Group #16019298 — subgroups

Subgroups — #16019298

Order 3328.

496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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	#13125406	C₂	1	2	yes	maximal, complemented
2	#13117001	C₂	1	2	yes	maximal, complemented
3	#13116994	C₂	1	2	yes	maximal, complemented
4	#13116949	C₂	1	2	yes	maximal, complemented
5	#13116944	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116939	C₂	1	1	yes	maximal, characteristic
7	#13116899	C₂	1	2	yes	maximal, complemented
8	#13116892	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719184	—	2	2	no	—
11	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	#11718777	C₂²	1	2	yes	—
15	#11718776	C₂²	1	2	yes	—
16	#11718775	—	2	2	no	—
17	C₂×Dic₁₀₄	C₂²	1	1	yes	characteristic
18	C₂×#88040	C₂²	1	2	yes	—
19	C₂×D₂₀₈	C₂²	1	1	yes	characteristic
20	C₄×Dic₅₂	C₂²	1	2	yes	—
21	#11718358	—	2	2	no	—
22	#11718357	C₂²	1	2	yes	—
23	C₄×D₁₀₄	C₂²	1	2	yes	—
24	C₄×#6095	—	2	2	no	—
25	#11718344	C₂²	1	2	yes	—
26	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
27	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
28	#11718101	C₂²	1	2	yes	—
29	#11718101	C₂²	1	2	yes	—
30	#11718097	C₂²	1	1	yes	characteristic
31	#11718097	C₂²	1	1	yes	characteristic
32	#11718096	C₂²	1	2	yes	—
33	#11718095	C₂²	1	2	yes	—
34	#11718095	C₂²	1	2	yes	—
35	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
37	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
38	#88184	—	2	2	no	—
39	#88183	—	4	2	no	—
40	C₄×C₂²⋊D₁₃	—	4	2	no	—
41	#88178	—	2	2	no	—
42	C₂×Dic₅₂	C₂³	1	2	yes	—
43	C₂×D₁₀₄	C₂³	1	2	yes	—
44	C₂×#6095	—	2	2	no	—
45	#88130	—	4	2	no	—
46	#88129	—	2	2	no	—
47	C₄×D₅₂	—	2	2	no	—
48	#88126	—	4	2	no	—
49	#88124	—	2	2	no	—
50	C₄×Dic₂₆	—	2	2	no	—
51	C₁₃×M₃₂	—	4	1	no	—
52	C₁₃×M₃₂	—	4	1	no	—
53	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
55	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
56	C₄×C₈×C₁₃	D₄	1	2	yes	—
57	C₄×C₈×C₁₃	C₂³	1	2	yes	—
58	#88061	—	2	2	no	—
59	#88061	—	2	2	no	—
60	#88058	C₂³	1	2	yes	—
61	#88058	C₂³	1	2	yes	—
62	#88057	—	2	2	no	—
63	#88056	—	2	2	no	—
64	#88056	—	2	2	no	—
65	Dic₁₀₄	—	4	1	no	—
66	#88040	—	4	2	no	—
67	D₂₀₈	—	4	1	no	—
68	#33822	—	13	1	no	maximal, Sylow
69	C₂²×C₄×C₁₃	D₈	1	2	yes	—
70	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
71	C₂×C₂²⋊D₁₃	—	4	2	no	—
72	C₂×D₅₂	—	2	2	no	—
73	C₂×C₄×D₁₃	—	4	2	no	—
74	C₂×Dic₂₆	—	2	2	no	—
75	C₂×C₈×C₁₃	—	2	1	no	—
76	C₂×C₈×C₁₃	—	2	1	no	—
77	C₂×C₈×C₁₃	—	4	1	no	—
78	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
80	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
81	C₄²×C₁₃	D₈	1	1	yes	characteristic
82	C₄²×C₁₃	D₈	1	1	yes	characteristic
83	C₄²×C₁₃	C₂×D₄	1	2	yes	—
84	C₂²⋊Dic₁₃	—	4	2	no	—
85	#6103	—	4	2	no	—
86	#6103	—	4	2	no	—
87	#6103	—	4	2	no	—
