Group #18087520 — subgroups

Subgroups — #18087520

Order 4864.

372 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 95 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	#14564434	C₂	1	1	yes	maximal, characteristic
2	#14563809	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562407	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562406	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562060	C₂	1	1	yes	maximal, characteristic
6	#14561465	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1486	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	C₂×#10597279	—	2	2	no	—
10	#11926568	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
13	C₂×#10597260	C₂²	1	1	yes	characteristic
14	#11926295	—	2	2	no	—
15	#11926294	—	2	2	no	—
16	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#431	C₂²	1	1	yes	characteristic
19	C₁₉×#423	C₂²	1	1	yes	characteristic
20	C₁₉×D₄⋊C₈	—	2	2	no	—
21	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	—	2	1	no	—
23	C₂×M₁₆×C₁₉	—	2	1	no	—
24	C₄×D₄×C₁₉	—	2	1	no	—
25	C₄×D₄×C₁₉	—	2	1	no	—
26	C₄×D₄×C₁₉	—	2	1	no	—
27	C₄×D₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×#64520	—	2	1	no	—
32	C₂²×C₁₉⋊C₈	—	2	1	no	—
33	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
34	C₁₉×C₄⋊C₈	—	2	1	no	—
35	C₁₉×C₄⋊C₈	—	2	1	no	—
36	C₁₉×C₄⋊C₈	—	2	1	no	—
37	C₁₉×C₂²⋊C₈	—	2	1	no	—
38	C₄×C₈×C₁₉	D₄	1	2	yes	—
39	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
40	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
41	#10597279	—	4	4	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
47	#10597260	—	2	1	no	—
48	#10597260	—	2	1	no	—
49	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
50	C₂⁴×C₁₉	—	2	1	no	—
51	C₂×D₄×C₁₉	—	2	1	no	—
52	C₂×D₄×C₁₉	—	2	1	no	—
53	C₂×D₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	2	1	no	—
55	C₂²×C₄×C₁₉	—	4	1	no	—
56	C₂²×C₄×C₁₉	—	4	1	no	—
57	C₂²×C₄×C₁₉	—	4	2	no	—
58	C₂²×C₄×C₁₉	—	4	2	no	—
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
62	M₁₆×C₁₉	—	4	2	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	4	1	no	—
65	C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂²⋊C₄×C₁₉	—	4	1	no	—
68	C₂²⋊C₄×C₁₉	—	4	1	no	—
69	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₉	#41	1	1	yes	characteristic
72	C₄²×C₁₉	#41	1	1	yes	characteristic
73	#64520	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	2	2	no	—
75	C₂×C₁₉⋊C₈	—	2	2	no	—
76	C₂×C₁₉⋊C₈	—	2	2	no	—
77	C₂×C₁₉⋊C₈	—	4	1	no	—
