Group #36473290 — subgroups

Subgroups — #36473290

Order 22784.

558 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 558 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	C₂²×Dic₇₁₂	C₂	1	2	yes	maximal
2	C₂×#19151978	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151403	C₂	1	2	yes	maximal
4	#26021113	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#1374	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₅₆	—	2	1	no	—
7	C₂²×Dic₃₅₆	C₂²	1	2	yes	—
8	C₂²×Dic₃₅₆	C₂²	1	1	yes	characteristic
9	C₂×#15668012	—	2	1	no	—
10	C₂×Dic₇₁₂	—	2	4	no	—
11	C₂×Dic₇₁₂	—	2	4	no	—
12	C₂×Dic₇₁₂	—	2	4	no	—
13	#19151978	—	2	4	no	—
14	C₂×#15667946	C₂²	1	1	yes	characteristic
15	C₂×#15667937	—	2	1	no	—
16	#19151504	—	2	1	no	—
17	#19151403	—	2	4	no	—
18	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×Dic₁₇₈	—	2	2	no	—
21	C₂²×Dic₁₇₈	—	2	1	no	—
22	C₂×Dic₃₅₆	—	2	4	no	—
23	C₂×Dic₃₅₆	—	2	2	no	—
24	C₂×Dic₃₅₆	—	2	2	no	—
25	C₂×Dic₃₅₆	—	2	2	no	—
26	C₂×Dic₃₅₆	—	2	2	no	—
27	C₂×Dic₃₅₆	—	2	2	no	—
28	C₂×Dic₃₅₆	—	2	2	no	—
29	C₂×Dic₃₅₆	—	2	2	no	—
30	C₂×Dic₃₅₆	—	2	1	no	—
31	C₂×Dic₃₅₆	—	4	2	no	—
32	C₂×Dic₃₅₆	—	4	2	no	—
33	C₂×Dic₃₅₆	D₄	1	4	yes	—
34	C₂×Dic₃₅₆	D₄	1	2	yes	—
35	#15668012	—	2	4	no	—
36	#15668012	—	4	2	no	—
37	C₂×C₄⋊Dic₈₉	—	2	1	no	—
38	C₂×C₄⋊Dic₈₉	—	4	2	no	—
39	Dic₇₁₂	—	2	16	no	—
40	#15667946	—	2	2	no	—
41	#15667937	—	4	2	no	—
42	#15667919	—	4	2	no	—
43	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
45	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
46	C₂×C₁₆×C₈₉	—	2	2	no	—
47	C₂×C₁₆×C₈₉	—	2	2	no	—
48	C₂×C₁₆×C₈₉	D₄	1	4	yes	—
49	C₄×C₈×C₈₉	—	2	2	no	—
50	C₂×Dic₁₇₈	—	2	4	no	—
51	C₂×Dic₁₇₈	—	2	2	no	—
52	C₂×Dic₁₇₈	—	4	1	no	—
53	C₂×Dic₁₇₈	—	4	2	no	—
54	C₂×Dic₁₇₈	—	4	2	no	—
55	C₂×Dic₁₇₈	—	4	1	no	—
56	C₂×Dic₁₇₈	—	4	2	no	—
57	C₂×Dic₁₇₈	—	4	1	no	—
58	C₂×Dic₁₇₈	—	4	2	no	—
59	C₂×Dic₁₇₈	—	4	1	no	—
60	C₂×Dic₁₇₈	—	4	2	no	—
61	C₂×Dic₁₇₈	—	4	1	no	—
62	C₂²×Dic₈₉	—	4	1	no	—
63	C₂²×Dic₈₉	—	4	2	no	—
64	C₂²×Dic₈₉	—	4	1	no	—
65	Dic₃₅₆	—	2	4	no	—
66	Dic₃₅₆	—	2	4	no	—
67	Dic₃₅₆	—	2	4	no	—
68	Dic₃₅₆	—	4	8	no	—
69	Dic₃₅₆	—	4	2	no	—
70	Dic₃₅₆	—	4	2	no	—
71	Dic₃₅₆	—	4	2	no	—
72	C₄⋊Dic₈₉	—	4	8	no	—
73	C₄⋊Dic₈₉	—	4	1	no	—
74	C₄⋊Dic₈₉	—	4	1	no	—
75	C₂²×C₄×C₈₉	D₈	1	2	yes	—
76	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₈₉	—	2	1	no	—
78	C₂×C₈×C₈₉	—	2	1	no	—
79	C₂×C₈×C₈₉	D₈	1	2	yes	—
80	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
82	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
83	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
84	C₄²×C₈₉	—	2	1	no	—
85	C₄²×C₈₉	—	2	1	no	—
86	C₁₆×C₈₉	—	2	4	no	—
87	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
88	C₂×C₄×C₈₉	—	2	2	no	—
