Group #28488145 — subgroups

Subgroups — #28488145

Order 15104.

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×#16837805	C₂	1	1	yes	maximal, characteristic
2	#21424267	C₂	1	1	yes	maximal, characteristic
3	#21422782	C₂	1	1	yes	maximal, characteristic
4	#21422781	C₂	1	1	yes	maximal, characteristic
5	#21422776	C₂	1	1	yes	maximal, characteristic
6	#21422380	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1548	C₂	1	1	yes	maximal, characteristic
8	C₂×#14273727	C₂²	1	1	yes	characteristic
9	#16837805	—	2	1	no	—
10	#16837805	—	2	1	no	—
11	#16837805	C₄	1	4	yes	—
12	#16837455	C₂²	1	1	yes	characteristic
13	C₂×#14273662	—	2	2	no	—
14	C₂×#14273660	—	2	2	no	—
15	#16837426	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
17	#16837150	—	2	2	no	—
18	#16837148	—	2	2	no	—
19	#16837147	—	2	2	no	—
20	#16837124	—	2	1	no	—
21	C₈×C₅₉⋊C₈	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₅₉×#431	C₂²	1	1	yes	characteristic
24	C₅₉×#423	C₂²	1	1	yes	characteristic
25	C₅₉×#333	—	2	2	no	—
26	C₂²×Dic₁₁₈	—	2	1	no	—
27	C₂×#11745664	—	2	1	no	—
28	C₂²×C₅₉⋊C₈	D₄	1	2	yes	—
29	#14273727	—	2	1	no	—
30	#14273727	—	2	1	no	—
31	#14273727	—	2	1	no	—
32	#14273727	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊Dic₅₉	—	2	1	no	—
34	C₂×C₄⋊Dic₅₉	—	2	1	no	—
35	#14273662	—	4	4	no	—
36	#14273660	—	2	4	no	—
37	#14273660	—	2	4	no	—
38	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
39	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
40	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
41	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
42	C₄×C₅₉⋊C₈	—	2	1	no	—
43	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
44	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
45	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₅₉	—	2	1	no	—
47	C₂×M₁₆×C₅₉	—	2	1	no	—
48	C₄⋊Q₈×C₅₉	—	2	1	no	—
49	C₄⋊Q₈×C₅₉	—	2	1	no	—
50	C₄⋊Q₈×C₅₉	—	2	1	no	—
51	C₄⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
54	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
55	C₄⋊C₈×C₅₉	—	2	1	no	—
56	C₄⋊C₈×C₅₉	—	2	1	no	—
57	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
58	C₂²⋊C₈×C₅₉	—	2	1	no	—
59	C₄×C₈×C₅₉	—	2	1	no	—
60	C₂×Q₈×C₅₉	—	2	2	no	—
61	C₂×Q₈×C₅₉	—	4	1	no	—
62	C₂×Q₈×C₅₉	—	8	2	no	—
63	C₂²×C₄×C₅₉	—	4	1	no	—
64	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
66	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
67	C₂²×Dic₅₉	—	4	1	no	—
68	C₂×Dic₁₁₈	—	2	2	no	—
69	C₂×Dic₁₁₈	—	4	1	no	—
70	C₂×Dic₁₁₈	—	8	2	no	—
71	M₁₆×C₅₉	—	4	2	no	—
72	C₂×C₈×C₅₉	—	2	2	no	—
73	C₂×C₈×C₅₉	—	4	1	no	—
74	C₄⋊C₄×C₅₉	—	2	2	no	—
75	C₄⋊C₄×C₅₉	—	2	2	no	—
76	C₄⋊C₄×C₅₉	—	4	1	no	—
77	C₄⋊C₄×C₅₉	—	4	1	no	—
78	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
