Subgroups — #34018032

Order 18688.

666 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626853	C₂	1	2	yes	maximal
2	#22625496	C₂	1	2	yes	maximal, complemented
3	#22625495	C₂	1	2	yes	maximal, complemented
4	#22625494	C₂	1	1	yes	maximal, characteristic, complemented
5	#22625493	C₂	1	1	yes	maximal, characteristic, complemented
6	#22625487	C₂	1	1	yes	maximal, characteristic, complemented
7	#22625485	C₂	1	1	yes	maximal, characteristic, complemented
8	#22625483	C₂	1	2	yes	maximal, complemented
9	#22625481	C₂	1	1	yes	maximal, characteristic, complemented
10	#22625473	C₂	1	1	yes	maximal, characteristic, complemented
11	#22618353	C₂	1	1	yes	maximal, characteristic
12	#17989639	—	2	2	no	—
13	#17989620	—	2	2	no	—
14	#17989619	—	2	2	no	—
15	#17989617	—	2	2	no	—
16	#17989609	C₂²	1	2	yes	—
17	#17989608	C₂²	1	2	yes	—
18	#17989606	C₂²	1	2	yes	—
19	#17989591	C₂²	1	2	yes	—
20	#17989590	C₂²	1	2	yes	—
21	#17989588	C₂²	1	2	yes	—
22	#17989451	C₂²	1	2	yes	—
23	#17989450	C₂²	1	2	yes	—
24	#17989450	C₂²	1	2	yes	—
25	#17989449	C₂²	1	1	yes	characteristic
26	#17989449	C₂²	1	1	yes	characteristic
27	#17989449	C₂²	1	1	yes	characteristic
28	#17989449	C₂²	1	1	yes	characteristic
29	#17989449	C₂²	1	2	yes	—
30	#17989448	C₂²	1	2	yes	—
31	#17989448	C₂²	1	2	yes	—
32	C₂×#14556599	C₄	1	1	yes	characteristic
33	C₂×#14556597	C₄	1	1	yes	characteristic
34	#17989055	C₂²	1	1	yes	characteristic
35	#17988544	C₄	1	1	yes	characteristic
36	#17988544	C₄	1	1	yes	characteristic
37	#17988543	C₄	1	1	yes	characteristic
38	#17988541	C₄	1	1	yes	characteristic
39	#17988541	C₄	1	1	yes	characteristic
40	#17988539	C₂²	1	1	yes	characteristic
41	#17988539	C₂²	1	1	yes	characteristic
42	M₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
46	#405×C₇₃	C₄	1	1	yes	characteristic
47	C₂×#11924038	—	2	2	no	—
48	C₂×#11924037	—	2	2	no	—
49	C₂×#11924036	—	2	2	no	—
50	#14556658	—	2	2	no	—
51	#14556658	—	2	2	no	—
52	C₄⋊#10596833	—	2	2	no	—
53	C₄⋊#10596833	C₂³	1	2	yes	—
54	C₄⋊#10596833	C₂³	1	2	yes	—
55	C₄⋊#10596833	C₂³	1	2	yes	—
56	C₄⋊#10596833	C₂³	1	2	yes	—
57	#14556648	—	2	2	no	—
58	#14556648	—	2	2	no	—
59	C₂²⋊#10596833	—	2	2	no	—
60	#14556646	—	2	2	no	—
61	#14556646	—	2	2	no	—
62	C₄×#10596833	—	2	2	no	—
63	C₂×#11924028	C₂×C₄	1	1	yes	characteristic
64	#14556599	—	2	4	no	—
65	#14556597	—	2	4	no	—
66	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
67	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
68	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
69	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
70	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
71	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
76	#14556556	D₄	1	1	yes	characteristic
77	#14556556	Q₈	1	1	yes	characteristic
78	#14556553	D₄	1	1	yes	characteristic
79	#14556553	Q₈	1	1	yes	characteristic
80	#14556551	D₄	1	1	yes	characteristic
