Subgroups — C₂²×#14582997 #25960626

Order 11008.

3222 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10621884	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582997	C₂	1	24	yes	maximal, direct product factor
4	C₂²×#13063258	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13063249	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13063245	C₂	1	1	yes	maximal, characteristic
7	C₂²×#13063236	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic
10	C₂³×C₄×D₄₃	—	2	1	no	—
11	C₂²×#10621884	C₄	1	16	yes	complemented
12	C₂²×#10621884	C₂²	1	12	yes	—
13	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₁₇₂	—	2	6	no	—
16	C₂×C₄×D₁₇₂	C₂²	1	12	yes	—
17	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
18	C₂²×(C₂×D₄₃)⋊C₄	—	2	1	no	—
19	#14582997	C₂²	1	64	yes	direct product factor
20	C₂×#13063258	C₂²	1	12	yes	complemented
21	C₂×#13063249	C₂²	1	12	yes	complemented
22	C₂×#13063245	C₂²	1	12	yes	—
23	C₂×#13063236	C₂²	1	12	yes	complemented
24	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₄₃	—	2	6	no	—
26	C₂×C₄×Q₈×C₄₃	C₂²	1	12	yes	complemented
27	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
28	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₄₃	—	2	1	no	—
30	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
31	C₂⁴×D₄₃	—	2	1	no	—
32	C₂²×D₁₇₂	—	2	3	no	—
33	C₂²×D₁₇₂	—	2	4	no	—
34	C₂²×D₁₇₂	C₂×C₄	1	8	yes	—
35	C₂²×D₁₇₂	C₂³	1	6	yes	—
36	C₂³×Dic₄₃	—	2	1	no	—
37	C₂²×C₄×D₄₃	—	2	12	no	—
38	C₂²×C₄×D₄₃	—	4	8	no	—
39	C₂×#10621884	C₂×C₄	1	96	yes	complemented
40	C₂×#10621884	C₂³	1	16	yes	—
41	C₂²×C₄₃⋊C₈	—	2	4	no	—
42	C₂²×C₄₃⋊C₈	C₂×C₄	1	8	yes	complemented
43	C₂²×C₄₃⋊C₈	C₂³	1	6	yes	—
44	C₂²×C₄₃⋊C₈	C₂³	1	6	yes	—
45	C₄×D₁₇₂	—	2	24	no	—
46	C₄×D₁₇₂	C₂³	1	16	yes	—
47	C₂×C₄⋊Dic₄₃	—	2	3	no	—
48	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
49	C₂×(C₂×D₄₃)⋊C₄	—	2	12	no	—
50	#13063258	C₂³	1	16	yes	complemented
51	#13063249	C₂³	1	16	yes	complemented
52	#13063245	C₂³	1	16	yes	—
53	#13063236	C₂³	1	16	yes	complemented
54	C₂²×Q₈×C₄₃	—	2	3	no	—
55	C₂²×Q₈×C₄₃	—	2	4	no	—
56	C₂²×Q₈×C₄₃	C₂×C₄	1	8	yes	complemented
57	C₂²×Q₈×C₄₃	C₂³	1	6	yes	—
58	C₂³×C₄×C₄₃	—	2	1	no	—
59	C₂³×C₄×C₄₃	—	2	1	no	—
60	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₄₃	—	2	24	no	—
64	C₄×Q₈×C₄₃	C₂³	1	16	yes	complemented
65	C₂×C₄⋊C₄×C₄₃	—	2	12	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	3	no	—
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	6	yes	—
68	C₂×C₄²×C₄₃	—	2	12	no	—
69	C₂×C₄²×C₄₃	D₄	1	6	yes	—
70	C₂×C₄²×C₄₃	C₂³	1	6	yes	—
