Subgroups — C₂×#20242152 #26185293

Order 12032.

758 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689179	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689145	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
4	#20242152	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688876	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688875	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688873	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625324	—	2	1	no	—
10	C₂²×#10625324	C₄	1	1	yes	characteristic
11	C₂²×#10625324	C₄	1	1	yes	characteristic
12	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
13	#15689179	—	2	2	no	—
14	#15689179	C₂²	1	4	yes	—
15	#15689145	—	2	2	no	—
16	#15689145	C₂²	1	4	yes	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×Dic₄₇⋊C₈	—	2	1	no	—
20	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
21	C₄×#10625324	C₄	1	4	yes	—
22	C₄×#10625324	C₂²	1	4	yes	—
23	C₂×#13093934	—	2	1	no	—
24	C₂×#13093934	C₄	1	1	yes	characteristic
25	C₂×#13093934	C₄	1	1	yes	characteristic
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	#15688876	C₂²	1	4	yes	complemented
28	#15688875	C₂²	1	4	yes	complemented
29	#15688873	C₂²	1	4	yes	complemented
30	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#334	C₂²	1	4	yes	complemented
34	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₄₇	Q₈	1	1	yes	characteristic
37	C₂×#10625324	—	2	4	no	—
38	C₂×#10625324	—	2	4	no	—
39	C₂×#10625324	—	2	4	no	—
40	C₂×#10625324	—	4	4	no	—
41	C₂×#10625324	C₂×C₄	1	4	yes	—
42	C₂×#10625324	C₂×C₄	1	4	yes	—
43	C₂²×C₄₇⋊C₈	—	2	1	no	—
44	C₂²×C₄₇⋊C₈	—	2	1	no	—
45	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
49	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
50	C₄²×D₄₇	C₂×C₄	1	2	yes	—
51	C₄²×D₄₇	D₄	1	2	yes	—
52	C₄²×D₄₇	Q₈	1	2	yes	—
53	C₄²×D₄₇	C₂³	1	2	yes	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
57	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
58	Dic₄₇⋊C₈	—	2	4	no	—
59	(C₂×D₄₇)⋊C₈	—	2	4	no	—
60	#13093934	—	2	4	no	—
61	#13093934	C₂×C₄	1	4	yes	—
62	#13093934	C₂×C₄	1	4	yes	—
63	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
64	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
65	C₂²×C₈×C₄₇	—	2	1	no	—
66	C₂²×C₈×C₄₇	—	2	1	no	—
67	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₄₇	—	2	1	no	—
71	C₄⋊C₈×C₄₇	—	2	1	no	—
72	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
73	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
74	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
75	C₄×C₈×C₄₇	C₂³	1	2	yes	—
76	C₂³×D₄₇	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
80	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₄₇	—	2	2	no	—
84	C₂×C₄×D₄₇	—	2	2	no	—
85	C₂×C₄×D₄₇	—	2	2	no	—
86	C₂×C₄×D₄₇	—	2	2	no	—
87	C₂×C₄×D₄₇	—	4	2	no	—
88	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
89	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
90	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
91	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
92	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