81	#14556551	D₄	1	1	yes	characteristic
82	#14556551	Q₈	1	1	yes	characteristic
83	#14556551	Q₈	1	1	yes	characteristic
84	#14556548	C₂×C₄	1	1	yes	characteristic
85	#14556548	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
87	C₄²×D₇₃	C₂³	1	1	yes	characteristic
88	C₄²×D₇₃	C₂³	1	1	yes	characteristic
89	#14556502	C₂×C₄	1	1	yes	characteristic
90	#14556502	C₂×C₄	1	1	yes	characteristic
91	#14556501	C₂×C₄	1	1	yes	characteristic
92	#14556501	C₂×C₄	1	1	yes	characteristic
93	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
94	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
98	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
99	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
100	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
102	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
103	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
104	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
105	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
106	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
107	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
108	#11924038	—	8	2	no	—
109	#11924037	—	8	2	no	—
110	#11924036	—	8	2	no	—
111	C₂×#10596833	—	2	2	no	—
112	C₂×#10596833	—	2	2	no	—
113	C₂×#10596833	—	2	2	no	—
114	C₂×#10596833	—	2	2	no	—
115	#11924028	—	2	2	no	—
116	#11924028	—	2	2	no	—
117	C₂×Dic₁₄₆	C₄⋊C₄	1	1	yes	characteristic
118	C₂×D₂₉₂	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₂²⋊D₇₃	C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₂²⋊D₇₃	C₄⋊C₄	1	1	yes	characteristic
121	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
123	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
128	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
129	#11924012	—	2	2	no	—
130	#11924011	—	2	2	no	—
131	#11924011	—	2	2	no	—
132	#11924011	—	2	2	no	—
133	#11924011	M₁₆	1	4	yes	complemented
134	C₂×#10596831	—	2	2	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	C₂²×C₄	1	1	yes	characteristic
139	C₈×D₇₃	—	2	2	no	—
140	C₈×D₇₃	—	2	2	no	—
141	C₈×D₇₃	—	2	2	no	—
142	C₈×D₇₃	M₁₆	1	4	yes	complemented
143	#11924007	C₄⋊C₄	1	1	yes	characteristic
144	#11924007	C₄⋊C₄	1	1	yes	characteristic
145	#11924007	C₄⋊C₄	1	1	yes	characteristic
146	#11924007	C₄⋊C₄	1	1	yes	characteristic
147	#11924005	C₄⋊C₄	1	1	yes	characteristic
148	#11924005	C₄⋊C₄	1	1	yes	characteristic
149	#11924005	C₄⋊C₄	1	1	yes	characteristic
150	#11924005	C₄⋊C₄	1	1	yes	characteristic
151	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
153	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
154	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
155	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
156	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
157	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
158	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
160	M₁₆×C₇₃	—	2	2	no	—
