Group #18081708 — subgroups

Subgroups — #18081708

Order 4864.

498 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14574214	C₂	1	1	yes	maximal, characteristic
2	#14564553	C₂	1	2	yes	maximal, complemented
3	#14562129	C₂	1	2	yes	maximal, complemented
4	#14561924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927094	C₂²	1	2	yes	—
7	#11926949	C₄	1	1	yes	characteristic, complemented
8	#11926921	C₄	1	1	yes	characteristic, complemented
9	#11926891	C₄	1	2	yes	complemented
10	#11926780	—	2	1	no	—
11	#11926780	—	2	1	no	—
12	C₄×D₁₅₂	—	2	1	no	—
13	C₄×D₁₅₂	—	2	1	no	—
14	#11926597	C₂²	1	1	yes	characteristic
15	C₂×#10597262	—	2	4	no	—
16	C₄×#64520	C₂²	1	1	yes	characteristic
17	#11926277	—	2	4	no	—
18	#11926266	—	2	1	no	—
19	#11926265	—	2	1	no	—
20	C₂×C₁₉×#106	—	2	1	no	—
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#340	—	2	1	no	—
24	C₂×#64541	—	2	2	no	—
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄²×C₁₉	—	2	2	no	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	#10597376	—	2	2	no	—
31	#10597376	—	2	2	no	—
32	C₂×#64520	D₄	1	2	yes	—
33	C₂×D₁₅₂	—	2	1	no	—
34	C₂×D₁₅₂	—	2	1	no	—
35	#10597321	—	2	2	no	—
36	#10597320	C₂×C₄	1	2	yes	—
37	C₄×D₇₆	—	2	2	no	—
38	C₄×D₇₆	—	2	2	no	—
39	#10597315	C₂×C₄	1	2	yes	—
40	C₁₉×#106	—	2	4	no	—
41	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
45	C₁₉×#95	—	2	2	no	—
46	C₂²⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
47	#10597278	—	2	2	no	—
48	#10597278	—	2	2	no	—
49	#10597275	—	2	1	no	—
50	#10597275	—	2	1	no	—
51	#10597262	—	4	8	no	—
52	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
53	#10597260	—	2	1	no	—
54	C₄×C₁₉⋊C₈	—	2	1	no	—
55	C₄×C₁₉⋊C₈	—	2	1	no	—
56	C₂²×C₄×C₁₉	—	4	2	no	—
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂×C₂²⋊D₁₉	—	4	2	no	—
61	#64541	—	4	4	no	—
62	#64541	—	4	4	no	—
63	C₂×D₇₆	—	2	2	no	—
64	C₂×D₇₆	—	2	2	no	—
65	C₂×D₇₆	—	2	2	no	—
66	C₂×C₄×D₁₉	—	4	2	no	—
67	C₂×Dic₃₈	—	2	2	no	—
68	C₂×C₈×C₁₉	—	2	2	no	—
69	C₂×C₈×C₁₉	—	4	1	no	—
70	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₄⋊C₄×C₁₉	—	4	2	no	—
76	C₄²×C₁₉	—	4	4	no	—
77	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₉	#41	1	1	yes	characteristic
80	C₄²×C₁₉	#41	1	1	yes	characteristic
81	(C₂×D₁₉)⋊C₄	—	4	2	no	—
82	(C₂×D₁₉)⋊C₄	—	4	2	no	—
83	C₄⋊Dic₁₉	—	2	2	no	—
84	C₄⋊Dic₁₉	—	2	2	no	—
85	#64520	—	2	4	no	—
86	C₂×C₁₉⋊C₈	—	2	2	no	—
87	C₂×C₁₉⋊C₈	—	2	2	no	—
88	D₁₅₂	—	4	2	no	—
89	D₁₅₂	—	4	2	no	—
90	#9721	—	19	1	no	maximal, Sylow
91	C₂³×C₁₉	#127	1	1	yes	characteristic
92	C₂²×D₁₉	—	4	2	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	4	1	no	—
