Group #18081655 — subgroups

Subgroups — #18081655

Order 4864.

590 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 143 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	#14571992	C₂	1	1	yes	maximal, characteristic
2	#14563488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11926291	C₂	1	2	yes	maximal, complemented
4	C₂×#11926287	C₂	1	2	yes	maximal
5	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597320	C₂²	1	1	yes	characteristic
8	C₂×#10597321	—	2	2	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
10	C₂×#10597260	—	2	1	no	—
11	#11926446	—	2	1	no	—
12	#11926446	—	2	1	no	—
13	#11926446	C₄	1	4	yes	—
14	#11926299	—	2	1	no	—
15	#11926291	—	2	4	no	—
16	#11926287	—	2	4	no	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₄³×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#336	—	2	2	no	—
20	C₂²×D₇₆	—	2	1	no	—
21	C₂²×D₇₆	—	2	1	no	—
22	C₂²×D₇₆	C₂×C₄	1	2	yes	—
23	C₂²×Dic₃₈	—	2	1	no	—
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	2	yes	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×(C₂×D₁₉)⋊C₄	—	2	4	no	—
31	C₂×(C₂×D₁₉)⋊C₄	—	2	4	no	—
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
34	C₂²×C₁₉⋊C₈	—	2	2	no	—
35	#10597321	—	4	8	no	—
36	#10597320	—	2	2	no	—
37	#10597320	—	2	2	no	—
38	#10597315	—	2	2	no	—
39	#10597315	—	2	2	no	—
40	C₁₉×C₄⋊C₈	—	2	2	no	—
41	C₁₉×C₄⋊C₈	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
44	#10597260	—	4	2	no	—
45	C₂³×D₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×Dic₁₉	—	2	2	no	—
52	C₂×D₇₆	—	2	4	no	—
53	C₂×D₇₆	—	4	4	no	—
54	C₂×D₇₆	—	4	2	no	—
55	C₂×D₇₆	—	4	1	no	—
56	C₂×D₇₆	—	4	1	no	—
57	C₂×D₇₆	—	4	2	no	—
58	C₂×D₇₆	—	4	1	no	—
59	C₂×D₇₆	—	4	4	no	—
60	C₂×D₇₆	—	4	1	no	—
61	C₂×Dic₃₈	—	4	1	no	—
62	C₂×Dic₃₈	—	4	1	no	—
63	C₂×Dic₃₈	—	4	4	no	—
64	C₂×C₈×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	—	4	4	no	—
66	C₄²×C₁₉	—	2	2	no	—
67	C₄²×C₁₉	—	2	1	no	—
68	C₄²×C₁₉	—	2	4	no	—
69	C₄²×C₁₉	—	2	1	no	—
70	C₄²×C₁₉	—	4	2	no	—
71	C₄²×C₁₉	C₂×D₄	1	2	yes	—
72	C₄²×C₁₉	#41	1	2	yes	—
73	(C₂×D₁₉)⋊C₄	—	4	8	no	—
74	(C₂×D₁₉)⋊C₄	—	4	8	no	—
75	C₄⋊Dic₁₉	—	2	4	no	—
76	C₄⋊Dic₁₉	—	4	2	no	—
77	C₂×C₁₉⋊C₈	—	2	4	no	—
78	C₂×C₁₉⋊C₈	—	4	2	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	#9710	—	19	1	no	maximal, Sylow
81	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×D₁₉	—	4	2	no	—
83	C₂²×D₁₉	—	4	4	no	—
84	C₂²×D₁₉	—	4	2	no	—
85	C₂²×D₁₉	—	4	2	no	—
