Subgroups — #26187211

Order 12032.

602 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	#20253428	C₂	1	1	yes	maximal, characteristic
2	#20252339	C₂	1	1	yes	maximal, characteristic
3	#20252331	C₂	1	1	yes	maximal, characteristic
4	#20242284	C₂	1	2	yes	maximal, complemented
5	#20242237	C₂	1	2	yes	maximal, complemented
6	#20242237	C₂	1	2	yes	maximal, complemented
7	#20242194	C₂	1	2	yes	maximal, complemented
8	#20241842	C₂	1	1	yes	maximal, characteristic
9	C₂×#15688853	C₂	1	1	yes	maximal, characteristic
10	#20241669	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1571	C₂	1	1	yes	maximal, characteristic
12	#15689680	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
14	#15689459	C₄	1	2	yes	—
15	#15689419	C₄	1	1	yes	characteristic
16	#15689419	C₄	1	1	yes	characteristic
17	#15689334	C₄	1	1	yes	characteristic
18	#15689334	C₄	1	1	yes	characteristic
19	#15689281	C₄	1	2	yes	—
20	#15689252	—	2	2	no	—
21	#15689252	—	2	2	no	—
22	#15689250	C₂²	1	2	yes	—
23	#15689250	C₂²	1	2	yes	—
24	#15689247	C₂²	1	2	yes	—
25	#15689247	C₂²	1	2	yes	—
26	C₄×Dic₁₈₈	C₂²	1	2	yes	—
27	C₄×Dic₁₈₈	C₂²	1	2	yes	—
28	#15689149	—	2	1	no	—
29	#15689146	—	2	1	no	—
30	#15689078	—	2	1	no	—
31	C₄×#10625329	C₂²	1	1	yes	characteristic
32	M₁₆×Dic₄₇	—	2	1	no	—
33	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
34	#15688853	C₂²	1	1	yes	characteristic
35	#15688853	C₂²	1	2	yes	—
36	#15688853	C₂²	1	1	yes	characteristic
37	#15688853	C₂²	1	1	yes	characteristic
38	#15688853	C₂²	1	2	yes	—
39	#15688853	C₂²	1	1	yes	characteristic
40	#15688845	C₂²	1	2	yes	—
41	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
42	C₄₇×#431	C₂²	1	1	yes	characteristic
43	C₄₇×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#335	C₂²	1	2	yes	—
46	C₄₇×#335	C₂²	1	2	yes	—
47	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
48	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
49	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
50	C₂×#10625329	D₄	1	1	yes	characteristic
51	C₂×#10625329	D₄	1	1	yes	characteristic
52	C₂²×C₄₇⋊C₈	—	2	1	no	—
53	#13094024	C₂×C₄	1	1	yes	characteristic
54	#13094024	C₂×C₄	1	1	yes	characteristic
55	#13094016	—	2	1	no	—
56	#13094003	—	2	1	no	—
57	#13094003	C₂×C₄	1	2	yes	—
58	C₄×Dic₉₄	—	2	1	no	—
59	C₄×Dic₉₄	—	2	1	no	—
60	C₄×Dic₉₄	—	2	1	no	—
61	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
64	C₄×Dic₉₄	C₂³	1	2	yes	—
65	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
66	#13093983	—	2	1	no	—
67	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₄₇⋊C₄	—	2	1	no	—
69	C₂×C₄×Dic₄₇	—	2	1	no	—
70	#13093958	C₂×C₄	1	2	yes	—
71	#13093958	C₂×C₄	1	2	yes	—
72	Dic₄₇⋊C₈	—	2	2	no	—
73	Dic₄₇⋊C₈	—	2	2	no	—
74	Dic₄₇⋊C₈	—	2	2	no	—
75	Dic₄₇⋊C₈	—	2	2	no	—
76	#13093949	C₂×C₄	1	2	yes	—
77	#13093949	C₂×C₄	1	2	yes	—
78	#13093949	C₂×C₄	1	2	yes	—
79	#13093949	C₂×C₄	1	2	yes	—
80	#13093935	D₄	1	2	yes	—
81	#13093934	—	2	2	no	—
82	#13093934	—	2	2	no	—
83	C₄×C₄₇⋊C₈	—	2	1	no	—
84	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
86	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
87	C₈×Dic₄₇	—	2	2	no	—
88	C₈×Dic₄₇	—	2	2	no	—
89	C₂×M₁₆×C₄₇	—	2	1	no	—
