Subgroups — C₂×#19139621 #25268349

Order 11008.

3182 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063325	C₂	1	2	yes	maximal
2	C₂²×#13063324	C₂	1	2	yes	maximal
3	#19139621	C₂	1	16	yes	maximal, direct product factor
4	C₂×#14582820	C₂	1	4	yes	maximal
5	C₂×#14582798	C₂	1	2	yes	maximal
6	C₂×#14582797	C₂	1	2	yes	maximal
7	C₂×#14582769	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂³×Dic₈₆	C₂²	1	4	yes	—
11	C₂×#13063325	—	2	16	no	—
12	C₂×#13063325	C₂²	1	16	yes	—
13	C₂×#13063324	—	2	16	no	—
14	C₂×#13063324	C₂²	1	16	yes	—
15	C₂²×C₄⋊Dic₄₃	C₂²	1	4	yes	—
16	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	—
17	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	—
18	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	—
19	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
21	C₂²×Dic₄₃⋊C₄	C₂²	1	4	yes	—
22	C₂²×C₄×Dic₄₃	C₂²	1	2	yes	—
23	#14582820	C₂²	1	32	yes	—
24	#14582798	C₂²	1	16	yes	—
25	#14582797	C₂²	1	16	yes	—
26	#14582769	C₂²	1	8	yes	—
27	C₄×C₄⋊Dic₄₃	C₂²	1	8	yes	—
28	C₂×C₄₃⋊#95	C₂²	1	2	yes	—
29	C₂×C₄₃⋊#95	C₂²	1	4	yes	—
30	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
33	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₄₃	C₂²	1	8	yes	—
35	C₂×#95×C₄₃	C₂²	1	2	yes	—
36	C₂²×Dic₈₆	—	2	16	no	—
37	C₂²×Dic₈₆	—	2	16	no	—
38	C₂²×Dic₈₆	—	4	8	no	—
39	C₂²×Dic₈₆	C₂³	1	16	yes	—
40	C₂³×Dic₄₃	C₂³	1	4	yes	—
41	C₂³×Dic₄₃	C₂³	1	2	yes	—
42	C₂³×Dic₄₃	C₂³	1	2	yes	—
43	#13063325	—	2	64	no	—
44	#13063324	—	2	64	no	—
45	C₂×C₄⋊Dic₄₃	—	2	8	no	—
46	C₂×C₄⋊Dic₄₃	—	2	8	no	—
47	C₂×C₄⋊Dic₄₃	—	2	16	no	—
48	C₂×C₄⋊Dic₄₃	—	4	4	no	—
49	C₂×C₄⋊Dic₄₃	D₄	1	8	yes	—
50	C₂×C₄⋊Dic₄₃	Q₈	1	8	yes	complemented
51	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
52	C₂×C₄⋊Dic₄₃	C₂³	1	16	yes	—
53	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
54	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
55	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
56	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
57	C₂×Dic₄₃⋊C₄	—	2	16	no	—
58	C₂×Dic₄₃⋊C₄	C₂³	1	16	yes	—
59	C₂×C₄×Dic₄₃	—	2	8	no	—
60	C₂×C₄×Dic₄₃	C₂³	1	8	yes	—
61	C₄₃⋊#95	C₂³	1	16	yes	—
62	C₄₃⋊#95	C₂³	1	8	yes	—
63	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₃	D₄	1	8	yes	—
69	C₂×C₄⋊C₄×C₄₃	Q₈	1	8	yes	complemented
70	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
72	C₂×C₄²×C₄₃	—	2	8	no	—
73	C₂×C₄²×C₄₃	Q₈	1	8	yes	complemented
74	C₂×C₄²×C₄₃	C₂³	1	8	yes	—
75	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
76	#95×C₄₃	C₂³	1	8	yes	—
77	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
78	C₂²×C₄×C₄₃	—	2	4	no	—
79	C₂²×C₄×C₄₃	—	2	4	no	—
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	4	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	4	no	—
84	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
