Subgroups — #46824907

Order 34432.

1252 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771318	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771314	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771305	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771304	C₂	1	2	yes	maximal, complemented
5	#31771299	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771276	C₂	1	1	yes	maximal, characteristic, complemented
7	#31771251	C₂	1	2	yes	maximal, complemented
8	#31771245	C₂	1	2	yes	maximal, complemented
9	#31771245	C₂	1	2	yes	maximal, complemented
10	D₄×D₁₀₇₆	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₂²⋊D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771210	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771206	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771193	C₂	1	2	yes	maximal, complemented
16	#31771188	C₂	1	2	yes	maximal, complemented
17	#31771152	C₂	1	1	yes	maximal, characteristic, complemented
18	#31771133	C₂	1	1	yes	maximal, characteristic, complemented
19	#31771114	C₂	1	2	yes	maximal, complemented
20	C₂×#22575426	C₂	1	2	yes	maximal, complemented
21	#31771077	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#518×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16864402	C₂²	1	2	yes	complemented
25	C₂×#16864402	C₂²	1	2	yes	complemented
26	C₂²×D₁₀₇₆	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
29	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic
30	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	complemented
32	#22575452	C₂²	1	1	yes	characteristic, complemented
33	#22575450	C₂²	1	1	yes	characteristic, complemented
34	#22575449	C₂²	1	1	yes	characteristic, complemented
35	#22575449	C₂²	1	1	yes	characteristic, complemented
36	#22575448	C₂²	1	1	yes	characteristic, complemented
37	#22575447	C₂²	1	2	yes	complemented
38	#22575446	C₂²	1	1	yes	characteristic, complemented
39	#22575446	C₂²	1	2	yes	complemented
40	#22575445	C₂²	1	1	yes	characteristic, complemented
41	#22575444	C₂²	1	1	yes	characteristic, complemented
42	#22575443	C₂²	1	1	yes	characteristic, complemented
43	#22575441	C₂²	1	2	yes	complemented
44	#22575439	C₂²	1	2	yes	complemented
45	#22575439	C₂²	1	2	yes	complemented
46	#22575439	C₂²	1	1	yes	characteristic, complemented
47	#22575438	C₂²	1	2	yes	complemented
48	#22575438	C₂²	1	2	yes	complemented
49	#22575438	C₂²	1	1	yes	characteristic, complemented
50	#22575436	C₂²	1	2	yes	complemented
51	#22575436	C₂²	1	2	yes	complemented
52	#22575435	C₂²	1	2	yes	complemented
53	#22575435	C₂²	1	2	yes	complemented
54	#22575435	C₂²	1	1	yes	characteristic, complemented
55	#22575432	C₂²	1	2	yes	complemented
56	#22575431	C₂²	1	1	yes	characteristic, complemented
57	#22575430	C₂²	1	2	yes	complemented
58	#22575430	C₂²	1	2	yes	complemented
59	#22575428	C₂²	1	1	yes	characteristic, complemented
60	#22575428	C₂²	1	1	yes	characteristic, complemented
61	#22575427	C₂²	1	2	yes	complemented
62	#22575427	C₂²	1	2	yes	complemented
63	#22575427	C₂²	1	2	yes	complemented
64	#22575427	C₂²	1	1	yes	characteristic, complemented
65	#22575427	C₂²	1	1	yes	characteristic, complemented
66	#22575426	C₂²	1	1	yes	characteristic
67	#22575426	C₂²	1	2	yes	complemented
