Group #18074035 — subgroups

Subgroups — #18074035

Order 4864.

1030 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 227 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	#14563615	C₂	1	2	yes	maximal
2	C₂×#11926293	C₂	1	4	yes	maximal, complemented
3	C₂²×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
5	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
6	#11926299	—	2	2	no	—
7	#11926293	—	2	8	no	—
8	C₂³×Q₈×C₁₉	C₄	1	2	yes	—
9	C₂×C₁₉×C₄⋊Q₈	—	2	8	no	—
10	C₂×C₁₉×C₄⋊Q₈	—	2	2	no	—
11	C₂×C₁₉×C₄⋊Q₈	C₄	1	2	yes	—
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₉	—	2	2	no	—
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×Q₈×C₁₉	—	2	8	no	—
16	C₂²×Q₈×C₁₉	—	2	2	no	—
17	C₂²×Q₈×C₁₉	—	4	4	no	—
18	C₂²×Q₈×C₁₉	—	4	4	no	—
19	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
20	C₂³×C₄×C₁₉	—	2	2	no	—
21	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	D₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	—	2	16	no	—
24	C₁₉×C₄⋊Q₈	—	2	8	no	—
25	C₁₉×C₄⋊Q₈	—	2	4	no	—
26	C₁₉×C₄⋊Q₈	D₄	1	8	yes	—
27	C₂×C₄⋊C₄×C₁₉	—	2	16	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
30	C₂×C₄²×C₁₉	—	2	4	no	—
31	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	D₄	1	2	yes	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²×C₁₉⋊C₈	—	2	4	no	—
35	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
37	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×Q₈×C₁₉	—	2	8	no	—
39	C₂×Q₈×C₁₉	—	2	4	no	—
40	C₂×Q₈×C₁₉	—	4	32	no	—
41	C₂×Q₈×C₁₉	—	4	4	no	—
42	C₂×Q₈×C₁₉	—	4	4	no	—
43	C₂×Q₈×C₁₉	—	4	4	no	—
44	C₂×Q₈×C₁₉	—	4	4	no	—
45	C₂×Q₈×C₁₉	C₂²⋊C₄	1	8	yes	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	—	2	4	no	—
50	C₂²×C₄×C₁₉	—	2	4	no	—
51	C₂²×C₄×C₁₉	—	2	8	no	—
52	C₂²×C₄×C₁₉	—	2	4	no	—
53	C₂²×C₄×C₁₉	—	4	4	no	—
54	C₂²×C₄×C₁₉	—	4	4	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	—
58	C₂²×C₄×C₁₉	Q₁₆	1	4	yes	—
59	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
61	C₄⋊C₄×C₁₉	—	2	16	no	—
62	C₄⋊C₄×C₁₉	—	2	16	no	—
63	C₄²×C₁₉	—	2	2	no	—
64	C₄²×C₁₉	—	2	4	no	—
65	C₄²×C₁₉	C₂×D₄	1	4	yes	—
66	C₂×C₁₉⋊C₈	—	4	4	no	—
67	C₂×C₁₉⋊C₈	—	4	4	no	—
68	C₂×C₁₉⋊C₈	—	4	4	no	—
69	#8342	—	19	1	no	maximal, Sylow
70	C₂³×C₁₉	—	2	1	no	—
71	C₂³×C₁₉	—	2	1	no	—
72	C₂³×C₁₉	—	2	2	no	—
73	C₂³×C₁₉	#100	1	2	yes	—
74	C₂³×C₁₉	#103	1	4	yes	—
75	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	Q₈×C₁₉	—	4	8	no	—
77	Q₈×C₁₉	—	4	16	no	—
