Subgroups — C₂×#31771403 #46825630

Order 34432.

1484 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#16864402	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771403	C₂	1	16	yes	maximal, direct product factor
3	C₂×#22575484	C₂	1	2	yes	maximal, complemented
4	C₂×#22575483	C₂	1	2	yes	maximal, complemented
5	C₂×#22575479	C₂	1	2	yes	maximal, complemented
6	C₂×#22575478	C₂	1	2	yes	maximal, complemented
7	C₂×#22575473	C₂	1	4	yes	maximal, complemented
8	C₂²×#16864386	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16864402	—	2	1	no	—
11	C₂×#16864402	—	2	1	no	—
12	C₂×#16864402	—	2	4	no	—
13	C₂×#16864402	C₂²	1	2	yes	—
14	C₂×#16864402	C₂²	1	2	yes	complemented
15	C₂×#16864402	C₂²	1	8	yes	complemented
16	C₂²×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊D₂₆₉	—	2	1	no	—
19	C₂²×C₄×D₂₆₉	—	2	1	no	—
20	#22575484	C₂²	1	16	yes	complemented
21	#22575483	C₂²	1	16	yes	complemented
22	#22575479	C₂²	1	16	yes	complemented
23	#22575478	C₂²	1	16	yes	complemented
24	#22575473	C₂²	1	32	yes	complemented
25	C₂×#16864392	C₂²	1	4	yes	complemented
26	C₂×#16864390	C₂²	1	4	yes	complemented
27	C₂×#16864389	C₂²	1	4	yes	complemented
28	C₂×#16864387	C₂²	1	4	yes	complemented
29	C₂×#16864386	C₂²	1	2	yes	complemented
30	C₂×#16864386	C₂²	1	2	yes	complemented
31	C₂×#16864386	C₂²	1	8	yes	complemented
32	C₂²×#14524130	C₂²	1	2	yes	complemented
33	C₂×#41×C₂₆₉	—	2	1	no	—
34	C₂×#41×C₂₆₉	—	2	1	no	—
35	C₂×#41×C₂₆₉	—	2	4	no	—
36	C₂×#41×C₂₆₉	C₂²	1	2	yes	—
37	C₂×#41×C₂₆₉	C₂²	1	2	yes	complemented
38	C₂×#41×C₂₆₉	C₂²	1	8	yes	complemented
39	C₂²×Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
40	C₂²×D₄×C₂₆₉	—	2	1	no	—
41	C₂²×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
42	C₂³×C₄×C₂₆₉	—	2	1	no	—
43	C₂³×C₄×C₂₆₉	C₂²	1	1	yes	characteristic
44	C₂³×D₂₆₉	—	2	1	no	—
45	#16864402	—	2	4	no	—
46	#16864402	—	2	8	no	—
47	#16864402	—	2	8	no	—
48	#16864402	—	2	4	no	—
49	#16864402	C₂³	1	8	yes	—
50	#16864402	C₂³	1	8	yes	complemented
51	C₂×Dic₅₃₈	—	2	1	no	—
52	C₂×Dic₅₃₈	—	2	2	no	—
53	C₂×Dic₅₃₈	C₂³	1	2	yes	—
54	C₂×Dic₅₃₈	C₂³	1	4	yes	complemented
55	C₂×D₁₀₇₆	—	2	1	no	—
56	C₂×D₁₀₇₆	—	2	2	no	—
57	C₂×D₁₀₇₆	C₂³	1	2	yes	—
58	C₂×D₁₀₇₆	C₂³	1	4	yes	complemented
59	C₂×C₂²⋊D₂₆₉	—	2	2	no	—
60	C₂×C₂²⋊D₂₆₉	—	2	2	no	—
61	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
62	C₂²×Dic₂₆₉	—	2	1	no	—
63	C₂×C₄×D₂₆₉	—	2	2	no	—
64	C₂×C₄×D₂₆₉	—	2	8	no	—
65	C₂×C₄×D₂₆₉	—	2	2	no	—
66	#16864392	C₂³	1	16	yes	complemented
67	#16864390	C₂³	1	16	yes	complemented
68	#16864389	C₂³	1	16	yes	complemented
69	#16864387	C₂³	1	16	yes	complemented
70	#16864386	C₂³	1	8	yes	complemented
71	#16864386	C₂³	1	8	yes	complemented
72	C₂×#14524130	C₂³	1	4	yes	—
