Subgroups — #34030383

Order 18688.

618 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626314	C₂	1	2	yes	maximal, complemented
2	#22626313	C₂	1	2	yes	maximal, complemented
3	#22626312	C₂	1	2	yes	maximal, complemented
4	#22626311	C₂	1	2	yes	maximal, complemented
5	#22626295	C₂	1	1	yes	maximal, characteristic, complemented
6	#22626294	C₂	1	1	yes	maximal, characteristic, complemented
7	#22626160	C₂	1	1	yes	maximal, characteristic, complemented
8	#22626159	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#17989482	C₂	1	1	yes	maximal, characteristic, complemented
10	#22626156	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₄×D₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#14556666	C₂²	1	2	yes	complemented
13	C₂×#14556665	C₂²	1	2	yes	complemented
14	C₂×#14556664	C₂²	1	2	yes	complemented
15	C₂²×#11924031	C₂²	1	2	yes	complemented
16	#17989508	C₂²	1	2	yes	complemented
17	C₄⋊#11924031	C₂²	1	2	yes	complemented
18	#17989482	C₂²	1	1	yes	characteristic
19	#17989482	C₂²	1	1	yes	characteristic
20	#17989482	C₂²	1	1	yes	characteristic
21	#17989482	C₂²	1	1	yes	characteristic
22	#17989482	C₂²	1	2	yes	complemented
23	#17989482	C₂²	1	2	yes	complemented
24	C₂²⋊#11924031	C₂²	1	2	yes	complemented
25	C₂²⋊#11924031	C₂²	1	2	yes	complemented
26	#17989476	C₂²	1	2	yes	complemented
27	#17989475	C₂²	1	2	yes	complemented
28	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
29	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
30	C₄×D₄×D₇₃	C₄	1	1	yes	characteristic
31	C₈×D₂₉₂	C₄	1	1	yes	characteristic
32	D₄×#10596831	C₂²	1	1	yes	characteristic
33	#17988652	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
35	C₈×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
36	#17988650	C₂²	1	1	yes	characteristic
37	#17988650	C₂²	1	1	yes	characteristic
38	C₄⋊C₈×D₇₃	C₄	1	1	yes	characteristic
39	C₂²⋊C₈×D₇₃	C₄	1	1	yes	characteristic
40	C₂²⋊C₈×D₇₃	C₄	1	1	yes	characteristic
41	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₇₃	C₄	1	1	yes	characteristic
43	#14556666	—	4	2	no	—
44	#14556665	—	4	2	no	—
45	#14556664	—	4	2	no	—
46	C₂×#11924031	—	4	2	no	—
47	C₂×#11924031	C₂³	1	2	yes	—
48	C₂×#11924031	C₂³	1	2	yes	—
49	C₂×#11924031	C₂³	1	2	yes	—
50	C₂×#11924031	C₂³	1	2	yes	—
51	C₂×D₄×D₇₃	C₈	1	1	yes	characteristic
52	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×#10596831	C₂³	1	1	yes	characteristic
55	C₂²×#10596831	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₇₃	—	4	2	no	—
57	C₂×C₈×D₇₃	—	4	2	no	—
58	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
64	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
65	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
66	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
67	D₄×Dic₇₃	C₈	1	1	yes	characteristic
68	#14556553	C₈	1	1	yes	characteristic
69	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
70	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
71	#14556551	C₈	1	1	yes	characteristic
72	#14556551	C₈	1	1	yes	characteristic
73	C₄⋊C₄×D₇₃	C₈	1	1	yes	characteristic
74	C₂²⋊C₄×D₇₃	C₈	1	1	yes	characteristic
75	C₂²⋊C₄×D₇₃	C₈	1	1	yes	characteristic
76	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
77	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
