Group #18087170 — subgroups

Subgroups — #18087170

Order 4864.

322 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14564479	C₂	1	1	yes	maximal, characteristic
2	#14564410	C₂	1	1	yes	maximal, characteristic
3	#14562410	C₂	1	1	yes	maximal, characteristic
4	#14562306	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926289	C₂	1	1	yes	maximal, characteristic
6	#14561510	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1565	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	C₂×#10597279	—	2	1	no	—
10	#11926568	C₂²	1	1	yes	characteristic
11	#11926568	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#10597281	—	2	1	no	—
14	C₂×#10597281	—	2	1	no	—
15	#11926308	—	2	1	no	—
16	#11926297	—	2	2	no	—
17	#11926289	—	2	1	no	—
18	#11926289	—	2	1	no	—
19	#11926289	—	2	2	no	—
20	C₁₉×#431	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#335	—	2	1	no	—
24	C₁₉×#334	—	2	1	no	—
25	C₂²×Dic₃₈	—	2	1	no	—
26	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
27	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₉	—	2	1	no	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×C₄⋊Dic₁₉	Q₈	1	2	yes	—
32	C₂×#64520	—	2	1	no	—
33	C₂×#64520	—	2	1	no	—
34	C₂²×C₁₉⋊C₈	—	2	1	no	—
35	#10597315	—	2	1	no	—
36	#10597315	—	2	1	no	—
37	#10597315	—	2	1	no	—
38	#10597315	—	2	1	no	—
39	C₁₉×C₄⋊C₈	—	2	1	no	—
40	C₁₉×C₄⋊C₈	—	2	1	no	—
41	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
42	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
43	C₁₉×C₂²⋊C₈	—	2	1	no	—
44	C₁₉×#97	—	2	1	no	—
45	C₄×C₈×C₁₉	—	2	1	no	—
46	C₄×C₈×C₁₉	—	2	1	no	—
47	#10597281	—	4	2	no	—
48	#10597281	—	4	2	no	—
49	#10597279	—	4	2	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
52	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
53	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
54	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
55	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
59	C₂²×Dic₁₉	—	2	2	no	—
60	C₂×Dic₃₈	—	4	1	no	—
61	C₂×Dic₃₈	—	4	1	no	—
62	C₂×Dic₃₈	—	4	1	no	—
63	C₂×Dic₃₈	—	4	1	no	—
64	C₂×Dic₃₈	—	4	1	no	—
65	C₂×Dic₃₈	—	4	1	no	—
66	M₁₆×C₁₉	—	2	1	no	—
67	M₁₆×C₁₉	—	2	1	no	—
68	M₁₆×C₁₉	—	2	1	no	—
69	M₁₆×C₁₉	D₈	1	2	yes	—
70	C₂×C₈×C₁₉	—	2	1	no	—
71	C₂×C₈×C₁₉	—	2	1	no	—
72	C₂×C₈×C₁₉	—	2	1	no	—
73	C₂×C₈×C₁₉	—	2	1	no	—
74	C₂×C₈×C₁₉	—	4	1	no	—
75	C₂×C₈×C₁₉	—	8	1	no	—
76	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₁₉	#41	1	1	yes	characteristic
79	C₄²×C₁₉	#41	1	1	yes	characteristic
80	C₄⋊Dic₁₉	—	2	2	no	—
81	C₄⋊Dic₁₉	—	2	2	no	—
82	C₄⋊Dic₁₉	—	4	1	no	—
83	C₄⋊Dic₁₉	—	4	1	no	—
84	#64520	—	4	1	no	—
85	#64520	—	4	1	no	—
86	#64520	—	4	1	no	—
87	#64520	—	4	1	no	—
88	C₂×C₁₉⋊C₈	—	2	2	no	—
89	C₂×C₁₉⋊C₈	—	4	1	no	—
