Group #18082120 — subgroups

Subgroups — #18082120

Order 4864.

426 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 121 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×#11926940	C₂	1	1	yes	maximal, characteristic
2	#14564623	C₂	1	1	yes	maximal, characteristic
3	#14564480	C₂	1	1	yes	maximal, characteristic
4	#14562390	C₂	1	1	yes	maximal, characteristic
5	#14562319	C₂	1	1	yes	maximal, characteristic
6	#14561916	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	#11926940	—	2	2	no	—
10	#11926940	—	2	1	no	—
11	#11926940	—	2	1	no	—
12	C₂×#10597265	C₄	1	4	yes	—
13	#11926568	C₂²	1	1	yes	characteristic
14	C₂×#10597293	—	2	2	no	—
15	C₄×#64520	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	#11926312	—	2	2	no	—
18	#11926294	—	2	2	no	—
19	#11926291	—	2	2	no	—
20	#11926266	—	2	1	no	—
21	C₈×C₁₉⋊C₈	—	2	1	no	—
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₉×#431	C₂²	1	1	yes	characteristic
24	C₁₉×#423	C₂²	1	1	yes	characteristic
25	C₁₉×#332	—	2	2	no	—
26	C₂²×Q₈×C₁₉	—	2	1	no	—
27	C₂²×Dic₃₈	—	2	1	no	—
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₁₉×C₄⋊Q₈	—	2	1	no	—
30	C₁₉×C₄⋊Q₈	—	2	1	no	—
31	C₁₉×C₄⋊Q₈	—	2	1	no	—
32	C₁₉×C₄⋊Q₈	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×C₄⋊Dic₁₉	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
38	C₂×#64520	—	2	1	no	—
39	C₂×#64520	D₄	1	2	yes	—
40	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
41	#10597315	—	2	1	no	—
42	#10597315	—	2	1	no	—
43	#10597315	—	2	1	no	—
44	#10597315	—	2	1	no	—
45	C₁₉×C₄⋊C₈	—	2	1	no	—
46	C₁₉×C₄⋊C₈	—	2	1	no	—
47	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
48	C₁₉×C₂²⋊C₈	—	2	1	no	—
49	C₄×C₈×C₁₉	—	2	1	no	—
50	#10597293	—	4	4	no	—
51	#10597265	—	2	4	no	—
52	#10597265	—	2	4	no	—
53	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
54	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
55	#10597260	—	2	1	no	—
56	C₄×C₁₉⋊C₈	—	2	1	no	—
57	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
58	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
59	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
60	C₂×Q₈×C₁₉	—	4	1	no	—
61	C₂×Q₈×C₁₉	—	4	1	no	—
62	C₂×Q₈×C₁₉	—	4	2	no	—
63	C₂×Q₈×C₁₉	—	4	2	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
68	C₂²×Dic₁₉	—	2	2	no	—
69	C₂×Dic₃₈	—	4	1	no	—
70	C₂×Dic₃₈	—	4	1	no	—
71	C₂×Dic₃₈	—	8	2	no	—
72	M₁₆×C₁₉	—	4	2	no	—
73	C₂×C₈×C₁₉	—	2	2	no	—
74	C₂×C₈×C₁₉	—	4	1	no	—
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₄⋊C₄×C₁₉	—	4	1	no	—
78	C₄⋊C₄×C₁₉	—	4	1	no	—
79	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₁₉	#41	1	1	yes	characteristic
83	C₄⋊Dic₁₉	—	2	2	no	—
84	C₄⋊Dic₁₉	—	2	2	no	—
85	C₄⋊Dic₁₉	—	4	1	no	—
