Subgroups — #33101889

Order 18688.

1378 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22618783	C₂	1	2	yes	maximal, complemented
2	#22618392	C₂	1	2	yes	maximal, complemented
3	#22610830	C₂	1	2	yes	maximal, complemented
4	#22610420	C₂	1	4	yes	maximal, complemented
5	#22609977	C₂	1	1	yes	maximal, characteristic, complemented
6	#22609901	C₂	1	2	yes	maximal, complemented
7	#22609731	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#576×C₇₃	C₂	1	1	yes	maximal, characteristic
9	#17989062	C₂²	1	4	yes	complemented
10	#17988699	—	2	4	no	—
11	D₈×Dic₇₃	—	2	4	no	—
12	#17988625	C₂²	1	2	yes	complemented
13	#17988604	C₂²	1	4	yes	complemented
14	#17988592	C₂²	1	4	yes	complemented
15	#17988571	C₂²	1	1	yes	characteristic
16	#17988561	C₂²	1	2	yes	—
17	#17988561	C₂²	1	1	yes	characteristic
18	#17988561	C₂²	1	4	yes	complemented
19	C₂×#14556506	—	2	8	no	—
20	#17988542	C₂²	1	2	yes	complemented
21	#17988358	C₂²	1	2	yes	complemented
22	#17988344	C₂²	1	2	yes	complemented
23	C₂×H(5,𝔽₂)×C₇₃	C₂²	1	2	yes	—
24	#576×C₇₃	—	2	4	no	—
25	#576×C₇₃	—	2	4	no	—
26	C₂×AGL(1,ℤ/8)×C₇₃	C₄	1	4	yes	complemented
27	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
28	C₂×#135×C₇₃	C₄	1	2	yes	complemented
29	C₂×#135×C₇₃	C₂²	1	1	yes	characteristic
30	C₂²×D₈×C₇₃	C₄	1	2	yes	complemented
31	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×#11924012	C₂³	1	2	yes	—
34	D₄×Dic₇₃	—	2	8	no	—
35	D₄×Dic₇₃	—	4	4	no	—
36	#14556550	C₂³	1	4	yes	—
37	#14556550	C₂³	1	2	yes	—
38	C₂×C₂²⋊Dic₇₃	—	2	8	no	—
39	#14556525	—	2	2	no	—
40	#14556523	—	2	2	no	—
41	#14556518	—	4	4	no	—
42	#14556512	—	2	8	no	—
43	#14556510	—	2	1	no	—
44	#14556508	—	2	1	no	—
45	#14556506	—	2	8	no	—
46	#14556506	—	2	4	no	—
47	#14556506	D₄	1	4	yes	—
48	#14556501	—	2	2	no	—
49	C₈×Dic₇₃	—	2	2	no	—
50	H(5,𝔽₂)×C₇₃	—	2	8	no	—
51	H(5,𝔽₂)×C₇₃	—	4	4	no	—
52	C₂×#41×C₇₃	—	2	2	no	—
53	C₂×#41×C₇₃	C₂×C₄	1	4	yes	complemented
54	C₂×#41×C₇₃	C₂³	1	2	yes	—
55	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₇₃	—	2	4	no	—
57	C₂²×D₄×C₇₃	—	2	2	no	—
58	C₂²×D₄×C₇₃	C₂×C₄	1	4	yes	complemented
59	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
60	AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
61	AGL(1,ℤ/8)×C₇₃	—	2	16	no	—
62	#135×C₇₃	—	2	4	no	—
63	#135×C₇₃	—	2	4	no	—
64	#135×C₇₃	—	2	2	no	—
65	#135×C₇₃	—	2	2	no	—
66	C₂×Q₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×SD₁₆×C₇₃	C₂×C₄	1	4	yes	complemented
68	C₂×SD₁₆×C₇₃	C₂×C₄	1	2	yes	complemented
69	C₂×D₈×C₇₃	—	2	4	no	—
70	C₂×D₈×C₇₃	—	2	4	no	—
71	C₂×D₈×C₇₃	C₂×C₄	1	2	yes	—
72	C₂×D₈×C₇₃	C₂×C₄	1	2	yes	—
73	C₂×D₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
74	C₂×D₈×C₇₃	C₂×C₄	1	4	yes	complemented
