Group #14574864 — subgroups

Subgroups — #14574864

Order 2432.

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

normal subgroups only

This group has 362 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	C₄⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927076	C₂	1	1	yes	maximal, characteristic
3	#11926952	C₂	1	2	yes	maximal, complemented
4	#11926902	C₂	1	2	yes	maximal, complemented
5	#11926881	C₂	1	2	yes	maximal, complemented
6	#11926861	C₂	1	2	yes	maximal
7	#11926830	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926826	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926824	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926600	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#474	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×D₁₉	—	2	1	no	—
13	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	#10597390	—	2	1	no	—
16	#10597384	C₂²	1	1	yes	characteristic
17	#10597382	C₂²	1	1	yes	characteristic
18	C₄×C₂²⋊D₁₉	—	2	1	no	—
19	#10597372	—	2	1	no	—
20	#10597343	C₂²	1	1	yes	characteristic
21	C₄⋊C₄×D₁₉	—	2	1	no	—
22	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
23	#10597336	C₂²	1	1	yes	characteristic
24	#10597334	—	2	1	no	—
25	#10597334	C₂²	1	2	yes	—
26	#10597329	—	2	1	no	—
27	#10597325	—	2	1	no	—
28	C₄²×D₁₉	C₂²	1	1	yes	characteristic
29	#10597315	C₂²	1	1	yes	characteristic
30	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
31	C₁₉×#107	C₂²	1	2	yes	—
32	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₉×#102	C₂²	1	2	yes	—
34	#10597289	C₂²	1	2	yes	—
35	(C₂×D₁₉)⋊C₈	C₂²	1	2	yes	—
36	#10597274	C₂²	1	2	yes	—
37	#10597273	C₂²	1	2	yes	—
38	#10597272	C₂²	1	2	yes	—
39	#10597267	C₂²	1	2	yes	—
40	#10597265	C₂²	1	2	yes	—
41	#10597264	C₂²	1	2	yes	—
42	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
43	C₂×Q₈×C₁₉	—	2	1	no	—
44	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂×C₂²⋊D₁₉	—	2	1	no	—
47	Q₈×D₁₉	—	4	4	no	—
48	C₂×C₄×D₁₉	—	2	2	no	—
49	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
52	C₂×Dic₃₈	—	2	1	no	—
53	C₂×Dic₃₈	—	2	2	no	—
54	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
55	C₂×C₈×C₁₉	C₂³	1	2	yes	—
56	C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
59	C₂²⋊C₄×C₁₉	—	2	1	no	—
60	C₄²×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²⋊Dic₁₉	—	2	1	no	—
62	C₂²⋊Dic₁₉	—	2	1	no	—
63	C₂²⋊Dic₁₉	—	2	1	no	—
64	(C₂×D₁₉)⋊C₄	—	2	1	no	—
65	C₄⋊Dic₁₉	—	2	1	no	—
66	C₄⋊Dic₁₉	—	2	1	no	—
67	C₄⋊Dic₁₉	—	2	1	no	—
68	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
69	C₄⋊Dic₁₉	C₂³	1	2	yes	—