71	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
72	C₂³×D₄₃	—	2	8	no	—
73	C₂³×D₄₃	—	2	6	no	—
74	C₂³×D₄₃	—	4	4	no	—
75	C₂³×D₄₃	—	4	4	no	—
76	C₂×Q₈×C₄₃	—	2	24	no	—
77	C₂×Q₈×C₄₃	—	2	6	no	—
78	C₂×Q₈×C₄₃	—	2	12	no	—
79	C₂×Q₈×C₄₃	C₂²×C₄	1	24	yes	complemented
80	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
81	C₂²×C₄×C₄₃	—	2	8	no	—
82	C₂²×C₄×C₄₃	—	2	4	no	—
83	C₂²×C₄×C₄₃	—	2	4	no	—
84	C₂²×C₄×C₄₃	—	2	6	no	—
85	C₂²×C₄×C₄₃	—	2	6	no	—
86	C₂²×C₄×C₄₃	—	4	4	no	—
87	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
89	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
90	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
91	C₂²×C₄×C₄₃	#41	1	4	yes	—
92	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
93	C₂²×Dic₄₃	—	2	6	no	—
94	C₂²×Dic₄₃	—	4	4	no	—
95	C₂×D₁₇₂	—	2	24	no	—
96	C₂×D₁₇₂	—	2	6	no	—
97	C₂×D₁₇₂	—	2	12	no	—
98	C₂×D₁₇₂	C₂²×C₄	1	24	yes	—
99	C₂×D₁₇₂	C₂⁴	1	4	yes	—
100	C₂×C₄×D₄₃	—	2	16	no	—
101	C₂×C₄×D₄₃	—	4	48	no	—
102	C₄⋊C₄×C₄₃	—	2	16	no	—
103	C₄⋊C₄×C₄₃	—	2	6	no	—
104	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
105	C₄²×C₄₃	—	2	16	no	—
106	C₄²×C₄₃	C₂×D₄	1	12	yes	—
107	C₄²×C₄₃	C₂⁴	1	4	yes	—
108	#10621884	C₂²×C₄	1	64	yes	complemented
109	(C₂×D₄₃)⋊C₄	—	2	16	no	—
110	C₄⋊Dic₄₃	—	2	6	no	—
111	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
112	C₂×C₄₃⋊C₈	—	2	12	no	—
113	C₂×C₄₃⋊C₈	C₂²×C₄	1	24	yes	complemented
114	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
115	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
116	C₂³×C₄₃	C₄×D₄	1	4	yes	—
117	C₂³×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
118	C₂³×C₄₃	#137	1	4	yes	—
119	C₂³×C₄₃	C₂²×D₄	1	3	yes	—
120	C₂²×D₄₃	—	2	24	no	—
121	C₂²×D₄₃	—	2	4	no	—
122	C₂²×D₄₃	—	4	12	no	—
123	C₂²×D₄₃	—	4	12	no	—
124	C₂²×D₄₃	—	4	32	no	—
125	Q₈×C₄₃	—	2	24	no	—
126	Q₈×C₄₃	—	2	4	no	—
127	Q₈×C₄₃	C₂³×C₄	1	8	yes	complemented
128	C₂×C₄×C₄₃	—	2	24	no	—
129	C₂×C₄×C₄₃	—	2	12	no	—
130	C₂×C₄×C₄₃	—	2	12	no	—
131	C₂×C₄×C₄₃	—	2	4	no	—
132	C₂×C₄×C₄₃	—	2	4	no	—
133	C₂×C₄×C₄₃	—	4	12	no	—
134	C₂×C₄×C₄₃	C₄×D₄	1	12	yes	—
135	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
136	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
137	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
138	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
139	C₂×C₄×C₄₃	C₂×#41	1	6	yes	—
140	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
141	C₂×Dic₄₃	—	2	4	no	—
142	C₂×Dic₄₃	—	4	12	no	—
143	D₁₇₂	—	2	24	no	—
144	D₁₇₂	—	2	4	no	—
145	D₁₇₂	C₂³×C₄	1	8	yes	—
146	C₄×D₄₃	—	4	32	no	—
147	C₄₃⋊C₈	—	2	4	no	—
