Subgroups — C₂×#20242813 #26198565

Order 12032.

758 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×#15689475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689403	C₂	1	1	yes	maximal, characteristic
3	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#20242813	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688873	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688869	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688868	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#461	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₄₇⋊C₈	—	2	1	no	—
10	C₂×#13094024	C₂²	1	1	yes	characteristic
11	#15689475	—	2	2	no	—
12	#15689475	C₂²	1	4	yes	complemented
13	#15689403	—	2	2	no	—
14	#15689403	C₂²	1	4	yes	—
15	D₄×C₄₇⋊C₈	—	2	2	no	—
16	D₄×C₄₇⋊C₈	C₂²	1	4	yes	—
17	C₂×#13093957	—	2	1	no	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093947	—	2	1	no	—
21	C₂×#13093947	—	2	1	no	—
22	C₂×#13093945	—	2	1	no	—
23	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	#15688873	C₂²	1	4	yes	complemented
26	#15688869	C₂²	1	4	yes	complemented
27	#15688868	C₂²	1	4	yes	complemented
28	C₂²×SD₁₆×C₄₇	—	2	1	no	—
29	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#461	—	2	2	no	—
32	C₄₇×#461	C₂²	1	4	yes	—
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#103×C₄₇	—	2	1	no	—
35	C₂²×Dic₉₄	—	2	1	no	—
36	C₂²×C₄₇⋊C₈	—	2	1	no	—
37	C₂²×C₄₇⋊C₈	—	2	1	no	—
38	C₂²×C₄₇⋊C₈	—	2	4	no	—
39	C₂²×C₄₇⋊C₈	—	4	4	no	—
40	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
41	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
42	#13094024	—	2	1	no	—
43	#13094024	—	2	1	no	—
44	#13094024	—	2	1	no	—
45	#13094024	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₄₇	—	2	1	no	—
47	C₂×C₄⋊Dic₄₇	—	2	1	no	—
48	#13093957	—	2	4	no	—
49	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
50	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
51	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
52	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
53	#13093947	—	2	4	no	—
54	#13093947	—	2	4	no	—
55	#13093945	—	2	4	no	—
56	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
57	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
58	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
59	C₂²×Q₈×C₄₇	—	2	1	no	—
60	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	—	2	1	no	—
62	C₂×SD₁₆×C₄₇	—	2	4	no	—
63	C₂×SD₁₆×C₄₇	—	4	4	no	—
64	C₂²×C₈×C₄₇	—	2	1	no	—
65	C₄⋊Q₈×C₄₇	—	2	1	no	—
66	C₄⋊Q₈×C₄₇	—	2	1	no	—
67	C₄⋊Q₈×C₄₇	—	2	1	no	—
68	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
69	C₄×D₄×C₄₇	—	2	1	no	—
70	C₄×D₄×C₄₇	—	2	1	no	—
71	C₄×D₄×C₄₇	D₄	1	2	yes	—
72	C₄×D₄×C₄₇	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₄₇	—	2	1	no	—
79	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
80	#103×C₄₇	—	2	4	no	—
81	C₂⁴×C₄₇	—	2	1	no	—
82	C₂×Q₈×C₄₇	—	2	2	no	—
83	C₂×Q₈×C₄₇	—	4	1	no	—
84	C₂×Q₈×C₄₇	—	4	2	no	—
85	C₂×Q₈×C₄₇	—	4	2	no	—
86	C₂×D₄×C₄₇	—	2	1	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	SD₁₆	1	4	yes	—
89	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₇	—	2	1	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	4	2	no	—
94	C₂²×C₄×C₄₇	—	4	2	no	—
95	C₂²×C₄×C₄₇	—	4	1	no	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
99	C₂²×Dic₄₇	—	4	1	no	—
100	C₂×Dic₉₄	—	2	2	no	—
101	C₂×Dic₉₄	—	4	2	no	—
102	C₂×Dic₉₄	—	4	2	no	—
103	C₂×Dic₉₄	—	4	1	no	—
104	SD₁₆×C₄₇	—	4	8	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	4	2	no	—
107	C₄⋊C₄×C₄₇	—	2	1	no	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	4	1	no	—
111	C₄⋊C₄×C₄₇	—	4	1	no	—
112	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
113	C₂²⋊C₄×C₄₇	—	2	2	no	—
114	C₂²⋊C₄×C₄₇	—	2	2	no	—
115	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₄₇	#41	1	1	yes	characteristic
118	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
