Subgroups — C₂×#20245506 #26370833

Order 12032.

678 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093965	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689540	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689393	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245506	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688952	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688936	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688935	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#472	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13094049	—	2	1	no	—
10	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
11	C₂×#13093965	—	2	1	no	—
12	C₂×#13093965	—	2	1	no	—
13	C₂×#13093965	—	2	2	no	—
14	C₂×#13093965	C₂²	1	4	yes	complemented
15	#15689540	—	2	2	no	—
16	#15689540	C₂²	1	4	yes	complemented
17	C₂×#13093964	—	2	1	no	—
18	C₂×#13093964	C₂²	1	1	yes	characteristic
19	C₂²×C₄₇⋊C₁₆	—	2	1	no	—
20	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
21	#15689393	—	2	2	no	—
22	#15689393	C₂²	1	4	yes	complemented
23	C₂×#13093960	C₂²	1	1	yes	characteristic
24	C₂×#13093940	—	2	1	no	—
25	#15688952	C₂²	1	4	yes	complemented
26	#15688936	C₂²	1	4	yes	complemented
27	#15688935	C₂²	1	4	yes	complemented
28	C₂×AGL(1,ℤ/8)×C₄₇	—	2	1	no	—
29	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#472	—	2	2	no	—
32	C₄₇×#472	C₂²	1	4	yes	complemented
33	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#100×C₄₇	—	2	1	no	—
35	C₂²×D₁₈₈	—	2	1	no	—
36	#13094049	—	2	4	no	—
37	#13094049	—	4	2	no	—
38	C₂×#10625336	—	4	1	no	—
39	C₂×D₃₇₆	—	2	1	no	—
40	C₂×D₃₇₆	—	2	1	no	—
41	C₂×D₃₇₆	—	2	1	no	—
42	C₂×D₃₇₆	—	2	1	no	—
43	C₂×D₃₇₆	—	2	1	no	—
44	C₂×D₃₇₆	C₂³	1	2	yes	—
45	C₂×#10625334	—	4	1	no	—
46	C₂×#10625329	—	2	1	no	—
47	#13093965	—	2	4	no	—
48	#13093965	—	2	4	no	—
49	#13093964	—	2	1	no	—
50	#13093964	—	2	4	no	—
51	#13093964	C₂³	1	2	yes	—
52	C₂×C₄₇⋊C₁₆	—	2	1	no	—
53	C₂×C₄₇⋊C₁₆	—	2	4	no	—
54	C₂×C₄₇⋊C₁₆	D₄	1	1	yes	characteristic
55	C₂×C₄₇⋊C₁₆	D₄	1	1	yes	characteristic
56	C₂×C₄₇⋊C₁₆	D₄	1	2	yes	—
57	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
58	#13093960	—	2	1	no	—
59	#13093960	C₂³	1	2	yes	—
60	#13093940	—	2	4	no	—
61	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₄₇	—	2	1	no	—
63	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
64	AGL(1,ℤ/8)×C₄₇	—	4	2	no	—
65	C₂×SD₁₆×C₄₇	—	4	1	no	—
66	C₂×D₈×C₄₇	—	2	1	no	—
67	C₂×D₈×C₄₇	—	2	1	no	—
68	C₂×D₈×C₄₇	—	2	1	no	—
69	C₂×D₈×C₄₇	—	2	1	no	—
70	C₂×D₈×C₄₇	—	2	1	no	—
71	C₂×D₈×C₄₇	—	4	1	no	—
72	C₂×D₈×C₄₇	C₂³	1	2	yes	—
73	#131×C₄₇	—	2	1	no	—
74	#131×C₄₇	—	2	1	no	—
75	#131×C₄₇	D₄	1	2	yes	—
76	#131×C₄₇	C₂³	1	2	yes	—
77	C₂×M₁₆×C₄₇	—	2	1	no	—
78	C₂×M₁₆×C₄₇	—	2	1	no	—
79	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	—	2	1	no	—
81	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	#108×C₄₇	—	2	1	no	—
83	#108×C₄₇	C₂³	1	2	yes	—
84	#100×C₄₇	—	2	4	no	—
85	C₂⁴×C₄₇	—	4	1	no	—
86	C₂³×D₄₇	—	4	1	no	—
87	#41×C₄₇	—	2	1	no	—
88	#41×C₄₇	—	2	1	no	—
89	#41×C₄₇	D₈	1	2	yes	—
90	#41×C₄₇	C₂×D₄	1	2	yes	—
91	C₂×Q₈×C₄₇	D₈	1	1	yes	characteristic