88	#6103	—	4	2	no	—
89	C₄⋊Dic₁₃	—	2	2	no	—
90	C₄⋊Dic₁₃	—	2	2	no	—
91	#6101	—	4	2	no	—
92	#6101	—	4	2	no	—
93	#6101	—	4	2	no	—
94	#6101	—	4	2	no	—
95	C₄×Dic₁₃	—	4	2	no	—
96	Dic₅₂	—	2	2	no	—
97	Dic₅₂	—	2	2	no	—
98	D₁₀₄	—	2	2	no	—
99	D₁₀₄	—	2	2	no	—
100	#6095	—	4	4	no	—
101	C₁₃×C₁₆	—	2	1	no	—
102	C₁₃×C₁₆	—	2	2	no	—
103	C₁₃×C₁₆	—	2	1	no	—
104	#3168	—	13	2	no	—
105	#2229	—	13	2	no	—
106	#2228	—	13	2	no	—
107	#2220	—	13	2	no	—
108	#2219	—	13	1	no	—
109	#2218	—	13	1	no	—
110	#2211	—	13	2	no	—
111	#2210	—	13	2	no	—
112	#2150	D₁₃	1	1	yes	characteristic, complemented
113	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
114	C₂²×D₁₃	—	4	2	no	—
115	C₂×C₄×C₁₃	—	2	1	no	—
116	C₂×C₄×C₁₃	—	2	1	no	—
117	C₂×C₄×C₁₃	—	4	2	no	—
118	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
119	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
120	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
121	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
122	C₂²⋊D₁₃	—	8	4	no	—
123	C₂×Dic₁₃	—	4	2	no	—
124	C₂×Dic₁₃	—	4	2	no	—
125	C₂×Dic₁₃	—	4	2	no	—
126	D₅₂	—	4	2	no	—
127	D₅₂	—	4	2	no	—
128	C₄×D₁₃	—	8	4	no	—
129	Dic₂₆	—	4	2	no	—
130	Dic₂₆	—	4	2	no	—
131	C₈×C₁₃	—	2	1	no	—
132	C₈×C₁₃	—	2	2	no	—
133	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
134	C₈×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
135	#529	—	26	2	no	—
136	C₂×Q₃₂	—	13	1	no	—
137	C₂×SD₃₂	—	13	2	no	—
138	C₂×D₁₆	—	13	1	no	—
139	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
140	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
141	#499	—	13	2	no	—
142	#495	—	13	2	no	—
143	#488	—	26	2	no	—
144	#467	—	13	2	no	—
145	#466	—	13	2	no	—
146	#465	—	26	2	no	—
147	C₄×Q₁₆	—	13	2	no	—
148	C₄×SD₁₆	—	26	2	no	—
149	C₄×D₈	—	13	2	no	—
150	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
151	#367	—	13	1	no	—
152	#367	—	13	1	no	—
153	#366	—	13	2	no	—
154	C₄⋊C₁₆	C₂×D₁₃	1	2	yes	—
155	C₄⋊C₁₆	C₂×D₁₃	1	2	yes	—
156	#358	—	13	2	no	—
157	#358	—	13	2	no	—
158	#357	—	13	2	no	—
159	#357	—	13	2	no	—
160	C₂²×C₁₃	—	2	2	no	—
161	C₂²×C₁₃	—	2	1	no	—
162	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
163	C₂×D₁₃	—	8	2	no	—
164	C₂×D₁₃	—	8	2	no	—
165	C₂×D₁₃	—	8	2	no	—
166	C₄×C₁₃	—	2	2	no	—
167	C₄×C₁₃	—	2	2	no	—
168	C₄×C₁₃	—	2	1	no	—
169	C₄×C₁₃	#537	1	1	yes	characteristic
170	C₄×C₁₃	#575	1	1	yes	characteristic
171	Dic₁₃	—	8	2	no	—
172	Dic₁₃	—	8	2	no	—
173	Dic₁₃	—	8	2	no	—
174	C₂×Q₁₆	—	13	2	no	—
175	C₂×SD₁₆	—	26	2	no	—
176	C₂×D₈	—	13	2	no	—
177	C₂²×C₈	D₅₂	1	1	yes	characteristic
178	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
179	#126	—	52	2	no	—
180	#125	—	26	2	no	—
181	#124	—	26	2	no	—
182	#123	—	52	2	no	—
183	C₂²⋊Q₈	—	26	2	no	—
184	#121	—	26	2	no	—
185	C₄×Q₈	—	26	2	no	—
186	C₄×D₄	—	26	2	no	—
