Group #14574814 — subgroups

Subgroups — #14574814

Order 2432.

332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 121 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	#11927078	C₂	1	1	yes	maximal, characteristic
2	#11926943	C₂	1	2	yes	maximal, complemented
3	#11926901	C₂	1	2	yes	maximal, complemented
4	#11926885	C₂	1	2	yes	maximal, complemented
5	#11926868	C₂	1	2	yes	maximal
6	#11926836	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926831	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926826	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926821	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926597	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₁₉×#125	C₂²	1	2	yes	—
15	C₁₉×C₂²⋊Q₈	—	2	1	no	—
16	C₁₉×C₂²⋊Q₈	—	2	1	no	—
17	C₄×Q₈×C₁₉	—	2	1	no	—
18	C₄×Q₈×C₁₉	—	2	1	no	—
19	C₁₉×#117	C₂²	1	2	yes	—
20	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	#10597376	C₂²	1	1	yes	characteristic
22	#10597375	—	2	1	no	—
23	C₄×C₂²⋊D₁₉	—	2	1	no	—
24	#10597370	C₂²	1	1	yes	characteristic
25	#10597322	—	2	1	no	—
26	#10597321	C₂²	1	1	yes	characteristic
27	C₄×D₇₆	C₂²	1	1	yes	characteristic
28	#10597318	—	2	1	no	—
29	#10597316	C₂²	1	1	yes	characteristic
30	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
31	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
32	#10597267	C₂²	1	2	yes	—
33	#10597267	C₂²	1	2	yes	—
34	#10597266	C₂²	1	2	yes	—
35	#10597266	C₂²	1	2	yes	—
36	#10597265	C₂²	1	2	yes	—
37	#10597265	C₂²	1	2	yes	—
38	#10597264	C₂²	1	2	yes	—
39	#10597264	C₂²	1	2	yes	—
40	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
41	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
42	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
43	C₂×Q₈×C₁₉	—	2	1	no	—
44	C₂×Q₈×C₁₉	—	2	1	no	—
45	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×C₂²⋊D₁₉	—	2	1	no	—
49	C₂×D₇₆	C₂³	1	1	yes	characteristic
50	C₂×C₄×D₁₉	—	2	1	no	—
51	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
52	C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
57	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
58	C₂²⋊C₄×C₁₉	—	2	2	no	—
59	C₄²×C₁₉	—	2	2	no	—
60	C₄²×C₁₉	D₄	1	1	yes	characteristic
61	C₄²×C₁₉	D₄	1	1	yes	characteristic
62	C₄²×C₁₉	C₂³	1	1	yes	characteristic
63	C₄²×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²⋊Dic₁₉	—	2	1	no	—
65	(C₂×D₁₉)⋊C₄	—	2	1	no	—
66	(C₂×D₁₉)⋊C₄	—	2	1	no	—
67	(C₂×D₁₉)⋊C₄	—	2	1	no	—
68	(C₂×D₁₉)⋊C₄	—	2	1	no	—
69	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
70	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
71	Dic₁₉⋊C₄	—	2	1	no	—
72	Dic₁₉⋊C₄	—	2	1	no	—
73	Dic₁₉⋊C₄	—	2	1	no	—
74	Dic₁₉⋊C₄	—	2	1	no	—
75	C₄×Dic₁₉	—	2	1	no	—
76	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
77	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
78	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×D₁₉	—	2	1	no	—
80	Q₈×C₁₉	—	4	2	no	—
81	Q₈×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	4	1	no	—
88	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
94	C₂²⋊D₁₉	—	4	2	no	—
95	C₂×Dic₁₉	—	2	1	no	—
96	C₂×Dic₁₉	—	2	1	no	—
97	C₂×Dic₁₉	—	2	1	no	—
98	D₇₆	—	2	1	no	—
99	D₇₆	—	2	1	no	—
100	C₄×D₁₉	—	4	2	no	—
101	Dic₃₈	—	2	1	no	—
102	Dic₃₈	—	2	1	no	—
103	C₁₉⋊C₈	—	2	2	no	—
104	C₁₉⋊C₈	—	2	2	no	—
105	#3233	—	19	1	no	maximal, Sylow
106	C₂²×C₁₉	—	2	1	no	—
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	—	2	1	no	—
109	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
110	C₂×D₁₉	—	4	1	no	—
111	C₂×D₁₉	—	4	1	no	—
112	C₂×D₁₉	—	4	1	no	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	4	2	no	—
118	C₄×C₁₉	—	4	2	no	—
119	C₄×C₁₉	#135	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	—	4	1	no	—
123	Dic₁₉	—	4	1	no	—
