Subgroups — C₄×#41×#261 #16807451

Order 3328.

4086 conjugacy classes of subgroups.

The subgroup lattice has 394 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	2	yes	maximal
2	C₄×Q₈×#261	C₂	1	4	yes	maximal, complemented
3	C₄×D₄×#261	C₂	1	12	yes	maximal, complemented
4	#117×#261	C₂	1	6	yes	maximal, complemented
5	C₄×#88237	C₂	1	3	yes	maximal, complemented
6	C₂×C₄²×#261	C₂	1	3	yes	maximal, complemented
7	C₄×#41×D₁₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#41×D₁₃	C₂²	1	1	yes	characteristic
9	#41×#261	C₄	1	32	yes	direct product factor
10	C₂×Q₈×#261	C₂²	1	4	yes	—
11	C₂×D₄×#261	C₂²	1	12	yes	—
12	C₂×#88237	C₂²	1	6	yes	—
13	C₂²×C₄×#261	C₂²	1	12	yes	—
14	C₂²×C₄×#261	C₂²	1	6	yes	—
15	C₄×C₁₃×#41	C₄	1	1	yes	characteristic, complemented
16	#41×Dic₁₃	C₄	1	1	yes	characteristic, complemented
17	C₄×#6131	C₄	1	2	yes	complemented
18	C₄×Q₈×D₁₃	C₂²	1	2	yes	—
19	C₄×D₄×D₁₃	C₂²	1	6	yes	—
20	C₄×#6129	C₄	1	6	yes	complemented
21	#11719227	C₄	1	3	yes	complemented
22	D₁₃×#117	C₂²	1	3	yes	—
23	C₄×#6127	C₄	1	3	yes	complemented
24	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
25	C₄×C₂²⋊#261	C₂²	1	12	yes	—
26	C₄⋊C₄×#261	C₂²	1	24	yes	—
27	C₂²⋊C₄×#261	C₂²	1	24	yes	—
28	C₄×C₄⋊#261	C₂²	1	12	yes	—
29	#11719057	C₂²	1	6	yes	—
30	C₄²×#261	C₂²	1	3	yes	—
31	C₄²×#261	C₂²	1	6	yes	—
32	C₄²×#261	C₂²	1	12	yes	—
33	C₄²×#261	C₂²	1	1	yes	characteristic
34	C₂³×#261	C₂³	1	12	yes	—
35	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
36	#41×D₁₃	C₂×C₄	1	16	yes	—
37	C₂×#6131	C₂×C₄	1	1	yes	characteristic
38	C₂×Q₈×D₁₃	C₂³	1	1	yes	characteristic
39	C₂×#6129	C₂×C₄	1	3	yes	—
40	C₂×D₄×D₁₃	C₂³	1	3	yes	—
41	C₂×#6127	C₂×C₄	1	3	yes	—
42	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
43	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
44	C₂×C₂²⋊#261	C₂³	1	12	yes	—
45	Q₈×#261	C₂×C₄	1	32	yes	complemented
46	D₄×#261	C₂×C₄	1	96	yes	complemented
47	#88237	C₂×C₄	1	48	yes	complemented
48	C₂×C₄⋊#261	C₂³	1	12	yes	—
49	C₂×C₄×#261	—	2	48	no	—
50	C₂×C₄×#261	C₂×C₄	1	48	yes	complemented
51	C₂×C₄×#261	C₂³	1	12	yes	—
52	C₂×C₄×#261	C₂³	1	24	yes	—
53	C₂×C₄×#261	C₂³	1	2	yes	—
54	C₂×C₄×#261	C₂³	1	6	yes	—
55	C₂×C₄×#261	C₂³	1	12	yes	—
56	C₂×C₄×#261	C₂³	1	4	yes	—
57	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	complemented
58	C₄×D₄×C₁₃	C₂×C₄	1	6	yes	complemented
59	C₁₃×#117	C₂×C₄	1	3	yes	complemented
60	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	complemented
