Group #15778564 — subgroups

Subgroups — #15778564

Order 3328.

934 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 934 conjugacy classes of subgroups — too many to draw. Only its 171 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	C₂³×Dic₅₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718084	C₂	1	4	yes	maximal, complemented
3	C₂×C₂²⋊#6090	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₂₆	—	2	1	no	—
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₅₂	—	2	2	no	—
8	C₂²×Dic₅₂	—	2	1	no	—
9	C₂²×Dic₅₂	—	2	8	no	—
10	C₂²×Dic₅₂	C₄	1	4	yes	complemented
11	C₂²×Dic₅₂	C₂²	1	2	yes	—
12	C₂×C₁₃×#107	C₂²	1	2	yes	—
13	C₁₃×#380	—	2	1	no	—
14	C₂²×#6090	C₂²	1	2	yes	—
15	C₁₃×#340	—	2	1	no	—
16	C₂²⋊#6090	—	2	2	no	—
17	#11718084	—	2	8	no	—
18	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
19	C₂³×Dic₁₃	—	4	1	no	—
20	C₂²×Dic₂₆	—	2	8	no	—
21	C₂²×Dic₂₆	—	2	4	no	—
22	C₂²×Dic₂₆	—	2	2	no	—
23	C₂²×Dic₂₆	—	4	4	no	—
24	C₂²×Dic₂₆	—	4	1	no	—
25	C₂²×Dic₂₆	—	4	2	no	—
26	C₂²×C₈×C₁₃	—	2	4	no	—
27	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₁₃	D₄	1	2	yes	—
29	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
32	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
33	C₂×Dic₅₂	—	2	8	no	—
34	C₂×Dic₅₂	—	2	16	no	—
35	C₂×Dic₅₂	—	2	4	no	—
36	C₂×Dic₅₂	—	2	2	no	—
37	C₂×Dic₅₂	—	2	4	no	—
38	C₂×Dic₅₂	—	2	16	no	—
39	C₂×Dic₅₂	C₂×C₄	1	4	yes	—
40	C₂×Dic₅₂	D₄	1	8	yes	—
41	C₁₃×#107	—	2	4	no	—
42	C₁₃×#95	—	4	1	no	—
43	C₂×#6090	—	2	4	no	—
44	C₂×#6090	—	2	2	no	—
45	#12732	—	13	1	no	maximal, Sylow
46	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	—	2	2	no	—
48	C₂²×C₄×C₁₃	—	2	2	no	—
49	C₂²×C₄×C₁₃	—	4	2	no	—
50	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
53	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×Dic₁₃	—	4	8	no	—
55	C₂²×Dic₁₃	—	4	4	no	—
56	C₂²×Dic₁₃	—	4	2	no	—
57	C₂×Dic₂₆	—	2	16	no	—
58	C₂×Dic₂₆	—	2	4	no	—
59	C₂×Dic₂₆	—	2	8	no	—
60	C₂×Dic₂₆	—	4	8	no	—
61	C₂×Dic₂₆	—	4	8	no	—
62	C₂×Dic₂₆	—	4	16	no	—
63	C₂×Dic₂₆	—	4	4	no	—
64	C₂×Dic₂₆	—	4	2	no	—
65	C₂×Dic₂₆	—	4	4	no	—
66	C₂×C₈×C₁₃	—	2	2	no	—
67	C₂×C₈×C₁₃	—	2	4	no	—
68	C₂×C₈×C₁₃	—	2	4	no	—
69	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
70	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
72	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₁₃×C₄⋊C₄	—	4	2	no	—
74	C₁₃×C₄⋊C₄	—	4	2	no	—
75	C₁₃×C₂²⋊C₄	—	8	2	no	—
76	Dic₅₂	—	2	16	no	—
77	Dic₅₂	—	2	4	no	—
78	Dic₅₂	—	2	8	no	—
79	Dic₅₂	C₂²⋊C₄	1	8	yes	complemented
80	#6090	—	4	2	no	—
81	C₂³×Q₁₆	—	13	1	no	—
82	C₂×#358	—	13	4	no	—
83	C₂×C₂²⋊C₁₆	—	13	1	no	—