78	#14556520	C₂×C₄	1	1	yes	characteristic
79	#14556520	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
82	#14556503	C₂×C₄	1	1	yes	characteristic
83	#14556503	C₂×C₄	1	1	yes	characteristic
84	#14556503	C₂×C₄	1	1	yes	characteristic
85	#14556503	C₂×C₄	1	1	yes	characteristic
86	C₄×#10596831	C₂³	1	1	yes	characteristic
87	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₇₃	C₂³	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×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
92	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
96	#11924031	—	2	2	no	—
97	#11924031	—	2	2	no	—
98	#11924031	—	2	2	no	—
99	#11924031	—	2	2	no	—
100	C₂³×D₇₃	C₂×C₈	1	1	yes	characteristic
101	C₂³×D₇₃	C₂×C₈	1	1	yes	characteristic
102	C₂×D₂₉₂	C₂×C₈	1	1	yes	characteristic
103	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
104	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
105	D₄×D₇₃	—	2	4	no	—
106	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
107	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
108	C₂×C₄×D₇₃	—	4	1	no	—
109	C₂×C₄×D₇₃	—	4	1	no	—
110	C₂×C₄×D₇₃	—	4	1	no	—
111	C₂×C₄×D₇₃	—	4	1	no	—
112	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
113	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
114	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
115	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
116	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
117	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
118	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×#10596831	—	2	2	no	—
122	C₂×#10596831	—	2	2	no	—
123	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
124	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
125	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
126	C₂×#10596831	C₂⁴	1	1	yes	characteristic
127	C₈×D₇₃	—	2	2	no	—
128	C₈×D₇₃	—	2	2	no	—
129	C₈×D₇₃	—	2	2	no	—
130	C₈×D₇₃	—	4	1	no	—
131	C₈×D₇₃	—	4	1	no	—
132	C₈×D₇₃	—	4	1	no	—
133	C₈×D₇₃	—	4	1	no	—
134	C₈×D₇₃	—	4	1	no	—
135	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
136	#11924007	C₂×C₈	1	1	yes	characteristic
137	#11924007	C₂×C₈	1	1	yes	characteristic
138	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
139	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
140	#11924005	C₂×C₈	1	1	yes	characteristic
141	#11924005	C₂×C₈	1	1	yes	characteristic
142	#11924005	C₂×C₈	1	1	yes	characteristic
143	#11924005	C₂×C₈	1	1	yes	characteristic
144	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
145	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
146	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₄×C₇₃	C₂×C₈	1	1	yes	characteristic
148	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₇₃	—	4	1	no	—
151	C₂×C₈×C₇₃	—	4	1	no	—
152	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
156	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
157	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
158	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
159	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
160	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
161	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
162	C₂²×D₇₃	—	2	2	no	—
163	C₂²×D₇₃	—	4	1	no	—
164	C₂²×D₇₃	—	4	1	no	—
165	C₂²×D₇₃	—	4	1	no	—