96	C₂×C₄×C₁₉	—	4	4	no	—
97	C₂×C₄×C₁₉	—	8	2	no	—
98	C₂×C₄×C₁₉	—	8	2	no	—
99	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
105	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
106	C₂²⋊D₁₉	—	8	2	no	—
107	C₂²⋊D₁₉	—	8	2	no	—
108	C₂×Dic₁₉	—	4	2	no	—
109	D₇₆	—	4	2	no	—
110	D₇₆	—	4	2	no	—
111	D₇₆	—	4	4	no	—
112	D₇₆	—	8	2	no	—
113	C₄×D₁₉	—	8	4	no	—
114	Dic₃₈	—	4	4	no	—
115	C₈×C₁₉	—	2	1	no	—
116	C₈×C₁₉	—	2	1	no	—
117	C₈×C₁₉	—	2	1	no	—
118	C₈×C₁₉	#104	1	2	yes	complemented
119	C₁₉⋊C₈	—	4	2	no	—
120	C₁₉⋊C₈	—	4	2	no	—
121	#3169	—	19	1	no	—
122	#1980	—	19	2	no	—
123	C₄×#106	D₁₉	1	1	yes	characteristic, complemented
124	#1502	—	19	2	no	—
125	#1451	—	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	#496	1	2	yes	—
130	C₂×D₁₉	—	8	2	no	—
131	C₂×D₁₉	—	8	2	no	—
132	C₂×D₁₉	—	8	2	no	—
133	C₄×C₁₉	—	2	1	no	—
134	C₄×C₁₉	—	2	1	no	—
135	C₄×C₁₉	—	2	1	no	—
136	C₄×C₁₉	—	8	4	no	—
137	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
138	C₄×C₁₉	#421	1	1	yes	characteristic
139	C₄×C₁₉	#442	1	2	yes	—
140	C₄×C₁₉	#469	1	2	yes	—
141	Dic₁₉	—	8	2	no	—
142	#532	—	19	2	no	—
143	#500	—	19	1	no	—
144	#493	—	19	1	no	—
145	#486	—	19	2	no	—
146	#466	—	38	1	no	—
147	#466	—	38	1	no	—
148	C₄×D₈	—	38	1	no	—
149	C₄×D₈	—	38	1	no	—
150	#431	—	19	1	no	—
151	C₂×#106	—	2	1	no	—
152	C₂×#104	—	38	4	no	—
153	C₄×M₁₆	—	19	1	no	—
154	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
155	C₄×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
156	#340	—	2	1	no	—
157	#327	—	38	4	no	—
158	#322	—	38	1	no	—
159	#322	—	38	1	no	—
160	C₂×C₁₉	—	2	2	no	—
161	C₂×C₁₉	#1972	1	1	yes	characteristic
162	C₂×C₁₉	#1976	1	1	yes	characteristic
163	C₂×C₁₉	#1980	1	1	yes	characteristic
164	D₁₉	—	16	2	no	—
165	C₂×#41	—	38	2	no	—
166	C₂×D₈	—	38	1	no	—
167	C₂×D₈	—	38	1	no	—
168	C₂×M₁₆	—	19	2	no	—
169	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
170	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
171	C₄⋊Q₈	—	19	2	no	—
172	#127	—	19	2	no	—
173	#124	—	38	2	no	—
174	#121	—	38	2	no	—
175	#121	—	38	2	no	—
176	C₄×D₄	—	38	2	no	—
177	C₄×D₄	—	38	2	no	—
178	C₂×C₄⋊C₄	—	2	2	no	—
179	C₂×C₄²	—	2	2	no	—
180	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
181	#107	—	38	1	no	—
182	#107	—	38	1	no	—
183	#106	—	2	4	no	—
184	C₄⋊C₈	—	38	1	no	—
185	#104	—	76	8	no	—
186	#102	—	38	2	no	—
187	#102	—	38	2	no	—
188	C₂²⋊C₈	—	19	2	no	—
189	#97	—	38	1	no	—
190	C₄×C₈	—	38	1	no	—
191	C₄×C₈	—	38	1	no	—
192	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
193	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
194	C₄×C₈	D₇₆	1	1	yes	characteristic
195	C₄×C₈	D₇₆	1	1	yes	characteristic
