Group #28487126 — subgroups

Subgroups — #28487126

Order 15104.

338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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	#21425072	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×Dic₅₉	C₂	1	1	yes	maximal, characteristic
3	#21422868	C₂	1	1	yes	maximal, characteristic
4	#21422754	C₂	1	1	yes	maximal, characteristic
5	#21422500	C₂	1	1	yes	maximal, characteristic
6	#21421928	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1301	C₂	1	1	yes	maximal, characteristic
8	#16837959	C₂²	1	1	yes	characteristic
9	#16837455	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₈×Dic₅₉	—	2	1	no	—
12	C₄²×Dic₅₉	C₂²	1	1	yes	characteristic
13	#16837163	—	2	1	no	—
14	#16837163	—	2	1	no	—
15	#16837156	—	2	1	no	—
16	#16837152	—	2	2	no	—
17	#16837150	C₄	1	2	yes	complemented
18	#16837147	C₄	1	2	yes	complemented
19	#16837134	—	2	2	no	—
20	C₅₉×#431	C₂²	1	1	yes	characteristic
21	C₅₉×#423	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₂²×C₅₉⋊C₈	—	2	1	no	—
24	#14273727	C₂×C₄	1	1	yes	characteristic
25	#14273727	C₂×C₄	1	1	yes	characteristic
26	#14273719	—	2	1	no	—
27	#14273706	—	2	1	no	—
28	#14273706	—	2	1	no	—
29	C₄×Dic₁₁₈	—	2	1	no	—
30	C₄×Dic₁₁₈	—	2	1	no	—
31	#14273686	—	2	1	no	—
32	C₂×C₄×Dic₅₉	—	2	1	no	—
33	C₂×C₄×Dic₅₉	—	2	1	no	—
34	C₂×C₄×Dic₅₉	D₄	1	1	yes	characteristic
35	C₂×C₄×Dic₅₉	D₄	1	1	yes	characteristic
36	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
37	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
38	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
39	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
40	C₄×C₅₉⋊C₈	—	2	1	no	—
41	C₈×Dic₅₉	—	4	2	no	—
42	C₂×M₁₆×C₅₉	—	2	1	no	—
43	C₂²×C₈×C₅₉	—	2	1	no	—
44	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
45	C₄⋊C₈×C₅₉	—	2	1	no	—
46	C₄⋊C₈×C₅₉	—	2	1	no	—
47	C₄⋊C₈×C₅₉	—	2	1	no	—
48	C₄⋊C₈×C₅₉	—	2	1	no	—
49	C₄⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
50	C₂²⋊C₈×C₅₉	—	2	1	no	—
51	C₄×C₈×C₅₉	—	2	1	no	—
52	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
54	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
55	C₂²×Dic₅₉	—	2	1	no	—
56	C₂²×Dic₅₉	—	2	1	no	—
57	C₂×Dic₁₁₈	—	2	1	no	—
58	C₂×Dic₁₁₈	—	2	1	no	—
59	M₁₆×C₅₉	—	4	1	no	—
60	M₁₆×C₅₉	—	4	1	no	—
61	C₂×C₈×C₅₉	—	2	2	no	—
62	C₂×C₈×C₅₉	—	4	1	no	—
63	C₂×C₈×C₅₉	—	4	1	no	—
64	C₂×C₈×C₅₉	—	4	1	no	—
65	C₂×C₈×C₅₉	—	4	1	no	—
66	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₅₉	#41	1	1	yes	characteristic
69	C₄²×C₅₉	#41	1	1	yes	characteristic
70	C₂²⋊Dic₅₉	—	4	1	no	—
71	C₄⋊Dic₅₉	—	2	1	no	—
72	C₄⋊Dic₅₉	—	2	1	no	—
73	C₄⋊Dic₅₉	—	2	1	no	—
74	C₄⋊Dic₅₉	—	2	1	no	—
75	Dic₅₉⋊C₄	—	4	1	no	—
76	Dic₅₉⋊C₄	—	4	1	no	—
77	C₄×Dic₅₉	—	2	4	no	—
78	C₄×Dic₅₉	—	2	1	no	—
79	C₄×Dic₅₉	—	2	1	no	—
80	C₄×Dic₅₉	—	2	1	no	—
81	C₄×Dic₅₉	—	4	2	no	—
82	C₄×Dic₅₉	—	4	1	no	—
