Group #18081991 — subgroups

Subgroups — #18081991

Order 4864.

398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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×#11926895	C₂	1	1	yes	maximal, characteristic
2	#14563773	C₂	1	1	yes	maximal, characteristic
3	#14562319	C₂	1	1	yes	maximal, characteristic
4	#14562315	C₂	1	1	yes	maximal, characteristic
5	#14562306	C₂	1	1	yes	maximal, characteristic
6	#14562306	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1450	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	C₂×#10597315	C₂²	1	1	yes	characteristic
10	#11926895	—	2	1	no	—
11	#11926895	—	2	1	no	—
12	#11926895	C₄	1	4	yes	—
13	#11926568	C₂²	1	1	yes	characteristic
14	#11926568	C₂²	1	1	yes	characteristic
15	C₂×#10597273	—	2	2	no	—
16	#11926309	—	2	2	no	—
17	#11926292	—	2	2	no	—
18	#11926291	—	2	2	no	—
19	#11926289	—	2	2	no	—
20	#11926289	—	2	2	no	—
21	C₁₉×#431	C₂²	1	1	yes	characteristic
22	C₁₉×#431	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#322	—	2	1	no	—
25	C₈²×C₁₉	—	2	1	no	—
26	C₂²×Dic₃₈	—	2	1	no	—
27	C₂²×Dic₃₈	—	2	1	no	—
28	C₂²×C₈×C₁₉	D₄	1	2	yes	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×C₄⋊Dic₁₉	—	2	1	no	—
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	C₂×C₄⋊Dic₁₉	—	2	1	no	—
34	C₂×#64520	—	2	1	no	—
35	C₂×#64520	—	2	1	no	—
36	#10597315	—	2	1	no	—
37	#10597315	—	2	1	no	—
38	#10597315	—	2	1	no	—
39	#10597315	—	2	1	no	—
40	#10597315	—	2	1	no	—
41	#10597315	—	2	1	no	—
42	#10597315	C₂×C₄	1	2	yes	—
43	#10597315	C₂×C₄	1	2	yes	—
44	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
45	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
46	C₁₉×C₂²⋊C₈	—	2	1	no	—
47	C₁₉×C₂²⋊C₈	—	2	1	no	—
48	C₄×C₈×C₁₉	—	2	1	no	—
49	C₄×C₈×C₁₉	—	2	1	no	—
50	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
51	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
52	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
53	#10597273	—	2	4	no	—
54	#10597273	—	2	4	no	—
55	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
56	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
62	C₂²×Dic₁₉	—	4	1	no	—
63	C₂²×Dic₁₉	—	4	1	no	—
64	C₂×Dic₃₈	—	2	2	no	—
65	C₂×Dic₃₈	—	2	2	no	—
66	C₂×Dic₃₈	—	4	2	no	—
67	C₂×Dic₃₈	—	4	2	no	—
68	C₂×Dic₃₈	—	4	1	no	—
69	C₂×Dic₃₈	—	4	1	no	—
70	C₂×Dic₃₈	—	8	2	no	—
71	C₂×C₈×C₁₉	—	2	2	no	—
72	C₂×C₈×C₁₉	—	2	2	no	—
73	C₂×C₈×C₁₉	—	2	2	no	—
74	C₂×C₈×C₁₉	—	2	2	no	—
75	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
76	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
77	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₄⋊Dic₁₉	—	2	2	no	—
