Subgroups — #26244389

Order 12032.

1082 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256793	C₂	1	1	yes	maximal, characteristic
2	#20251978	C₂	1	1	yes	maximal, characteristic
3	#20251977	C₂	1	1	yes	maximal, characteristic
4	#20245795	C₂	1	1	yes	maximal, characteristic
5	#20244737	C₂	1	4	yes	maximal, complemented
6	#20244732	C₂	1	4	yes	maximal, complemented
7	#20243126	C₂	1	1	yes	maximal, characteristic
8	C₂×#15688883	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄₇×#339	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	#15689754	—	2	2	no	—
12	#15689751	—	2	2	no	—
13	#15689751	C₂²	1	4	yes	—
14	#15689749	—	2	2	no	—
15	#15689680	—	2	2	no	—
16	#15689676	—	2	2	no	—
17	#15689676	—	2	2	no	—
18	C₂×#13093983	C₂²	1	1	yes	characteristic
19	C₂×#13093983	C₂²	1	1	yes	characteristic
20	C₂×#13093983	C₂²	1	1	yes	characteristic
21	#15689166	C₂²	1	4	yes	—
22	#15689165	—	2	2	no	—
23	#15689165	C₂²	1	4	yes	—
24	#15689163	—	2	2	no	—
25	#15689161	—	2	2	no	—
26	#15689159	—	2	2	no	—
27	#15688993	C₂²	1	2	yes	—
28	#15688989	C₂²	1	2	yes	—
29	#15688983	—	2	2	no	—
30	C₄×C₄⋊Dic₄₇	—	2	2	no	—
31	#15688891	C₂²	1	4	yes	—
32	#15688883	C₂²	1	2	yes	—
33	#15688883	C₂²	1	2	yes	—
34	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#339	C₂²	1	2	yes	—
38	C₄₇×#339	C₂²	1	2	yes	—
39	C₂×#10625329	—	2	1	no	—
40	C₂×#10625329	—	2	2	no	—
41	C₂×#10625329	Q₈	1	4	yes	complemented
42	C₂×#10625329	C₂³	1	2	yes	—
43	C₂²×C₄₇⋊C₈	—	2	1	no	—
44	#13094024	—	2	4	no	—
45	#13094023	—	2	4	no	—
46	#13094023	—	2	4	no	—
47	#13094016	—	2	4	no	—
48	#13094015	—	2	4	no	—
49	#13094015	—	2	4	no	—
50	#13094003	—	2	8	no	—
51	#13094001	—	2	8	no	—
52	#13094001	—	2	8	no	—
53	C₄×Dic₉₄	—	2	8	no	—
54	#13093983	—	2	1	no	—
55	#13093983	—	2	1	no	—
56	#13093983	—	2	1	no	—
57	#13093983	—	2	1	no	—
58	#13093983	—	2	1	no	—
59	#13093983	—	2	1	no	—
60	#13093983	—	2	1	no	—
61	#13093983	—	2	1	no	—
62	#13093983	—	2	1	no	—
63	#13093983	—	2	1	no	—
64	#13093983	D₄	1	2	yes	—
65	#13093983	C₂³	1	2	yes	—
66	C₂×C₄⋊Dic₄₇	—	2	4	no	—
67	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
68	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
69	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
70	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
71	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
72	C₂×C₂²⋊Dic₄₇	D₄	1	2	yes	—
73	C₂×C₄×Dic₄₇	—	2	1	no	—
74	C₂×C₄×Dic₄₇	—	2	1	no	—
75	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
76	#13093958	—	2	4	no	—
77	#13093957	—	2	4	no	—
78	#13093956	—	2	4	no	—
79	#13093955	—	2	4	no	—
80	C₄₇⋊#95	—	2	4	no	—
81	C₂³×C₄×C₄₇	—	2	1	no	—
82	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₄₇	—	2	1	no	—
84	C₂×M₁₆×C₄₇	—	2	2	no	—
85	C₂×M₁₆×C₄₇	Q₈	1	4	yes	complemented
86	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
87	C₂²×C₈×C₄₇	—	2	1	no	—
88	#117×C₄₇	—	2	1	no	—
89	#117×C₄₇	—	2	1	no	—
90	#117×C₄₇	D₄	1	2	yes	—
91	#117×C₄₇	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
93	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
94	C₂×C₄²×C₄₇	—	2	1	no	—
95	C₂×C₄²×C₄₇	—	2	1	no	—
96	C₂×C₄²×C₄₇	—	2	2	no	—
97	C₂×C₄²×C₄₇	Q₈	1	4	yes	complemented
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	4	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	4	4	no	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
114	C₂²×C₄×C₄₇	#41	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂²×Dic₄₇	—	2	2	no	—
