Subgroups — D₄×#13063269 #25253267

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063269	C₂	1	2	yes	maximal, complemented
2	D₄×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#19136850	C₂	1	1	yes	maximal, characteristic, complemented
4	#19136689	C₂	1	2	yes	maximal, complemented
5	#19136640	C₂	1	1	yes	maximal, characteristic, complemented
6	#19136632	C₂	1	1	yes	maximal, characteristic, complemented
7	#19136524	C₂	1	2	yes	maximal, complemented
8	#19136511	C₂	1	2	yes	maximal, complemented
9	C₄×#13063269	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₁₇₂	C₂²	1	2	yes	complemented
13	D₄×Dic₈₆	—	2	1	no	—
14	C₂×#13063269	—	2	8	no	—
15	C₂×#13063269	C₂²	1	2	yes	—
16	C₂×#13063269	C₂²	1	1	yes	characteristic
17	C₂×#13063269	C₂²	1	2	yes	complemented
18	C₂×#13063269	C₂²	1	2	yes	complemented
19	C₂×#13063269	C₂²	1	2	yes	complemented
20	C₂²×C₄₃⋊C₁₆	C₂²	1	2	yes	complemented
21	#14583279	C₂²	1	1	yes	characteristic, complemented
22	#14583140	C₂²	1	2	yes	complemented
23	#14583110	—	2	1	no	—
24	#14583057	—	2	2	no	—
25	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
26	#14582726	C₂²	1	1	yes	characteristic, complemented
27	C₄⋊(C₄₃⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
28	#14582702	C₂²	1	2	yes	complemented
29	#14582702	C₂²	1	1	yes	characteristic, complemented
30	#14582700	C₂²	1	1	yes	characteristic
31	#14582700	C₂²	1	2	yes	complemented
32	C₂²⋊(C₄₃⋊C₁₆)	C₂²	1	2	yes	complemented
33	C₄×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
35	D₄²×C₄₃	—	2	1	no	—
36	C₄₃×#493	C₂²	1	1	yes	characteristic
37	C₄₃×#466	C₂²	1	2	yes	—
38	C₄₃×#459	—	2	1	no	—
39	C₄₃×#447	—	2	2	no	—
40	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic
42	C₂²×Dic₈₆	—	2	2	no	—
43	C₂×Dic₁₇₂	—	2	4	no	—
44	C₂×Dic₁₇₂	—	2	2	no	—
45	C₂×Dic₁₇₂	—	2	1	no	—
46	C₂×Dic₁₇₂	—	4	2	no	—
47	C₂×Dic₁₇₂	C₂³	1	2	yes	—
48	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
49	#13063325	—	2	1	no	—
50	#13063324	—	4	1	no	—
51	#13063304	—	2	2	no	—
52	#13063302	—	4	2	no	—
53	C₄×Dic₈₆	—	2	1	no	—
54	D₄×Dic₄₃	—	4	1	no	—
55	#13063269	—	2	4	no	—
56	#13063269	—	2	4	no	—
57	#13063269	—	2	4	no	—
58	#13063269	—	4	2	no	—
59	#13063269	D₄	1	4	yes	direct product factor
60	C₂×C₄₃⋊C₁₆	—	2	4	no	—
61	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
62	C₂×C₄₃⋊C₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₄₃⋊C₁₆	C₂³	1	1	yes	characteristic
64	#13063259	C₂³	1	1	yes	characteristic
65	#13063250	—	2	1	no	—
66	#13063250	—	2	2	no	—
67	C₂²×D₄×C₄₃	—	2	2	no	—
68	C₂²×D₄×C₄₃	—	4	1	no	—
69	C₂×D₈×C₄₃	—	2	4	no	—
70	C₂×D₈×C₄₃	—	2	2	no	—
71	C₂×D₈×C₄₃	—	2	1	no	—
