Subgroups — D₄×#14556523 #33104083

Order 18688.

1126 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556523	C₂	1	2	yes	maximal, complemented
2	D₄×C₄⋊Dic₇₃	C₂	1	2	yes	maximal
3	#22610695	C₂	1	2	yes	maximal, complemented
4	#22610126	C₂	1	4	yes	maximal, complemented
5	#22610088	C₂	1	1	yes	maximal, characteristic, complemented
6	#22609956	C₂	1	2	yes	maximal, complemented
7	C₄×#14556523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₇₃	C₂	1	1	yes	maximal, characteristic
9	C₂×D₄×Dic₇₃	—	2	2	no	—
10	C₂²×C₄⋊Dic₇₃	C₂²	1	4	yes	—
11	C₂×#14556523	—	2	8	no	—
12	C₂×#14556523	C₂²	1	4	yes	—
13	C₂×#14556523	C₂²	1	1	yes	characteristic
14	C₂×#14556523	C₂²	1	2	yes	—
15	C₂×#14556523	C₂²	1	2	yes	—
16	C₂×#14556523	C₂²	1	1	yes	characteristic
17	#17988486	—	2	2	no	—
18	#17988462	—	2	4	no	—
19	#17988457	C₂²	1	2	yes	—
20	#17988447	C₂²	1	4	yes	—
21	C₄×C₄⋊Dic₇₃	C₂²	1	2	yes	—
22	#17988350	C₂²	1	4	yes	—
23	#17988350	C₂²	1	2	yes	—
24	C₂³×C₈×C₇₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
26	C₈×D₄×C₇₃	C₄	1	8	yes	complemented
27	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂³×Dic₇₃	—	2	4	no	—
31	D₄×Dic₇₃	—	4	8	no	—
32	C₂×C₄⋊Dic₇₃	—	2	8	no	—
33	C₂×C₄⋊Dic₇₃	—	2	2	no	—
34	C₂×C₄⋊Dic₇₃	—	2	4	no	—
35	C₂×C₄⋊Dic₇₃	—	2	2	no	—
36	C₂×C₄⋊Dic₇₃	—	4	4	no	—
37	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
38	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
39	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
40	C₂×C₂²⋊Dic₇₃	—	2	4	no	—
41	C₂×C₄×Dic₇₃	—	2	2	no	—
42	#14556523	—	2	8	no	—
43	#14556523	—	2	4	no	—
44	#14556523	—	2	2	no	—
45	#14556523	—	4	2	no	—
46	#14556523	D₄	1	4	yes	direct product factor
47	#14556498	—	2	2	no	—
48	#14556498	—	2	4	no	—
49	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₇₃	—	2	4	no	—
52	C₂²×C₈×C₇₃	—	2	4	no	—
53	C₂²×C₈×C₇₃	C₂×C₄	1	8	yes	complemented
54	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
57	C₄×D₄×C₇₃	C₂×C₄	1	4	yes	—
58	C₄×D₄×C₇₃	Q₈	1	4	yes	—
59	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
61	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₇₃	C₂×C₄	1	4	yes	complemented
63	C₂²⋊C₈×C₇₃	C₂×C₄	1	8	yes	complemented
64	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	complemented
65	C₂²×Dic₇₃	—	2	2	no	—
66	C₂²×Dic₇₃	—	2	2	no	—
67	C₂²×Dic₇₃	—	2	4	no	—
68	C₂²×Dic₇₃	—	4	8	no	—
69	C₂²×Dic₇₃	—	4	8	no	—
70	C₂²×Dic₇₃	—	8	4	no	—
71	C₄⋊Dic₇₃	—	2	2	no	—
