Group #18087178 — subgroups

Subgroups — #18087178

Order 4864.

306 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 97 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	#14564625	C₂	1	1	yes	maximal, characteristic
2	#14564408	C₂	1	1	yes	maximal, characteristic
3	#14562410	C₂	1	1	yes	maximal, characteristic
4	#14562388	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926293	C₂	1	1	yes	maximal, characteristic
6	#14561509	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1548	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597279	—	2	1	no	—
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₄×#64520	C₂²	1	1	yes	characteristic
13	#11926313	—	2	1	no	—
14	#11926313	—	2	1	no	—
15	#11926308	—	2	1	no	—
16	#11926297	—	2	2	no	—
17	#11926296	—	2	1	no	—
18	#11926294	—	2	1	no	—
19	#11926293	—	2	2	no	—
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₉×#431	C₂²	1	1	yes	characteristic
22	C₁₉×#423	C₂²	1	1	yes	characteristic
23	C₁₉×#333	—	2	1	no	—
24	C₁₉×#333	—	2	1	no	—
25	C₂²×Q₈×C₁₉	Q₈	1	2	yes	—
26	C₂×M₁₆×C₁₉	—	2	1	no	—
27	C₁₉×C₄⋊Q₈	—	2	1	no	—
28	C₁₉×C₄⋊Q₈	—	2	1	no	—
29	C₁₉×C₄⋊Q₈	—	2	1	no	—
30	C₁₉×C₄⋊Q₈	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×#64520	—	2	1	no	—
35	C₂×#64520	D₄	1	1	yes	characteristic
36	C₂×#64520	D₄	1	1	yes	characteristic
37	C₂²×C₁₉⋊C₈	—	2	1	no	—
38	C₂²×C₁₉⋊C₈	—	2	1	no	—
39	C₁₉×C₄⋊C₈	—	2	1	no	—
40	C₁₉×C₄⋊C₈	—	2	1	no	—
41	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
42	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
43	C₁₉×C₂²⋊C₈	—	2	1	no	—
44	C₄×C₈×C₁₉	—	2	1	no	—
45	#10597279	—	4	2	no	—
46	C₄⋊(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	2	yes	—
52	#10597260	—	2	1	no	—
53	C₄×C₁₉⋊C₈	—	2	1	no	—
54	C₂×Q₈×C₁₉	—	2	2	no	—
55	C₂×Q₈×C₁₉	—	2	2	no	—
56	C₂×Q₈×C₁₉	—	8	2	no	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
61	M₁₆×C₁₉	—	4	1	no	—
62	M₁₆×C₁₉	—	4	1	no	—
63	C₂×C₈×C₁₉	—	2	1	no	—
64	C₂×C₈×C₁₉	—	2	1	no	—
65	C₂×C₈×C₁₉	—	4	1	no	—
66	C₄⋊C₄×C₁₉	—	4	1	no	—
67	C₄⋊C₄×C₁₉	—	4	1	no	—
68	C₄⋊C₄×C₁₉	—	4	1	no	—
69	C₄⋊C₄×C₁₉	—	4	1	no	—
70	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₉	#41	1	1	yes	characteristic
73	C₄²×C₁₉	#41	1	1	yes	characteristic
74	#64520	—	2	1	no	—
75	#64520	—	2	1	no	—
76	#64520	—	2	1	no	—
77	#64520	—	4	1	no	—
78	#64520	—	4	1	no	—
79	#64520	Q₁₆	1	2	yes	—
80	C₂×C₁₉⋊C₈	—	2	1	no	—
81	C₂×C₁₉⋊C₈	—	2	1	no	—
82	C₂×C₁₉⋊C₈	—	2	2	no	—
83	C₂×C₁₉⋊C₈	—	4	1	no	—
84	C₂×C₁₉⋊C₈	—	4	1	no	—
85	C₂×C₁₉⋊C₈	—	4	1	no	—
