Subgroups — #26207545

Order 12032.

798 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#20254988	C₂	1	2	yes	maximal, complemented
3	#20242981	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242855	C₂	1	2	yes	maximal, complemented
5	#20242774	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242743	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242566	C₂	1	2	yes	maximal, complemented
8	#20242477	C₂	1	2	yes	maximal, complemented
9	#20242273	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#10625334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3334	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094049	—	2	2	no	—
13	C₂×D₈×D₄₇	—	2	1	no	—
14	D₄×D₁₈₈	C₂²	1	2	yes	—
15	#15689500	C₂²	1	1	yes	characteristic
16	#15689497	C₂²	1	2	yes	complemented
17	#15689471	C₂²	1	2	yes	complemented
18	#15689371	—	2	2	no	—
19	#15689360	—	2	1	no	—
20	#15689325	C₂²	1	2	yes	—
21	#15689318	C₂²	1	2	yes	—
22	#15689318	C₂²	1	2	yes	complemented
23	#15689273	—	2	2	no	—
24	#15689268	—	2	2	no	—
25	#15689258	—	2	2	no	—
26	C₄×#10625334	C₂²	1	1	yes	characteristic
27	#15689201	C₂²	1	2	yes	complemented
28	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
29	#15688876	C₂²	1	1	yes	characteristic, complemented
30	#15688875	C₂²	1	1	yes	characteristic, complemented
31	#15688869	C₂²	1	2	yes	complemented
32	#15688866	C₂²	1	2	yes	complemented
33	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
34	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
35	#15688850	C₂²	1	1	yes	characteristic
36	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
37	C₄₇×#547	C₂²	1	2	yes	complemented
38	C₄₇×#500	C₂²	1	1	yes	characteristic, complemented
39	C₄₇×#480	—	2	2	no	—
40	C₄₇×#474	C₂²	1	2	yes	complemented
41	C₄₇×#466	—	2	1	no	—
42	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
44	C₂×#107×C₄₇	—	2	1	no	—
45	C₂²×D₁₈₈	—	2	2	no	—
46	C₂×D₄×D₄₇	—	2	2	no	—
47	#13094049	—	4	8	no	—
48	C₂×#10625336	—	2	2	no	—
49	C₂×#10625336	—	2	2	no	—
50	C₂×#10625336	—	2	2	no	—
51	C₂×D₃₇₆	—	2	1	no	—
52	C₂×D₃₇₆	—	2	1	no	—
53	C₂×#10625334	—	2	2	no	—
54	C₂×#10625334	—	2	2	no	—
55	C₂×#10625334	D₄	1	1	yes	characteristic
56	D₈×D₄₇	—	4	4	no	—
57	C₂×#10625329	—	2	2	no	—
58	C₂×C₈×D₄₇	—	2	1	no	—
59	#13094021	C₂³	1	2	yes	—
60	#13093999	—	2	2	no	—
61	#13093998	—	2	2	no	—
62	#13093994	—	4	2	no	—
63	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
64	#13093957	D₄	1	1	yes	characteristic
65	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
66	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
67	#13093948	—	2	2	no	—
68	#13093945	D₄	1	1	yes	characteristic
69	#13093944	—	2	2	no	—
70	#13093944	—	2	2	no	—
71	#13093944	—	4	2	no	—
72	#13093944	D₄	1	1	yes	characteristic
73	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
