Subgroups — C₂×#19147733 #26003106

Order 11008.

2126 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583701	C₂	1	2	yes	maximal, complemented
2	#19147733	C₂	1	16	yes	maximal, direct product factor
3	C₂×#14583336	C₂	1	4	yes	maximal, complemented
4	C₂×#14583334	C₂	1	2	yes	maximal, complemented
5	C₂×#14583332	C₂	1	2	yes	maximal, complemented
6	C₂²×D₆₈₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₁₆×D₄₃	C₂	1	2	yes	maximal, complemented
8	C₂×#14583315	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13063371	—	2	2	no	—
11	#14583701	—	2	8	no	—
12	#14583701	C₂²	1	16	yes	complemented
13	C₂×#13063352	—	2	4	no	—
14	C₂×#13063350	—	2	2	no	—
15	C₂×#13063348	C₂²	1	4	yes	complemented
16	C₂²×D₃₄₄	C₂²	1	2	yes	complemented
17	C₂×D₈×D₄₃	C₂²	1	4	yes	complemented
18	C₂×#13063331	C₂²	1	1	yes	characteristic
19	#14583336	C₂²	1	32	yes	complemented
20	#14583334	C₂²	1	16	yes	complemented
21	#14583332	C₂²	1	16	yes	complemented
22	C₂×#13063268	C₂²	1	4	yes	complemented
23	C₂×D₆₈₈	C₂²	1	2	yes	complemented
24	C₂×D₆₈₈	C₂²	1	2	yes	complemented
25	C₂×D₆₈₈	C₂²	1	8	yes	complemented
26	C₂×#13063266	C₂²	1	4	yes	complemented
27	D₁₆×D₄₃	C₂²	1	16	yes	complemented
28	#14583315	C₂²	1	8	yes	complemented
29	C₂×#13063265	C₂²	1	1	yes	characteristic, complemented
30	C₂×#13063264	C₂²	1	2	yes	complemented
31	C₂×C₁₆×D₄₃	C₂²	1	2	yes	complemented
32	C₂×#135×C₄₃	C₂²	1	2	yes	complemented
33	C₄₃×#508	C₂²	1	8	yes	complemented
34	C₂×Q₃₂×C₄₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×SD₃₂×C₄₃	C₂²	1	2	yes	complemented
36	C₂×D₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
38	#13063371	—	2	16	no	—
39	#13063371	—	4	8	no	—
40	C₂×#10621902	—	2	4	no	—
41	C₂×#10621898	—	4	2	no	—
42	C₂×#10621898	D₄	1	1	yes	characteristic
43	C₂²×D₁₇₂	—	2	2	no	—
44	C₂²×D₁₇₂	—	4	2	no	—
45	C₂×D₄×D₄₃	—	2	4	no	—
46	C₂×D₄×D₄₃	—	4	4	no	—
47	#13063352	—	2	32	no	—
48	#13063350	—	2	16	no	—
49	#13063348	—	2	8	no	—
50	#13063348	C₂³	1	16	yes	complemented
51	C₂×#10621884	—	2	4	no	—
52	C₂×D₃₄₄	—	2	2	no	—
53	C₂×D₃₄₄	—	2	4	no	—
54	C₂×D₃₄₄	C₂³	1	4	yes	—
55	C₂×D₃₄₄	C₂³	1	8	yes	complemented
56	C₂×#10621882	—	2	4	no	—
57	D₈×D₄₃	—	2	8	no	—
58	D₈×D₄₃	C₂³	1	16	yes	complemented
59	#13063331	D₄	1	4	yes	—
60	#13063331	C₂³	1	4	yes	—
61	C₂×#10621877	D₄	1	1	yes	characteristic
62	C₂×#10621872	D₄	1	2	yes	—