79	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
82	C₄⋊Dic₅₉	—	2	2	no	—
83	C₄⋊Dic₅₉	—	2	2	no	—
84	C₄⋊Dic₅₉	—	4	1	no	—
85	C₄⋊Dic₅₉	—	4	1	no	—
86	#11745664	—	4	2	no	—
87	C₂×C₅₉⋊C₈	—	2	2	no	—
88	C₂×C₅₉⋊C₈	—	4	1	no	—
89	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	2	yes	—
90	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	2	yes	—
91	C₂×C₅₉⋊C₈	SD₁₆	1	4	yes	—
92	C₂×C₅₉⋊C₈	Q₁₆	1	4	yes	—
93	C₂³×C₅₉	#124	1	1	yes	characteristic
94	Q₈×C₅₉	—	8	2	no	—
95	Q₈×C₅₉	—	8	2	no	—
96	C₂×C₄×C₅₉	—	2	2	no	—
97	C₂×C₄×C₅₉	—	2	2	no	—
98	C₂×C₄×C₅₉	—	4	2	no	—
99	C₂×C₄×C₅₉	—	8	2	no	—
100	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
102	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
103	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
104	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
105	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
106	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
107	C₂×C₄×C₅₉	C₂×Q₁₆	1	2	yes	—
108	C₂×Dic₅₉	—	4	2	no	—
109	C₂×Dic₅₉	—	8	2	no	—
110	Dic₁₁₈	—	8	2	no	—
111	Dic₁₁₈	—	8	2	no	—
112	C₈×C₅₉	—	4	2	no	—
113	C₈×C₅₉	—	8	1	no	—
114	C₅₉⋊C₈	—	4	2	no	—
115	C₅₉⋊C₈	—	8	1	no	—
116	C₅₉⋊C₈	#103	1	4	yes	—
117	C₅₉⋊C₈	#103	1	4	yes	—
118	#9771	—	59	1	no	maximal, Sylow
119	C₂²×C₅₉	—	2	1	no	—
120	C₂²×C₅₉	—	2	1	no	—
121	C₂²×C₅₉	#390	1	1	yes	characteristic
122	C₂²×C₅₉	#487	1	2	yes	—
123	C₄×C₅₉	—	2	1	no	—
124	C₄×C₅₉	—	2	1	no	—
125	C₄×C₅₉	—	8	2	no	—
126	C₄×C₅₉	C₂×#103	1	2	yes	—
127	C₄×C₅₉	#472	1	2	yes	—
128	C₄×C₅₉	#473	1	2	yes	—
129	C₄×C₅₉	#492	1	1	yes	characteristic
130	C₄×C₅₉	#494	1	1	yes	characteristic
131	Dic₅₉	—	8	2	no	—
132	C₂×#500	—	59	1	no	—
133	#1848	—	59	1	no	—
134	#1549	—	59	1	no	—
135	#1549	—	59	1	no	—
136	#1548	—	59	1	no	—
137	#1548	D₅₉	1	1	yes	characteristic
138	#1450	—	59	1	no	—
139	C₂×C₅₉	—	2	2	no	—
140	C₂×C₅₉	#1956	1	1	yes	characteristic
141	C₂×C₅₉	#1978	1	1	yes	characteristic
142	C₂×C₅₉	#1979	1	1	yes	characteristic
143	C₂×C₄⋊Q₈	—	59	1	no	—
144	C₂×C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
145	#500	—	59	4	no	—
146	#500	—	118	1	no	—
147	#500	—	118	1	no	—
148	#431	—	59	1	no	—
149	#431	C₂×D₅₉	1	1	yes	characteristic
150	C₂×#108	—	118	2	no	—
151	C₂×#107	—	118	2	no	—
152	#423	—	59	1	no	—
153	#423	C₂×D₅₉	1	1	yes	characteristic
154	C₂×C₄×C₈	—	59	1	no	—
155	#333	—	2	2	no	—
156	#333	—	118	2	no	—
157	#332	—	118	2	no	—
158	#332	—	118	2	no	—
159	#322	—	118	1	no	—
160	C₈²	—	118	1	no	—
161	C₅₉	#9771	1	1	yes	characteristic, complemented, Sylow
162	C₂²×Q₈	—	2	1	no	—
163	C₂²×Q₈	—	118	1	no	—
164	C₂×M₁₆	—	2	1	no	—
165	C₂×M₁₆	—	118	1	no	—
166	C₂²×C₈	—	59	2	no	—
167	C₄⋊Q₈	—	2	1	no	—
168	C₄⋊Q₈	—	2	1	no	—
169	C₄⋊Q₈	—	2	1	no	—
170	C₄⋊Q₈	—	59	2	no	—
171	C₄⋊Q₈	—	118	1	no	—
172	C₄⋊Q₈	—	118	1	no	—