74	(C₂×D₄₇)⋊C₈	—	2	1	no	—
75	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
76	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
77	C₂×#41×C₄₇	—	2	2	no	—
78	C₂×D₈×C₄₇	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	—	2	1	no	—
80	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
81	#123×C₄₇	—	4	2	no	—
82	C₂²⋊Q₈×C₄₇	—	2	2	no	—
83	#121×C₄₇	—	2	2	no	—
84	C₄×D₄×C₄₇	C₂³	1	2	yes	—
85	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
87	#107×C₄₇	—	2	1	no	—
88	#107×C₄₇	—	2	1	no	—
89	#107×C₄₇	—	2	2	no	—
90	#107×C₄₇	D₄	1	1	yes	characteristic
91	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
92	#102×C₄₇	—	2	2	no	—
93	#102×C₄₇	D₄	1	2	yes	—
94	C₂²⋊C₈×C₄₇	—	2	1	no	—
95	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
96	C₂³×D₄₇	—	4	2	no	—
97	#41×C₄₇	—	4	4	no	—
98	#41×C₄₇	—	8	2	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	4	2	no	—
101	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	4	2	no	—
106	C₂×C₂²⋊D₄₇	—	4	2	no	—
107	D₄×D₄₇	—	4	4	no	—
108	D₄×D₄₇	—	8	2	no	—
109	C₂×D₁₈₈	—	2	2	no	—
110	C₂×D₁₈₈	—	2	2	no	—
111	C₂×D₁₈₈	—	2	2	no	—
112	C₂×D₁₈₈	—	4	4	no	—
113	C₂×D₁₈₈	—	4	2	no	—
114	C₂×D₁₈₈	—	8	2	no	—
115	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₄₇	—	2	1	no	—
117	D₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	4	2	no	—
120	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	4	2	no	—
125	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
127	C₂²⋊C₄×C₄₇	—	2	1	no	—
128	C₂²⋊C₄×C₄₇	—	2	2	no	—
129	C₂²⋊C₄×C₄₇	—	4	2	no	—
130	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
131	#10625336	—	4	4	no	—
132	#10625336	—	4	4	no	—
133	#10625336	—	8	2	no	—
134	#10625334	—	4	4	no	—
135	#10625334	—	4	4	no	—
136	#10625334	D₈	1	4	yes	complemented
137	(C₂×D₄₇)⋊C₄	—	2	1	no	—
138	(C₂×D₄₇)⋊C₄	—	4	2	no	—
139	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
140	#10625329	—	4	4	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
146	D₃₇₆	—	4	2	no	—
147	D₃₇₆	—	8	1	no	—
148	C₈×D₄₇	—	4	2	no	—
149	C₂³×C₄₇	—	2	1	no	—
150	C₂³×C₄₇	—	2	2	no	—
151	C₂²×D₄₇	—	2	1	no	—
152	C₂²×D₄₇	—	4	2	no	—
153	C₂²×D₄₇	—	8	4	no	—
154	C₂²×D₄₇	—	8	4	no	—
155	C₂²×D₄₇	—	16	2	no	—
156	Q₈×C₄₇	—	4	2	no	—
157	Q₈×C₄₇	—	4	2	no	—
158	D₄×C₄₇	—	2	2	no	—
159	D₄×C₄₇	—	2	1	no	—
160	D₄×C₄₇	—	2	2	no	—
161	D₄×C₄₇	—	8	4	no	—
162	D₄×C₄₇	C₂×D₈	1	2	yes	complemented
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	8	4	no	—
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂²⋊D₄₇	—	8	4	no	—
175	C₂×Dic₄₇	—	2	1	no	—
176	D₁₈₈	—	2	1	no	—
177	D₁₈₈	—	4	2	no	—
178	D₁₈₈	—	4	2	no	—
179	D₁₈₈	—	4	2	no	—
180	D₁₈₈	—	4	2	no	—
181	D₁₈₈	—	8	2	no	—
182	D₁₈₈	—	8	4	no	—
183	D₁₈₈	C₂×D₈	1	2	yes	—
184	C₄×D₄₇	—	4	1	no	—
185	C₄×D₄₇	—	4	1	no	—
186	C₈×C₄₇	—	2	1	no	—