84	#1808	D₁₃	1	1	yes	characteristic
85	C₂³×C₁₃	—	2	2	no	—
86	C₂³×C₁₃	—	2	2	no	—
87	C₂³×C₁₃	#102	1	2	yes	—
88	C₂³×C₁₃	SD₃₂	1	2	yes	—
89	C₂³×C₁₃	Q₃₂	1	2	yes	—
90	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₁₃	—	2	2	no	—
92	C₂×C₄×C₁₃	—	2	2	no	—
93	C₂×C₄×C₁₃	—	2	2	no	—
94	C₂×C₄×C₁₃	—	2	4	no	—
95	C₂×C₄×C₁₃	—	8	2	no	—
96	C₂×C₄×C₁₃	—	8	2	no	—
97	C₂×C₄×C₁₃	—	8	2	no	—
98	C₂×C₄×C₁₃	#102	1	2	yes	—
99	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₃	#120	1	2	yes	—
101	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
102	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
103	C₂×Dic₁₃	—	4	16	no	—
104	C₂×Dic₁₃	—	4	4	no	—
105	C₂×Dic₁₃	—	4	8	no	—
106	Dic₂₆	—	2	8	no	—
107	Dic₂₆	—	4	16	no	—
108	Dic₂₆	—	4	4	no	—
109	Dic₂₆	—	4	8	no	—
110	C₈×C₁₃	—	2	2	no	—
111	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
112	C₈×C₁₃	#120	1	2	yes	—
113	C₂³×Q₈	—	26	1	no	—
114	C₂²×Q₁₆	—	13	4	no	—
115	C₂²×Q₁₆	—	13	2	no	—
116	C₂²×Q₁₆	—	26	8	no	—
117	C₂²×Q₁₆	—	26	2	no	—
118	C₂²×Q₁₆	—	26	1	no	—
119	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
120	C₂²×C₁₆	—	13	2	no	—
121	C₂×#107	C₂×D₁₃	1	2	yes	—
122	#380	—	2	1	no	—
123	#358	—	26	8	no	—
124	C₂²⋊C₁₆	—	26	2	no	—
125	#340	—	2	1	no	—
126	C₂²×C₁₃	—	2	2	no	—
127	C₂²×C₁₃	—	2	4	no	—
128	C₂²×C₁₃	—	2	4	no	—
129	C₂²×C₁₃	—	2	2	no	—
130	C₂²×C₁₃	#358	1	4	yes	complemented
131	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
132	C₂²×C₁₃	#447	1	2	yes	—
133	C₂²×C₁₃	C₂×SD₃₂	1	1	yes	characteristic
134	C₂²×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
135	C₂²×C₁₃	#510	1	2	yes	—
136	C₄×C₁₃	—	2	2	no	—
137	C₄×C₁₃	—	16	2	no	—
138	C₄×C₁₃	#379	1	1	yes	characteristic
139	C₄×C₁₃	#418	1	1	yes	characteristic
140	C₄×C₁₃	#450	1	2	yes	—
141	Dic₁₃	—	4	8	no	—
142	C₂²×Q₈	—	26	8	no	—
143	C₂²×Q₈	—	26	4	no	—
144	C₂²×Q₈	—	26	2	no	—
145	C₂²×Q₈	—	52	4	no	—
146	C₂²×Q₈	—	52	1	no	—
147	C₂²×Q₈	—	52	2	no	—
148	C₂³×C₄	—	52	1	no	—
149	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
150	C₂×Q₁₆	—	13	4	no	—
151	C₂×Q₁₆	—	13	8	no	—
152	C₂×Q₁₆	—	26	16	no	—
153	C₂×Q₁₆	—	26	8	no	—
154	C₂×Q₁₆	—	26	16	no	—
155	C₂×Q₁₆	—	26	4	no	—
156	C₂×Q₁₆	—	26	2	no	—
157	C₂×Q₁₆	—	26	4	no	—
158	C₂²×C₈	—	2	4	no	—
159	C₂²×C₈	C₄×D₁₃	1	2	yes	—
160	C₂²×C₈	D₅₂	1	2	yes	—
161	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
162	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
163	C₂×C₄⋊C₄	—	2	2	no	—
164	C₂×C₂²⋊C₄	—	4	1	no	—
165	C₂×C₁₆	—	26	2	no	—
166	C₂×C₁₆	—	26	4	no	—
167	#107	—	2	4	no	—
168	#95	—	4	1	no	—
169	C₂×C₁₃	—	2	4	no	—
170	C₂×C₁₃	#1786	1	1	yes	characteristic