72	C₂×D₈×C₄₃	—	4	2	no	—
73	C₂×D₈×C₄₃	C₂³	1	2	yes	—
74	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
76	#127×C₄₃	—	2	1	no	—
77	#121×C₄₃	—	2	2	no	—
78	#121×C₄₃	—	4	1	no	—
79	#120×C₄₃	—	4	2	no	—
80	C₄×D₄×C₄₃	—	2	1	no	—
81	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
82	#107×C₄₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
84	#102×C₄₃	—	2	1	no	—
85	#102×C₄₃	—	2	2	no	—
86	C₂²⋊C₈×C₄₃	D₄	1	2	yes	—
87	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₂⁴×C₄₃	—	4	2	no	—
89	C₂×D₄×C₄₃	—	2	1	no	—
90	C₂×D₄×C₄₃	—	2	2	no	—
91	C₂×D₄×C₄₃	—	4	2	no	—
92	C₂×D₄×C₄₃	—	4	1	no	—
93	C₂×D₄×C₄₃	—	4	1	no	—
94	C₂×D₄×C₄₃	—	4	2	no	—
95	C₂×D₄×C₄₃	—	4	4	no	—
96	C₂×D₄×C₄₃	—	8	2	no	—
97	C₂×D₄×C₄₃	—	8	4	no	—
98	C₂×D₄×C₄₃	D₈	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	—	4	1	no	—
100	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
101	C₂²×Dic₄₃	—	4	2	no	—
102	C₂×Dic₈₆	—	2	1	no	—
103	C₂×Dic₈₆	—	2	2	no	—
104	C₂×Dic₈₆	—	4	4	no	—
105	C₂×Dic₈₆	—	4	2	no	—
106	C₂×Dic₈₆	—	8	2	no	—
107	D₈×C₄₃	—	2	2	no	—
108	D₈×C₄₃	—	2	1	no	—
109	D₈×C₄₃	—	2	2	no	—
110	D₈×C₄₃	—	4	4	no	—
111	D₈×C₄₃	—	8	1	no	—
112	D₈×C₄₃	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
118	C₄⋊C₄×C₄₃	—	2	1	no	—
119	C₄⋊C₄×C₄₃	D₈	1	1	yes	characteristic
120	C₂²⋊C₄×C₄₃	—	4	1	no	—
121	C₂²⋊C₄×C₄₃	—	4	2	no	—
122	C₂²⋊C₄×C₄₃	D₈	1	2	yes	—
123	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²⋊Dic₄₃	—	4	2	no	—
125	C₄⋊Dic₄₃	—	2	1	no	—
126	C₄⋊Dic₄₃	—	4	1	no	—
127	C₄⋊Dic₄₃	—	4	1	no	—
128	Dic₄₃⋊C₄	—	4	1	no	—
129	Dic₄₃⋊C₄	—	4	2	no	—
130	C₄×Dic₄₃	—	4	1	no	—
131	Dic₁₇₂	—	2	2	no	—
132	Dic₁₇₂	—	2	1	no	—
133	Dic₁₇₂	—	2	2	no	—
134	Dic₁₇₂	—	4	4	no	—
135	Dic₁₇₂	—	8	1	no	—
136	Dic₁₇₂	C₂×D₄	1	2	yes	complemented
137	C₄₃⋊C₁₆	—	2	2	no	—
138	C₄₃⋊C₁₆	—	2	1	no	—
139	C₄₃⋊C₁₆	C₂×D₄	1	2	yes	complemented
140	C₂³×C₄₃	—	4	1	no	—
141	C₂³×C₄₃	—	4	2	no	—
142	C₂³×C₄₃	—	8	4	no	—
143	C₂³×C₄₃	—	8	4	no	—
144	C₂³×C₄₃	—	16	2	no	—
145	C₂³×C₄₃	C₂×D₈	1	2	yes	—
146	D₄×C₄₃	—	2	2	no	—
147	D₄×C₄₃	—	4	2	no	—
148	D₄×C₄₃	—	4	1	no	—
149	D₄×C₄₃	—	4	2	no	—
150	D₄×C₄₃	—	8	4	no	—
151	D₄×C₄₃	—	8	4	no	—
152	D₄×C₄₃	—	8	2	no	—
153	D₄×C₄₃	—	16	1	no	—
154	D₄×C₄₃	SD₃₂	1	4	yes	complemented
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	4	1	no	—
158	C₂×C₄×C₄₃	—	8	2	no	—
159	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
161	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×Dic₄₃	—	4	1	no	—
164	C₂×Dic₄₃	—	4	1	no	—
165	C₂×Dic₄₃	—	4	2	no	—
166	C₂×Dic₄₃	—	8	4	no	—
167	Dic₈₆	—	2	2	no	—
168	Dic₈₆	—	4	1	no	—
169	Dic₈₆	—	4	2	no	—
170	Dic₈₆	—	4	2	no	—
171	Dic₈₆	—	8	4	no	—
172	C₈×C₄₃	—	2	2	no	—