93	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
94	C₂×C₈×C₄₇	—	2	2	no	—
95	C₂×C₈×C₄₇	—	2	2	no	—
96	C₂×C₈×C₄₇	—	2	2	no	—
97	C₂×C₈×C₄₇	—	4	2	no	—
98	C₂×C₈×C₄₇	—	4	2	no	—
99	C₂×C₈×C₄₇	M₁₆	1	4	yes	complemented
100	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
102	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
105	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
107	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
108	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
109	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
110	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
111	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
112	C₂×C₄₇⋊C₈	—	2	2	no	—
113	C₂×C₄₇⋊C₈	—	2	2	no	—
114	C₂×C₄₇⋊C₈	—	2	2	no	—
115	C₂×C₄₇⋊C₈	—	4	2	no	—
116	C₂×C₄₇⋊C₈	—	4	2	no	—
117	C₂×C₄₇⋊C₈	M₁₆	1	4	yes	complemented
118	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
119	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
120	#10625324	—	2	8	no	—
121	#10625324	—	2	8	no	—
122	#10625324	—	4	8	no	—
123	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂²×D₄₇	—	2	2	no	—
125	C₂²×D₄₇	—	2	2	no	—
126	C₂²×D₄₇	—	2	2	no	—
127	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
133	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
134	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
135	C₂×C₄×C₄₇	#137	1	2	yes	—
136	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
139	C₂×Dic₄₇	—	2	2	no	—
140	C₂×Dic₄₇	—	2	2	no	—
141	C₂×Dic₄₇	—	2	2	no	—
142	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
145	C₄×D₄₇	—	2	2	no	—
146	C₄×D₄₇	—	2	2	no	—
147	C₄×D₄₇	—	2	2	no	—
148	C₄×D₄₇	—	2	2	no	—
149	C₄×D₄₇	—	2	4	no	—
150	C₄×D₄₇	—	2	4	no	—
151	C₄×D₄₇	—	4	2	no	—
152	C₄×D₄₇	—	4	2	no	—
153	C₈×C₄₇	—	2	2	no	—
154	C₈×C₄₇	—	4	2	no	—
155	C₈×C₄₇	—	4	2	no	—
156	C₈×C₄₇	C₂×M₁₆	1	4	yes	complemented
157	C₄₇⋊C₈	—	2	2	no	—
158	C₄₇⋊C₈	—	4	2	no	—
159	C₄₇⋊C₈	—	4	2	no	—
160	C₄₇⋊C₈	C₂×M₁₆	1	4	yes	complemented
161	C₂×#1569	—	47	1	no	maximal, Sylow
162	C₂²×C₄₇	#423	1	2	yes	—
163	C₂²×C₄₇	#428	1	2	yes	—
164	C₂²×C₄₇	#430	1	2	yes	—
165	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
166	C₂×D₄₇	—	2	2	no	—
167	C₂×D₄₇	—	2	2	no	—
168	C₂×D₄₇	—	2	2	no	—
169	C₂×D₄₇	—	4	4	no	—
170	C₄×C₄₇	—	2	1	no	—
171	C₄×C₄₇	—	2	1	no	—
172	C₄×C₄₇	#423	1	2	yes	—
173	C₄×C₄₇	#428	1	2	yes	—
174	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
175	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
176	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
178	Dic₄₇	—	2	2	no	—
179	Dic₄₇	—	2	2	no	—
180	Dic₄₇	—	2	2	no	—
181	C₂×#432	—	47	1	no	—
182	C₂×#423	—	47	1	no	—
183	C₂×C₄×M₁₆	—	47	1	no	—
184	#1569	—	47	8	no	—
185	C₂×#335	—	47	1	no	—
186	C₂×#335	—	47	1	no	—
187	C₂×#334	—	47	1	no	—
188	C₂×#334	D₄₇	1	1	yes	characteristic, complemented
189	C₂×C₄₇	#1569	1	4	yes	complemented
190	C₂×C₄₇	C₂×#423	1	1	yes	characteristic
191	C₂×C₄₇	C₂×#428	1	1	yes	characteristic
192	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
193	D₄₇	—	4	2	no	—
194	C₂²×M₁₆	—	47	1	no	—
