Group #18081444 — subgroups

Subgroups — #18081444

Order 4864.

586 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 147 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×C₄×D₁₅₂	C₂	1	1	yes	maximal, characteristic
2	#14564428	C₂	1	2	yes	maximal, complemented
3	C₂×#11926271	C₂	1	2	yes	maximal, complemented
4	C₂×#11926266	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₅₂	C₄	1	1	yes	characteristic
7	C₂×C₄×D₇₆	C₂²	1	2	yes	—
8	C₄×D₁₅₂	—	2	2	no	—
9	C₄×D₁₅₂	—	2	2	no	—
10	C₂×#10597275	C₄	1	1	yes	characteristic
11	C₂×#10597278	C₄	1	2	yes	—
12	C₂×(C₂×D₁₉)⋊C₈	—	2	4	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	#11926271	—	2	4	no	—
16	#11926266	—	2	2	no	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#334	—	2	2	no	—
20	C₂²×D₇₆	C₂×C₄	1	2	yes	—
21	C₂²×C₄×D₁₉	—	2	2	no	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
27	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
28	C₂²×C₁₉⋊C₈	—	2	1	no	—
29	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
30	C₂×D₁₅₂	—	2	4	no	—
31	C₂×D₁₅₂	—	2	2	no	—
32	C₄×D₇₆	—	2	2	no	—
33	C₄×D₇₆	—	2	2	no	—
34	C₄×D₇₆	—	2	2	no	—
35	C₄×D₇₆	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₄×C₈×C₁₉	D₄	1	2	yes	—
39	C₄×C₈×C₁₉	D₄	1	2	yes	—
40	#10597278	—	2	4	no	—
41	(C₂×D₁₉)⋊C₈	—	4	8	no	—
42	#10597275	—	2	2	no	—
43	C₄×C₁₉⋊C₈	—	2	1	no	—
44	C₄×C₁₉⋊C₈	—	2	1	no	—
45	C₄×C₁₉⋊C₈	—	2	1	no	—
46	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
47	C₂³×D₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
51	C₂²×Dic₁₉	—	2	2	no	—
52	C₂×D₇₆	—	2	2	no	—
53	C₂×D₇₆	—	2	2	no	—
54	C₂×D₇₆	—	2	2	no	—
55	C₂×D₇₆	—	2	2	no	—
56	C₂×D₇₆	—	2	2	no	—
57	C₂×D₇₆	M₁₆	1	4	yes	—
58	C₂×C₄×D₁₉	—	4	2	no	—
59	C₂×C₄×D₁₉	—	4	2	no	—
60	C₂×C₄×D₁₉	—	4	4	no	—
61	C₂×C₄×D₁₉	—	4	4	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	—	4	4	no	—
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
68	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₉	#41	1	1	yes	characteristic
72	(C₂×D₁₉)⋊C₄	—	4	2	no	—
73	(C₂×D₁₉)⋊C₄	—	4	2	no	—
74	C₄⋊Dic₁₉	—	2	2	no	—
75	C₄⋊Dic₁₉	—	2	2	no	—
76	C₂×C₁₉⋊C₈	—	2	4	no	—
77	C₂×C₁₉⋊C₈	—	2	2	no	—
78	C₂×C₁₉⋊C₈	—	2	2	no	—
79	C₂×C₁₉⋊C₈	—	2	4	no	—
80	D₁₅₂	—	2	8	no	—
81	#9665	—	19	1	no	maximal, Sylow
82	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
83	C₂²×D₁₉	—	2	4	no	—
84	C₂²×D₁₉	—	4	2	no	—
85	C₂²×D₁₉	—	4	2	no	—
86	C₂²×D₁₉	—	4	4	no	—
87	C₂²×D₁₉	—	4	4	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
96	C₂×C₄×C₁₉	#131	1	2	yes	—
