Subgroups — C₂×#31771118 #46824129

Order 34432.

1880 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#16864403	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771118	C₂	1	16	yes	maximal, direct product factor
4	C₂×#22575438	C₂	1	2	yes	maximal, complemented
5	C₂×#22575429	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22575428	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#22575427	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#22575423	C₂	1	2	yes	maximal, complemented
9	C₂×#22575415	C₂	1	2	yes	maximal, complemented
10	C₂×#22575413	C₂	1	2	yes	maximal, complemented
11	C₂×#22575411	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂²⋊Q₈×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₂₆₉	C₂²	1	1	yes	characteristic
14	C₂×#16864403	—	2	8	no	—
15	C₂×#16864403	C₂²	1	8	yes	complemented
16	C₂²×D₁₀₇₆	C₂²	1	2	yes	—
17	C₂²×D₁₀₇₆	C₂²	1	2	yes	—
18	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
20	C₂³×Dic₂₆₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₂₆₉	—	2	8	no	—
22	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₂₆₉	C₂²	1	8	yes	complemented
27	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	complemented
28	#22575438	C₂²	1	16	yes	complemented
29	#22575429	C₂²	1	8	yes	complemented
30	#22575428	C₂²	1	8	yes	complemented
31	#22575427	C₂²	1	8	yes	complemented
32	#22575423	C₂²	1	16	yes	complemented
33	#22575415	C₂²	1	16	yes	complemented
34	#22575413	C₂²	1	16	yes	complemented
35	#22575411	C₂²	1	8	yes	complemented
36	C₂×C₄⋊Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×#16864381	C₂²	1	2	yes	complemented
38	C₂×#16864379	C₂²	1	2	yes	—
39	C₂×#16864379	C₂²	1	2	yes	—
40	C₂×#16864379	C₂²	1	2	yes	complemented
41	C₂×#16864379	C₂²	1	2	yes	complemented
42	C₂×C₄×Dic₂₆₉	C₂²	1	2	yes	complemented
43	C₂²×Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
44	C₂³×C₄×C₂₆₉	C₂²	1	1	yes	characteristic
45	C₂²⋊Q₈×C₂₆₉	C₂²	1	8	yes	complemented
46	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
48	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	—
49	C₂³×D₂₆₉	—	2	4	no	—
50	C₂³×D₂₆₉	—	2	4	no	—
51	C₂³×D₂₆₉	—	2	4	no	—
52	C₂³×D₂₆₉	C₂³	1	2	yes	—
53	C₂³×D₂₆₉	C₂³	1	4	yes	—
54	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
55	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
56	#16864403	—	2	32	no	—
57	C₂×D₁₀₇₆	—	2	8	no	—
58	C₂×D₁₀₇₆	—	2	8	no	—
59	C₂×D₁₀₇₆	—	2	4	no	—
60	C₂×D₁₀₇₆	C₂³	1	8	yes	—
61	C₂×D₁₀₇₆	C₂³	1	8	yes	—
62	C₂×D₁₀₇₆	C₂³	1	4	yes	complemented
63	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
64	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	—
65	C₂²×Dic₂₆₉	—	2	4	no	—
66	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
67	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
68	C₂²×Dic₂₆₉	C₂³	1	4	yes	—
69	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
70	C₂×C₄×D₂₆₉	—	2	4	no	—