195	C₂²×M₁₆	—	47	1	no	—
196	C₂²×M₁₆	—	94	1	no	—
197	C₂²×C₄²	—	47	1	no	—
198	#432	—	47	4	no	—
199	#432	—	94	2	no	—
200	#423	—	47	4	no	—
201	#423	—	94	2	no	—
202	C₂×C₄⋊C₈	—	47	1	no	—
203	C₂×C₄⋊C₈	—	47	1	no	—
204	C₂×C₄⋊C₈	—	94	1	no	—
205	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
206	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
207	C₂×C₂²⋊C₈	—	94	1	no	—
208	C₄×M₁₆	—	47	4	no	—
209	C₄×M₁₆	—	47	4	no	—
210	C₂×#97	—	47	1	no	—
211	C₂×#97	—	47	1	no	—
212	C₂×#97	—	94	1	no	—
213	C₂×C₄×C₈	—	47	1	no	—
214	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
215	#335	—	47	4	no	—
216	#335	—	47	4	no	—
217	#334	—	47	4	no	—
218	#334	C₂×D₄₇	1	4	yes	complemented
219	C₄₇	C₂×#1569	1	1	yes	characteristic, complemented, Sylow
220	C₂³×C₄	—	47	1	no	—
221	C₂³×C₄	—	47	1	no	—
222	C₂³×C₄	—	47	1	no	—
223	C₂×M₁₆	—	47	4	no	—
224	C₂×M₁₆	—	47	4	no	—
225	C₂×M₁₆	—	94	4	no	—
226	C₂×M₁₆	—	94	4	no	—
227	C₂×M₁₆	—	94	4	no	—
228	C₂×M₁₆	—	188	4	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	47	1	no	—
232	C₂²×C₈	—	47	1	no	—
233	C₂²×C₈	—	94	1	no	—
234	C₂²×C₈	—	94	1	no	—
235	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
236	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
237	C₂×C₄²	—	47	1	no	—
238	C₂×C₄²	—	47	1	no	—
239	C₂×C₄²	—	47	1	no	—
240	C₂×C₄²	—	47	2	no	—
241	C₂×C₄²	—	47	2	no	—
242	C₂×C₄²	—	47	2	no	—
243	C₂×C₄²	—	47	2	no	—
244	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	47	2	no	—
248	C₄⋊C₈	—	47	2	no	—
249	C₄⋊C₈	—	94	4	no	—
250	C₄⋊C₈	—	94	1	no	—
251	C₄⋊C₈	—	94	1	no	—
252	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
253	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
254	C₂²⋊C₈	—	94	4	no	—
255	#97	—	47	4	no	—
256	#97	—	47	4	no	—
257	#97	—	94	4	no	—
258	C₄×C₈	—	47	2	no	—
259	C₄×C₈	—	47	2	no	—
260	C₄×C₈	C₄×D₄₇	1	2	yes	—
261	C₄×C₈	C₂²×D₄₇	1	2	yes	—
262	C₂⁴	—	47	1	no	—
263	C₂²×C₄	—	47	1	no	—
264	C₂²×C₄	—	47	1	no	—
265	C₂²×C₄	—	47	1	no	—
266	C₂²×C₄	—	47	2	no	—
267	C₂²×C₄	—	47	2	no	—
268	C₂²×C₄	—	47	2	no	—
269	C₂²×C₄	—	47	2	no	—
270	C₂²×C₄	—	47	2	no	—
271	C₂²×C₄	—	47	2	no	—
272	C₂²×C₄	—	94	2	no	—
273	C₂²×C₄	—	94	2	no	—
274	C₂²×C₄	—	94	2	no	—
275	C₂²×C₄	—	94	2	no	—
276	C₂²×C₄	—	188	2	no	—
277	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
278	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
279	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
280	M₁₆	—	94	8	no	—
281	M₁₆	—	94	8	no	—
282	M₁₆	—	188	8	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	4	2	no	—
287	C₂×C₈	—	4	2	no	—
288	C₂×C₈	—	47	4	no	—
289	C₂×C₈	—	47	2	no	—
290	C₂×C₈	—	47	2	no	—
291	C₂×C₈	—	94	2	no	—
292	C₂×C₈	—	94	2	no	—
293	C₂×C₈	—	94	2	no	—
294	C₂×C₈	—	188	2	no	—
295	C₂×C₈	—	188	2	no	—
296	C₂×C₈	#10625324	1	4	yes	complemented
297	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
298	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
299	C₄²	—	47	2	no	—
300	C₄²	—	47	2	no	—
301	C₄²	—	47	2	no	—
302	C₄²	—	47	2	no	—
303	C₄²	—	47	2	no	—
304	C₄²	—	47	2	no	—
305	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
306	C₄²	D₄×D₄₇	1	1	yes	characteristic