85	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
86	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
87	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
88	C₂²×C₄×C₄₃	C₂×Q₈	1	8	yes	—
89	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
90	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
92	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
93	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
94	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
95	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
97	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
98	C₂²×Dic₄₃	—	2	4	no	—
99	C₂²×Dic₄₃	—	2	4	no	—
100	C₂²×Dic₄₃	—	2	8	no	—
101	C₂²×Dic₄₃	—	2	8	no	—
102	C₂²×Dic₄₃	—	2	4	no	—
103	C₂²×Dic₄₃	—	2	8	no	—
104	C₂²×Dic₄₃	—	2	4	no	—
105	C₂²×Dic₄₃	C₂×D₄	1	8	yes	—
106	C₂²×Dic₄₃	C₂×Q₈	1	8	yes	—
107	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
108	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
109	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
110	C₂×Dic₈₆	—	2	32	no	—
111	C₂×Dic₈₆	—	2	32	no	—
112	C₂×Dic₈₆	—	4	16	no	—
113	C₂×Dic₈₆	—	4	64	no	—
114	C₄⋊C₄×C₄₃	C₂×D₄	1	16	yes	—
115	C₄⋊C₄×C₄₃	C₂×Q₈	1	16	yes	complemented
116	C₄²×C₄₃	—	2	16	no	—
117	C₄²×C₄₃	C₂×Q₈	1	16	yes	complemented
118	C₄⋊Dic₄₃	—	2	16	no	—
119	C₄⋊Dic₄₃	—	2	16	no	—
120	C₄⋊Dic₄₃	—	2	32	no	—
121	C₄⋊Dic₄₃	—	4	8	no	—
122	C₄⋊Dic₄₃	C₂×D₄	1	16	yes	—
123	C₄⋊Dic₄₃	C₂×Q₈	1	16	yes	complemented
124	Dic₄₃⋊C₄	—	2	32	no	—
125	C₄×Dic₄₃	—	2	16	no	—
126	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
127	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
128	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
129	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
130	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
131	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
132	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
133	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
134	C₂×C₄×C₄₃	—	2	8	no	—
135	C₂×C₄×C₄₃	—	2	16	no	—
136	C₂×C₄×C₄₃	—	2	16	no	—
137	C₂×C₄×C₄₃	—	2	4	no	—
138	C₂×C₄×C₄₃	—	2	4	no	—
139	C₂×C₄×C₄₃	—	2	2	no	—
140	C₂×C₄×C₄₃	—	2	4	no	—
141	C₂×C₄×C₄₃	—	2	2	no	—
142	C₂×C₄×C₄₃	—	2	4	no	—
143	C₂×C₄×C₄₃	C₄⋊Q₈	1	16	yes	complemented
144	C₂×C₄×C₄₃	C₄⋊Q₈	1	16	yes	complemented
145	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
146	C₂×C₄×C₄₃	C₂²×D₄	1	8	yes	—
147	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
148	C₂×C₄×C₄₃	C₂²×Q₈	1	4	yes	—
149	C₂×C₄×C₄₃	C₂²×Q₈	1	4	yes	—
150	C₂×C₄×C₄₃	C₂²×Q₈	1	8	yes	—
151	C₂×C₄×C₄₃	C₂²×Q₈	1	4	yes	—
152	C₂×C₄×C₄₃	C₂²×Q₈	1	4	yes	—
153	C₂×C₄×C₄₃	C₂²×Q₈	1	4	yes	—
154	C₂×Dic₄₃	—	2	16	no	—
155	C₂×Dic₄₃	—	2	16	no	—
156	C₂×Dic₄₃	—	2	4	no	—
157	C₂×Dic₄₃	—	2	4	no	—
158	C₂×Dic₄₃	—	2	4	no	—
159	C₂×Dic₄₃	—	2	4	no	—
160	C₂×Dic₄₃	—	2	8	no	—
