Group #18076689 — subgroups

Subgroups — #18076689

Order 4864.

364 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14572572	C₂	1	1	yes	maximal, characteristic
2	#14564356	C₂	1	1	yes	maximal, characteristic
3	#14562135	C₂	1	1	yes	maximal, characteristic
4	#14562037	C₂	1	1	yes	maximal, characteristic
5	#14561536	C₂	1	1	yes	maximal, characteristic
6	#14561479	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1570	C₂	1	1	yes	maximal, characteristic
8	#11927101	C₂²	1	1	yes	characteristic
9	#11926673	—	2	2	no	—
10	#11926673	—	2	2	no	—
11	#11926597	C₂²	1	1	yes	characteristic
12	#11926572	—	2	1	no	—
13	C₂×Dic₁₉⋊C₈	—	2	1	no	—
14	#11926502	—	2	1	no	—
15	C₂×#10597260	C₂²	1	1	yes	characteristic
16	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
17	#11926298	—	2	1	no	—
18	#11926282	C₄	1	2	yes	—
19	#11926282	C₄	1	2	yes	—
20	#11926274	—	2	2	no	—
21	C₁₉×#431	C₂²	1	1	yes	characteristic
22	C₁₉×#423	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₁₉×#334	—	2	2	no	—
25	C₂×M₁₆×C₁₉	—	2	1	no	—
26	C₂²×C₈×C₁₉	—	2	1	no	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	#10597372	—	2	1	no	—
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	#10597370	—	2	1	no	—
31	#10597370	C₂×C₄	1	2	yes	—
32	C₂×C₄×Dic₁₉	—	2	1	no	—
33	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
34	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
35	#10597316	—	2	1	no	—
36	#10597315	Q₈	1	1	yes	characteristic
37	#10597315	Q₈	1	1	yes	characteristic
38	C₄×Dic₃₈	—	2	1	no	—
39	C₄×Dic₃₈	D₄	1	2	yes	—
40	C₁₉×C₄⋊C₈	—	2	1	no	—
41	C₁₉×C₄⋊C₈	—	2	1	no	—
42	C₁₉×C₄⋊C₈	—	2	1	no	—
43	C₁₉×C₄⋊C₈	—	2	1	no	—
44	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
45	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
46	C₄×C₈×C₁₉	—	2	1	no	—
47	C₁₉⋊#95	C₂×C₄	1	1	yes	characteristic
48	C₁₉⋊#95	C₂×C₄	1	1	yes	characteristic
49	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
50	#10597272	—	2	2	no	—
51	Dic₁₉⋊C₈	—	2	4	no	—
52	Dic₁₉⋊C₈	—	4	2	no	—
53	C₈×Dic₁₉	—	2	2	no	—
54	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
55	#10597260	—	2	1	no	—
56	#10597260	—	2	1	no	—
57	C₄×C₁₉⋊C₈	—	2	1	no	—
58	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
61	C₂²×Dic₁₉	—	2	1	no	—
62	C₂²×Dic₁₉	—	2	1	no	—
63	C₂×Dic₃₈	—	2	1	no	—
64	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
65	M₁₆×C₁₉	—	4	1	no	—
66	M₁₆×C₁₉	—	4	1	no	—
67	C₂×C₈×C₁₉	—	2	2	no	—
68	C₂×C₈×C₁₉	—	2	2	no	—
69	C₂×C₈×C₁₉	—	4	1	no	—
70	C₂×C₈×C₁₉	—	4	1	no	—
71	C₂×C₈×C₁₉	—	4	1	no	—
72	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
75	C₄²×C₁₉	#41	1	1	yes	characteristic
76	C₂²⋊Dic₁₉	—	2	2	no	—
77	C₄⋊Dic₁₉	—	2	1	no	—
78	C₄⋊Dic₁₉	—	2	1	no	—
79	C₄⋊Dic₁₉	—	2	1	no	—
80	C₄⋊Dic₁₉	—	4	2	no	—
81	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
82	Dic₁₉⋊C₄	—	2	2	no	—
83	Dic₁₉⋊C₄	—	2	2	no	—
84	C₄×Dic₁₉	—	2	2	no	—
85	C₄×Dic₁₉	—	4	1	no	—
