Subgroups — C₂×#22625725 #34020191

Order 18688.

1310 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	C₂×#17989588	C₂	1	1	yes	maximal, characteristic
2	C₂²×#14556645	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊#64408	C₂	1	1	yes	maximal, characteristic
4	#22625725	C₂	1	8	yes	maximal, direct product factor
5	C₂×#17989452	C₂	1	2	yes	maximal
6	C₂×C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×#11924036	C₂²	1	2	yes	—
8	C₂²×C₄⋊#64408	C₄	1	2	yes	—
9	C₂²×C₄×#64408	C₂²	1	2	yes	—
10	C₂×#14556658	C₄	1	2	yes	complemented
11	#17989588	C₄	1	4	yes	complemented
12	#17989588	C₂²	1	4	yes	—
13	C₂×C₄⋊#10596833	C₄	1	2	yes	complemented
14	C₂×#14556645	—	2	8	no	—
15	C₂×#14556645	C₂²	1	8	yes	—
16	C₄×C₄⋊#64408	C₄	1	4	yes	—
17	C₄×C₄⋊#64408	C₂²	1	4	yes	—
18	C₂×(C₂×#64408)⋊C₄	C₄	1	2	yes	—
19	#17989452	C₂²	1	8	yes	—
20	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
21	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×#10596831	C₄	1	1	yes	characteristic, complemented
24	C₂×C₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
25	C₂×C₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
26	C₄×C₈×D₇₃	C₄	1	4	yes	complemented
27	C₄×C₈×D₇₃	C₂²	1	4	yes	—
28	C₂×C₄×C₈×C₇₃	C₄	1	1	yes	characteristic, complemented
29	C₂³×#64408	C₂×C₄	1	4	yes	—
30	C₂×#11924036	—	2	4	no	—
31	C₂×#11924036	—	2	4	no	—
32	C₂×#11924036	C₂×C₄	1	4	yes	—
33	C₂×#11924036	C₂³	1	4	yes	—
34	C₂²×#10596833	C₂×C₄	1	4	yes	—
35	C₂×C₄⋊#64408	—	2	8	no	—
36	C₂×C₄⋊#64408	C₂×C₄	1	8	yes	—
37	C₂×C₄×#64408	—	2	4	no	—
38	C₂×C₄×#64408	—	2	4	no	—
39	C₂×C₄×#64408	C₂×C₄	1	4	yes	—
40	C₂×C₄×#64408	C₂³	1	4	yes	—
41	#14556658	C₂×C₄	1	8	yes	complemented
42	C₄⋊#10596833	C₂×C₄	1	8	yes	complemented
43	#14556645	—	2	16	no	—
44	(C₂×#64408)⋊C₄	C₂×C₄	1	8	yes	—
45	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
48	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
49	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₇₃	—	2	2	no	—
51	C₂×C₈×D₇₃	—	2	2	no	—
52	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
54	C₂×C₈×D₇₃	D₄	1	4	yes	—
55	C₂×C₈×D₇₃	Q₈	1	4	yes	—
56	C₂×C₈×D₇₃	C₂³	1	2	yes	—
57	C₂×C₈×D₇₃	C₂³	1	2	yes	—
58	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₇₃	C₂×C₄	1	2	yes	—
62	C₄²×D₇₃	C₂×C₄	1	2	yes	—
63	C₄²×D₇₃	C₂×C₄	1	2	yes	—
64	C₄²×D₇₃	C₂³	1	2	yes	—
65	C₄×#10596831	C₂×C₄	1	4	yes	complemented
66	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
67	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
68	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	complemented
72	C₂²×#64408	—	2	8	no	—
73	C₂²×#64408	—	2	8	no	—
74	C₂²×#64408	—	2	8	no	—
75	C₂²×#64408	C₂²×C₄	1	8	yes	—
76	#11924036	—	2	8	no	—
77	#11924036	—	2	4	no	—
78	#11924036	—	2	4	no	—
79	C₂×#10596833	—	2	8	no	—
80	C₂×#10596833	C₂²×C₄	1	8	yes	—
81	C₄⋊#64408	—	2	16	no	—
82	C₄×#64408	—	2	8	no	—
83	C₄×#64408	—	2	4	no	—
84	C₄×#64408	—	2	4	no	—
