Subgroups — C₂²×#41×#261 #16809630

Order 3328.

12878 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×#261	C₂	1	48	yes	maximal, direct product factor
2	C₂²×Q₈×#261	C₂	1	2	yes	maximal, complemented
3	C₂²×D₄×#261	C₂	1	6	yes	maximal, complemented
4	C₂²×#88237	C₂	1	3	yes	maximal, complemented
5	C₂³×C₄×#261	C₂	1	3	yes	maximal, complemented
6	C₂²×#41×D₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂⁴×#261	C₂²	1	6	yes	—
8	C₂²×C₁₃×#41	C₄	1	1	yes	characteristic, complemented
9	C₂×#41×D₁₃	C₄	1	24	yes	complemented
10	C₂×#41×D₁₃	C₂²	1	24	yes	—
11	C₂²×#6131	C₄	1	1	yes	characteristic, complemented
12	C₂²×Q₈×D₁₃	C₂²	1	1	yes	characteristic
13	C₂²×#6129	C₄	1	3	yes	complemented
14	C₂²×D₄×D₁₃	C₂²	1	3	yes	—
15	C₂²×#6127	C₄	1	3	yes	complemented
16	C₂³×C₄×D₁₃	C₂²	1	3	yes	—
17	C₂²×C₂²⋊#261	C₂²	1	6	yes	—
18	#41×#261	C₂²	1	256	yes	direct product factor
19	C₂×Q₈×#261	C₂²	1	48	yes	complemented
20	C₂×D₄×#261	C₂²	1	144	yes	complemented
21	C₂×#88237	C₂²	1	72	yes	complemented
22	C₂²×C₄⋊#261	C₂²	1	6	yes	—
23	C₂²×C₄×#261	C₂²	1	1	yes	characteristic
24	C₂²×C₄×#261	C₂²	1	3	yes	—
25	C₂²×C₄×#261	C₂²	1	6	yes	—
26	C₂²×C₄×#261	C₂²	1	72	yes	complemented
27	C₂⁴×D₁₃	C₂³	1	3	yes	—
28	C₂³×#261	—	2	48	no	—
29	C₂³×#261	C₂³	1	6	yes	—
30	C₂³×#261	C₂³	1	72	yes	—
31	C₂³×#261	C₂³	1	2	yes	—
32	C₂×C₁₃×#41	C₂×C₄	1	24	yes	complemented
33	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
34	C₂²×D₄×C₁₃	C₂×C₄	1	3	yes	complemented
35	C₂³×C₄×C₁₃	C₂×C₄	1	3	yes	complemented
36	C₂²×C₂²⋊D₁₃	C₂×C₄	1	6	yes	complemented
37	C₂³×Dic₁₃	C₂×C₄	1	3	yes	complemented
38	#41×D₁₃	C₂×C₄	1	192	yes	complemented
39	#41×D₁₃	C₂³	1	64	yes	—
40	C₂×#6131	C₂×C₄	1	24	yes	complemented
41	C₂×Q₈×D₁₃	C₂×C₄	1	12	yes	complemented
42	C₂×Q₈×D₁₃	C₂³	1	12	yes	—
43	C₂×#6129	C₂×C₄	1	72	yes	complemented
44	C₂×D₄×D₁₃	C₂×C₄	1	36	yes	complemented
45	C₂×D₄×D₁₃	C₂³	1	36	yes	—
46	C₂×#6127	C₂×C₄	1	72	yes	complemented
47	C₂²×D₅₂	C₂×C₄	1	3	yes	complemented
48	C₂²×C₄×D₁₃	C₂×C₄	1	36	yes	complemented
49	C₂²×C₄×D₁₃	C₂×C₄	1	3	yes	complemented
50	C₂²×C₄×D₁₃	C₂×C₄	1	3	yes	complemented
51	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
53	C₂²×C₄×D₁₃	C₂³	1	36	yes	—
54	C₂²×Dic₂₆	C₂×C₄	1	3	yes	complemented
55	C₂×C₂²⋊#261	C₂³	1	72	yes	—
56	Q₈×#261	C₂³	1	128	yes	complemented
