Subgroups — #41×D₃₇₆ #27097685

Order 12032.

2406 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×D₁₈₈	C₂	1	2	yes	maximal, complemented
2	#20256363	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256024	C₂	1	2	yes	maximal, complemented
5	#20255736	C₂	1	3	yes	maximal, complemented
6	#20255202	C₂	1	6	yes	maximal, complemented
7	D₄×D₃₇₆	C₂	1	3	yes	maximal, complemented
8	#20253967	C₂	1	3	yes	maximal, complemented
9	#20253389	C₂	1	6	yes	maximal, complemented
10	C₂×C₄×D₃₇₆	C₂	1	3	yes	maximal, complemented
11	C₈×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×D₄₇	—	2	2	no	—
13	C₂²×D₃₇₆	C₂²	1	3	yes	—
14	#15689795	C₂²	1	2	yes	complemented
15	Q₈×D₁₈₈	C₂²	1	2	yes	complemented
16	#15689785	—	2	2	no	—
17	#15689777	C₂²	1	6	yes	complemented
18	#15689768	—	2	6	no	—
19	D₄×D₁₈₈	C₂²	1	6	yes	complemented
20	#15689673	C₂²	1	6	yes	complemented
21	#15689635	—	2	6	no	—
22	C₂×C₄×D₁₈₈	C₂²	1	6	yes	complemented
23	#15689528	C₂²	1	3	yes	complemented
24	#15689500	C₂²	1	3	yes	complemented
25	#15689470	C₂²	1	6	yes	complemented
26	#15689437	C₂²	1	12	yes	complemented
27	#15689404	C₂²	1	6	yes	complemented
28	#15689404	C₂²	1	6	yes	complemented
29	#15689359	C₂²	1	6	yes	complemented
30	#15689359	C₂²	1	6	yes	complemented
31	#15689319	C₂²	1	6	yes	complemented
32	#15689319	C₂²	1	6	yes	complemented
33	#15689259	C₂²	1	12	yes	complemented
34	C₄×D₃₇₆	C₂²	1	3	yes	—
35	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
36	C₄×D₃₇₆	C₂²	1	3	yes	complemented
37	C₄×D₃₇₆	C₂²	1	6	yes	complemented
38	C₄×D₃₇₆	C₂²	1	6	yes	complemented
39	C₄×D₃₇₆	C₂²	1	3	yes	complemented
40	C₄×D₃₇₆	C₂²	1	6	yes	complemented
41	C₂×#13093958	C₂²	1	3	yes	complemented
42	C₂×#13093946	C₂²	1	6	yes	complemented
43	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
44	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
45	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
46	C₈×D₄×C₄₇	C₂²	1	3	yes	complemented
47	C₈×D₄×C₄₇	C₂²	1	3	yes	complemented
48	C₄₇×#431	C₂²	1	3	yes	complemented
49	C₂×C₄×C₈×C₄₇	C₂²	1	3	yes	complemented
50	C₂×#10625354	—	2	2	no	—
51	C₂×#10625350	—	2	6	no	—
52	C₂×#10625352	—	2	6	no	—
53	#41×D₄₇	—	4	16	no	—
54	C₂×Q₈×D₄₇	—	2	2	no	—
55	C₂²×D₁₈₈	C₂³	1	6	yes	—
56	C₂×D₄×D₄₇	—	2	6	no	—