71	C₂×C₄×D₂₆₉	—	2	4	no	—
72	C₂×C₄×D₂₆₉	—	2	8	no	—
73	C₂×C₄×D₂₆₉	—	2	32	no	—
74	C₂×C₄×D₂₆₉	—	2	4	no	—
75	C₂×C₄×D₂₆₉	D₄	1	8	yes	complemented
76	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
77	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
78	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
79	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
80	C₂×C₄×D₂₆₉	C₂³	1	8	yes	complemented
81	C₄⋊Dic₂₆₉	C₂³	1	4	yes	complemented
82	#16864381	C₂³	1	8	yes	complemented
83	#16864379	C₂³	1	8	yes	—
84	#16864379	C₂³	1	8	yes	—
85	#16864379	C₂³	1	8	yes	complemented
86	#16864379	C₂³	1	8	yes	complemented
87	C₄×Dic₂₆₉	C₂³	1	8	yes	complemented
88	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
89	C₂×Q₈×C₂₆₉	—	2	4	no	—
90	C₂×Q₈×C₂₆₉	C₂³	1	4	yes	complemented
91	C₂²×C₄×C₂₆₉	—	2	4	no	—
92	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
93	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
94	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₂₆₉	C₂³	1	4	yes	—
96	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	complemented
98	C₄⋊C₄×C₂₆₉	C₂³	1	8	yes	complemented
99	C₂²⋊C₄×C₂₆₉	C₂³	1	8	yes	—
100	C₂²×D₂₆₉	—	2	32	no	—
101	C₂²×D₂₆₉	—	2	2	no	—
102	C₂²×D₂₆₉	—	2	2	no	—
103	C₂²×D₂₆₉	—	2	2	no	—
104	C₂²×D₂₆₉	—	2	2	no	—
105	C₂²×D₂₆₉	—	2	8	no	—
106	C₂²×D₂₆₉	—	2	8	no	—
107	C₂²×D₂₆₉	—	2	8	no	—
108	C₂²×D₂₆₉	—	2	4	no	—
109	C₂²×D₂₆₉	—	2	4	no	—
110	C₂²×D₂₆₉	—	2	4	no	—
111	C₂²×D₂₆₉	C₂×D₄	1	4	yes	—
112	C₂²×D₂₆₉	#41	1	4	yes	complemented
113	C₂²×D₂₆₉	C₂⁴	1	4	yes	—
114	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
115	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
116	D₁₀₇₆	—	2	16	no	—
117	D₁₀₇₆	—	2	16	no	—
118	D₁₀₇₆	—	2	8	no	—
119	C₂²⋊D₂₆₉	—	2	16	no	—
120	C₂×Dic₂₆₉	—	2	2	no	—
121	C₂×Dic₂₆₉	—	2	4	no	—
122	C₂×Dic₂₆₉	—	2	8	no	—
123	C₂×Dic₂₆₉	C₂×D₄	1	4	yes	—
124	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
125	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
126	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
127	C₄×D₂₆₉	—	2	8	no	—
128	C₄×D₂₆₉	—	2	8	no	—
129	C₄×D₂₆₉	—	2	8	no	—
130	C₄×D₂₆₉	—	2	16	no	—
131	C₄×D₂₆₉	C₂×D₄	1	16	yes	complemented
132	C₂³×C₂₆₉	—	2	2	no	—
133	C₂³×C₂₆₉	—	2	2	no	—
134	C₂³×C₂₆₉	#41	1	4	yes	complemented
135	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
136	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
137	Q₈×C₂₆₉	—	2	8	no	—
138	C₂×C₄×C₂₆₉	—	2	2	no	—
139	C₂×C₄×C₂₆₉	—	2	4	no	—
140	C₂×C₄×C₂₆₉	—	2	4	no	—
141	C₂×C₄×C₂₆₉	—	2	8	no	—
142	C₂×C₄×C₂₆₉	C₂×D₄	1	4	yes	—
143	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
144	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
145	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
146	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
147	C₂²×C₂₆₉	—	2	8	no	—
148	C₂²×C₂₆₉	—	2	2	no	—
149	C₂²×C₂₆₉	—	2	2	no	—
150	C₂²×C₂₆₉	C₂²×D₄	1	2	yes	—