78	Q₈×C₁₉	—	4	8	no	—
79	C₂×C₄×C₁₉	—	2	8	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	8	no	—
87	C₂×C₄×C₁₉	—	2	8	no	—
88	C₂×C₄×C₁₉	—	2	8	no	—
89	C₂×C₄×C₁₉	—	4	16	no	—
90	C₂×C₄×C₁₉	—	4	4	no	—
91	C₂×C₄×C₁₉	—	4	4	no	—
92	C₂×C₄×C₁₉	#100	1	2	yes	—
93	C₂×C₄×C₁₉	#103	1	4	yes	—
94	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
95	C₂×C₄×C₁₉	#120	1	4	yes	—
96	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
97	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
98	C₂×C₄×C₁₉	#137	1	4	yes	—
99	C₁₉⋊C₈	—	8	4	no	—
100	C₂²×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
101	#1797	—	19	2	no	—
102	C₂×#333	—	19	4	no	—
103	C₂²×C₁₉	—	2	4	no	—
104	C₂²×C₁₉	—	2	2	no	—
105	C₂²×C₁₉	—	2	2	no	—
106	C₂²×C₁₉	—	2	4	no	—
107	C₂²×C₁₉	#333	1	4	yes	complemented
108	C₂²×C₁₉	#379	1	1	yes	characteristic
109	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
110	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
111	C₂²×C₁₉	C₂×#103	1	2	yes	—
112	C₂²×C₁₉	#419	1	2	yes	—
113	C₄×C₁₉	—	2	2	no	—
114	C₄×C₁₉	—	2	2	no	—
115	C₄×C₁₉	—	2	4	no	—
116	C₄×C₁₉	—	4	8	no	—
117	C₄×C₁₉	#448	1	4	yes	—
118	C₄×C₁₉	#451	1	4	yes	—
119	C₂³×Q₈	Dic₁₉	1	2	yes	—
120	C₂×C₄⋊Q₈	—	2	8	no	—
121	C₂×C₄⋊Q₈	—	2	2	no	—
122	C₂×C₄⋊Q₈	Dic₁₉	1	2	yes	—
123	C₂×C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
124	C₂²×C₄⋊C₄	—	2	2	no	—
125	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
126	C₂×C₄⋊C₈	—	19	4	no	—
127	C₂×C₂²⋊C₈	—	38	2	no	—
128	#336	—	38	2	no	—
129	#333	—	38	8	no	—
130	C₂×C₁₉	—	2	4	no	—
131	C₂×C₁₉	C₂×#333	1	1	yes	characteristic
132	C₂×C₁₉	#1548	1	2	yes	—
133	C₂×C₁₉	#1558	1	1	yes	characteristic
134	C₂×C₁₉	#1783	1	1	yes	characteristic
135	C₂×C₁₉	#1787	1	2	yes	—
136	C₂²×Q₈	—	2	8	no	—
137	C₂²×Q₈	—	2	2	no	—
138	C₂²×Q₈	—	4	4	no	—
139	C₂²×Q₈	—	4	4	no	—
140	C₂²×Q₈	C₂×Dic₁₉	1	4	yes	—
141	C₂³×C₄	—	2	2	no	—
142	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
143	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
144	C₂²×C₈	—	38	4	no	—
145	C₄⋊Q₈	—	2	16	no	—
146	C₄⋊Q₈	—	2	8	no	—
147	C₄⋊Q₈	—	2	4	no	—
148	C₄⋊Q₈	C₂²⋊D₁₉	1	8	yes	—
149	C₂×C₄⋊C₄	—	2	16	no	—
150	C₂×C₄⋊C₄	—	2	4	no	—
151	C₂×C₄⋊C₄	—	2	4	no	—
152	C₂×C₄²	—	2	4	no	—
153	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
154	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
155	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
156	C₄⋊C₈	—	38	8	no	—
157	C₂²⋊C₈	—	76	4	no	—
