Group #18081971 — subgroups

Subgroups — #18081971

Order 4864.

414 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 129 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	C₂×#11926940	C₂	1	1	yes	maximal, characteristic
2	#14563806	C₂	1	1	yes	maximal, characteristic
3	#14562320	C₂	1	1	yes	maximal, characteristic
4	#14562319	C₂	1	1	yes	maximal, characteristic
5	#14562317	C₂	1	1	yes	maximal, characteristic
6	#14561919	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1548	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	#11926940	—	2	1	no	—
10	#11926940	—	2	1	no	—
11	#11926940	C₄	1	4	yes	—
12	#11926597	C₂²	1	1	yes	characteristic
13	C₂×#10597279	—	2	2	no	—
14	C₂×#10597265	—	2	2	no	—
15	#11926568	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	#11926292	—	2	2	no	—
18	#11926291	—	2	2	no	—
19	#11926290	—	2	2	no	—
20	#11926266	—	2	1	no	—
21	C₈×C₁₉⋊C₈	—	2	1	no	—
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₉×#431	C₂²	1	1	yes	characteristic
24	C₁₉×#423	C₂²	1	1	yes	characteristic
25	C₁₉×#333	—	2	2	no	—
26	C₂²×Q₈×C₁₉	—	2	1	no	—
27	C₂²×Dic₃₈	—	2	1	no	—
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₁₉×C₄⋊Q₈	—	2	1	no	—
30	C₁₉×C₄⋊Q₈	—	2	1	no	—
31	C₁₉×C₄⋊Q₈	—	2	1	no	—
32	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×C₄⋊Dic₁₉	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	—	2	1	no	—
38	C₂×#64520	—	2	1	no	—
39	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
40	#10597315	—	2	1	no	—
41	#10597315	—	2	1	no	—
42	#10597315	—	2	1	no	—
43	#10597315	C₂×C₄	1	2	yes	—
44	C₁₉×C₄⋊C₈	—	2	1	no	—
45	C₁₉×C₄⋊C₈	—	2	1	no	—
46	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
47	C₁₉×C₂²⋊C₈	—	2	1	no	—
48	C₄×C₈×C₁₉	—	2	1	no	—
49	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
50	#10597279	—	4	4	no	—
51	#10597265	—	2	4	no	—
52	#10597265	—	2	4	no	—
53	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
54	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
55	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
56	C₄×C₁₉⋊C₈	—	2	1	no	—
57	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
58	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
59	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
60	C₂×Q₈×C₁₉	—	2	2	no	—
61	C₂×Q₈×C₁₉	—	4	1	no	—
62	C₂×Q₈×C₁₉	—	8	2	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
67	C₂²×Dic₁₉	—	4	1	no	—
68	C₂×Dic₃₈	—	2	2	no	—
69	C₂×Dic₃₈	—	4	1	no	—
70	C₂×Dic₃₈	—	8	2	no	—
71	M₁₆×C₁₉	—	4	2	no	—
72	C₂×C₈×C₁₉	—	2	2	no	—
73	C₂×C₈×C₁₉	—	4	1	no	—
74	C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₄⋊C₄×C₁₉	—	4	1	no	—
77	C₄⋊C₄×C₁₉	—	4	1	no	—
