Subgroups — #26370671

Order 12032.

696 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256522	C₂	1	2	yes	maximal, complemented
2	#20253816	C₂	1	1	yes	maximal, characteristic, complemented
3	#20245469	C₂	1	2	yes	maximal, complemented
4	#20245464	C₂	1	2	yes	maximal, complemented
5	#20245457	C₂	1	4	yes	maximal, complemented
6	C₂×#15688944	C₂	1	1	yes	maximal, characteristic, complemented
7	#20245135	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₇×#443	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13094046	—	2	1	no	—
10	C₂×#13094046	C₂²	1	2	yes	—
11	#15689673	—	2	1	no	—
12	#15689564	—	2	2	no	—
13	#15689563	C₂²	1	4	yes	—
14	#15689559	—	2	2	no	—
15	#15689558	C₂²	1	4	yes	—
16	#15689553	—	2	4	no	—
17	C₂×#13093964	C₂²	1	2	yes	—
18	#15689507	—	2	1	no	—
19	#15689507	C₂²	1	2	yes	complemented
20	#15689503	C₂²	1	1	yes	characteristic, complemented
21	#15689500	C₂²	1	1	yes	characteristic, complemented
22	#15689496	—	2	1	no	—
23	#15688944	C₂²	1	2	yes	complemented
24	#15688944	C₂²	1	2	yes	complemented
25	#15688938	C₂²	1	4	yes	complemented
26	#15688935	C₂²	1	4	yes	complemented
27	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#131×C₄₇	—	2	1	no	—
29	C₄₇×#443	—	2	1	no	—
30	C₄₇×#443	—	2	1	no	—
31	C₄₇×#443	C₂²	1	2	yes	—
32	C₄₇×#443	C₂²	1	2	yes	—
33	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#104×C₄₇	—	2	1	no	—
35	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#10625350	—	2	2	no	—
37	#13094046	—	2	2	no	—
38	#13094046	—	2	2	no	—
39	#13094046	—	2	2	no	—
40	#13094046	—	2	2	no	—
41	#13094046	—	4	1	no	—
42	#13094046	—	4	1	no	—
43	#13094046	—	4	1	no	—
44	#13094046	—	4	1	no	—
45	C₂×Dic₁₈₈	—	2	1	no	—
46	C₂×Dic₁₈₈	C₂³	1	2	yes	—
47	C₂×#10625325	—	2	2	no	—
48	C₂×#10625325	—	2	2	no	—
49	C₂×D₃₇₆	—	2	1	no	—
50	C₂×D₃₇₆	C₂³	1	2	yes	—
51	#13094024	—	2	1	no	—
52	#13094021	—	2	1	no	—
53	#13094012	—	2	2	no	—
54	#13093998	—	4	2	no	—
55	C₄×D₁₈₈	—	4	2	no	—
56	#13093970	—	2	4	no	—
57	#13093968	—	2	4	no	—
58	#13093967	—	2	4	no	—
59	#13093965	—	2	4	no	—
60	#13093964	—	2	2	no	—
61	#13093964	C₂³	1	4	yes	—
62	C₂×C₄₇⋊C₁₆	—	2	2	no	—
63	C₂×#41×C₄₇	—	2	1	no	—
64	#135×C₄₇	—	2	1	no	—
65	#135×C₄₇	—	2	1	no	—
66	#135×C₄₇	D₄	1	2	yes	complemented
67	#135×C₄₇	C₂³	1	2	yes	—
68	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic, complemented
69	C₂×SD₁₆×C₄₇	—	2	1	no	—
70	C₂×D₈×C₄₇	D₄	1	1	yes	characteristic, complemented
71	#131×C₄₇	—	2	2	no	—
72	#131×C₄₇	—	2	2	no	—
73	#131×C₄₇	—	4	1	no	—
74	#131×C₄₇	—	4	1	no	—
75	C₂×M₁₆×C₄₇	—	2	1	no	—
76	C₂×M₁₆×C₄₇	—	4	1	no	—
77	C₂²×C₈×C₄₇	—	4	1	no	—
78	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
81	#108×C₄₇	—	2	1	no	—
82	#108×C₄₇	C₂³	1	2	yes	—
83	#104×C₄₇	—	2	2	no	—
84	#104×C₄₇	—	2	2	no	—
85	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
86	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
87	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
89	#41×C₄₇	—	2	2	no	—
90	#41×C₄₇	—	2	2	no	—
91	#41×C₄₇	—	4	1	no	—
92	#41×C₄₇	—	4	1	no	—
93	C₂×Q₈×C₄₇	—	2	1	no	—
94	C₂×D₄×C₄₇	—	2	1	no	—
95	C₂×D₄×C₄₇	—	4	1	no	—
96	C₂²×C₄×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	—	4	1	no	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂×C₂²⋊D₄₇	—	4	2	no	—
100	#10625350	—	4	2	no	—
101	#10625350	—	4	2	no	—
