Group #18077210 — subgroups

Subgroups — #18077210

Order 4864.

510 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14572720	C₂	1	1	yes	maximal, characteristic
2	#14562030	C₂	1	2	yes	maximal
3	#14561959	C₂	1	1	yes	maximal, characteristic
4	#14561468	C₂	1	2	yes	maximal
5	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
6	#11926675	—	2	4	no	—
7	#11926601	—	2	2	no	—
8	#11926597	C₂²	1	2	yes	—
9	#11926597	C₂²	1	2	yes	—
10	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
11	#11926270	—	2	2	no	—
12	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#391	C₄	1	1	yes	characteristic
16	C₁₉×#391	C₄	1	1	yes	characteristic
17	C₁₉×#389	—	2	2	no	—
18	C₁₉×#384	C₄	1	1	yes	characteristic
19	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₄³×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	—	2	2	no	—
25	C₄×Q₈×C₁₉	—	2	2	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₄×Q₈×C₁₉	—	2	2	no	—
28	C₄×Q₈×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	—	2	1	no	—
37	C₂×C₄²×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	D₄	1	2	yes	—
41	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
42	C₁₉×#95	—	2	2	no	—
43	C₁₉×#95	—	2	2	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
49	#10597260	—	2	4	no	—
50	C₄×C₁₉⋊C₈	—	2	2	no	—
51	C₄×C₁₉⋊C₈	—	2	2	no	—
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	2	1	no	—
54	C₂×Q₈×C₁₉	—	2	1	no	—
55	C₂×Q₈×C₁₉	—	2	1	no	—
56	C₂×Q₈×C₁₉	—	2	2	no	—
57	C₂×Q₈×C₁₉	—	2	2	no	—
58	C₂×Q₈×C₁₉	—	2	2	no	—
59	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₄⋊C₄×C₁₉	—	2	8	no	—
70	C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₄⋊C₄×C₁₉	—	2	4	no	—
72	C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₄⋊C₄×C₁₉	—	4	4	no	—
74	C₄⋊C₄×C₁₉	—	4	2	no	—
75	C₄²×C₁₉	—	2	4	no	—
76	C₄²×C₁₉	—	2	2	no	—
77	C₄²×C₁₉	—	2	2	no	—
78	C₄²×C₁₉	—	2	1	no	—
79	C₄²×C₁₉	—	2	2	no	—
80	C₄²×C₁₉	—	4	2	no	—
81	C₄²×C₁₉	—	4	1	no	—
82	C₄²×C₁₉	—	4	1	no	—
83	C₄²×C₁₉	M₁₆	1	2	yes	—
84	C₄²×C₁₉	C₂×D₄	1	2	yes	—
85	C₄²×C₁₉	#41	1	2	yes	—
86	C₂×C₁₉⋊C₈	—	2	4	no	—
87	C₂×C₁₉⋊C₈	—	4	2	no	—
88	#8962	—	19	1	no	maximal, Sylow
89	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	Q₈×C₁₉	—	2	4	no	—
91	Q₈×C₁₉	—	4	2	no	—
92	Q₈×C₁₉	—	4	2	no	—
93	Q₈×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	2	2	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	2	2	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	2	2	no	—
102	C₂×C₄×C₁₉	—	2	2	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	1	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	—	4	2	no	—