82	C₄⋊Dic₁₉	—	2	2	no	—
83	C₄⋊Dic₁₉	—	2	2	no	—
84	C₄⋊Dic₁₉	—	2	2	no	—
85	C₄⋊Dic₁₉	—	4	1	no	—
86	C₄⋊Dic₁₉	—	4	1	no	—
87	C₄⋊Dic₁₉	—	4	1	no	—
88	C₄⋊Dic₁₉	—	4	1	no	—
89	#64520	—	4	2	no	—
90	#64520	—	4	2	no	—
91	C₂×C₁₉⋊C₈	—	4	1	no	—
92	C₂×C₁₉⋊C₈	—	4	1	no	—
93	#9770	—	19	1	no	maximal, Sylow
94	C₂³×C₁₉	#124	1	1	yes	characteristic
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#135	1	2	yes	—
104	C₂×C₄×C₁₉	#135	1	2	yes	—
105	C₂×Dic₁₉	—	4	2	no	—
106	C₂×Dic₁₉	—	4	2	no	—
107	C₂×Dic₁₉	—	8	2	no	—
108	C₂×Dic₁₉	—	8	2	no	—
109	Dic₃₈	—	4	4	no	—
110	Dic₃₈	—	8	2	no	—
111	Dic₃₈	—	8	1	no	—
112	Dic₃₈	—	8	1	no	—
113	Dic₃₈	—	8	2	no	—
114	C₈×C₁₉	—	2	2	no	—
115	C₈×C₁₉	—	2	2	no	—
116	C₈×C₁₉	—	4	2	no	—
117	C₈×C₁₉	—	4	2	no	—
118	C₁₉⋊C₈	—	8	1	no	—
119	C₁₉⋊C₈	—	8	1	no	—
120	C₂×#487	—	19	1	no	—
121	#1837	—	19	1	no	—
122	#1549	—	19	1	no	—
123	#1548	—	19	1	no	—
124	#1546	—	19	1	no	—
125	#1546	—	19	1	no	—
126	#1450	D₁₉	1	1	yes	characteristic
127	C₂²×C₁₉	—	2	1	no	—
128	C₂²×C₁₉	—	2	1	no	—
129	C₂²×C₁₉	#390	1	1	yes	characteristic
130	C₂²×C₁₉	#488	1	2	yes	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	#416	1	2	yes	—
134	C₄×C₁₉	#471	1	2	yes	—
135	C₄×C₁₉	#473	1	2	yes	—
136	C₄×C₁₉	#495	1	1	yes	characteristic
137	C₄×C₁₉	#495	1	1	yes	characteristic
138	Dic₁₉	—	8	2	no	—
139	Dic₁₉	—	8	2	no	—
140	C₂×C₄⋊Q₈	—	19	1	no	—
141	C₂×C₄⋊Q₈	—	19	1	no	—
142	#487	—	19	4	no	—
143	#487	—	38	1	no	—
144	#487	—	38	1	no	—
145	#431	C₂×D₁₉	1	1	yes	characteristic
146	#431	C₂×D₁₉	1	1	yes	characteristic
147	#423	—	19	1	no	—
148	#423	—	19	1	no	—
149	C₂×#103	—	38	2	no	—
150	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
151	#341	—	38	2	no	—
152	#333	—	38	2	no	—
153	#332	—	38	2	no	—
154	#332	—	38	2	no	—
155	#332	—	38	2	no	—
156	#322	—	2	1	no	—
157	C₈²	—	2	1	no	—
158	C₂×C₁₉	—	2	2	no	—
159	C₂×C₁₉	#1958	1	1	yes	characteristic
160	C₂×C₁₉	#1977	1	1	yes	characteristic
161	C₂×C₁₉	#1979	1	1	yes	characteristic
162	C₂²×Q₈	—	38	1	no	—
163	C₂²×Q₈	—	38	1	no	—
164	C₂×M₁₆	—	38	1	no	—
165	C₂×M₁₆	—	38	1	no	—
166	C₂²×C₈	D₇₆	1	2	yes	—
167	C₄⋊Q₈	—	19	2	no	—
168	C₄⋊Q₈	—	19	2	no	—
169	C₄⋊Q₈	—	38	1	no	—
170	C₄⋊Q₈	—	38	1	no	—
171	C₄⋊Q₈	—	38	1	no	—
172	C₄⋊Q₈	—	38	1	no	—
173	C₄⋊Q₈	—	38	1	no	—
174	C₄⋊Q₈	—	38	1	no	—
175	C₂×C₄⋊C₄	—	38	1	no	—
176	C₂×C₄⋊C₄	—	38	1	no	—
177	C₂×C₄⋊C₄	—	38	1	no	—
178	C₂×C₄⋊C₄	—	38	1	no	—
179	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
180	C₄⋊C₈	—	38	1	no	—
181	C₄⋊C₈	—	38	1	no	—
182	C₄⋊C₈	—	38	1	no	—
183	C₄⋊C₈	—	38	1	no	—
184	C₄⋊C₈	D₇₆	1	2	yes	—
185	C₄⋊C₈	D₇₆	1	2	yes	—
186	#103	—	38	4	no	—
187	#103	—	38	4	no	—
188	C₂²⋊C₈	—	2	1	no	—