90	C₂×C₁₉⋊C₈	—	4	1	no	—
91	C₂×C₁₉⋊C₈	—	4	1	no	—
92	C₂×C₁₉⋊C₈	—	4	1	no	—
93	#10604	—	19	1	no	maximal, Sylow
94	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	4	1	no	—
98	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
102	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
105	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
106	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
108	C₂×Dic₁₉	—	4	2	no	—
109	C₂×Dic₁₉	—	4	2	no	—
110	C₂×Dic₁₉	—	4	2	no	—
111	Dic₃₈	—	8	1	no	—
112	Dic₃₈	—	8	1	no	—
113	Dic₃₈	—	8	1	no	—
114	Dic₃₈	—	8	1	no	—
115	C₈×C₁₉	—	2	2	no	—
116	C₈×C₁₉	—	4	1	no	—
117	C₈×C₁₉	—	4	1	no	—
118	C₈×C₁₉	—	4	1	no	—
119	C₈×C₁₉	—	8	1	no	—
120	C₁₉⋊C₈	—	4	2	no	—
121	C₁₉⋊C₈	—	8	1	no	—
122	C₁₉⋊C₈	—	8	1	no	—
123	#1966	—	19	1	no	—
124	#1950	—	19	1	no	—
125	#1571	—	19	1	no	—
126	#1565	D₁₉	1	1	yes	characteristic
127	#1546	—	19	1	no	—
128	C₂×#332	—	19	1	no	—
129	#1292	—	19	1	no	—
130	C₂²×C₁₉	—	2	1	no	—
131	C₂²×C₁₉	—	2	1	no	—
132	C₂²×C₁₉	#396	1	1	yes	characteristic
133	C₂²×C₁₉	#474	1	1	yes	characteristic
134	C₂²×C₁₉	#478	1	1	yes	characteristic
135	C₄×C₁₉	—	2	1	no	—
136	C₄×C₁₉	—	2	1	no	—
137	C₄×C₁₉	—	2	1	no	—
138	C₄×C₁₉	#459	1	1	yes	characteristic
139	C₄×C₁₉	#464	1	1	yes	characteristic
140	C₄×C₁₉	#466	1	1	yes	characteristic
141	C₄×C₁₉	#468	1	1	yes	characteristic
142	C₄×C₁₉	#471	1	1	yes	characteristic
143	C₄×C₁₉	#473	1	1	yes	characteristic
144	Dic₁₉	—	8	2	no	—
145	C₂×C₄⋊Q₈	—	19	1	no	—
146	#431	C₂×D₁₉	1	1	yes	characteristic
147	C₂×#108	—	38	1	no	—
148	#423	—	19	1	no	—
149	#423	—	19	1	no	—
150	C₂×C₄⋊C₈	—	19	1	no	—
151	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
152	C₂×#101	—	38	1	no	—
153	C₂×#101	—	38	1	no	—
154	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
155	#341	—	38	1	no	—
156	#335	—	2	1	no	—
157	#335	—	38	2	no	—
158	#334	—	2	1	no	—
159	#332	—	38	2	no	—
160	#332	—	38	1	no	—
161	#332	—	38	1	no	—
162	C₂×C₁₉	—	2	1	no	—
163	C₂×C₁₉	—	2	1	no	—
164	C₂×C₁₉	#2064	1	1	yes	characteristic
165	C₂×C₁₉	#2067	1	1	yes	characteristic
166	C₂×C₁₉	#2070	1	1	yes	characteristic
167	C₂²×Q₈	—	38	1	no	—
168	C₂×M₁₆	—	38	1	no	—
169	C₂×M₁₆	—	38	1	no	—
170	C₂×M₁₆	D₇₆	1	1	yes	characteristic
171	C₂×M₁₆	D₇₆	1	1	yes	characteristic
172	C₂²×C₈	—	2	1	no	—
173	C₂²×C₈	—	38	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	—	19	2	no	—
179	C₂×C₄⋊C₄	—	38	1	no	—
180	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
181	#108	—	76	2	no	—
182	C₄⋊C₈	—	2	1	no	—
183	C₄⋊C₈	—	2	1	no	—
184	C₄⋊C₈	—	19	2	no	—
185	C₄⋊C₈	—	38	1	no	—
186	C₄⋊C₈	—	38	1	no	—
187	C₄⋊C₈	—	38	1	no	—
188	C₄⋊C₈	—	38	1	no	—
189	C₄⋊C₈	—	38	1	no	—
190	C₄⋊C₈	C₂²⋊D₁₉	1	1	yes	characteristic
191	C₄⋊C₈	C₂²⋊D₁₉	1	1	yes	characteristic