57	C₂²×C₄×D₄₇	—	2	6	no	—
58	C₂×D₃₇₆	—	2	12	no	—
59	C₂×D₃₇₆	C₂³	1	3	yes	—
60	C₂×D₃₇₆	C₂³	1	6	yes	—
61	C₂×D₃₇₆	C₂³	1	6	yes	—
62	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
63	#13094024	C₂³	1	6	yes	—
64	#13094021	C₂³	1	6	yes	—
65	#13094012	—	2	6	no	—
66	#13094008	—	2	12	no	—
67	#13094004	—	2	6	no	—
68	#13094004	—	2	6	no	—
69	#13093999	—	2	6	no	—
70	#13093999	—	2	6	no	—
71	#13093998	—	2	6	no	—
72	#13093998	C₂³	1	12	yes	—
73	#13093994	—	2	12	no	—
74	C₄×D₁₈₈	—	2	6	no	—
75	C₄×D₁₈₈	—	2	6	no	—
76	C₄×D₁₈₈	—	2	6	no	—
77	C₄×D₁₈₈	C₂³	1	6	yes	—
78	C₄×D₁₈₈	C₂³	1	6	yes	—
79	C₄×D₁₈₈	C₂³	1	2	yes	—
80	C₄×D₁₈₈	C₂³	1	6	yes	—
81	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
82	C₂×(C₂×D₄₇)⋊C₄	—	2	6	no	—
83	#13093958	C₂³	1	3	yes	—
84	#13093958	C₂³	1	6	yes	—
85	#13093958	C₂³	1	6	yes	—
86	#13093958	C₂³	1	1	yes	characteristic
87	#13093946	C₂³	1	6	yes	—
88	#13093946	C₂³	1	12	yes	—
89	#13093946	C₂³	1	6	yes	—
90	#13093946	C₂³	1	6	yes	—
91	#13093946	C₂³	1	2	yes	—
92	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₇	C₂³	1	3	yes	—
94	C₂²×C₈×C₄₇	C₂³	1	3	yes	—
95	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
96	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₄₇	D₄	1	3	yes	—
98	C₄×D₄×C₄₇	C₂³	1	3	yes	—
99	#117×C₄₇	D₄	1	3	yes	—
100	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
101	C₄⋊C₈×C₄₇	C₂³	1	3	yes	—
102	C₄⋊C₈×C₄₇	C₂³	1	3	yes	—
103	C₂²⋊C₈×C₄₇	C₂³	1	6	yes	—
104	C₄×C₈×C₄₇	C₂³	1	3	yes	—
105	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
106	C₄×C₈×C₄₇	C₂³	1	3	yes	—
107	C₄×C₈×C₄₇	C₂³	1	3	yes	—
108	C₂³×D₄₇	—	2	6	no	—
109	#41×C₄₇	D₈	1	8	yes	complemented
110	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂×D₄×C₄₇	C₂×D₄	1	3	yes	—
112	C₂²×C₄×C₄₇	C₂×D₄	1	3	yes	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	3	yes	—
114	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
115	C₂×C₂²⋊D₄₇	—	2	12	no	—
116	C₂²×Dic₄₇	—	2	6	no	—
117	#10625354	—	4	8	no	—
118	Q₈×D₄₇	—	4	8	no	—
119	#10625352	—	4	24	no	—
120	D₄×D₄₇	—	4	24	no	—
121	#10625350	—	4	24	no	—
122	C₂×D₁₈₈	—	2	12	no	—
123	C₂×D₁₈₈	—	2	6	no	—
124	C₂×D₁₈₈	—	2	6	no	—
125	C₂×D₁₈₈	—	2	6	no	—
126	C₂×D₁₈₈	—	4	6	no	—
127	C₂×D₁₈₈	C₂⁴	1	6	yes	—
128	C₂×D₁₈₈	C₂⁴	1	2	yes	—