75	C₂×D₈×C₇₃	D₄	1	4	yes	—
76	C₂×D₈×C₇₃	D₄	1	4	yes	—
77	#131×C₇₃	—	2	2	no	—
78	#131×C₇₃	—	2	2	no	—
79	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	complemented
80	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
82	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
83	C₂²×Dic₇₃	—	4	8	no	—
84	#11924012	—	2	2	no	—
85	#11924012	—	2	2	no	—
86	C₂×#10596831	—	2	2	no	—
87	C₄⋊Dic₇₃	—	2	2	no	—
88	C₄⋊Dic₇₃	—	2	4	no	—
89	C₂²⋊Dic₇₃	—	2	4	no	—
90	C₂²⋊Dic₇₃	—	4	8	no	—
91	C₂²⋊Dic₇₃	C₂×D₄	1	4	yes	—
92	C₄×Dic₇₃	—	2	2	no	—
93	C₄×Dic₇₃	—	2	4	no	—
94	C₂⁴×C₇₃	—	2	2	no	—
95	C₂⁴×C₇₃	—	2	4	no	—
96	#41×C₇₃	—	2	2	no	—
97	#41×C₇₃	—	2	2	no	—
98	#41×C₇₃	—	2	8	no	—
99	#41×C₇₃	—	2	4	no	—
100	#41×C₇₃	—	2	4	no	—
101	#41×C₇₃	—	4	4	no	—
102	#41×C₇₃	—	4	8	no	—
103	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
104	C₂×Q₈×C₇₃	#41	1	1	yes	characteristic
105	C₂×D₄×C₇₃	—	2	8	no	—
106	C₂×D₄×C₇₃	—	2	4	no	—
107	C₂×D₄×C₇₃	—	2	2	no	—
108	C₂×D₄×C₇₃	—	2	4	no	—
109	C₂×D₄×C₇₃	—	2	2	no	—
110	C₂×D₄×C₇₃	—	2	4	no	—
111	C₂×D₄×C₇₃	—	4	4	no	—
112	C₂×D₄×C₇₃	—	4	8	no	—
113	C₂×D₄×C₇₃	—	4	16	no	—
114	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₇₃	C₂²×C₄	1	4	yes	—
116	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₇₃	C₂×D₄	1	8	yes	—
118	C₂×D₄×C₇₃	#41	1	1	yes	characteristic
119	C₂²×C₄×C₇₃	—	2	4	no	—
120	C₂²×C₄×C₇₃	—	2	2	no	—
121	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
123	Q₁₆×C₇₃	—	2	1	no	—
124	Q₁₆×C₇₃	—	2	1	no	—
125	SD₁₆×C₇₃	—	2	8	no	—
126	SD₁₆×C₇₃	—	2	4	no	—
127	D₈×C₇₃	—	2	8	no	—
128	D₈×C₇₃	—	2	1	no	—
129	D₈×C₇₃	—	2	1	no	—
130	D₈×C₇₃	C₂²⋊C₄	1	4	yes	—
131	D₈×C₇₃	C₂²⋊C₄	1	4	yes	—
132	D₈×C₇₃	C₂²⋊C₄	1	8	yes	—
133	M₁₆×C₇₃	—	2	2	no	—
134	M₁₆×C₇₃	—	2	4	no	—
135	C₂×C₈×C₇₃	—	2	2	no	—
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
142	C₂³×C₇₃	—	2	4	no	—
143	C₂³×C₇₃	—	2	8	no	—
144	C₂³×C₇₃	—	2	2	no	—
145	C₂³×C₇₃	—	4	8	no	—
146	C₂³×C₇₃	—	16	2	no	—
147	C₂³×C₇₃	—	16	4	no	—
148	C₂³×C₇₃	C₄×D₄	1	2	yes	—
149	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₇₃	—	2	2	no	—
151	Q₈×C₇₃	—	2	2	no	—
152	Q₈×C₇₃	—	2	2	no	—
153	D₄×C₇₃	—	2	4	no	—
154	D₄×C₇₃	—	2	2	no	—
155	D₄×C₇₃	—	2	4	no	—
156	D₄×C₇₃	—	2	2	no	—
157	D₄×C₇₃	—	2	8	no	—
158	D₄×C₇₃	—	2	2	no	—
159	D₄×C₇₃	—	4	8	no	—
160	D₄×C₇₃	—	4	8	no	—
161	D₄×C₇₃	—	4	4	no	—
162	D₄×C₇₃	C₂×C₂²⋊C₄	1	8	yes	—
163	C₂×C₄×C₇₃	—	2	2	no	—
164	C₂×C₄×C₇₃	—	2	2	no	—
165	C₂×C₄×C₇₃	—	2	2	no	—
166	C₂×C₄×C₇₃	—	4	8	no	—
167	C₂×C₄×C₇₃	—	4	4	no	—
168	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
173	C₂×Dic₇₃	—	2	4	no	—
174	C₂×Dic₇₃	—	4	4	no	—
175	C₂×Dic₇₃	—	16	8	no	—
176	C₈×C₇₃	—	2	2	no	—