161	C₂×C₈×C₇₃	—	2	2	no	—
162	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
166	C₄⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
167	C₄⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
168	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
169	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
170	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
172	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₇₃	—	2	1	no	—
176	C₂×C₄×C₇₃	—	2	1	no	—
177	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
183	C₂²⋊D₇₃	—	2	2	no	—
184	C₂²⋊D₇₃	—	2	2	no	—
185	C₂×Dic₇₃	—	2	2	no	—
186	C₂×Dic₇₃	—	4	1	no	—
187	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
193	D₂₉₂	—	2	2	no	—
194	C₄×D₇₃	—	2	1	no	—
195	C₄×D₇₃	—	2	1	no	—
196	C₄×D₇₃	—	2	2	no	—
197	C₄×D₇₃	—	2	2	no	—
198	C₄×D₇₃	—	4	1	no	—
199	C₄×D₇₃	—	4	1	no	—
200	C₄×D₇₃	C₂×M₁₆	1	2	yes	—
201	C₄×D₇₃	C₂×M₁₆	1	2	yes	—
202	Dic₁₄₆	—	2	2	no	—
203	#10596833	—	4	2	no	—
204	#10596833	—	4	2	no	—
205	#10596833	—	4	2	no	—
206	#10596833	—	4	2	no	—
207	C₈×C₇₃	—	2	1	no	—
208	C₈×C₇₃	—	2	1	no	—
209	C₈×C₇₃	C₂×M₁₆	1	2	yes	—
210	C₈×C₇₃	C₂×M₁₆	1	2	yes	—
211	#10596831	—	2	1	no	—
212	#10596831	—	2	1	no	—
213	#10596831	C₂×M₁₆	1	2	yes	—
214	#10596831	C₂×M₁₆	1	2	yes	—
215	C₂²×C₇₃	—	2	1	no	—
216	C₂²×C₇₃	—	2	1	no	—
217	C₂²×C₇₃	—	2	1	no	—
218	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
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	#423	1	2	yes	—
225	C₄×C₇₃	—	2	1	no	—
226	C₄×C₇₃	—	2	1	no	—
227	C₄×C₇₃	—	2	1	no	—
228	C₄×C₇₃	—	2	1	no	—
229	C₄×C₇₃	—	2	1	no	—
230	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
231	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
232	Dic₇₃	—	2	1	no	—
233	Dic₇₃	—	2	1	no	—
234	Dic₇₃	—	2	1	no	—
235	Dic₇₃	—	2	1	no	—
236	Dic₇₃	#423	1	2	yes	—
237	Dic₇₃	#577	1	2	yes	—
238	#17798	—	73	1	no	maximal, Sylow
239	C₂×C₇₃	—	4	1	no	—
240	C₂×C₇₃	C₂×#423	1	1	yes	characteristic
241	C₂×C₇₃	#2912	1	1	yes	characteristic
242	C₂×C₇₃	#2916	1	1	yes	characteristic
243	D₇₃	—	2	2	no	—
244	D₇₃	—	4	1	no	—
245	#2989	—	73	2	no	—
246	C₄×#131	—	73	1	no	—
247	#1569	—	73	2	no	—
248	#1569	—	73	2	no	—
249	#1568	—	73	1	no	—
250	#1568	—	73	1	no	—
251	#1566	—	73	1	no	—
252	#1566	—	73	1	no	—
253	#1565	—	73	2	no	—
254	#1564	—	73	1	no	—
255	C₂×#334	—	73	1	no	—
256	C₇₃	#17798	1	1	yes	characteristic, complemented, Sylow
257	C₂×#131	—	73	1	no	—
258	C₂×#131	—	73	1	no	—
259	C₄×#41	—	73	1	no	—
260	#446	—	146	2	no	—
261	#436	—	146	2	no	—
262	#435	—	146	2	no	—
263	#435	—	146	2	no	—
264	#432	—	73	2	no	—
265	#432	—	73	2	no	—
266	#431	—	73	2	no	—
267	#423	—	73	2	no	—
268	#423	—	73	2	no	—
269	C₂×C₄⋊C₈	—	73	2	no	—
270	#405	—	73	1	no	—
271	#405	—	73	1	no	—
272	#405	—	73	1	no	—
273	#405	—	73	1	no	—
274	#405	—	73	1	no	—
275	#405	#64408	1	1	yes	characteristic
276	C₄×M₁₆	—	73	1	no	—
277	C₄×M₁₆	—	73	1	no	—
278	C₄×M₁₆	—	73	1	no	—
