Group #18085136 — subgroups

Subgroups — #18085136

Order 4864.

626 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 139 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×#11926924	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926825	C₂	1	2	yes	maximal
3	#14564429	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926289	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Dic₇₆	—	2	2	no	—
7	C₂×#10597315	C₂²	1	2	yes	—
8	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
9	#11926924	—	2	4	no	—
10	#11926825	—	2	4	no	—
11	#11926825	—	2	4	no	—
12	C₂×#10597275	—	2	2	no	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#10597278	—	2	2	no	—
15	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
16	#11926289	—	2	4	no	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×D₇₆	D₄	1	1	yes	characteristic
20	C₂²×C₄×D₁₉	—	2	1	no	—
21	C₂²×Dic₃₈	—	2	2	no	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₂²×C₈×C₁₉	D₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
29	C₂²×C₁₉⋊C₈	—	2	1	no	—
30	C₂×Dic₇₆	—	2	8	no	—
31	C₂×Dic₇₆	—	4	4	no	—
32	C₂×Dic₇₆	—	4	4	no	—
33	C₄×D₇₆	—	2	2	no	—
34	C₄×D₇₆	—	2	2	no	—
35	#10597315	—	2	2	no	—
36	#10597315	—	2	2	no	—
37	#10597315	—	2	2	no	—
38	#10597315	D₄	1	4	yes	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
41	C₄×C₈×C₁₉	—	2	2	no	—
42	#10597278	—	2	8	no	—
43	(C₂×D₁₉)⋊C₈	—	4	4	no	—
44	#10597275	—	2	8	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₂³×D₁₉	—	2	1	no	—
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
50	C₂²×Dic₁₉	—	2	1	no	—
51	C₂²×Dic₁₉	—	4	2	no	—
52	C₂×D₇₆	—	2	2	no	—
53	C₂×D₇₆	—	2	2	no	—
54	C₂×D₇₆	—	2	1	no	—
55	C₂×D₇₆	Q₁₆	1	2	yes	complemented
56	C₂×C₄×D₁₉	—	4	1	no	—
57	C₂×C₄×D₁₉	—	4	1	no	—
58	C₂×C₄×D₁₉	—	4	2	no	—
59	C₂×C₄×D₁₉	—	4	2	no	—
60	C₂×Dic₃₈	—	2	4	no	—
61	C₂×Dic₃₈	—	4	4	no	—
62	C₂×Dic₃₈	—	4	4	no	—
63	C₂×Dic₃₈	—	4	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	2	4	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₂×C₈×C₁₉	—	4	2	no	—
69	C₂×C₈×C₁₉	D₈	1	4	yes	—
70	C₄²×C₁₉	C₂×D₄	1	2	yes	—
71	C₄²×C₁₉	C₂×D₄	1	2	yes	—
72	(C₂×D₁₉)⋊C₄	—	4	2	no	—
73	C₄⋊Dic₁₉	—	2	2	no	—
74	C₄⋊Dic₁₉	—	2	4	no	—
75	C₄⋊Dic₁₉	—	2	4	no	—
76	C₄⋊Dic₁₉	—	4	2	no	—
77	C₄⋊Dic₁₉	—	4	2	no	—
78	C₂×C₁₉⋊C₈	—	4	1	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	Dic₇₆	—	4	16	no	—
81	#10274	—	19	1	no	maximal, Sylow
82	C₂³×C₁₉	#121	1	1	yes	characteristic
83	C₂²×D₁₉	—	2	2	no	—
84	C₂²×D₁₉	—	4	1	no	—
85	C₂²×D₁₉	—	4	2	no	—
86	C₂²×D₁₉	—	4	1	no	—
