Subgroups — #34030341

Order 18688.

558 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626348	C₂	1	2	yes	maximal, complemented
2	#22626316	C₂	1	2	yes	maximal, complemented
3	#22626313	C₂	1	2	yes	maximal, complemented
4	#22626311	C₂	1	2	yes	maximal, complemented
5	#22626291	C₂	1	1	yes	maximal, characteristic, complemented
6	#22626289	C₂	1	1	yes	maximal, characteristic, complemented
7	#22626289	C₂	1	1	yes	maximal, characteristic, complemented
8	#22626138	C₂	1	1	yes	maximal, characteristic, complemented
9	#22626137	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#17989473	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#11924027	C₂	1	1	yes	maximal, characteristic
12	C₂×#14556666	C₂²	1	2	yes	—
13	C₂×#14556665	C₂²	1	2	yes	—
14	C₂²×#11924031	C₂²	1	2	yes	—
15	#17989508	C₂²	1	2	yes	—
16	#17989508	C₂²	1	2	yes	—
17	C₄⋊#11924031	C₂²	1	2	yes	—
18	#17989482	C₂²	1	2	yes	—
19	C₂²⋊#11924031	C₂²	1	2	yes	—
20	C₂²⋊#11924031	C₂²	1	2	yes	—
21	#17989476	C₂²	1	2	yes	—
22	#17989475	C₂²	1	2	yes	—
23	#17989473	C₂²	1	2	yes	—
24	#17989473	C₂²	1	1	yes	characteristic
25	#17989473	C₂²	1	1	yes	characteristic
26	#17989473	C₂²	1	1	yes	characteristic
27	#17989473	C₂²	1	1	yes	characteristic
28	C₄×#11924027	C₄	1	1	yes	characteristic
29	C₈×Dic₁₄₆	C₄	1	1	yes	characteristic
30	#17988711	C₂²	1	1	yes	characteristic
31	D₄×#10596831	C₂²	1	1	yes	characteristic
32	C₈×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
33	C₈×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
34	#17988650	C₂²	1	1	yes	characteristic
35	#17988650	C₂²	1	1	yes	characteristic
36	#17988639	C₄	1	1	yes	characteristic
37	#17988637	C₄	1	1	yes	characteristic
38	#17988637	C₄	1	1	yes	characteristic
39	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
40	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₇₃	C₄	1	1	yes	characteristic
43	#14556666	—	2	4	no	—
44	#14556665	—	2	4	no	—
45	C₂×#11924031	—	2	4	no	—
46	C₂×#11924031	C₂³	1	2	yes	—
47	C₂×#11924031	C₂³	1	2	yes	—
48	C₂×#11924031	C₂³	1	2	yes	—
49	C₂×#11924031	C₂³	1	2	yes	—
50	C₂×#11924027	C₈	1	1	yes	characteristic
51	C₂²×#10596831	C₂³	1	1	yes	characteristic
52	C₂²×#10596831	C₂³	1	1	yes	characteristic
53	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
55	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
56	#14556556	C₈	1	1	yes	characteristic
57	D₄×Dic₇₃	C₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
59	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
60	#14556551	C₈	1	1	yes	characteristic
61	#14556551	C₈	1	1	yes	characteristic
62	#14556549	C₈	1	1	yes	characteristic
63	#14556547	C₈	1	1	yes	characteristic
64	#14556547	C₈	1	1	yes	characteristic
65	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
68	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
69	#14556520	C₂×C₄	1	1	yes	characteristic
70	#14556520	C₂×C₄	1	1	yes	characteristic
71	#14556520	C₂×C₄	1	1	yes	characteristic
72	#14556520	C₂×C₄	1	1	yes	characteristic
73	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
74	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
75	#14556503	C₂×C₄	1	1	yes	characteristic
76	#14556503	C₂×C₄	1	1	yes	characteristic
77	C₄×#10596831	C₂³	1	1	yes	characteristic
78	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
84	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
85	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
88	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
