Subgroups — #34034618

Order 18688.

864 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22627078	C₂	1	2	yes	maximal, complemented
2	#22627078	C₂	1	2	yes	maximal, complemented
3	#22627076	C₂	1	2	yes	maximal
4	#22627074	C₂	1	1	yes	maximal, characteristic, complemented
5	#22627073	C₂	1	1	yes	maximal, characteristic, complemented
6	#22627072	C₂	1	1	yes	maximal, characteristic
7	C₄×C₄⋊#10596842	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²⋊C₄×#10596842	C₂	1	2	yes	maximal
9	#22627065	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×(C₂×#10596842)⋊C₄	C₂	1	1	yes	maximal, characteristic
11	#117×#64408	C₂	1	1	yes	maximal, characteristic
12	C₂³×#10596842	C₂²	1	2	yes	—
13	C₂×C₄⋊#10596842	C₂²	1	2	yes	—
14	C₂×C₄⋊#10596842	C₂²	1	2	yes	—
15	C₂×C₂²⋊#10596842	C₂²	1	2	yes	—
16	C₂×C₄×#10596842	C₂²	1	2	yes	—
17	C₂×C₄×#10596842	C₂²	1	2	yes	—
18	(C₂×#10596842)⋊C₄	C₂²	1	1	yes	characteristic
19	(C₂×#10596842)⋊C₄	C₂²	1	1	yes	characteristic
20	(C₂×#10596842)⋊C₄	C₂²	1	2	yes	—
21	(C₂×#10596842)⋊C₄	C₂²	1	1	yes	characteristic
22	(C₂×#10596842)⋊C₄	C₂²	1	2	yes	—
23	(C₂×#10596842)⋊C₄	C₂²	1	2	yes	—
24	(C₂×#10596842)⋊C₄	C₂²	1	2	yes	—
25	(C₂×#10596842)⋊C₄	C₂²	1	2	yes	—
26	(C₂×#10596842)⋊C₄	C₂²	1	2	yes	—
27	(C₂×#10596842)⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×#14556670	C₄	1	1	yes	characteristic
29	C₂²×C₄×#64408	C₂²	1	1	yes	characteristic
30	C₄⋊C₄×#64408	C₄	1	1	yes	characteristic
31	C₄⋊C₄×#64408	C₄	1	1	yes	characteristic
32	C₄⋊C₄×#64408	C₂²	1	1	yes	characteristic
33	C₄⋊C₄×#64408	C₂²	1	1	yes	characteristic
34	C₂²⋊C₄×#64408	C₄	1	1	yes	characteristic
35	C₂²⋊C₄×#64408	C₄	1	1	yes	characteristic
36	C₂²⋊C₄×#64408	C₂²	1	1	yes	characteristic
37	C₂²⋊C₄×#64408	C₂²	1	1	yes	characteristic
38	#17989523	C₄	1	1	yes	characteristic
39	#17989523	C₄	1	1	yes	characteristic
40	C₄²×#64408	C₂²	1	1	yes	characteristic
41	C₄²×#64408	C₂²	1	1	yes	characteristic
42	#117×D₇₃	C₄	1	1	yes	characteristic
43	C₂²×#10596842	—	2	4	no	—
44	C₂²×#10596842	—	2	4	no	—
45	C₂²×#10596842	—	4	2	no	—
46	C₂²×#10596842	C₂³	1	2	yes	—
47	C₂²×#10596842	C₂³	1	2	yes	—
48	C₂²×#10596842	C₂³	1	2	yes	—
49	C₂²×#10596842	C₂³	1	2	yes	—
50	C₄⋊#10596842	—	2	4	no	—
51	C₄⋊#10596842	—	4	2	no	—
52	C₂²⋊#10596842	—	2	4	no	—
53	C₄×#10596842	—	2	4	no	—
54	C₄×#10596842	—	4	2	no	—
55	C₂³×#64408	C₂×C₄	1	1	yes	characteristic
56	C₂³×#64408	C₂³	1	1	yes	characteristic
57	#14556670	—	2	4	no	—
58	C₂×C₄⋊#64408	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊#64408	C₂×C₄	1	1	yes	characteristic
60	C₂×C₂²⋊#64408	C₂×C₄	1	1	yes	characteristic
61	C₂×C₂²⋊#64408	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×#64408	—	2	4	no	—
63	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
72	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
73	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
74	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
75	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
76	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
77	(C₂×#64408)⋊C₄	C₂×C₄	1	1	yes	characteristic
78	(C₂×#64408)⋊C₄	C₂×C₄	1	1	yes	characteristic
79	(C₂×#64408)⋊C₄	C₂×C₄	1	1	yes	characteristic
80	(C₂×#64408)⋊C₄	C₂×C₄	1	1	yes	characteristic
81	(C₂×#64408)⋊C₄	C₂×C₄	1	1	yes	characteristic
82	(C₂×#64408)⋊C₄	C₂×C₄	1	1	yes	characteristic
83	(C₂×#64408)⋊C₄	C₂×C₄	1	1	yes	characteristic
84	(C₂×#64408)⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
