Subgroups — C₂×#22625752 #34020280

Order 18688.

1046 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×#64408	C₂	1	2	yes	maximal
3	C₂²×#14556645	C₂	1	1	yes	maximal, characteristic
4	#22625752	C₂	1	8	yes	maximal, direct product factor
5	C₂×#17989462	C₂	1	2	yes	maximal
6	C₂×#108×D₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂×D₇₃⋊M₁₆	C₂²	1	2	yes	—
8	C₂²×#11924036	C₂²	1	1	yes	characteristic
9	C₂²×C₄×#64408	C₂²	1	1	yes	characteristic
10	C₂×#14556662	C₄	1	2	yes	complemented
11	D₇₃⋊#108	C₄	1	4	yes	complemented
12	D₇₃⋊#108	C₂²	1	4	yes	—
13	C₂×#14556661	C₄	1	2	yes	complemented
14	M₁₆×#64408	—	2	4	no	—
15	M₁₆×#64408	C₂²	1	8	yes	—
16	C₂×#14556645	—	2	2	no	—
17	C₂×#14556645	C₄	1	2	yes	—
18	C₂×#14556645	C₄	1	2	yes	—
19	C₂×#14556645	C₄	1	4	yes	—
20	C₂×#14556645	C₂²	1	4	yes	—
21	C₂×C₈×#64408	—	2	2	no	—
22	#17989462	C₂²	1	8	yes	—
23	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
24	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
25	C₂×#14556527	C₄	1	1	yes	characteristic, complemented
26	C₂×#14556526	C₄	1	2	yes	complemented
27	#108×D₇₃	C₄	1	4	yes	complemented
28	#108×D₇₃	C₂²	1	4	yes	—
29	C₂×#108×C₇₃	C₄	1	1	yes	characteristic, complemented
30	C₂³×#64408	Q₈	1	2	yes	—
31	C₂×#11924038	C₂×C₄	1	4	yes	—
32	D₇₃⋊M₁₆	—	2	2	no	—
33	D₇₃⋊M₁₆	—	2	2	no	—
34	D₇₃⋊M₁₆	C₂×C₄	1	4	yes	—
35	D₇₃⋊M₁₆	C₂³	1	4	yes	—
36	C₂×#11924037	—	2	2	no	—
37	C₂×#11924036	—	2	2	no	—
38	C₂×#11924036	—	2	1	no	—
39	C₂×#11924036	—	2	1	no	—
40	C₂×#11924036	—	2	1	no	—
41	C₂×#11924036	C₂×C₄	1	2	yes	—
42	C₂×#11924036	C₂×C₄	1	2	yes	—
43	C₂×#11924036	C₂³	1	2	yes	—
44	C₂²×#10596833	—	2	1	no	—
45	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
46	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
47	C₂×C₄×#64408	D₄	1	2	yes	—
48	C₂×C₄×#64408	D₄	1	2	yes	—
49	C₂×C₄×#64408	Q₈	1	2	yes	—
50	C₂×C₄×#64408	C₂³	1	2	yes	—
51	#14556662	C₂×C₄	1	8	yes	complemented
52	#14556661	C₂×C₄	1	8	yes	complemented
53	#14556645	—	2	8	no	—
54	#14556645	C₂×C₄	1	8	yes	—
55	#14556645	C₂×C₄	1	8	yes	—
56	C₈×#64408	—	2	8	no	—
57	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
58	C₂×#11924012	C₂×C₄	1	2	yes	—
59	C₂×#11924011	—	2	2	no	—
60	M₁₆×D₇₃	—	2	2	no	—
61	M₁₆×D₇₃	—	2	2	no	—
62	M₁₆×D₇₃	C₂×C₄	1	4	yes	—
63	M₁₆×D₇₃	C₂³	1	4	yes	—
64	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₇₃	—	2	2	no	—
66	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
68	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
71	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
73	C₂×C₈×D₇₃	C₂³	1	2	yes	—
74	#14556527	C₂×C₄	1	4	yes	complemented
75	#14556526	C₂×C₄	1	8	yes	complemented
76	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
77	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
78	#108×C₇₃	C₂×C₄	1	4	yes	complemented
79	C₂²×#64408	—	4	4	no	—
80	C₂²×#64408	C₄⋊C₄	1	4	yes	—
81	C₂²×#64408	C₄⋊C₄	1	4	yes	—
82	C₂²×#64408	C₂×Q₈	1	4	yes	—
83	#11924038	—	2	4	no	—