61	Q₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
62	D₄×Dic₁₃	C₂×C₄	1	6	yes	complemented
63	C₄×C₂²⋊D₁₃	C₂×C₄	1	12	yes	complemented
64	#88180	C₂×C₄	1	3	yes	complemented
65	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	complemented
66	C₂×C₄×Dic₁₃	C₂×C₄	1	6	yes	complemented
67	#88147	C₂×C₄	1	6	yes	complemented
68	#88146	C₂×C₄	1	6	yes	complemented
69	C₄⋊C₄×D₁₃	C₂³	1	6	yes	—
70	#88141	C₂×C₄	1	6	yes	complemented
71	#88135	C₂×C₄	1	12	yes	complemented
72	C₂²⋊C₄×D₁₃	C₂³	1	6	yes	—
73	#88131	C₂×C₄	1	6	yes	complemented
74	C₄×D₅₂	C₂×C₄	1	6	yes	complemented
75	#88126	C₂×C₄	1	6	yes	complemented
76	C₄²×D₁₃	C₂×C₄	1	3	yes	complemented
77	C₄²×D₁₃	C₂×C₄	1	3	yes	complemented
78	C₄²×D₁₃	C₂×C₄	1	6	yes	complemented
79	C₄²×D₁₃	C₂³	1	1	yes	characteristic
80	C₄²×D₁₃	C₂³	1	3	yes	—
81	C₄²×D₁₃	C₂³	1	6	yes	—
82	C₄×Dic₂₆	C₂×C₄	1	6	yes	complemented
83	(C₂×#261)⋊C₄	C₂³	1	24	yes	—
84	C₄²×#41	—	13	1	no	maximal, Sylow
85	C₂³×D₁₃	C₂⁴	1	3	yes	—
86	C₂²×#261	—	2	48	no	—
87	C₂²×#261	C₂²×C₄	1	48	yes	—
88	C₂²×#261	C₂⁴	1	12	yes	—
89	C₂²×#261	C₂⁴	1	4	yes	—
90	C₁₃×#41	C₄²	1	8	yes	complemented
91	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×D₄×C₁₃	C₂²×C₄	1	3	yes	—
93	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
94	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
95	C₂×C₂²⋊D₁₃	C₂²×C₄	1	6	yes	—
96	C₂²×Dic₁₃	C₂²×C₄	1	6	yes	—
97	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
98	#6131	C₄²	1	8	yes	complemented
99	Q₈×D₁₃	C₂²×C₄	1	8	yes	—
100	#6129	C₄²	1	24	yes	complemented
101	D₄×D₁₃	C₂²×C₄	1	24	yes	—
102	#6127	C₄²	1	24	yes	complemented
103	C₂×D₅₂	C₂²×C₄	1	3	yes	—
104	C₂×C₄×D₁₃	—	2	24	no	—
105	C₂×C₄×D₁₃	C₂²×C₄	1	6	yes	—
106	C₂×C₄×D₁₃	C₂²×C₄	1	6	yes	—
107	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
108	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
109	C₂×C₄×D₁₃	C₂²×C₄	1	24	yes	—
110	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
111	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
113	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
114	C₂×Dic₂₆	C₂²×C₄	1	3	yes	—
115	C₂²⋊#261	C₂²×C₄	1	48	yes	—
116	C₄⋊#261	C₂²×C₄	1	48	yes	—
117	C₄×#261	—	2	48	no	—
118	C₄×#261	—	2	24	no	—
119	C₄×#261	C₂²×C₄	1	8	yes	—
120	C₄×#261	C₂²×C₄	1	24	yes	—
121	C₄×#261	C₂²×C₄	1	48	yes	—
122	C₄×#261	#41	1	16	yes	direct product factor
123	C₁₃×C₄⋊C₄	C₂²×C₄	1	6	yes	—
124	C₁₃×C₂²⋊C₄	C₂²×C₄	1	6	yes	—
125	C₄²×C₁₃	C₂²×C₄	1	6	yes	—
126	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
