Group #18075335 — subgroups

Subgroups — #18075335

Order 4864.

516 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 169 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	C₄⋊Q₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	#14563786	C₂	1	2	yes	maximal
3	C₂×#11926293	C₂	1	1	yes	maximal, characteristic
4	#14561519	C₂	1	2	yes	maximal
5	C₂×C₁₉×#333	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×Dic₁₉	C₄	1	2	yes	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×Dic₁₉⋊C₈	—	2	2	no	—
9	C₂×Dic₁₉⋊C₈	—	2	2	no	—
10	#11926451	C₄	1	2	yes	—
11	#11926443	—	2	2	no	—
12	#11926414	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×Dic₁₉	—	2	2	no	—
14	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
15	#11926293	—	2	2	no	—
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₁₉×#333	—	2	2	no	—
19	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₁₉	—	2	2	no	—
21	C₁₉×C₄⋊Q₈	—	2	2	no	—
22	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	Q₈	1	2	yes	—
24	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	Q₈×Dic₁₉	—	4	4	no	—
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
30	C₂×C₄×Dic₁₉	—	2	2	no	—
31	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
34	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
35	C₂²×C₁₉⋊C₈	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉⋊#95	—	2	4	no	—
39	Dic₁₉⋊C₈	—	4	4	no	—
40	Dic₁₉⋊C₈	—	4	4	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₂×Q₈×C₁₉	—	2	2	no	—
44	C₂×Q₈×C₁₉	—	4	2	no	—
45	C₂×Q₈×C₁₉	—	4	2	no	—
46	C₂×Q₈×C₁₉	C₄⋊C₄	1	4	yes	—
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
50	C₂²×Dic₁₉	—	2	2	no	—
51	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
53	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₈×C₁₉	—	4	2	no	—
55	C₂×C₈×C₁₉	—	4	2	no	—
56	C₂×C₈×C₁₉	—	4	2	no	—
57	C₄⋊C₄×C₁₉	—	2	4	no	—
58	C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
61	C₄²×C₁₉	#41	1	2	yes	—
62	C₄⋊Dic₁₉	—	4	4	no	—
63	C₄⋊Dic₁₉	—	4	2	no	—
64	C₄⋊Dic₁₉	—	4	2	no	—
65	C₄⋊Dic₁₉	—	4	2	no	—
66	C₄×Dic₁₉	—	2	2	no	—
67	C₄×Dic₁₉	—	2	2	no	—
68	C₄×Dic₁₉	—	2	2	no	—
69	C₄×Dic₁₉	—	4	1	no	—
70	C₄×Dic₁₉	—	4	4	no	—
71	C₄×Dic₁₉	SD₁₆	1	4	yes	—
72	C₄×Dic₁₉	Q₁₆	1	4	yes	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	#8587	—	19	1	no	maximal, Sylow
77	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	Q₈×C₁₉	—	4	4	no	—