73	C₂×#14524130	C₂³	1	8	yes	complemented
74	C₂⁴×C₂₆₉	—	2	1	no	—
75	C₂⁴×C₂₆₉	D₄	1	1	yes	characteristic
76	#41×C₂₆₉	—	2	4	no	—
77	#41×C₂₆₉	—	2	8	no	—
78	#41×C₂₆₉	—	2	8	no	—
79	#41×C₂₆₉	—	2	4	no	—
80	#41×C₂₆₉	C₂³	1	8	yes	—
81	#41×C₂₆₉	C₂³	1	8	yes	complemented
82	C₂×Q₈×C₂₆₉	—	2	1	no	—
83	C₂×Q₈×C₂₆₉	—	2	2	no	—
84	C₂×Q₈×C₂₆₉	C₂³	1	2	yes	—
85	C₂×Q₈×C₂₆₉	C₂³	1	4	yes	complemented
86	C₂×D₄×C₂₆₉	—	2	2	no	—
87	C₂×D₄×C₂₆₉	—	2	2	no	—
88	C₂×D₄×C₂₆₉	—	2	8	no	—
89	C₂×D₄×C₂₆₉	—	2	1	no	—
90	C₂×D₄×C₂₆₉	—	2	2	no	—
91	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
92	C₂×D₄×C₂₆₉	C₂³	1	4	yes	complemented
93	C₂²×C₄×C₂₆₉	—	2	1	no	—
94	C₂²×C₄×C₂₆₉	—	2	2	no	—
95	C₂²×C₄×C₂₆₉	—	2	8	no	—
96	C₂²×C₄×C₂₆₉	—	2	2	no	—
97	C₂²×C₄×C₂₆₉	D₄	1	1	yes	characteristic
98	C₂²×C₄×C₂₆₉	D₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₆₉	D₄	1	1	yes	characteristic
100	C₂²×C₄×C₂₆₉	D₄	1	4	yes	—
101	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₂₆₉	C₂³	1	4	yes	—
105	C₂²×D₂₆₉	—	2	2	no	—
106	C₂²×D₂₆₉	—	2	4	no	—
107	C₂²×D₂₆₉	—	4	4	no	—
108	Dic₅₃₈	—	2	2	no	—
109	Dic₅₃₈	—	2	4	no	—
110	Dic₅₃₈	C₂⁴	1	4	yes	—
111	D₁₀₇₆	—	2	2	no	—
112	D₁₀₇₆	—	2	4	no	—
113	D₁₀₇₆	C₂⁴	1	4	yes	—
114	C₂²⋊D₂₆₉	—	2	8	no	—
115	C₂²⋊D₂₆₉	—	2	8	no	—
116	C₂×Dic₂₆₉	—	2	2	no	—
117	C₂×Dic₂₆₉	—	2	4	no	—
118	C₄×D₂₆₉	—	2	8	no	—
119	C₄×D₂₆₉	—	2	8	no	—
120	#14524130	C₂⁴	1	8	yes	—
121	C₂³×C₂₆₉	—	2	2	no	—
122	C₂³×C₂₆₉	—	2	4	no	—
123	C₂³×C₂₆₉	—	4	2	no	—
124	C₂³×C₂₆₉	—	4	4	no	—
125	C₂³×C₂₆₉	C₂×D₄	1	1	yes	characteristic
126	C₂³×C₂₆₉	C₂×D₄	1	1	yes	characteristic
127	C₂³×C₂₆₉	C₂×D₄	1	1	yes	characteristic
128	C₂³×C₂₆₉	C₂×D₄	1	4	yes	—
129	Q₈×C₂₆₉	—	2	2	no	—
130	Q₈×C₂₆₉	—	2	4	no	—
131	Q₈×C₂₆₉	C₂⁴	1	4	yes	—
132	D₄×C₂₆₉	—	2	8	no	—
133	D₄×C₂₆₉	—	2	8	no	—
134	D₄×C₂₆₉	—	2	2	no	—
135	D₄×C₂₆₉	—	2	4	no	—
136	D₄×C₂₆₉	C₂⁴	1	4	yes	—
137	C₂×C₄×C₂₆₉	—	2	2	no	—
138	C₂×C₄×C₂₆₉	—	2	4	no	—
139	C₂×C₄×C₂₆₉	—	2	8	no	—
140	C₂×C₄×C₂₆₉	—	2	8	no	—
141	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×C₂₆₉	C₂×D₄	1	4	yes	—
143	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×C₂₆₉	C₂×D₄	1	2	yes	—
145	C₂×C₄×C₂₆₉	C₂×D₄	1	4	yes	—
146	C₂×C₄×C₂₆₉	C₂×D₄	1	2	yes	—
147	C₂×C₄×C₂₆₉	C₂×D₄	1	2	yes	—
148	C₂×C₄×C₂₆₉	C₂×D₄	1	4	yes	—
149	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
151	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
152	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
153	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
154	C₂²×C₂₆₉	—	2	2	no	—
155	C₂²×C₂₆₉	—	2	2	no	—
156	C₂²×C₂₆₉	—	2	2	no	—
157	C₂²×C₂₆₉	—	2	4	no	—
158	C₂²×C₂₆₉	—	4	4	no	—
159	C₂²×C₂₆₉	—	4	8	no	—
160	C₂²×C₂₆₉	—	4	4	no	—
161	C₂²×C₂₆₉	C₂²×D₄	1	2	yes	—
162	C₂²×C₂₆₉	C₂²×D₄	1	2	yes	—
163	C₂²×C₂₆₉	C₂²×D₄	1	2	yes	—
