Subgroups — C₂×#15689927 #20258140

Order 6016.

1512 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13094070	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13094069	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689927	C₂	1	16	yes	maximal, direct product factor
4	C₂×#13094052	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13094051	C₂	1	2	yes	maximal, complemented
6	C₂×#13094048	C₂	1	2	yes	maximal, complemented
7	C₂×#13094045	C₂	1	2	yes	maximal, complemented
8	C₂×#13094044	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625334	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₈×D₄₇	C₂	1	2	yes	maximal, complemented
11	C₂×#13094032	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#13094070	—	2	4	no	—
14	#13094070	C₂²	1	8	yes	complemented
15	#13094069	—	2	4	no	—
16	#13094069	C₂²	1	8	yes	complemented
17	C₂×#10625354	C₂²	1	2	yes	complemented
18	C₂×#10625350	—	2	1	no	—
19	C₂×#10625350	C₂²	1	1	yes	characteristic
20	C₂×#10625350	C₂²	1	1	yes	characteristic, complemented
21	C₂×#10625352	—	2	1	no	—
22	C₂×#10625352	C₂²	1	2	yes	complemented
23	C₂²×D₁₈₈	—	2	1	no	—
24	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₂²⋊D₄₇	—	2	2	no	—
26	C₂×D₄×D₄₇	—	2	2	no	—
27	C₂×D₄×D₄₇	—	2	1	no	—
28	C₂×D₄×D₄₇	C₂²	1	2	yes	complemented
29	C₂×D₄×D₄₇	C₂²	1	2	yes	complemented
30	#13094052	C₂²	1	8	yes	complemented
31	#13094051	C₂²	1	16	yes	complemented
32	#13094048	C₂²	1	16	yes	complemented
33	#13094045	C₂²	1	16	yes	complemented
34	#13094044	C₂²	1	8	yes	complemented
35	C₂×#10625337	C₂²	1	1	yes	characteristic, complemented
36	C₂×#10625325	C₂²	1	2	yes	complemented
37	C₂×#10625335	C₂²	1	1	yes	characteristic, complemented
38	C₂×#10625336	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₃₇₆	C₂²	1	2	yes	complemented
40	C₂×#10625334	C₂²	1	1	yes	characteristic, complemented
41	C₂×#10625334	C₂²	1	2	yes	complemented
42	C₂×#10625334	C₂²	1	2	yes	complemented
43	C₂×#10625334	C₂²	1	8	yes	complemented
44	D₈×D₄₇	C₂²	1	16	yes	complemented
45	#13094032	C₂²	1	8	yes	complemented
46	C₂×#10625324	C₂²	1	2	yes	complemented
47	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₈×D₄₇	C₂²	1	2	yes	complemented
49	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
50	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
51	AGL(1,ℤ/8)×C₄₇	C₂²	1	8	yes	complemented
52	C₂×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
53	C₂×D₈×C₄₇	C₂²	1	2	yes	complemented
