Subgroups — C₄×#15689404 #26223842

Order 12032.

1000 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689404	C₂	1	1	yes	maximal, characteristic
2	C₄×#13094024	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×D₁₈₈	C₂	1	1	yes	maximal, characteristic
4	#20244339	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244147	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243960	C₂	1	2	yes	maximal, complemented
7	#20243638	C₂	1	2	yes	maximal
8	#20243389	C₂	1	1	yes	maximal, characteristic
9	C₄×#13093958	C₂	1	2	yes	maximal, complemented
10	C₄×#13093946	C₂	1	2	yes	maximal
11	C₄×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094024	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₉₄	—	2	1	no	—
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
17	C₂×C₄²×D₄₇	—	2	1	no	—
18	#15689404	C₄	1	8	yes	direct product factor
19	C₂×#13093958	C₂²	1	2	yes	—
20	C₂×#13093958	C₂²	1	2	yes	—
21	C₂×#13093946	C₂²	1	2	yes	—
22	C₂×#13093946	C₂²	1	2	yes	—
23	#15689029	—	2	1	no	—
24	#15689021	—	2	1	no	—
25	#15689021	C₂²	1	2	yes	—
26	#15688993	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊Dic₄₇	—	2	1	no	—
28	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
33	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
34	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
35	#15688886	C₂²	1	2	yes	—
36	#15688886	C₂²	1	2	yes	—
37	#15688886	C₂²	1	2	yes	—
38	#15688886	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
42	C₄³×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#336	C₂²	1	2	yes	—
44	C₂²×Dic₉₄	—	2	1	no	—
45	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	—	2	1	no	—
47	C₂²×C₄×D₄₇	—	2	1	no	—
48	C₂²×C₄×D₄₇	—	2	1	no	—
49	#13094024	—	2	2	no	—
50	#13094024	C₂×C₄	1	4	yes	complemented
51	C₄×Dic₉₄	—	4	4	no	—
52	C₄×D₁₈₈	—	2	2	no	—
53	C₄×D₁₈₈	—	2	2	no	—
54	C₄×D₁₈₈	—	2	2	no	—
55	C₄×D₁₈₈	—	2	2	no	—
56	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
57	C₄×D₁₈₈	Q₈	1	4	yes	complemented
58	C₂×C₄⋊Dic₄₇	—	2	1	no	—
59	C₂×C₄⋊Dic₄₇	—	2	1	no	—
60	C₂×C₄⋊Dic₄₇	—	2	1	no	—
61	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
62	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
66	C₂×Dic₄₇⋊C₄	—	2	2	no	—
67	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
68	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
69	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
70	C₂×C₄×Dic₄₇	—	2	1	no	—
71	C₂×C₄×Dic₄₇	—	2	1	no	—
72	C₂×C₄×Dic₄₇	—	2	1	no	—
73	C₂×C₄×Dic₄₇	—	2	2	no	—
74	C₄²×D₄₇	—	4	4	no	—