173	C₈×C₄₃	—	2	1	no	—
174	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
175	C₈×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
176	D₄×SD₃₂	—	43	1	no	maximal, Sylow
177	C₂²×C₄₃	—	2	2	no	—
178	C₂²×C₄₃	—	2	2	no	—
179	C₂²×C₄₃	—	4	2	no	—
180	C₂²×C₄₃	—	8	1	no	—
181	C₂²×C₄₃	—	8	1	no	—
182	C₂²×C₄₃	—	8	2	no	—
183	C₂²×C₄₃	—	8	2	no	—
184	C₂²×C₄₃	—	8	2	no	—
185	C₂²×C₄₃	—	16	8	no	—
186	C₂²×C₄₃	C₂×SD₃₂	1	4	yes	complemented
187	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
188	C₄×C₄₃	—	2	1	no	—
189	C₄×C₄₃	—	2	2	no	—
190	C₄×C₄₃	—	8	1	no	—
191	C₄×C₄₃	C₂×SD₃₂	1	2	yes	complemented
192	C₄×C₄₃	D₄²	1	1	yes	characteristic
193	C₄×C₄₃	#576	1	1	yes	characteristic
194	Dic₄₃	—	4	2	no	—
195	Dic₄₃	—	8	1	no	—
196	Dic₄₃	—	8	2	no	—
197	C₂²×SD₃₂	—	43	2	no	—
198	D₄×Q₁₆	—	43	1	no	—
199	D₄×D₈	D₄₃	1	1	yes	characteristic
200	#2248	—	43	1	no	—
201	#2217	—	43	2	no	—
202	#2208	—	43	1	no	—
203	#2207	—	43	1	no	—
204	#2187	—	43	2	no	—
205	#2185	—	43	2	no	—
206	C₄×SD₃₂	—	43	1	no	—
207	D₄×C₁₆	—	43	1	no	—
208	C₂×C₄₃	—	2	4	no	—
209	C₂×C₄₃	—	8	2	no	—
210	C₂×C₄₃	—	16	2	no	—
211	C₂×C₄₃	D₄×D₈	1	1	yes	characteristic
212	C₂×C₄₃	C₂²×SD₃₂	1	1	yes	characteristic
213	C₂×C₄₃	#3416	1	1	yes	characteristic
214	C₂²×Q₁₆	—	43	2	no	—
215	C₂²×D₈	C₂×D₄₃	1	2	yes	—
216	D₄×Q₈	—	86	1	no	—
217	D₄²	—	2	1	no	—
218	C₂×SD₃₂	—	43	1	no	—
219	C₂×SD₃₂	—	43	2	no	—
220	C₂×SD₃₂	—	43	2	no	—
221	C₂×SD₃₂	—	43	2	no	—
222	C₂×SD₃₂	—	43	2	no	—
223	C₂×SD₃₂	—	86	8	no	—
224	C₂²×C₁₆	—	43	2	no	—
225	#494	—	43	1	no	—
226	#493	C₂×D₄₃	1	1	yes	characteristic
227	#467	—	43	2	no	—
228	#466	C₂×D₄₃	1	2	yes	—
229	#462	—	86	1	no	—
230	#459	—	2	1	no	—
231	#451	—	86	2	no	—
232	#447	—	2	2	no	—
233	C₄×Q₁₆	—	43	1	no	—
234	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
235	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic
236	#367	—	43	1	no	—
237	C₄⋊C₁₆	—	43	1	no	—
238	#358	—	43	1	no	—
239	#358	—	43	2	no	—
240	#357	—	43	1	no	—
241	#357	—	43	2	no	—
242	C₂²⋊C₁₆	—	43	2	no	—
243	C₄×C₁₆	—	43	1	no	—
244	C₄₃	D₄×SD₃₂	1	1	yes	characteristic, complemented, Sylow
245	C₂²×Q₈	—	86	2	no	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	—	4	1	no	—
248	C₂×Q₁₆	—	43	1	no	—
249	C₂×Q₁₆	—	43	2	no	—
250	C₂×Q₁₆	—	86	4	no	—
251	C₂×Q₁₆	—	86	1	no	—
252	C₂×Q₁₆	—	86	2	no	—
253	C₂×Q₁₆	—	172	2	no	—
254	C₂×D₈	—	2	4	no	—
255	C₂×D₈	—	2	2	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	4	2	no	—
258	C₂×D₈	C₂²×D₄₃	1	2	yes	—
259	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
260	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
261	C₄⋊Q₈	—	86	1	no	—
262	C₄⋊Q₈	—	172	1	no	—
