Group #18081647 — subgroups

Subgroups — #18081647

Order 4864.

486 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 155 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	#14572013	C₂	1	1	yes	maximal, characteristic
2	#14563787	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926291	C₂	1	2	yes	maximal
4	C₂×#11926289	C₂	1	2	yes	maximal
5	C₁₉×#1767	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597315	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
10	#11926450	—	2	2	no	—
11	#11926450	—	2	1	no	—
12	#11926450	—	2	1	no	—
13	#11926410	C₄	1	4	yes	—
14	#11926291	—	2	4	no	—
15	#11926289	—	2	4	no	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₉×#97	—	2	1	no	—
18	C₄³×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#336	—	2	1	no	—
20	C₂²×Dic₃₈	—	2	1	no	—
21	C₂²×Dic₃₈	—	2	1	no	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	—	2	1	no	—
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
32	C₂²×C₁₉⋊C₈	—	2	2	no	—
33	#10597315	—	2	2	no	—
34	#10597315	—	2	2	no	—
35	#10597315	—	2	2	no	—
36	#10597315	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
39	C₁₉×#97	—	4	2	no	—
40	C₁₉⋊#95	—	2	4	no	—
41	C₁₉⋊#95	—	2	4	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
45	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
47	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₁₉	—	2	2	no	—
51	C₂²×Dic₁₉	—	2	2	no	—
52	C₂×Dic₃₈	—	4	2	no	—
53	C₂×Dic₃₈	—	4	1	no	—
54	C₂×Dic₃₈	—	4	1	no	—
55	C₂×Dic₃₈	—	4	2	no	—
56	C₂×Dic₃₈	—	4	1	no	—
57	C₂×Dic₃₈	—	4	2	no	—
58	C₂×Dic₃₈	—	4	1	no	—
59	C₂×Dic₃₈	—	4	2	no	—
60	C₂×C₈×C₁₉	—	2	4	no	—
61	C₂×C₈×C₁₉	—	4	2	no	—
62	C₂×C₈×C₁₉	—	4	2	no	—
63	C₄²×C₁₉	—	2	4	no	—
64	C₄²×C₁₉	—	2	2	no	—
65	C₄²×C₁₉	—	2	2	no	—
66	C₄²×C₁₉	—	2	1	no	—
67	C₄²×C₁₉	—	2	1	no	—
68	C₄²×C₁₉	—	2	2	no	—
69	C₄²×C₁₉	C₂×D₄	1	2	yes	—
70	C₄²×C₁₉	#41	1	2	yes	—
71	C₄⋊Dic₁₉	—	2	4	no	—
72	C₄⋊Dic₁₉	—	2	4	no	—
73	C₄⋊Dic₁₉	—	4	2	no	—
74	C₄⋊Dic₁₉	—	4	1	no	—
75	C₄⋊Dic₁₉	—	4	1	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	C₂×C₁₉⋊C₈	—	4	4	no	—
78	#9708	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	#101	1	4	yes	—
87	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
88	C₂×C₄×C₁₉	#121	1	2	yes	—
89	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#135	1	2	yes	—