161	C₂×Dic₄₃	—	2	8	no	—
162	C₂×Dic₄₃	—	2	8	no	—
163	C₂×Dic₄₃	—	4	16	no	—
164	C₂×Dic₄₃	C₂²×D₄	1	8	yes	—
165	C₂×Dic₄₃	C₂²×Q₈	1	8	yes	—
166	Dic₈₆	—	4	64	no	—
167	C₂×#2551	—	43	1	no	maximal, Sylow
168	C₂²×C₄₃	C₂×C₄⋊Q₈	1	4	yes	—
169	C₂²×C₄₃	C₂×C₄⋊Q₈	1	4	yes	—
170	C₂²×C₄₃	#544	1	4	yes	—
171	C₂²×C₄₃	D₄²	1	4	yes	—
172	C₂²×C₄₃	D₄×Q₈	1	4	yes	—
173	C₂²×C₄₃	D₄×Q₈	1	4	yes	—
174	C₂²×C₄₃	Q₈²	1	4	yes	—
175	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
176	C₂²×C₄₃	C₂³×D₄	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	C₂³×Q₈	1	1	yes	characteristic
180	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
181	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
182	C₄×C₄₃	—	2	4	no	—
183	C₄×C₄₃	—	2	8	no	—
184	C₄×C₄₃	—	2	8	no	—
185	C₄×C₄₃	C₂×C₄⋊Q₈	1	8	yes	complemented
186	C₄×C₄₃	C₂×C₄⋊Q₈	1	8	yes	complemented
187	Dic₄₃	—	2	8	no	—
188	Dic₄₃	—	2	8	no	—
189	Dic₄₃	—	4	8	no	—
190	C₂²×C₄⋊Q₈	—	43	2	no	—
191	C₂²×C₄⋊Q₈	—	43	2	no	—
192	#2551	—	43	16	no	—
193	C₂×#395	—	43	4	no	—
194	C₂×#389	—	43	2	no	—
195	C₂×#389	—	43	2	no	—
196	C₂×#384	—	43	1	no	—
197	C₂×C₄×C₄⋊C₄	—	43	1	no	—
198	C₂×C₄×C₄⋊C₄	D₄₃	1	1	yes	characteristic
199	C₂×C₄₃	#2551	1	8	yes	complemented
200	C₂×C₄₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
201	C₂×C₄₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
202	C₂×C₄₃	C₂×#544	1	1	yes	characteristic
203	C₂×C₄₃	C₂×D₄²	1	1	yes	characteristic
204	C₂×C₄₃	C₂×D₄×Q₈	1	1	yes	characteristic
205	C₂×C₄₃	C₂×D₄×Q₈	1	1	yes	characteristic
206	C₂×C₄₃	C₂×Q₈²	1	1	yes	characteristic
207	C₂³×Q₈	—	43	4	no	—
208	C₂×C₄⋊Q₈	—	43	16	no	—
209	C₂×C₄⋊Q₈	—	43	16	no	—
210	C₂×C₄⋊Q₈	—	86	16	no	—
211	C₂×C₄⋊Q₈	—	86	16	no	—
212	C₂²×C₄⋊C₄	—	43	1	no	—
213	C₂²×C₄⋊C₄	—	43	1	no	—
214	C₂²×C₄⋊C₄	—	43	4	no	—
215	C₂²×C₄⋊C₄	—	43	4	no	—
216	C₂²×C₄⋊C₄	—	43	2	no	—
217	C₂²×C₄⋊C₄	—	43	2	no	—
218	C₂²×C₄⋊C₄	—	43	2	no	—
219	C₂²×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
221	C₂²×C₄²	—	43	2	no	—
222	C₂²×C₄²	C₂×D₄₃	1	2	yes	—
223	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
224	#395	—	43	32	no	—
225	#389	—	43	16	no	—
226	#389	—	43	16	no	—
227	#384	—	43	8	no	—
228	C₄×C₄⋊C₄	—	43	8	no	—
229	C₄×C₄⋊C₄	C₂×D₄₃	1	8	yes	—
230	C₂×#95	—	43	2	no	—
231	C₂×#95	—	43	4	no	—
232	C₂×#95	C₂×D₄₃	1	2	yes	—
233	C₄₃	C₂×#2551	1	1	yes	characteristic, complemented, Sylow
234	C₂²×Q₈	—	43	16	no	—
235	C₂²×Q₈	—	86	16	no	—
236	C₂²×Q₈	—	86	16	no	—
237	C₂²×Q₈	—	172	8	no	—
238	C₂³×C₄	—	43	2	no	—
239	C₂³×C₄	—	43	2	no	—
240	C₂³×C₄	—	43	4	no	—
241	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
242	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
243	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
244	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
245	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
246	C₄⋊Q₈	—	86	64	no	—