127	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²⋊Dic₁₃	C₂²×C₄	1	6	yes	—
129	#6103	C₂²×C₄	1	12	yes	—
130	C₄⋊Dic₁₃	C₂²×C₄	1	6	yes	—
131	#6101	C₂²×C₄	1	12	yes	—
132	C₄×Dic₁₃	C₂²×C₄	1	6	yes	—
133	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
135	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
136	C₄×Dic₁₃	C₂²×C₄	1	6	yes	—
137	C₄×Dic₁₃	C₂²×C₄	1	6	yes	—
138	C₄×Dic₁₃	C₂²×C₄	1	6	yes	—
139	C₂×C₄×#41	—	13	2	no	—
140	C₂×C₄×#41	—	13	1	no	—
141	C₄²×Q₈	—	13	4	no	—
142	C₄²×D₄	—	13	12	no	—
143	C₄×#117	—	13	3	no	—
144	C₄×#117	—	13	6	no	—
145	C₂×C₄³	—	13	3	no	—
146	C₂³×C₁₃	C₂³×C₄	1	3	yes	—
147	C₂²×D₁₃	—	2	12	no	—
148	C₂²×D₁₃	C₂³×C₄	1	12	yes	—
149	C₂²×D₁₃	C₂³×C₄	1	3	yes	—
150	C₂²×D₁₃	C₂⁵	1	1	yes	characteristic
151	C₂×#261	—	2	24	no	—
152	C₂×#261	—	2	96	no	—
153	C₂×#261	C₂³×C₄	1	24	yes	—
154	C₂×#261	C₂³×C₄	1	8	yes	—
155	C₂×#261	C₂×#41	1	16	yes	—
156	Q₈×C₁₃	C₂×C₄²	1	4	yes	complemented
157	D₄×C₁₃	C₂×C₄²	1	12	yes	complemented
158	C₂×C₄×C₁₃	—	2	12	no	—
159	C₂×C₄×C₁₃	C₂×C₄²	1	12	yes	complemented
160	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
161	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
162	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
164	C₂²⋊D₁₃	C₂×C₄²	1	24	yes	complemented
165	C₂×Dic₁₃	—	2	12	no	—
166	C₂×Dic₁₃	C₂×C₄²	1	12	yes	complemented
167	C₂×Dic₁₃	C₂³×C₄	1	6	yes	—
168	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
169	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
170	C₂×Dic₁₃	C₂³×C₄	1	3	yes	—
171	D₅₂	C₂×C₄²	1	12	yes	complemented
172	C₄×D₁₃	—	2	12	no	—
173	C₄×D₁₃	—	2	12	no	—
174	C₄×D₁₃	—	2	12	no	—
175	C₄×D₁₃	C₂×C₄²	1	12	yes	complemented
176	C₄×D₁₃	C₂×C₄²	1	12	yes	complemented
177	C₄×D₁₃	C₂³×C₄	1	4	yes	—
178	C₄×D₁₃	C₂³×C₄	1	12	yes	—
179	C₄×D₁₃	C₂×#41	1	8	yes	—
180	Dic₂₆	C₂×C₄²	1	12	yes	complemented
181	C₂²×#41	—	13	1	no	—
182	C₄×#41	—	13	32	no	—
183	C₄×#41	—	13	1	no	—
184	C₄×#41	—	13	2	no	—
185	C₄×#41	—	13	6	no	—
186	C₄×#41	—	13	3	no	—
187	C₄×#41	—	13	3	no	—
188	C₄×#41	#261	1	1	yes	characteristic, direct product factor
189	C₂×C₄×Q₈	—	13	4	no	—
190	C₂×C₄×Q₈	—	13	2	no	—
191	C₂×C₄×D₄	—	13	12	no	—
192	C₂×C₄×D₄	—	13	6	no	—
193	C₂×#117	—	13	6	no	—
194	C₂×#117	—	13	3	no	—
195	C₂²×C₄²	—	13	6	no	—
196	C₂²×C₄²	—	13	3	no	—
197	C₂²×C₄²	—	13	12	no	—
198	C₄×C₄⋊C₄	—	13	12	no	—
199	C₄×C₄⋊C₄	—	13	24	no	—
200	C₄×C₂²⋊C₄	—	13	24	no	—
201	C₄×C₂²⋊C₄	—	13	12	no	—
202	#376	—	13	6	no	—
203	C₄³	—	13	1	no	—
204	C₄³	—	13	3	no	—