119	C₄⋊Dic₄₇	—	2	2	no	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	4	1	no	—
122	C₄⋊Dic₄₇	—	4	1	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	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	4	8	no	—
128	C₂×C₄₇⋊C₈	—	4	2	no	—
129	C₂×C₄₇⋊C₈	—	4	2	no	—
130	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
131	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	4	no	—
134	C₂³×C₄₇	—	4	2	no	—
135	C₂³×C₄₇	—	4	2	no	—
136	C₂³×C₄₇	#121	1	1	yes	characteristic
137	Q₈×C₄₇	—	4	2	no	—
138	Q₈×C₄₇	—	4	2	no	—
139	Q₈×C₄₇	—	8	2	no	—
140	D₄×C₄₇	—	2	2	no	—
141	D₄×C₄₇	—	2	4	no	—
142	D₄×C₄₇	C₂×SD₁₆	1	4	yes	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	8	2	no	—
151	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
152	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
155	C₂×C₄×C₄₇	#135	1	2	yes	—
156	C₂×C₄×C₄₇	#135	1	2	yes	—
157	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
158	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	8	2	no	—
163	Dic₉₄	—	4	2	no	—
164	Dic₉₄	—	4	2	no	—
165	Dic₉₄	—	8	2	no	—
166	C₈×C₄₇	—	4	2	no	—
167	C₄₇⋊C₈	—	2	2	no	—
168	C₄₇⋊C₈	—	2	2	no	—
169	C₄₇⋊C₈	—	4	2	no	—
170	C₄₇⋊C₈	—	4	2	no	—
171	C₂×#1679	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	—	2	4	no	—
173	C₂²×C₄₇	—	4	8	no	—
174	C₂²×C₄₇	—	4	2	no	—
175	C₂²×C₄₇	—	4	2	no	—
176	C₂²×C₄₇	#463	1	2	yes	—
177	C₂²×C₄₇	#465	1	2	yes	—
178	C₂²×C₄₇	#473	1	2	yes	—
179	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
180	C₄×C₄₇	—	2	1	no	—
181	C₄×C₄₇	—	2	1	no	—
182	C₄×C₄₇	—	4	2	no	—
183	C₄×C₄₇	—	8	2	no	—
184	C₄×C₄₇	#463	1	2	yes	—
185	C₄×C₄₇	#465	1	2	yes	—
186	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
187	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
188	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
189	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
190	Dic₄₇	—	8	2	no	—
191	C₂×#487	—	47	1	no	—
192	C₂×#474	—	47	1	no	—
193	C₂×#461	D₄₇	1	1	yes	characteristic
194	C₂×C₈×D₄	—	47	1	no	—
195	#1679	—	47	8	no	—
196	C₂×#334	—	47	1	no	—
197	C₂×#332	—	47	1	no	—
198	C₂×#332	—	47	1	no	—
199	C₂×C₄₇	—	4	4	no	—
200	C₂×C₄₇	#1679	1	4	yes	complemented
201	C₂×C₄₇	C₂×#463	1	1	yes	characteristic
202	C₂×C₄₇	C₂×#465	1	1	yes	characteristic
203	C₂×C₄₇	C₂×#473	1	1	yes	characteristic
204	C₂²×SD₁₆	—	2	1	no	—
205	C₂³×C₈	—	94	1	no	—
206	C₂×C₄⋊Q₈	—	47	1	no	—
207	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
208	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
209	#487	—	47	4	no	—
210	#487	—	94	2	no	—
211	#474	—	47	4	no	—
212	#474	—	94	2	no	—
213	#461	—	2	2	no	—
214	#461	C₂×D₄₇	1	4	yes	—
215	C₈×D₄	—	47	4	no	—
216	C₈×D₄	—	94	2	no	—
217	C₂×#107	—	94	1	no	—
218	C₂×C₄⋊C₈	—	47	1	no	—
219	C₂×C₄⋊C₈	—	47	1	no	—
220	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
221	C₂×#103	—	2	1	no	—
222	C₂×#103	—	94	1	no	—
223	C₂×#103	—	94	1	no	—
224	C₂×#102	—	94	1	no	—
225	C₂×C₂²⋊C₈	—	94	1	no	—
226	C₂×C₄×C₈	—	47	1	no	—
227	#334	—	47	4	no	—
228	#332	—	47	4	no	—
229	#332	—	47	4	no	—
230	C₄₇	C₂×#1679	1	1	yes	characteristic, complemented, Sylow
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×Q₈	—	94	1	no	—
233	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
234	C₂³×C₄	—	2	1	no	—
235	C₂×SD₁₆	—	2	4	no	—
236	C₂×SD₁₆	—	4	4	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	47	1	no	—
239	C₂²×C₈	—	47	1	no	—
240	C₂²×C₈	—	94	4	no	—
241	C₂²×C₈	—	94	1	no	—
242	C₂²×C₈	—	94	1	no	—
243	C₂²×C₈	—	188	4	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	47	2	no	—
248	C₄⋊Q₈	—	94	1	no	—
249	C₄⋊Q₈	—	94	1	no	—
250	C₄⋊Q₈	—	94	1	no	—
251	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
255	C₄×D₄	C₂²×D₄₇	1	2	yes	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	94	1	no	—
259	C₂×C₄⋊C₄	—	94	1	no	—
260	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
263	#107	—	94	4	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	47	2	no	—