57	D₄×#261	C₂³	1	384	yes	complemented
58	#88237	C₂³	1	192	yes	complemented
59	C₂×C₄⋊#261	C₂³	1	72	yes	—
60	C₂×C₄×#261	C₂³	1	12	yes	—
61	C₂×C₄×#261	C₂³	1	36	yes	—
62	C₂×C₄×#261	C₂³	1	72	yes	—
63	C₂×C₄×#261	C₂³	1	192	yes	complemented
64	C₂²×C₄×#41	—	13	1	no	maximal, Sylow
65	C₂⁴×C₁₃	C₂²×C₄	1	3	yes	—
66	C₂³×D₁₃	—	2	24	no	—
67	C₂³×D₁₃	C₂²×C₄	1	3	yes	—
68	C₂³×D₁₃	C₂²×C₄	1	18	yes	—
69	C₂³×D₁₃	C₂⁴	1	18	yes	—
70	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
71	C₂²×#261	—	2	24	no	—
72	C₂²×#261	—	2	288	no	—
73	C₂²×#261	#41	1	16	yes	direct product factor
74	C₂²×#261	C₂⁴	1	36	yes	—
75	C₂²×#261	C₂⁴	1	96	yes	—
76	C₂²×#261	C₂⁴	1	12	yes	—
77	C₁₃×#41	C₂²×C₄	1	64	yes	complemented
78	C₂×Q₈×C₁₃	C₂²×C₄	1	12	yes	complemented
79	C₂×D₄×C₁₃	C₂²×C₄	1	36	yes	complemented
80	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂²×C₄	1	36	yes	complemented
83	C₂×C₂²⋊D₁₃	C₂²×C₄	1	72	yes	complemented
84	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
85	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×Dic₁₃	C₂²×C₄	1	36	yes	complemented
87	#6131	C₂²×C₄	1	64	yes	complemented
88	Q₈×D₁₃	C₂²×C₄	1	48	yes	complemented
89	Q₈×D₁₃	C₂⁴	1	16	yes	—
90	#6129	C₂²×C₄	1	192	yes	complemented
91	D₄×D₁₃	C₂²×C₄	1	144	yes	complemented
92	D₄×D₁₃	C₂⁴	1	48	yes	—
93	#6127	C₂²×C₄	1	192	yes	complemented
94	C₂×D₅₂	C₂²×C₄	1	36	yes	complemented
95	C₂×C₄×D₁₃	C₂²×C₄	1	6	yes	—
96	C₂×C₄×D₁₃	C₂²×C₄	1	18	yes	—
97	C₂×C₄×D₁₃	C₂²×C₄	1	144	yes	complemented
98	C₂×C₄×D₁₃	C₂²×C₄	1	36	yes	complemented
99	C₂×C₄×D₁₃	C₂²×C₄	1	36	yes	complemented
100	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
101	C₂×C₄×D₁₃	C₂⁴	1	18	yes	—
102	C₂×C₄×D₁₃	C₂⁴	1	48	yes	—
103	C₂×Dic₂₆	C₂²×C₄	1	36	yes	complemented
104	C₂²⋊#261	C₂⁴	1	96	yes	—
105	C₄⋊#261	C₂⁴	1	96	yes	—
106	C₄×#261	C₂⁴	1	16	yes	—
107	C₄×#261	C₂⁴	1	48	yes	—
108	C₄×#261	C₂⁴	1	96	yes	—
109	C₂³×#41	—	13	1	no	—
110	C₂×C₄×#41	—	13	48	no	—
111	C₂²×C₄×Q₈	—	13	2	no	—
112	C₂²×C₄×D₄	—	13	6	no	—
113	C₂²×#117	—	13	3	no	—
114	C₂³×C₄²	—	13	3	no	—
115	C₂³×C₁₃	—	2	12	no	—
116	C₂³×C₁₃	C₂³×C₄	1	18	yes	—
117	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
118	C₂²×D₁₃	—	2	12	no	—
119	C₂²×D₁₃	—	2	72	no	—
120	C₂²×D₁₃	—	2	72	no	—
121	C₂²×D₁₃	C₂³×C₄	1	18	yes	—
122	C₂²×D₁₃	C₂³×C₄	1	36	yes	—
123	C₂²×D₁₃	C₂³×C₄	1	3	yes	—