164	C₂²×C₂₆₉	C₂²×D₄	1	1	yes	characteristic
165	C₂×D₂₆₉	—	2	4	no	—
166	C₂×D₂₆₉	—	4	8	no	—
167	C₂×D₂₆₉	—	4	4	no	—
168	C₄×C₂₆₉	—	2	4	no	—
169	C₄×C₂₆₉	C₂²×D₄	1	2	yes	—
170	C₄×C₂₆₉	C₂²×D₄	1	2	yes	—
171	C₄×C₂₆₉	C₂²×D₄	1	2	yes	—
172	C₄×C₂₆₉	C₂²×D₄	1	1	yes	characteristic
173	C₄×C₂₆₉	C₂⁵	1	1	yes	characteristic
174	Dic₂₆₉	—	2	4	no	—
175	C₂×C₂₆₉	—	2	2	no	—
176	C₂×C₂₆₉	—	2	2	no	—
177	C₂×C₂₆₉	—	2	2	no	—
178	C₂×C₂₆₉	—	4	4	no	—
179	C₂×C₂₆₉	#575	1	2	yes	complemented
180	C₂×C₂₆₉	C₂³×D₄	1	1	yes	characteristic
181	D₂₆₉	—	4	4	no	—
182	C₂₆₉	C₂×#575	1	1	yes	characteristic, complemented, Sylow
183	C₂×#575	—	269	1	no	maximal, Sylow
184	C₂²×#41	—	269	1	no	—
185	C₂²×#41	D₂₆₉	1	1	yes	characteristic, complemented
186	#575	—	269	16	no	—
187	C₂×#137	—	269	2	no	—
188	C₂×#137	—	269	2	no	—
189	C₂×AGL(1,ℤ/8)	—	269	2	no	—
190	C₂×AGL(1,ℤ/8)	—	269	2	no	—
191	C₂×#135	—	269	4	no	—
192	C₂²×M₁₆	—	269	1	no	—
193	C₂×#41	—	2	1	no	—
194	C₂×#41	—	2	4	no	—
195	C₂×#41	—	2	1	no	—
196	C₂×#41	—	269	2	no	—
197	C₂×#41	—	269	2	no	—
198	C₂×#41	—	269	8	no	—
199	C₂×#41	—	538	1	no	—
200	C₂×#41	—	538	4	no	—
201	C₂×#41	—	538	1	no	—
202	C₂×#41	C₂×D₂₆₉	1	2	yes	—
203	C₂×#41	C₂×D₂₆₉	1	2	yes	complemented
204	C₂×#41	C₂×D₂₆₉	1	8	yes	complemented
205	C₂²×Q₈	—	269	1	no	—
206	C₂²×Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
207	C₂²×D₄	—	2	1	no	—
208	C₂²×D₄	—	269	1	no	—
209	C₂²×D₄	—	538	1	no	—
210	C₂²×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
211	C₂³×C₄	—	2	1	no	—
212	C₂³×C₄	—	538	1	no	—
213	C₂³×C₄	C₂×D₂₆₉	1	1	yes	characteristic
214	#137	—	269	16	no	—
215	#137	—	269	16	no	—
216	AGL(1,ℤ/8)	—	269	16	no	—
217	AGL(1,ℤ/8)	—	269	16	no	—
218	#135	—	269	32	no	—
219	C₂×Q₁₆	—	269	4	no	—
220	C₂×SD₁₆	—	269	4	no	—
221	C₂×SD₁₆	—	269	4	no	—
222	C₂×D₈	—	269	4	no	—
223	C₂×M₁₆	—	269	2	no	—
224	C₂×M₁₆	—	269	2	no	—
225	C₂×M₁₆	—	269	8	no	—
226	C₂²×C₈	—	269	2	no	—
227	C₂⁴	—	2	1	no	—
228	C₂⁴	—	538	1	no	—
229	C₂⁴	C₂²⋊D₂₆₉	1	1	yes	characteristic
230	#41	—	2	4	no	—
231	#41	—	2	8	no	—
232	#41	—	2	8	no	—
233	#41	—	2	4	no	—
234	#41	—	269	8	no	—
235	#41	—	269	8	no	—
236	#41	—	538	8	no	—
237	#41	—	538	4	no	—
238	#41	—	538	4	no	—
239	#41	—	538	8	no	—
240	#41	C₂²×D₂₆₉	1	8	yes	—
241	#41	C₂²×D₂₆₉	1	8	yes	complemented
242	C₂×Q₈	—	2	1	no	—
243	C₂×Q₈	—	2	2	no	—
244	C₂×Q₈	—	269	2	no	—
245	C₂×Q₈	—	269	4	no	—
246	C₂×Q₈	—	538	1	no	—
247	C₂×Q₈	—	538	2	no	—
248	C₂×Q₈	C₂²×D₂₆₉	1	2	yes	—
249	C₂×Q₈	C₂²×D₂₆₉	1	4	yes	complemented
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	1	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	269	2	no	—
256	C₂×D₄	—	269	4	no	—
257	C₂×D₄	—	538	2	no	—
258	C₂×D₄	—	538	2	no	—
259	C₂×D₄	—	538	8	no	—
260	C₂×D₄	—	538	1	no	—
261	C₂×D₄	—	538	2	no	—
