Subgroups — D₄×#14556660 #34026968

Order 18688.

1126 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556660	C₂	1	2	yes	maximal, complemented
2	D₄×C₄⋊#64408	C₂	1	2	yes	maximal
3	#22626042	C₂	1	2	yes	maximal, complemented
4	#22625880	C₂	1	4	yes	maximal, complemented
5	#22625867	C₂	1	1	yes	maximal, characteristic, complemented
6	#22625808	C₂	1	2	yes	maximal, complemented
7	C₄×#14556660	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×D₄×D₇₃	C₂	1	1	yes	maximal, characteristic
9	C₂×D₄×#64408	—	2	2	no	—
10	C₂²×C₄⋊#64408	C₂²	1	4	yes	—
11	C₂×#14556660	—	2	8	no	—
12	C₂×#14556660	C₂²	1	1	yes	characteristic
13	C₂×#14556660	C₂²	1	2	yes	—
14	C₂×#14556660	C₂²	1	4	yes	—
15	C₂×#14556660	C₂²	1	2	yes	—
16	C₂×#14556660	C₂²	1	1	yes	characteristic
17	#17989538	—	2	2	no	—
18	#17989534	—	2	4	no	—
19	#17989533	C₂²	1	2	yes	—
20	#17989529	C₂²	1	4	yes	—
21	C₄×C₄⋊#64408	C₂²	1	2	yes	—
22	#17989461	C₂²	1	4	yes	—
23	#17989461	C₂²	1	2	yes	—
24	C₂²×C₈×D₇₃	C₂²	1	2	yes	—
25	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
26	C₈×D₂₉₂	C₄	1	1	yes	characteristic, complemented
27	D₄×#10596831	C₄	1	1	yes	characteristic, complemented
28	#17988652	C₄	1	1	yes	characteristic, complemented
29	C₈×C₂²⋊D₇₃	C₄	1	2	yes	complemented
30	#17988650	C₄	1	2	yes	complemented
31	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
32	C₂²⋊C₈×D₇₃	C₂²	1	2	yes	—
33	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
34	C₈×D₄×C₇₃	C₄	1	1	yes	characteristic, complemented
35	C₂³×#64408	—	2	4	no	—
36	D₄×#64408	—	4	8	no	—
37	C₂×C₄⋊#64408	—	2	8	no	—
38	C₂×C₄⋊#64408	—	2	4	no	—
39	C₂×C₄⋊#64408	—	2	2	no	—
40	C₂×C₄⋊#64408	—	2	2	no	—
41	C₂×C₄⋊#64408	—	4	4	no	—
42	C₂×C₄⋊#64408	C₂³	1	4	yes	—
43	C₂×C₄⋊#64408	C₂³	1	2	yes	—
44	C₂×C₄⋊#64408	C₂³	1	2	yes	—
45	C₂×C₂²⋊#64408	—	2	4	no	—
46	C₂×C₄×#64408	—	2	2	no	—
47	#14556660	—	2	8	no	—
48	#14556660	—	2	4	no	—
49	#14556660	—	2	2	no	—
50	#14556660	—	4	2	no	—
51	#14556660	D₄	1	4	yes	direct product factor
52	(C₂×#64408)⋊C₄	—	2	2	no	—
53	(C₂×#64408)⋊C₄	—	2	4	no	—
54	C₂×D₄×D₇₃	D₄	1	1	yes	characteristic
55	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
56	C₂²×#10596831	C₂×C₄	1	2	yes	complemented
57	C₂×C₈×D₇₃	—	2	4	no	—
58	C₂×C₈×D₇₃	—	2	4	no	—
59	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	complemented
60	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	complemented