86	C₂²×D₁₉	—	4	4	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
95	C₂×C₄×C₁₉	#121	1	2	yes	—
96	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#135	1	2	yes	—
99	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
100	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
102	C₂×Dic₁₉	—	4	2	no	—
103	C₂×Dic₁₉	—	4	4	no	—
104	D₇₆	—	8	4	no	—
105	D₇₆	—	8	2	no	—
106	D₇₆	—	8	2	no	—
107	D₇₆	—	8	2	no	—
108	D₇₆	—	8	2	no	—
109	Dic₃₈	—	8	2	no	—
110	Dic₃₈	—	8	2	no	—
111	C₈×C₁₉	—	8	2	no	—
112	C₁₉⋊C₈	—	4	4	no	—
113	#2858	—	19	1	no	—
114	#1831	D₁₉	1	1	yes	characteristic, complemented
115	#1767	—	19	1	no	—
116	C₂×#332	—	19	2	no	—
117	C₂×#331	—	19	2	no	—
118	C₂²×C₁₉	#390	1	1	yes	characteristic
119	C₂²×C₁₉	#413	1	2	yes	—
120	C₂²×C₁₉	#416	1	1	yes	characteristic
121	C₂²×C₁₉	#417	1	1	yes	characteristic
122	C₂²×C₁₉	#418	1	2	yes	—
123	C₂×D₁₉	—	8	4	no	—
124	C₂×D₁₉	—	8	4	no	—
125	C₂×D₁₉	—	8	2	no	—
126	C₂×D₁₉	—	8	2	no	—
127	C₂×D₁₉	—	8	2	no	—
128	C₄×C₁₉	—	2	2	no	—
129	C₄×C₁₉	—	4	2	no	—
130	C₄×C₁₉	—	4	2	no	—
131	C₄×C₁₉	#463	1	2	yes	—
132	C₄×C₁₉	#464	1	2	yes	—
133	C₄×C₁₉	#490	1	2	yes	—
134	C₄×C₁₉	#496	1	2	yes	—
135	Dic₁₉	—	8	2	no	—
136	C₂×C₄⋊Q₈	—	19	1	no	—
137	C₂×#127	—	19	1	no	—
138	C₂×#124	—	38	2	no	—
139	C₂×C₄⋊C₈	—	19	2	no	—
140	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
141	C₂×#97	—	38	1	no	—
142	#390	—	19	4	no	—
143	#390	—	38	1	no	—
144	#390	—	38	1	no	—
145	C₄³	C₂×D₁₉	1	1	yes	characteristic
146	#336	—	2	2	no	—
147	#336	—	38	1	no	—
148	#332	—	38	4	no	—
149	#331	—	38	4	no	—
150	C₂×C₁₉	#1553	1	2	yes	—
151	C₂×C₁₉	#1557	1	2	yes	—
152	C₂×C₁₉	#1961	1	1	yes	characteristic
153	C₂×C₁₉	#1967	1	1	yes	characteristic
154	C₂×C₁₉	#1983	1	1	yes	characteristic
155	D₁₉	—	16	2	no	—
156	C₂²×Q₈	—	38	1	no	—
157	C₂²×D₄	—	19	2	no	—
158	C₂²×D₄	—	38	1	no	—
159	C₂²×D₄	—	38	1	no	—
160	C₂²×C₈	—	2	2	no	—
161	C₂²×C₈	—	38	2	no	—
162	C₄⋊Q₈	—	38	2	no	—
163	C₄⋊Q₈	—	38	2	no	—
164	#127	—	38	2	no	—
165	#127	—	38	2	no	—
166	#124	—	76	8	no	—
167	C₂×C₄⋊C₄	—	19	2	no	—
168	C₂×C₄⋊C₄	—	38	1	no	—
169	C₂×C₂²⋊C₄	—	38	4	no	—
170	C₂×C₂²⋊C₄	—	38	4	no	—
171	C₂×C₄²	C₄×D₁₉	1	2	yes	—
172	C₂×C₄²	D₇₆	1	1	yes	characteristic
173	C₂×C₄²	D₇₆	1	1	yes	characteristic
174	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
175	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
176	C₄⋊C₈	—	2	2	no	—
177	C₄⋊C₈	—	2	2	no	—
178	C₄⋊C₈	—	19	4	no	—
179	C₄⋊C₈	—	38	2	no	—
180	#97	—	76	2	no	—
181	C₁₉	#9710	1	1	yes	characteristic, complemented, Sylow
