Group #18081478 — subgroups

Subgroups — #18081478

Order 4864.

434 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 119 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	C₂×C₄×Dic₇₆	C₂	1	1	yes	maximal, characteristic
2	#14562031	C₂	1	2	yes	maximal
3	#14561958	C₂	1	2	yes	maximal
4	#14561927	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₇₆	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₃₈	C₂²	1	2	yes	—
8	C₄×Dic₇₆	—	2	1	no	—
9	C₄×Dic₇₆	—	2	1	no	—
10	C₄×Dic₇₆	—	2	1	no	—
11	C₄×Dic₇₆	—	2	1	no	—
12	#11926597	C₂²	1	1	yes	characteristic
13	#11926597	C₂²	1	1	yes	characteristic
14	C₂×#10597275	C₄	1	1	yes	characteristic
15	C₂×#10597273	C₄	1	2	yes	—
16	#11926276	—	2	4	no	—
17	#11926269	—	2	4	no	—
18	#11926266	—	2	1	no	—
19	#11926266	—	2	1	no	—
20	C₁₉×#431	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#335	—	2	1	no	—
23	C₁₉×#334	—	2	1	no	—
24	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
29	C₂×Dic₁₉⋊C₄	—	2	2	no	—
30	C₂×C₄×Dic₁₉	—	2	2	no	—
31	C₂×Dic₇₆	—	2	4	no	—
32	C₂×Dic₇₆	—	2	1	no	—
33	C₂×Dic₇₆	—	2	1	no	—
34	C₄×Dic₃₈	—	2	2	no	—
35	C₄×Dic₃₈	—	2	2	no	—
36	C₄×Dic₃₈	—	2	2	no	—
37	C₄×Dic₃₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₁₉×C₂²⋊C₈	—	2	2	no	—
40	C₄×C₈×C₁₉	—	2	2	no	—
41	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
45	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
46	C₂²⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
47	#10597275	—	2	1	no	—
48	#10597275	—	2	1	no	—
49	#10597273	—	2	2	no	—
50	#10597273	—	2	2	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
52	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
53	C₄×C₁₉⋊C₈	—	2	1	no	—
54	C₄×C₁₉⋊C₈	—	2	1	no	—
55	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
58	C₂²×Dic₁₉	—	2	2	no	—
59	C₂²×Dic₁₉	—	2	2	no	—
60	C₂×Dic₃₈	—	2	2	no	—
61	C₂×Dic₃₈	—	2	2	no	—
62	C₂×Dic₃₈	—	2	2	no	—
63	C₂×Dic₃₈	—	2	2	no	—
64	C₂×Dic₃₈	—	2	2	no	—
65	C₂×Dic₃₈	M₁₆	1	4	yes	—
66	C₂×C₈×C₁₉	—	2	2	no	—
67	C₂×C₈×C₁₉	—	2	2	no	—
68	C₂×C₈×C₁₉	—	4	2	no	—
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₁₉	#41	1	1	yes	characteristic
77	C₄⋊Dic₁₉	—	2	2	no	—
78	C₄⋊Dic₁₉	—	2	2	no	—
79	Dic₁₉⋊C₄	—	4	2	no	—
80	Dic₁₉⋊C₄	—	4	2	no	—
81	C₄×Dic₁₉	—	4	2	no	—
82	C₄×Dic₁₉	—	4	2	no	—
83	C₂×C₁₉⋊C₈	—	2	2	no	—
84	C₂×C₁₉⋊C₈	—	2	2	no	—
85	Dic₇₆	—	2	4	no	—
86	Dic₇₆	—	2	4	no	—
87	#9671	—	19	1	no	maximal, Sylow
88	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
