Subgroups — #34030342

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	#22626314	C₂	1	2	yes	maximal, complemented
4	#22626312	C₂	1	2	yes	maximal, complemented
5	#22626290	C₂	1	1	yes	maximal, characteristic, complemented
6	#22626290	C₂	1	1	yes	maximal, characteristic, complemented
7	#22626288	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#14556666	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#14556665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14556664	C₂	1	1	yes	maximal, characteristic, complemented
11	#22618887	C₂	1	1	yes	maximal, characteristic
12	C₂×#14556666	C₂²	1	2	yes	—
13	C₂×#14556665	C₂²	1	2	yes	—
14	C₂×#14556664	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	#17989482	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	C₄×#11924031	C₂²	1	1	yes	characteristic
25	C₄×#11924031	C₂²	1	1	yes	characteristic
26	C₄×#11924031	C₂²	1	1	yes	characteristic
27	C₄×#11924031	C₂²	1	1	yes	characteristic
28	C₄×#11924028	C₄	1	1	yes	characteristic
29	#17988711	C₄	1	1	yes	characteristic
30	#17988711	C₂²	1	1	yes	characteristic
31	#17988652	C₄	1	1	yes	characteristic
32	#17988652	C₂²	1	1	yes	characteristic
33	#17988650	C₄	1	1	yes	characteristic
34	#17988650	C₄	1	1	yes	characteristic
35	#17988650	C₂²	1	1	yes	characteristic
36	#17988650	C₂²	1	1	yes	characteristic
37	#17988638	C₄	1	1	yes	characteristic
38	#17988638	C₄	1	1	yes	characteristic
39	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
42	#431×C₇₃	C₄	1	1	yes	characteristic
43	#14556666	—	2	4	no	—
44	#14556665	—	2	4	no	—
45	#14556664	—	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×#11924028	C₈	1	1	yes	characteristic
51	C₂²×#10596831	C₂×C₄	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	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
57	C₄×Dic₁₄₆	C₈	1	1	yes	characteristic
58	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
59	C₄×D₂₉₂	C₈	1	1	yes	characteristic
60	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
61	C₄×C₂²⋊D₇₃	C₈	1	1	yes	characteristic
62	C₄×C₂²⋊D₇₃	C₈	1	1	yes	characteristic
63	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
64	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
65	#14556550	C₈	1	1	yes	characteristic
66	#14556548	C₈	1	1	yes	characteristic
67	#14556548	C₈	1	1	yes	characteristic
68	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₇₃	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	#14556520	C₂×C₄	1	1	yes	characteristic
74	#14556503	C₂×C₄	1	1	yes	characteristic
75	#14556503	C₂×C₄	1	1	yes	characteristic
76	#14556503	C₂×C₄	1	1	yes	characteristic
77	#14556503	C₂×C₄	1	1	yes	characteristic
78	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
79	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
80	C₄×#10596831	C₂³	1	1	yes	characteristic
81	C₄×#10596831	C₂³	1	1	yes	characteristic
82	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
85	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
87	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
91	C₄×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	#11924028	—	2	4	no	—
98	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
99	C₂×D₂₉₂	C₂×C₈	1	1	yes	characteristic
100	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
101	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₇₃	C₂×C₈	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×#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	C₈×D₇₃	—	2	2	no	—
117	C₈×D₇₃	—	2	2	no	—
118	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
119	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
120	#11924007	C₂×C₈	1	1	yes	characteristic
121	#11924007	C₂×C₈	1	1	yes	characteristic
122	#11924007	C₂×C₈	1	1	yes	characteristic
123	#11924007	C₂×C₈	1	1	yes	characteristic
124	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
125	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
126	#11924005	C₂×C₈	1	1	yes	characteristic
127	#11924005	C₂×C₈	1	1	yes	characteristic
128	#11924005	C₂×C₈	1	1	yes	characteristic
129	#11924005	C₂×C₈	1	1	yes	characteristic
130	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
137	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
138	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
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	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic
144	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic
145	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
147	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
148	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₇₃	—	2	1	no	—
151	C₂×C₄×C₇₃	—	2	1	no	—
152	C₂×C₄×C₇₃	—	2	2	no	—
153	C₂×C₄×C₇₃	—	2	2	no	—
154	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
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	C₂²×C₈	1	1	yes	characteristic