85	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
87	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
88	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₄×D₇₃	—	2	4	no	—
90	C₂×C₄×D₇₃	C₄²	1	2	yes	—
91	C₂×C₄×D₇₃	C₄²	1	2	yes	—
92	C₂×C₄×D₇₃	M₁₆	1	8	yes	—
93	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
94	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
98	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
99	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
100	C₂×C₄×D₇₃	#41	1	2	yes	—
101	C₂×C₄×D₇₃	#41	1	2	yes	—
102	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
103	C₂×#10596831	—	2	2	no	—
104	C₂×#10596831	C₄⋊C₄	1	4	yes	complemented
105	C₂×#10596831	C₂²×C₄	1	2	yes	—
106	C₂×#10596831	C₂²×C₄	1	2	yes	—
107	C₈×D₇₃	—	2	4	no	—
108	C₈×D₇₃	—	2	2	no	—
109	C₈×D₇₃	—	2	2	no	—
110	C₈×D₇₃	C₄⋊C₄	1	8	yes	complemented
111	C₈×D₇₃	C₂×D₄	1	4	yes	—
112	C₈×D₇₃	C₂×Q₈	1	4	yes	—
113	C₄×Dic₇₃	C₄²	1	2	yes	—
114	C₄×Dic₇₃	C₄²	1	2	yes	—
115	C₄×Dic₇₃	C₄²	1	2	yes	—
116	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
117	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
118	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
120	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
121	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₇₃	—	2	2	no	—
123	C₂×C₈×C₇₃	C₄⋊C₄	1	4	yes	complemented
124	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₇₃	C₄²	1	2	yes	—
127	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
128	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
129	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
130	C₂²×D₇₃	C₄×D₄	1	2	yes	—
131	C₂²×D₇₃	C₄×Q₈	1	2	yes	—
132	C₂²×D₇₃	C₂×M₁₆	1	4	yes	—
133	C₂²×D₇₃	#131	1	4	yes	—
134	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
135	C₂×#64408	—	2	8	no	—
136	C₂×#64408	—	2	8	no	—
137	C₂×#64408	—	2	8	no	—
138	C₂×#64408	—	4	16	no	—
139	C₂×C₄×C₇₃	—	2	2	no	—
140	C₂×C₄×C₇₃	#97	1	4	yes	complemented
141	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
142	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
144	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₇₃	#117	1	2	yes	—
146	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
147	C₂×Dic₇₃	—	2	2	no	—
148	C₂×Dic₇₃	#97	1	4	yes	complemented
149	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
150	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
151	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
152	C₂×Dic₇₃	C₄×D₄	1	2	yes	—
153	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
154	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
155	C₄×D₇₃	—	2	4	no	—
156	C₄×D₇₃	—	2	4	no	—
157	C₄×D₇₃	#97	1	8	yes	complemented
158	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
159	C₄×D₇₃	#117	1	2	yes	—
160	C₄×D₇₃	C₄×D₄	1	2	yes	—
161	C₄×D₇₃	C₄×D₄	1	2	yes	—
162	C₄×D₇₃	C₄×Q₈	1	2	yes	—