89	C₂×C₄×C₈₉	—	2	2	no	—
90	C₂×C₄×C₈₉	Q₃₂	1	4	yes	complemented
91	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
92	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
93	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
94	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
95	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
96	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
97	C₂×Dic₈₉	—	4	4	no	—
98	C₂×Dic₈₉	—	4	2	no	—
99	C₂×Dic₈₉	—	8	1	no	—
100	C₂×Dic₈₉	—	8	2	no	—
101	C₂×Dic₈₉	—	8	1	no	—
102	C₂×Dic₈₉	—	8	2	no	—
103	C₂×Dic₈₉	—	8	1	no	—
104	C₂×Dic₈₉	—	8	2	no	—
105	Dic₁₇₈	—	4	2	no	—
106	Dic₁₇₈	—	4	4	no	—
107	Dic₁₇₈	—	4	4	no	—
108	Dic₁₇₈	—	4	2	no	—
109	Dic₁₇₈	—	8	1	no	—
110	Dic₁₇₈	—	8	2	no	—
111	Dic₁₇₈	—	8	2	no	—
112	Dic₁₇₈	—	8	1	no	—
113	C₈×C₈₉	—	2	2	no	—
114	C₈×C₈₉	#120	1	2	yes	—
115	C₈×C₈₉	#121	1	2	yes	—
116	C₂²×C₈₉	#447	1	1	yes	characteristic
117	C₂²×C₈₉	#459	1	1	yes	characteristic
118	C₂²×C₈₉	#493	1	1	yes	characteristic
119	C₂²×C₈₉	C₂×Q₃₂	1	2	yes	—
120	C₂²×C₈₉	#510	1	2	yes	—
121	C₄×C₈₉	—	2	4	no	—
122	C₄×C₈₉	#392	1	1	yes	characteristic
123	C₄×C₈₉	#447	1	1	yes	characteristic
124	C₄×C₈₉	#459	1	1	yes	characteristic
125	C₄×C₈₉	#496	1	1	yes	characteristic
126	Dic₈₉	—	8	4	no	—
127	Dic₈₉	—	8	2	no	—
128	Dic₈₉	—	16	1	no	—
129	#13330	—	89	1	no	maximal, Sylow
130	C₂×C₈₉	#2011	1	1	yes	characteristic
131	C₂×C₈₉	#2188	1	2	yes	—
132	C₂×C₈₉	#2209	1	2	yes	—
133	C₂×C₈₉	#2247	1	1	yes	characteristic
134	C₂×C₈₉	#2251	1	1	yes	characteristic
135	C₂²×Q₃₂	—	89	2	no	—
136	C₂×#494	—	89	1	no	—
137	C₂×#358	—	89	2	no	—
138	#1969	—	89	1	no	—
139	#1374	D₈₉	1	1	yes	characteristic
140	C₈₉	#13330	1	1	yes	characteristic, complemented, Sylow
141	C₂²×Q₁₆	—	89	2	no	—
142	C₂²×Q₁₆	—	89	1	no	—
143	C₂²×Q₁₆	—	178	1	no	—
144	C₂×C₄⋊Q₈	—	178	1	no	—
145	C₂×Q₃₂	—	178	4	no	—
146	C₂×Q₃₂	—	178	4	no	—
147	C₂×Q₃₂	—	178	4	no	—
148	C₂²×C₁₆	C₂×D₈₉	1	2	yes	—
149	#494	—	178	4	no	—
150	C₂×#107	—	89	1	no	—
151	C₂×#103	—	178	1	no	—
152	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
153	#391	—	178	1	no	—
154	#358	—	178	4	no	—
155	C₂²×Q₈	—	178	2	no	—
156	C₂²×Q₈	—	178	1	no	—
157	C₂×Q₁₆	—	89	4	no	—
158	C₂×Q₁₆	—	89	2	no	—
159	C₂×Q₁₆	—	356	2	no	—
160	C₂×Q₁₆	—	356	2	no	—
161	C₂×Q₁₆	—	178	4	no	—
162	C₂×Q₁₆	—	178	2	no	—
163	C₂×Q₁₆	—	178	2	no	—
164	C₂×Q₁₆	—	178	2	no	—
165	C₂×Q₁₆	—	178	2	no	—
166	C₂×Q₁₆	—	178	2	no	—
167	C₂×Q₁₆	—	178	2	no	—
168	C₂×Q₁₆	—	178	1	no	—
169	C₂×Q₁₆	—	178	2	no	—
170	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
171	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
172	C₄⋊Q₈	—	356	2	no	—
173	C₄⋊Q₈	—	178	4	no	—
174	C₂×C₄⋊C₄	—	356	2	no	—
175	C₂×C₄⋊C₄	—	178	1	no	—
