Group #28476896 — subgroups

Subgroups — #28476896

Order 15104.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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	C₄×#14273727	C₂	1	1	yes	maximal, characteristic
2	#21423949	C₂	1	1	yes	maximal, characteristic
3	#21421920	C₂	1	4	yes	maximal
4	C₅₉×#1839	C₂	1	1	yes	maximal, characteristic
5	C₂×#14273727	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₁₁₈	—	2	1	no	—
7	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
8	C₂×#14273638	—	2	1	no	—
9	#16837308	—	2	1	no	—
10	#16837300	—	2	1	no	—
11	#16837300	C₂²	1	2	yes	—
12	#16837272	C₄	1	1	yes	characteristic
13	C₄×C₄⋊Dic₅₉	—	2	1	no	—
14	C₄×C₄⋊Dic₅₉	C₄	1	2	yes	—
15	#16837157	C₂²	1	2	yes	—
16	C₄³×C₅₉	C₂²	1	1	yes	characteristic
17	C₅₉×#336	—	2	1	no	—
18	C₅₉×#336	—	2	1	no	—
19	C₅₉×#336	C₂²	1	2	yes	—
20	C₂²×Dic₁₁₈	—	2	1	no	—
21	C₂²×C₅₉⋊C₈	—	2	2	no	—
22	#14273727	—	2	4	no	—
23	C₄×Dic₁₁₈	—	4	4	no	—
24	C₂×C₄⋊Dic₅₉	—	2	1	no	—
25	C₂×C₄⋊Dic₅₉	—	2	1	no	—
26	C₂×C₄⋊Dic₅₉	—	2	1	no	—
27	C₂×C₄⋊Dic₅₉	C₂×C₄	1	2	yes	—
28	C₂×C₄⋊Dic₅₉	C₂×C₄	1	2	yes	—
29	C₂×Dic₅₉⋊C₄	—	2	2	no	—
30	C₂×C₄×Dic₅₉	—	2	2	no	—
31	C₄⋊(C₅₉⋊C₈)	—	2	4	no	—
32	#14273638	—	4	2	no	—
33	C₅₉⋊#95	—	2	2	no	—
34	C₅₉⋊#95	—	2	2	no	—
35	C₂²×C₈×C₅₉	—	2	2	no	—
36	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₅₉	—	2	2	no	—
51	C₂²×Dic₅₉	—	2	2	no	—
52	C₂×Dic₁₁₈	—	2	4	no	—
53	C₂×Dic₁₁₈	—	4	2	no	—
54	C₂×Dic₁₁₈	—	4	2	no	—
55	C₂×C₈×C₅₉	—	4	2	no	—
56	C₂×C₈×C₅₉	—	4	2	no	—
57	C₂×C₈×C₅₉	—	4	2	no	—
58	C₄²×C₅₉	—	2	2	no	—
59	C₄²×C₅₉	—	2	2	no	—
60	C₄²×C₅₉	—	2	2	no	—
61	C₄²×C₅₉	—	2	2	no	—
62	C₄²×C₅₉	—	4	1	no	—
63	C₄²×C₅₉	—	4	1	no	—
64	C₄²×C₅₉	SD₁₆	1	2	yes	—
65	C₄²×C₅₉	Q₁₆	1	2	yes	—
66	C₄⋊Dic₅₉	—	2	4	no	—
67	C₄⋊Dic₅₉	—	2	2	no	—
68	C₄⋊Dic₅₉	—	4	2	no	—
69	C₄⋊Dic₅₉	—	4	2	no	—
70	C₄⋊Dic₅₉	—	4	2	no	—
71	C₄⋊Dic₅₉	M₁₆	1	4	yes	—
72	Dic₅₉⋊C₄	—	4	4	no	—
73	C₄×Dic₅₉	—	4	4	no	—
74	C₂×C₅₉⋊C₈	—	2	4	no	—
75	C₂×C₅₉⋊C₈	—	4	2	no	—
76	C₂×C₅₉⋊C₈	—	4	2	no	—
77	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄×C₅₉	—	2	1	no	—
79	C₂×C₄×C₅₉	—	2	1	no	—
80	C₂×C₄×C₅₉	—	2	1	no	—
81	C₂×C₄×C₅₉	—	2	1	no	—
82	C₂×C₄×C₅₉	—	2	1	no	—
83	C₂×C₄×C₅₉	—	2	1	no	—
84	C₂×C₄×C₅₉	—	2	1	no	—
85	C₂×C₄×C₅₉	—	2	1	no	—
86	C₂×C₄×C₅₉	—	2	1	no	—
87	C₂×C₄×C₅₉	—	2	1	no	—
88	C₂×C₄×C₅₉	—	2	1	no	—
89	C₂×C₄×C₅₉	—	2	1	no	—
90	C₂×C₄×C₅₉	—	2	1	no	—
91	C₂×C₄×C₅₉	—	2	1	no	—
92	C₂×C₄×C₅₉	#101	1	2	yes	—
93	C₂×C₄×C₅₉	#103	1	2	yes	—
94	C₂×C₄×C₅₉	#103	1	2	yes	—
