Group #36473276 — subgroups

Subgroups — #36473276

Order 22784.

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

normal subgroups only

This group has 662 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×#15667956	C₂	1	2	yes	maximal, complemented
2	C₂×#19151399	C₂	1	2	yes	maximal, complemented
3	#26021113	C₂	1	1	yes	maximal, characteristic, complemented
4	#26018330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#493×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₅₆	C₂²	1	1	yes	characteristic
7	C₂×#15667956	—	2	4	no	—
8	C₂×#15667956	—	2	4	no	—
9	C₂×#15667956	—	2	4	no	—
10	C₂²×#13083549	C₂²	1	2	yes	—
11	C₂×#15667946	C₂²	1	1	yes	characteristic
12	C₂×#15667937	—	2	1	no	—
13	#19151504	—	2	1	no	—
14	#19151399	—	2	4	no	—
15	C₂²×D₈×C₈₉	—	2	1	no	—
16	C₂²×D₈×C₈₉	C₂²	1	2	yes	—
17	C₂×#127×C₈₉	—	2	1	no	—
18	#493×C₈₉	—	2	4	no	—
19	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×Dic₁₇₈	—	2	1	no	—
21	C₂×Dic₃₅₆	—	2	2	no	—
22	C₂×Dic₃₅₆	—	2	2	no	—
23	C₂×Dic₃₅₆	—	2	1	no	—
24	C₂×Dic₃₅₆	D₄	1	2	yes	complemented
25	C₂×C₄⋊Dic₈₉	—	2	1	no	—
26	#15667956	—	2	16	no	—
27	C₂×#13083549	—	2	2	no	—
28	C₂×#13083549	—	2	2	no	—
29	C₂×#13083549	D₄	1	4	yes	complemented
30	#15667946	—	2	2	no	—
31	#15667937	—	4	2	no	—
32	#15667919	—	4	2	no	—
33	C₂²×D₄×C₈₉	—	2	2	no	—
34	C₂²×D₄×C₈₉	—	4	2	no	—
35	C₂×D₈×C₈₉	—	2	4	no	—
36	C₂×D₈×C₈₉	—	2	2	no	—
37	C₂×D₈×C₈₉	—	2	2	no	—
38	C₂×D₈×C₈₉	—	2	2	no	—
39	C₂×D₈×C₈₉	—	2	2	no	—
40	C₂×D₈×C₈₉	—	2	2	no	—
41	C₂×D₈×C₈₉	—	4	2	no	—
42	C₂×D₈×C₈₉	—	4	2	no	—
43	C₂×D₈×C₈₉	D₄	1	4	yes	—
44	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
46	#127×C₈₉	—	2	4	no	—
47	#127×C₈₉	—	4	2	no	—
48	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₈₉	—	2	2	no	—
50	C₂×Dic₁₇₈	—	2	2	no	—
51	C₂×Dic₁₇₈	—	4	1	no	—
52	C₂×Dic₁₇₈	—	4	1	no	—
53	C₂×Dic₁₇₈	—	4	1	no	—
54	C₂×Dic₁₇₈	—	4	1	no	—
55	C₂×Dic₁₇₈	—	4	1	no	—
56	C₂²×Dic₈₉	—	4	1	no	—
57	C₂²×Dic₈₉	—	4	1	no	—
58	Dic₃₅₆	—	2	4	no	—
59	Dic₃₅₆	—	4	2	no	—
60	C₄⋊Dic₈₉	—	4	1	no	—
61	C₄⋊Dic₈₉	—	4	1	no	—
62	#13083549	—	2	4	no	—
63	C₂⁴×C₈₉	—	4	2	no	—
64	C₂×D₄×C₈₉	—	2	4	no	—
65	C₂×D₄×C₈₉	—	4	8	no	—
66	C₂×D₄×C₈₉	—	4	2	no	—
67	C₂×D₄×C₈₉	—	4	2	no	—
68	C₂×D₄×C₈₉	—	4	2	no	—
69	C₂×D₄×C₈₉	—	4	2	no	—
70	C₂×D₄×C₈₉	—	4	2	no	—
71	C₂×D₄×C₈₉	—	8	4	no	—
72	C₂×D₄×C₈₉	—	8	4	no	—
73	C₂²×C₄×C₈₉	D₈	1	2	yes	—
74	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
75	D₈×C₈₉	—	2	4	no	—
76	D₈×C₈₉	—	2	4	no	—
77	D₈×C₈₉	—	4	8	no	—
78	D₈×C₈₉	—	4	2	no	—
79	D₈×C₈₉	—	4	2	no	—
80	C₂×C₈×C₈₉	—	2	1	no	—
81	C₂×C₈×C₈₉	—	2	1	no	—
82	C₂×C₈×C₈₉	D₈	1	2	yes	—
83	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
85	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
86	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
87	C₄²×C₈₉	—	2	1	no	—
88	C₄²×C₈₉	—	2	1	no	—
89	C₂³×C₈₉	—	4	4	no	—
90	C₂³×C₈₉	—	8	2	no	—
91	C₂³×C₈₉	—	8	2	no	—
92	C₂³×C₈₉	—	8	4	no	—