87	C₂²×D₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#120	1	2	yes	—
91	C₂×C₄×C₁₉	#121	1	2	yes	—
92	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
94	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
96	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
97	C₂×C₄×C₁₉	#137	1	2	yes	—
98	C₂×Dic₁₉	—	4	4	no	—
99	C₂×Dic₁₉	—	4	1	no	—
100	C₂×Dic₁₉	—	4	2	no	—
101	C₂×Dic₁₉	—	8	4	no	—
102	D₇₆	—	2	4	no	—
103	D₇₆	—	4	2	no	—
104	C₄×D₁₉	—	8	2	no	—
105	C₄×D₁₉	—	8	1	no	—
106	C₄×D₁₉	—	8	1	no	—
107	Dic₃₈	—	4	8	no	—
108	Dic₃₈	—	8	2	no	—
109	Dic₃₈	—	8	2	no	—
110	C₈×C₁₉	—	2	4	no	—
111	C₈×C₁₉	—	4	4	no	—
112	C₁₉⋊C₈	—	8	1	no	—
113	C₂×#494	—	19	1	no	—
114	C₂×#474	—	19	2	no	—
115	#1954	—	19	1	no	—
116	C₂×#332	—	19	2	no	—
117	#1277	D₁₉	1	1	yes	characteristic, complemented
118	C₂²×C₁₉	#392	1	1	yes	characteristic
119	C₂²×C₁₉	#459	1	2	yes	—
120	C₂²×C₁₉	#467	1	1	yes	characteristic
121	C₂²×C₁₉	#470	1	1	yes	characteristic
122	C₂²×C₁₉	#473	1	2	yes	—
123	C₂×D₁₉	—	4	4	no	—
124	C₂×D₁₉	—	4	2	no	—
125	C₂×D₁₉	—	8	2	no	—
126	C₂×D₁₉	—	8	1	no	—
127	C₂×D₁₉	—	8	1	no	—
128	C₄×C₁₉	—	2	2	no	—
129	C₄×C₁₉	#447	1	2	yes	—
130	C₄×C₁₉	#451	1	2	yes	—
131	C₄×C₁₉	#452	1	2	yes	—
132	C₄×C₁₉	#493	1	1	yes	characteristic
133	C₄×C₁₉	#496	1	1	yes	characteristic
134	Dic₁₉	—	8	4	no	—
135	Dic₁₉	—	8	1	no	—
136	C₂²×Q₁₆	—	38	2	no	—
137	C₂×C₄⋊Q₈	—	19	2	no	—
138	C₂×C₄×D₄	—	19	1	no	—
139	#494	—	38	4	no	—
140	#474	—	38	4	no	—
141	#474	—	38	4	no	—
142	C₂×#107	—	38	2	no	—
143	C₂×C₄⋊C₈	—	19	1	no	—
144	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
145	C₂×#102	—	38	2	no	—
146	C₂×C₂²⋊C₈	—	38	2	no	—
147	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
148	#332	—	38	4	no	—
149	C₂×C₁₉	#1669	1	2	yes	—
150	C₂×C₁₉	#1689	1	2	yes	—
151	C₂×C₁₉	#2001	1	1	yes	characteristic
152	C₂×C₁₉	#2011	1	1	yes	characteristic
153	C₂×C₁₉	#2020	1	1	yes	characteristic
154	D₁₉	—	8	2	no	—
155	C₂²×Q₈	—	38	2	no	—
156	C₂²×D₄	—	19	1	no	—
157	C₂³×C₄	—	38	1	no	—
158	C₂×Q₁₆	—	38	8	no	—
159	C₂×Q₁₆	—	76	4	no	—
160	C₂×Q₁₆	—	76	4	no	—
161	C₂²×C₈	—	2	2	no	—
162	C₂²×C₈	—	38	1	no	—
163	C₂²×C₈	D₇₆	1	2	yes	—
164	C₄⋊Q₈	—	19	4	no	—
165	C₄⋊Q₈	—	38	2	no	—
166	C₄⋊Q₈	—	38	2	no	—
167	C₄⋊Q₈	—	38	2	no	—
168	C₄×D₄	—	38	2	no	—
169	C₄×D₄	—	38	2	no	—
170	C₂×C₄⋊C₄	—	19	1	no	—
171	C₂×C₄⋊C₄	—	38	2	no	—
172	C₂×C₄⋊C₄	—	38	2	no	—
173	C₂×C₂²⋊C₄	—	38	1	no	—
174	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
175	#107	—	38	8	no	—
176	C₄⋊C₈	—	2	2	no	—
177	C₄⋊C₈	—	38	2	no	—
178	C₄⋊C₈	D₇₆	1	4	yes	—
179	#102	—	38	8	no	—
180	C₂²⋊C₈	—	76	4	no	—
181	C₄×C₈	—	2	2	no	—