262	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
263	C₂×D₄	C₂²×D₂₆₉	1	4	yes	complemented
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	538	1	no	—
269	C₂²×C₄	—	538	2	no	—
270	C₂²×C₄	—	538	8	no	—
271	C₂²×C₄	—	538	2	no	—
272	C₂²×C₄	C₂²⋊D₂₆₉	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊D₂₆₉	1	4	yes	—
274	C₂²×C₄	C₂²⋊D₂₆₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊D₂₆₉	1	1	yes	characteristic
276	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
277	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
278	C₂²×C₄	C₂²×D₂₆₉	1	4	yes	—
279	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
280	Q₁₆	—	269	16	no	—
281	SD₁₆	—	269	16	no	—
282	SD₁₆	—	269	16	no	—
283	D₈	—	269	16	no	—
284	M₁₆	—	269	8	no	—
285	M₁₆	—	269	8	no	—
286	C₂×C₈	—	269	4	no	—
287	C₂×C₈	—	269	8	no	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	4	2	no	—
291	C₂³	—	4	4	no	—
292	C₂³	—	538	4	no	—
293	C₂³	—	538	2	no	—
294	C₂³	—	1076	4	no	—
295	C₂³	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
296	C₂³	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
297	C₂³	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
298	C₂³	C₂×C₂²⋊D₂₆₉	1	4	yes	—
299	Q₈	—	2	2	no	—
300	Q₈	—	2	4	no	—
301	Q₈	—	269	4	no	—
302	Q₈	—	538	4	no	—
303	Q₈	—	538	2	no	—
304	Q₈	C₂³×D₂₆₉	1	4	yes	—
305	D₄	—	2	8	no	—
306	D₄	—	2	8	no	—
307	D₄	—	2	2	no	—
308	D₄	—	2	4	no	—
309	D₄	—	269	4	no	—
310	D₄	—	538	8	no	—
311	D₄	—	538	8	no	—
312	D₄	—	538	4	no	—
313	D₄	—	538	2	no	—
314	D₄	C₂³×D₂₆₉	1	4	yes	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	538	4	no	—
320	C₂×C₄	—	538	2	no	—
321	C₂×C₄	—	538	8	no	—
322	C₂×C₄	—	538	8	no	—
323	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
324	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	4	yes	—
325	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
326	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	4	yes	—
327	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	2	yes	—
328	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	2	yes	—
329	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	2	yes	—
330	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	4	yes	—
331	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
332	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
333	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
334	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
335	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
336	C₈	—	269	8	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	4	8	no	—
343	C₂²	—	4	4	no	—
344	C₂²	—	538	4	no	—
345	C₂²	—	1076	8	no	—
346	C₂²	—	1076	4	no	—
347	C₂²	C₂²×C₂²⋊D₂₆₉	1	2	yes	—
348	C₂²	C₂²×C₂²⋊D₂₆₉	1	2	yes	—