93	C₂³×C₈₉	—	8	4	no	—
94	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
95	D₄×C₈₉	—	4	4	no	—
96	D₄×C₈₉	—	4	4	no	—
97	D₄×C₈₉	—	8	16	no	—
98	D₄×C₈₉	—	8	2	no	—
99	D₄×C₈₉	—	8	2	no	—
100	C₂×C₄×C₈₉	—	2	2	no	—
101	C₂×C₄×C₈₉	—	2	2	no	—
102	C₂×C₄×C₈₉	SD₃₂	1	4	yes	complemented
103	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
104	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
105	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
106	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
107	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
108	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
109	C₂×Dic₈₉	—	4	2	no	—
110	C₂×Dic₈₉	—	8	1	no	—
111	C₂×Dic₈₉	—	8	1	no	—
112	C₂×Dic₈₉	—	8	1	no	—
113	C₂×Dic₈₉	—	8	2	no	—
114	Dic₁₇₈	—	4	2	no	—
115	Dic₁₇₈	—	4	2	no	—
116	Dic₁₇₈	—	8	1	no	—
117	Dic₁₇₈	—	8	1	no	—
118	C₈×C₈₉	—	2	2	no	—
119	C₈×C₈₉	#120	1	2	yes	—
120	C₈×C₈₉	#121	1	2	yes	—
121	C₂²×C₈₉	—	8	8	no	—
122	C₂²×C₈₉	—	8	4	no	—
123	C₂²×C₈₉	—	16	4	no	—
124	C₂²×C₈₉	—	16	2	no	—
125	C₂²×C₈₉	—	16	2	no	—
126	C₂²×C₈₉	#447	1	1	yes	characteristic
127	C₂²×C₈₉	#459	1	1	yes	characteristic
128	C₂²×C₈₉	#493	1	1	yes	characteristic
129	C₂²×C₈₉	C₂×SD₃₂	1	2	yes	—
130	C₂²×C₈₉	#509	1	2	yes	—
131	C₄×C₈₉	—	2	4	no	—
132	C₄×C₈₉	#392	1	1	yes	characteristic
133	C₄×C₈₉	#447	1	1	yes	characteristic
134	C₄×C₈₉	#459	1	1	yes	characteristic
135	C₄×C₈₉	#496	1	1	yes	characteristic
136	Dic₈₉	—	8	2	no	—
137	Dic₈₉	—	16	1	no	—
138	#13328	—	89	1	no	maximal, Sylow
139	C₂×C₈₉	—	16	4	no	—
140	C₂×C₈₉	#2011	1	1	yes	characteristic
141	C₂×C₈₉	#2187	1	2	yes	—
142	C₂×C₈₉	#2207	1	2	yes	—
143	C₂×C₈₉	#2248	1	1	yes	characteristic
144	C₂×C₈₉	#2250	1	1	yes	characteristic
145	C₂²×SD₃₂	—	89	2	no	—
146	C₂×#493	D₈₉	1	1	yes	characteristic
147	C₂×#357	—	89	2	no	—
148	#1969	—	89	1	no	—
149	#1374	—	89	1	no	—
150	C₈₉	#13328	1	1	yes	characteristic, complemented, Sylow
151	C₂²×Q₁₆	—	89	1	no	—
152	C₂²×D₈	—	2	1	no	—
153	C₂²×D₈	C₂×D₈₉	1	2	yes	—
154	C₂×#127	—	2	1	no	—
155	C₂×SD₃₂	—	178	4	no	—
156	C₂×SD₃₂	—	178	4	no	—
157	C₂×SD₃₂	—	178	4	no	—
158	C₂²×C₁₆	—	89	2	no	—
159	#493	—	2	4	no	—
160	C₂×#107	—	89	1	no	—
161	C₂×#103	—	178	1	no	—
162	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
163	#391	—	178	1	no	—
164	#357	—	178	4	no	—
165	C₂²×Q₈	—	178	1	no	—
166	C₂²×D₄	—	2	2	no	—
167	C₂²×D₄	—	4	2	no	—
168	C₂×Q₁₆	—	89	2	no	—
169	C₂×Q₁₆	—	178	2	no	—
170	C₂×Q₁₆	—	178	2	no	—
171	C₂×Q₁₆	—	178	1	no	—
172	C₂×D₈	—	2	4	no	—
173	C₂×D₈	—	2	2	no	—
174	C₂×D₈	—	2	2	no	—
175	C₂×D₈	—	2	2	no	—
176	C₂×D₈	—	2	2	no	—
177	C₂×D₈	—	2	2	no	—
178	C₂×D₈	—	4	2	no	—
179	C₂×D₈	—	4	2	no	—
180	C₂×D₈	C₂²⋊D₈₉	1	4	yes	—
181	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
182	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
183	#127	—	2	4	no	—
184	#127	—	4	2	no	—
185	C₂×C₄⋊C₄	—	178	1	no	—