124	Dic₁₉	—	4	1	no	—
125	#533	D₁₉	1	1	yes	characteristic, complemented
126	#529	—	19	1	no	—
127	#499	—	19	2	no	—
128	#488	—	19	2	no	—
129	#485	—	19	2	no	—
130	#482	—	19	2	no	—
131	#477	—	19	1	no	—
132	#476	—	19	1	no	—
133	#475	—	19	1	no	—
134	#474	—	19	1	no	—
135	#431	—	19	1	no	—
136	C₂×C₁₉	—	4	1	no	—
137	C₂×C₁₉	#536	1	1	yes	characteristic
138	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
139	C₂×C₁₉	#575	1	1	yes	characteristic
140	D₁₉	—	8	1	no	—
141	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
142	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
143	#126	—	38	1	no	—
144	#125	—	19	1	no	—
145	#125	C₂×D₁₉	1	2	yes	—
146	#124	—	19	1	no	—
147	#123	—	38	1	no	—
148	C₂²⋊Q₈	—	2	1	no	—
149	C₂²⋊Q₈	—	2	1	no	—
150	C₂²⋊Q₈	—	19	1	no	—
151	#121	—	19	1	no	—
152	C₄×Q₈	—	2	1	no	—
153	C₄×Q₈	—	2	1	no	—
154	C₄×Q₈	—	19	1	no	—
155	C₄×D₄	—	19	1	no	—
156	C₄×D₄	—	38	1	no	—
157	#117	—	38	1	no	—
158	#117	C₂×D₁₉	1	2	yes	—
159	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
160	#107	—	19	2	no	—
161	#107	—	19	2	no	—
162	#106	—	19	2	no	—
163	#106	—	19	2	no	—
164	C₄⋊C₈	—	19	1	no	—
165	C₄⋊C₈	—	19	1	no	—
166	#103	—	19	2	no	—
167	#103	—	19	2	no	—
168	#102	—	19	2	no	—
169	#102	—	19	2	no	—
170	C₂²⋊C₈	—	19	2	no	—
171	C₄×C₈	—	19	2	no	—
172	C₁₉	#3233	1	1	yes	characteristic, complemented, Sylow
173	C₂×Q₈	—	2	1	no	—
174	C₂×Q₈	—	2	1	no	—
175	C₂×Q₈	—	19	1	no	—
176	C₂×D₄	—	19	1	no	—
177	C₂×D₄	—	38	1	no	—
178	C₂²×C₄	—	38	1	no	—
179	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
180	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
181	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
182	C₂×C₈	—	19	2	no	—
183	C₂×C₈	—	19	2	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	2	1	no	—
187	C₄⋊C₄	—	2	1	no	—
188	C₄⋊C₄	—	19	1	no	—
189	C₄⋊C₄	—	19	1	no	—
190	C₄⋊C₄	—	38	1	no	—
191	C₄⋊C₄	—	38	1	no	—
192	C₄⋊C₄	—	38	1	no	—
193	C₄⋊C₄	—	38	1	no	—
194	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
195	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
196	C₂²⋊C₄	—	2	2	no	—
197	C₂²⋊C₄	—	38	1	no	—
198	C₂²⋊C₄	—	38	1	no	—
199	C₂²⋊C₄	—	38	1	no	—
200	C₂²⋊C₄	—	38	1	no	—
201	C₂²⋊C₄	—	38	1	no	—
202	C₄²	—	2	2	no	—
203	C₄²	—	38	1	no	—
204	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
205	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
206	C₄²	C₂²×D₁₉	1	1	yes	characteristic
207	C₄²	C₂²×D₁₉	1	1	yes	characteristic
208	C₂³	—	38	1	no	—
209	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
210	Q₈	—	4	2	no	—
211	Q₈	—	4	2	no	—
212	Q₈	—	38	1	no	—
213	Q₈	—	38	1	no	—
214	D₄	—	38	1	no	—
215	D₄	—	38	1	no	—
216	D₄	—	76	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	4	1	no	—
223	C₂×C₄	—	38	1	no	—
224	C₂×C₄	—	38	1	no	—
225	C₂×C₄	—	38	1	no	—
226	C₂×C₄	—	76	2	no	—
227	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
228	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
229	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
230	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
231	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
232	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
233	C₈	—	38	2	no	—
234	C₈	—	38	2	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	76	1	no	—
239	C₂²	—	76	1	no	—
240	C₂²	—	76	1	no	—
241	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	4	2	no	—
247	C₄	—	4	2	no	—
248	C₄	—	76	1	no	—
249	C₄	—	76	1	no	—
250	C₄	—	76	1	no	—
251	C₄	#10597396	1	2	yes	—
252	C₄	#10597433	1	1	yes	characteristic
253	C₄	#10597433	1	1	yes	characteristic
254	C₂	—	4	1	no	—
255	C₂	—	152	1	no	—
256	C₂	#11927118	1	1	yes	characteristic
257	C₂	C₂×#10597396	1	1	yes	characteristic
258	C₂	#11927342	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927078

