Group #14573424 — subgroups

Subgroups — #14573424

Order 2432.

388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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	#11927099	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#64543	C₂	1	1	yes	maximal, characteristic
3	#11926854	C₂	1	2	yes	maximal, complemented
4	#11926846	C₂	1	2	yes	maximal, complemented
5	#11926836	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926830	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926824	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926579	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926537	C₂	1	2	yes	maximal
11	C₁₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#64543	C₂²	1	1	yes	characteristic
13	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	#10597392	—	2	1	no	—
16	Q₈×Dic₁₉	—	2	1	no	—
17	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
18	C₄×C₂²⋊D₁₉	—	2	1	no	—
19	C₂×C₄×Dic₁₉	—	2	1	no	—
20	C₂×C₈×D₁₉	C₂²	1	2	yes	—
21	#10597343	—	2	1	no	—
22	#10597338	C₂²	1	2	yes	—
23	#10597338	C₂²	1	1	yes	characteristic
24	#10597336	C₂²	1	2	yes	—
25	#10597333	—	2	1	no	—
26	#10597333	C₂²	1	1	yes	characteristic
27	(C₂²⋊D₁₉)⋊C₄	—	2	1	no	—
28	#10597323	—	2	1	no	—
29	C₄²×D₁₉	C₂²	1	1	yes	characteristic
30	#10597315	C₂²	1	1	yes	characteristic
31	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
32	C₁₉×#106	C₂²	1	2	yes	—
33	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₁₉×#102	C₂²	1	2	yes	—
35	#10597289	C₂²	1	2	yes	—
36	#10597274	C₂²	1	2	yes	—
37	#10597273	C₂²	1	2	yes	—
38	Dic₁₉⋊C₈	C₂²	1	2	yes	—
39	#10597267	C₂²	1	2	yes	—
40	#10597264	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	C₂²×Dic₁₉	—	2	1	no	—
48	C₂²×Dic₁₉	—	2	1	no	—
49	#64543	—	2	2	no	—
50	#64543	Q₈	1	4	yes	complemented
51	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
53	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
54	C₂×Dic₃₈	—	2	1	no	—
55	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
56	C₂×C₈×C₁₉	C₂³	1	2	yes	—
57	C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
60	C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²⋊Dic₁₉	—	2	1	no	—
63	(C₂×D₁₉)⋊C₄	—	2	2	no	—
64	(C₂×D₁₉)⋊C₄	—	2	1	no	—
65	C₄⋊Dic₁₉	—	2	1	no	—
66	C₄⋊Dic₁₉	—	2	2	no	—
67	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
68	C₄⋊Dic₁₉	C₂³	1	2	yes	—
69	Dic₁₉⋊C₄	—	2	1	no	—
70	Dic₁₉⋊C₄	—	2	2	no	—
71	Dic₁₉⋊C₄	—	2	1	no	—
72	C₄×Dic₁₉	—	2	1	no	—
73	C₄×Dic₁₉	—	2	2	no	—
74	C₄×Dic₁₉	—	2	1	no	—
75	C₄×Dic₁₉	—	2	1	no	—
76	C₄×Dic₁₉	D₄	1	1	yes	characteristic
77	C₄×Dic₁₉	D₄	1	1	yes	characteristic
78	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
80	C₈×D₁₉	—	2	4	no	—
81	C₂³×C₁₉	—	2	1	no	—
82	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
83	Q₈×C₁₉	—	4	2	no	—
84	D₄×C₁₉	—	2	1	no	—
85	D₄×C₁₉	C₂×Q₈	1	2	yes	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
92	C₂²⋊D₁₉	—	2	4	no	—
93	C₂×Dic₁₉	—	2	1	no	—
94	C₂×Dic₁₉	—	2	4	no	—
95	C₂×Dic₁₉	—	2	1	no	—
96	C₂×Dic₁₉	—	2	2	no	—
97	C₂×Dic₁₉	—	4	2	no	—
98	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
101	C₄×D₁₉	—	2	2	no	—
102	C₄×D₁₉	—	4	1	no	—
103	C₄×D₁₉	C₂×Q₈	1	2	yes	—
104	C₄×D₁₉	#41	1	2	yes	—
105	Dic₃₈	—	2	1	no	—
106	Dic₃₈	—	4	2	no	—
107	Dic₃₈	C₂×Q₈	1	2	yes	—
108	C₈×C₁₉	—	2	2	no	—
109	C₁₉⋊C₈	—	2	2	no	—
110	#3076	—	19	1	no	maximal, Sylow
111	C₂²×C₁₉	—	2	2	no	—
112	C₂²×C₁₉	—	4	1	no	—
113	C₂²×C₁₉	—	4	1	no	—
114	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
115	C₂×D₁₉	—	2	1	no	—
116	C₂×D₁₉	—	2	1	no	—
117	C₂×D₁₉	C₂²⋊Q₈	1	2	yes	—
118	C₄×C₁₉	—	2	1	no	—
119	C₄×C₁₉	—	4	1	no	—
120	C₄×C₁₉	—	4	2	no	—
121	C₄×C₁₉	#135	1	2	yes	—
122	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
123	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
124	Dic₁₉	—	2	2	no	—
125	Dic₁₉	—	2	1	no	—