117	C₂²×Dic₄₇	—	2	2	no	—
118	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
119	C₂×Dic₉₄	—	2	8	no	—
120	M₁₆×C₄₇	—	2	4	no	—
121	M₁₆×C₄₇	—	2	2	no	—
122	M₁₆×C₄₇	C₂×Q₈	1	4	yes	—
123	C₂×C₈×C₄₇	—	2	4	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
127	C₂²⋊C₄×C₄₇	—	2	2	no	—
128	C₂²⋊C₄×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	2	4	no	—
131	C₄²×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	2	1	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
135	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
136	C₂²⋊Dic₄₇	—	2	2	no	—
137	C₂²⋊Dic₄₇	—	2	2	no	—
138	C₂²⋊Dic₄₇	—	2	2	no	—
139	C₂²⋊Dic₄₇	—	2	2	no	—
140	C₂²⋊Dic₄₇	—	4	1	no	—
141	C₂²⋊Dic₄₇	—	4	1	no	—
142	C₄⋊Dic₄₇	—	2	8	no	—
143	C₄⋊Dic₄₇	—	2	2	no	—
144	C₄⋊Dic₄₇	—	2	2	no	—
145	C₄⋊Dic₄₇	—	2	2	no	—
146	C₄⋊Dic₄₇	—	2	2	no	—
147	C₄⋊Dic₄₇	—	2	2	no	—
148	C₄⋊Dic₄₇	—	4	8	no	—
149	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
150	Dic₄₇⋊C₄	—	2	8	no	—
151	Dic₄₇⋊C₄	—	2	8	no	—
152	C₄×Dic₄₇	—	2	2	no	—
153	C₄×Dic₄₇	—	2	2	no	—
154	C₄×Dic₄₇	—	2	2	no	—
155	C₄×Dic₄₇	—	2	2	no	—
156	C₄×Dic₄₇	—	4	1	no	—
157	C₄×Dic₄₇	—	4	1	no	—
158	#10625329	—	2	4	no	—
159	#10625329	—	2	2	no	—
160	#10625329	C₂×Q₈	1	4	yes	—
161	C₂×C₄₇⋊C₈	—	2	4	no	—
162	C₂×C₄₇⋊C₈	—	2	2	no	—
163	C₂³×C₄₇	—	4	2	no	—
164	C₂³×C₄₇	#120	1	1	yes	characteristic
165	C₂³×C₄₇	#120	1	1	yes	characteristic
166	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
167	C₂³×C₄₇	C₄⋊Q₈	1	2	yes	—
168	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	4	8	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	8	2	no	—
176	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
177	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
180	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
181	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
182	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
183	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
184	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
185	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
186	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
187	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
188	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
194	C₂×Dic₄₇	—	2	4	no	—
195	C₂×Dic₄₇	—	2	4	no	—
196	C₂×Dic₄₇	—	4	4	no	—
197	C₂×Dic₄₇	—	4	4	no	—
198	C₂×Dic₄₇	—	4	2	no	—
199	C₂×Dic₄₇	—	8	2	no	—
200	Dic₉₄	—	8	8	no	—
201	C₈×C₄₇	—	2	4	no	—
202	C₄₇⋊C₈	—	2	4	no	—
203	#23560	—	47	1	no	maximal, Sylow
204	C₂²×C₄₇	—	2	2	no	—
205	C₂²×C₄₇	—	2	2	no	—
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	4	2	no	—
208	C₂²×C₄₇	—	4	2	no	—
209	C₂²×C₄₇	#395	1	2	yes	—
210	C₂²×C₄₇	#395	1	2	yes	—
211	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
212	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
213	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
214	C₄×C₄₇	—	2	4	no	—
215	C₄×C₄₇	—	4	2	no	—
216	C₄×C₄₇	—	4	4	no	—
217	C₄×C₄₇	#395	1	2	yes	—
218	C₄×C₄₇	#395	1	2	yes	—
219	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
220	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
221	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
222	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
223	Dic₄₇	—	4	4	no	—
224	Dic₄₇	—	4	4	no	—
225	Dic₄₇	—	8	2	no	—
226	#3458	—	47	1	no	—
227	#2911	—	47	1	no	—
228	#2911	—	47	1	no	—
229	#2285	—	47	1	no	—
230	#2061	—	47	4	no	—