163	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
164	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
165	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
166	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
167	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
168	D₂₉₂	—	2	2	no	—
169	C₄×D₇₃	—	2	1	no	—
170	C₄×D₇₃	—	2	1	no	—
171	C₄×D₇₃	—	2	1	no	—
172	C₄×D₇₃	—	2	1	no	—
173	C₄×D₇₃	—	2	2	no	—
174	C₄×D₇₃	—	2	2	no	—
175	C₄×D₇₃	—	2	2	no	—
176	C₄×D₇₃	M₃₂	1	4	yes	complemented
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	—	2	1	no	—
182	#10596831	—	2	1	no	—
183	#10596831	—	2	1	no	—
184	#10596831	#131	1	2	yes	—
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	C₂³×C₈	1	1	yes	characteristic
190	C₂×D₇₃	—	2	1	no	—
191	C₂×D₇₃	—	2	1	no	—
192	C₂×D₇₃	—	2	1	no	—
193	C₂×D₇₃	—	2	1	no	—
194	C₂×D₇₃	—	2	1	no	—
195	C₂×D₇₃	C₂×M₃₂	1	2	yes	—
196	C₄×C₇₃	—	2	1	no	—
197	C₄×C₇₃	—	2	1	no	—
198	C₄×C₇₃	—	2	1	no	—
199	C₄×C₇₃	C₂×M₃₂	1	2	yes	—
200	C₄×C₇₃	#504	1	2	yes	—
201	C₄×C₇₃	C₄×#41	1	1	yes	characteristic
202	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
203	Dic₇₃	—	2	1	no	—
204	Dic₇₃	—	2	1	no	—
205	Dic₇₃	—	2	1	no	—
206	Dic₇₃	—	2	1	no	—
207	Dic₇₃	—	2	1	no	—
208	Dic₇₃	C₂×M₃₂	1	2	yes	—
209	#33479	—	73	1	no	maximal, Sylow
210	C₂×C₇₃	—	4	1	no	—
211	C₂×C₇₃	C₈×#41	1	1	yes	characteristic
212	C₂×C₇₃	C₂²×M₃₂	1	1	yes	characteristic
213	C₂×C₇₃	C₂×#504	1	1	yes	characteristic
214	D₇₃	—	2	2	no	—
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	—	73	1	no	—
240	#431	—	73	1	no	—
241	#431	—	73	1	no	—
242	#431	#64408	1	1	yes	characteristic
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	—	73	1	no	—
265	C₂²×C₈	—	73	1	no	—
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	—	73	1	no	—
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	C₂×#64408	1	1	yes	characteristic
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	C₂×#64408	1	1	yes	characteristic
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	C₂×#64408	1	1	yes	characteristic
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	—	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	1	no	—
319	C₂²×C₄	—	73	1	no	—
320	C₂²×C₄	#11924036	1	1	yes	characteristic
321	C₂²×C₄	#11924036	1	1	yes	characteristic
322	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
323	C₂×C₈	—	73	1	no	—
324	C₂×C₈	—	73	1	no	—
325	C₂×C₈	—	73	1	no	—
326	C₂×C₈	—	73	1	no	—
327	C₂×C₈	—	146	2	no	—
328	C₂×C₈	—	146	2	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	—	73	1	no	—
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	—	73	1	no	—
348	C₂²⋊C₄	—	73	1	no	—
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	#11924036	1	1	yes	characteristic
356	C₄²	#11924036	1	1	yes	characteristic
357	C₄²	C₂²×#64408	1	1	yes	characteristic
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	—	73	1	no	—
365	C₂³	C₂×#11924036	1	1	yes	characteristic
366	Q₈	—	146	2	no	—
367	D₄	—	146	2	no	—
368	D₄	—	146	2	no	—
369	D₄	—	146	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	73	1	no	—
375	C₂×C₄	—	73	4	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	—	146	2	no	—
382	C₂×C₄	—	146	2	no	—
383	C₂×C₄	—	146	2	no	—
384	C₂×C₄	—	146	1	no	—
385	C₂×C₄	—	146	1	no	—
386	C₂×C₄	—	146	1	no	—
387	C₂×C₄	—	146	1	no	—
388	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
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	—	2	1	no	—
398	C₈	—	73	2	no	—
399	C₈	—	73	2	no	—
400	C₈	—	146	1	no	—
401	C₈	—	146	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	73	2	no	—
406	C₂²	—	146	1	no	—
407	C₂²	—	146	1	no	—
408	C₂²	—	146	1	no	—
409	C₂²	—	146	1	no	—
410	C₂²	—	146	1	no	—
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	—	73	2	no	—
416	C₄	—	146	1	no	—
417	C₄	—	146	1	no	—
418	C₄	—	146	1	no	—
419	C₄	—	146	1	no	—
420	C₄	—	146	1	no	—
421	C₄	#17989643	1	2	yes	—
422	C₄	#17989646	1	2	yes	—
423	C₄	#41×#64408	1	1	yes	characteristic
424	C₄	D₇₃⋊#131	1	1	yes	characteristic
425	C₂	—	4	1	no	—
426	C₂	—	292	1	no	—
427	C₂	—	146	2	no	—
428	C₂	#22626735	1	1	yes	characteristic
429	C₂	C₂×#17989643	1	1	yes	characteristic
430	C₂	C₂×#17989646	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×#64408
Fitting	#431×C₇₃	C₄
prime radical	C₂×#11924028	C₈
cosocle	C₂×#10596831	C₂⁴
hypercenter	#431	#64408
hypocenter	C₇₃	#33479
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄² ◁ #431

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. #22626314	C₂	semidirect
4. #22626312	C₂	semidirect
5. #22626290	C₂	semidirect
6. #22626290	C₂	semidirect
7. #22626288	C₂	semidirect
8. C₄×#14556666	C₂	semidirect
9. C₄×#14556665	C₂	semidirect
10. C₄×#14556664	C₂	semidirect
96. #11924031	#41	semidirect
176. C₄×D₇₃	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
#22626314	2
#22626312	2
#22626290	2
#22626288	2
C₄×#14556666	2
C₄×#14556665	2
C₄×#14556664	2
#22618887	2
#33479	73