126	Dic₁₉	—	2	1	no	—
127	Dic₁₉	—	4	2	no	—
128	Dic₁₉	—	4	1	no	—
129	Dic₁₉	C₂²⋊Q₈	1	2	yes	—
130	#533	—	19	1	no	—
131	C₄×#41	—	19	1	no	—
132	#479	—	19	2	no	—
133	#478	—	19	2	no	—
134	#477	—	19	1	no	—
135	#476	D₁₉	1	1	yes	characteristic, complemented
136	#475	—	19	1	no	—
137	#474	—	19	1	no	—
138	#427	—	19	2	no	—
139	C₂×C₄⋊C₈	—	19	1	no	—
140	#416	—	19	2	no	—
141	C₂×C₁₉	—	4	2	no	—
142	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
143	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
144	C₂×C₁₉	#575	1	1	yes	characteristic
145	D₁₉	—	2	2	no	—
146	C₂×#41	—	19	1	no	—
147	C₂²×C₈	—	19	2	no	—
148	C₄⋊Q₈	—	19	1	no	—
149	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
150	#125	—	19	2	no	—
151	C₂²⋊Q₈	—	38	1	no	—
152	C₂²⋊Q₈	—	38	1	no	—
153	C₄×Q₈	—	19	1	no	—
154	C₄×Q₈	—	19	1	no	—
155	C₄×Q₈	—	38	1	no	—
156	C₄×Q₈	—	38	1	no	—
157	C₄×D₄	—	19	1	no	—
158	C₄×D₄	—	38	1	no	—
159	C₄×D₄	—	38	1	no	—
160	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
161	#117	—	19	1	no	—
162	#117	—	19	2	no	—
163	#117	—	38	1	no	—
164	C₂×C₄²	—	19	1	no	—
165	C₂×C₄²	—	38	1	no	—
166	#107	—	19	2	no	—
167	#107	—	19	2	no	—
168	#106	—	19	2	no	—
169	#106	C₂×D₁₉	1	2	yes	—
170	C₄⋊C₈	—	19	2	no	—
171	C₄⋊C₈	—	19	1	no	—
172	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
173	#103	—	19	2	no	—
174	#103	—	19	2	no	—
175	#102	—	19	2	no	—
176	#102	C₂×D₁₉	1	2	yes	—
177	C₁₉	#3076	1	1	yes	characteristic, complemented, Sylow
178	#41	—	19	4	no	—
179	#41	—	38	2	no	—
180	C₂×Q₈	—	2	1	no	—
181	C₂×Q₈	—	19	1	no	—
182	C₂×Q₈	—	38	1	no	—
183	C₂×D₄	—	38	1	no	—
184	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	—	19	1	no	—
187	C₂²×C₄	—	19	1	no	—
188	C₂²×C₄	—	19	1	no	—
189	C₂²×C₄	—	38	1	no	—
190	C₂²×C₄	—	38	1	no	—
191	C₂×C₈	—	19	2	no	—
192	C₂×C₈	—	38	4	no	—
193	C₂×C₈	C₂²×D₁₉	1	2	yes	—
194	C₄⋊C₄	—	2	1	no	—
195	C₄⋊C₄	—	19	2	no	—
196	C₄⋊C₄	—	19	1	no	—
197	C₄⋊C₄	—	38	1	no	—
198	C₄⋊C₄	—	38	2	no	—
199	C₄⋊C₄	—	38	2	no	—
200	C₄⋊C₄	—	38	1	no	—
201	C₄⋊C₄	—	38	1	no	—
202	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
203	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
204	C₂²⋊C₄	—	2	1	no	—
205	C₂²⋊C₄	—	38	1	no	—
206	C₂²⋊C₄	—	38	2	no	—
207	C₂²⋊C₄	—	38	1	no	—
208	C₄²	—	19	1	no	—
209	C₄²	—	19	1	no	—
210	C₄²	—	19	1	no	—
211	C₄²	—	38	1	no	—
212	C₄²	—	38	1	no	—
213	C₄²	—	38	2	no	—
214	C₄²	—	38	1	no	—
215	C₄²	C₂²×D₁₉	1	1	yes	characteristic
216	C₂³	—	2	1	no	—
217	C₂³	—	19	1	no	—
218	Q₈	—	4	2	no	—
219	Q₈	—	19	2	no	—
220	Q₈	—	38	1	no	—
221	Q₈	—	76	2	no	—
222	D₄	—	2	1	no	—
223	D₄	—	38	4	no	—
224	D₄	Q₈×D₁₉	1	2	yes	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	19	1	no	—
229	C₂×C₄	—	19	2	no	—
230	C₂×C₄	—	19	2	no	—
231	C₂×C₄	—	19	1	no	—
232	C₂×C₄	—	19	1	no	—
233	C₂×C₄	—	38	4	no	—
234	C₂×C₄	—	38	1	no	—
235	C₂×C₄	—	38	2	no	—
236	C₂×C₄	—	38	1	no	—
237	C₂×C₄	—	38	2	no	—
238	C₂×C₄	—	76	1	no	—
239	C₂×C₄	—	76	2	no	—
240	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
241	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
242	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
243	C₈	—	2	2	no	—
244	C₈	—	38	2	no	—
245	C₂²	—	2	2	no	—
246	C₂²	—	4	1	no	—
247	C₂²	—	4	1	no	—
248	C₂²	—	19	2	no	—
249	C₂²	—	38	1	no	—
250	C₂²	—	38	1	no	—
251	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
252	C₄	—	2	1	no	—
253	C₄	—	4	1	no	—
254	C₄	—	4	2	no	—
255	C₄	—	19	2	no	—
256	C₄	—	38	1	no	—
257	C₄	—	38	1	no	—
258	C₄	—	38	2	no	—
259	C₄	—	76	2	no	—
260	C₄	—	76	1	no	—
261	C₄	#10597362	1	2	yes	—
262	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
263	C₄	#41×D₁₉	1	1	yes	characteristic
264	C₂	—	4	2	no	—
265	C₂	—	38	2	no	—
266	C₂	C₂²⋊Q₈×D₁₉	1	1	yes	characteristic
267	C₂	C₂×#10597362	1	1	yes	characteristic
268	C₂	#11927340	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927099