163	C₄×D₇₃	C₄×Q₈	1	2	yes	—
164	C₄×D₇₃	C₂×M₁₆	1	8	yes	—
165	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
166	C₄×D₇₃	C₂²×Q₈	1	1	yes	characteristic
167	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
168	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
169	#10596833	—	2	8	no	—
170	C₈×C₇₃	—	2	2	no	—
171	C₈×C₇₃	C₂×C₄⋊C₄	1	4	yes	complemented
172	#10596831	—	2	2	no	—
173	#10596831	C₂×C₄⋊C₄	1	4	yes	complemented
174	C₂²×C₇₃	C₄×C₄⋊C₄	1	2	yes	—
175	C₂²×C₇₃	C₂×#97	1	2	yes	—
176	C₂²×C₇₃	#405	1	2	yes	—
177	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
178	C₂×D₇₃	C₄×C₄⋊C₄	1	2	yes	—
179	C₂×D₇₃	C₂×#97	1	2	yes	—
180	C₂×D₇₃	#405	1	2	yes	—
181	C₂×D₇₃	#436	1	8	yes	—
182	C₂×D₇₃	#446	1	8	yes	—
183	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂×D₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
185	C₂×D₇₃	C₂²×M₁₆	1	2	yes	—
186	C₂×D₇₃	C₂×#131	1	2	yes	—
187	#64408	—	4	8	no	—
188	C₄×C₇₃	—	2	2	no	—
189	C₄×C₇₃	C₄×C₄⋊C₄	1	2	yes	—
190	C₄×C₇₃	C₂×#97	1	4	yes	complemented
191	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
192	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
193	Dic₇₃	—	2	2	no	—
194	Dic₇₃	C₄×C₄⋊C₄	1	2	yes	—
195	Dic₇₃	C₂×#97	1	4	yes	complemented
196	Dic₇₃	C₂×C₄×D₄	1	1	yes	characteristic
197	Dic₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
198	C₂×#1770	—	73	1	no	maximal, Sylow
199	C₂×C₇₃	#1770	1	4	yes	complemented
200	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
201	C₂×C₇₃	C₂²×#97	1	1	yes	characteristic
202	C₂×C₇₃	C₂×#405	1	1	yes	characteristic
203	D₇₃	#1770	1	4	yes	complemented
204	D₇₃	C₂×#436	1	2	yes	—
205	D₇₃	C₂×#446	1	2	yes	—
206	C₂²×C₄⋊C₈	—	73	1	no	—
207	C₂²×#97	—	73	2	no	—
208	C₂²×C₄×C₈	—	73	1	no	—
209	C₂×C₄×C₄⋊C₄	—	73	1	no	—
210	#1770	—	73	8	no	—
211	C₂×#336	—	73	2	no	—
212	C₇₃	C₂×#1770	1	1	yes	characteristic, complemented, Sylow
213	C₂³×C₈	—	73	1	no	—
214	C₂³×C₈	—	73	2	no	—
215	C₂³×C₈	—	73	1	no	—
216	C₂²×C₄⋊C₄	—	73	2	no	—
217	C₂²×C₄²	—	73	1	no	—
218	C₂²×C₄²	—	73	2	no	—
219	C₂×C₄⋊C₈	—	73	2	no	—
220	C₂×C₄⋊C₈	—	73	4	no	—
221	C₂×C₄⋊C₈	—	73	4	no	—
222	C₂×C₄⋊C₈	—	73	2	no	—
223	C₂×#97	—	73	8	no	—
224	C₂×#97	—	146	8	no	—
225	C₂×C₄×C₈	—	73	1	no	—
226	C₂×C₄×C₈	—	73	1	no	—
227	C₂×C₄×C₈	—	73	1	no	—
228	C₂×C₄×C₈	—	73	4	no	—
229	C₂×C₄×C₈	—	73	4	no	—
230	C₂×C₄×C₈	#64408	1	1	yes	characteristic, complemented
231	C₄×C₄⋊C₄	—	73	4	no	—
232	C₄×C₄⋊C₄	—	73	4	no	—
233	C₂×#95	—	73	2	no	—
234	#336	—	73	8	no	—
235	C₂³×C₄	—	73	1	no	—
236	C₂³×C₄	—	73	1	no	—
237	C₂³×C₄	—	73	1	no	—
238	C₂³×C₄	—	73	4	no	—
239	C₂²×C₈	—	73	1	no	—
240	C₂²×C₈	—	73	4	no	—
241	C₂²×C₈	—	73	4	no	—
242	C₂²×C₈	—	73	2	no	—
243	C₂²×C₈	—	73	2	no	—
244	C₂²×C₈	—	73	4	no	—
245	C₂²×C₈	—	73	4	no	—
246	C₂²×C₈	—	73	4	no	—
247	C₂²×C₈	—	73	1	no	—
248	C₂²×C₈	—	73	2	no	—
249	C₂²×C₈	—	73	2	no	—
250	C₂²×C₈	—	146	2	no	—
251	C₂²×C₈	—	146	2	no	—
252	C₂²×C₈	—	146	4	no	—