61	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₇₃	C₂³	1	2	yes	—
63	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
64	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
65	D₄×Dic₇₃	Q₈	1	1	yes	characteristic
66	#14556553	Q₈	1	1	yes	characteristic
67	C₄×C₂²⋊D₇₃	C₂×C₄	1	2	yes	—
68	#14556551	Q₈	1	2	yes	—
69	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
70	C₂²⋊C₄×D₇₃	D₄	1	2	yes	—
71	C₄²×D₇₃	C₂³	1	1	yes	characteristic
72	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic, complemented
73	#14556520	C₂×C₄	1	2	yes	complemented
74	C₂²⋊#10596831	C₂×C₄	1	2	yes	complemented
75	#14556503	C₂×C₄	1	2	yes	complemented
76	#14556503	C₂×C₄	1	2	yes	complemented
77	C₄×#10596831	C₂×C₄	1	1	yes	characteristic, complemented
78	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic, complemented
79	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic, complemented
80	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
81	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
82	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
83	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	complemented
84	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
85	C₂²×#64408	—	2	2	no	—
86	C₂²×#64408	—	2	4	no	—
87	C₂²×#64408	—	2	2	no	—
88	C₂²×#64408	—	4	8	no	—
89	C₂²×#64408	—	4	8	no	—
90	C₂²×#64408	—	8	4	no	—
91	C₄⋊#64408	—	2	4	no	—
92	C₄⋊#64408	—	2	2	no	—
93	C₄⋊#64408	—	2	2	no	—
94	C₄⋊#64408	—	2	4	no	—
95	C₄⋊#64408	—	2	2	no	—
96	C₄⋊#64408	—	4	8	no	—
97	C₄⋊#64408	—	4	4	no	—
98	C₄⋊#64408	—	8	2	no	—
99	C₄⋊#64408	C₂×D₄	1	4	yes	—
100	C₂²⋊#64408	—	4	8	no	—
101	C₄×#64408	—	4	4	no	—
102	C₂³×D₇₃	C₂×D₄	1	2	yes	—
103	C₂×D₂₉₂	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₂²⋊D₇₃	C₄⋊C₄	1	2	yes	—
105	D₄×D₇₃	D₈	1	4	yes	—
106	D₄×D₇₃	Q₁₆	1	4	yes	—
107	C₂²×Dic₇₃	C₂×Q₈	1	2	yes	—
108	C₂×C₄×D₇₃	—	2	2	no	—
109	C₂×C₄×D₇₃	—	2	2	no	—
110	C₂×C₄×D₇₃	—	2	2	no	—
111	C₂×C₄×D₇₃	—	2	2	no	—
112	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
113	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
115	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
117	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
118	C₂×#10596831	—	2	4	no	—
119	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
120	C₂×#10596831	C₂²×C₄	1	2	yes	—
121	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
122	C₈×D₇₃	—	2	2	no	—
123	C₈×D₇₃	—	2	2	no	—
124	C₈×D₇₃	—	2	1	no	—
