Subgroups — #34030347

Order 18688.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626348	C₂	1	1	yes	maximal, characteristic, complemented
2	#22626345	C₂	1	1	yes	maximal, characteristic, complemented
3	#22626316	C₂	1	1	yes	maximal, characteristic, complemented
4	#22626313	C₂	1	1	yes	maximal, characteristic, complemented
5	#22626311	C₂	1	1	yes	maximal, characteristic, complemented
6	#22626309	C₂	1	1	yes	maximal, characteristic, complemented
7	#22626309	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×#11924031	C₂	1	1	yes	maximal, characteristic, complemented
9	#22626299	C₂	1	1	yes	maximal, characteristic, complemented
10	#22626297	C₂	1	1	yes	maximal, characteristic, complemented
11	#22626293	C₂	1	1	yes	maximal, characteristic, complemented
12	#22626142	C₂	1	1	yes	maximal, characteristic, complemented
13	#22626141	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#17989473	C₂	1	1	yes	maximal, characteristic, complemented
15	#22618901	C₂	1	1	yes	maximal, characteristic
16	C₂×#14556666	C₂²	1	1	yes	characteristic
17	C₂×#14556665	C₂²	1	1	yes	characteristic
18	C₂×#14556664	C₂²	1	1	yes	characteristic
19	C₂²×#11924031	C₂²	1	1	yes	characteristic
20	C₂²×#11924031	C₂²	1	1	yes	characteristic
21	C₂²×#11924031	C₂²	1	1	yes	characteristic
22	#17989508	C₂²	1	1	yes	characteristic
23	#17989508	C₂²	1	1	yes	characteristic
24	#17989508	C₂²	1	1	yes	characteristic
25	#17989508	C₂²	1	1	yes	characteristic
26	C₄⋊#11924031	C₂²	1	1	yes	characteristic
27	C₄⋊#11924031	C₂²	1	1	yes	characteristic
28	#17989482	C₂²	1	1	yes	characteristic
29	#17989482	C₂²	1	1	yes	characteristic
30	C₂²⋊#11924031	C₂²	1	1	yes	characteristic
31	C₂²⋊#11924031	C₂²	1	1	yes	characteristic
32	C₂²⋊#11924031	C₂²	1	1	yes	characteristic
33	C₂²⋊#11924031	C₂²	1	1	yes	characteristic
34	#17989476	C₂²	1	1	yes	characteristic
35	#17989476	C₂²	1	1	yes	characteristic
36	#17989476	C₂²	1	1	yes	characteristic
37	#17989475	C₂²	1	1	yes	characteristic
38	#17989473	C₂²	1	1	yes	characteristic
39	#17989473	C₂²	1	1	yes	characteristic
40	#17989473	C₂²	1	1	yes	characteristic
41	#17989473	C₂²	1	1	yes	characteristic
42	#17989473	C₂²	1	1	yes	characteristic
43	C₄×#11924031	C₂²	1	1	yes	characteristic
44	#17989117	C₄	1	1	yes	characteristic
45	#17988715	C₄	1	1	yes	characteristic
46	#17988711	C₂²	1	1	yes	characteristic
47	#17988663	C₄	1	1	yes	characteristic
48	#17988658	C₄	1	1	yes	characteristic
49	D₄×#10596831	C₂²	1	1	yes	characteristic
50	#17988650	C₂²	1	1	yes	characteristic
51	#17988650	C₂²	1	1	yes	characteristic
52	#17988647	C₄	1	1	yes	characteristic
53	#17988645	C₄	1	1	yes	characteristic
54	#17988641	C₄	1	1	yes	characteristic
55	#17988545	C₂²	1	1	yes	characteristic
56	#17988544	C₂²	1	1	yes	characteristic
57	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
58	#435×C₇₃	C₄	1	1	yes	characteristic
59	#14556666	—	2	2	no	—
60	#14556665	—	2	2	no	—
61	#14556664	—	2	2	no	—
62	C₂×#11924031	—	2	2	no	—
63	C₂×#11924031	—	2	2	no	—
64	C₂×#11924031	—	2	2	no	—
65	C₂×#11924031	C₂³	1	1	yes	characteristic
66	C₂×#11924031	C₂³	1	1	yes	characteristic
67	C₂×#11924031	C₂³	1	1	yes	characteristic
68	C₂×#11924031	C₂³	1	1	yes	characteristic
69	C₂×#11924031	C₂³	1	1	yes	characteristic
70	C₂×#11924031	C₂³	1	1	yes	characteristic
71	C₂×#11924031	C₂³	1	1	yes	characteristic
72	C₂×#11924031	C₂³	1	1	yes	characteristic
73	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
74	C₂²×#10596831	C₂³	1	1	yes	characteristic