205	C₄³	—	13	6	no	—
206	C₄³	—	13	12	no	—
207	C₂²×C₁₃	—	2	6	no	—
208	C₂²×C₁₃	C₂²×C₄²	1	6	yes	—
209	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
210	C₂×D₁₃	—	2	6	no	—
211	C₂×D₁₃	—	2	24	no	—
212	C₂×D₁₃	C₂²×C₄²	1	6	yes	—
213	C₂×D₁₃	C₂⁴×C₄	1	2	yes	—
214	C₂×D₁₃	C₂²×#41	1	4	yes	—
215	#261	—	2	24	no	—
216	#261	C₄×#41	1	16	yes	direct product factor
217	C₄×C₁₃	—	2	6	no	—
218	C₄×C₁₃	C₂²×C₄²	1	6	yes	—
219	C₄×C₁₃	C₂²×C₄²	1	2	yes	—
220	C₄×C₁₃	C₄×#41	1	4	yes	complemented
221	Dic₁₃	—	2	6	no	—
222	Dic₁₃	C₂²×C₄²	1	6	yes	—
223	Dic₁₃	C₂²×C₄²	1	2	yes	—
224	Dic₁₃	C₄×#41	1	4	yes	complemented
225	C₂×#41	—	13	16	no	—
226	C₂×#41	—	13	1	no	—
227	C₂×#41	—	13	3	no	—
228	C₂×#41	—	13	3	no	—
229	C₂×#41	C₂×#261	1	1	yes	characteristic
230	C₂²×Q₈	—	13	1	no	—
231	C₂²×D₄	—	13	3	no	—
232	C₂³×C₄	—	13	3	no	—
233	C₂³×C₄	—	13	12	no	—
234	C₂³×C₄	—	13	6	no	—
235	C₄×Q₈	—	13	32	no	—
236	C₄×Q₈	—	13	2	no	—
237	C₄×Q₈	—	13	6	no	—
238	C₄×Q₈	—	13	6	no	—
239	C₄×Q₈	C₂×#261	1	2	yes	complemented
240	C₄×D₄	—	13	96	no	—
241	C₄×D₄	—	13	6	no	—
242	C₄×D₄	—	13	12	no	—
243	C₄×D₄	—	13	6	no	—
244	C₄×D₄	—	13	12	no	—
245	C₄×D₄	—	13	6	no	—
246	C₄×D₄	C₂×#261	1	6	yes	complemented
247	#117	—	13	48	no	—
248	#117	—	13	3	no	—
249	#117	—	13	6	no	—
250	#117	—	13	6	no	—
251	#117	—	13	6	no	—
252	#117	C₂×#261	1	3	yes	complemented
253	C₂×C₄⋊C₄	—	13	12	no	—
254	C₂×C₄⋊C₄	—	13	6	no	—
255	C₂×C₂²⋊C₄	—	13	12	no	—
256	C₂×C₂²⋊C₄	—	13	6	no	—
257	C₂×C₄²	—	13	6	no	—
258	C₂×C₄²	—	13	12	no	—
259	C₂×C₄²	—	13	48	no	—
260	C₂×C₄²	—	13	2	no	—
261	C₂×C₄²	—	13	4	no	—
262	C₂×C₄²	—	13	6	no	—
263	C₂×C₄²	—	13	3	no	—
264	C₂×C₄²	—	13	3	no	—
265	C₂×C₄²	—	13	6	no	—
266	C₂×C₄²	—	13	6	no	—
267	C₂×C₄²	—	13	3	no	—
268	C₂×C₄²	—	13	3	no	—
269	C₂×C₄²	—	13	1	no	—
270	C₂×C₄²	—	13	24	no	—
271	C₂×C₄²	—	13	12	no	—
272	C₂×C₄²	—	26	48	no	—
273	C₂×C₄²	C₂×#261	1	3	yes	complemented
274	#95	—	13	24	no	—
275	C₂×C₁₃	—	2	6	no	—
276	C₂×C₁₃	C₂³×C₄²	1	1	yes	characteristic
277	C₂×C₁₃	C₂×C₄×#41	1	2	yes	—
278	D₁₃	—	2	6	no	—
279	D₁₃	C₂×C₄×#41	1	4	yes	—
280	C₂⁴	—	13	3	no	—
281	#41	—	13	8	no	—
282	#41	—	13	24	no	—
283	#41	—	13	24	no	—
284	#41	C₄×#261	1	8	yes	direct product factor
285	C₂×Q₈	—	13	8	no	—
286	C₂×Q₈	—	13	3	no	—
287	C₂×Q₈	C₂²×#261	1	1	yes	characteristic
288	C₂×D₄	—	13	6	no	—
289	C₂×D₄	—	13	24	no	—
290	C₂×D₄	—	13	3	no	—
291	C₂×D₄	C₂²×#261	1	3	yes	—
292	C₂²×C₄	—	13	4	no	—
293	C₂²×C₄	—	13	3	no	—
294	C₂²×C₄	—	13	24	no	—
295	C₂²×C₄	—	13	1	no	—
296	C₂²×C₄	—	13	2	no	—
