Subgroups — #26123550

Order 12032.

974 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	C₂×#15689172	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689087	C₂	1	2	yes	maximal
3	#20243114	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₇⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×#407	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×#10625329	C₂²	1	2	yes	—
8	#15689172	—	2	4	no	—
9	C₂×#13093960	—	2	2	no	—
10	#15689087	—	2	4	no	—
11	#15689087	—	2	4	no	—
12	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
13	#15688887	—	2	4	no	—
14	C₄₇⋊#338	—	2	2	no	—
15	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#407	—	2	2	no	—
19	C₄₇×#407	C₄	1	4	yes	—
20	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
21	C₂×#10625329	—	2	2	no	—
22	C₂×#10625329	—	2	2	no	—
23	C₂×#10625329	—	2	2	no	—
24	C₂×#10625329	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	—	2	2	no	—
32	C₂×#10625329	D₄	1	4	yes	—
33	C₂²×C₄₇⋊C₈	—	2	2	no	—
34	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
35	#13093960	—	2	8	no	—
36	C₂²⋊(C₄₇⋊C₈)	—	2	16	no	—
37	C₂⁵×C₄₇	Q₈	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	—	2	2	no	—
39	C₂³×C₄×C₄₇	—	2	2	no	—
40	C₂³×C₄×C₄₇	—	2	1	no	—
41	C₂³×C₄×C₄₇	—	2	1	no	—
42	C₂³×C₄×C₄₇	—	2	1	no	—
43	C₂³×C₄×C₄₇	—	2	1	no	—
44	C₂³×C₄×C₄₇	—	2	2	no	—
45	C₂³×C₄×C₄₇	—	2	2	no	—
46	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₄₇	D₄	1	2	yes	—
48	C₂³×C₄×C₄₇	Q₈	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₄₇	—	2	2	no	—
51	C₂×M₁₆×C₄₇	—	2	2	no	—
52	C₂×M₁₆×C₄₇	—	2	1	no	—
53	C₂×M₁₆×C₄₇	—	2	2	no	—
54	C₂×M₁₆×C₄₇	—	2	2	no	—
55	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
56	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
58	C₂²×C₈×C₄₇	—	2	1	no	—
59	C₂²×C₈×C₄₇	D₄	1	2	yes	—
60	C₂²⋊C₈×C₄₇	—	2	8	no	—
61	C₂⁴×C₄₇	—	2	1	no	—
62	C₂⁴×C₄₇	—	2	2	no	—
63	C₂⁴×C₄₇	—	2	1	no	—
64	C₂⁴×C₄₇	—	2	2	no	—
65	C₂⁴×C₄₇	—	4	4	no	—
66	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
67	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	—	2	1	no	—
69	C₂²×C₄×C₄₇	—	2	1	no	—
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	—	2	4	no	—
75	C₂²×C₄×C₄₇	—	2	4	no	—
76	C₂²×C₄×C₄₇	—	2	4	no	—
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	4	1	no	—
81	C₂²×C₄×C₄₇	—	4	2	no	—
82	C₂²×C₄×C₄₇	—	4	2	no	—
83	C₂²×C₄×C₄₇	—	4	2	no	—
84	C₂²×C₄×C₄₇	—	4	1	no	—
85	C₂²×C₄×C₄₇	—	4	2	no	—
86	C₂²×C₄×C₄₇	—	4	2	no	—
87	C₂²×C₄×C₄₇	—	4	1	no	—
88	C₂²×C₄×C₄₇	—	4	2	no	—
89	C₂²×C₄×C₄₇	—	4	1	no	—
90	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	#41	1	2	yes	—
100	C₂²×C₄×C₄₇	#41	1	2	yes	—
101	M₁₆×C₄₇	—	2	4	no	—
102	M₁₆×C₄₇	—	2	4	no	—
103	M₁₆×C₄₇	—	2	4	no	—
104	M₁₆×C₄₇	—	4	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	4	1	no	—
109	C₂×C₈×C₄₇	—	4	1	no	—
110	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
111	#10625329	—	2	4	no	—
112	#10625329	—	2	4	no	—
113	#10625329	—	4	2	no	—
114	#10625329	—	4	2	no	—
115	#10625329	—	4	2	no	—
116	#10625329	—	4	2	no	—
117	#10625329	—	4	2	no	—
118	#10625329	—	4	2	no	—
119	C₂×C₄₇⋊C₈	—	2	4	no	—
120	C₂×C₄₇⋊C₈	—	2	4	no	—
121	C₂×C₄₇⋊C₈	—	2	4	no	—
122	C₂×C₄₇⋊C₈	—	2	4	no	—
123	C₂×C₄₇⋊C₈	—	4	2	no	—
124	C₂×C₄₇⋊C₈	—	4	2	no	—
125	C₂³×C₄₇	—	2	8	no	—
126	C₂³×C₄₇	—	2	4	no	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	—	2	4	no	—
129	C₂³×C₄₇	—	4	4	no	—
130	C₂³×C₄₇	—	4	2	no	—
131	C₂³×C₄₇	—	4	4	no	—
132	C₂³×C₄₇	—	4	2	no	—
133	C₂³×C₄₇	—	4	8	no	—
134	C₂³×C₄₇	—	4	4	no	—
135	C₂³×C₄₇	—	4	1	no	—
136	C₂³×C₄₇	—	4	2	no	—
137	C₂³×C₄₇	—	4	1	no	—
138	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