124	C₂²×D₁₃	C₂×#41	1	8	yes	—
125	C₂²×D₁₃	C₂⁵	1	12	yes	—
126	C₂²×D₁₃	C₂⁵	1	3	yes	—
127	C₂×#261	—	2	72	no	—
128	C₂×#261	—	2	192	no	—
129	C₂×#261	C₂×#41	1	48	yes	direct product factor
130	C₂×#261	C₂⁵	1	24	yes	—
131	C₂×#261	C₂⁵	1	8	yes	—
132	Q₈×C₁₃	C₂³×C₄	1	16	yes	complemented
133	D₄×C₁₃	C₂³×C₄	1	48	yes	complemented
134	C₂×C₄×C₁₃	C₂³×C₄	1	18	yes	—
135	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
136	C₂×C₄×C₁₃	C₂³×C₄	1	48	yes	complemented
137	C₂²⋊D₁₃	C₂³×C₄	1	96	yes	complemented
138	C₂×Dic₁₃	C₂³×C₄	1	18	yes	—
139	C₂×Dic₁₃	C₂³×C₄	1	6	yes	—
140	C₂×Dic₁₃	C₂³×C₄	1	48	yes	complemented
141	D₅₂	C₂³×C₄	1	48	yes	complemented
142	C₄×D₁₃	C₂³×C₄	1	12	yes	—
143	C₄×D₁₃	C₂³×C₄	1	36	yes	—
144	C₄×D₁₃	C₂³×C₄	1	48	yes	complemented
145	C₄×D₁₃	C₂³×C₄	1	48	yes	complemented
146	C₄×D₁₃	C₂⁵	1	4	yes	—
147	C₄×D₁₃	C₂⁵	1	12	yes	—
148	Dic₂₆	C₂³×C₄	1	48	yes	complemented
149	C₂²×#41	—	13	24	no	—
150	C₂²×#41	—	13	24	no	—
151	C₂²×#41	—	13	1	no	—
152	C₂²×#41	—	13	3	no	—
153	C₂²×#41	—	13	3	no	—
154	C₂²×#41	#261	1	1	yes	characteristic, direct product factor
155	C₂³×Q₈	—	13	1	no	—
156	C₂³×D₄	—	13	3	no	—
157	C₂⁴×C₄	—	13	3	no	—
158	C₂⁴×C₄	—	13	6	no	—
159	C₄×#41	—	13	256	no	—
160	C₂×C₄×Q₈	—	13	48	no	—
161	C₂×C₄×D₄	—	13	144	no	—
162	C₂×#117	—	13	72	no	—
163	C₂²×C₄⋊C₄	—	13	6	no	—
164	C₂²×C₂²⋊C₄	—	13	6	no	—
165	C₂²×C₄²	—	13	1	no	—
166	C₂²×C₄²	—	13	3	no	—
167	C₂²×C₄²	—	13	6	no	—
168	C₂²×C₄²	—	13	72	no	—
169	C₂²×C₁₃	—	2	36	no	—
170	C₂²×C₁₃	C₄×#41	1	4	yes	complemented
171	C₂²×C₁₃	C₂⁴×C₄	1	12	yes	—
172	C₂²×C₁₃	C₂⁴×C₄	1	3	yes	—
173	C₂×D₁₃	—	2	36	no	—
174	C₂×D₁₃	—	2	24	no	—
175	C₂×D₁₃	—	2	72	no	—
176	C₂×D₁₃	C₄×#41	1	12	yes	complemented
177	C₂×D₁₃	C₂⁴×C₄	1	12	yes	—
178	C₂×D₁₃	C₂⁴×C₄	1	3	yes	—
179	C₂×D₁₃	C₂²×#41	1	12	yes	—
180	C₂×D₁₃	C₂⁶	1	1	yes	characteristic
181	#261	—	2	24	no	—
182	#261	C₂²×#41	1	16	yes	direct product factor
183	C₄×C₁₃	C₂⁴×C₄	1	12	yes	—
184	C₄×C₁₃	C₂⁴×C₄	1	4	yes	—
185	Dic₁₃	C₂⁴×C₄	1	12	yes	—
186	Dic₁₃	C₂⁴×C₄	1	4	yes	—
187	C₂⁵	—	13	3	no	—
188	C₂×#41	—	13	64	no	—
189	C₂×#41	—	13	192	no	—
190	C₂×#41	—	13	24	no	—
191	C₂×#41	—	13	72	no	—
192	C₂×#41	—	13	72	no	—
193	C₂×#41	C₂×#261	1	24	yes	direct product factor
194	C₂²×Q₈	—	13	12	no	—
195	C₂²×Q₈	—	13	12	no	—
196	C₂²×Q₈	—	13	3	no	—
