Group #28503967 — subgroups

Subgroups — #28503967

Order 15104.

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

normal subgroups only

This group has 422 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	C₂×#16837508	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837219	C₂	1	1	yes	maximal, characteristic
3	#21425815	C₂	1	1	yes	maximal, characteristic
4	C₂×#16837179	C₂	1	1	yes	maximal, characteristic
5	#21423982	C₂	1	1	yes	maximal, characteristic
6	#21422194	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1386	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₂₃₆	C₂²	1	1	yes	characteristic
9	C₂×#14273692	—	2	1	no	—
10	C₂×#14273667	C₂²	1	1	yes	characteristic
11	#16837508	—	2	2	no	—
12	#16837508	C₄	1	4	yes	complemented
13	C₂×#14273663	C₂²	1	1	yes	characteristic
14	C₂×#14273650	—	2	1	no	—
15	#16837358	—	2	1	no	—
16	C₂×#14273637	C₂²	1	1	yes	characteristic
17	#16837219	C₄	1	4	yes	complemented
18	#16837205	C₄	1	4	yes	complemented
19	#16837179	—	2	2	no	—
20	#16837161	—	2	1	no	—
21	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic
22	C₅₉×#427	C₂²	1	1	yes	characteristic
23	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
24	C₂²×Dic₁₁₈	—	2	1	no	—
25	C₂×Dic₂₃₆	—	2	1	no	—
26	C₂×Dic₂₃₆	—	2	1	no	—
27	C₂×Dic₂₃₆	—	2	1	no	—
28	C₂×Dic₂₃₆	C₂×C₄	1	2	yes	—
29	C₂×Dic₂₃₆	C₂×C₄	1	2	yes	—
30	C₂×Dic₂₃₆	C₂×C₄	1	2	yes	—
31	C₂×#11745664	—	2	1	no	—
32	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
33	#14273692	—	2	4	no	—
34	#14273692	—	4	2	no	—
35	C₂×Dic₅₉⋊C₄	—	4	1	no	—
36	C₂×C₄×Dic₅₉	—	4	1	no	—
37	C₂×C₄×Dic₅₉	D₄	1	1	yes	characteristic
38	#14273667	—	2	1	no	—
39	#14273667	—	2	1	no	—
40	C₂×C₅₉⋊C₁₆	C₂×C₄	1	2	yes	—
41	#14273663	—	2	1	no	—
42	#14273663	C₂×C₄	1	2	yes	—
43	#14273650	—	2	4	no	—
44	#14273638	—	4	1	no	—
45	#14273637	C₂×C₄	1	2	yes	—
46	#14273637	D₄	1	2	yes	—
47	C₄×C₅₉⋊C₈	—	4	1	no	—
48	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
49	#117×C₅₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
51	M₃₂×C₅₉	—	2	1	no	—
52	M₃₂×C₅₉	C₂×C₄	1	2	yes	—
53	C₂×C₁₆×C₅₉	—	2	1	no	—
54	#107×C₅₉	C₂×C₄	1	2	yes	—
55	#106×C₅₉	—	2	1	no	—
56	#106×C₅₉	—	2	1	no	—
57	#106×C₅₉	C₂×C₄	1	2	yes	—
58	C₂²×C₄×C₅₉	—	4	1	no	—
59	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×Dic₅₉	—	2	1	no	—
61	C₂²×Dic₅₉	—	4	1	no	—
62	C₂×Dic₁₁₈	—	2	2	no	—
63	C₂×Dic₁₁₈	—	2	2	no	—
64	C₂×Dic₁₁₈	—	2	2	no	—
65	C₂×Dic₁₁₈	—	4	1	no	—
66	C₂×Dic₁₁₈	—	4	1	no	—
67	C₂×Dic₁₁₈	—	4	1	no	—
68	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
73	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
74	C₄⋊C₄×C₅₉	—	2	2	no	—
75	C₄⋊C₄×C₅₉	—	2	2	no	—
76	C₄⋊C₄×C₅₉	—	4	1	no	—
77	C₂²⋊C₄×C₅₉	—	4	1	no	—
78	C₄²×C₅₉	—	4	1	no	—
79	Dic₅₉⋊C₄	—	4	4	no	—
80	C₄×Dic₅₉	—	2	1	no	—
81	C₄×Dic₅₉	—	4	4	no	—
82	C₄×Dic₅₉	C₂²⋊C₄	1	2	yes	—
83	#11745664	—	2	2	no	—