90	C₂²×C₈×C₄₇	—	2	1	no	—
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₄₇	—	2	1	no	—
93	C₄⋊C₈×C₄₇	—	2	1	no	—
94	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
96	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
98	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
100	C₄×C₈×C₄₇	C₂³	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
104	C₂²×Dic₄₇	—	2	1	no	—
105	C₂²×Dic₄₇	—	2	1	no	—
106	C₂×Dic₉₄	—	2	2	no	—
107	C₂×Dic₉₄	—	2	1	no	—
108	C₂×Dic₉₄	—	2	1	no	—
109	C₂×Dic₉₄	—	4	1	no	—
110	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
111	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
112	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
113	M₁₆×C₄₇	—	4	2	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	4	2	no	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
120	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₇	#41	1	1	yes	characteristic
123	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
124	C₂²⋊Dic₄₇	—	2	2	no	—
125	C₄⋊Dic₄₇	—	2	1	no	—
126	C₄⋊Dic₄₇	—	2	1	no	—
127	C₄⋊Dic₄₇	—	2	1	no	—
128	C₄⋊Dic₄₇	—	2	1	no	—
129	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
132	Dic₄₇⋊C₄	—	2	1	no	—
133	Dic₄₇⋊C₄	—	2	1	no	—
134	Dic₄₇⋊C₄	—	2	2	no	—
135	Dic₄₇⋊C₄	—	2	1	no	—
136	Dic₄₇⋊C₄	—	2	1	no	—
137	Dic₄₇⋊C₄	—	2	2	no	—
138	C₄×Dic₄₇	—	2	1	no	—
139	C₄×Dic₄₇	—	2	1	no	—
140	C₄×Dic₄₇	—	2	1	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	#10625329	—	2	2	no	—
144	#10625329	Q₁₆	1	4	yes	complemented
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	4	2	no	—
148	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
149	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
150	Dic₁₈₈	—	2	4	no	—
151	Dic₁₈₈	—	4	2	no	—
152	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	4	1	no	—
156	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
160	C₂×C₄×C₄₇	#135	1	2	yes	—
161	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	2	1	no	—
166	C₂×Dic₄₇	—	2	1	no	—
167	C₂×Dic₄₇	—	2	1	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	8	1	no	—
172	Dic₉₄	—	2	1	no	—
173	Dic₉₄	—	2	2	no	—
174	Dic₉₄	—	2	1	no	—
175	Dic₉₄	—	2	1	no	—
176	Dic₉₄	—	2	2	no	—
177	Dic₉₄	—	4	2	no	—
178	Dic₉₄	—	8	1	no	—
179	Dic₉₄	#131	1	2	yes	—
180	C₈×C₄₇	—	2	2	no	—
181	C₈×C₄₇	—	2	2	no	—
182	C₈×C₄₇	—	4	1	no	—
183	C₈×C₄₇	—	4	1	no	—
184	C₈×C₄₇	—	4	2	no	—
185	C₄₇⋊C₈	—	2	2	no	—
186	C₄₇⋊C₈	—	2	2	no	—
187	C₄₇⋊C₈	—	4	1	no	—
188	C₄₇⋊C₈	C₂×Q₁₆	1	4	yes	—
189	#17998	—	47	1	no	maximal, Sylow
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	C₄×Q₁₆	1	2	yes	—
193	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₄₇	—	2	1	no	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	C₄×Q₁₆	1	2	yes	—
198	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
199	C₄×C₄₇	#568	1	1	yes	characteristic
200	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
201	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
202	Dic₄₇	—	2	2	no	—
203	Dic₄₇	—	4	1	no	—
204	Dic₄₇	—	4	2	no	—
205	Dic₄₇	—	4	2	no	—
206	Dic₄₇	—	4	1	no	—
207	Dic₄₇	—	4	1	no	—
208	#3104	—	47	1	no	—
209	Q₈×M₁₆	—	47	1	no	—
210	#2962	—	47	1	no	—
211	#1591	—	47	2	no	—
212	#1584	—	47	2	no	—