197	C₂²×Q₈	C₂×#261	1	1	yes	characteristic, complemented
198	C₂²×D₄	—	13	6	no	—
199	C₂²×D₄	—	13	36	no	—
200	C₂²×D₄	—	13	36	no	—
201	C₂²×D₄	—	13	3	no	—
202	C₂²×D₄	C₂×#261	1	3	yes	complemented
203	C₂³×C₄	—	13	2	no	—
204	C₂³×C₄	—	13	3	no	—
205	C₂³×C₄	—	13	3	no	—
206	C₂³×C₄	—	13	3	no	—
207	C₂³×C₄	—	13	1	no	—
208	C₂³×C₄	—	13	3	no	—
209	C₂³×C₄	—	13	36	no	—
210	C₂³×C₄	—	13	36	no	—
211	C₂³×C₄	—	13	6	no	—
212	C₂³×C₄	—	13	72	no	—
213	C₂³×C₄	—	26	48	no	—
214	C₂³×C₄	C₂×#261	1	3	yes	complemented
215	C₄×Q₈	—	13	128	no	—
216	C₄×D₄	—	13	384	no	—
217	#117	—	13	192	no	—
218	C₂×C₄⋊C₄	—	13	72	no	—
219	C₂×C₂²⋊C₄	—	13	72	no	—
220	C₂×C₄²	—	13	36	no	—
221	C₂×C₄²	—	13	72	no	—
222	C₂×C₄²	—	13	192	no	—
223	C₂×C₄²	—	13	12	no	—
224	C₂×C₁₃	—	2	12	no	—
225	C₂×C₁₃	C₂×C₄×#41	1	6	yes	complemented
226	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
227	D₁₃	—	2	12	no	—
228	D₁₃	C₂×C₄×#41	1	6	yes	complemented
229	D₁₃	C₂³×#41	1	2	yes	—
230	C₂⁴	—	13	1	no	—
231	C₂⁴	—	13	18	no	—
232	C₂⁴	—	13	18	no	—
233	C₂⁴	—	13	3	no	—
234	C₂⁴	—	26	24	no	—
235	C₂⁴	C₂²×#261	1	3	yes	—
236	#41	—	13	64	no	—
237	#41	—	13	192	no	—
238	#41	—	13	192	no	—
239	#41	C₂²×#261	1	64	yes	direct product factor
240	C₂×Q₈	—	13	16	no	—
241	C₂×Q₈	—	13	48	no	—
242	C₂×Q₈	—	13	36	no	—
243	C₂×Q₈	C₂²×#261	1	12	yes	complemented
244	C₂×D₄	—	13	72	no	—
245	C₂×D₄	—	13	48	no	—
246	C₂×D₄	—	13	144	no	—
247	C₂×D₄	—	13	36	no	—
248	C₂×D₄	C₂²×#261	1	36	yes	complemented
249	C₂²×C₄	—	13	12	no	—
250	C₂²×C₄	—	13	16	no	—
251	C₂²×C₄	—	13	1	no	—
252	C₂²×C₄	—	13	3	no	—
253	C₂²×C₄	—	13	36	no	—
254	C₂²×C₄	—	13	6	no	—
255	C₂²×C₄	—	13	18	no	—
256	C₂²×C₄	—	13	6	no	—
257	C₂²×C₄	—	13	18	no	—
258	C₂²×C₄	—	13	36	no	—
259	C₂²×C₄	—	13	36	no	—
260	C₂²×C₄	—	13	48	no	—
261	C₂²×C₄	—	13	144	no	—
262	C₂²×C₄	—	13	36	no	—
263	C₂²×C₄	—	13	96	no	—
264	C₂²×C₄	—	26	288	no	—
265	C₂²×C₄	—	26	24	no	—
266	C₂²×C₄	C₂²×#261	1	3	yes	—
267	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
268	C₂²×C₄	C₂²×#261	1	36	yes	complemented
269	C₄⋊C₄	—	13	96	no	—
270	C₂²⋊C₄	—	13	96	no	—
271	C₄²	—	13	16	no	—
272	C₄²	—	13	48	no	—
273	C₄²	—	13	96	no	—
274	C₁₃	C₂²×C₄×#41	1	1	yes	characteristic, complemented, Sylow
275	C₂³	—	2	12	no	—
276	C₂³	—	13	8	no	—
277	C₂³	—	13	3	no	—
278	C₂³	—	13	3	no	—
279	C₂³	—	13	12	no	—
280	C₂³	—	13	36	no	—