84	#11745664	—	4	1	no	—
85	C₂×C₅₉⋊C₈	—	2	1	no	—
86	C₂×C₅₉⋊C₈	—	2	1	no	—
87	C₂×C₅₉⋊C₈	—	4	1	no	—
88	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	2	yes	—
89	Dic₂₃₆	—	2	2	no	—
90	Dic₂₃₆	—	2	2	no	—
91	Dic₂₃₆	—	2	2	no	—
92	Dic₂₃₆	C₄²	1	4	yes	—
93	C₁₆×C₅₉	—	2	2	no	—
94	C₅₉⋊C₁₆	—	2	2	no	—
95	C₂³×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
96	C₂×C₄×C₅₉	—	4	2	no	—
97	C₂×C₄×C₅₉	—	4	2	no	—
98	C₂×C₄×C₅₉	—	8	2	no	—
99	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
101	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
102	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
104	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
105	C₂×Dic₅₉	—	2	2	no	—
106	C₂×Dic₅₉	—	4	2	no	—
107	C₂×Dic₅₉	—	4	2	no	—
108	C₂×Dic₅₉	—	4	2	no	—
109	C₂×Dic₅₉	—	4	2	no	—
110	Dic₁₁₈	—	2	4	no	—
111	Dic₁₁₈	—	4	2	no	—
112	Dic₁₁₈	—	4	2	no	—
113	Dic₁₁₈	—	4	2	no	—
114	C₈×C₅₉	C₂×C₄²	1	1	yes	characteristic
115	C₈×C₅₉	#117	1	1	yes	characteristic
116	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
117	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
118	C₅₉⋊C₈	—	2	2	no	—
119	C₅₉⋊C₈	—	4	2	no	—
120	#12648	—	59	1	no	maximal, Sylow
121	C₂²×C₅₉	—	2	2	no	—
122	C₂²×C₅₉	#418	1	1	yes	characteristic
123	C₂²×C₅₉	#440	1	1	yes	characteristic
124	C₂²×C₅₉	#442	1	1	yes	characteristic
125	C₄×C₅₉	—	8	2	no	—
126	C₄×C₅₉	—	8	2	no	—
127	C₄×C₅₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
128	C₄×C₅₉	#417	1	1	yes	characteristic
129	C₄×C₅₉	#440	1	1	yes	characteristic
130	C₄×C₅₉	#442	1	1	yes	characteristic
131	Dic₅₉	—	4	2	no	—
132	Dic₅₉	—	4	4	no	—
133	C₂×#441	—	59	1	no	—
134	C₂×#362	—	59	1	no	—
135	#2141	—	59	1	no	—
136	C₂×#347	—	59	1	no	—
137	#1773	—	59	1	no	—
138	#1386	D₅₉	1	1	yes	characteristic
139	#1383	—	59	1	no	—
140	C₂×C₅₉	—	2	1	no	—
141	C₂×C₅₉	—	2	1	no	—
142	C₂×C₅₉	#1762	1	1	yes	characteristic
143	C₂×C₅₉	#2180	1	2	yes	—
144	C₂²×Q₁₆	—	59	1	no	—
145	C₂×C₄×Q₈	—	118	1	no	—
146	C₂×M₃₂	—	59	1	no	—
147	C₂×M₃₂	C₂×D₅₉	1	1	yes	characteristic
148	#441	—	59	4	no	—
149	#441	—	118	2	no	—
150	C₂×#108	—	59	1	no	—
151	#427	C₂×D₅₉	1	1	yes	characteristic
152	C₂×#106	C₂×D₅₉	1	1	yes	characteristic
153	C₂×#103	—	118	1	no	—
154	#405	—	118	1	no	—
155	C₂×#97	—	59	1	no	—
156	#362	—	59	4	no	—
157	#358	—	59	4	no	—
158	#347	—	118	2	no	—
159	#339	—	118	1	no	—
160	C₅₉	#12648	1	1	yes	characteristic, complemented, Sylow
161	C₂²×Q₈	—	118	1	no	—
162	C₂×Q₁₆	—	59	2	no	—
163	C₂×Q₁₆	—	59	2	no	—
164	C₂×Q₁₆	—	59	2	no	—
165	C₂×Q₁₆	—	118	1	no	—
166	C₂×Q₁₆	—	118	1	no	—
167	C₂×Q₁₆	—	118	1	no	—
168	C₂×M₁₆	—	118	1	no	—
169	C₂²×C₈	—	59	1	no	—
170	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
171	C₄×Q₈	—	118	4	no	—
172	C₄×Q₈	—	236	2	no	—
173	#117	—	2	1	no	—
174	C₂×C₄⋊C₄	—	2	1	no	—
175	C₂×C₄⋊C₄	—	236	1	no	—
176	C₂×C₄²	—	59	1	no	—
177	C₂×C₄²	—	236	1	no	—