84	#11924038	C₂²×C₄	1	8	yes	—
85	#11924037	—	2	4	no	—
86	#11924037	—	2	4	no	—
87	#11924036	—	2	2	no	—
88	#11924036	—	2	2	no	—
89	#11924036	—	2	4	no	—
90	#11924036	—	2	4	no	—
91	#11924036	—	2	2	no	—
92	#11924036	C₂²×C₄	1	4	yes	—
93	C₂×#10596833	—	2	2	no	—
94	C₂×#10596833	—	2	2	no	—
95	C₂×#10596833	—	2	4	no	—
96	C₂×#10596833	—	2	2	no	—
97	C₄×#64408	C₄⋊C₄	1	4	yes	—
98	C₄×#64408	C₄⋊C₄	1	4	yes	—
99	C₄×#64408	C₂²×C₄	1	4	yes	—
100	C₄×#64408	C₂×D₄	1	4	yes	—
101	C₂³×D₇₃	C₂×Q₈	1	1	yes	characteristic
102	C₂²×Dic₇₃	#41	1	1	yes	characteristic
103	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
111	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
112	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
113	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
114	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
115	#11924012	—	2	2	no	—
116	#11924012	C₂²×C₄	1	4	yes	—
117	#11924011	—	2	4	no	—
118	#11924011	—	2	4	no	—
119	C₂×#10596831	—	2	2	no	—
120	C₂×#10596831	C₄²	1	1	yes	characteristic
121	C₂×#10596831	C₄²	1	2	yes	—
122	C₂×#10596831	C₄²	1	1	yes	characteristic
123	C₂×#10596831	C₂²×C₄	1	2	yes	—
124	C₈×D₇₃	—	2	4	no	—
125	C₈×D₇₃	—	2	4	no	—
126	C₈×D₇₃	C₄²	1	2	yes	—
127	C₈×D₇₃	C₄²	1	2	yes	—
128	C₈×D₇₃	C₄²	1	2	yes	—
129	C₈×D₇₃	C₄²	1	2	yes	—
130	C₈×D₇₃	C₂²×C₄	1	2	yes	—
131	C₈×D₇₃	C₂²×C₄	1	2	yes	—
132	C₈×D₇₃	C₂²×C₄	1	2	yes	—
133	C₈×D₇₃	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
135	M₁₆×C₇₃	—	2	2	no	—
136	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
137	C₂×C₈×C₇₃	—	2	2	no	—
138	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
139	C₂×C₈×C₇₃	C₄²	1	2	yes	—
140	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
141	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
142	C₂³×C₇₃	C₄×Q₈	1	1	yes	characteristic
143	C₂²×D₇₃	—	2	4	no	—
144	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂²×D₇₃	C₄×Q₈	1	1	yes	characteristic
147	C₂²×D₇₃	C₄×Q₈	1	1	yes	characteristic
148	C₂²×D₇₃	C₄×Q₈	1	1	yes	characteristic
149	C₂²×D₇₃	C₂²×Q₈	1	1	yes	characteristic
150	C₂×#64408	—	2	8	no	—
151	C₂×#64408	—	4	4	no	—
152	C₂×#64408	—	4	4	no	—
153	C₂×#64408	C₂×C₄⋊C₄	1	8	yes	—
154	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×Dic₇₃	#117	1	1	yes	characteristic
161	C₂×Dic₇₃	#117	1	1	yes	characteristic
162	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
163	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
164	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
165	C₂×Dic₇₃	C₂×#41	1	1	yes	characteristic
166	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
167	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
168	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₄×D₇₃	#117	1	1	yes	characteristic
171	C₄×D₇₃	#117	1	1	yes	characteristic
172	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
173	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
174	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