54	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
55	C₂⁴×C₄₇	—	2	1	no	—
56	C₂³×D₄₇	—	2	1	no	—
57	C₂³×D₄₇	—	2	2	no	—
58	C₂³×D₄₇	—	2	2	no	—
59	#41×C₄₇	—	2	2	no	—
60	#41×C₄₇	C₂³	1	4	yes	complemented
61	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₄₇	—	2	1	no	—
63	C₂×D₄×C₄₇	—	2	1	no	—
64	C₂×D₄×C₄₇	—	2	2	no	—
65	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₄₇	C₂³	1	2	yes	—
67	C₂×D₄×C₄₇	C₂³	1	4	yes	complemented
68	C₂²×C₄×C₄₇	—	2	1	no	—
69	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₄₇	—	2	1	no	—
71	C₂×C₂²⋊D₄₇	—	2	2	no	—
72	C₂×C₂²⋊D₄₇	—	2	16	no	—
73	C₂×C₂²⋊D₄₇	—	2	2	no	—
74	C₂×C₂²⋊D₄₇	—	2	2	no	—
75	C₂×C₂²⋊D₄₇	D₄	1	2	yes	—
76	C₂²×Dic₄₇	—	2	2	no	—
77	#10625354	—	2	4	no	—
78	#10625354	C₂³	1	8	yes	complemented
79	#10625352	—	2	4	no	—
80	#10625352	—	2	8	no	—
81	#10625352	C₂³	1	8	yes	complemented
82	D₄×D₄₇	—	2	16	no	—
83	D₄×D₄₇	—	2	8	no	—
84	D₄×D₄₇	—	2	4	no	—
85	D₄×D₄₇	—	2	4	no	—
86	D₄×D₄₇	C₂³	1	8	yes	complemented
87	D₄×D₄₇	C₂³	1	8	yes	complemented
88	#10625350	—	2	2	no	—
89	#10625350	—	2	8	no	—
90	#10625350	D₄	1	4	yes	—
91	#10625350	C₂³	1	4	yes	—
92	#10625350	C₂³	1	4	yes	complemented
93	C₂×D₁₈₈	—	2	2	no	—
94	C₂×D₁₈₈	—	2	1	no	—
95	C₂×D₁₈₈	—	2	2	no	—
96	C₂×D₁₈₈	—	2	8	no	—
97	C₂×D₁₈₈	D₄	1	1	yes	characteristic
98	C₂×D₁₈₈	C₂³	1	2	yes	—
99	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
100	C₂×D₁₈₈	C₂³	1	4	yes	complemented
101	C₂×C₄×D₄₇	—	2	1	no	—
102	C₂×C₄×D₄₇	—	2	2	no	—
103	C₂×C₄×D₄₇	C₂³	1	2	yes	—
104	C₂×Dic₉₄	D₄	1	1	yes	characteristic
105	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
106	SD₁₆×C₄₇	C₂³	1	8	yes	complemented
107	D₈×C₄₇	C₂³	1	8	yes	complemented
108	M₁₆×C₄₇	C₂³	1	4	yes	complemented
109	C₂×C₈×C₄₇	C₂³	1	2	yes	—
110	#10625337	C₂³	1	4	yes	complemented
111	#10625336	C₂³	1	4	yes	complemented
112	#10625335	C₂³	1	4	yes	complemented
113	#10625334	C₂³	1	4	yes	complemented
114	#10625334	C₂³	1	8	yes	complemented
115	#10625334	C₂³	1	8	yes	complemented
116	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
117	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
118	C₂×C₄₇⋊C₈	C₂³	1	4	yes	complemented
119	D₃₇₆	C₂³	1	8	yes	complemented
120	#10625325	C₂³	1	8	yes	complemented
121	#10625324	C₂³	1	8	yes	complemented
122	C₈×D₄₇	C₂³	1	8	yes	complemented
123	C₂³×C₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	2	1	no	—
125	C₂³×C₄₇	—	2	4	no	—
126	C₂³×C₄₇	—	8	2	no	—
127	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×D₄₇	—	2	2	no	—
129	C₂²×D₄₇	—	2	1	no	—