86	C₄×Dic₁₉	—	4	1	no	—
87	C₂×C₁₉⋊C₈	—	2	1	no	—
88	C₂×C₁₉⋊C₈	—	2	1	no	—
89	C₂×C₁₉⋊C₈	—	2	1	no	—
90	C₂×C₁₉⋊C₈	—	2	1	no	—
91	C₂×C₁₉⋊C₈	—	2	1	no	—
92	C₂×C₁₉⋊C₈	—	4	1	no	—
93	C₂×C₁₉⋊C₈	SD₁₆	1	2	yes	—
94	#8881	—	19	1	no	maximal, Sylow
95	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
96	C₂×C₄×C₁₉	—	4	1	no	—
97	C₂×C₄×C₁₉	—	4	1	no	—
98	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#120	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	#123	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
105	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
108	C₂×Dic₁₉	—	2	2	no	—
109	C₂×Dic₁₉	—	2	2	no	—
110	C₂×Dic₁₉	—	2	2	no	—
111	C₂×Dic₁₉	—	4	1	no	—
112	C₂×Dic₁₉	—	4	1	no	—
113	C₂×Dic₁₉	—	4	1	no	—
114	C₂×Dic₁₉	—	4	1	no	—
115	C₂×Dic₁₉	—	4	1	no	—
116	Dic₃₈	—	4	2	no	—
117	Dic₃₈	—	8	1	no	—
118	C₈×C₁₉	—	4	2	no	—
119	C₈×C₁₉	—	4	2	no	—
120	C₈×C₁₉	—	8	1	no	—
121	C₁₉⋊C₈	—	2	2	no	—
122	C₁₉⋊C₈	—	4	1	no	—
123	C₁₉⋊C₈	—	8	1	no	—
124	#2961	—	19	1	no	—
125	#1940	—	19	1	no	—
126	#1570	D₁₉	1	1	yes	characteristic
127	#1503	—	19	1	no	—
128	#1481	—	19	1	no	—
129	#1303	—	19	1	no	—
130	#1281	—	19	1	no	—
131	C₂²×C₁₉	—	2	1	no	—
132	C₂²×C₁₉	—	2	1	no	—
133	C₂²×C₁₉	#385	1	1	yes	characteristic
134	C₂²×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
135	C₂²×C₁₉	#441	1	1	yes	characteristic
136	C₄×C₁₉	—	2	1	no	—
137	C₄×C₁₉	—	2	1	no	—
138	C₄×C₁₉	—	2	1	no	—
139	C₄×C₁₉	—	2	1	no	—
140	C₄×C₁₉	#448	1	1	yes	characteristic
141	C₄×C₁₉	#452	1	1	yes	characteristic
142	C₄×C₁₉	#475	1	1	yes	characteristic
143	C₄×C₁₉	#479	1	1	yes	characteristic
144	Dic₁₉	—	4	2	no	—
145	Dic₁₉	—	4	2	no	—
146	Dic₁₉	—	4	2	no	—
147	Dic₁₉	—	8	1	no	—
148	#533	—	19	1	no	—
149	#446	—	38	2	no	—
150	#446	—	38	2	no	—
151	#431	—	19	1	no	—
152	#431	C₂×D₁₉	1	1	yes	characteristic
153	#424	—	38	1	no	—
154	#423	C₂×D₁₉	1	1	yes	characteristic
155	C₂×C₄⋊C₈	—	38	1	no	—
156	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
157	#405	—	38	1	no	—
158	C₂×#97	—	19	1	no	—
159	C₄×C₄⋊C₄	—	19	1	no	—
160	#336	—	38	1	no	—
161	#334	—	2	2	no	—
162	#328	—	19	2	no	—
163	#328	—	19	2	no	—
164	Q₈⋊C₈	—	38	2	no	—
165	C₂×C₁₉	—	2	1	no	—
166	C₂×C₁₉	—	2	1	no	—
167	C₂×C₁₉	#1861	1	1	yes	characteristic
168	C₂×C₁₉	#1865	1	1	yes	characteristic
169	C₂×C₁₉	#1868	1	1	yes	characteristic
170	C₂×M₁₆	—	2	1	no	—
171	C₂²×C₈	—	2	1	no	—
172	C₂²×C₈	—	19	1	no	—
173	C₂²×C₈	—	19	1	no	—
174	C₄⋊Q₈	—	19	1	no	—
175	C₄⋊Q₈	—	19	1	no	—
176	#125	—	38	1	no	—
177	C₂²⋊Q₈	—	19	2	no	—
178	C₂²⋊Q₈	—	38	1	no	—
179	C₄×Q₈	—	19	2	no	—
180	C₄×Q₈	—	38	1	no	—
181	#117	—	38	1	no	—
182	C₂×C₄⋊C₄	—	38	1	no	—
183	C₂×C₄²	—	38	1	no	—
184	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
185	C₄⋊C₈	—	2	1	no	—
186	C₄⋊C₈	—	2	1	no	—
187	C₄⋊C₈	—	2	1	no	—
188	C₄⋊C₈	—	2	1	no	—
189	C₄⋊C₈	—	38	4	no	—
190	C₄⋊C₈	—	38	1	no	—
191	C₄⋊C₈	—	76	2	no	—
192	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
