Subgroups — C₄×#15689477 #26224261

Order 12032.

858 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689477	C₂	1	1	yes	maximal, characteristic
2	C₄×#13094016	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244352	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244200	C₂	1	1	yes	maximal, characteristic
5	#20244074	C₂	1	2	yes	maximal
6	#20244067	C₂	1	2	yes	maximal, complemented
7	#20243518	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#13093948	C₂	1	2	yes	maximal, complemented
9	C₄×#13093945	C₂	1	2	yes	maximal
10	C₄²×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#124×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094016	C₂²	1	1	yes	characteristic
13	#15689477	C₄	1	8	yes	direct product factor
14	C₂×#13093948	C₂²	1	2	yes	—
15	C₂×#13093948	C₂²	1	2	yes	—
16	C₂×#13093945	C₂²	1	2	yes	—
17	C₂×#13093945	C₂²	1	2	yes	—
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	#15689021	C₂²	1	2	yes	—
23	#15689007	—	2	2	no	—
24	#15688989	C₂²	1	1	yes	characteristic
25	C₄×Dic₄₇⋊C₄	—	2	2	no	—
26	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
27	#15688885	C₂²	1	2	yes	—
28	#15688885	C₂²	1	2	yes	—
29	#15688885	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#391	C₂²	1	1	yes	characteristic
35	C₄₇×#390	C₂²	1	1	yes	characteristic
36	C₄₇×#388	—	2	2	no	—
37	C₄₇×#382	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₄₇	—	2	2	no	—
39	C₄³×C₄₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
41	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
42	#13094016	—	2	2	no	—
43	#13094016	C₂×C₄	1	4	yes	complemented
44	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
45	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
46	C₂×Dic₄₇⋊C₄	—	2	2	no	—
47	C₂×Dic₄₇⋊C₄	—	2	2	no	—
48	C₂×C₄×Dic₄₇	—	2	2	no	—
49	#13093948	—	2	4	no	—
50	#13093948	C₂×C₄	1	8	yes	complemented
51	#13093945	—	2	4	no	—
52	#13093945	C₂×C₄	1	8	yes	—
53	C₄×C₄₇⋊C₈	—	2	2	no	—
54	C₄×C₄₇⋊C₈	—	2	4	no	—
55	C₄×C₄₇⋊C₈	—	2	4	no	—
56	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
57	C₄₇⋊#95	—	2	2	no	—
58	C₄₇⋊#95	—	2	2	no	—
59	C₄₇⋊#95	—	2	2	no	—
60	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	—	2	1	no	—
63	#124×C₄₇	—	2	2	no	—
64	#124×C₄₇	C₂×C₄	1	4	yes	—
65	C₄×Q₈×C₄₇	—	2	4	no	—
66	C₄×D₄×C₄₇	—	2	4	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₄²×C₄₇	—	2	1	no	—
74	C₂×C₄²×C₄₇	D₄	1	2	yes	—
75	C₂×C₄²×C₄₇	D₄	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	#95×C₄₇	—	2	2	no	—
80	#95×C₄₇	—	2	2	no	—
81	C₂⁴×C₄₇	—	2	1	no	—
82	C₂×Q₈×C₄₇	—	2	1	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
86	C₂×D₄×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	1	no	—
89	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	—	2	1	no	—
91	C₂²×C₄×C₄₇	—	2	1	no	—
92	C₂²×C₄×C₄₇	—	2	1	no	—
93	C₂²×C₄×C₄₇	—	4	2	no	—
94	C₂²×C₄×C₄₇	—	4	4	no	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₇	—	2	2	no	—
101	C₂²×Dic₄₇	—	2	2	no	—
102	C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	—	4	2	no	—
105	C₂²⋊C₄×C₄₇	—	2	8	no	—
106	C₂²⋊C₄×C₄₇	—	4	2	no	—
107	C₂²⋊C₄×C₄₇	—	4	4	no	—
108	C₄²×C₄₇	—	2	4	no	—
109	C₄²×C₄₇	—	2	4	no	—
110	C₄²×C₄₇	—	2	2	no	—
111	C₄²×C₄₇	—	4	2	no	—
112	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
113	C₄²×C₄₇	#41	1	2	yes	—
114	C₄²×C₄₇	#41	1	4	yes	—
115	C₄⋊Dic₄₇	—	2	2	no	—
116	C₄⋊Dic₄₇	—	2	2	no	—
117	C₄⋊Dic₄₇	—	2	2	no	—
118	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
119	Dic₄₇⋊C₄	—	2	8	no	—
120	Dic₄₇⋊C₄	—	4	4	no	—
121	C₄×Dic₄₇	—	4	4	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
127	C₂×C₄₇⋊C₈	#41	1	4	yes	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	—	4	1	no	—