98	C₂×C₄×C₁₉	#131	1	2	yes	—
99	C₂×Dic₁₉	—	2	4	no	—
100	C₂×Dic₁₉	—	4	2	no	—
101	C₂×Dic₁₉	—	4	2	no	—
102	C₂×Dic₁₉	—	4	2	no	—
103	C₂×Dic₁₉	—	8	2	no	—
104	Dic₃₈	—	2	4	no	—
105	Dic₃₈	—	2	4	no	—
106	Dic₃₈	—	4	2	no	—
107	Dic₃₈	—	4	2	no	—
108	C₈×C₁₉	—	2	1	no	—
109	C₈×C₁₉	—	2	1	no	—
110	C₈×C₁₉	—	2	1	no	—
111	C₈×C₁₉	—	2	1	no	—
112	C₈×C₁₉	—	8	2	no	—
113	C₁₉⋊C₈	—	4	2	no	—
114	C₁₉⋊C₈	—	4	2	no	—
115	C₂×C₄×Q₁₆	—	19	1	no	—
116	#1564	D₁₉	1	1	yes	characteristic
117	#1479	—	19	2	no	—
118	#1461	—	19	2	no	—
119	#1452	—	19	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	#390	1	1	yes	characteristic
123	C₂²×C₁₉	#435	1	2	yes	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	#407	1	1	yes	characteristic
128	C₄×C₁₉	#408	1	1	yes	characteristic
129	C₄×C₁₉	#435	1	2	yes	—
130	C₄×C₁₉	#473	1	2	yes	—
131	Dic₁₉	—	4	4	no	—
132	Dic₁₉	—	8	2	no	—
133	C₂²×Q₁₆	—	19	1	no	—
134	C₂×C₄×Q₈	—	19	2	no	—
135	C₄×Q₁₆	—	38	1	no	—
136	C₄×Q₁₆	—	38	1	no	—
137	C₄×Q₁₆	—	38	1	no	—
138	C₄×Q₁₆	—	38	1	no	—
139	#431	—	19	1	no	—
140	#431	—	19	1	no	—
141	#431	C₂×D₁₉	1	2	yes	—
142	C₂×#107	—	19	1	no	—
143	C₂×#103	—	19	2	no	—
144	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
145	#335	—	2	1	no	—
146	#334	—	2	1	no	—
147	Q₈⋊C₈	—	38	4	no	—
148	#324	—	38	4	no	—
149	#322	—	38	1	no	—
150	#322	—	38	1	no	—
151	C₂×C₁₉	—	2	2	no	—
152	C₂×C₁₉	#1955	1	1	yes	characteristic
153	C₂×C₁₉	#1976	1	1	yes	characteristic
154	C₂×C₁₉	#1979	1	1	yes	characteristic
155	C₂²×Q₈	—	19	2	no	—
156	C₂×Q₁₆	—	38	4	no	—
157	C₂×Q₁₆	—	38	1	no	—
158	C₂×Q₁₆	—	38	1	no	—
159	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
160	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
161	C₄×Q₈	—	38	2	no	—
162	C₄×Q₈	—	38	2	no	—
163	C₄×Q₈	—	38	2	no	—
164	C₄×Q₈	—	38	2	no	—
165	C₂×C₄⋊C₄	—	19	2	no	—
166	C₂×C₄⋊C₄	—	38	2	no	—
167	C₂×C₄²	—	38	2	no	—
168	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
169	#107	—	38	1	no	—
170	#107	—	38	1	no	—
171	C₄⋊C₈	—	2	2	no	—
172	C₄⋊C₈	—	19	2	no	—
173	C₄⋊C₈	—	38	1	no	—
174	#103	—	38	2	no	—
175	#103	—	38	2	no	—
176	C₂²⋊C₈	—	2	2	no	—
177	C₂²⋊C₈	—	19	2	no	—
178	C₂²⋊C₈	—	38	1	no	—
179	C₄×C₈	—	2	2	no	—
180	C₄×C₈	—	38	1	no	—
181	C₄×C₈	—	38	1	no	—
182	C₄×C₈	D₇₆	1	1	yes	characteristic
183	C₄×C₈	D₇₆	1	1	yes	characteristic
184	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
185	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