C₂

yes

maximal, characteristic

#11926943

C₂

yes

maximal, complemented

#11926901

C₂

yes

maximal, complemented

#11926885

C₂

yes

maximal, complemented

#11926868

C₂

yes

maximal

#11926836

C₂

yes

maximal, characteristic, complemented

#11926831

C₂

yes

maximal, characteristic, complemented

#11926826

C₂

yes

maximal, characteristic, complemented

#11926821

C₂

yes

maximal, characteristic, complemented

#11926597

C₂

yes

maximal, characteristic, complemented

C₁₉×#533

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#125

C₂²

yes

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597376

C₂²

yes

characteristic

#10597375

—

C₄×C₂²⋊D₁₉

—

#10597370

C₂²

yes

characteristic

#10597322

—

#10597321

C₂²

yes

characteristic

C₄×D₇₆

C₂²

yes

characteristic

#10597318

—

#10597316

C₂²

yes

characteristic

C₄×Dic₃₈

C₂²

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597267

C₂²

yes

—

#10597267

C₂²

yes

—

#10597266

C₂²

yes

—

#10597266

C₂²

yes

—

#10597265

C₂²

yes

—

#10597265

C₂²

yes

—

#10597264

C₂²

yes

—

#10597264

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×D₇₆

C₂³

yes

characteristic

C₂×C₄×D₁₉

—

C₂×Dic₃₈

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

C₂³

yes

characteristic

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×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