75	C₂²×#10596831	C₂³	1	1	yes	characteristic
76	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
77	#14556586	C₈	1	1	yes	characteristic
78	#14556584	C₈	1	1	yes	characteristic
79	#14556581	C₈	1	1	yes	characteristic
80	#14556577	C₈	1	1	yes	characteristic
81	#14556575	C₈	1	1	yes	characteristic
82	#14556572	C₈	1	1	yes	characteristic
83	#14556568	C₈	1	1	yes	characteristic
84	#14556563	C₈	1	1	yes	characteristic
85	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
86	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
87	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
88	#14556550	C₂×C₄	1	1	yes	characteristic
89	#14556548	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
91	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
92	#14556520	C₂×C₄	1	1	yes	characteristic
93	#14556520	C₂×C₄	1	1	yes	characteristic
94	#14556520	C₂×C₄	1	1	yes	characteristic
95	#14556520	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
97	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
98	#14556503	C₂×C₄	1	1	yes	characteristic
99	#14556503	C₂×C₄	1	1	yes	characteristic
100	#14556501	C₂×C₄	1	1	yes	characteristic
101	#14556501	C₂×C₄	1	1	yes	characteristic
102	#14556501	C₂×C₄	1	1	yes	characteristic
103	C₄×#10596831	C₂³	1	1	yes	characteristic
104	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
105	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
106	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
107	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
108	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
110	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
111	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
112	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
115	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
116	#11924031	—	2	1	no	—
117	#11924031	—	2	1	no	—
118	#11924031	—	2	1	no	—
119	#11924031	—	2	1	no	—
120	#11924031	—	2	1	no	—
121	#11924031	—	2	1	no	—
122	#11924031	#41	1	2	yes	—
123	#11924031	#41	1	2	yes	—
124	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
125	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
126	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
127	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
128	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
129	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
130	#11924011	—	2	2	no	—
131	C₂×#10596831	—	2	1	no	—
132	C₂×#10596831	—	2	1	no	—
133	C₂×#10596831	—	2	1	no	—
134	C₂×#10596831	—	2	1	no	—
135	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
136	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
137	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
138	C₂×#10596831	C₂⁴	1	1	yes	characteristic
139	C₈×D₇₃	—	2	1	no	—
140	C₈×D₇₃	—	2	1	no	—
141	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
142	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
143	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
144	#11924007	C₂×C₈	1	1	yes	characteristic
145	#11924007	C₂×C₈	1	1	yes	characteristic
146	#11924007	C₂×C₈	1	1	yes	characteristic
147	#11924007	C₂×C₈	1	1	yes	characteristic
148	#11924007	C₂×C₈	1	1	yes	characteristic
149	#11924007	C₂×C₈	1	1	yes	characteristic
150	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
151	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
152	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