125	C₈×D₇₃	—	2	1	no	—
126	C₈×D₇₃	—	2	4	no	—
127	C₈×D₇₃	—	2	4	no	—
128	C₈×D₇₃	C₂×D₄	1	2	yes	—
129	C₈×D₇₃	#41	1	2	yes	—
130	C₄⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
131	#11924007	C₄⋊C₄	1	2	yes	—
132	C₂²⋊Dic₇₃	C₄⋊C₄	1	2	yes	—
133	#11924005	C₄⋊C₄	1	2	yes	—
134	#11924005	C₄⋊C₄	1	2	yes	—
135	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
137	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
138	C₂×D₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₇₃	—	2	4	no	—
141	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
144	C₄⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
145	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
146	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
147	C₂³×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
148	C₂²×D₇₃	—	2	2	no	—
149	C₂²×D₇₃	—	2	2	no	—
150	C₂²×D₇₃	—	2	2	no	—
151	C₂²×D₇₃	—	2	2	no	—
152	C₂²×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
153	C₂²×D₇₃	C₂×D₈	1	4	yes	—
154	C₂²×D₇₃	C₂×Q₁₆	1	4	yes	—
155	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
156	C₂×#64408	—	2	4	no	—
157	C₂×#64408	—	4	2	no	—
158	C₂×#64408	—	4	2	no	—
159	C₂×#64408	—	4	4	no	—
160	C₂×#64408	—	4	2	no	—
161	C₂×#64408	—	4	2	no	—
162	C₂×#64408	—	4	4	no	—
163	C₂×#64408	—	4	4	no	—
164	C₂×#64408	—	4	2	no	—
165	C₂×#64408	—	8	16	no	—
166	D₄×C₇₃	#107	1	4	yes	complemented
167	C₂×C₄×C₇₃	—	2	2	no	—
168	C₂×C₄×C₇₃	—	2	2	no	—
169	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
171	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
173	C₂²⋊D₇₃	#107	1	8	yes	complemented
174	C₂×Dic₇₃	—	2	2	no	—
175	C₂×Dic₇₃	—	2	2	no	—
176	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×Dic₇₃	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
180	D₂₉₂	#107	1	4	yes	complemented
181	C₄×D₇₃	—	2	2	no	—
182	C₄×D₇₃	—	2	2	no	—
183	C₄×D₇₃	—	2	1	no	—
184	C₄×D₇₃	—	2	1	no	—
185	C₄×D₇₃	—	2	2	no	—
186	C₄×D₇₃	—	2	2	no	—
187	C₄×D₇₃	—	2	2	no	—
188	C₄×D₇₃	—	2	2	no	—
189	C₄×D₇₃	C₂×D₈	1	2	yes	—
190	C₄×D₇₃	C₂×Q₁₆	1	2	yes	—
191	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
192	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
193	C₄×D₇₃	H(5,𝔽₂)	1	1	yes	characteristic
194	C₄×D₇₃	2₋¹⁺⁴	1	1	yes	characteristic
195	C₈×C₇₃	—	2	2	no	—
196	C₈×C₇₃	—	2	1	no	—
197	C₈×C₇₃	C₄×D₄	1	2	yes	complemented
198	#10596831	—	2	2	no	—
199	#10596831	—	2	1	no	—