86	C₄⋊Dic₁₉	—	4	1	no	—
87	#64520	—	2	2	no	—
88	#64520	—	4	2	no	—
89	#64520	SD₁₆	1	4	yes	—
90	C₂×C₁₉⋊C₈	—	2	2	no	—
91	C₂×C₁₉⋊C₈	—	2	4	no	—
92	C₂×C₁₉⋊C₈	—	4	1	no	—
93	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
94	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
95	#9794	—	19	1	no	maximal, Sylow
96	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
97	Q₈×C₁₉	—	8	2	no	—
98	Q₈×C₁₉	—	8	1	no	—
99	Q₈×C₁₉	—	8	1	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	2	2	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	4	no	—
104	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
108	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
111	C₂×C₄×C₁₉	#135	1	2	yes	—
112	C₂×Dic₁₉	—	4	2	no	—
113	C₂×Dic₁₉	—	8	2	no	—
114	Dic₃₈	—	8	2	no	—
115	Dic₃₈	—	8	2	no	—
116	C₈×C₁₉	—	4	2	no	—
117	C₈×C₁₉	—	8	1	no	—
118	C₁₉⋊C₈	—	2	2	no	—
119	C₁₉⋊C₈	—	2	4	no	—
120	C₁₉⋊C₈	—	8	1	no	—
121	C₁₉⋊C₈	#101	1	4	yes	complemented
122	C₂×#498	—	19	1	no	—
123	#1997	—	19	1	no	—
124	#1966	—	19	1	no	—
125	#1566	—	19	1	no	—
126	#1549	—	19	1	no	—
127	#1546	D₁₉	1	1	yes	characteristic
128	C₈×M₁₆	—	19	1	no	—
129	C₂²×C₁₉	—	2	1	no	—
130	C₂²×C₁₉	—	2	1	no	—
131	C₂²×C₁₉	#390	1	1	yes	characteristic
132	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
133	C₄×C₁₉	—	2	1	no	—
134	C₄×C₁₉	—	2	1	no	—
135	C₄×C₁₉	—	8	2	no	—
136	C₄×C₁₉	C₂×#101	1	2	yes	—
137	C₄×C₁₉	#465	1	2	yes	—
138	C₄×C₁₉	#471	1	2	yes	—
139	C₄×C₁₉	#492	1	1	yes	characteristic
140	C₄×C₁₉	#495	1	1	yes	characteristic
141	Dic₁₉	—	8	2	no	—
142	C₂×C₄⋊Q₈	—	19	1	no	—
143	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
144	#498	—	38	1	no	—
145	#498	—	38	1	no	—
146	#498	—	38	2	no	—
147	#431	C₂×D₁₉	1	1	yes	characteristic
148	C₂×#106	—	19	4	no	—
149	#423	—	19	1	no	—
150	#423	C₂×D₁₉	1	1	yes	characteristic
151	C₂×#101	—	38	2	no	—
152	C₄×M₁₆	—	19	1	no	—
153	C₂×C₄×C₈	—	19	1	no	—
154	#343	—	38	2	no	—
155	#334	—	38	2	no	—
156	#332	—	2	2	no	—
157	#332	—	38	2	no	—
158	#322	—	38	1	no	—
159	C₈²	—	38	1	no	—
160	C₂×C₁₉	—	2	2	no	—
161	C₂×C₁₉	#1966	1	1	yes	characteristic
162	C₂×C₁₉	#1968	1	1	yes	characteristic
163	C₂×C₁₉	#1977	1	1	yes	characteristic
164	C₂²×Q₈	—	2	1	no	—
165	C₂²×Q₈	—	38	1	no	—
166	C₂×M₁₆	—	2	1	no	—
167	C₂×M₁₆	—	19	2	no	—
168	C₂×M₁₆	—	38	1	no	—
169	C₂²×C₈	—	19	2	no	—
170	C₄⋊Q₈	—	2	1	no	—
171	C₄⋊Q₈	—	2	1	no	—
172	C₄⋊Q₈	—	2	1	no	—
173	C₄⋊Q₈	—	2	1	no	—
174	C₄⋊Q₈	—	38	1	no	—
175	C₄⋊Q₈	—	38	1	no	—
176	C₄⋊Q₈	—	38	1	no	—
177	C₄⋊Q₈	—	38	1	no	—
178	C₂×C₄⋊C₄	—	2	1	no	—
179	C₂×C₄⋊C₄	—	19	2	no	—
180	C₂×C₄⋊C₄	—	38	1	no	—
181	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
182	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
183	#106	—	38	4	no	—
