Group #18087188 — subgroups

Subgroups — #18087188

Order 4864.

306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14564624	C₂	1	1	yes	maximal, characteristic
2	#14562409	C₂	1	1	yes	maximal, characteristic
3	#14562387	C₂	1	1	yes	maximal, characteristic
4	#14562321	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926289	C₂	1	1	yes	maximal, characteristic
6	#14561509	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1950	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	#11926597	C₂²	1	1	yes	characteristic
10	#11926568	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	#11926312	—	2	1	no	—
13	#11926312	—	2	1	no	—
14	#11926297	—	2	1	no	—
15	#11926296	—	2	2	no	—
16	#11926295	—	2	1	no	—
17	#11926289	—	2	2	no	—
18	#11926289	—	2	1	no	—
19	#11926289	—	2	1	no	—
20	C₂×C₁₉×#108	—	2	1	no	—
21	C₁₉×#423	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#341	—	2	1	no	—
25	C₂²×Dic₃₈	—	2	1	no	—
26	C₂×M₁₆×C₁₉	—	2	1	no	—
27	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
28	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×C₄⋊Dic₁₉	—	2	1	no	—
32	C₂×C₄⋊Dic₁₉	Q₈	1	2	yes	—
33	C₂×#64520	—	2	1	no	—
34	C₂²×C₁₉⋊C₈	—	2	1	no	—
35	#10597315	—	2	1	no	—
36	#10597315	—	2	1	no	—
37	#10597315	—	2	1	no	—
38	#10597315	—	2	1	no	—
39	C₁₉×#108	—	4	2	no	—
40	C₁₉×C₄⋊C₈	—	2	1	no	—
41	C₁₉×C₄⋊C₈	—	2	1	no	—
42	C₁₉×C₄⋊C₈	—	2	1	no	—
43	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
44	C₁₉×#97	—	2	1	no	—
45	C₄×C₈×C₁₉	—	2	1	no	—
46	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
51	C₄⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
52	C₄⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
53	C₄×C₁₉⋊C₈	—	2	1	no	—
54	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
57	C₂²×Dic₁₉	—	2	2	no	—
58	C₂×Dic₃₈	—	4	1	no	—
59	C₂×Dic₃₈	—	4	1	no	—
60	C₂×Dic₃₈	—	8	1	no	—
61	C₂×Dic₃₈	—	8	1	no	—
62	M₁₆×C₁₉	—	2	1	no	—
63	M₁₆×C₁₉	—	2	1	no	—
64	M₁₆×C₁₉	—	2	1	no	—
65	M₁₆×C₁₉	—	4	1	no	—
66	M₁₆×C₁₉	—	4	1	no	—
67	M₁₆×C₁₉	Q₁₆	1	2	yes	—
68	C₂×C₈×C₁₉	—	2	1	no	—
69	C₂×C₈×C₁₉	—	2	2	no	—
70	C₂×C₈×C₁₉	—	2	1	no	—
71	C₂×C₈×C₁₉	—	4	1	no	—
72	C₂×C₈×C₁₉	—	4	1	no	—
73	C₂×C₈×C₁₉	—	4	1	no	—
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	C₄²×C₁₉	#41	1	1	yes	characteristic
78	C₄⋊Dic₁₉	—	2	2	no	—
79	C₄⋊Dic₁₉	—	2	2	no	—
80	C₄⋊Dic₁₉	—	4	1	no	—
81	C₄⋊Dic₁₉	—	4	1	no	—
82	#64520	—	4	1	no	—
83	#64520	—	4	1	no	—
84	C₂×C₁₉⋊C₈	—	2	1	no	—
85	C₂×C₁₉⋊C₈	—	2	1	no	—
86	C₂×C₁₉⋊C₈	—	4	1	no	—
87	C₂×C₁₉⋊C₈	—	4	1	no	—
88	C₂×C₁₉⋊C₈	—	8	1	no	—