130	C₂²×D₄₇	—	2	4	no	—
131	C₂²×D₄₇	—	2	8	no	—
132	C₂²×D₄₇	—	2	8	no	—
133	C₂²×D₄₇	—	8	4	no	—
134	C₂²×D₄₇	—	8	4	no	—
135	C₂²×D₄₇	—	8	2	no	—
136	C₂²×D₄₇	C₂×D₄	1	2	yes	—
137	Q₈×C₄₇	—	2	1	no	—
138	Q₈×C₄₇	C₂⁴	1	2	yes	—
139	D₄×C₄₇	—	2	4	no	—
140	D₄×C₄₇	—	2	1	no	—
141	D₄×C₄₇	—	2	2	no	—
142	D₄×C₄₇	—	2	4	no	—
143	D₄×C₄₇	C₂⁴	1	4	yes	—
144	D₄×C₄₇	C₂⁴	1	2	yes	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
151	C₂²⋊D₄₇	—	2	4	no	—
152	C₂²⋊D₄₇	—	2	8	no	—
153	C₂²⋊D₄₇	—	2	8	no	—
154	C₂²⋊D₄₇	—	2	8	no	—
155	C₂²⋊D₄₇	C₂×D₄	1	8	yes	—
156	C₂×Dic₄₇	—	2	1	no	—
157	C₂×Dic₄₇	—	2	8	no	—
158	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
159	D₁₈₈	—	2	8	no	—
160	D₁₈₈	—	2	4	no	—
161	D₁₈₈	—	2	2	no	—
162	D₁₈₈	—	2	1	no	—
163	D₁₈₈	C₂×D₄	1	4	yes	—
164	D₁₈₈	C₂⁴	1	4	yes	—
165	D₁₈₈	C₂⁴	1	2	yes	—
166	C₄×D₄₇	—	2	4	no	—
167	C₄×D₄₇	—	2	8	no	—
168	C₄×D₄₇	C₂×D₄	1	4	yes	—
169	C₄×D₄₇	C₂⁴	1	4	yes	—
170	Dic₉₄	—	2	1	no	—
171	Dic₉₄	C₂×D₄	1	4	yes	—
172	Dic₉₄	C₂⁴	1	2	yes	—
173	C₈×C₄₇	C₂⁴	1	4	yes	—
174	C₄₇⋊C₈	C₂⁴	1	2	yes	—
175	C₄₇⋊C₈	C₂⁴	1	2	yes	—
176	C₂²×C₄₇	—	2	2	no	—
177	C₂²×C₄₇	—	2	4	no	—
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	—	4	2	no	—
180	C₂²×C₄₇	—	4	4	no	—
181	C₂²×C₄₇	—	8	4	no	—
182	C₂²×C₄₇	C₂²×D₄	1	2	yes	—
183	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×D₄₇	—	2	4	no	—
185	C₂×D₄₇	—	2	4	no	—
186	C₂×D₄₇	—	2	2	no	—
187	C₂×D₄₇	—	4	4	no	—
188	C₂×D₄₇	—	4	2	no	—
189	C₂×D₄₇	—	8	8	no	—
190	C₂×D₄₇	—	8	8	no	—
191	C₂×D₄₇	—	8	4	no	—
192	C₂×D₄₇	C₂²×D₄	1	4	yes	—
193	C₄×C₄₇	—	2	2	no	—
194	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₄×C₄₇	C₂²×D₄	1	2	yes	—
196	C₄×C₄₇	C₂⁵	1	1	yes	characteristic
197	Dic₄₇	—	2	2	no	—
198	Dic₄₇	C₂²×D₄	1	4	yes	—
199	C₂×#576	—	47	1	no	maximal, Sylow
200	C₂×C₄₇	—	2	2	no	—
201	C₂×C₄₇	—	4	2	no	—
202	C₂×C₄₇	—	4	4	no	—
203	C₂×C₄₇	#576	1	2	yes	complemented
204	C₂×C₄₇	C₂³×D₄	1	1	yes	characteristic
205	D₄₇	—	2	4	no	—
206	D₄₇	—	4	4	no	—
207	D₄₇	—	4	2	no	—
208	C₂×H(5,𝔽₂)	—	47	1	no	—
209	C₂×H(5,𝔽₂)	—	47	1	no	—
210	#576	—	47	16	no	—
211	C₂×AGL(1,ℤ/8)	—	47	2	no	—
212	C₂×AGL(1,ℤ/8)	—	47	2	no	—
213	C₂×AGL(1,ℤ/8)	—	47	1	no	—
214	C₂×AGL(1,ℤ/8)	D₄₇	1	1	yes	characteristic, complemented
215	C₂×#135	—	47	1	no	—
216	C₂×#135	—	47	2	no	—
217	C₂²×D₈	—	47	1	no	—
218	C₂²×D₈	—	47	2	no	—
219	C₂×#131	—	47	1	no	—
220	C₄₇	C₂×#576	1	1	yes	characteristic, complemented, Sylow
221	H(5,𝔽₂)	—	47	8	no	—
222	H(5,𝔽₂)	—	47	8	no	—
223	H(5,𝔽₂)	—	94	4	no	—
224	H(5,𝔽₂)	—	94	4	no	—