79	Q₈×C₁₉	—	4	4	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	4	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#121	1	2	yes	—
88	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
89	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
90	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
91	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
92	C₂×C₄×C₁₉	#137	1	2	yes	—
93	C₂×Dic₁₉	—	2	2	no	—
94	C₂×Dic₁₉	—	2	2	no	—
95	C₂×Dic₁₉	—	2	1	no	—
96	C₂×Dic₁₉	—	2	2	no	—
97	C₂×Dic₁₉	—	4	2	no	—
98	C₂×Dic₁₉	—	4	4	no	—
99	C₂×Dic₁₉	#100	1	2	yes	—
100	C₂×Dic₁₉	#103	1	4	yes	—
101	C₂×Dic₁₉	#103	1	4	yes	—
102	C₈×C₁₉	—	8	2	no	—
103	C₁₉⋊C₈	—	8	2	no	—
104	C₄×C₄⋊Q₈	—	19	1	no	—
105	#1842	—	19	2	no	—
106	C₂×#333	—	19	1	no	—
107	C₂×#333	D₁₉	1	1	yes	characteristic
108	#1296	—	19	2	no	—
109	C₂²×C₁₉	#380	1	1	yes	characteristic
110	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
111	C₂²×C₁₉	#413	1	1	yes	characteristic
112	C₂²×C₁₉	C₂×#103	1	2	yes	—
113	C₂²×C₁₉	#417	1	2	yes	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	4	4	no	—
117	C₄×C₁₉	#460	1	2	yes	—
118	C₄×C₁₉	#462	1	2	yes	—
119	C₄×C₁₉	#475	1	2	yes	—
120	C₄×C₁₉	#477	1	2	yes	—
121	Dic₁₉	—	2	4	no	—
122	Dic₁₉	—	4	1	no	—
123	Dic₁₉	—	8	2	no	—
124	Dic₁₉	#333	1	4	yes	complemented
125	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
126	C₂×C₄×Q₈	—	19	2	no	—
127	C₂×C₄⋊C₈	—	19	2	no	—
128	C₂×C₄⋊C₈	—	38	2	no	—
129	C₂×C₄⋊C₈	—	38	2	no	—
130	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
131	#391	—	19	2	no	—
132	#389	—	38	2	no	—
133	#384	—	19	1	no	—
134	C₄×C₄⋊C₄	—	38	2	no	—
135	C₄³	—	19	1	no	—
136	#333	—	2	2	no	—
137	#333	—	38	2	no	—
138	C₂×C₁₉	C₂×#333	1	1	yes	characteristic
139	C₂×C₁₉	#1550	1	2	yes	—
140	C₂×C₁₉	#1560	1	1	yes	characteristic
141	C₂×C₁₉	#1800	1	1	yes	characteristic
142	C₂×C₁₉	#1803	1	2	yes	—
143	C₂²×Q₈	C₄×D₁₉	1	2	yes	—
144	C₂²×C₈	—	2	2	no	—
145	C₂²×C₈	—	38	2	no	—
146	C₄⋊Q₈	—	2	2	no	—
147	C₄⋊Q₈	Dic₃₈	1	2	yes	—
148	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
149	C₄×Q₈	—	76	4	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	19	2	no	—
152	C₂×C₄⋊C₄	—	38	2	no	—
153	C₂×C₄⋊C₄	—	38	2	no	—
154	C₂×C₄²	—	19	2	no	—
155	C₂×C₄²	—	19	1	no	—
156	C₂×C₄²	—	19	2	no	—
157	C₂×C₄²	—	19	1	no	—
158	C₂×C₄²	—	38	2	no	—
159	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
160	C₄⋊C₈	—	2	2	no	—
161	C₄⋊C₈	—	2	2	no	—
162	C₄⋊C₈	—	38	2	no	—
163	C₄⋊C₈	—	38	2	no	—
164	C₄⋊C₈	—	76	4	no	—
165	C₄⋊C₈	—	76	4	no	—
166	#95	—	38	4	no	—