68	#22575426	C₂²	1	2	yes	complemented
69	#22575426	C₂²	1	2	yes	complemented
70	#22575426	C₂²	1	2	yes	complemented
71	#22575426	C₂²	1	2	yes	complemented
72	#22575426	C₂²	1	2	yes	complemented
73	#22575426	C₂²	1	2	yes	complemented
74	#22575426	C₂²	1	2	yes	complemented
75	#22575426	C₂²	1	2	yes	complemented
76	#22575425	C₂²	1	2	yes	complemented
77	#22575425	C₂²	1	2	yes	complemented
78	#22575424	C₂²	1	1	yes	characteristic, complemented
79	#22575424	C₂²	1	1	yes	characteristic, complemented
80	#22575423	C₂²	1	2	yes	complemented
81	#22575423	C₂²	1	2	yes	complemented
82	#22575422	C₂²	1	2	yes	complemented
83	#22575422	C₂²	1	2	yes	complemented
84	#22575421	C₂²	1	2	yes	complemented
85	#22575421	C₂²	1	2	yes	complemented
86	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
88	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
89	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
90	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
91	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
92	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
93	#22575415	C₂²	1	1	yes	characteristic, complemented
94	#22575415	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
101	#22575413	C₂²	1	2	yes	complemented
102	#22575413	C₂²	1	2	yes	complemented
103	#22575411	C₂²	1	1	yes	characteristic, complemented
104	#22575410	C₂²	1	1	yes	characteristic, complemented
105	#22575410	C₂²	1	2	yes	complemented
106	C₂×#16864381	C₂²	1	2	yes	complemented
107	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
108	C₂×#16864379	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
111	C₄²×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
112	C₂²×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
113	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
114	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
115	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₄×C₂₆₉	C₂²	1	2	yes	complemented
117	C₄×D₄×C₂₆₉	C₂²	1	2	yes	complemented
118	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
119	#117×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
120	#117×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
122	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
123	C₂³×D₂₆₉	C₂³	1	2	yes	—
124	C₂³×D₂₆₉	C₂³	1	2	yes	—
125	#16864402	—	4	4	no	—
126	#16864402	—	4	4	no	—
127	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₅₃₈	C₂³	1	2	yes	—
129	C₂×D₁₀₇₆	—	4	4	no	—
130	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
131	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
132	C₂×D₁₀₇₆	C₂³	1	2	yes	—
133	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
134	C₂×D₁₀₇₆	C₂³	1	2	yes	—
135	C₂×D₁₀₇₆	C₂³	1	2	yes	—
136	C₂×D₁₀₇₆	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₂₆₉	—	4	4	no	—
138	C₂×C₂²⋊D₂₆₉	—	4	4	no	—
139	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
151	D₄×D₂₆₉	—	2	4	no	—
152	D₄×D₂₆₉	—	2	4	no	—
153	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
154	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
155	C₂×C₄×D₂₆₉	—	4	4	no	—
156	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
161	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
162	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