75	#13093958	—	2	4	no	—
76	#13093958	C₂×C₄	1	8	yes	complemented
77	#13093946	—	2	4	no	—
78	#13093946	C₂×C₄	1	8	yes	—
79	C₄₇⋊#95	—	2	1	no	—
80	C₄₇⋊#95	—	2	1	no	—
81	C₄₇⋊#95	—	2	1	no	—
82	C₄₇⋊#95	—	2	2	no	—
83	C₄₇⋊#95	—	2	2	no	—
84	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
85	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₄₇	—	2	2	no	—
94	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
95	C₄×C₈×C₄₇	—	2	4	no	—
96	C₂³×D₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
104	C₂²×Dic₄₇	—	2	1	no	—
105	C₂²×Dic₄₇	—	2	1	no	—
106	C₂²×Dic₄₇	—	2	1	no	—
107	C₂²×Dic₄₇	—	2	2	no	—
108	C₂²×Dic₄₇	—	2	2	no	—
109	C₂×D₁₈₈	—	2	1	no	—
110	C₂×D₁₈₈	—	2	1	no	—
111	C₂×D₁₈₈	—	2	1	no	—
112	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
113	C₂×D₁₈₈	C₂×Q₈	1	2	yes	—
114	C₂×D₁₈₈	#41	1	2	yes	—
115	C₂×C₄×D₄₇	—	2	4	no	—
116	C₂×C₄×D₄₇	—	2	4	no	—
117	C₂×C₄×D₄₇	—	2	4	no	—
118	C₂×C₄×D₄₇	—	4	2	no	—
119	C₂×C₄×D₄₇	—	4	2	no	—
120	C₂×C₄×D₄₇	—	4	2	no	—
121	C₂×C₄×D₄₇	—	4	2	no	—
122	C₂×C₄×D₄₇	—	4	2	no	—
123	C₂×C₄×D₄₇	—	4	2	no	—
124	C₂×Dic₉₄	—	2	4	no	—
125	C₂×Dic₉₄	—	4	2	no	—
126	C₂×Dic₉₄	—	4	2	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	—	2	2	no	—
129	C₂×C₈×C₄₇	—	2	2	no	—
130	C₂×C₈×C₄₇	—	2	2	no	—
131	C₂×C₈×C₄₇	—	2	2	no	—
132	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
133	C₄²×C₄₇	—	2	2	no	—
134	C₄²×C₄₇	—	2	2	no	—
135	C₄²×C₄₇	—	2	1	no	—
136	C₄²×C₄₇	—	2	1	no	—
137	C₄²×C₄₇	—	4	1	no	—
138	C₄²×C₄₇	D₈	1	4	yes	—
139	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
140	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
141	C₄²×C₄₇	#41	1	2	yes	—
142	C₄²×C₄₇	#41	1	2	yes	—
143	(C₂×D₄₇)⋊C₄	—	2	4	no	—
144	(C₂×D₄₇)⋊C₄	—	2	4	no	—
145	(C₂×D₄₇)⋊C₄	—	2	4	no	—
146	C₄⋊Dic₄₇	—	2	4	no	—
147	C₄⋊Dic₄₇	—	2	1	no	—
148	C₄⋊Dic₄₇	—	2	1	no	—
149	C₄⋊Dic₄₇	—	2	1	no	—
150	C₄⋊Dic₄₇	—	2	2	no	—
151	C₄⋊Dic₄₇	—	2	2	no	—
152	C₄⋊Dic₄₇	—	2	2	no	—
153	C₄⋊Dic₄₇	—	4	2	no	—
154	C₄⋊Dic₄₇	—	4	2	no	—
155	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
156	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
157	C₄⋊Dic₄₇	C₂×Q₈	1	2	yes	—
158	C₄⋊Dic₄₇	#41	1	2	yes	—
159	Dic₄₇⋊C₄	—	4	4	no	—
160	C₄×Dic₄₇	—	4	2	no	—
161	C₄×Dic₄₇	—	4	2	no	—
162	C₄×Dic₄₇	—	4	2	no	—
163	C₄×Dic₄₇	—	4	4	no	—
164	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
165	C₂²×D₄₇	—	2	2	no	—
166	C₂²×D₄₇	—	2	2	no	—
167	C₂²×D₄₇	—	2	2	no	—
168	C₂²×D₄₇	—	4	1	no	—
169	C₂²×D₄₇	—	4	1	no	—
170	C₂²×D₄₇	—	4	1	no	—
171	C₂²×D₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