86	#14556550	C₈	1	1	yes	characteristic, complemented
87	#14556549	C₈	1	1	yes	characteristic, complemented
88	#14556549	C₈	1	1	yes	characteristic, complemented
89	#14556548	C₈	1	1	yes	characteristic, complemented
90	#14556548	C₈	1	1	yes	characteristic, complemented
91	#14556547	C₈	1	1	yes	characteristic, complemented
92	#14556547	C₈	1	1	yes	characteristic, complemented
93	C₄⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
94	C₄⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
97	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
98	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
99	#117×C₇₃	C₈	1	1	yes	characteristic, complemented
100	C₂×#10596842	—	2	2	no	—
101	C₂×#10596842	—	2	2	no	—
102	C₂×#10596842	—	2	2	no	—
103	C₂×#10596842	—	2	2	no	—
104	C₂×#10596842	—	2	2	no	—
105	C₂×#10596842	—	2	2	no	—
106	C₂×#10596842	—	2	2	no	—
107	C₂×#10596842	—	2	2	no	—
108	C₂×#10596842	—	2	2	no	—
109	C₂×#10596842	—	2	2	no	—
110	C₂×#10596842	—	2	2	no	—
111	C₂×#10596842	—	4	8	no	—
112	C₂×#10596842	#41	1	4	yes	—
113	C₂²×#64408	—	2	2	no	—
114	C₂²×#64408	—	2	1	no	—
115	C₂²×#64408	—	2	1	no	—
116	C₂²×#64408	—	2	2	no	—
117	C₂²×#64408	—	2	2	no	—
118	C₂²×#64408	—	4	1	no	—
119	C₂²×#64408	C₂²×C₄	1	1	yes	characteristic
120	C₂²×#64408	C₂²×C₄	1	1	yes	characteristic
121	C₂²×#64408	C₂²×C₄	1	1	yes	characteristic
122	C₂²×#64408	C₂²×C₄	1	1	yes	characteristic
123	C₂²×#64408	C₂²×C₄	1	1	yes	characteristic
124	C₂²×#64408	C₂²×C₄	1	1	yes	characteristic
125	C₂²×#64408	C₂²×C₄	1	1	yes	characteristic
126	C₂²×#64408	#41	1	4	yes	—
127	C₂²×#64408	C₂⁴	1	1	yes	characteristic
128	C₄⋊#64408	—	2	2	no	—
129	C₄⋊#64408	—	2	2	no	—
130	C₂²⋊#64408	—	2	2	no	—
131	C₂²⋊#64408	M₁₆	1	4	yes	—
132	C₄×#64408	—	2	2	no	—
133	C₄×#64408	—	2	2	no	—
134	C₄×#64408	—	2	2	no	—
135	C₄×#64408	—	2	2	no	—
136	C₄×#64408	—	2	2	no	—
137	C₄×#64408	—	2	2	no	—
138	C₄×#64408	—	2	2	no	—
139	C₄×#64408	—	2	2	no	—
140	C₄×#64408	—	2	2	no	—
141	C₄×#64408	—	2	2	no	—
142	C₄×#64408	—	2	1	no	—
143	C₄×#64408	—	2	1	no	—
144	C₄×#64408	—	2	1	no	—
145	C₄×#64408	—	2	1	no	—
146	C₄×#64408	—	4	1	no	—
147	C₄×#64408	—	4	1	no	—
148	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
150	C₂×C₄×D₇₃	—	2	2	no	—
151	C₂×C₄×D₇₃	—	2	2	no	—
152	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
153	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
154	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
160	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic, complemented
161	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic, complemented
162	#11924007	C₂×C₈	1	1	yes	characteristic, complemented
163	#11924007	C₂×C₈	1	1	yes	characteristic, complemented
164	#11924007	C₂×C₈	1	1	yes	characteristic, complemented
165	#11924007	C₂×C₈	1	1	yes	characteristic, complemented
166	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
167	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
168	#11924005	C₂×C₈	1	1	yes	characteristic
169	#11924005	C₂×C₈	1	1	yes	characteristic
170	#11924005	C₂×C₈	1	1	yes	characteristic
171	#11924005	C₂×C₈	1	1	yes	characteristic
172	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic, complemented
173	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic, complemented
174	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic, complemented