196	#95	—	2	2	no	—
197	C₁₉	#9721	1	1	yes	characteristic, complemented, Sylow
198	#41	—	76	4	no	—
199	#41	—	76	4	no	—
200	C₂×Q₈	—	38	2	no	—
201	C₂×D₄	—	38	2	no	—
202	C₂×D₄	—	38	2	no	—
203	C₂×D₄	—	38	2	no	—
204	C₂×D₄	—	76	2	no	—
205	C₂²×C₄	—	4	2	no	—
206	C₂²×C₄	—	76	2	no	—
207	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
208	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
209	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
210	D₈	—	76	2	no	—
211	D₈	—	76	2	no	—
212	M₁₆	—	38	4	no	—
213	C₂×C₈	—	2	2	no	—
214	C₂×C₈	—	4	1	no	—
215	C₂×C₈	—	38	2	no	—
216	C₂×C₈	—	38	2	no	—
217	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
218	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
219	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
220	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
221	C₄⋊C₄	—	2	4	no	—
222	C₄⋊C₄	—	4	2	no	—
223	C₄⋊C₄	—	38	2	no	—
224	C₄⋊C₄	—	38	2	no	—
225	C₂²⋊C₄	—	76	2	no	—
226	C₂²⋊C₄	—	76	2	no	—
227	C₄²	—	4	4	no	—
228	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
229	C₄²	C₂×D₇₆	1	1	yes	characteristic
230	C₄²	#64545	1	1	yes	characteristic
231	C₄²	#64545	1	1	yes	characteristic
232	C₂³	—	76	2	no	—
233	C₂³	#10597386	1	1	yes	characteristic
234	Q₈	—	76	4	no	—
235	D₄	—	76	2	no	—
236	D₄	—	76	2	no	—
237	D₄	—	76	4	no	—
238	D₄	—	152	2	no	—
239	D₄	—	152	2	no	—
240	D₄	—	152	2	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	4	4	no	—
245	C₂×C₄	—	8	2	no	—
246	C₂×C₄	—	8	2	no	—
247	C₂×C₄	—	76	2	no	—
248	C₂×C₄	—	152	4	no	—
249	C₂×C₄	#10597339	1	1	yes	characteristic
250	C₂×C₄	#10597339	1	1	yes	characteristic
251	C₂×C₄	#10597341	1	1	yes	characteristic
252	C₂×C₄	#10597341	1	1	yes	characteristic
253	C₂×C₄	#10597360	1	4	yes	—
254	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
255	C₂×C₄	#10597393	1	1	yes	characteristic
256	C₈	—	2	1	no	—
257	C₈	—	2	1	no	—
258	C₈	—	2	1	no	—
259	C₈	—	76	2	no	—
260	C₈	—	76	2	no	—
261	C₈	#10597262	1	2	yes	complemented
262	C₂²	—	2	1	no	—
263	C₂²	—	2	1	no	—
264	C₂²	—	152	2	no	—
265	C₂²	—	152	2	no	—
266	C₂²	—	152	2	no	—
267	C₂²	#11926445	1	1	yes	characteristic
268	C₂²	#11926930	1	2	yes	—
269	C₄	—	2	1	no	—
270	C₄	—	2	1	no	—
271	C₄	—	2	1	no	—
272	C₄	—	8	4	no	—
273	C₄	—	152	2	no	—
274	C₄	C₂×#10597262	1	1	yes	characteristic
275	C₄	#11926562	1	1	yes	characteristic
276	C₄	#11926655	1	2	yes	—
277	C₄	#11926798	1	2	yes	—
278	C₂	—	2	2	no	—
279	C₂	—	304	2	no	—
280	C₂	#14564509	1	1	yes	characteristic
281	C₂	#14564531	1	1	yes	characteristic
282	C₂	#14564553	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574214