89	#10606	—	19	1	no	maximal, Sylow
90	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
102	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
104	C₂×Dic₁₉	—	4	2	no	—
105	C₂×Dic₁₉	—	8	2	no	—
106	Dic₃₈	—	8	2	no	—
107	Dic₃₈	—	8	1	no	—
108	Dic₃₈	—	8	1	no	—
109	C₈×C₁₉	—	2	2	no	—
110	C₈×C₁₉	—	4	2	no	—
111	C₈×C₁₉	—	4	1	no	—
112	C₈×C₁₉	—	8	1	no	—
113	C₁₉⋊C₈	—	4	1	no	—
114	C₁₉⋊C₈	—	4	1	no	—
115	C₁₉⋊C₈	—	8	1	no	—
116	C₁₉⋊C₈	—	8	1	no	—
117	#1997	—	19	1	no	—
118	#1950	D₁₉	1	1	yes	characteristic
119	#1571	—	19	1	no	—
120	#1565	—	19	1	no	—
121	#1549	—	19	1	no	—
122	C₂×#332	—	19	1	no	—
123	#1292	—	19	1	no	—
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	#396	1	1	yes	characteristic
127	C₂²×C₁₉	#477	1	1	yes	characteristic
128	C₂²×C₁₉	#479	1	1	yes	characteristic
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	#462	1	1	yes	characteristic
133	C₄×C₁₉	#463	1	1	yes	characteristic
134	C₄×C₁₉	#467	1	1	yes	characteristic
135	C₄×C₁₉	#468	1	1	yes	characteristic
136	C₄×C₁₉	#471	1	1	yes	characteristic
137	C₄×C₁₉	#472	1	1	yes	characteristic
138	Dic₁₉	—	8	2	no	—
139	C₂×C₄⋊Q₈	—	19	1	no	—
140	#431	—	19	1	no	—
141	C₂×#108	—	2	1	no	—
142	#423	—	19	1	no	—
143	#423	C₂×D₁₉	1	1	yes	characteristic
144	C₂×C₄⋊C₈	—	19	1	no	—
145	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
146	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
147	#343	—	38	1	no	—
148	#343	—	38	1	no	—
149	#341	—	2	1	no	—
150	#335	—	38	1	no	—
151	#335	—	38	2	no	—
152	#334	—	38	1	no	—
153	#332	—	38	1	no	—
154	#332	—	38	1	no	—
155	#332	—	38	2	no	—
156	C₂×C₁₉	—	2	1	no	—
157	C₂×C₁₉	—	2	1	no	—
158	C₂×C₁₉	#2063	1	1	yes	characteristic
159	C₂×C₁₉	#2068	1	1	yes	characteristic
160	C₂×C₁₉	#2070	1	1	yes	characteristic
161	C₂²×Q₈	—	38	1	no	—
162	C₂×M₁₆	—	2	1	no	—
163	C₂×M₁₆	—	38	1	no	—
164	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
165	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
166	C₂²×C₈	—	2	1	no	—
167	C₂²×C₈	—	38	1	no	—
168	C₄⋊Q₈	—	38	1	no	—
169	C₄⋊Q₈	—	38	1	no	—
170	C₄⋊Q₈	—	38	1	no	—
171	C₄⋊Q₈	—	38	1	no	—
172	C₂×C₄⋊C₄	—	19	2	no	—
173	C₂×C₄⋊C₄	—	38	1	no	—
174	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
175	#108	—	4	2	no	—
176	C₄⋊C₈	—	2	1	no	—
177	C₄⋊C₈	—	2	1	no	—
178	C₄⋊C₈	—	2	1	no	—
179	C₄⋊C₈	—	19	1	no	—
180	C₄⋊C₈	—	19	1	no	—
181	C₄⋊C₈	—	38	1	no	—
182	C₄⋊C₈	—	38	1	no	—
183	C₄⋊C₈	—	38	1	no	—
184	C₄⋊C₈	—	38	1	no	—
185	C₄⋊C₈	D₇₆	1	2	yes	—
186	C₂²⋊C₈	—	38	1	no	—
187	#97	—	2	1	no	—
188	C₄×C₈	—	2	1	no	—
189	C₄×C₈	—	38	1	no	—