93	#11924031	—	2	2	no	—
94	#11924031	—	2	2	no	—
95	#11924031	—	2	2	no	—
96	#11924031	#41	1	4	yes	complemented
97	#11924027	—	2	4	no	—
98	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
99	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
100	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
101	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
102	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
103	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
104	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
107	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×#10596831	—	2	2	no	—
109	C₂×#10596831	—	2	2	no	—
110	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
111	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
112	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
113	C₂×#10596831	C₂⁴	1	1	yes	characteristic
114	C₈×D₇₃	—	2	2	no	—
115	C₈×D₇₃	—	2	2	no	—
116	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
117	#11924007	C₂×C₈	1	1	yes	characteristic
118	#11924007	C₂×C₈	1	1	yes	characteristic
119	#11924007	C₂×C₈	1	1	yes	characteristic
120	#11924007	C₂×C₈	1	1	yes	characteristic
121	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
122	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
123	#11924005	C₂×C₈	1	1	yes	characteristic
124	#11924005	C₂×C₈	1	1	yes	characteristic
125	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
126	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
127	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
128	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
129	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
130	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×D₄×C₇₃	C₂×C₈	1	1	yes	characteristic
135	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₇₃	—	2	2	no	—
138	C₂×C₈×C₇₃	—	2	2	no	—
139	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
143	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
144	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
145	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
146	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
147	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
148	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
150	D₄×C₇₃	—	2	2	no	—
151	C₂×C₄×C₇₃	—	2	1	no	—
152	C₂×C₄×C₇₃	—	2	1	no	—
153	C₂×C₄×C₇₃	—	2	1	no	—
154	C₂×C₄×C₇₃	—	2	1	no	—
155	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
160	C₂²⋊D₇₃	—	2	2	no	—
161	C₂²⋊D₇₃	—	2	2	no	—
162	C₂×Dic₇₃	—	2	2	no	—
163	C₂×Dic₇₃	—	2	2	no	—
164	C₂×Dic₇₃	—	2	2	no	—
165	C₂×Dic₇₃	M₃₂	1	4	yes	complemented
166	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
167	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
168	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
169	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
170	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
171	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
172	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
173	C₄×D₇₃	—	2	1	no	—
174	C₄×D₇₃	—	2	1	no	—
175	C₄×D₇₃	—	2	2	no	—
176	C₄×D₇₃	—	2	2	no	—
177	Dic₁₄₆	—	2	2	no	—
178	C₈×C₇₃	—	2	1	no	—
179	C₈×C₇₃	—	2	1	no	—
180	C₈×C₇₃	—	2	1	no	—
181	C₈×C₇₃	#131	1	2	yes	—
182	#10596831	—	2	1	no	—
183	#10596831	—	2	1	no	—
184	#10596831	—	2	1	no	—
185	#10596831	C₂×#41	1	2	yes	—
186	C₂²×C₇₃	—	2	1	no	—
187	C₂²×C₇₃	—	2	1	no	—
188	C₂²×C₇₃	—	2	1	no	—
189	C₂²×C₇₃	—	2	1	no	—