166	C₂²×D₇₃	—	4	1	no	—
167	C₂²×D₇₃	M₃₂	1	4	yes	complemented
168	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
169	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
170	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
171	D₄×C₇₃	—	2	2	no	—
172	C₂×C₄×C₇₃	—	2	1	no	—
173	C₂×C₄×C₇₃	—	2	1	no	—
174	C₂×C₄×C₇₃	—	2	1	no	—
175	C₂×C₄×C₇₃	—	2	1	no	—
176	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
177	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
181	C₂²⋊D₇₃	—	2	2	no	—
182	C₂²⋊D₇₃	—	2	2	no	—
183	C₂×Dic₇₃	—	4	1	no	—
184	C₂×Dic₇₃	—	4	1	no	—
185	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
186	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
187	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
188	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
189	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
190	D₂₉₂	—	2	2	no	—
191	C₄×D₇₃	—	2	2	no	—
192	C₄×D₇₃	—	2	1	no	—
193	C₄×D₇₃	—	2	1	no	—
194	C₄×D₇₃	—	2	1	no	—
195	C₄×D₇₃	—	2	1	no	—
196	C₄×D₇₃	—	2	1	no	—
197	C₄×D₇₃	—	2	1	no	—
198	C₄×D₇₃	—	4	1	no	—
199	C₄×D₇₃	—	4	1	no	—
200	C₄×D₇₃	—	4	1	no	—
201	C₄×D₇₃	—	4	1	no	—
202	C₄×D₇₃	—	4	1	no	—
203	C₈×C₇₃	—	2	1	no	—
204	C₈×C₇₃	—	2	1	no	—
205	C₈×C₇₃	—	2	1	no	—
206	C₈×C₇₃	—	2	1	no	—
207	#10596831	—	2	1	no	—
208	#10596831	—	2	1	no	—
209	#10596831	—	2	1	no	—
210	#10596831	H(5,𝔽₂)	1	2	yes	—
211	C₂²×C₇₃	—	2	1	no	—
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	C₂×M₃₂	1	2	yes	—
217	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
218	C₂×D₇₃	—	2	1	no	—
219	C₂×D₇₃	—	2	1	no	—
220	C₂×D₇₃	—	2	1	no	—
221	C₂×D₇₃	—	2	1	no	—
222	C₂×D₇₃	—	2	1	no	—
223	C₂×D₇₃	—	2	1	no	—
224	C₂×D₇₃	—	2	1	no	—
225	C₂×D₇₃	—	4	4	no	—
226	C₂×D₇₃	—	4	4	no	—
227	C₂×D₇₃	C₂×M₃₂	1	2	yes	—
228	C₂×D₇₃	C₂×M₃₂	1	2	yes	—
229	C₄×C₇₃	—	2	1	no	—
230	C₄×C₇₃	—	2	1	no	—
231	C₄×C₇₃	—	2	1	no	—
232	C₄×C₇₃	—	2	1	no	—
233	C₄×C₇₃	#518	1	1	yes	characteristic
234	C₄×C₇₃	#568	1	1	yes	characteristic
235	Dic₇₃	—	2	1	no	—
236	Dic₇₃	—	2	1	no	—
237	Dic₇₃	—	2	1	no	—
238	Dic₇₃	—	2	1	no	—
239	Dic₇₃	—	2	1	no	—
240	#33487	—	73	1	no	maximal, Sylow
241	C₂×C₇₃	—	2	2	no	—
242	C₂×C₇₃	—	4	1	no	—
243	C₂×C₇₃	#2972	1	1	yes	characteristic
244	C₂×C₇₃	C₂²×M₃₂	1	1	yes	characteristic
245	C₂×C₇₃	#3407	1	1	yes	characteristic
246	D₇₃	—	2	2	no	—
247	D₇₃	—	2	2	no	—
248	D₇₃	—	4	1	no	—
249	C₂×C₈×D₄	—	73	1	no	—
250	#2168	—	73	2	no	—
251	#2168	—	73	2	no	—
252	#2168	—	73	2	no	—
253	#2168	—	73	2	no	—
254	#2163	—	73	1	no	—
255	#2163	—	73	1	no	—
256	#2112	—	73	1	no	—
257	#2112	—	73	1	no	—
258	C₂×C₂²⋊C₁₆	—	73	1	no	—
259	C₂×C₂²⋊C₁₆	—	73	1	no	—
260	C₇₃	#33487	1	1	yes	characteristic, complemented, Sylow
261	C₂³×C₈	—	73	1	no	—
262	C₂³×C₈	—	73	1	no	—
263	C₂×C₄×D₄	—	73	1	no	—
264	C₂×M₃₂	—	73	2	no	—
265	C₂×M₃₂	—	73	2	no	—
266	C₂²×C₁₆	—	73	2	no	—
267	C₂²×C₁₆	—	73	2	no	—
268	C₈×D₄	—	73	1	no	—
269	C₈×D₄	—	73	1	no	—
270	C₈×D₄	—	73	1	no	—
271	C₈×D₄	—	73	1	no	—
272	C₈×D₄	—	73	1	no	—
273	C₈×D₄	—	73	1	no	—
274	C₈×D₄	—	73	1	no	—
275	C₈×D₄	#64408	1	1	yes	characteristic
276	C₂×C₄⋊C₈	—	73	1	no	—
277	C₂×C₂²⋊C₈	—	73	1	no	—
278	C₂×C₂²⋊C₈	—	73	1	no	—
279	C₂×C₄×C₈	—	73	1	no	—
280	C₄⋊C₁₆	—	73	2	no	—
281	C₄⋊C₁₆	—	73	2	no	—
282	C₂²⋊C₁₆	—	73	1	no	—
283	C₂²⋊C₁₆	—	73	1	no	—
284	C₂²⋊C₁₆	—	73	1	no	—
285	C₂²⋊C₁₆	—	73	1	no	—