184	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
187	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
188	C₂×C₄×C₄₇	#135	1	2	yes	—
189	C₂×C₄×C₄₇	#137	1	2	yes	—
190	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
196	C₂×Dic₄₇	—	2	4	no	—
197	C₂×Dic₄₇	—	2	2	no	—
198	C₂×Dic₄₇	—	2	2	no	—
199	C₂×Dic₄₇	—	2	2	no	—
200	C₂×Dic₄₇	—	4	1	no	—
201	C₂×Dic₄₇	—	4	1	no	—
202	C₂×Dic₄₇	—	4	1	no	—
203	C₂×Dic₄₇	—	4	2	no	—
204	C₂×Dic₄₇	—	4	2	no	—
205	C₂×Dic₄₇	—	4	1	no	—
206	C₂×Dic₄₇	—	4	1	no	—
207	C₂×Dic₄₇	—	4	1	no	—
208	C₂×Dic₄₇	—	4	2	no	—
209	C₂×Dic₄₇	—	4	2	no	—
210	C₂×Dic₄₇	—	4	2	no	—
211	D₁₈₈	—	2	2	no	—
212	D₁₈₈	—	2	2	no	—
213	D₁₈₈	—	2	2	no	—
214	D₁₈₈	C₄×Q₈	1	4	yes	complemented
215	C₄×D₄₇	—	4	8	no	—
216	C₄×D₄₇	—	4	8	no	—
217	C₄×D₄₇	—	4	8	no	—
218	Dic₉₄	—	4	8	no	—
219	C₈×C₄₇	—	2	4	no	—
220	C₈×C₄₇	—	4	2	no	—
221	C₄×#474	—	47	1	no	maximal, Sylow
222	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
223	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
224	C₂²×C₄₇	#525	1	1	yes	characteristic
225	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
226	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
227	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
228	C₂²×C₄₇	#575	1	1	yes	characteristic
229	C₂×D₄₇	—	2	4	no	—
230	C₂×D₄₇	—	4	2	no	—
231	C₂×D₄₇	—	4	2	no	—
232	C₂×D₄₇	—	4	2	no	—
233	C₂×D₄₇	—	4	2	no	—
234	C₂×D₄₇	—	4	2	no	—
235	C₂×D₄₇	—	4	2	no	—
236	C₄×C₄₇	—	2	2	no	—
237	C₄×C₄₇	—	2	2	no	—
238	C₄×C₄₇	—	2	2	no	—
239	C₄×C₄₇	—	4	1	no	—
240	C₄×C₄₇	C₄×D₈	1	4	yes	—
241	C₄×C₄₇	#474	1	4	yes	complemented
242	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
243	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
244	C₄×C₄₇	#529	1	1	yes	characteristic
245	C₄×C₄₇	#533	1	1	yes	characteristic
246	Dic₄₇	—	4	2	no	—
247	Dic₄₇	—	4	4	no	—
248	Dic₄₇	—	4	2	no	—
249	Dic₄₇	—	4	2	no	—
250	Dic₄₇	—	8	2	no	—
251	C₂×#474	—	47	1	no	—
252	C₄×C₄⋊Q₈	—	47	1	no	—
253	C₄²×D₄	—	47	1	no	—
254	#1988	—	47	1	no	—
255	#1947	—	47	1	no	—
256	#1918	—	47	2	no	—
257	#1862	—	47	2	no	—
258	#1802	—	47	1	no	—
259	C₄×#107	—	47	2	no	—
260	C₄×C₄⋊C₈	D₄₇	1	1	yes	characteristic, complemented
261	C₄×#102	—	47	2	no	—
262	C₂×C₄₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
263	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
264	C₂×C₄₇	C₄×#137	1	1	yes	characteristic
265	C₂×C₄₇	C₂×#474	1	1	yes	characteristic
266	C₂×C₄₇	#3076	1	1	yes	characteristic
267	C₂×C₄₇	#3100	1	1	yes	characteristic
268	C₂×C₄₇	#3107	1	1	yes	characteristic
