Group #18071288 — subgroups

Subgroups — #18071288

Order 4864.

492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 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	#14571623	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564866	C₂	1	2	yes	maximal
3	#14561461	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561457	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2014	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597289	—	2	2	no	—
7	C₂×#10597289	—	2	2	no	—
8	#11926483	—	2	1	no	—
9	#11926476	—	2	2	no	—
10	#11926451	—	2	1	no	—
11	#11926442	C₂²	1	2	yes	—
12	#11926431	—	2	2	no	—
13	#11926299	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₁₉	—	2	1	no	—
15	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#102	—	2	1	no	—
17	C₁₉×#391	C₂²	1	1	yes	characteristic
18	C₁₉×#336	C₂²	1	1	yes	characteristic
19	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×D₄×C₁₉	—	2	2	no	—
21	C₂²×D₄×C₁₉	—	2	1	no	—
22	C₂×SD₁₆×C₁₉	—	4	2	no	—
23	C₂×SD₁₆×C₁₉	—	4	2	no	—
24	C₂×SD₁₆×C₁₉	—	4	2	no	—
25	C₂²×C₈×C₁₉	—	2	1	no	—
26	C₁₉×#127	—	4	2	no	—
27	C₂×C₄⋊C₄×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	D₄	1	2	yes	—
32	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
33	C₂×Dic₁₉⋊C₄	—	2	2	no	—
34	C₂×C₄×Dic₁₉	—	2	1	no	—
35	C₂²×C₁₉⋊C₈	—	2	2	no	—
36	C₁₉×#102	—	4	2	no	—
37	C₁₉×#95	—	2	2	no	—
38	#10597289	—	4	4	no	—
39	#10597289	—	4	4	no	—
40	C₁₉⋊#95	—	2	1	no	—
41	C₁₉⋊#95	—	2	2	no	—
42	C₁₉⋊#95	—	2	2	no	—
43	C₁₉⋊#95	—	2	2	no	—
44	C₂⁴×C₁₉	—	4	1	no	—
45	C₂×Q₈×C₁₉	—	2	1	no	—
46	C₂×Q₈×C₁₉	—	4	1	no	—
47	C₂×Q₈×C₁₉	—	4	1	no	—
48	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
49	C₂×D₄×C₁₉	—	2	2	no	—
50	C₂×D₄×C₁₉	—	2	4	no	—
51	C₂×D₄×C₁₉	—	4	1	no	—
52	C₂×D₄×C₁₉	—	4	2	no	—
53	C₂×D₄×C₁₉	—	4	2	no	—
54	C₂×D₄×C₁₉	—	4	1	no	—
55	C₂×D₄×C₁₉	—	4	2	no	—
56	C₂×D₄×C₁₉	—	4	1	no	—
57	C₂×D₄×C₁₉	—	4	1	no	—
58	C₂×D₄×C₁₉	—	4	2	no	—
59	C₂×D₄×C₁₉	—	4	2	no	—
60	C₂×D₄×C₁₉	—	4	1	no	—
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×Dic₁₉	—	2	2	no	—
66	C₂²×Dic₁₉	—	2	2	no	—
67	SD₁₆×C₁₉	—	4	8	no	—
68	C₂×C₈×C₁₉	—	2	2	no	—
69	C₂×C₈×C₁₉	—	4	1	no	—
70	C₂×C₈×C₁₉	—	4	1	no	—
71	C₄⋊C₄×C₁₉	—	4	1	no	—
72	C₄²×C₁₉	—	4	1	no	—
73	C₄⋊Dic₁₉	—	2	2	no	—
74	C₄⋊Dic₁₉	—	2	2	no	—
75	C₄⋊Dic₁₉	—	4	2	no	—
76	C₄⋊Dic₁₉	—	8	1	no	—
77	C₄⋊Dic₁₉	—	8	1	no	—
78	Dic₁₉⋊C₄	—	4	2	no	—
79	Dic₁₉⋊C₄	—	4	2	no	—
80	C₄×Dic₁₉	—	8	1	no	—
81	C₂×C₁₉⋊C₈	—	4	2	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	C₂×C₁₉⋊C₈	—	4	2	no	—
84	#7743	—	19	1	no	maximal, Sylow
85	C₂³×C₁₉	—	4	2	no	—
86	C₂³×C₁₉	—	8	1	no	—
87	C₂³×C₁₉	—	8	2	no	—
88	C₂³×C₁₉	—	8	1	no	—
89	C₂³×C₁₉	—	8	2	no	—