163	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
164	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
165	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
166	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
167	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
168	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
169	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
170	#16864381	C₂³	1	2	yes	—
171	#16864381	C₂³	1	1	yes	characteristic
172	#16864381	C₂³	1	2	yes	—
173	#16864381	C₂³	1	2	yes	—
174	#16864381	C₂³	1	2	yes	—
175	#16864381	C₂³	1	1	yes	characteristic
176	#16864381	C₂³	1	1	yes	characteristic
177	#16864381	C₂³	1	1	yes	characteristic
178	#16864381	C₂³	1	1	yes	characteristic
179	#16864381	C₂³	1	2	yes	—
180	#16864381	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
186	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
187	#16864379	C₂³	1	1	yes	characteristic
188	#16864379	C₂³	1	2	yes	—
189	#16864379	C₂³	1	2	yes	—
190	#16864379	C₂³	1	2	yes	—
191	#16864379	C₂³	1	1	yes	characteristic
192	#16864379	C₂³	1	2	yes	—
193	#16864379	C₂³	1	2	yes	—
194	#16864379	C₂³	1	2	yes	—
195	#16864379	C₂³	1	2	yes	—
196	#16864379	C₂³	1	1	yes	characteristic
197	#16864379	C₂³	1	1	yes	characteristic
198	#16864379	C₂³	1	1	yes	characteristic
199	#16864379	C₂³	1	2	yes	—
200	#16864379	C₂³	1	2	yes	—
201	#16864379	C₂³	1	1	yes	characteristic
202	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
204	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
205	C₄×Dic₂₆₉	C₂³	1	2	yes	—
206	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
207	C₂⁴×C₂₆₉	C₂³	1	2	yes	—
208	C₂×D₄×C₂₆₉	—	2	4	no	—
209	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
210	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
214	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
215	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
216	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
217	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
226	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
228	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
229	C₄²×C₂₆₉	C₂³	1	2	yes	—
230	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
231	C₂²×D₂₆₉	—	2	4	no	—
232	C₂²×D₂₆₉	—	2	4	no	—
233	C₂²×D₂₆₉	—	2	4	no	—
234	C₂²×D₂₆₉	—	4	2	no	—
235	C₂²×D₂₆₉	—	4	2	no	—
236	C₂²×D₂₆₉	—	4	2	no	—
237	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
238	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
239	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
240	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
241	Dic₅₃₈	—	2	2	no	—
242	Dic₅₃₈	—	4	2	no	—
243	D₁₀₇₆	—	2	2	no	—
244	D₁₀₇₆	—	2	4	no	—
245	D₁₀₇₆	—	2	2	no	—
246	D₁₀₇₆	—	2	2	no	—
247	D₁₀₇₆	—	4	2	no	—
248	D₁₀₇₆	—	4	2	no	—
249	D₁₀₇₆	—	4	2	no	—
250	C₂²⋊D₂₆₉	—	2	4	no	—
251	C₂²⋊D₂₆₉	—	2	4	no	—
252	C₂²⋊D₂₆₉	—	2	2	no	—
253	C₂²⋊D₂₆₉	—	2	4	no	—
254	C₂²⋊D₂₆₉	—	2	2	no	—
255	C₂²⋊D₂₆₉	—	2	4	no	—
256	C₂²⋊D₂₆₉	—	4	2	no	—
257	C₂²⋊D₂₆₉	—	4	2	no	—
258	C₂²⋊D₂₆₉	—	4	2	no	—
259	C₂²⋊D₂₆₉	—	4	2	no	—
260	C₂²⋊D₂₆₉	—	4	2	no	—
261	C₂²⋊D₂₆₉	—	4	2	no	—
262	C₂×Dic₂₆₉	—	2	4	no	—
263	C₂×Dic₂₆₉	—	4	2	no	—
264	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
268	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