279	C₂×C₄×C₈	—	73	1	no	—
280	C₂×C₄×C₈	—	73	1	no	—
281	C₂×C₄×C₈	—	73	1	no	—
282	#335	—	73	2	no	—
283	#335	—	73	2	no	—
284	#335	—	73	2	no	—
285	#334	—	73	1	no	—
286	#334	—	73	1	no	—
287	#334	—	73	2	no	—
288	#334	—	73	1	no	—
289	#334	—	73	1	no	—
290	#334	—	73	2	no	—
291	#334	—	73	2	no	—
292	C₂×#41	—	73	1	no	—
293	#131	—	146	4	no	—
294	#131	—	146	4	no	—
295	C₂×M₁₆	—	73	1	no	—
296	C₂×M₁₆	—	73	1	no	—
297	C₂×M₁₆	—	73	1	no	—
298	C₂×M₁₆	—	73	1	no	—
299	C₂×M₁₆	—	73	1	no	—
300	C₂×M₁₆	—	146	2	no	—
301	C₂×M₁₆	—	146	2	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	—	73	1	no	—
307	C₂²×C₈	—	73	1	no	—
308	C₂²×C₈	—	146	2	no	—
309	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
310	C₄×Q₈	—	73	1	no	—
311	C₄×Q₈	—	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	—	73	1	no	—
317	C₄×D₄	—	73	1	no	—
318	#117	—	73	1	no	—
319	#117	—	73	1	no	—
320	#117	C₂×#64408	1	1	yes	characteristic
321	C₂×C₄²	—	73	1	no	—
322	C₂×C₄²	—	73	1	no	—
323	C₂×C₄²	—	73	1	no	—
324	C₄⋊C₈	—	73	2	no	—
325	C₄⋊C₈	—	73	2	no	—
326	C₄⋊C₈	—	73	2	no	—
327	C₄⋊C₈	—	73	2	no	—
328	C₄⋊C₈	—	146	2	no	—
329	C₄⋊C₈	—	146	2	no	—
330	C₄⋊C₈	—	146	2	no	—
331	C₂²⋊C₈	—	146	2	no	—
332	C₂²⋊C₈	—	146	2	no	—
333	C₂²⋊C₈	—	146	2	no	—
334	#97	—	73	1	no	—
335	#97	—	73	1	no	—
336	#97	—	73	1	no	—
337	#97	—	73	1	no	—
338	#97	—	146	2	no	—
339	#97	—	146	2	no	—
340	#97	C₂×#64408	1	1	yes	characteristic
341	#97	C₂×#64408	1	1	yes	characteristic
342	C₄×C₈	—	73	1	no	—
343	C₄×C₈	—	73	1	no	—
344	C₄×C₈	—	73	1	no	—
345	C₄×C₈	—	73	1	no	—
346	C₄×C₈	—	73	1	no	—
347	C₄×C₈	—	73	1	no	—
348	C₄×C₈	—	73	1	no	—
349	C₄×C₈	—	73	1	no	—
350	C₄×C₈	—	146	2	no	—
351	C₄×C₈	C₂×#64408	1	1	yes	characteristic
352	C₄×C₈	C₂×#64408	1	1	yes	characteristic
353	#41	—	146	2	no	—
354	#41	—	146	2	no	—
355	C₂×Q₈	—	73	1	no	—
356	C₂×D₄	—	73	1	no	—
357	C₂×D₄	—	73	1	no	—
358	C₂×D₄	—	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	M₁₆	—	2	2	no	—
369	M₁₆	—	584	2	no	—
370	M₁₆	—	584	2	no	—
371	M₁₆	—	73	4	no	—
372	M₁₆	—	146	2	no	—
373	M₁₆	—	146	2	no	—
374	M₁₆	—	146	2	no	—
375	M₁₆	—	146	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	584	2	no	—
378	C₂×C₈	—	73	1	no	—
379	C₂×C₈	—	73	1	no	—
380	C₂×C₈	—	73	4	no	—
381	C₂×C₈	—	73	1	no	—
382	C₂×C₈	—	73	1	no	—
383	C₂×C₈	—	146	2	no	—
384	C₂×C₈	—	146	2	no	—
385	C₂×C₈	—	146	2	no	—
386	C₂×C₈	—	146	2	no	—
387	C₂×C₈	—	146	2	no	—
388	C₂×C₈	—	146	2	no	—
389	C₂×C₈	—	146	2	no	—
390	C₂×C₈	—	146	2	no	—
391	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
392	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
393	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
394	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
395	C₄⋊C₄	—	73	1	no	—
396	C₄⋊C₄	—	73	1	no	—
397	C₄⋊C₄	—	73	1	no	—
398	C₄⋊C₄	—	73	1	no	—
399	C₄⋊C₄	C₄⋊#64408	1	1	yes	characteristic
400	C₄⋊C₄	C₄⋊#64408	1	1	yes	characteristic
401	C₂²⋊C₄	—	73	1	no	—
402	C₂²⋊C₄	—	73	1	no	—
403	C₂²⋊C₄	—	73	1	no	—