83	C₄×Dic₅₉	SD₁₆	1	2	yes	—
84	C₂×C₅₉⋊C₈	—	2	2	no	—
85	C₂×C₅₉⋊C₈	—	2	2	no	—
86	C₂×C₅₉⋊C₈	—	4	1	no	—
87	C₂×C₅₉⋊C₈	—	4	1	no	—
88	C₂³×C₅₉	#123	1	1	yes	characteristic
89	C₂×C₄×C₅₉	—	2	2	no	—
90	C₂×C₄×C₅₉	—	4	1	no	—
91	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
92	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
93	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
95	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
96	C₂×C₄×C₅₉	#126	1	1	yes	characteristic
97	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
99	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
100	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
101	C₂×Dic₅₉	—	2	2	no	—
102	C₂×Dic₅₉	—	2	2	no	—
103	C₂×Dic₅₉	—	2	2	no	—
104	C₂×Dic₅₉	—	2	2	no	—
105	C₂×Dic₅₉	—	4	1	no	—
106	C₂×Dic₅₉	—	4	1	no	—
107	C₂×Dic₅₉	—	4	1	no	—
108	C₂×Dic₅₉	—	4	1	no	—
109	Dic₁₁₈	—	4	2	no	—
110	Dic₁₁₈	—	8	1	no	—
111	C₈×C₅₉	—	4	2	no	—
112	C₈×C₅₉	—	8	1	no	—
113	C₈×C₅₉	—	8	1	no	—
114	C₅₉⋊C₈	—	4	2	no	—
115	C₅₉⋊C₈	—	4	2	no	—
116	#9579	—	59	1	no	maximal, Sylow
117	C₂²×C₅₉	—	2	1	no	—
118	C₂²×C₅₉	—	2	1	no	—
119	C₂²×C₅₉	#388	1	1	yes	characteristic
120	C₂²×C₅₉	#483	1	1	yes	characteristic
121	C₂²×C₅₉	#485	1	1	yes	characteristic
122	C₄×C₅₉	—	2	1	no	—
123	C₄×C₅₉	—	2	1	no	—
124	C₄×C₅₉	—	2	1	no	—
125	C₄×C₅₉	C₄×SD₁₆	1	1	yes	characteristic
126	C₄×C₅₉	#441	1	1	yes	characteristic
127	C₄×C₅₉	#443	1	2	yes	—
128	C₄×C₅₉	#461	1	1	yes	characteristic
129	C₄×C₅₉	#464	1	1	yes	characteristic
130	Dic₅₉	—	2	4	no	—
131	Dic₅₉	—	4	2	no	—
132	Dic₅₉	—	8	1	no	—
133	Dic₅₉	—	8	1	no	—
134	#1994	—	59	1	no	—
135	C₄×C₄⋊C₈	—	59	1	no	—
136	#1570	—	59	1	no	—
137	#1542	—	59	1	no	—
138	#1481	—	59	1	no	—
139	#1301	D₅₉	1	1	yes	characteristic
140	#1276	—	59	1	no	—
141	C₂×C₅₉	—	2	1	no	—
142	C₂×C₅₉	—	2	1	no	—
143	C₂×C₅₉	#1927	1	1	yes	characteristic
144	C₂×C₅₉	#1932	1	1	yes	characteristic
145	C₂×C₅₉	#1937	1	1	yes	characteristic
146	#533	—	59	1	no	—
147	#431	—	59	1	no	—
148	#431	C₂×D₅₉	1	1	yes	characteristic
149	#423	C₂×D₅₉	1	1	yes	characteristic
150	C₂×C₄⋊C₈	—	59	1	no	—
151	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
152	C₂×C₄×C₈	—	118	1	no	—
153	C₄³	—	59	1	no	—
154	#339	—	118	1	no	—
155	#339	—	118	1	no	—
156	#336	—	118	1	no	—
157	#334	—	118	2	no	—
158	#333	—	59	2	no	—
159	#332	—	59	2	no	—
160	Q₈⋊C₈	—	118	2	no	—
161	C₅₉	#9579	1	1	yes	characteristic, complemented, Sylow
162	C₂×M₁₆	—	2	1	no	—
163	C₂²×C₈	—	2	1	no	—
164	C₂²×C₈	—	118	1	no	—
165	C₄⋊Q₈	—	59	1	no	—
166	C₄⋊Q₈	—	59	1	no	—
167	#125	—	118	1	no	—
168	C₂²⋊Q₈	—	118	1	no	—
169	C₂²⋊Q₈	—	118	1	no	—
170	C₄×Q₈	—	118	1	no	—
171	C₄×Q₈	—	118	1	no	—
172	#117	—	118	1	no	—
173	C₂×C₄²	—	59	1	no	—
174	C₂×C₄²	—	59	1	no	—
175	C₂×C₄²	—	118	1	no	—
176	C₂×C₄²	—	118	1	no	—
177	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
178	C₄⋊C₈	—	2	1	no	—
179	C₄⋊C₈	—	2	1	no	—