186	C₁₉	#9671	1	1	yes	characteristic, complemented, Sylow
187	C₂×Q₈	—	19	4	no	—
188	C₂×Q₈	—	38	2	no	—
189	C₂×Q₈	—	38	2	no	—
190	C₂×Q₈	—	38	2	no	—
191	C₂×Q₈	—	38	2	no	—
192	C₂×Q₈	—	38	2	no	—
193	C₂²×C₄	—	38	2	no	—
194	C₂²×C₄	—	38	2	no	—
195	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
196	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
197	C₂²×C₄	#64545	1	1	yes	characteristic
198	Q₁₆	—	38	4	no	—
199	Q₁₆	—	38	4	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	4	2	no	—
203	C₂×C₈	—	38	2	no	—
204	C₂×C₈	—	38	2	no	—
205	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
206	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
207	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
208	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
209	C₄⋊C₄	—	38	2	no	—
210	C₄⋊C₄	—	38	2	no	—
211	C₄⋊C₄	—	76	2	no	—
212	C₄⋊C₄	—	76	2	no	—
213	C₄²	—	76	2	no	—
214	C₄²	—	76	2	no	—
215	C₄²	C₂×D₇₆	1	1	yes	characteristic
216	C₄²	D₄×D₁₉	1	1	yes	characteristic
217	C₄²	#64545	1	1	yes	characteristic
218	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
219	C₂³	#10597339	1	1	yes	characteristic
220	Q₈	—	38	4	no	—
221	Q₈	—	38	4	no	—
222	Q₈	—	76	2	no	—
223	Q₈	—	76	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	4	1	no	—
226	C₂×C₄	—	38	4	no	—
227	C₂×C₄	—	76	2	no	—
228	C₂×C₄	—	76	2	no	—
229	C₂×C₄	—	76	2	no	—
230	C₂×C₄	—	152	2	no	—
231	C₂×C₄	#10597339	1	1	yes	characteristic
232	C₂×C₄	#10597341	1	1	yes	characteristic
233	C₂×C₄	#10597341	1	1	yes	characteristic
234	C₂×C₄	#10597347	1	2	yes	—
235	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
236	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
237	C₂×C₄	#10597386	1	1	yes	characteristic
238	C₂×C₄	#10597393	1	1	yes	characteristic
239	C₈	—	2	1	no	—
240	C₈	—	2	1	no	—
241	C₈	—	2	1	no	—
242	C₈	—	2	1	no	—
243	C₈	—	8	2	no	—
244	C₈	—	76	2	no	—
245	C₈	—	76	2	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	2	1	no	—
248	C₂²	#11926445	1	1	yes	characteristic
249	C₂²	#11926614	1	2	yes	—
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	1	no	—
253	C₄	—	76	4	no	—
254	C₄	—	152	2	no	—
255	C₄	#11926507	1	1	yes	characteristic
256	C₄	#11926510	1	1	yes	characteristic
257	C₄	#11926614	1	2	yes	—
258	C₄	#11926820	1	2	yes	—
259	C₂	—	2	2	no	—
260	C₂	#14564432	1	1	yes	characteristic
261	C₂	#14564531	1	1	yes	characteristic
262	C₂	#14564548	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₇₆