253	C₂²×C₈	—	146	4	no	—
254	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
255	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
256	C₂×C₄⋊C₄	—	73	8	no	—
257	C₂×C₄⋊C₄	—	146	8	no	—
258	C₂×C₄²	—	73	1	no	—
259	C₂×C₄²	—	73	1	no	—
260	C₂×C₄²	—	73	1	no	—
261	C₂×C₄²	—	73	2	no	—
262	C₂×C₄²	—	73	2	no	—
263	C₂×C₄²	—	73	2	no	—
264	C₂×C₄²	—	73	2	no	—
265	C₂×C₄²	—	73	4	no	—
266	C₂×C₄²	—	73	4	no	—
267	C₂×C₄²	—	146	4	no	—
268	C₂×C₄²	—	146	4	no	—
269	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
270	C₄⋊C₈	—	73	8	no	—
271	C₄⋊C₈	—	73	8	no	—
272	#97	—	146	16	no	—
273	C₄×C₈	—	73	4	no	—
274	C₄×C₈	—	73	4	no	—
275	C₄×C₈	—	73	4	no	—
276	C₄×C₈	C₂×#64408	1	4	yes	complemented
277	#95	—	73	8	no	—
278	C₂⁴	—	73	1	no	—
279	C₂²×C₄	—	73	1	no	—
280	C₂²×C₄	—	73	1	no	—
281	C₂²×C₄	—	73	1	no	—
282	C₂²×C₄	—	73	1	no	—
283	C₂²×C₄	—	73	8	no	—
284	C₂²×C₄	—	73	2	no	—
285	C₂²×C₄	—	73	1	no	—
286	C₂²×C₄	—	73	2	no	—
287	C₂²×C₄	—	73	1	no	—
288	C₂²×C₄	—	73	2	no	—
289	C₂²×C₄	—	73	2	no	—
290	C₂²×C₄	—	73	2	no	—
291	C₂²×C₄	—	73	2	no	—
292	C₂²×C₄	—	73	1	no	—
293	C₂²×C₄	—	73	2	no	—
294	C₂²×C₄	—	73	2	no	—
295	C₂²×C₄	—	73	8	no	—
296	C₂²×C₄	—	146	4	no	—
297	C₂²×C₄	—	146	8	no	—
298	C₂²×C₄	—	146	8	no	—
299	C₂²×C₄	—	146	8	no	—
300	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
301	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
302	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	73	2	no	—
305	C₂×C₈	—	73	4	no	—
306	C₂×C₈	—	73	8	no	—
307	C₂×C₈	—	73	4	no	—
308	C₂×C₈	—	73	4	no	—
309	C₂×C₈	—	73	8	no	—
310	C₂×C₈	—	73	2	no	—
311	C₂×C₈	—	146	2	no	—
312	C₂×C₈	—	146	2	no	—
313	C₂×C₈	—	146	4	no	—
314	C₂×C₈	—	146	8	no	—
315	C₂×C₈	—	146	4	no	—
316	C₂×C₈	—	146	4	no	—
317	C₂×C₈	—	146	8	no	—
318	C₂×C₈	—	146	2	no	—
319	C₂×C₈	C₄⋊#64408	1	4	yes	complemented
320	C₂×C₈	C₂²×#64408	1	2	yes	—
321	C₂×C₈	C₂²×#64408	1	2	yes	—
322	C₄⋊C₄	—	146	16	no	—
323	C₄²	—	73	2	no	—
324	C₄²	—	73	2	no	—
325	C₄²	—	73	2	no	—
326	C₄²	—	73	2	no	—
327	C₄²	—	73	2	no	—
328	C₄²	—	73	2	no	—
329	C₄²	—	146	4	no	—
330	C₄²	—	146	4	no	—
331	C₄²	—	146	8	no	—
332	C₄²	C₄×#64408	1	2	yes	—
333	C₄²	C₂²×#64408	1	2	yes	—
334	C₂³	—	73	1	no	—
335	C₂³	—	73	1	no	—
336	C₂³	—	73	2	no	—
337	C₂³	—	73	2	no	—
338	C₂³	—	73	4	no	—
339	C₂³	—	73	4	no	—
340	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	292	16	no	—
343	C₂×C₄	—	73	1	no	—
344	C₂×C₄	—	73	1	no	—
345	C₂×C₄	—	73	2	no	—
346	C₂×C₄	—	73	2	no	—
347	C₂×C₄	—	73	2	no	—
348	C₂×C₄	—	73	4	no	—
349	C₂×C₄	—	73	1	no	—
350	C₂×C₄	—	73	2	no	—
351	C₂×C₄	—	73	1	no	—
352	C₂×C₄	—	73	1	no	—
353	C₂×C₄	—	73	1	no	—
354	C₂×C₄	—	73	2	no	—
355	C₂×C₄	—	73	2	no	—
356	C₂×C₄	—	73	2	no	—
357	C₂×C₄	—	73	2	no	—
358	C₂×C₄	—	73	2	no	—
359	C₂×C₄	—	73	8	no	—
360	C₂×C₄	—	73	8	no	—
361	C₂×C₄	—	73	2	no	—
362	C₂×C₄	—	146	4	no	—
363	C₂×C₄	—	146	4	no	—
364	C₂×C₄	—	146	8	no	—
365	C₂×C₄	—	146	8	no	—
366	C₂×C₄	—	146	8	no	—
367	C₂×C₄	—	146	2	no	—