153	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
154	#11924005	C₂×C₈	1	1	yes	characteristic
155	#11924005	C₂×C₈	1	1	yes	characteristic
156	#11924005	C₂×C₈	1	1	yes	characteristic
157	#11924005	C₂×C₈	1	1	yes	characteristic
158	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
159	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
160	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
161	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
162	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×D₄×C₇₃	C₂×C₈	1	1	yes	characteristic
164	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
166	M₁₆×C₇₃	—	2	2	no	—
167	C₂×C₈×C₇₃	—	2	2	no	—
168	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
172	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
173	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
174	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
175	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
176	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
177	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
178	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
179	D₄×C₇₃	—	2	2	no	—
180	C₂×C₄×C₇₃	—	2	1	no	—
181	C₂×C₄×C₇₃	—	2	1	no	—
182	C₂×C₄×C₇₃	—	2	1	no	—
183	C₂×C₄×C₇₃	—	2	1	no	—
184	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
185	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
186	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
187	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
188	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
189	C₂²⋊D₇₃	—	2	2	no	—
190	C₂²⋊D₇₃	—	2	2	no	—
191	C₂×Dic₇₃	—	2	2	no	—
192	C₂×Dic₇₃	—	2	2	no	—
193	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
194	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
195	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
196	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
197	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
198	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
199	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
200	C₄×D₇₃	—	2	1	no	—
201	C₄×D₇₃	—	2	1	no	—
202	Dic₁₄₆	—	2	2	no	—
203	C₈×C₇₃	—	2	1	no	—
204	C₈×C₇₃	—	2	1	no	—
205	C₈×C₇₃	—	2	1	no	—
206	C₈×C₇₃	#131	1	2	yes	—
207	#10596831	—	2	1	no	—
208	#10596831	—	2	1	no	—
209	#10596831	—	2	1	no	—
210	#10596831	C₂×#41	1	1	yes	characteristic
211	#10596831	C₂×#41	1	1	yes	characteristic
212	C₂²×C₇₃	—	2	1	no	—
213	C₂²×C₇₃	—	2	1	no	—
214	C₂²×C₇₃	—	2	1	no	—
215	C₂²×C₇₃	—	2	1	no	—
216	C₂²×C₇₃	—	2	1	no	—
217	C₂²×C₇₃	#504	1	2	yes	—
218	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
219	C₂×D₇₃	—	2	1	no	—
220	C₂×D₇₃	—	2	1	no	—
221	C₂×D₇₃	—	2	1	no	—
222	C₄×C₇₃	—	2	1	no	—
223	C₄×C₇₃	—	2	1	no	—
224	C₄×C₇₃	—	2	1	no	—
225	C₄×C₇₃	—	2	1	no	—
226	C₄×C₇₃	C₄×#41	1	1	yes	characteristic
227	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
228	Dic₇₃	—	2	1	no	—
229	Dic₇₃	—	2	1	no	—
230	Dic₇₃	—	2	1	no	—
231	Dic₇₃	—	2	1	no	—
232	Dic₇₃	—	2	1	no	—
233	Dic₇₃	—	2	1	no	—
234	Dic₇₃	#504	1	2	yes	—
235	#33480	—	73	1	no	maximal, Sylow
236	C₂×C₇₃	—	2	2	no	—
237	C₂×C₇₃	—	4	1	no	—
238	C₂×C₇₃	C₈×#41	1	1	yes	characteristic
239	C₂×C₇₃	C₂×#504	1	1	yes	characteristic
240	C₂×C₇₃	C₂×#504	1	1	yes	characteristic
241	D₇₃	—	4	1	no	—
242	#2966	—	73	1	no	—
243	#2183	—	73	1	no	—
244	Q₈×C₁₆	—	73	1	no	—
245	#2169	—	73	1	no	—
246	#2168	—	73	1	no	—
247	#2168	—	73	1	no	—
248	D₄×C₁₆	—	73	1	no	—
249	D₄×C₁₆	—	73	1	no	—