63	C₂×C₈×D₄₃	C₂³	1	2	yes	—
64	#13063268	C₂³	1	16	yes	complemented
65	D₆₈₈	C₂³	1	8	yes	complemented
66	D₆₈₈	C₂³	1	8	yes	complemented
67	#13063266	C₂³	1	16	yes	complemented
68	#13063265	C₂³	1	4	yes	complemented
69	#13063264	C₂³	1	8	yes	complemented
70	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
71	C₁₆×D₄₃	C₂³	1	8	yes	complemented
72	C₂×#41×C₄₃	—	2	2	no	—
73	#135×C₄₃	—	2	4	no	—
74	#135×C₄₃	C₂³	1	8	yes	complemented
75	C₂×Q₁₆×C₄₃	C₂³	1	2	yes	—
76	C₂×SD₁₆×C₄₃	—	2	2	no	—
77	C₂×D₈×C₄₃	C₂³	1	2	yes	—
78	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
79	Q₃₂×C₄₃	C₂³	1	4	yes	complemented
80	SD₃₂×C₄₃	C₂³	1	8	yes	complemented
81	D₁₆×C₄₃	C₂³	1	4	yes	complemented
82	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
83	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₁₆×C₄₃	C₂³	1	4	yes	complemented
85	C₂³×D₄₃	—	4	2	no	—
86	C₂³×D₄₃	—	4	4	no	—
87	#41×C₄₃	—	2	8	no	—
88	#41×C₄₃	—	4	4	no	—
89	C₂×Q₈×C₄₃	—	2	2	no	—
90	C₂×D₄×C₄₃	—	2	2	no	—
91	C₂×D₄×C₄₃	—	4	2	no	—
92	C₂²×C₄×C₄₃	—	4	2	no	—
93	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
94	C₂×C₂²⋊D₄₃	—	4	4	no	—
95	C₂×C₂²⋊D₄₃	D₈	1	2	yes	—
96	#10621902	—	2	16	no	—
97	#10621902	—	4	8	no	—
98	D₄×D₄₃	—	2	16	no	—
99	D₄×D₄₃	—	4	32	no	—
100	D₄×D₄₃	—	4	8	no	—
101	#10621898	—	4	16	no	—
102	#10621898	D₈	1	4	yes	—
103	#10621898	C₂×D₄	1	4	yes	—
104	C₂×D₁₇₂	—	2	4	no	—
105	C₂×D₁₇₂	—	2	8	no	—
106	C₂×D₁₇₂	—	4	2	no	—
107	C₂×D₁₇₂	—	4	4	no	—
108	C₂×D₁₇₂	—	4	16	no	—
109	C₂×D₁₇₂	—	4	4	no	—
110	C₂×D₁₇₂	D₈	1	1	yes	characteristic
111	C₂×C₄×D₄₃	—	4	4	no	—
112	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
113	C₂×Dic₈₆	D₈	1	1	yes	characteristic
114	Q₁₆×C₄₃	—	2	2	no	—
115	Q₁₆×C₄₃	C₂⁴	1	4	yes	—
116	SD₁₆×C₄₃	—	2	8	no	—
117	D₈×C₄₃	—	2	2	no	—
118	D₈×C₄₃	C₂⁴	1	4	yes	—
119	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
122	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
123	#10621884	—	2	16	no	—
124	#10621882	—	2	16	no	—
125	#10621877	C₂×D₄	1	4	yes	—
126	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
127	D₃₄₄	—	2	4	no	—
128	D₃₄₄	—	2	8	no	—
129	D₃₄₄	C₂⁴	1	8	yes	—
130	#10621872	C₂×D₄	1	8	yes	—
131	C₈×D₄₃	C₂×D₄	1	4	yes	—
132	C₈×D₄₃	C₂⁴	1	4	yes	—
133	C₁₆×C₄₃	C₂⁴	1	2	yes	—
134	C₁₆×C₄₃	C₂⁴	1	2	yes	—
135	C₄₃⋊C₁₆	C₂⁴	1	4	yes	—
136	C₂³×C₄₃	—	4	2	no	—
137	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