175	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
176	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
177	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
178	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
179	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
180	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
181	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
182	#10596833	—	2	4	no	—
183	#10596833	—	2	8	no	—
184	C₈×C₇₃	—	2	4	no	—
185	C₈×C₇₃	C₂×C₄²	1	2	yes	—
186	C₈×C₇₃	C₂×C₄²	1	2	yes	—
187	#10596831	—	2	4	no	—
188	#10596831	C₂×C₄²	1	2	yes	—
189	#10596831	C₂×C₄²	1	2	yes	—
190	C₂²×C₇₃	—	2	2	no	—
191	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
192	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
194	C₂×D₇₃	—	2	2	no	—
195	C₂×D₇₃	—	2	2	no	—
196	C₂×D₇₃	—	2	2	no	—
197	C₂×D₇₃	—	2	2	no	—
198	C₂×D₇₃	—	2	2	no	—
199	C₂×D₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
200	C₂×D₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
201	C₂×D₇₃	#430	1	4	yes	—
202	C₂×D₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
203	C₂×D₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
204	#64408	—	2	8	no	—
205	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
206	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
207	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
208	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
209	Dic₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
210	Dic₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
211	Dic₇₃	C₂×#117	1	1	yes	characteristic
212	Dic₇₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₂×#1778	—	73	1	no	maximal, Sylow
214	C₂×C₇₃	—	2	1	no	—
215	C₂×C₇₃	—	2	1	no	—
216	C₂×C₇₃	#1778	1	2	yes	complemented
217	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
218	D₇₃	—	2	1	no	—
219	D₇₃	—	2	1	no	—
220	D₇₃	#1778	1	2	yes	complemented
221	D₇₃	C₂×#430	1	2	yes	—
222	C₂²×#108	—	73	1	no	—
223	C₂²×#108	—	73	1	no	—
224	C₂×C₄×M₁₆	—	73	2	no	—
225	C₂²×#97	—	73	1	no	—
226	#1778	—	73	8	no	—
227	C₂×#341	—	73	2	no	—
228	C₇₃	C₂×#1778	1	1	yes	characteristic, complemented, Sylow
229	C₂²×M₁₆	—	73	2	no	—
230	C₂²×M₁₆	—	73	2	no	—
231	C₂³×C₈	—	73	1	no	—
232	C₂³×C₈	—	73	1	no	—
233	C₂²×C₄²	—	73	1	no	—
234	C₂×#108	—	73	2	no	—
235	C₂×#108	—	73	4	no	—
236	C₂×#108	—	73	4	no	—
237	C₂×#108	—	73	2	no	—
238	C₂×#108	—	73	2	no	—
239	C₂×#108	—	73	1	no	—
240	C₂×#108	—	73	4	no	—
241	C₂×#108	—	73	4	no	—
242	C₂×#108	#64408	1	1	yes	characteristic, complemented
243	C₄×M₁₆	—	73	8	no	—
244	C₄×M₁₆	—	146	4	no	—
245	C₂×#97	—	73	4	no	—
246	C₂×#97	—	73	2	no	—
247	C₂×#97	—	73	2	no	—
248	C₂×#97	—	73	4	no	—
249	C₂×#97	—	146	2	no	—
250	C₂×C₄×C₈	—	146	2	no	—
251	#341	—	73	8	no	—
252	C₂³×C₄	—	73	2	no	—
253	C₂³×C₄	—	73	1	no	—
254	C₂×M₁₆	—	73	4	no	—
255	C₂×M₁₆	—	73	4	no	—
256	C₂×M₁₆	—	73	4	no	—
257	C₂×M₁₆	—	73	2	no	—
258	C₂×M₁₆	—	73	4	no	—