225	C₂×#41	—	47	1	no	—
226	C₂×#41	—	47	2	no	—
227	C₂×#41	—	47	2	no	—
228	C₂×#41	—	47	1	no	—
229	C₂×#41	—	94	1	no	—
230	C₂×#41	—	94	1	no	—
231	C₂×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
232	C₂²×D₄	—	47	2	no	—
233	C₂²×D₄	—	47	2	no	—
234	C₂²×D₄	—	47	1	no	—
235	C₂²×D₄	—	94	1	no	—
236	C₂²×D₄	—	94	2	no	—
237	C₂²×D₄	—	94	1	no	—
238	C₂²×D₄	—	94	2	no	—
239	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
240	AGL(1,ℤ/8)	—	47	16	no	—
241	AGL(1,ℤ/8)	—	47	16	no	—
242	AGL(1,ℤ/8)	—	47	8	no	—
243	AGL(1,ℤ/8)	C₂×D₄₇	1	8	yes	complemented
244	#135	—	47	8	no	—
245	#135	—	47	16	no	—
246	C₂×Q₁₆	—	47	1	no	—
247	C₂×SD₁₆	—	47	1	no	—
248	C₂×SD₁₆	—	47	1	no	—
249	C₂×SD₁₆	—	47	2	no	—
250	C₂×SD₁₆	C₂×D₄₇	1	2	yes	complemented
251	C₂×D₈	—	47	2	no	—
252	C₂×D₈	—	47	1	no	—
253	C₂×D₈	—	47	2	no	—
254	C₂×D₈	—	47	8	no	—
255	C₂×D₈	—	47	16	no	—
256	C₂×D₈	—	47	2	no	—
257	C₂×D₈	C₂×D₄₇	1	2	yes	complemented
258	#131	—	47	8	no	—
259	C₂×M₁₆	—	47	2	no	—
260	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
261	C₂²×C₈	—	47	1	no	—
262	C₂²×C₈	—	47	2	no	—
263	C₂⁴	—	2	1	no	—
264	C₂⁴	—	94	2	no	—
265	C₂⁴	—	94	2	no	—
266	C₂⁴	—	94	1	no	—
267	#41	—	2	2	no	—
268	#41	—	47	4	no	—
269	#41	—	47	4	no	—
270	#41	—	47	8	no	—
271	#41	—	47	8	no	—
272	#41	—	47	4	no	—
273	#41	—	94	8	no	—
274	#41	—	94	4	no	—
275	#41	—	94	4	no	—
276	#41	—	94	8	no	—
277	#41	—	94	2	no	—
278	#41	C₂²×D₄₇	1	4	yes	complemented
279	C₂×Q₈	—	47	1	no	—
280	C₂×Q₈	—	47	1	no	—
281	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	47	2	no	—
286	C₂×D₄	—	47	8	no	—
287	C₂×D₄	—	47	8	no	—
288	C₂×D₄	—	47	1	no	—
289	C₂×D₄	—	47	2	no	—
290	C₂×D₄	—	47	1	no	—
291	C₂×D₄	—	47	4	no	—
292	C₂×D₄	—	94	8	no	—
293	C₂×D₄	—	94	2	no	—
294	C₂×D₄	—	94	4	no	—
295	C₂×D₄	—	94	4	no	—
296	C₂×D₄	—	94	2	no	—
297	C₂×D₄	—	94	2	no	—
298	C₂×D₄	—	94	16	no	—
299	C₂×D₄	—	94	8	no	—
300	C₂×D₄	—	94	16	no	—
301	C₂×D₄	—	94	2	no	—
302	C₂×D₄	—	94	1	no	—
303	C₂×D₄	—	94	1	no	—
304	C₂×D₄	—	94	2	no	—
305	C₂×D₄	C₂²×D₄₇	1	2	yes	—
306	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
307	C₂×D₄	C₂²×D₄₇	1	4	yes	complemented
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	47	2	no	—
310	C₂²×C₄	—	94	2	no	—
311	C₂²×C₄	—	94	2	no	—
312	C₂²×C₄	—	94	1	no	—
313	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
314	Q₁₆	—	47	4	no	—
315	SD₁₆	—	47	4	no	—
316	SD₁₆	—	47	4	no	—
317	SD₁₆	—	47	8	no	—
318	SD₁₆	C₂²×D₄₇	1	8	yes	complemented
319	D₈	—	47	8	no	—
320	D₈	—	47	4	no	—
321	D₈	—	47	8	no	—
322	D₈	—	47	8	no	—
