Subgroups — #34018162

Order 18688.

610 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626626	C₂	1	2	yes	maximal
2	#22625503	C₂	1	2	yes	maximal, complemented
3	#22625502	C₂	1	2	yes	maximal, complemented
4	#22625498	C₂	1	2	yes	maximal, complemented
5	#22625493	C₂	1	1	yes	maximal, characteristic, complemented
6	#22625492	C₂	1	1	yes	maximal, characteristic, complemented
7	#22625488	C₂	1	1	yes	maximal, characteristic, complemented
8	#22625481	C₂	1	1	yes	maximal, characteristic, complemented
9	#22625478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#17989450	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#11924027	C₂	1	1	yes	maximal, characteristic
12	#17989612	—	2	2	no	—
13	#17989611	—	2	2	no	—
14	#17989609	C₂²	1	2	yes	—
15	#17989608	C₂²	1	2	yes	—
16	#17989606	C₂²	1	2	yes	—
17	#17989603	C₂²	1	2	yes	—
18	#17989590	C₂²	1	2	yes	—
19	C₂×C₄⋊#10596833	C₂²	1	2	yes	—
20	#17989560	—	2	2	no	—
21	#17989551	—	2	2	no	—
22	#17989451	C₂²	1	2	yes	—
23	#17989450	C₂²	1	1	yes	characteristic
24	#17989450	C₂²	1	1	yes	characteristic
25	#17989450	C₂²	1	2	yes	—
26	#17989450	C₂²	1	1	yes	characteristic
27	#17989450	C₂²	1	1	yes	characteristic
28	#17989449	C₂²	1	2	yes	—
29	#17989449	C₂²	1	2	yes	—
30	#17989448	C₂²	1	2	yes	—
31	#17989448	C₂²	1	2	yes	—
32	C₄×#11924027	C₂²	1	1	yes	characteristic
33	C₈×Dic₁₄₆	C₄	1	1	yes	characteristic
34	#17988711	C₄	1	1	yes	characteristic
35	D₄×#10596831	C₄	1	1	yes	characteristic
36	C₈×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
37	C₈×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
38	#17988650	C₄	1	1	yes	characteristic
39	#17988650	C₄	1	1	yes	characteristic
40	#17988639	C₂²	1	1	yes	characteristic
41	#17988637	C₂²	1	1	yes	characteristic
42	#17988637	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
46	C₈×D₄×C₇₃	C₄	1	1	yes	characteristic
47	C₂×#11924037	—	2	2	no	—
48	C₂²×#10596833	—	2	2	no	—
49	#14556658	—	2	2	no	—
50	C₄⋊#10596833	—	2	2	no	—
51	C₄⋊#10596833	C₂³	1	2	yes	—
52	C₄⋊#10596833	C₂³	1	2	yes	—
53	C₄⋊#10596833	C₂³	1	2	yes	—
54	C₄⋊#10596833	C₂³	1	2	yes	—
55	#14556648	—	2	2	no	—
56	#14556648	—	2	2	no	—
57	C₂²⋊#10596833	—	2	2	no	—
58	C₂²⋊#10596833	—	2	2	no	—
59	#14556646	—	2	2	no	—
60	#14556646	—	2	2	no	—
61	C₄×#10596833	—	2	2	no	—
62	C₄×#10596833	—	2	2	no	—
63	C₂×#11924027	D₄	1	1	yes	characteristic
64	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
65	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
68	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
69	#14556556	Q₈	1	1	yes	characteristic
70	D₄×Dic₇₃	Q₈	1	1	yes	characteristic
71	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
73	#14556551	Q₈	1	1	yes	characteristic
74	#14556551	Q₈	1	1	yes	characteristic
75	#14556549	D₄	1	1	yes	characteristic
76	#14556547	D₄	1	1	yes	characteristic
77	#14556547	D₄	1	1	yes	characteristic
78	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