C₂

yes

maximal, characteristic

#14564553

C₂

yes

maximal, complemented

#14562129

C₂

yes

maximal, complemented

#14561924

C₂

yes

maximal, characteristic, complemented

C₄×C₁₉×#106

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

—

#11926949

C₄

yes

characteristic, complemented

#11926921

C₄

yes

characteristic, complemented

#11926891

C₄

yes

complemented

#11926780

—

#11926780

—

C₄×D₁₅₂

—

C₄×D₁₅₂

—

#11926597

C₂²

yes

characteristic

C₂×#10597262

—

C₄×#64520

C₂²

yes

—

—

—

C₂×C₁₉×#106

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₉

C₂²

yes

—

C₁₉×#340

—

C₂×#64541

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

D₄

yes

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

#10597321

—

#10597320

C₂×C₄

yes

—

C₄×D₇₆

—

C₄×D₇₆

—

#10597315

C₂×C₄

yes

—

C₁₉×#106

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

D₄

yes

—

—

—

—

—

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

D₁₅₂

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

100

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

101

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

102

C₂×C₄×C₁₉

#121

yes

characteristic

103

C₂×C₄×C₁₉

#121

yes

characteristic

104

C₂×C₄×C₁₉

#124

yes

characteristic

105

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

106

C₂²⋊D₁₉

—

107

C₂²⋊D₁₉

—

108

C₂×Dic₁₉

—

109

D₇₆

—

110

D₇₆

—

111

D₇₆

—

112

D₇₆

—

113

C₄×D₁₉

—

114

Dic₃₈

—

115

C₈×C₁₉

—

116

C₈×C₁₉

—

117

C₈×C₁₉

—

118

C₈×C₁₉

#104

yes

complemented

119

C₁₉⋊C₈

—

120

C₁₉⋊C₈

—

121

#3169

—

122

#1980

—

123

C₄×#106

D₁₉

yes

characteristic, complemented

124

#1502

—

125

#1451

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

#390

yes

characteristic

129

C₂²×C₁₉

#496

yes

—

130

C₂×D₁₉

—

131

C₂×D₁₉

—

132

C₂×D₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

C₂×#104

yes

characteristic

138

C₄×C₁₉

#421

yes

characteristic

139

C₄×C₁₉

#442

yes

—

140

C₄×C₁₉

#469

yes

—

141

Dic₁₉

—

142

#532

—

143

#500

—

144

#493

—

145

#486

—

146

#466

—

147

#466

—

148

C₄×D₈

—

149

C₄×D₈

—

150

#431

—

151

C₂×#106

—

152

C₂×#104

—

153

C₄×M₁₆

—

154

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

155

C₄×C₄⋊C₄

C₂×D₁₉

yes

—

156

#340

—

157

#327

—

158

#322

—

159

#322

—

160

C₂×C₁₉

—

161

C₂×C₁₉

#1972

yes

characteristic

162

C₂×C₁₉

#1976

yes

characteristic

163

C₂×C₁₉

#1980

yes

characteristic

164

D₁₉

—

165

C₂×#41

—

166

C₂×D₈

—

167

C₂×D₈

—

168

C₂×M₁₆

—

169

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

170

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

171

C₄⋊Q₈

—

172

#127

—

173

#124

—

174

#121

—

175

#121

—

176

C₄×D₄

—

177

C₄×D₄

—

178

C₂×C₄⋊C₄

—

179

C₂×C₄²

—

180

C₂×C₄²

C₂²×D₁₉

yes

characteristic

181

#107

—

182

#107

—

183

#106

—

184

C₄⋊C₈

—

185

#104

—

186

#102

—

187

#102

—

188

C₂²⋊C₈

—

189

#97

—

190

C₄×C₈

—

191

C₄×C₈

—

192

C₄×C₈

C₄×D₁₉

yes

characteristic

193

C₄×C₈

C₄×D₁₉

yes

characteristic

194

C₄×C₈

D₇₆

yes

characteristic

195

C₄×C₈

D₇₆

yes

characteristic

196

#95

—

197

C₁₉

#9721

yes

characteristic, complemented, Sylow