97	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
98	C₂×Dic₁₉	—	4	2	no	—
99	C₂×Dic₁₉	—	4	4	no	—
100	D₇₆	—	2	4	no	—
101	D₇₆	—	2	4	no	—
102	D₇₆	—	4	2	no	—
103	D₇₆	—	4	2	no	—
104	C₄×D₁₉	—	8	4	no	—
105	C₄×D₁₉	—	8	2	no	—
106	C₄×D₁₉	—	8	2	no	—
107	C₈×C₁₉	—	2	2	no	—
108	C₈×C₁₉	—	2	2	no	—
109	C₈×C₁₉	—	8	2	no	—
110	C₁₉⋊C₈	—	2	4	no	—
111	C₁₉⋊C₈	—	4	2	no	—
112	C₂×C₄×D₈	—	19	1	no	—
113	#1954	—	19	2	no	—
114	C₂×#334	D₁₉	1	1	yes	characteristic, complemented
115	C₂×D₄⋊C₈	—	19	2	no	—
116	C₂×#322	—	19	1	no	—
117	C₂²×C₁₉	#390	1	1	yes	characteristic
118	C₂²×C₁₉	#435	1	2	yes	—
119	C₂²×C₁₉	#442	1	2	yes	—
120	C₂²×C₁₉	#443	1	2	yes	—
121	C₂×D₁₉	—	4	8	no	—
122	C₂×D₁₉	—	4	4	no	—
123	C₂×D₁₉	—	8	4	no	—
124	C₂×D₁₉	—	8	2	no	—
125	C₂×D₁₉	—	8	2	no	—
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	#407	1	1	yes	characteristic
129	C₄×C₁₉	#408	1	1	yes	characteristic
130	C₄×C₁₉	#435	1	2	yes	—
131	C₄×C₁₉	#469	1	2	yes	—
132	C₄×C₁₉	#496	1	2	yes	—
133	Dic₁₉	—	8	2	no	—
134	C₂²×D₈	—	19	1	no	—
135	C₂×C₄×D₄	—	19	2	no	—
136	C₄×D₈	—	38	2	no	—
137	C₄×D₈	—	38	2	no	—
138	C₂×#107	—	19	1	no	—
139	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
140	C₂×#102	—	19	2	no	—
141	C₂×C₂²⋊C₈	—	38	4	no	—
142	C₂×C₄×C₈	—	19	1	no	—
143	C₂×C₄×C₈	—	19	1	no	—
144	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
145	#334	—	2	2	no	—
146	D₄⋊C₈	—	38	4	no	—
147	#322	—	38	2	no	—
148	C₂×C₁₉	#1586	1	4	yes	—
149	C₂×C₁₉	#1955	1	1	yes	characteristic
150	C₂×C₁₉	#1972	1	1	yes	characteristic
151	C₂×C₁₉	#1974	1	1	yes	characteristic
152	D₁₉	—	8	4	no	—
153	C₂²×D₄	—	19	2	no	—
154	C₂³×C₄	—	38	2	no	—
155	C₂×D₈	—	38	4	no	—
156	C₂×D₈	—	38	2	no	—
157	C₂²×C₈	—	2	2	no	—
158	C₂²×C₈	—	19	2	no	—
159	C₂²×C₈	—	38	1	no	—
160	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
161	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
162	C₄×D₄	—	38	2	no	—
163	C₄×D₄	—	38	2	no	—
164	C₄×D₄	—	38	2	no	—
165	C₄×D₄	—	38	2	no	—
166	C₂×C₄⋊C₄	—	19	2	no	—
167	C₂×C₂²⋊C₄	—	38	2	no	—
168	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
169	#107	—	38	2	no	—
170	C₄⋊C₈	—	2	2	no	—
171	C₄⋊C₈	—	2	2	no	—
172	#102	—	38	4	no	—
173	C₂²⋊C₈	—	76	8	no	—
174	C₄×C₈	—	19	2	no	—
175	C₄×C₈	—	38	1	no	—
176	C₄×C₈	—	38	1	no	—
177	C₄×C₈	—	38	1	no	—
178	C₄×C₈	D₇₆	1	2	yes	—
179	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
180	C₁₉	#9665	1	1	yes	characteristic, complemented, Sylow
181	C₂⁴	—	38	2	no	—
182	C₂×D₄	—	19	4	no	—
183	C₂×D₄	—	38	2	no	—
184	C₂×D₄	—	38	2	no	—