78	C₂×C₁₉⋊C₈	—	4	1	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	C₂×C₁₉⋊C₈	SD₁₆	1	4	yes	—
81	#10661	—	19	1	no	maximal, Sylow
82	C₂³×C₁₉	—	2	2	no	—
83	C₂³×C₁₉	—	4	1	no	—
84	C₂³×C₁₉	—	4	2	no	—
85	C₂³×C₁₉	—	4	1	no	—
86	C₂³×C₁₉	—	4	2	no	—
87	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
88	D₄×C₁₉	—	2	2	no	—
89	D₄×C₁₉	—	2	2	no	—
90	D₄×C₁₉	—	4	1	no	—
91	D₄×C₁₉	—	4	1	no	—
92	C₂×C₄×C₁₉	—	4	1	no	—
93	C₂×C₄×C₁₉	—	4	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	—	8	1	no	—
98	C₂×C₄×C₁₉	—	8	1	no	—
99	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
106	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
107	C₈×C₁₉	—	4	2	no	—
108	C₈×C₁₉	—	8	1	no	—
109	C₁₉⋊C₈	—	2	4	no	—
110	C₁₉⋊C₈	—	4	2	no	—
111	C₁₉⋊C₈	—	8	1	no	—
112	C₁₉⋊C₈	—	8	1	no	—
113	#1955	—	19	1	no	—
114	#1849	—	19	1	no	—
115	#1570	—	19	1	no	—
116	#1570	—	19	1	no	—
117	#1486	—	19	1	no	—
118	#1486	D₁₉	1	1	yes	characteristic
119	#1275	—	19	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	—	4	4	no	—
123	C₂²×C₁₉	—	4	2	no	—
124	C₂²×C₁₉	—	8	2	no	—
125	C₂²×C₁₉	—	8	1	no	—
126	C₂²×C₁₉	—	8	1	no	—
127	C₂²×C₁₉	#399	1	1	yes	characteristic
128	C₂²×C₁₉	#476	1	2	yes	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	—	8	1	no	—
134	C₄×C₁₉	#481	1	2	yes	—
135	C₄×C₁₉	#492	1	1	yes	characteristic
136	C₄×C₁₉	#496	1	1	yes	characteristic
137	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
138	#431	—	19	1	no	—
139	#431	C₂×D₁₉	1	1	yes	characteristic
140	C₂×#108	—	38	2	no	—
141	#423	—	19	1	no	—
142	#423	C₂×D₁₉	1	1	yes	characteristic
143	C₂×C₄⋊C₈	—	19	1	no	—
144	C₂×C₂²⋊C₈	—	38	2	no	—
145	C₂×#97	—	19	1	no	—
146	#334	—	38	2	no	—
147	#334	—	38	2	no	—
148	D₄⋊C₈	—	2	2	no	—
149	D₄⋊C₈	—	38	2	no	—
150	C₂×C₁₉	—	2	2	no	—
151	C₂×C₁₉	—	8	2	no	—
152	C₂×C₁₉	#2091	1	1	yes	characteristic
153	C₂×C₁₉	#2094	1	1	yes	characteristic
154	C₂×C₁₉	#2098	1	1	yes	characteristic
155	C₂²×D₄	Dic₃₈	1	1	yes	characteristic
156	C₂³×C₄	—	2	1	no	—
157	C₂×M₁₆	—	2	1	no	—
158	C₂×M₁₆	—	38	1	no	—
159	C₂²×C₈	—	19	2	no	—
160	C₂²×C₈	—	38	1	no	—
161	C₄×D₄	—	2	1	no	—
162	C₄×D₄	—	2	1	no	—
163	C₄×D₄	—	2	1	no	—
164	C₄×D₄	—	2	1	no	—
165	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
166	C₂×C₂²⋊C₄	—	2	1	no	—
167	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
168	#108	—	76	4	no	—
169	C₄⋊C₈	—	2	1	no	—
170	C₄⋊C₈	—	2	1	no	—
171	C₄⋊C₈	—	2	1	no	—
172	C₄⋊C₈	—	38	1	no	—
173	C₄⋊C₈	—	38	1	no	—
174	C₄⋊C₈	—	38	1	no	—
175	C₄⋊C₈	—	38	1	no	—
176	C₄⋊C₈	—	38	1	no	—
177	C₂²⋊C₈	—	2	1	no	—
178	C₂²⋊C₈	—	38	1	no	—