151	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
152	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
153	C₂²×C₂₆₉	C₂×#41	1	4	yes	complemented
154	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
155	C₂×D₂₆₉	—	2	32	no	—
156	C₂×D₂₆₉	—	2	8	no	—
157	C₂×D₂₆₉	—	2	8	no	—
158	C₂×D₂₆₉	—	2	2	no	—
159	C₂×D₂₆₉	—	2	2	no	—
160	C₂×D₂₆₉	—	2	2	no	—
161	C₂×D₂₆₉	—	2	2	no	—
162	C₂×D₂₆₉	—	2	4	no	—
163	C₂×D₂₆₉	—	2	4	no	—
164	C₂×D₂₆₉	—	2	4	no	—
165	C₂×D₂₆₉	—	4	8	no	—
166	C₂×D₂₆₉	C₂²×D₄	1	4	yes	—
167	C₂×D₂₆₉	C₂×#41	1	4	yes	complemented
168	C₄×C₂₆₉	—	2	2	no	—
169	C₄×C₂₆₉	—	2	4	no	—
170	C₄×C₂₆₉	—	2	4	no	—
171	C₄×C₂₆₉	C₂²×D₄	1	4	yes	—
172	Dic₂₆₉	—	2	2	no	—
173	Dic₂₆₉	—	2	4	no	—
174	Dic₂₆₉	C₂²×D₄	1	4	yes	—
175	C₂×C₂₆₉	—	2	4	no	—
176	C₂×C₂₆₉	#525	1	4	yes	complemented
177	C₂×C₂₆₉	C₂³×D₄	1	1	yes	characteristic
178	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
179	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
180	D₂₆₉	—	2	4	no	—
181	D₂₆₉	—	2	4	no	—
182	D₂₆₉	—	4	4	no	—
183	C₂₆₉	C₂×#525	1	1	yes	characteristic, complemented, Sylow
184	C₂×#525	—	269	1	no	maximal, Sylow
185	C₂²×#41	—	269	1	no	—
186	C₂⁴×C₄	—	269	1	no	—
187	#525	—	269	16	no	—
188	C₂×#123	—	269	2	no	—
189	C₂×C₂²⋊Q₈	—	269	1	no	—
190	C₂×C₂²⋊Q₈	D₂₆₉	1	1	yes	characteristic, complemented
191	C₂×#121	—	269	1	no	—
192	C₂×#121	—	269	1	no	—
193	C₂×#120	—	269	2	no	—
194	C₂×C₄×D₄	—	269	2	no	—
195	C₂×C₄×D₄	—	269	2	no	—
196	C₂×#117	—	269	1	no	—
197	C₂⁵	—	269	1	no	—
198	C₂×#41	—	269	8	no	—
199	C₂×#41	—	538	8	no	—
200	C₂²×Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
201	C₂²×D₄	—	269	2	no	—
202	C₂²×D₄	—	269	2	no	—
203	C₂²×D₄	—	269	2	no	—
204	C₂²×D₄	—	269	1	no	—
205	C₂³×C₄	—	269	1	no	—
206	C₂³×C₄	—	269	1	no	—
207	C₂³×C₄	—	269	1	no	—
208	C₂³×C₄	—	269	2	no	—
209	C₂³×C₄	—	269	1	no	—
210	C₂³×C₄	—	269	1	no	—
211	C₂³×C₄	—	269	8	no	—
212	C₂³×C₄	—	538	8	no	—
213	C₂³×C₄	C₂×D₂₆₉	1	1	yes	characteristic
214	#123	—	269	16	no	—
215	C₂²⋊Q₈	—	269	8	no	—
216	C₂²⋊Q₈	C₂×D₂₆₉	1	8	yes	complemented
217	#121	—	269	8	no	—
218	#121	—	269	8	no	—
219	#120	—	269	16	no	—
220	C₄×D₄	—	269	16	no	—
221	C₄×D₄	—	269	16	no	—
222	#117	—	269	8	no	—
223	C₂×C₄⋊C₄	—	269	1	no	—
224	C₂×C₄⋊C₄	—	269	2	no	—
225	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
226	C₂×C₄⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
227	C₂×C₂²⋊C₄	—	269	2	no	—
228	C₂×C₂²⋊C₄	—	269	2	no	—
229	C₂×C₂²⋊C₄	—	269	2	no	—
230	C₂×C₂²⋊C₄	—	269	2	no	—
231	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	—
232	C₂×C₄²	—	269	2	no	—
233	C₂⁴	—	269	1	no	—
234	C₂⁴	—	269	1	no	—
235	C₂⁴	—	269	4	no	—
236	C₂⁴	—	269	2	no	—
237	C₂⁴	—	538	4	no	—
238	C₂⁴	—	538	4	no	—
239	C₂⁴	—	538	4	no	—
240	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
241	#41	—	538	32	no	—
242	C₂×Q₈	—	2	4	no	—
243	C₂×Q₈	C₂²×D₂₆₉	1	4	yes	complemented
244	C₂×D₄	—	269	8	no	—
245	C₂×D₄	—	269	8	no	—