200	#10596831	C₄×D₄	1	2	yes	complemented
201	C₂²×C₇₃	—	2	2	no	—
202	C₂²×C₇₃	—	2	2	no	—
203	C₂²×C₇₃	C₂×#107	1	4	yes	complemented
204	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
205	C₂×D₇₃	—	2	2	no	—
206	C₂×D₇₃	—	2	2	no	—
207	C₂×D₇₃	—	2	4	no	—
208	C₂×D₇₃	—	2	4	no	—
209	C₂×D₇₃	—	2	4	no	—
210	C₂×D₇₃	—	2	4	no	—
211	C₂×D₇₃	C₂×#107	1	4	yes	complemented
212	C₂×D₇₃	D₄²	1	1	yes	characteristic
213	C₂×D₇₃	#547	1	1	yes	characteristic
214	C₂×D₇₃	C₂²×D₈	1	1	yes	characteristic
215	C₂×D₇₃	C₂²×Q₁₆	1	1	yes	characteristic
216	C₂×D₇₃	#576	1	1	yes	characteristic
217	C₂×D₇₃	#578	1	1	yes	characteristic
218	#64408	—	4	4	no	—
219	#64408	—	8	2	no	—
220	#64408	—	8	4	no	—
221	C₄×C₇₃	—	2	2	no	—
222	C₄×C₇₃	—	2	1	no	—
223	C₄×C₇₃	C₂×#107	1	2	yes	complemented
224	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
225	C₄×C₇₃	#520	1	1	yes	characteristic
226	Dic₇₃	—	2	2	no	—
227	Dic₇₃	—	2	1	no	—
228	Dic₇₃	C₂×#107	1	2	yes	complemented
229	Dic₇₃	D₄×Q₈	1	1	yes	characteristic
230	Dic₇₃	#554	1	1	yes	characteristic
231	D₄×#107	—	73	1	no	maximal, Sylow
232	C₂×C₇₃	—	2	4	no	—
233	C₂×C₇₃	D₄×C₄⋊C₄	1	1	yes	characteristic
234	C₂×C₇₃	C₂²×#107	1	1	yes	characteristic
235	C₂×C₇₃	#2913	1	1	yes	characteristic
236	D₇₃	—	2	4	no	—
237	D₇₃	D₄×D₈	1	1	yes	characteristic
238	D₇₃	D₄×Q₁₆	1	1	yes	characteristic
239	D₇₃	#3334	1	1	yes	characteristic
240	D₇₃	#3338	1	1	yes	characteristic
241	C₂×C₈×D₄	—	73	1	no	—
242	C₂²×#107	—	73	2	no	—
243	D₄×C₄⋊C₄	—	73	2	no	—
244	#1947	—	73	2	no	—
245	#1852	—	73	4	no	—
246	#1845	—	73	1	no	—
247	#1808	—	73	2	no	—
248	C₄×#107	—	73	1	no	—
249	C₇₃	D₄×#107	1	1	yes	characteristic, complemented, Sylow
250	C₂³×C₈	—	73	2	no	—
251	C₂×C₄×D₄	—	73	1	no	—
252	C₂×C₄×D₄	—	146	2	no	—
253	C₂²×C₄⋊C₄	—	73	4	no	—
254	C₈×D₄	—	73	2	no	—
255	C₈×D₄	—	73	1	no	—
256	C₈×D₄	—	73	1	no	—
257	C₈×D₄	—	73	2	no	—
258	C₈×D₄	—	73	1	no	—
259	C₈×D₄	#64408	1	1	yes	characteristic, complemented
260	C₂×#107	—	73	2	no	—
261	C₂×#107	—	73	1	no	—
262	C₂×#107	—	73	1	no	—
263	C₂×#107	—	73	2	no	—
264	C₂×#107	—	73	4	no	—
265	C₂×#107	—	146	8	no	—
266	C₂×C₄⋊C₈	—	73	1	no	—
267	C₂×C₂²⋊C₈	—	73	2	no	—
268	C₂×C₄×C₈	—	73	1	no	—
269	#389	—	146	2	no	—
270	#385	—	146	4	no	—
271	#384	—	73	2	no	—
272	#380	—	73	4	no	—
273	C₄×C₄⋊C₄	—	73	2	no	—
274	#340	—	73	4	no	—
275	#340	—	73	2	no	—
276	C₂²×D₄	—	73	1	no	—
277	C₂³×C₄	—	73	2	no	—
278	C₂³×C₄	—	146	4	no	—
279	C₂²×C₈	—	73	1	no	—
280	C₂²×C₈	—	73	2	no	—