C₂

yes

maximal, characteristic, complemented

C₄×#64543

C₂

yes

maximal, characteristic

#11926854

C₂

yes

maximal, complemented

#11926846

C₂

yes

maximal, complemented

#11926836

C₂

yes

maximal, characteristic, complemented

#11926830

C₂

yes

maximal, characteristic, complemented

#11926824

C₂

yes

maximal, characteristic, complemented

#11926579

C₂

yes

maximal, complemented

C₄⋊C₈×D₁₉

C₂

yes

maximal, characteristic, complemented

#11926537

C₂

yes

maximal

C₁₉×#476

C₂

yes

maximal, characteristic, complemented

C₂×#64543

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₄×D₄×C₁₉

C₂²

yes

characteristic

#10597392

—

Q₈×Dic₁₉

—

D₄×Dic₁₉

C₂²

yes

characteristic

C₄×C₂²⋊D₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₈×D₁₉

C₂²

yes

—

#10597343

—

#10597338

C₂²

yes

—

#10597338

C₂²

yes

characteristic

#10597336

C₂²

yes

—

#10597333

—

#10597333

C₂²

yes

characteristic

(C₂²⋊D₁₉)⋊C₄

—

#10597323

—

C₄²×D₁₉

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×#106

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#102

C₂²

yes

—

#10597289

C₂²

yes

—

#10597274

C₂²

yes

—

#10597273

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

#10597267

C₂²

yes

—

#10597264

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

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

#64543

—

#64543

Q₈

yes

complemented

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

C₂³

yes

characteristic

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

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

C₈×D₁₉

—

C₂³×C₁₉

—

C₂²×D₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

C₂×Q₈

yes

—

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×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