198

#41

—

199

#41

—

200

C₂×Q₈

—

201

C₂×D₄

—

202

C₂×D₄

—

203

C₂×D₄

—

204

C₂×D₄

—

205

C₂²×C₄

—

206

C₂²×C₄

—

207

C₂²×C₄

D₄×D₁₉

yes

characteristic

208

C₂²×C₄

D₄×D₁₉

yes

characteristic

209

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

210

D₈

—

211

D₈

—

212

M₁₆

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

218

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

219

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

220

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₂²⋊C₄

—

226

C₂²⋊C₄

—

227

C₄²

—

228

C₄²

C₂×C₄×D₁₉

yes

characteristic

229

C₄²

C₂×D₇₆

yes

characteristic

230

C₄²

#64545

yes

characteristic

231

C₄²

#64545

yes

characteristic

232

C₂³

—

233

C₂³

#10597386

yes

characteristic

234

Q₈

—

235

D₄

—

236

D₄

—

237

D₄

—

238

D₄

—

152

—

239

D₄

—

152

—

240

D₄

—

152

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

152

—

249

C₂×C₄

#10597339

yes

characteristic

250

C₂×C₄

#10597339

yes

characteristic

251

C₂×C₄

#10597341

yes

characteristic

252

C₂×C₄

#10597341

yes

characteristic

253

C₂×C₄

#10597360

yes

—

254

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

255

C₂×C₄

#10597393

yes

characteristic

256

C₈

—

257

C₈

—

258

C₈

—

259

C₈

—

260

C₈

—

261

C₈

#10597262

yes

complemented

262

C₂²

—

263

C₂²

—

264

C₂²

—

152

—

265

C₂²

—

152

—

266

C₂²

—

152

—

267

C₂²

#11926445

yes

characteristic

268

C₂²

#11926930

yes

—

269

C₄

—

270

C₄

—

271

C₄

—

272

C₄

—

273

C₄

—

152

—

274

C₄

C₂×#10597262

yes

characteristic

275

C₄

#11926562

yes

characteristic

276

C₄

#11926655

yes

—

277

C₄

#11926798

yes

—

278

C₂

—

279

C₂

—

304

—

280

C₂

#14564509

yes

characteristic

281

C₂

#14564531

yes

characteristic

282

C₂

#14564553

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597341
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#106	C₂
socle	C₂²×C₁₉	#390
prime radical	#14574214	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#106	D₁₉
hypocenter	C₁₉	#9721
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#106

subgroup

G/H

center

C₂×C₄

#10597341

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#106

C₂

C₂²×C₁₉

C₂

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#106

N	H ≅ G/N	type
2. #14564553	C₂	semidirect
3. #14562129	C₂	semidirect
4. #14561924	C₂	semidirect
5. C₄×C₁₉×#106	C₂	semidirect
7. #11926949	C₄	semidirect
8. #11926921	C₄	semidirect
9. #11926891	C₄	semidirect
118. C₈×C₁₉	#104	semidirect
123. C₄×#106	D₁₉	semidirect
197. C₁₉	#9721	semidirect
261. C₈	#10597262	semidirect

H ≅ G/N

type

2. #14564553

C₂

semidirect

3. #14562129

C₂

semidirect

4. #14561924

C₂

semidirect

5. C₄×C₁₉×#106

C₂

semidirect

7. #11926949

C₄

semidirect

8. #11926921

C₄

semidirect

9. #11926891

C₄

semidirect

118. C₈×C₁₉

#104

semidirect

123. C₄×#106

D₁₉

semidirect

197. C₁₉

#9721

semidirect

261. C₈

#10597262

semidirect

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

subgroup	index
#14574214	2
#14564553	2
#14562129	2
#14561924	2
C₄×C₁₉×#106	2
#9721	19

subgroup

index

C₄×C₁₉×#106

Subgroups — #18081708

Conjugacy classes of subgroups

Complements

Maximal subgroups