187	C₄×D₄	—	52	2	no	—
188	#117	—	52	2	no	—
189	C₂×C₄²	D₅₂	1	1	yes	characteristic
190	Q₃₂	—	52	1	no	—
191	SD₃₂	—	52	2	no	—
192	D₁₆	—	52	1	no	—
193	M₃₂	—	4	1	no	—
194	M₃₂	—	4	1	no	—
195	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
196	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
197	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
198	#107	—	13	2	no	—
199	#107	—	13	2	no	—
200	#106	—	26	2	no	—
201	#103	—	26	2	no	—
202	#103	—	26	2	no	—
203	#102	—	26	2	no	—
204	#102	—	26	2	no	—
205	C₄×C₈	D₅₂	1	2	yes	—
206	C₄×C₈	C₂²×D₁₃	1	2	yes	—
207	C₂×C₁₃	—	4	1	no	—
208	C₂×C₁₃	#3245	1	1	yes	characteristic
209	C₂×C₁₃	#3414	1	2	yes	—
210	D₁₃	—	16	2	no	—
211	C₂×Q₈	—	26	2	no	—
212	C₂×D₄	—	26	2	no	—
213	C₂×D₄	—	52	2	no	—
214	C₂²×C₄	—	52	2	no	—
215	C₂²×C₄	D₁₀₄	1	2	yes	—
216	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
217	Q₁₆	—	26	2	no	—
218	Q₁₆	—	26	2	no	—
219	SD₁₆	—	52	4	no	—
220	D₈	—	26	2	no	—
221	D₈	—	26	2	no	—
222	C₂×C₈	—	2	1	no	—
223	C₂×C₈	—	2	1	no	—
224	C₂×C₈	—	4	1	no	—
225	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
226	C₂×C₈	C₂×D₅₂	1	2	yes	—
227	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
228	C₄⋊C₄	—	26	2	no	—
229	C₄⋊C₄	—	26	2	no	—
230	C₄⋊C₄	—	52	2	no	—
231	C₄⋊C₄	—	52	2	no	—
232	C₄⋊C₄	—	52	2	no	—
233	C₄⋊C₄	—	52	2	no	—
234	C₂²⋊C₄	—	52	2	no	—
235	C₂²⋊C₄	—	52	2	no	—
236	C₂²⋊C₄	—	52	2	no	—
237	C₂²⋊C₄	—	52	2	no	—
238	C₂²⋊C₄	—	52	2	no	—
239	C₄²	—	52	2	no	—
240	C₄²	D₁₀₄	1	1	yes	characteristic
241	C₄²	D₁₀₄	1	1	yes	characteristic
242	C₄²	C₂×D₅₂	1	2	yes	—
243	C₁₆	—	2	1	no	—
244	C₁₆	—	2	2	no	—
245	C₁₆	—	2	1	no	—
246	C₁₃	#33822	1	1	yes	characteristic, complemented, Sylow
247	C₂³	—	52	2	no	—
248	C₂³	C₂×D₁₀₄	1	1	yes	characteristic
249	Q₈	—	52	2	no	—
250	Q₈	—	52	2	no	—
251	D₄	—	52	2	no	—
252	D₄	—	52	2	no	—
253	D₄	—	104	4	no	—
254	C₂×C₄	—	2	1	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	4	2	no	—
257	C₂×C₄	—	52	2	no	—
258	C₂×C₄	—	52	2	no	—
259	C₂×C₄	—	52	2	no	—
260	C₂×C₄	—	104	4	no	—
261	C₂×C₄	C₂×D₁₀₄	1	2	yes	—
262	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
263	C₂×C₄	C₂×D₁₀₄	1	2	yes	—
264	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
265	C₈	—	2	2	no	—
266	C₈	—	2	1	no	—
267	C₈	#88251	1	1	yes	characteristic
268	C₈	#88254	1	1	yes	characteristic
269	C₂²	—	2	1	no	—
270	C₂²	—	2	2	no	—
271	C₂²	—	104	2	no	—
272	C₂²	—	104	2	no	—
273	C₂²	—	104	2	no	—
274	C₂²	C₂²×D₁₀₄	1	1	yes	characteristic
275	C₄	—	2	1	no	—
276	C₄	—	2	2	no	—
277	C₄	—	2	2	no	—
278	C₄	—	104	2	no	—
279	C₄	—	104	2	no	—
280	C₄	—	104	2	no	—
281	C₄	#11719215	1	1	yes	characteristic
282	C₄	#11719453	1	1	yes	characteristic
283	C₂	—	4	1	no	—
284	C₂	—	208	2	no	—
285	C₂	#13126146	1	1	yes	characteristic
286	C₂	#13127972	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13125406