192	#101	—	76	2	no	—
193	#101	—	76	2	no	—
194	C₂²⋊C₈	—	2	1	no	—
195	#97	—	2	1	no	—
196	C₄×C₈	—	2	1	no	—
197	C₄×C₈	—	2	1	no	—
198	C₁₉	#10604	1	1	yes	characteristic, complemented, Sylow
199	C₂×Q₈	—	76	1	no	—
200	C₂×Q₈	—	76	1	no	—
201	C₂×Q₈	—	76	1	no	—
202	C₂×Q₈	—	76	1	no	—
203	C₂×Q₈	—	76	1	no	—
204	C₂×Q₈	—	76	1	no	—
205	C₂²×C₄	—	38	2	no	—
206	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
207	C₂²×C₄	#64543	1	1	yes	characteristic
208	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
209	M₁₆	—	2	1	no	—
210	M₁₆	—	2	1	no	—
211	M₁₆	—	2	1	no	—
212	M₁₆	—	76	1	no	—
213	M₁₆	—	76	1	no	—
214	M₁₆	—	76	1	no	—
215	M₁₆	—	76	1	no	—
216	M₁₆	D₁₅₂	1	2	yes	—
217	C₂×C₈	—	2	1	no	—
218	C₂×C₈	—	2	1	no	—
219	C₂×C₈	—	2	1	no	—
220	C₂×C₈	—	2	1	no	—
221	C₂×C₈	—	4	1	no	—
222	C₂×C₈	—	8	1	no	—
223	C₂×C₈	—	38	2	no	—
224	C₂×C₈	—	76	1	no	—
225	C₂×C₈	—	76	1	no	—
226	C₂×C₈	—	76	1	no	—
227	C₂×C₈	—	76	1	no	—
228	C₄⋊C₄	—	38	2	no	—
229	C₄⋊C₄	—	38	2	no	—
230	C₄⋊C₄	—	76	1	no	—
231	C₄⋊C₄	—	76	1	no	—
232	C₄²	#64541	1	1	yes	characteristic
233	C₄²	D₄×D₁₉	1	1	yes	characteristic
234	C₄²	#64545	1	1	yes	characteristic
235	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
236	C₂³	#10597343	1	1	yes	characteristic
237	Q₈	—	152	1	no	—
238	Q₈	—	152	1	no	—
239	Q₈	—	152	1	no	—
240	Q₈	—	152	1	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	76	2	no	—
245	C₂×C₄	—	76	2	no	—
246	C₂×C₄	—	76	2	no	—
247	C₂×C₄	#10597341	1	1	yes	characteristic
248	C₂×C₄	#10597342	1	1	yes	characteristic
249	C₂×C₄	#10597344	1	1	yes	characteristic
250	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
251	C₂×C₄	#10597350	1	1	yes	characteristic
252	C₂×C₄	#10597354	1	1	yes	characteristic
253	C₂×C₄	#10597355	1	1	yes	characteristic
254	C₂×C₄	#10597376	1	1	yes	characteristic
255	C₂×C₄	#10597385	1	1	yes	characteristic
256	C₂×C₄	#10597392	1	1	yes	characteristic
257	C₈	—	2	2	no	—
258	C₈	—	4	1	no	—
259	C₈	—	4	1	no	—
260	C₈	—	4	1	no	—
261	C₈	—	8	1	no	—
262	C₈	—	76	2	no	—
263	C₈	—	152	1	no	—
264	C₈	—	152	1	no	—
265	C₂²	—	2	1	no	—
266	C₂²	—	2	1	no	—
267	C₂²	#11926466	1	1	yes	characteristic
268	C₂²	#11926825	1	1	yes	characteristic
269	C₂²	#11926845	1	1	yes	characteristic
270	C₄	—	2	1	no	—
271	C₄	—	2	1	no	—
272	C₄	—	2	1	no	—
273	C₄	—	152	2	no	—
274	C₄	#11926740	1	1	yes	characteristic
275	C₄	#11926767	1	1	yes	characteristic
276	C₄	#11926780	1	1	yes	characteristic
277	C₄	#11926790	1	1	yes	characteristic
278	C₄	#11926805	1	1	yes	characteristic
279	C₄	#11926817	1	1	yes	characteristic
280	C₂	—	2	1	no	—
281	C₂	—	2	1	no	—
282	C₂	#14564999	1	1	yes	characteristic
283	C₂	#14565022	1	1	yes	characteristic
284	C₂	#14565035	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564479