286	C₂²⋊C₁₆	—	73	2	no	—
287	C₂²⋊C₁₆	—	73	2	no	—
288	C₂²⋊C₁₆	—	73	2	no	—
289	C₂²⋊C₁₆	—	73	2	no	—
290	#346	—	73	2	no	—
291	#346	—	73	2	no	—
292	C₂²×D₄	—	73	1	no	—
293	C₂³×C₄	—	73	1	no	—
294	C₂³×C₄	—	73	1	no	—
295	C₂²×C₈	—	292	2	no	—
296	C₂²×C₈	—	292	2	no	—
297	C₂²×C₈	—	73	1	no	—
298	C₂²×C₈	—	73	1	no	—
299	C₂²×C₈	—	73	1	no	—
300	C₂²×C₈	—	73	1	no	—
301	C₂²×C₈	—	73	1	no	—
302	C₂²×C₈	—	73	1	no	—
303	C₂²×C₈	—	73	1	no	—
304	C₂²×C₈	—	73	1	no	—
305	C₂²×C₈	—	73	1	no	—
306	C₂²×C₈	—	73	1	no	—
307	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
308	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
309	C₄×D₄	—	73	1	no	—
310	C₄×D₄	—	73	1	no	—
311	C₄×D₄	—	73	1	no	—
312	C₄×D₄	—	73	1	no	—
313	C₄×D₄	—	73	1	no	—
314	C₄×D₄	—	73	1	no	—
315	C₄×D₄	—	73	1	no	—
316	C₄×D₄	C₂×#64408	1	1	yes	characteristic
317	C₂×C₄⋊C₄	—	73	1	no	—
318	C₂×C₂²⋊C₄	—	73	1	no	—
319	C₂×C₂²⋊C₄	—	73	1	no	—
320	C₂×C₄²	—	73	1	no	—
321	M₃₂	—	292	2	no	—
322	M₃₂	—	292	2	no	—
323	C₂×C₁₆	—	292	2	no	—
324	C₂×C₁₆	—	292	2	no	—
325	C₂×C₁₆	—	73	2	no	—
326	C₂×C₁₆	—	73	2	no	—
327	C₂×C₁₆	—	73	2	no	—
328	C₂×C₁₆	—	73	2	no	—
329	C₄⋊C₈	—	73	1	no	—
330	C₄⋊C₈	—	73	1	no	—
331	C₄⋊C₈	—	73	1	no	—
332	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic
333	C₂²⋊C₈	—	73	1	no	—
334	C₂²⋊C₈	—	73	1	no	—
335	C₂²⋊C₈	—	73	1	no	—
336	C₂²⋊C₈	—	73	1	no	—
337	C₂²⋊C₈	—	73	1	no	—
338	C₂²⋊C₈	—	73	1	no	—
339	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
340	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
341	C₄×C₈	—	73	1	no	—
342	C₄×C₈	—	73	1	no	—
343	C₄×C₈	—	73	1	no	—
344	C₄×C₈	C₂×#64408	1	1	yes	characteristic
345	C₂⁴	—	73	1	no	—
346	C₂⁴	—	73	1	no	—
347	C₂×D₄	—	73	1	no	—
348	C₂×D₄	—	73	1	no	—
349	C₂×D₄	—	73	1	no	—
350	C₂×D₄	—	146	4	no	—
351	C₂×D₄	#11924036	1	1	yes	characteristic
352	C₂²×C₄	—	292	1	no	—
353	C₂²×C₄	—	292	1	no	—
354	C₂²×C₄	—	292	1	no	—
355	C₂²×C₄	—	292	1	no	—
356	C₂²×C₄	—	73	1	no	—
357	C₂²×C₄	—	73	1	no	—
358	C₂²×C₄	—	73	1	no	—
359	C₂²×C₄	—	73	1	no	—
360	C₂²×C₄	—	73	1	no	—
361	C₂²×C₄	—	73	1	no	—
362	C₂²×C₄	—	73	1	no	—
363	C₂²×C₄	—	73	1	no	—
364	C₂²×C₄	—	73	1	no	—
365	C₂²×C₄	—	73	1	no	—
366	C₂²×C₄	—	73	1	no	—
367	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
368	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	292	1	no	—
372	C₂×C₈	—	292	1	no	—
373	C₂×C₈	—	292	1	no	—
374	C₂×C₈	—	292	1	no	—
375	C₂×C₈	—	292	1	no	—
376	C₂×C₈	—	73	1	no	—
377	C₂×C₈	—	73	1	no	—
378	C₂×C₈	—	73	1	no	—
379	C₂×C₈	—	73	1	no	—
380	C₂×C₈	—	146	2	no	—
381	C₂×C₈	—	146	2	no	—
382	C₂×C₈	—	146	2	no	—
383	C₂×C₈	—	146	2	no	—
384	C₂×C₈	—	146	2	no	—
385	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
386	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
387	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
388	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
389	C₄⋊C₄	—	73	1	no	—
390	C₄⋊C₄	—	73	1	no	—
391	C₄⋊C₄	—	73	1	no	—
392	C₄⋊C₄	#11924036	1	1	yes	characteristic
393	C₂²⋊C₄	—	73	1	no	—
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	#11924036	1	1	yes	characteristic
400	C₂²⋊C₄	#11924036	1	1	yes	characteristic
401	C₄²	—	73	1	no	—
402	C₄²	—	73	1	no	—
403	C₄²	—	73	1	no	—
404	C₄²	C₂²×#64408	1	1	yes	characteristic
405	C₁₆	—	146	2	no	—
406	C₁₆	—	146	2	no	—
407	C₁₆	—	146	2	no	—
