Subgroups — C₄×Q₈×Dic₈₆ #25256601

Order 11008.

2324 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic
2	#19137684	C₂	1	3	yes	maximal
3	#19137682	C₂	1	6	yes	maximal
4	Q₈×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₄×Dic₈₆	C₂	1	3	yes	maximal
6	Q₈×Dic₄₃⋊C₄	C₂	1	2	yes	maximal
7	C₄×#13063325	C₂	1	3	yes	maximal
8	C₄×#13063324	C₂	1	6	yes	maximal
9	C₄×Q₈×Dic₄₃	C₂	1	2	yes	maximal
10	C₄²×Dic₈₆	C₂	1	3	yes	maximal
11	C₄²×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
12	Q₈×Dic₈₆	C₄	1	16	yes	direct product factor
13	C₂×#13063325	C₂²	1	3	yes	—
14	C₂×#13063324	C₂²	1	6	yes	—
15	C₂×Q₈×Dic₄₃	C₂²	1	2	yes	—
16	C₂×Q₈×Dic₄₃	C₂²	1	2	yes	—
17	C₂×C₄×Dic₈₆	C₂²	1	3	yes	—
18	C₂×C₄×Dic₈₆	C₂²	1	6	yes	—
19	C₂×C₄×Dic₈₆	C₂²	1	3	yes	—
20	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
21	#14582805	C₂²	1	6	yes	—
22	#14582803	C₂²	1	12	yes	—
23	#14582798	C₂²	1	6	yes	—
24	#14582797	C₂²	1	6	yes	—
25	#14582797	C₂²	1	6	yes	—
26	#14582796	C₂²	1	12	yes	—
27	#14582795	C₂²	1	6	yes	—
28	#14582769	C₂²	1	3	yes	—
29	#14582768	C₂²	1	6	yes	—
30	C₄⋊C₄×Dic₄₃	C₂²	1	6	yes	—
31	C₄⋊C₄×Dic₄₃	C₂²	1	6	yes	—
32	C₄×Dic₄₃⋊C₄	C₂²	1	6	yes	—
33	C₄×Dic₄₃⋊C₄	C₂²	1	6	yes	—
34	C₄×Dic₄₃⋊C₄	C₂²	1	6	yes	—
35	C₄×C₄⋊Dic₄₃	C₂²	1	6	yes	—
36	C₄×C₄⋊Dic₄₃	C₂²	1	3	yes	—
37	C₄×C₄⋊Dic₄₃	C₂²	1	3	yes	—
38	C₄×C₄⋊Dic₄₃	C₂²	1	3	yes	—
39	C₄²×Dic₄₃	C₂²	1	6	yes	—
40	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
44	C₄×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
45	C₄×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
46	C₄³×C₄₃	C₂²	1	3	yes	—
47	C₂²×Dic₈₆	C₂³	1	6	yes	—
48	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
49	#13063325	C₂×C₄	1	24	yes	—
50	#13063324	C₂×C₄	1	48	yes	—
51	Q₈×Dic₄₃	—	2	8	no	—
52	Q₈×Dic₄₃	C₂×C₄	1	16	yes	—
53	C₄×Dic₈₆	—	2	12	no	—
54	C₄×Dic₈₆	—	4	12	no	—
55	C₄×Dic₈₆	C₂×C₄	1	24	yes	—
56	C₄×Dic₈₆	Q₈	1	8	yes	direct product factor
57	C₂×C₄⋊Dic₄₃	C₂³	1	3	yes	—
58	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
59	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
60	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
61	C₂×C₄⋊Dic₄₃	C₂³	1	3	yes	—
62	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
63	C₂×Dic₄₃⋊C₄	C₂³	1	6	yes	—
64	C₂×Dic₄₃⋊C₄	C₂³	1	12	yes	—
65	C₂×Dic₄₃⋊C₄	C₂³	1	6	yes	—
66	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
67	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
68	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
69	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
70	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
71	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
72	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
73	C₄₃⋊#95	C₂³	1	6	yes	—
74	C₄₃⋊#95	C₂³	1	12	yes	—
75	C₄₃⋊#95	C₂³	1	6	yes	—
76	C₄₃⋊#95	C₂³	1	6	yes	—
77	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
78	C₄×Q₈×C₄₃	—	2	4	no	—
79	C₄×Q₈×C₄₃	C₂×C₄	1	8	yes	—