184	#106	—	38	4	no	—
185	C₄⋊C₈	—	2	1	no	—
186	C₄⋊C₈	—	2	1	no	—
187	C₄⋊C₈	—	38	1	no	—
188	C₄⋊C₈	—	38	1	no	—
189	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
190	#101	—	76	4	no	—
191	C₂²⋊C₈	—	2	1	no	—
192	#97	—	38	1	no	—
193	C₄×C₈	—	2	1	no	—
194	C₄×C₈	—	19	1	no	—
195	C₄×C₈	—	19	1	no	—
196	C₄×C₈	—	19	2	no	—
197	C₄×C₈	—	38	1	no	—
198	C₁₉	#9794	1	1	yes	characteristic, complemented, Sylow
199	C₂×Q₈	—	4	1	no	—
200	C₂×Q₈	—	4	1	no	—
201	C₂×Q₈	—	4	2	no	—
202	C₂×Q₈	—	4	2	no	—
203	C₂×Q₈	—	76	1	no	—
204	C₂×Q₈	—	76	1	no	—
205	C₂×Q₈	—	152	2	no	—
206	C₂²×C₄	—	2	2	no	—
207	C₂²×C₄	—	38	2	no	—
208	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
209	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
210	C₂²×C₄	#64543	1	1	yes	characteristic
211	M₁₆	—	4	2	no	—
212	M₁₆	—	19	4	no	—
213	M₁₆	—	38	2	no	—
214	M₁₆	—	76	2	no	—
215	C₂×C₈	—	2	2	no	—
216	C₂×C₈	—	4	1	no	—
217	C₂×C₈	—	19	2	no	—
218	C₂×C₈	—	19	2	no	—
219	C₂×C₈	—	38	4	no	—
220	C₂×C₈	—	38	2	no	—
221	C₂×C₈	—	76	1	no	—
222	C₄⋊C₄	—	2	2	no	—
223	C₄⋊C₄	—	2	2	no	—
224	C₄⋊C₄	—	4	1	no	—
225	C₄⋊C₄	—	4	1	no	—
226	C₄⋊C₄	—	38	2	no	—
227	C₄⋊C₄	—	38	2	no	—
228	C₄⋊C₄	—	76	1	no	—
229	C₄⋊C₄	—	76	1	no	—
230	C₄²	#64541	1	1	yes	characteristic
231	C₄²	D₄×D₁₉	1	1	yes	characteristic
232	C₄²	D₄×D₁₉	1	1	yes	characteristic
233	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
234	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
235	Q₈	—	8	1	no	—
236	Q₈	—	8	1	no	—
237	Q₈	—	8	2	no	—
238	Q₈	—	152	2	no	—
239	Q₈	—	152	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	4	4	no	—
243	C₂×C₄	—	4	2	no	—
244	C₂×C₄	—	76	2	no	—
245	C₂×C₄	—	152	2	no	—
246	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
247	C₂×C₄	#10597330	1	1	yes	characteristic
248	C₂×C₄	#10597331	1	1	yes	characteristic
249	C₂×C₄	#10597358	1	2	yes	—
250	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
251	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
252	C₂×C₄	#10597385	1	1	yes	characteristic
253	C₂×C₄	#10597386	1	1	yes	characteristic
254	C₈	—	4	2	no	—
255	C₈	—	8	1	no	—
256	C₈	—	19	4	no	—
257	C₈	—	38	4	no	—
258	C₈	—	38	2	no	—
259	C₈	—	152	1	no	—
260	C₂²	—	2	1	no	—
261	C₂²	—	2	1	no	—
262	C₂²	#11926444	1	1	yes	characteristic
263	C₂²	#11926635	1	2	yes	—
264	C₄	—	2	1	no	—
265	C₄	—	2	1	no	—
266	C₄	—	8	2	no	—
267	C₄	—	152	2	no	—
268	C₄	#101×D₁₉	1	2	yes	—
269	C₄	#11926772	1	2	yes	—
270	C₄	#11926809	1	2	yes	—
271	C₄	#11926915	1	1	yes	characteristic
272	C₄	#11926927	1	1	yes	characteristic
273	C₂	—	2	2	no	—
274	C₂	#14564477	1	1	yes	characteristic
275	C₂	#14564490	1	1	yes	characteristic
276	C₂	#14564537	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926940