182	C₁₉	#10274	1	1	yes	characteristic, complemented, Sylow
183	C₂⁴	—	38	1	no	—
184	C₂×Q₈	—	38	4	no	—
185	C₂×Q₈	—	76	2	no	—
186	C₂×Q₈	—	76	4	no	—
187	C₂×Q₈	—	76	4	no	—
188	C₂×D₄	—	19	2	no	—
189	C₂×D₄	—	38	2	no	—
190	C₂×D₄	—	38	1	no	—
191	C₂×D₄	—	38	2	no	—
192	C₂²×C₄	—	38	1	no	—
193	C₂²×C₄	—	76	2	no	—
194	C₂²×C₄	—	76	1	no	—
195	C₂²×C₄	—	76	1	no	—
196	C₂²×C₄	—	76	2	no	—
197	C₂²×C₄	—	76	2	no	—
198	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
199	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
200	C₂²×C₄	#64545	1	1	yes	characteristic
201	Q₁₆	—	76	16	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	2	4	no	—
205	C₂×C₈	—	4	2	no	—
206	C₂×C₈	—	4	2	no	—
207	C₂×C₈	—	76	1	no	—
208	C₂×C₈	—	76	2	no	—
209	C₂×C₈	D₁₅₂	1	4	yes	—
210	C₄⋊C₄	—	38	4	no	—
211	C₄⋊C₄	—	38	2	no	—
212	C₄⋊C₄	—	38	4	no	—
213	C₄⋊C₄	—	76	2	no	—
214	C₄⋊C₄	—	76	2	no	—
215	C₂²⋊C₄	—	76	2	no	—
216	C₄²	C₂×D₇₆	1	2	yes	—
217	C₄²	D₄×D₁₉	1	2	yes	—
218	C₂³	—	38	2	no	—
219	C₂³	—	76	1	no	—
220	C₂³	—	76	2	no	—
221	C₂³	—	76	1	no	—
222	C₂³	—	76	2	no	—
223	C₂³	#10597341	1	1	yes	characteristic
224	Q₈	—	76	8	no	—
225	Q₈	—	152	2	no	—
226	Q₈	—	152	2	no	—
227	D₄	—	38	4	no	—
228	D₄	—	76	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	76	1	no	—
231	C₂×C₄	—	76	4	no	—
232	C₂×C₄	—	76	2	no	—
233	C₂×C₄	—	152	4	no	—
234	C₂×C₄	—	152	1	no	—
235	C₂×C₄	—	152	1	no	—
236	C₂×C₄	—	152	2	no	—
237	C₂×C₄	#10597320	1	1	yes	characteristic
238	C₂×C₄	#10597328	1	1	yes	characteristic
239	C₂×C₄	#10597328	1	2	yes	—
240	C₂×C₄	#10597341	1	2	yes	—
241	C₂×C₄	C₂×D₁₅₂	1	2	yes	—
242	C₂×C₄	#10597354	1	2	yes	—
243	C₂×C₄	#10597358	1	1	yes	characteristic
244	C₂×C₄	#10597361	1	2	yes	—
245	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
246	C₈	—	2	4	no	—
247	C₈	—	4	4	no	—
248	C₈	—	152	1	no	—
249	C₂²	—	76	2	no	—
250	C₂²	—	76	4	no	—
251	C₂²	—	152	2	no	—
252	C₂²	—	152	1	no	—
253	C₂²	—	152	1	no	—
254	C₂²	#11926454	1	1	yes	characteristic
255	C₂²	#11926740	1	2	yes	—
256	C₂²	#11926786	1	1	yes	characteristic
257	C₂²	#11926803	1	1	yes	characteristic
258	C₂²	#11926820	1	2	yes	—
259	C₄	—	2	2	no	—
260	C₄	—	152	1	no	—
261	C₄	—	152	4	no	—
262	C₄	#11926680	1	2	yes	—
263	C₄	#11926701	1	2	yes	—
264	C₄	#11926707	1	2	yes	—
265	C₄	#11926921	1	1	yes	characteristic
266	C₄	#11926933	1	1	yes	characteristic
267	C₂	—	152	2	no	—
268	C₂	#14563001	1	2	yes	—
269	C₂	#14563125	1	2	yes	—
270	C₂	#14564646	1	1	yes	characteristic
271	C₂	#14564708	1	1	yes	characteristic
272	C₂	#14564757	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926924