72	C₄⋊Dic₇₃	—	2	4	no	—
73	C₄⋊Dic₇₃	—	2	2	no	—
74	C₄⋊Dic₇₃	—	2	4	no	—
75	C₄⋊Dic₇₃	—	2	2	no	—
76	C₄⋊Dic₇₃	—	4	8	no	—
77	C₄⋊Dic₇₃	—	4	4	no	—
78	C₄⋊Dic₇₃	—	8	2	no	—
79	C₄⋊Dic₇₃	C₂×D₄	1	4	yes	—
80	C₂²⋊Dic₇₃	—	4	8	no	—
81	C₄×Dic₇₃	—	4	4	no	—
82	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
83	C₂×D₄×C₇₃	C₄⋊C₄	1	4	yes	—
84	C₂×D₄×C₇₃	SD₁₆	1	8	yes	—
85	C₂²×C₄×C₇₃	—	2	2	no	—
86	C₂²×C₄×C₇₃	—	2	2	no	—
87	C₂²×C₄×C₇₃	—	2	2	no	—
88	C₂²×C₄×C₇₃	—	2	2	no	—
89	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₃	C₂×Q₈	1	4	yes	—
94	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₇₃	—	2	2	no	—
96	C₂×C₈×C₇₃	—	2	2	no	—
97	C₂×C₈×C₇₃	—	2	1	no	—
98	C₂×C₈×C₇₃	—	2	1	no	—
99	C₂×C₈×C₇₃	—	2	16	no	—
100	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₇₃	#41	1	2	yes	—
105	C₄⋊C₄×C₇₃	C₄⋊C₄	1	4	yes	—
106	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	8	yes	—
107	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
108	C₄²×C₇₃	C₂×Q₈	1	2	yes	—
109	C₂³×C₇₃	—	2	2	no	—
110	C₂³×C₇₃	—	2	2	no	—
111	C₂³×C₇₃	—	2	4	no	—
112	C₂³×C₇₃	C₂×C₄⋊C₄	1	4	yes	—
113	C₂³×C₇₃	C₂×SD₁₆	1	8	yes	—
114	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
115	D₄×C₇₃	#106	1	16	yes	complemented
116	C₂×C₄×C₇₃	—	2	2	no	—
117	C₂×C₄×C₇₃	—	2	2	no	—
118	C₂×C₄×C₇₃	—	2	2	no	—
119	C₂×C₄×C₇₃	—	2	4	no	—
120	C₂×C₄×C₇₃	—	2	4	no	—
121	C₂×C₄×C₇₃	—	2	4	no	—
122	C₂×C₄×C₇₃	—	2	4	no	—
123	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
124	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	4	yes	—
125	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
126	C₂×C₄×C₇₃	C₂×SD₁₆	1	4	yes	—
127	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
128	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
129	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
130	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
131	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
132	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
133	C₂×Dic₇₃	—	2	4	no	—
134	C₂×Dic₇₃	—	4	2	no	—
135	C₂×Dic₇₃	—	4	2	no	—
136	C₂×Dic₇₃	—	4	4	no	—
137	C₂×Dic₇₃	—	4	2	no	—
138	C₂×Dic₇₃	—	4	2	no	—
139	C₂×Dic₇₃	—	4	4	no	—
140	C₂×Dic₇₃	—	4	4	no	—
141	C₂×Dic₇₃	—	4	2	no	—
142	C₂×Dic₇₃	—	8	16	no	—
143	C₈×C₇₃	—	2	4	no	—
144	C₈×C₇₃	—	2	2	no	—
145	C₈×C₇₃	C₄×D₄	1	4	yes	complemented
146	C₂²×C₇₃	—	2	8	no	—
147	C₂²×C₇₃	—	2	4	no	—
148	C₂²×C₇₃	—	2	4	no	—
149	C₂²×C₇₃	—	2	8	no	—
150	C₂²×C₇₃	C₂×#106	1	8	yes	complemented
