Subgroups — D₄×#13063259 #25114715

Order 11008.

1126 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063259	C₂	1	2	yes	maximal, complemented
2	D₄×C₄⋊Dic₄₃	C₂	1	2	yes	maximal
3	#19135354	C₂	1	2	yes	maximal, complemented
4	#19134785	C₂	1	4	yes	maximal, complemented
5	#19134755	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134624	C₂	1	2	yes	maximal, complemented
7	C₄×#13063259	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
9	C₂×D₄×Dic₄₃	—	2	2	no	—
10	C₂²×C₄⋊Dic₄₃	C₂²	1	4	yes	—
11	C₂×#13063259	—	2	8	no	—
12	C₂×#13063259	C₂²	1	2	yes	—
13	C₂×#13063259	C₂²	1	4	yes	—
14	C₂×#13063259	C₂²	1	1	yes	characteristic
15	C₂×#13063259	C₂²	1	2	yes	—
16	C₂×#13063259	C₂²	1	1	yes	characteristic
17	#14582798	—	2	2	no	—
18	#14582774	—	2	4	no	—
19	#14582769	C₂²	1	2	yes	—
20	#14582759	C₂²	1	4	yes	—
21	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
22	#14582662	C₂²	1	2	yes	—
23	#14582662	C₂²	1	4	yes	—
24	C₂³×C₈×C₄₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
26	C₈×D₄×C₄₃	C₄	1	8	yes	complemented
27	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂³×Dic₄₃	—	2	4	no	—
31	D₄×Dic₄₃	—	4	8	no	—
32	C₂×C₄⋊Dic₄₃	—	2	8	no	—
33	C₂×C₄⋊Dic₄₃	—	2	4	no	—
34	C₂×C₄⋊Dic₄₃	—	2	2	no	—
35	C₂×C₄⋊Dic₄₃	—	2	2	no	—
36	C₂×C₄⋊Dic₄₃	—	4	4	no	—
37	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
38	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
39	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
40	C₂×C₂²⋊Dic₄₃	—	2	4	no	—
41	C₂×C₄×Dic₄₃	—	2	2	no	—
42	#13063259	—	2	4	no	—
43	#13063259	—	2	2	no	—
44	#13063259	—	2	8	no	—
45	#13063259	—	4	2	no	—
46	#13063259	D₄	1	4	yes	direct product factor
47	C₄₃⋊#95	—	2	4	no	—
48	C₄₃⋊#95	—	2	2	no	—
49	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₄₃	—	2	4	no	—
52	C₂²×C₈×C₄₃	—	2	4	no	—
53	C₂²×C₈×C₄₃	C₂×C₄	1	8	yes	complemented
54	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
57	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
58	C₄×D₄×C₄₃	Q₈	1	4	yes	—
59	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
61	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	complemented
63	C₂²⋊C₈×C₄₃	C₂×C₄	1	8	yes	complemented
64	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
65	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
66	C₂×D₄×C₄₃	C₄⋊C₄	1	4	yes	—
67	C₂×D₄×C₄₃	D₈	1	4	yes	—
68	C₂×D₄×C₄₃	Q₁₆	1	4	yes	—
69	C₂²×C₄×C₄₃	—	2	2	no	—
70	C₂²×C₄×C₄₃	—	2	2	no	—
71	C₂²×C₄×C₄₃	—	2	2	no	—
72	C₂²×C₄×C₄₃	—	2	2	no	—
73	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
74	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
78	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
79	C₂²×Dic₄₃	—	2	2	no	—
80	C₂²×Dic₄₃	—	2	2	no	—
81	C₂²×Dic₄₃	—	2	4	no	—
82	C₂²×Dic₄₃	—	4	8	no	—
83	C₂²×Dic₄₃	—	4	8	no	—
84	C₂²×Dic₄₃	—	8	4	no	—
85	C₂×C₈×C₄₃	—	2	2	no	—
86	C₂×C₈×C₄₃	—	2	2	no	—
87	C₂×C₈×C₄₃	—	2	1	no	—
88	C₂×C₈×C₄₃	—	2	1	no	—
89	C₂×C₈×C₄₃	—	2	16	no	—
90	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
91	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
92	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
93	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
94	C₂×C₈×C₄₃	#41	1	2	yes	—
95	C₄⋊C₄×C₄₃	C₄⋊C₄	1	4	yes	—
96	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	8	yes	—