269	D₄₇	—	4	4	no	—
270	C₂×C₄⋊Q₈	—	47	1	no	—
271	C₂×C₄×Q₈	—	94	1	no	—
272	C₂×C₄×D₄	—	47	1	no	—
273	C₂×C₄×D₄	—	47	1	no	—
274	C₂×C₄×D₄	—	47	1	no	—
275	C₂²×C₄²	—	94	1	no	—
276	#474	—	47	8	no	—
277	C₂×#107	—	47	2	no	—
278	C₂×#107	—	47	2	no	—
279	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
281	C₂×#102	—	47	2	no	—
282	C₂×#102	—	47	2	no	—
283	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
284	#391	—	94	1	no	—
285	#389	—	47	2	no	—
286	#389	—	94	1	no	—
287	#384	—	47	1	no	—
288	C₄×C₄⋊C₄	—	47	2	no	—
289	C₄×C₄⋊C₄	—	47	1	no	—
290	C₄×C₄⋊C₄	—	47	1	no	—
291	C₄×C₄⋊C₄	—	47	1	no	—
292	C₄×C₄⋊C₄	—	94	1	no	—
293	C₄×C₂²⋊C₄	—	94	1	no	—
294	C₄×C₂²⋊C₄	—	94	1	no	—
295	C₄×C₂²⋊C₄	—	94	1	no	—
296	C₄³	C₂×D₄₇	1	1	yes	characteristic
297	#340	—	47	2	no	—
298	#340	—	47	2	no	—
299	#340	—	47	2	no	—
300	#340	—	47	2	no	—
301	#336	C₂×D₄₇	1	2	yes	—
302	C₄₇	C₄×#474	1	1	yes	characteristic, complemented, Sylow
303	C₂²×Q₈	—	94	1	no	—
304	C₂²×D₄	—	47	1	no	—
305	C₂³×C₄	—	94	1	no	—
306	C₂³×C₄	—	94	1	no	—
307	C₂³×C₄	—	94	1	no	—
308	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
309	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
310	C₄⋊Q₈	—	47	4	no	—
311	C₄⋊Q₈	—	94	2	no	—
312	C₄×Q₈	—	188	4	no	—
313	C₄×D₄	—	47	4	no	—
314	C₄×D₄	—	47	4	no	—
315	C₄×D₄	—	94	2	no	—
316	C₄×D₄	—	94	2	no	—
317	C₄×D₄	—	94	2	no	—
318	C₄×D₄	—	94	2	no	—
319	C₂×C₄⋊C₄	—	47	1	no	—
320	C₂×C₄⋊C₄	—	47	1	no	—
321	C₂×C₄⋊C₄	—	47	1	no	—
322	C₂×C₄⋊C₄	—	47	2	no	—
323	C₂×C₄⋊C₄	—	47	2	no	—
324	C₂×C₄⋊C₄	—	94	1	no	—
325	C₂×C₄⋊C₄	—	94	2	no	—
326	C₂×C₄⋊C₄	—	94	1	no	—
327	C₂×C₄⋊C₄	—	94	1	no	—
328	C₂×C₂²⋊C₄	—	94	1	no	—
329	C₂×C₂²⋊C₄	—	94	1	no	—
330	C₂×C₂²⋊C₄	—	94	1	no	—
331	C₂×C₄²	—	94	1	no	—
332	C₂×C₄²	—	94	1	no	—
333	C₂×C₄²	—	94	2	no	—
334	C₂×C₄²	—	94	1	no	—
335	C₂×C₄²	—	188	4	no	—
336	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
337	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
338	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
339	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
340	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
341	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
342	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
343	#107	—	47	8	no	—
344	#107	—	94	4	no	—
345	C₄⋊C₈	—	2	2	no	—
346	C₄⋊C₈	C₄×D₄₇	1	4	yes	complemented
347	#102	—	47	8	no	—
348	#102	—	94	4	no	—
349	C₄×C₈	—	2	4	no	—
350	#95	—	94	1	no	—
351	#95	—	94	1	no	—
352	#95	—	94	1	no	—
353	#95	—	94	2	no	—
354	#95	—	94	2	no	—
355	C₂⁴	—	94	1	no	—