129	C₂×C₄×D₄₇	—	2	2	no	—
130	C₂×C₄×D₄₇	—	2	6	no	—
131	C₂×C₄×D₄₇	—	2	6	no	—
132	C₂×C₄×D₄₇	—	2	6	no	—
133	C₂×C₄×D₄₇	—	4	24	no	—
134	C₂×Dic₉₄	—	2	6	no	—
135	C₂×C₈×C₄₇	—	2	6	no	—
136	C₂×C₈×C₄₇	—	4	3	no	—
137	C₂×C₈×C₄₇	C₂⁴	1	3	yes	—
138	C₂×C₈×C₄₇	C₂⁴	1	3	yes	—
139	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
140	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
141	C₄⋊C₄×C₄₇	C₂×D₄	1	3	yes	—
142	C₄⋊C₄×C₄₇	C₂×D₄	1	3	yes	—
143	C₂²⋊C₄×C₄₇	C₂×D₄	1	6	yes	—
144	C₄²×C₄₇	C₂×D₄	1	3	yes	—
145	C₄²×C₄₇	C₂×D₄	1	3	yes	—
146	C₄²×C₄₇	C₂⁴	1	3	yes	—
147	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
148	(C₂×D₄₇)⋊C₄	—	2	2	no	—
149	(C₂×D₄₇)⋊C₄	—	2	6	no	—
150	(C₂×D₄₇)⋊C₄	—	2	6	no	—
151	(C₂×D₄₇)⋊C₄	—	2	6	no	—
152	(C₂×D₄₇)⋊C₄	—	2	12	no	—
153	C₄⋊Dic₄₇	—	2	6	no	—
154	C₄⋊Dic₄₇	—	2	6	no	—
155	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
156	C₄⋊Dic₄₇	C₂⁴	1	6	yes	—
157	D₃₇₆	—	2	12	no	—
158	D₃₇₆	—	2	6	no	—
159	D₃₇₆	—	4	6	no	—
160	D₃₇₆	#41	1	4	yes	direct product factor
161	C₂³×C₄₇	C₂²×D₄	1	3	yes	—
162	C₂²×D₄₇	—	2	2	no	—
163	C₂²×D₄₇	—	2	6	no	—
164	C₂²×D₄₇	—	4	12	no	—
165	C₂²×D₄₇	—	4	12	no	—
166	C₂²×D₄₇	—	8	6	no	—
167	Q₈×C₄₇	C₂×D₈	1	4	yes	complemented
168	D₄×C₄₇	C₂×D₈	1	12	yes	complemented
169	C₂×C₄×C₄₇	—	2	3	no	—
170	C₂×C₄×C₄₇	—	2	3	no	—
171	C₂×C₄×C₄₇	—	4	3	no	—
172	C₂×C₄×C₄₇	C₂×D₈	1	12	yes	complemented
173	C₂×C₄×C₄₇	C₂²×D₄	1	3	yes	—
174	C₂×C₄×C₄₇	C₂²×D₄	1	3	yes	—
175	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×D₄	1	3	yes	—
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
179	C₂²⋊D₄₇	—	4	24	no	—
180	C₂×Dic₄₇	—	2	6	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	4	12	no	—
183	D₁₈₈	—	2	6	no	—
184	D₁₈₈	—	2	2	no	—
185	D₁₈₈	—	2	6	no	—
186	D₁₈₈	—	4	12	no	—
187	D₁₈₈	—	4	12	no	—
188	D₁₈₈	—	8	6	no	—
189	D₁₈₈	C₂×#41	1	4	yes	complemented
190	C₄×D₄₇	—	4	4	no	—
191	C₄×D₄₇	—	4	12	no	—
192	C₄×D₄₇	—	4	12	no	—
193	C₄×D₄₇	—	4	12	no	—
194	Dic₉₄	—	4	12	no	—
195	C₈×C₄₇	—	2	3	no	—
196	C₈×C₄₇	—	2	3	no	—
197	C₈×C₄₇	—	2	1	no	—
198	C₈×C₄₇	C₂×#41	1	2	yes	complemented
199	D₈×#41	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	—	2	3	no	—
201	C₂²×C₄₇	—	2	3	no	—
202	C₂²×C₄₇	C₂²×D₈	1	6	yes	—
203	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