190	C₁₉	#10606	1	1	yes	characteristic, complemented, Sylow
191	C₂×Q₈	—	76	1	no	—
192	C₂×Q₈	—	76	1	no	—
193	C₂×Q₈	—	152	1	no	—
194	C₂×Q₈	—	152	1	no	—
195	C₂²×C₄	—	38	2	no	—
196	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
197	C₂²×C₄	#64545	1	1	yes	characteristic
198	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
199	M₁₆	—	2	1	no	—
200	M₁₆	—	2	1	no	—
201	M₁₆	—	2	1	no	—
202	M₁₆	—	4	1	no	—
203	M₁₆	—	4	1	no	—
204	M₁₆	—	76	1	no	—
205	M₁₆	—	76	1	no	—
206	M₁₆	#64528	1	2	yes	—
207	C₂×C₈	—	2	1	no	—
208	C₂×C₈	—	2	2	no	—
209	C₂×C₈	—	2	1	no	—
210	C₂×C₈	—	4	1	no	—
211	C₂×C₈	—	4	1	no	—
212	C₂×C₈	—	4	1	no	—
213	C₂×C₈	—	38	1	no	—
214	C₂×C₈	—	38	1	no	—
215	C₂×C₈	—	76	1	no	—
216	C₂×C₈	—	76	1	no	—
217	C₂×C₈	—	152	1	no	—
218	C₄⋊C₄	—	38	2	no	—
219	C₄⋊C₄	—	38	2	no	—
220	C₄⋊C₄	—	76	1	no	—
221	C₄⋊C₄	—	76	1	no	—
222	C₄²	C₂×D₇₆	1	1	yes	characteristic
223	C₄²	#64541	1	1	yes	characteristic
224	C₄²	D₄×D₁₉	1	1	yes	characteristic
225	C₄²	#64543	1	1	yes	characteristic
226	C₂³	#10597392	1	1	yes	characteristic
227	Q₈	—	152	2	no	—
228	Q₈	—	152	1	no	—
229	Q₈	—	152	1	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	4	1	no	—
233	C₂×C₄	—	76	2	no	—
234	C₂×C₄	—	152	2	no	—
235	C₂×C₄	#10597341	1	1	yes	characteristic
236	C₂×C₄	#10597342	1	1	yes	characteristic
237	C₂×C₄	#10597343	1	1	yes	characteristic
238	C₂×C₄	#10597344	1	1	yes	characteristic
239	C₂×C₄	#10597376	1	1	yes	characteristic
240	C₂×C₄	#10597378	1	1	yes	characteristic
241	C₂×C₄	#10597385	1	1	yes	characteristic
242	C₂×C₄	C₂×#64528	1	1	yes	characteristic
243	C₂×C₄	#10597396	1	1	yes	characteristic
244	C₂×C₄	#10597397	1	1	yes	characteristic
245	C₈	—	2	2	no	—
246	C₈	—	4	1	no	—
247	C₈	—	4	2	no	—
248	C₈	—	8	1	no	—
249	C₈	—	76	1	no	—
250	C₈	—	76	1	no	—
251	C₈	—	152	1	no	—
252	C₈	—	152	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	—	2	1	no	—
255	C₂²	#11926466	1	1	yes	characteristic
256	C₂²	#11926836	1	1	yes	characteristic
257	C₂²	#11926848	1	1	yes	characteristic
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	2	1	no	—
261	C₄	—	152	2	no	—
262	C₄	#11926754	1	1	yes	characteristic
263	C₄	#11926759	1	1	yes	characteristic
264	C₄	#11926783	1	1	yes	characteristic
265	C₄	#11926788	1	1	yes	characteristic
266	C₄	#11926808	1	1	yes	characteristic
267	C₄	#11926815	1	1	yes	characteristic
268	C₂	—	2	1	no	—
269	C₂	—	2	1	no	—
270	C₂	#14564990	1	1	yes	characteristic
271	C₂	#14565027	1	1	yes	characteristic
272	C₂	#14565035	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564624