78	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₄⋊Dic₁₉	—	2	2	no	—
83	C₄⋊Dic₁₉	—	2	2	no	—
84	C₄⋊Dic₁₉	—	4	1	no	—
85	C₄⋊Dic₁₉	—	4	1	no	—
86	#64520	—	4	2	no	—
87	C₂×C₁₉⋊C₈	—	2	2	no	—
88	C₂×C₁₉⋊C₈	—	4	1	no	—
89	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
90	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
91	C₂×C₁₉⋊C₈	SD₁₆	1	4	yes	—
92	C₂×C₁₉⋊C₈	Q₁₆	1	4	yes	—
93	#9767	—	19	1	no	maximal, Sylow
94	C₂³×C₁₉	#124	1	1	yes	characteristic
95	Q₈×C₁₉	—	8	2	no	—
96	Q₈×C₁₉	—	8	2	no	—
97	C₂×C₄×C₁₉	—	2	2	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	—	8	2	no	—
101	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
105	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
107	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
108	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
109	C₂×Dic₁₉	—	4	2	no	—
110	C₂×Dic₁₉	—	8	2	no	—
111	Dic₃₈	—	8	2	no	—
112	Dic₃₈	—	8	2	no	—
113	C₈×C₁₉	—	4	2	no	—
114	C₈×C₁₉	—	8	1	no	—
115	C₁₉⋊C₈	—	4	2	no	—
116	C₁₉⋊C₈	—	8	1	no	—
117	C₁₉⋊C₈	#103	1	4	yes	—
118	C₁₉⋊C₈	#103	1	4	yes	—
119	C₂×#498	—	19	1	no	—
120	#1848	—	19	1	no	—
121	#1549	—	19	1	no	—
122	#1549	—	19	1	no	—
123	#1548	—	19	1	no	—
124	#1548	D₁₉	1	1	yes	characteristic
125	#1450	—	19	1	no	—
126	C₂²×C₁₉	—	2	1	no	—
127	C₂²×C₁₉	—	2	1	no	—
128	C₂²×C₁₉	#390	1	1	yes	characteristic
129	C₂²×C₁₉	#487	1	2	yes	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	8	2	no	—
133	C₄×C₁₉	C₂×#103	1	2	yes	—
134	C₄×C₁₉	#471	1	2	yes	—
135	C₄×C₁₉	#471	1	2	yes	—
136	C₄×C₁₉	#492	1	1	yes	characteristic
137	C₄×C₁₉	#494	1	1	yes	characteristic
138	Dic₁₉	—	8	2	no	—
139	C₂×C₄⋊Q₈	—	19	1	no	—
140	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
141	#498	—	19	4	no	—
142	#498	—	38	1	no	—
143	#498	—	38	1	no	—
144	#431	—	19	1	no	—
145	#431	C₂×D₁₉	1	1	yes	characteristic
146	C₂×#108	—	38	2	no	—
147	C₂×#106	—	38	2	no	—
148	#423	—	19	1	no	—
149	#423	C₂×D₁₉	1	1	yes	characteristic
150	C₂×C₄×C₈	—	19	1	no	—
151	#333	—	2	2	no	—
152	#333	—	38	2	no	—
153	#332	—	38	2	no	—
154	#332	—	38	2	no	—
155	#322	—	38	1	no	—
156	C₈²	—	38	1	no	—
157	C₂×C₁₉	—	2	2	no	—
158	C₂×C₁₉	#1956	1	1	yes	characteristic
159	C₂×C₁₉	#1977	1	1	yes	characteristic
160	C₂×C₁₉	#1977	1	1	yes	characteristic
161	C₂²×Q₈	—	2	1	no	—
162	C₂²×Q₈	—	38	1	no	—
163	C₂×M₁₆	—	2	1	no	—
164	C₂×M₁₆	—	38	1	no	—
165	C₂²×C₈	—	19	2	no	—
166	C₄⋊Q₈	—	2	1	no	—
167	C₄⋊Q₈	—	2	1	no	—
168	C₄⋊Q₈	—	2	1	no	—
169	C₄⋊Q₈	—	19	2	no	—
170	C₄⋊Q₈	—	38	1	no	—
171	C₄⋊Q₈	—	38	1	no	—
172	C₄⋊Q₈	—	38	1	no	—
173	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
174	C₂×C₄⋊C₄	—	2	1	no	—
175	C₂×C₄⋊C₄	—	2	1	no	—
176	C₂×C₄⋊C₄	—	38	1	no	—
177	C₂×C₄⋊C₄	—	38	1	no	—