297	C₂²×C₄	—	13	3	no	—
298	C₂²×C₄	—	13	3	no	—
299	C₂²×C₄	—	13	3	no	—
300	C₂²×C₄	—	13	12	no	—
301	C₂²×C₄	—	13	48	no	—
302	C₂²×C₄	—	13	6	no	—
303	C₂²×C₄	—	13	6	no	—
304	C₂²×C₄	—	13	6	no	—
305	C₂²×C₄	—	13	6	no	—
306	C₂²×C₄	—	26	24	no	—
307	C₂²×C₄	—	26	48	no	—
308	C₂²×C₄	C₂²×#261	1	6	yes	—
309	C₂²×C₄	C₂²×#261	1	3	yes	—
310	C₄⋊C₄	—	13	48	no	—
311	C₄⋊C₄	—	13	12	no	—
312	C₄⋊C₄	—	13	6	no	—
313	C₄⋊C₄	C₂²×#261	1	6	yes	—
314	C₂²⋊C₄	—	13	48	no	—
315	C₂²⋊C₄	—	13	6	no	—
316	C₂²⋊C₄	—	13	12	no	—
317	C₂²⋊C₄	C₂²×#261	1	6	yes	—
318	C₄²	—	13	8	no	—
319	C₄²	—	13	24	no	—
320	C₄²	—	13	48	no	—
321	C₄²	—	13	16	no	—
322	C₄²	—	13	1	no	—
323	C₄²	—	13	2	no	—
324	C₄²	—	13	6	no	—
325	C₄²	—	13	3	no	—
326	C₄²	—	13	6	no	—
327	C₄²	—	13	6	no	—
328	C₄²	—	13	6	no	—
329	C₄²	—	26	48	no	—
330	C₄²	—	26	24	no	—
331	C₄²	C₂²×#261	1	3	yes	—
332	C₄²	C₂²×#261	1	6	yes	—
333	C₄²	C₂²×#261	1	1	yes	characteristic
334	C₁₃	C₄²×#41	1	1	yes	characteristic, complemented, Sylow
335	C₂³	—	13	1	no	—
336	C₂³	—	13	12	no	—
337	C₂³	—	13	3	no	—
338	C₂³	—	26	12	no	—
339	C₂³	C₂³×#261	1	3	yes	—
340	Q₈	—	13	12	no	—
341	Q₈	C₂×C₄×#261	1	4	yes	complemented
342	D₄	—	13	24	no	—
343	D₄	—	13	12	no	—
344	D₄	C₂×C₄×#261	1	12	yes	complemented
345	C₂×C₄	—	2	12	no	—
346	C₂×C₄	—	13	8	no	—
347	C₂×C₄	—	13	16	no	—
348	C₂×C₄	—	13	12	no	—
349	C₂×C₄	—	13	1	no	—
350	C₂×C₄	—	13	2	no	—
351	C₂×C₄	—	13	3	no	—
352	C₂×C₄	—	13	4	no	—
353	C₂×C₄	—	13	12	no	—
354	C₂×C₄	—	13	12	no	—
355	C₂×C₄	—	13	12	no	—
356	C₂×C₄	—	13	8	no	—
357	C₂×C₄	—	13	24	no	—
358	C₂×C₄	—	13	6	no	—
359	C₂×C₄	—	26	12	no	—
360	C₂×C₄	—	26	12	no	—
361	C₂×C₄	—	26	12	no	—
362	C₂×C₄	—	26	96	no	—
363	C₂×C₄	—	26	24	no	—
364	C₂×C₄	—	26	12	no	—
365	C₂×C₄	C₂×C₄×#261	1	12	yes	complemented
366	C₂×C₄	C₂³×#261	1	6	yes	—
367	C₂×C₄	C₂³×#261	1	1	yes	characteristic
368	C₂×C₄	C₂³×#261	1	3	yes	—
369	C₂×C₄	C₂³×#261	1	2	yes	—
370	C₂²	—	2	6	no	—
371	C₂²	—	13	2	no	—
372	C₂²	—	13	4	no	—
373	C₂²	—	13	6	no	—
374	C₂²	—	26	24	no	—
375	C₂²	—	26	6	no	—
376	C₂²	C₂²×C₄×#261	1	6	yes	—
377	C₂²	C₂⁴×#261	1	1	yes	characteristic
378	C₄	—	2	6	no	—
379	C₄	—	13	16	no	—
380	C₄	—	13	2	no	—
381	C₄	—	13	6	no	—
382	C₄	—	13	4	no	—
383	C₄	—	26	24	no	—
384	C₄	—	26	6	no	—
385	C₄	C₂²×C₄×#261	1	2	yes	—
386	C₄	C₂²×C₄×#261	1	6	yes	—
387	C₄	#41×#261	1	4	yes	direct product factor
388	C₂	—	2	6	no	—
389	C₂	—	13	4	no	—
390	C₂	—	26	6	no	—
391	C₂	C₂³×C₄×#261	1	1	yes	characteristic
392	C₂	C₂×#41×#261	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂²×#261