158	C₁₉	#8342	1	1	yes	characteristic, complemented, Sylow
159	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
160	C₂×Q₈	—	2	8	no	—
161	C₂×Q₈	—	2	4	no	—
162	C₂×Q₈	—	4	32	no	—
163	C₂×Q₈	—	4	4	no	—
164	C₂×Q₈	—	4	4	no	—
165	C₂×Q₈	—	4	4	no	—
166	C₂×Q₈	—	4	4	no	—
167	C₂×Q₈	C₂²⋊Dic₁₉	1	8	yes	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	4	no	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	2	4	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	8	no	—
174	C₂²×C₄	—	2	4	no	—
175	C₂²×C₄	—	4	4	no	—
176	C₂²×C₄	—	4	4	no	—
177	C₂²×C₄	#64527	1	4	yes	—
178	C₂²×C₄	#64528	1	4	yes	—
179	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
180	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
181	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
182	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
183	C₂×C₈	—	76	4	no	—
184	C₂×C₈	—	76	4	no	—
185	C₂×C₈	—	76	4	no	—
186	C₄⋊C₄	—	2	16	no	—
187	C₄⋊C₄	—	2	16	no	—
188	C₄²	—	2	2	no	—
189	C₄²	—	2	4	no	—
190	C₄²	C₂×C₂²⋊D₁₉	1	4	yes	—
191	C₂³	—	2	2	no	—
192	C₂³	—	2	1	no	—
193	C₂³	—	2	1	no	—
194	C₂³	#10597290	1	2	yes	—
195	C₂³	#10597292	1	4	yes	—
196	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
197	Q₈	—	4	8	no	—
198	Q₈	—	4	8	no	—
199	Q₈	—	4	16	no	—
200	C₂×C₄	—	2	8	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	8	no	—
208	C₂×C₄	—	2	8	no	—
209	C₂×C₄	—	2	8	no	—
210	C₂×C₄	—	4	16	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	4	no	—
213	C₂×C₄	#10597290	1	2	yes	—
214	C₂×C₄	#10597292	1	4	yes	—
215	C₂×C₄	C₂×#64527	1	2	yes	—
216	C₂×C₄	#10597388	1	4	yes	—
217	C₂×C₄	C₂×#64528	1	2	yes	—
218	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	2	yes	—
219	C₂×C₄	#10597399	1	4	yes	—
220	C₈	—	152	4	no	—
221	C₂²	—	2	4	no	—
222	C₂²	—	2	2	no	—
223	C₂²	—	2	2	no	—
224	C₂²	—	2	4	no	—
225	C₂²	#11926293	1	4	yes	complemented
226	C₂²	#11926400	1	1	yes	characteristic
227	C₂²	C₂×#10597290	1	1	yes	characteristic
228	C₂²	C₂×#10597290	1	1	yes	characteristic
229	C₂²	C₂×#10597292	1	2	yes	—
230	C₂²	#11926553	1	2	yes	—
231	C₄	—	2	2	no	—
232	C₄	—	2	2	no	—
233	C₄	—	2	4	no	—
234	C₄	—	4	8	no	—
235	C₄	#11926683	1	4	yes	—
236	C₄	#11926700	1	4	yes	—
237	C₂	—	2	4	no	—
238	C₂	C₂×#11926293	1	1	yes	characteristic
239	C₂	#14562316	1	2	yes	—
240	C₂	#14562361	1	1	yes	characteristic
241	C₂	#14563556	1	1	yes	characteristic
242	C₂	#14563570	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563615