182	C₂⁴	—	38	2	no	—
183	C₂×Q₈	—	76	1	no	—
184	C₂×Q₈	—	76	1	no	—
185	C₂×Q₈	—	76	4	no	—
186	C₂×D₄	—	38	4	no	—
187	C₂×D₄	—	76	4	no	—
188	C₂×D₄	—	76	1	no	—
189	C₂×D₄	—	76	1	no	—
190	C₂×D₄	—	76	4	no	—
191	C₂×D₄	—	76	2	no	—
192	C₂×D₄	—	76	2	no	—
193	C₂×D₄	—	76	1	no	—
194	C₂×D₄	—	76	1	no	—
195	C₂²×C₄	—	38	2	no	—
196	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
197	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
198	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
199	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
200	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
201	C₂×C₈	—	4	2	no	—
202	C₂×C₈	—	4	4	no	—
203	C₂×C₈	—	38	4	no	—
204	C₂×C₈	—	76	2	no	—
205	C₂×C₈	—	76	2	no	—
206	C₄⋊C₄	—	38	4	no	—
207	C₄⋊C₄	—	76	2	no	—
208	C₂²⋊C₄	—	76	8	no	—
209	C₂²⋊C₄	—	76	8	no	—
210	C₄²	—	2	4	no	—
211	C₄²	—	2	2	no	—
212	C₄²	—	2	1	no	—
213	C₄²	—	2	1	no	—
214	C₄²	—	4	2	no	—
215	C₄²	D₄×D₁₉	1	2	yes	—
216	C₄²	#64545	1	2	yes	—
217	C₂³	—	76	2	no	—
218	C₂³	—	76	2	no	—
219	C₂³	—	76	4	no	—
220	C₂³	—	76	2	no	—
221	C₂³	—	76	4	no	—
222	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
223	Q₈	—	152	2	no	—
224	Q₈	—	152	2	no	—
225	D₄	—	152	4	no	—
226	D₄	—	152	2	no	—
227	D₄	—	152	2	no	—
228	D₄	—	152	2	no	—
229	D₄	—	152	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	76	4	no	—
238	C₂×C₄	—	76	2	no	—
239	C₂×C₄	#10597339	1	2	yes	—
240	C₂×C₄	#10597341	1	2	yes	—
241	C₂×C₄	#10597350	1	2	yes	—
242	C₂×C₄	#10597354	1	1	yes	characteristic
243	C₂×C₄	#10597355	1	1	yes	characteristic
244	C₂×C₄	#10597386	1	1	yes	characteristic
245	C₂×C₄	#10597393	1	1	yes	characteristic
246	C₂×C₄	#10597395	1	4	yes	—
247	C₈	—	8	2	no	—
248	C₈	—	76	4	no	—
249	C₂²	—	152	4	no	—
250	C₂²	—	152	4	no	—
251	C₂²	—	152	2	no	—
252	C₂²	—	152	2	no	—
253	C₂²	—	152	2	no	—
254	C₂²	#11926445	1	1	yes	characteristic
255	C₂²	#11926526	1	2	yes	—
256	C₂²	#11926541	1	1	yes	characteristic
257	C₂²	#11926546	1	1	yes	characteristic
258	C₂²	#11926548	1	2	yes	—
259	C₄	—	2	2	no	—
260	C₄	—	4	2	no	—
261	C₄	—	4	2	no	—
262	C₄	—	152	2	no	—
263	C₄	#11926760	1	2	yes	—
264	C₄	#11926767	1	2	yes	—
265	C₄	#11926910	1	2	yes	—
266	C₄	#11926934	1	2	yes	—
267	C₂	—	304	2	no	—
268	C₂	#14562338	1	2	yes	—
269	C₂	#14562358	1	2	yes	—
270	C₂	#14564458	1	1	yes	characteristic
271	C₂	#14564482	1	1	yes	characteristic
272	C₂	#14564565	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14571992