70	Dic₁₉⋊C₄	—	2	1	no	—
71	Dic₁₉⋊C₄	—	2	2	no	—
72	Dic₁₉⋊C₄	—	2	2	no	—
73	Dic₁₉⋊C₄	—	2	1	no	—
74	C₄×Dic₁₉	—	2	1	no	—
75	C₄×Dic₁₉	D₄	1	1	yes	characteristic
76	C₄×Dic₁₉	D₄	1	1	yes	characteristic
77	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
79	C₂³×C₁₉	—	2	1	no	—
80	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
81	Q₈×C₁₉	—	4	2	no	—
82	D₄×C₁₉	—	2	1	no	—
83	D₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
90	C₂²⋊D₁₉	—	4	2	no	—
91	C₂×Dic₁₉	—	2	1	no	—
92	C₂×Dic₁₉	—	2	1	no	—
93	C₂×Dic₁₉	—	2	2	no	—
94	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
97	C₄×D₁₉	—	2	2	no	—
98	C₄×D₁₉	—	2	2	no	—
99	C₄×D₁₉	—	2	1	no	—
100	C₄×D₁₉	—	2	1	no	—
101	C₄×D₁₉	—	4	4	no	—
102	Dic₃₈	—	2	1	no	—
103	Dic₃₈	—	2	1	no	—
104	Dic₃₈	—	4	4	no	—
105	Dic₃₈	—	4	2	no	—
106	C₈×C₁₉	—	2	2	no	—
107	C₁₉⋊C₈	—	2	2	no	—
108	#3239	—	19	1	no	maximal, Sylow
109	C₂²×C₁₉	—	4	1	no	—
110	C₂²×C₁₉	—	4	1	no	—
111	C₂²×C₁₉	—	4	1	no	—
112	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
113	C₂×D₁₉	—	2	1	no	—
114	C₂×D₁₉	—	2	1	no	—
115	C₂×D₁₉	#137	1	2	yes	—
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	4	2	no	—
118	C₄×C₁₉	—	4	1	no	—
119	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
120	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
121	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
122	Dic₁₉	—	2	1	no	—
123	Dic₁₉	—	2	1	no	—
124	Dic₁₉	—	2	1	no	—
125	Dic₁₉	—	4	1	no	—
126	Dic₁₉	—	4	2	no	—
127	Dic₁₉	—	4	1	no	—
128	C₂×C₄⋊Q₈	—	19	1	no	—
129	#529	—	19	1	no	—
130	#501	—	19	2	no	—
131	#489	—	19	2	no	—
132	#484	—	19	2	no	—
133	#481	—	19	2	no	—
134	#475	—	19	1	no	—
135	#475	—	19	1	no	—
136	#474	—	19	1	no	—
137	#474	D₁₉	1	1	yes	characteristic, complemented
138	#432	—	19	1	no	—
139	C₂×C₁₉	—	8	1	no	—
140	C₂×C₁₉	#536	1	1	yes	characteristic
141	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
142	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
143	D₁₉	—	2	2	no	—
144	C₂²×Q₈	—	38	1	no	—
145	C₄⋊Q₈	—	19	2	no	—
146	C₄⋊Q₈	—	19	1	no	—
147	C₄⋊Q₈	—	38	1	no	—
148	C₄⋊Q₈	—	38	1	no	—
149	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
150	#126	—	38	1	no	—
151	#125	—	19	1	no	—
152	#124	—	19	1	no	—
153	#123	—	38	1	no	—
154	C₂²⋊Q₈	—	19	1	no	—
155	#121	—	19	1	no	—
156	C₄×Q₈	—	19	1	no	—
157	C₄×D₄	—	38	1	no	—
158	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
159	#117	—	38	1	no	—
160	C₂×C₄⋊C₄	—	19	2	no	—
161	C₂×C₄⋊C₄	—	38	1	no	—
162	C₂×C₄²	—	19	1	no	—
163	#107	—	19	2	no	—
164	#107	C₂×D₁₉	1	2	yes	—
165	#106	—	19	2	no	—
166	#106	—	19	2	no	—