193	C₂²⋊C₈	—	38	1	no	—
194	C₂²⋊C₈	C₄×D₁₉	1	2	yes	—
195	#97	—	38	2	no	—
196	#97	—	38	1	no	—
197	#97	—	38	1	no	—
198	C₄×C₈	—	2	1	no	—
199	C₄×C₈	—	38	2	no	—
200	C₄×C₈	—	38	1	no	—
201	#95	—	19	1	no	—
202	#95	—	19	1	no	—
203	C₁₉	#8881	1	1	yes	characteristic, complemented, Sylow
204	C₂×Q₈	—	19	2	no	—
205	C₂×Q₈	—	38	1	no	—
206	C₂²×C₄	—	38	1	no	—
207	C₂²×C₄	—	38	1	no	—
208	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
209	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
210	C₂²×C₄	#64545	1	1	yes	characteristic
211	M₁₆	—	4	1	no	—
212	M₁₆	—	4	1	no	—
213	C₂×C₈	—	2	2	no	—
214	C₂×C₈	—	2	2	no	—
215	C₂×C₈	—	4	1	no	—
216	C₂×C₈	—	4	1	no	—
217	C₂×C₈	—	4	1	no	—
218	C₂×C₈	—	19	2	no	—
219	C₂×C₈	—	38	1	no	—
220	C₂×C₈	—	38	1	no	—
221	C₂×C₈	—	38	1	no	—
222	C₂×C₈	—	38	1	no	—
223	C₂×C₈	—	38	1	no	—
224	C₂×C₈	—	76	1	no	—
225	C₄⋊C₄	—	19	2	no	—
226	C₄⋊C₄	—	38	1	no	—
227	C₄⋊C₄	—	38	2	no	—
228	C₄⋊C₄	—	38	1	no	—
229	C₄⋊C₄	—	38	1	no	—
230	C₄⋊C₄	—	38	2	no	—
231	C₄⋊C₄	—	76	2	no	—
232	C₂²⋊C₄	—	38	2	no	—
233	C₄²	—	38	2	no	—
234	C₄²	—	76	1	no	—
235	C₄²	—	76	1	no	—
236	C₄²	#64541	1	1	yes	characteristic
237	C₄²	D₄×D₁₉	1	1	yes	characteristic
238	C₄²	Q₈×D₁₉	1	1	yes	characteristic
239	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
240	C₂³	#10597339	1	1	yes	characteristic
241	Q₈	—	76	2	no	—
242	Q₈	—	152	1	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	4	1	no	—
245	C₂×C₄	—	38	2	no	—
246	C₂×C₄	—	38	2	no	—
247	C₂×C₄	—	38	2	no	—
248	C₂×C₄	—	76	1	no	—
249	C₂×C₄	—	76	1	no	—
250	C₂×C₄	—	76	1	no	—
251	C₂×C₄	—	76	1	no	—
252	C₂×C₄	—	76	1	no	—
253	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
254	C₂×C₄	#10597340	1	1	yes	characteristic
255	C₂×C₄	#10597342	1	1	yes	characteristic
256	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
257	C₂×C₄	#10597361	1	1	yes	characteristic
258	C₂×C₄	#10597361	1	1	yes	characteristic
259	C₂×C₄	#10597362	1	1	yes	characteristic
260	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
261	C₂×C₄	#10597383	1	1	yes	characteristic
262	C₂×C₄	#10597392	1	1	yes	characteristic
263	C₈	—	4	2	no	—
264	C₈	—	4	2	no	—
265	C₈	—	8	1	no	—
266	C₈	—	38	2	no	—
267	C₈	—	76	1	no	—
268	C₈	—	152	1	no	—
269	C₂²	—	2	1	no	—
270	C₂²	—	2	1	no	—
271	C₂²	#11926415	1	1	yes	characteristic
272	C₂²	#11926631	1	1	yes	characteristic
273	C₂²	#11926650	1	1	yes	characteristic
274	C₄	—	2	1	no	—
275	C₄	—	2	1	no	—
276	C₄	—	2	1	no	—
277	C₄	—	2	1	no	—
278	C₄	—	76	2	no	—
279	C₄	—	76	2	no	—
280	C₄	—	76	2	no	—
281	C₄	—	152	1	no	—
282	C₄	#11926681	1	1	yes	characteristic
283	C₄	#11926703	1	1	yes	characteristic
284	C₄	#11926828	1	1	yes	characteristic
285	C₄	#11926854	1	1	yes	characteristic
286	C₂	—	2	1	no	—
287	C₂	—	2	1	no	—
288	C₂	#14563872	1	1	yes	characteristic
289	C₂	#14563900	1	1	yes	characteristic
290	C₂	#14563919	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572572