C₂

yes

maximal, complemented

#13117001

C₂

yes

maximal, complemented

#13116994

C₂

yes

maximal, complemented

#13116949

C₂

yes

maximal, complemented

#13116944

C₂

yes

maximal, characteristic, complemented

#13116939

C₂

yes

maximal, characteristic

#13116899

C₂

yes

maximal, complemented

#13116892

C₂

yes

maximal, complemented

C₁₃×#2150

C₂

yes

maximal, characteristic, complemented

#11719184

—

C₂×C₁₃×M₃₂

C₂²

yes

characteristic

C₂×C₁₃×M₃₂

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

#11718777

C₂²

yes

—

#11718776

C₂²

yes

—

#11718775

—

C₂×Dic₁₀₄

C₂²

yes

characteristic

C₂×#88040

C₂²

yes

—

C₂×D₂₀₈

C₂²

yes

characteristic

C₄×Dic₅₂

C₂²

yes

—

#11718358

—

#11718357

C₂²

yes

—

C₄×D₁₀₄

C₂²

yes

—

C₄×#6095

—

#11718344

C₂²

yes

—

C₁₃×C₄⋊C₁₆

C₂²

yes

—

C₁₃×C₄⋊C₁₆

C₂²

yes

—

#11718101

C₂²

yes

—

#11718101

C₂²

yes

—

#11718097

C₂²

yes

characteristic

#11718097

C₂²

yes

characteristic

#11718096

C₂²

yes

—

#11718095

C₂²

yes

—

#11718095

C₂²

yes

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

characteristic

#88184

—

#88183

—

C₄×C₂²⋊D₁₃

—

#88178

—

C₂×Dic₅₂

C₂³

yes

—

C₂×D₁₀₄

C₂³

yes

—

C₂×#6095

—

#88130

—

#88129

—

C₄×D₅₂

—

#88126

—

#88124

—

C₄×Dic₂₆

—

C₁₃×M₃₂

—

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

C₂³

yes

characteristic

C₂×C₁₃×C₁₆

C₂³

yes

—

C₂×C₁₃×C₁₆

C₂³

yes

characteristic

C₄×C₈×C₁₃

D₄

yes

—

C₄×C₈×C₁₃

C₂³

yes

—

#88061

—

#88061

—

#88058

C₂³

yes

—

#88058

C₂³

yes

—

#88057

—

#88056

—

#88056

—

Dic₁₀₄

—

#88040

—

D₂₀₈

—

#33822

—

maximal, Sylow

C₂²×C₄×C₁₃

D₈

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₁₃

—

C₂×D₅₂

—

C₂×C₄×D₁₃

—

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂⁴

yes

characteristic

C₄²×C₁₃

D₈

yes

characteristic

C₄²×C₁₃

D₈

yes

characteristic

C₄²×C₁₃

C₂×D₄

yes

—

C₂²⋊Dic₁₃

—

—

—

—

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

—

—

—

—

C₄×Dic₁₃

—

Dic₅₂

—

Dic₅₂

—

D₁₀₄

—

D₁₀₄

—

100

#6095

—

101

C₁₃×C₁₆

—

102

C₁₃×C₁₆

—

103

C₁₃×C₁₆

—

104

#3168

—

105

#2229

—

106

#2228

—

107

#2220

—

108

#2219

—

109

#2218

—

110

#2211

—

111

#2210

—

112

#2150

D₁₃

yes

characteristic, complemented

113

C₂³×C₁₃

C₂×D₈

yes

characteristic

114

C₂²×D₁₃

—

115

C₂×C₄×C₁₃

—

116

C₂×C₄×C₁₃

—

117

C₂×C₄×C₁₃

—

118

C₂×C₄×C₁₃

C₂×D₈

yes

—

119

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

120

C₂×C₄×C₁₃

C₂×D₈

yes

—

121

C₂×C₄×C₁₃

C₂²×D₄

yes

characteristic

122

C₂²⋊D₁₃

—

123

C₂×Dic₁₃

—

124

C₂×Dic₁₃

—

125

C₂×Dic₁₃

—

126

D₅₂

—

127

D₅₂

—

128

C₄×D₁₃

—

129

Dic₂₆

—

130

Dic₂₆

—

131

C₈×C₁₃

—

132

C₈×C₁₃

—

133

C₈×C₁₃

H(5,𝔽₂)