204	C₂×D₄₇	—	2	4	no	—
205	C₂×D₄₇	—	4	2	no	—
206	C₂×D₄₇	—	4	2	no	—
207	C₂×D₄₇	—	4	6	no	—
208	C₂×D₄₇	—	4	6	no	—
209	C₂×D₄₇	—	4	6	no	—
210	C₂×D₄₇	—	8	24	no	—
211	C₄×C₄₇	—	2	3	no	—
212	C₄×C₄₇	—	2	1	no	—
213	C₄×C₄₇	—	2	3	no	—
214	C₄×C₄₇	C₂²×D₈	1	6	yes	—
215	C₄×C₄₇	C₂²×D₈	1	2	yes	—
216	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
217	C₄×C₄₇	#585	1	1	yes	characteristic
218	Dic₄₇	—	4	6	no	—
219	Dic₄₇	—	4	2	no	—
220	D₄×#41	—	47	2	no	—
221	#3391	—	47	1	no	—
222	Q₈×D₈	—	47	1	no	—
223	#3358	—	47	2	no	—
224	#3334	—	47	3	no	—
225	#3294	—	47	6	no	—
226	D₄×D₈	—	47	3	no	—
227	#3169	—	47	3	no	—
228	#3100	—	47	6	no	—
229	C₈×#41	D₄₇	1	1	yes	characteristic, complemented
230	C₂×C₄×D₈	—	47	3	no	—
231	C₂×C₄₇	—	2	6	no	—
232	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
233	C₂×C₄₇	C₂³×D₈	1	1	yes	characteristic
234	C₂×C₄₇	#3584	1	1	yes	characteristic
235	D₄₇	—	4	4	no	—
236	D₄₇	—	8	6	no	—
237	C₂²×#41	—	94	2	no	—
238	C₂²×D₈	—	47	3	no	—
239	#550	—	47	2	no	—
240	D₄×Q₈	—	47	2	no	—
241	#548	—	94	2	no	—
242	#547	—	47	6	no	—
243	#546	—	94	6	no	—
244	D₄²	—	47	6	no	—
245	#532	—	47	6	no	—
246	#525	—	94	6	no	—
247	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
248	C₂×C₄×D₄	—	47	6	no	—
249	#500	—	47	3	no	—
250	#493	—	47	3	no	—
251	#486	—	47	6	no	—
252	#480	—	47	12	no	—
253	#474	—	47	6	no	—
254	#474	—	47	6	no	—
255	#466	—	47	6	no	—
256	#466	—	47	6	no	—
257	#459	—	47	6	no	—
258	#459	—	47	6	no	—
259	#447	—	47	12	no	—
260	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
261	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
262	C₄×D₈	—	47	3	no	—
263	C₄×D₈	—	47	6	no	—
264	C₄×D₈	—	47	6	no	—
265	C₄×D₈	—	47	6	no	—
266	C₄×D₈	—	47	3	no	—
267	C₄×D₈	—	47	3	no	—
268	C₄×D₈	—	47	1	no	—
269	C₈×D₄	C₂×D₄₇	1	3	yes	complemented
270	C₈×D₄	C₂×D₄₇	1	3	yes	complemented
271	#431	C₂×D₄₇	1	3	yes	complemented
272	C₂×#107	—	47	3	no	—
273	C₂×#102	—	47	6	no	—
274	C₂×C₄×C₈	C₂×D₄₇	1	3	yes	complemented
275	C₄₇	D₈×#41	1	1	yes	characteristic, complemented, Sylow
276	C₂×#41	—	94	2	no	—
277	C₂×#41	—	94	6	no	—
278	C₂×#41	—	94	6	no	—
279	C₂×#41	—	188	16	no	—
280	C₂×#41	D₁₈₈	1	1	yes	characteristic
281	C₂²×Q₈	—	94	2	no	—
282	C₂²×D₄	—	47	6	no	—
283	C₂²×D₄	—	94	6	no	—
284	C₂³×C₄	—	94	6	no	—