167	C₁₉	#8587	1	1	yes	characteristic, complemented, Sylow
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	—	4	2	no	—
170	C₂×Q₈	—	4	2	no	—
171	C₂×Q₈	Dic₁₉⋊C₄	1	4	yes	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	19	1	no	—
174	C₂²×C₄	—	19	2	no	—
175	C₂²×C₄	—	19	1	no	—
176	C₂²×C₄	—	38	2	no	—
177	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
178	C₂²×C₄	D₄×D₁₉	1	2	yes	—
179	C₂×C₈	—	4	2	no	—
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	76	2	no	—
183	C₂×C₈	—	76	2	no	—
184	C₂×C₈	—	76	2	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	2	4	no	—
187	C₄⋊C₄	—	76	2	no	—
188	C₄⋊C₄	—	76	4	no	—
189	C₄⋊C₄	—	76	2	no	—
190	C₄⋊C₄	—	76	2	no	—
191	C₄²	—	19	4	no	—
192	C₄²	—	19	4	no	—
193	C₄²	—	38	2	no	—
194	C₄²	—	38	2	no	—
195	C₄²	—	38	2	no	—
196	C₄²	—	76	1	no	—
197	C₄²	—	76	4	no	—
198	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
199	C₄²	#64543	1	2	yes	—
200	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
201	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
202	Q₈	—	4	4	no	—
203	Q₈	—	4	4	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	4	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	19	4	no	—
210	C₂×C₄	—	19	2	no	—
211	C₂×C₄	—	19	4	no	—
212	C₂×C₄	—	38	2	no	—
213	C₂×C₄	—	38	2	no	—
214	C₂×C₄	—	38	2	no	—
215	C₂×C₄	—	38	1	no	—
216	C₂×C₄	—	76	4	no	—
217	C₂×C₄	—	76	2	no	—
218	C₂×C₄	#10597323	1	1	yes	characteristic
219	C₂×C₄	#10597324	1	2	yes	—
220	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
221	C₂×C₄	#10597360	1	2	yes	—
222	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
223	C₂×C₄	#10597364	1	2	yes	—
224	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
225	C₂×C₄	#10597385	1	2	yes	—
226	C₈	—	8	2	no	—
227	C₈	—	152	2	no	—
228	C₂²	#11926402	1	1	yes	characteristic
229	C₂²	#100×D₁₉	1	1	yes	characteristic
230	C₂²	#11926525	1	1	yes	characteristic
231	C₂²	#103×D₁₉	1	2	yes	—
232	C₂²	#11926544	1	2	yes	—
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	4	4	no	—
236	C₄	—	19	4	no	—
237	C₄	—	38	4	no	—
238	C₄	—	76	1	no	—
239	C₄	—	152	2	no	—
240	C₄	#11926742	1	2	yes	—
241	C₄	#11926752	1	2	yes	—
242	C₄	#11926827	1	2	yes	—
243	C₄	#11926837	1	2	yes	—
244	C₂	D₁₉×#333	1	1	yes	characteristic
245	C₂	#14562322	1	2	yes	—
246	C₂	#14562369	1	1	yes	characteristic
247	C₂	#14563625	1	1	yes	characteristic
248	C₂	#14563638	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×Dic₁₉