281	C₂²×C₈	—	73	2	no	—
282	C₂²×C₈	—	73	2	no	—
283	C₂²×C₈	—	73	2	no	—
284	C₂²×C₈	—	73	1	no	—
285	C₂²×C₈	—	146	4	no	—
286	C₂²×C₈	—	146	4	no	—
287	C₂²×C₈	C₂×#64408	1	2	yes	complemented
288	C₄×D₄	—	292	8	no	—
289	C₄×D₄	—	73	1	no	—
290	C₄×D₄	—	73	2	no	—
291	C₄×D₄	—	73	1	no	—
292	C₄×D₄	—	73	2	no	—
293	C₄×D₄	—	73	1	no	—
294	C₄×D₄	C₂×#64408	1	1	yes	characteristic
295	C₂×C₄⋊C₄	—	292	4	no	—
296	C₂×C₄⋊C₄	—	73	1	no	—
297	C₂×C₄⋊C₄	—	73	2	no	—
298	C₂×C₄⋊C₄	—	73	4	no	—
299	C₂×C₄⋊C₄	—	73	2	no	—
300	C₂×C₄⋊C₄	—	146	4	no	—
301	C₂×C₄⋊C₄	—	146	2	no	—
302	C₂×C₄⋊C₄	—	146	8	no	—
303	C₂×C₄⋊C₄	—	146	2	no	—
304	C₂×C₂²⋊C₄	—	73	2	no	—
305	C₂×C₂²⋊C₄	—	146	4	no	—
306	C₂×C₄²	—	73	1	no	—
307	C₂×C₄²	—	146	2	no	—
308	#107	—	292	2	no	—
309	#107	—	73	4	no	—
310	#107	—	146	8	no	—
311	#107	—	146	4	no	—
312	#107	—	146	2	no	—
313	C₄⋊C₈	—	73	2	no	—
314	C₄⋊C₈	—	73	1	no	—
315	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic, complemented
316	C₂²⋊C₈	—	73	2	no	—
317	C₂²⋊C₈	—	73	2	no	—
318	C₂²⋊C₈	—	73	2	no	—
319	C₂²⋊C₈	C₂×#64408	1	2	yes	complemented
320	C₄×C₈	—	73	1	no	—
321	C₄×C₈	—	73	1	no	—
322	C₄×C₈	—	73	1	no	—
323	C₄×C₈	C₂×#64408	1	1	yes	characteristic, complemented
324	#95	—	146	2	no	—
325	#95	—	146	4	no	—
326	C₂⁴	—	73	2	no	—
327	C₂×D₄	—	73	2	no	—
328	C₂×D₄	—	73	4	no	—
329	C₂×D₄	—	73	4	no	—
330	C₂×D₄	—	73	1	no	—
331	C₂×D₄	C₄⋊#64408	1	1	yes	characteristic
332	C₂²×C₄	—	292	8	no	—
333	C₂²×C₄	—	292	8	no	—
334	C₂²×C₄	—	584	4	no	—
335	C₂²×C₄	—	73	1	no	—
336	C₂²×C₄	—	73	1	no	—
337	C₂²×C₄	—	73	2	no	—
338	C₂²×C₄	—	73	2	no	—
339	C₂²×C₄	—	73	1	no	—
340	C₂²×C₄	—	73	2	no	—
341	C₂²×C₄	—	73	2	no	—
342	C₂²×C₄	—	146	2	no	—
343	C₂²×C₄	—	146	2	no	—
344	C₂²×C₄	—	146	2	no	—
345	C₂²×C₄	—	146	2	no	—
346	C₂²×C₄	—	146	2	no	—
347	C₂²×C₄	—	146	4	no	—
348	C₂²×C₄	—	146	2	no	—
349	C₂²×C₄	C₂²×#64408	1	2	yes	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	73	1	no	—
352	C₂×C₈	—	73	2	no	—
353	C₂×C₈	—	73	2	no	—
354	C₂×C₈	—	73	1	no	—
355	C₂×C₈	—	73	2	no	—
356	C₂×C₈	—	146	4	no	—
357	C₂×C₈	—	146	1	no	—
358	C₂×C₈	—	146	2	no	—
359	C₂×C₈	—	146	1	no	—
360	C₂×C₈	—	146	2	no	—
361	C₂×C₈	—	146	4	no	—
362	C₂×C₈	—	146	4	no	—
363	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
364	C₂×C₈	C₂²×#64408	1	2	yes	—
365	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
366	C₄⋊C₄	—	292	4	no	—
367	C₄⋊C₄	—	292	8	no	—
368	C₄⋊C₄	—	584	2	no	—
369	C₄⋊C₄	—	73	2	no	—