177	C₈×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₈×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₈×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
180	#10596831	—	4	2	no	—
181	C₂²×C₇₃	—	2	2	no	—
182	C₂²×C₇₃	—	2	8	no	—
183	C₂²×C₇₃	—	4	1	no	—
184	C₂²×C₇₃	—	4	2	no	—
185	C₂²×C₇₃	—	4	2	no	—
186	C₂²×C₇₃	—	8	8	no	—
187	C₂²×C₇₃	—	8	4	no	—
188	C₂²×C₇₃	—	8	2	no	—
189	C₂²×C₇₃	—	16	8	no	—
190	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
191	C₂²×C₇₃	D₄²	1	2	yes	—
192	C₄×C₇₃	—	2	2	no	—
193	C₄×C₇₃	—	4	2	no	—
194	C₄×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
195	C₄×C₇₃	#518	1	1	yes	characteristic
196	C₄×C₇₃	#546	1	2	yes	—
197	Dic₇₃	—	4	4	no	—
198	Dic₇₃	—	8	4	no	—
199	#22455	—	73	1	no	maximal, Sylow
200	C₂×C₇₃	—	2	2	no	—
201	C₂×C₇₃	—	2	1	no	—
202	C₂×C₇₃	—	4	2	no	—
203	C₂×C₇₃	—	4	8	no	—
204	C₂×C₇₃	—	8	2	no	—
205	C₂×C₇₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×#576	D₇₃	1	1	yes	characteristic
207	#2948	—	73	2	no	—
208	#2883	—	73	2	no	—
209	#1976	—	73	2	no	—
210	#1904	—	73	4	no	—
211	#1812	—	73	1	no	—
212	#1795	—	73	2	no	—
213	#1757	—	73	1	no	—
214	C₇₃	#22455	1	1	yes	characteristic, complemented, Sylow
215	C₂×H(5,𝔽₂)	C₂×D₇₃	1	2	yes	—
216	#576	—	2	4	no	—
217	#576	—	2	4	no	—
218	C₂×AGL(1,ℤ/8)	Dic₇₃	1	4	yes	complemented
219	C₂×AGL(1,ℤ/8)	C₂×D₇₃	1	2	yes	—
220	C₂×#135	Dic₇₃	1	2	yes	complemented
221	C₂×#135	C₂×D₇₃	1	1	yes	characteristic
222	C₂²×D₈	Dic₇₃	1	2	yes	complemented
223	C₂²×D₈	C₂×D₇₃	1	1	yes	characteristic
224	C₂×#131	C₂×D₇₃	1	1	yes	characteristic
225	#518	—	73	4	no	—
226	#442	—	146	4	no	—
227	C₄×D₈	—	146	4	no	—
228	#427	—	73	2	no	—
229	#421	—	73	4	no	—
230	#418	—	73	4	no	—
231	#413	—	73	1	no	—
232	#410	—	73	1	no	—
233	#410	—	73	2	no	—
234	#410	—	73	4	no	—
235	C₂×#99	—	146	8	no	—
236	#405	—	73	2	no	—
237	#344	—	73	2	no	—
238	H(3,ℤ/4)	—	73	2	no	—
239	H(5,𝔽₂)	—	2	8	no	—
240	H(5,𝔽₂)	—	4	4	no	—
241	C₂×#41	—	2	2	no	—
242	C₂×#41	C₂×Dic₇₃	1	4	yes	complemented
243	C₂×#41	C₂²×D₇₃	1	2	yes	—
244	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
245	C₂²×D₄	—	2	4	no	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	C₂×Dic₇₃	1	4	yes	complemented
248	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
249	AGL(1,ℤ/8)	—	2	8	no	—
250	AGL(1,ℤ/8)	—	2	16	no	—
251	#135	—	2	4	no	—
252	#135	—	2	4	no	—
253	#135	—	2	2	no	—
254	#135	—	2	2	no	—
255	C₂×Q₁₆	C₂×Dic₇₃	1	1	yes	characteristic, complemented
256	C₂×SD₁₆	C₂×Dic₇₃	1	4	yes	complemented
257	C₂×SD₁₆	C₂×Dic₇₃	1	2	yes	complemented
258	C₂×D₈	—	2	4	no	—
259	C₂×D₈	—	2	4	no	—
260	C₂×D₈	C₂×Dic₇₃	1	2	yes	—
261	C₂×D₈	C₂×Dic₇₃	1	2	yes	—
262	C₂×D₈	C₂×Dic₇₃	1	1	yes	characteristic, complemented
263	C₂×D₈	C₂×Dic₇₃	1	4	yes	complemented
264	C₂×D₈	C₂²⋊D₇₃	1	4	yes	—
265	C₂×D₈	C₂²⋊D₇₃	1	4	yes	—