95	C₂×C₄×C₅₉	#104	1	2	yes	—
96	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
97	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
99	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
100	C₂×Dic₅₉	—	2	4	no	—
101	C₂×Dic₅₉	—	4	2	no	—
102	C₂×Dic₅₉	—	4	2	no	—
103	C₂×Dic₅₉	—	4	2	no	—
104	C₂×Dic₅₉	—	4	2	no	—
105	C₂×Dic₅₉	—	4	2	no	—
106	Dic₁₁₈	—	4	8	no	—
107	C₈×C₅₉	—	8	2	no	—
108	C₅₉⋊C₈	—	4	4	no	—
109	#7622	—	59	1	no	maximal, Sylow
110	C₂²×C₅₉	#407	1	1	yes	characteristic
111	C₂²×C₅₉	#410	1	1	yes	characteristic
112	C₂²×C₅₉	C₂×#101	1	1	yes	characteristic
113	C₂²×C₅₉	C₂×#103	1	1	yes	characteristic
114	C₂²×C₅₉	#418	1	1	yes	characteristic
115	C₂²×C₅₉	C₂×#104	1	1	yes	characteristic
116	C₂²×C₅₉	#421	1	1	yes	characteristic
117	C₄×C₅₉	—	2	2	no	—
118	C₄×C₅₉	—	2	2	no	—
119	C₄×C₅₉	—	2	2	no	—
120	C₄×C₅₉	—	2	2	no	—
121	C₄×C₅₉	—	2	1	no	—
122	C₄×C₅₉	—	2	1	no	—
123	C₄×C₅₉	—	2	2	no	—
124	C₄×C₅₉	—	2	2	no	—
125	Dic₅₉	—	4	4	no	—
126	Dic₅₉	—	8	2	no	—
127	C₄×C₄⋊Q₈	—	59	1	no	—
128	#1839	D₅₉	1	1	yes	characteristic
129	#1767	—	59	1	no	—
130	#1271	—	59	4	no	—
131	C₂×C₅₉	#1467	1	1	yes	characteristic
132	C₂×C₅₉	#1487	1	1	yes	characteristic
133	C₂×C₅₉	#1490	1	1	yes	characteristic
134	C₂×C₅₉	#1503	1	1	yes	characteristic
135	C₂×C₅₉	#1514	1	1	yes	characteristic
136	C₂×C₅₉	#1531	1	1	yes	characteristic
137	C₂×C₅₉	#1549	1	1	yes	characteristic
138	C₂×C₄⋊Q₈	—	59	1	no	—
139	C₂×C₄×Q₈	—	118	1	no	—
140	C₂×C₄⋊C₈	—	118	1	no	—
141	C₂×#97	—	118	1	no	—
142	#391	—	118	1	no	—
143	#389	—	59	2	no	—
144	#389	—	118	1	no	—
145	#384	—	59	1	no	—
146	C₄×C₄⋊C₄	—	59	2	no	—
147	C₄×C₄⋊C₄	—	118	1	no	—
148	C₄³	C₂×D₅₉	1	1	yes	characteristic
149	#336	—	2	1	no	—
150	#336	—	2	1	no	—
151	#336	—	59	2	no	—
152	#336	C₂×D₅₉	1	2	yes	—
153	C₅₉	#7622	1	1	yes	characteristic, complemented, Sylow
154	C₂²×Q₈	—	118	1	no	—
155	C₂²×C₈	—	2	2	no	—
156	C₂²×C₈	—	118	2	no	—
157	C₄⋊Q₈	—	118	4	no	—
158	C₄×Q₈	—	236	4	no	—
159	C₂×C₄⋊C₄	—	59	2	no	—
160	C₂×C₄⋊C₄	—	59	2	no	—
161	C₂×C₄⋊C₄	—	118	1	no	—
162	C₂×C₄⋊C₄	—	118	1	no	—
163	C₂×C₄⋊C₄	—	118	1	no	—
164	C₂×C₄⋊C₄	—	118	2	no	—
165	C₂×C₄²	—	118	2	no	—
166	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
167	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
168	C₂×C₄²	D₂₃₆	1	1	yes	characteristic
169	C₂×C₄²	D₂₃₆	1	1	yes	characteristic
170	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
171	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