97	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
98	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
99	C₂²⋊Dic₄₃	—	4	8	no	—
100	C₄⋊Dic₄₃	—	2	2	no	—
101	C₄⋊Dic₄₃	—	2	4	no	—
102	C₄⋊Dic₄₃	—	2	2	no	—
103	C₄⋊Dic₄₃	—	2	4	no	—
104	C₄⋊Dic₄₃	—	2	2	no	—
105	C₄⋊Dic₄₃	—	4	8	no	—
106	C₄⋊Dic₄₃	—	4	4	no	—
107	C₄⋊Dic₄₃	—	8	2	no	—
108	C₄⋊Dic₄₃	C₂×D₄	1	4	yes	—
109	C₄×Dic₄₃	—	4	4	no	—
110	C₂³×C₄₃	—	2	2	no	—
111	C₂³×C₄₃	—	2	2	no	—
112	C₂³×C₄₃	—	2	2	no	—
113	C₂³×C₄₃	—	2	2	no	—
114	C₂³×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
115	C₂³×C₄₃	C₂×D₈	1	4	yes	—
116	C₂³×C₄₃	C₂×Q₁₆	1	4	yes	—
117	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
118	D₄×C₄₃	#107	1	16	yes	complemented
119	C₂×C₄×C₄₃	—	2	2	no	—
120	C₂×C₄×C₄₃	—	2	2	no	—
121	C₂×C₄×C₄₃	—	2	1	no	—
122	C₂×C₄×C₄₃	—	2	1	no	—
123	C₂×C₄×C₄₃	—	2	4	no	—
124	C₂×C₄×C₄₃	—	2	4	no	—
125	C₂×C₄×C₄₃	—	2	4	no	—
126	C₂×C₄×C₄₃	—	2	4	no	—
127	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
129	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
130	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
131	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
132	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
133	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
135	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
136	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
137	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
138	C₂×Dic₄₃	—	2	4	no	—
139	C₂×Dic₄₃	—	4	2	no	—
140	C₂×Dic₄₃	—	4	2	no	—
141	C₂×Dic₄₃	—	4	4	no	—
142	C₂×Dic₄₃	—	4	2	no	—
143	C₂×Dic₄₃	—	4	2	no	—
144	C₂×Dic₄₃	—	4	4	no	—
145	C₂×Dic₄₃	—	4	4	no	—
146	C₂×Dic₄₃	—	4	2	no	—
147	C₂×Dic₄₃	—	8	16	no	—
148	C₈×C₄₃	—	2	4	no	—
149	C₈×C₄₃	—	2	2	no	—
150	C₈×C₄₃	C₄×D₄	1	4	yes	complemented
151	D₄×#107	—	43	1	no	maximal, Sylow
152	C₂²×C₄₃	—	2	4	no	—
153	C₂²×C₄₃	—	2	4	no	—
154	C₂²×C₄₃	—	2	4	no	—
155	C₂²×C₄₃	—	2	4	no	—
156	C₂²×C₄₃	—	2	4	no	—
157	C₂²×C₄₃	—	2	4	no	—
158	C₂²×C₄₃	C₂×#107	1	8	yes	complemented
159	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
160	C₂²×C₄₃	D₄²	1	1	yes	characteristic
161	C₂²×C₄₃	#547	1	1	yes	characteristic
162	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
163	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
164	C₂²×C₄₃	#576	1	1	yes	characteristic
165	C₂²×C₄₃	#578	1	1	yes	characteristic
166	C₄×C₄₃	—	2	4	no	—
167	C₄×C₄₃	—	2	2	no	—
168	C₄×C₄₃	C₂×#107	1	4	yes	complemented
169	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
170	C₄×C₄₃	#520	1	1	yes	characteristic
171	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
172	C₄×C₄₃	#554	1	1	yes	characteristic
173	Dic₄₃	—	4	4	no	—
174	Dic₄₃	—	8	2	no	—
175	Dic₄₃	—	8	4	no	—
176	C₂×C₈×D₄	D₄₃	1	1	yes	characteristic
177	C₂²×#107	—	43	2	no	—
178	D₄×C₄⋊C₄	—	43	2	no	—
179	#1947	—	43	2	no	—
180	#1852	—	43	4	no	—
181	#1845	—	43	1	no	—
182	#1808	—	43	2	no	—
183	C₄×#107	—	43	1	no	—
184	C₂×C₄₃	—	2	8	no	—
185	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄₃	C₂²×#107	1	1	yes	characteristic
187	C₂×C₄₃	#2913	1	1	yes	characteristic
188	C₂×C₄₃	D₄×D₈	1	1	yes	characteristic
189	C₂×C₄₃	D₄×Q₁₆	1	1	yes	characteristic
190	C₂×C₄₃	#3334	1	1	yes	characteristic
191	C₂×C₄₃	#3338	1	1	yes	characteristic
192	C₂³×C₈	C₂×D₄₃	1	2	yes	—
193	C₂×C₄×D₄	—	86	2	no	—