176	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
177	Q₃₂	—	178	16	no	—
178	C₂×C₁₆	—	2	2	no	—
179	C₂×C₁₆	—	2	2	no	—
180	C₂×C₁₆	D₃₅₆	1	4	yes	—
181	#107	—	178	2	no	—
182	#103	—	356	2	no	—
183	C₄×C₈	—	2	2	no	—
184	#95	—	356	2	no	—
185	C₂×Q₈	—	356	2	no	—
186	C₂×Q₈	—	356	1	no	—
187	C₂×Q₈	—	356	1	no	—
188	C₂×Q₈	—	356	2	no	—
189	C₂×Q₈	—	356	2	no	—
190	C₂×Q₈	—	356	1	no	—
191	C₂×Q₈	—	356	1	no	—
192	C₂×Q₈	—	356	2	no	—
193	C₂×Q₈	—	356	2	no	—
194	C₂×Q₈	—	356	1	no	—
195	C₂×Q₈	—	178	4	no	—
196	C₂×Q₈	—	178	2	no	—
197	C₂²×C₄	—	356	1	no	—
198	C₂²×C₄	—	356	2	no	—
199	C₂²×C₄	—	356	1	no	—
200	C₂²×C₄	D₇₁₂	1	2	yes	—
201	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
202	Q₁₆	—	356	8	no	—
203	Q₁₆	—	356	2	no	—
204	Q₁₆	—	356	2	no	—
205	Q₁₆	—	356	2	no	—
206	Q₁₆	—	178	4	no	—
207	Q₁₆	—	178	4	no	—
208	Q₁₆	—	178	4	no	—
209	C₂×C₈	—	2	1	no	—
210	C₂×C₈	—	2	1	no	—
211	C₂×C₈	D₇₁₂	1	2	yes	—
212	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
213	C₂×C₈	D₄×D₈₉	1	2	yes	—
214	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
215	C₂×C₈	#13083575	1	1	yes	characteristic
216	C₄⋊C₄	—	356	8	no	—
217	C₄⋊C₄	—	356	1	no	—
218	C₄⋊C₄	—	356	1	no	—
219	C₄²	—	2	1	no	—
220	C₄²	—	2	1	no	—
221	C₁₆	—	2	4	no	—
222	C₂³	C₂×D₇₁₂	1	1	yes	characteristic
223	Q₈	—	356	4	no	—
224	Q₈	—	356	4	no	—
225	Q₈	—	356	2	no	—
226	Q₈	—	356	2	no	—
227	Q₈	—	712	2	no	—
228	Q₈	—	712	1	no	—
229	Q₈	—	712	1	no	—
230	Q₈	—	712	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	356	4	no	—
234	C₂×C₄	—	356	2	no	—
235	C₂×C₄	—	712	1	no	—
236	C₂×C₄	—	712	2	no	—
237	C₂×C₄	—	712	1	no	—
238	C₂×C₄	—	712	2	no	—
239	C₂×C₄	—	712	1	no	—
240	C₂×C₄	—	712	2	no	—
241	C₂×C₄	Dic₇₁₂	1	4	yes	complemented
242	C₂×C₄	#15667982	1	1	yes	characteristic
243	C₂×C₄	#15667987	1	1	yes	characteristic
244	C₂×C₄	#15668009	1	1	yes	characteristic
245	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
246	C₂×C₄	#15668040	1	1	yes	characteristic
247	C₂×C₄	#15668040	1	1	yes	characteristic
248	C₈	—	2	2	no	—
249	C₈	#15667982	1	2	yes	—
250	C₈	#15667987	1	2	yes	—
251	C₂²	#19151734	1	1	yes	characteristic
252	C₂²	#19151794	1	1	yes	characteristic
253	C₂²	#19151975	1	1	yes	characteristic
254	C₂²	C₂×Dic₇₁₂	1	2	yes	—
255	C₂²	#19152041	1	2	yes	—
256	C₄	—	2	4	no	—
257	C₄	—	1424	1	no	—
258	C₄	—	712	4	no	—
259	C₄	—	712	2	no	—
260	C₄	#19151508	1	1	yes	characteristic
261	C₄	#19151734	1	1	yes	characteristic
262	C₄	#19151794	1	1	yes	characteristic
263	C₄	#19151987	1	1	yes	characteristic
264	C₂	#26021325	1	1	yes	characteristic
265	C₂	#26022188	1	2	yes	—
266	C₂	#26022303	1	2	yes	—
267	C₂	#26022505	1	1	yes	characteristic
268	C₂	#26022523	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₇₁₂