102	#10625350	—	4	2	no	—
103	#10625350	—	4	2	no	—
104	C₂×D₁₈₈	—	2	2	no	—
105	C₂×D₁₈₈	—	4	2	no	—
106	C₂×C₄×D₄₇	—	4	2	no	—
107	C₂×Dic₉₄	—	2	2	no	—
108	Q₁₆×C₄₇	—	2	1	no	—
109	Q₁₆×C₄₇	C₂×D₄	1	2	yes	—
110	SD₁₆×C₄₇	—	2	2	no	—
111	SD₁₆×C₄₇	—	2	2	no	—
112	D₈×C₄₇	—	2	1	no	—
113	D₈×C₄₇	C₂×D₄	1	2	yes	—
114	M₁₆×C₄₇	—	2	2	no	—
115	M₁₆×C₄₇	—	4	1	no	—
116	M₁₆×C₄₇	—	4	2	no	—
117	M₁₆×C₄₇	—	4	2	no	—
118	C₂×C₈×C₄₇	—	4	1	no	—
119	C₂×C₈×C₄₇	—	4	2	no	—
120	C₂×C₈×C₄₇	—	4	2	no	—
121	C₂×C₈×C₄₇	D₈	1	1	yes	characteristic
122	C₂×C₈×C₄₇	D₈	1	1	yes	characteristic
123	C₂×C₈×C₄₇	D₈	1	1	yes	characteristic
124	C₂×C₈×C₄₇	D₈	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	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
131	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
132	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
136	(C₂×D₄₇)⋊C₄	—	4	4	no	—
137	C₄⋊Dic₄₇	—	4	2	no	—
138	Dic₁₈₈	—	2	2	no	—
139	Dic₁₈₈	—	2	2	no	—
140	Dic₁₈₈	—	4	1	no	—
141	Dic₁₈₈	—	4	1	no	—
142	D₃₇₆	—	2	2	no	—
143	D₃₇₆	—	2	2	no	—
144	D₃₇₆	—	4	1	no	—
145	D₃₇₆	—	4	1	no	—
146	#10625325	—	4	2	no	—
147	#10625325	—	4	2	no	—
148	#10625325	—	4	2	no	—
149	#10625325	—	4	2	no	—
150	C₄₇⋊C₁₆	—	2	4	no	—
151	C₂³×C₄₇	—	4	1	no	—
152	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂²×D₄₇	—	4	2	no	—
154	Q₈×C₄₇	—	2	2	no	—
155	Q₈×C₄₇	—	4	1	no	—
156	D₄×C₄₇	—	2	2	no	—
157	D₄×C₄₇	—	4	2	no	—
158	D₄×C₄₇	—	4	2	no	—
159	D₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂²⋊D₄₇	—	8	2	no	—
173	C₂²⋊D₄₇	—	8	2	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	D₁₈₈	—	4	2	no	—
176	D₁₈₈	—	4	2	no	—
177	D₁₈₈	—	8	4	no	—
178	C₄×D₄₇	—	8	2	no	—
179	C₄×D₄₇	—	8	2	no	—
180	Dic₉₄	—	4	2	no	—
181	Dic₉₄	—	4	2	no	—
182	C₈×C₄₇	—	4	2	no	—
183	C₈×C₄₇	#121	1	1	yes	characteristic
184	C₈×C₄₇	#121	1	1	yes	characteristic
185	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
186	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
187	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
188	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
189	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
191	#33594	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	—	4	1	no	—
193	C₂²×C₄₇	—	4	2	no	—
194	C₂²×C₄₇	—	8	2	no	—
195	C₂²×C₄₇	#459	1	1	yes	characteristic
196	C₂²×C₄₇	#459	1	1	yes	characteristic
197	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₂×D₄₇	—	8	4	no	—
199	C₂×D₄₇	—	8	2	no	—
200	C₄×C₄₇	—	2	2	no	—
201	C₄×C₄₇	—	4	1	no	—
202	C₄×C₄₇	—	4	2	no	—
203	C₄×C₄₇	#459	1	1	yes	characteristic
204	C₄×C₄₇	#459	1	1	yes	characteristic
205	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
206	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
207	Dic₄₇	—	8	2	no	—
208	#3414	—	47	2	no	—
209	#3147	—	47	1	no	—
210	C₂×#443	D₄₇	1	1	yes	characteristic, complemented
211	#2214	—	47	2	no	—
212	#2213	—	47	2	no	—
213	#2212	—	47	4	no	—
214	C₂×#364	—	47	1	no	—
215	#2148	—	47	2	no	—
216	C₂×C₄₇	—	2	1	no	—
217	C₂×C₄₇	—	2	1	no	—
218	C₂×C₄₇	—	2	1	no	—
219	C₂×C₄₇	—	8	2	no	—
220	C₂×C₄₇	C₂×#459	1	1	yes	characteristic
221	D₄₇	—	16	2	no	—
222	C₂×#135	—	47	2	no	—
223	C₂×#135	—	94	1	no	—
224	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
225	C₂×#131	—	2	1	no	—
226	#532	—	94	1	no	—
227	#510	—	47	4	no	—
228	#510	—	94	2	no	—