130	C₂³×C₄₇	—	4	1	no	—
131	C₂³×C₄₇	—	4	2	no	—
132	C₂³×C₄₇	—	4	2	no	—
133	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₄₇	—	2	4	no	—
135	Q₈×C₄₇	—	4	2	no	—
136	D₄×C₄₇	—	2	4	no	—
137	D₄×C₄₇	—	4	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	4	1	no	—
145	C₂×C₄×C₄₇	—	4	1	no	—
146	C₂×C₄×C₄₇	—	4	1	no	—
147	C₂×C₄×C₄₇	—	4	1	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	8	4	no	—
151	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
152	C₂×C₄×C₄₇	#124	1	2	yes	—
153	C₂×C₄×C₄₇	#124	1	2	yes	—
154	C₂×C₄×C₄₇	#135	1	4	yes	—
155	C₂×C₄×C₄₇	#135	1	4	yes	—
156	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
159	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂×Dic₄₇	—	2	4	no	—
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₄₇⋊C₈	—	2	4	no	—
167	C₄₇⋊C₈	—	2	4	no	—
168	C₄×#488	—	47	1	no	maximal, Sylow
169	C₂²×C₄₇	—	4	4	no	—
170	C₂²×C₄₇	—	4	2	no	—
171	C₂²×C₄₇	—	8	1	no	—
172	C₂²×C₄₇	—	8	1	no	—
173	C₂²×C₄₇	—	8	2	no	—
174	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
175	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
176	C₂²×C₄₇	#532	1	1	yes	characteristic
177	C₂²×C₄₇	C₂×#135	1	2	yes	—
178	C₂²×C₄₇	C₂×#135	1	2	yes	—
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	2	4	no	—
181	C₄×C₄₇	—	2	4	no	—
182	C₄×C₄₇	—	4	2	no	—
183	C₄×C₄₇	—	8	1	no	—
184	C₄×C₄₇	—	8	1	no	—
185	C₄×C₄₇	#488	1	4	yes	complemented
186	C₄×C₄₇	C₄×#41	1	2	yes	—
187	C₄×C₄₇	#529	1	2	yes	—
188	Dic₄₇	—	4	4	no	—
189	Dic₄₇	—	8	2	no	—
190	C₂×#488	—	47	1	no	—
191	C₄×#125	—	47	1	no	—
192	C₄×#124	D₄₇	1	1	yes	characteristic
193	#1991	—	47	1	no	—
194	#1958	—	47	1	no	—
195	#1934	—	47	2	no	—
196	#1933	—	47	2	no	—
197	#1835	—	47	1	no	—
198	C₄×#103	—	47	2	no	—
199	C₄×#102	—	47	2	no	—
200	C₄²×C₈	—	47	1	no	—
201	C₂×C₄₇	—	8	2	no	—
202	C₂×C₄₇	C₄×#124	1	1	yes	characteristic
203	C₂×C₄₇	C₄×#135	1	2	yes	—
204	C₂×C₄₇	C₂×#488	1	1	yes	characteristic
205	C₂×C₄₇	#3131	1	1	yes	characteristic
206	C₂×C₄₇	#3168	1	2	yes	—
207	C₂×#125	—	47	1	no	—
208	C₂×#124	C₂×D₄₇	1	1	yes	characteristic
209	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
210	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
211	#488	—	47	8	no	—
212	C₂×#103	—	47	2	no	—
213	C₂×#103	—	47	2	no	—
214	C₂×#102	—	47	2	no	—
215	C₂×#102	—	47	2	no	—
216	C₂×C₄×C₈	—	47	1	no	—
217	C₂×C₄×C₈	—	47	2	no	—
218	C₂×C₄×C₈	—	47	1	no	—
219	C₂×C₄×C₈	—	47	2	no	—
220	#391	C₂×D₄₇	1	1	yes	characteristic
221	#390	C₂×D₄₇	1	1	yes	characteristic
222	#389	—	47	2	no	—
223	#388	—	2	2	no	—
224	#387	—	94	2	no	—
225	#382	—	47	1	no	—
226	#382	C₂×D₄₇	1	1	yes	characteristic
227	C₄×C₄⋊C₄	—	47	2	no	—
228	C₄×C₄⋊C₄	—	94	2	no	—
229	C₄×C₂²⋊C₄	—	2	2	no	—
230	C₄³	C₂×D₄₇	1	1	yes	characteristic
231	#340	—	47	2	no	—
232	#340	—	47	2	no	—
233	#340	—	47	2	no	—
234	#340	—	47	2	no	—
235	C₄₇	C₄×#488	1	1	yes	characteristic, complemented, Sylow
236	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
237	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
238	C₂³×C₄	—	2	1	no	—
239	C₂²×C₈	—	47	2	no	—
240	C₂²×C₈	—	47	2	no	—
241	#125	—	47	4	no	—
242	#125	—	94	2	no	—
243	#124	—	2	2	no	—
244	#124	C₄×D₄₇	1	4	yes	—
245	C₄×Q₈	—	2	4	no	—
246	C₄×D₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	47	2	no	—
249	C₂×C₄⋊C₄	—	47	2	no	—
250	C₂×C₄⋊C₄	—	94	2	no	—
251	C₂×C₄⋊C₄	—	94	2	no	—
252	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	94	2	no	—
259	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
260	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
261	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
263	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
264	#103	—	47	8	no	—
265	#103	—	94	4	no	—