92	C₂×D₄×C₄₇	—	2	1	no	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	—	4	1	no	—
95	C₂×D₄×C₄₇	—	4	1	no	—
96	C₂×D₄×C₄₇	—	4	1	no	—
97	C₂×D₄×C₄₇	—	4	1	no	—
98	C₂×D₄×C₄₇	—	4	1	no	—
99	C₂×D₄×C₄₇	D₈	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂×D₁₈₈	—	2	2	no	—
103	C₂×D₁₈₈	—	4	1	no	—
104	C₂×D₁₈₈	—	4	1	no	—
105	C₂×D₁₈₈	—	4	1	no	—
106	C₂×D₁₈₈	—	4	1	no	—
107	C₂×D₁₈₈	—	4	1	no	—
108	SD₁₆×C₄₇	—	4	4	no	—
109	D₈×C₄₇	—	2	2	no	—
110	D₈×C₄₇	—	2	2	no	—
111	D₈×C₄₇	—	4	4	no	—
112	D₈×C₄₇	—	4	1	no	—
113	D₈×C₄₇	—	4	1	no	—
114	M₁₆×C₄₇	—	2	1	no	—
115	M₁₆×C₄₇	—	2	2	no	—
116	M₁₆×C₄₇	—	2	2	no	—
117	M₁₆×C₄₇	—	2	2	no	—
118	M₁₆×C₄₇	—	4	1	no	—
119	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	4	1	no	—
124	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
128	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
130	#10625336	—	4	4	no	—
131	#10625334	—	4	4	no	—
132	#10625329	—	2	2	no	—
133	#10625329	—	4	1	no	—
134	C₂×C₄₇⋊C₈	—	4	1	no	—
135	D₃₇₆	—	2	2	no	—
136	D₃₇₆	—	2	2	no	—
137	D₃₇₆	—	4	1	no	—
138	D₃₇₆	—	4	1	no	—
139	C₄₇⋊C₁₆	—	2	2	no	—
140	C₄₇⋊C₁₆	C₂×D₄	1	2	yes	—
141	C₄₇⋊C₁₆	C₂×D₄	1	2	yes	—
142	C₂³×C₄₇	—	2	1	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	—	8	1	no	—
145	C₂³×C₄₇	—	8	1	no	—
146	C₂³×C₄₇	—	16	2	no	—
147	C₂³×C₄₇	#135	1	1	yes	characteristic
148	C₂²×D₄₇	—	4	2	no	—
149	C₂²×D₄₇	—	8	1	no	—
150	C₂²×D₄₇	—	8	1	no	—
151	C₂²×D₄₇	—	16	2	no	—
152	Q₈×C₄₇	—	2	1	no	—
153	Q₈×C₄₇	C₂×D₈	1	2	yes	—
154	D₄×C₄₇	—	2	2	no	—
155	D₄×C₄₇	—	2	2	no	—
156	D₄×C₄₇	—	2	1	no	—
157	D₄×C₄₇	—	4	2	no	—
158	D₄×C₄₇	—	4	2	no	—
159	D₄×C₄₇	—	8	1	no	—
160	D₄×C₄₇	—	8	1	no	—
161	D₄×C₄₇	C₂×D₈	1	2	yes	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	D₁₈₈	—	4	2	no	—
172	D₁₈₈	—	4	2	no	—
173	D₁₈₈	—	8	1	no	—
174	D₁₈₈	—	8	1	no	—
175	C₈×C₄₇	—	2	2	no	—
176	C₈×C₄₇	—	4	2	no	—
177	C₈×C₄₇	#121	1	1	yes	characteristic
178	C₈×C₄₇	#121	1	1	yes	characteristic
179	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₄₇⋊C₈	—	4	2	no	—
182	C₂×#2221	—	47	1	no	maximal, Sylow
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	2	2	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	—	8	2	no	—
187	C₂²×C₄₇	—	16	2	no	—
188	C₂²×C₄₇	—	16	2	no	—
189	C₂²×C₄₇	—	16	2	no	—
190	C₂²×C₄₇	#466	1	1	yes	characteristic
191	C₂²×C₄₇	#466	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
193	C₂×D₄₇	—	8	2	no	—
194	C₂×D₄₇	—	16	2	no	—
195	C₂×D₄₇	—	16	2	no	—
196	C₂×D₄₇	—	16	2	no	—
197	C₄×C₄₇	—	2	2	no	—
198	C₄×C₄₇	#466	1	1	yes	characteristic
199	C₄×C₄₇	#466	1	1	yes	characteristic
200	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
201	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
202	C₂²×D₁₆	—	47	1	no	—
203	C₂×#504	—	47	1	no	—
204	C₂×#472	—	47	1	no	—
205	C₂×#472	D₄₇	1	1	yes	characteristic, complemented
206	#2221	—	47	8	no	—
207	C₂×#368	—	47	1	no	—
208	C₂×#361	—	47	1	no	—
209	C₂×#361	—	47	1	no	—
210	C₂×C₄₇	—	2	1	no	—
211	C₂×C₄₇	—	2	1	no	—
212	C₂×C₄₇	—	4	2	no	—
213	C₂×C₄₇	—	16	2	no	—
214	C₂×C₄₇	#2221	1	2	yes	complemented
215	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
216	D₄₇	—	16	2	no	—
217	C₂×AGL(1,ℤ/8)	—	2	1	no	—