80	C₄²×D₇₃	C₂³	1	1	yes	characteristic
81	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
82	#14556520	C₂×C₄	1	1	yes	characteristic
83	#14556520	C₂×C₄	1	1	yes	characteristic
84	#14556520	C₂×C₄	1	1	yes	characteristic
85	#14556520	C₂×C₄	1	1	yes	characteristic
86	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
88	#14556503	C₂×C₄	1	1	yes	characteristic
89	#14556503	C₂×C₄	1	1	yes	characteristic
90	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
91	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
96	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
97	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
98	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
100	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
101	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
102	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
103	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
105	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
106	#11924037	—	4	4	no	—
107	C₂×#10596833	—	2	2	no	—
108	C₂×#10596833	—	2	2	no	—
109	C₂×#10596833	—	2	2	no	—
110	C₂×#10596833	—	2	2	no	—
111	C₂×#10596833	—	4	4	no	—
112	#11924027	—	2	2	no	—
113	#11924027	—	2	2	no	—
114	C₂×Dic₁₄₆	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₂²⋊D₇₃	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₂²⋊D₇₃	C₄⋊C₄	1	1	yes	characteristic
117	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
120	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
124	C₂×#10596831	—	4	1	no	—
125	C₂×#10596831	—	4	1	no	—
126	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
127	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
128	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
129	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
130	C₈×D₇₃	—	2	2	no	—
131	C₈×D₇₃	—	4	1	no	—
132	C₄⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
133	#11924007	C₄⋊C₄	1	1	yes	characteristic
134	#11924007	C₄⋊C₄	1	1	yes	characteristic
135	#11924007	C₄⋊C₄	1	1	yes	characteristic
136	#11924007	C₄⋊C₄	1	1	yes	characteristic
137	C₂²⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
138	C₂²⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
139	#11924005	C₄⋊C₄	1	1	yes	characteristic
140	#11924005	C₄⋊C₄	1	1	yes	characteristic
141	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
144	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
145	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
146	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
147	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
148	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
149	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
150	C₂×D₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₇₃	—	2	2	no	—
154	C₂×C₈×C₇₃	—	2	2	no	—
155	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
160	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