86	C₂×C₁₉⋊C₈	—	4	1	no	—
87	C₂×C₁₉⋊C₈	—	8	1	no	—
88	#10605	—	19	1	no	maximal, Sylow
89	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
90	Q₈×C₁₉	—	8	2	no	—
91	Q₈×C₁₉	—	8	2	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	4	1	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	8	2	no	—
97	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
105	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
107	C₈×C₁₉	—	4	1	no	—
108	C₈×C₁₉	—	4	1	no	—
109	C₈×C₁₉	—	8	1	no	—
110	C₁₉⋊C₈	—	2	2	no	—
111	C₁₉⋊C₈	—	4	2	no	—
112	C₁₉⋊C₈	—	4	1	no	—
113	C₁₉⋊C₈	—	8	1	no	—
114	C₁₉⋊C₈	—	8	1	no	—
115	#1997	—	19	1	no	—
116	#1950	—	19	1	no	—
117	#1571	—	19	1	no	—
118	#1565	—	19	1	no	—
119	#1548	D₁₉	1	1	yes	characteristic
120	C₂×#333	—	19	1	no	—
121	#1292	—	19	1	no	—
122	C₂²×C₁₉	—	2	1	no	—
123	C₂²×C₁₉	—	2	1	no	—
124	C₂²×C₁₉	#396	1	1	yes	characteristic
125	C₂²×C₁₉	#477	1	1	yes	characteristic
126	C₂²×C₁₉	#479	1	1	yes	characteristic
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	8	2	no	—
131	C₄×C₁₉	#462	1	1	yes	characteristic
132	C₄×C₁₉	#463	1	1	yes	characteristic
133	C₄×C₁₉	#467	1	1	yes	characteristic
134	C₄×C₁₉	#468	1	1	yes	characteristic
135	C₄×C₁₉	#471	1	1	yes	characteristic
136	C₄×C₁₉	#473	1	1	yes	characteristic
137	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
138	#431	C₂×D₁₉	1	1	yes	characteristic
139	C₂×#108	—	38	1	no	—
140	#423	—	19	1	no	—
141	#423	C₂×D₁₉	1	1	yes	characteristic
142	C₂×C₄⋊C₈	—	19	1	no	—
143	C₂×C₄⋊C₈	—	19	1	no	—
144	C₄×M₁₆	—	19	1	no	—
145	#343	—	38	1	no	—
146	#343	—	38	1	no	—
147	#341	—	38	1	no	—
148	#335	—	38	2	no	—
149	#335	—	38	1	no	—
150	#334	—	38	1	no	—
151	#333	—	2	1	no	—
152	#333	—	2	1	no	—
153	#333	—	38	2	no	—
154	C₂×C₁₉	—	2	1	no	—
155	C₂×C₁₉	—	2	1	no	—
156	C₂×C₁₉	#2064	1	1	yes	characteristic
157	C₂×C₁₉	#2068	1	1	yes	characteristic
158	C₂×C₁₉	#2069	1	1	yes	characteristic
159	C₂²×Q₈	Dic₃₈	1	2	yes	—
160	C₂×M₁₆	—	2	1	no	—
161	C₂×M₁₆	—	19	1	no	—
162	C₂×M₁₆	—	19	1	no	—
163	C₂×M₁₆	—	38	1	no	—
164	C₂²×C₈	—	38	1	no	—
165	C₂²×C₈	—	38	1	no	—
166	C₄⋊Q₈	—	2	1	no	—
167	C₄⋊Q₈	—	2	1	no	—
168	C₄⋊Q₈	—	2	1	no	—
169	C₄⋊Q₈	—	2	1	no	—
170	C₂×C₄⋊C₄	—	2	1	no	—
171	C₂×C₄⋊C₄	—	2	1	no	—
172	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
173	#108	—	76	2	no	—
174	C₄⋊C₈	—	2	1	no	—
175	C₄⋊C₈	—	2	1	no	—
176	C₄⋊C₈	—	19	2	no	—
177	C₄⋊C₈	—	38	1	no	—
178	C₄⋊C₈	—	38	1	no	—
179	C₄⋊C₈	—	38	1	no	—
180	C₄⋊C₈	—	38	1	no	—
181	C₄⋊C₈	—	38	1	no	—
182	C₄⋊C₈	C₂²⋊D₁₉	1	1	yes	characteristic