173	C₄⋊Q₈	—	118	1	no	—
174	C₄⋊Q₈	C₄×D₅₉	1	2	yes	—
175	C₂×C₄⋊C₄	—	2	1	no	—
176	C₂×C₄⋊C₄	—	2	1	no	—
177	C₂×C₄⋊C₄	—	118	1	no	—
178	C₂×C₄⋊C₄	—	118	1	no	—
179	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
180	#108	—	236	4	no	—
181	#107	—	118	4	no	—
182	#107	—	118	4	no	—
183	C₄⋊C₈	—	2	1	no	—
184	C₄⋊C₈	—	2	1	no	—
185	C₄⋊C₈	—	59	2	no	—
186	C₄⋊C₈	—	118	1	no	—
187	C₄⋊C₈	—	118	1	no	—
188	C₄⋊C₈	C₂²⋊D₅₉	1	2	yes	—
189	C₂²⋊C₈	—	2	1	no	—
190	C₂²⋊C₈	—	118	1	no	—
191	C₄×C₈	—	2	1	no	—
192	C₄×C₈	—	59	2	no	—
193	C₄×C₈	—	59	1	no	—
194	C₄×C₈	—	59	1	no	—
195	C₄×C₈	—	118	1	no	—
196	C₂×Q₈	—	2	2	no	—
197	C₂×Q₈	—	4	1	no	—
198	C₂×Q₈	—	8	2	no	—
199	C₂×Q₈	—	118	2	no	—
200	C₂×Q₈	—	472	2	no	—
201	C₂×Q₈	—	236	1	no	—
202	C₂²×C₄	—	4	1	no	—
203	C₂²×C₄	—	236	1	no	—
204	C₂²×C₄	#11745685	1	1	yes	characteristic
205	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
206	C₂²×C₄	#11745687	1	1	yes	characteristic
207	M₁₆	—	4	2	no	—
208	M₁₆	—	236	2	no	—
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	—	4	1	no	—
211	C₂×C₈	—	59	2	no	—
212	C₂×C₈	—	59	2	no	—
213	C₂×C₈	—	59	4	no	—
214	C₂×C₈	—	59	4	no	—
215	C₂×C₈	—	118	2	no	—
216	C₂×C₈	—	236	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	—	118	2	no	—
222	C₄⋊C₄	—	118	2	no	—
223	C₄⋊C₄	—	236	1	no	—
224	C₄⋊C₄	—	236	1	no	—
225	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
226	C₄²	D₄×D₅₉	1	1	yes	characteristic
227	C₄²	D₄×D₅₉	1	1	yes	characteristic
228	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
229	C₂³	#14273713	1	1	yes	characteristic
230	Q₈	—	8	2	no	—
231	Q₈	—	8	2	no	—
232	Q₈	—	472	2	no	—
233	Q₈	—	472	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	—	472	2	no	—
239	C₂×C₄	—	236	2	no	—
240	C₂×C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
241	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
242	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
243	C₂×C₄	#14273699	1	1	yes	characteristic
244	C₂×C₄	#14273700	1	1	yes	characteristic
245	C₂×C₄	#14273723	1	1	yes	characteristic
246	C₂×C₄	SD₁₆×D₅₉	1	2	yes	—
247	C₂×C₄	Q₁₆×D₅₉	1	2	yes	—
248	C₈	—	4	2	no	—
249	C₈	—	8	1	no	—
250	C₈	—	59	4	no	—
251	C₈	—	59	4	no	—
252	C₈	—	472	1	no	—
253	C₈	—	236	2	no	—
254	C₂²	—	2	1	no	—
255	C₂²	—	2	1	no	—
256	C₂²	#16837302	1	1	yes	characteristic
257	C₂²	#16837751	1	2	yes	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	8	2	no	—
261	C₄	—	472	2	no	—
262	C₄	#103×D₅₉	1	2	yes	—
263	C₄	#16837671	1	2	yes	—
264	C₄	#16837675	1	2	yes	—
265	C₄	#16837773	1	1	yes	characteristic
266	C₄	#16837780	1	1	yes	characteristic
267	C₂	—	2	2	no	—
268	C₂	#21424896	1	1	yes	characteristic
269	C₂	#21425003	1	1	yes	characteristic
270	C₂	#21425010	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837805

