Subgroups — #26234717

Order 12032.

910 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689217	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689217	C₂	1	1	yes	maximal, characteristic
4	#20246307	C₂	1	2	yes	maximal
5	#20244122	C₂	1	1	yes	maximal, characteristic
6	#20243657	C₂	1	2	yes	maximal
7	#20243655	C₂	1	2	yes	maximal
8	#20243551	C₂	1	1	yes	maximal, characteristic
9	#20243402	C₂	1	2	yes	maximal
10	C₈×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1942	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₁₈₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
14	C₂×#13093989	C₂²	1	2	yes	—
15	C₂×#13093989	C₂²	1	2	yes	—
16	C₄×Dic₁₈₈	—	2	4	no	—
17	#15689217	—	2	4	no	—
18	#15689217	C₄	1	8	yes	complemented
19	C₂×#13093958	C₂²	1	1	yes	characteristic
20	C₂×#13093955	C₂²	1	2	yes	—
21	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×#13093949	C₂²	1	2	yes	—
23	C₂×#13093947	C₂²	1	2	yes	—
24	C₂×#13093947	C₂²	1	2	yes	—
25	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
27	#15689022	C₂²	1	2	yes	—
28	#15689020	—	2	2	no	—
29	#15689018	—	2	2	no	—
30	#15688988	C₂²	1	2	yes	—
31	#15688987	—	2	2	no	—
32	C₄⋊C₄×Dic₄₇	—	2	2	no	—
33	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
34	#15688885	C₂²	1	2	yes	—
35	#15688878	C₂²	1	1	yes	characteristic
36	#15688877	C₂²	1	1	yes	characteristic
37	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#389	C₂²	1	2	yes	—
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₂²×Dic₉₄	C₂³	1	2	yes	—
43	C₂×Dic₁₈₈	C₂×C₄	1	4	yes	—
44	C₂×Dic₁₈₈	D₄	1	4	yes	—
45	C₂×Dic₁₈₈	Q₈	1	4	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₄×Dic₉₄	—	2	4	no	—
49	C₄×Dic₉₄	—	4	2	no	—
50	#13093989	—	2	4	no	—
51	#13093989	—	2	4	no	—
52	#13093989	—	4	2	no	—
53	#13093989	C₂×C₄	1	8	yes	—
54	C₂×C₄⋊Dic₄₇	—	2	2	no	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
56	C₂×Dic₄₇⋊C₄	—	2	2	no	—
57	C₂×Dic₄₇⋊C₄	—	2	2	no	—
58	C₂×Dic₄₇⋊C₄	—	2	2	no	—
59	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
60	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	—	2	2	no	—
62	C₂×C₄×Dic₄₇	—	2	2	no	—
63	C₂×C₄×Dic₄₇	—	2	2	no	—
64	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	#13093958	—	2	2	no	—
67	#13093955	—	4	2	no	—
68	Dic₄₇⋊C₈	—	2	2	no	—
69	#13093949	—	2	4	no	—
70	#13093947	—	2	4	no	—
71	#13093947	C₂×C₄	1	8	yes	—
72	C₈×Dic₄₇	—	2	2	no	—
73	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	—	2	2	no	—
76	C₄₇⋊#95	—	2	2	no	—
77	C₄₇⋊#95	D₄	1	1	yes	characteristic
78	C₄₇⋊#95	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	#107×C₄₇	—	2	2	no	—
86	#107×C₄₇	C₂×C₄	1	4	yes	—
87	C₄×C₈×C₄₇	—	2	2	no	—
88	#95×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	2	2	no	—
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂×Dic₉₄	—	2	2	no	—
101	C₂×Dic₉₄	—	2	2	no	—
102	C₂×Dic₉₄	—	2	2	no	—
103	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