281	C₂³	—	13	18	no	—
282	C₂³	—	26	72	no	—
283	C₂³	—	26	72	no	—
284	C₂³	—	26	12	no	—
285	C₂³	C₂³×#261	1	18	yes	—
286	C₂³	C₂³×#261	1	1	yes	characteristic
287	Q₈	—	13	48	no	—
288	Q₈	C₂³×#261	1	16	yes	complemented
289	D₄	—	13	96	no	—
290	D₄	—	13	48	no	—
291	D₄	C₂³×#261	1	48	yes	complemented
292	C₂×C₄	—	13	8	no	—
293	C₂×C₄	—	13	48	no	—
294	C₂×C₄	—	13	6	no	—
295	C₂×C₄	—	13	18	no	—
296	C₂×C₄	—	13	48	no	—
297	C₂×C₄	—	13	4	no	—
298	C₂×C₄	—	13	12	no	—
299	C₂×C₄	—	13	12	no	—
300	C₂×C₄	—	13	36	no	—
301	C₂×C₄	—	13	48	no	—
302	C₂×C₄	—	13	48	no	—
303	C₂×C₄	—	13	24	no	—
304	C₂×C₄	—	26	192	no	—
305	C₂×C₄	—	26	72	no	—
306	C₂×C₄	C₂³×#261	1	6	yes	—
307	C₂×C₄	C₂³×#261	1	18	yes	—
308	C₂×C₄	C₂³×#261	1	48	yes	complemented
309	C₂²	—	2	36	no	—
310	C₂²	—	13	12	no	—
311	C₂²	—	13	12	no	—
312	C₂²	—	13	3	no	—
313	C₂²	—	13	1	no	—
314	C₂²	—	13	12	no	—
315	C₂²	—	26	24	no	—
316	C₂²	—	26	72	no	—
317	C₂²	—	26	36	no	—
318	C₂²	#41×#261	1	4	yes	direct product factor
319	C₂²	C₂⁴×#261	1	12	yes	—
320	C₂²	C₂⁴×#261	1	3	yes	—
321	C₄	—	13	16	no	—
322	C₄	—	13	4	no	—
323	C₄	—	13	12	no	—
324	C₄	—	26	24	no	—
325	C₄	C₂⁴×#261	1	4	yes	—
326	C₄	C₂⁴×#261	1	12	yes	—
327	C₂	—	2	12	no	—
328	C₂	—	13	2	no	—
329	C₂	—	13	6	no	—
330	C₂	—	26	12	no	—
331	C₂	C₂×#41×#261	1	6	yes	direct product factor
332	C₂	C₂⁵×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×#261
commutator	C₂×C₁₃	C₂⁵×C₄
Frattini	C₂	C₂⁵×#261
Fitting	C₂²×C₁₃×#41	C₄
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂²×#41×D₁₃	C₂
cosocle	C₂×D₁₃	C₂⁶
hypercenter	C₂²×#41	#261
hypocenter	C₁₃	C₂²×C₄×#41
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#41×#261	C₂	direct (N × H)
2. C₂²×Q₈×#261	C₂	semidirect
3. C₂²×D₄×#261	C₂	semidirect
4. C₂²×#88237	C₂	semidirect
5. C₂³×C₄×#261	C₂	semidirect
8. C₂²×C₁₃×#41	C₄	semidirect
9. C₂×#41×D₁₃	C₄	semidirect
11. C₂²×#6131	C₄	semidirect
13. C₂²×#6129	C₄	semidirect
15. C₂²×#6127	C₄	semidirect
18. #41×#261	C₂²	direct (N × H)
19. C₂×Q₈×#261	C₂²	semidirect
20. C₂×D₄×#261	C₂²	semidirect
21. C₂×#88237	C₂²	semidirect
26. C₂²×C₄×#261	C₂²	semidirect
32. C₂×C₁₃×#41	C₂×C₄	semidirect
33. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
34. C₂²×D₄×C₁₃	C₂×C₄	semidirect
35. C₂³×C₄×C₁₃	C₂×C₄	semidirect
36. C₂²×C₂²⋊D₁₃	C₂×C₄	semidirect