187	C₈×C₄₇	—	4	1	no	—
188	C₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	complemented
189	C₄₇⋊C₈	—	2	1	no	—
190	C₄₇⋊C₈	—	4	1	no	—
191	C₄₇⋊C₈	—	4	2	no	—
192	C₄₇⋊C₈	—	4	1	no	—
193	C₄₇⋊C₈	C₂×D₈	1	2	yes	complemented
194	#19883	—	47	1	no	maximal, Sylow
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	—	4	1	no	—
197	C₂²×C₄₇	—	4	1	no	—
198	C₂²×C₄₇	—	4	2	no	—
199	C₂²×C₄₇	—	4	2	no	—
200	C₂²×C₄₇	—	4	2	no	—
201	C₂²×C₄₇	D₄²	1	1	yes	characteristic
202	C₂×D₄₇	—	2	2	no	—
203	C₂×D₄₇	—	4	1	no	—
204	C₂×D₄₇	—	4	1	no	—
205	C₂×D₄₇	—	8	2	no	—
206	C₂×D₄₇	—	8	2	no	—
207	C₂×D₄₇	—	8	2	no	—
208	C₂×D₄₇	—	16	8	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	4	1	no	—
211	C₄×C₄₇	—	4	2	no	—
212	C₄×C₄₇	—	8	2	no	—
213	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
214	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₄×C₄₇	#576	1	1	yes	characteristic
216	C₄×C₄₇	#577	1	1	yes	characteristic
217	Dic₄₇	—	4	1	no	—
218	#3334	D₄₇	1	1	yes	characteristic, complemented
219	D₄×D₈	—	47	1	no	—
220	#3272	—	47	2	no	—
221	#1706	—	47	1	no	—
222	#1685	—	47	2	no	—
223	#1673	—	47	1	no	—
224	#1667	—	47	1	no	—
225	#1639	—	47	2	no	—
226	#1625	—	47	2	no	—
227	#1589	—	47	1	no	—
228	C₈×D₈	—	47	1	no	—
229	C₂×C₄₇	—	4	2	no	—
230	C₂×C₄₇	—	8	2	no	—
231	C₂×C₄₇	#3272	1	1	yes	characteristic
232	C₂×C₄₇	D₄×D₈	1	1	yes	characteristic
233	C₂×C₄₇	#3290	1	1	yes	characteristic
234	D₄₇	—	4	2	no	—
235	D₄₇	—	16	2	no	—
236	C₂×AGL(1,ℤ/8)	—	94	2	no	—
237	C₂²×D₈	—	94	1	no	—
238	#547	C₂×D₄₇	1	2	yes	complemented
239	D₄²	—	47	2	no	—
240	#500	C₂×D₄₇	1	1	yes	characteristic, complemented
241	#493	—	47	1	no	—
242	#492	—	47	2	no	—
243	#486	—	47	2	no	—
244	#480	—	2	2	no	—
245	#474	C₂×D₄₇	1	2	yes	complemented
246	#468	—	94	2	no	—
247	#466	—	2	1	no	—
248	#466	—	94	1	no	—
249	#461	—	47	2	no	—
250	#459	—	47	2	no	—
251	#459	—	47	2	no	—
252	#450	—	94	2	no	—
253	#449	—	94	2	no	—
254	#447	—	94	2	no	—
255	C₄×D₈	—	47	1	no	—
256	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
257	#436	—	47	2	no	—
258	C₈×D₄	—	47	1	no	—
259	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
260	C₂×#107	—	2	1	no	—
261	#335	—	47	1	no	—
262	#335	—	47	1	no	—
263	#332	—	47	2	no	—
264	#331	—	47	2	no	—
265	D₄⋊C₈	—	47	1	no	—
266	D₄⋊C₈	—	47	2	no	—
267	D₄⋊C₈	—	47	1	no	—
268	C₈²	—	47	1	no	—
269	C₄₇	#19883	1	1	yes	characteristic, complemented, Sylow
270	C₂×#41	—	2	2	no	—
271	C₂²×D₄	—	94	2	no	—
272	C₂²×D₄	—	94	2	no	—
273	AGL(1,ℤ/8)	—	188	8	no	—
274	C₂×SD₁₆	—	94	2	no	—
275	C₂×SD₁₆	—	94	2	no	—
276	C₂×SD₁₆	—	94	2	no	—
277	C₂×D₈	—	47	1	no	—
278	C₂×D₈	—	94	2	no	—
279	C₂×D₈	—	94	2	no	—
280	C₂×D₈	—	94	1	no	—
281	C₂×D₈	—	94	1	no	—
282	C₂×D₈	—	188	4	no	—
283	C₂×D₈	C₂²⋊D₄₇	1	1	yes	characteristic
284	C₂×M₁₆	—	94	2	no	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	—	94	1	no	—