186	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
187	SD₃₂	—	178	16	no	—
188	C₂×C₁₆	—	89	4	no	—
189	C₂×C₁₆	—	178	2	no	—
190	C₂×C₁₆	—	178	2	no	—
191	#107	—	178	2	no	—
192	#103	—	356	2	no	—
193	C₄×C₈	—	2	2	no	—
194	#95	—	356	2	no	—
195	C₂⁴	—	4	2	no	—
196	C₂×Q₈	—	356	1	no	—
197	C₂×Q₈	—	356	1	no	—
198	C₂×Q₈	—	356	1	no	—
199	C₂×Q₈	—	356	1	no	—
200	C₂×Q₈	—	356	1	no	—
201	C₂×Q₈	—	178	2	no	—
202	C₂×D₄	—	2	4	no	—
203	C₂×D₄	—	4	8	no	—
204	C₂×D₄	—	4	2	no	—
205	C₂×D₄	—	4	2	no	—
206	C₂×D₄	—	4	2	no	—
207	C₂×D₄	—	4	2	no	—
208	C₂×D₄	—	4	2	no	—
209	C₂×D₄	—	8	4	no	—
210	C₂×D₄	—	8	4	no	—
211	C₂²×C₄	—	356	1	no	—
212	C₂²×C₄	—	356	1	no	—
213	C₂²×C₄	#13083559	1	2	yes	—
214	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
215	Q₁₆	—	356	2	no	—
216	Q₁₆	—	178	4	no	—
217	D₈	—	2	4	no	—
218	D₈	—	2	4	no	—
219	D₈	—	4	8	no	—
220	D₈	—	4	2	no	—
221	D₈	—	4	2	no	—
222	C₂×C₈	—	2	1	no	—
223	C₂×C₈	—	2	1	no	—
224	C₂×C₈	#13083559	1	2	yes	—
225	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
226	C₂×C₈	D₄×D₈₉	1	2	yes	—
227	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
228	C₂×C₈	#13083573	1	1	yes	characteristic
229	C₄⋊C₄	—	356	1	no	—
230	C₄⋊C₄	—	356	1	no	—
231	C₄²	—	2	1	no	—
232	C₄²	—	2	1	no	—
233	C₁₆	—	178	4	no	—
234	C₂³	—	4	4	no	—
235	C₂³	—	8	2	no	—
236	C₂³	—	8	4	no	—
237	C₂³	—	8	4	no	—
238	C₂³	—	8	2	no	—
239	C₂³	C₂×#13083559	1	1	yes	characteristic
240	Q₈	—	356	2	no	—
241	Q₈	—	356	2	no	—
242	Q₈	—	712	1	no	—
243	Q₈	—	712	1	no	—
244	D₄	—	4	4	no	—
245	D₄	—	4	4	no	—
246	D₄	—	8	16	no	—
247	D₄	—	8	2	no	—
248	D₄	—	8	2	no	—
249	C₂×C₄	—	2	2	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	356	2	no	—
252	C₂×C₄	—	712	1	no	—
253	C₂×C₄	—	712	2	no	—
254	C₂×C₄	—	712	1	no	—
255	C₂×C₄	—	712	1	no	—
256	C₂×C₄	#15667956	1	4	yes	complemented
257	C₂×C₄	#15667981	1	1	yes	characteristic
258	C₂×C₄	#15667983	1	1	yes	characteristic
259	C₂×C₄	#15668008	1	1	yes	characteristic
260	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
261	C₂×C₄	#15668038	1	1	yes	characteristic
262	C₂×C₄	#15668038	1	1	yes	characteristic
263	C₈	—	2	2	no	—
264	C₈	#15667980	1	2	yes	—
265	C₈	#15667984	1	2	yes	—
266	C₂²	—	8	8	no	—
267	C₂²	—	8	4	no	—
268	C₂²	—	16	2	no	—
269	C₂²	—	16	2	no	—
270	C₂²	—	16	4	no	—
271	C₂²	#19151732	1	1	yes	characteristic
272	C₂²	#19151790	1	1	yes	characteristic
273	C₂²	#19151974	1	1	yes	characteristic
274	C₂²	C₂×#15667956	1	2	yes	—
275	C₂²	#19152034	1	2	yes	—
276	C₄	—	2	4	no	—
277	C₄	—	1424	1	no	—
278	C₄	—	712	2	no	—
279	C₄	#19151506	1	1	yes	characteristic
280	C₄	#19151732	1	1	yes	characteristic
281	C₄	#19151790	1	1	yes	characteristic
282	C₄	#19151985	1	1	yes	characteristic
283	C₂	—	16	4	no	—
284	C₂	#26021323	1	1	yes	characteristic
285	C₂	#26022181	1	2	yes	—
286	C₂	#26022289	1	2	yes	—
287	C₂	#26022507	1	1	yes	characteristic
288	C₂	#26022516	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#15667956