259	C₂×M₁₆	—	73	4	no	—
260	C₂×M₁₆	—	146	2	no	—
261	C₂×M₁₆	—	146	2	no	—
262	C₂×M₁₆	—	146	2	no	—
263	C₂×M₁₆	—	146	2	no	—
264	C₂×M₁₆	—	146	2	no	—
265	C₂×M₁₆	—	146	2	no	—
266	C₂×M₁₆	C₂×#64408	1	2	yes	—
267	C₂²×C₈	—	73	1	no	—
268	C₂²×C₈	—	73	1	no	—
269	C₂²×C₈	—	73	1	no	—
270	C₂²×C₈	—	73	2	no	—
271	C₂²×C₈	—	73	1	no	—
272	C₂²×C₈	—	73	2	no	—
273	C₂²×C₈	—	73	1	no	—
274	C₂²×C₈	—	73	2	no	—
275	C₂²×C₈	—	73	2	no	—
276	C₂²×C₈	—	73	2	no	—
277	C₂²×C₈	—	73	2	no	—
278	C₂²×C₈	—	73	2	no	—
279	C₂²×C₈	—	146	2	no	—
280	C₂²×C₈	—	146	1	no	—
281	C₂²×C₈	—	146	1	no	—
282	C₂²×C₈	—	146	1	no	—
283	C₂²×C₈	—	146	1	no	—
284	C₂²×C₈	—	146	2	no	—
285	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
286	C₂×C₄²	—	73	2	no	—
287	C₂×C₄²	—	73	2	no	—
288	C₂×C₄²	—	73	2	no	—
289	C₂×C₄²	—	73	2	no	—
290	C₂×C₄²	—	73	2	no	—
291	C₂×C₄²	—	73	2	no	—
292	#108	—	73	8	no	—
293	#108	—	73	8	no	—
294	#108	—	73	8	no	—
295	#108	—	73	4	no	—
296	#108	C₂×#64408	1	4	yes	complemented
297	#97	—	73	8	no	—
298	#97	—	73	8	no	—
299	#97	—	146	8	no	—
300	C₄×C₈	—	146	8	no	—
301	C₂⁴	—	73	1	no	—
302	C₂²×C₄	—	292	4	no	—
303	C₂²×C₄	—	73	4	no	—
304	C₂²×C₄	—	73	4	no	—
305	C₂²×C₄	—	73	1	no	—
306	C₂²×C₄	—	73	1	no	—
307	C₂²×C₄	—	73	1	no	—
308	C₂²×C₄	—	73	1	no	—
309	C₂²×C₄	—	73	1	no	—
310	C₂²×C₄	—	73	1	no	—
311	C₂²×C₄	—	73	1	no	—
312	C₂²×C₄	—	73	1	no	—
313	C₂²×C₄	—	73	1	no	—
314	C₂²×C₄	—	73	1	no	—
315	C₂²×C₄	—	73	1	no	—
316	C₂²×C₄	—	73	1	no	—
317	C₂²×C₄	—	73	1	no	—
318	C₂²×C₄	—	73	4	no	—
319	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
320	M₁₆	—	2	2	no	—
321	M₁₆	—	73	8	no	—
322	M₁₆	—	73	4	no	—
323	M₁₆	—	146	4	no	—
324	M₁₆	—	146	4	no	—
325	M₁₆	—	146	4	no	—
326	M₁₆	—	146	4	no	—
327	M₁₆	—	146	4	no	—
328	M₁₆	—	146	2	no	—
329	M₁₆	C₂²×#64408	1	4	yes	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	73	2	no	—
332	C₂×C₈	—	73	1	no	—
333	C₂×C₈	—	73	1	no	—
334	C₂×C₈	—	73	2	no	—
335	C₂×C₈	—	73	2	no	—
336	C₂×C₈	—	73	2	no	—
337	C₂×C₈	—	73	2	no	—
338	C₂×C₈	—	73	2	no	—
339	C₂×C₈	—	73	2	no	—
340	C₂×C₈	—	73	2	no	—
341	C₂×C₈	—	73	2	no	—
342	C₂×C₈	—	73	2	no	—
343	C₂×C₈	—	73	4	no	—
344	C₂×C₈	—	146	4	no	—
345	C₂×C₈	—	146	4	no	—
346	C₂×C₈	—	146	2	no	—
347	C₂×C₈	—	146	2	no	—
348	C₂×C₈	—	146	2	no	—
349	C₂×C₈	—	146	4	no	—
350	C₂×C₈	—	146	4	no	—
351	C₂×C₈	—	146	2	no	—
352	C₂×C₈	—	146	2	no	—
353	C₂×C₈	—	146	2	no	—
354	C₂×C₈	—	146	4	no	—
355	C₂×C₈	—	146	2	no	—
356	C₂×C₈	C₄×#64408	1	1	yes	characteristic
357	C₂×C₈	C₄×#64408	1	1	yes	characteristic
358	C₂×C₈	C₄×#64408	1	2	yes	—
359	C₂×C₈	C₂²×#64408	1	2	yes	—
360	C₄²	—	73	4	no	—
361	C₄²	—	73	4	no	—
362	C₄²	—	73	4	no	—
363	C₄²	—	73	4	no	—
364	C₂³	—	73	1	no	—
365	C₂³	—	73	1	no	—
366	C₂³	—	73	1	no	—
367	C₂³	—	73	1	no	—
368	C₂³	—	73	1	no	—
369	C₂³	—	73	1	no	—
370	C₂³	—	146	4	no	—
371	C₂³	Q₈×#64408	1	1	yes	characteristic
372	C₂×C₄	—	292	4	no	—
373	C₂×C₄	—	292	4	no	—
374	C₂×C₄	—	73	1	no	—
375	C₂×C₄	—	73	1	no	—
376	C₂×C₄	—	73	1	no	—
377	C₂×C₄	—	73	1	no	—
378	C₂×C₄	—	73	1	no	—