231	#2060	—	47	4	no	—
232	#1742	—	47	1	no	—
233	C₂×#339	—	47	1	no	—
234	C₂×#339	D₄₇	1	1	yes	characteristic
235	C₂×C₄₇	—	2	1	no	—
236	C₂×C₄₇	—	2	1	no	—
237	C₂×C₄₇	—	2	2	no	—
238	C₂×C₄₇	—	2	2	no	—
239	C₂×C₄₇	C₂×#395	1	1	yes	characteristic
240	C₂×C₄₇	#3018	1	2	yes	—
241	C₂²×M₁₆	—	47	1	no	—
242	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
243	#544	—	47	4	no	—
244	#544	—	94	2	no	—
245	#544	—	94	2	no	—
246	#543	—	94	2	no	—
247	#533	—	94	2	no	—
248	#533	—	94	2	no	—
249	#533	—	94	2	no	—
250	C₂×#117	—	47	1	no	—
251	C₂×#117	—	47	1	no	—
252	C₂×#117	—	47	1	no	—
253	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
254	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
255	#428	—	47	4	no	—
256	#428	—	47	4	no	—
257	#428	—	94	2	no	—
258	#428	—	94	2	no	—
259	#427	—	94	2	no	—
260	#427	—	94	2	no	—
261	#384	—	47	2	no	—
262	#382	—	47	2	no	—
263	#380	—	94	2	no	—
264	C₄×C₄⋊C₄	—	94	2	no	—
265	#343	—	47	4	no	—
266	#339	—	47	2	no	—
267	#339	—	47	2	no	—
268	#339	C₂×D₄₇	1	2	yes	—
269	#339	C₂×D₄₇	1	2	yes	—
270	C₄₇	#23560	1	1	yes	characteristic, complemented, Sylow
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	—	47	4	no	—
276	C₂×M₁₆	—	47	2	no	—
277	C₂×M₁₆	—	94	1	no	—
278	C₂×M₁₆	—	94	2	no	—
279	C₂×M₁₆	Dic₉₄	1	4	yes	complemented
280	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	94	1	no	—
283	C₄⋊Q₈	—	94	4	no	—
284	C₄⋊Q₈	—	94	4	no	—
285	C₄⋊Q₈	—	94	4	no	—
286	#125	—	94	4	no	—
287	#125	—	94	4	no	—
288	#125	—	94	4	no	—
289	C₂²⋊Q₈	—	94	8	no	—
290	C₂²⋊Q₈	—	94	8	no	—
291	C₂²⋊Q₈	—	94	8	no	—
292	C₄×Q₈	—	94	8	no	—
293	#117	—	2	1	no	—
294	#117	—	2	1	no	—
295	#117	—	47	2	no	—
296	#117	—	47	2	no	—
297	#117	—	94	1	no	—
298	#117	—	94	1	no	—
299	#117	—	94	1	no	—
300	#117	—	94	1	no	—
301	#117	—	94	1	no	—
302	#117	—	94	1	no	—
303	#117	—	94	1	no	—
304	#117	—	94	1	no	—
305	#117	—	94	1	no	—
306	#117	—	94	1	no	—
307	#117	D₁₈₈	1	2	yes	—
308	#117	C₂²×D₄₇	1	2	yes	—
309	C₂×C₄⋊C₄	—	47	2	no	—
310	C₂×C₄⋊C₄	—	47	2	no	—
311	C₂×C₄⋊C₄	—	47	2	no	—
312	C₂×C₄⋊C₄	—	94	4	no	—
313	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	47	2	no	—
316	C₂×C₂²⋊C₄	—	94	1	no	—
317	C₂×C₂²⋊C₄	—	94	1	no	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	47	2	no	—
322	C₂×C₄²	—	94	1	no	—
323	C₂×C₄²	—	94	1	no	—
324	C₂×C₄²	Dic₉₄	1	4	yes	complemented
325	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
326	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
327	#107	—	94	4	no	—
328	#107	—	94	4	no	—
329	#106	—	94	4	no	—
330	#106	—	94	4	no	—
331	#95	—	94	4	no	—
332	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
333	C₂×Q₈	—	94	8	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	—	47	4	no	—
340	C₂²×C₄	—	94	2	no	—
341	C₂²×C₄	—	94	2	no	—
342	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
343	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
344	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
347	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
349	C₂²×C₄	#10625352	1	2	yes	—
350	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
351	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
352	M₁₆	—	2	4	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	47	4	no	—
355	M₁₆	—	94	4	no	—
356	M₁₆	—	94	2	no	—
357	M₁₆	C₂×Dic₉₄	1	4	yes	—
358	C₂×C₈	—	2	4	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	94	4	no	—
361	C₂×C₈	—	94	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	47	4	no	—