263	#127	—	2	1	no	—
264	C₂²⋊Q₈	—	86	2	no	—
265	C₂²⋊Q₈	—	172	2	no	—
266	#121	—	2	2	no	—
267	#121	—	4	1	no	—
268	#120	—	4	2	no	—
269	C₄×Q₈	—	86	1	no	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	172	1	no	—
272	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
273	SD₃₂	—	43	4	no	—
274	SD₃₂	—	86	4	no	—
275	SD₃₂	—	86	4	no	—
276	SD₃₂	—	86	4	no	—
277	SD₃₂	—	172	2	no	—
278	C₂×C₁₆	—	43	1	no	—
279	C₂×C₁₆	—	43	1	no	—
280	C₂×C₁₆	—	43	2	no	—
281	C₂×C₁₆	—	86	4	no	—
282	#107	—	43	1	no	—
283	#107	C₂²×D₄₃	1	1	yes	characteristic
284	C₄⋊C₈	C₂²⋊D₄₃	1	1	yes	characteristic
285	#103	—	86	1	no	—
286	#103	—	86	2	no	—
287	#102	—	2	1	no	—
288	#102	—	2	2	no	—
289	C₂²⋊C₈	C₂²⋊D₄₃	1	2	yes	—
290	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
291	C₂⁴	—	4	2	no	—
292	C₂×Q₈	—	86	1	no	—
293	C₂×Q₈	—	86	2	no	—
294	C₂×Q₈	—	344	2	no	—
295	C₂×Q₈	—	172	4	no	—
296	C₂×Q₈	—	172	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	4	4	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	8	2	no	—
305	C₂×D₄	—	8	4	no	—
306	C₂×D₄	#10621882	1	1	yes	characteristic
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	172	2	no	—
309	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
310	Q₁₆	—	43	2	no	—
311	Q₁₆	—	86	2	no	—
312	Q₁₆	—	86	1	no	—
313	Q₁₆	—	86	2	no	—
314	Q₁₆	—	344	1	no	—
315	Q₁₆	—	172	4	no	—
316	D₈	—	2	2	no	—
317	D₈	—	2	1	no	—
318	D₈	—	2	2	no	—
319	D₈	—	4	4	no	—
320	D₈	—	8	1	no	—
321	D₈	D₄×D₄₃	1	2	yes	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
325	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
326	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	86	1	no	—
329	C₄⋊C₄	—	172	1	no	—
330	C₄⋊C₄	—	172	1	no	—
331	C₄⋊C₄	—	172	2	no	—
332	C₄⋊C₄	—	172	1	no	—
333	C₄⋊C₄	#10621882	1	1	yes	characteristic
334	C₂²⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	172	2	no	—
337	C₂²⋊C₄	#10621882	1	2	yes	—
338	C₄²	—	172	1	no	—
339	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
340	C₁₆	—	43	2	no	—
341	C₁₆	—	86	2	no	—
342	C₁₆	—	86	1	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	4	no	—
346	C₂³	—	8	4	no	—
347	C₂³	—	16	2	no	—
348	C₂³	C₂×#10621882	1	2	yes	—
349	Q₈	—	86	2	no	—
350	Q₈	—	344	4	no	—
351	Q₈	—	172	2	no	—
352	Q₈	—	172	2	no	—
353	Q₈	—	172	1	no	—
354	D₄	—	2	2	no	—
355	D₄	—	4	1	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	8	4	no	—
359	D₄	—	8	4	no	—
360	D₄	—	8	2	no	—
361	D₄	—	16	1	no	—
362	D₄	#13063269	1	4	yes	direct product factor
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	8	2	no	—
367	C₂×C₄	—	344	4	no	—
368	C₂×C₄	—	172	1	no	—
369	C₂×C₄	—	172	2	no	—
370	C₂×C₄	—	172	1	no	—
