Group #18070808 — subgroups

Subgroups — #18070808

Order 4864.

468 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 115 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×#10597315	C₂	1	1	yes	maximal, characteristic
2	#14563384	C₂	1	1	yes	maximal, characteristic
3	#14561457	C₂	1	4	yes	maximal
4	C₁₉×#1745	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597315	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₃₈	—	2	1	no	—
7	C₂×#10597260	—	2	1	no	—
8	#11926450	—	2	1	no	—
9	#11926442	—	2	1	no	—
10	#11926442	C₂²	1	2	yes	—
11	#11926414	C₄	1	1	yes	characteristic
12	C₄×C₄⋊Dic₁₉	—	2	1	no	—
13	C₄×C₄⋊Dic₁₉	C₄	1	2	yes	—
14	#11926299	—	2	1	no	—
15	#11926299	C₂²	1	2	yes	—
16	C₂×C₁₉×#97	—	2	1	no	—
17	C₄³×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#336	—	2	1	no	—
19	C₁₉×#336	C₂²	1	2	yes	—
20	C₂²×Dic₃₈	—	2	1	no	—
21	C₂²×C₈×C₁₉	—	2	2	no	—
22	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×C₄⋊Dic₁₉	—	2	1	no	—
32	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
34	C₂×Dic₁₉⋊C₄	—	2	2	no	—
35	C₂×C₄×Dic₁₉	—	2	2	no	—
36	C₂²×C₁₉⋊C₈	—	2	2	no	—
37	#10597315	—	2	4	no	—
38	C₄×Dic₃₈	—	4	4	no	—
39	C₁₉×#97	—	2	4	no	—
40	C₁₉⋊#95	—	2	2	no	—
41	C₁₉⋊#95	—	2	2	no	—
42	#10597260	—	2	4	no	—
43	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₁₉	—	2	2	no	—
51	C₂²×Dic₁₉	—	2	2	no	—
52	C₂×Dic₃₈	—	2	4	no	—
53	C₂×Dic₃₈	—	4	2	no	—
54	C₂×Dic₃₈	—	4	2	no	—
55	C₂×C₈×C₁₉	—	2	4	no	—
56	C₂×C₈×C₁₉	—	4	2	no	—
57	C₂×C₈×C₁₉	—	4	2	no	—
58	C₄²×C₁₉	—	2	2	no	—
59	C₄²×C₁₉	—	2	2	no	—
60	C₄²×C₁₉	—	2	2	no	—
61	C₄²×C₁₉	—	2	2	no	—
62	C₄²×C₁₉	—	2	2	no	—
63	C₄²×C₁₉	—	2	2	no	—
64	C₄²×C₁₉	—	4	1	no	—
65	C₄⋊Dic₁₉	—	2	4	no	—
66	C₄⋊Dic₁₉	—	2	2	no	—
67	C₄⋊Dic₁₉	—	4	2	no	—
68	C₄⋊Dic₁₉	—	4	2	no	—
69	C₄⋊Dic₁₉	—	4	2	no	—
70	C₄⋊Dic₁₉	M₁₆	1	4	yes	—
71	Dic₁₉⋊C₄	—	4	4	no	—
72	C₄×Dic₁₉	—	4	4	no	—
73	C₂×C₁₉⋊C₈	—	2	4	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	#7638	—	19	1	no	maximal, Sylow
77	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	#101	1	2	yes	—
94	C₂×C₄×C₁₉	#104	1	2	yes	—
95	C₂×C₄×C₁₉	#104	1	2	yes	—
96	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
97	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
98	C₂×C₄×C₁₉	#137	1	2	yes	—
99	C₂×Dic₁₉	—	2	4	no	—
100	C₂×Dic₁₉	—	4	2	no	—
101	C₂×Dic₁₉	—	4	2	no	—