229	#509	—	47	4	no	—
230	#509	—	94	2	no	—
231	#508	—	94	4	no	—
232	C₂×M₃₂	—	47	2	no	—
233	#495	—	47	2	no	—
234	#495	—	94	1	no	—
235	#494	—	47	1	no	—
236	#493	—	47	1	no	—
237	#492	—	94	1	no	—
238	#443	—	2	1	no	—
239	#443	—	2	1	no	—
240	#443	C₂×D₄₇	1	2	yes	—
241	#443	C₂×D₄₇	1	2	yes	—
242	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
243	C₂×#104	—	2	1	no	—
244	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
245	#364	—	47	2	no	—
246	#364	—	47	2	no	—
247	#362	—	47	4	no	—
248	#361	—	47	4	no	—
249	C₄₇	#33594	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	2	1	no	—
251	C₂×#41	—	94	2	no	—
252	#135	—	2	1	no	—
253	#135	—	2	1	no	—
254	#135	—	94	2	no	—
255	#135	—	94	2	no	—
256	#135	—	94	2	no	—
257	#135	—	94	2	no	—
258	#135	—	188	1	no	—
259	#135	—	188	1	no	—
260	#135	—	188	1	no	—
261	#135	—	188	1	no	—
262	#135	D₁₈₈	1	2	yes	complemented
263	#135	C₂²×D₄₇	1	2	yes	—
264	C₂×Q₁₆	—	47	2	no	—
265	C₂×Q₁₆	—	94	1	no	—
266	C₂×Q₁₆	D₁₈₈	1	1	yes	characteristic, complemented
267	C₂×SD₁₆	—	2	1	no	—
268	C₂×SD₁₆	—	94	2	no	—
269	C₂×SD₁₆	—	94	2	no	—
270	C₂×D₈	—	47	2	no	—
271	C₂×D₈	—	94	1	no	—
272	C₂×D₈	D₁₈₈	1	1	yes	characteristic, complemented
273	#131	—	2	2	no	—
274	#131	—	2	2	no	—
275	#131	—	4	1	no	—
276	#131	—	4	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	4	1	no	—
279	C₂²×C₈	—	4	1	no	—
280	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
282	C₄⋊Q₈	—	94	1	no	—
283	#127	—	94	1	no	—
284	#124	—	94	2	no	—
285	#121	—	188	2	no	—
286	C₄×D₄	—	188	2	no	—
287	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
288	Q₃₂	—	94	4	no	—
289	SD₃₂	—	94	4	no	—
290	SD₃₂	—	94	4	no	—
291	D₁₆	—	94	4	no	—
292	M₃₂	—	47	4	no	—
293	M₃₂	—	94	2	no	—
294	C₂×C₁₆	—	94	2	no	—
295	#108	—	2	1	no	—
296	#108	C₂²×D₄₇	1	2	yes	—
297	#104	—	2	2	no	—
298	#104	—	2	2	no	—
299	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
300	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
301	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
303	#41	—	2	2	no	—
304	#41	—	2	2	no	—
305	#41	—	4	1	no	—
306	#41	—	4	1	no	—
307	#41	—	188	2	no	—
308	#41	—	188	2	no	—
309	#41	—	188	2	no	—
310	#41	—	188	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	94	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	94	2	no	—
316	C₂×D₄	—	188	2	no	—
317	C₂×D₄	—	188	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	188	2	no	—
321	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
322	Q₁₆	—	2	1	no	—
323	Q₁₆	—	94	2	no	—
324	Q₁₆	—	94	2	no	—
325	Q₁₆	—	188	1	no	—
326	Q₁₆	—	188	1	no	—
327	Q₁₆	C₂×D₁₈₈	1	2	yes	—
328	SD₁₆	—	2	2	no	—
329	SD₁₆	—	2	2	no	—
330	SD₁₆	—	188	2	no	—
331	SD₁₆	—	188	2	no	—
332	SD₁₆	—	188	2	no	—
333	SD₁₆	—	188	2	no	—
334	D₈	—	2	1	no	—
335	D₈	—	94	2	no	—
336	D₈	—	94	2	no	—
337	D₈	—	188	1	no	—
338	D₈	—	188	1	no	—
339	D₈	C₂×D₁₈₈	1	2	yes	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	4	1	no	—
342	M₁₆	—	4	2	no	—
343	M₁₆	—	4	2	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	4	2	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	#10625334	1	1	yes	characteristic
348	C₂×C₈	#10625334	1	1	yes	characteristic
349	C₂×C₈	#10625334	1	1	yes	characteristic
350	C₂×C₈	#10625334	1	1	yes	characteristic
351	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