323	D₈	C₂²×D₄₇	1	8	yes	complemented
324	M₁₆	—	47	8	no	—
325	M₁₆	C₂²×D₄₇	1	4	yes	complemented
326	C₂×C₈	—	47	1	no	—
327	C₂×C₈	—	47	1	no	—
328	C₂×C₈	—	47	4	no	—
329	C₂×C₈	—	47	8	no	—
330	C₂×C₈	C₂²×D₄₇	1	2	yes	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	8	2	no	—
335	C₂³	—	47	2	no	—
336	C₂³	—	94	8	no	—
337	C₂³	—	94	8	no	—
338	C₂³	—	94	4	no	—
339	C₂³	—	94	2	no	—
340	C₂³	—	94	1	no	—
341	C₂³	—	376	2	no	—
342	C₂³	—	376	4	no	—
343	C₂³	—	376	4	no	—
344	C₂³	D₄×D₄₇	1	1	yes	characteristic
345	Q₈	—	2	1	no	—
346	Q₈	—	47	4	no	—
347	Q₈	—	47	2	no	—
348	Q₈	—	94	1	no	—
349	Q₈	C₂³×D₄₇	1	2	yes	—
350	D₄	—	2	4	no	—
351	D₄	—	2	2	no	—
352	D₄	—	2	4	no	—
353	D₄	—	2	1	no	—
354	D₄	—	47	8	no	—
355	D₄	—	47	4	no	—
356	D₄	—	47	4	no	—
357	D₄	—	47	2	no	—
358	D₄	—	94	8	no	—
359	D₄	—	94	8	no	—
360	D₄	—	94	8	no	—
361	D₄	—	94	8	no	—
362	D₄	—	94	4	no	—
363	D₄	—	94	4	no	—
364	D₄	—	94	2	no	—
365	D₄	—	94	1	no	—
366	D₄	C₂³×D₄₇	1	4	yes	—
367	D₄	C₂³×D₄₇	1	2	yes	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	47	2	no	—
371	C₂×C₄	—	47	4	no	—
372	C₂×C₄	—	47	4	no	—
373	C₂×C₄	—	94	8	no	—
374	C₂×C₄	—	94	8	no	—
375	C₂×C₄	—	94	1	no	—
376	C₂×C₄	—	94	4	no	—
377	C₂×C₄	D₄×D₄₇	1	2	yes	—
378	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
379	C₂×C₄	C₂³×D₄₇	1	2	yes	—
380	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
381	C₈	—	47	2	no	—
382	C₈	—	47	2	no	—
383	C₈	C₂³×D₄₇	1	4	yes	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	8	4	no	—
390	C₂²	—	47	4	no	—
391	C₂²	—	94	4	no	—
392	C₂²	—	94	4	no	—
393	C₂²	—	94	2	no	—
394	C₂²	—	376	4	no	—
395	C₂²	—	376	8	no	—
396	C₂²	—	376	8	no	—
397	C₂²	—	188	4	no	—
398	C₂²	—	188	2	no	—
399	C₂²	C₂×D₄×D₄₇	1	2	yes	—
400	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	47	4	no	—
403	C₄	—	94	2	no	—
404	C₄	C₂×D₄×D₄₇	1	2	yes	—
405	C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
406	C₄	C₂⁴×D₄₇	1	1	yes	characteristic
407	C₂	—	2	2	no	—
408	C₂	—	4	4	no	—
409	C₂	—	4	2	no	—
410	C₂	—	94	4	no	—
411	C₂	—	188	4	no	—
412	C₂	—	188	2	no	—
413	C₂	#15689927	1	2	yes	direct product factor
414	C₂	C₂²×D₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁵
Frattini	C₄	C₂⁴×D₄₇
Fitting	C₂×AGL(1,ℤ/8)×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₄₇
hypocenter	C₄₇	C₂×#576
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×#13094070	C₂	semidirect
2. C₂×#13094069	C₂	semidirect
3. #15689927	C₂	direct (N × H)
4. C₂×#13094052	C₂	semidirect
5. C₂×#13094051	C₂	semidirect