287	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
288	#127	—	47	2	no	—
289	#123	—	4	2	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	#121	—	2	2	no	—
292	#121	—	94	2	no	—
293	#121	—	94	2	no	—
294	#120	—	188	2	no	—
295	C₄×D₄	—	47	1	no	—
296	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
297	C₄×D₄	C₂²×D₄₇	1	2	yes	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	#107	—	2	1	no	—
300	#107	—	2	1	no	—
301	#107	—	2	2	no	—
302	#107	—	47	1	no	—
303	#107	C₂²⋊D₄₇	1	1	yes	characteristic
304	C₄⋊C₈	—	47	2	no	—
305	C₄⋊C₈	—	47	1	no	—
306	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
307	#103	—	94	2	no	—
308	#102	—	2	2	no	—
309	#102	—	47	1	no	—
310	#102	—	47	1	no	—
311	#102	—	94	2	no	—
312	#102	—	94	2	no	—
313	#102	—	188	2	no	—
314	#102	C₂²⋊D₄₇	1	2	yes	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	94	2	no	—
317	C₂²⋊C₈	—	94	1	no	—
318	C₄×C₈	—	47	1	no	—
319	C₄×C₈	—	47	1	no	—
320	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
321	C₂⁴	—	188	2	no	—
322	#41	—	4	4	no	—
323	#41	—	8	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	—	47	1	no	—
327	C₂×D₄	—	94	2	no	—
328	C₂×D₄	—	94	2	no	—
329	C₂×D₄	—	94	2	no	—
330	C₂×D₄	—	376	2	no	—
331	C₂×D₄	—	376	2	no	—
332	C₂×D₄	—	188	2	no	—
333	C₂×D₄	—	188	4	no	—
334	C₂×D₄	—	188	2	no	—
335	C₂×D₄	—	188	4	no	—
336	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
337	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	94	1	no	—
342	SD₁₆	—	376	2	no	—
343	SD₁₆	—	188	4	no	—
344	SD₁₆	—	188	4	no	—
345	D₈	—	2	2	no	—
346	D₈	—	47	4	no	—
347	D₈	—	376	1	no	—
348	D₈	—	188	4	no	—
349	D₈	—	188	4	no	—
350	D₈	—	188	2	no	—
351	M₁₆	—	188	4	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	4	2	no	—
354	C₂×C₈	—	47	1	no	—
355	C₂×C₈	—	47	1	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	—	94	1	no	—
358	C₂×C₈	—	94	1	no	—
359	C₂×C₈	—	188	2	no	—
360	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
361	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	47	1	no	—
366	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
367	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₂²⋊C₄	—	94	1	no	—
372	C₂²⋊C₄	—	188	2	no	—
373	C₄²	C₂³×D₄₇	1	1	yes	characteristic
374	C₂³	—	2	1	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	94	1	no	—
377	C₂³	—	376	4	no	—
378	C₂³	—	376	4	no	—
379	C₂³	—	188	2	no	—
380	C₂³	—	752	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	1	no	—
385	D₄	—	2	2	no	—
386	D₄	—	8	4	no	—
387	D₄	—	47	2	no	—
388	D₄	—	94	1	no	—
389	D₄	—	376	2	no	—
390	D₄	—	376	4	no	—
391	D₄	—	376	4	no	—
392	D₄	—	188	2	no	—
393	D₄	—	188	2	no	—
394	D₄	—	188	2	no	—
395	D₄	—	188	2	no	—
396	D₄	D₈×D₄₇	1	2	yes	complemented
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	8	4	no	—
405	C₂×C₄	—	94	1	no	—