151	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
152	C₂²×C₇₃	D₄²	1	1	yes	characteristic
153	C₂²×C₇₃	#547	1	1	yes	characteristic
154	C₂²×C₇₃	C₂²×SD₁₆	1	2	yes	—
155	C₂²×C₇₃	#577	1	2	yes	—
156	C₄×C₇₃	—	2	4	no	—
157	C₄×C₇₃	—	2	2	no	—
158	C₄×C₇₃	C₂×#106	1	4	yes	complemented
159	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
160	C₄×C₇₃	#520	1	1	yes	characteristic
161	C₄×C₇₃	D₄×Q₈	1	1	yes	characteristic
162	C₄×C₇₃	#554	1	1	yes	characteristic
163	Dic₇₃	—	4	4	no	—
164	Dic₇₃	—	8	2	no	—
165	Dic₇₃	—	8	4	no	—
166	D₄×#106	—	73	1	no	maximal, Sylow
167	C₂×C₇₃	—	2	8	no	—
168	C₂×C₇₃	D₄×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₇₃	C₂²×#106	1	1	yes	characteristic
170	C₂×C₇₃	#2912	1	1	yes	characteristic
171	C₂×C₇₃	D₄×SD₁₆	1	2	yes	—
172	C₂×C₇₃	#3335	1	2	yes	—
173	C₂×C₈×D₄	D₇₃	1	1	yes	characteristic
174	C₂²×#106	—	73	2	no	—
175	D₄×C₄⋊C₄	—	73	2	no	—
176	#1948	—	73	2	no	—
177	#1853	—	73	4	no	—
178	#1844	—	73	1	no	—
179	#1807	—	73	2	no	—
180	C₄×#106	—	73	1	no	—
181	C₇₃	D₄×#106	1	1	yes	characteristic, complemented, Sylow
182	C₂³×C₈	C₂×D₇₃	1	2	yes	—
183	C₂×C₄×D₄	—	146	2	no	—
184	C₂×C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
185	C₂²×C₄⋊C₄	—	73	4	no	—
186	C₈×D₄	Dic₇₃	1	8	yes	complemented
187	C₂×#106	—	73	2	no	—
188	C₂×#106	—	73	1	no	—
189	C₂×#106	—	73	1	no	—
190	C₂×#106	—	73	2	no	—
191	C₂×#106	—	73	4	no	—
192	C₂×#106	—	146	8	no	—
193	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
194	C₂×C₂²⋊C₈	C₂×D₇₃	1	2	yes	—
195	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
196	#389	—	146	2	no	—
197	#385	—	146	4	no	—
198	#384	—	73	2	no	—
199	#380	—	73	4	no	—
200	C₄×C₄⋊C₄	—	73	2	no	—
201	#340	—	73	4	no	—
202	#340	—	73	2	no	—
203	C₂²×D₄	D₂₉₂	1	1	yes	characteristic
204	C₂³×C₄	—	146	4	no	—
205	C₂³×C₄	C₂²×D₇₃	1	2	yes	—
206	C₂²×C₈	—	2	4	no	—
207	C₂²×C₈	—	2	4	no	—
208	C₂²×C₈	C₂×Dic₇₃	1	8	yes	complemented
209	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
210	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
211	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
212	C₄×D₄	—	292	8	no	—
213	C₄×D₄	Dic₁₄₆	1	4	yes	—
214	C₄×D₄	C₂×Dic₇₃	1	4	yes	—
215	C₂×C₄⋊C₄	—	292	4	no	—
216	C₂×C₄⋊C₄	—	73	2	no	—
217	C₂×C₄⋊C₄	—	73	4	no	—
218	C₂×C₄⋊C₄	—	73	2	no	—
219	C₂×C₄⋊C₄	—	146	4	no	—
220	C₂×C₄⋊C₄	—	146	2	no	—
221	C₂×C₄⋊C₄	—	146	8	no	—
222	C₂×C₄⋊C₄	—	146	2	no	—
223	C₂×C₄⋊C₄	D₂₉₂	1	1	yes	characteristic