247	C₄⋊Q₈	—	86	64	no	—
248	C₂×C₄⋊C₄	—	43	8	no	—
249	C₂×C₄⋊C₄	—	43	8	no	—
250	C₂×C₄⋊C₄	—	43	4	no	—
251	C₂×C₄⋊C₄	—	43	4	no	—
252	C₂×C₄⋊C₄	—	43	16	no	—
253	C₂×C₄⋊C₄	—	43	8	no	—
254	C₂×C₄⋊C₄	—	43	8	no	—
255	C₂×C₄⋊C₄	—	43	16	no	—
256	C₂×C₄⋊C₄	—	43	8	no	—
257	C₂×C₄⋊C₄	—	86	16	no	—
258	C₂×C₄⋊C₄	—	86	16	no	—
259	C₂×C₄⋊C₄	—	86	8	no	—
260	C₂×C₄⋊C₄	—	86	8	no	—
261	C₂×C₄⋊C₄	—	172	4	no	—
262	C₂×C₄⋊C₄	Dic₈₆	1	8	yes	complemented
263	C₂×C₄⋊C₄	D₁₇₂	1	8	yes	—
264	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
265	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
266	C₂×C₄²	—	2	8	no	—
267	C₂×C₄²	—	43	8	no	—
268	C₂×C₄²	—	86	8	no	—
269	C₂×C₄²	Dic₈₆	1	8	yes	complemented
270	C₂×C₄²	C₂²×D₄₃	1	8	yes	—
271	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
272	#95	—	43	8	no	—
273	#95	—	43	16	no	—
274	#95	C₂²×D₄₃	1	8	yes	—
275	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
276	C₂×Q₈	—	86	32	no	—
277	C₂×Q₈	—	86	32	no	—
278	C₂×Q₈	—	172	16	no	—
279	C₂×Q₈	—	172	64	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	43	8	no	—
287	C₂²×C₄	—	43	8	no	—
288	C₂²×C₄	—	43	4	no	—
289	C₂²×C₄	—	43	4	no	—
290	C₂²×C₄	—	43	8	no	—
291	C₂²×C₄	—	86	4	no	—
292	C₂²×C₄	—	86	4	no	—
293	C₂²×C₄	—	86	4	no	—
294	C₂²×C₄	—	86	4	no	—
295	C₂²×C₄	—	86	8	no	—
296	C₂²×C₄	—	86	8	no	—
297	C₂²×C₄	—	86	8	no	—
298	C₂²×C₄	C₂×Dic₈₆	1	4	yes	—
299	C₂²×C₄	C₂×Dic₈₆	1	8	yes	—
300	C₂²×C₄	C₂×Dic₈₆	1	4	yes	—
301	C₂²×C₄	C₂×Dic₈₆	1	4	yes	—
302	C₂²×C₄	C₂×Dic₈₆	1	4	yes	—
303	C₂²×C₄	C₂×D₁₇₂	1	8	yes	—
304	C₂²×C₄	C₂×D₁₇₂	1	4	yes	—
305	C₂²×C₄	D₄×D₄₃	1	4	yes	—
306	C₂²×C₄	Q₈×D₄₃	1	4	yes	—
307	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
308	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
309	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
310	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
311	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
312	C₄⋊C₄	—	43	16	no	—
313	C₄⋊C₄	—	43	16	no	—
314	C₄⋊C₄	—	86	32	no	—
315	C₄⋊C₄	—	86	16	no	—
316	C₄⋊C₄	—	86	32	no	—
317	C₄⋊C₄	—	86	16	no	—
318	C₄⋊C₄	—	172	8	no	—
319	C₄⋊C₄	C₂×Dic₈₆	1	16	yes	complemented
320	C₄⋊C₄	C₂×D₁₇₂	1	16	yes	—
321	C₄²	—	2	16	no	—
322	C₄²	—	86	16	no	—
323	C₄²	C₂×Dic₈₆	1	16	yes	complemented
324	C₂³	C₂×D₄×D₄₃	1	2	yes	—
325	C₂³	C₂²×D₁₇₂	1	2	yes	—
326	C₂³	C₂×Q₈×D₄₃	1	2	yes	—
327	C₂³	C₂²×Dic₈₆	1	2	yes	—
328	C₂³	C₂²×Dic₈₆	1	2	yes	—
329	C₂³	#13063371	1	2	yes	—
330	C₂³	#13063372	1	2	yes	—
331	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
332	Q₈	—	172	64	no	—
333	C₂×C₄	—	2	16	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	2	16	no	—
342	C₂×C₄	—	43	8	no	—
343	C₂×C₄	—	43	8	no	—
344	C₂×C₄	—	86	16	no	—
345	C₂×C₄	—	86	4	no	—
346	C₂×C₄	—	86	4	no	—
347	C₂×C₄	—	86	4	no	—
348	C₂×C₄	—	86	4	no	—
349	C₂×C₄	—	86	16	no	—
350	C₂×C₄	—	86	8	no	—
351	C₂×C₄	—	86	8	no	—