C₂

yes

maximal, complemented

C₂×#19151399

C₂

yes

maximal, complemented

#26021113

C₂

yes

maximal, characteristic, complemented

#26018330

C₂

yes

maximal, characteristic, complemented

C₂×#493×C₈₉

C₂

yes

maximal, characteristic

C₂²×Dic₃₅₆

C₂²

yes

—

—

—

C₂²

yes

—

C₂×#15667946

C₂²

yes

—

—

—

C₂²×D₈×C₈₉

—

C₂²×D₈×C₈₉

C₂²

yes

—

C₂×#127×C₈₉

—

#493×C₈₉

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

C₂²×Dic₁₇₈

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

D₄

yes

complemented

C₂×C₄⋊Dic₈₉

—

—

—

—

D₄

yes

—

—

—

C₂²×D₄×C₈₉

—

C₂²×D₄×C₈₉

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

D₄

yes

—

C₂²×C₈×C₈₉

D₄

yes

characteristic

C₂²×C₈×C₈₉

C₂³

yes

characteristic

#127×C₈₉

—

#127×C₈₉

—

C₂×C₄²×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

Dic₃₅₆

—

Dic₃₅₆

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

#13083549

—

C₂⁴×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂²×C₄×C₈₉

D₈

yes

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

D₈×C₈₉

—

D₈×C₈₉

—

D₈×C₈₉

—

D₈×C₈₉

—

D₈×C₈₉

—

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

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

C₂×D₈

yes

characteristic

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

100

C₂×C₄×C₈₉

—

101

C₂×C₄×C₈₉

—

102

C₂×C₄×C₈₉

SD₃₂

yes

complemented

103

C₂×C₄×C₈₉

#120

yes

characteristic

104

C₂×C₄×C₈₉

#121

yes

characteristic

105

C₂×C₄×C₈₉

#127

yes

characteristic

106

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

107

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

characteristic

108

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

characteristic

109

C₂×Dic₈₉

—

110

C₂×Dic₈₉

—

111

C₂×Dic₈₉

—

112

C₂×Dic₈₉

—

113

C₂×Dic₈₉

—

114

Dic₁₇₈

—

115

Dic₁₇₈

—

116

Dic₁₇₈

—

117

Dic₁₇₈

—

118

C₈×C₈₉

—

119

C₈×C₈₉

#120

yes

—

120

C₈×C₈₉

#121

yes

—

121

C₂²×C₈₉

—

122

C₂²×C₈₉

—

123

C₂²×C₈₉

—

124

C₂²×C₈₉

—

125

C₂²×C₈₉

—

126

C₂²×C₈₉

#447

yes

characteristic

127

C₂²×C₈₉

#459

yes

characteristic

128

C₂²×C₈₉

#493

yes

characteristic

129

C₂²×C₈₉

C₂×SD₃₂

yes

—

130

C₂²×C₈₉

#509

yes

—

131

C₄×C₈₉

—

132

C₄×C₈₉

#392

yes

characteristic

133

C₄×C₈₉

#447

yes

characteristic

134

C₄×C₈₉

#459

yes

characteristic

135

C₄×C₈₉

#496

yes

characteristic

136

Dic₈₉

—

137

Dic₈₉

—

138

#13328

—

maximal, Sylow

139

C₂×C₈₉

—

140

C₂×C₈₉

#2011

yes

characteristic