104	C₂×Dic₉₄	C₂×D₄	1	4	yes	—
105	C₂×Dic₉₄	C₂×Q₈	1	4	yes	—
106	C₂×C₈×C₄₇	—	2	1	no	—
107	C₂×C₈×C₄₇	—	2	1	no	—
108	C₂×C₈×C₄₇	—	2	1	no	—
109	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	4	4	no	—
116	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
117	C₄²×C₄₇	—	2	1	no	—
118	C₄²×C₄₇	—	2	1	no	—
119	C₄⋊Dic₄₇	—	2	2	no	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	4	4	no	—
122	Dic₄₇⋊C₄	—	2	2	no	—
123	Dic₄₇⋊C₄	—	2	8	no	—
124	Dic₄₇⋊C₄	—	2	2	no	—
125	Dic₄₇⋊C₄	—	4	4	no	—
126	Dic₄₇⋊C₄	—	4	4	no	—
127	C₄×Dic₄₇	—	2	1	no	—
128	C₄×Dic₄₇	—	2	1	no	—
129	C₄×Dic₄₇	—	2	8	no	—
130	C₄×Dic₄₇	—	4	4	no	—
131	C₄×Dic₄₇	—	4	4	no	—
132	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
133	C₄×Dic₄₇	#41	1	2	yes	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
140	Dic₁₈₈	C₄⋊C₄	1	16	yes	complemented
141	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	#135	1	2	yes	—
154	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
160	C₂×Dic₄₇	—	2	4	no	—
161	C₂×Dic₄₇	—	2	1	no	—
162	C₂×Dic₄₇	—	2	4	no	—
163	C₂×Dic₄₇	—	2	4	no	—
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	1	no	—
169	C₂×Dic₄₇	—	2	1	no	—
170	C₂×Dic₄₇	—	2	1	no	—
171	C₂×Dic₄₇	—	2	1	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
176	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
177	C₂×Dic₄₇	#135	1	2	yes	—
178	Dic₉₄	—	2	4	no	—
179	Dic₉₄	—	2	4	no	—
180	Dic₉₄	—	2	4	no	—
181	Dic₉₄	C₂×C₄⋊C₄	1	8	yes	—
182	C₈×C₄₇	—	4	1	no	—
183	C₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
184	C₄₇⋊C₈	—	2	2	no	—
185	C₄₇⋊C₈	—	4	1	no	—
186	#22685	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂²×C₄₇	D₄²	1	1	yes	characteristic
189	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
190	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
192	C₂²×C₄₇	#578	1	1	yes	characteristic
193	C₂²×C₄₇	#578	1	1	yes	characteristic
194	C₄×C₄₇	—	2	2	no	—
195	C₄×C₄₇	—	4	4	no	—
196	C₄×C₄₇	—	4	1	no	—
197	C₄×C₄₇	—	8	2	no	—
198	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
199	C₄×C₄₇	#520	1	1	yes	characteristic
200	C₄×C₄₇	#547	1	1	yes	characteristic
201	C₄×C₄₇	#554	1	1	yes	characteristic
202	Dic₄₇	—	2	8	no	—
203	Dic₄₇	—	2	2	no	—
204	Dic₄₇	—	2	2	no	—
205	Dic₄₇	—	2	2	no	—
206	Dic₄₇	—	4	1	no	—
207	Dic₄₇	—	8	2	no	—
208	C₂×C₄×Q₁₆	—	47	1	no	—
209	C₂×C₄×Q₁₆	—	47	1	no	—
210	C₂×C₄×Q₁₆	—	47	1	no	—
211	#2351	—	47	2	no	—
212	#1942	—	47	1	no	—
213	#1942	D₄₇	1	1	yes	characteristic
214	#1865	—	47	2	no	—
215	#1865	—	47	2	no	—
216	#1846	—	47	1	no	—
217	#1805	—	47	2	no	—
218	C₈×C₄⋊C₄	—	47	1	no	—
219	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₄₇	C₄×#135	1	1	yes	characteristic
221	C₂×C₄₇	#2950	1	1	yes	characteristic
222	C₂×C₄₇	#3285	1	1	yes	characteristic
223	C₂×C₄₇	#3285	1	1	yes	characteristic
224	C₂×C₄₇	#3383	1	1	yes	characteristic
225	C₂×C₄₇	#3383	1	1	yes	characteristic