178	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
179	#108	—	76	4	no	—
180	#106	—	38	4	no	—
181	#106	—	38	4	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	C₂²⋊D₁₉	1	2	yes	—
188	C₂²⋊C₈	—	2	1	no	—
189	C₂²⋊C₈	—	38	1	no	—
190	C₄×C₈	—	2	1	no	—
191	C₄×C₈	—	19	2	no	—
192	C₄×C₈	—	19	1	no	—
193	C₄×C₈	—	19	1	no	—
194	C₄×C₈	—	38	1	no	—
195	C₁₉	#9767	1	1	yes	characteristic, complemented, Sylow
196	C₂×Q₈	—	2	2	no	—
197	C₂×Q₈	—	4	1	no	—
198	C₂×Q₈	—	8	2	no	—
199	C₂×Q₈	—	38	2	no	—
200	C₂×Q₈	—	76	1	no	—
201	C₂×Q₈	—	152	2	no	—
202	C₂²×C₄	—	4	1	no	—
203	C₂²×C₄	—	76	1	no	—
204	C₂²×C₄	#64541	1	1	yes	characteristic
205	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
206	C₂²×C₄	#64543	1	1	yes	characteristic
207	M₁₆	—	4	2	no	—
208	M₁₆	—	76	2	no	—
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	—	4	1	no	—
211	C₂×C₈	—	19	2	no	—
212	C₂×C₈	—	19	2	no	—
213	C₂×C₈	—	19	4	no	—
214	C₂×C₈	—	19	4	no	—
215	C₂×C₈	—	38	2	no	—
216	C₂×C₈	—	76	1	no	—
217	C₄⋊C₄	—	2	2	no	—
218	C₄⋊C₄	—	2	2	no	—
219	C₄⋊C₄	—	4	1	no	—
220	C₄⋊C₄	—	4	1	no	—
221	C₄⋊C₄	—	38	2	no	—
222	C₄⋊C₄	—	38	2	no	—
223	C₄⋊C₄	—	76	1	no	—
224	C₄⋊C₄	—	76	1	no	—
225	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
226	C₄²	D₄×D₁₉	1	1	yes	characteristic
227	C₄²	D₄×D₁₉	1	1	yes	characteristic
228	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
229	C₂³	#10597331	1	1	yes	characteristic
230	Q₈	—	8	2	no	—
231	Q₈	—	8	2	no	—
232	Q₈	—	152	2	no	—
233	Q₈	—	152	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	8	2	no	—
238	C₂×C₄	—	76	2	no	—
239	C₂×C₄	—	152	2	no	—
240	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
241	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
242	C₂×C₄	#10597330	1	1	yes	characteristic
243	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
244	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
245	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
246	C₂×C₄	#10597385	1	1	yes	characteristic
247	C₂×C₄	#10597386	1	1	yes	characteristic
248	C₈	—	4	2	no	—
249	C₈	—	8	1	no	—
250	C₈	—	19	4	no	—
251	C₈	—	19	4	no	—
252	C₈	—	76	2	no	—
253	C₈	—	152	1	no	—
254	C₂²	—	2	1	no	—
255	C₂²	—	2	1	no	—
256	C₂²	#11926444	1	1	yes	characteristic
257	C₂²	#11926893	1	2	yes	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	8	2	no	—
261	C₄	—	152	2	no	—
262	C₄	#103×D₁₉	1	2	yes	—
263	C₄	#11926806	1	2	yes	—
264	C₄	#11926809	1	2	yes	—
265	C₄	#11926915	1	1	yes	characteristic
266	C₄	#11926922	1	1	yes	characteristic
267	C₂	—	2	2	no	—
268	C₂	#14564435	1	1	yes	characteristic
269	C₂	#14564535	1	1	yes	characteristic
270	C₂	#14564537	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926940