368	C₂×C₄	#14556645	1	4	yes	complemented
369	C₂×C₄	C₂×C₄×#64408	1	2	yes	—
370	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×#64408	1	2	yes	—
372	C₂×C₄	C₂×C₄⋊#64408	1	2	yes	—
373	C₂×C₄	#14556670	1	2	yes	—
374	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	73	4	no	—
377	C₈	—	146	8	no	—
378	C₈	—	146	2	no	—
379	C₈	C₂×C₄⋊#64408	1	4	yes	complemented
380	C₂²	—	73	1	no	—
381	C₂²	—	73	1	no	—
382	C₂²	—	73	2	no	—
383	C₂²	—	73	2	no	—
384	C₂²	—	73	2	no	—
385	C₂²	—	73	2	no	—
386	C₂²	—	73	2	no	—
387	C₂²	—	73	8	no	—
388	C₂²	—	73	8	no	—
389	C₂²	C₄×C₄⋊#64408	1	2	yes	—
390	C₂²	C₂×#14556645	1	2	yes	—
391	C₂²	#17989550	1	2	yes	—
392	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	292	8	no	—
395	C₄	—	73	1	no	—
396	C₄	—	73	1	no	—
397	C₄	—	73	2	no	—
398	C₄	—	73	4	no	—
399	C₄	—	146	2	no	—
400	C₄	C₄×C₄⋊#64408	1	2	yes	—
401	C₄	C₂×#14556645	1	4	yes	complemented
402	C₄	C₂²×C₄⋊#64408	1	1	yes	characteristic
403	C₄	C₂×#14556670	1	1	yes	characteristic
404	C₂	—	73	2	no	—
405	C₂	—	73	2	no	—
406	C₂	—	73	4	no	—
407	C₂	#22625725	1	4	yes	direct product factor
408	C₂	C₂×C₄×C₄⋊#64408	1	1	yes	characteristic
409	C₂	C₂²×#14556645	1	1	yes	characteristic
410	C₂	C₂×#17989550	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×#64408
commutator	C₂²×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₂×C₄×C₈×C₇₃	C₄
socle	C₂³×C₇₃	C₂×C₄²
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	C₂×C₄×C₈	#64408
hypocenter	C₇₃	C₂×#1770
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #22625725	C₂	direct (N × H)
10. C₂×#14556658	C₄	semidirect
11. #17989588	C₄	semidirect
13. C₂×C₄⋊#10596833	C₄	semidirect
23. C₂×C₄×#10596831	C₄	semidirect
24. C₂×C₈×Dic₇₃	C₄	semidirect
25. C₂×C₈×Dic₇₃	C₄	semidirect
26. C₄×C₈×D₇₃	C₄	semidirect
28. C₂×C₄×C₈×C₇₃	C₄	semidirect
41. #14556658	C₂×C₄	semidirect
42. C₄⋊#10596833	C₂×C₄	semidirect
65. C₄×#10596831	C₂×C₄	semidirect
66. C₈×Dic₇₃	C₂×C₄	semidirect
67. C₈×Dic₇₃	C₂×C₄	semidirect
71. C₄×C₈×C₇₃	C₂×C₄	semidirect
104. C₂×#10596831	C₄⋊C₄	semidirect
110. C₈×D₇₃	C₄⋊C₄	semidirect
123. C₂×C₈×C₇₃	C₄⋊C₄	semidirect
140. C₂×C₄×C₇₃	#97	semidirect
148. C₂×Dic₇₃	#97	semidirect
157. C₄×D₇₃	#97	semidirect
171. C₈×C₇₃	C₂×C₄⋊C₄	semidirect
173. #10596831	C₂×C₄⋊C₄	semidirect
190. C₄×C₇₃	C₂×#97	semidirect
195. Dic₇₃	C₂×#97	semidirect
199. C₂×C₇₃	#1770	semidirect
203. D₇₃	#1770	semidirect
212. C₇₃	C₂×#1770	semidirect
230. C₂×C₄×C₈	#64408	semidirect
276. C₄×C₈	C₂×#64408	semidirect
319. C₂×C₈	C₄⋊#64408	semidirect
368. C₂×C₄	#14556645	semidirect
379. C₈	C₂×C₄⋊#64408	semidirect
401. C₄	C₂×#14556645	semidirect
407. C₂	#22625725	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#17989588	2
C₂²×#14556645	2
C₂×C₄×C₄⋊#64408	2
#22625725	2
C₂×#17989452	2
C₂×C₄×C₈×D₇₃	2
C₂×#1770	73

Subgroups — C2×#22625725 #34020191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22625725 #34020191