271	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
272	C₄×D₂₆₉	—	2	2	no	—
273	C₄×D₂₆₉	—	2	2	no	—
274	C₄×D₂₆₉	—	2	2	no	—
275	C₄×D₂₆₉	—	2	2	no	—
276	C₄×D₂₆₉	—	2	4	no	—
277	C₄×D₂₆₉	—	4	2	no	—
278	C₄×D₂₆₉	—	4	2	no	—
279	C₄×D₂₆₉	—	4	2	no	—
280	C₄×D₂₆₉	—	4	2	no	—
281	C₂³×C₂₆₉	—	2	4	no	—
282	C₂³×C₂₆₉	—	4	2	no	—
283	C₂³×C₂₆₉	—	4	2	no	—
284	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
285	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
286	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
287	D₄×C₂₆₉	—	2	4	no	—
288	D₄×C₂₆₉	—	2	2	no	—
289	D₄×C₂₆₉	#41	1	4	yes	complemented
290	C₂×C₄×C₂₆₉	—	2	2	no	—
291	C₂×C₄×C₂₆₉	—	4	2	no	—
292	C₂×C₄×C₂₆₉	—	4	2	no	—
293	C₂×C₄×C₂₆₉	—	4	2	no	—
294	C₂×C₄×C₂₆₉	—	4	2	no	—
295	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
296	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
297	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
298	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
299	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
300	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
301	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
302	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
303	C₂²×C₂₆₉	—	2	2	no	—
304	C₂²×C₂₆₉	—	2	2	no	—
305	C₂²×C₂₆₉	—	2	1	no	—
306	C₂²×C₂₆₉	—	2	2	no	—
307	C₂²×C₂₆₉	—	2	2	no	—
308	C₂²×C₂₆₉	—	2	2	no	—
309	C₂²×C₂₆₉	—	2	1	no	—
310	C₂²×C₂₆₉	—	2	1	no	—
311	C₂²×C₂₆₉	—	8	4	no	—
312	C₂²×C₂₆₉	C₂×#41	1	4	yes	—
313	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
314	C₂×D₂₆₉	—	2	1	no	—
315	C₂×D₂₆₉	—	2	1	no	—
316	C₂×D₂₆₉	—	2	1	no	—
317	C₂×D₂₆₉	—	2	2	no	—
318	C₂×D₂₆₉	—	2	2	no	—
319	C₂×D₂₆₉	—	2	2	no	—
320	C₂×D₂₆₉	—	2	2	no	—
321	C₂×D₂₆₉	—	2	2	no	—
322	C₂×D₂₆₉	—	2	1	no	—
323	C₂×D₂₆₉	—	2	2	no	—
324	C₂×D₂₆₉	—	2	1	no	—
325	C₂×D₂₆₉	—	4	8	no	—
326	C₂×D₂₆₉	—	8	4	no	—
327	C₂×D₂₆₉	H(5,𝔽₂)	1	2	yes	—
328	C₄×C₂₆₉	—	2	1	no	—
329	C₄×C₂₆₉	—	2	1	no	—
330	C₄×C₂₆₉	—	2	1	no	—
331	C₄×C₂₆₉	—	2	2	no	—
332	C₄×C₂₆₉	—	2	1	no	—
333	C₄×C₂₆₉	—	2	2	no	—
334	C₄×C₂₆₉	—	2	1	no	—
335	C₄×C₂₆₉	C₂×#41	1	2	yes	—
336	Dic₂₆₉	—	2	1	no	—
337	Dic₂₆₉	—	2	1	no	—
338	Dic₂₆₉	—	2	1	no	—
339	Dic₂₆₉	—	2	2	no	—
340	Dic₂₆₉	—	2	1	no	—
341	Dic₂₆₉	—	2	2	no	—
342	Dic₂₆₉	—	2	1	no	—
343	Dic₂₆₉	H(5,𝔽₂)	1	2	yes	—
344	C₂×C₂₆₉	—	2	4	no	—
345	C₂×C₂₆₉	—	4	2	no	—
346	C₂×C₂₆₉	—	4	1	no	—
347	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
348	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
350	D₂₆₉	—	2	2	no	—
351	D₂₆₉	—	4	2	no	—
352	D₂₆₉	—	4	2	no	—
353	D₂₆₉	—	4	1	no	—
354	C₂₆₉	#3519	1	1	yes	characteristic, complemented, Sylow
355	#3519	—	269	1	no	maximal, Sylow
356	#555	—	269	1	no	—
357	#554	—	269	1	no	—
358	#553	—	269	2	no	—
359	#553	—	269	1	no	—
360	#553	—	269	1	no	—
361	#550	—	269	1	no	—
362	#546	—	269	2	no	—
363	#546	—	269	2	no	—
364	#546	—	269	2	no	—
365	D₄²	—	269	1	no	—
366	D₄²	—	269	1	no	—
367	D₄²	—	269	1	no	—
368	#540	—	269	1	no	—
369	#540	—	269	1	no	—
370	#538	—	269	2	no	—
371	#538	—	269	2	no	—
372	#532	—	269	1	no	—
373	#529	—	269	1	no	—
374	#525	—	269	2	no	—
375	C₂×#121	—	269	2	no	—
376	#518	—	269	1	no	—
377	#518	D₂₆₉	1	1	yes	characteristic, complemented
378	C₂×C₄×D₄	—	269	1	no	—
379	C₂×#41	—	269	2	no	—
380	C₂×#41	—	269	2	no	—