C₂

yes

maximal, characteristic

#14564410

C₂

yes

maximal, characteristic

#14562410

C₂

yes

maximal, characteristic

#14562306

C₂

yes

maximal, characteristic

C₂×#11926289

C₂

yes

maximal, characteristic

#14561510

C₂

yes

maximal, characteristic

C₁₉×#1565

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×#10597279

—

#11926568

C₂²

yes

characteristic

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

—

—

—

—

—

—

C₁₉×#431

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₂²×Dic₃₈

—

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

Q₈

yes

—

C₂×#64520

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

—

—

—

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

characteristic

C₁₉×C₄⋊C₈

D₄

yes

characteristic

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

#10597281

—

#10597281

—

#10597279

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10604

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

100

C₂×C₄×C₁₉

#121

yes

characteristic

101

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

102

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

103

C₂×C₄×C₁₉

#126

yes

characteristic

104

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

105

C₂×C₄×C₁₉

#135

yes

characteristic

106

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

107

C₂×C₄×C₁₉

#137

yes

characteristic

108

C₂×Dic₁₉

—

109

C₂×Dic₁₉

—

110

C₂×Dic₁₉

—

111

Dic₃₈

—

112

Dic₃₈

—

113

Dic₃₈

—

114

Dic₃₈

—

115

C₈×C₁₉

—

116

C₈×C₁₉

—

117

C₈×C₁₉

—

118

C₈×C₁₉

—

119

C₈×C₁₉

—

120

C₁₉⋊C₈

—

121

C₁₉⋊C₈

—

122

C₁₉⋊C₈

—

123

#1966

—

124

#1950

—

125

#1571

—

126

#1565

D₁₉

yes

characteristic

127

#1546

—

128

C₂×#332

—

129

#1292

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

#396

yes

characteristic

133

C₂²×C₁₉

#474

yes

characteristic

134

C₂²×C₁₉

#478

yes

characteristic

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

—

138

C₄×C₁₉

#459

yes

characteristic

139

C₄×C₁₉

#464

yes

characteristic

140

C₄×C₁₉

#466

yes

characteristic

141

C₄×C₁₉

#468

yes

characteristic

142

C₄×C₁₉

#471

yes

characteristic

143

C₄×C₁₉

#473

yes

characteristic

144

Dic₁₉

—

145

C₂×C₄⋊Q₈

—

146

#431

C₂×D₁₉

yes

characteristic

147

C₂×#108

—

148

#423

—

149

#423

—

150

C₂×C₄⋊C₈

—

151

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

152

C₂×#101

—

153

C₂×#101

—

154

C₄×M₁₆

C₂×D₁₉

yes

characteristic

155

#341

—

156

#335

—

157

#335

—

158

#334

—

159

#332

—

160

#332

—

161

#332

—

162

C₂×C₁₉

—

163

C₂×C₁₉

—

164

C₂×C₁₉

#2064

yes

characteristic

165

C₂×C₁₉

#2067

yes

characteristic

166

C₂×C₁₉

#2070

yes

characteristic

167

C₂²×Q₈

—

168

C₂×M₁₆

—

169

C₂×M₁₆

—

170

C₂×M₁₆

D₇₆

yes

characteristic

171

C₂×M₁₆

D₇₆

yes

characteristic

172

C₂²×C₈

—

173

C₂²×C₈

—

174

C₄⋊Q₈

—

175

C₄⋊Q₈

—

176

C₄⋊Q₈

—

177

C₄⋊Q₈

—

178

C₂×C₄⋊C₄

—

179

C₂×C₄⋊C₄

—

180

C₂×C₄²

C₂²×D₁₉

yes

characteristic

181

#108

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