180	C₄⋊C₈	—	2	1	no	—
181	C₄⋊C₈	—	2	1	no	—
182	C₄⋊C₈	—	59	2	no	—
183	C₄⋊C₈	—	59	2	no	—
184	C₄⋊C₈	—	118	1	no	—
185	C₄⋊C₈	C₄×D₅₉	1	2	yes	—
186	C₂²⋊C₈	—	2	1	no	—
187	C₂²⋊C₈	—	118	1	no	—
188	C₄×C₈	—	2	1	no	—
189	C₄×C₈	—	118	1	no	—
190	C₄×C₈	—	236	2	no	—
191	C₂×Q₈	—	118	1	no	—
192	C₂×Q₈	—	118	1	no	—
193	C₂²×C₄	—	118	1	no	—
194	C₂²×C₄	—	118	1	no	—
195	C₂²×C₄	#11745685	1	1	yes	characteristic
196	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
197	C₂²×C₄	#11745689	1	1	yes	characteristic
198	M₁₆	—	4	1	no	—
199	M₁₆	—	4	1	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	4	1	no	—
202	C₂×C₈	—	4	1	no	—
203	C₂×C₈	—	4	1	no	—
204	C₂×C₈	—	4	1	no	—
205	C₂×C₈	—	118	2	no	—
206	C₂×C₈	—	118	2	no	—
207	C₂×C₈	—	236	1	no	—
208	C₂×C₈	—	236	1	no	—
209	C₄⋊C₄	—	118	1	no	—
210	C₄⋊C₄	—	118	1	no	—
211	C₄⋊C₄	—	118	1	no	—
212	C₄⋊C₄	—	118	1	no	—
213	C₄⋊C₄	—	236	1	no	—
214	C₄⋊C₄	—	236	1	no	—
215	C₂²⋊C₄	—	236	1	no	—
216	C₄²	—	59	2	no	—
217	C₄²	—	118	4	no	—
218	C₄²	—	118	1	no	—
219	C₄²	—	118	1	no	—
220	C₄²	—	118	1	no	—
221	C₄²	—	236	2	no	—
222	C₄²	—	236	1	no	—
223	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
224	C₄²	#11745685	1	1	yes	characteristic
225	C₄²	D₄×D₅₉	1	1	yes	characteristic
226	C₄²	#11745687	1	1	yes	characteristic
227	C₂³	#14273712	1	1	yes	characteristic
228	Q₈	—	472	1	no	—
229	Q₈	—	236	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	4	1	no	—
232	C₂×C₄	—	118	2	no	—
233	C₂×C₄	—	118	2	no	—
234	C₂×C₄	—	118	2	no	—
235	C₂×C₄	—	118	2	no	—
236	C₂×C₄	—	236	1	no	—
237	C₂×C₄	—	236	1	no	—
238	C₂×C₄	—	236	1	no	—
239	C₂×C₄	—	236	1	no	—
240	C₂×C₄	#14273684	1	1	yes	characteristic
241	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
242	C₂×C₄	#14273689	1	1	yes	characteristic
243	C₂×C₄	#14273700	1	1	yes	characteristic
244	C₂×C₄	#14273713	1	1	yes	characteristic
245	C₂×C₄	#14273722	1	1	yes	characteristic
246	C₂×C₄	SD₁₆×D₅₉	1	1	yes	characteristic
247	C₂×C₄	#14273746	1	1	yes	characteristic
248	C₂×C₄	#14273756	1	1	yes	characteristic
249	C₂×C₄	#14273759	1	1	yes	characteristic
250	C₈	—	4	2	no	—
251	C₈	—	8	1	no	—
252	C₈	—	8	1	no	—
253	C₈	—	236	2	no	—
254	C₈	—	236	2	no	—
255	C₂²	—	2	1	no	—
256	C₂²	—	2	1	no	—
257	C₂²	#16837291	1	1	yes	characteristic
258	C₂²	#16837734	1	1	yes	characteristic
259	C₂²	#16837745	1	1	yes	characteristic
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	2	1	no	—
263	C₄	—	118	4	no	—
264	C₄	—	472	1	no	—
265	C₄	—	472	1	no	—
266	C₄	—	236	2	no	—
267	C₄	#16837493	1	1	yes	characteristic
268	C₄	#16837506	1	1	yes	characteristic
269	C₄	#16837518	1	2	yes	—
270	C₄	#16837606	1	1	yes	characteristic
271	C₄	#16837623	1	1	yes	characteristic
272	C₂	—	2	1	no	—
273	C₂	—	2	1	no	—
274	C₂	#21424728	1	1	yes	characteristic
275	C₂	#21424763	1	1	yes	characteristic
276	C₂	#21424798	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21425072