178	M₃₂	—	2	1	no	—
179	M₃₂	—	118	1	no	—
180	M₃₂	—	118	1	no	—
181	M₃₂	C₄×D₅₉	1	2	yes	—
182	C₂×C₁₆	—	2	1	no	—
183	C₂×C₁₆	—	59	2	no	—
184	#108	—	59	2	no	—
185	#108	—	118	1	no	—
186	#107	C₄×D₅₉	1	2	yes	—
187	#106	—	2	1	no	—
188	#106	—	2	1	no	—
189	#106	C₄×D₅₉	1	2	yes	—
190	#103	—	118	4	no	—
191	#97	—	59	2	no	—
192	#97	—	59	2	no	—
193	#97	—	236	1	no	—
194	C₄×C₈	—	236	1	no	—
195	C₂×Q₈	—	118	2	no	—
196	C₂×Q₈	—	118	2	no	—
197	C₂×Q₈	—	118	2	no	—
198	C₂×Q₈	—	236	1	no	—
199	C₂×Q₈	—	236	1	no	—
200	C₂×Q₈	—	236	1	no	—
201	C₂²×C₄	—	4	1	no	—
202	C₂²×C₄	—	118	1	no	—
203	C₂²×C₄	—	236	1	no	—
204	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
205	Q₁₆	—	59	4	no	—
206	Q₁₆	—	118	2	no	—
207	Q₁₆	—	118	2	no	—
208	Q₁₆	—	118	2	no	—
209	M₁₆	—	118	2	no	—
210	M₁₆	—	236	1	no	—
211	C₂×C₈	—	59	2	no	—
212	C₂×C₈	—	118	1	no	—
213	C₂×C₈	—	118	1	no	—
214	C₂×C₈	—	236	1	no	—
215	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
216	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
217	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
218	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
219	C₂×C₈	#11745687	1	1	yes	characteristic
220	C₂×C₈	#11745689	1	1	yes	characteristic
221	C₄⋊C₄	—	2	2	no	—
222	C₄⋊C₄	—	2	2	no	—
223	C₄⋊C₄	—	4	1	no	—
224	C₄⋊C₄	—	236	4	no	—
225	C₂²⋊C₄	—	4	1	no	—
226	C₄²	—	4	1	no	—
227	C₄²	—	59	2	no	—
228	C₄²	—	118	1	no	—
229	C₄²	—	236	4	no	—
230	C₁₆	—	2	2	no	—
231	C₁₆	—	118	2	no	—
232	C₂³	#14273751	1	1	yes	characteristic
233	Q₈	—	118	4	no	—
234	Q₈	—	236	2	no	—
235	Q₈	—	236	2	no	—
236	Q₈	—	236	2	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	8	2	no	—
240	C₂×C₄	—	118	2	no	—
241	C₂×C₄	—	236	2	no	—
242	C₂×C₄	—	236	2	no	—
243	C₂×C₄	—	236	2	no	—
244	C₂×C₄	—	236	2	no	—
245	C₂×C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
246	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
247	C₂×C₄	#14273689	1	1	yes	characteristic
248	C₂×C₄	#14273754	1	1	yes	characteristic
249	C₂×C₄	#14273754	1	1	yes	characteristic
250	C₂×C₄	#14273759	1	1	yes	characteristic
251	C₈	—	118	2	no	—
252	C₈	—	236	2	no	—
253	C₈	C₄²×D₅₉	1	1	yes	characteristic
254	C₈	#14273685	1	1	yes	characteristic
255	C₈	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
256	C₈	#14273689	1	1	yes	characteristic
257	C₂²	—	2	2	no	—
258	C₂²	#16837405	1	1	yes	characteristic
259	C₂²	#16837501	1	1	yes	characteristic
260	C₂²	#16837511	1	1	yes	characteristic
261	C₄	—	8	2	no	—
262	C₄	—	8	2	no	—
263	C₄	—	236	2	no	—
264	C₄	—	236	4	no	—
265	C₄	#16837249	1	1	yes	characteristic
266	C₄	#16837402	1	1	yes	characteristic
267	C₄	#16837505	1	1	yes	characteristic
268	C₄	#16837513	1	1	yes	characteristic
269	C₂	—	2	1	no	—
270	C₂	—	2	1	no	—
271	C₂	#21423920	1	1	yes	characteristic
272	C₂	#21425984	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837508