80	C₄×Q₈×C₄₃	Q₈	1	8	yes	complemented
81	C₂×C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
82	C₂×C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
84	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
85	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
86	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
87	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
88	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
89	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
90	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
91	#95×C₄₃	C₂³	1	6	yes	—
92	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
93	C₂×Q₈×C₄₃	C₂×Q₈	1	4	yes	—
94	C₂×Q₈×C₄₃	#41	1	4	yes	—
95	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
96	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
97	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
98	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
101	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₄₃	C₂⁴	1	6	yes	—
103	C₂²×Dic₄₃	C₂⁴	1	6	yes	—
104	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
105	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
106	C₂×Dic₈₆	—	4	6	no	—
107	C₂×Dic₈₆	—	4	6	no	—
108	C₂×Dic₈₆	C₂²×C₄	1	24	yes	—
109	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
110	C₂×Dic₈₆	C₂×Q₈	1	4	yes	—
111	C₂×Dic₈₆	#41	1	4	yes	—
112	C₄⋊C₄×C₄₃	—	2	6	no	—
113	C₄⋊C₄×C₄₃	C₂²×C₄	1	12	yes	—
114	C₄⋊C₄×C₄₃	C₂×Q₈	1	12	yes	—
115	C₄²×C₄₃	—	2	6	no	—
116	C₄²×C₄₃	—	2	6	no	—
117	C₄²×C₄₃	—	2	6	no	—
118	C₄²×C₄₃	—	4	3	no	—
119	C₄²×C₄₃	C₂²×C₄	1	12	yes	—
120	C₄²×C₄₃	C₂×Q₈	1	12	yes	—
121	C₄²×C₄₃	C₂×Q₈	1	4	yes	—
122	C₄⋊Dic₄₃	—	2	6	no	—
123	C₄⋊Dic₄₃	—	2	12	no	—
124	C₄⋊Dic₄₃	—	4	6	no	—
125	C₄⋊Dic₄₃	C₂²×C₄	1	12	yes	—
126	C₄⋊Dic₄₃	C₂²×C₄	1	24	yes	—
127	C₄⋊Dic₄₃	C₂×Q₈	1	4	yes	—
128	Dic₄₃⋊C₄	—	2	12	no	—
129	Dic₄₃⋊C₄	—	4	12	no	—
130	Dic₄₃⋊C₄	C₂²×C₄	1	24	yes	—
131	Dic₄₃⋊C₄	C₂×Q₈	1	8	yes	—
132	C₄×Dic₄₃	—	2	12	no	—
133	C₄×Dic₄₃	—	2	12	no	—
134	C₄×Dic₄₃	—	2	12	no	—
135	C₄×Dic₄₃	—	4	6	no	—
136	C₄×Dic₄₃	C₂²×C₄	1	24	yes	—
137	C₄×Dic₄₃	C₂×Q₈	1	8	yes	—
138	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
139	Q₈×C₄₃	C₄×Q₈	1	16	yes	complemented
140	C₂×C₄×C₄₃	—	2	3	no	—
141	C₂×C₄×C₄₃	—	2	1	no	—
142	C₂×C₄×C₄₃	—	2	3	no	—
143	C₂×C₄×C₄₃	—	2	3	no	—
144	C₂×C₄×C₄₃	—	2	1	no	—
145	C₂×C₄×C₄₃	—	2	3	no	—
146	C₂×C₄×C₄₃	—	2	3	no	—
147	C₂×C₄×C₄₃	—	2	3	no	—
148	C₂×C₄×C₄₃	—	2	3	no	—
149	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
150	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
151	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
152	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
153	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
154	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
155	C₂×C₄×C₄₃	C₂²×Q₈	1	6	yes	—
156	C₂×C₄×C₄₃	C₂²×Q₈	1	6	yes	—
157	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