148	C₄₃⋊C₈	C₂³×C₄	1	8	yes	complemented
149	C₂²×#440	—	43	1	no	maximal, Sylow
150	C₂²×C₄₃	#440	1	16	yes	complemented
151	C₂²×C₄₃	C₂×C₄×D₄	1	6	yes	—
152	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
153	C₂²×C₄₃	C₂×#137	1	6	yes	—
154	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
155	C₂×D₄₃	—	2	8	no	—
156	C₂×D₄₃	—	4	48	no	—
157	C₂×D₄₃	—	4	4	no	—
158	C₂×D₄₃	—	4	4	no	—
159	C₄×C₄₃	—	2	8	no	—
160	C₄×C₄₃	—	2	4	no	—
161	C₄×C₄₃	—	2	4	no	—
162	C₄×C₄₃	—	4	4	no	—
163	C₄×C₄₃	C₂×C₄×D₄	1	6	yes	—
164	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
165	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
166	Dic₄₃	—	4	4	no	—
167	C₂³×SD₁₆	—	43	1	no	—
168	C₂²×C₄×Q₈	D₄₃	1	1	yes	characteristic, complemented
169	C₂²×C₄×D₄	—	43	1	no	—
170	C₂×#440	—	43	24	no	—
171	C₂²×#107	—	43	1	no	—
172	C₂²×#103	—	43	1	no	—
173	C₂²×#102	—	43	1	no	—
174	C₂²×#97	—	43	1	no	—
175	C₂×C₄₃	C₂×#440	1	12	yes	complemented
176	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
177	C₂×C₄₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
178	C₂×C₄₃	C₂²×#137	1	1	yes	characteristic
179	D₄₃	—	4	8	no	—
180	C₂³×Q₈	C₂×D₄₃	1	1	yes	characteristic
181	C₂³×D₄	—	43	1	no	—
182	C₂⁴×C₄	—	86	1	no	—
183	C₂²×SD₁₆	—	43	12	no	—
184	C₂²×SD₁₆	—	43	16	no	—
185	C₂³×C₈	—	43	1	no	—
186	C₂³×C₈	—	43	1	no	—
187	C₂×C₄×Q₈	—	2	6	no	—
188	C₂×C₄×Q₈	C₂×D₄₃	1	12	yes	complemented
189	C₂×C₄×D₄	—	43	12	no	—
190	C₂×C₄×D₄	—	86	6	no	—
191	C₂²×C₄⋊C₄	—	2	1	no	—
192	C₂²×C₄⋊C₄	—	43	1	no	—
193	C₂²×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
194	C₂²×C₂²⋊C₄	—	86	1	no	—
195	C₂²×C₄²	—	2	1	no	—
196	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
197	#440	—	43	64	no	—
198	C₂×#107	—	43	12	no	—
199	C₂×#103	—	43	12	no	—
200	C₂×#102	—	43	12	no	—
201	C₂×#97	—	43	12	no	—
202	C₄₃	C₂²×#440	1	1	yes	characteristic, complemented, Sylow
203	C₂⁵	—	86	1	no	—
204	C₂²×Q₈	—	2	4	no	—
205	C₂²×Q₈	—	2	3	no	—
206	C₂²×Q₈	C₄×D₄₃	1	8	yes	complemented
207	C₂²×Q₈	C₂²×D₄₃	1	6	yes	—
208	C₂²×D₄	—	43	8	no	—
209	C₂²×D₄	—	43	6	no	—
210	C₂²×D₄	—	86	4	no	—
211	C₂²×D₄	—	86	3	no	—
212	C₂³×C₄	—	2	1	no	—
213	C₂³×C₄	—	2	1	no	—
214	C₂³×C₄	—	86	1	no	—
215	C₂³×C₄	—	86	12	no	—
216	C₂³×C₄	—	172	8	no	—
217	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
218	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
219	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
220	C₂×SD₁₆	—	43	96	no	—
221	C₂×SD₁₆	—	43	16	no	—
222	C₂²×C₈	—	43	8	no	—
223	C₂²×C₈	—	43	6	no	—
224	C₂²×C₈	—	43	6	no	—
225	C₂²×C₈	—	86	4	no	—