138	C₂²×D₄₃	—	4	4	no	—
139	C₂²×D₄₃	—	4	8	no	—
140	C₂²×D₄₃	—	4	16	no	—
141	C₂²×D₄₃	—	16	8	no	—
142	C₂²×D₄₃	—	16	4	no	—
143	C₂²×D₄₃	C₂×D₈	1	2	yes	—
144	Q₈×C₄₃	—	2	4	no	—
145	Q₈×C₄₃	—	4	2	no	—
146	D₄×C₄₃	—	2	4	no	—
147	D₄×C₄₃	—	4	8	no	—
148	D₄×C₄₃	—	4	2	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	—	4	8	no	—
151	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
153	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
155	C₂²⋊D₄₃	—	4	16	no	—
156	C₂²⋊D₄₃	C₂×D₈	1	8	yes	—
157	C₂×Dic₄₃	C₂×D₈	1	2	yes	—
158	D₁₇₂	—	2	8	no	—
159	D₁₇₂	—	4	16	no	—
160	D₁₇₂	—	4	8	no	—
161	D₁₇₂	—	4	4	no	—
162	D₁₇₂	C₂×D₈	1	4	yes	—
163	C₄×D₄₃	—	4	16	no	—
164	C₄×D₄₃	C₂×D₈	1	4	yes	—
165	C₄×D₄₃	C₂²×D₄	1	4	yes	—
166	Dic₈₆	C₂×D₈	1	4	yes	—
167	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
168	C₈×C₄₃	C₂²×D₄	1	2	yes	—
169	C₈×C₄₃	C₂⁵	1	1	yes	characteristic
170	C₄₃⋊C₈	C₂²×D₄	1	4	yes	—
171	C₂×#3415	—	43	1	no	maximal, Sylow
172	C₂²×C₄₃	—	2	2	no	—
173	C₂²×C₄₃	—	4	4	no	—
174	C₂²×C₄₃	—	8	4	no	—
175	C₂²×C₄₃	C₂²×D₈	1	2	yes	—
176	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
177	C₂×D₄₃	—	2	4	no	—
178	C₂×D₄₃	—	4	8	no	—
179	C₂×D₄₃	—	8	8	no	—
180	C₂×D₄₃	—	16	16	no	—
181	C₂×D₄₃	—	16	8	no	—
182	C₂×D₄₃	C₂²×D₈	1	4	yes	—
183	C₄×C₄₃	—	4	4	no	—
184	C₄×C₄₃	C₂²×D₈	1	2	yes	—
185	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
186	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
187	Dic₄₃	C₂²×D₈	1	4	yes	—
188	C₂×#576	—	43	2	no	—
189	#3415	—	43	16	no	—
190	C₂×#509	—	43	4	no	—
191	C₂×#509	—	43	2	no	—
192	C₂×#508	—	43	2	no	—
193	C₂×#508	D₄₃	1	1	yes	characteristic, complemented
194	C₂²×D₁₆	—	43	2	no	—
195	C₂²×D₁₆	—	43	1	no	—
196	C₂×#504	—	43	1	no	—
197	C₂×C₄₃	—	2	2	no	—
198	C₂×C₄₃	—	8	4	no	—
199	C₂×C₄₃	#3415	1	2	yes	complemented
200	C₂×C₄₃	C₂³×D₈	1	1	yes	characteristic
201	D₄₃	—	2	4	no	—
202	D₄₃	—	8	8	no	—
203	C₂×H(5,𝔽₂)	—	86	2	no	—
204	#576	—	43	16	no	—
205	#576	—	86	8	no	—
206	C₂×AGL(1,ℤ/8)	—	86	4	no	—
207	C₂×AGL(1,ℤ/8)	—	86	2	no	—
208	C₂×#135	—	43	4	no	—
209	C₂×#135	C₂×D₄₃	1	2	yes	complemented
210	C₂²×D₈	—	43	4	no	—
211	C₂²×D₈	—	43	2	no	—
212	C₂×#131	—	43	1	no	—
213	#509	—	43	16	no	—
214	#509	—	43	32	no	—
215	#508	—	43	16	no	—
216	#508	C₂×D₄₃	1	8	yes	complemented
217	C₂×Q₃₂	C₂×D₄₃	1	1	yes	characteristic, complemented
218	C₂×SD₃₂	—	43	4	no	—