yes

characteristic

134

C₈×C₁₃

2₋¹⁺⁴

yes

characteristic

135

#529

—

136

C₂×Q₃₂

—

137

C₂×SD₃₂

—

138

C₂×D₁₆

—

139

C₂×M₃₂

C₂×D₁₃

yes

characteristic

140

C₂×M₃₂

C₂×D₁₃

yes

characteristic

141

#499

—

142

#495

—

143

#488

—

144

#467

—

145

#466

—

146

#465

—

147

C₄×Q₁₆

—

148

C₄×SD₁₆

—

149

C₄×D₈

—

150

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

151

#367

—

152

#367

—

153

#366

—

154

C₄⋊C₁₆

C₂×D₁₃

yes

—

155

C₄⋊C₁₆

C₂×D₁₃

yes

—

156

#358

—

157

#358

—

158

#357

—

159

#357

—

160

C₂²×C₁₃

—

161

C₂²×C₁₃

—

162

C₂²×C₁₃

C₂²×D₈

yes

characteristic

163

C₂×D₁₃

—

164

C₂×D₁₃

—

165

C₂×D₁₃

—

166

C₄×C₁₃

—

167

C₄×C₁₃

—

168

C₄×C₁₃

—

169

C₄×C₁₃

#537

yes

characteristic

170

C₄×C₁₃

#575

yes

characteristic

171

Dic₁₃

—

172

Dic₁₃

—

173

Dic₁₃

—

174

C₂×Q₁₆

—

175

C₂×SD₁₆

—

176

C₂×D₈

—

177

C₂²×C₈

D₅₂

yes

characteristic

178

C₂²×C₈

C₂²×D₁₃

yes

characteristic

179

#126

—

180

#125

—

181

#124

—

182

#123

—

183

C₂²⋊Q₈

—

184

#121

—

185

C₄×Q₈

—

186

C₄×D₄

—

187

C₄×D₄

—

188

#117

—

189

C₂×C₄²

D₅₂

yes

characteristic

190

Q₃₂

—

191

SD₃₂

—

192

D₁₆

—

193

M₃₂

—

194

M₃₂

—

195

C₂×C₁₆

C₂²×D₁₃

yes

characteristic

196

C₂×C₁₆

C₂²×D₁₃

yes

—

197

C₂×C₁₆

C₂²×D₁₃

yes

characteristic

198

#107

—

199

#107

—

200

#106

—

201

#103

—

202

#103

—

203

#102

—

204

#102

—

205

C₄×C₈

D₅₂

yes

—

206

C₄×C₈

C₂²×D₁₃

yes

—

207

C₂×C₁₃

—

208

C₂×C₁₃

#3245

yes

characteristic

209

C₂×C₁₃

#3414

yes

—

210

D₁₃

—

211

C₂×Q₈

—

212

C₂×D₄

—

213

C₂×D₄

—

214

C₂²×C₄

—

215

C₂²×C₄

D₁₀₄

yes

—

216

C₂²×C₄

C₂×D₅₂

yes

characteristic

217

Q₁₆

—

218

Q₁₆

—

219

SD₁₆

—

220

D₈

—

221

D₈

—

222

C₂×C₈

—

223

C₂×C₈

—

224

C₂×C₈

—

225

C₂×C₈

C₂×D₅₂

yes

characteristic

226

C₂×C₈

C₂×D₅₂

yes

—

227

C₂×C₈

C₂³×D₁₃

yes

characteristic

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₂²⋊C₄

—

235

C₂²⋊C₄

—

236

C₂²⋊C₄

—

237

C₂²⋊C₄

—

238

C₂²⋊C₄

—

239

C₄²

—

240

C₄²

D₁₀₄

yes

characteristic

241

C₄²

D₁₀₄

yes

characteristic

242

C₄²

C₂×D₅₂

yes

—

243

C₁₆

—

244

C₁₆

—

245

C₁₆

—

246

C₁₃

#33822

yes