C₂

yes

maximal, characteristic

#14563488

C₂

yes

maximal, characteristic, complemented

C₂×#11926291

C₂

yes

maximal, complemented

C₂×#11926287

C₂

yes

maximal

C₁₉×#1831

C₂

yes

maximal, characteristic, complemented

C₂×#10597315

C₂²

yes

characteristic

C₂×#10597320

C₂²

yes

characteristic

C₂×#10597321

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

—

—

—

C₄

yes

—

#11926299

—

#11926291

—

#11926287

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×D₇₆

C₂×C₄

yes

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

—

—

—

—

—

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

C₂³×D₁₉

—

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

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9710

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

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

—

100

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

101

C₂×C₄×C₁₉

#137

yes

characteristic

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

D₇₆

—

105

D₇₆

—

106

D₇₆

—

107

D₇₆

—

108

D₇₆

—

109

Dic₃₈

—

110

Dic₃₈

—

111

C₈×C₁₉

—

112

C₁₉⋊C₈

—

113

#2858

—

114

#1831

D₁₉

yes

characteristic, complemented

115

#1767

—

116

C₂×#332

—

117

C₂×#331

—

118

C₂²×C₁₉

#390

yes

characteristic

119

C₂²×C₁₉

#413

yes

—

120

C₂²×C₁₉

#416

yes

characteristic

121

C₂²×C₁₉

#417

yes

characteristic

122

C₂²×C₁₉

#418

yes

—

123

C₂×D₁₉

—

124

C₂×D₁₉

—

125

C₂×D₁₉

—

126

C₂×D₁₉

—

127

C₂×D₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

#463

yes

—

132

C₄×C₁₉

#464

yes

—

133

C₄×C₁₉

#490

yes

—

134

C₄×C₁₉

#496

yes

—

135

Dic₁₉

—

136

C₂×C₄⋊Q₈

—

137

C₂×#127

—

138

C₂×#124

—

139

C₂×C₄⋊C₈

—

140

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

141

C₂×#97

—

142

#390

—

143

#390

—

144

#390

—

145

C₄³

C₂×D₁₉

yes

characteristic

146

#336

—

147

#336

—

148

#332

—

149

#331

—

150

C₂×C₁₉

#1553

yes

—

151

C₂×C₁₉

#1557

yes

—

152

C₂×C₁₉

#1961

yes

characteristic

153

C₂×C₁₉

#1967

yes

characteristic

154

C₂×C₁₉

#1983

yes

characteristic

155

D₁₉

—

156

C₂²×Q₈

—

157

C₂²×D₄

—

158

C₂²×D₄

—

159

C₂²×D₄

—

160

C₂²×C₈

—

161

C₂²×C₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

—

164

#127

—

165

#127

—

166

#124

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₂²⋊C₄

—

170

C₂×C₂²⋊C₄

—

171

C₂×C₄²

C₄×D₁₉

yes

—

172

C₂×C₄²

D₇₆

yes

characteristic

173

C₂×C₄²

D₇₆

yes

characteristic

174

C₂×C₄²

C₂²⋊D₁₉

yes

—

175

C₂×C₄²

C₂²×D₁₉

yes

characteristic

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

#97

—

181

C₁₉

#9710

yes

characteristic, complemented, Sylow

182

C₂⁴

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂²×C₄

—

196

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

197

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

198

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

199

C₂²×C₄

C₂×D₇₆

yes

characteristic

200

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₂²⋊C₄

—

209

C₂²⋊C₄

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

215

C₄²

D₄×D₁₉

yes

—

216

C₄²

#64545

yes

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

223

Q₈

—

152

—

224

Q₈

—

152

—

225

D₄

—

152

—

226

D₄

—

152

—

227

D₄

—

152

—

228

D₄

—

152

—

229

D₄

—

152

—

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

#10597339

yes

—

240

C₂×C₄

#10597341

yes

—

241

C₂×C₄

#10597350

yes

—

242

C₂×C₄

#10597354

yes

characteristic

243

C₂×C₄

#10597355

yes

characteristic

244

C₂×C₄

#10597386

yes

characteristic

245

C₂×C₄

#10597393

yes

characteristic

246

C₂×C₄

#10597395

yes

—

247

C₈

—

248

C₈

—

249

C₂²

—

152

—

250

C₂²

—

152

—

251

C₂²

—

152

—

252

C₂²

—

152

—

253

C₂²

—

152

—

254

C₂²

#11926445

yes

characteristic

255

C₂²

#11926526

yes

—

256

C₂²

#11926541

yes

characteristic

257

C₂²

#11926546

yes

characteristic

258

C₂²

#11926548

yes

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

152

—

263

C₄

#11926760

yes

—

264

C₄

#11926767

yes

—

265

C₄

#11926910

yes

—

266

C₄

#11926934

yes

—

267

C₂

—

304

—

268

C₂

#14562338

yes

—

269

C₂

#14562358

yes

—

270

C₂

#14564458

yes

characteristic

271

C₂

#14564482

yes

characteristic

272

C₂

#14564565

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1831	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×#10597320	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1831	D₁₉
hypocenter	C₁₉	#9710
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1831

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂×#10597320

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

N	H ≅ G/N	type
2. #14563488	C₂	semidirect
3. C₂×#11926291	C₂	semidirect
5. C₁₉×#1831	C₂	semidirect
114. #1831	D₁₉	semidirect
181. C₁₉	#9710	semidirect

H ≅ G/N

type

2. #14563488

C₂

semidirect

3. C₂×#11926291

C₂

semidirect

5. C₁₉×#1831

C₂

semidirect

114. #1831

D₁₉

semidirect

181. C₁₉

#9710

semidirect

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

subgroup	index
#14571992	2
#14563488	2
C₂×#11926291	2
C₂×#11926287	2
C₁₉×#1831	2
#9710	19

subgroup

index

C₁₉×#1831

Subgroups — #18081655

Conjugacy classes of subgroups

Complements

Maximal subgroups