179	C₂²⋊C₈	—	76	4	no	—
180	#97	—	38	1	no	—
181	#97	—	38	1	no	—
182	C₄×C₈	—	19	2	no	—
183	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
184	C₁₉	#10661	1	1	yes	characteristic, complemented, Sylow
185	C₂⁴	—	2	1	no	—
186	C₂×D₄	—	2	1	no	—
187	C₂×D₄	—	2	1	no	—
188	C₂×D₄	—	4	2	no	—
189	C₂²×C₄	—	2	1	no	—
190	C₂²×C₄	—	4	1	no	—
191	C₂²×C₄	—	4	1	no	—
192	C₂²×C₄	—	4	2	no	—
193	C₂²×C₄	—	4	2	no	—
194	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
195	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
196	C₂²×C₄	#64543	1	1	yes	characteristic
197	M₁₆	—	4	2	no	—
198	M₁₆	—	76	2	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	19	4	no	—
202	C₂×C₈	—	38	2	no	—
203	C₂×C₈	—	38	2	no	—
204	C₂×C₈	—	38	2	no	—
205	C₂×C₈	—	76	1	no	—
206	C₂×C₈	—	76	1	no	—
207	C₂×C₈	—	76	2	no	—
208	C₄⋊C₄	—	2	1	no	—
209	C₄⋊C₄	—	2	1	no	—
210	C₂²⋊C₄	—	4	1	no	—
211	C₂²⋊C₄	—	4	1	no	—
212	C₄²	#64541	1	1	yes	characteristic
213	C₄²	D₄×D₁₉	1	1	yes	characteristic
214	C₄²	#64543	1	1	yes	characteristic
215	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
216	C₂³	—	2	2	no	—
217	C₂³	—	4	1	no	—
218	C₂³	—	4	2	no	—
219	C₂³	—	4	2	no	—
220	C₂³	—	4	1	no	—
221	C₂³	#10597324	1	1	yes	characteristic
222	D₄	—	2	2	no	—
223	D₄	—	2	2	no	—
224	D₄	—	4	1	no	—
225	D₄	—	4	1	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	8	2	no	—
231	C₂×C₄	—	8	1	no	—
232	C₂×C₄	—	8	1	no	—
233	C₂×C₄	#10597324	1	1	yes	characteristic
234	C₂×C₄	#10597329	1	1	yes	characteristic
235	C₂×C₄	#10597329	1	1	yes	characteristic
236	C₂×C₄	#10597357	1	2	yes	—
237	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
238	C₂×C₄	#10597370	1	1	yes	characteristic
239	C₂×C₄	#10597381	1	1	yes	characteristic
240	C₂×C₄	#10597386	1	1	yes	characteristic
241	C₈	—	4	2	no	—
242	C₈	—	8	1	no	—
243	C₈	—	38	4	no	—
244	C₈	—	76	2	no	—
245	C₈	—	152	1	no	—
246	C₈	—	152	1	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	2	1	no	—
249	C₂²	—	4	4	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	8	2	no	—
252	C₂²	—	8	1	no	—
253	C₂²	—	8	1	no	—
254	C₂²	#11926480	1	1	yes	characteristic
255	C₂²	#11926832	1	2	yes	—
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	8	1	no	—
261	C₄	#11926861	1	2	yes	—
262	C₄	#11926915	1	1	yes	characteristic
263	C₄	#11926932	1	1	yes	characteristic
264	C₂	—	2	2	no	—
265	C₂	—	8	2	no	—
266	C₂	#14565151	1	1	yes	characteristic
267	C₂	#14565166	1	1	yes	characteristic
268	C₂	#14565190	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564434

