Subgroups — #26370818

Order 12032.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689540	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253036	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245503	C₂	1	2	yes	maximal, complemented
5	#20245489	C₂	1	2	yes	maximal, complemented
6	#20245486	C₂	1	2	yes	maximal, complemented
7	#20245472	C₂	1	2	yes	maximal, complemented
8	#20245174	C₂	1	1	yes	maximal, characteristic, complemented
9	#20245095	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688923	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3061	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
13	#15689687	—	2	1	no	—
14	#15689558	—	2	4	no	—
15	C₂×#13093967	C₂²	1	2	yes	—
16	C₂×#13093965	C₂²	1	2	yes	—
17	#15689540	—	2	4	no	—
18	C₂×#13093964	C₂²	1	1	yes	characteristic
19	C₂×#13093964	C₂²	1	2	yes	complemented
20	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₄₇⋊C₁₆	C₂²	1	2	yes	complemented
22	#15689376	—	2	2	no	—
23	#15689359	C₂²	1	2	yes	—
24	#15689359	C₂²	1	2	yes	—
25	#15689161	C₂²	1	1	yes	characteristic
26	#15689129	—	2	1	no	—
27	#15688950	C₂²	1	2	yes	complemented
28	#15688948	C₂²	1	2	yes	complemented
29	#15688927	C₂²	1	1	yes	characteristic, complemented
30	#15688927	C₂²	1	1	yes	characteristic, complemented
31	#15688924	C₂²	1	1	yes	characteristic, complemented
32	#15688924	C₂²	1	1	yes	characteristic, complemented
33	#15688923	C₂²	1	2	yes	—
34	#15688923	C₂²	1	2	yes	—
35	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#537	—	2	1	no	—
38	C₄₇×#468	—	2	2	no	—
39	C₄₇×#467	C₂²	1	2	yes	complemented
40	C₄₇×#466	C₂²	1	2	yes	complemented
41	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#417	—	2	1	no	—
43	C₂²×D₁₈₈	—	2	1	no	—
44	C₂×D₃₇₆	—	2	2	no	—
45	C₂×D₃₇₆	—	2	2	no	—
46	C₂×D₃₇₆	—	2	1	no	—
47	C₂×D₃₇₆	C₂³	1	2	yes	—
48	#13094020	—	4	1	no	—
49	#13094013	—	4	1	no	—
50	#13093998	—	2	2	no	—
51	#13093998	—	2	2	no	—
52	#13093992	—	4	2	no	—
53	#13093983	—	2	1	no	—
54	#13093967	—	2	4	no	—
55	#13093965	—	2	4	no	—
56	#13093964	—	2	4	no	—
57	#13093964	D₄	1	4	yes	complemented
58	C₂×C₄₇⋊C₁₆	—	2	2	no	—
59	C₂×C₄₇⋊C₁₆	—	2	4	no	—
60	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
63	#13093958	C₂³	1	1	yes	characteristic
64	#13093958	C₂³	1	1	yes	characteristic
65	#13093956	—	2	1	no	—
66	#13093946	—	2	2	no	—
67	#13093946	—	2	2	no	—
68	C₂×#41×C₄₇	—	2	1	no	—
69	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
70	#135×C₄₇	—	2	2	no	—
71	#135×C₄₇	—	2	2	no	—
72	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×SD₁₆×C₄₇	—	2	1	no	—
74	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
75	#131×C₄₇	—	2	2	no	—
76	#131×C₄₇	—	2	2	no	—
77	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
78	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂²⋊Q₈×C₄₇	—	2	2	no	—
82	C₂²⋊Q₈×C₄₇	—	4	1	no	—
83	#121×C₄₇	—	2	2	no	—
84	#121×C₄₇	—	4	1	no	—
85	#121×C₄₇	—	4	2	no	—
86	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
87	#107×C₄₇	—	2	1	no	—
88	#107×C₄₇	C₂³	1	2	yes	—
89	#103×C₄₇	—	2	2	no	—
90	#102×C₄₇	—	2	2	no	—
91	C₂³×D₄₇	—	4	1	no	—
92	#41×C₄₇	—	2	2	no	—
93	#41×C₄₇	—	2	2	no	—
94	#41×C₄₇	—	4	2	no	—