370	C₄⋊C₄	—	73	1	no	—
371	C₄⋊C₄	—	73	4	no	—
372	C₄⋊C₄	—	146	4	no	—
373	C₄⋊C₄	—	146	4	no	—
374	C₄⋊C₄	—	146	2	no	—
375	C₄⋊C₄	—	146	2	no	—
376	C₄⋊C₄	—	146	2	no	—
377	C₄⋊C₄	C₄⋊#64408	1	1	yes	characteristic
378	C₂²⋊C₄	—	292	8	no	—
379	C₂²⋊C₄	—	73	2	no	—
380	C₂²⋊C₄	—	73	2	no	—
381	C₂²⋊C₄	—	73	2	no	—
382	C₂²⋊C₄	C₄⋊#64408	1	2	yes	—
383	C₄²	—	292	4	no	—
384	C₄²	—	73	1	no	—
385	C₄²	—	73	1	no	—
386	C₄²	—	73	1	no	—
387	C₄²	C₂²×#64408	1	1	yes	characteristic
388	C₂³	—	73	1	no	—
389	C₂³	—	73	2	no	—
390	C₂³	—	73	4	no	—
391	C₂³	—	73	4	no	—
392	C₂³	—	146	2	no	—
393	C₂³	—	146	2	no	—
394	C₂³	—	146	2	no	—
395	C₂³	—	146	2	no	—
396	C₂³	C₂×C₄⋊#64408	1	2	yes	—
397	D₄	—	73	8	no	—
398	D₄	—	73	4	no	—
399	D₄	#14556660	1	4	yes	direct product factor
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	292	2	no	—
403	C₂×C₄	—	292	2	no	—
404	C₂×C₄	—	292	2	no	—
405	C₂×C₄	—	292	4	no	—
406	C₂×C₄	—	292	4	no	—
407	C₂×C₄	—	292	4	no	—
408	C₂×C₄	—	292	2	no	—
409	C₂×C₄	—	292	2	no	—
410	C₂×C₄	—	584	16	no	—
411	C₂×C₄	—	73	1	no	—
412	C₂×C₄	—	73	1	no	—
413	C₂×C₄	—	73	1	no	—
414	C₂×C₄	—	73	1	no	—
415	C₂×C₄	—	73	1	no	—
416	C₂×C₄	—	73	1	no	—
417	C₂×C₄	—	73	2	no	—
418	C₂×C₄	—	73	2	no	—
419	C₂×C₄	—	73	1	no	—
420	C₂×C₄	—	73	2	no	—
421	C₂×C₄	—	146	2	no	—
422	C₂×C₄	—	146	2	no	—
423	C₂×C₄	—	146	2	no	—
424	C₂×C₄	—	146	1	no	—
425	C₂×C₄	—	146	2	no	—
426	C₂×C₄	—	146	1	no	—
427	C₂×C₄	—	146	4	no	—
428	C₂×C₄	—	146	2	no	—
429	C₂×C₄	—	146	2	no	—
430	C₂×C₄	—	146	2	no	—
431	C₂×C₄	—	146	2	no	—
432	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
433	C₂×C₄	C₂×C₄⋊#64408	1	2	yes	—
434	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
435	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
436	C₈	—	2	2	no	—
437	C₈	—	2	1	no	—
438	C₈	—	73	2	no	—
439	C₈	—	146	2	no	—
440	C₈	—	146	1	no	—
441	C₈	D₄×#64408	1	2	yes	complemented
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	73	1	no	—
445	C₂²	—	73	1	no	—
446	C₂²	—	73	1	no	—
447	C₂²	—	73	1	no	—
448	C₂²	—	73	1	no	—
449	C₂²	—	73	1	no	—
450	C₂²	—	73	4	no	—
451	C₂²	—	146	4	no	—
452	C₂²	—	146	4	no	—
453	C₂²	—	146	4	no	—
454	C₂²	—	146	4	no	—
455	C₂²	—	146	2	no	—
456	C₂²	—	146	2	no	—
457	C₂²	C₂×#14556660	1	4	yes	complemented
458	C₂²	C₂²×C₄⋊#64408	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	2	no	—
461	C₄	—	292	4	no	—
462	C₄	—	584	4	no	—
463	C₄	—	584	2	no	—
464	C₄	—	73	2	no	—
465	C₄	—	73	1	no	—
466	C₄	—	73	1	no	—