C₂

yes

maximal, characteristic

#14564356

C₂

yes

maximal, characteristic

#14562135

C₂

yes

maximal, characteristic

#14562037

C₂

yes

maximal, characteristic

#14561536

C₂

yes

maximal, characteristic

#14561479

C₂

yes

maximal, characteristic

C₁₉×#1570

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

—

C₂²

yes

characteristic

#11926572

—

C₂×Dic₁₉⋊C₈

—

#11926502

—

C₂×#10597260

C₂²

yes

characteristic

C₄×C₄⋊Dic₁₉

C₂²

yes

characteristic

#11926298

—

#11926282

C₄

yes

—

#11926282

C₄

yes

—

#11926274

—

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#334

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

—

C₂×C₄⋊Dic₁₉

—

#10597370

—

#10597370

C₂×C₄

yes

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

#10597316

—

#10597315

Q₈

yes

characteristic

#10597315

Q₈

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

C₂×C₄

yes

characteristic

C₁₉⋊#95

C₂×C₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

#10597272

—

Dic₁₉⋊C₈

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₄⋊C₄

yes

—

M₁₆×C₁₉

—

M₁₆×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

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₄⋊C₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

SD₁₆

yes

—

#8881

—

maximal, Sylow

C₂³×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

100

C₂×C₄×C₁₉

#120

yes

characteristic

101

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

102

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

103

C₂×C₄×C₁₉

#123

yes

characteristic

104

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

105

C₂×C₄×C₁₉

#135

yes

characteristic

106

C₂×C₄×C₁₉

#137

yes

characteristic

107

C₂×C₄×C₁₉

#137

yes

characteristic

108

C₂×Dic₁₉

—

109

C₂×Dic₁₉

—

110

C₂×Dic₁₉

—

111

C₂×Dic₁₉

—

112

C₂×Dic₁₉

—

113

C₂×Dic₁₉

—

114

C₂×Dic₁₉

—

115

C₂×Dic₁₉

—

116

Dic₃₈

—

117

Dic₃₈

—

118

C₈×C₁₉

—

119

C₈×C₁₉

—

120

C₈×C₁₉

—

121

C₁₉⋊C₈

—

122

C₁₉⋊C₈

—

123

C₁₉⋊C₈

—

124

#2961

—

125

#1940

—

126

#1570

D₁₉

yes

characteristic

127

#1503

—

128

#1481

—

129

#1303

—

130

#1281

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

#385

yes

characteristic

134

C₂²×C₁₉

C₄×SD₁₆

yes

characteristic

135

C₂²×C₁₉

#441

yes

characteristic

136

C₄×C₁₉

—

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

—

140

C₄×C₁₉

#448

yes

characteristic

141

C₄×C₁₉

#452

yes

characteristic

142

C₄×C₁₉

#475

yes

characteristic

143

C₄×C₁₉

#479

yes

characteristic

144

Dic₁₉

—

145

Dic₁₉

—

146

Dic₁₉

—

147

Dic₁₉

—

148

#533

—

149

#446

—

150

#446

—

151

#431

—

152

#431

C₂×D₁₉

yes

characteristic

153

#424

—

154

#423

C₂×D₁₉

yes

characteristic

155

C₂×C₄⋊C₈

—

156

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

157

#405

—

158

C₂×#97

—

159

C₄×C₄⋊C₄

—

160

#336

—

161

#334

—

162

#328

—

163

#328

—

164

Q₈⋊C₈

—

165

C₂×C₁₉

—

166

C₂×C₁₉

—

167

C₂×C₁₉

#1861

yes

characteristic

168

C₂×C₁₉

#1865

yes

characteristic

169

C₂×C₁₉

#1868

yes

characteristic

170

C₂×M₁₆

—

171

C₂²×C₈

—

172

C₂²×C₈

—

173

C₂²×C₈

—

174

C₄⋊Q₈

—

175

C₄⋊Q₈