381	C₂²×D₄	—	269	2	no	—
382	C₂²×D₄	—	269	2	no	—
383	C₂²×D₄	—	269	1	no	—
384	C₂²×D₄	—	269	1	no	—
385	C₂²×D₄	—	269	2	no	—
386	C₂²×D₄	C₂×D₂₆₉	1	1	yes	characteristic
387	C₂³×C₄	—	269	2	no	—
388	C₄⋊Q₈	—	269	1	no	—
389	#127	—	269	1	no	—
390	#127	—	269	1	no	—
391	#127	—	269	1	no	—
392	#126	—	269	1	no	—
393	#126	—	269	1	no	—
394	#126	—	269	2	no	—
395	#126	—	269	2	no	—
396	#125	—	269	1	no	—
397	#125	—	269	1	no	—
398	#125	—	269	1	no	—
399	#124	—	269	1	no	—
400	#124	—	269	2	no	—
401	#124	—	269	2	no	—
402	#124	—	269	2	no	—
403	#123	—	269	2	no	—
404	#123	—	269	2	no	—
405	#123	—	269	2	no	—
406	#123	—	269	1	no	—
407	#123	—	269	2	no	—
408	#123	—	269	2	no	—
409	#123	—	269	1	no	—
410	#123	—	269	2	no	—
411	C₂²⋊Q₈	—	269	2	no	—
412	C₂²⋊Q₈	—	269	1	no	—
413	C₂²⋊Q₈	—	269	2	no	—
414	C₂²⋊Q₈	—	269	2	no	—
415	#121	—	269	2	no	—
416	#121	—	269	1	no	—
417	#121	—	269	2	no	—
418	#121	—	269	1	no	—
419	#121	—	269	2	no	—
420	#121	—	269	2	no	—
421	#121	—	269	1	no	—
422	#121	—	269	1	no	—
423	#121	—	269	2	no	—
424	#121	—	269	1	no	—
425	#121	—	269	1	no	—
426	#121	—	269	1	no	—
427	#121	—	269	2	no	—
428	#121	—	269	2	no	—
429	#121	—	269	2	no	—
430	#121	—	269	2	no	—
431	#121	—	269	2	no	—
432	#121	—	269	2	no	—
433	#121	—	269	2	no	—
434	#121	—	269	2	no	—
435	#121	—	269	2	no	—
436	#120	—	269	2	no	—
437	#120	—	269	2	no	—
438	#120	—	269	2	no	—
439	#120	—	269	2	no	—
440	#120	—	269	2	no	—
441	#120	—	269	2	no	—
442	C₄×Q₈	—	269	1	no	—
443	C₄×D₄	—	269	1	no	—
444	C₄×D₄	—	269	1	no	—
445	C₄×D₄	—	269	2	no	—
446	C₄×D₄	—	269	2	no	—
447	C₄×D₄	—	269	2	no	—
448	C₄×D₄	—	269	1	no	—
449	C₄×D₄	—	269	1	no	—
450	C₄×D₄	—	269	2	no	—
451	C₄×D₄	—	269	1	no	—
452	C₄×D₄	—	269	1	no	—
453	C₄×D₄	—	269	2	no	—
454	C₄×D₄	—	269	2	no	—
455	C₄×D₄	—	269	1	no	—
456	C₄×D₄	—	269	1	no	—
457	C₄×D₄	—	269	2	no	—
458	C₄×D₄	—	269	1	no	—
459	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
460	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
461	C₄×D₄	C₂×D₂₆₉	1	2	yes	complemented
462	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
463	C₄×D₄	C₂×D₂₆₉	1	2	yes	complemented
464	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
465	#117	—	269	1	no	—
466	#117	—	269	1	no	—
467	#117	—	269	2	no	—
468	#117	C₂×D₂₆₉	1	1	yes	characteristic, complemented
469	#117	C₂×D₂₆₉	1	1	yes	characteristic, complemented
470	C₂×C₄⋊C₄	—	269	2	no	—
471	C₂×C₄⋊C₄	—	269	1	no	—
472	C₂×C₂²⋊C₄	—	269	2	no	—
473	C₂×C₂²⋊C₄	—	269	2	no	—
474	C₂×C₂²⋊C₄	—	269	2	no	—
475	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
476	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
477	C₂×C₄²	—	269	1	no	—
478	C₂⁴	—	269	2	no	—
479	C₂⁴	—	269	2	no	—
480	C₂⁴	C₂²×D₂₆₉	1	2	yes	—
481	#41	—	1076	4	no	—
482	#41	—	1076	4	no	—
483	C₂×Q₈	—	269	1	no	—
484	C₂×Q₈	—	269	2	no	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	269	2	no	—
487	C₂×D₄	—	269	2	no	—
488	C₂×D₄	—	269	2	no	—
489	C₂×D₄	—	269	1	no	—
490	C₂×D₄	—	269	1	no	—
491	C₂×D₄	—	269	2	no	—
492	C₂×D₄	—	269	2	no	—
493	C₂×D₄	—	269	2	no	—
494	C₂×D₄	—	269	2	no	—
495	C₂×D₄	—	269	2	no	—
496	C₂×D₄	—	269	2	no	—
497	C₂×D₄	—	269	2	no	—
498	C₂×D₄	—	269	1	no	—
499	C₂×D₄	—	269	1	no	—
500	C₂×D₄	—	269	2	no	—
501	C₂×D₄	—	269	1	no	—
502	C₂×D₄	—	269	2	no	—
503	C₂×D₄	—	269	2	no	—
504	C₂×D₄	—	269	2	no	—
505	C₂×D₄	—	538	4	no	—