161	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
162	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
163	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	D₄×C₇₃	—	2	2	no	—
167	C₂×C₄×C₇₃	—	2	1	no	—
168	C₂×C₄×C₇₃	—	2	1	no	—
169	C₂×C₄×C₇₃	—	2	1	no	—
170	C₂×C₄×C₇₃	—	2	1	no	—
171	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
176	C₂²⋊D₇₃	—	2	2	no	—
177	C₂²⋊D₇₃	—	2	2	no	—
178	C₂×Dic₇₃	—	2	1	no	—
179	C₂×Dic₇₃	—	2	1	no	—
180	C₂×Dic₇₃	—	4	1	no	—
181	C₂×Dic₇₃	—	4	1	no	—
182	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×Dic₇₃	#135	1	2	yes	—
188	C₂×Dic₇₃	#135	1	2	yes	—
189	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
191	C₄×D₇₃	—	2	1	no	—
192	C₄×D₇₃	—	2	1	no	—
193	C₄×D₇₃	—	2	1	no	—
194	C₄×D₇₃	—	2	1	no	—
195	C₄×D₇₃	—	4	1	no	—
196	Dic₁₄₆	—	2	2	no	—
197	#10596833	—	4	2	no	—
198	#10596833	—	4	2	no	—
199	#10596833	—	4	2	no	—
200	#10596833	—	4	2	no	—
201	C₈×C₇₃	—	2	1	no	—
202	C₈×C₇₃	—	2	1	no	—
203	C₈×C₇₃	—	2	1	no	—
204	C₈×C₇₃	#131	1	2	yes	—
205	#10596831	—	2	1	no	—
206	#10596831	—	2	1	no	—
207	#10596831	—	2	1	no	—
208	#10596831	—	2	1	no	—
209	C₂²×C₇₃	—	2	1	no	—
210	C₂²×C₇₃	—	2	1	no	—
211	C₂²×C₇₃	—	2	1	no	—
212	C₂²×C₇₃	—	2	1	no	—
213	C₂²×C₇₃	—	2	1	no	—
214	C₂²×C₇₃	#427	1	2	yes	—
215	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
216	C₂×D₇₃	—	2	1	no	—
217	C₂×D₇₃	—	2	1	no	—
218	C₂×D₇₃	—	2	1	no	—
219	C₄×C₇₃	—	2	1	no	—
220	C₄×C₇₃	—	2	1	no	—
221	C₄×C₇₃	—	2	1	no	—
222	C₄×C₇₃	—	2	1	no	—
223	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
224	C₄×C₇₃	#568	1	1	yes	characteristic
225	Dic₇₃	—	2	1	no	—
226	Dic₇₃	—	2	1	no	—
227	Dic₇₃	—	2	1	no	—
228	Dic₇₃	—	2	1	no	—
229	Dic₇₃	—	2	1	no	—
230	Dic₇₃	#427	1	2	yes	—
231	Dic₇₃	C₂×#135	1	1	yes	characteristic
232	Dic₇₃	C₂×#135	1	1	yes	characteristic
233	#17829	—	73	1	no	maximal, Sylow
234	C₂×C₇₃	—	2	2	no	—
235	C₂×C₇₃	—	4	1	no	—
236	C₂×C₇₃	#2906	1	1	yes	characteristic
237	C₂×C₇₃	C₂×#427	1	1	yes	characteristic
238	C₂×C₇₃	#2916	1	1	yes	characteristic
239	D₇₃	—	4	1	no	—
240	C₈×#41	—	73	1	no	—
241	#2925	—	73	2	no	—
242	#1572	—	73	2	no	—
243	#1572	—	73	2	no	—
244	#1570	—	73	2	no	—
245	#1568	—	73	1	no	—
246	#1568	—	73	1	no	—
247	#1567	—	73	1	no	—
248	#1564	—	73	1	no	—
249	#1564	—	73	1	no	—
250	C₂×#335	—	73	1	no	—
251	C₇₃	#17829	1	1	yes	characteristic, complemented, Sylow
252	C₄×#41	—	73	1	no	—
253	C₈×Q₈	—	73	1	no	—
254	C₈×Q₈	—	73	1	no	—
255	C₈×D₄	—	73	1	no	—
256	C₈×D₄	—	73	1	no	—
257	C₈×D₄	—	73	1	no	—
258	C₈×D₄	—	73	1	no	—
259	C₈×D₄	—	73	1	no	—
260	C₈×D₄	#64408	1	1	yes	characteristic
261	#433	—	146	2	no	—
262	#433	—	146	2	no	—
263	#432	—	73	2	no	—
264	#432	—	73	2	no	—
265	#431	—	73	1	no	—
266	#431	—	73	1	no	—
267	#431	—	73	1	no	—
268	#431	—	73	2	no	—
269	#431	—	73	2	no	—
270	#423	—	73	2	no	—
271	C₂×C₄⋊C₈	—	73	2	no	—
272	#408	—	146	2	no	—
273	#405	—	146	2	no	—
274	C₂×C₄×C₈	—	73	1	no	—
275	C₂×C₄×C₈	—	73	1	no	—
276	C₂×C₄×C₈	—	73	1	no	—