183	C₄⋊C₈	C₂²⋊D₁₉	1	1	yes	characteristic
184	C₂²⋊C₈	—	2	1	no	—
185	#97	—	38	1	no	—
186	C₄×C₈	—	2	1	no	—
187	C₄×C₈	—	38	1	no	—
188	C₁₉	#10605	1	1	yes	characteristic, complemented, Sylow
189	C₂×Q₈	—	2	2	no	—
190	C₂×Q₈	—	2	2	no	—
191	C₂×Q₈	—	8	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
194	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
195	C₂²×C₄	#64543	1	1	yes	characteristic
196	M₁₆	—	4	1	no	—
197	M₁₆	—	4	1	no	—
198	M₁₆	—	19	2	no	—
199	M₁₆	—	38	1	no	—
200	M₁₆	—	38	1	no	—
201	M₁₆	—	38	1	no	—
202	M₁₆	—	76	1	no	—
203	M₁₆	—	76	1	no	—
204	C₂×C₈	—	2	1	no	—
205	C₂×C₈	—	2	1	no	—
206	C₂×C₈	—	4	1	no	—
207	C₂×C₈	—	38	1	no	—
208	C₂×C₈	—	38	1	no	—
209	C₂×C₈	—	38	2	no	—
210	C₂×C₈	—	76	1	no	—
211	C₂×C₈	—	76	1	no	—
212	C₂×C₈	—	76	1	no	—
213	C₂×C₈	—	76	1	no	—
214	C₂×C₈	—	152	1	no	—
215	C₄⋊C₄	—	4	1	no	—
216	C₄⋊C₄	—	4	1	no	—
217	C₄⋊C₄	—	4	1	no	—
218	C₄⋊C₄	—	4	1	no	—
219	C₄²	#64541	1	1	yes	characteristic
220	C₄²	D₄×D₁₉	1	1	yes	characteristic
221	C₄²	#64543	1	1	yes	characteristic
222	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
223	C₂³	#10597324	1	1	yes	characteristic
224	Q₈	—	8	2	no	—
225	Q₈	—	8	2	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	8	2	no	—
231	C₂×C₄	#10597324	1	1	yes	characteristic
232	C₂×C₄	#10597325	1	1	yes	characteristic
233	C₂×C₄	#10597330	1	1	yes	characteristic
234	C₂×C₄	#10597360	1	1	yes	characteristic
235	C₂×C₄	#10597361	1	1	yes	characteristic
236	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
237	C₂×C₄	#10597365	1	1	yes	characteristic
238	C₂×C₄	#10597370	1	1	yes	characteristic
239	C₂×C₄	#10597384	1	1	yes	characteristic
240	C₂×C₄	#10597385	1	1	yes	characteristic
241	C₈	—	4	1	no	—
242	C₈	—	4	1	no	—
243	C₈	—	8	1	no	—
244	C₈	—	38	2	no	—
245	C₈	—	76	1	no	—
246	C₈	—	76	2	no	—
247	C₈	—	152	1	no	—
248	C₈	—	152	1	no	—
249	C₂²	—	2	1	no	—
250	C₂²	—	2	1	no	—
251	C₂²	#11926467	1	1	yes	characteristic
252	C₂²	#11926837	1	1	yes	characteristic
253	C₂²	#11926853	1	1	yes	characteristic
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	8	2	no	—
258	C₄	#11926753	1	1	yes	characteristic
259	C₄	#11926762	1	1	yes	characteristic
260	C₄	#11926782	1	1	yes	characteristic
261	C₄	#11926787	1	1	yes	characteristic
262	C₄	#11926809	1	1	yes	characteristic
263	C₄	#11926817	1	1	yes	characteristic
264	C₂	—	2	1	no	—
265	C₂	—	2	1	no	—
266	C₂	#14565002	1	1	yes	characteristic
267	C₂	#14565028	1	1	yes	characteristic
268	C₂	#14565033	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564625