506	C₂×D₄	—	538	4	no	—
507	C₂×D₄	—	1076	4	no	—
508	C₂×D₄	—	1076	4	no	—
509	C₂×D₄	—	1076	4	no	—
510	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
511	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
512	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
513	C₂²×C₄	—	269	2	no	—
514	C₂²×C₄	—	269	2	no	—
515	C₂²×C₄	—	269	1	no	—
516	C₂²×C₄	—	269	1	no	—
517	C₂²×C₄	—	269	1	no	—
518	C₂²×C₄	—	269	1	no	—
519	C₂²×C₄	—	269	2	no	—
520	C₂²×C₄	—	269	2	no	—
521	C₂²×C₄	—	269	2	no	—
522	C₂²×C₄	—	269	2	no	—
523	C₂²×C₄	—	269	2	no	—
524	C₂²×C₄	—	1076	4	no	—
525	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
526	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
527	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
528	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
529	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
530	C₄⋊C₄	—	269	1	no	—
531	C₄⋊C₄	—	269	2	no	—
532	C₄⋊C₄	—	269	1	no	—
533	C₄⋊C₄	—	269	2	no	—
534	C₄⋊C₄	—	269	2	no	—
535	C₄⋊C₄	—	269	2	no	—
536	C₄⋊C₄	—	269	1	no	—
537	C₄⋊C₄	—	269	1	no	—
538	C₄⋊C₄	—	269	1	no	—
539	C₄⋊C₄	—	269	1	no	—
540	C₄⋊C₄	—	269	1	no	—
541	C₄⋊C₄	—	269	1	no	—
542	C₄⋊C₄	—	269	2	no	—
543	C₄⋊C₄	—	269	2	no	—
544	C₄⋊C₄	—	269	1	no	—
545	C₄⋊C₄	—	269	1	no	—
546	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
548	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
549	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
550	C₂²⋊C₄	—	269	2	no	—
551	C₂²⋊C₄	—	269	2	no	—
552	C₂²⋊C₄	—	269	1	no	—
553	C₂²⋊C₄	—	269	1	no	—
554	C₂²⋊C₄	—	269	2	no	—
555	C₂²⋊C₄	—	269	2	no	—
556	C₂²⋊C₄	—	269	1	no	—
557	C₂²⋊C₄	—	269	2	no	—
558	C₂²⋊C₄	—	269	1	no	—
559	C₂²⋊C₄	—	269	2	no	—
560	C₂²⋊C₄	—	269	2	no	—
561	C₂²⋊C₄	—	269	2	no	—
562	C₂²⋊C₄	—	269	2	no	—
563	C₂²⋊C₄	—	269	2	no	—
564	C₂²⋊C₄	—	269	2	no	—
565	C₂²⋊C₄	—	269	1	no	—
566	C₂²⋊C₄	—	269	1	no	—
567	C₂²⋊C₄	—	269	1	no	—
568	C₂²⋊C₄	—	269	1	no	—
569	C₂²⋊C₄	—	269	2	no	—
570	C₂²⋊C₄	—	269	2	no	—
571	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
573	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
575	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
576	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
577	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
578	C₄²	—	269	1	no	—
579	C₄²	—	269	1	no	—
580	C₄²	—	269	1	no	—
581	C₄²	—	269	2	no	—
582	C₄²	—	269	1	no	—
583	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
584	C₄²	C₂²×D₂₆₉	1	2	yes	—
585	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
586	C₂³	—	2	4	no	—
587	C₂³	—	4	2	no	—
588	C₂³	—	4	2	no	—
589	C₂³	—	269	1	no	—
590	C₂³	—	269	1	no	—
591	C₂³	—	269	2	no	—
592	C₂³	—	269	2	no	—
593	C₂³	—	538	4	no	—
594	C₂³	—	538	4	no	—
595	C₂³	—	538	4	no	—
596	C₂³	—	1076	2	no	—
597	C₂³	—	1076	2	no	—
598	C₂³	—	1076	2	no	—
599	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
600	C₂³	C₂³×D₂₆₉	1	2	yes	—
601	C₂³	C₂³×D₂₆₉	1	2	yes	—
602	Q₈	—	538	2	no	—
603	Q₈	—	1076	2	no	—
604	D₄	—	2	4	no	—
605	D₄	—	2	2	no	—
606	D₄	—	538	2	no	—
607	D₄	—	538	4	no	—
608	D₄	—	538	2	no	—
609	D₄	—	538	4	no	—
610	D₄	—	538	2	no	—
611	D₄	—	538	4	no	—
612	D₄	—	538	4	no	—
613	D₄	—	538	4	no	—
614	D₄	—	538	2	no	—
615	D₄	—	538	2	no	—
616	D₄	—	1076	2	no	—
617	D₄	—	1076	2	no	—
618	D₄	—	1076	2	no	—