219	C₂×SD₃₂	C₂×D₄₃	1	2	yes	complemented
220	C₂×D₁₆	—	43	4	no	—
221	C₂×D₁₆	—	43	16	no	—
222	C₂×D₁₆	—	43	2	no	—
223	C₂×D₁₆	—	43	2	no	—
224	C₂×D₁₆	—	43	8	no	—
225	C₂×D₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
226	#504	—	43	8	no	—
227	C₂×M₃₂	—	43	1	no	—
228	C₂×M₃₂	—	43	2	no	—
229	C₂²×C₁₆	—	43	2	no	—
230	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
231	C₄₃	C₂×#3415	1	1	yes	characteristic, complemented, Sylow
232	H(5,𝔽₂)	—	86	16	no	—
233	H(5,𝔽₂)	—	172	8	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	43	1	no	—
236	C₂×#41	—	86	4	no	—
237	C₂×#41	—	172	2	no	—
238	C₂²×D₄	—	86	4	no	—
239	C₂²×D₄	—	86	2	no	—
240	C₂²×D₄	—	172	2	no	—
241	C₂²×D₄	—	172	4	no	—
242	AGL(1,ℤ/8)	—	86	32	no	—
243	AGL(1,ℤ/8)	—	86	16	no	—
244	#135	—	2	4	no	—
245	#135	—	43	16	no	—
246	#135	—	86	8	no	—
247	#135	C₂²×D₄₃	1	8	yes	complemented
248	C₂×Q₁₆	C₂²×D₄₃	1	2	yes	—
249	C₂×SD₁₆	—	2	2	no	—
250	C₂×SD₁₆	—	86	4	no	—
251	C₂×D₈	—	43	16	no	—
252	C₂×D₈	—	43	4	no	—
253	C₂×D₈	—	43	8	no	—
254	C₂×D₈	—	86	8	no	—
255	C₂×D₈	—	86	4	no	—
256	C₂×D₈	—	86	2	no	—
257	C₂×D₈	—	86	4	no	—
258	C₂×D₈	C₂²×D₄₃	1	2	yes	—
259	#131	—	43	4	no	—
260	#131	—	43	4	no	—
261	C₂×M₁₆	—	43	1	no	—
262	C₂×M₁₆	—	43	2	no	—
263	C₂²×C₈	—	43	2	no	—
264	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
265	Q₃₂	C₂²×D₄₃	1	4	yes	complemented
266	SD₃₂	—	43	16	no	—
267	SD₃₂	C₂²×D₄₃	1	8	yes	complemented
268	D₁₆	—	43	16	no	—
269	D₁₆	—	43	8	no	—
270	D₁₆	—	43	8	no	—
271	D₁₆	C₂²×D₄₃	1	4	yes	complemented
272	M₃₂	—	43	4	no	—
273	M₃₂	—	43	8	no	—
274	C₂×C₁₆	—	43	2	no	—
275	C₂×C₁₆	—	43	8	no	—
276	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
277	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
278	C₂×C₁₆	C₂²×D₄₃	1	4	yes	complemented
279	C₂⁴	—	172	4	no	—
280	C₂⁴	—	172	2	no	—
281	#41	—	2	8	no	—
282	#41	—	4	4	no	—
283	#41	—	43	4	no	—
284	#41	—	43	4	no	—
285	#41	—	86	16	no	—
286	#41	—	172	16	no	—
287	#41	—	172	8	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	43	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	43	2	no	—
293	C₂×D₄	—	43	1	no	—
294	C₂×D₄	—	86	16	no	—
295	C₂×D₄	—	86	4	no	—
296	C₂×D₄	—	86	8	no	—
297	C₂×D₄	—	172	16	no	—
298	C₂×D₄	—	172	4	no	—
299	C₂×D₄	—	172	8	no	—
300	C₂×D₄	—	172	4	no	—
301	C₂×D₄	—	172	32	no	—
302	C₂×D₄	—	172	2	no	—