102	C₂×Dic₁₉	—	4	2	no	—
103	C₂×Dic₁₉	—	4	2	no	—
104	C₂×Dic₁₉	—	4	2	no	—
105	Dic₃₈	—	4	8	no	—
106	C₈×C₁₉	—	4	4	no	—
107	C₁₉⋊C₈	—	4	4	no	—
108	C₄×C₄⋊Q₈	—	19	1	no	—
109	#1745	—	19	1	no	—
110	#1745	D₁₉	1	1	yes	characteristic
111	#1271	—	19	4	no	—
112	C₂²×C₁₉	#407	1	1	yes	characteristic
113	C₂²×C₁₉	#410	1	1	yes	characteristic
114	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
115	C₂²×C₁₉	#418	1	1	yes	characteristic
116	C₂²×C₁₉	#419	1	1	yes	characteristic
117	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
118	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
119	C₄×C₁₉	—	2	2	no	—
120	C₄×C₁₉	—	2	2	no	—
121	C₄×C₁₉	—	2	2	no	—
122	C₄×C₁₉	—	2	2	no	—
123	C₄×C₁₉	—	2	2	no	—
124	C₄×C₁₉	—	2	2	no	—
125	C₄×C₁₉	—	4	1	no	—
126	Dic₁₉	—	4	4	no	—
127	Dic₁₉	—	8	2	no	—
128	C₂×C₄⋊Q₈	—	19	1	no	—
129	C₂×C₄×Q₈	—	38	1	no	—
130	C₂×#97	—	2	1	no	—
131	C₂×#97	—	38	1	no	—
132	#391	—	38	1	no	—
133	#389	—	19	2	no	—
134	#389	—	38	1	no	—
135	#384	—	19	1	no	—
136	C₄×C₄⋊C₄	—	19	2	no	—
137	C₄×C₄⋊C₄	—	38	1	no	—
138	C₄³	C₂×D₁₉	1	1	yes	characteristic
139	#336	—	2	1	no	—
140	#336	—	19	2	no	—
141	#336	—	38	1	no	—
142	#336	C₂×D₁₉	1	2	yes	—
143	C₂×C₁₉	#1467	1	1	yes	characteristic
144	C₂×C₁₉	#1490	1	1	yes	characteristic
145	C₂×C₁₉	#1491	1	1	yes	characteristic
146	C₂×C₁₉	#1505	1	1	yes	characteristic
147	C₂×C₁₉	#1506	1	1	yes	characteristic
148	C₂×C₁₉	#1526	1	1	yes	characteristic
149	C₂×C₁₉	#1556	1	1	yes	characteristic
150	C₂²×Q₈	—	38	1	no	—
151	C₂²×C₈	—	2	2	no	—
152	C₂²×C₈	—	38	2	no	—
153	C₄⋊Q₈	—	38	4	no	—
154	C₄×Q₈	—	76	4	no	—
155	C₂×C₄⋊C₄	—	19	2	no	—
156	C₂×C₄⋊C₄	—	19	2	no	—
157	C₂×C₄⋊C₄	—	38	1	no	—
158	C₂×C₄⋊C₄	—	38	1	no	—
159	C₂×C₄⋊C₄	—	38	1	no	—
160	C₂×C₄⋊C₄	—	38	2	no	—
161	C₂×C₄²	—	38	2	no	—
162	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
163	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
164	C₂×C₄²	D₇₆	1	1	yes	characteristic
165	C₂×C₄²	D₇₆	1	1	yes	characteristic
166	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
167	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
168	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
169	#97	—	2	4	no	—
170	#97	—	38	4	no	—
171	#95	—	38	2	no	—
172	#95	—	38	2	no	—
173	C₁₉	#7638	1	1	yes	characteristic, complemented, Sylow
174	C₂×Q₈	—	38	4	no	—