190	C₂²×C₇₃	—	2	1	no	—
191	C₂²×C₇₃	C₂×M₃₂	1	2	yes	—
192	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
193	C₂×D₇₃	—	2	1	no	—
194	C₂×D₇₃	—	2	1	no	—
195	C₂×D₇₃	—	2	1	no	—
196	C₄×C₇₃	—	2	1	no	—
197	C₄×C₇₃	—	2	1	no	—
198	C₄×C₇₃	—	2	1	no	—
199	C₄×C₇₃	—	2	1	no	—
200	C₄×C₇₃	C₄×#41	1	1	yes	characteristic
201	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
202	Dic₇₃	—	2	1	no	—
203	Dic₇₃	—	2	1	no	—
204	Dic₇₃	—	2	1	no	—
205	Dic₇₃	—	2	1	no	—
206	Dic₇₃	C₂×M₃₂	1	2	yes	—
207	Dic₇₃	C₂×M₃₂	1	2	yes	—
208	Dic₇₃	#504	1	2	yes	—
209	#33479	—	73	1	no	maximal, Sylow
210	C₂×C₇₃	—	2	2	no	—
211	C₂×C₇₃	—	4	1	no	—
212	C₂×C₇₃	C₈×#41	1	1	yes	characteristic
213	C₂×C₇₃	C₂²×M₃₂	1	1	yes	characteristic
214	C₂×C₇₃	C₂×#504	1	1	yes	characteristic
215	D₇₃	—	4	1	no	—
216	C₈×#41	—	73	1	no	—
217	#2183	—	73	2	no	—
218	#2169	—	73	2	no	—
219	#2168	—	73	2	no	—
220	#2168	—	73	2	no	—
221	#2162	—	73	1	no	—
222	#2162	—	73	1	no	—
223	#2162	—	73	1	no	—
224	C₄×M₃₂	—	73	1	no	—
225	C₄×M₃₂	—	73	1	no	—
226	C₂×C₄×C₁₆	—	73	1	no	—
227	C₇₃	#33479	1	1	yes	characteristic, complemented, Sylow
228	C₄×#41	—	73	1	no	—
229	C₂×M₃₂	—	73	2	no	—
230	C₂×M₃₂	—	73	2	no	—
231	C₂²×C₁₆	—	73	2	no	—
232	C₈×Q₈	—	73	1	no	—
233	C₈×Q₈	—	73	1	no	—
234	C₈×D₄	—	73	1	no	—
235	C₈×D₄	—	73	1	no	—
236	C₈×D₄	—	73	1	no	—
237	C₈×D₄	—	73	1	no	—
238	C₈×D₄	—	73	1	no	—
239	C₈×D₄	#64408	1	1	yes	characteristic
240	#431	—	73	1	no	—
241	#431	—	73	1	no	—
242	#431	—	73	1	no	—
243	C₂×C₄×C₈	—	73	1	no	—
244	C₂×C₄×C₈	—	73	1	no	—
245	C₂×C₄×C₈	—	73	1	no	—
246	C₄⋊C₁₆	—	73	2	no	—
247	C₄⋊C₁₆	—	73	2	no	—
248	C₄⋊C₁₆	—	73	2	no	—
249	C₂²⋊C₁₆	—	73	2	no	—
250	C₂²⋊C₁₆	—	73	2	no	—
251	C₂²⋊C₁₆	—	73	2	no	—
252	#346	—	73	2	no	—
253	#346	—	73	2	no	—
254	C₄×C₁₆	—	73	1	no	—
255	C₄×C₁₆	—	73	1	no	—
256	C₄×C₁₆	—	73	2	no	—
257	C₄×C₁₆	—	73	1	no	—
258	C₄×C₁₆	—	73	1	no	—
259	C₂×#41	—	73	1	no	—
260	C₂²×C₈	—	73	1	no	—
261	C₂²×C₈	—	73	1	no	—
262	C₂²×C₈	—	73	1	no	—
263	C₂²×C₈	—	73	1	no	—
264	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
265	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
266	C₄×Q₈	—	73	1	no	—
267	C₄×Q₈	—	73	1	no	—
268	C₄×D₄	—	73	1	no	—
269	C₄×D₄	—	73	1	no	—
270	C₄×D₄	—	73	1	no	—
271	C₄×D₄	—	73	1	no	—
272	C₄×D₄	—	73	1	no	—
273	C₄×D₄	C₂×#64408	1	1	yes	characteristic
274	#117	—	73	1	no	—
275	#117	—	73	1	no	—
276	#117	—	73	1	no	—
277	C₂×C₄²	—	73	1	no	—
278	C₂×C₄²	—	73	1	no	—
279	C₂×C₄²	—	73	1	no	—
280	M₃₂	—	146	4	no	—
281	M₃₂	—	146	4	no	—
282	C₂×C₁₆	—	73	2	no	—
283	C₂×C₁₆	—	73	2	no	—
284	C₂×C₁₆	—	73	2	no	—
285	C₂×C₁₆	—	73	2	no	—
286	C₂×C₁₆	—	146	4	no	—
287	C₄⋊C₈	—	73	1	no	—
288	C₄⋊C₈	—	73	1	no	—
289	C₄⋊C₈	—	73	1	no	—
290	C₄⋊C₈	—	73	1	no	—
291	C₄⋊C₈	—	73	1	no	—
292	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic
293	C₂²⋊C₈	—	73	1	no	—
294	C₂²⋊C₈	—	73	1	no	—
295	C₂²⋊C₈	—	73	1	no	—
296	C₂²⋊C₈	—	73	1	no	—
297	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
298	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
299	C₄×C₈	—	73	1	no	—
300	C₄×C₈	—	73	1	no	—
301	C₄×C₈	—	73	1	no	—
302	C₄×C₈	—	73	1	no	—
303	C₄×C₈	—	73	1	no	—
304	C₄×C₈	—	73	1	no	—
305	C₄×C₈	—	73	1	no	—
306	C₄×C₈	—	73	1	no	—
307	C₄×C₈	—	73	1	no	—
308	C₄×C₈	C₂×#64408	1	1	yes	characteristic
309	#41	—	146	4	no	—
310	C₂×Q₈	—	73	1	no	—
311	C₂×D₄	—	73	1	no	—
312	C₂×D₄	—	73	1	no	—
313	C₂×D₄	#11924036	1	1	yes	characteristic
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	1	no	—
319	C₂²×C₄	—	73	1	no	—
320	C₂²×C₄	—	73	1	no	—