141

C₂×C₈₉

#2187

yes

—

142

C₂×C₈₉

#2207

yes

—

143

C₂×C₈₉

#2248

yes

characteristic

144

C₂×C₈₉

#2250

yes

characteristic

145

C₂²×SD₃₂

—

146

C₂×#493

D₈₉

yes

characteristic

147

C₂×#357

—

148

#1969

—

149

#1374

—

150

C₈₉

#13328

yes

characteristic, complemented, Sylow

151

C₂²×Q₁₆

—

152

C₂²×D₈

—

153

C₂²×D₈

C₂×D₈₉

yes

—

154

C₂×#127

—

155

C₂×SD₃₂

—

178

—

156

C₂×SD₃₂

—

178

—

157

C₂×SD₃₂

—

178

—

158

C₂²×C₁₆

—

159

#493

—

160

C₂×#107

—

161

C₂×#103

—

178

—

162

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

163

#391

—

178

—

164

#357

—

178

—

165

C₂²×Q₈

—

178

—

166

C₂²×D₄

—

167

C₂²×D₄

—

168

C₂×Q₁₆

—

169

C₂×Q₁₆

—

178

—

170

C₂×Q₁₆

—

178

—

171

C₂×Q₁₆

—

178

—

172

C₂×D₈

—

173

C₂×D₈

—

174

C₂×D₈

—

175

C₂×D₈

—

176

C₂×D₈

—

177

C₂×D₈

—

178

C₂×D₈

—

179

C₂×D₈

—

180

C₂×D₈

C₂²⋊D₈₉

yes

—

181

C₂²×C₈

C₂²⋊D₈₉

yes

characteristic

182

C₂²×C₈

C₂²×D₈₉

yes

characteristic

183

#127

—

184

#127

—

185

C₂×C₄⋊C₄

—

178

—

186

C₂×C₄²

C₂²⋊D₈₉

yes

characteristic

187

SD₃₂

—

178

—

188

C₂×C₁₆

—

189

C₂×C₁₆

—

178

—

190

C₂×C₁₆

—

178

—

191

#107

—

178

—

192

#103

—

356

—

193

C₄×C₈

—

194

#95

—

356

—

195

C₂⁴

—

196

C₂×Q₈

—

356

—

197

C₂×Q₈

—

356

—

198

C₂×Q₈

—

356

—

199

C₂×Q₈

—

356

—

200

C₂×Q₈

—

356

—

201

C₂×Q₈

—

178

—

202

C₂×D₄

—

203

C₂×D₄

—

204

C₂×D₄

—

205

C₂×D₄

—

206

C₂×D₄

—

207

C₂×D₄

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂²×C₄

—

356

—

212

C₂²×C₄

—

356

—

213

C₂²×C₄

#13083559

yes

—

214

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

215

Q₁₆

—

356

—

216

Q₁₆

—

178

—

217

D₈

—

218

D₈

—

219

D₈

—

220

D₈

—

221

D₈

—

222

C₂×C₈

—

223

C₂×C₈

—

224

C₂×C₈

#13083559

yes

—

225

C₂×C₈

D₄×D₈₉

yes

characteristic

226

C₂×C₈

D₄×D₈₉

yes

—

227

C₂×C₈

C₂×C₂²⋊D₈₉

yes

—

228

C₂×C₈

#13083573

yes

characteristic

229

C₄⋊C₄

—

356

—

230

C₄⋊C₄

—

356

—

231

C₄²

—

232

C₄²

—

233

C₁₆

—

178

—

234

C₂³

—

235

C₂³

—

236

C₂³

—

237

C₂³

—

238

C₂³

—

239

C₂³

C₂×#13083559

yes

characteristic

240

Q₈

—

356

—

241

Q₈

—

356

—

242

Q₈

—

712

—

243

Q₈

—

712

—

244

D₄

—

245

D₄

—

246

D₄

—

247

D₄

—

248

D₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

356

—

252

C₂×C₄

—

712

—

253

C₂×C₄

—

712

—

254

C₂×C₄

—

712

—

255

C₂×C₄

—

712

—

256