404	C₂²⋊C₄	—	73	1	no	—
405	C₂²⋊C₄	C₄⋊#64408	1	1	yes	characteristic
406	C₂²⋊C₄	C₄⋊#64408	1	1	yes	characteristic
407	C₄²	—	73	1	no	—
408	C₄²	—	73	1	no	—
409	C₄²	—	73	1	no	—
410	C₄²	—	73	1	no	—
411	C₄²	—	73	1	no	—
412	C₄²	—	73	1	no	—
413	C₄²	—	73	1	no	—
414	C₄²	—	73	1	no	—
415	C₄²	C₂²×#64408	1	1	yes	characteristic
416	C₄²	C₂²×#64408	1	1	yes	characteristic
417	C₂³	—	73	1	no	—
418	C₂³	—	73	1	no	—
419	C₂³	C₂×C₄⋊#64408	1	1	yes	characteristic
420	Q₈	—	146	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	—	292	1	no	—
427	C₂×C₄	—	292	1	no	—
428	C₂×C₄	—	292	1	no	—
429	C₂×C₄	—	73	1	no	—
430	C₂×C₄	—	73	1	no	—
431	C₂×C₄	—	73	2	no	—
432	C₂×C₄	—	73	2	no	—
433	C₂×C₄	—	73	1	no	—
434	C₂×C₄	—	73	1	no	—
435	C₂×C₄	—	73	1	no	—
436	C₂×C₄	—	73	1	no	—
437	C₂×C₄	—	146	2	no	—
438	C₂×C₄	—	146	2	no	—
439	C₂×C₄	—	146	2	no	—
440	C₂×C₄	—	146	1	no	—
441	C₂×C₄	—	146	1	no	—
442	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
443	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
444	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
445	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
446	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
447	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	292	2	no	—
451	C₈	—	292	2	no	—
452	C₈	—	292	2	no	—
453	C₈	—	292	2	no	—
454	C₈	—	73	2	no	—
455	C₈	—	73	2	no	—
456	C₈	—	146	1	no	—
457	C₈	—	146	1	no	—
458	C₈	D₇₃⋊M₁₆	1	2	yes	—
459	C₈	D₇₃⋊M₁₆	1	2	yes	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	73	2	no	—
464	C₂²	—	146	1	no	—
465	C₂²	—	146	1	no	—
466	C₂²	—	146	1	no	—
467	C₂²	—	146	1	no	—
468	C₂²	—	146	1	no	—
469	C₂²	C₂²×C₄⋊#64408	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	73	2	no	—
476	C₄	—	73	2	no	—
477	C₄	—	146	1	no	—
478	C₄	—	146	1	no	—
479	C₄	—	146	1	no	—
480	C₄	—	146	1	no	—
481	C₄	C₂×D₇₃⋊M₁₆	1	1	yes	characteristic
482	C₄	C₂×D₇₃⋊M₁₆	1	1	yes	characteristic
483	C₂	—	4	1	no	—
484	C₂	—	292	1	no	—
485	C₂	—	146	2	no	—
486	C₂	D₇₃⋊#423	1	1	yes	characteristic
487	C₂	#22626585	1	1	yes	characteristic
488	C₂	#22626593	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#64408
Fitting	#405×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂×#11924028	C₂×C₄
cosocle	C₄×Dic₇₃	C₂⁴
hypercenter	#405	#64408
hypocenter	C₇₃	#17798
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #22625496	C₂	semidirect
3. #22625495	C₂	semidirect
4. #22625494	C₂	semidirect
5. #22625493	C₂	semidirect
6. #22625487	C₂	semidirect
7. #22625485	C₂	semidirect
8. #22625483	C₂	semidirect
9. #22625481	C₂	semidirect
10. #22625473	C₂	semidirect
133. #11924011	M₁₆	semidirect
142. C₈×D₇₃	M₁₆	semidirect
256. C₇₃	#17798	semidirect

Maximal subgroups

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

subgroup	index
#22626853	2
#22625496	2
#22625495	2
#22625494	2
#22625493	2
#22625487	2
#22625485	2
#22625483	2
#22625481	2
#22625473	2
#22618353	2
#17798	73