250	D₄×C₁₆	—	73	1	no	—
251	#2164	—	73	1	no	—
252	#2164	—	73	1	no	—
253	#2163	—	73	1	no	—
254	#2108	—	73	1	no	—
255	#2108	—	73	1	no	—
256	C₂×C₄×C₁₆	—	73	1	no	—
257	C₇₃	#33480	1	1	yes	characteristic, complemented, Sylow
258	#529	—	73	1	no	—
259	C₂×M₃₂	—	73	1	no	—
260	C₂×M₃₂	—	73	1	no	—
261	C₂²×C₁₆	—	73	1	no	—
262	C₂²×C₁₆	—	73	1	no	—
263	C₂²×C₁₆	—	73	1	no	—
264	C₂²×C₁₆	—	73	1	no	—
265	#446	—	73	1	no	—
266	C₈×Q₈	—	73	1	no	—
267	#436	—	73	1	no	—
268	#435	—	73	1	no	—
269	#435	#64408	1	1	yes	characteristic
270	C₈×D₄	—	73	1	no	—
271	C₈×D₄	—	73	1	no	—
272	C₈×D₄	—	73	1	no	—
273	#433	—	73	1	no	—
274	#433	—	73	1	no	—
275	#432	—	73	1	no	—
276	#405	—	73	1	no	—
277	#405	—	73	1	no	—
278	C₂×C₄×C₈	—	73	1	no	—
279	C₄⋊C₁₆	—	73	1	no	—
280	C₄⋊C₁₆	—	73	1	no	—
281	C₄⋊C₁₆	—	73	1	no	—
282	C₄⋊C₁₆	—	73	1	no	—
283	C₄⋊C₁₆	—	73	1	no	—
284	C₄⋊C₁₆	—	73	1	no	—
285	C₂²⋊C₁₆	—	73	1	no	—
286	C₂²⋊C₁₆	—	73	1	no	—
287	C₂²⋊C₁₆	—	73	1	no	—
288	C₂²⋊C₁₆	—	73	1	no	—
289	C₂²⋊C₁₆	—	73	1	no	—
290	C₂²⋊C₁₆	—	73	1	no	—
291	#346	—	73	1	no	—
292	#346	—	73	1	no	—
293	#346	—	73	1	no	—
294	#346	—	73	1	no	—
295	C₄×C₁₆	—	73	1	no	—
296	C₄×C₁₆	—	73	1	no	—
297	C₄×C₁₆	—	73	1	no	—
298	C₄×C₁₆	—	73	1	no	—
299	C₄×C₁₆	—	73	1	no	—
300	C₄×C₁₆	—	73	1	no	—
301	C₂×M₁₆	—	73	1	no	—
302	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
303	C₂²×C₈	—	73	1	no	—
304	C₂²×C₈	—	73	1	no	—
305	C₂²×C₈	—	73	1	no	—
306	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
307	#126	—	73	1	no	—
308	#126	—	73	1	no	—
309	#125	—	73	1	no	—
310	#124	—	73	1	no	—
311	#123	—	73	1	no	—
312	#123	—	73	1	no	—
313	C₂²⋊Q₈	—	73	1	no	—
314	#121	—	73	1	no	—
315	C₄×Q₈	—	73	1	no	—
316	C₄×D₄	—	73	1	no	—
317	C₄×D₄	—	73	1	no	—
318	C₄×D₄	C₂×#64408	1	1	yes	characteristic
319	#117	—	73	1	no	—
320	#117	—	73	1	no	—
321	C₂×C₄²	—	73	1	no	—
322	M₃₂	—	146	2	no	—
323	M₃₂	—	146	2	no	—
324	C₂×C₁₆	—	73	1	no	—
325	C₂×C₁₆	—	73	1	no	—
326	C₂×C₁₆	—	73	1	no	—
327	C₂×C₁₆	—	73	1	no	—
328	C₂×C₁₆	—	73	1	no	—
329	C₂×C₁₆	—	73	1	no	—
330	C₂×C₁₆	—	73	1	no	—
331	C₂×C₁₆	—	73	1	no	—
332	C₂×C₁₆	—	146	2	no	—
333	C₂×C₁₆	—	146	2	no	—
334	C₂×C₁₆	—	146	2	no	—
335	C₂×C₁₆	—	146	2	no	—
336	C₄⋊C₈	—	73	1	no	—
337	C₄⋊C₈	—	73	1	no	—
338	C₄⋊C₈	—	73	1	no	—
339	C₄⋊C₈	—	73	1	no	—
340	C₄⋊C₈	—	73	1	no	—
341	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic
342	C₂²⋊C₈	—	73	1	no	—
343	C₂²⋊C₈	—	73	1	no	—
344	C₂²⋊C₈	—	73	1	no	—
345	C₂²⋊C₈	—	73	1	no	—
346	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
347	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
348	#97	—	73	1	no	—
349	#97	—	73	1	no	—
350	#97	—	73	1	no	—
351	#97	C₂×#64408	1	1	yes	characteristic
352	C₄×C₈	—	73	1	no	—
353	C₄×C₈	—	73	1	no	—
354	C₄×C₈	—	73	1	no	—
355	C₄×C₈	—	73	1	no	—
356	C₄×C₈	—	73	1	no	—
357	C₄×C₈	—	73	1	no	—
358	C₂×Q₈	—	73	1	no	—
359	C₂×D₄	—	73	1	no	—
360	C₂×D₄	—	73	1	no	—
361	C₂×D₄	#11924036	1	1	yes	characteristic
362	C₂²×C₄	—	73	1	no	—
363	C₂²×C₄	—	73	1	no	—
364	C₂²×C₄	—	73	1	no	—
365	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
366	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
367	M₁₆	—	2	2	no	—
368	M₁₆	—	146	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	73	1	no	—
371	C₂×C₈	—	73	1	no	—
372	C₂×C₈	—	73	1	no	—
373	C₂×C₈	—	73	1	no	—
374	C₂×C₈	—	146	1	no	—
375	C₂×C₈	—	146	1	no	—
376	C₂×C₈	—	146	1	no	—
377	C₂×C₈	—	146	1	no	—
378	C₂×C₈	—	146	1	no	—
379	C₂×C₈	—	146	1	no	—
380	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