619	D₄	—	1076	2	no	—
620	D₄	—	1076	2	no	—
621	D₄	—	1076	2	no	—
622	D₄	—	1076	2	no	—
623	D₄	—	1076	2	no	—
624	D₄	—	1076	2	no	—
625	D₄	#16864402	1	4	yes	complemented
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	269	1	no	—
632	C₂×C₄	—	269	1	no	—
633	C₂×C₄	—	269	1	no	—
634	C₂×C₄	—	269	1	no	—
635	C₂×C₄	—	269	2	no	—
636	C₂×C₄	—	269	1	no	—
637	C₂×C₄	—	269	1	no	—
638	C₂×C₄	—	269	2	no	—
639	C₂×C₄	—	538	2	no	—
640	C₂×C₄	—	538	4	no	—
641	C₂×C₄	—	538	2	no	—
642	C₂×C₄	—	538	4	no	—
643	C₂×C₄	—	538	2	no	—
644	C₂×C₄	—	538	2	no	—
645	C₂×C₄	—	1076	2	no	—
646	C₂×C₄	—	1076	2	no	—
647	C₂×C₄	—	1076	2	no	—
648	C₂×C₄	—	1076	2	no	—
649	C₂×C₄	—	1076	2	no	—
650	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
653	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
655	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
656	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
657	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	8	4	no	—
667	C₂²	—	269	2	no	—
668	C₂²	—	538	1	no	—
669	C₂²	—	538	1	no	—
670	C₂²	—	538	1	no	—
671	C₂²	—	538	2	no	—
672	C₂²	—	538	2	no	—
673	C₂²	—	538	2	no	—
674	C₂²	—	538	2	no	—
675	C₂²	—	538	2	no	—
676	C₂²	—	538	1	no	—
677	C₂²	—	538	1	no	—
678	C₂²	—	538	2	no	—
679	C₂²	—	1076	8	no	—
680	C₂²	—	2152	4	no	—
681	C₂²	C₂×#16864402	1	4	yes	—
682	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	1	no	—
690	C₄	—	269	2	no	—
691	C₄	—	538	1	no	—
692	C₄	—	538	1	no	—
693	C₄	—	538	2	no	—
694	C₄	—	538	1	no	—
695	C₄	—	538	1	no	—
696	C₄	—	538	2	no	—
697	C₄	—	538	1	no	—
698	C₄	C₂×#16864402	1	2	yes	—
699	C₂	—	2	4	no	—
700	C₂	—	4	1	no	—
701	C₂	—	4	2	no	—
702	C₂	—	538	2	no	—
703	C₂	—	1076	2	no	—
704	C₂	—	1076	1	no	—
705	C₂	—	1076	2	no	—
706	C₂	C₂²×#16864402	1	1	yes	characteristic
707	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic
708	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#518×C₂₆₉	C₂
hypercenter	#518	D₂₆₉
hypocenter	C₂₆₉	#3519
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #518

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #31771318	C₂	semidirect
2. #31771314	C₂	semidirect
3. #31771305	C₂	semidirect
4. #31771304	C₂	semidirect
5. #31771299	C₂	semidirect
6. #31771276	C₂	semidirect
7. #31771251	C₂	semidirect
8. #31771245	C₂	semidirect
9. #31771245	C₂	semidirect
10. D₄×D₁₀₇₆	C₂	semidirect
11. D₄×C₂²⋊D₂₆₉	C₂	semidirect
12. D₄×C₂²⋊D₂₆₉	C₂	semidirect
13. #31771210	C₂	semidirect
14. #31771206	C₂	semidirect
15. #31771193	C₂	semidirect
16. #31771188	C₂	semidirect
17. #31771152	C₂	semidirect
18. #31771133	C₂	semidirect
19. #31771114	C₂	semidirect
20. C₂×#22575426	C₂	semidirect
21. #31771077	C₂	semidirect
22. C₄×D₄×D₂₆₉	C₂	semidirect
23. #518×C₂₆₉	C₂	semidirect
24. C₂×#16864402	C₂²	semidirect
25. C₂×#16864402	C₂²	semidirect
26. C₂²×D₁₀₇₆	C₂²	semidirect
27. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
28. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
31. C₂²×C₄×D₂₆₉	C₂²	semidirect
32. #22575452	C₂²	semidirect
33. #22575450	C₂²	semidirect
34. #22575449	C₂²	semidirect
35. #22575449	C₂²	semidirect
36. #22575448	C₂²	semidirect
37. #22575447	C₂²	semidirect
38. #22575446	C₂²	semidirect
39. #22575446	C₂²	semidirect
40. #22575445	C₂²	semidirect
41. #22575444	C₂²	semidirect