175	C₂×Q₈	—	76	2	no	—
176	C₂×Q₈	—	76	2	no	—
177	C₂²×C₄	—	38	2	no	—
178	C₂²×C₄	—	38	2	no	—
179	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
180	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
181	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
182	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
183	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
184	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
185	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
186	C₂×C₈	—	2	4	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	4	2	no	—
189	C₂×C₈	—	38	4	no	—
190	C₂×C₈	—	76	2	no	—
191	C₂×C₈	—	76	2	no	—
192	C₄⋊C₄	—	19	4	no	—
193	C₄⋊C₄	—	38	4	no	—
194	C₄⋊C₄	—	38	2	no	—
195	C₄⋊C₄	—	76	2	no	—
196	C₄⋊C₄	—	76	2	no	—
197	C₄⋊C₄	—	76	2	no	—
198	C₄⋊C₄	—	76	4	no	—
199	C₄²	—	2	2	no	—
200	C₄²	—	2	2	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	2	2	no	—
203	C₄²	—	2	2	no	—
204	C₄²	—	2	2	no	—
205	C₄²	—	4	1	no	—
206	C₄²	—	76	4	no	—
207	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
208	Q₈	—	76	8	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	38	4	no	—
225	C₂×C₄	—	76	2	no	—
226	C₂×C₄	—	76	2	no	—
227	C₂×C₄	—	76	2	no	—
228	C₂×C₄	—	76	2	no	—
229	C₂×C₄	—	76	2	no	—
230	C₂×C₄	#10597262	1	2	yes	—
231	C₂×C₄	#10597281	1	2	yes	—
232	C₂×C₄	#10597282	1	2	yes	—
233	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
234	C₂×C₄	#10597354	1	2	yes	—
235	C₂×C₄	#10597397	1	2	yes	—
236	C₈	—	4	4	no	—
237	C₈	—	76	4	no	—
238	C₂²	#11926507	1	1	yes	characteristic
239	C₂²	#11926517	1	1	yes	characteristic
240	C₂²	C₂×#10597281	1	1	yes	characteristic
241	C₂²	#11926550	1	1	yes	characteristic
242	C₂²	#11926552	1	1	yes	characteristic
243	C₂²	C₂×#10597282	1	1	yes	characteristic
244	C₂²	C₂×#10597262	1	1	yes	characteristic
245	C₄	—	2	2	no	—
246	C₄	—	2	2	no	—
247	C₄	—	2	2	no	—
248	C₄	—	2	2	no	—
249	C₄	—	2	2	no	—
250	C₄	—	2	2	no	—
251	C₄	—	4	1	no	—
252	C₄	—	76	4	no	—
253	C₄	—	152	2	no	—
254	C₂	#14561978	1	1	yes	characteristic
255	C₂	#14562079	1	1	yes	characteristic
256	C₂	#14562081	1	1	yes	characteristic
257	C₂	#14562144	1	1	yes	characteristic
258	C₂	#14562146	1	1	yes	characteristic
259	C₂	#14562229	1	1	yes	characteristic
260	C₂	#14562351	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597315