171	C₂×C₁₃	C₂×#358	1	1	yes	characteristic
172	C₂×C₁₃	#2141	1	1	yes	characteristic
173	C₂×C₁₃	#2185	1	2	yes	—
174	C₂×C₁₃	#2188	1	2	yes	—
175	C₂⁴	#6104	1	1	yes	characteristic
176	C₂×Q₈	—	26	16	no	—
177	C₂×Q₈	—	26	4	no	—
178	C₂×Q₈	—	26	8	no	—
179	C₂×Q₈	—	52	8	no	—
180	C₂×Q₈	—	52	8	no	—
181	C₂×Q₈	—	52	16	no	—
182	C₂×Q₈	—	52	2	no	—
183	C₂×Q₈	—	52	4	no	—
184	C₂×Q₈	—	52	4	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	—	2	2	no	—
187	C₂²×C₄	—	4	2	no	—
188	C₂²×C₄	—	52	8	no	—
189	C₂²×C₄	—	52	2	no	—
190	C₂²×C₄	—	52	4	no	—
191	C₂²×C₄	#6103	1	2	yes	—
192	C₂²×C₄	#6104	1	1	yes	characteristic
193	C₂²×C₄	#6106	1	2	yes	—
194	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
195	Q₁₆	—	13	8	no	—
196	Q₁₆	—	26	16	no	—
197	Q₁₆	—	26	4	no	—
198	Q₁₆	—	26	8	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	2	4	no	—
201	C₂×C₈	—	2	4	no	—
202	C₂×C₈	#6103	1	2	yes	—
203	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
204	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
205	C₂×C₈	D₄×D₁₃	1	4	yes	—
206	C₄⋊C₄	—	4	2	no	—
207	C₄⋊C₄	—	4	2	no	—
208	C₂²⋊C₄	—	8	2	no	—
209	C₁₆	—	52	2	no	—
210	C₁₃	#12732	1	1	yes	characteristic, complemented, Sylow
211	C₂³	—	2	2	no	—
212	C₂³	—	2	2	no	—
213	C₂³	#88049	1	2	yes	—
214	C₂³	#88067	1	2	yes	—
215	C₂³	#88069	1	2	yes	—
216	C₂³	C₂×#6104	1	1	yes	characteristic
217	Q₈	—	26	8	no	—
218	Q₈	—	52	16	no	—
219	Q₈	—	52	4	no	—
220	Q₈	—	52	8	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	4	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	8	2	no	—
226	C₂×C₄	—	8	2	no	—
227	C₂×C₄	—	8	2	no	—
228	C₂×C₄	—	52	16	no	—
229	C₂×C₄	—	52	8	no	—
230	C₂×C₄	—	52	4	no	—
231	C₂×C₄	#88049	1	2	yes	—
232	C₂×C₄	C₂×#6103	1	1	yes	characteristic
233	C₂×C₄	#88191	1	2	yes	—
234	C₂×C₄	C₂×#6106	1	1	yes	characteristic
235	C₂×C₄	#88203	1	2	yes	—
236	C₈	—	2	2	no	—
237	C₈	C₂²⋊C₄×D₁₃	1	2	yes	—
238	C₈	#88136	1	2	yes	—
239	C₂²	—	2	4	no	—
240	C₂²	—	2	4	no	—
241	C₂²	—	2	2	no	—
242	C₂²	—	2	2	no	—
243	C₂²	#11718084	1	4	yes	complemented
244	C₂²	C₂×#88049	1	1	yes	characteristic
245	C₂²	#11718697	1	2	yes	—
246	C₂²	C₂×#88067	1	1	yes	characteristic
247	C₂²	C₂×#88069	1	1	yes	characteristic
248	C₂²	#11718856	1	2	yes	—
249	C₄	—	2	2	no	—
250	C₄	—	16	2	no	—
251	C₄	—	52	8	no	—
252	C₄	#11718616	1	1	yes	characteristic
253	C₄	#11718662	1	1	yes	characteristic
254	C₄	#11718707	1	2	yes	—
255	C₂	—	2	4	no	—
256	C₂	#13114766	1	1	yes	characteristic
257	C₂	C₂×#11718084	1	1	yes	characteristic
258	C₂	#13116555	1	1	yes	characteristic
259	C₂	#13116752	1	2	yes	—
260	C₂	#13116769	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×Dic₅₂