C₂

yes

maximal, characteristic

#21424267

C₂

yes

maximal, characteristic

#21422782

C₂

yes

maximal, characteristic

#21422781

C₂

yes

maximal, characteristic

#21422776

C₂

yes

maximal, characteristic

#21422380

C₂

yes

maximal, characteristic

C₅₉×#1548

C₂

yes

maximal, characteristic

C₂×#14273727

C₂²

yes

—

—

C₄

yes

—

#16837455

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×C₄×C₅₉⋊C₈

C₂²

yes

—

—

—

—

C₈×C₅₉⋊C₈

—

C₂×C₄⋊Q₈×C₅₉

C₂²

yes

characteristic

C₅₉×#431

C₂²

yes

characteristic

C₅₉×#423

C₂²

yes

characteristic

C₅₉×#333

—

C₂²×Dic₁₁₈

—

C₂×#11745664

—

C₂²×C₅₉⋊C₈

D₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

#14273662

—

#14273660

—

#14273660

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

D₄

yes

—

C₂²⋊(C₅₉⋊C₈)

—

C₄×C₅₉⋊C₈

—

C₄×C₅₉⋊C₈

C₂×C₄

yes

—

C₄×C₅₉⋊C₈

D₄

yes

characteristic

C₄×C₅₉⋊C₈

D₄

yes

characteristic

C₂²×Q₈×C₅₉

—

C₂×M₁₆×C₅₉

—

C₄⋊Q₈×C₅₉

—

C₄⋊Q₈×C₅₉

—

C₄⋊Q₈×C₅₉

—

C₄⋊Q₈×C₅₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

D₄

yes

—

C₂²⋊C₈×C₅₉

—

C₄×C₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

C₂²×C₄×C₅₉

yes

C₂²×C₄×C₅₉

yes

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

C₂²×C₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₅₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₅₉⋊C₈