172	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
173	C₄⋊C₈	—	118	4	no	—
174	#97	—	236	2	no	—
175	#95	—	118	2	no	—
176	#95	—	118	2	no	—
177	C₂×Q₈	—	118	4	no	—
178	C₂×Q₈	—	236	2	no	—
179	C₂×Q₈	—	236	2	no	—
180	C₂²×C₄	—	118	2	no	—
181	C₂²×C₄	—	118	2	no	—
182	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
183	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
184	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
185	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
187	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	4	2	no	—
192	C₂×C₈	—	118	4	no	—
193	C₂×C₈	—	236	2	no	—
194	C₂×C₈	—	236	2	no	—
195	C₄⋊C₄	—	59	4	no	—
196	C₄⋊C₄	—	118	4	no	—
197	C₄⋊C₄	—	118	2	no	—
198	C₄⋊C₄	—	236	2	no	—
199	C₄⋊C₄	—	236	2	no	—
200	C₄⋊C₄	—	236	2	no	—
201	C₄⋊C₄	—	236	4	no	—
202	C₄²	—	2	2	no	—
203	C₄²	—	2	2	no	—
204	C₄²	—	2	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	4	1	no	—
207	C₄²	—	4	1	no	—
208	C₄²	—	236	4	no	—
209	C₄²	#11745660	1	2	yes	—
210	C₄²	Dic₂₃₆	1	2	yes	—
211	C₂³	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
212	Q₈	—	236	8	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	118	4	no	—
228	C₂×C₄	—	236	2	no	—
229	C₂×C₄	—	236	2	no	—
230	C₂×C₄	—	236	2	no	—
231	C₂×C₄	—	236	2	no	—
232	C₂×C₄	—	236	2	no	—
233	C₂×C₄	#14273645	1	2	yes	—
234	C₂×C₄	#14273652	1	2	yes	—
235	C₂×C₄	#14273652	1	2	yes	—
236	C₂×C₄	#14273653	1	2	yes	—
237	C₂×C₄	M₁₆×D₅₉	1	2	yes	—
238	C₂×C₄	C₂×#11745660	1	1	yes	characteristic
239	C₂×C₄	C₂×Dic₂₃₆	1	1	yes	characteristic
240	C₂×C₄	#14273752	1	2	yes	—
241	C₈	—	8	2	no	—
242	C₈	—	236	4	no	—
243	C₂²	#16837365	1	1	yes	characteristic
244	C₂²	#16837375	1	1	yes	characteristic
245	C₂²	C₂×#14273645	1	1	yes	characteristic
246	C₂²	C₂×#14273652	1	1	yes	characteristic
247	C₂²	#16837406	1	1	yes	characteristic
248	C₂²	C₂×#14273653	1	1	yes	characteristic
249	C₂²	#16837420	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	2	no	—
253	C₄	—	2	2	no	—
254	C₄	—	2	2	no	—
255	C₄	—	2	2	no	—
256	C₄	—	2	2	no	—
257	C₄	—	2	2	no	—
258	C₄	—	472	2	no	—
259	C₄	—	236	4	no	—
260	C₂	#21422439	1	1	yes	characteristic
261	C₂	#21422526	1	1	yes	characteristic
262	C₂	#21422538	1	1	yes	characteristic
263	C₂	#21422596	1	1	yes	characteristic
264	C₂	#21422642	1	1	yes	characteristic
265	C₂	#21422712	1	1	yes	characteristic
266	C₂	#21422780	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#14273727