303	C₂×D₄	—	172	4	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	—	43	2	no	—
306	C₂²×C₄	—	172	4	no	—
307	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
308	Q₁₆	—	2	2	no	—
309	Q₁₆	C₂³×D₄₃	1	4	yes	—
310	SD₁₆	—	2	8	no	—
311	SD₁₆	—	86	16	no	—
312	D₈	—	2	2	no	—
313	D₈	—	43	8	no	—
314	D₈	—	86	16	no	—
315	D₈	—	86	4	no	—
316	D₈	—	86	8	no	—
317	D₈	C₂³×D₄₃	1	4	yes	—
318	M₁₆	—	43	4	no	—
319	M₁₆	—	43	8	no	—
320	C₂×C₈	—	43	2	no	—
321	C₂×C₈	—	43	4	no	—
322	C₂×C₈	—	43	4	no	—
323	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
324	C₂×C₈	D₄×D₄₃	1	2	yes	—
325	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
326	C₂×C₈	C₂³×D₄₃	1	2	yes	—
327	C₁₆	—	43	4	no	—
328	C₁₆	C₂³×D₄₃	1	2	yes	—
329	C₁₆	C₂³×D₄₃	1	2	yes	—
330	C₂³	—	4	2	no	—
331	C₂³	—	43	2	no	—
332	C₂³	—	172	16	no	—
333	C₂³	—	172	4	no	—
334	C₂³	—	172	8	no	—
335	C₂³	—	688	4	no	—
336	C₂³	—	688	8	no	—
337	C₂³	D₈×D₄₃	1	1	yes	characteristic
338	Q₈	—	2	4	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	43	4	no	—
341	D₄	—	2	4	no	—
342	D₄	—	4	8	no	—
343	D₄	—	4	2	no	—
344	D₄	—	43	8	no	—
345	D₄	—	43	4	no	—
346	D₄	—	86	8	no	—
347	D₄	—	172	16	no	—
348	D₄	—	172	16	no	—
349	D₄	—	172	8	no	—
350	D₄	—	172	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	—	43	2	no	—
354	C₂×C₄	—	43	4	no	—
355	C₂×C₄	—	43	4	no	—
356	C₂×C₄	—	172	16	no	—
357	C₂×C₄	D₈×D₄₃	1	2	yes	—
358	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
360	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
361	C₈	—	43	4	no	—
362	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
363	C₈	C₂×D₄×D₄₃	1	2	yes	—
364	C₈	C₂⁴×D₄₃	1	1	yes	characteristic
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	8	4	no	—
368	C₂²	—	43	4	no	—
369	C₂²	—	86	4	no	—
370	C₂²	—	344	8	no	—
371	C₂²	—	172	8	no	—
372	C₂²	—	688	8	no	—
373	C₂²	—	688	16	no	—
374	C₂²	C₂×D₈×D₄₃	1	2	yes	—
375	C₂²	C₂×D₈×D₄₃	1	1	yes	characteristic
376	C₄	—	4	4	no	—
377	C₄	—	43	4	no	—
378	C₄	C₂×D₈×D₄₃	1	2	yes	—
379	C₄	C₂×D₈×D₄₃	1	1	yes	characteristic
380	C₄	C₂²×D₄×D₄₃	1	1	yes	characteristic
381	C₂	—	2	2	no	—
382	C₂	—	8	4	no	—
383	C₂	—	86	4	no	—
384	C₂	—	344	8	no	—
385	C₂	#19147733	1	2	yes	direct product factor
386	C₂	C₂²×D₈×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₄₃
commutator, cosocle	C₈×C₄₃	C₂⁵
Frattini	C₈	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#508	C₂
socle	C₂²×C₄₃	C₂²×D₈