—

176

#125

—

177

C₂²⋊Q₈

—

178

C₂²⋊Q₈

—

179

C₄×Q₈

—

180

C₄×Q₈

—

181

#117

—

182

C₂×C₄⋊C₄

—

183

C₂×C₄²

—

184

C₂×C₄²

C₂²×D₁₉

yes

characteristic

185

C₄⋊C₈

—

186

C₄⋊C₈

—

187

C₄⋊C₈

—

188

C₄⋊C₈

—

189

C₄⋊C₈

—

190

C₄⋊C₈

—

191

C₄⋊C₈

—

192

C₄⋊C₈

C₂²⋊D₁₉

yes

—

193

C₂²⋊C₈

—

194

C₂²⋊C₈

C₄×D₁₉

yes

—

195

#97

—

196

#97

—

197

#97

—

198

C₄×C₈

—

199

C₄×C₈

—

200

C₄×C₈

—

201

#95

—

202

#95

—

203

C₁₉

#8881

yes

characteristic, complemented, Sylow

204

C₂×Q₈

—

205

C₂×Q₈

—

206

C₂²×C₄

—

207

C₂²×C₄

—

208

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

209

C₂²×C₄

D₄×D₁₉

yes

characteristic

210

C₂²×C₄

#64545

yes

characteristic

211

M₁₆

—

212

M₁₆

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

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

C₄⋊C₄

—

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₂²⋊C₄

—

233

C₄²

—

234

C₄²

—

235

C₄²

—

236

C₄²

#64541

yes

characteristic

237

C₄²

D₄×D₁₉

yes

characteristic

238

C₄²

Q₈×D₁₉

yes

characteristic

239

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

240

C₂³

#10597339

yes

characteristic

241

Q₈

—

242

Q₈

—

152

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

252

C₂×C₄

—

253

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

254

C₂×C₄

#10597340

yes

characteristic

255

C₂×C₄

#10597342

yes

characteristic

256

C₂×C₄

SD₁₆×D₁₉

yes

characteristic

257

C₂×C₄

#10597361

yes

characteristic

258

C₂×C₄

#10597361

yes

characteristic

259

C₂×C₄

#10597362

yes

characteristic

260

C₂×C₄

C₄×C₂²⋊D₁₉

yes

characteristic

261

C₂×C₄

#10597383

yes

characteristic

262

C₂×C₄

#10597392

yes

characteristic

263

C₈

—

264

C₈

—

265

C₈

—

266

C₈

—

267

C₈

—

268

C₈

—

152

—

269

C₂²

—

270

C₂²

—

271

C₂²

#11926415

yes

characteristic

272

C₂²

#11926631

yes

characteristic

273

C₂²

#11926650

yes

characteristic

274

C₄

—

275

C₄

—

276

C₄

—

277

C₄

—

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

—

152

—

282

C₄

#11926681

yes

characteristic

283

C₄

#11926703

yes

characteristic

284

C₄

#11926828

yes

characteristic

285

C₄

#11926854

yes

characteristic

286

C₂

—

287

C₂

—

288

C₂

#14563872

yes

characteristic

289

C₂

#14563900

yes

characteristic

290

C₂

#14563919

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1570	C₂
socle	C₂²×C₁₉	#385
prime radical	C₂³×C₁₉	C₄×D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1570	D₁₉
hypocenter	C₁₉	#8881
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1570

subgroup

G/H

center

C₂×C₄

#10597383

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1570

C₂

socle

C₂²×C₁₉

#385

prime radical

C₂³×C₁₉

C₄×D₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1570

N	H ≅ G/N	type
203. C₁₉	#8881	semidirect

H ≅ G/N

type

203. C₁₉

#8881

semidirect

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

subgroup	index
#14572572	2
#14564356	2
#14562135	2
#14562037	2
#14561536	2
#14561479	2
C₁₉×#1570	2
#8881	19

subgroup

index

C₁₉×#1570

Subgroups — #18076689

Conjugacy classes of subgroups

Complements

Maximal subgroups