356	C₂×Q₈	—	94	4	no	—
357	C₂×Q₈	—	188	2	no	—
358	C₂×Q₈	—	188	2	no	—
359	C₂×D₄	—	47	2	no	—
360	C₂×D₄	—	47	2	no	—
361	C₂×D₄	—	47	2	no	—
362	C₂×D₄	—	94	1	no	—
363	C₂×D₄	—	94	1	no	—
364	C₂×D₄	—	94	1	no	—
365	C₂²×C₄	—	94	4	no	—
366	C₂²×C₄	—	94	1	no	—
367	C₂²×C₄	—	94	1	no	—
368	C₂²×C₄	—	94	1	no	—
369	C₂²×C₄	—	94	2	no	—
370	C₂²×C₄	—	94	4	no	—
371	C₂²×C₄	—	94	4	no	—
372	C₂²×C₄	—	94	2	no	—
373	C₂²×C₄	—	188	2	no	—
374	C₂²×C₄	—	188	2	no	—
375	C₂²×C₄	—	188	2	no	—
376	C₂²×C₄	—	188	2	no	—
377	C₂²×C₄	—	188	2	no	—
378	C₂²×C₄	—	188	2	no	—
379	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
385	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
392	C₄⋊C₄	—	47	4	no	—
393	C₄⋊C₄	—	47	2	no	—
394	C₄⋊C₄	—	47	2	no	—
395	C₄⋊C₄	—	47	2	no	—
396	C₄⋊C₄	—	94	4	no	—
397	C₄⋊C₄	—	94	1	no	—
398	C₄⋊C₄	—	94	1	no	—
399	C₄⋊C₄	—	94	1	no	—
400	C₄⋊C₄	—	94	2	no	—
401	C₄⋊C₄	—	94	2	no	—
402	C₄⋊C₄	—	94	2	no	—
403	C₄⋊C₄	—	188	2	no	—
404	C₄⋊C₄	—	188	4	no	—
405	C₄⋊C₄	—	188	2	no	—
406	C₂²⋊C₄	—	94	4	no	—
407	C₂²⋊C₄	—	94	4	no	—
408	C₂²⋊C₄	—	94	4	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	4	1	no	—
414	C₄²	—	188	2	no	—
415	C₄²	—	188	2	no	—
416	C₄²	—	188	2	no	—
417	C₄²	—	188	4	no	—
418	C₄²	D₃₇₆	1	4	yes	—
419	C₄²	C₂×C₄×D₄₇	1	2	yes	—
420	C₄²	#10625350	1	2	yes	—
421	C₄²	#10625352	1	2	yes	—
422	C₄²	Q₈×D₄₇	1	2	yes	—
423	C₂³	—	94	2	no	—
424	C₂³	—	94	2	no	—
425	C₂³	—	94	2	no	—
426	C₂³	—	188	1	no	—
427	C₂³	—	188	1	no	—
428	C₂³	—	188	1	no	—
429	C₂³	—	188	1	no	—
430	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
431	Q₈	—	188	8	no	—
432	D₄	—	47	4	no	—
433	D₄	—	94	2	no	—
434	D₄	—	94	2	no	—
435	D₄	—	94	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	94	2	no	—
446	C₂×C₄	—	94	4	no	—
447	C₂×C₄	—	94	2	no	—
448	C₂×C₄	—	94	2	no	—
449	C₂×C₄	—	188	8	no	—
450	C₂×C₄	—	188	2	no	—
451	C₂×C₄	—	188	2	no	—
452	C₂×C₄	—	188	2	no	—
453	C₂×C₄	—	188	1	no	—
454	C₂×C₄	—	188	1	no	—
455	C₂×C₄	—	188	1	no	—
456	C₂×C₄	—	188	2	no	—
457	C₂×C₄	—	188	1	no	—
458	C₂×C₄	—	188	2	no	—
459	C₂×C₄	—	188	1	no	—
460	C₂×C₄	—	188	1	no	—
461	C₂×C₄	—	188	8	no	—
462	C₂×C₄	—	188	8	no	—
463	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
464	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
465	C₂×C₄	#13094004	1	2	yes	—
466	C₂×C₄	#13094004	1	2	yes	—
467	C₂×C₄	C₂×D₃₇₆	1	2	yes	—
468	C₂×C₄	C₂×D₃₇₆	1	2	yes	—
469	C₂×C₄	C₂×D₃₇₆	1	2	yes	—
470	C₂×C₄	#13094046	1	2	yes	—
471	C₂×C₄	#13094057	1	2	yes	—
472	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
473	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