C₂

yes

maximal, characteristic

#14564623

C₂

yes

maximal, characteristic

#14564480

C₂

yes

maximal, characteristic

#14562390

C₂

yes

maximal, characteristic

#14562319

C₂

yes

maximal, characteristic

#14561916

C₂

yes

maximal, characteristic

C₁₉×#1546

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

—

—

—

C₄

yes

—

#11926568

C₂²

yes

characteristic

C₂×#10597293

—

C₄×#64520

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

—

C₈×C₁₉⋊C₈

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#332

—

C₂²×Q₈×C₁₉

—

C₂²×Dic₃₈

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×#64520

—

C₂×#64520

D₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

—

—

—

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

#10597293

—

#10597265

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×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

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

#64520

SD₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

#9794

—

maximal, Sylow

C₂³×C₁₉

C₄×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

105

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

106

C₂×C₄×C₁₉

#121

yes

characteristic

107

C₂×C₄×C₁₉

#121

yes

characteristic

108

C₂×C₄×C₁₉

#124

yes

characteristic

109

C₂×C₄×C₁₉

#127

yes

characteristic

110

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

111

C₂×C₄×C₁₉

#135

yes

—

112

C₂×Dic₁₉

—

113

C₂×Dic₁₉

—

114

Dic₃₈

—

115

Dic₃₈

—

116

C₈×C₁₉

—

117

C₈×C₁₉

—

118

C₁₉⋊C₈

—

119

C₁₉⋊C₈

—

120

C₁₉⋊C₈

—

121

C₁₉⋊C₈

#101

yes

complemented

122

C₂×#498

—

123

#1997

—

124

#1966

—

125

#1566

—

126

#1549

—

127

#1546

D₁₉

yes

characteristic

128

C₈×M₁₆

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

#390

yes

characteristic

132

C₂²×C₁₉

C₄×SD₁₆

yes

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

C₂×#101

yes

—

137

C₄×C₁₉

#465

yes

—

138

C₄×C₁₉

#471

yes

—

139

C₄×C₁₉

#492

yes

characteristic

140

C₄×C₁₉

#495

yes

characteristic

141

Dic₁₉

—

142

C₂×C₄⋊Q₈

—

143

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

144

#498

—

145

#498

—

146

#498

—

147

#431

C₂×D₁₉

yes

characteristic

148

C₂×#106

—

149

#423

—

150

#423

C₂×D₁₉

yes

characteristic

151

C₂×#101

—

152

C₄×M₁₆

—

153

C₂×C₄×C₈

—

154

#343

—

155

#334

—

156

#332

—

157

#332

—

158

#322

—

159

C₈²

—

160

C₂×C₁₉

—

161

C₂×C₁₉

#1966

yes

characteristic

162

C₂×C₁₉

#1968

yes

characteristic

163

C₂×C₁₉

#1977

yes

characteristic

164

C₂²×Q₈

—

165

C₂²×Q₈

—

166

C₂×M₁₆

—

167

C₂×M₁₆

—

168

C₂×M₁₆

—

169

C₂²×C₈

—

170

C₄⋊Q₈

—

171

C₄⋊Q₈

—

172

C₄⋊Q₈

—

173

C₄⋊Q₈

—

174

C₄⋊Q₈

—

175

C₄⋊Q₈

—

176

C₄⋊Q₈

—

177

C₄⋊Q₈

—

178

C₂×C₄⋊C₄

—

179

C₂×C₄⋊C₄

—

180

C₂×C₄⋊C₄

—

181

C₂×C₄⋊C₄

C₄×D₁₉

yes

—

182

C₂×C₄²

C₂²×D₁₉

yes

characteristic

183

#106

—

184

#106

—

185

C₄⋊C₈

—

186

C₄⋊C₈