218	C₂×AGL(1,ℤ/8)	—	94	1	no	—
219	C₂²×D₈	—	47	1	no	—
220	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
221	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
222	C₂×D₁₆	—	47	4	no	—
223	C₂×D₁₆	—	94	1	no	—
224	C₂×D₁₆	—	94	1	no	—
225	C₂×D₁₆	—	94	2	no	—
226	#504	—	47	4	no	—
227	#504	—	94	2	no	—
228	C₂×M₃₂	—	47	1	no	—
229	C₂×M₃₂	—	94	1	no	—
230	C₂²×C₁₆	—	47	1	no	—
231	C₂²×C₁₆	—	94	1	no	—
232	#472	—	2	2	no	—
233	#472	—	47	4	no	—
234	#472	—	94	2	no	—
235	#472	C₂×D₄₇	1	4	yes	complemented
236	C₂×#108	—	47	1	no	—
237	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
238	C₂×#100	—	2	1	no	—
239	C₂×#100	—	94	1	no	—
240	#368	—	47	4	no	—
241	#361	—	47	4	no	—
242	#361	—	47	4	no	—
243	C₄₇	C₂×#2221	1	1	yes	characteristic, complemented, Sylow
244	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	—	94	1	no	—
247	AGL(1,ℤ/8)	—	2	4	no	—
248	AGL(1,ℤ/8)	—	4	2	no	—
249	AGL(1,ℤ/8)	—	94	4	no	—
250	AGL(1,ℤ/8)	—	188	2	no	—
251	C₂×SD₁₆	—	4	1	no	—
252	C₂×SD₁₆	—	188	1	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂×D₈	—	2	1	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	4	1	no	—
259	C₂×D₈	—	47	2	no	—
260	C₂×D₈	—	94	1	no	—
261	C₂×D₈	—	94	1	no	—
262	C₂×D₈	—	94	1	no	—
263	C₂×D₈	—	94	1	no	—
264	C₂×D₈	—	94	1	no	—
265	C₂×D₈	—	188	1	no	—
266	C₂×D₈	C₂²×D₄₇	1	2	yes	—
267	#131	—	2	1	no	—
268	#131	—	2	1	no	—
269	#131	C₂²⋊D₄₇	1	2	yes	—
270	#131	C₂²×D₄₇	1	2	yes	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	94	1	no	—
274	C₂×M₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
275	C₂²×C₈	—	2	1	no	—
276	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
277	D₁₆	—	94	4	no	—
278	D₁₆	—	94	4	no	—
279	M₃₂	—	47	2	no	—
280	M₃₂	—	94	4	no	—
281	M₃₂	—	94	1	no	—
282	C₂×C₁₆	—	47	1	no	—
283	C₂×C₁₆	—	47	1	no	—
284	C₂×C₁₆	—	47	2	no	—
285	C₂×C₁₆	—	47	2	no	—
286	C₂×C₁₆	—	94	4	no	—
287	C₂×C₁₆	—	94	1	no	—
288	#108	—	2	1	no	—
289	#108	—	47	2	no	—
290	#108	—	94	1	no	—
291	#108	C₂²×D₄₇	1	2	yes	—
292	#100	—	2	4	no	—
293	#100	—	94	4	no	—
294	C₂⁴	—	4	1	no	—
295	C₂⁴	—	188	1	no	—
296	#41	—	2	1	no	—
297	#41	—	2	1	no	—
298	#41	#10625334	1	2	yes	—
299	#41	C₂×C₂²⋊D₄₇	1	2	yes	—
300	C₂×Q₈	#10625334	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	94	2	no	—
309	C₂×D₄	—	188	1	no	—
310	C₂×D₄	—	188	1	no	—
311	C₂×D₄	—	188	1	no	—
312	C₂×D₄	—	188	1	no	—
313	C₂×D₄	—	188	1	no	—
314	C₂×D₄	#10625334	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
317	SD₁₆	—	4	4	no	—
318	SD₁₆	—	188	4	no	—
319	D₈	—	2	2	no	—
320	D₈	—	2	2	no	—
321	D₈	—	4	4	no	—
322	D₈	—	4	1	no	—
323	D₈	—	4	1	no	—
324	D₈	—	94	2	no	—
325	D₈	—	94	2	no	—
326	D₈	—	188	4	no	—
327	D₈	—	188	1	no	—
328	D₈	—	188	1	no	—
329	M₁₆	—	2	1	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	4	1	no	—
334	M₁₆	—	94	2	no	—
335	M₁₆	—	188	1	no	—
336	M₁₆	C₂×C₂²⋊D₄₇	1	2	yes	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	188	1	no	—
342	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
343	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
344	C₂×C₈	#10625352	1	1	yes	characteristic
345	C₂×C₈	#10625352	1	1	yes	characteristic
346	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