158	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
159	C₂×C₄×C₄₃	C₂×#41	1	6	yes	—
160	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
161	C₂×Dic₄₃	—	2	2	no	—
162	C₂×Dic₄₃	—	2	6	no	—
163	C₂×Dic₄₃	—	2	2	no	—
164	C₂×Dic₄₃	—	2	6	no	—
165	C₂×Dic₄₃	—	2	6	no	—
166	C₂×Dic₄₃	—	2	6	no	—
167	C₂×Dic₄₃	—	2	6	no	—
168	C₂×Dic₄₃	C₂³×C₄	1	12	yes	—
169	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
170	C₂×Dic₄₃	C₂²×Q₈	1	4	yes	—
171	C₂×Dic₄₃	C₂²×Q₈	1	4	yes	—
172	C₂×Dic₄₃	C₂×#41	1	4	yes	—
173	Dic₈₆	—	4	24	no	—
174	Dic₈₆	C₄×Q₈	1	16	yes	direct product factor
175	C₄×Q₈²	—	43	1	no	maximal, Sylow
176	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
177	C₂²×C₄₃	C₂³×Q₈	1	1	yes	characteristic
178	C₂²×C₄₃	C₂³×Q₈	1	1	yes	characteristic
179	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
180	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
181	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
182	C₂²×C₄₃	#585	1	1	yes	characteristic
183	C₄×C₄₃	—	2	6	no	—
184	C₄×C₄₃	—	2	6	no	—
185	C₄×C₄₃	—	2	2	no	—
186	C₄×C₄₃	—	4	3	no	—
187	C₄×C₄₃	C₂×C₄×Q₈	1	4	yes	—
188	C₄×C₄₃	C₂×C₄×Q₈	1	12	yes	—
189	C₄×C₄₃	Q₈²	1	4	yes	complemented
190	Dic₄₃	—	2	12	no	—
191	Dic₄₃	—	2	4	no	—
192	Dic₄₃	—	4	6	no	—
193	Dic₄₃	C₂×C₄×Q₈	1	8	yes	—
194	C₂×Q₈²	—	43	1	no	—
195	#2369	—	43	6	no	—
196	#2369	—	43	3	no	—
197	Q₈×C₄⋊C₄	—	43	3	no	—
198	Q₈×C₄⋊C₄	—	43	2	no	—
199	Q₈×C₄⋊C₄	—	43	1	no	—
200	C₄×C₄⋊Q₈	—	43	6	no	—
201	C₄×C₄⋊Q₈	—	43	3	no	—
202	C₄²×Q₈	—	43	3	no	—
203	C₄²×Q₈	—	43	2	no	—
204	C₄²×Q₈	D₄₃	1	1	yes	characteristic
205	C₂×C₄₃	C₂²×C₄×Q₈	1	1	yes	characteristic
206	C₂×C₄₃	C₂²×C₄×Q₈	1	1	yes	characteristic
207	C₂×C₄₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄₃	C₂×Q₈²	1	1	yes	characteristic
209	C₂×C₄₃	Q₈×#41	1	1	yes	characteristic
210	C₂×C₄₃	Q₈×#41	1	1	yes	characteristic
211	C₂×C₄₃	#3483	1	1	yes	characteristic
212	Q₈²	—	43	16	no	—
213	C₂×C₄⋊Q₈	—	43	6	no	—
214	C₂×C₄⋊Q₈	—	43	3	no	—
215	C₂×C₄×Q₈	—	43	2	no	—
216	C₂×C₄×Q₈	—	43	2	no	—
217	C₂×C₄×Q₈	—	43	3	no	—
218	C₂×C₄×Q₈	—	43	1	no	—
219	C₂×C₄×Q₈	—	43	3	no	—
220	C₂×C₄×Q₈	—	43	6	no	—
221	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
222	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
224	#391	—	43	6	no	—
225	#391	—	43	12	no	—
226	#389	—	43	6	no	—
227	#389	—	43	6	no	—
228	#389	—	43	6	no	—
229	#389	—	43	6	no	—
230	#389	—	43	12	no	—
231	#384	—	43	6	no	—
232	#384	—	43	3	no	—
233	C₄×C₄⋊C₄	—	43	6	no	—
234	C₄×C₄⋊C₄	—	43	6	no	—
235	C₄×C₄⋊C₄	—	43	6	no	—
236	C₄×C₄⋊C₄	—	43	3	no	—
237	C₄×C₄⋊C₄	—	43	6	no	—
238	C₄×C₄⋊C₄	—	43	3	no	—
239	C₄×C₄⋊C₄	—	43	6	no	—
240	C₄×C₄⋊C₄	—	43	3	no	—
241	C₄×C₄⋊C₄	—	43	6	no	—
242	C₄×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
243	C₄×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
244	C₄×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
245	C₄³	—	43	6	no	—
246	C₄³	C₂×D₄₃	1	3	yes	—
247	C₄₃	C₄×Q₈²	1	1	yes	characteristic, complemented, Sylow
