Group #18075368 — subgroups

Subgroups — #18075368

Order 4864.

476 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 149 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	C₄⋊Q₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	#14563751	C₂	1	2	yes	maximal
3	C₂×#11926293	C₂	1	1	yes	maximal, characteristic
4	#14561519	C₂	1	2	yes	maximal
5	C₂×C₁₉×#333	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×Dic₁₉	C₄	1	2	yes	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	#11926451	C₄	1	2	yes	—
9	#11926443	—	2	2	no	—
10	#11926414	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×Dic₁₉	—	2	2	no	—
12	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
13	#11926298	—	2	2	no	—
14	#11926298	—	2	2	no	—
15	#11926293	—	2	2	no	—
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₁₉×#333	—	2	2	no	—
19	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₁₉	—	2	2	no	—
21	C₁₉×C₄⋊Q₈	—	2	2	no	—
22	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	Q₈	1	2	yes	—
24	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	Q₈×Dic₁₉	—	4	4	no	—
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
30	C₂×C₄×Dic₁₉	—	2	2	no	—
31	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
34	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
35	C₂²×C₁₉⋊C₈	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉⋊#95	—	2	4	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₂×Q₈×C₁₉	—	2	2	no	—
42	C₂×Q₈×C₁₉	—	4	2	no	—
43	C₂×Q₈×C₁₉	—	4	2	no	—
44	C₂×Q₈×C₁₉	C₄⋊C₄	1	4	yes	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
48	C₂²×Dic₁₉	—	2	2	no	—
49	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
50	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×C₈×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	—	4	2	no	—
54	C₂×C₈×C₁₉	—	4	2	no	—
55	C₄⋊C₄×C₁₉	—	2	4	no	—
56	C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
59	C₄²×C₁₉	#41	1	2	yes	—
60	C₄⋊Dic₁₉	—	4	4	no	—
61	C₄⋊Dic₁₉	—	4	2	no	—
62	C₄⋊Dic₁₉	—	4	2	no	—
63	C₄⋊Dic₁₉	—	4	2	no	—
64	C₄×Dic₁₉	—	2	2	no	—
65	C₄×Dic₁₉	—	2	2	no	—
66	C₄×Dic₁₉	—	2	2	no	—
67	C₄×Dic₁₉	—	2	2	no	—
68	C₄×Dic₁₉	—	2	2	no	—
69	C₄×Dic₁₉	—	4	1	no	—
70	C₄×Dic₁₉	—	4	4	no	—
71	C₂×C₁₉⋊C₈	—	4	2	no	—
72	C₂×C₁₉⋊C₈	—	4	2	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	#8594	—	19	1	no	maximal, Sylow
75	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	Q₈×C₁₉	—	4	4	no	—
77	Q₈×C₁₉	—	4	4	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	4	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#121	1	2	yes	—
86	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
87	C₂×C₄×C₁₉	#135	1	2	yes	—
88	C₂×C₄×C₁₉	#135	1	2	yes	—
89	C₂×C₄×C₁₉	#137	1	2	yes	—
90	C₂×C₄×C₁₉	#137	1	2	yes	—
91	C₂×Dic₁₉	—	2	2	no	—
92	C₂×Dic₁₉	—	2	1	no	—
93	C₂×Dic₁₉	—	2	2	no	—
94	C₂×Dic₁₉	—	2	2	no	—
95	C₂×Dic₁₉	—	2	2	no	—
96	C₂×Dic₁₉	—	2	2	no	—
97	C₂×Dic₁₉	—	4	2	no	—
98	C₂×Dic₁₉	—	4	4	no	—
99	C₂×Dic₁₉	#100	1	2	yes	—
100	C₈×C₁₉	—	8	2	no	—
101	C₁₉⋊C₈	—	8	2	no	—
102	C₄×C₄⋊Q₈	—	19	1	no	—
103	#1831	—	19	2	no	—
104	C₂×#333	—	19	1	no	—
105	C₂×#333	D₁₉	1	1	yes	characteristic
106	#1296	—	19	2	no	—
107	C₂²×C₁₉	#380	1	1	yes	characteristic
108	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
109	C₂²×C₁₉	#413	1	1	yes	characteristic
110	C₂²×C₁₉	#416	1	2	yes	—
111	C₂²×C₁₉	#419	1	2	yes	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	4	4	no	—
115	C₄×C₁₉	#464	1	2	yes	—