285	C₂×D₈	—	47	1	no	—
286	C₂×D₈	—	47	6	no	—
287	C₂×D₈	—	47	3	no	—
288	C₂×D₈	—	47	6	no	—
289	C₂×D₈	—	94	12	no	—
290	C₂²×C₈	C₂²×D₄₇	1	3	yes	—
291	C₂²×C₈	C₂²×D₄₇	1	3	yes	—
292	C₄⋊Q₈	—	47	6	no	—
293	#127	—	47	6	no	—
294	#124	—	94	6	no	—
295	#123	—	94	12	no	—
296	C₂²⋊Q₈	—	94	6	no	—
297	C₂²⋊Q₈	—	94	6	no	—
298	#121	—	47	12	no	—
299	#121	—	94	6	no	—
300	#121	—	94	6	no	—
301	#121	—	94	6	no	—
302	#120	—	94	12	no	—
303	C₄×Q₈	D₁₈₈	1	1	yes	characteristic
304	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
305	C₄×D₄	—	47	2	no	—
306	C₄×D₄	—	47	6	no	—
307	C₄×D₄	—	47	6	no	—
308	C₄×D₄	—	47	6	no	—
309	C₄×D₄	—	94	6	no	—
310	C₄×D₄	—	94	6	no	—
311	C₄×D₄	—	94	6	no	—
312	C₄×D₄	D₁₈₈	1	3	yes	—
313	C₄×D₄	C₂²×D₄₇	1	3	yes	—
314	#117	D₁₈₈	1	3	yes	—
315	C₂×C₄⋊C₄	—	47	6	no	—
316	C₂×C₂²⋊C₄	—	94	6	no	—
317	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
318	#107	—	47	1	no	—
319	#107	—	47	3	no	—
320	#107	—	47	6	no	—
321	#107	—	47	6	no	—
322	C₄⋊C₈	C₂²×D₄₇	1	3	yes	—
323	C₄⋊C₈	C₂²×D₄₇	1	3	yes	—
324	#102	—	47	2	no	—
325	#102	—	47	6	no	—
326	#102	—	47	6	no	—
327	#102	—	47	6	no	—
328	#102	—	47	12	no	—
329	C₂²⋊C₈	C₂²×D₄₇	1	6	yes	—
330	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
331	C₄×C₈	C₂²×D₄₇	1	3	yes	—
332	C₄×C₈	C₂²×D₄₇	1	3	yes	—
333	C₄×C₈	C₂²×D₄₇	1	3	yes	—
334	C₂⁴	—	94	6	no	—
335	#41	—	188	8	no	—
336	#41	—	188	24	no	—
337	#41	—	188	24	no	—
338	#41	D₃₇₆	1	8	yes	direct product factor
339	C₂×Q₈	—	94	6	no	—
340	C₂×Q₈	—	188	8	no	—
341	C₂×Q₈	C₂×D₁₈₈	1	1	yes	characteristic
342	C₂×D₄	—	47	2	no	—
343	C₂×D₄	—	47	6	no	—
344	C₂×D₄	—	94	12	no	—
345	C₂×D₄	—	94	12	no	—
346	C₂×D₄	—	94	6	no	—
347	C₂×D₄	—	94	6	no	—
348	C₂×D₄	—	94	6	no	—
349	C₂×D₄	—	188	6	no	—
350	C₂×D₄	—	188	24	no	—
351	C₂×D₄	C₂×D₁₈₈	1	3	yes	—
352	C₂²×C₄	—	94	6	no	—
353	C₂²×C₄	—	94	6	no	—
354	C₂²×C₄	—	94	6	no	—
355	C₂²×C₄	—	94	2	no	—
356	C₂²×C₄	—	94	6	no	—
357	C₂²×C₄	—	188	24	no	—
358	C₂²×C₄	C₂×D₁₈₈	1	3	yes	—
359	C₂²×C₄	C₂×D₁₈₈	1	3	yes	—
360	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
361	D₈	—	47	4	no	—
362	D₈	—	94	12	no	—
363	D₈	—	94	6	no	—
364	D₈	—	188	6	no	—
365	C₂×C₈	—	2	6	no	—
366	C₂×C₈	—	4	3	no	—
367	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
368	C₂×C₈	C₂³×D₄₇	1	3	yes	—