349	C₂²	C₂²×C₂²⋊D₂₆₉	1	2	yes	—
350	C₂²	C₂²×C₂²⋊D₂₆₉	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	538	4	no	—
353	C₄	C₂²×C₂²⋊D₂₆₉	1	2	yes	—
354	C₄	C₂²×C₂²⋊D₂₆₉	1	2	yes	—
355	C₄	C₂²×C₂²⋊D₂₆₉	1	2	yes	—
356	C₄	C₂²×C₂²⋊D₂₆₉	1	1	yes	characteristic
357	C₄	C₂⁴×D₂₆₉	1	1	yes	characteristic
358	C₂	—	2	2	no	—
359	C₂	—	2	2	no	—
360	C₂	—	2	2	no	—
361	C₂	—	4	4	no	—
362	C₂	—	1076	4	no	—
363	C₂	#31771403	1	2	yes	direct product factor
364	C₂	C₂³×C₂²⋊D₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₂₆₉
commutator, cosocle	C₄×C₂₆₉	C₂⁵
Frattini	C₄	C₂⁴×D₂₆₉
Fitting	C₂²×#41×C₂₆₉	C₂
socle	C₂²×C₂₆₉	C₂²×D₄
hypercenter	C₂²×#41	D₂₆₉
hypocenter	C₂₆₉	C₂×#575
LCS	G ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×#16864402	C₂	semidirect
2. #31771403	C₂	direct (N × H)
3. C₂×#22575484	C₂	semidirect
4. C₂×#22575483	C₂	semidirect
5. C₂×#22575479	C₂	semidirect
6. C₂×#22575478	C₂	semidirect
7. C₂×#22575473	C₂	semidirect
8. C₂²×#16864386	C₂	semidirect
9. C₂²×#41×C₂₆₉	C₂	semidirect
14. C₂×#16864402	C₂²	semidirect
15. C₂×#16864402	C₂²	semidirect
16. C₂²×Dic₅₃₈	C₂²	semidirect
17. C₂²×D₁₀₇₆	C₂²	semidirect
20. #22575484	C₂²	semidirect
21. #22575483	C₂²	semidirect
22. #22575479	C₂²	semidirect
23. #22575478	C₂²	semidirect
24. #22575473	C₂²	semidirect
25. C₂×#16864392	C₂²	semidirect
26. C₂×#16864390	C₂²	semidirect
27. C₂×#16864389	C₂²	semidirect
28. C₂×#16864387	C₂²	semidirect
29. C₂×#16864386	C₂²	semidirect
30. C₂×#16864386	C₂²	semidirect
31. C₂×#16864386	C₂²	semidirect
32. C₂²×#14524130	C₂²	semidirect
37. C₂×#41×C₂₆₉	C₂²	semidirect
38. C₂×#41×C₂₆₉	C₂²	semidirect
39. C₂²×Q₈×C₂₆₉	C₂²	semidirect
41. C₂²×D₄×C₂₆₉	C₂²	semidirect
50. #16864402	C₂³	semidirect
54. C₂×Dic₅₃₈	C₂³	semidirect
58. C₂×D₁₀₇₆	C₂³	semidirect
66. #16864392	C₂³	semidirect
67. #16864390	C₂³	semidirect
68. #16864389	C₂³	semidirect
69. #16864387	C₂³	semidirect
70. #16864386	C₂³	semidirect
71. #16864386	C₂³	semidirect
73. C₂×#14524130	C₂³	semidirect
81. #41×C₂₆₉	C₂³	semidirect
85. C₂×Q₈×C₂₆₉	C₂³	semidirect
92. C₂×D₄×C₂₆₉	C₂³	semidirect
179. C₂×C₂₆₉	#575	semidirect
182. C₂₆₉	C₂×#575	semidirect
185. C₂²×#41	D₂₆₉	semidirect
203. C₂×#41	C₂×D₂₆₉	semidirect
204. C₂×#41	C₂×D₂₆₉	semidirect
206. C₂²×Q₈	C₂×D₂₆₉	semidirect
210. C₂²×D₄	C₂×D₂₆₉	semidirect
241. #41	C₂²×D₂₆₉	semidirect
249. C₂×Q₈	C₂²×D₂₆₉	semidirect
263. C₂×D₄	C₂²×D₂₆₉	semidirect
363. C₂	#31771403	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×#16864402	2
#31771403	2
C₂×#22575484	2
C₂×#22575483	2
C₂×#22575479	2
C₂×#22575478	2
C₂×#22575473	2
C₂²×#16864386	2
C₂²×#41×C₂₆₉	2
C₂×#575	269

Subgroups — C2×#31771403 #46825630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#31771403 #46825630