226	C₄×Q₈	—	2	24	no	—
227	C₄×Q₈	C₂²×D₄₃	1	16	yes	complemented
228	C₄×D₄	—	43	16	no	—
229	C₄×D₄	—	86	24	no	—
230	C₂×C₄⋊C₄	—	2	12	no	—
231	C₂×C₄⋊C₄	—	2	3	no	—
232	C₂×C₄⋊C₄	—	43	6	no	—
233	C₂×C₄⋊C₄	—	86	3	no	—
234	C₂×C₄⋊C₄	C₂²×D₄₃	1	6	yes	—
235	C₂×C₂²⋊C₄	—	86	12	no	—
236	C₂×C₄²	—	2	12	no	—
237	C₂×C₄²	C₂²⋊D₄₃	1	6	yes	—
238	C₂×C₄²	C₂²×D₄₃	1	6	yes	—
239	#107	—	43	16	no	—
240	#103	—	43	16	no	—
241	#102	—	43	16	no	—
242	#97	—	43	16	no	—
243	C₂⁴	—	86	8	no	—
244	C₂⁴	—	86	6	no	—
245	C₂⁴	—	172	4	no	—
246	C₂⁴	—	172	4	no	—
247	C₂⁴	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
248	C₂×Q₈	—	2	24	no	—
249	C₂×Q₈	—	2	6	no	—
250	C₂×Q₈	—	2	12	no	—
251	C₂×Q₈	C₂×C₄×D₄₃	1	24	yes	complemented
252	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
253	C₂×D₄	—	43	24	no	—
254	C₂×D₄	—	43	4	no	—
255	C₂×D₄	—	86	24	no	—
256	C₂×D₄	—	86	6	no	—
257	C₂×D₄	—	86	12	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	6	no	—
262	C₂²×C₄	—	2	6	no	—
263	C₂²×C₄	—	4	4	no	—
264	C₂²×C₄	—	86	6	no	—
265	C₂²×C₄	—	86	16	no	—
266	C₂²×C₄	—	172	48	no	—
267	C₂²×C₄	—	172	4	no	—
268	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
269	C₂²×C₄	#10621898	1	4	yes	—
270	C₂²×C₄	C₂×C₂²⋊D₄₃	1	6	yes	—
271	C₂²×C₄	C₂×C₂²⋊D₄₃	1	6	yes	—
272	C₂²×C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
273	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
274	SD₁₆	—	43	64	no	—
275	C₂×C₈	—	43	24	no	—
276	C₂×C₈	—	43	4	no	—
277	C₂×C₈	—	43	4	no	—
278	C₂×C₈	—	86	12	no	—
279	C₄⋊C₄	—	2	16	no	—
280	C₄⋊C₄	—	2	6	no	—
281	C₄⋊C₄	—	43	4	no	—
282	C₄⋊C₄	—	86	6	no	—
283	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
284	C₂²⋊C₄	—	86	16	no	—
285	C₄²	—	2	16	no	—
286	C₄²	C₂×C₂²⋊D₄₃	1	12	yes	—
287	C₄²	C₂³×D₄₃	1	4	yes	—
288	C₂³	—	86	24	no	—
289	C₂³	—	86	4	no	—
290	C₂³	—	172	12	no	—
291	C₂³	—	172	12	no	—
292	C₂³	—	172	32	no	—
293	C₂³	C₄×C₂²⋊D₄₃	1	4	yes	—
294	C₂³	#13063350	1	4	yes	—
295	C₂³	#13063356	1	4	yes	—
296	C₂³	C₂²×C₂²⋊D₄₃	1	3	yes	—
297	Q₈	—	2	24	no	—
298	Q₈	—	2	4	no	—
299	Q₈	C₂²×C₄×D₄₃	1	8	yes	complemented
300	D₄	—	43	8	no	—
301	D₄	—	86	24	no	—
302	D₄	—	86	4	no	—
303	C₂×C₄	—	2	24	no	—
304	C₂×C₄	—	2	12	no	—
305	C₂×C₄	—	2	12	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	4	12	no	—
309	C₂×C₄	—	86	4	no	—
310	C₂×C₄	—	172	32	no	—
311	C₂×C₄	—	172	12	no	—
312	C₂×C₄	C₄×C₂²⋊D₄₃	1	12	yes	—
313	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
314	C₂×C₄	C₂²×C₂²⋊D₄₃	1	4	yes	—
315	C₂×C₄	C₂²×C₂²⋊D₄₃	1	4	yes	—
316	C₂×C₄	C₂²×C₂²⋊D₄₃	1	3	yes	—
317	C₂×C₄	C₂×#10621898	1	6	yes	—