189	C₂²⋊C₈	—	2	1	no	—
190	C₄×C₈	—	2	1	no	—
191	C₄×C₈	—	2	1	no	—
192	C₄×C₈	C₄×D₁₉	1	2	yes	—
193	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
194	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
195	C₁₉	#9770	1	1	yes	characteristic, complemented, Sylow
196	C₂×Q₈	—	38	2	no	—
197	C₂×Q₈	—	38	2	no	—
198	C₂×Q₈	—	76	1	no	—
199	C₂×Q₈	—	76	1	no	—
200	C₂×Q₈	—	76	2	no	—
201	C₂×Q₈	—	76	2	no	—
202	C₂×Q₈	—	152	2	no	—
203	C₂²×C₄	—	76	1	no	—
204	C₂²×C₄	—	76	1	no	—
205	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
206	C₂²×C₄	#64541	1	1	yes	characteristic
207	C₂²×C₄	#64541	1	1	yes	characteristic
208	M₁₆	—	76	2	no	—
209	M₁₆	—	76	2	no	—
210	C₂×C₈	—	2	2	no	—
211	C₂×C₈	—	2	2	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	2	2	no	—
214	C₂×C₈	—	76	1	no	—
215	C₂×C₈	—	76	1	no	—
216	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
217	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
218	C₄⋊C₄	—	38	2	no	—
219	C₄⋊C₄	—	38	2	no	—
220	C₄⋊C₄	—	38	2	no	—
221	C₄⋊C₄	—	38	2	no	—
222	C₄⋊C₄	—	76	1	no	—
223	C₄⋊C₄	—	76	1	no	—
224	C₄⋊C₄	—	76	1	no	—
225	C₄⋊C₄	—	76	1	no	—
226	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
227	C₄²	C₂×D₇₆	1	1	yes	characteristic
228	C₄²	C₂×D₇₆	1	1	yes	characteristic
229	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
230	C₂³	#10597321	1	1	yes	characteristic
231	Q₈	—	76	4	no	—
232	Q₈	—	152	2	no	—
233	Q₈	—	152	2	no	—
234	Q₈	—	152	1	no	—
235	Q₈	—	152	1	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	76	2	no	—
239	C₂×C₄	—	76	2	no	—
240	C₂×C₄	—	152	2	no	—
241	C₂×C₄	—	152	2	no	—
242	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
243	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
244	C₂×C₄	#10597320	1	1	yes	characteristic
245	C₂×C₄	#10597350	1	2	yes	—
246	C₂×C₄	#10597350	1	2	yes	—
247	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
248	C₂×C₄	#10597376	1	1	yes	characteristic
249	C₂×C₄	#10597376	1	1	yes	characteristic
250	C₈	—	2	2	no	—
251	C₈	—	2	2	no	—
252	C₈	—	4	2	no	—
253	C₈	—	4	2	no	—
254	C₈	—	152	1	no	—
255	C₈	—	152	1	no	—
256	C₂²	—	2	1	no	—
257	C₂²	—	2	1	no	—
258	C₂²	#11926446	1	1	yes	characteristic
259	C₂²	#11926899	1	2	yes	—
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	152	2	no	—
263	C₄	—	152	2	no	—
264	C₄	#11926541	1	2	yes	—
265	C₄	#11926807	1	2	yes	—
266	C₄	#11926819	1	2	yes	—
267	C₄	#11926928	1	1	yes	characteristic
268	C₄	#11926928	1	1	yes	characteristic
269	C₂	—	2	2	no	—
270	C₂	#14564446	1	1	yes	characteristic
271	C₂	#14564538	1	1	yes	characteristic
272	C₂	#14564550	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926895