248	C₂²×Q₈	—	43	1	no	—
249	C₂²×Q₈	—	43	6	no	—
250	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
251	C₄⋊Q₈	—	43	48	no	—
252	C₄⋊Q₈	—	43	24	no	—
253	C₄×Q₈	—	2	4	no	—
254	C₄×Q₈	—	43	16	no	—
255	C₄×Q₈	—	43	24	no	—
256	C₄×Q₈	—	43	8	no	—
257	C₄×Q₈	—	86	12	no	—
258	C₄×Q₈	—	86	8	no	—
259	C₄×Q₈	—	172	12	no	—
260	C₄×Q₈	Dic₈₆	1	8	yes	direct product factor
261	C₄×Q₈	C₄×D₄₃	1	8	yes	—
262	C₂×C₄⋊C₄	—	43	6	no	—
263	C₂×C₄⋊C₄	—	43	3	no	—
264	C₂×C₄⋊C₄	—	43	6	no	—
265	C₂×C₄⋊C₄	—	43	2	no	—
266	C₂×C₄⋊C₄	—	43	1	no	—
267	C₂×C₄⋊C₄	—	43	6	no	—
268	C₂×C₄⋊C₄	—	43	3	no	—
269	C₂×C₄⋊C₄	—	43	6	no	—
270	C₂×C₄⋊C₄	—	43	12	no	—
271	C₂×C₄⋊C₄	—	43	6	no	—
272	C₂×C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
273	C₂×C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
274	C₂×C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
275	C₂×C₄²	—	43	6	no	—
276	C₂×C₄²	—	43	2	no	—
277	C₂×C₄²	—	43	6	no	—
278	C₂×C₄²	—	43	6	no	—
279	C₂×C₄²	—	43	6	no	—
280	C₂×C₄²	—	43	6	no	—
281	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
282	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
283	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
284	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
285	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
286	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
287	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
288	#95	—	43	6	no	—
289	#95	—	43	6	no	—
290	#95	—	43	6	no	—
291	#95	—	43	12	no	—
292	#95	C₂²×D₄₃	1	6	yes	—
293	C₂×Q₈	—	43	4	no	—
294	C₂×Q₈	—	43	24	no	—
295	C₂×Q₈	—	43	4	no	—
296	C₂×Q₈	—	43	4	no	—
297	C₂×Q₈	—	172	6	no	—
298	C₂×Q₈	—	172	6	no	—
299	C₂×Q₈	C₂×Dic₈₆	1	4	yes	—
300	C₂×Q₈	C₂×C₄×D₄₃	1	4	yes	—
301	C₂×Q₈	#10621898	1	4	yes	—
302	C₂²×C₄	—	43	2	no	—
303	C₂²×C₄	—	43	2	no	—
304	C₂²×C₄	—	43	6	no	—
305	C₂²×C₄	—	43	6	no	—
306	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
307	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
308	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
309	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
310	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
311	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
312	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
313	C₄⋊C₄	—	2	6	no	—
314	C₄⋊C₄	—	43	24	no	—
315	C₄⋊C₄	—	43	12	no	—
316	C₄⋊C₄	—	43	24	no	—
317	C₄⋊C₄	—	43	8	no	—
318	C₄⋊C₄	—	43	4	no	—
319	C₄⋊C₄	—	86	12	no	—
320	C₄⋊C₄	—	86	6	no	—
321	C₄⋊C₄	—	86	12	no	—
322	C₄⋊C₄	—	172	12	no	—
323	C₄⋊C₄	—	172	6	no	—
324	C₄⋊C₄	C₂×Dic₈₆	1	12	yes	—
325	C₄⋊C₄	C₂×C₄×D₄₃	1	12	yes	—
326	C₄²	—	2	6	no	—
327	C₄²	—	2	6	no	—
328	C₄²	—	2	6	no	—
329	C₄²	—	4	3	no	—
330	C₄²	—	43	24	no	—
331	C₄²	—	43	8	no	—
332	C₄²	—	86	12	no	—
333	C₄²	—	86	12	no	—
334	C₄²	—	86	12	no	—
335	C₄²	—	172	6	no	—
336	C₄²	C₂×Dic₈₆	1	12	yes	—
337	C₄²	C₂×C₄×D₄₃	1	12	yes	—
338	C₄²	Q₈×D₄₃	1	4	yes	—
339	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