37. C₂³×Dic₁₃	C₂×C₄	semidirect
38. #41×D₁₃	C₂×C₄	semidirect
40. C₂×#6131	C₂×C₄	semidirect
41. C₂×Q₈×D₁₃	C₂×C₄	semidirect
43. C₂×#6129	C₂×C₄	semidirect
44. C₂×D₄×D₁₃	C₂×C₄	semidirect
46. C₂×#6127	C₂×C₄	semidirect
47. C₂²×D₅₂	C₂×C₄	semidirect
48. C₂²×C₄×D₁₃	C₂×C₄	semidirect
49. C₂²×C₄×D₁₃	C₂×C₄	semidirect
50. C₂²×C₄×D₁₃	C₂×C₄	semidirect
54. C₂²×Dic₂₆	C₂×C₄	semidirect
56. Q₈×#261	C₂³	semidirect
57. D₄×#261	C₂³	semidirect
58. #88237	C₂³	semidirect
63. C₂×C₄×#261	C₂³	semidirect
73. C₂²×#261	#41	direct (N × H)
77. C₁₃×#41	C₂²×C₄	semidirect
78. C₂×Q₈×C₁₃	C₂²×C₄	semidirect
79. C₂×D₄×C₁₃	C₂²×C₄	semidirect
82. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
83. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
86. C₂²×Dic₁₃	C₂²×C₄	semidirect
87. #6131	C₂²×C₄	semidirect
88. Q₈×D₁₃	C₂²×C₄	semidirect
90. #6129	C₂²×C₄	semidirect
91. D₄×D₁₃	C₂²×C₄	semidirect
93. #6127	C₂²×C₄	semidirect
94. C₂×D₅₂	C₂²×C₄	semidirect
97. C₂×C₄×D₁₃	C₂²×C₄	semidirect
98. C₂×C₄×D₁₃	C₂²×C₄	semidirect
99. C₂×C₄×D₁₃	C₂²×C₄	semidirect
103. C₂×Dic₂₆	C₂²×C₄	semidirect
129. C₂×#261	C₂×#41	direct (N × H)
132. Q₈×C₁₃	C₂³×C₄	semidirect
133. D₄×C₁₃	C₂³×C₄	semidirect
136. C₂×C₄×C₁₃	C₂³×C₄	semidirect
137. C₂²⋊D₁₃	C₂³×C₄	semidirect
140. C₂×Dic₁₃	C₂³×C₄	semidirect
141. D₅₂	C₂³×C₄	semidirect
144. C₄×D₁₃	C₂³×C₄	semidirect
145. C₄×D₁₃	C₂³×C₄	semidirect
148. Dic₂₆	C₂³×C₄	semidirect
154. C₂²×#41	#261	direct (N × H)
170. C₂²×C₁₃	C₄×#41	semidirect
176. C₂×D₁₃	C₄×#41	semidirect
182. #261	C₂²×#41	direct (N × H)
193. C₂×#41	C₂×#261	direct (N × H)
197. C₂²×Q₈	C₂×#261	semidirect
202. C₂²×D₄	C₂×#261	semidirect
214. C₂³×C₄	C₂×#261	semidirect
225. C₂×C₁₃	C₂×C₄×#41	semidirect
228. D₁₃	C₂×C₄×#41	semidirect
239. #41	C₂²×#261	direct (N × H)
243. C₂×Q₈	C₂²×#261	semidirect
248. C₂×D₄	C₂²×#261	semidirect
268. C₂²×C₄	C₂²×#261	semidirect
274. C₁₃	C₂²×C₄×#41	semidirect
288. Q₈	C₂³×#261	semidirect
291. D₄	C₂³×#261	semidirect
308. C₂×C₄	C₂³×#261	semidirect
318. C₂²	#41×#261	direct (N × H)
331. C₂	C₂×#41×#261	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#41×#261	2
C₂²×Q₈×#261	2
C₂²×D₄×#261	2
C₂²×#88237	2
C₂³×C₄×#261	2
C₂²×#41×D₁₃	2
C₂²×C₄×#41	13

Subgroups — C22×#41×#261 #16809630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#41×#261 #16809630