commutator	C₂×C₁₃	C₂³×C₄²
Frattini	C₂²	C₂⁴×#261
Fitting	C₄×C₁₃×#41	C₄
socle	C₂²×C₁₃	C₂⁴×C₄
prime radical	C₂×#41×D₁₃	C₂²
cosocle	C₂²×D₁₃	C₂⁵
hypercenter	C₄×#41	#261
hypocenter	C₁₃	C₄²×#41
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×#261	C₂	semidirect
3. C₄×D₄×#261	C₂	semidirect
4. #117×#261	C₂	semidirect
5. C₄×#88237	C₂	semidirect
6. C₂×C₄²×#261	C₂	semidirect
9. #41×#261	C₄	direct (N × H)
15. C₄×C₁₃×#41	C₄	semidirect
16. #41×Dic₁₃	C₄	semidirect
17. C₄×#6131	C₄	semidirect
20. C₄×#6129	C₄	semidirect
21. #11719227	C₄	semidirect
23. C₄×#6127	C₄	semidirect
45. Q₈×#261	C₂×C₄	semidirect
46. D₄×#261	C₂×C₄	semidirect
47. #88237	C₂×C₄	semidirect
50. C₂×C₄×#261	C₂×C₄	semidirect
57. C₄×Q₈×C₁₃	C₂×C₄	semidirect
58. C₄×D₄×C₁₃	C₂×C₄	semidirect
59. C₁₃×#117	C₂×C₄	semidirect
60. C₂×C₄²×C₁₃	C₂×C₄	semidirect
61. Q₈×Dic₁₃	C₂×C₄	semidirect
62. D₄×Dic₁₃	C₂×C₄	semidirect
63. C₄×C₂²⋊D₁₃	C₂×C₄	semidirect
64. #88180	C₂×C₄	semidirect
65. C₂×C₄×Dic₁₃	C₂×C₄	semidirect
66. C₂×C₄×Dic₁₃	C₂×C₄	semidirect
67. #88147	C₂×C₄	semidirect
68. #88146	C₂×C₄	semidirect
70. #88141	C₂×C₄	semidirect
71. #88135	C₂×C₄	semidirect
73. #88131	C₂×C₄	semidirect
74. C₄×D₅₂	C₂×C₄	semidirect
75. #88126	C₂×C₄	semidirect
76. C₄²×D₁₃	C₂×C₄	semidirect
77. C₄²×D₁₃	C₂×C₄	semidirect
78. C₄²×D₁₃	C₂×C₄	semidirect
82. C₄×Dic₂₆	C₂×C₄	semidirect
90. C₁₃×#41	C₄²	semidirect
98. #6131	C₄²	semidirect
100. #6129	C₄²	semidirect
102. #6127	C₄²	semidirect
122. C₄×#261	#41	direct (N × H)
156. Q₈×C₁₃	C₂×C₄²	semidirect
157. D₄×C₁₃	C₂×C₄²	semidirect
159. C₂×C₄×C₁₃	C₂×C₄²	semidirect
164. C₂²⋊D₁₃	C₂×C₄²	semidirect
166. C₂×Dic₁₃	C₂×C₄²	semidirect
171. D₅₂	C₂×C₄²	semidirect
175. C₄×D₁₃	C₂×C₄²	semidirect
176. C₄×D₁₃	C₂×C₄²	semidirect
180. Dic₂₆	C₂×C₄²	semidirect
188. C₄×#41	#261	direct (N × H)
216. #261	C₄×#41	direct (N × H)
220. C₄×C₁₃	C₄×#41	semidirect
224. Dic₁₃	C₄×#41	semidirect
239. C₄×Q₈	C₂×#261	semidirect
246. C₄×D₄	C₂×#261	semidirect
252. #117	C₂×#261	semidirect
273. C₂×C₄²	C₂×#261	semidirect
284. #41	C₄×#261	direct (N × H)
334. C₁₃	C₄²×#41	semidirect
341. Q₈	C₂×C₄×#261	semidirect
344. D₄	C₂×C₄×#261	semidirect
365. C₂×C₄	C₂×C₄×#261	semidirect
387. C₄	#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
C₄×Q₈×#261	2
C₄×D₄×#261	2
#117×#261	2
C₄×#88237	2
C₂×C₄²×#261	2
C₄×#41×D₁₃	2
C₄²×#41	13

Subgroups — C4×#41×#261 #16807451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#41×#261 #16807451