140	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
141	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	4	1	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	1	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	4	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	4	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
159	C₂×C₄×C₄₇	#120	1	2	yes	—
160	C₂×C₄×C₄₇	#121	1	2	yes	—
161	C₂×C₄×C₄₇	#121	1	2	yes	—
162	C₂×C₄×C₄₇	#121	1	2	yes	—
163	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#123	1	2	yes	—
167	C₂×C₄×C₄₇	#123	1	2	yes	—
168	C₂×C₄×C₄₇	#124	1	2	yes	—
169	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
170	C₂×C₄×C₄₇	#126	1	2	yes	—
171	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
172	C₈×C₄₇	—	2	4	no	—
173	C₈×C₄₇	—	4	2	no	—
174	C₄₇⋊C₈	—	4	4	no	—
175	C₄₇⋊C₈	—	4	4	no	—
176	#11101	—	47	1	no	maximal, Sylow
177	C₂²×C₄₇	—	2	4	no	—
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	—	2	4	no	—
180	C₂²×C₄₇	—	2	8	no	—
181	C₂²×C₄₇	—	4	1	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	—	4	1	no	—
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	—	4	4	no	—
186	C₂²×C₄₇	—	4	4	no	—
187	C₂²×C₄₇	—	4	8	no	—
188	C₂²×C₄₇	—	4	4	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	#380	1	1	yes	characteristic
191	C₂²×C₄₇	#385	1	2	yes	—
192	C₂²×C₄₇	#393	1	1	yes	characteristic
193	C₂²×C₄₇	#396	1	2	yes	—
194	C₂²×C₄₇	#399	1	1	yes	characteristic
195	C₄×C₄₇	—	4	2	no	—
196	C₄×C₄₇	#386	1	1	yes	characteristic
197	C₄×C₄₇	#388	1	2	yes	—
198	C₄×C₄₇	#390	1	1	yes	characteristic
199	C₄×C₄₇	#392	1	1	yes	characteristic
200	C₄×C₄₇	#394	1	2	yes	—
201	C₄×C₄₇	#397	1	1	yes	characteristic
202	C₂×#430	—	47	1	no	—
203	C₂×#407	—	47	2	no	—
204	C₂×#407	D₄₇	1	1	yes	characteristic
205	#1738	—	47	2	no	—
206	C₂×#338	—	47	1	no	—
207	C₂×C₄₇	—	2	1	no	—
208	C₂×C₄₇	—	2	2	no	—
209	C₂×C₄₇	—	2	1	no	—
210	C₂×C₄₇	—	2	2	no	—
211	C₂×C₄₇	—	4	4	no	—
212	C₂×C₄₇	#1439	1	1	yes	characteristic
213	C₂×C₄₇	#2091	1	2	yes	—
214	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
215	C₂²×M₁₆	—	47	2	no	—
216	C₂²×M₁₆	—	47	2	no	—
217	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
218	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
219	#430	—	94	4	no	—
220	C₂×#108	—	94	2	no	—
221	#407	—	2	2	no	—
222	#407	—	94	4	no	—
223	#407	—	94	4	no	—
224	#407	Dic₄₇	1	4	yes	—
225	C₂×C₂²⋊C₈	—	2	2	no	—
226	C₂×C₂²⋊C₈	—	94	4	no	—
227	#341	—	94	4	no	—
228	#338	—	94	2	no	—
229	C₄₇	#11101	1	1	yes	characteristic, complemented, Sylow
230	C₂⁵	Dic₉₄	1	1	yes	characteristic
231	C₂³×C₄	—	2	1	no	—
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	—	2	2	no	—
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	—	2	1	no	—
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	Dic₉₄	1	1	yes	characteristic
240	C₂³×C₄	D₁₈₈	1	2	yes	—
241	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
242	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	47	4	no	—
249	C₂×M₁₆	—	94	2	no	—
250	C₂×M₁₆	—	94	2	no	—
251	C₂×M₁₆	—	94	2	no	—
252	C₂×M₁₆	—	94	2	no	—
253	C₂×M₁₆	—	94	2	no	—
254	C₂×M₁₆	—	94	2	no	—
255	C₂×M₁₆	—	94	2	no	—
256	C₂×M₁₆	—	94	2	no	—
257	C₂×M₁₆	—	94	2	no	—
258	C₂×M₁₆	—	94	2	no	—
259	C₂×M₁₆	—	94	2	no	—
260	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
261	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
262	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	47	4	no	—
265	C₂²×C₈	—	94	2	no	—
266	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
267	#108	—	94	8	no	—
268	C₂²⋊C₈	—	2	8	no	—
269	C₂²⋊C₈	—	94	16	no	—
270	C₂⁴	—	2	2	no	—