111	C₂×C₄×C₁₉	—	4	1	no	—
112	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
113	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
114	C₂×C₄×C₁₉	#121	1	2	yes	—
115	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
116	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
117	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
118	C₂×C₄×C₁₉	#131	1	2	yes	—
119	C₁₉⋊C₈	—	4	4	no	—
120	C₁₉⋊C₈	—	8	2	no	—
121	#2983	—	19	1	no	—
122	C₄×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
123	#1479	—	19	2	no	—
124	#1461	—	19	1	no	—
125	#1276	—	19	2	no	—
126	C₂²×C₁₉	—	2	1	no	—
127	C₂²×C₁₉	—	2	1	no	—
128	C₂²×C₁₉	#386	1	1	yes	characteristic
129	C₂²×C₁₉	#407	1	1	yes	characteristic
130	C₂²×C₁₉	#408	1	1	yes	characteristic
131	C₄×C₁₉	—	2	4	no	—
132	C₄×C₁₉	—	2	2	no	—
133	C₄×C₁₉	—	2	1	no	—
134	C₄×C₁₉	—	4	2	no	—
135	C₄×C₁₉	—	4	2	no	—
136	C₄×C₁₉	—	4	2	no	—
137	C₄×C₁₉	—	4	2	no	—
138	C₄×C₁₉	—	8	1	no	—
139	C₄×C₁₉	#435	1	2	yes	—
140	C₄×C₁₉	#436	1	2	yes	—
141	C₄×C₁₉	#456	1	2	yes	—
142	C₂×C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic
143	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
144	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
145	#446	—	38	4	no	—
146	#432	—	38	2	no	—
147	#431	—	19	2	no	—
148	#431	—	19	2	no	—
149	#391	Dic₁₉	1	1	yes	characteristic
150	#391	Dic₁₉	1	1	yes	characteristic
151	#389	—	2	2	no	—
152	#384	Dic₁₉	1	1	yes	characteristic
153	C₄×C₄⋊C₄	—	2	2	no	—
154	C₄³	C₂×D₁₉	1	1	yes	characteristic
155	Q₈⋊C₈	—	38	4	no	—
156	#324	—	38	2	no	—
157	C₂×C₁₉	—	2	1	no	—
158	C₂×C₁₉	—	2	1	no	—
159	C₂×C₁₉	#1870	1	1	yes	characteristic
160	C₂×C₁₉	#1884	1	1	yes	characteristic
161	C₂×C₁₉	#1886	1	1	yes	characteristic
162	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
163	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
164	C₄⋊Q₈	—	2	2	no	—
165	C₄⋊Q₈	—	2	2	no	—
166	C₄×Q₈	—	2	2	no	—
167	C₄×Q₈	—	2	2	no	—
168	C₄×Q₈	—	2	2	no	—
169	C₄×Q₈	—	2	2	no	—
170	C₂×C₄⋊C₄	—	2	2	no	—
171	C₂×C₄⋊C₄	—	2	2	no	—
172	C₂×C₄⋊C₄	—	2	1	no	—
173	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
174	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
175	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
176	C₂×C₄²	—	2	1	no	—
177	C₂×C₄²	—	2	1	no	—
178	C₂×C₄²	—	2	1	no	—
179	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
180	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
181	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
182	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