352	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
353	C₂×C₈	#10625350	1	1	yes	characteristic
354	C₂×C₈	#10625350	1	1	yes	characteristic
355	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
356	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
357	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
358	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
359	C₄⋊C₄	—	188	2	no	—
360	C₂²⋊C₄	—	188	4	no	—
361	C₄²	—	2	1	no	—
362	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
364	C₁₆	—	94	4	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	188	2	no	—
367	C₂³	#13094049	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	4	1	no	—
370	Q₈	—	188	2	no	—
371	Q₈	—	188	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	1	no	—
376	D₄	—	376	4	no	—
377	D₄	—	376	2	no	—
378	D₄	—	376	2	no	—
379	D₄	—	188	2	no	—
380	D₄	—	188	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	376	2	no	—
388	C₂×C₄	—	376	2	no	—
389	C₂×C₄	—	188	2	no	—
390	C₂×C₄	#13093998	1	1	yes	characteristic
391	C₂×C₄	#13093998	1	1	yes	characteristic
392	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
393	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
394	C₂×C₄	#13094049	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
396	C₈	—	4	2	no	—
397	C₈	#13093998	1	1	yes	characteristic
398	C₈	#13093998	1	1	yes	characteristic
399	C₈	C₂×#10625334	1	1	yes	characteristic
400	C₈	C₂×#10625334	1	1	yes	characteristic
401	C₈	C₂×#10625334	1	1	yes	characteristic
402	C₈	C₂×#10625334	1	1	yes	characteristic
403	C₈	C₂²×D₁₈₈	1	1	yes	characteristic
404	C₈	C₂×#10625350	1	1	yes	characteristic
405	C₂²	—	4	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	376	4	no	—
409	C₂²	—	376	2	no	—
410	C₂²	#15689318	1	1	yes	characteristic
411	C₂²	#15689318	1	1	yes	characteristic
412	C₂²	C₂×#13094049	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	376	2	no	—
417	C₄	#15689318	1	1	yes	characteristic
418	C₄	#15689318	1	1	yes	characteristic
419	C₄	C₂×#13093998	1	1	yes	characteristic
420	C₄	C₂²×#10625334	1	1	yes	characteristic
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	8	2	no	—
425	C₂	—	752	2	no	—
426	C₂	C₂×#15689318	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15689318
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₂×C₄₇×#443	C₂
socle	C₂×C₄₇	C₂×#459
hypercenter	C₂×#443	D₄₇
hypocenter	C₄₇	#33594
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
1. #20256522	C₂	semidirect
2. #20253816	C₂	semidirect
3. #20245469	C₂	semidirect
4. #20245464	C₂	semidirect
5. #20245457	C₂	semidirect
6. C₂×#15688944	C₂	semidirect
7. #20245135	C₂	semidirect
8. C₂×C₄₇×#443	C₂	semidirect
19. #15689507	C₂²	semidirect
20. #15689503	C₂²	semidirect
21. #15689500	C₂²	semidirect
23. #15688944	C₂²	semidirect
24. #15688944	C₂²	semidirect
25. #15688938	C₂²	semidirect
26. #15688935	C₂²	semidirect
66. #135×C₄₇	D₄	semidirect
68. C₂×Q₁₆×C₄₇	D₄	semidirect
70. C₂×D₈×C₄₇	D₄	semidirect
210. C₂×#443	D₄₇	semidirect
249. C₄₇	#33594	semidirect
262. #135	D₁₈₈	semidirect
266. C₂×Q₁₆	D₁₈₈	semidirect
272. C₂×D₈	D₁₈₈	semidirect

Maximal subgroups

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

subgroup	index
#20256522	2
#20253816	2
#20245469	2
#20245464	2
#20245457	2
C₂×#15688944	2
#20245135	2
C₂×C₄₇×#443	2
#33594	47