—

187

C₄⋊C₈

—

188

C₄⋊C₈

—

189

C₄⋊C₈

C₂²⋊D₁₉

yes

—

190

#101

—

191

C₂²⋊C₈

—

192

#97

—

193

C₄×C₈

—

194

C₄×C₈

—

195

C₄×C₈

—

196

C₄×C₈

—

197

C₄×C₈

—

198

C₁₉

#9794

yes

characteristic, complemented, Sylow

199

C₂×Q₈

—

200

C₂×Q₈

—

201

C₂×Q₈

—

202

C₂×Q₈

—

203

C₂×Q₈

—

204

C₂×Q₈

—

205

C₂×Q₈

—

152

—

206

C₂²×C₄

—

207

C₂²×C₄

—

208

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

209

C₂²×C₄

D₄×D₁₉

yes

characteristic

210

C₂²×C₄

#64543

yes

characteristic

211

M₁₆

—

212

M₁₆

—

213

M₁₆

—

214

M₁₆

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

—

218

C₂×C₈

—

219

C₂×C₈

—

220

C₂×C₈

—

221

C₂×C₈

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₄⋊C₄

—

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄²

#64541

yes

characteristic

231

C₄²

D₄×D₁₉

yes

characteristic

232

C₄²

D₄×D₁₉

yes

characteristic

233

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

234

C₂³

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

235

Q₈

—

236

Q₈

—

237

Q₈

—

238

Q₈

—

152

—

239

Q₈

—

152

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

152

—

246

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

247

C₂×C₄

#10597330

yes

characteristic

248

C₂×C₄

#10597331

yes

characteristic

249

C₂×C₄

#10597358

yes

—

250

C₂×C₄

SD₁₆×D₁₉

yes

—

251

C₂×C₄

C₄×C₂²⋊D₁₉

yes

characteristic

252

C₂×C₄

#10597385

yes

characteristic

253

C₂×C₄

#10597386

yes

characteristic

254

C₈

—

255

C₈

—

256

C₈

—

257

C₈

—

258

C₈

—

259

C₈

—

152

—

260

C₂²

—

261

C₂²

—

262

C₂²

#11926444

yes

characteristic

263

C₂²

#11926635

yes

—

264

C₄

—

265

C₄

—

266

C₄

—

267

C₄

—

152

—

268

C₄

#101×D₁₉

yes

—

269

C₄

#11926772

yes

—

270

C₄

#11926809

yes

—

271

C₄

#11926915

yes

characteristic

272

C₄

#11926927

yes

characteristic

273

C₂

—

274

C₂

#14564477

yes

characteristic

275

C₂

#14564490

yes

characteristic

276

C₂

#14564537

yes

characteristic

	subgroup	G/H
center	C₂²	#11926444
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1546	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	C₄×D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1546	D₁₉
hypocenter	C₁₉	#9794
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1546

subgroup

G/H

center

C₂²

#11926444

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1546

C₂

socle

C₂²×C₁₉

#390

prime radical

C₂³×C₁₉

C₄×D₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1546

N	H ≅ G/N	type
121. C₁₉⋊C₈	#101	semidirect
198. C₁₉	#9794	semidirect

H ≅ G/N

type

121. C₁₉⋊C₈

#101

semidirect

198. C₁₉

#9794

semidirect

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

subgroup	index
C₂×#11926940	2
#14564623	2
#14564480	2
#14562390	2
#14562319	2
#14561916	2
C₁₉×#1546	2
#9794	19

subgroup

index

C₁₉×#1546

Subgroups — #18082120

Conjugacy classes of subgroups

Complements

Maximal subgroups