C₂×D₄

yes

characteristic

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

—

D₇₆

—

D₇₆

—

100

C₄×D₁₉

—

101

Dic₃₈

—

102

Dic₃₈

—

103

C₁₉⋊C₈

—

104

C₁₉⋊C₈

—

105

#3233

—

maximal, Sylow

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

C₂²×D₄

yes

characteristic

110

C₂×D₁₉

—

111

C₂×D₁₉

—

112

C₂×D₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

#135

yes

—

120

C₄×C₁₉

2₋¹⁺⁴

yes

characteristic

121

C₄×C₁₉

2₋¹⁺⁴

yes

characteristic

122

Dic₁₉

—

123

Dic₁₉

—

124

Dic₁₉

—

125

#533

D₁₉

yes

characteristic, complemented

126

#529

—

127

#499

—

128

#488

—

129

#485

—

130

#482

—

131

#477

—

132

#476

—

133

#475

—

134

#474

—

135

#431

—

136

C₂×C₁₉

—

137

C₂×C₁₉

#536

yes

characteristic

138

C₂×C₁₉

C₂×#135

yes

characteristic

139

C₂×C₁₉

#575

yes

characteristic

140

D₁₉

—

141

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

142

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

143

#126

—

144

#125

—

145

#125

C₂×D₁₉

yes

—

146

#124

—

147

#123

—

148

C₂²⋊Q₈

—

149

C₂²⋊Q₈

—

150

C₂²⋊Q₈

—

151

#121

—

152

C₄×Q₈

—

153

C₄×Q₈

—

154

C₄×Q₈

—

155

C₄×D₄

—

156

C₄×D₄

—

157

#117

—

158

#117

C₂×D₁₉

yes

—

159

C₂×C₄²

C₂×D₁₉

yes

characteristic

160

#107

—

161

#107

—

162

#106

—

163

#106

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

#103

—

167

#103

—

168

#102

—

169

#102

—

170

C₂²⋊C₈

—

171

C₄×C₈

—

172

C₁₉

#3233

yes

characteristic, complemented, Sylow

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂²×C₄

—

179

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

180

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

181

C₂²×C₄

C₂²×D₁₉

yes

characteristic

182

C₂×C₈

—

183

C₂×C₈

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

C₂²×D₁₉

yes

—

195

C₄⋊C₄

C₂²×D₁₉

yes

—

196

C₂²⋊C₄

—

197

C₂²⋊C₄

—

198

C₂²⋊C₄

—

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

202

C₄²

—

203

C₄²

—

204

C₄²

C₂²⋊D₁₉

yes

characteristic

205

C₄²

C₂²⋊D₁₉

yes

characteristic

206

C₄²

C₂²×D₁₉

yes

characteristic

207

C₄²

C₂²×D₁₉

yes

characteristic

208

C₂³

—

209

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

210

Q₈

—

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

D₄

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

228

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

229

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

230

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

231

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

232

C₂×C₄

C₂³×D₁₉

yes

characteristic

233

C₈

—

234

C₈

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

#10597396

yes

—

252

C₄

#10597433

yes

characteristic

253

C₄

#10597433

yes

characteristic

254

C₂

—

255

C₂

—

152

—

256

C₂

#11927118

yes

characteristic

257

C₂

C₂×#10597396

yes

characteristic

258

C₂

#11927342

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#533	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#10597376	C₂²
hypercenter	#533	D₁₉
hypocenter	C₁₉	#3233
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#533

C₂

socle

C₂²×C₁₉

C₂²×D₄

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

N	H ≅ G/N	type
2. #11926943	C₂	semidirect
3. #11926901	C₂	semidirect
4. #11926885	C₂	semidirect
6. #11926836	C₂	semidirect
7. #11926831	C₂	semidirect
8. #11926826	C₂	semidirect
9. #11926821	C₂	semidirect
10. #11926597	C₂	semidirect
11. C₁₉×#533	C₂	semidirect
125. #533	D₁₉	semidirect
172. C₁₉	#3233	semidirect

H ≅ G/N

type

2. #11926943

C₂

semidirect

3. #11926901

C₂

semidirect

4. #11926885

C₂

semidirect

6. #11926836

C₂

semidirect

7. #11926831

C₂

semidirect

8. #11926826

C₂

semidirect

9. #11926821

C₂

semidirect

10. #11926597

C₂

semidirect

11. C₁₉×#533

C₂

semidirect

125. #533

D₁₉

semidirect

172. C₁₉

#3233

semidirect

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

subgroup	index
#11927078	2
#11926943	2
#11926901	2
#11926885	2
#11926868	2
#11926836	2
#11926831	2
#11926826	2
#11926821	2
#11926597	2
C₁₉×#533	2
#3233	19

subgroup

index

C₁₉×#533

Subgroups — #14574814

Conjugacy classes of subgroups

Complements

Maximal subgroups