C₂

yes

maximal, characteristic

C₄⋊C₈×Dic₅₉

C₂

yes

maximal, characteristic

#21422868

C₂

yes

maximal, characteristic

#21422754

C₂

yes

maximal, characteristic

#21422500

C₂

yes

maximal, characteristic

#21421928

C₂

yes

maximal, characteristic

C₅₉×#1301

C₂

yes

maximal, characteristic

#16837959

C₂²

yes

characteristic

#16837455

C₂²

yes

characteristic

C₂×C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

C₂×C₈×Dic₅₉

—

C₄²×Dic₅₉

C₂²

yes

—

—

—

—

C₄

yes

complemented

#16837147

C₄

yes

complemented

#16837134

—

C₅₉×#431

C₂²

yes

characteristic

C₅₉×#423

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₅₉

C₂²

yes

characteristic

C₂²×C₅₉⋊C₈

—

#14273727

C₂×C₄

yes

characteristic

#14273727

C₂×C₄

yes

—

—

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

—

#14273686

—

C₂×C₄×Dic₅₉

—

C₂×C₄×Dic₅₉

—

C₂×C₄×Dic₅₉

D₄

yes

characteristic

C₂×C₄×Dic₅₉

D₄

yes

characteristic

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

C₂×C₄

yes

—

C₄⋊(C₅₉⋊C₈)

D₄

yes

—

C₂²⋊(C₅₉⋊C₈)