266	#102	—	47	8	no	—
267	#102	—	94	4	no	—
268	C₄×C₈	—	47	4	no	—
269	C₄×C₈	—	94	4	no	—
270	C₄×C₈	—	94	2	no	—
271	C₄×C₈	—	94	4	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	94	2	no	—
275	#95	—	94	2	no	—
276	#95	—	94	2	no	—
277	C₂⁴	—	2	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	94	2	no	—
292	C₂²×C₄	—	94	2	no	—
293	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
294	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
296	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
298	C₂×C₈	—	47	4	no	—
299	C₂×C₈	—	47	4	no	—
300	C₂×C₈	—	94	2	no	—
301	C₂×C₈	—	94	2	no	—
302	C₂×C₈	—	94	2	no	—
303	C₂×C₈	—	94	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	47	4	no	—
308	C₄⋊C₄	—	94	8	no	—
309	C₄⋊C₄	—	94	2	no	—
310	C₄⋊C₄	—	94	2	no	—
311	C₄⋊C₄	—	94	2	no	—
312	C₄⋊C₄	—	188	4	no	—
313	C₂²⋊C₄	—	2	8	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	4	4	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	4	2	no	—
320	C₄²	—	188	4	no	—
321	C₄²	C₂×C₄×D₄₇	1	2	yes	—
322	C₄²	#10625350	1	2	yes	—
323	C₄²	#10625352	1	4	yes	—
324	C₂³	—	2	2	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	1	no	—
329	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
330	Q₈	—	2	4	no	—
331	Q₈	—	4	2	no	—
332	D₄	—	2	4	no	—
333	D₄	—	4	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	8	4	no	—
347	C₂×C₄	—	94	4	no	—
348	C₂×C₄	—	188	2	no	—
349	C₂×C₄	—	188	2	no	—
350	C₂×C₄	—	188	2	no	—
351	C₂×C₄	—	188	2	no	—
352	C₂×C₄	—	188	2	no	—
353	C₂×C₄	C₄×C₂²⋊D₄₇	1	4	yes	—
354	C₂×C₄	#13094011	1	2	yes	—
355	C₂×C₄	#13094011	1	2	yes	—
356	C₂×C₄	#13094044	1	4	yes	—
357	C₂×C₄	#13094044	1	4	yes	—
358	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
359	C₂×C₄	#41×D₄₇	1	2	yes	—
360	C₂×C₄	C₂×#10625352	1	2	yes	—
361	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
362	C₈	—	94	4	no	—
363	C₈	—	94	4	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
370	C₂²	C₂×#13094011	1	1	yes	characteristic
371	C₂²	#15689669	1	1	yes	characteristic
372	C₂²	C₂×#13094044	1	2	yes	—
373	C₂²	C₂×#13094044	1	2	yes	—
374	C₄	—	2	4	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	4	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	1	no	—
379	C₄	—	8	1	no	—
380	C₄	—	376	2	no	—
381	C₄	—	188	4	no	—
382	C₄	#15689477	1	4	yes	direct product factor
383	C₄	C₄×#10625352	1	2	yes	—
384	C₄	#15689655	1	2	yes	—
385	C₂	—	8	2	no	—
386	C₂	C₄×#13094011	1	1	yes	characteristic
387	C₂	C₄×#13094044	1	2	yes	—
388	C₂	C₂×#15689477	1	1	yes	characteristic
389	C₂	#20253710	1	1	yes	characteristic
390	C₂	#20253952	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#124×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₄×C₄₇	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#124	D₄₇
hypocenter	C₄₇	C₄×#488
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#124

Complements

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

N	H ≅ G/N	type
2. C₄×#13094016	C₂	semidirect
3. #20244352	C₂	semidirect
6. #20244067	C₂	semidirect
7. #20243518	C₂	semidirect
8. C₄×#13093948	C₂	semidirect
10. C₄²×C₄₇⋊C₈	C₂	semidirect
13. #15689477	C₄	direct (N × H)
43. #13094016	C₂×C₄	semidirect
50. #13093948	C₂×C₄	semidirect
56. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
185. C₄×C₄₇	#488	semidirect
235. C₄₇	C₄×#488	semidirect
382. C₄	#15689477	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×#15689477	2
C₄×#13094016	2
#20244352	2
#20244200	2
#20244074	2
#20244067	2
#20243518	2
C₄×#13093948	2
C₄×#13093945	2
C₄²×C₄₇⋊C₈	2
C₄×#124×C₄₇	2
C₄×#488	47

Subgroups — C4×#15689477 #26224261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689477 #26224261