277	#335	—	73	1	no	—
278	#335	—	73	1	no	—
279	#335	—	73	2	no	—
280	#335	—	73	1	no	—
281	#335	—	73	1	no	—
282	#335	—	73	2	no	—
283	#334	—	73	2	no	—
284	#334	—	73	2	no	—
285	#334	—	73	2	no	—
286	#334	—	73	2	no	—
287	C₂×#41	—	73	1	no	—
288	C₂×M₁₆	—	146	2	no	—
289	C₂²×C₈	—	73	1	no	—
290	C₂²×C₈	—	73	1	no	—
291	C₂²×C₈	—	73	1	no	—
292	C₂²×C₈	—	73	1	no	—
293	C₂²×C₈	—	146	2	no	—
294	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
295	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
296	C₄×Q₈	—	73	1	no	—
297	C₄×Q₈	—	73	1	no	—
298	C₄×D₄	—	73	1	no	—
299	C₄×D₄	—	73	1	no	—
300	C₄×D₄	—	73	1	no	—
301	C₄×D₄	—	73	1	no	—
302	C₄×D₄	—	73	1	no	—
303	C₄×D₄	C₂×#64408	1	1	yes	characteristic
304	#117	—	73	1	no	—
305	#117	—	73	1	no	—
306	#117	—	73	1	no	—
307	C₂×C₄²	—	73	1	no	—
308	C₂×C₄²	—	73	1	no	—
309	C₂×C₄²	—	73	1	no	—
310	C₄⋊C₈	—	73	1	no	—
311	C₄⋊C₈	—	73	1	no	—
312	C₄⋊C₈	—	73	1	no	—
313	C₄⋊C₈	—	73	1	no	—
314	C₄⋊C₈	—	73	2	no	—
315	C₄⋊C₈	—	73	2	no	—
316	C₄⋊C₈	—	73	2	no	—
317	C₄⋊C₈	—	73	2	no	—
318	C₄⋊C₈	—	73	1	no	—
319	C₄⋊C₈	—	146	2	no	—
320	C₄⋊C₈	—	146	2	no	—
321	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic
322	C₂²⋊C₈	—	73	1	no	—
323	C₂²⋊C₈	—	73	1	no	—
324	C₂²⋊C₈	—	73	1	no	—
325	C₂²⋊C₈	—	73	1	no	—
326	C₂²⋊C₈	—	146	2	no	—
327	C₂²⋊C₈	—	146	2	no	—
328	C₂²⋊C₈	—	146	2	no	—
329	C₂²⋊C₈	—	146	2	no	—
330	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
331	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
332	#97	—	146	2	no	—
333	#97	—	146	2	no	—
334	C₄×C₈	—	73	1	no	—
335	C₄×C₈	—	73	1	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	—	73	1	no	—
342	C₄×C₈	—	73	1	no	—
343	C₄×C₈	—	146	2	no	—
344	C₄×C₈	—	146	2	no	—
345	C₄×C₈	C₂×#64408	1	1	yes	characteristic
346	#41	—	146	2	no	—
347	#41	—	146	2	no	—
348	C₂×Q₈	—	73	1	no	—
349	C₂×D₄	—	73	1	no	—
350	C₂×D₄	—	73	1	no	—
351	C₂×D₄	C₄⋊#64408	1	1	yes	characteristic
352	C₂²×C₄	—	73	1	no	—
353	C₂²×C₄	—	73	1	no	—
354	C₂²×C₄	—	73	1	no	—
355	C₂²×C₄	—	73	1	no	—
356	C₂²×C₄	—	73	1	no	—
357	C₂²×C₄	—	73	1	no	—
358	C₂²×C₄	—	73	1	no	—
359	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
360	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
361	M₁₆	—	292	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	292	1	no	—
365	C₂×C₈	—	292	4	no	—
366	C₂×C₈	—	292	1	no	—
367	C₂×C₈	—	292	1	no	—
368	C₂×C₈	—	73	1	no	—
369	C₂×C₈	—	73	1	no	—
370	C₂×C₈	—	73	1	no	—
371	C₂×C₈	—	73	1	no	—
372	C₂×C₈	—	146	2	no	—
373	C₂×C₈	—	146	2	no	—
374	C₂×C₈	—	146	2	no	—
375	C₂×C₈	—	146	2	no	—
376	C₂×C₈	—	146	2	no	—
377	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
378	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
379	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
380	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
381	C₄⋊C₄	—	73	1	no	—
382	C₄⋊C₄	—	73	1	no	—
383	C₄⋊C₄	—	73	1	no	—
384	C₄⋊C₄	—	73	1	no	—
385	C₄⋊C₄	—	73	1	no	—
386	C₄⋊C₄	C₄⋊#64408	1	1	yes	characteristic