371	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
372	C₂×C₄	C₂×#10621882	1	2	yes	—
373	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	2	no	—
377	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
378	C₈	#13063370	1	1	yes	characteristic
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	16	8	no	—
388	C₂²	C₂×#13063269	1	4	yes	complemented
389	C₂²	C₂²×#10621882	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	1	no	—
392	C₄	—	8	1	no	—
393	C₄	—	344	2	no	—
394	C₄	—	344	1	no	—
395	C₄	—	172	2	no	—
396	C₄	C₂×#13063269	1	2	yes	complemented
397	C₄	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
398	C₄	#14583702	1	1	yes	characteristic
399	C₂	—	2	4	no	—
400	C₂	—	8	2	no	—
401	C₂	—	16	2	no	—
402	C₂	D₄×#10621882	1	1	yes	characteristic
403	C₂	C₂²×#13063269	1	1	yes	characteristic
404	C₂	#19147742	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#10621882
commutator, cosocle	C₂×C₈×C₄₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₃
Fitting, prime radical	D₄×D₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×D₈
hypercenter	D₄×D₈	D₄₃
hypocenter	C₄₃	D₄×SD₃₂
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄ ◁ D₄×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#13063269	C₂	semidirect
2. D₄×Dic₁₇₂	C₂	semidirect
3. #19136850	C₂	semidirect
4. #19136689	C₂	semidirect
5. #19136640	C₂	semidirect
6. #19136632	C₂	semidirect
7. #19136524	C₂	semidirect
8. #19136511	C₂	semidirect
9. C₄×#13063269	C₂	semidirect
10. D₄×C₄₃⋊C₁₆	C₂	semidirect
12. C₂²×Dic₁₇₂	C₂²	semidirect
17. C₂×#13063269	C₂²	semidirect
18. C₂×#13063269	C₂²	semidirect
19. C₂×#13063269	C₂²	semidirect
20. C₂²×C₄₃⋊C₁₆	C₂²	semidirect
21. #14583279	C₂²	semidirect
22. #14583140	C₂²	semidirect
25. C₄×Dic₁₇₂	C₂²	semidirect
26. #14582726	C₂²	semidirect
27. C₄⋊(C₄₃⋊C₁₆)	C₂²	semidirect
28. #14582702	C₂²	semidirect
29. #14582702	C₂²	semidirect
31. #14582700	C₂²	semidirect
32. C₂²⋊(C₄₃⋊C₁₆)	C₂²	semidirect
33. C₄×C₄₃⋊C₁₆	C₂²	semidirect
59. #13063269	D₄	direct (N × H)
136. Dic₁₇₂	C₂×D₄	semidirect
139. C₄₃⋊C₁₆	C₂×D₄	semidirect
154. D₄×C₄₃	SD₃₂	semidirect
186. C₂²×C₄₃	C₂×SD₃₂	semidirect
191. C₄×C₄₃	C₂×SD₃₂	semidirect
244. C₄₃	D₄×SD₃₂	semidirect
362. D₄	#13063269	direct (N × H)
388. C₂²	C₂×#13063269	semidirect
396. C₄	C₂×#13063269	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13063269	2
D₄×Dic₁₇₂	2
#19136850	2
#19136689	2
#19136640	2
#19136632	2
#19136524	2
#19136511	2
C₄×#13063269	2
D₄×C₄₃⋊C₁₆	2
D₄×D₈×C₄₃	2
D₄×SD₃₂	43

Subgroups — D4×#13063269 #25253267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#13063269 #25253267