364	C₄⋊C₄	—	94	8	no	—
365	C₄⋊C₄	—	94	8	no	—
366	C₄⋊C₄	—	94	8	no	—
367	C₄⋊C₄	—	94	2	no	—
368	C₄⋊C₄	—	94	2	no	—
369	C₄⋊C₄	—	94	2	no	—
370	C₄⋊C₄	—	94	2	no	—
371	C₄⋊C₄	—	94	2	no	—
372	C₄⋊C₄	—	188	8	no	—
373	C₄⋊C₄	C₂×D₁₈₈	1	4	yes	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	94	2	no	—
377	C₂²⋊C₄	—	94	2	no	—
378	C₂²⋊C₄	—	94	2	no	—
379	C₂²⋊C₄	—	94	2	no	—
380	C₂²⋊C₄	—	188	1	no	—
381	C₂²⋊C₄	—	188	1	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	4	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	94	2	no	—
388	C₄²	—	94	2	no	—
389	C₄²	—	94	2	no	—
390	C₄²	—	94	2	no	—
391	C₄²	—	188	1	no	—
392	C₄²	—	188	1	no	—
393	C₄²	C₂×Dic₉₄	1	2	yes	—
394	C₄²	C₂×Dic₉₄	1	2	yes	—
395	C₂³	—	4	2	no	—
396	C₂³	#13093994	1	1	yes	characteristic
397	C₂³	#13093994	1	1	yes	characteristic
398	C₂³	#13094001	1	2	yes	—
399	C₂³	#13094023	1	2	yes	—
400	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
401	Q₈	—	376	8	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	8	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	2	no	—
409	C₂×C₄	—	94	4	no	—
410	C₂×C₄	—	94	4	no	—
411	C₂×C₄	—	376	2	no	—
412	C₂×C₄	—	188	4	no	—
413	C₂×C₄	—	188	2	no	—
414	C₂×C₄	—	188	4	no	—
415	C₂×C₄	#13093994	1	1	yes	characteristic
416	C₂×C₄	#13093994	1	1	yes	characteristic
417	C₂×C₄	#13094001	1	2	yes	—
418	C₂×C₄	#13094001	1	2	yes	—
419	C₂×C₄	#13094001	1	2	yes	—
420	C₂×C₄	#13094004	1	2	yes	—
421	C₂×C₄	#13094004	1	2	yes	—
422	C₂×C₄	#13094023	1	2	yes	—
423	C₂×C₄	#13094023	1	2	yes	—
424	C₂×C₄	#13094023	1	2	yes	—
425	C₂×C₄	#13094024	1	2	yes	—
426	C₂×C₄	#13094024	1	2	yes	—
427	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
429	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
430	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
431	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
432	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
433	C₈	—	2	4	no	—
434	C₈	—	94	4	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	#15689044	1	2	yes	—
441	C₂²	#15689044	1	2	yes	—
442	C₂²	C₂×#13093994	1	1	yes	characteristic
443	C₂²	C₂×#13094001	1	1	yes	characteristic
444	C₂²	C₂×#13094023	1	1	yes	characteristic
445	C₄	—	2	4	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	4	no	—
448	C₄	—	376	2	no	—
449	C₄	—	188	4	no	—
450	C₄	—	188	4	no	—
451	C₄	#15689044	1	2	yes	—
452	C₄	#15689044	1	2	yes	—
453	C₄	C₂×#13094001	1	1	yes	characteristic
454	C₄	C₂×#13094004	1	1	yes	characteristic
455	C₄	C₂×#13094023	1	1	yes	characteristic
456	C₄	C₂×#13094024	1	1	yes	characteristic
457	C₂	—	2	1	no	—
458	C₂	—	2	2	no	—
459	C₂	—	2	2	no	—
460	C₂	—	2	1	no	—
461	C₂	C₂×#15689044	1	1	yes	characteristic
462	C₂	#20252739	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13093994
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#339	C₂
socle	C₂²×C₄₇	C₂×#120
prime radical	C₂⁴×C₄₇	C₂×D₄
hypercenter	C₂×#339	D₄₇
hypocenter	C₄₇	#23560
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
5. #20244737	C₂	semidirect
6. #20244732	C₂	semidirect
41. C₂×#10625329	Q₈	semidirect
85. C₂×M₁₆×C₄₇	Q₈	semidirect
97. C₂×C₄²×C₄₇	Q₈	semidirect
270. C₄₇	#23560	semidirect
279. C₂×M₁₆	Dic₉₄	semidirect
324. C₂×C₄²	Dic₉₄	semidirect

Maximal subgroups

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

subgroup	index
#20256793	2
#20251978	2
#20251977	2
#20245795	2
#20244737	2
#20244732	2
#20243126	2
C₂×#15688883	2
C₂×C₄₇×#339	2
#23560	47