C₂

yes

maximal

C₂×#19151978

C₂

yes

maximal, characteristic

C₂×#19151403

C₂

yes

maximal

#26021113

C₂

yes

maximal, characteristic

C₈₉×#1374

C₂

yes

maximal, characteristic

C₂²×Dic₃₅₆

—

C₂²×Dic₃₅₆

C₂²

yes

—

C₂²×Dic₃₅₆

C₂²

yes

characteristic

C₂×#15668012

—

C₂×Dic₇₁₂

—

C₂×Dic₇₁₂

—

C₂×Dic₇₁₂

—

#19151978

—

C₂×#15667946

C₂²

yes

—

—

—

C₂²×C₁₆×C₈₉

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

C₂²×Dic₁₇₈

—

C₂²×Dic₁₇₈

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

D₄

yes

—

C₂×Dic₃₅₆

D₄

yes

—

#15668012

—

#15668012

—

C₂×C₄⋊Dic₈₉

—

C₂×C₄⋊Dic₈₉

—

Dic₇₁₂

—

#15667946

—

#15667937

—

#15667919

—

C₂²×C₈×C₈₉

D₄

yes

characteristic

C₂²×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₄²×C₈₉

D₄

yes

characteristic

C₂×C₁₆×C₈₉

—

C₂×C₁₆×C₈₉

—

C₂×C₁₆×C₈₉

D₄

yes

—

C₄×C₈×C₈₉

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₂²×C₄×C₈₉

D₈

yes

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

D₈

yes

—

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

—

C₂×C₈×C₈₉

C₂×D₄

yes

—

C₂×C₈×C₈₉

#41

yes

characteristic

C₄²×C₈₉

—

C₄²×C₈₉

—

C₁₆×C₈₉

—

C₂³×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

Q₃₂

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

C₂×D₈

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

100

C₂×Dic₈₉

—

101

C₂×Dic₈₉

—

102

C₂×Dic₈₉

—

103

C₂×Dic₈₉

—

104

C₂×Dic₈₉

—

105

Dic₁₇₈

—

106

Dic₁₇₈

—

107

Dic₁₇₈

—

108

Dic₁₇₈

—

109

Dic₁₇₈

—

110

Dic₁₇₈

—

111

Dic₁₇₈

—

112

Dic₁₇₈

—

113

C₈×C₈₉

—

114

C₈×C₈₉

#120

yes

—

115

C₈×C₈₉

#121

yes

—

116

C₂²×C₈₉

#447

yes

characteristic

117

C₂²×C₈₉

#459

yes

characteristic

118

C₂²×C₈₉

#493

yes

characteristic

119

C₂²×C₈₉

C₂×Q₃₂

yes

—

120

C₂²×C₈₉

#510

yes

—

121

C₄×C₈₉

—

122

C₄×C₈₉

#392

yes

characteristic

123

C₄×C₈₉

#447

yes

characteristic

124

C₄×C₈₉

#459

yes

characteristic

125

C₄×C₈₉

#496

yes

characteristic

126

Dic₈₉

—

127

Dic₈₉

—

128

Dic₈₉

—

129

#13330

—

maximal, Sylow

130

C₂×C₈₉

#2011

yes

characteristic

131

C₂×C₈₉

#2188

yes

—

132

C₂×C₈₉

#2209

yes

—

133

C₂×C₈₉

#2247

yes

characteristic

134

C₂×C₈₉

#2251

yes

characteristic

135

C₂²×Q₃₂

—

136