246	C₂×D₄	—	269	8	no	—
247	C₂×D₄	—	269	4	no	—
248	C₂×D₄	—	538	8	no	—
249	C₂×D₄	—	538	8	no	—
250	C₂×D₄	—	538	8	no	—
251	C₂×D₄	—	538	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	269	1	no	—
254	C₂²×C₄	—	269	8	no	—
255	C₂²×C₄	—	269	4	no	—
256	C₂²×C₄	—	269	4	no	—
257	C₂²×C₄	—	269	2	no	—
258	C₂²×C₄	—	269	1	no	—
259	C₂²×C₄	—	269	4	no	—
260	C₂²×C₄	—	269	8	no	—
261	C₂²×C₄	—	269	4	no	—
262	C₂²×C₄	—	269	4	no	—
263	C₂²×C₄	—	538	4	no	—
264	C₂²×C₄	—	538	32	no	—
265	C₂²×C₄	—	538	8	no	—
266	C₂²×C₄	—	538	4	no	—
267	C₂²×C₄	—	538	4	no	—
268	C₂²×C₄	—	538	4	no	—
269	C₂²×C₄	C₂²×D₂₆₉	1	4	yes	—
270	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
271	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
273	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
274	C₄⋊C₄	—	269	4	no	—
275	C₄⋊C₄	—	269	8	no	—
276	C₄⋊C₄	C₂²×D₂₆₉	1	4	yes	complemented
277	C₄⋊C₄	C₂²×D₂₆₉	1	8	yes	complemented
278	C₂²⋊C₄	—	269	8	no	—
279	C₂²⋊C₄	—	269	8	no	—
280	C₂²⋊C₄	—	269	8	no	—
281	C₂²⋊C₄	—	269	8	no	—
282	C₂²⋊C₄	C₂²×D₂₆₉	1	8	yes	—
283	C₄²	—	269	8	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	269	4	no	—
287	C₂³	—	269	4	no	—
288	C₂³	—	269	2	no	—
289	C₂³	—	269	2	no	—
290	C₂³	—	269	4	no	—
291	C₂³	—	538	8	no	—
292	C₂³	—	538	8	no	—
293	C₂³	—	538	32	no	—
294	C₂³	—	538	2	no	—
295	C₂³	—	538	2	no	—
296	C₂³	—	538	2	no	—
297	C₂³	—	538	2	no	—
298	C₂³	—	538	8	no	—
299	C₂³	—	538	4	no	—
300	C₂³	—	538	4	no	—
301	C₂³	—	538	4	no	—
302	C₂³	#16864403	1	4	yes	complemented
303	C₂³	C₂³×D₂₆₉	1	2	yes	—
304	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
305	Q₈	—	2	8	no	—
306	D₄	—	538	16	no	—
307	D₄	—	538	16	no	—
308	D₄	—	538	16	no	—
309	D₄	—	538	8	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	269	4	no	—
315	C₂×C₄	—	269	2	no	—
316	C₂×C₄	—	269	16	no	—
317	C₂×C₄	—	269	4	no	—
318	C₂×C₄	—	269	2	no	—
319	C₂×C₄	—	538	8	no	—
320	C₂×C₄	—	538	16	no	—
321	C₂×C₄	—	538	8	no	—
322	C₂×C₄	—	538	8	no	—
323	C₂×C₄	—	538	2	no	—
324	C₂×C₄	—	538	4	no	—
325	C₂×C₄	—	538	8	no	—
326	C₂×C₄	D₄×D₂₆₉	1	4	yes	—
327	C₂×C₄	C₂³×D₂₆₉	1	4	yes	—
328	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
329	C₂×C₄	C₂³×D₂₆₉	1	4	yes	—
330	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	8	no	—
334	C₂²	—	269	4	no	—
335	C₂²	—	269	4	no	—
336	C₂²	—	538	32	no	—
337	C₂²	—	538	2	no	—
338	C₂²	—	538	2	no	—
339	C₂²	—	538	2	no	—
340	C₂²	—	538	2	no	—
341	C₂²	—	538	8	no	—
342	C₂²	—	538	8	no	—
343	C₂²	—	538	4	no	—
344	C₂²	—	538	4	no	—
345	C₂²	—	538	4	no	—
346	C₂²	—	1076	8	no	—
347	C₂²	C₂×D₄×D₂₆₉	1	2	yes	—
348	C₂²	#41×D₂₆₉	1	2	yes	—
349	C₂²	C₂×#16864403	1	2	yes	—
350	C₂²	C₂×#16864403	1	4	yes	complemented
351	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
352	C₄	—	2	2	no	—
353	C₄	—	2	4	no	—
354	C₄	—	2	4	no	—
355	C₄	—	269	4	no	—
356	C₄	—	538	2	no	—
357	C₄	—	538	4	no	—
358	C₄	C₂×D₄×D₂₆₉	1	4	yes	—
359	C₂	—	2	4	no	—