90	C₂³×C₁₉	#120	1	1	yes	characteristic
91	Q₈×C₁₉	—	4	2	no	—
92	Q₈×C₁₉	—	8	1	no	—
93	D₄×C₁₉	—	4	2	no	—
94	D₄×C₁₉	—	4	2	no	—
95	D₄×C₁₉	—	4	4	no	—
96	D₄×C₁₉	—	4	4	no	—
97	D₄×C₁₉	—	8	1	no	—
98	D₄×C₁₉	—	8	1	no	—
99	D₄×C₁₉	—	8	2	no	—
100	D₄×C₁₉	—	8	2	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	2	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	2	1	no	—
105	C₂×C₄×C₁₉	—	2	2	no	—
106	C₂×C₄×C₁₉	—	4	1	no	—
107	C₂×C₄×C₁₉	—	4	1	no	—
108	C₂×C₄×C₁₉	—	4	1	no	—
109	C₂×C₄×C₁₉	—	4	2	no	—
110	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
111	C₂×C₄×C₁₉	#135	1	2	yes	—
112	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
113	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
114	C₂×Dic₁₉	—	4	2	no	—
115	C₂×Dic₁₉	—	4	2	no	—
116	C₂×Dic₁₉	—	4	2	no	—
117	C₂×Dic₁₉	—	4	2	no	—
118	C₂×Dic₁₉	—	4	2	no	—
119	C₂×Dic₁₉	—	4	2	no	—
120	C₈×C₁₉	—	4	2	no	—
121	C₁₉⋊C₈	—	8	2	no	—
122	#2809	—	19	1	no	—
123	#2041	—	19	2	no	—
124	#2014	D₁₉	1	1	yes	characteristic
125	#1272	—	19	1	no	—
126	#1271	—	19	2	no	—
127	C₂²×C₁₉	—	8	2	no	—
128	C₂²×C₁₉	—	8	4	no	—
129	C₂²×C₁₉	—	16	1	no	—
130	C₂²×C₁₉	—	16	2	no	—
131	C₂²×C₁₉	—	16	1	no	—
132	C₂²×C₁₉	#448	1	1	yes	characteristic
133	C₂²×C₁₉	#449	1	2	yes	—
134	C₂²×C₁₉	#453	1	1	yes	characteristic
135	C₂²×C₁₉	#454	1	2	yes	—
136	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
137	C₄×C₁₉	—	2	1	no	—
138	C₄×C₁₉	—	2	1	no	—
139	C₄×C₁₉	—	2	2	no	—
140	C₄×C₁₉	—	2	2	no	—
141	C₄×C₁₉	—	4	2	no	—
142	C₄×C₁₉	—	8	1	no	—
143	Dic₁₉	—	8	2	no	—
144	Dic₁₉	—	8	2	no	—
145	C₂²×SD₁₆	—	2	1	no	—
146	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
147	C₂×#102	—	2	1	no	—
148	C₂×#102	—	38	2	no	—
149	C₂×#102	—	38	2	no	—
150	#400	—	38	1	no	—
151	#398	—	38	2	no	—
152	#391	—	38	1	no	—
153	#391	C₂×D₁₉	1	1	yes	characteristic
154	#389	—	19	2	no	—
155	#387	—	38	2	no	—
156	#336	—	19	2	no	—
157	#336	C₂×D₁₉	1	1	yes	characteristic
158	C₂×C₁₉	—	16	2	no	—
159	C₂×C₁₉	#1596	1	1	yes	characteristic
160	C₂×C₁₉	#1597	1	2	yes	—
161	C₂×C₁₉	#1624	1	1	yes	characteristic
162	C₂×C₁₉	#1626	1	2	yes	—
163	C₂×C₁₉	#1657	1	1	yes	characteristic
164	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
165	C₂²×D₄	—	2	2	no	—
166	C₂²×D₄	—	2	1	no	—
167	C₂×SD₁₆	—	4	2	no	—
168	C₂×SD₁₆	—	4	2	no	—
169	C₂×SD₁₆	—	4	2	no	—
170	C₂²×C₈	—	2	1	no	—
171	C₂²×C₈	—	38	2	no	—
172	#127	—	4	2	no	—
173	C₂×C₄⋊C₄	—	19	2	no	—
174	C₂×C₄⋊C₄	—	19	2	no	—
175	C₂×C₄⋊C₄	—	38	2	no	—
176	C₂×C₄⋊C₄	—	38	1	no	—
177	C₂×C₄⋊C₄	—	38	1	no	—
178	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
179	C₂×C₄²	—	38	1	no	—
180	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
181	#102	—	4	2	no	—
182	#102	—	76	4	no	—
183	#102	—	76	4	no	—