—

C₄×C₅₉⋊C₈

—

C₈×Dic₅₉

—

C₂×M₁₆×C₅₉

—

C₂²×C₈×C₅₉

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

C₂×C₄

yes

—

C₂²⋊C₈×C₅₉

—

C₄×C₈×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

C₂²×C₄×C₅₉

yes

C₂²×C₄×C₅₉

yes

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄²×C₅₉

C₂²×C₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

C₄²×C₅₉

yes

C₄²×C₅₉

yes

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

SD₁₆

yes

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

#123

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#117

yes

characteristic

C₂×C₄×C₅₉

C₄×D₄

yes

characteristic

C₂×C₄×C₅₉

C₄×D₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

C₂×SD₁₆

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

100

C₂×C₄×C₅₉

#137

yes

characteristic

101

C₂×Dic₅₉

—

102

C₂×Dic₅₉

—

103

C₂×Dic₅₉

—

104

C₂×Dic₅₉

—

105

C₂×Dic₅₉

—

106

C₂×Dic₅₉

—

107

C₂×Dic₅₉

—

108

C₂×Dic₅₉

—

109

Dic₁₁₈

—

110

Dic₁₁₈

—

111

C₈×C₅₉

—

112

C₈×C₅₉

—

113

C₈×C₅₉

—

114

C₅₉⋊C₈

—

115

C₅₉⋊C₈

—

116

#9579

—

maximal, Sylow

117

C₂²×C₅₉

—

118

C₂²×C₅₉

—

119

C₂²×C₅₉

#388

yes

characteristic

120

C₂²×C₅₉

#483

yes

characteristic

121

C₂²×C₅₉

#485

yes

characteristic

122

C₄×C₅₉

—

123

C₄×C₅₉

—

124

C₄×C₅₉

—

125

C₄×C₅₉

C₄×SD₁₆

yes

characteristic

126

C₄×C₅₉

#441

yes

characteristic

127

C₄×C₅₉

#443

yes

—

128

C₄×C₅₉

#461

yes

characteristic

129

C₄×C₅₉

#464

yes

characteristic

130

Dic₅₉

—

131

Dic₅₉

—

132

Dic₅₉

—

133

Dic₅₉

—

134

#1994

—

135

C₄×C₄⋊C₈

—

136

#1570

—

137

#1542

—

138

#1481

—

139

#1301

D₅₉

yes

characteristic

140

#1276

—

141

C₂×C₅₉

—

142

C₂×C₅₉

—

143

C₂×C₅₉

#1927

yes

characteristic

144

C₂×C₅₉

#1932

yes

characteristic

145

C₂×C₅₉

#1937

yes

characteristic

146

#533

—

147

#431

—

148

#431

C₂×D₅₉

yes

characteristic

149

#423

C₂×D₅₉

yes

characteristic

150

C₂×C₄⋊C₈

—

151

C₂×C₄⋊C₈

C₂×D₅₉

yes

characteristic

152

C₂×C₄×C₈

—

118

—

153

C₄³

—

154

#339

—

118

—

155

#339

—

118

—

156

#336

—

118

—

157

#334

—

118

—

158

#333

—

159

#332

—

160

Q₈⋊C₈

—

118

—

161

C₅₉

#9579

yes

characteristic, complemented, Sylow

162

C₂×M₁₆

—

163

C₂²×C₈

—

164

C₂²×C₈

—

118

—

165

C₄⋊Q₈

—

166

C₄⋊Q₈

—

167

#125

—

118

—

168

C₂²⋊Q₈

—

118

—

169

C₂²⋊Q₈

—

118

—

170

C₄×Q₈

—

118

—

171

C₄×Q₈

—

118

—

172

#117

—

118

—

173

C₂×C₄²

—

174

C₂×C₄²

—

175

C₂×C₄²

—

118

—

176

C₂×C₄²

—

118

—

177

C₂×C₄²

C₂²×D₅₉

yes

characteristic

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

118

—

185

C₄⋊C₈

C₄×D₅₉

yes

—

186

C₂²⋊C₈

—

187

C₂²⋊C₈

—

118

—

188

C₄×C₈

—

189

C₄×C₈

—

118

—

190

C₄×C₈

—

236

—

191

C₂×Q₈

—

118

—

192

C₂×Q₈

—

118

—

193

C₂²×C₄

—

118

—

194

C₂²×C₄

—

118

—

195

C₂²×C₄

#11745685

yes

characteristic

196

C₂²×C₄

D₄×D₅₉

yes

characteristic

197

C₂²×C₄

#11745689

yes

characteristic

198

M₁₆

—

199