369	C₂×C₈	C₂³×D₄₇	1	3	yes	—
370	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
371	C₄⋊C₄	—	47	2	no	—
372	C₄⋊C₄	—	47	6	no	—
373	C₄⋊C₄	—	94	6	no	—
374	C₄⋊C₄	—	94	6	no	—
375	C₄⋊C₄	C₂×D₁₈₈	1	3	yes	—
376	C₄⋊C₄	C₂×D₁₈₈	1	3	yes	—
377	C₂²⋊C₄	—	94	2	no	—
378	C₂²⋊C₄	—	94	6	no	—
379	C₂²⋊C₄	—	94	6	no	—
380	C₂²⋊C₄	—	94	6	no	—
381	C₂²⋊C₄	—	94	12	no	—
382	C₂²⋊C₄	C₂×D₁₈₈	1	6	yes	—
383	C₄²	C₂×D₁₈₈	1	3	yes	—
384	C₄²	C₂×D₁₈₈	1	3	yes	—
385	C₄²	C₂³×D₄₇	1	3	yes	—
386	C₄²	C₂³×D₄₇	1	1	yes	characteristic
387	C₂³	—	94	2	no	—
388	C₂³	—	94	6	no	—
389	C₂³	—	376	6	no	—
390	C₂³	—	188	12	no	—
391	C₂³	—	188	12	no	—
392	C₂³	C₂²×D₁₈₈	1	3	yes	—
393	Q₈	—	188	12	no	—
394	Q₈	C₂×D₃₇₆	1	4	yes	complemented
395	D₄	—	47	4	no	—
396	D₄	—	94	6	no	—
397	D₄	—	94	2	no	—
398	D₄	—	94	6	no	—
399	D₄	—	376	6	no	—
400	D₄	—	188	12	no	—
401	D₄	—	188	24	no	—
402	D₄	—	188	12	no	—
403	D₄	C₂×D₃₇₆	1	12	yes	complemented
404	C₂×C₄	—	2	3	no	—
405	C₂×C₄	—	2	3	no	—
406	C₂×C₄	—	4	3	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	6	no	—
409	C₂×C₄	—	188	12	no	—
410	C₂×C₄	—	188	4	no	—
411	C₂×C₄	—	188	12	no	—
412	C₂×C₄	—	188	12	no	—
413	C₂×C₄	—	188	12	no	—
414	C₂×C₄	C₂×D₃₇₆	1	12	yes	complemented
415	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₁₈₈	1	3	yes	—
417	C₂×C₄	C₂²×D₁₈₈	1	3	yes	—
418	C₂×C₄	C₂²×D₁₈₈	1	3	yes	—
419	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
420	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
421	C₈	—	2	3	no	—
422	C₈	—	2	1	no	—
423	C₈	—	2	3	no	—
424	C₈	#41×D₄₇	1	2	yes	complemented
425	C₂²	—	2	3	no	—
426	C₂²	—	2	3	no	—
427	C₂²	—	94	4	no	—
428	C₂²	—	376	24	no	—
429	C₂²	—	188	6	no	—
430	C₂²	—	188	6	no	—
431	C₂²	—	188	6	no	—
432	C₂²	—	188	2	no	—
433	C₂²	—	188	2	no	—
434	C₂²	C₂²×D₃₇₆	1	6	yes	—
435	C₂²	C₂³×D₁₈₈	1	1	yes	characteristic
436	C₄	—	2	3	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	3	no	—
439	C₄	—	188	2	no	—
440	C₄	—	188	6	no	—
441	C₄	C₂²×D₃₇₆	1	2	yes	—
442	C₄	C₂²×D₃₇₆	1	6	yes	—
443	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
444	C₄	#15689959	1	1	yes	characteristic
445	C₂	—	2	6	no	—
446	C₂	—	376	6	no	—
447	C₂	—	188	4	no	—
448	C₂	#41×D₁₈₈	1	1	yes	characteristic
449	C₂	C₂³×D₃₇₆	1	1	yes	characteristic