224	C₂×C₂²⋊C₄	—	146	4	no	—
225	C₂×C₂²⋊C₄	D₂₉₂	1	2	yes	—
226	C₂×C₄²	—	146	2	no	—
227	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
228	#106	—	292	2	no	—
229	#106	—	73	4	no	—
230	#106	—	146	8	no	—
231	#106	—	146	4	no	—
232	#106	—	146	2	no	—
233	C₄⋊C₈	C₂×Dic₇₃	1	4	yes	complemented
234	C₂²⋊C₈	C₂×Dic₇₃	1	8	yes	complemented
235	C₄×C₈	C₂×Dic₇₃	1	4	yes	complemented
236	#95	—	146	2	no	—
237	#95	—	146	4	no	—
238	C₂⁴	C₂×D₂₉₂	1	2	yes	—
239	C₂×D₄	C₄⋊Dic₇₃	1	4	yes	—
240	C₂×D₄	#11924017	1	8	yes	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	292	8	no	—
246	C₂²×C₄	—	292	8	no	—
247	C₂²×C₄	—	584	4	no	—
248	C₂²×C₄	—	146	2	no	—
249	C₂²×C₄	—	146	4	no	—
250	C₂²×C₄	—	146	2	no	—
251	C₂²×C₄	C₂²×Dic₇₃	1	4	yes	—
252	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
253	C₂²×C₄	C₂×D₂₉₂	1	2	yes	—
254	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
255	C₂²×C₄	C₂×Dic₁₄₆	1	4	yes	—
256	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	1	no	—
260	C₂×C₈	—	2	1	no	—
261	C₂×C₈	—	2	16	no	—
262	C₂×C₈	C₂²×Dic₇₃	1	2	yes	—
263	C₂×C₈	C₂²×Dic₇₃	1	4	yes	—
264	C₂×C₈	C₂²×Dic₇₃	1	2	yes	—
265	C₂×C₈	D₄×D₇₃	1	2	yes	—
266	C₂×C₈	#11924027	1	2	yes	—
267	C₄⋊C₄	—	292	8	no	—
268	C₄⋊C₄	—	292	4	no	—
269	C₄⋊C₄	—	584	2	no	—
270	C₄⋊C₄	—	73	4	no	—
271	C₄⋊C₄	—	146	4	no	—
272	C₄⋊C₄	—	146	2	no	—
273	C₄⋊C₄	—	146	4	no	—
274	C₄⋊C₄	—	146	2	no	—
275	C₄⋊C₄	—	146	2	no	—
276	C₄⋊C₄	C₄⋊Dic₇₃	1	4	yes	—
277	C₂²⋊C₄	—	292	8	no	—
278	C₂²⋊C₄	C₄⋊Dic₇₃	1	8	yes	—
279	C₄²	—	292	4	no	—
280	C₄²	C₂²×Dic₇₃	1	2	yes	—
281	C₄²	C₂×Dic₁₄₆	1	2	yes	—
282	C₂³	—	2	4	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	C₂×C₄⋊Dic₇₃	1	4	yes	—
286	C₂³	C₂×#11924017	1	8	yes	—
287	C₂³	C₂²×D₂₉₂	1	1	yes	characteristic
288	D₄	#14556523	1	16	yes	direct product factor
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	292	2	no	—
297	C₂×C₄	—	292	2	no	—
298	C₂×C₄	—	292	4	no	—
299	C₂×C₄	—	292	2	no	—
300	C₂×C₄	—	292	4	no	—
301	C₂×C₄	—	292	2	no	—
302	C₂×C₄	—	292	2	no	—
303	C₂×C₄	—	292	4	no	—
304	C₂×C₄	—	584	16	no	—
305	C₂×C₄	—	146	4	no	—
306	C₂×C₄	C₂×C₄⋊Dic₇₃	1	2	yes	—
307	C₂×C₄	C₂×C₄⋊Dic₇₃	1	4	yes	—
308	C₂×C₄	C₂×C₄⋊Dic₇₃	1	2	yes	—
309	C₂×C₄	C₂×#11924017	1	4	yes	—
310	C₂×C₄	C₂³×Dic₇₃	1	1	yes	characteristic
311	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
312	C₂×C₄	C₂²×Dic₁₄₆	1	1	yes	characteristic
313	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