92	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
93	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
94	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#137	1	2	yes	—
96	C₂×Dic₁₉	—	4	2	no	—
97	C₂×Dic₁₉	—	4	2	no	—
98	C₂×Dic₁₉	—	4	2	no	—
99	C₂×Dic₁₉	—	4	2	no	—
100	C₂×Dic₁₉	—	4	4	no	—
101	Dic₃₈	—	8	2	no	—
102	Dic₃₈	—	8	2	no	—
103	Dic₃₈	—	8	2	no	—
104	Dic₃₈	—	8	1	no	—
105	Dic₃₈	—	8	1	no	—
106	C₈×C₁₉	—	4	4	no	—
107	C₁₉⋊C₈	—	8	2	no	—
108	#2862	—	19	1	no	—
109	#1842	—	19	1	no	—
110	#1767	D₁₉	1	1	yes	characteristic
111	C₂×#332	—	19	2	no	—
112	C₂×#332	—	19	2	no	—
113	C₂²×C₁₉	#390	1	1	yes	characteristic
114	C₂²×C₁₉	C₂×#101	1	2	yes	—
115	C₂²×C₁₉	#416	1	1	yes	characteristic
116	C₂²×C₁₉	#417	1	1	yes	characteristic
117	C₂²×C₁₉	#417	1	2	yes	—
118	C₄×C₁₉	—	2	4	no	—
119	C₄×C₁₉	—	2	2	no	—
120	C₄×C₁₉	—	4	2	no	—
121	C₄×C₁₉	#463	1	2	yes	—
122	C₄×C₁₉	#464	1	2	yes	—
123	C₄×C₁₉	#489	1	2	yes	—
124	C₄×C₁₉	#496	1	1	yes	characteristic
125	C₄×C₁₉	#497	1	1	yes	characteristic
126	Dic₁₉	—	8	2	no	—
127	Dic₁₉	—	8	2	no	—
128	C₂×C₄⋊Q₈	—	19	1	no	—
129	C₂×C₄⋊Q₈	—	19	1	no	—
130	C₂×C₄⋊C₈	—	19	2	no	—
131	C₂×C₄⋊C₈	—	38	2	no	—
132	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
133	C₂×#97	—	2	1	no	—
134	#391	—	38	2	no	—
135	#391	—	38	1	no	—
136	#391	—	38	1	no	—
137	#382	—	19	4	no	—
138	C₄³	C₂×D₁₉	1	1	yes	characteristic
139	#336	—	2	1	no	—
140	#332	—	38	4	no	—
141	#332	—	38	4	no	—
142	C₂×C₁₉	#1552	1	2	yes	—
143	C₂×C₁₉	#1561	1	2	yes	—
144	C₂×C₁₉	#1959	1	1	yes	characteristic
145	C₂×C₁₉	#1966	1	1	yes	characteristic
146	C₂×C₁₉	#1983	1	1	yes	characteristic
147	C₂²×Q₈	—	38	1	no	—
148	C₂²×Q₈	—	38	1	no	—
149	C₂²×C₈	—	2	2	no	—
150	C₂²×C₈	—	38	2	no	—
151	C₄⋊Q₈	—	38	2	no	—
152	C₄⋊Q₈	—	38	2	no	—
153	C₄⋊Q₈	—	38	2	no	—
154	C₄⋊Q₈	—	38	2	no	—
155	C₂×C₄⋊C₄	—	19	2	no	—
156	C₂×C₄⋊C₄	—	19	2	no	—
157	C₂×C₄⋊C₄	—	38	1	no	—
158	C₂×C₄⋊C₄	—	38	1	no	—
159	C₂×C₄²	C₄×D₁₉	1	2	yes	—
160	C₂×C₄²	D₇₆	1	2	yes	—
161	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
162	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
163	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	38	2	no	—
166	C₄⋊C₈	—	38	2	no	—
167	C₄⋊C₈	—	76	4	no	—
168	C₄⋊C₈	D₇₆	1	4	yes	—
169	#97	—	4	2	no	—
170	#95	—	38	4	no	—
171	#95	—	38	4	no	—
172	C₁₉	#9708	1	1	yes	characteristic, complemented, Sylow