340	Q₈	—	43	16	no	—
341	Q₈	—	172	24	no	—
342	Q₈	C₄×Dic₈₆	1	16	yes	direct product factor
343	C₂×C₄	—	2	3	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	3	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	3	no	—
348	C₂×C₄	—	2	3	no	—
349	C₂×C₄	—	2	3	no	—
350	C₂×C₄	—	2	3	no	—
351	C₂×C₄	—	2	3	no	—
352	C₂×C₄	—	43	4	no	—
353	C₂×C₄	—	43	4	no	—
354	C₂×C₄	—	43	4	no	—
355	C₂×C₄	—	43	12	no	—
356	C₂×C₄	—	43	4	no	—
357	C₂×C₄	—	86	2	no	—
358	C₂×C₄	—	86	6	no	—
359	C₂×C₄	—	86	2	no	—
360	C₂×C₄	—	86	6	no	—
361	C₂×C₄	—	86	6	no	—
362	C₂×C₄	—	86	6	no	—
363	C₂×C₄	—	86	6	no	—
364	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
365	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
366	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
367	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
368	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
369	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
370	C₂×C₄	C₂²×Dic₈₆	1	6	yes	—
371	C₂×C₄	C₂²×Dic₈₆	1	6	yes	—
372	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
373	C₂×C₄	#41×D₄₃	1	2	yes	—
374	C₂×C₄	C₂×#10621898	1	6	yes	—
375	C₂×C₄	#13063371	1	2	yes	—
376	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
377	C₂²	C₂²×Q₈×D₄₃	1	1	yes	characteristic
378	C₂²	C₂³×Dic₈₆	1	1	yes	characteristic
379	C₂²	C₂×#41×D₄₃	1	1	yes	characteristic
380	C₂²	C₂²×#10621898	1	1	yes	characteristic
381	C₂²	C₂×#13063371	1	1	yes	characteristic
382	C₂²	#14583735	1	1	yes	characteristic
383	C₄	—	2	6	no	—
384	C₄	—	2	6	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	3	no	—
387	C₄	—	43	8	no	—
388	C₄	—	86	12	no	—
389	C₄	—	86	4	no	—
390	C₄	—	172	6	no	—
391	C₄	C₄×Q₈×D₄₃	1	4	yes	—
392	C₄	C₂×C₄×Dic₈₆	1	12	yes	—
393	C₄	Q₈×Dic₈₆	1	4	yes	direct product factor
394	C₂	C₂×C₄×Q₈×D₄₃	1	1	yes	characteristic
395	C₂	C₂²×C₄×Dic₈₆	1	1	yes	characteristic
396	C₂	C₄×#13063371	1	1	yes	characteristic
397	C₂	C₂×Q₈×Dic₈₆	1	1	yes	characteristic
398	C₂	#41×Dic₈₆	1	1	yes	characteristic
399	C₂	Q₈×#10621898	1	1	yes	characteristic
400	C₂	#19148221	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₃
Fitting	C₄²×Q₈×C₄₃	C₂
socle, prime radical, cosocle	C₂³×C₄₃	C₂⁵
hypercenter	C₄²×Q₈	D₄₃
hypocenter	C₄₃	C₄×Q₈²
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
12. Q₈×Dic₈₆	C₄	direct (N × H)
56. C₄×Dic₈₆	Q₈	direct (N × H)
80. C₄×Q₈×C₄₃	Q₈	semidirect
139. Q₈×C₄₃	C₄×Q₈	semidirect
174. Dic₈₆	C₄×Q₈	direct (N × H)
189. C₄×C₄₃	Q₈²	semidirect
247. C₄₃	C₄×Q₈²	semidirect
260. C₄×Q₈	Dic₈₆	direct (N × H)
342. Q₈	C₄×Dic₈₆	direct (N × H)
393. C₄	Q₈×Dic₈₆	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×Q₈×Dic₈₆	2
#19137684	2
#19137682	2
Q₈×C₄⋊Dic₄₃	2
C₄⋊C₄×Dic₈₆	2
Q₈×Dic₄₃⋊C₄	2
C₄×#13063325	2
C₄×#13063324	2
C₄×Q₈×Dic₄₃	2
C₄²×Dic₈₆	2
C₄²×Q₈×C₄₃	2
C₄×Q₈²	43

Subgroups — C4×Q8×Dic86 #25256601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Q₈×Dic₈₆ #25256601