C₂×C₄

#15667956

yes

complemented

257

C₂×C₄

#15667981

yes

characteristic

258

C₂×C₄

#15667983

yes

characteristic

259

C₂×C₄

#15668008

yes

characteristic

260

C₂×C₄

C₂×#13083559

yes

characteristic

261

C₂×C₄

#15668038

yes

characteristic

262

C₂×C₄

#15668038

yes

characteristic

263

C₈

—

264

C₈

#15667980

yes

—

265

C₈

#15667984

yes

—

266

C₂²

—

267

C₂²

—

268

C₂²

—

269

C₂²

—

270

C₂²

—

271

C₂²

#19151732

yes

characteristic

272

C₂²

#19151790

yes

characteristic

273

C₂²

#19151974

yes

characteristic

274

C₂²

C₂×#15667956

yes

—

275

C₂²

#19152034

yes

—

276

C₄

—

277

C₄

—

1424

—

278

C₄

—

712

—

279

C₄

#19151506

yes

characteristic

280

C₄

#19151732

yes

characteristic

281

C₄

#19151790

yes

characteristic

282

C₄

#19151985

yes

characteristic

283

C₂

—

284

C₂

#26021323

yes

characteristic

285

C₂

#26022181

yes

—

286

C₂

#26022289

yes

—

287

C₂

#26022507

yes

characteristic

288

C₂

#26022516

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×#13083559
commutator, cosocle	C₂²×C₈×C₈₉	C₂³
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting, prime radical	C₂×#493×C₈₉	C₂
socle	C₂³×C₈₉	C₂×D₈
hypercenter	C₂×#493	D₈₉
hypocenter	C₈₉	#13328
LCS	G ▷ C₂²×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#493

subgroup

G/H

center

C₂³

C₂×#13083559

commutator, cosocle

C₂²×C₈×C₈₉

C₂³

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting, prime radical

C₂×#493×C₈₉

C₂

socle

C₂³×C₈₉

C₂×D₈

D₈₉

C₈₉

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

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#493

N	H ≅ G/N	type
1. C₂²×#15667956	C₂	semidirect
2. C₂×#19151399	C₂	semidirect
3. #26021113	C₂	semidirect
4. #26018330	C₂	semidirect
24. C₂×Dic₃₅₆	D₄	semidirect
29. C₂×#13083549	D₄	semidirect
102. C₂×C₄×C₈₉	SD₃₂	semidirect
150. C₈₉	#13328	semidirect
256. C₂×C₄	#15667956	semidirect

H ≅ G/N

type

1. C₂²×#15667956

C₂

semidirect

2. C₂×#19151399

C₂

semidirect

3. #26021113

C₂

semidirect

4. #26018330

C₂

semidirect

24. C₂×Dic₃₅₆

D₄

semidirect

29. C₂×#13083549

D₄

semidirect

102. C₂×C₄×C₈₉

SD₃₂

semidirect

150. C₈₉

#13328

semidirect

256. C₂×C₄

#15667956

semidirect

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

subgroup	index
C₂²×#15667956	2
C₂×#19151399	2
#26021113	2
#26018330	2
C₂×#493×C₈₉	2
#13328	89

subgroup

index

C₂×#493×C₈₉

Subgroups — #36473276

Conjugacy classes of subgroups

Complements

Maximal subgroups