318	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
319	C₈	—	43	8	no	—
320	C₈	—	86	4	no	—
321	C₂²	—	86	8	no	—
322	C₂²	—	172	4	no	—
323	C₂²	—	172	4	no	—
324	C₂²	—	172	48	no	—
325	C₂²	#14582997	1	16	yes	direct product factor
326	C₂²	C₂×C₄×C₂²⋊D₄₃	1	6	yes	—
327	C₂²	C₂×#13063350	1	6	yes	—
328	C₂²	C₂×#13063356	1	6	yes	—
329	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	2	4	no	—
332	C₄	—	2	8	no	—
333	C₄	—	4	4	no	—
334	C₄	—	172	4	no	—
335	C₄	C₂×C₄×C₂²⋊D₄₃	1	6	yes	—
336	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
337	C₄	C₂²×#10621898	1	1	yes	characteristic
338	C₂	—	172	8	no	—
339	C₂	C₂×#14582997	1	12	yes	direct product factor
340	C₂	C₂²×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
341	C₂	C₂²×#13063350	1	1	yes	characteristic
342	C₂	C₂²×#13063356	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₃
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂²×C₄×Q₈×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂×D₄
prime radical	C₂³×D₁₇₂	C₂²
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂²×C₄×Q₈	D₄₃
hypocenter	C₄₃	C₂²×#440
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
3. C₂×#14582997	C₂	direct (N × H)
4. C₂²×#13063258	C₂	semidirect
5. C₂²×#13063249	C₂	semidirect
7. C₂²×#13063236	C₂	semidirect
8. C₂²×C₄×Q₈×C₄₃	C₂	semidirect
11. C₂²×#10621884	C₄	semidirect
19. #14582997	C₂²	direct (N × H)
20. C₂×#13063258	C₂²	semidirect
21. C₂×#13063249	C₂²	semidirect
23. C₂×#13063236	C₂²	semidirect
26. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
39. C₂×#10621884	C₂×C₄	semidirect
42. C₂²×C₄₃⋊C₈	C₂×C₄	semidirect
50. #13063258	C₂³	semidirect
51. #13063249	C₂³	semidirect
53. #13063236	C₂³	semidirect
56. C₂²×Q₈×C₄₃	C₂×C₄	semidirect
64. C₄×Q₈×C₄₃	C₂³	semidirect
79. C₂×Q₈×C₄₃	C₂²×C₄	semidirect
108. #10621884	C₂²×C₄	semidirect
113. C₂×C₄₃⋊C₈	C₂²×C₄	semidirect
127. Q₈×C₄₃	C₂³×C₄	semidirect
148. C₄₃⋊C₈	C₂³×C₄	semidirect
150. C₂²×C₄₃	#440	semidirect
168. C₂²×C₄×Q₈	D₄₃	semidirect
175. C₂×C₄₃	C₂×#440	semidirect
188. C₂×C₄×Q₈	C₂×D₄₃	semidirect
202. C₄₃	C₂²×#440	semidirect
206. C₂²×Q₈	C₄×D₄₃	semidirect
227. C₄×Q₈	C₂²×D₄₃	semidirect
251. C₂×Q₈	C₂×C₄×D₄₃	semidirect
299. Q₈	C₂²×C₄×D₄₃	semidirect
325. C₂²	#14582997	direct (N × H)
339. C₂	C₂×#14582997	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#10621884	2
C₂²×C₄×D₁₇₂	2
C₂×#14582997	2
C₂²×#13063258	2
C₂²×#13063249	2
C₂²×#13063245	2
C₂²×#13063236	2
C₂²×C₄×Q₈×C₄₃	2
C₂²×#440	43

Subgroups — C22×#14582997 #25960626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#14582997 #25960626