450	C₂	#20258162	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₈×#41×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₈×#41	D₄₇
hypocenter	C₄₇	D₈×#41
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #41×D₁₈₈	C₂	semidirect
2. #20256363	C₂	semidirect
3. Q₈×D₃₇₆	C₂	semidirect
4. #20256024	C₂	semidirect
5. #20255736	C₂	semidirect
6. #20255202	C₂	semidirect
7. D₄×D₃₇₆	C₂	semidirect
8. #20253967	C₂	semidirect
9. #20253389	C₂	semidirect
10. C₂×C₄×D₃₇₆	C₂	semidirect
11. C₈×#41×C₄₇	C₂	semidirect
14. #15689795	C₂²	semidirect
15. Q₈×D₁₈₈	C₂²	semidirect
17. #15689777	C₂²	semidirect
19. D₄×D₁₈₈	C₂²	semidirect
20. #15689673	C₂²	semidirect
22. C₂×C₄×D₁₈₈	C₂²	semidirect
23. #15689528	C₂²	semidirect
24. #15689500	C₂²	semidirect
25. #15689470	C₂²	semidirect
26. #15689437	C₂²	semidirect
27. #15689404	C₂²	semidirect
28. #15689404	C₂²	semidirect
29. #15689359	C₂²	semidirect
30. #15689359	C₂²	semidirect
31. #15689319	C₂²	semidirect
32. #15689319	C₂²	semidirect
33. #15689259	C₂²	semidirect
36. C₄×D₃₇₆	C₂²	semidirect
37. C₄×D₃₇₆	C₂²	semidirect
38. C₄×D₃₇₆	C₂²	semidirect
39. C₄×D₃₇₆	C₂²	semidirect
40. C₄×D₃₇₆	C₂²	semidirect
41. C₂×#13093958	C₂²	semidirect
42. C₂×#13093946	C₂²	semidirect
44. C₈×Q₈×C₄₇	C₂²	semidirect
45. C₈×Q₈×C₄₇	C₂²	semidirect
46. C₈×D₄×C₄₇	C₂²	semidirect
47. C₈×D₄×C₄₇	C₂²	semidirect
48. C₄₇×#431	C₂²	semidirect
49. C₂×C₄×C₈×C₄₇	C₂²	semidirect
109. #41×C₄₇	D₈	semidirect
160. D₃₇₆	#41	direct (N × H)
167. Q₈×C₄₇	C₂×D₈	semidirect
168. D₄×C₄₇	C₂×D₈	semidirect
172. C₂×C₄×C₄₇	C₂×D₈	semidirect
189. D₁₈₈	C₂×#41	semidirect
198. C₈×C₄₇	C₂×#41	semidirect
229. C₈×#41	D₄₇	semidirect
260. C₈×Q₈	C₂×D₄₇	semidirect
261. C₈×Q₈	C₂×D₄₇	semidirect
269. C₈×D₄	C₂×D₄₇	semidirect
270. C₈×D₄	C₂×D₄₇	semidirect
271. #431	C₂×D₄₇	semidirect
274. C₂×C₄×C₈	C₂×D₄₇	semidirect
275. C₄₇	D₈×#41	semidirect
338. #41	D₃₇₆	direct (N × H)
394. Q₈	C₂×D₃₇₆	semidirect
403. D₄	C₂×D₃₇₆	semidirect
414. C₂×C₄	C₂×D₃₇₆	semidirect
424. C₈	#41×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#41×D₁₈₈	2
#20256363	2
Q₈×D₃₇₆	2
#20256024	2
#20255736	2
#20255202	2
D₄×D₃₇₆	2
#20253967	2
#20253389	2
C₂×C₄×D₃₇₆	2
C₈×#41×C₄₇	2
D₈×#41	47

Subgroups — #41×D376 #27097685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×D₃₇₆ #27097685