C₂×#494

—

137

C₂×#358

—

138

#1969

—

139

#1374

D₈₉

yes

characteristic

140

C₈₉

#13330

yes

characteristic, complemented, Sylow

141

C₂²×Q₁₆

—

142

C₂²×Q₁₆

—

143

C₂²×Q₁₆

—

178

—

144

C₂×C₄⋊Q₈

—

178

—

145

C₂×Q₃₂

—

178

—

146

C₂×Q₃₂

—

178

—

147

C₂×Q₃₂

—

178

—

148

C₂²×C₁₆

C₂×D₈₉

yes

—

149

#494

—

178

—

150

C₂×#107

—

151

C₂×#103

—

178

—

152

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

153

#391

—

178

—

154

#358

—

178

—

155

C₂²×Q₈

—

178

—

156

C₂²×Q₈

—

178

—

157

C₂×Q₁₆

—

158

C₂×Q₁₆

—

159

C₂×Q₁₆

—

356

—

160

C₂×Q₁₆

—

356

—

161

C₂×Q₁₆

—

178

—

162

C₂×Q₁₆

—

178

—

163

C₂×Q₁₆

—

178

—

164

C₂×Q₁₆

—

178

—

165

C₂×Q₁₆

—

178

—

166

C₂×Q₁₆

—

178

—

167

C₂×Q₁₆

—

178

—

168

C₂×Q₁₆

—

178

—

169

C₂×Q₁₆

—

178

—

170

C₂²×C₈

D₃₅₆

yes

characteristic

171

C₂²×C₈

C₂²×D₈₉

yes

characteristic

172

C₄⋊Q₈

—

356

—

173

C₄⋊Q₈

—

178

—

174

C₂×C₄⋊C₄

—

356

—

175

C₂×C₄⋊C₄

—

178

—

176

C₂×C₄²

D₃₅₆

yes

characteristic

177

Q₃₂

—

178

—

178

C₂×C₁₆

—

179

C₂×C₁₆

—

180

C₂×C₁₆

D₃₅₆

yes

—

181

#107

—

178

—

182

#103

—

356

—

183

C₄×C₈

—

184

#95

—

356

—

185

C₂×Q₈

—

356

—

186

C₂×Q₈

—

356

—

187

C₂×Q₈

—

356

—

188

C₂×Q₈

—

356

—

189

C₂×Q₈

—

356

—

190

C₂×Q₈

—

356

—

191

C₂×Q₈

—

356

—

192

C₂×Q₈

—

356

—

193

C₂×Q₈

—

356

—

194

C₂×Q₈

—

356

—

195

C₂×Q₈

—

178

—

196

C₂×Q₈

—

178

—

197

C₂²×C₄

—

356

—

198

C₂²×C₄

—

356

—

199

C₂²×C₄

—

356

—

200

C₂²×C₄

D₇₁₂

yes

—

201

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

202

Q₁₆

—

356

—

203

Q₁₆

—

356

—

204

Q₁₆

—

356

—

205

Q₁₆

—

356

—

206

Q₁₆

—

178

—

207

Q₁₆

—

178

—

208

Q₁₆

—

178

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

D₇₁₂

yes

—

212

C₂×C₈

D₄×D₈₉

yes

characteristic

213

C₂×C₈

D₄×D₈₉

yes

—

214

C₂×C₈

C₂×D₃₅₆

yes

—

215

C₂×C₈

#13083575

yes

characteristic

216

C₄⋊C₄

—

356

—

217

C₄⋊C₄

—

356

—

218

C₄⋊C₄

—

356

—

219

C₄²

—

220

C₄²

—

221

C₁₆

—

222

C₂³

C₂×D₇₁₂

yes

characteristic

223

Q₈

—

356

—

224

Q₈

—

356

—

225

Q₈

—

356

—

226

Q₈

—

356

—

227

Q₈

—

712

—

228

Q₈