307	C₄²	Q₈×D₄₇	1	1	yes	characteristic
308	C₄²	C₂³×D₄₇	1	1	yes	characteristic
309	C₂³	—	47	2	no	—
310	C₂³	—	94	2	no	—
311	C₂³	—	94	2	no	—
312	C₂³	—	94	2	no	—
313	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	47	2	no	—
316	C₂×C₄	—	47	2	no	—
317	C₂×C₄	—	47	2	no	—
318	C₂×C₄	—	94	2	no	—
319	C₂×C₄	—	94	2	no	—
320	C₂×C₄	—	94	2	no	—
321	C₂×C₄	—	94	2	no	—
322	C₂×C₄	—	94	2	no	—
323	C₂×C₄	—	94	2	no	—
324	C₂×C₄	—	94	4	no	—
325	C₂×C₄	—	94	2	no	—
326	C₂×C₄	—	94	4	no	—
327	C₂×C₄	—	188	2	no	—
328	C₂×C₄	—	188	2	no	—
329	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
330	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
331	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
332	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
333	C₂×C₄	C₂×#10625324	1	2	yes	—
334	C₂×C₄	#13094051	1	2	yes	—
335	C₂×C₄	#13094053	1	2	yes	—
336	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
337	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
338	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
339	C₈	—	2	2	no	—
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₈	—	47	4	no	—
343	C₈	—	94	2	no	—
344	C₈	—	188	2	no	—
345	C₈	—	188	2	no	—
346	C₈	C₂×#10625324	1	4	yes	complemented
347	C₂²	—	94	2	no	—
348	C₂²	—	94	2	no	—
349	C₂²	—	94	2	no	—
350	C₂²	—	188	4	no	—
351	C₂²	#15689145	1	2	yes	—
352	C₂²	#15689162	1	2	yes	—
353	C₂²	#15689170	1	2	yes	—
354	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	94	2	no	—
358	C₄	—	94	2	no	—
359	C₄	—	94	2	no	—
360	C₄	#15689145	1	2	yes	—
361	C₄	#15689162	1	2	yes	—
362	C₄	C₂×M₁₆×D₄₇	1	1	yes	characteristic
363	C₄	C₂²×#10625324	1	1	yes	characteristic
364	C₄	C₂×#13094051	1	1	yes	characteristic
365	C₄	C₂×#13094053	1	1	yes	characteristic
366	C₂	—	188	2	no	—
367	C₂	#20242152	1	4	yes	direct product factor
368	C₂	C₂×#15689145	1	1	yes	characteristic
369	C₂	C₂×#15689162	1	1	yes	characteristic
370	C₂	C₂×#15689170	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#334	C₂
socle	C₂³×C₄₇	C₂×C₄⋊C₄
prime radical	C₂³×D₄₇	C₄⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×#334	D₄₇
hypocenter	C₄₇	C₂×#1569
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
4. #20242152	C₂	direct (N × H)
5. C₂×#15688876	C₂	semidirect
6. C₂×#15688875	C₂	semidirect
7. C₂×#15688873	C₂	semidirect
8. C₂×C₄₇×#334	C₂	semidirect
27. #15688876	C₂²	semidirect
28. #15688875	C₂²	semidirect
29. #15688873	C₂²	semidirect
33. C₄₇×#334	C₂²	semidirect
99. C₂×C₈×C₄₇	M₁₆	semidirect
117. C₂×C₄₇⋊C₈	M₁₆	semidirect
156. C₈×C₄₇	C₂×M₁₆	semidirect
160. C₄₇⋊C₈	C₂×M₁₆	semidirect
188. C₂×#334	D₄₇	semidirect
189. C₂×C₄₇	#1569	semidirect
218. #334	C₂×D₄₇	semidirect
219. C₄₇	C₂×#1569	semidirect
296. C₂×C₈	#10625324	semidirect
346. C₈	C₂×#10625324	semidirect
367. C₂	#20242152	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×#15689179	2
C₂×#15689145	2
C₂×C₄×#10625324	2
#20242152	2
C₂×#15688876	2
C₂×#15688875	2
C₂×#15688873	2
C₂×C₄₇×#334	2
C₂×#1569	47

Subgroups — C2×#20242152 #26185293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242152 #26185293