194	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
195	C₂²×C₄⋊C₄	—	43	4	no	—
196	C₈×D₄	Dic₄₃	1	8	yes	complemented
197	C₂×#107	—	43	1	no	—
198	C₂×#107	—	43	1	no	—
199	C₂×#107	—	43	2	no	—
200	C₂×#107	—	43	4	no	—
201	C₂×#107	—	43	2	no	—
202	C₂×#107	—	86	8	no	—
203	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
204	C₂×C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
205	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
206	#389	—	86	2	no	—
207	#385	—	86	4	no	—
208	#384	—	43	2	no	—
209	#380	—	43	4	no	—
210	C₄×C₄⋊C₄	—	43	2	no	—
211	#340	—	43	4	no	—
212	#340	—	43	2	no	—
213	C₄₃	D₄×#107	1	1	yes	characteristic, complemented, Sylow
214	C₂²×D₄	D₁₇₂	1	1	yes	characteristic
215	C₂³×C₄	—	86	4	no	—
216	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
217	C₂²×C₈	—	2	4	no	—
218	C₂²×C₈	—	2	4	no	—
219	C₂²×C₈	C₂×Dic₄₃	1	8	yes	complemented
220	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
221	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
222	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
223	C₄×D₄	—	172	8	no	—
224	C₄×D₄	Dic₈₆	1	4	yes	—
225	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
226	C₂×C₄⋊C₄	—	43	2	no	—
227	C₂×C₄⋊C₄	—	43	4	no	—
228	C₂×C₄⋊C₄	—	43	2	no	—
229	C₂×C₄⋊C₄	—	86	8	no	—
230	C₂×C₄⋊C₄	—	86	2	no	—
231	C₂×C₄⋊C₄	—	86	4	no	—
232	C₂×C₄⋊C₄	—	86	2	no	—
233	C₂×C₄⋊C₄	—	172	4	no	—
234	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	—	86	4	no	—
236	C₂×C₂²⋊C₄	D₁₇₂	1	2	yes	—
237	C₂×C₄²	—	86	2	no	—
238	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
239	#107	—	43	4	no	—
240	#107	—	86	8	no	—
241	#107	—	86	4	no	—
242	#107	—	86	2	no	—
243	#107	—	172	2	no	—
244	C₄⋊C₈	C₂×Dic₄₃	1	4	yes	complemented
245	C₂²⋊C₈	C₂×Dic₄₃	1	8	yes	complemented
246	C₄×C₈	C₂×Dic₄₃	1	4	yes	complemented
247	#95	—	86	2	no	—
248	#95	—	86	4	no	—
249	C₂⁴	C₂×D₁₇₂	1	2	yes	—
250	C₂×D₄	D₃₄₄	1	4	yes	—
251	C₂×D₄	Dic₁₇₂	1	4	yes	—
252	C₂×D₄	C₄⋊Dic₄₃	1	4	yes	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	86	2	no	—
258	C₂²×C₄	—	86	2	no	—
259	C₂²×C₄	—	86	4	no	—
260	C₂²×C₄	—	344	4	no	—
261	C₂²×C₄	—	172	8	no	—
262	C₂²×C₄	—	172	8	no	—
263	C₂²×C₄	C₂×Dic₈₆	1	4	yes	—
264	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
266	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
267	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
268	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	—	2	1	no	—
273	C₂×C₈	—	2	16	no	—
274	C₂×C₈	D₄×D₄₃	1	2	yes	—
275	C₂×C₈	#10621900	1	2	yes	—
276	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
277	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
278	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
279	C₄⋊C₄	—	43	4	no	—
280	C₄⋊C₄	—	86	2	no	—
281	C₄⋊C₄	—	86	4	no	—
282	C₄⋊C₄	—	86	2	no	—
283	C₄⋊C₄	—	86	4	no	—
284	C₄⋊C₄	—	86	2	no	—
285	C₄⋊C₄	—	344	2	no	—
286	C₄⋊C₄	—	172	8	no	—
287	C₄⋊C₄	—	172	4	no	—
288	C₄⋊C₄	C₄⋊Dic₄₃	1	4	yes	—
289	C₂²⋊C₄	—	172	8	no	—
290	C₂²⋊C₄	C₄⋊Dic₄₃	1	8	yes	—
291	C₄²	—	172	4	no	—
292	C₄²	C₂×Dic₈₆	1	2	yes	—
293	C₄²	C₂²×Dic₄₃	1	2	yes	—
294	C₂³	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	C₂×C₄⋊Dic₄₃	1	4	yes	—
299	C₂³	C₂×D₃₄₄	1	4	yes	—
300	C₂³	C₂×Dic₁₇₂	1	4	yes	—
301	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
302	D₄	#13063259	1	16	yes	direct product factor