213	#1584	—	47	2	no	—
214	C₈×Q₁₆	—	47	2	no	—
215	#1571	D₄₇	1	1	yes	characteristic
216	#1493	—	47	1	no	—
217	C₂×Q₈⋊C₈	—	47	1	no	—
218	C₈×M₁₆	—	47	1	no	—
219	C₂×C₄₇	—	2	2	no	—
220	C₂×C₄₇	#2933	1	1	yes	characteristic
221	C₂×C₄₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
222	C₂×C₄₇	#2956	1	1	yes	characteristic
223	#533	—	47	1	no	—
224	C₂×C₄×Q₈	—	47	1	no	—
225	#484	—	47	2	no	—
226	#477	—	47	1	no	—
227	#477	—	47	1	no	—
228	#462	—	47	1	no	—
229	#462	—	47	1	no	—
230	#451	—	47	2	no	—
231	#446	—	47	2	no	—
232	#446	—	47	2	no	—
233	#446	—	94	2	no	—
234	#446	—	94	2	no	—
235	C₈×Q₈	—	47	2	no	—
236	C₈×Q₈	—	47	2	no	—
237	C₄×Q₁₆	—	47	2	no	—
238	C₄×Q₁₆	—	47	2	no	—
239	#431	C₂×D₄₇	1	1	yes	characteristic
240	#424	—	94	1	no	—
241	#423	—	94	1	no	—
242	#423	C₂×D₄₇	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
244	#405	—	94	1	no	—
245	C₄×M₁₆	—	47	1	no	—
246	C₄×M₁₆	—	94	1	no	—
247	C₂×C₄×C₈	—	47	1	no	—
248	#335	C₂×D₄₇	1	2	yes	—
249	#335	C₂×D₄₇	1	2	yes	—
250	Q₈⋊C₈	—	47	1	no	—
251	Q₈⋊C₈	—	47	2	no	—
252	Q₈⋊C₈	—	47	1	no	—
253	Q₈⋊C₈	—	47	1	no	—
254	Q₈⋊C₈	—	47	2	no	—
255	Q₈⋊C₈	—	47	1	no	—
256	#322	—	47	2	no	—
257	C₈²	—	47	2	no	—
258	C₄₇	#17998	1	1	yes	characteristic, complemented, Sylow
259	C₂²×Q₈	—	47	1	no	—
260	C₂×Q₁₆	—	47	2	no	—
261	C₂×Q₁₆	—	47	2	no	—
262	C₂×M₁₆	—	2	1	no	—
263	C₂×M₁₆	—	47	1	no	—
264	C₂×M₁₆	—	47	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	94	1	no	—
267	C₄⋊Q₈	—	47	1	no	—
268	C₄⋊Q₈	—	47	1	no	—
269	#125	—	94	1	no	—
270	C₂²⋊Q₈	—	47	2	no	—
271	C₂²⋊Q₈	—	94	1	no	—
272	C₄×Q₈	—	47	1	no	—
273	C₄×Q₈	—	47	1	no	—
274	C₄×Q₈	—	47	1	no	—
275	C₄×Q₈	—	47	1	no	—
276	C₄×Q₈	—	47	2	no	—
277	C₄×Q₈	—	94	1	no	—
278	C₄×Q₈	—	94	1	no	—
279	C₄×Q₈	—	94	1	no	—
280	#117	—	94	1	no	—
281	C₂×C₄⋊C₄	—	47	1	no	—
282	C₂×C₄⋊C₄	—	94	1	no	—
283	C₂×C₄²	—	94	1	no	—
284	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
285	#107	—	47	2	no	—
286	#107	—	47	2	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	94	2	no	—
290	C₄⋊C₈	—	94	2	no	—
291	C₄⋊C₈	—	94	2	no	—
292	C₄⋊C₈	—	94	2	no	—
293	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
294	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
295	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
296	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
298	#103	—	47	2	no	—
299	#103	—	47	2	no	—
300	#103	—	47	2	no	—
301	#103	—	47	2	no	—
302	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
303	#97	—	47	2	no	—
304	#97	—	94	2	no	—
305	#97	—	94	2	no	—
306	C₄×C₈	—	47	2	no	—
307	C₄×C₈	—	47	1	no	—
308	C₄×C₈	—	47	1	no	—
309	C₄×C₈	—	94	2	no	—
310	C₄×C₈	—	94	2	no	—
311	C₄×C₈	—	94	1	no	—
312	C₄×C₈	C₂²×D₄₇	1	2	yes	—
313	C₂×Q₈	—	47	1	no	—
314	C₂×Q₈	—	47	1	no	—
315	C₂×Q₈	—	47	2	no	—
316	C₂×Q₈	—	94	2	no	—
317	C₂×Q₈	—	94	1	no	—
318	C₂×Q₈	—	94	1	no	—
319	C₂×Q₈	—	188	1	no	—
320	C₂²×C₄	—	94	1	no	—
321	C₂²×C₄	—	94	1	no	—
322	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
324	C₂²×C₄	#10625354	1	1	yes	characteristic
325	Q₁₆	—	94	4	no	—
326	Q₁₆	—	188	2	no	—
327	M₁₆	—	4	2	no	—
328	M₁₆	—	47	4	no	—
329	M₁₆	—	94	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	—	47	2	no	—
335	C₂×C₈	—	47	2	no	—