—

186

C₄⋊C₈

—

187

C₄⋊C₈

—

188

C₄⋊C₈

—

189

C₄⋊C₈

—

190

C₄⋊C₈

C₂²⋊D₁₉

yes

characteristic

191

C₄⋊C₈

C₂²⋊D₁₉

yes

characteristic

192

#101

—

193

#101

—

194

C₂²⋊C₈

—

195

#97

—

196

C₄×C₈

—

197

C₄×C₈

—

198

C₁₉

#10604

yes

characteristic, complemented, Sylow

199

C₂×Q₈

—

200

C₂×Q₈

—

201

C₂×Q₈

—

202

C₂×Q₈

—

203

C₂×Q₈

—

204

C₂×Q₈

—

205

C₂²×C₄

—

206

C₂²×C₄

C₂×D₇₆

yes

characteristic

207

C₂²×C₄

#64543

yes

characteristic

208

C₂²×C₄

Q₈×D₁₉

yes

characteristic

209

M₁₆

—

210

M₁₆

—

211

M₁₆

—

212

M₁₆

—

213

M₁₆

—

214

M₁₆

—

215

M₁₆

—

216

M₁₆

D₁₅₂

yes

—

217

C₂×C₈

—

218

C₂×C₈

—

219

C₂×C₈

—

220

C₂×C₈

—

221

C₂×C₈

—

222

C₂×C₈

—

223

C₂×C₈

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₄²

#64541

yes

characteristic

233

C₄²

D₄×D₁₉

yes

characteristic

234

C₄²

#64545

yes

characteristic

235

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

236

C₂³

#10597343

yes

characteristic

237

Q₈

—

152

—

238

Q₈

—

152

—

239

Q₈

—

152

—

240

Q₈

—

152

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

#10597341

yes

characteristic

248

C₂×C₄

#10597342

yes

characteristic

249

C₂×C₄

#10597344

yes

characteristic

250

C₂×C₄

C₂×D₁₅₂

yes

characteristic

251

C₂×C₄

#10597350

yes

characteristic

252

C₂×C₄

#10597354

yes

characteristic

253

C₂×C₄

#10597355

yes

characteristic

254

C₂×C₄

#10597376

yes

characteristic

255

C₂×C₄

#10597385

yes

characteristic

256

C₂×C₄

#10597392

yes

characteristic

257

C₈

—

258

C₈

—

259

C₈

—

260

C₈

—

261

C₈

—

262

C₈

—

263

C₈

—

152

—

264

C₈

—

152

—

265

C₂²

—

266

C₂²

—

267

C₂²

#11926466

yes

characteristic

268

C₂²

#11926825

yes

characteristic

269

C₂²

#11926845

yes

characteristic

270

C₄

—

271

C₄

—

272

C₄

—

273

C₄

—

152

—

274

C₄

#11926740

yes

characteristic

275

C₄

#11926767

yes

characteristic

276

C₄

#11926780

yes

characteristic

277

C₄

#11926790

yes

characteristic

278

C₄

#11926805

yes

characteristic

279

C₄

#11926817

yes

characteristic

280

C₂

—

281

C₂

—

282

C₂

#14564999

yes

characteristic

283

C₂

#14565022

yes

characteristic

284

C₂

#14565035

yes

characteristic

	subgroup	G/H
center	C₂²	#11926466
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1565	C₂
socle	C₂²×C₁₉	#396
prime radical	C₂³×C₁₉	C₂²⋊Q₈
hypercenter	#1565	D₁₉
hypocenter	C₁₉	#10604
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1565

subgroup

G/H

center

C₂²

#11926466

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1565

C₂

socle

C₂²×C₁₉

#396

prime radical

C₂³×C₁₉

C₂²⋊Q₈

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1565

N	H ≅ G/N	type
198. C₁₉	#10604	semidirect

H ≅ G/N

type

198. C₁₉

#10604

semidirect

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

subgroup	index
#14564479	2
#14564410	2
#14562410	2
#14562306	2
C₂×#11926289	2
#14561510	2
C₁₉×#1565	2
#10604	19

subgroup

index

C₁₉×#1565

Subgroups — #18087170

Conjugacy classes of subgroups

Complements

Maximal subgroups