116	C₄×C₁₉	#464	1	2	yes	—
117	C₄×C₁₉	#479	1	2	yes	—
118	C₄×C₁₉	#479	1	2	yes	—
119	Dic₁₉	—	2	2	no	—
120	Dic₁₉	—	4	1	no	—
121	Dic₁₉	—	4	2	no	—
122	Dic₁₉	—	8	2	no	—
123	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
124	C₂×C₄×Q₈	—	19	2	no	—
125	C₂×C₄⋊C₈	—	19	2	no	—
126	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
127	#391	—	19	2	no	—
128	#389	—	38	2	no	—
129	#384	—	19	1	no	—
130	C₄×C₄⋊C₄	—	38	2	no	—
131	C₄³	—	19	1	no	—
132	#336	—	38	2	no	—
133	#336	—	38	2	no	—
134	#333	—	2	2	no	—
135	#333	—	38	2	no	—
136	C₂×C₁₉	#1543	1	1	yes	characteristic
137	C₂×C₁₉	#1554	1	2	yes	—
138	C₂×C₁₉	#1558	1	1	yes	characteristic
139	C₂×C₁₉	#1800	1	1	yes	characteristic
140	C₂×C₁₉	#1805	1	2	yes	—
141	C₂²×Q₈	C₄×D₁₉	1	2	yes	—
142	C₂²×C₈	—	2	2	no	—
143	C₂²×C₈	—	38	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₄⋊Q₈	Dic₃₈	1	2	yes	—
146	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
147	C₄×Q₈	—	76	4	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	19	2	no	—
150	C₂×C₄⋊C₄	—	38	2	no	—
151	C₂×C₄⋊C₄	—	38	2	no	—
152	C₂×C₄²	—	19	1	no	—
153	C₂×C₄²	—	19	2	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	#95	—	38	4	no	—
163	C₁₉	#8594	1	1	yes	characteristic, complemented, Sylow
164	C₂×Q₈	—	2	2	no	—
165	C₂×Q₈	—	4	2	no	—
166	C₂×Q₈	—	4	2	no	—
167	C₂×Q₈	Dic₁₉⋊C₄	1	4	yes	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	19	1	no	—
170	C₂²×C₄	—	19	2	no	—
171	C₂²×C₄	—	19	1	no	—
172	C₂²×C₄	—	38	2	no	—
173	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
174	C₂²×C₄	D₄×D₁₉	1	2	yes	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	76	2	no	—
179	C₂×C₈	—	76	2	no	—
180	C₂×C₈	—	76	2	no	—
181	C₄⋊C₄	—	2	4	no	—
182	C₄⋊C₄	—	2	4	no	—
183	C₄⋊C₄	—	76	2	no	—
184	C₄⋊C₄	—	76	4	no	—
185	C₄⋊C₄	—	76	2	no	—
186	C₄⋊C₄	—	76	2	no	—
187	C₄²	—	38	2	no	—
188	C₄²	—	38	2	no	—
189	C₄²	—	38	2	no	—
190	C₄²	—	38	2	no	—
191	C₄²	—	38	2	no	—
192	C₄²	—	76	1	no	—
193	C₄²	—	76	4	no	—
194	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
195	C₄²	#64543	1	2	yes	—
196	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
197	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
198	Q₈	—	4	4	no	—
199	Q₈	—	4	4	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	19	2	no	—
206	C₂×C₄	—	38	2	no	—
207	C₂×C₄	—	38	2	no	—
208	C₂×C₄	—	38	2	no	—
209	C₂×C₄	—	38	2	no	—
210	C₂×C₄	—	38	1	no	—
211	C₂×C₄	—	38	2	no	—
212	C₂×C₄	—	76	4	no	—
213	C₂×C₄	—	76	2	no	—
214	C₂×C₄	#10597323	1	1	yes	characteristic
215	C₂×C₄	#10597324	1	2	yes	—
216	C₂×C₄	#10597361	1	2	yes	—
217	C₂×C₄	#10597362	1	2	yes	—
218	C₂×C₄	#10597364	1	2	yes	—
219	C₂×C₄	#10597365	1	2	yes	—
220	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
221	C₂×C₄	#10597385	1	2	yes	—
222	C₈	—	8	2	no	—
223	C₈	—	152	2	no	—
224	C₂²	#11926402	1	1	yes	characteristic
225	C₂²	#100×D₁₉	1	1	yes	characteristic
226	C₂²	#11926525	1	1	yes	characteristic
227	C₂²	#11926539	1	2	yes	—
228	C₂²	#11926551	1	2	yes	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	4	4	no	—
232	C₄	—	38	2	no	—
233	C₄	—	76	2	no	—
234	C₄	—	76	1	no	—
235	C₄	—	152	2	no	—
236	C₄	#11926764	1	2	yes	—
237	C₄	#11926768	1	2	yes	—
238	C₄	#11926849	1	2	yes	—
239	C₄	#11926853	1	2	yes	—
240	C₂	#14562296	1	1	yes	characteristic
241	C₂	#14562344	1	2	yes	—
242	C₂	#14562359	1	1	yes	characteristic
243	C₂	#14563625	1	1	yes	characteristic
244	C₂	#14563648	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×Dic₁₉