381	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
382	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
383	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
384	C₄⋊C₄	—	73	1	no	—
385	C₄⋊C₄	—	73	1	no	—
386	C₄⋊C₄	—	73	1	no	—
387	C₄⋊C₄	—	73	1	no	—
388	C₄⋊C₄	—	73	1	no	—
389	C₄⋊C₄	—	73	1	no	—
390	C₄⋊C₄	—	73	1	no	—
391	C₄⋊C₄	—	73	1	no	—
392	C₄⋊C₄	—	73	1	no	—
393	C₄⋊C₄	#11924036	1	1	yes	characteristic
394	C₂²⋊C₄	—	73	1	no	—
395	C₂²⋊C₄	—	73	1	no	—
396	C₂²⋊C₄	—	73	1	no	—
397	C₂²⋊C₄	—	73	1	no	—
398	C₂²⋊C₄	—	73	1	no	—
399	C₂²⋊C₄	—	73	1	no	—
400	C₂²⋊C₄	—	73	1	no	—
401	C₂²⋊C₄	—	73	1	no	—
402	C₂²⋊C₄	#11924036	1	1	yes	characteristic
403	C₂²⋊C₄	#11924036	1	1	yes	characteristic
404	C₄²	—	73	1	no	—
405	C₄²	—	73	1	no	—
406	C₄²	—	73	1	no	—
407	C₄²	—	73	1	no	—
408	C₄²	—	73	1	no	—
409	C₄²	C₂²×#64408	1	1	yes	characteristic
410	C₁₆	—	73	2	no	—
411	C₁₆	—	73	2	no	—
412	C₁₆	—	146	1	no	—
413	C₁₆	—	146	1	no	—
414	C₁₆	—	146	1	no	—
415	C₁₆	—	146	1	no	—
416	C₁₆	—	146	1	no	—
417	C₁₆	—	146	1	no	—
418	C₂³	—	73	1	no	—
419	C₂³	C₂×#11924036	1	1	yes	characteristic
420	C₂³	C₂×#11924036	1	1	yes	characteristic
421	Q₈	—	146	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	146	2	no	—
424	D₄	—	146	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	73	1	no	—
430	C₂×C₄	—	73	1	no	—
431	C₂×C₄	—	73	1	no	—
432	C₂×C₄	—	73	1	no	—
433	C₂×C₄	—	73	1	no	—
434	C₂×C₄	—	73	1	no	—
435	C₂×C₄	—	73	1	no	—
436	C₂×C₄	—	146	2	no	—
437	C₂×C₄	—	146	2	no	—
438	C₂×C₄	—	146	1	no	—
439	C₂×C₄	—	146	1	no	—
440	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
441	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
442	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
443	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
444	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	73	1	no	—
449	C₈	—	73	1	no	—
450	C₈	—	146	1	no	—
451	C₈	—	146	1	no	—
452	C₈	—	146	1	no	—
453	C₈	#14556678	1	2	yes	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	146	1	no	—
460	C₂²	—	146	1	no	—
461	C₂²	—	146	1	no	—
462	C₂²	#17989646	1	2	yes	—
463	C₂²	C₂²×#11924036	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	73	2	no	—
469	C₄	—	146	1	no	—
470	C₄	—	146	1	no	—
471	C₄	—	146	1	no	—
472	C₄	—	146	1	no	—
473	C₄	—	146	1	no	—
474	C₄	—	146	1	no	—
475	C₄	#41×#64408	1	1	yes	characteristic
476	C₄	C₂×#14556678	1	1	yes	characteristic
477	C₂	—	2	2	no	—
478	C₂	—	4	1	no	—
479	C₂	—	292	1	no	—
480	C₂	#22626736	1	1	yes	characteristic
481	C₂	#22626896	1	1	yes	characteristic
482	C₂	C₂×#17989646	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂³×C₈
Fitting	#435×C₇₃	C₄
prime radical	#14556563	C₈
cosocle	C₂×#10596831	C₂⁴
hypercenter	#435	#64408
hypocenter	C₇₃	#33480
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. #22626348	C₂	semidirect
2. #22626345	C₂	semidirect
3. #22626316	C₂	semidirect
4. #22626313	C₂	semidirect
5. #22626311	C₂	semidirect
6. #22626309	C₂	semidirect
7. #22626309	C₂	semidirect
8. D₄×#11924031	C₂	semidirect
9. #22626299	C₂	semidirect
10. #22626297	C₂	semidirect
11. #22626293	C₂	semidirect
12. #22626142	C₂	semidirect
13. #22626141	C₂	semidirect
14. C₂×#17989473	C₂	semidirect
257. C₇₃	#33480	semidirect

Maximal subgroups

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

subgroup	index
#22626348	2
#22626345	2
#22626316	2
#22626313	2
#22626311	2
#22626309	2
D₄×#11924031	2
#22626299	2
#22626297	2
#22626293	2
#22626142	2
#22626141	2
C₂×#17989473	2
#22618901	2
#33480	73