467	C₄	—	146	1	no	—
468	C₄	—	146	2	no	—
469	C₄	C₂×#14556660	1	2	yes	complemented
470	C₄	C₂×D₄×#64408	1	1	yes	characteristic
471	C₄	#17989656	1	1	yes	characteristic
472	C₂	—	2	4	no	—
473	C₂	—	73	1	no	—
474	C₂	—	73	1	no	—
475	C₂	—	73	1	no	—
476	C₂	—	73	1	no	—
477	C₂	—	146	4	no	—
478	C₂	D₄×C₄⋊#64408	1	1	yes	characteristic
479	C₂	C₂²×#14556660	1	1	yes	characteristic
480	C₂	#22626586	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₈×D₄×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂×D₄×D₇₃	D₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	C₈×D₄	#64408
hypocenter	C₇₃	D₄×#107
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#14556660	C₂	semidirect
3. #22626042	C₂	semidirect
4. #22625880	C₂	semidirect
5. #22625867	C₂	semidirect
6. #22625808	C₂	semidirect
7. C₄×#14556660	C₂	semidirect
26. C₈×D₂₉₂	C₄	semidirect
27. D₄×#10596831	C₄	semidirect
28. #17988652	C₄	semidirect
29. C₈×C₂²⋊D₇₃	C₄	semidirect
30. #17988650	C₄	semidirect
34. C₈×D₄×C₇₃	C₄	semidirect
51. #14556660	D₄	direct (N × H)
56. C₂²×#10596831	C₂×C₄	semidirect
59. C₂×C₈×D₇₃	C₂×C₄	semidirect
60. C₂×C₈×D₇₃	C₂×C₄	semidirect
72. C₄⋊#10596831	C₂×C₄	semidirect
73. #14556520	C₂×C₄	semidirect
74. C₂²⋊#10596831	C₂×C₄	semidirect
75. #14556503	C₂×C₄	semidirect
76. #14556503	C₂×C₄	semidirect
77. C₄×#10596831	C₂×C₄	semidirect
78. C₈×Dic₇₃	C₂×C₄	semidirect
79. C₈×Dic₇₃	C₂×C₄	semidirect
80. C₂²×C₈×C₇₃	C₂×C₄	semidirect
82. C₄⋊C₈×C₇₃	C₂×C₄	semidirect
83. C₂²⋊C₈×C₇₃	C₂×C₄	semidirect
84. C₄×C₈×C₇₃	C₂×C₄	semidirect
166. D₄×C₇₃	#107	semidirect
173. C₂²⋊D₇₃	#107	semidirect
180. D₂₉₂	#107	semidirect
197. C₈×C₇₃	C₄×D₄	semidirect
200. #10596831	C₄×D₄	semidirect
203. C₂²×C₇₃	C₂×#107	semidirect
211. C₂×D₇₃	C₂×#107	semidirect
223. C₄×C₇₃	C₂×#107	semidirect
228. Dic₇₃	C₂×#107	semidirect
249. C₇₃	D₄×#107	semidirect
259. C₈×D₄	#64408	semidirect
287. C₂²×C₈	C₂×#64408	semidirect
315. C₄⋊C₈	C₂×#64408	semidirect
319. C₂²⋊C₈	C₂×#64408	semidirect
323. C₄×C₈	C₂×#64408	semidirect
399. D₄	#14556660	direct (N × H)
441. C₈	D₄×#64408	semidirect
457. C₂²	C₂×#14556660	semidirect
469. C₄	C₂×#14556660	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14556660	2
D₄×C₄⋊#64408	2
#22626042	2
#22625880	2
#22625867	2
#22625808	2
C₄×#14556660	2
C₈×D₄×D₇₃	2
D₄×#107	73

Subgroups — D4×#14556660 #34026968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#14556660 #34026968