M₁₆

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

118

—

206

C₂×C₈

—

118

—

207

C₂×C₈

—

236

—

208

C₂×C₈

—

236

—

209

C₄⋊C₄

—

118

—

210

C₄⋊C₄

—

118

—

211

C₄⋊C₄

—

118

—

212

C₄⋊C₄

—

118

—

213

C₄⋊C₄

—

236

—

214

C₄⋊C₄

—

236

—

215

C₂²⋊C₄

—

236

—

216

C₄²

—

217

C₄²

—

118

—

218

C₄²

—

118

—

219

C₄²

—

118

—

220

C₄²

—

118

—

221

C₄²

—

236

—

222

C₄²

—

236

—

223

C₄²

C₂×C₄×D₅₉

yes

characteristic

224

C₄²

#11745685

yes

characteristic

225

C₄²

D₄×D₅₉

yes

characteristic

226

C₄²

#11745687

yes

characteristic

227

C₂³

#14273712

yes

characteristic

228

Q₈

—

472

—

229

Q₈

—

236

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

118

—

233

C₂×C₄

—

118

—

234

C₂×C₄

—

118

—

235

C₂×C₄

—

118

—

236

C₂×C₄

—

236

—

237

C₂×C₄

—

236

—

238

C₂×C₄

—

236

—

239

C₂×C₄

—

236

—

240

C₂×C₄

#14273684

yes

characteristic

241

C₂×C₄

(C₂²⋊D₅₉)⋊C₄

yes

characteristic

242

C₂×C₄

#14273689

yes

characteristic

243

C₂×C₄

#14273700

yes

characteristic

244

C₂×C₄

#14273713

yes

characteristic

245

C₂×C₄

#14273722

yes

characteristic

246

C₂×C₄

SD₁₆×D₅₉

yes

characteristic

247

C₂×C₄

#14273746

yes

characteristic

248

C₂×C₄

#14273756

yes

characteristic

249

C₂×C₄

#14273759

yes

characteristic

250

C₈

—

251

C₈

—

252

C₈

—

253

C₈

—

236

—

254

C₈

—

236

—

255

C₂²

—

256

C₂²

—

257

C₂²

#16837291

yes

characteristic

258

C₂²

#16837734

yes

characteristic

259

C₂²

#16837745

yes

characteristic

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

118

—

264

C₄

—

472

—

265

C₄

—

472

—

266

C₄

—

236

—

267

C₄

#16837493

yes

characteristic

268

C₄

#16837506

yes

characteristic

269

C₄

#16837518

yes

—

270

C₄

#16837606

yes

characteristic

271

C₄

#16837623

yes

characteristic

272

C₂

—

273

C₂

—

274

C₂

#21424728

yes

characteristic

275

C₂

#21424763

yes

characteristic

276

C₂

#21424798

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14273700
commutator	C₄²×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1301	C₂
socle	C₂²×C₅₉	#388
prime radical	C₂³×C₅₉	#123
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1301	D₅₉
hypocenter	C₅₉	#9579
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

subgroup

G/H

center

C₂×C₄

#14273700

commutator

C₄²×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1301

C₂

C₂²×C₅₉

C₂³×C₅₉

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

N	H ≅ G/N	type
17. #16837150	C₄	semidirect
18. #16837147	C₄	semidirect
161. C₅₉	#9579	semidirect

H ≅ G/N

type

17. #16837150

C₄

semidirect

18. #16837147

C₄

semidirect

161. C₅₉

#9579

semidirect

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

subgroup	index
#21425072	2
C₄⋊C₈×Dic₅₉	2
#21422868	2
#21422754	2
#21422500	2
#21421928	2
C₅₉×#1301	2
#9579	59

subgroup

index

C₄⋊C₈×Dic₅₉

C₅₉×#1301

Subgroups — #28487126

Conjugacy classes of subgroups

Complements

Maximal subgroups