183	C₄⋊C₈	—	19	4	no	—
184	C₄⋊C₈	—	38	4	no	—
185	C₄⋊C₈	—	38	2	no	—
186	C₂²⋊C₈	—	38	2	no	—
187	C₂²⋊C₈	—	38	2	no	—
188	#97	—	38	4	no	—
189	C₄×C₈	—	38	2	no	—
190	C₄×C₈	—	38	2	no	—
191	#95	—	2	2	no	—
192	#95	—	2	2	no	—
193	C₁₉	#8962	1	1	yes	characteristic, complemented, Sylow
194	C₂×Q₈	—	2	2	no	—
195	C₂×Q₈	—	2	2	no	—
196	C₂×Q₈	—	2	1	no	—
197	C₂×Q₈	—	2	1	no	—
198	C₂×Q₈	—	2	1	no	—
199	C₂×Q₈	—	2	2	no	—
200	C₂×Q₈	—	2	2	no	—
201	C₂×Q₈	#64520	1	2	yes	—
202	C₂²×C₄	—	2	1	no	—
203	C₂²×C₄	—	2	1	no	—
204	C₂²×C₄	—	2	1	no	—
205	C₂²×C₄	—	2	1	no	—
206	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
207	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
208	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
209	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
210	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
211	C₂×C₈	—	38	4	no	—
212	C₂×C₈	—	76	2	no	—
213	C₄⋊C₄	—	2	8	no	—
214	C₄⋊C₄	—	2	2	no	—
215	C₄⋊C₄	—	2	4	no	—
216	C₄⋊C₄	—	2	2	no	—
217	C₄⋊C₄	—	4	4	no	—
218	C₄⋊C₄	—	4	2	no	—
219	C₄²	—	2	4	no	—
220	C₄²	—	2	2	no	—
221	C₄²	—	2	2	no	—
222	C₄²	—	2	1	no	—
223	C₄²	—	2	2	no	—
224	C₄²	—	4	2	no	—
225	C₄²	—	4	1	no	—
226	C₄²	—	4	1	no	—
227	C₄²	#64520	1	2	yes	—
228	C₄²	D₄×D₁₉	1	2	yes	—
229	C₄²	#64543	1	2	yes	—
230	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
231	Q₈	—	2	4	no	—
232	Q₈	—	4	2	no	—
233	Q₈	—	4	2	no	—
234	Q₈	—	4	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	4	1	no	—
246	C₂×C₄	—	4	1	no	—
247	C₂×C₄	—	4	1	no	—
248	C₂×C₄	—	4	1	no	—
249	C₂×C₄	—	4	1	no	—
250	C₂×C₄	—	4	2	no	—
251	C₂×C₄	—	4	2	no	—
252	C₂×C₄	—	4	1	no	—
253	C₂×C₄	C₂×#64520	1	1	yes	characteristic
254	C₂×C₄	C₂×#64520	1	1	yes	characteristic
255	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
256	C₂×C₄	#10597381	1	1	yes	characteristic
257	C₂×C₄	#10597383	1	1	yes	characteristic
258	C₂×C₄	#10597385	1	2	yes	—
259	C₂×C₄	#10597394	1	2	yes	—
260	C₈	—	76	4	no	—
261	C₈	—	152	2	no	—
262	C₂²	—	2	1	no	—
263	C₂²	—	2	1	no	—
264	C₂²	#11926424	1	1	yes	characteristic
265	C₂²	#11926508	1	1	yes	characteristic
266	C₂²	#11926511	1	1	yes	characteristic
267	C₄	—	2	4	no	—
268	C₄	—	2	2	no	—
269	C₄	—	2	1	no	—
270	C₄	—	4	2	no	—
271	C₄	—	4	2	no	—
272	C₄	—	4	2	no	—
273	C₄	—	4	2	no	—
274	C₄	—	8	1	no	—
275	C₄	#11926616	1	2	yes	—
276	C₄	#11926622	1	2	yes	—
277	C₄	#11926726	1	2	yes	—
278	C₂	—	2	1	no	—
279	C₂	—	2	1	no	—
280	C₂	#14563933	1	1	yes	characteristic
281	C₂	#14564019	1	1	yes	characteristic
282	C₂	#14564029	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572720