185	C₂×D₄	—	38	2	no	—
186	C₂×D₄	—	38	2	no	—
187	C₂×D₄	—	38	2	no	—
188	C₂²×C₄	—	38	2	no	—
189	C₂²×C₄	—	76	2	no	—
190	C₂²×C₄	—	76	2	no	—
191	C₂²×C₄	—	76	4	no	—
192	C₂²×C₄	—	76	4	no	—
193	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
194	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
195	C₂²×C₄	#64545	1	1	yes	characteristic
196	D₈	—	38	8	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	4	2	no	—
200	C₂×C₈	—	4	4	no	—
201	C₂×C₈	—	38	4	no	—
202	C₂×C₈	—	38	2	no	—
203	C₂×C₈	—	38	2	no	—
204	C₂×C₈	—	38	4	no	—
205	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
206	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
207	C₄⋊C₄	—	38	2	no	—
208	C₄⋊C₄	—	38	2	no	—
209	C₂²⋊C₄	—	76	2	no	—
210	C₂²⋊C₄	—	76	2	no	—
211	C₄²	C₂×D₇₆	1	1	yes	characteristic
212	C₄²	D₄×D₁₉	1	1	yes	characteristic
213	C₄²	#64545	1	1	yes	characteristic
214	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
215	C₂³	—	38	4	no	—
216	C₂³	—	76	2	no	—
217	C₂³	—	76	4	no	—
218	C₂³	—	76	4	no	—
219	C₂³	—	76	2	no	—
220	C₂³	#10597339	1	1	yes	characteristic
221	D₄	—	38	4	no	—
222	D₄	—	38	4	no	—
223	D₄	—	76	2	no	—
224	D₄	—	76	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	76	4	no	—
227	C₂×C₄	—	76	2	no	—
228	C₂×C₄	—	152	4	no	—
229	C₂×C₄	—	152	2	no	—
230	C₂×C₄	—	152	2	no	—
231	C₂×C₄	#10597339	1	1	yes	characteristic
232	C₂×C₄	#10597341	1	1	yes	characteristic
233	C₂×C₄	#10597341	1	1	yes	characteristic
234	C₂×C₄	#10597347	1	2	yes	—
235	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
236	C₂×C₄	#10597360	1	4	yes	—
237	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
238	C₂×C₄	#10597386	1	1	yes	characteristic
239	C₂×C₄	#10597393	1	1	yes	characteristic
240	C₈	—	2	2	no	—
241	C₈	—	2	2	no	—
242	C₈	—	8	2	no	—
243	C₈	—	38	4	no	—
244	C₈	—	76	2	no	—
245	C₂²	—	76	4	no	—
246	C₂²	—	76	8	no	—
247	C₂²	—	152	2	no	—
248	C₂²	—	152	2	no	—
249	C₂²	—	152	4	no	—
250	C₂²	#11926445	1	1	yes	characteristic
251	C₂²	#11926614	1	2	yes	—
252	C₂²	#11926655	1	2	yes	—
253	C₂²	#11926660	1	2	yes	—
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	152	2	no	—
257	C₄	#11926507	1	1	yes	characteristic
258	C₄	#11926510	1	1	yes	characteristic
259	C₄	#11926614	1	2	yes	—
260	C₄	#11926798	1	2	yes	—
261	C₄	#11926930	1	2	yes	—
262	C₂	—	152	4	no	—
263	C₂	#14562498	1	4	yes	—
264	C₂	#14564432	1	1	yes	characteristic
265	C₂	#14564509	1	1	yes	characteristic
266	C₂	#14564521	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×D₁₅₂