hypercenter	C₂×#508	D₄₃
hypocenter	C₄₃	C₂×#3415
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#508

Complements

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

N	H ≅ G/N	type
1. C₂×#14583701	C₂	semidirect
2. #19147733	C₂	direct (N × H)
3. C₂×#14583336	C₂	semidirect
4. C₂×#14583334	C₂	semidirect
5. C₂×#14583332	C₂	semidirect
6. C₂²×D₆₈₈	C₂	semidirect
7. C₂×D₁₆×D₄₃	C₂	semidirect
8. C₂×#14583315	C₂	semidirect
9. C₂×C₄₃×#508	C₂	semidirect
12. #14583701	C₂²	semidirect
15. C₂×#13063348	C₂²	semidirect
16. C₂²×D₃₄₄	C₂²	semidirect
17. C₂×D₈×D₄₃	C₂²	semidirect
19. #14583336	C₂²	semidirect
20. #14583334	C₂²	semidirect
21. #14583332	C₂²	semidirect
22. C₂×#13063268	C₂²	semidirect
23. C₂×D₆₈₈	C₂²	semidirect
24. C₂×D₆₈₈	C₂²	semidirect
25. C₂×D₆₈₈	C₂²	semidirect
26. C₂×#13063266	C₂²	semidirect
27. D₁₆×D₄₃	C₂²	semidirect
28. #14583315	C₂²	semidirect
29. C₂×#13063265	C₂²	semidirect
30. C₂×#13063264	C₂²	semidirect
31. C₂×C₁₆×D₄₃	C₂²	semidirect
32. C₂×#135×C₄₃	C₂²	semidirect
33. C₄₃×#508	C₂²	semidirect
34. C₂×Q₃₂×C₄₃	C₂²	semidirect
35. C₂×SD₃₂×C₄₃	C₂²	semidirect
36. C₂×D₁₆×C₄₃	C₂²	semidirect
37. C₂²×C₁₆×C₄₃	C₂²	semidirect
50. #13063348	C₂³	semidirect
55. C₂×D₃₄₄	C₂³	semidirect
58. D₈×D₄₃	C₂³	semidirect
64. #13063268	C₂³	semidirect
65. D₆₈₈	C₂³	semidirect
66. D₆₈₈	C₂³	semidirect
67. #13063266	C₂³	semidirect
68. #13063265	C₂³	semidirect
69. #13063264	C₂³	semidirect
71. C₁₆×D₄₃	C₂³	semidirect
74. #135×C₄₃	C₂³	semidirect
79. Q₃₂×C₄₃	C₂³	semidirect
80. SD₃₂×C₄₃	C₂³	semidirect
81. D₁₆×C₄₃	C₂³	semidirect
84. C₂×C₁₆×C₄₃	C₂³	semidirect
193. C₂×#508	D₄₃	semidirect
199. C₂×C₄₃	#3415	semidirect
209. C₂×#135	C₂×D₄₃	semidirect
216. #508	C₂×D₄₃	semidirect
217. C₂×Q₃₂	C₂×D₄₃	semidirect
219. C₂×SD₃₂	C₂×D₄₃	semidirect
225. C₂×D₁₆	C₂×D₄₃	semidirect
230. C₂²×C₁₆	C₂×D₄₃	semidirect
231. C₄₃	C₂×#3415	semidirect
247. #135	C₂²×D₄₃	semidirect
265. Q₃₂	C₂²×D₄₃	semidirect
267. SD₃₂	C₂²×D₄₃	semidirect
271. D₁₆	C₂²×D₄₃	semidirect
278. C₂×C₁₆	C₂²×D₄₃	semidirect
385. C₂	#19147733	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×#14583701	2
#19147733	2
C₂×#14583336	2
C₂×#14583334	2
C₂×#14583332	2
C₂²×D₆₈₈	2
C₂×D₁₆×D₄₃	2
C₂×#14583315	2
C₂×C₄₃×#508	2
C₂×#3415	43

Subgroups — C2×#19147733 #26003106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19147733 #26003106