SD₁₆

yes

—

C₂×C₅₉⋊C₈

Q₁₆

yes

—

C₂³×C₅₉

#124

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

100

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

101

C₂×C₄×C₅₉

C₄×D₄

yes

characteristic

102

C₂×C₄×C₅₉

C₄×D₄

yes

characteristic

103

C₂×C₄×C₅₉

#121

yes

characteristic

104

C₂×C₄×C₅₉

#121

yes

characteristic

105

C₂×C₄×C₅₉

#127

yes

characteristic

106

C₂×C₄×C₅₉

C₂×SD₁₆

yes

—

107

C₂×C₄×C₅₉

C₂×Q₁₆

yes

—

108

C₂×Dic₅₉

—

109

C₂×Dic₅₉

—

110

Dic₁₁₈

—

111

Dic₁₁₈

—

112

C₈×C₅₉

—

113

C₈×C₅₉

—

114

C₅₉⋊C₈

—

115

C₅₉⋊C₈

—

116

C₅₉⋊C₈

#103

yes

—

117

C₅₉⋊C₈

#103

yes

—

118

#9771

—

maximal, Sylow

119

C₂²×C₅₉

—

120

C₂²×C₅₉

—

121

C₂²×C₅₉

#390

yes

characteristic

122

C₂²×C₅₉

#487

yes

—

123

C₄×C₅₉

—

124

C₄×C₅₉

—

125

C₄×C₅₉

—

126

C₄×C₅₉

C₂×#103

yes

—

127

C₄×C₅₉

#472

yes

—

128

C₄×C₅₉

#473

yes

—

129

C₄×C₅₉

#492

yes

characteristic

130

C₄×C₅₉

#494

yes

characteristic

131

Dic₅₉

—

132

C₂×#500

—

133

#1848

—

134

#1549

—

135

#1549

—

136

#1548

—

137

#1548

D₅₉

yes

characteristic

138

#1450

—

139

C₂×C₅₉

—

140

C₂×C₅₉

#1956

yes

characteristic

141

C₂×C₅₉

#1978

yes

characteristic

142

C₂×C₅₉

#1979

yes

characteristic

143

C₂×C₄⋊Q₈

—

144

C₂×C₄⋊Q₈

C₂×D₅₉

yes

characteristic

145

#500

—

146

#500

—

118

—

147

#500

—

118

—

148

#431

—

149

#431

C₂×D₅₉

yes

characteristic

150

C₂×#108

—

118

—

151

C₂×#107

—

118

—

152

#423

—

153

#423

C₂×D₅₉

yes

characteristic

154

C₂×C₄×C₈

—

155

#333

—

156

#333

—

118

—

157

#332

—

118

—

158

#332

—

118

—

159

#322

—

118

—

160

C₈²

—

118

—

161

C₅₉

#9771

yes

characteristic, complemented, Sylow

162

C₂²×Q₈

—

163

C₂²×Q₈

—

118

—

164

C₂×M₁₆

—

165

C₂×M₁₆

—

118

—

166

C₂²×C₈

—

167

C₄⋊Q₈

—

168

C₄⋊Q₈

—

169

C₄⋊Q₈

—

170

C₄⋊Q₈

—

171

C₄⋊Q₈

—

118

—

172

C₄⋊Q₈

—

118

—

173

C₄⋊Q₈

—

118

—

174

C₄⋊Q₈

C₄×D₅₉

yes

—

175

C₂×C₄⋊C₄

—

176

C₂×C₄⋊C₄

—

177

C₂×C₄⋊C₄

—

118

—

178

C₂×C₄⋊C₄

—

118

—

179

C₂×C₄²

C₂²×D₅₉

yes

characteristic

180

#108

—

236

—

181

#107

—

118

—

182

#107

—

118

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

—

186

C₄⋊C₈

—

118

—

187

C₄⋊C₈

—

118

—

188

C₄⋊C₈

C₂²⋊D₅₉

yes

—

189

C₂²⋊C₈

—

190

C₂²⋊C₈

—

118

—

191

C₄×C₈

—

192

C₄×C₈

—

193

C₄×C₈

—

194

C₄×C₈

—

195

C₄×C₈

—

118

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×Q₈

—

199

C₂×Q₈

—

118

—

200

C₂×Q₈

—

472

—

201

C₂×Q₈

—

236

—

202

C₂²×C₄

—

203

C₂²×C₄

—

236

—

204

C₂²×C₄

#11745685

yes

characteristic

205

C₂²×C₄

D₄×D₅₉

yes

characteristic

206

C₂²×C₄

#11745687

yes

characteristic

207

M₁₆

—

208

M₁₆

—

236

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

118

—

216

C₂×C₈

—

236

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

118

—

222

C₄⋊C₄

—

118

—

223

C₄⋊C₄

—

236

—

224

C₄⋊C₄

—

236

—

225

C₄²

C₂×C₄×D₅₉

yes

characteristic

226

C₄²

D₄×D₅₉

yes

characteristic

227

C₄²

D₄×D₅₉

yes

characteristic

228

C₄²

C₂×C₂²⋊D₅₉

yes

characteristic

229

C₂³

#14273713

yes

characteristic

230

Q₈

—

231

Q₈

—

232

Q₈

—

472

—

233

Q₈

—

472

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

472

—

239

C₂×C₄

—

236

—

240

C₂×C₄

C₂²⋊C₄×D₅₉

yes

characteristic

241

C₂×C₄

(C₂²⋊D₅₉)⋊C₄

yes

characteristic

242

C₂×C₄

C₄×C₂²⋊D₅₉

yes

characteristic

243

C₂×C₄

#14273699

yes

characteristic

244

C₂×C₄

#14273700

yes

characteristic

245

C₂×C₄

#14273723

yes

characteristic

246

C₂×C₄

SD₁₆×D₅₉

yes

—

247

C₂×C₄

Q₁₆×D₅₉

yes

—

248

C₈

—

249

C₈

—

250

C₈

—

251

C₈

—

252

C₈

—

472

—

253

C₈

—

236

—

254

C₂²

—

255

C₂²

—

256

C₂²

#16837302

yes

characteristic

257

C₂²

#16837751

yes

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

472

—

262

C₄

#103×D₅₉

yes

—

263

C₄

#16837671

yes

—

264

C₄

#16837675

yes

—

265

C₄

#16837773

yes

characteristic

266

C₄

#16837780

yes

characteristic

267

C₂

—

268

C₂

#21424896

yes

characteristic

269

C₂

#21425003

yes

characteristic

270

C₂

#21425010

yes

characteristic

	subgroup	G/H
center	C₂²	#16837302
commutator	C₄²×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1548	C₂
socle	C₂²×C₅₉	#390
prime radical	C₂³×C₅₉	#124
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1548	D₅₉
hypocenter	C₅₉	#9771
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

subgroup

G/H

center

C₂²

#16837302

commutator

C₄²×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1548

C₂

C₂²×C₅₉

C₂³×C₅₉

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

N	H ≅ G/N	type
161. C₅₉	#9771	semidirect

H ≅ G/N

type

161. C₅₉

#9771

semidirect

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

subgroup	index
C₂×#16837805	2
#21424267	2
#21422782	2
#21422781	2
#21422776	2
#21422380	2
C₅₉×#1548	2
#9771	59

subgroup

index

C₅₉×#1548

Subgroups — #28488145

Conjugacy classes of subgroups

Complements

Maximal subgroups