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	86	4	no	—
312	C₂×C₄	—	344	16	no	—
313	C₂×C₄	—	172	2	no	—
314	C₂×C₄	—	172	2	no	—
315	C₂×C₄	—	172	4	no	—
316	C₂×C₄	—	172	4	no	—
317	C₂×C₄	—	172	2	no	—
318	C₂×C₄	—	172	4	no	—
319	C₂×C₄	—	172	2	no	—
320	C₂×C₄	—	172	2	no	—
321	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
322	C₂×C₄	C₂×C₄⋊Dic₄₃	1	4	yes	—
323	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
324	C₂×C₄	C₂×D₃₄₄	1	2	yes	—
325	C₂×C₄	C₂×Dic₁₇₂	1	2	yes	—
326	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
327	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
328	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
329	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
330	C₂×C₄	#13063371	1	1	yes	characteristic
331	C₂×C₄	#13063372	1	1	yes	characteristic
332	C₈	—	2	4	no	—
333	C₈	—	2	2	no	—
334	C₈	D₄×Dic₄₃	1	4	yes	complemented
335	C₂²	—	2	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	2	4	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	4	no	—
341	C₂²	C₂×#13063259	1	8	yes	complemented
342	C₂²	C₂²×C₄⋊Dic₄₃	1	1	yes	characteristic
343	C₂²	D₄×D₁₇₂	1	1	yes	characteristic
344	C₂²	#14583553	1	1	yes	characteristic
345	C₂²	C₂²×D₃₄₄	1	1	yes	characteristic
346	C₂²	C₂²×Dic₁₇₂	1	1	yes	characteristic
347	C₂²	#14583704	1	1	yes	characteristic
348	C₂²	#14583716	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	2	4	no	—
351	C₄	—	344	4	no	—
352	C₄	—	344	2	no	—
353	C₄	—	172	4	no	—
354	C₄	C₂×#13063259	1	4	yes	complemented
355	C₄	C₂×D₄×Dic₄₃	1	1	yes	characteristic
356	C₄	#14583382	1	1	yes	characteristic
357	C₄	D₄×Dic₈₆	1	1	yes	characteristic
358	C₄	#14583606	1	1	yes	characteristic
359	C₂	—	2	8	no	—
360	C₂	D₄×C₄⋊Dic₄₃	1	1	yes	characteristic
361	C₂	C₂²×#13063259	1	1	yes	characteristic
362	C₂	#19143195	1	1	yes	characteristic
363	C₂	D₄×D₃₄₄	1	1	yes	characteristic
364	C₂	D₄×Dic₁₇₂	1	1	yes	characteristic
365	C₂	#19146943	1	1	yes	characteristic
366	C₂	#19146988	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₈×D₄×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₄×C₄₃	D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×C₈×D₄	D₄₃
hypocenter	C₄₃	D₄×#107
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#13063259	C₂	semidirect
3. #19135354	C₂	semidirect
4. #19134785	C₂	semidirect
5. #19134755	C₂	semidirect
6. #19134624	C₂	semidirect
7. C₄×#13063259	C₂	semidirect
26. C₈×D₄×C₄₃	C₄	semidirect
46. #13063259	D₄	direct (N × H)
53. C₂²×C₈×C₄₃	C₂×C₄	semidirect
62. C₄⋊C₈×C₄₃	C₂×C₄	semidirect
63. C₂²⋊C₈×C₄₃	C₂×C₄	semidirect
64. C₄×C₈×C₄₃	C₂×C₄	semidirect
118. D₄×C₄₃	#107	semidirect
150. C₈×C₄₃	C₄×D₄	semidirect
158. C₂²×C₄₃	C₂×#107	semidirect
168. C₄×C₄₃	C₂×#107	semidirect
196. C₈×D₄	Dic₄₃	semidirect
213. C₄₃	D₄×#107	semidirect
219. C₂²×C₈	C₂×Dic₄₃	semidirect
244. C₄⋊C₈	C₂×Dic₄₃	semidirect
245. C₂²⋊C₈	C₂×Dic₄₃	semidirect
246. C₄×C₈	C₂×Dic₄₃	semidirect
302. D₄	#13063259	direct (N × H)
334. C₈	D₄×Dic₄₃	semidirect
341. C₂²	C₂×#13063259	semidirect
354. C₄	C₂×#13063259	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13063259	2
D₄×C₄⋊Dic₄₃	2
#19135354	2
#19134785	2
#19134755	2
#19134624	2
C₄×#13063259	2
C₂×C₈×D₄×C₄₃	2
D₄×#107	43

Subgroups — D4×#13063259 #25114715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#13063259 #25114715