266	#131	—	2	2	no	—
267	#131	—	2	2	no	—
268	C₂×M₁₆	—	73	2	no	—
269	C₂×M₁₆	C₂×Dic₇₃	1	2	yes	complemented
270	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
271	C₂²×C₈	C₂×Dic₇₃	1	2	yes	complemented
272	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
273	C₄×D₄	—	292	4	no	—
274	C₄×D₄	—	146	8	no	—
275	#117	—	73	2	no	—
276	#117	—	73	4	no	—
277	C₂×C₂²⋊C₄	—	146	8	no	—
278	#107	—	146	2	no	—
279	#106	—	146	2	no	—
280	#104	—	292	4	no	—
281	#102	—	146	8	no	—
282	#101	—	146	1	no	—
283	#100	—	146	1	no	—
284	#99	—	73	4	no	—
285	#99	—	146	8	no	—
286	#99	—	146	4	no	—
287	#97	—	146	2	no	—
288	C₄×C₈	—	146	2	no	—
289	C₂⁴	—	2	2	no	—
290	C₂⁴	—	2	4	no	—
291	#41	—	2	2	no	—
292	#41	—	2	2	no	—
293	#41	—	2	8	no	—
294	#41	—	2	4	no	—
295	#41	—	2	4	no	—
296	#41	—	4	4	no	—
297	#41	—	4	8	no	—
298	C₂×Q₈	C₂²×Dic₇₃	1	2	yes	—
299	C₂×Q₈	#11924027	1	1	yes	characteristic
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	4	4	no	—
307	C₂×D₄	—	4	8	no	—
308	C₂×D₄	—	4	16	no	—
309	C₂×D₄	C₂²×Dic₇₃	1	2	yes	—
310	C₂×D₄	C₂²×Dic₇₃	1	4	yes	—
311	C₂×D₄	D₄×D₇₃	1	2	yes	—
312	C₂×D₄	C₂×C₂²⋊D₇₃	1	8	yes	—
313	C₂×D₄	#11924027	1	1	yes	characteristic
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	292	8	no	—
317	C₂²×C₄	C₂²×Dic₇₃	1	2	yes	—
318	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
319	Q₁₆	—	2	1	no	—
320	Q₁₆	—	2	1	no	—
321	SD₁₆	—	2	8	no	—
322	SD₁₆	—	2	4	no	—
323	D₈	—	2	8	no	—
324	D₈	—	2	1	no	—
325	D₈	—	2	1	no	—
326	D₈	C₂²⋊Dic₇₃	1	4	yes	—
327	D₈	C₂²⋊Dic₇₃	1	4	yes	—
328	D₈	C₂²⋊Dic₇₃	1	8	yes	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	4	no	—
331	M₁₆	—	146	2	no	—
332	M₁₆	—	146	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	146	2	no	—
336	C₂×C₈	C₂²×Dic₇₃	1	2	yes	—
337	C₂×C₈	C₂²×Dic₇₃	1	1	yes	characteristic
338	C₂×C₈	C₂²×Dic₇₃	1	1	yes	characteristic
339	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
340	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
341	C₄⋊C₄	—	146	4	no	—
342	C₄⋊C₄	—	146	2	no	—
343	C₂²⋊C₄	—	292	8	no	—
344	C₂²⋊C₄	—	73	4	no	—
345	C₂²⋊C₄	—	146	4	no	—
346	C₄²	—	146	4	no	—
347	C₄²	—	146	2	no	—
348	C₂³	—	2	8	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	4	8	no	—
352	C₂³	—	16	2	no	—
353	C₂³	—	16	4	no	—
354	C₂³	D₄×Dic₇₃	1	2	yes	—
355	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
356	Q₈	—	2	2	no	—
357	Q₈	—	2	2	no	—
358	Q₈	—	2	2	no	—
359	D₄	—	2	4	no	—
360	D₄	—	2	8	no	—
361	D₄	—	2	2	no	—
362	D₄	—	2	2	no	—
363	D₄	—	2	4	no	—
364	D₄	—	2	2	no	—
365	D₄	—	4	8	no	—
366	D₄	—	4	8	no	—
367	D₄	—	4	4	no	—
368	D₄	C₂×C₂²⋊Dic₇₃	1	8	yes	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	292	4	no	—
375	C₂×C₄	—	1168	8	no	—
376	C₂×C₄	—	146	4	no	—
