₈	—	76	2	no	—
227	C₈	—	152	1	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	#11926441	1	1	yes	characteristic
231	C₂²	#11926846	1	1	yes	characteristic
232	C₂²	#11926849	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	2	1	no	—
236	C₄	—	4	4	no	—
237	C₄	#11926579	1	1	yes	characteristic
238	C₄	#11926585	1	1	yes	characteristic
239	C₄	#11926658	1	2	yes	—
240	C₄	#11926758	1	1	yes	characteristic
241	C₄	#11926769	1	1	yes	characteristic
242	C₂	—	2	1	no	—
243	C₂	—	2	1	no	—
244	C₂	#14564382	1	1	yes	characteristic
245	C₂	#14564402	1	1	yes	characteristic
246	C₂	#14564424	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563772

C₂

yes

maximal, characteristic

C₄⋊C₄×C₁₉⋊C₈

C₂

yes

maximal, characteristic

#14562411

C₂

yes

maximal, characteristic

#14562406

C₂

yes

maximal, characteristic

#14562381

C₂

yes

maximal, characteristic

#14561538

C₂

yes

maximal, characteristic

C₁₉×#1303

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

characteristic

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

—

C₄

yes

complemented

#11926295

—

#11926294

C₄

yes

complemented

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

C₂×C₄

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉×#95

Q₈

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₁₉⋊C₈

Q₈

yes

characteristic

C₄×C₁₉⋊C₈

Q₈

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

C₄²×C₁₉

yes

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

characteristic

#9629

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₄⋊Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

100

C₁₉⋊C₈

—

101

C₁₉⋊C₈

—

102

C₁₉⋊C₈

—

103

C₁₉⋊C₈

—

104

C₁₉⋊C₈

—

105

#1837

—

106

C₈×C₄⋊C₄

—

107

#1571

—

108

#1570

—

109

#1564

—

110

#1303

—

111

#1303

D₁₉

yes

characteristic

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

#389

yes

characteristic

115

C₂²×C₁₉

#478

yes

characteristic

116

C₂²×C₁₉

#479

yes

characteristic

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

#427

yes

characteristic

122

C₄×C₁₉

#428

yes

characteristic

123

C₄×C₁₉

#443

yes

—

124

C₄×C₁₉

#463

yes

characteristic

125

C₄×C₁₉

#464

yes

characteristic

126

#431

—

127

#431

C₂×D₁₉

yes

characteristic

128

#423

—

129

#423

C₂×D₁₉

yes

characteristic

130

C₂×C₄⋊C₈

—

131

C₂×C₄×C₈

—

132

C₂×C₄×C₈

—

133

C₄×C₄⋊C₄

C₂×D₁₉

yes

characteristic

134

#341

—

135

#341

—

136

#336

—

137

#335

—

138

#335

—

139

#334

—

140

#334

—

141

C₂×C₁₉

—

142

C₂×C₁₉

—

143

C₂×C₁₉

#1945

yes

characteristic

144

C₂×C₁₉

#1949

yes

characteristic

145

C₂×C₁₉

#1953

yes

characteristic

146

C₂×M₁₆

—

147

C₂×M₁₆

—

148

C₂²×C₈

—

149

C₂²×C₈

—

150

C₂²×C₈

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄²

—

153

C₂×C₄²

C₂²×D₁₉

yes

characteristic

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

C₄×D₁₉

yes

—

162

C₂²⋊C₈

—

163

C₂²⋊C₈

—

164

C₄×C₈

—

165

C₄×C₈

—

166

C₄×C₈

—

167

C₄×C₈

—

168

C₄×C₈

—

169

C₄×C₈

—

170

C₄×C₈

—

171

#95

Dic₃₈

yes

—

172

C₁₉

#9629

yes

characteristic, complemented, Sylow

173

C₂²×C₄

—

174

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

175

C₂²×C₄

D₄×D₁₉

yes

characteristic

176

C₂²×C₄

#64543

yes

characteristic

177

M₁₆

—

178

M₁₆

—

179

M₁₆

—

180

M₁₆

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₄⋊C₄

—

197

C₄²

—

198

C₄²

—

199

C₄²

C₂×C₄×D₁₉

yes

characteristic

200

C₄²

#64541

yes

characteristic

201

C₄²

D₄×D₁₉

yes

characteristic

202

C₄²

Q₈×D₁₉

yes

characteristic

203

C₂³

#10597324

yes

characteristic

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

C₄×Dic₃₈

yes

characteristic

210

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

211

C₂×C₄

#10597330

yes

characteristic

212

C₂×C₄

#10597334

yes

characteristic

213

C₂×C₄

#10597335

yes

characteristic

214

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

215

C₂×C₄

#10597357

yes

characteristic

216

C₂×C₄

#10597362

yes

characteristic

217

C₂×C₄

#10597362

yes

characteristic

218

C₂×C₄

#10597364

yes

characteristic

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

225

C₈

—

226

C₈

—

227

C₈

—

152

—

228

C₂²

—

229

C₂²

—

230

C₂²

#11926441

yes

characteristic

231

C₂²

#11926846

yes

characteristic

232

C₂²

#11926849

yes

characteristic

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

#11926579

yes

characteristic

238

C₄

#11926585

yes

characteristic

239

C₄

#11926658

yes

—

240

C₄

#11926758

yes

characteristic

241

C₄

#11926769

yes

characteristic

242

C₂

—

243

C₂

—

244

C₂

#14564382

yes

characteristic

245

C₂

#14564402

yes

characteristic

246

C₂

#14564424

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597330
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1303	C₂
socle	C₂²×C₁₉	#389
prime radical	C₂³×C₁₉	C₂²⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1303	D₁₉
hypocenter	C₁₉	#9629
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

subgroup

G/H

center

C₂×C₄

#10597330

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1303

C₂

socle

C₂²×C₁₉

#389

prime radical

C₂³×C₁₉

C₂²⋊Q₈

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

N	H ≅ G/N	type
17. #11926296	C₄	semidirect
19. #11926294	C₄	semidirect
172. C₁₉	#9629	semidirect

H ≅ G/N

type

17. #11926296

C₄

semidirect

19. #11926294

C₄

semidirect

172. C₁₉

#9629

semidirect

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

subgroup	index
#14563772	2
C₄⋊C₄×C₁₉⋊C₈	2
#14562411	2
#14562406	2
#14562381	2
#14561538	2
C₁₉×#1303	2
#9629	19

subgroup

index

C₄⋊C₄×C₁₉⋊C₈

C₁₉×#1303

Subgroups — #18081267

Conjugacy classes of subgroups

Complements

Maximal subgroups