C₂

yes

maximal

C₂×#11926293

C₂

yes

maximal, complemented

C₂²×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926299

—

#11926293

—

C₂³×Q₈×C₁₉

C₄

yes

—

C₂×C₁₉×C₄⋊Q₈

—

C₂×C₁₉×C₄⋊Q₈

—

C₂×C₁₉×C₄⋊Q₈

C₄

yes

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

—

C₂²×C₄⋊C₄×C₁₉

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8342

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#100

yes

—

C₂³×C₁₉

#103

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#100

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₁₉⋊C₈

—

100

C₂²×C₄⋊Q₈

D₁₉

yes

characteristic

101

#1797

—

102

C₂×#333

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

#333

yes

complemented

108

C₂²×C₁₉

#379

yes

characteristic

109

C₂²×C₁₉

C₂×#100

yes

characteristic

110

C₂²×C₁₉

C₂×#100

yes

characteristic

111

C₂²×C₁₉

C₂×#103

yes

—

112

C₂²×C₁₉

#419

yes

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

#448

yes

—

118

C₄×C₁₉

#451

yes

—

119

C₂³×Q₈

Dic₁₉

yes

—

120

C₂×C₄⋊Q₈

—

121

C₂×C₄⋊Q₈

—

122

C₂×C₄⋊Q₈

Dic₁₉

yes

—

123

C₂×C₄⋊Q₈

C₂×D₁₉

yes

—

124

C₂²×C₄⋊C₄

—

125

C₂²×C₄²

C₂×D₁₉

yes

characteristic

126

C₂×C₄⋊C₈

—

127

C₂×C₂²⋊C₈

—

128

#336

—

129

#333

—

130

C₂×C₁₉

—

131

C₂×C₁₉

C₂×#333

yes

characteristic

132

C₂×C₁₉

#1548

yes

—

133

C₂×C₁₉

#1558

yes

characteristic

134

C₂×C₁₉

#1783

yes

characteristic

135

C₂×C₁₉

#1787

yes

—

136

C₂²×Q₈

—

137

C₂²×Q₈

—

138

C₂²×Q₈

—

139

C₂²×Q₈

—

140

C₂²×Q₈

C₂×Dic₁₉

yes

—

141

C₂³×C₄

—

142

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

143

C₂³×C₄

C₂²⋊D₁₉

yes

—

144

C₂²×C₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄²

—

153

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

154

C₂×C₄²

C₂²⋊D₁₉

yes

—

155

C₂×C₄²

C₂²×D₁₉

yes

characteristic

156

C₄⋊C₈

—

157

C₂²⋊C₈

—

158

C₁₉

#8342

yes

characteristic, complemented, Sylow

159

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

C₂²⋊Dic₁₉

yes

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

#64527

yes

—

178

C₂²×C₄

#64528

yes

—

179

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

180

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

181

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

182

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄²

—

189

C₄²

—

190

C₄²

C₂×C₂²⋊D₁₉

yes

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

#10597290

yes

—

195

C₂³

#10597292

yes

—

196

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

197

Q₈

—

198

Q₈

—

199

Q₈

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

#10597290

yes

—

214

C₂×C₄

#10597292

yes

—

215

C₂×C₄

C₂×#64527

yes

—

216

C₂×C₄

#10597388

yes

—

217

C₂×C₄

C₂×#64528

yes

—

218

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

—

219

C₂×C₄

#10597399

yes

—

220

C₈

—

152

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

#11926293

yes

complemented

226

C₂²

#11926400

yes

characteristic

227

C₂²

C₂×#10597290

yes

characteristic

228

C₂²

C₂×#10597290

yes

characteristic

229

C₂²

C₂×#10597292

yes

—

230

C₂²

#11926553

yes

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

#11926683

yes

—

236

C₄

#11926700

yes

—

237

C₂

—

238

C₂

C₂×#11926293

yes

characteristic

239

C₂

#14562316

yes

—

240

C₂

#14562361

yes

characteristic

241

C₂

#14563556

yes

characteristic

242

C₂

#14563570

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂²×C₁₉×C₄⋊Q₈	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂²×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#8342
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂²×C₁₉×C₄⋊Q₈

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₂²×C₄⋊Q₈

D₁₉

hypocenter

C₁₉

#8342

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×C₄⋊Q₈

N	H ≅ G/N	type
2. C₂×#11926293	C₂	semidirect
107. C₂²×C₁₉	#333	semidirect
158. C₁₉	#8342	semidirect
225. C₂²	#11926293	semidirect

H ≅ G/N

type

2. C₂×#11926293

C₂

semidirect

107. C₂²×C₁₉

#333

semidirect

158. C₁₉

#8342

semidirect

225. C₂²

#11926293

semidirect

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

subgroup	index
#14563615	2
C₂×#11926293	2
C₂²×C₁₉×C₄⋊Q₈	2
#8342	19

subgroup

index

#14563615

C₂×#11926293

C₂²×C₁₉×C₄⋊Q₈

#8342

Subgroups — #18074035

Conjugacy classes of subgroups

Complements

Maximal subgroups