347	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
348	C₁₆	—	47	2	no	—
349	C₁₆	—	47	2	no	—
350	C₁₆	—	94	2	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	8	1	no	—
354	C₂³	—	8	1	no	—
355	C₂³	—	16	2	no	—
356	C₂³	—	376	1	no	—
357	C₂³	—	376	1	no	—
358	C₂³	—	188	2	no	—
359	C₂³	—	752	2	no	—
360	C₂³	#13094044	1	1	yes	characteristic
361	Q₈	—	2	1	no	—
362	Q₈	C₂×#10625334	1	2	yes	—
363	D₄	—	2	2	no	—
364	D₄	—	2	2	no	—
365	D₄	—	2	1	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	8	1	no	—
369	D₄	—	8	1	no	—
370	D₄	—	376	1	no	—
371	D₄	—	376	1	no	—
372	D₄	—	188	2	no	—
373	D₄	—	188	2	no	—
374	D₄	C₂×#10625334	1	2	yes	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	#13093996	1	1	yes	characteristic
379	C₂×C₄	#13093996	1	1	yes	characteristic
380	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
381	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
382	C₂×C₄	#13094044	1	1	yes	characteristic
383	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	188	2	no	—
387	C₈	#13093996	1	1	yes	characteristic
388	C₈	#13093996	1	1	yes	characteristic
389	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
390	C₈	C₂×#10625352	1	1	yes	characteristic
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	16	2	no	—
396	C₂²	—	16	2	no	—
397	C₂²	—	16	2	no	—
398	C₂²	—	376	2	no	—
399	C₂²	—	752	2	no	—
400	C₂²	—	752	2	no	—
401	C₂²	—	752	2	no	—
402	C₂²	#15689357	1	1	yes	characteristic
403	C₂²	#15689357	1	1	yes	characteristic
404	C₂²	C₂×#13094044	1	1	yes	characteristic
405	C₄	—	2	2	no	—
406	C₄	#15689357	1	1	yes	characteristic
407	C₄	#15689357	1	1	yes	characteristic
408	C₄	C₂×#13093996	1	1	yes	characteristic
409	C₄	C₂²×#10625334	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	4	2	no	—
413	C₂	—	16	2	no	—
414	C₂	—	752	2	no	—
415	C₂	#20245506	1	2	yes	direct product factor
416	C₂	C₂×#15689357	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15689357
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₂×C₄₇×#472	C₂
socle	C₂²×C₄₇	#466
hypercenter	C₂×#472	D₄₇
hypocenter	C₄₇	C₂×#2221
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131 ◁ C₂×#472

Complements

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

N	H ≅ G/N	type
1. C₂²×#13093965	C₂	semidirect
2. C₂×#15689540	C₂	semidirect
3. C₂×#15689393	C₂	semidirect
4. #20245506	C₂	direct (N × H)
5. C₂×#15688952	C₂	semidirect
6. C₂×#15688936	C₂	semidirect
7. C₂×#15688935	C₂	semidirect
8. C₂×C₄₇×#472	C₂	semidirect
14. C₂×#13093965	C₂²	semidirect
16. #15689540	C₂²	semidirect
22. #15689393	C₂²	semidirect
25. #15688952	C₂²	semidirect
26. #15688936	C₂²	semidirect
27. #15688935	C₂²	semidirect
32. C₄₇×#472	C₂²	semidirect
205. C₂×#472	D₄₇	semidirect
214. C₂×C₄₇	#2221	semidirect
235. #472	C₂×D₄₇	semidirect
243. C₄₇	C₂×#2221	semidirect
415. C₂	#20245506	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#13093965	2
C₂×#15689540	2
C₂×#15689393	2
#20245506	2
C₂×#15688952	2
C₂×#15688936	2
C₂×#15688935	2
C₂×C₄₇×#472	2
C₂×#2221	47

Subgroups — C2×#20245506 #26370833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20245506 #26370833