360	C₂	—	538	4	no	—
361	C₂	—	538	4	no	—
362	C₂	—	1076	4	no	—
363	C₂	#31771118	1	4	yes	direct product factor
364	C₂	C₂²×D₄×D₂₆₉	1	1	yes	characteristic
365	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
366	C₂	C₂²×#16864403	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₆₉
commutator, cosocle	C₂²×C₂₆₉	C₂⁵
Frattini	C₂²	C₂⁴×D₂₆₉
Fitting	C₂×C₂²⋊Q₈×C₂₆₉	C₂
socle	C₂³×C₂₆₉	C₂⁴
hypercenter	C₂×C₂²⋊Q₈	D₂₆₉
hypocenter	C₂₆₉	C₂×#525
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#16864403	C₂	semidirect
2. C₂³×C₄×D₂₆₉	C₂	semidirect
3. #31771118	C₂	direct (N × H)
4. C₂×#22575438	C₂	semidirect
5. C₂×#22575429	C₂	semidirect
6. C₂×#22575428	C₂	semidirect
7. C₂×#22575427	C₂	semidirect
8. C₂×#22575423	C₂	semidirect
9. C₂×#22575415	C₂	semidirect
10. C₂×#22575413	C₂	semidirect
11. C₂×#22575411	C₂	semidirect
12. C₂×C₂²⋊Q₈×C₂₆₉	C₂	semidirect
15. C₂×#16864403	C₂²	semidirect
18. C₂²×D₁₀₇₆	C₂²	semidirect
26. C₂²×C₄×D₂₆₉	C₂²	semidirect
27. C₂²×C₄×D₂₆₉	C₂²	semidirect
28. #22575438	C₂²	semidirect
29. #22575429	C₂²	semidirect
30. #22575428	C₂²	semidirect
31. #22575427	C₂²	semidirect
32. #22575423	C₂²	semidirect
33. #22575415	C₂²	semidirect
34. #22575413	C₂²	semidirect
35. #22575411	C₂²	semidirect
36. C₂×C₄⋊Dic₂₆₉	C₂²	semidirect
37. C₂×#16864381	C₂²	semidirect
40. C₂×#16864379	C₂²	semidirect
41. C₂×#16864379	C₂²	semidirect
42. C₂×C₄×Dic₂₆₉	C₂²	semidirect
43. C₂²×Q₈×C₂₆₉	C₂²	semidirect
45. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
46. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
47. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
62. C₂×D₁₀₇₆	C₂³	semidirect
75. C₂×C₄×D₂₆₉	D₄	semidirect
80. C₂×C₄×D₂₆₉	C₂³	semidirect
81. C₄⋊Dic₂₆₉	C₂³	semidirect
82. #16864381	C₂³	semidirect
85. #16864379	C₂³	semidirect
86. #16864379	C₂³	semidirect
87. C₄×Dic₂₆₉	C₂³	semidirect
90. C₂×Q₈×C₂₆₉	C₂³	semidirect
97. C₄⋊C₄×C₂₆₉	C₂³	semidirect
98. C₄⋊C₄×C₂₆₉	C₂³	semidirect
112. C₂²×D₂₆₉	#41	semidirect
131. C₄×D₂₆₉	C₂×D₄	semidirect
134. C₂³×C₂₆₉	#41	semidirect
153. C₂²×C₂₆₉	C₂×#41	semidirect
167. C₂×D₂₆₉	C₂×#41	semidirect
176. C₂×C₂₆₉	#525	semidirect
183. C₂₆₉	C₂×#525	semidirect
190. C₂×C₂²⋊Q₈	D₂₆₉	semidirect
200. C₂²×Q₈	C₂×D₂₆₉	semidirect
216. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
225. C₂×C₄⋊C₄	C₂×D₂₆₉	semidirect
226. C₂×C₄⋊C₄	C₂×D₂₆₉	semidirect
243. C₂×Q₈	C₂²×D₂₆₉	semidirect
276. C₄⋊C₄	C₂²×D₂₆₉	semidirect
277. C₄⋊C₄	C₂²×D₂₆₉	semidirect
302. C₂³	#16864403	semidirect
350. C₂²	C₂×#16864403	semidirect
363. C₂	#31771118	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#16864403	2
C₂³×C₄×D₂₆₉	2
#31771118	2
C₂×#22575438	2
C₂×#22575429	2
C₂×#22575428	2
C₂×#22575427	2
C₂×#22575423	2
C₂×#22575415	2
C₂×#22575413	2
C₂×#22575411	2
C₂×C₂²⋊Q₈×C₂₆₉	2
C₂×#525	269

Subgroups — C2×#31771118 #46824129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#31771118 #46824129