408	C₁₆	—	146	2	no	—
409	C₂³	—	292	1	no	—
410	C₂³	—	292	1	no	—
411	C₂³	—	292	1	no	—
412	C₂³	—	292	1	no	—
413	C₂³	—	73	4	no	—
414	C₂³	—	73	1	no	—
415	C₂³	—	73	1	no	—
416	C₂³	—	73	1	no	—
417	C₂³	—	146	2	no	—
418	C₂³	C₂×#11924036	1	1	yes	characteristic
419	C₂³	C₂×#11924036	1	1	yes	characteristic
420	D₄	—	2	2	no	—
421	D₄	—	146	2	no	—
422	D₄	—	146	2	no	—
423	D₄	—	146	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	292	1	no	—
429	C₂×C₄	—	292	1	no	—
430	C₂×C₄	—	292	1	no	—
431	C₂×C₄	—	292	1	no	—
432	C₂×C₄	—	292	1	no	—
433	C₂×C₄	—	292	1	no	—
434	C₂×C₄	—	292	1	no	—
435	C₂×C₄	—	73	1	no	—
436	C₂×C₄	—	73	1	no	—
437	C₂×C₄	—	73	1	no	—
438	C₂×C₄	—	73	1	no	—
439	C₂×C₄	—	73	1	no	—
440	C₂×C₄	—	146	2	no	—
441	C₂×C₄	—	146	1	no	—
442	C₂×C₄	—	146	1	no	—
443	C₂×C₄	—	146	1	no	—
444	C₂×C₄	—	146	1	no	—
445	C₂×C₄	—	146	1	no	—
446	C₂×C₄	—	146	1	no	—
447	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
448	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
449	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
450	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
451	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
452	C₈	—	2	1	no	—
453	C₈	—	2	1	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	73	2	no	—
457	C₈	—	146	1	no	—
458	C₈	—	146	1	no	—
459	C₈	—	146	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	292	4	no	—
466	C₂²	—	292	4	no	—
467	C₂²	—	73	2	no	—
468	C₂²	—	73	2	no	—
469	C₂²	—	146	1	no	—
470	C₂²	—	146	1	no	—
471	C₂²	—	146	1	no	—
472	C₂²	—	146	1	no	—
473	C₂²	—	146	1	no	—
474	C₂²	—	146	1	no	—
475	C₂²	—	146	1	no	—
476	C₂²	#17989643	1	2	yes	—
477	C₂²	C₂²×#11924036	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	146	1	no	—
483	C₄	—	146	1	no	—
484	C₄	—	146	1	no	—
485	C₄	—	146	1	no	—
486	C₄	—	146	1	no	—
487	C₄	#17989654	1	1	yes	characteristic
488	C₄	#17989666	1	1	yes	characteristic
489	C₂	—	2	2	no	—
490	C₂	—	4	1	no	—
491	C₂	—	292	1	no	—
492	C₂	—	146	2	no	—
493	C₂	—	146	2	no	—
494	C₂	#22626779	1	1	yes	characteristic
495	C₂	C₂×#17989643	1	1	yes	characteristic
496	C₂	#22626899	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂³×C₈
Fitting	C₈×D₄×C₇₃	C₄
prime radical	C₂×D₄×D₇₃	C₈
cosocle	C₂×#10596831	C₂⁴
hypercenter	C₈×D₄	#64408
hypocenter	C₇₃	#33487
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. #22626314	C₂	semidirect
2. #22626313	C₂	semidirect
3. #22626312	C₂	semidirect
4. #22626311	C₂	semidirect
5. #22626295	C₂	semidirect
6. #22626294	C₂	semidirect
7. #22626160	C₂	semidirect
8. #22626159	C₂	semidirect
9. C₂×#17989482	C₂	semidirect
10. #22626156	C₂	semidirect
12. C₂×#14556666	C₂²	semidirect
13. C₂×#14556665	C₂²	semidirect
14. C₂×#14556664	C₂²	semidirect
15. C₂²×#11924031	C₂²	semidirect
16. #17989508	C₂²	semidirect
17. C₄⋊#11924031	C₂²	semidirect
22. #17989482	C₂²	semidirect
23. #17989482	C₂²	semidirect
24. C₂²⋊#11924031	C₂²	semidirect
25. C₂²⋊#11924031	C₂²	semidirect
26. #17989476	C₂²	semidirect
27. #17989475	C₂²	semidirect
167. C₂²×D₇₃	M₃₂	semidirect
260. C₇₃	#33487	semidirect

Maximal subgroups

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

subgroup	index
#22626314	2
#22626313	2
#22626312	2
#22626311	2
#22626295	2
#22626294	2
#22626160	2
#22626159	2
C₂×#17989482	2
#22626156	2
C₈×D₄×D₇₃	2
#33487	73