C₂

yes

maximal, characteristic

#14562030

C₂

yes

maximal

#14561959

C₂

yes

maximal, characteristic

#14561468

C₂

yes

maximal

C₄×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

#11926675

—

#11926601

—

#11926597

C₂²

yes

—

#11926597

C₂²

yes

—

Q₈⋊(C₁₉⋊C₈)

—

#11926270

—

C₂×C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#391

C₄

yes

characteristic

C₁₉×#391

C₄

yes

characteristic

C₁₉×#389

—

C₁₉×#384

C₄

yes

characteristic

C₄×C₄⋊C₄×C₁₉

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8962

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×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

—

111

C₂×C₄×C₁₉

—

112

C₂×C₄×C₁₉

C₄×D₄

yes

—

113

C₂×C₄×C₁₉

#120

yes

characteristic

114

C₂×C₄×C₁₉

#121

yes

—

115

C₂×C₄×C₁₉

#123

yes

characteristic

116

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

117

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

118

C₂×C₄×C₁₉

#131

yes

—

119

C₁₉⋊C₈

—

120

C₁₉⋊C₈

—

121

#2983

—

122

C₄×C₄⋊Q₈

D₁₉

yes

characteristic

123

#1479

—

124

#1461

—

125

#1276

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

#386

yes

characteristic

129

C₂²×C₁₉

#407

yes

characteristic

130

C₂²×C₁₉

#408

yes

characteristic

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

#435

yes

—

140

C₄×C₁₉

#436

yes

—

141

C₄×C₁₉

#456

yes

—

142

C₂×C₄⋊Q₈

Dic₁₉

yes

characteristic

143

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

144

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

145

#446

—

146

#432

—

147

#431

—

148

#431

—

149

#391

Dic₁₉

yes

characteristic

150

#391

Dic₁₉

yes

characteristic

151

#389

—

152

#384

Dic₁₉

yes

characteristic

153

C₄×C₄⋊C₄

—

154

C₄³

C₂×D₁₉

yes

characteristic

155

Q₈⋊C₈

—

156

#324

—

157

C₂×C₁₉

—

158

C₂×C₁₉

—

159

C₂×C₁₉

#1870

yes

characteristic

160

C₂×C₁₉

#1884

yes

characteristic

161

C₂×C₁₉

#1886

yes

characteristic

162

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

163

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

164

C₄⋊Q₈

—

165

C₄⋊Q₈

—

166

C₄×Q₈

—

167

C₄×Q₈

—

168

C₄×Q₈

—

169

C₄×Q₈

—

170

C₂×C₄⋊C₄

—

171

C₂×C₄⋊C₄

—

172

C₂×C₄⋊C₄

—

173

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

174

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

175

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

176

C₂×C₄²

—

177

C₂×C₄²

—

178

C₂×C₄²

—

179

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

180

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

181

C₂×C₄²

C₂²⋊D₁₉

yes

—

182

C₂×C₄²

C₂²×D₁₉

yes

characteristic

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

—

186

C₂²⋊C₈

—

187

C₂²⋊C₈

—

188

#97

—

189

C₄×C₈

—

190

C₄×C₈

—

191

#95

—

192

#95

—

193

C₁₉

#8962

yes

characteristic, complemented, Sylow

194

C₂×Q₈

—

195

C₂×Q₈

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×Q₈

—

199

C₂×Q₈

—

200

C₂×Q₈

—

201

C₂×Q₈

#64520

yes

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

—

205

C₂²×C₄

—

206

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

207

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

208

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

209

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

210

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

211

C₂×C₈

—

212

C₂×C₈

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄²

—

220

C₄²

—

221

C₄²

—

222

C₄²

—

223

C₄²

—

224

C₄²

—

225

C₄²

—

226

C₄²

—

227

C₄²

#64520

yes

—

228

C₄²

D₄×D₁₉

yes

—

229

C₄²

#64543

yes

—

230

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

231

Q₈

—

232

Q₈

—

233

Q₈

—

234

Q₈

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

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

C₂×#64520

yes

characteristic

254

C₂×C₄

C₂×#64520

yes

characteristic

255

C₂×C₄

D₄×Dic₁₉

yes

—

256

C₂×C₄

#10597381

yes

characteristic

257

C₂×C₄

#10597383

yes

characteristic

258

C₂×C₄

#10597385

yes

—

259

C₂×C₄

#10597394

yes

—

260

C₈

—

261

C₈

—

152

—

262

C₂²

—

263

C₂²

—

264

C₂²

#11926424

yes

characteristic

265

C₂²

#11926508

yes

characteristic

266

C₂²

#11926511

yes

characteristic

267

C₄

—

268

C₄

—

269

C₄

—

270

C₄

—

271

C₄

—

272

C₄

—

273

C₄

—

274

C₄

—

275

C₄

#11926616

yes

—

276

C₄

#11926622

yes

—

277

C₄

#11926726

yes

—

278

C₂

—

279

C₂

—

280

C₂

#14563933

yes

characteristic

281

C₂

#14564019

yes

characteristic

282

C₂

#14564029

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×C₄⋊Q₈	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#8962
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×C₄⋊Q₈

subgroup

G/H

center

C₂×C₄

#10597383

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×C₄⋊Q₈

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₄×C₄⋊Q₈

D₁₉

hypocenter

C₁₉

#8962

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×C₄⋊Q₈

N	H ≅ G/N	type
193. C₁₉	#8962	semidirect

H ≅ G/N

type

193. C₁₉

#8962

semidirect

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

subgroup	index
#14572720	2
#14562030	2
#14561959	2
#14561468	2
C₄×C₁₉×C₄⋊Q₈	2
#8962	19

subgroup

index

C₄×C₁₉×C₄⋊Q₈

Subgroups — #18077210

Conjugacy classes of subgroups

Complements

Maximal subgroups