C₂

yes

maximal, characteristic

#21423949

C₂

yes

maximal, characteristic

#21421920

C₂

yes

maximal

C₅₉×#1839

C₂

yes

maximal, characteristic

C₂×#14273727

C₄

yes

characteristic

C₂×C₄×Dic₁₁₈

—

C₂×C₄⋊(C₅₉⋊C₈)

—

—

—

—

C₂²

yes

—

#16837272

C₄

yes

characteristic

C₄×C₄⋊Dic₅₉

—

C₄×C₄⋊Dic₅₉

C₄

yes

—

#16837157

C₂²

yes

—

C₄³×C₅₉

C₂²

yes

characteristic

C₅₉×#336

—

C₅₉×#336

—

C₅₉×#336

C₂²

yes

—

C₂²×Dic₁₁₈

—

C₂²×C₅₉⋊C₈

—

#14273727

—

C₄×Dic₁₁₈

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

C₂×C₄

yes

—

C₂×C₄⋊Dic₅₉

C₂×C₄

yes

—

C₂×Dic₅₉⋊C₄

—

C₂×C₄×Dic₅₉

—

C₄⋊(C₅₉⋊C₈)

—

#14273638

—

C₅₉⋊#95

—

C₅₉⋊#95

—

C₂²×C₈×C₅₉

—

C₂×C₄²×C₅₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₅₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₅₉

D₄

yes

characteristic

C₂×C₄²×C₅₉

D₄

yes

characteristic

C₂×C₄²×C₅₉

D₄

yes

characteristic

C₂×C₄²×C₅₉

D₄

yes

characteristic

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₂²×C₄×C₅₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

SD₁₆

yes

—

C₄²×C₅₉

Q₁₆

yes

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

M₁₆

yes

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#101

yes

—

C₂×C₄×C₅₉

#103

yes

—

C₂×C₄×C₅₉

#103

yes

—

C₂×C₄×C₅₉

#104

yes

—

C₂×C₄×C₅₉

C₂×M₁₆

yes

—

C₂×C₄×C₅₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₅₉

AGL(1,ℤ/8)