226	C₂²×Q₁₆	—	47	1	no	—
227	C₂×C₄×Q₈	—	47	2	no	—
228	C₂×C₄×Q₈	—	47	2	no	—
229	C₂×C₄×Q₈	—	47	2	no	—
230	C₄×Q₁₆	—	47	8	no	—
231	C₄×Q₁₆	—	94	4	no	—
232	C₄×Q₁₆	—	94	4	no	—
233	C₂×#107	—	47	1	no	—
234	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
235	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
236	C₂×#106	—	47	2	no	—
237	C₂×C₄⋊C₈	—	47	1	no	—
238	C₂×#103	—	47	2	no	—
239	C₂×#103	—	47	2	no	—
240	C₂×#103	—	47	2	no	—
241	C₂×C₄×C₈	—	47	1	no	—
242	C₂×C₄×C₈	—	47	1	no	—
243	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
244	#389	—	47	2	no	—
245	#389	—	94	2	no	—
246	#389	—	94	2	no	—
247	#389	C₂×D₄₇	1	2	yes	—
248	#382	—	47	2	no	—
249	#382	—	94	2	no	—
250	C₄×C₄⋊C₄	—	47	1	no	—
251	C₄×C₄⋊C₄	—	94	2	no	—
252	#340	—	47	2	no	—
253	#340	C₂×D₄₇	1	2	yes	—
254	#336	—	47	1	no	—
255	#336	—	47	1	no	—
256	C₄₇	#22685	1	1	yes	characteristic, complemented, Sylow
257	C₂²×Q₈	—	47	2	no	—
258	C₂×Q₁₆	—	47	4	no	—
259	C₂×Q₁₆	—	47	4	no	—
260	C₂×Q₁₆	—	47	4	no	—
261	C₂²×C₈	—	47	1	no	—
262	C₂²×C₈	—	47	1	no	—
263	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
264	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
265	C₄×Q₈	—	47	8	no	—
266	C₄×Q₈	—	94	4	no	—
267	C₄×Q₈	—	94	4	no	—
268	C₄×Q₈	—	94	4	no	—
269	C₄×Q₈	—	188	2	no	—
270	C₄×Q₈	—	188	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	47	1	no	—
273	C₂×C₄⋊C₄	—	47	1	no	—
274	C₂×C₄⋊C₄	—	47	2	no	—
275	C₂×C₄⋊C₄	—	94	2	no	—
276	C₂×C₄⋊C₄	—	94	2	no	—
277	C₂×C₄⋊C₄	—	94	2	no	—
278	C₂×C₄⋊C₄	—	94	2	no	—
279	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
280	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
281	C₂×C₄²	—	47	1	no	—
282	C₂×C₄²	—	47	1	no	—
283	C₂×C₄²	—	94	2	no	—
284	C₂×C₄²	—	94	2	no	—
285	C₂×C₄²	—	94	2	no	—
286	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
287	#107	—	2	2	no	—
288	#107	—	94	2	no	—
289	#107	C₄×D₄₇	1	4	yes	—
290	#106	—	188	2	no	—
291	C₄⋊C₈	—	94	2	no	—
292	#103	—	47	8	no	—
293	#103	—	94	4	no	—
294	#103	—	94	4	no	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	—	47	4	no	—
297	C₄×C₈	—	94	2	no	—
298	#95	—	2	2	no	—
299	#95	—	47	1	no	—
300	#95	—	47	1	no	—
301	#95	—	94	2	no	—
302	#95	—	94	2	no	—
303	#95	—	94	2	no	—
304	C₂×Q₈	—	47	4	no	—
305	C₂×Q₈	—	47	4	no	—
306	C₂×Q₈	—	47	4	no	—
307	C₂×Q₈	—	94	2	no	—
308	C₂×Q₈	—	94	2	no	—
309	C₂×Q₈	—	94	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	47	1	no	—
313	C₂²×C₄	—	47	1	no	—
314	C₂²×C₄	—	47	1	no	—
315	C₂²×C₄	—	47	1	no	—
316	C₂²×C₄	—	94	2	no	—
317	C₂²×C₄	—	94	2	no	—
318	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
321	Q₁₆	—	47	16	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	47	2	no	—
326	C₂×C₈	—	94	1	no	—
327	C₂×C₈	—	94	1	no	—
328	C₂×C₈	—	94	1	no	—
329	C₂×C₈	—	94	1	no	—
330	C₂×C₈	—	94	1	no	—
331	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
332	C₂×C₈	D₄×D₄₇	1	2	yes	—