C₂

yes

maximal, characteristic

#14563786

C₂

yes

maximal

C₂×#11926293

C₂

yes

maximal, characteristic

#14561519

C₂

yes

maximal

C₂×C₁₉×#333

C₂

yes

maximal, characteristic

C₂×Q₈×Dic₁₉

C₄

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×Dic₁₉⋊C₈

—

C₂×Dic₁₉⋊C₈

—

#11926451

C₄

yes

—

#11926443

—

#11926414

C₂²

yes

characteristic

C₄⋊C₄×Dic₁₉

—

C₄²×Dic₁₉

C₂²

yes

characteristic

#11926293

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#333

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

Q₈

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

Q₈×Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

D₄

yes

—

C₂×C₄×Dic₁₉

D₄

yes

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

Dic₁₉⋊C₈

—

Dic₁₉⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂²⋊C₄

yes

characteristic

C₂²×Dic₁₉

C₂²⋊C₄

yes

—

C₂²×Dic₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

SD₁₆

yes

—

C₄×Dic₁₉

Q₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8587

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#100

yes

—

100

C₂×Dic₁₉

#103

yes

—

101

C₂×Dic₁₉

#103

yes

—

102

C₈×C₁₉

—

103

C₁₉⋊C₈

—

104

C₄×C₄⋊Q₈

—

105

#1842

—

106

C₂×#333

—

107

C₂×#333

D₁₉

yes

characteristic

108

#1296

—

109

C₂²×C₁₉

#380

yes

characteristic

110

C₂²×C₁₉

C₂×#100

yes

characteristic

111

C₂²×C₁₉

#413

yes

characteristic

112

C₂²×C₁₉

C₂×#103

yes

—

113

C₂²×C₁₉

#417

yes

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

#460

yes

—

118

C₄×C₁₉

#462

yes

—

119

C₄×C₁₉

#475

yes

—

120

C₄×C₁₉

#477

yes

—

121

Dic₁₉

—

122

Dic₁₉

—

123

Dic₁₉

—

124

Dic₁₉

#333

yes

complemented

125

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

126

C₂×C₄×Q₈

—

127

C₂×C₄⋊C₈

—

128

C₂×C₄⋊C₈

—

129

C₂×C₄⋊C₈

—

130

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

131

#391

—

132

#389

—

133

#384

—

134

C₄×C₄⋊C₄

—

135

C₄³

—

136

#333

—

137

#333

—

138

C₂×C₁₉

C₂×#333

yes

characteristic

139

C₂×C₁₉

#1550

yes

—

140

C₂×C₁₉

#1560

yes

characteristic

141

C₂×C₁₉

#1800

yes

characteristic

142

C₂×C₁₉

#1803

yes

—

143

C₂²×Q₈

C₄×D₁₉

yes

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

Dic₃₈

yes

—

148

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

149

C₄×Q₈

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄²

—

155

C₂×C₄²

—

156

C₂×C₄²

—

157

C₂×C₄²

—

158

C₂×C₄²

—

159

C₂×C₄²

C₂²×D₁₉

yes

characteristic

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

#95

—

167

C₁₉

#8587

yes

characteristic, complemented, Sylow

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

Dic₁₉⋊C₄

yes

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

178

C₂²×C₄

D₄×D₁₉

yes

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

—

195

C₄²

—

196

C₄²

—

197

C₄²

—

198

C₄²

C₂×Dic₃₈

yes

characteristic

199

C₄²

#64543

yes

—

200

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

201

C₂³

C₂²⋊C₄×D₁₉

yes

characteristic

202

Q₈

—

203

Q₈

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

#10597323

yes

characteristic

219

C₂×C₄

#10597324

yes

—

220

C₂×C₄

SD₁₆×D₁₉

yes

—

221

C₂×C₄

#10597360

yes

—

222

C₂×C₄

Q₁₆×D₁₉

yes

—

223

C₂×C₄

#10597364

yes

—

224

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

225

C₂×C₄

#10597385

yes

—

226

C₈

—

227

C₈

—

152

—

228

C₂²

#11926402

yes

characteristic

229

C₂²

#100×D₁₉

yes

characteristic

230

C₂²

#11926525

yes

characteristic

231

C₂²

#103×D₁₉

yes

—

232

C₂²

#11926544

yes

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

152

—

240

C₄

#11926742

yes

—

241

C₄

#11926752

yes

—

242

C₄

#11926827

yes

—

243

C₄

#11926837

yes

—

244

C₂

D₁₉×#333

yes

characteristic

245

C₂

#14562322

yes

—

246

C₂

#14562369

yes

characteristic

247

C₂

#14563625

yes

characteristic

248

C₂

#14563638

yes

—

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#333	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#333	D₁₉
hypocenter	C₁₉	#8587
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

subgroup

G/H

center

C₂³

C₂²⋊C₄×D₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#333

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

N	H ≅ G/N	type
124. Dic₁₉	#333	semidirect
167. C₁₉	#8587	semidirect

H ≅ G/N

type

124. Dic₁₉

#333

semidirect

167. C₁₉

#8587

semidirect

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

subgroup	index
C₄⋊Q₈×Dic₁₉	2
#14563786	2
C₂×#11926293	2
#14561519	2
C₂×C₁₉×#333	2
#8587	19

subgroup

index

C₄⋊Q₈×Dic₁₉

C₂×C₁₉×#333

Subgroups — #18075335

Conjugacy classes of subgroups

Complements

Maximal subgroups