C₂

yes

maximal, characteristic

C₂×#11718084

C₂

yes

maximal, complemented

C₂×C₂²⋊#6090

C₂

yes

maximal, characteristic

C₁₃×#1808

C₂

yes

maximal, characteristic

C₂³×Dic₂₆

—

C₂³×C₈×C₁₃

C₂²

yes

characteristic

C₂²×Dic₅₂

—

C₂²×Dic₅₂

—

C₂²×Dic₅₂

—

C₂²×Dic₅₂

C₄

yes

complemented

C₂²×Dic₅₂

C₂²

yes

—

C₂×C₁₃×#107

C₂²

yes

—

C₁₃×#380

—

C₂²×#6090

C₂²

yes

—

C₁₃×#340

—

C₂²⋊#6090

—

#11718084

—

C₂³×C₄×C₁₃

D₄

yes

characteristic

C₂³×Dic₁₃

—

C₂²×Dic₂₆

—

C₂²×Dic₂₆

—

C₂²×Dic₂₆

—

C₂²×Dic₂₆

—

C₂²×Dic₂₆

—

C₂²×Dic₂₆

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂²×C₈×C₁₃

D₄

yes

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

C₂×C₄

yes

—

C₂×Dic₅₂

D₄

yes

—

C₁₃×#107

—

C₁₃×#95

—

—

—

—

C₂⁴×C₁₃

D₈

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

D₈

yes

characteristic

C₂²×C₄×C₁₃

SD₁₆

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

Dic₅₂

—

Dic₅₂

—

Dic₅₂

—

Dic₅₂

C₂²⋊C₄

yes

complemented

#6090

—

C₂³×Q₁₆

—

C₂×#358

—

C₂×C₂²⋊C₁₆

—

#1808

D₁₃

yes

characteristic

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

#102

yes

—

C₂³×C₁₃

SD₃₂

yes

—

C₂³×C₁₃

Q₃₂

yes

—

C₂³×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#102

yes

—

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

100

C₂×C₄×C₁₃

#120

yes

—

101

C₂×C₄×C₁₃

C₂×SD₁₆

yes

characteristic

102

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

103

C₂×Dic₁₃

—

104

C₂×Dic₁₃

—

105

C₂×Dic₁₃

—

106

Dic₂₆

—

107

Dic₂₆

—

108

Dic₂₆

—

109

Dic₂₆

—

110

C₈×C₁₃

—

111

C₈×C₁₃

C₂×C₂²⋊C₄

yes

—

112

C₈×C₁₃

#120

yes

—

113

C₂³×Q₈

—

114

C₂²×Q₁₆

—

115

C₂²×Q₁₆

—

116

C₂²×Q₁₆

—

117

C₂²×Q₁₆

—

118

C₂²×Q₁₆

—

119

C₂³×C₈

C₂×D₁₃

yes

characteristic

120

C₂²×C₁₆

—

121

C₂×#107

C₂×D₁₃

yes

—

122

#380

—

123

#358

—

124

C₂²⋊C₁₆

—

125

#340

—

126

C₂²×C₁₃

—

127

C₂²×C₁₃

—

128

C₂²×C₁₃

—

129

C₂²×C₁₃

—

130

C₂²×C₁₃

#358

yes

complemented

131

C₂²×C₁₃

C₂×#102

yes

characteristic

132

C₂²×C₁₃

#447

yes

—

133

C₂²×C₁₃

C₂×SD₃₂

yes

characteristic

134

C₂²×C₁₃

C₂×Q₃₂

yes

characteristic

135

C₂²×C₁₃

#510

yes

—

136

C₄×C₁₃

—

137

C₄×C₁₃

—

138

C₄×C₁₃

#379

yes

characteristic

139

C₄×C₁₃

#418

yes

characteristic

140

C₄×C₁₃

#450

yes

—

141

Dic₁₃

—

142

C₂²×Q₈

—

143

C₂²×Q₈

—

144

C₂²×Q₈

—

145

C₂²×Q₈

—

146

C₂²×Q₈

—

147

C₂²×Q₈

—

148

C₂³×C₄

—

149

C₂³×C₄

C₂²⋊D₁₃

yes

characteristic

150

C₂×Q₁₆

—

151

C₂×Q₁₆

—

152

C₂×Q₁₆

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂²×C₈

—

159

C₂²×C₈

C₄×D₁₃

yes

—

160

C₂²×C₈

D₅₂

yes

—

161

C₂²×C₈

C₂²⋊D₁₃

yes

characteristic

162

C₂²×C₈

C₂²×D₁₃

yes

characteristic

163

C₂×C₄⋊C₄

—

164

C₂×C₂²⋊C₄

—

165

C₂×C₁₆

—

166

C₂×C₁₆

—

167

#107

—

168

#95

—

169

C₂×C₁₃

—

170

C₂×C₁₃

#1786

yes

characteristic

171

C₂×C₁₃

C₂×#358

yes

characteristic

172

C₂×C₁₃

#2141

yes

characteristic