C₂

yes

maximal, characteristic

#14563751

C₂

yes

maximal

C₂×#11926293

C₂

yes

maximal, characteristic

#14561519

C₂

yes

maximal

C₂×C₁₉×#333

C₂

yes

maximal, characteristic

C₂×Q₈×Dic₁₉

C₄

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926451

C₄

yes

—

#11926443

—

#11926414

C₂²

yes

characteristic

C₄⋊C₄×Dic₁₉

—

C₄²×Dic₁₉

C₂²

yes

—

—

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#333

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

Q₈

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

Q₈×Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

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

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂²⋊C₄

yes

—

C₂²×Dic₁₉

C₂²⋊C₄

yes

characteristic

C₂²×Dic₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×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

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8594

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

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

#135

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#100

yes

—

100

C₈×C₁₉

—

101

C₁₉⋊C₈

—

102

C₄×C₄⋊Q₈

—

103

#1831

—

104

C₂×#333

—

105

C₂×#333

D₁₉

yes

characteristic

106

#1296

—

107

C₂²×C₁₉

#380

yes

characteristic

108

C₂²×C₁₉

C₂×#100

yes

characteristic

109

C₂²×C₁₉

#413

yes

characteristic

110

C₂²×C₁₉

#416

yes

—

111

C₂²×C₁₉

#419

yes

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

#464

yes

—

116

C₄×C₁₉

#464

yes

—

117

C₄×C₁₉

#479

yes

—

118

C₄×C₁₉

#479

yes

—

119

Dic₁₉

—

120

Dic₁₉

—

121

Dic₁₉

—

122

Dic₁₉

—

123

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

124

C₂×C₄×Q₈

—

125

C₂×C₄⋊C₈

—

126

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

127

#391

—

128

#389

—

129

#384

—

130

C₄×C₄⋊C₄

—

131

C₄³

—

132

#336

—

133

#336

—

134

#333

—

135

#333

—

136

C₂×C₁₉

#1543

yes

characteristic

137

C₂×C₁₉

#1554

yes

—

138

C₂×C₁₉

#1558

yes

characteristic

139

C₂×C₁₉

#1800

yes

characteristic

140

C₂×C₁₉

#1805

yes

—

141

C₂²×Q₈

C₄×D₁₉

yes

—

142

C₂²×C₈

—

143

C₂²×C₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

Dic₃₈

yes

—

146

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

147

C₄×Q₈

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

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

#95

—

163

C₁₉

#8594

yes

characteristic, complemented, Sylow

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

Dic₁₉⋊C₄

yes

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

174

C₂²×C₄

D₄×D₁₉

yes

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

C₂×Dic₃₈

yes

characteristic

195

C₄²

#64543

yes

—

196

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

197

C₂³

C₂²⋊C₄×D₁₉

yes

characteristic

198

Q₈

—

199

Q₈

—

200

C₂×C₄

—

201

C₂×C₄

—

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

#10597323

yes

characteristic

215

C₂×C₄

#10597324

yes

—

216

C₂×C₄

#10597361

yes

—

217

C₂×C₄

#10597362

yes

—

218

C₂×C₄

#10597364

yes

—

219

C₂×C₄

#10597365

yes

—

220

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

221

C₂×C₄

#10597385

yes

—

222

C₈

—

223

C₈

—

152

—

224

C₂²

#11926402

yes

characteristic

225

C₂²

#100×D₁₉

yes

characteristic

226

C₂²

#11926525

yes

characteristic

227

C₂²

#11926539

yes

—

228

C₂²

#11926551

yes

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

152

—

236

C₄

#11926764

yes

—

237

C₄

#11926768

yes

—

238

C₄

#11926849

yes

—

239

C₄

#11926853

yes

—

240

C₂

#14562296

yes

characteristic

241

C₂

#14562344

yes

—

242

C₂

#14562359

yes

characteristic

243

C₂

#14563625

yes

characteristic

244

C₂

#14563648

yes

—

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#333	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#333	D₁₉
hypocenter	C₁₉	#8594
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

subgroup

G/H

center

C₂³

C₂²⋊C₄×D₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#333

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 ◁ C₂×#333

N	H ≅ G/N	type
163. C₁₉	#8594	semidirect

H ≅ G/N

type

163. C₁₉

#8594

semidirect

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

subgroup	index
C₄⋊Q₈×Dic₁₉	2
#14563751	2
C₂×#11926293	2
#14561519	2
C₂×C₁₉×#333	2
#8594	19

subgroup

index

C₄⋊Q₈×Dic₁₉

C₂×C₁₉×#333

Subgroups — #18075368

Conjugacy classes of subgroups

Complements

Maximal subgroups