173	C₂×Q₈	—	76	2	no	—
174	C₂×Q₈	—	76	1	no	—
175	C₂×Q₈	—	76	1	no	—
176	C₂×Q₈	—	76	2	no	—
177	C₂×Q₈	—	76	1	no	—
178	C₂×Q₈	—	76	1	no	—
179	C₂×Q₈	—	76	2	no	—
180	C₂×Q₈	—	76	2	no	—
181	C₂²×C₄	—	38	2	no	—
182	C₂²×C₄	—	38	2	no	—
183	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
184	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
185	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
186	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
187	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
188	C₂×C₈	—	2	4	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	76	2	no	—
192	C₂×C₈	—	76	4	no	—
193	C₄⋊C₄	—	38	4	no	—
194	C₄⋊C₄	—	38	4	no	—
195	C₄⋊C₄	—	76	2	no	—
196	C₄⋊C₄	—	76	1	no	—
197	C₄⋊C₄	—	76	1	no	—
198	C₄²	—	2	1	no	—
199	C₄²	—	2	1	no	—
200	C₄²	—	2	2	no	—
201	C₄²	—	2	4	no	—
202	C₄²	—	2	2	no	—
203	C₄²	—	2	2	no	—
204	C₄²	C₂×D₇₆	1	2	yes	—
205	C₄²	#64541	1	2	yes	—
206	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
207	Q₈	—	152	2	no	—
208	Q₈	—	152	1	no	—
209	Q₈	—	152	1	no	—
210	Q₈	—	152	2	no	—
211	Q₈	—	152	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	76	2	no	—
219	C₂×C₄	—	76	2	no	—
220	C₂×C₄	—	76	4	no	—
221	C₂×C₄	—	76	2	no	—
222	C₂×C₄	—	76	2	no	—
223	C₂×C₄	#10597281	1	4	yes	—
224	C₂×C₄	C₄×D₇₆	1	2	yes	—
225	C₂×C₄	#10597320	1	1	yes	characteristic
226	C₂×C₄	#10597321	1	1	yes	characteristic
227	C₂×C₄	#10597354	1	2	yes	—
228	C₂×C₄	#10597355	1	2	yes	—
229	C₂×C₄	#10597376	1	2	yes	—
230	C₂×C₄	#10597378	1	1	yes	characteristic
231	C₂×C₄	#10597388	1	1	yes	characteristic
232	C₂×C₄	#10597396	1	2	yes	—
233	C₈	—	4	4	no	—
234	C₈	—	152	2	no	—
235	C₂²	#11926446	1	1	yes	characteristic
236	C₂²	C₂×#10597281	1	2	yes	—
237	C₂²	#11926538	1	1	yes	characteristic
238	C₂²	#11926543	1	1	yes	characteristic
239	C₂²	#11926546	1	2	yes	—
240	C₄	—	2	4	no	—
241	C₄	—	2	2	no	—
242	C₄	—	4	2	no	—
243	C₄	—	152	2	no	—
244	C₄	—	152	2	no	—
245	C₄	#11926759	1	2	yes	—
246	C₄	#11926766	1	2	yes	—
247	C₄	#11926904	1	2	yes	—
248	C₄	#11926933	1	1	yes	characteristic
249	C₄	#11926938	1	1	yes	characteristic
250	C₂	#14562336	1	2	yes	—
251	C₂	#14562372	1	2	yes	—
252	C₂	#14564451	1	1	yes	characteristic
253	C₂	#14564479	1	1	yes	characteristic
254	C₂	#14564567	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572013