characteristic, complemented, Sylow

247

C₂³

—

248

C₂³

C₂×D₁₀₄

yes

characteristic

249

Q₈

—

250

Q₈

—

251

D₄

—

252

D₄

—

253

D₄

—

104

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

104

—

261

C₂×C₄

C₂×D₁₀₄

yes

—

262

C₂×C₄

C₂×D₁₀₄

yes

characteristic

263

C₂×C₄

C₂×D₁₀₄

yes

—

264

C₂×C₄

C₂²×D₅₂

yes

characteristic

265

C₈

—

266

C₈

—

267

C₈

#88251

yes

characteristic

268

C₈

#88254

yes

characteristic

269

C₂²

—

270

C₂²

—

271

C₂²

—

104

—

272

C₂²

—

104

—

273

C₂²

—

104

—

274

C₂²

C₂²×D₁₀₄

yes

characteristic

275

C₄

—

276

C₄

—

277

C₄

—

278

C₄

—

104

—

279

C₄

—

104

—

280

C₄

—

104

—

281

C₄

#11719215

yes

characteristic

282

C₄

#11719453

yes

characteristic

283

C₂

—

284

C₂

—

208

—

285

C₂

#13126146

yes

characteristic

286

C₂

#13127972

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₁₀₄
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2150	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	#13116939	C₂
hypercenter	#2150	D₁₃
hypocenter	C₁₃	#33822
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2150

subgroup

G/H

center

C₂²

C₂²×D₁₀₄

commutator, cosocle

C₂×C₈×C₁₃

C₂⁴

Frattini

C₂×C₈

C₂³×D₁₃

Fitting

C₁₃×#2150

C₂

socle

C₂²×C₁₃

C₂²×D₈

C₂

D₁₃

C₁₃

G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2150

N	H ≅ G/N	type
1. #13125406	C₂	semidirect
2. #13117001	C₂	semidirect
3. #13116994	C₂	semidirect
4. #13116949	C₂	semidirect
5. #13116944	C₂	semidirect
7. #13116899	C₂	semidirect
8. #13116892	C₂	semidirect
9. C₁₃×#2150	C₂	semidirect
112. #2150	D₁₃	semidirect
246. C₁₃	#33822	semidirect

H ≅ G/N

type

1. #13125406

C₂

semidirect

2. #13117001

C₂

semidirect

3. #13116994

C₂

semidirect

4. #13116949

C₂

semidirect

5. #13116944

C₂

semidirect

7. #13116899

C₂

semidirect

8. #13116892

C₂

semidirect

9. C₁₃×#2150

C₂

semidirect

112. #2150

D₁₃

semidirect

246. C₁₃

#33822

semidirect

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

subgroup	index
#13125406	2
#13117001	2
#13116994	2
#13116949	2
#13116944	2
#13116939	2
#13116899	2
#13116892	2
C₁₃×#2150	2
#33822	13

subgroup

index

C₁₃×#2150

Subgroups — #16019298

Conjugacy classes of subgroups

Complements

Maximal subgroups