377	C₂×C₄	D₄×Dic₇₃	1	2	yes	—
378	C₂×C₄	C₂³×Dic₇₃	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₂²⋊D₇₃	1	2	yes	—
380	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
381	C₂×C₄	#14556636	1	2	yes	—
382	C₈	—	2	2	no	—
383	C₈	—	292	2	no	—
384	C₈	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
385	C₈	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
386	C₈	C₂×C₂²⋊Dic₇₃	1	2	yes	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	8	8	no	—
393	C₂²	—	8	4	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	16	8	no	—
396	C₂²	C₂×D₄×Dic₇₃	1	1	yes	characteristic
397	C₂²	D₄×C₂²⋊D₇₃	1	2	yes	—
398	C₄	—	2	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	292	4	no	—
401	C₄	—	584	4	no	—
402	C₄	C₂²×C₂²⋊Dic₇₃	1	1	yes	characteristic
403	C₄	#17989062	1	1	yes	characteristic
404	C₄	#17989231	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	2	1	no	—
407	C₂	—	4	2	no	—
408	C₂	—	4	8	no	—
409	C₂	—	8	2	no	—
410	C₂	D₄×C₂²⋊Dic₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×C₂²⋊Dic₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting, prime radical	C₂×#576×C₇₃	C₂
socle	C₂×C₇₃	D₄×C₂²⋊C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₂×#576	D₇₃
hypocenter	C₇₃	#22455
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. #22618783	C₂	semidirect
2. #22618392	C₂	semidirect
3. #22610830	C₂	semidirect
4. #22610420	C₂	semidirect
5. #22609977	C₂	semidirect
6. #22609901	C₂	semidirect
7. #22609731	C₂	semidirect
9. #17989062	C₂²	semidirect
12. #17988625	C₂²	semidirect
13. #17988604	C₂²	semidirect
14. #17988592	C₂²	semidirect
18. #17988561	C₂²	semidirect
20. #17988542	C₂²	semidirect
21. #17988358	C₂²	semidirect
22. #17988344	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₇₃	C₄	semidirect
28. C₂×#135×C₇₃	C₄	semidirect
30. C₂²×D₈×C₇₃	C₄	semidirect
53. C₂×#41×C₇₃	C₂×C₄	semidirect
58. C₂²×D₄×C₇₃	C₂×C₄	semidirect
66. C₂×Q₁₆×C₇₃	C₂×C₄	semidirect
67. C₂×SD₁₆×C₇₃	C₂×C₄	semidirect
68. C₂×SD₁₆×C₇₃	C₂×C₄	semidirect
73. C₂×D₈×C₇₃	C₂×C₄	semidirect
74. C₂×D₈×C₇₃	C₂×C₄	semidirect
79. C₂×M₁₆×C₇₃	C₂×C₄	semidirect
81. C₂²×C₈×C₇₃	C₂×C₄	semidirect
214. C₇₃	#22455	semidirect
218. C₂×AGL(1,ℤ/8)	Dic₇₃	semidirect
220. C₂×#135	Dic₇₃	semidirect
222. C₂²×D₈	Dic₇₃	semidirect
242. C₂×#41	C₂×Dic₇₃	semidirect
247. C₂²×D₄	C₂×Dic₇₃	semidirect
255. C₂×Q₁₆	C₂×Dic₇₃	semidirect
256. C₂×SD₁₆	C₂×Dic₇₃	semidirect
257. C₂×SD₁₆	C₂×Dic₇₃	semidirect
262. C₂×D₈	C₂×Dic₇₃	semidirect
263. C₂×D₈	C₂×Dic₇₃	semidirect
269. C₂×M₁₆	C₂×Dic₇₃	semidirect
271. C₂²×C₈	C₂×Dic₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22618783	2
#22618392	2
#22610830	2
#22610420	2
#22609977	2
#22609901	2
#22609731	2
C₂×#576×C₇₃	2
#22455	73