C₂

yes

maximal, characteristic

#14563787

C₂

yes

maximal, characteristic

C₂×#11926291

C₂

yes

maximal

C₂×#11926289

C₂

yes

maximal

C₁₉×#1767

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

—

—

—

C₄

yes

—

#11926291

—

#11926289

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₂×C₁₉×#97

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×Dic₃₈

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

—

—

—

—

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×#97

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9708

—

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×C₁₉

—

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

characteristic

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

Dic₃₈

—

102

Dic₃₈

—

103

Dic₃₈

—

104

Dic₃₈

—

105

Dic₃₈

—

106

C₈×C₁₉

—

107

C₁₉⋊C₈

—

108

#2862

—

109

#1842

—

110

#1767

D₁₉

yes

characteristic

111

C₂×#332

—

112

C₂×#332

—

113

C₂²×C₁₉

#390

yes

characteristic

114

C₂²×C₁₉

C₂×#101

yes

—

115

C₂²×C₁₉

#416

yes

characteristic

116

C₂²×C₁₉

#417

yes

characteristic

117

C₂²×C₁₉

#417

yes

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

#463

yes

—

122

C₄×C₁₉

#464

yes

—

123

C₄×C₁₉

#489

yes

—

124

C₄×C₁₉

#496

yes

characteristic

125

C₄×C₁₉

#497

yes

characteristic

126

Dic₁₉

—

127

Dic₁₉

—

128

C₂×C₄⋊Q₈

—

129

C₂×C₄⋊Q₈

—

130

C₂×C₄⋊C₈

—

131

C₂×C₄⋊C₈

—

132

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

133

C₂×#97

—

134

#391

—

135

#391

—

136

#391

—

137

#382

—

138

C₄³

C₂×D₁₉

yes

characteristic

139

#336

—

140

#332

—

141

#332

—

142

C₂×C₁₉

#1552

yes

—

143

C₂×C₁₉

#1561

yes

—

144

C₂×C₁₉

#1959

yes

characteristic

145

C₂×C₁₉

#1966

yes

characteristic

146

C₂×C₁₉

#1983

yes

characteristic

147

C₂²×Q₈

—

148

C₂²×Q₈

—

149

C₂²×C₈

—

150

C₂²×C₈

—

151

C₄⋊Q₈

—

152

C₄⋊Q₈

—

153

C₄⋊Q₈

—

154

C₄⋊Q₈

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄²

C₄×D₁₉

yes

—

160

C₂×C₄²

D₇₆

yes

—

161

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

162

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

163

C₂×C₄²

C₂²×D₁₉

yes

characteristic

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₄⋊C₈

D₇₆

yes

—

169

#97

—

170

#95

—

171

#95

—

172

C₁₉

#9708

yes

characteristic, complemented, Sylow

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

184

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

185

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

186

C₂²×C₄

C₂×D₇₆

yes

characteristic

187

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

C₂×D₇₆

yes

—

205

C₄²

#64541

yes

—

206

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

207

Q₈

—

152

—

208

Q₈

—

152

—

209

Q₈

—

152

—

210

Q₈

—

152

—

211

Q₈

—

152

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

#10597281

yes

—

224

C₂×C₄

C₄×D₇₆

yes

—

225

C₂×C₄

#10597320

yes

characteristic

226

C₂×C₄

#10597321

yes

characteristic

227

C₂×C₄

#10597354

yes

—

228

C₂×C₄

#10597355

yes

—

229

C₂×C₄

#10597376

yes

—

230

C₂×C₄

#10597378

yes

characteristic

231

C₂×C₄

#10597388

yes

characteristic

232

C₂×C₄

#10597396

yes

—

233

C₈

—

234

C₈

—

152

—

235

C₂²

#11926446

yes

characteristic

236

C₂²

C₂×#10597281

yes

—

237

C₂²

#11926538

yes

characteristic

238

C₂²

#11926543

yes

characteristic

239

C₂²

#11926546

yes

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

152

—

244

C₄

—

152

—

245

C₄

#11926759

yes

—

246

C₄

#11926766

yes

—

247

C₄

#11926904

yes

—

248

C₄

#11926933

yes

characteristic

249

C₄

#11926938

yes

characteristic

250

C₂

#14562336

yes

—

251

C₂

#14562372

yes

—

252

C₂

#14564451

yes

characteristic

253

C₂

#14564479

yes

characteristic

254

C₂

#14564567

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1767	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1767	D₁₉
hypocenter	C₁₉	#9708
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1767

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 ◁ C₄³ ◁ #1767

N	H ≅ G/N	type
172. C₁₉	#9708	semidirect

H ≅ G/N

type

172. C₁₉

#9708

semidirect

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

subgroup	index
#14572013	2
#14563787	2
C₂×#11926291	2
C₂×#11926289	2
C₁₉×#1767	2
#9708	19

subgroup

index

C₁₉×#1767

Subgroups — #18081647

Conjugacy classes of subgroups

Complements

Maximal subgroups