yes

—

100

C₂×Dic₅₉

—

101

C₂×Dic₅₉

—

102

C₂×Dic₅₉

—

103

C₂×Dic₅₉

—

104

C₂×Dic₅₉

—

105

C₂×Dic₅₉

—

106

Dic₁₁₈

—

107

C₈×C₅₉

—

108

C₅₉⋊C₈

—

109

#7622

—

maximal, Sylow

110

C₂²×C₅₉

#407

yes

characteristic

111

C₂²×C₅₉

#410

yes

characteristic

112

C₂²×C₅₉

C₂×#101

yes

characteristic

113

C₂²×C₅₉

C₂×#103

yes

characteristic

114

C₂²×C₅₉

#418

yes

characteristic

115

C₂²×C₅₉

C₂×#104

yes

characteristic

116

C₂²×C₅₉

#421

yes

characteristic

117

C₄×C₅₉

—

118

C₄×C₅₉

—

119

C₄×C₅₉

—

120

C₄×C₅₉

—

121

C₄×C₅₉

—

122

C₄×C₅₉

—

123

C₄×C₅₉

—

124

C₄×C₅₉

—

125

Dic₅₉

—

126

Dic₅₉

—

127

C₄×C₄⋊Q₈

—

128

#1839

D₅₉

yes

characteristic

129

#1767

—

130

#1271

—

131

C₂×C₅₉

#1467

yes

characteristic

132

C₂×C₅₉

#1487

yes

characteristic

133

C₂×C₅₉

#1490

yes

characteristic

134

C₂×C₅₉

#1503

yes

characteristic

135

C₂×C₅₉

#1514

yes

characteristic

136

C₂×C₅₉

#1531

yes

characteristic

137

C₂×C₅₉

#1549

yes

characteristic

138

C₂×C₄⋊Q₈

—

139

C₂×C₄×Q₈

—

118

—

140

C₂×C₄⋊C₈

—

118

—

141

C₂×#97

—

118

—

142

#391

—

118

—

143

#389

—

144

#389

—

118

—

145

#384

—

146

C₄×C₄⋊C₄

—

147

C₄×C₄⋊C₄

—

118

—

148

C₄³

C₂×D₅₉

yes

characteristic

149

#336

—

150

#336

—

151

#336

—

152

#336

C₂×D₅₉

yes

—

153

C₅₉

#7622

yes

characteristic, complemented, Sylow

154

C₂²×Q₈

—

118

—

155

C₂²×C₈

—

156

C₂²×C₈

—

118

—

157

C₄⋊Q₈

—

118

—

158

C₄×Q₈

—

236

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

118

—

162

C₂×C₄⋊C₄

—

118

—

163

C₂×C₄⋊C₄

—

118

—

164

C₂×C₄⋊C₄

—

118

—

165

C₂×C₄²

—

118

—

166

C₂×C₄²

C₄×D₅₉

yes

characteristic

167

C₂×C₄²

C₄×D₅₉

yes

characteristic

168

C₂×C₄²

D₂₃₆

yes

characteristic

169

C₂×C₄²

D₂₃₆

yes

characteristic

170

C₂×C₄²

C₂²⋊D₅₉

yes

characteristic

171

C₂×C₄²

C₂²⋊D₅₉

yes

characteristic

172

C₂×C₄²

C₂²×D₅₉

yes

characteristic

173

C₄⋊C₈

—

118

—

174

#97

—

236

—

175

#95

—

118

—

176

#95

—

118

—

177

C₂×Q₈

—

118

—

178

C₂×Q₈

—

236

—

179

C₂×Q₈

—

236

—

180

C₂²×C₄

—

118

—

181

C₂²×C₄

—

118

—

182

C₂²×C₄

(C₂×D₅₉)⋊C₄

yes

characteristic

183

C₂²×C₄

(C₂×D₅₉)⋊C₄

yes

characteristic

184

C₂²×C₄

(C₂×D₅₉)⋊C₄

yes

characteristic

185

C₂²×C₄

(C₂×D₅₉)⋊C₄

yes

characteristic

186

C₂²×C₄

C₂×C₄×D₅₉

yes

characteristic

187

C₂²×C₄

C₂×D₂₃₆

yes

characteristic

188

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

118

—

193

C₂×C₈

—

236

—

194

C₂×C₈

—

236

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

118

—

197

C₄⋊C₄

—

118

—

198

C₄⋊C₄

—

236

—

199

C₄⋊C₄

—

236

—

200

C₄⋊C₄

—

236

—

201

C₄⋊C₄

—

236

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

236

—

209

C₄²

#11745660

yes

—

210

C₄²

Dic₂₃₆

yes

—

211

C₂³

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

212

Q₈

—

236

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

118

—

228

C₂×C₄

—

236

—

229

C₂×C₄

—

236

—

230

C₂×C₄

—

236

—

231

C₂×C₄

—

236

—

232

C₂×C₄

—

236

—

233

C₂×C₄

#14273645

yes

—

234

C₂×C₄

#14273652

yes

—

235

C₂×C₄

#14273652

yes

—

236

C₂×C₄

#14273653

yes

—

237

C₂×C₄

M₁₆×D₅₉

yes

—

238

C₂×C₄

C₂×#11745660

yes

characteristic

239

C₂×C₄

C₂×Dic₂₃₆

yes

characteristic

240

C₂×C₄

#14273752

yes

—

241

C₈

—

242

C₈

—

236

—

243

C₂²

#16837365

yes

characteristic

244

C₂²

#16837375

yes

characteristic

245

C₂²

C₂×#14273645

yes

characteristic

246

C₂²

C₂×#14273652

yes

characteristic

247

C₂²

#16837406

yes

characteristic

248

C₂²

C₂×#14273653

yes

characteristic

249

C₂²

#16837420

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

472

—

259

C₄

—

236

—

260

C₂

#21422439

yes

characteristic

261

C₂

#21422526

yes

characteristic

262

C₂

#21422538

yes

characteristic

263

C₂

#21422596

yes

characteristic

264

C₂

#21422642

yes

characteristic

265

C₂

#21422712

yes

characteristic

266

C₂

#21422780

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₅₉)⋊C₄
commutator	C₂²×C₄×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1839	C₂
socle, prime radical	C₂³×C₅₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1839	D₅₉
hypocenter	C₅₉	#7622
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

subgroup

G/H

center

C₂³

C₂×(C₂×D₅₉)⋊C₄

commutator

C₂²×C₄×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1839

C₂

socle, prime radical

C₂³×C₅₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂²×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

N	H ≅ G/N	type
153. C₅₉	#7622	semidirect

H ≅ G/N

type

153. C₅₉

#7622

semidirect

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

subgroup	index
C₄×#14273727	2
#21423949	2
#21421920	2
C₅₉×#1839	2
#7622	59

subgroup

index

C₅₉×#1839

Subgroups — #28476896

Conjugacy classes of subgroups

Complements

Maximal subgroups