C₂

yes

maximal, characteristic

#14562409

C₂

yes

maximal, characteristic

#14562387

C₂

yes

maximal, characteristic

#14562321

C₂

yes

maximal, characteristic

C₂×#11926289

C₂

yes

maximal, characteristic

#14561509

C₂

yes

maximal, characteristic

C₁₉×#1950

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

#11926597

C₂²

yes

characteristic

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

—

—

—

—

—

—

—

C₂×C₁₉×#108

—

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#341

—

C₂²×Dic₃₈

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

Q₈

yes

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

—

—

—

—

C₁₉×#108

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

characteristic

C₄⋊(C₁₉⋊C₈)

D₄

yes

characteristic

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

Q₁₆

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10606

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#126

yes

characteristic

100

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

101

C₂×C₄×C₁₉

#135

yes

characteristic

102

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

103

C₂×C₄×C₁₉

#137

yes

characteristic

104

C₂×Dic₁₉

—

105

C₂×Dic₁₉

—

106

Dic₃₈

—

107

Dic₃₈

—

108

Dic₃₈

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

C₈×C₁₉

—

112

C₈×C₁₉

—

113

C₁₉⋊C₈

—

114

C₁₉⋊C₈

—

115

C₁₉⋊C₈

—

116

C₁₉⋊C₈

—

117

#1997

—

118

#1950

D₁₉

yes

characteristic

119

#1571

—

120

#1565

—

121

#1549

—

122

C₂×#332

—

123

#1292

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

#396

yes

characteristic

127

C₂²×C₁₉

#477

yes

characteristic

128

C₂²×C₁₉

#479

yes

characteristic

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

#462

yes

characteristic

133

C₄×C₁₉

#463

yes

characteristic

134

C₄×C₁₉

#467

yes

characteristic

135

C₄×C₁₉

#468

yes

characteristic

136

C₄×C₁₉

#471

yes

characteristic

137

C₄×C₁₉

#472

yes

characteristic

138

Dic₁₉

—

139

C₂×C₄⋊Q₈

—

140

#431

—

141

C₂×#108

—

142

#423

—

143

#423

C₂×D₁₉

yes

characteristic

144

C₂×C₄⋊C₈

—

145

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

146

C₄×M₁₆

C₂×D₁₉

yes

characteristic

147

#343

—

148

#343

—

149

#341

—

150

#335

—

151

#335

—

152

#334

—

153

#332

—

154

#332

—

155

#332

—

156

C₂×C₁₉

—

157

C₂×C₁₉

—

158

C₂×C₁₉

#2063

yes

characteristic

159

C₂×C₁₉

#2068

yes

characteristic

160

C₂×C₁₉

#2070

yes

characteristic

161

C₂²×Q₈

—

162

C₂×M₁₆

—

163

C₂×M₁₆

—

164

C₂×M₁₆

C₂²⋊D₁₉

yes

characteristic

165

C₂×M₁₆

C₂²⋊D₁₉

yes

characteristic

166

C₂²×C₈

—

167

C₂²×C₈

—

168

C₄⋊Q₈

—

169

C₄⋊Q₈

—

170

C₄⋊Q₈

—

171

C₄⋊Q₈

—

172

C₂×C₄⋊C₄

—

173

C₂×C₄⋊C₄

—

174

C₂×C₄²

C₂²×D₁₉

yes

characteristic

175

#108

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

D₇₆

yes

—

186

C₂²⋊C₈

—

187

#97

—

188

C₄×C₈

—

189

C₄×C₈

—

190

C₁₉

#10606

yes

characteristic, complemented, Sylow

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×Q₈

—

152

—

194

C₂×Q₈

—

152

—

195

C₂²×C₄

—

196

C₂²×C₄

Q₈×D₁₉

yes

characteristic

197

C₂²×C₄

#64545

yes

characteristic

198

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

199

M₁₆

—

200

M₁₆

—

201

M₁₆

—

202

M₁₆

—

203

M₁₆

—

204

M₁₆

—

205

M₁₆

—

206

M₁₆

#64528

yes

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

—

152

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄²

C₂×D₇₆

yes

characteristic

223

C₄²

#64541

yes

characteristic

224

C₄²

D₄×D₁₉

yes

characteristic

225

C₄²

#64543

yes

characteristic

226

C₂³

#10597392

yes

characteristic

227

Q₈

—

152

—

228

Q₈

—

152

—

229

Q₈

—

152

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

152

—

235

C₂×C₄

#10597341

yes

characteristic

236

C₂×C₄

#10597342

yes

characteristic

237

C₂×C₄

#10597343

yes

characteristic

238

C₂×C₄

#10597344

yes

characteristic

239

C₂×C₄

#10597376

yes

characteristic

240

C₂×C₄

#10597378

yes

characteristic

241

C₂×C₄

#10597385

yes

characteristic

242

C₂×C₄

C₂×#64528

yes

characteristic

243

C₂×C₄

#10597396

yes

characteristic

244

C₂×C₄

#10597397

yes

characteristic

245

C₈

—

246

C₈

—

247

C₈

—

248

C₈

—

249

C₈

—

250

C₈

—

251

C₈

—

152

—

252

C₈

—

152

—

253

C₂²

—

254

C₂²

—

255

C₂²

#11926466

yes

characteristic

256

C₂²

#11926836

yes

characteristic

257

C₂²

#11926848

yes

characteristic

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

152

—

262

C₄

#11926754

yes

characteristic

263

C₄

#11926759

yes

characteristic

264

C₄

#11926783

yes

characteristic

265

C₄

#11926788

yes

characteristic

266

C₄

#11926808

yes

characteristic

267

C₄

#11926815

yes

characteristic

268

C₂

—

269

C₂

—

270

C₂

#14564990

yes

characteristic

271

C₂

#14565027

yes

characteristic

272

C₂

#14565035

yes

characteristic

	subgroup	G/H
center	C₂²	#11926466
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1950	C₂
socle	C₂²×C₁₉	#396
prime radical	C₂³×C₁₉	C₂²⋊Q₈
hypercenter	#1950	D₁₉
hypocenter	C₁₉	#10606
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1950

subgroup

G/H

center

C₂²

#11926466

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1950

C₂

socle

C₂²×C₁₉

#396

prime radical

C₂³×C₁₉

C₂²⋊Q₈

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1950

N	H ≅ G/N	type
190. C₁₉	#10606	semidirect

H ≅ G/N

type

190. C₁₉

#10606

semidirect

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

subgroup	index
#14564624	2
#14562409	2
#14562387	2
#14562321	2
C₂×#11926289	2
#14561509	2
C₁₉×#1950	2
#10606	19

subgroup

index

C₁₉×#1950

Subgroups — #18087188

Conjugacy classes of subgroups

Complements

Maximal subgroups