95	#41×C₄₇	—	4	2	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	D₈	1	1	yes	characteristic
98	C₂×D₄×C₄₇	—	2	1	no	—
99	C₂×D₄×C₄₇	—	4	1	no	—
100	C₂×D₄×C₄₇	—	4	2	no	—
101	C₂×D₄×C₄₇	D₈	1	2	yes	—
102	C₂×D₄×C₄₇	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	—	4	1	no	—
104	C₂²×C₄×C₄₇	—	4	1	no	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂×C₂²⋊D₄₇	—	4	2	no	—
108	C₂×C₂²⋊D₄₇	—	4	2	no	—
109	C₂×D₁₈₈	—	2	2	no	—
110	C₂×D₁₈₈	—	4	2	no	—
111	C₂×D₁₈₈	—	4	2	no	—
112	C₂×D₁₈₈	—	4	1	no	—
113	Q₁₆×C₄₇	—	2	1	no	—
114	Q₁₆×C₄₇	—	2	1	no	—
115	SD₁₆×C₄₇	—	4	2	no	—
116	D₈×C₄₇	—	2	1	no	—
117	D₈×C₄₇	—	2	1	no	—
118	M₁₆×C₄₇	—	2	2	no	—
119	M₁₆×C₄₇	—	2	4	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₄₇	#41	1	2	yes	—
126	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	—	4	1	no	—
129	C₄⋊C₄×C₄₇	—	4	2	no	—
130	C₂²⋊C₄×C₄₇	—	4	2	no	—
131	C₂²⋊C₄×C₄₇	—	4	2	no	—
132	C₂²⋊Dic₄₇	—	4	1	no	—
133	(C₂×D₄₇)⋊C₄	—	4	2	no	—
134	(C₂×D₄₇)⋊C₄	—	4	2	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	C₄⋊Dic₄₇	—	2	1	no	—
137	C₄×Dic₄₇	—	4	1	no	—
138	D₃₇₆	—	2	2	no	—
139	D₃₇₆	—	2	2	no	—
140	D₃₇₆	—	4	2	no	—
141	C₄₇⋊C₁₆	—	2	1	no	—
142	C₄₇⋊C₁₆	—	2	1	no	—
143	C₄₇⋊C₁₆	C₂×D₄	1	4	yes	—
144	C₂³×C₄₇	—	4	1	no	—
145	C₂³×C₄₇	C₂×D₈	1	2	yes	—
146	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
147	C₂²×D₄₇	—	4	2	no	—
148	C₂²×D₄₇	—	8	2	no	—
149	C₂²×D₄₇	—	16	1	no	—
150	C₂²×D₄₇	—	16	1	no	—
151	Q₈×C₄₇	—	2	2	no	—
152	Q₈×C₄₇	—	4	1	no	—
153	Q₈×C₄₇	—	4	1	no	—
154	D₄×C₄₇	—	2	4	no	—
155	D₄×C₄₇	—	2	2	no	—
156	D₄×C₄₇	—	4	1	no	—
157	D₄×C₄₇	—	4	1	no	—
158	D₄×C₄₇	—	8	2	no	—
159	D₄×C₄₇	—	16	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	8	2	no	—
165	C₂×C₄×C₄₇	—	16	1	no	—
166	C₂×C₄×C₄₇	#121	1	2	yes	—
167	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
168	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₄₇	#135	1	2	yes	—
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂²⋊D₄₇	—	16	2	no	—
172	C₂²⋊D₄₇	—	16	2	no	—
173	C₂×Dic₄₇	—	4	1	no	—
174	C₂×Dic₄₇	—	4	1	no	—
175	D₁₈₈	—	4	2	no	—
176	D₁₈₈	—	4	2	no	—
177	D₁₈₈	—	8	2	no	—
178	C₈×C₄₇	—	2	2	no	—
179	C₈×C₄₇	#121	1	2	yes	—
180	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
182	#33612	—	47	1	no	maximal, Sylow
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	8	1	no	—
189	C₂²×C₄₇	—	8	1	no	—
190	C₂²×C₄₇	—	8	1	no	—
191	C₂²×C₄₇	#466	1	2	yes	—
192	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
193	C₂×D₄₇	—	8	2	no	—
194	C₂×D₄₇	—	8	2	no	—
195	C₂×D₄₇	—	8	2	no	—
196	C₂×D₄₇	—	16	4	no	—
197	C₄×C₄₇	—	2	2	no	—
198	C₄×C₄₇	—	8	2	no	—
199	C₄×C₄₇	—	8	1	no	—
200	C₄×C₄₇	#466	1	2	yes	—
201	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
202	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
203	Dic₄₇	—	8	1	no	—
204	Dic₄₇	—	8	1	no	—
205	C₂×#509	—	47	1	no	—
206	C₂×#504	—	47	1	no	—
207	#3061	D₄₇	1	1	yes	characteristic, complemented
208	#3058	—	47	1	no	—
209	#2220	—	47	2	no	—
210	#2218	—	47	2	no	—
211	#2217	—	47	2	no	—
212	#2215	—	47	2	no	—
213	#2159	—	47	1	no	—
214	#2138	—	47	1	no	—
215	C₂×#357	—	47	1	no	—
216	C₂×C₄₇	—	2	2	no	—
217	C₂×C₄₇	—	4	2	no	—
218	C₂×C₄₇	—	16	1	no	—
219	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
220	C₂×C₄₇	#3415	1	1	yes	characteristic