C₂

yes

maximal, characteristic

#14564428

C₂

yes

maximal, complemented

C₂×#11926271

C₂

yes

maximal, complemented

C₂×#11926266

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#334

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₅₂

C₄

yes

characteristic

C₂×C₄×D₇₆

C₂²

yes

—

C₄×D₁₅₂

—

C₄×D₁₅₂

—

C₂×#10597275

C₄

yes

characteristic

C₂×#10597278

C₄

yes

—

C₂×(C₂×D₁₉)⋊C₈

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926271

—

#11926266

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#334

—

C₂²×D₇₆

C₂×C₄

yes

—

C₂²×C₄×D₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₄×D₇₆

—

C₄×D₇₆

—

C₄×D₇₆

—

C₄×D₇₆

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

#10597278

—

(C₂×D₁₉)⋊C₈

—

#10597275

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

M₁₆

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

#9665

—

maximal, Sylow

C₂³×C₁₉

C₄×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

100

D₇₆

—

101

D₇₆

—

102

D₇₆

—

103

D₇₆

—

104

C₄×D₁₉

—

105

C₄×D₁₉

—

106

C₄×D₁₉

—

107

C₈×C₁₉

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₁₉⋊C₈

—

111

C₁₉⋊C₈

—

112

C₂×C₄×D₈

—

113

#1954

—

114

C₂×#334

D₁₉

yes

characteristic, complemented

115

C₂×D₄⋊C₈

—

116

C₂×#322

—

117

C₂²×C₁₉

#390

yes

characteristic

118

C₂²×C₁₉

#435

yes

—

119

C₂²×C₁₉

#442

yes

—

120

C₂²×C₁₉

#443

yes

—

121

C₂×D₁₉

—

122

C₂×D₁₉

—

123

C₂×D₁₉

—

124

C₂×D₁₉

—

125

C₂×D₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

#407

yes

characteristic

129

C₄×C₁₉

#408

yes

characteristic

130

C₄×C₁₉

#435

yes

—

131

C₄×C₁₉

#469

yes

—

132

C₄×C₁₉

#496

yes

—

133

Dic₁₉

—

134

C₂²×D₈

—

135

C₂×C₄×D₄

—

136

C₄×D₈

—

137

C₄×D₈

—

138

C₂×#107

—

139

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

140

C₂×#102

—

141

C₂×C₂²⋊C₈

—

142

C₂×C₄×C₈

—

143

C₂×C₄×C₈

—

144

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

145

#334

—

146

D₄⋊C₈

—

147

#322

—

148

C₂×C₁₉

#1586

yes

—

149

C₂×C₁₉

#1955

yes

characteristic

150

C₂×C₁₉

#1972

yes

characteristic

151

C₂×C₁₉

#1974

yes

characteristic

152

D₁₉

—

153

C₂²×D₄

—

154

C₂³×C₄

—

155

C₂×D₈

—

156

C₂×D₈

—

157

C₂²×C₈

—

158

C₂²×C₈

—

159

C₂²×C₈

—

160

C₂²×C₈

C₄×D₁₉

yes

characteristic

161

C₂²×C₈

C₄×D₁₉

yes

characteristic

162

C₄×D₄

—

163

C₄×D₄

—

164

C₄×D₄

—

165

C₄×D₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₂²⋊C₄

—

168

C₂×C₄²

C₂²×D₁₉

yes

characteristic

169

#107

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

#102

—

173

C₂²⋊C₈

—

174

C₄×C₈

—

175

C₄×C₈

—

176

C₄×C₈

—

177

C₄×C₈

—

178

C₄×C₈

D₇₆

yes

—

179

C₄×C₈

C₂²⋊D₁₉

yes

—

180

C₁₉

#9665

yes

characteristic, complemented, Sylow

181

C₂⁴

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

194

C₂²×C₄

D₄×D₁₉

yes

characteristic

195

C₂²×C₄

#64545

yes

characteristic

196

D₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

206

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₂²⋊C₄

—

210

C₂²⋊C₄

—

211

C₄²

C₂×D₇₆

yes

characteristic

212

C₄²

D₄×D₁₉

yes

characteristic

213

C₄²

#64545

yes

characteristic

214

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

215

C₂³

—

216

C₂³

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

#10597339

yes

characteristic

221

D₄

—

222

D₄

—

223

D₄

—

224

D₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

152

—

229

C₂×C₄

—

152

—

230

C₂×C₄

—

152

—

231

C₂×C₄

#10597339

yes

characteristic

232

C₂×C₄

#10597341

yes

characteristic

233

C₂×C₄

#10597341

yes

characteristic

234

C₂×C₄

#10597347

yes

—

235

C₂×C₄

M₁₆×D₁₉

yes

—

236

C₂×C₄

#10597360

yes

—

237

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

238

C₂×C₄

#10597386

yes

characteristic

239

C₂×C₄

#10597393

yes

characteristic

240

C₈

—

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

152

—

248

C₂²

—

152

—

249

C₂²

—

152

—

250

C₂²

#11926445

yes

characteristic

251

C₂²

#11926614

yes

—

252

C₂²

#11926655

yes

—

253

C₂²

#11926660

yes

—

254

C₄

—

255

C₄

—

256

C₄

—

152

—

257

C₄

#11926507

yes

characteristic

258

C₄

#11926510

yes

characteristic

259

C₄

#11926614

yes

—

260

C₄

#11926798

yes

—

261

C₄

#11926930

yes

—

262

C₂

—

152

—

263

C₂

#14562498

yes

—

264

C₂

#14564432

yes

characteristic

265

C₂

#14564509

yes

characteristic

266

C₂

#14564521

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#334	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂²×D₁₅₂	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#334	D₁₉
hypocenter	C₁₉	#9665
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

subgroup

G/H

center

C₂²×C₄

D₄×D₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#334

C₂

socle

C₂³×C₁₉

C₄×D₄

prime radical

C₂²×D₁₅₂

C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

N	H ≅ G/N	type
2. #14564428	C₂	semidirect
3. C₂×#11926271	C₂	semidirect
4. C₂×#11926266	C₂	semidirect
5. C₂×C₁₉×#334	C₂	semidirect
114. C₂×#334	D₁₉	semidirect
180. C₁₉	#9665	semidirect

H ≅ G/N

type

2. #14564428

C₂

semidirect

3. C₂×#11926271

C₂

semidirect

4. C₂×#11926266

C₂

semidirect

5. C₂×C₁₉×#334

C₂

semidirect

114. C₂×#334

D₁₉

semidirect

180. C₁₉

#9665

semidirect

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

subgroup	index
C₂×C₄×D₁₅₂	2
#14564428	2
C₂×#11926271	2
C₂×#11926266	2
C₂×C₁₉×#334	2
#9665	19

subgroup

index

C₂×C₄×D₁₅₂

C₂×C₁₉×#334

Subgroups — #18081444

Conjugacy classes of subgroups

Complements

Maximal subgroups