C₂

yes

maximal, characteristic

#14564408

C₂

yes

maximal, characteristic

#14562410

C₂

yes

maximal, characteristic

#14562388

C₂

yes

maximal, characteristic

C₂×#11926293

C₂

yes

maximal, characteristic

#14561509

C₂

yes

maximal, characteristic

C₁₉×#1548

C₂

yes

maximal, characteristic

C₂×#10597279

—

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄×#64520

C₂²

yes

—

—

—

—

—

—

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#333

—

C₁₉×#333

—

C₂²×Q₈×C₁₉

Q₈

yes

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂×#64520

D₄

yes

characteristic

C₂×#64520

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

characteristic

C₁₉×C₄⋊C₈

D₄

yes

characteristic

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

#10597279

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

—

—

—

—

Q₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10605

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

100

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

101

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

102

C₂×C₄×C₁₉

#126

yes

characteristic

103

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

104

C₂×C₄×C₁₉

#135

yes

characteristic

105

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

106

C₂×C₄×C₁₉

#137

yes

characteristic

107

C₈×C₁₉

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₁₉⋊C₈

—

111

C₁₉⋊C₈

—

112

C₁₉⋊C₈

—

113

C₁₉⋊C₈

—

114

C₁₉⋊C₈

—

115

#1997

—

116

#1950

—

117

#1571

—

118

#1565

—

119

#1548

D₁₉

yes

characteristic

120

C₂×#333

—

121

#1292

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

#396

yes

characteristic

125

C₂²×C₁₉

#477

yes

characteristic

126

C₂²×C₁₉

#479

yes

characteristic

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

#462

yes

characteristic

132

C₄×C₁₉

#463

yes

characteristic

133

C₄×C₁₉

#467

yes

characteristic

134

C₄×C₁₉

#468

yes

characteristic

135

C₄×C₁₉

#471

yes

characteristic

136

C₄×C₁₉

#473

yes

characteristic

137

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

138

#431

C₂×D₁₉

yes

characteristic

139

C₂×#108

—

140

#423

—

141

#423

C₂×D₁₉

yes

characteristic

142

C₂×C₄⋊C₈

—

143

C₂×C₄⋊C₈

—

144

C₄×M₁₆

—

145

#343

—

146

#343

—

147

#341

—

148

#335

—

149

#335

—

150

#334

—

151

#333

—

152

#333

—

153

#333

—

154

C₂×C₁₉

—

155

C₂×C₁₉

—

156

C₂×C₁₉

#2064

yes

characteristic

157

C₂×C₁₉

#2068

yes

characteristic

158

C₂×C₁₉

#2069

yes

characteristic

159

C₂²×Q₈

Dic₃₈

yes

—

160

C₂×M₁₆

—

161

C₂×M₁₆

—

162

C₂×M₁₆

—

163

C₂×M₁₆

—

164

C₂²×C₈

—

165

C₂²×C₈

—

166

C₄⋊Q₈

—

167

C₄⋊Q₈

—

168

C₄⋊Q₈

—

169

C₄⋊Q₈

—

170

C₂×C₄⋊C₄

—

171

C₂×C₄⋊C₄

—

172

C₂×C₄²

C₂²×D₁₉

yes

characteristic

173

#108

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

C₄⋊C₈

C₂²⋊D₁₉

yes

characteristic

183

C₄⋊C₈

C₂²⋊D₁₉

yes

characteristic

184

C₂²⋊C₈

—

185

#97

—

186

C₄×C₈

—

187

C₄×C₈

—

188

C₁₉

#10605

yes

characteristic, complemented, Sylow

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂²×C₄

—

193

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

194

C₂²×C₄

D₄×D₁₉

yes

characteristic

195

C₂²×C₄

#64543

yes

characteristic

196

M₁₆

—

197

M₁₆

—

198

M₁₆

—

199

M₁₆

—

200

M₁₆

—

201

M₁₆

—

202

M₁₆

—

203

M₁₆

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

152

—

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄²

#64541

yes

characteristic

220

C₄²

D₄×D₁₉

yes

characteristic

221

C₄²

#64543

yes

characteristic

222

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

223

C₂³

#10597324

yes

characteristic

224

Q₈

—

225

Q₈

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

#10597324

yes

characteristic

232

C₂×C₄

#10597325

yes

characteristic

233

C₂×C₄

#10597330

yes

characteristic

234

C₂×C₄

#10597360

yes

characteristic

235

C₂×C₄

#10597361

yes

characteristic

236

C₂×C₄

Q₁₆×D₁₉

yes

characteristic

237

C₂×C₄

#10597365

yes

characteristic

238

C₂×C₄

#10597370

yes

characteristic

239

C₂×C₄

#10597384

yes

characteristic

240

C₂×C₄

#10597385

yes

characteristic

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

245

C₈

—

246

C₈

—

247

C₈

—

152

—

248

C₈

—

152

—

249

C₂²

—

250

C₂²

—

251

C₂²

#11926467

yes

characteristic

252

C₂²

#11926837

yes

characteristic

253

C₂²

#11926853

yes

characteristic

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

#11926753

yes

characteristic

259

C₄

#11926762

yes

characteristic

260

C₄

#11926782

yes

characteristic

261

C₄

#11926787

yes

characteristic

262

C₄

#11926809

yes

characteristic

263

C₄

#11926817

yes

characteristic

264

C₂

—

265

C₂

—

266

C₂

#14565002

yes

characteristic

267

C₂

#14565028

yes

characteristic

268

C₂

#14565033

yes

characteristic

	subgroup	G/H
center	C₂²	#11926467
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1548	C₂
socle	C₂²×C₁₉	#396
prime radical	C₂³×C₁₉	C₂²⋊Q₈
hypercenter	#1548	D₁₉
hypocenter	C₁₉	#10605
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

subgroup

G/H

center

C₂²

#11926467

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1548

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 ◁ #1548

N	H ≅ G/N	type
188. C₁₉	#10605	semidirect

H ≅ G/N

type

188. C₁₉

#10605

semidirect

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

subgroup	index
#14564625	2
#14564408	2
#14562410	2
#14562388	2
C₂×#11926293	2
#14561509	2
C₁₉×#1548	2
#10605	19

subgroup

index

C₁₉×#1548

Subgroups — #18087178

Conjugacy classes of subgroups

Complements

Maximal subgroups