—

712

—

229

Q₈

—

712

—

230

Q₈

—

712

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

356

—

234

C₂×C₄

—

356

—

235

C₂×C₄

—

712

—

236

C₂×C₄

—

712

—

237

C₂×C₄

—

712

—

238

C₂×C₄

—

712

—

239

C₂×C₄

—

712

—

240

C₂×C₄

—

712

—

241

C₂×C₄

Dic₇₁₂

yes

complemented

242

C₂×C₄

#15667982

yes

characteristic

243

C₂×C₄

#15667987

yes

characteristic

244

C₂×C₄

#15668009

yes

characteristic

245

C₂×C₄

C₂×D₇₁₂

yes

characteristic

246

C₂×C₄

#15668040

yes

characteristic

247

C₂×C₄

#15668040

yes

characteristic

248

C₈

—

249

C₈

#15667982

yes

—

250

C₈

#15667987

yes

—

251

C₂²

#19151734

yes

characteristic

252

C₂²

#19151794

yes

characteristic

253

C₂²

#19151975

yes

characteristic

254

C₂²

C₂×Dic₇₁₂

yes

—

255

C₂²

#19152041

yes

—

256

C₄

—

257

C₄

—

1424

—

258

C₄

—

712

—

259

C₄

—

712

—

260

C₄

#19151508

yes

characteristic

261

C₄

#19151734

yes

characteristic

262

C₄

#19151794

yes

characteristic

263

C₄

#19151987

yes

characteristic

264

C₂

#26021325

yes

characteristic

265

C₂

#26022188

yes

—

266

C₂

#26022303

yes

—

267

C₂

#26022505

yes

characteristic

268

C₂

#26022523

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₇₁₂
commutator, cosocle	C₂²×C₈×C₈₉	C₂³
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₈₉×#1374	C₂
socle, prime radical	C₂³×C₈₉	C₂×D₈
hypercenter	#1374	D₈₉
hypocenter	C₈₉	#13330
LCS	G ▷ C₂²×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

subgroup

G/H

center

C₂³

C₂×D₇₁₂

commutator, cosocle

C₂²×C₈×C₈₉

C₂³

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting

C₈₉×#1374

C₂

socle, prime radical

C₂³×C₈₉

C₂×D₈

D₈₉

C₈₉

G ▷ C₂²×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

N	H ≅ G/N	type
90. C₂×C₄×C₈₉	Q₃₂	semidirect
140. C₈₉	#13330	semidirect
241. C₂×C₄	Dic₇₁₂	semidirect

H ≅ G/N

type

90. C₂×C₄×C₈₉

Q₃₂

semidirect

140. C₈₉

#13330

semidirect

241. C₂×C₄

Dic₇₁₂

semidirect

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

subgroup	index
C₂²×Dic₇₁₂	2
C₂×#19151978	2
C₂×#19151403	2
#26021113	2
C₈₉×#1374	2
#13330	89

subgroup

index

C₂²×Dic₇₁₂

C₈₉×#1374

Subgroups — #36473290

Conjugacy classes of subgroups

Complements

Maximal subgroups