184	#95	—	2	2	no	—
185	#95	—	38	1	no	—
186	#95	—	38	2	no	—
187	#95	—	38	2	no	—
188	#95	—	38	2	no	—
189	C₁₉	#7743	1	1	yes	characteristic, complemented, Sylow
190	C₂⁴	—	4	1	no	—
191	C₂×Q₈	—	2	1	no	—
192	C₂×Q₈	—	4	1	no	—
193	C₂×Q₈	—	4	1	no	—
194	C₂×Q₈	#64526	1	2	yes	—
195	C₂×D₄	—	2	4	no	—
196	C₂×D₄	—	2	2	no	—
197	C₂×D₄	—	4	1	no	—
198	C₂×D₄	—	4	1	no	—
199	C₂×D₄	—	4	2	no	—
200	C₂×D₄	—	4	2	no	—
201	C₂×D₄	—	4	2	no	—
202	C₂×D₄	—	4	1	no	—
203	C₂×D₄	—	4	1	no	—
204	C₂×D₄	—	4	1	no	—
205	C₂×D₄	—	4	2	no	—
206	C₂×D₄	—	4	2	no	—
207	C₂²×C₄	—	2	1	no	—
208	C₂²×C₄	—	2	1	no	—
209	C₂²×C₄	—	38	2	no	—
210	C₂²×C₄	—	38	2	no	—
211	C₂²×C₄	D₄×D₁₉	1	2	yes	—
212	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
213	SD₁₆	—	4	8	no	—
214	C₂×C₈	—	2	2	no	—
215	C₂×C₈	—	4	1	no	—
216	C₂×C₈	—	4	1	no	—
217	C₂×C₈	—	76	2	no	—
218	C₂×C₈	—	76	2	no	—
219	C₂×C₈	—	76	2	no	—
220	C₄⋊C₄	—	4	1	no	—
221	C₄⋊C₄	—	38	2	no	—
222	C₄⋊C₄	—	38	2	no	—
223	C₄⋊C₄	—	76	2	no	—
224	C₄⋊C₄	—	76	2	no	—
225	C₄⋊C₄	—	76	2	no	—
226	C₄⋊C₄	—	152	1	no	—
227	C₄⋊C₄	—	152	1	no	—
228	C₄²	—	4	1	no	—
229	C₄²	—	152	1	no	—
230	C₂³	—	4	2	no	—
231	C₂³	—	8	1	no	—
232	C₂³	—	8	2	no	—
233	C₂³	—	8	1	no	—
234	C₂³	—	8	2	no	—
235	C₂³	#10597383	1	1	yes	characteristic
236	Q₈	—	4	2	no	—
237	Q₈	—	8	1	no	—
238	D₄	—	4	2	no	—
239	D₄	—	4	4	no	—
240	D₄	—	4	4	no	—
241	D₄	—	4	2	no	—
242	D₄	—	8	2	no	—
243	D₄	—	8	2	no	—
244	D₄	—	8	1	no	—
245	D₄	—	8	1	no	—
246	C₂×C₄	—	2	1	no	—
247	C₂×C₄	—	2	2	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	2	1	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	4	1	no	—
252	C₂×C₄	—	4	1	no	—
253	C₂×C₄	—	4	1	no	—
254	C₂×C₄	—	4	2	no	—
255	C₂×C₄	—	76	2	no	—
256	C₂×C₄	—	76	2	no	—
257	C₂×C₄	—	76	2	no	—
258	C₂×C₄	—	76	2	no	—
259	C₂×C₄	—	76	2	no	—
260	C₂×C₄	—	76	2	no	—
261	C₂×C₄	#10597360	1	2	yes	—
262	C₂×C₄	#10597362	1	2	yes	—
263	C₂×C₄	C₂×#64526	1	1	yes	characteristic
264	C₂×C₄	#10597397	1	1	yes	characteristic
265	C₈	—	4	2	no	—
266	C₈	—	152	2	no	—
267	C₂²	—	8	4	no	—
268	C₂²	—	8	2	no	—
269	C₂²	—	16	1	no	—
270	C₂²	—	16	1	no	—
271	C₂²	—	16	2	no	—
272	C₂²	#11926682	1	1	yes	characteristic
273	C₂²	#11926688	1	2	yes	—
274	C₂²	#11926711	1	1	yes	characteristic
275	C₂²	#11926715	1	2	yes	—
276	C₂²	#11926730	1	1	yes	characteristic
277	C₄	—	2	2	no	—
278	C₄	—	2	2	no	—
279	C₄	—	2	1	no	—
280	C₄	—	2	1	no	—
281	C₄	—	4	2	no	—
282	C₄	—	8	1	no	—
283	C₄	—	152	2	no	—
284	C₄	—	152	2	no	—
285	C₂	—	16	2	no	—
286	C₂	#14562557	1	1	yes	characteristic
287	C₂	#14562563	1	2	yes	—
288	C₂	#14562716	1	1	yes	characteristic
289	C₂	#14562730	1	2	yes	—
290	C₂	#14562931	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14571623