321	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
322	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	73	1	no	—
326	C₂×C₈	—	73	1	no	—
327	C₂×C₈	—	73	1	no	—
328	C₂×C₈	—	73	1	no	—
329	C₂×C₈	—	146	2	no	—
330	C₂×C₈	—	146	2	no	—
331	C₂×C₈	—	146	2	no	—
332	C₂×C₈	—	146	2	no	—
333	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
334	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
335	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
336	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
337	C₄⋊C₄	—	73	1	no	—
338	C₄⋊C₄	—	73	1	no	—
339	C₄⋊C₄	—	73	1	no	—
340	C₄⋊C₄	—	73	1	no	—
341	C₄⋊C₄	—	73	1	no	—
342	C₄⋊C₄	#11924036	1	1	yes	characteristic
343	C₂²⋊C₄	—	73	1	no	—
344	C₂²⋊C₄	—	73	1	no	—
345	C₂²⋊C₄	—	73	1	no	—
346	C₂²⋊C₄	—	73	1	no	—
347	C₂²⋊C₄	#11924036	1	1	yes	characteristic
348	C₂²⋊C₄	#11924036	1	1	yes	characteristic
349	C₄²	—	73	1	no	—
350	C₄²	—	73	1	no	—
351	C₄²	—	73	1	no	—
352	C₄²	—	73	1	no	—
353	C₄²	—	73	1	no	—
354	C₄²	—	73	1	no	—
355	C₄²	—	73	1	no	—
356	C₄²	—	73	1	no	—
357	C₄²	—	73	1	no	—
358	C₄²	C₂²×#64408	1	1	yes	characteristic
359	C₁₆	—	73	4	no	—
360	C₁₆	—	146	2	no	—
361	C₁₆	—	146	2	no	—
362	C₁₆	—	146	2	no	—
363	C₂³	—	73	1	no	—
364	C₂³	C₂×#11924036	1	1	yes	characteristic
365	C₂³	C₂×#11924036	1	1	yes	characteristic
366	Q₈	—	146	2	no	—
367	D₄	—	2	2	no	—
368	D₄	—	146	2	no	—
369	D₄	—	146	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	73	4	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	—	146	2	no	—
383	C₂×C₄	—	146	2	no	—
384	C₂×C₄	—	146	2	no	—
385	C₂×C₄	—	146	2	no	—
386	C₂×C₄	—	146	2	no	—
387	C₂×C₄	—	146	1	no	—
388	C₂×C₄	—	146	1	no	—
389	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
390	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
391	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
392	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
393	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	—	73	2	no	—
398	C₈	—	146	1	no	—
399	C₈	—	146	1	no	—
400	C₈	—	146	1	no	—
401	C₈	#14556678	1	2	yes	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	146	1	no	—
408	C₂²	—	146	1	no	—
409	C₂²	—	146	1	no	—
410	C₂²	#17989643	1	2	yes	—
411	C₂²	C₂²×#11924036	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	73	2	no	—
417	C₄	—	73	2	no	—
418	C₄	—	73	2	no	—
419	C₄	—	146	1	no	—
420	C₄	—	146	1	no	—
421	C₄	—	146	1	no	—
422	C₄	—	146	1	no	—
423	C₄	#41×#64408	1	1	yes	characteristic
424	C₄	C₂×#14556678	1	1	yes	characteristic
425	C₂	—	2	2	no	—
426	C₂	—	4	1	no	—
427	C₂	—	292	1	no	—
428	C₂	#22626736	1	1	yes	characteristic
429	C₂	C₂×#17989643	1	1	yes	characteristic
430	C₂	#22626896	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₈×D₄×C₇₃	C₄
prime radical	C₂×#11924027	C₈
cosocle	C₂×#10596831	C₂⁴
hypercenter	C₈×D₄	#64408
hypocenter	C₇₃	#33479
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. #22626348	C₂	semidirect
2. #22626316	C₂	semidirect
3. #22626313	C₂	semidirect
4. #22626311	C₂	semidirect
5. #22626291	C₂	semidirect
6. #22626289	C₂	semidirect
7. #22626289	C₂	semidirect
8. #22626138	C₂	semidirect
9. #22626137	C₂	semidirect
10. C₂×#17989473	C₂	semidirect
96. #11924031	#41	semidirect
165. C₂×Dic₇₃	M₃₂	semidirect
227. C₇₃	#33479	semidirect

Maximal subgroups

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

subgroup	index
#22626348	2
#22626316	2
#22626313	2
#22626311	2
#22626291	2
#22626289	2
#22626138	2
#22626137	2
C₂×#17989473	2
C₈×#11924027	2
#33479	73