221	C₂×C₄₇	#3416	1	1	yes	characteristic
222	D₄₇	—	16	2	no	—
223	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
224	C₂²×D₈	—	47	1	no	—
225	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
226	#537	—	2	1	no	—
227	#535	—	94	1	no	—
228	#509	—	94	4	no	—
229	C₂×SD₃₂	—	47	2	no	—
230	C₂×D₁₆	—	47	2	no	—
231	#504	—	94	4	no	—
232	C₂×M₃₂	—	47	1	no	—
233	C₂×M₃₂	—	47	2	no	—
234	C₂²×C₁₆	—	47	1	no	—
235	C₂²×C₁₆	—	47	2	no	—
236	#469	—	94	2	no	—
237	#468	—	2	2	no	—
238	#467	C₂×D₄₇	1	2	yes	complemented
239	#466	—	47	2	no	—
240	#466	—	47	2	no	—
241	#466	C₂×D₄₇	1	2	yes	complemented
242	#427	—	47	1	no	—
243	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
244	#418	—	94	1	no	—
245	#417	—	2	1	no	—
246	#367	—	47	2	no	—
247	#366	—	47	2	no	—
248	#358	—	47	1	no	—
249	#358	—	47	1	no	—
250	#357	—	47	1	no	—
251	#357	—	47	1	no	—
252	#357	—	47	2	no	—
253	#357	—	47	2	no	—
254	C₄₇	#33612	1	1	yes	characteristic, complemented, Sylow
255	C₂×#41	—	2	1	no	—
256	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
257	C₂²×D₄	—	94	1	no	—
258	#135	—	2	2	no	—
259	#135	—	2	2	no	—
260	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
261	C₂×SD₁₆	—	2	1	no	—
262	C₂×D₈	—	47	2	no	—
263	C₂×D₈	—	94	2	no	—
264	C₂×D₈	—	94	2	no	—
265	C₂×D₈	—	94	1	no	—
266	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
267	#131	—	2	2	no	—
268	#131	—	2	2	no	—
269	C₂×M₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
270	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
271	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
272	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
273	#127	—	188	1	no	—
274	#124	—	188	1	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₂²⋊Q₈	—	4	1	no	—
277	#121	—	2	2	no	—
278	#121	—	4	1	no	—
279	#121	—	4	2	no	—
280	#121	—	94	2	no	—
281	#121	—	94	2	no	—
282	#120	—	188	2	no	—
283	#117	—	94	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	SD₃₂	—	94	4	no	—
286	D₁₆	—	94	4	no	—
287	M₃₂	—	47	4	no	—
288	M₃₂	—	94	4	no	—
289	C₂×C₁₆	—	47	2	no	—
290	C₂×C₁₆	—	47	1	no	—
291	C₂×C₁₆	—	47	1	no	—
292	C₂×C₁₆	—	94	4	no	—
293	C₂×C₁₆	—	94	2	no	—
294	#107	—	2	1	no	—
295	#107	—	47	1	no	—
296	#107	—	47	1	no	—
297	#107	C₂²×D₄₇	1	2	yes	—
298	#106	—	94	1	no	—
299	#103	—	2	2	no	—
300	#102	—	2	2	no	—
301	#102	—	94	2	no	—
302	#102	—	94	2	no	—
303	C₂⁴	—	188	1	no	—
304	#41	—	2	2	no	—
305	#41	—	2	2	no	—
306	#41	—	4	2	no	—
307	#41	—	4	2	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	#10625334	1	1	yes	characteristic
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	94	2	no	—
314	C₂×D₄	—	188	2	no	—
315	C₂×D₄	—	188	2	no	—
316	C₂×D₄	—	188	2	no	—
317	C₂×D₄	—	188	1	no	—
318	C₂×D₄	—	188	2	no	—
319	C₂×D₄	#10625334	1	2	yes	—
320	C₂×D₄	#10625334	1	1	yes	characteristic
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
324	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
325	Q₁₆	—	2	1	no	—
326	Q₁₆	—	2	1	no	—
327	SD₁₆	—	4	2	no	—
328	D₈	—	2	1	no	—
329	D₈	—	2	1	no	—
330	D₈	—	94	2	no	—
331	D₈	—	94	2	no	—
332	D₈	—	188	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	4	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	D₄×D₄₇	1	2	yes	—
338	C₂×C₈	#10625352	1	2	yes	—