C₂

yes

maximal, characteristic, complemented

#14564866

C₂

yes

maximal

#14561461

C₂

yes

maximal, characteristic, complemented

#14561457

C₂

yes

maximal, complemented

C₁₉×#2014

C₂

yes

maximal, characteristic

—

—

—

—

—

C₂²

yes

—

#11926431

—

#11926299

C₂²

yes

—

C₂²×SD₁₆×C₁₉

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₂×C₁₉×#102

—

C₁₉×#391

C₂²

yes

characteristic

C₁₉×#336

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×#127

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×#102

—

C₁₉×#95

—

#10597289

—

#10597289

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

SD₁₆

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

SD₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7743

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

100

D₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

—

110

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

111

C₂×C₄×C₁₉

#135

yes

—

112

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

113

C₂×C₄×C₁₉

#137

yes

characteristic

114

C₂×Dic₁₉

—

115

C₂×Dic₁₉

—

116

C₂×Dic₁₉

—

117

C₂×Dic₁₉

—

118

C₂×Dic₁₉

—

119

C₂×Dic₁₉

—

120

C₈×C₁₉

—

121

C₁₉⋊C₈

—

122

#2809

—

123

#2041

—

124

#2014

D₁₉

yes

characteristic

125

#1272

—

126

#1271

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

#448

yes

characteristic

133

C₂²×C₁₉

#449

yes

—

134

C₂²×C₁₉

#453

yes

characteristic

135

C₂²×C₁₉

#454

yes

—

136

C₂²×C₁₉

B(4,𝔽₂)