C₂

yes

maximal, characteristic

#14563773

C₂

yes

maximal, characteristic

#14562319

C₂

yes

maximal, characteristic

#14562315

C₂

yes

maximal, characteristic

#14562306

C₂

yes

maximal, characteristic

#14562306

C₂

yes

maximal, characteristic

C₁₉×#1450

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×#10597315

C₂²

yes

—

—

C₄

yes

—

#11926568

C₂²

yes

characteristic

#11926568

C₂²

yes

—

—

—

—

—

—

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₈²×C₁₉

—

C₂²×Dic₃₈

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

—

—

—

—

—

—

—

—

C₂×C₄

yes

—

#10597315

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597273

—

#10597273

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

100

C₂×C₄×C₁₉

#121

yes

characteristic

101

C₂×C₄×C₁₉

#121

yes

characteristic

102

C₂×C₄×C₁₉

#127

yes

characteristic

103

C₂×C₄×C₁₉

#135

yes

—

104

C₂×C₄×C₁₉

#135

yes

—

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

C₂×Dic₁₉

—

108

C₂×Dic₁₉

—

109

Dic₃₈

—

110

Dic₃₈

—

111

Dic₃₈

—

112

Dic₃₈

—

113

Dic₃₈

—

114

C₈×C₁₉

—

115

C₈×C₁₉

—

116

C₈×C₁₉

—

117

C₈×C₁₉

—

118

C₁₉⋊C₈

—

119

C₁₉⋊C₈

—

120

C₂×#487

—

121

#1837

—

122

#1549

—

123

#1548

—

124

#1546

—

125

#1546

—

126

#1450

D₁₉

yes

characteristic

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

#390

yes

characteristic

130

C₂²×C₁₉

#488

yes

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

#416

yes

—

134

C₄×C₁₉

#471

yes

—

135

C₄×C₁₉

#473

yes

—

136

C₄×C₁₉

#495

yes

characteristic

137

C₄×C₁₉

#495

yes

characteristic

138

Dic₁₉

—

139

Dic₁₉

—

140

C₂×C₄⋊Q₈

—

141

C₂×C₄⋊Q₈

—

142

#487

—

143

#487

—

144

#487

—

145

#431

C₂×D₁₉

yes

characteristic

146

#431

C₂×D₁₉

yes

characteristic

147

#423

—

148

#423

—

149

C₂×#103

—

150

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

151

#341

—

152

#333

—

153

#332

—

154

#332

—

155

#332

—

156

#322

—

157

C₈²

—

158

C₂×C₁₉

—

159

C₂×C₁₉

#1958

yes

characteristic

160

C₂×C₁₉

#1977

yes

characteristic

161

C₂×C₁₉

#1979

yes

characteristic

162

C₂²×Q₈

—

163

C₂²×Q₈

—

164

C₂×M₁₆

—

165

C₂×M₁₆

—

166

C₂²×C₈

D₇₆

yes

—

167

C₄⋊Q₈

—

168

C₄⋊Q₈

—

169

C₄⋊Q₈

—

170

C₄⋊Q₈

—

171

C₄⋊Q₈

—

172

C₄⋊Q₈

—

173

C₄⋊Q₈

—

174

C₄⋊Q₈

—

175

C₂×C₄⋊C₄

—

176

C₂×C₄⋊C₄

—

177

C₂×C₄⋊C₄

—

178

C₂×C₄⋊C₄

—

179

C₂×C₄²

C₂²×D₁₉

yes

characteristic

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

D₇₆

yes

—

185

C₄⋊C₈

D₇₆

yes

—

186

#103

—

187

#103

—

188

C₂²⋊C₈

—

189

C₂²⋊C₈

—

190

C₄×C₈

—

191

C₄×C₈

—

192

C₄×C₈

C₄×D₁₉

yes

—

193

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

194

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

195

C₁₉

#9770

yes

characteristic, complemented, Sylow

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×Q₈

—

199

C₂×Q₈

—

200

C₂×Q₈

—

201

C₂×Q₈

—

202

C₂×Q₈

—

152

—

203

C₂²×C₄

—

204

C₂²×C₄

—

205

C₂²×C₄

C₂×D₇₆

yes

characteristic

206

C₂²×C₄

#64541

yes

characteristic

207

C₂²×C₄

#64541

yes

characteristic

208

M₁₆

—

209

M₁₆

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

217

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₄⋊C₄

—

226

C₄²

C₂×C₄×D₁₉

yes

characteristic

227

C₄²

C₂×D₇₆

yes

characteristic

228

C₄²

C₂×D₇₆

yes

characteristic

229

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

230

C₂³

#10597321

yes

characteristic

231

Q₈

—

232

Q₈

—

152

—

233

Q₈

—

152

—

234

Q₈

—

152

—

235

Q₈

—

152

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

152

—

241

C₂×C₄

—

152

—

242

C₂×C₄

C₄×D₇₆

yes

characteristic

243

C₂×C₄

C₄×D₇₆

yes

characteristic

244

C₂×C₄

#10597320

yes

characteristic

245

C₂×C₄

#10597350

yes

—

246

C₂×C₄

#10597350

yes

—

247

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

248

C₂×C₄

#10597376

yes

characteristic

249

C₂×C₄

#10597376

yes

characteristic

250

C₈

—

251

C₈

—

252

C₈

—

253

C₈

—

254

C₈

—

152

—

255

C₈

—

152

—

256

C₂²

—

257

C₂²

—

258

C₂²

#11926446

yes

characteristic

259

C₂²

#11926899

yes

—

260

C₄

—

261

C₄

—

262

C₄

—

152

—

263

C₄

—

152

—

264

C₄

#11926541

yes

—

265

C₄

#11926807

yes

—

266

C₄

#11926819

yes

—

267

C₄

#11926928

yes

characteristic

268

C₄

#11926928

yes

characteristic

269

C₂

—

270

C₂

#14564446

yes

characteristic

271

C₂

#14564538

yes

characteristic

272

C₂

#14564550

yes

characteristic

	subgroup	G/H
center	C₂²	#11926446
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1450	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#124
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1450	D₁₉
hypocenter	C₁₉	#9770
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1450

subgroup

G/H

center

C₂²

#11926446

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1450

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1450

N	H ≅ G/N	type
195. C₁₉	#9770	semidirect

H ≅ G/N

type

195. C₁₉

#9770

semidirect

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

subgroup	index
C₂×#11926895	2
#14563773	2
#14562319	2
#14562315	2
#14562306	2
C₁₉×#1450	2
#9770	19

subgroup

index

C₁₉×#1450

Subgroups — #18081991

Conjugacy classes of subgroups

Complements

Maximal subgroups