333	C₂×C₈	Q₈×D₄₇	1	2	yes	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	94	2	no	—
339	C₄⋊C₄	—	94	8	no	—
340	C₄⋊C₄	—	94	2	no	—
341	C₄⋊C₄	—	94	2	no	—
342	C₄⋊C₄	—	94	2	no	—
343	C₄⋊C₄	—	188	4	no	—
344	C₄⋊C₄	—	188	4	no	—
345	C₄⋊C₄	—	188	4	no	—
346	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	47	2	no	—
350	C₄²	—	47	2	no	—
351	C₄²	—	94	8	no	—
352	C₄²	—	94	1	no	—
353	C₄²	—	94	1	no	—
354	C₄²	—	188	4	no	—
355	C₄²	—	188	4	no	—
356	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
357	Q₈	—	47	8	no	—
358	Q₈	—	94	4	no	—
359	Q₈	—	94	4	no	—
360	Q₈	—	94	4	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	47	2	no	—
373	C₂×C₄	—	47	2	no	—
374	C₂×C₄	—	47	2	no	—
375	C₂×C₄	—	94	1	no	—
376	C₂×C₄	—	94	4	no	—
377	C₂×C₄	—	94	4	no	—
378	C₂×C₄	—	94	4	no	—
379	C₂×C₄	—	94	1	no	—
380	C₂×C₄	—	94	1	no	—
381	C₂×C₄	—	94	1	no	—
382	C₂×C₄	—	94	1	no	—
383	C₂×C₄	—	94	1	no	—
384	C₂×C₄	—	94	1	no	—
385	C₂×C₄	—	94	1	no	—
386	C₂×C₄	—	94	1	no	—
387	C₂×C₄	—	188	2	no	—
388	C₂×C₄	—	188	2	no	—
389	C₂×C₄	—	188	2	no	—
390	C₂×C₄	#13094043	1	2	yes	—
391	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
393	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
394	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
395	C₂×C₄	#13094070	1	1	yes	characteristic
396	C₂×C₄	#13094072	1	1	yes	characteristic
397	C₈	—	4	1	no	—
398	C₈	—	94	2	no	—
399	C₈	—	188	1	no	—
400	C₈	C₄⋊C₄×D₄₇	1	4	yes	—
401	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
402	C₂²	#15689757	1	1	yes	characteristic
403	C₂²	#15689788	1	1	yes	characteristic
404	C₂²	#135×D₄₇	1	1	yes	characteristic
405	C₂²	C₂×#13094043	1	1	yes	characteristic
406	C₂²	#15689936	1	1	yes	characteristic
407	C₂²	#15689937	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	4	no	—
411	C₄	—	8	2	no	—
412	C₄	—	94	8	no	—
413	C₄	—	94	2	no	—
414	C₄	—	94	2	no	—
415	C₄	—	94	2	no	—
416	C₄	—	376	2	no	—
417	C₄	—	188	1	no	—
418	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
419	C₄	#15689605	1	1	yes	characteristic
420	C₄	#15689775	1	1	yes	characteristic
421	C₄	#15689829	1	1	yes	characteristic
422	C₂	#20246289	1	1	yes	characteristic
423	C₂	C₄×#13094043	1	1	yes	characteristic
424	C₂	#20252251	1	1	yes	characteristic
425	C₂	#20255126	1	1	yes	characteristic
426	C₂	#20255132	1	1	yes	characteristic
427	C₂	#20256276	1	1	yes	characteristic
428	C₂	#20256281	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1942	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1942	D₄₇
hypocenter	C₄₇	#22685
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1942

Complements

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

N	H ≅ G/N	type
18. #15689217	C₄	semidirect
140. Dic₁₈₈	C₄⋊C₄	semidirect
256. C₄₇	#22685	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₁₈₈	2
C₂×#15689217	2
#20246307	2
#20244122	2
#20243657	2
#20243655	2
#20243551	2
#20243402	2
C₈×Dic₄₇⋊C₄	2
C₄₇×#1942	2
#22685	47