C₂

yes

maximal, characteristic

#14563809

C₂

yes

maximal, characteristic, complemented

#14562407

C₂

yes

maximal, characteristic, complemented

#14562406

C₂

yes

maximal, characteristic, complemented

#14562060

C₂

yes

maximal, characteristic

#14561465

C₂

yes

maximal, characteristic, complemented

C₁₉×#1486

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

characteristic

C₂×#10597279

—

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×#10597260

C₂²

yes

characteristic

#11926295

—

#11926294

—

D₄⋊(C₁₉⋊C₈)

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×D₄⋊C₈

—

C₂²×D₄×C₁₉

Q₈

yes

characteristic

C₂³×C₄×C₁₉

—

C₂×M₁₆×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

#10597279

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×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

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

SD₁₆

yes

—

#10661

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

C₂²⋊Q₈

yes

characteristic

100

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

101

C₂×C₄×C₁₉

#123

yes

characteristic

102

C₂×C₄×C₁₉

#123

yes

characteristic

103

C₂×C₄×C₁₉

#123

yes

characteristic

104

C₂×C₄×C₁₉

#127

yes

characteristic

105

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

106

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

107

C₈×C₁₉

—

108

C₈×C₁₉

—

109

C₁₉⋊C₈

—

110

C₁₉⋊C₈

—

111

C₁₉⋊C₈

—

112

C₁₉⋊C₈

—

113

#1955

—

114

#1849

—

115

#1570

—

116

#1570

—

117

#1486

—

118

#1486

D₁₉

yes

characteristic

119

#1275

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

#399

yes

characteristic

128

C₂²×C₁₉

#476

yes

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

#481

yes

—

135

C₄×C₁₉

#492

yes

characteristic

136

C₄×C₁₉

#496

yes

characteristic

137

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

138

#431

—

139

#431

C₂×D₁₉

yes

characteristic

140

C₂×#108

—

141

#423

—

142

#423

C₂×D₁₉

yes

characteristic

143

C₂×C₄⋊C₈

—

144

C₂×C₂²⋊C₈

—

145

C₂×#97

—

146

#334

—

147

#334

—

148

D₄⋊C₈

—

149

D₄⋊C₈

—

150

C₂×C₁₉

—

151

C₂×C₁₉

—

152

C₂×C₁₉

#2091

yes

characteristic

153

C₂×C₁₉

#2094

yes

characteristic

154

C₂×C₁₉

#2098

yes

characteristic

155

C₂²×D₄

Dic₃₈

yes

characteristic

156

C₂³×C₄

—

157

C₂×M₁₆

—

158

C₂×M₁₆

—

159

C₂²×C₈

—

160

C₂²×C₈

—

161

C₄×D₄

—

162

C₄×D₄

—

163

C₄×D₄

—

164

C₄×D₄

—

165

C₂×C₄⋊C₄

Dic₃₈

yes

characteristic

166

C₂×C₂²⋊C₄

—

167

C₂×C₄²

C₂²×D₁₉

yes

characteristic

168

#108

—

169

C₄⋊C₈

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₂²⋊C₈

—

178

C₂²⋊C₈

—

179

C₂²⋊C₈

—

180

#97

—

181

#97

—

182

C₄×C₈

—

183

C₄×C₈

C₂²⋊D₁₉

yes

—

184

C₁₉

#10661

yes

characteristic, complemented, Sylow

185

C₂⁴

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

195

C₂²×C₄

D₄×D₁₉

yes

characteristic

196

C₂²×C₄

#64543

yes

characteristic

197

M₁₆

—

198

M₁₆

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₂²⋊C₄

—

211

C₂²⋊C₄

—

212

C₄²

#64541

yes

characteristic

213

C₄²

D₄×D₁₉

yes

characteristic

214

C₄²

#64543

yes

characteristic

215

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

216

C₂³

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

#10597324

yes

characteristic

222

D₄

—

223

D₄

—

224

D₄

—

225

D₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

#10597324

yes

characteristic

234

C₂×C₄

#10597329

yes

characteristic

235

C₂×C₄

#10597329

yes

characteristic

236

C₂×C₄

#10597357

yes

—

237

C₂×C₄

SD₁₆×D₁₉

yes

—

238

C₂×C₄

#10597370

yes

characteristic

239

C₂×C₄

#10597381

yes

characteristic

240

C₂×C₄

#10597386

yes

characteristic

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

245

C₈

—

152

—

246

C₈

—

152

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

#11926480

yes

characteristic

255

C₂²

#11926832

yes

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

#11926861

yes

—

262

C₄

#11926915

yes

characteristic

263

C₄

#11926932

yes

characteristic

264

C₂

—

265

C₂

—

266

C₂

#14565151

yes

characteristic

267

C₂

#14565166

yes

characteristic

268

C₂

#14565190

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1486	C₂
socle	C₂²×C₁₉	#399
prime radical	C₂²×D₄×C₁₉	Q₈
hypercenter	#1486	D₁₉
hypocenter	C₁₉	#10661
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1486

subgroup

G/H

center

C₂×C₄

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1486

C₂

socle

C₂²×C₁₉

#399

prime radical

C₂²×D₄×C₁₉

Q₈

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1486

N	H ≅ G/N	type
2. #14563809	C₂	semidirect
3. #14562407	C₂	semidirect
4. #14562406	C₂	semidirect
6. #14561465	C₂	semidirect
184. C₁₉	#10661	semidirect

H ≅ G/N

type

2. #14563809

C₂

semidirect

3. #14562407

C₂

semidirect

4. #14562406

C₂

semidirect

6. #14561465

C₂

semidirect

184. C₁₉

#10661

semidirect

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

subgroup	index
#14564434	2
#14563809	2
#14562407	2
#14562406	2
#14562060	2
#14561465	2
C₁₉×#1486	2
#10661	19

subgroup

index

C₁₉×#1486

Subgroups — #18087520

Conjugacy classes of subgroups

Complements

Maximal subgroups