C₂

yes

maximal, characteristic

C₂×#16837219

C₂

yes

maximal, characteristic

#21425815

C₂

yes

maximal, characteristic

C₂×#16837179

C₂

yes

maximal, characteristic

#21423982

C₂

yes

maximal, characteristic

#21422194

C₂

yes

maximal, characteristic

C₅₉×#1386

C₂

yes

maximal, characteristic

C₂²×Dic₂₃₆

C₂²

yes

characteristic

C₂×#14273692

—

C₂×#14273667

C₂²

yes

characteristic

#16837508

—

#16837508

C₄

yes

complemented

C₂×#14273663

C₂²

yes

—

—

C₂²

yes

characteristic

#16837219

C₄

yes

complemented

#16837205

C₄

yes

complemented

#16837179

—

#16837161

—

C₂×M₃₂×C₅₉

C₂²

yes

characteristic

C₅₉×#427

C₂²

yes

characteristic

C₂×#106×C₅₉

C₂²

yes

characteristic

C₂²×Dic₁₁₈

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

C₂×C₄

yes

—

C₂×Dic₂₃₆

C₂×C₄

yes

—

C₂×Dic₂₃₆

C₂×C₄

yes

—

C₂×#11745664

—

C₂²×C₅₉⋊C₈

D₄

yes

characteristic

#14273692

—

#14273692

—

C₂×Dic₅₉⋊C₄

—

C₂×C₄×Dic₅₉

—

C₂×C₄×Dic₅₉

D₄

yes

characteristic

#14273667

—

#14273667

—

C₂×C₅₉⋊C₁₆

C₂×C₄

yes

—

#14273663

—

#14273663

C₂×C₄

yes

—

#14273650

—

#14273638

—

#14273637

C₂×C₄

yes

—

#14273637

D₄

yes

—

C₄×C₅₉⋊C₈

—

C₂²×C₈×C₅₉

C₂³

yes

characteristic

#117×C₅₉

—

C₂×C₄⋊C₄×C₅₉

—

M₃₂×C₅₉

—

M₃₂×C₅₉

C₂×C₄

yes

—

C₂×C₁₆×C₅₉

—

#107×C₅₉

C₂×C₄

yes

—

#106×C₅₉

—

#106×C₅₉

—

#106×C₅₉

C₂×C₄

yes

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

C₂×C₈×C₅₉

yes

C₂×C₈×C₅₉

yes

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

C₂²⋊C₄

yes

—

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂²⋊C₄

yes

—

Dic₂₃₆

—

Dic₂₃₆

—

Dic₂₃₆

—

Dic₂₃₆

C₄²

yes

—

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

100

C₂×C₄×C₅₉

C₄×D₄

yes

characteristic

101

C₂×C₄×C₅₉

C₄×D₄

yes

characteristic

102

C₂×C₄×C₅₉

AGL(1,ℤ/8)