42. #22575443	C₂²	semidirect
43. #22575441	C₂²	semidirect
44. #22575439	C₂²	semidirect
45. #22575439	C₂²	semidirect
46. #22575439	C₂²	semidirect
47. #22575438	C₂²	semidirect
48. #22575438	C₂²	semidirect
49. #22575438	C₂²	semidirect
50. #22575436	C₂²	semidirect
51. #22575436	C₂²	semidirect
52. #22575435	C₂²	semidirect
53. #22575435	C₂²	semidirect
54. #22575435	C₂²	semidirect
55. #22575432	C₂²	semidirect
56. #22575431	C₂²	semidirect
57. #22575430	C₂²	semidirect
58. #22575430	C₂²	semidirect
59. #22575428	C₂²	semidirect
60. #22575428	C₂²	semidirect
61. #22575427	C₂²	semidirect
62. #22575427	C₂²	semidirect
63. #22575427	C₂²	semidirect
64. #22575427	C₂²	semidirect
65. #22575427	C₂²	semidirect
67. #22575426	C₂²	semidirect
68. #22575426	C₂²	semidirect
69. #22575426	C₂²	semidirect
70. #22575426	C₂²	semidirect
71. #22575426	C₂²	semidirect
72. #22575426	C₂²	semidirect
73. #22575426	C₂²	semidirect
74. #22575426	C₂²	semidirect
75. #22575426	C₂²	semidirect
76. #22575425	C₂²	semidirect
77. #22575425	C₂²	semidirect
78. #22575424	C₂²	semidirect
79. #22575424	C₂²	semidirect
80. #22575423	C₂²	semidirect
81. #22575423	C₂²	semidirect
82. #22575422	C₂²	semidirect
83. #22575422	C₂²	semidirect
84. #22575421	C₂²	semidirect
85. #22575421	C₂²	semidirect
86. C₄×Dic₅₃₈	C₂²	semidirect
87. C₄×D₁₀₇₆	C₂²	semidirect
88. C₄×D₁₀₇₆	C₂²	semidirect
89. C₄×D₁₀₇₆	C₂²	semidirect
90. C₄×D₁₀₇₆	C₂²	semidirect
93. #22575415	C₂²	semidirect
94. #22575415	C₂²	semidirect
95. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
96. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
97. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
98. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
99. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
100. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
101. #22575413	C₂²	semidirect
102. #22575413	C₂²	semidirect
103. #22575411	C₂²	semidirect
104. #22575410	C₂²	semidirect
105. #22575410	C₂²	semidirect
106. C₂×#16864381	C₂²	semidirect
107. C₄⋊C₄×D₂₆₉	C₂²	semidirect
108. C₂×#16864379	C₂²	semidirect
109. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
110. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
111. C₄²×D₂₆₉	C₂²	semidirect
115. C₄×D₄×C₂₆₉	C₂²	semidirect
116. C₄×D₄×C₂₆₉	C₂²	semidirect
117. C₄×D₄×C₂₆₉	C₂²	semidirect
118. C₄×D₄×C₂₆₉	C₂²	semidirect
119. #117×C₂₆₉	C₂²	semidirect
120. #117×C₂₆₉	C₂²	semidirect
121. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
289. D₄×C₂₆₉	#41	semidirect
354. C₂₆₉	#3519	semidirect
377. #518	D₂₆₉	semidirect
461. C₄×D₄	C₂×D₂₆₉	semidirect
462. C₄×D₄	C₂×D₂₆₉	semidirect
463. C₄×D₄	C₂×D₂₆₉	semidirect
464. C₄×D₄	C₂×D₂₆₉	semidirect
468. #117	C₂×D₂₆₉	semidirect
469. #117	C₂×D₂₆₉	semidirect
475. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
476. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
625. D₄	#16864402	semidirect

Maximal subgroups

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

subgroup	index
#31771318	2
#31771314	2
#31771305	2
#31771304	2
#31771299	2
#31771276	2
#31771251	2
#31771245	2
D₄×D₁₀₇₆	2
D₄×C₂²⋊D₂₆₉	2
#31771210	2
#31771206	2
#31771193	2
#31771188	2
#31771152	2
#31771133	2
#31771114	2
C₂×#22575426	2
#31771077	2
C₄×D₄×D₂₆₉	2
#518×C₂₆₉	2
#3519	269