474	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
475	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
476	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
477	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
478	C₈	—	2	4	no	—
479	C₈	—	4	2	no	—
480	C₂²	—	94	4	no	—
481	C₂²	—	188	2	no	—
482	C₂²	—	188	2	no	—
483	C₂²	—	188	2	no	—
484	C₂²	—	188	2	no	—
485	C₂²	—	188	2	no	—
486	C₂²	—	188	2	no	—
487	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
488	C₂²	C₂×#13094004	1	1	yes	characteristic
489	C₂²	#15689635	1	1	yes	characteristic
490	C₂²	C₂²×D₃₇₆	1	1	yes	characteristic
491	C₂²	C₂×#13094046	1	1	yes	characteristic
492	C₂²	C₂×#13094057	1	1	yes	characteristic
493	C₂²	#15689923	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	4	1	no	—
498	C₄	—	376	2	no	—
499	C₄	—	188	2	no	—
500	C₄	—	188	2	no	—
501	C₄	—	188	2	no	—
502	C₄	—	188	4	no	—
503	C₄	C₄×D₃₇₆	1	4	yes	—
504	C₄	#15689404	1	4	yes	direct product factor
505	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
506	C₄	C₄×#10625352	1	1	yes	characteristic
507	C₄	#15689655	1	1	yes	characteristic
508	C₄	#15689677	1	1	yes	characteristic
509	C₂	—	188	4	no	—
510	C₂	C₄×#13094004	1	1	yes	characteristic
511	C₂	C₂×C₄×D₃₇₆	1	1	yes	characteristic
512	C₂	C₄×#13094057	1	1	yes	characteristic
513	C₂	C₂×#15689404	1	1	yes	characteristic
514	C₂	#20253178	1	1	yes	characteristic
515	C₂	#20253389	1	1	yes	characteristic
516	C₂	#20253460	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×C₄⋊C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×C₄⋊C₈	D₄₇
hypocenter	C₄₇	C₄×#474
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₄×#13094024	C₂	semidirect
4. #20244339	C₂	semidirect
5. #20244147	C₂	semidirect
6. #20243960	C₂	semidirect
9. C₄×#13093958	C₂	semidirect
11. C₄×C₄⋊C₈×C₄₇	C₂	semidirect
18. #15689404	C₄	direct (N × H)
50. #13094024	C₂×C₄	semidirect
57. C₄×D₁₈₈	Q₈	semidirect
76. #13093958	C₂×C₄	semidirect
94. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
214. D₁₈₈	C₄×Q₈	semidirect
241. C₄×C₄₇	#474	semidirect
260. C₄×C₄⋊C₈	D₄₇	semidirect
302. C₄₇	C₄×#474	semidirect
346. C₄⋊C₈	C₄×D₄₇	semidirect
504. C₄	#15689404	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689404	2
C₄×#13094024	2
C₄²×D₁₈₈	2
#20244339	2
#20244147	2
#20243960	2
#20243638	2
#20243389	2
C₄×#13093958	2
C₄×#13093946	2
C₄×C₄⋊C₈×C₄₇	2
C₄×#474	47

Subgroups — C4×#15689404 #26223842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689404 #26223842