173

C₂×C₁₃

#2185

yes

—

174

C₂×C₁₃

#2188

yes

—

175

C₂⁴

#6104

yes

characteristic

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

#6103

yes

—

192

C₂²×C₄

#6104

yes

characteristic

193

C₂²×C₄

#6106

yes

—

194

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

195

Q₁₆

—

196

Q₁₆

—

197

Q₁₆

—

198

Q₁₆

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

#6103

yes

—

203

C₂×C₈

C₂×C₄×D₁₃

yes

characteristic

204

C₂×C₈

C₂×D₅₂

yes

characteristic

205

C₂×C₈

D₄×D₁₃

yes

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₂²⋊C₄

—

209

C₁₆

—

210

C₁₃

#12732

yes

characteristic, complemented, Sylow

211

C₂³

—

212

C₂³

—

213

C₂³

#88049

yes

—

214

C₂³

#88067

yes

—

215

C₂³

#88069

yes

—

216

C₂³

C₂×#6104

yes

characteristic

217

Q₈

—

218

Q₈

—

219

Q₈

—

220

Q₈

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

#88049

yes

—

232

C₂×C₄

C₂×#6103

yes

characteristic

233

C₂×C₄

#88191

yes

—

234

C₂×C₄

C₂×#6106

yes

characteristic

235

C₂×C₄

#88203

yes

—

236

C₈

—

237

C₈

C₂²⋊C₄×D₁₃

yes

—

238

C₈

#88136

yes

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

#11718084

yes

complemented

244

C₂²

C₂×#88049

yes

characteristic

245

C₂²

#11718697

yes

—

246

C₂²

C₂×#88067

yes

characteristic

247

C₂²

C₂×#88069

yes

characteristic

248

C₂²

#11718856

yes

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

#11718616

yes

characteristic

253

C₄

#11718662

yes

characteristic

254

C₄

#11718707

yes

—

255

C₂

—

256

C₂

#13114766

yes

characteristic

257

C₂

C₂×#11718084

yes

characteristic

258

C₂

#13116555

yes

characteristic

259

C₂

#13116752

yes

—

260

C₂

#13116769

yes

—

	subgroup	G/H
center	C₂³	C₂×#6104
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1808	C₂
socle	C₂³×C₁₃	C₂×D₈
prime radical	C₂⁴×C₁₃	D₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1808	D₁₃
hypocenter	C₁₃	#12732
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1808

subgroup

G/H

center

C₂³

C₂×#6104

commutator

C₂×C₈×C₁₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₃

Fitting

C₁₃×#1808

C₂

socle

C₂³×C₁₃

C₂×D₈

prime radical

C₂⁴×C₁₃

D₈

cosocle

C₂²×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1808

N	H ≅ G/N	type
2. C₂×#11718084	C₂	semidirect
10. C₂²×Dic₅₂	C₄	semidirect
79. Dic₅₂	C₂²⋊C₄	semidirect
130. C₂²×C₁₃	#358	semidirect
210. C₁₃	#12732	semidirect
243. C₂²	#11718084	semidirect

H ≅ G/N

type

2. C₂×#11718084

C₂

semidirect

10. C₂²×Dic₅₂

C₄

semidirect

79. Dic₅₂

C₂²⋊C₄

semidirect

130. C₂²×C₁₃

#358

semidirect

210. C₁₃

#12732

semidirect

243. C₂²

#11718084

semidirect

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

subgroup	index
C₂³×Dic₅₂	2
C₂×#11718084	2
C₂×C₂²⋊#6090	2
C₁₃×#1808	2
#12732	13

subgroup

index

C₂³×Dic₅₂

C₂×#11718084

C₂×C₂²⋊#6090

C₁₃×#1808

#12732

Subgroups — #15778564

Conjugacy classes of subgroups

Complements

Maximal subgroups