271	C₂⁴	—	2	1	no	—
272	C₂⁴	—	2	2	no	—
273	C₂⁴	—	2	1	no	—
274	C₂⁴	—	4	4	no	—
275	C₂⁴	C₄⋊Dic₄₇	1	2	yes	—
276	C₂⁴	C₂×Dic₉₄	1	1	yes	characteristic
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
300	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
301	C₂²×C₄	#10625350	1	1	yes	characteristic
302	C₂²×C₄	#10625350	1	1	yes	characteristic
303	C₂²×C₄	D₄×D₄₇	1	2	yes	—
304	C₂²×C₄	D₄×D₄₇	1	2	yes	—
305	C₂²×C₄	#10625352	1	2	yes	—
306	C₂²×C₄	#10625352	1	2	yes	—
307	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
310	M₁₆	—	2	4	no	—
311	M₁₆	—	2	4	no	—
312	M₁₆	—	2	4	no	—
313	M₁₆	—	4	2	no	—
314	M₁₆	—	94	4	no	—
315	M₁₆	—	94	4	no	—
316	M₁₆	—	188	2	no	—
317	M₁₆	—	188	2	no	—
318	M₁₆	—	188	2	no	—
319	M₁₆	—	188	2	no	—
320	M₁₆	—	188	2	no	—
321	M₁₆	—	188	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	94	4	no	—
328	C₂×C₈	—	94	4	no	—
329	C₂×C₈	—	94	4	no	—
330	C₂×C₈	—	94	4	no	—
331	C₂×C₈	—	188	2	no	—
332	C₂×C₈	—	188	2	no	—
333	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
334	C₂³	—	2	8	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	4	4	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	8	no	—
343	C₂³	—	4	4	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	1	no	—
347	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
348	C₂³	#13094001	1	2	yes	—
349	C₂³	#13094001	1	2	yes	—
350	C₂³	#13094003	1	1	yes	characteristic
351	C₂³	#13094003	1	1	yes	characteristic
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
364	C₂×C₄	#13093983	1	1	yes	characteristic
365	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
366	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
367	C₂×C₄	#13093992	1	1	yes	characteristic
368	C₂×C₄	#13093994	1	2	yes	—
369	C₂×C₄	#13093995	1	2	yes	—
370	C₂×C₄	#13093996	1	2	yes	—
371	C₂×C₄	#13093997	1	2	yes	—
372	C₂×C₄	#13093998	1	1	yes	characteristic
373	C₂×C₄	#13093998	1	1	yes	characteristic
374	C₂×C₄	#13094005	1	1	yes	characteristic
375	C₂×C₄	#13094006	1	2	yes	—
376	C₂×C₄	#13094008	1	2	yes	—
377	C₂×C₄	#13094010	1	2	yes	—
378	C₂×C₄	#13094011	1	1	yes	characteristic
379	C₂×C₄	#13094017	1	2	yes	—
380	C₂×C₄	#13094020	1	1	yes	characteristic
381	C₈	—	2	4	no	—
382	C₈	—	4	2	no	—
383	C₈	—	188	4	no	—
384	C₈	—	188	4	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	8	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	2	no	—
398	C₂²	#15688983	1	1	yes	characteristic
399	C₂²	#15688998	1	2	yes	—
400	C₂²	#15689035	1	1	yes	characteristic
401	C₂²	#15689046	1	2	yes	—
402	C₂²	#15689059	1	1	yes	characteristic
403	C₄	—	4	2	no	—
404	C₄	#15689003	1	1	yes	characteristic
405	C₄	#15689016	1	2	yes	—
406	C₄	#15689026	1	1	yes	characteristic
407	C₄	#15689032	1	1	yes	characteristic
408	C₄	#15689039	1	2	yes	—
409	C₄	#15689048	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	2	no	—
412	C₂	—	2	1	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	4	no	—
415	C₂	#20241633	1	1	yes	characteristic
416	C₂	#20244904	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13094020
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#407	C₂
socle	C₂²×C₄₇	#399
prime radical	C₂⁵×C₄₇	Q₈
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#407	D₄₇
hypocenter	C₄₇	#11101
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#407

Complements

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

N	H ≅ G/N	type
1. C₂×#15689172	C₂	semidirect
3. #20243114	C₂	semidirect
4. C₂×C₄₇⋊#338	C₂	semidirect
229. C₄₇	#11101	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689172	2
C₂×#15689087	2
#20243114	2
C₂×C₄₇⋊#338	2
C₂×C₄₇×#407	2
#11101	47