167	C₄⋊C₈	—	19	1	no	—
168	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
169	#103	—	19	2	no	—
170	#103	—	19	2	no	—
171	#102	—	19	2	no	—
172	#102	C₂×D₁₉	1	2	yes	—
173	C₂²⋊C₈	—	19	2	no	—
174	#97	—	19	2	no	—
175	C₁₉	#3239	1	1	yes	characteristic, complemented, Sylow
176	C₂×Q₈	—	2	1	no	—
177	C₂×Q₈	—	19	1	no	—
178	C₂×Q₈	—	38	2	no	—
179	C₂×Q₈	—	38	1	no	—
180	C₂×Q₈	—	76	4	no	—
181	C₂×D₄	—	38	1	no	—
182	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	19	1	no	—
185	C₂²×C₄	—	19	1	no	—
186	C₂²×C₄	—	19	1	no	—
187	C₂²×C₄	—	38	2	no	—
188	C₂×C₈	—	19	2	no	—
189	C₂×C₈	C₂²×D₁₉	1	2	yes	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	19	2	no	—
192	C₄⋊C₄	—	19	1	no	—
193	C₄⋊C₄	—	38	2	no	—
194	C₄⋊C₄	—	38	2	no	—
195	C₄⋊C₄	—	38	1	no	—
196	C₄⋊C₄	—	38	1	no	—
197	C₄⋊C₄	—	38	1	no	—
198	C₄⋊C₄	—	38	1	no	—
199	C₄⋊C₄	—	38	1	no	—
200	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
201	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
202	C₂²⋊C₄	—	2	1	no	—
203	C₂²⋊C₄	—	38	1	no	—
204	C₂²⋊C₄	—	38	1	no	—
205	C₂²⋊C₄	—	38	1	no	—
206	C₂²⋊C₄	—	38	1	no	—
207	C₄²	—	19	1	no	—
208	C₄²	—	19	1	no	—
209	C₄²	—	19	1	no	—
210	C₄²	—	38	1	no	—
211	C₄²	C₂²×D₁₉	1	1	yes	characteristic
212	C₂³	—	2	1	no	—
213	C₂³	—	19	1	no	—
214	Q₈	—	4	2	no	—
215	Q₈	—	38	1	no	—
216	Q₈	—	38	1	no	—
217	Q₈	—	76	4	no	—
218	Q₈	—	76	2	no	—
219	D₄	—	2	1	no	—
220	D₄	—	2	1	no	—
221	D₄	—	76	2	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	19	1	no	—
226	C₂×C₄	—	19	1	no	—
227	C₂×C₄	—	19	1	no	—
228	C₂×C₄	—	38	2	no	—
229	C₂×C₄	—	38	1	no	—
230	C₂×C₄	—	38	1	no	—
231	C₂×C₄	—	38	2	no	—
232	C₂×C₄	—	38	1	no	—
233	C₂×C₄	—	38	1	no	—
234	C₂×C₄	—	38	2	no	—
235	C₂×C₄	—	76	4	no	—
236	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
237	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
238	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
239	C₈	—	2	2	no	—
240	C₈	—	38	2	no	—
241	C₂²	—	4	1	no	—
242	C₂²	—	4	1	no	—
243	C₂²	—	4	1	no	—
244	C₂²	—	19	2	no	—
245	C₂²	—	38	1	no	—
246	C₂²	—	38	1	no	—
247	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
248	C₄	—	2	1	no	—
249	C₄	—	4	1	no	—
250	C₄	—	4	2	no	—
251	C₄	—	38	1	no	—
252	C₄	—	38	1	no	—
253	C₄	—	38	1	no	—
254	C₄	—	76	2	no	—
255	C₄	—	76	1	no	—
256	C₄	—	76	1	no	—
257	C₄	#10597357	1	2	yes	—
258	C₄	#10597433	1	1	yes	characteristic
259	C₄	#10597436	1	1	yes	characteristic
260	C₂	—	8	1	no	—
261	C₂	—	38	2	no	—
262	C₂	#11927117	1	1	yes	characteristic
263	C₂	C₂×#10597357	1	1	yes	characteristic
264	C₂	#137×D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×D₁₉