314	C₂×C₄	#14556637	1	1	yes	characteristic
315	C₂×C₄	#14556638	1	1	yes	characteristic
316	C₈	—	2	4	no	—
317	C₈	—	2	2	no	—
318	C₈	D₄×Dic₇₃	1	4	yes	complemented
319	C₂²	—	2	8	no	—
320	C₂²	—	2	4	no	—
321	C₂²	—	2	4	no	—
322	C₂²	—	2	8	no	—
323	C₂²	C₂×#14556523	1	8	yes	complemented
324	C₂²	C₂²×C₄⋊Dic₇₃	1	1	yes	characteristic
325	C₂²	D₄×D₂₉₂	1	1	yes	characteristic
326	C₂²	#17989241	1	1	yes	characteristic
327	C₂²	C₂²×#11924017	1	2	yes	—
328	C₂²	#17989399	1	2	yes	—
329	C₄	—	2	4	no	—
330	C₄	—	2	2	no	—
331	C₄	—	292	4	no	—
332	C₄	—	584	2	no	—
333	C₄	—	584	4	no	—
334	C₄	C₂×#14556523	1	4	yes	complemented
335	C₄	C₂×D₄×Dic₇₃	1	1	yes	characteristic
336	C₄	#17989070	1	1	yes	characteristic
337	C₄	D₄×Dic₁₄₆	1	1	yes	characteristic
338	C₄	#17989294	1	1	yes	characteristic
339	C₂	—	2	8	no	—
340	C₂	D₄×C₄⋊Dic₇₃	1	1	yes	characteristic
341	C₂	C₂²×#14556523	1	1	yes	characteristic
342	C₂	#22618526	1	1	yes	characteristic
343	C₂	D₄×#11924017	1	2	yes	—
344	C₂	#22622289	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₂₉₂
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₂×C₈×D₄×C₇₃	C₂
socle	C₂³×C₇₃	C₂²×D₄
prime radical	C₂²×D₄×C₇₃	D₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₂×C₈×D₄	D₇₃
hypocenter	C₇₃	D₄×#106
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
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×#14556523	C₂	semidirect
3. #22610695	C₂	semidirect
4. #22610126	C₂	semidirect
5. #22610088	C₂	semidirect
6. #22609956	C₂	semidirect
7. C₄×#14556523	C₂	semidirect
26. C₈×D₄×C₇₃	C₄	semidirect
46. #14556523	D₄	direct (N × H)
53. C₂²×C₈×C₇₃	C₂×C₄	semidirect
62. C₄⋊C₈×C₇₃	C₂×C₄	semidirect
63. C₂²⋊C₈×C₇₃	C₂×C₄	semidirect
64. C₄×C₈×C₇₃	C₂×C₄	semidirect
115. D₄×C₇₃	#106	semidirect
145. C₈×C₇₃	C₄×D₄	semidirect
150. C₂²×C₇₃	C₂×#106	semidirect
158. C₄×C₇₃	C₂×#106	semidirect
181. C₇₃	D₄×#106	semidirect
186. C₈×D₄	Dic₇₃	semidirect
208. C₂²×C₈	C₂×Dic₇₃	semidirect
233. C₄⋊C₈	C₂×Dic₇₃	semidirect
234. C₂²⋊C₈	C₂×Dic₇₃	semidirect
235. C₄×C₈	C₂×Dic₇₃	semidirect
288. D₄	#14556523	direct (N × H)
318. C₈	D₄×Dic₇₃	semidirect
323. C₂²	C₂×#14556523	semidirect
334. C₄	C₂×#14556523	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14556523	2
D₄×C₄⋊Dic₇₃	2
#22610695	2
#22610126	2
#22610088	2
#22609956	2
C₄×#14556523	2
C₂×C₈×D₄×C₇₃	2
D₄×#106	73

Subgroups — D4×#14556523 #33104083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#14556523 #33104083