6. C₂×#13094048	C₂	semidirect
7. C₂×#13094045	C₂	semidirect
8. C₂×#13094044	C₂	semidirect
9. C₂²×#10625334	C₂	semidirect
10. C₂×D₈×D₄₇	C₂	semidirect
11. C₂×#13094032	C₂	semidirect
12. C₂×AGL(1,ℤ/8)×C₄₇	C₂	semidirect
14. #13094070	C₂²	semidirect
16. #13094069	C₂²	semidirect
17. C₂×#10625354	C₂²	semidirect
20. C₂×#10625350	C₂²	semidirect
22. C₂×#10625352	C₂²	semidirect
24. C₂²×D₁₈₈	C₂²	semidirect
28. C₂×D₄×D₄₇	C₂²	semidirect
29. C₂×D₄×D₄₇	C₂²	semidirect
30. #13094052	C₂²	semidirect
31. #13094051	C₂²	semidirect
32. #13094048	C₂²	semidirect
33. #13094045	C₂²	semidirect
34. #13094044	C₂²	semidirect
35. C₂×#10625337	C₂²	semidirect
36. C₂×#10625325	C₂²	semidirect
37. C₂×#10625335	C₂²	semidirect
38. C₂×#10625336	C₂²	semidirect
39. C₂×D₃₇₆	C₂²	semidirect
40. C₂×#10625334	C₂²	semidirect
41. C₂×#10625334	C₂²	semidirect
42. C₂×#10625334	C₂²	semidirect
43. C₂×#10625334	C₂²	semidirect
44. D₈×D₄₇	C₂²	semidirect
45. #13094032	C₂²	semidirect
46. C₂×#10625324	C₂²	semidirect
47. C₂²×C₄₇⋊C₈	C₂²	semidirect
48. C₂×C₈×D₄₇	C₂²	semidirect
49. C₂×#41×C₄₇	C₂²	semidirect
50. C₂²×D₄×C₄₇	C₂²	semidirect
51. AGL(1,ℤ/8)×C₄₇	C₂²	semidirect
52. C₂×SD₁₆×C₄₇	C₂²	semidirect
53. C₂×D₈×C₄₇	C₂²	semidirect
54. C₂×M₁₆×C₄₇	C₂²	semidirect
60. #41×C₄₇	C₂³	semidirect
67. C₂×D₄×C₄₇	C₂³	semidirect
78. #10625354	C₂³	semidirect
81. #10625352	C₂³	semidirect
86. D₄×D₄₇	C₂³	semidirect
87. D₄×D₄₇	C₂³	semidirect
92. #10625350	C₂³	semidirect
100. C₂×D₁₈₈	C₂³	semidirect
106. SD₁₆×C₄₇	C₂³	semidirect
107. D₈×C₄₇	C₂³	semidirect
108. M₁₆×C₄₇	C₂³	semidirect
110. #10625337	C₂³	semidirect
111. #10625336	C₂³	semidirect
112. #10625335	C₂³	semidirect
113. #10625334	C₂³	semidirect
114. #10625334	C₂³	semidirect
115. #10625334	C₂³	semidirect
118. C₂×C₄₇⋊C₈	C₂³	semidirect
119. D₃₇₆	C₂³	semidirect
120. #10625325	C₂³	semidirect
121. #10625324	C₂³	semidirect
122. C₈×D₄₇	C₂³	semidirect
203. C₂×C₄₇	#576	semidirect
214. C₂×AGL(1,ℤ/8)	D₄₇	semidirect
220. C₄₇	C₂×#576	semidirect
231. C₂×#41	C₂×D₄₇	semidirect
239. C₂²×D₄	C₂×D₄₇	semidirect
243. AGL(1,ℤ/8)	C₂×D₄₇	semidirect
250. C₂×SD₁₆	C₂×D₄₇	semidirect
257. C₂×D₈	C₂×D₄₇	semidirect
260. C₂×M₁₆	C₂×D₄₇	semidirect
278. #41	C₂²×D₄₇	semidirect
307. C₂×D₄	C₂²×D₄₇	semidirect
318. SD₁₆	C₂²×D₄₇	semidirect
323. D₈	C₂²×D₄₇	semidirect
325. M₁₆	C₂²×D₄₇	semidirect
413. C₂	#15689927	direct (N × H)

Subgroups — C2×#15689927 #20258140

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689927 #20258140