336	C₂×C₈	—	94	1	no	—
337	C₂×C₈	—	94	1	no	—
338	C₂×C₈	—	188	2	no	—
339	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
340	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
341	C₄⋊C₄	—	47	1	no	—
342	C₄⋊C₄	—	47	1	no	—
343	C₄⋊C₄	—	47	2	no	—
344	C₄⋊C₄	—	94	1	no	—
345	C₄⋊C₄	—	94	1	no	—
346	C₄⋊C₄	—	94	2	no	—
347	C₄⋊C₄	—	94	1	no	—
348	C₄⋊C₄	—	94	1	no	—
349	C₄⋊C₄	—	94	1	no	—
350	C₄⋊C₄	—	94	1	no	—
351	C₄⋊C₄	—	94	1	no	—
352	C₄⋊C₄	—	94	1	no	—
353	C₄⋊C₄	—	94	2	no	—
354	C₂²⋊C₄	—	94	2	no	—
355	C₄²	—	94	1	no	—
356	C₄²	—	94	1	no	—
357	C₄²	—	94	1	no	—
358	C₄²	—	94	2	no	—
359	C₄²	—	94	1	no	—
360	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
361	C₄²	D₄×D₄₇	1	1	yes	characteristic
362	C₄²	#10625354	1	1	yes	characteristic
363	C₄²	C₂³×D₄₇	1	1	yes	characteristic
364	C₂³	#13093986	1	1	yes	characteristic
365	Q₈	—	47	2	no	—
366	Q₈	—	94	1	no	—
367	Q₈	—	94	2	no	—
368	Q₈	—	94	1	no	—
369	Q₈	—	94	1	no	—
370	Q₈	—	94	2	no	—
371	Q₈	—	376	1	no	—
372	Q₈	—	188	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	94	1	no	—
377	C₂×C₄	—	94	1	no	—
378	C₂×C₄	—	94	1	no	—
379	C₂×C₄	—	94	1	no	—
380	C₂×C₄	—	94	2	no	—
381	C₂×C₄	—	94	2	no	—
382	C₂×C₄	—	376	1	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	#13093986	1	1	yes	characteristic
385	C₂×C₄	#13093986	1	1	yes	characteristic
386	C₂×C₄	#13093986	1	1	yes	characteristic
387	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
388	C₂×C₄	#13094043	1	2	yes	—
389	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
390	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
391	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
392	C₈	—	2	2	no	—
393	C₈	—	2	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	4	2	no	—
397	C₈	—	47	4	no	—
398	C₈	—	94	2	no	—
399	C₈	—	94	2	no	—
400	C₈	—	188	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	#15689217	1	2	yes	—
404	C₂²	C₂×#13093986	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	94	2	no	—
409	C₄	—	188	1	no	—
410	C₄	—	188	1	no	—
411	C₄	—	188	2	no	—
412	C₄	—	188	1	no	—
413	C₄	—	188	2	no	—
414	C₄	#15689217	1	2	yes	—
415	C₄	#131×D₄₇	1	1	yes	characteristic
416	C₄	#15689888	1	1	yes	characteristic
417	C₄	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
418	C₄	C₂×#13094043	1	1	yes	characteristic
419	C₂	—	2	2	no	—
420	C₂	#20252112	1	1	yes	characteristic
421	C₂	C₂×#15689217	1	1	yes	characteristic
422	C₂	#20252297	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1571	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂³×C₄₇	C₄×D₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1571	D₄₇
hypocenter	C₄₇	#17998
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

Complements

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

N	H ≅ G/N	type
4. #20242284	C₂	semidirect
5. #20242237	C₂	semidirect
6. #20242237	C₂	semidirect
7. #20242194	C₂	semidirect
144. #10625329	Q₁₆	semidirect
258. C₄₇	#17998	semidirect

Maximal subgroups

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

subgroup	index
#20253428	2
#20252339	2
#20252331	2
#20242284	2
#20242237	2
#20242194	2
#20241842	2
C₂×#15688853	2
#20241669	2
C₄₇×#1571	2
#17998	47