C₂

yes

maximal, characteristic

#14562031

C₂

yes

maximal

#14561958

C₂

yes

maximal

#14561927

C₂

yes

maximal, characteristic

C₁₉×#1564

C₂

yes

maximal, characteristic

C₂²×Dic₇₆

C₄

yes

characteristic

C₂×C₄×Dic₃₈

C₂²

yes

—

C₄×Dic₇₆

—

C₄×Dic₇₆

—

C₄×Dic₇₆

—

C₄×Dic₇₆

—

#11926597

C₂²

yes

characteristic

#11926597

C₂²

yes

characteristic

C₂×#10597275

C₄

yes

characteristic

C₂×#10597273

C₄

yes

—

—

—

—

—

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₂²×Dic₃₈

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

D₄

yes

—

—

—

—

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

M₁₆

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

Dic₇₆

—

#9671

—

maximal, Sylow

C₂³×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

Dic₃₈

—

105

Dic₃₈

—

106

Dic₃₈

—

107

Dic₃₈

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

C₈×C₁₉

—

112

C₈×C₁₉

—

113

C₁₉⋊C₈

—

114

C₁₉⋊C₈

—

115

C₂×C₄×Q₁₆

—

116

#1564

D₁₉

yes

characteristic

117

#1479

—

118

#1461

—

119

#1452

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

#390

yes

characteristic

123

C₂²×C₁₉

#435

yes

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

#407

yes

characteristic

128

C₄×C₁₉

#408

yes

characteristic

129

C₄×C₁₉

#435

yes

—

130

C₄×C₁₉

#473

yes

—

131

Dic₁₉

—

132

Dic₁₉

—

133

C₂²×Q₁₆

—

134

C₂×C₄×Q₈

—

135

C₄×Q₁₆

—

136

C₄×Q₁₆

—

137

C₄×Q₁₆

—

138

C₄×Q₁₆

—

139

#431

—

140

#431

—

141

#431

C₂×D₁₉

yes

—

142

C₂×#107

—

143

C₂×#103

—

144

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

145

#335

—

146

#334

—

147

Q₈⋊C₈

—

148

#324

—

149

#322

—

150

#322

—

151

C₂×C₁₉

—

152

C₂×C₁₉

#1955

yes

characteristic

153

C₂×C₁₉

#1976

yes

characteristic

154

C₂×C₁₉

#1979

yes

characteristic

155

C₂²×Q₈

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂×Q₁₆

—

159

C₂²×C₈

C₄×D₁₉

yes

characteristic

160

C₂²×C₈

C₄×D₁₉

yes

characteristic

161

C₄×Q₈

—

162

C₄×Q₈

—

163

C₄×Q₈

—

164

C₄×Q₈

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄²

—

168

C₂×C₄²

C₂²×D₁₉

yes

characteristic

169

#107

—

170

#107

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

#103

—

175

#103

—

176

C₂²⋊C₈

—

177

C₂²⋊C₈

—

178

C₂²⋊C₈

—

179

C₄×C₈

—

180

C₄×C₈

—

181

C₄×C₈

—

182

C₄×C₈

D₇₆

yes

characteristic

183

C₄×C₈

D₇₆

yes

characteristic

184

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

185

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

186

C₁₉

#9671

yes

characteristic, complemented, Sylow

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

196

C₂²×C₄

D₄×D₁₉

yes

characteristic

197

C₂²×C₄

#64545

yes

characteristic

198

Q₁₆

—

199

Q₁₆

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

206

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

207

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

208

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄²

—

214

C₄²

—

215

C₄²

C₂×D₇₆

yes

characteristic

216

C₄²

D₄×D₁₉

yes

characteristic

217

C₄²

#64545

yes

characteristic

218

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

219

C₂³

#10597339

yes

characteristic

220

Q₈

—

221

Q₈

—

222

Q₈

—

223

Q₈

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

152

—

231

C₂×C₄

#10597339

yes

characteristic

232

C₂×C₄

#10597341

yes

characteristic

233

C₂×C₄

#10597341

yes

characteristic

234

C₂×C₄

#10597347

yes

—

235

C₂×C₄

M₁₆×D₁₉

yes

—

236

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

237

C₂×C₄

#10597386

yes

characteristic

238

C₂×C₄

#10597393

yes

characteristic

239

C₈

—

240

C₈

—

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

245

C₈

—

246

C₂²

—

247

C₂²

—

248

C₂²

#11926445

yes

characteristic

249

C₂²

#11926614

yes

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

152

—

255

C₄

#11926507

yes

characteristic

256

C₄

#11926510

yes

characteristic

257

C₄

#11926614

yes

—

258

C₄

#11926820

yes

—

259

C₂

—

260

C₂

#14564432

yes

characteristic

261

C₂

#14564531

yes

characteristic

262

C₂

#14564548

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597341
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1564	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	C₄×D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1564	D₁₉
hypocenter	C₁₉	#9671
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂×C₄

#10597341

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1564

C₂

socle

C₂²×C₁₉

#390

prime radical

C₂³×C₁₉

C₄×D₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

N	H ≅ G/N	type
186. C₁₉	#9671	semidirect

H ≅ G/N

type

186. C₁₉

#9671

semidirect

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

subgroup	index
C₂×C₄×Dic₇₆	2
#14562031	2
#14561958	2
#14561927	2
C₁₉×#1564	2
#9671	19

subgroup

index

C₂×C₄×Dic₇₆

C₁₉×#1564

Subgroups — #18081478

Conjugacy classes of subgroups

Complements

Maximal subgroups