C₂

yes

maximal, characteristic

#14563806

C₂

yes

maximal, characteristic

#14562320

C₂

yes

maximal, characteristic

#14562319

C₂

yes

maximal, characteristic

#14562317

C₂

yes

maximal, characteristic

#14561919

C₂

yes

maximal, characteristic

C₁₉×#1548

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

—

—

C₄

yes

—

#11926597

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

—

C₈×C₁₉⋊C₈

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#333

—

C₂²×Q₈×C₁₉

—

C₂²×Dic₃₈

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

D₄

yes

—

—

—

—

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

#10597279

—

#10597265

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

SD₁₆

yes

—

C₂×C₁₉⋊C₈

Q₁₆

yes

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

102

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

103

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

104

C₂×C₄×C₁₉

#121

yes

characteristic

105

C₂×C₄×C₁₉

#121

yes

characteristic

106

C₂×C₄×C₁₉

#127

yes

characteristic

107

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

108

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

109

C₂×Dic₁₉

—

110

C₂×Dic₁₉

—

111

Dic₃₈

—

112

Dic₃₈

—

113

C₈×C₁₉

—

114

C₈×C₁₉

—

115

C₁₉⋊C₈

—

116

C₁₉⋊C₈

—

117

C₁₉⋊C₈

#103

yes

—

118

C₁₉⋊C₈

#103

yes

—

119

C₂×#498

—

120

#1848

—

121

#1549

—

122

#1549

—

123

#1548

—

124

#1548

D₁₉

yes

characteristic

125

#1450

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

#390

yes

characteristic

129

C₂²×C₁₉

#487

yes

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

C₂×#103

yes

—

134

C₄×C₁₉

#471

yes

—

135

C₄×C₁₉

#471

yes

—

136

C₄×C₁₉

#492

yes

characteristic

137

C₄×C₁₉

#494

yes

characteristic

138

Dic₁₉

—

139

C₂×C₄⋊Q₈

—

140

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

141

#498

—

142

#498

—

143

#498

—

144

#431

—

145

#431

C₂×D₁₉

yes

characteristic

146

C₂×#108

—

147

C₂×#106

—

148

#423

—

149

#423

C₂×D₁₉

yes

characteristic

150

C₂×C₄×C₈

—

151

#333

—

152

#333

—

153

#332

—

154

#332

—

155

#322

—

156

C₈²

—

157

C₂×C₁₉

—

158

C₂×C₁₉

#1956

yes

characteristic

159

C₂×C₁₉

#1977

yes

characteristic

160

C₂×C₁₉

#1977

yes

characteristic

161

C₂²×Q₈

—

162

C₂²×Q₈

—

163

C₂×M₁₆

—

164

C₂×M₁₆

—

165

C₂²×C₈

—

166

C₄⋊Q₈

—

167

C₄⋊Q₈

—

168

C₄⋊Q₈

—

169

C₄⋊Q₈

—

170

C₄⋊Q₈

—

171

C₄⋊Q₈

—

172

C₄⋊Q₈

—

173

C₄⋊Q₈

C₄×D₁₉

yes

—

174

C₂×C₄⋊C₄

—

175

C₂×C₄⋊C₄

—

176

C₂×C₄⋊C₄

—

177

C₂×C₄⋊C₄

—

178

C₂×C₄²

C₂²×D₁₉

yes

characteristic

179

#108

—

180

#106

—

181

#106

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

—

186

C₄⋊C₈

—

187

C₄⋊C₈

C₂²⋊D₁₉

yes

—

188

C₂²⋊C₈

—

189

C₂²⋊C₈

—

190

C₄×C₈

—

191

C₄×C₈

—

192

C₄×C₈

—

193

C₄×C₈

—

194

C₄×C₈

—

195

C₁₉

#9767

yes

characteristic, complemented, Sylow

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×Q₈

—

199

C₂×Q₈

—

200

C₂×Q₈

—

201

C₂×Q₈

—

152

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

#64541

yes

characteristic

205

C₂²×C₄

D₄×D₁₉

yes

characteristic

206

C₂²×C₄

#64543

yes

characteristic

207

M₁₆

—

208

M₁₆

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₄²

C₂×C₄×D₁₉

yes

characteristic

226

C₄²

D₄×D₁₉

yes

characteristic

227

C₄²

D₄×D₁₉

yes

characteristic

228

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

229

C₂³

#10597331

yes

characteristic

230

Q₈

—

231

Q₈

—

232

Q₈

—

152

—

233

Q₈

—

152

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

152

—

240

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

241

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

242

C₂×C₄

#10597330

yes

characteristic

243

C₂×C₄

SD₁₆×D₁₉

yes

—

244

C₂×C₄

Q₁₆×D₁₉

yes

—

245

C₂×C₄

C₄×C₂²⋊D₁₉

yes

characteristic

246

C₂×C₄

#10597385

yes

characteristic

247

C₂×C₄

#10597386

yes

characteristic

248

C₈

—

249

C₈

—

250

C₈

—

251

C₈

—

252

C₈

—

253

C₈

—

152

—

254

C₂²

—

255

C₂²

—

256

C₂²

#11926444

yes

characteristic

257

C₂²

#11926893

yes

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

152

—

262

C₄

#103×D₁₉

yes

—

263

C₄

#11926806

yes

—

264

C₄

#11926809

yes

—

265

C₄

#11926915

yes

characteristic

266

C₄

#11926922

yes

characteristic

267

C₂

—

268

C₂

#14564435

yes

characteristic

269

C₂

#14564535

yes

characteristic

270

C₂

#14564537

yes

characteristic

	subgroup	G/H
center	C₂²	#11926444
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1548	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#124
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1548	D₁₉
hypocenter	C₁₉	#9767
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

subgroup

G/H

center

C₂²

#11926444

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1548

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

N	H ≅ G/N	type
195. C₁₉	#9767	semidirect

H ≅ G/N

type

195. C₁₉

#9767

semidirect

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

subgroup	index
C₂×#11926940	2
#14563806	2
#14562320	2
#14562319	2
#14562317	2
#14561919	2
C₁₉×#1548	2
#9767	19

subgroup

index

C₁₉×#1548

Subgroups — #18081971

Conjugacy classes of subgroups

Complements

Maximal subgroups