yes

characteristic

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

—

140

C₄×C₁₉

—

141

C₄×C₁₉

—

142

C₄×C₁₉

—

143

Dic₁₉

—

144

Dic₁₉

—

145

C₂²×SD₁₆

—

146

C₂×#127

C₂×D₁₉

yes

characteristic

147

C₂×#102

—

148

C₂×#102

—

149

C₂×#102

—

150

#400

—

151

#398

—

152

#391

—

153

#391

C₂×D₁₉

yes

characteristic

154

#389

—

155

#387

—

156

#336

—

157

#336

C₂×D₁₉

yes

characteristic

158

C₂×C₁₉

—

159

C₂×C₁₉

#1596

yes

characteristic

160

C₂×C₁₉

#1597

yes

—

161

C₂×C₁₉

#1624

yes

characteristic

162

C₂×C₁₉

#1626

yes

—

163

C₂×C₁₉

#1657

yes

characteristic

164

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

165

C₂²×D₄

—

166

C₂²×D₄

—

167

C₂×SD₁₆

—

168

C₂×SD₁₆

—

169

C₂×SD₁₆

—

170

C₂²×C₈

—

171

C₂²×C₈

—

172

#127

—

173

C₂×C₄⋊C₄

—

174

C₂×C₄⋊C₄

—

175

C₂×C₄⋊C₄

—

176

C₂×C₄⋊C₄

—

177

C₂×C₄⋊C₄

—

178

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

179

C₂×C₄²

—

180

C₂×C₄²

C₂²×D₁₉

yes

characteristic

181

#102

—

182

#102

—

183

#102

—

184

#95

—

185

#95

—

186

#95

—

187

#95

—

188

#95

—

189

C₁₉

#7743

yes

characteristic, complemented, Sylow

190

C₂⁴

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×Q₈

—

194

C₂×Q₈

#64526

yes

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

—

201

C₂×D₄

—

202

C₂×D₄

—

203

C₂×D₄

—

204

C₂×D₄

—

205

C₂×D₄

—

206

C₂×D₄

—

207

C₂²×C₄

—

208

C₂²×C₄

—

209

C₂²×C₄

—

210

C₂²×C₄

—

211

C₂²×C₄

D₄×D₁₉

yes

—

212

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

213

SD₁₆

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

—

218

C₂×C₈

—

219

C₂×C₈

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₄⋊C₄

—

226

C₄⋊C₄

—

152

—

227

C₄⋊C₄

—

152

—

228

C₄²

—

229

C₄²

—

152

—

230

C₂³

—

231

C₂³

—

232

C₂³

—

233

C₂³

—

234

C₂³

—

235

C₂³

#10597383

yes

characteristic

236

Q₈

—

237

Q₈

—

238

D₄

—

239

D₄

—

240

D₄

—

241

D₄

—

242

D₄

—

243

D₄

—

244

D₄

—

245

D₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

252

C₂×C₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

#10597360

yes

—

262

C₂×C₄

#10597362

yes

—

263

C₂×C₄

C₂×#64526

yes

characteristic

264

C₂×C₄

#10597397

yes

characteristic

265

C₈

—

266

C₈

—

152

—

267

C₂²

—

268

C₂²

—

269

C₂²

—

270

C₂²

—

271

C₂²

—

272

C₂²

#11926682

yes

characteristic

273

C₂²

#11926688

yes

—

274

C₂²

#11926711

yes

characteristic

275

C₂²

#11926715

yes

—

276

C₂²

#11926730

yes

characteristic

277

C₄

—

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

—

282

C₄

—

283

C₄

—

152

—

284

C₄

—

152

—

285

C₂

—

286

C₂

#14562557

yes

characteristic

287

C₂

#14562563

yes

—

288

C₂

#14562716

yes

characteristic

289

C₂

#14562730

yes

—

290

C₂

#14562931

yes

characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2014	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×C₁₉×#127	C₂²
hypercenter	#2014	D₁₉
hypocenter	C₁₉	#7743
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2014

subgroup

G/H

center

C₂³

#10597383

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2014

C₂

socle

C₂³×C₁₉

#120

prime radical

C₂×C₁₉×#127

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂³×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2014

N	H ≅ G/N	type
1. #14571623	C₂	semidirect
3. #14561461	C₂	semidirect
4. #14561457	C₂	semidirect
189. C₁₉	#7743	semidirect

H ≅ G/N

type

1. #14571623

C₂

semidirect

3. #14561461

C₂

semidirect

4. #14561457

C₂

semidirect

189. C₁₉

#7743

semidirect

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

subgroup	index
#14571623	2
#14564866	2
#14561461	2
#14561457	2
C₁₉×#2014	2
#7743	19

subgroup

index

C₁₉×#2014

Subgroups — #18071288

Conjugacy classes of subgroups

Complements

Maximal subgroups