C₂

yes

maximal, characteristic, complemented

C₂×#11926825

C₂

yes

maximal

#14564429

C₂

yes

maximal, characteristic

C₂×#11926289

C₂

yes

maximal, complemented

C₁₉×#1277

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₇₆

—

C₂×#10597315

C₂²

yes

—

C₂×C₄×D₇₆

C₂²

yes

—

—

—

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597278

—

C₂×(C₂×D₁₉)⋊C₈

—

#11926289

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×D₇₆

D₄

yes

characteristic

C₂²×C₄×D₁₉

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₄×D₇₆

—

C₄×D₇₆

—

—

—

—

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₄×C₈×C₁₉

—

#10597278

—

(C₂×D₁₉)⋊C₈

—

#10597275

—

C₄⋊(C₁₉⋊C₈)

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

Q₁₆

yes

complemented

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

D₇₆

—

103

D₇₆

—

104

C₄×D₁₉

—

105

C₄×D₁₉

—

106

C₄×D₁₉

—

107

Dic₃₈

—

108

Dic₃₈

—

109

Dic₃₈

—

110

C₈×C₁₉

—

111

C₈×C₁₉

—

112

C₁₉⋊C₈

—

113

C₂×#494

—

114

C₂×#474

—

115

#1954

—

116

C₂×#332

—

117

#1277

D₁₉

yes

characteristic, complemented

118

C₂²×C₁₉

#392

yes

characteristic

119

C₂²×C₁₉

#459

yes

—

120

C₂²×C₁₉

#467

yes

characteristic

121

C₂²×C₁₉

#470

yes

characteristic

122

C₂²×C₁₉

#473

yes

—

123

C₂×D₁₉

—

124

C₂×D₁₉

—

125

C₂×D₁₉

—

126

C₂×D₁₉

—

127

C₂×D₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

#447

yes

—

130

C₄×C₁₉

#451

yes

—

131

C₄×C₁₉

#452

yes

—

132

C₄×C₁₉

#493

yes

characteristic

133

C₄×C₁₉

#496

yes

characteristic

134

Dic₁₉

—

135

Dic₁₉

—

136

C₂²×Q₁₆

—

137

C₂×C₄⋊Q₈

—

138

C₂×C₄×D₄

—

139

#494

—

140

#474

—

141

#474

—

142

C₂×#107

—

143

C₂×C₄⋊C₈

—

144

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

145

C₂×#102

—

146

C₂×C₂²⋊C₈

—

147

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

148

#332

—

149

C₂×C₁₉

#1669

yes

—

150

C₂×C₁₉

#1689

yes

—

151

C₂×C₁₉

#2001

yes

characteristic

152

C₂×C₁₉

#2011

yes

characteristic

153

C₂×C₁₉

#2020

yes

characteristic

154

D₁₉

—

155

C₂²×Q₈

—

156

C₂²×D₄

—

157

C₂³×C₄

—

158

C₂×Q₁₆

—

159

C₂×Q₁₆

—

160

C₂×Q₁₆

—

161

C₂²×C₈

—

162

C₂²×C₈

—

163

C₂²×C₈

D₇₆

yes

—

164

C₄⋊Q₈

—

165

C₄⋊Q₈

—

166

C₄⋊Q₈

—

167

C₄⋊Q₈

—

168

C₄×D₄

—

169

C₄×D₄

—

170

C₂×C₄⋊C₄

—

171

C₂×C₄⋊C₄

—

172

C₂×C₄⋊C₄

—

173

C₂×C₂²⋊C₄

—

174

C₂×C₄²

C₂²×D₁₉

yes

characteristic

175

#107

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

D₇₆

yes

—

179

#102

—

180

C₂²⋊C₈

—

181

C₄×C₈

—

182

C₁₉

#10274

yes

characteristic, complemented, Sylow

183

C₂⁴

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

C₂×D₇₆

yes

characteristic

199