yes

characteristic

103

C₂×C₄×C₅₉

AGL(1,ℤ/8)

yes

characteristic

104

C₂×C₄×C₅₉

#137

yes

characteristic

105

C₂×Dic₅₉

—

106

C₂×Dic₅₉

—

107

C₂×Dic₅₉

—

108

C₂×Dic₅₉

—

109

C₂×Dic₅₉

—

110

Dic₁₁₈

—

111

Dic₁₁₈

—

112

Dic₁₁₈

—

113

Dic₁₁₈

—

114

C₈×C₅₉

C₂×C₄²

yes

characteristic

115

C₈×C₅₉

#117

yes

characteristic

116

C₈×C₅₉

C₄×D₄

yes

characteristic

117

C₈×C₅₉

C₄×D₄

yes

characteristic

118

C₅₉⋊C₈

—

119

C₅₉⋊C₈

—

120

#12648

—

maximal, Sylow

121

C₂²×C₅₉

—

122

C₂²×C₅₉

#418

yes

characteristic

123

C₂²×C₅₉

#440

yes

characteristic

124

C₂²×C₅₉

#442

yes

characteristic

125

C₄×C₅₉

—

126

C₄×C₅₉

—

127

C₄×C₅₉

C₄×C₂²⋊C₄

yes

characteristic

128

C₄×C₅₉

#417

yes

characteristic

129

C₄×C₅₉

#440

yes

characteristic

130

C₄×C₅₉

#442

yes

characteristic

131

Dic₅₉

—

132

Dic₅₉

—

133

C₂×#441

—

134

C₂×#362

—

135

#2141

—

136

C₂×#347

—

137

#1773

—

138

#1386

D₅₉

yes

characteristic

139

#1383

—

140

C₂×C₅₉

—

141

C₂×C₅₉

—

142

C₂×C₅₉

#1762

yes

characteristic

143

C₂×C₅₉

#2180

yes

—

144

C₂²×Q₁₆

—

145

C₂×C₄×Q₈

—

118

—

146

C₂×M₃₂

—

147

C₂×M₃₂

C₂×D₅₉

yes

characteristic

148

#441

—

149

#441

—

118

—

150

C₂×#108

—

151

#427

C₂×D₅₉

yes

characteristic

152

C₂×#106

C₂×D₅₉

yes

characteristic

153

C₂×#103

—

118

—

154

#405

—

118

—

155

C₂×#97

—

156

#362

—

157

#358

—

158

#347

—

118

—

159

#339

—

118

—

160

C₅₉

#12648

yes

characteristic, complemented, Sylow

161

C₂²×Q₈

—

118

—

162

C₂×Q₁₆

—

163

C₂×Q₁₆

—

164

C₂×Q₁₆

—

165

C₂×Q₁₆

—

118

—

166

C₂×Q₁₆

—

118

—

167

C₂×Q₁₆

—

118

—

168

C₂×M₁₆

—

118

—

169

C₂²×C₈

—

170

C₂²×C₈

C₂²×D₅₉

yes

characteristic

171

C₄×Q₈

—

118

—

172

C₄×Q₈

—

236

—

173

#117

—

174

C₂×C₄⋊C₄

—

175

C₂×C₄⋊C₄

—

236

—

176

C₂×C₄²

—

177

C₂×C₄²

—

236

—

178

M₃₂

—

179

M₃₂

—

118

—

180

M₃₂

—

118

—

181

M₃₂

C₄×D₅₉

yes

—

182

C₂×C₁₆

—

183

C₂×C₁₆

—

184

#108

—

185

#108

—

118

—

186

#107

C₄×D₅₉

yes

—

187

#106

—

188

#106

—

189

#106

C₄×D₅₉

yes

—

190

#103

—

118

—

191

#97

—

192

#97

—

193

#97

—

236

—

194

C₄×C₈

—

236

—

195

C₂×Q₈

—

118

—

196

C₂×Q₈

—

118

—

197

C₂×Q₈

—

118

—

198

C₂×Q₈

—

236

—

199

C₂×Q₈

—

236

—

200

C₂×Q₈

—

236

—

201

C₂²×C₄

—

202

C₂²×C₄

—

118

—

203

C₂²×C₄

—

236

—

204

C₂²×C₄

D₄×D₅₉

yes

characteristic

205

Q₁₆

—

206

Q₁₆

—

118

—

207

Q₁₆

—

118

—

208

Q₁₆

—

118

—

209

M₁₆

—

118

—

210

M₁₆

—

236

—

211

C₂×C₈

—

212

C₂×C₈

—

118

—

213

C₂×C₈

—

118

—

214

C₂×C₈

—

236

—

215

C₂×C₈

C₂×C₄×D₅₉