339	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
340	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
341	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	94	1	no	—
346	C₄⋊C₄	—	94	1	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	188	1	no	—
350	C₂²⋊C₄	—	188	2	no	—
351	C₂²⋊C₄	—	188	2	no	—
352	C₄²	—	188	1	no	—
353	C₁₆	—	47	4	no	—
354	C₁₆	—	94	1	no	—
355	C₁₆	—	94	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	376	2	no	—
358	C₂³	—	188	2	no	—
359	C₂³	—	752	1	no	—
360	C₂³	—	752	1	no	—
361	C₂³	C₂×#10625334	1	2	yes	—
362	C₂³	C₂×#10625334	1	1	yes	characteristic
363	Q₈	—	2	2	no	—
364	Q₈	—	4	1	no	—
365	Q₈	—	4	1	no	—
366	D₄	—	2	4	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	D₄	—	8	2	no	—
371	D₄	—	16	2	no	—
372	D₄	—	376	2	no	—
373	D₄	—	188	2	no	—
374	D₄	—	188	2	no	—
375	D₄	—	752	2	no	—
376	D₄	—	752	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	—	16	1	no	—
383	C₂×C₄	—	188	1	no	—
384	C₂×C₄	—	188	1	no	—
385	C₂×C₄	#13093996	1	2	yes	—
386	C₂×C₄	C₂×#10625334	1	2	yes	—
387	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
388	C₂×C₄	#13094044	1	2	yes	—
389	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	#13093996	1	2	yes	—
392	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
393	C₈	C₂×#10625352	1	1	yes	characteristic
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	376	2	no	—
403	C₂²	—	376	2	no	—
404	C₂²	—	376	2	no	—
405	C₂²	—	752	4	no	—
406	C₂²	#15689357	1	2	yes	—
407	C₂²	C₂²×#10625334	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	1	no	—
411	C₄	—	376	1	no	—
412	C₄	—	376	1	no	—
413	C₄	#15689357	1	2	yes	—
414	C₄	C₂×#13093996	1	1	yes	characteristic
415	C₄	C₂×#13094044	1	1	yes	characteristic
416	C₂	—	2	2	no	—
417	C₂	—	4	2	no	—
418	C₂	—	16	1	no	—
419	C₂	—	752	2	no	—
420	C₂	C₂×#15689357	1	1	yes	characteristic
421	C₂	#20256527	1	1	yes	characteristic
422	C₂	#20256532	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#10625334
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#3061	C₂
socle	C₂²×C₄₇	C₂²×D₈
hypercenter	#3061	D₄₇
hypocenter	C₄₇	#33612
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×#41 ◁ C₂×#131 ◁ #3061

Complements

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

N	H ≅ G/N	type
1. C₂×#15689558	C₂	semidirect
2. C₂×#15689540	C₂	semidirect
3. #20253036	C₂	semidirect
4. #20245503	C₂	semidirect
5. #20245489	C₂	semidirect
6. #20245486	C₂	semidirect
7. #20245472	C₂	semidirect
8. #20245174	C₂	semidirect
9. #20245095	C₂	semidirect
10. C₂×#15688923	C₂	semidirect
11. C₄₇×#3061	C₂	semidirect
19. C₂×#13093964	C₂²	semidirect
21. C₂²×C₄₇⋊C₁₆	C₂²	semidirect
27. #15688950	C₂²	semidirect
28. #15688948	C₂²	semidirect
29. #15688927	C₂²	semidirect
30. #15688927	C₂²	semidirect
31. #15688924	C₂²	semidirect
32. #15688924	C₂²	semidirect
39. C₄₇×#467	C₂²	semidirect
40. C₄₇×#466	C₂²	semidirect
57. #13093964	D₄	semidirect
207. #3061	D₄₇	semidirect
238. #467	C₂×D₄₇	semidirect
241. #466	C₂×D₄₇	semidirect
254. C₄₇	#33612	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689558	2
C₂×#15689540	2
#20253036	2
#20245503	2
#20245489	2
#20245486	2
#20245472	2
#20245174	2
#20245095	2
C₂×#15688923	2
C₄₇×#3061	2
#33612	47