266	C₄⋊C₈	—	47	2	no	—
267	C₄⋊C₈	—	94	1	no	—
268	C₄⋊C₈	—	94	1	no	—
269	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
270	#103	—	2	4	no	—
271	#103	—	94	4	no	—
272	#103	—	94	4	no	—
273	#102	—	94	4	no	—
274	C₂²⋊C₈	—	94	4	no	—
275	C₄×C₈	—	47	2	no	—
276	C₄×C₈	—	47	2	no	—
277	C₂⁴	—	2	1	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×Q₈	—	94	2	no	—
283	C₂×Q₈	—	188	2	no	—
284	C₂×Q₈	—	188	2	no	—
285	C₂×Q₈	—	188	1	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	#10625335	1	4	yes	—
289	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	188	1	no	—
297	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
298	C₂²×C₄	#10625352	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
300	SD₁₆	—	4	8	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	—	47	2	no	—
304	C₂×C₈	—	47	2	no	—
305	C₂×C₈	—	94	2	no	—
306	C₂×C₈	—	94	2	no	—
307	C₂×C₈	—	94	2	no	—
308	C₂×C₈	—	94	2	no	—
309	C₂×C₈	—	188	8	no	—
310	C₂×C₈	—	188	2	no	—
311	C₂×C₈	—	188	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	94	2	no	—
318	C₄⋊C₄	—	94	2	no	—
319	C₄⋊C₄	—	188	1	no	—
320	C₄⋊C₄	—	188	1	no	—
321	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₄²	D₄×D₄₇	1	1	yes	characteristic
325	C₄²	#10625352	1	1	yes	characteristic
326	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
327	C₄²	C₂³×D₄₇	1	1	yes	characteristic
328	C₂³	—	2	4	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	#13093996	1	1	yes	characteristic
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	8	2	no	—
336	Q₈	—	376	2	no	—
337	Q₈	—	188	2	no	—
338	Q₈	—	188	2	no	—
339	D₄	—	2	4	no	—
340	D₄	—	2	2	no	—
341	D₄	C₂×#10625335	1	4	yes	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	376	2	no	—
351	C₂×C₄	—	188	2	no	—
352	C₂×C₄	#13093996	1	1	yes	characteristic
353	C₂×C₄	#13093996	1	1	yes	characteristic
354	C₂×C₄	#13093996	1	1	yes	characteristic
355	C₂×C₄	C₂×#10625335	1	2	yes	—
356	C₂×C₄	#13094044	1	2	yes	—
357	C₂×C₄	#13094045	1	2	yes	—
358	C₂×C₄	#13094051	1	2	yes	—
359	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
362	C₈	—	4	2	no	—
363	C₈	—	94	2	no	—
364	C₈	—	94	2	no	—
365	C₈	—	188	2	no	—
366	C₈	—	188	2	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	4	8	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	#15689340	1	2	yes	—
372	C₂²	#15689350	1	2	yes	—
373	C₂²	#15689396	1	2	yes	—
374	C₂²	C₂×#13093996	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	2	no	—
379	C₄	—	376	2	no	—
380	C₄	#15689340	1	2	yes	—
381	C₄	#15689350	1	2	yes	—
382	C₄	C₂²×#10625335	1	1	yes	characteristic
383	C₄	C₂×#13094044	1	1	yes	characteristic
384	C₄	C₂×#13094045	1	1	yes	characteristic
385	C₄	C₂×#13094051	1	1	yes	characteristic
386	C₂	—	4	4	no	—
387	C₂	#20242813	1	4	yes	direct product factor
388	C₂	C₂×#15689340	1	1	yes	characteristic
389	C₂	C₂×#15689350	1	1	yes	characteristic
390	C₂	C₂×#15689396	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#461	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂²×D₄×C₄₇	D₄
hypercenter	C₂×#461	D₄₇
hypocenter	C₄₇	C₂×#1679
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#461

Complements

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

N	H ≅ G/N	type
1. C₂×#15689475	C₂	semidirect
4. #20242813	C₂	direct (N × H)
5. C₂×#15688873	C₂	semidirect
6. C₂×#15688869	C₂	semidirect
7. C₂×#15688868	C₂	semidirect
12. #15689475	C₂²	semidirect
25. #15688873	C₂²	semidirect
26. #15688869	C₂²	semidirect
27. #15688868	C₂²	semidirect
200. C₂×C₄₇	#1679	semidirect
230. C₄₇	C₂×#1679	semidirect
387. C₂	#20242813	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×#15689475	2
C₂×#15689403	2
C₂×D₄×C₄₇⋊C₈	2
#20242813	2
C₂×#15688873	2
C₂×#15688869	2
C₂×#15688868	2
C₂×C₄₇×#461	2
C₂×#1679	47

Subgroups — C2×#20242813 #26198565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242813 #26198565