387	C₂²⋊C₄	—	73	1	no	—
388	C₂²⋊C₄	—	73	1	no	—
389	C₂²⋊C₄	—	73	1	no	—
390	C₂²⋊C₄	—	73	1	no	—
391	C₂²⋊C₄	C₄⋊#64408	1	1	yes	characteristic
392	C₂²⋊C₄	C₄⋊#64408	1	1	yes	characteristic
393	C₄²	—	73	1	no	—
394	C₄²	—	73	1	no	—
395	C₄²	—	73	1	no	—
396	C₄²	—	73	1	no	—
397	C₄²	—	73	1	no	—
398	C₄²	—	73	1	no	—
399	C₄²	—	73	1	no	—
400	C₄²	—	73	1	no	—
401	C₄²	—	73	1	no	—
402	C₄²	C₂²×#64408	1	1	yes	characteristic
403	C₂³	—	73	1	no	—
404	C₂³	C₂×C₄⋊#64408	1	1	yes	characteristic
405	C₂³	C₂×C₄⋊#64408	1	1	yes	characteristic
406	Q₈	—	146	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	146	2	no	—
409	D₄	—	146	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	292	1	no	—
415	C₂×C₄	—	292	1	no	—
416	C₂×C₄	—	292	1	no	—
417	C₂×C₄	—	73	1	no	—
418	C₂×C₄	—	73	1	no	—
419	C₂×C₄	—	73	2	no	—
420	C₂×C₄	—	73	2	no	—
421	C₂×C₄	—	73	1	no	—
422	C₂×C₄	—	73	1	no	—
423	C₂×C₄	—	73	1	no	—
424	C₂×C₄	—	73	1	no	—
425	C₂×C₄	—	73	1	no	—
426	C₂×C₄	—	146	1	no	—
427	C₂×C₄	—	146	1	no	—
428	C₂×C₄	—	146	1	no	—
429	C₂×C₄	—	146	1	no	—
430	C₂×C₄	—	146	1	no	—
431	C₂×C₄	—	146	1	no	—
432	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
433	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
434	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
435	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
436	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	292	2	no	—
441	C₈	—	292	2	no	—
442	C₈	—	292	2	no	—
443	C₈	—	292	2	no	—
444	C₈	—	146	1	no	—
445	C₈	—	146	1	no	—
446	C₈	—	146	1	no	—
447	C₈	—	146	1	no	—
448	C₈	#14556678	1	2	yes	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	146	1	no	—
455	C₂²	—	146	1	no	—
456	C₂²	—	146	1	no	—
457	C₂²	#17989597	1	2	yes	—
458	C₂²	C₂²×C₄⋊#64408	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	73	1	no	—
464	C₄	—	73	1	no	—
465	C₄	—	73	2	no	—
466	C₄	—	146	1	no	—
467	C₄	—	146	1	no	—
468	C₄	—	146	1	no	—
469	C₄	—	146	1	no	—
470	C₄	—	146	1	no	—
471	C₄	C₂×#14556678	1	1	yes	characteristic
472	C₄	#17989666	1	1	yes	characteristic
473	C₂	—	2	2	no	—
474	C₂	—	4	1	no	—
475	C₂	—	292	1	no	—
476	C₂	#22626576	1	1	yes	characteristic
477	C₂	C₂×#17989597	1	1	yes	characteristic
478	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	C₈×D₄×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂×#11924027	D₄
cosocle	C₄×Dic₇₃	C₂⁴
hypercenter	C₈×D₄	#64408
hypocenter	C₇₃	#17829
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
2. #22625503	C₂	semidirect
3. #22625502	C₂	semidirect
4. #22625498	C₂	semidirect
5. #22625493	C₂	semidirect
6. #22625492	C₂	semidirect
7. #22625488	C₂	semidirect
8. #22625481	C₂	semidirect
9. #22625478	C₂	semidirect
10. C₂×#17989450	C₂	semidirect
251. C₇₃	#17829	semidirect

Maximal subgroups

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

subgroup	index
#22626626	2
#22625503	2
#22625502	2
#22625498	2
#22625493	2
#22625492	2
#22625488	2
#22625481	2
#22625478	2
C₂×#17989450	2
C₈×#11924027	2
#17829	73