379	C₂×C₄	—	73	1	no	—
380	C₂×C₄	—	73	1	no	—
381	C₂×C₄	—	73	1	no	—
382	C₂×C₄	—	73	1	no	—
383	C₂×C₄	—	73	1	no	—
384	C₂×C₄	—	73	1	no	—
385	C₂×C₄	—	73	1	no	—
386	C₂×C₄	—	73	1	no	—
387	C₂×C₄	—	73	1	no	—
388	C₂×C₄	—	73	1	no	—
389	C₂×C₄	—	73	1	no	—
390	C₂×C₄	—	73	1	no	—
391	C₂×C₄	—	73	1	no	—
392	C₂×C₄	—	73	1	no	—
393	C₂×C₄	—	73	1	no	—
394	C₂×C₄	—	73	1	no	—
395	C₂×C₄	—	73	1	no	—
396	C₂×C₄	—	73	8	no	—
397	C₂×C₄	—	146	8	no	—
398	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
399	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
400	C₂×C₄	D₄×#64408	1	1	yes	characteristic
401	C₂×C₄	D₄×#64408	1	1	yes	characteristic
402	C₂×C₄	Q₈×#64408	1	1	yes	characteristic
403	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
404	C₈	—	2	4	no	—
405	C₈	—	73	2	no	—
406	C₈	—	73	2	no	—
407	C₈	—	146	4	no	—
408	C₈	—	146	8	no	—
409	C₈	—	146	4	no	—
410	C₈	C₂×C₄×#64408	1	2	yes	—
411	C₈	C₂×C₄×#64408	1	2	yes	—
412	C₂²	—	2	2	no	—
413	C₂²	—	73	1	no	—
414	C₂²	—	73	1	no	—
415	C₂²	—	73	4	no	—
416	C₂²	—	73	1	no	—
417	C₂²	—	73	1	no	—
418	C₂²	—	146	2	no	—
419	C₂²	—	146	2	no	—
420	C₂²	—	146	2	no	—
421	C₂²	—	146	2	no	—
422	C₂²	—	146	2	no	—
423	C₂²	C₄⋊C₄×#64408	1	1	yes	characteristic
424	C₂²	C₄⋊C₄×#64408	1	1	yes	characteristic
425	C₂²	C₂×Q₈×#64408	1	1	yes	characteristic
426	C₄	—	73	1	no	—
427	C₄	—	73	1	no	—
428	C₄	—	73	1	no	—
429	C₄	—	73	1	no	—
430	C₄	—	146	8	no	—
431	C₄	C₄⋊C₄×#64408	1	1	yes	characteristic
432	C₄	C₄⋊C₄×#64408	1	1	yes	characteristic
433	C₄	C₂²×C₄×#64408	1	1	yes	characteristic
434	C₄	C₂×D₄×#64408	1	1	yes	characteristic
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	73	2	no	—
438	C₂	—	73	2	no	—
439	C₂	—	146	1	no	—
440	C₂	—	146	1	no	—
441	C₂	#22625752	1	2	yes	direct product factor
442	C₂	C₂×C₄⋊C₄×#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#64408
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₂×#108×C₇₃	C₄
socle	C₂²×C₇₃	C₄×C₄⋊C₄
prime radical	C₂³×D₇₃	C₂×Q₈
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	C₂×#108	#64408
hypocenter	C₇₃	C₂×#1778
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
4. #22625752	C₂	direct (N × H)
10. C₂×#14556662	C₄	semidirect
11. D₇₃⋊#108	C₄	semidirect
13. C₂×#14556661	C₄	semidirect
25. C₂×#14556527	C₄	semidirect
26. C₂×#14556526	C₄	semidirect
27. #108×D₇₃	C₄	semidirect
29. C₂×#108×C₇₃	C₄	semidirect
51. #14556662	C₂×C₄	semidirect
52. #14556661	C₂×C₄	semidirect
74. #14556527	C₂×C₄	semidirect
75. #14556526	C₂×C₄	semidirect
78. #108×C₇₃	C₂×C₄	semidirect
216. C₂×C₇₃	#1778	semidirect
220. D₇₃	#1778	semidirect
228. C₇₃	C₂×#1778	semidirect
242. C₂×#108	#64408	semidirect
296. #108	C₂×#64408	semidirect
441. C₂	#22625752	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×D₇₃⋊#108	2
C₂×M₁₆×#64408	2
C₂²×#14556645	2
#22625752	2
C₂×#17989462	2
C₂×#108×D₇₃	2
C₂×#1778	73

Subgroups — C2×#22625752 #34020280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22625752 #34020280