406	C₂×C₄	—	188	1	no	—
407	C₂×C₄	—	188	1	no	—
408	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
409	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
410	C₂×C₄	#13094069	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	47	2	no	—
414	C₈	—	94	1	no	—
415	C₈	—	188	1	no	—
416	C₈	—	188	2	no	—
417	C₈	—	188	1	no	—
418	C₈	#13094049	1	2	yes	complemented
419	C₂²	—	2	2	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	94	2	no	—
426	C₂²	—	376	2	no	—
427	C₂²	—	376	2	no	—
428	C₂²	—	376	2	no	—
429	C₂²	—	188	1	no	—
430	C₂²	—	188	1	no	—
431	C₂²	—	752	8	no	—
432	C₂²	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	2	no	—
437	C₄	—	188	1	no	—
438	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
439	C₄	C₂×#13094049	1	1	yes	characteristic
440	C₄	#15689924	1	1	yes	characteristic
441	C₄	#15689931	1	1	yes	characteristic
442	C₂	—	4	2	no	—
443	C₂	—	8	2	no	—
444	C₂	—	188	2	no	—
445	C₂	—	752	2	no	—
446	C₂	#20254988	1	1	yes	characteristic
447	C₂	D₈×C₂²⋊D₄₇	1	1	yes	characteristic
448	C₂	#20255174	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×C₂²⋊D₄₇
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3334	C₂
socle	C₂²×C₄₇	D₄²
hypercenter	#3334	D₄₇
hypocenter	C₄₇	#19883
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #3334

Complements

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

N	H ≅ G/N	type
1. D₈×D₁₈₈	C₂	semidirect
2. #20254988	C₂	semidirect
3. #20242981	C₂	semidirect
4. #20242855	C₂	semidirect
5. #20242774	C₂	semidirect
6. #20242743	C₂	semidirect
7. #20242566	C₂	semidirect
8. #20242477	C₂	semidirect
9. #20242273	C₂	semidirect
10. C₈×#10625334	C₂	semidirect
11. C₄₇×#3334	C₂	semidirect
16. #15689497	C₂²	semidirect
17. #15689471	C₂²	semidirect
22. #15689318	C₂²	semidirect
27. #15689201	C₂²	semidirect
29. #15688876	C₂²	semidirect
30. #15688875	C₂²	semidirect
31. #15688869	C₂²	semidirect
32. #15688866	C₂²	semidirect
33. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
34. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
36. C₈×C₄₇⋊C₈	C₂²	semidirect
37. C₄₇×#547	C₂²	semidirect
38. C₄₇×#500	C₂²	semidirect
40. C₄₇×#474	C₂²	semidirect
43. C₈×D₄×C₄₇	C₂²	semidirect
136. #10625334	D₈	semidirect
162. D₄×C₄₇	C₂×D₈	semidirect
188. C₈×C₄₇	AGL(1,ℤ/8)	semidirect
193. C₄₇⋊C₈	C₂×D₈	semidirect
218. #3334	D₄₇	semidirect
238. #547	C₂×D₄₇	semidirect
240. #500	C₂×D₄₇	semidirect
245. #474	C₂×D₄₇	semidirect
259. C₈×D₄	C₂×D₄₇	semidirect
269. C₄₇	#19883	semidirect
396. D₄	D₈×D₄₇	semidirect
418. C₈	#13094049	semidirect

Maximal subgroups

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

subgroup	index
D₈×D₁₈₈	2
#20254988	2
#20242981	2
#20242855	2
#20242774	2
#20242743	2
#20242566	2
#20242477	2
#20242273	2
C₈×#10625334	2
C₄₇×#3334	2
#19883	47