C₂

yes

maximal, characteristic

#14563384

C₂

yes

maximal, characteristic

#14561457

C₂

yes

maximal

C₁₉×#1745

C₂

yes

maximal, characteristic

C₂×#10597315

C₄

yes

characteristic

C₂×C₄×Dic₃₈

—

—

—

—

C₂²

yes

—

#11926414

C₄

yes

characteristic

C₄×C₄⋊Dic₁₉

—

C₄×C₄⋊Dic₁₉

C₄

yes

—

#11926299

—

#11926299

C₂²

yes

—

C₂×C₁₉×#97

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₁₉×#336

C₂²

yes

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

#10597315

—

C₄×Dic₃₈

—

C₁₉×#97

—

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597260

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

M₁₆

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7638

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

C₂×Dic₁₉

—

105

Dic₃₈

—

106

C₈×C₁₉

—

107

C₁₉⋊C₈

—

108

C₄×C₄⋊Q₈

—

109

#1745

—

110

#1745

D₁₉

yes

characteristic

111

#1271

—

112

C₂²×C₁₉

#407

yes

characteristic

113

C₂²×C₁₉

#410

yes

characteristic

114

C₂²×C₁₉

C₂×#101

yes

characteristic

115

C₂²×C₁₉

#418

yes

characteristic

116

C₂²×C₁₉

#419

yes

characteristic

117

C₂²×C₁₉

C₂×#104

yes

characteristic

118

C₂²×C₁₉

C₂×#104

yes

characteristic

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

Dic₁₉

—

127

Dic₁₉

—

128

C₂×C₄⋊Q₈

—

129

C₂×C₄×Q₈

—

130

C₂×#97

—

131

C₂×#97

—

132

#391

—

133

#389

—

134

#389

—

135

#384

—

136

C₄×C₄⋊C₄

—

137

C₄×C₄⋊C₄

—

138

C₄³

C₂×D₁₉

yes

characteristic

139

#336

—

140

#336

—

141

#336

—

142

#336

C₂×D₁₉

yes

—

143

C₂×C₁₉

#1467

yes

characteristic

144

C₂×C₁₉

#1490

yes

characteristic

145

C₂×C₁₉

#1491

yes

characteristic

146

C₂×C₁₉

#1505

yes

characteristic

147

C₂×C₁₉

#1506

yes

characteristic

148

C₂×C₁₉

#1526

yes

characteristic

149

C₂×C₁₉

#1556

yes

characteristic

150

C₂²×Q₈

—

151

C₂²×C₈

—

152

C₂²×C₈

—

153

C₄⋊Q₈

—

154

C₄×Q₈

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄²

—

162

C₂×C₄²

C₄×D₁₉

yes

characteristic

163

C₂×C₄²

C₄×D₁₉

yes

characteristic

164

C₂×C₄²

D₇₆

yes

characteristic

165

C₂×C₄²

D₇₆

yes

characteristic

166

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

167

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

168

C₂×C₄²

C₂²×D₁₉

yes

characteristic

169

#97

—

170

#97

—

171

#95

—

172

#95

—

173

C₁₉

#7638

yes

characteristic, complemented, Sylow

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

180

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

181

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

182

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

183

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

184

C₂²×C₄

C₂×D₇₆

yes

characteristic

185

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄²

—

200

C₄²

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

208

Q₈

—

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

—

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

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

#10597262

yes

—

231

C₂×C₄

#10597281

yes

—

232

C₂×C₄

#10597282

yes

—

233

C₂×C₄

M₁₆×D₁₉

yes

—

234

C₂×C₄

#10597354

yes

—

235

C₂×C₄

#10597397

yes

—

236

C₈

—

237

C₈

—

238

C₂²

#11926507

yes

characteristic

239

C₂²

#11926517

yes

characteristic

240

C₂²

C₂×#10597281

yes

characteristic

241

C₂²

#11926550

yes

characteristic

242

C₂²

#11926552

yes

characteristic

243

C₂²

C₂×#10597282

yes

characteristic

244

C₂²

C₂×#10597262

yes

characteristic

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

152

—

254

C₂

#14561978

yes

characteristic

255

C₂

#14562079

yes

characteristic

256

C₂

#14562081

yes

characteristic

257

C₂

#14562144

yes

characteristic

258

C₂

#14562146

yes

characteristic

259

C₂

#14562229

yes

characteristic

260

C₂

#14562351

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1745	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1745	D₁₉
hypocenter	C₁₉	#7638
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1745

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1745

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 ◁ C₄³ ◁ #1745

N	H ≅ G/N	type
173. C₁₉	#7638	semidirect

H ≅ G/N

type

173. C₁₉

#7638

semidirect

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

subgroup	index
C₄×#10597315	2
#14563384	2
#14561457	2
C₁₉×#1745	2
#7638	19

subgroup

index

C₁₉×#1745

Subgroups — #18070808

Conjugacy classes of subgroups

Complements

Maximal subgroups