yes

characteristic

216

C₂×C₈

C₂×C₄×D₅₉

yes

characteristic

217

C₂×C₈

C₂×C₄×D₅₉

yes

characteristic

218

C₂×C₈

D₄×D₅₉

yes

characteristic

219

C₂×C₈

#11745687

yes

characteristic

220

C₂×C₈

#11745689

yes

characteristic

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

236

—

225

C₂²⋊C₄

—

226

C₄²

—

227

C₄²

—

228

C₄²

—

118

—

229

C₄²

—

236

—

230

C₁₆

—

231

C₁₆

—

118

—

232

C₂³

#14273751

yes

characteristic

233

Q₈

—

118

—

234

Q₈

—

236

—

235

Q₈

—

236

—

236

Q₈

—

236

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

118

—

241

C₂×C₄

—

236

—

242

C₂×C₄

—

236

—

243

C₂×C₄

—

236

—

244

C₂×C₄

—

236

—

245

C₂×C₄

C₂²⋊C₄×D₅₉

yes

characteristic

246

C₂×C₄

(C₂²⋊D₅₉)⋊C₄

yes

characteristic

247

C₂×C₄

#14273689

yes

characteristic

248

C₂×C₄

#14273754

yes

characteristic

249

C₂×C₄

#14273754

yes

characteristic

250

C₂×C₄

#14273759

yes

characteristic

251

C₈

—

118

—

252

C₈

—

236

—

253

C₈

C₄²×D₅₉

yes

characteristic

254

C₈

#14273685

yes

characteristic

255

C₈

(C₂²⋊D₅₉)⋊C₄

yes

characteristic

256

C₈

#14273689

yes

characteristic

257

C₂²

—

258

C₂²

#16837405

yes

characteristic

259

C₂²

#16837501

yes

characteristic

260

C₂²

#16837511

yes

characteristic

261

C₄

—

262

C₄

—

263

C₄

—

236

—

264

C₄

—

236

—

265

C₄

#16837249

yes

characteristic

266

C₄

#16837402

yes

characteristic

267

C₄

#16837505

yes

characteristic

268

C₄

#16837513

yes

characteristic

269

C₂

—

270

C₂

—

271

C₂

#21423920

yes

characteristic

272

C₂

#21425984

yes

—

	subgroup	G/H
center	C₂²	#16837511
commutator	C₈×C₅₉	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₅₉×#1386	C₂
socle	C₂²×C₅₉	#442
prime radical	C₂³×C₅₉	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	#1386	D₅₉
hypocenter	C₅₉	#12648
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1386

subgroup

G/H

center

C₂²

#16837511

commutator

C₈×C₅₉

C₂×C₄²

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₅₉×#1386

C₂

C₂²×C₅₉

C₂³×C₅₉

C₂²×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1386

N	H ≅ G/N	type
12. #16837508	C₄	semidirect
17. #16837219	C₄	semidirect
18. #16837205	C₄	semidirect
160. C₅₉	#12648	semidirect

H ≅ G/N

type

12. #16837508

C₄

semidirect

17. #16837219

C₄

semidirect

18. #16837205

C₄

semidirect

160. C₅₉

#12648

semidirect

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

subgroup	index
C₂×#16837508	2
C₂×#16837219	2
#21425815	2
C₂×#16837179	2
#21423982	2
#21422194	2
C₅₉×#1386	2
#12648	59

subgroup

index

C₅₉×#1386

Subgroups — #28503967

Conjugacy classes of subgroups

Complements

Maximal subgroups