100

C₂×Dic₁₉

C₂×D₄

yes

characteristic

101

C₄×D₁₉

—

102

C₄×D₁₉

—

103

C₄×D₁₉

C₂×Q₈

yes

—

104

C₄×D₁₉

#41

yes

—

105

Dic₃₈

—

106

Dic₃₈

—

107

Dic₃₈

C₂×Q₈

yes

—

108

C₈×C₁₉

—

109

C₁₉⋊C₈

—

110

#3076

—

maximal, Sylow

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

C₂²×D₄

yes

characteristic

115

C₂×D₁₉

—

116

C₂×D₁₉

—

117

C₂×D₁₉

C₂²⋊Q₈

yes

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

#135

yes

—

122

C₄×C₁₉

C₂²×Q₈

yes

characteristic

123

C₄×C₁₉

C₂×#41

yes

characteristic

124

Dic₁₉

—

125

Dic₁₉

—

126

Dic₁₉

—

127

Dic₁₉

—

128

Dic₁₉

—

129

Dic₁₉

C₂²⋊Q₈

yes

—

130

#533

—

131

C₄×#41

—

132

#479

—

133

#478

—

134

#477

—

135

#476

D₁₉

yes

characteristic, complemented

136

#475

—

137

#474

—

138

#427

—

139

C₂×C₄⋊C₈

—

140

#416

—

141

C₂×C₁₉

—

142

C₂×C₁₉

C₂×C₂²⋊Q₈

yes

characteristic

143

C₂×C₁₉

C₂×#135

yes

characteristic

144

C₂×C₁₉

#575

yes

characteristic

145

D₁₉

—

146

C₂×#41

—

147

C₂²×C₈

—

148

C₄⋊Q₈

—

149

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

150

#125

—

151

C₂²⋊Q₈

—

152

C₂²⋊Q₈

—

153

C₄×Q₈

—

154

C₄×Q₈

—

155

C₄×Q₈

—

156

C₄×Q₈

—

157

C₄×D₄

—

158

C₄×D₄

—

159

C₄×D₄

—

160

C₄×D₄

C₂×D₁₉

yes

characteristic

161

#117

—

162

#117

—

163

#117

—

164

C₂×C₄²

—

165

C₂×C₄²

—

166

#107

—

167

#107

—

168

#106

—

169

#106

C₂×D₁₉

yes

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

C₂×D₁₉

yes

characteristic

173

#103

—

174

#103

—

175

#102

—

176

#102

C₂×D₁₉

yes

—

177

C₁₉

#3076

yes

characteristic, complemented, Sylow

178

#41

—

179

#41

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×D₄

—

184

C₂×D₄

C₂²×D₁₉

yes

characteristic

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

C₂²×D₁₉

yes

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

C₂²×D₁₉

yes

—

203

C₄⋊C₄

C₂²×D₁₉

yes

characteristic

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₂²⋊C₄

—

208

C₄²

—

209

C₄²

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

215

C₄²

C₂²×D₁₉

yes

characteristic

216

C₂³

—

217

C₂³

—

218

Q₈

—

219

Q₈

—

220

Q₈

—

221

Q₈

—

222

D₄

—

223

D₄

—

224

D₄

Q₈×D₁₉

yes

—

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

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

D₄×D₁₉

yes

characteristic

241

C₂×C₄

D₄×D₁₉

yes

characteristic

242

C₂×C₄

C₂³×D₁₉

yes

characteristic

243

C₈

—

244

C₈

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

C₂×D₄×D₁₉

yes

characteristic

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

#10597362

yes

—

262

C₄

C₂×Q₈×D₁₉

yes

characteristic

263

C₄

#41×D₁₉

yes

characteristic

264

C₂

—

265

C₂

—

266

C₂

C₂²⋊Q₈×D₁₉

yes

characteristic

267

C₂

C₂×#10597362

yes

characteristic

268

C₂

#11927340

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#476	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂×#64543	C₂²
hypercenter	#476	D₁₉
hypocenter	C₁₉	#3076
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #476

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#476

C₂

socle

C₂²×C₁₉

C₂²×D₄

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #476

N	H ≅ G/N	type
1. #11927099	C₂	semidirect
3. #11926854	C₂	semidirect
4. #11926846	C₂	semidirect
5. #11926836	C₂	semidirect
6. #11926830	C₂	semidirect
7. #11926824	C₂	semidirect
8. #11926579	C₂	semidirect
9. C₄⋊C₈×D₁₉	C₂	semidirect
11. C₁₉×#476	C₂	semidirect
50. #64543	Q₈	semidirect
135. #476	D₁₉	semidirect
177. C₁₉	#3076	semidirect

H ≅ G/N

type

1. #11927099

C₂

semidirect

3. #11926854

C₂

semidirect

4. #11926846

C₂

semidirect

5. #11926836

C₂

semidirect

6. #11926830

C₂

semidirect

7. #11926824

C₂

semidirect

8. #11926579

C₂

semidirect

9. C₄⋊C₈×D₁₉

C₂

semidirect

11. C₁₉×#476

C₂

semidirect

50. #64543

Q₈

semidirect

135. #476

D₁₉

semidirect

177. C₁₉

#3076

semidirect

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

subgroup	index
#11927099	2
C₄×#64543	2
#11926854	2
#11926846	2
#11926836	2
#11926830	2
#11926824	2
#11926579	2
C₄⋊C₈×D₁₉	2
#11926537	2
C₁₉×#476	2
#3076	19

subgroup

index

C₄⋊C₈×D₁₉

C₁₉×#476

Subgroups — #14573424

Conjugacy classes of subgroups

Complements

Maximal subgroups