352	C₂×C₄	—	86	8	no	—
353	C₂×C₄	—	172	16	no	—
354	C₂×C₄	#13063324	1	16	yes	complemented
355	C₂×C₄	#13063325	1	16	yes	complemented
356	C₂×C₄	C₂×D₄×D₄₃	1	4	yes	—
357	C₂×C₄	C₂²×D₁₇₂	1	8	yes	—
358	C₂×C₄	C₂²×D₁₇₂	1	4	yes	—
359	C₂×C₄	C₂×Q₈×D₄₃	1	4	yes	—
360	C₂×C₄	C₂²×Dic₈₆	1	4	yes	—
361	C₂×C₄	C₂²×Dic₈₆	1	8	yes	—
362	C₂×C₄	C₂²×Dic₈₆	1	4	yes	—
363	C₂×C₄	C₂²×Dic₈₆	1	4	yes	—
364	C₂×C₄	C₂²×Dic₈₆	1	4	yes	—
365	C₂²	C₂×#13063324	1	4	yes	—
366	C₂²	C₂×#13063325	1	4	yes	—
367	C₂²	#14583527	1	4	yes	—
368	C₂²	D₄×D₁₇₂	1	4	yes	—
369	C₂²	D₄×Dic₈₆	1	4	yes	—
370	C₂²	Q₈×D₁₇₂	1	4	yes	—
371	C₂²	Q₈×Dic₈₆	1	4	yes	—
372	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
373	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
374	C₂²	C₂²×Q₈×D₄₃	1	1	yes	characteristic
375	C₂²	C₂³×Dic₈₆	1	1	yes	characteristic
376	C₂²	C₂³×Dic₈₆	1	1	yes	characteristic
377	C₂²	C₂×#13063371	1	1	yes	characteristic
378	C₂²	C₂×#13063372	1	1	yes	characteristic
379	C₄	—	2	8	no	—
380	C₄	—	2	8	no	—
381	C₄	—	2	4	no	—
382	C₄	—	86	8	no	—
383	C₄	—	86	8	no	—
384	C₄	—	172	8	no	—
385	C₄	C₂×#13063324	1	8	yes	complemented
386	C₄	C₂×#13063325	1	8	yes	complemented
387	C₂	#19139621	1	8	yes	direct product factor
388	C₂	C₂²×#13063324	1	1	yes	characteristic
389	C₂	C₂²×#13063325	1	1	yes	characteristic
390	C₂	C₂×#14583527	1	1	yes	characteristic
391	C₂	C₂×D₄×D₁₇₂	1	1	yes	characteristic
392	C₂	C₂×D₄×Dic₈₆	1	1	yes	characteristic
393	C₂	C₂×Q₈×D₁₇₂	1	1	yes	characteristic
394	C₂	C₂×Q₈×Dic₈₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₄₃
commutator, cosocle	C₂³×C₄₃	C₂⁵
Frattini	C₂³	C₂⁴×D₄₃
Fitting	C₂×C₄×C₄⋊C₄×C₄₃	C₂
socle, prime radical	C₂⁴×C₄₃	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₄₃
hypocenter	C₄₃	C₂×#2551
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #19139621	C₂	direct (N × H)
50. C₂×C₄⋊Dic₄₃	Q₈	semidirect
69. C₂×C₄⋊C₄×C₄₃	Q₈	semidirect
73. C₂×C₄²×C₄₃	Q₈	semidirect
115. C₄⋊C₄×C₄₃	C₂×Q₈	semidirect
117. C₄²×C₄₃	C₂×Q₈	semidirect
123. C₄⋊Dic₄₃	C₂×Q₈	semidirect
143. C₂×C₄×C₄₃	C₄⋊Q₈	semidirect
144. C₂×C₄×C₄₃	C₄⋊Q₈	semidirect
185. C₄×C₄₃	C₂×C₄⋊Q₈	semidirect
186. C₄×C₄₃	C₂×C₄⋊Q₈	semidirect
199. C₂×C₄₃	#2551	semidirect
233. C₄₃	C₂×#2551	semidirect
262. C₂×C₄⋊C₄	Dic₈₆	semidirect
269. C₂×C₄²	Dic₈₆	semidirect
319. C₄⋊C₄	C₂×Dic₈₆	semidirect
323. C₄²	C₂×Dic₈₆	semidirect
354. C₂×C₄	#13063324	semidirect
355. C₂×C₄	#13063325	semidirect
385. C₄	C₂×#13063324	semidirect
386. C₄	C₂×#13063325	semidirect
387. C₂	#19139621	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13063325	2
C₂²×#13063324	2
#19139621	2
C₂×#14582820	2
C₂×#14582798	2
C₂×#14582797	2
C₂×#14582769	2
C₂×C₄×C₄⋊Dic₄₃	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₂×#2551	43

Subgroups — C2×#19139621 #25268349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19139621 #25268349