C₂²×C₄

D₄×D₁₉

yes

characteristic

200

C₂²×C₄

#64545

yes

characteristic

201

Q₁₆

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

D₁₅₂

yes

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₂²⋊C₄

—

216

C₄²

C₂×D₇₆

yes

—

217

C₄²

D₄×D₁₉

yes

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

#10597341

yes

characteristic

224

Q₈

—

225

Q₈

—

152

—

226

Q₈

—

152

—

227

D₄

—

228

D₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

152

—

234

C₂×C₄

—

152

—

235

C₂×C₄

—

152

—

236

C₂×C₄

—

152

—

237

C₂×C₄

#10597320

yes

characteristic

238

C₂×C₄

#10597328

yes

characteristic

239

C₂×C₄

#10597328

yes

—

240

C₂×C₄

#10597341

yes

—

241

C₂×C₄

C₂×D₁₅₂

yes

—

242

C₂×C₄

#10597354

yes

—

243

C₂×C₄

#10597358

yes

characteristic

244

C₂×C₄

#10597361

yes

—

245

C₂×C₄

Q₁₆×D₁₉

yes

characteristic

246

C₈

—

247

C₈

—

248

C₈

—

152

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

152

—

252

C₂²

—

152

—

253

C₂²

—

152

—

254

C₂²

#11926454

yes

characteristic

255

C₂²

#11926740

yes

—

256

C₂²

#11926786

yes

characteristic

257

C₂²

#11926803

yes

characteristic

258

C₂²

#11926820

yes

—

259

C₄

—

260

C₄

—

152

—

261

C₄

—

152

—

262

C₄

#11926680

yes

—

263

C₄

#11926701

yes

—

264

C₄

#11926707

yes

—

265

C₄

#11926921

yes

characteristic

266

C₄

#11926933

yes

characteristic

267

C₂

—

152

—

268

C₂

#14563001

yes

—

269

C₂

#14563125

yes

—

270

C₂

#14564646

yes

characteristic

271

C₂

#14564708

yes

characteristic

272

C₂

#14564757

yes

characteristic

	subgroup	G/H
center	C₂³	#10597341
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1277	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×D₇₆	D₄
hypercenter	#1277	D₁₉
hypocenter	C₁₉	#10274
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

subgroup

G/H

center

C₂³

#10597341

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1277

C₂

socle

C₂³×C₁₉

#121

prime radical

C₂²×D₇₆

D₄

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

N	H ≅ G/N	type
1. C₂×#11926924	C₂	semidirect
4. C₂×#11926289	C₂	semidirect
5. C₁₉×#1277	C₂	semidirect
55. C₂×D₇₆	Q₁₆	semidirect
117. #1277	D₁₉	semidirect
182. C₁₉	#10274	semidirect

H ≅ G/N

type

1. C₂×#11926924

C₂

semidirect

4. C₂×#11926289

C₂

semidirect

5. C₁₉×#1277

C₂

semidirect

55. C₂×D₇₆

Q₁₆

semidirect

117. #1277

D₁₉

semidirect

182. C₁₉

#10274

semidirect

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

subgroup	index
C₂×#11926924	2
C₂×#11926825	2
#14564429	2
C₂×#11926289	2
C₁₉×#1277	2
#10274	19

subgroup

index

C₁₉×#1277

Subgroups — #18085136

Conjugacy classes of subgroups

Complements

Maximal subgroups