C₂

yes

maximal, characteristic, complemented

#11927076

C₂

yes

maximal, characteristic

#11926952

C₂

yes

maximal, complemented

#11926902

C₂

yes

maximal, complemented

#11926881

C₂

yes

maximal, complemented

#11926861

C₂

yes

maximal

#11926830

C₂

yes

maximal, characteristic, complemented

#11926826

C₂

yes

maximal, characteristic, complemented

#11926824

C₂

yes

maximal, characteristic, complemented

#11926600

C₂

yes

maximal, characteristic, complemented

C₁₉×#474

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₄×D₄×C₁₉

C₂²

yes

characteristic

#10597390

—

#10597384

C₂²

yes

characteristic

#10597382

C₂²

yes

characteristic

C₄×C₂²⋊D₁₉

—

#10597372

—

#10597343

C₂²

yes

characteristic

C₄⋊C₄×D₁₉

—

C₄⋊C₄×D₁₉

C₂²

yes

—

#10597336

C₂²

yes

characteristic

#10597334

—

#10597334

C₂²

yes

—

#10597329

—

#10597325

—

C₄²×D₁₉

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#102

C₂²

yes

—

#10597289

C₂²

yes

—

(C₂×D₁₉)⋊C₈

C₂²

yes

—

#10597274

C₂²

yes

—

#10597273

C₂²

yes

—

#10597272

C₂²

yes

—

#10597267

C₂²

yes

—

#10597265

C₂²

yes

—

#10597264

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂×C₂²⋊D₁₉

—

Q₈×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

—

C₂²×D₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

100

C₄×D₁₉

—

101

C₄×D₁₉

—

102

Dic₃₈

—

103

Dic₃₈

—

104

Dic₃₈

—

105

Dic₃₈

—

106

C₈×C₁₉

—

107

C₁₉⋊C₈

—

108

#3239

—

maximal, Sylow

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

C₂²×D₄

yes

characteristic

113

C₂×D₁₉

—

114

C₂×D₁₉

—

115

C₂×D₁₉

#137

yes

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

120

C₄×C₁₉

2₋¹⁺⁴

yes

characteristic

121

C₄×C₁₉

2₋¹⁺⁴

yes

characteristic

122

Dic₁₉

—

123

Dic₁₉

—

124

Dic₁₉

—

125

Dic₁₉

—

126

Dic₁₉

—

127

Dic₁₉

—

128

C₂×C₄⋊Q₈

—

129

#529

—

130

#501

—

131

#489

—

132

#484

—

133

#481

—

134

#475

—

135

#475

—

136

#474

—

137

#474

D₁₉

yes

characteristic, complemented

138

#432

—

139

C₂×C₁₉

—

140

C₂×C₁₉

#536

yes

characteristic

141

C₂×C₁₉

C₂×AGL(1,ℤ/8)

yes

characteristic

142

C₂×C₁₉

C₂×#137

yes

characteristic

143

D₁₉

—

144

C₂²×Q₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

150

#126

—

151

#125

—

152

#124

—

153

#123

—

154

C₂²⋊Q₈

—

155

#121

—

156

C₄×Q₈

—

157

C₄×D₄

—

158

C₄×D₄

C₂×D₁₉

yes

characteristic

159

#117

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄²

—

163

#107

—

164

#107

C₂×D₁₉

yes

—

165

#106

—

166

#106

—

167

C₄⋊C₈

—

168

C₄⋊C₈

C₂×D₁₉

yes

characteristic

169

#103

—

170

#103

—

171

#102

—

172

#102

C₂×D₁₉

yes

—

173

C₂²⋊C₈

—

174

#97

—

175

C₁₉

#3239

yes

characteristic, complemented, Sylow

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂×D₄

—

182

C₂×D₄

C₂²×D₁₉

yes

characteristic

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂×C₈

—

189

C₂×C₈

C₂²×D₁₉

yes

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

C₂²×D₁₉

yes

—

201

C₄⋊C₄

C₂²×D₁₉

yes

characteristic

202

C₂²⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

210

C₄²

—

211

C₄²

C₂²×D₁₉

yes

characteristic

212

C₂³

—

213

C₂³

—

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

Q₈

—

218

Q₈

—

219

D₄

—

220

D₄

—

221

D₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

D₄×D₁₉

yes

characteristic

237

C₂×C₄

D₄×D₁₉

yes

characteristic

238

C₂×C₄

C₂³×D₁₉

yes

characteristic

239

C₈

—

240

C₈

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

C₂×D₄×D₁₉

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

#10597357

yes

—

258

C₄

#10597433

yes

characteristic

259

C₄

#10597436

yes

characteristic

260

C₂

—

261

C₂

—

262

C₂

#11927117

yes

characteristic

263

C₂

C₂×#10597357

yes

characteristic

264

C₂

#137×D₁₉

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#474	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#10597384	C₂²
hypercenter	#474	D₁₉
hypocenter	C₁₉	#3239
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #474

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#474

C₂

socle

C₂²×C₁₉

C₂²×D₄

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #474

N	H ≅ G/N	type
1. C₄⋊Q₈×D₁₉	C₂	semidirect
3. #11926952	C₂	semidirect
4. #11926902	C₂	semidirect
5. #11926881	C₂	semidirect
7. #11926830	C₂	semidirect
8. #11926826	C₂	semidirect
9. #11926824	C₂	semidirect
10. #11926600	C₂	semidirect
11. C₁₉×#474	C₂	semidirect
137. #474	D₁₉	semidirect
175. C₁₉	#3239	semidirect

H ≅ G/N

type

1. C₄⋊Q₈×D₁₉

C₂

semidirect

3. #11926952

C₂

semidirect

4. #11926902

C₂

semidirect

5. #11926881

C₂

semidirect

7. #11926830

C₂

semidirect

8. #11926826

C₂

semidirect

9. #11926824

C₂

semidirect

10. #11926600

C₂

semidirect

11. C₁₉×#474

C₂

semidirect

137. #474

D₁₉

semidirect

175. C₁₉

#3239

semidirect

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

subgroup	index
C₄⋊Q₈×D₁₉	2
#11927076	2
#11926952	2
#11926902	2
#11926881	2
#11926861	2
#11926830	2
#11926826	2
#11926824	2
#11926600	2
C₁₉×#474	2
#3239	19

subgroup

index

C₄⋊Q₈×D₁₉

C₁₉×#474

Subgroups — #14574864

Conjugacy classes of subgroups

Complements

Maximal subgroups