175	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic, complemented
176	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic, complemented
177	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic, complemented
178	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
179	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic, complemented
180	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic, complemented
181	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
182	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
183	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic, complemented
184	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic, complemented
185	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
186	C₂²×D₇₃	—	2	1	no	—
187	C₂²×D₇₃	—	2	1	no	—
188	C₂²×D₇₃	—	2	1	no	—
189	C₂²×D₇₃	—	2	1	no	—
190	C₂²×D₇₃	#117	1	2	yes	—
191	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
192	C₂²×D₇₃	C₂×M₁₆	1	2	yes	—
193	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×#64408	—	2	1	no	—
195	C₂×#64408	—	2	1	no	—
196	C₂×#64408	—	2	1	no	—
197	C₂×#64408	—	2	1	no	—
198	C₂×#64408	—	2	1	no	—
199	C₂×#64408	—	2	1	no	—
200	C₂×#64408	—	2	1	no	—
201	C₂×#64408	—	2	1	no	—
202	C₂×#64408	—	2	4	no	—
203	C₂×#64408	—	2	4	no	—
204	C₂×#64408	—	2	1	no	—
205	C₂×#64408	—	2	1	no	—
206	C₂×#64408	—	2	1	no	—
207	C₂×#64408	—	2	1	no	—
208	C₂×#64408	—	2	1	no	—
209	C₂×#64408	—	2	1	no	—
210	C₂×#64408	—	2	1	no	—
211	C₂×#64408	—	2	1	no	—
212	C₂×#64408	—	2	1	no	—
213	C₂×#64408	—	4	4	no	—
214	C₂×#64408	#117	1	2	yes	—
215	C₂×#64408	C₂×M₁₆	1	2	yes	—
216	C₂×#64408	C₂×M₁₆	1	2	yes	—
217	C₂×#64408	#131	1	2	yes	—
218	C₂×#64408	C₂×#41	1	2	yes	—
219	C₂×#64408	C₂×#41	1	2	yes	—
220	C₂×#64408	H(5,𝔽₂)	1	1	yes	characteristic
221	C₂×#64408	2₋¹⁺⁴	1	1	yes	characteristic
222	#10596842	—	2	4	no	—
223	#10596842	—	4	2	no	—
224	#10596842	—	4	2	no	—
225	#10596842	—	4	2	no	—
226	C₂×C₄×C₇₃	—	2	2	no	—
227	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
228	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
229	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
230	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
231	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
232	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
233	C₂×Dic₇₃	—	2	2	no	—
234	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
235	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
236	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
237	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
238	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
239	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
240	C₄×D₇₃	—	2	1	no	—
241	C₄×D₇₃	—	2	1	no	—
242	C₄×D₇₃	—	2	1	no	—
243	C₄×D₇₃	—	2	1	no	—
244	C₄×D₇₃	—	2	1	no	—
245	C₄×D₇₃	—	2	1	no	—
246	C₄×D₇₃	—	2	1	no	—
247	C₄×D₇₃	—	2	1	no	—
248	C₄×D₇₃	—	2	1	no	—
249	C₄×D₇₃	—	2	1	no	—
250	C₄×D₇₃	—	2	1	no	—
251	C₄×D₇₃	—	2	1	no	—
252	C₄×D₇₃	—	2	2	no	—
253	C₄×D₇₃	—	2	2	no	—
254	C₂²×C₇₃	—	2	1	no	—
255	C₂²×C₇₃	—	2	1	no	—
256	C₂²×C₇₃	#431	1	2	yes	—
257	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
258	C₂×D₇₃	—	2	1	no	—
259	C₂×D₇₃	—	2	1	no	—
260	C₂×D₇₃	—	2	2	no	—
261	C₂×D₇₃	—	2	2	no	—
262	C₂×D₇₃	—	2	2	no	—
263	C₂×D₇₃	—	2	2	no	—
264	C₂×D₇₃	#431	1	2	yes	—
265	C₂×D₇₃	C₂×#117	1	1	yes	characteristic
266	C₂×D₇₃	C₄×#41	1	1	yes	characteristic
267	C₂×D₇₃	#520	1	1	yes	characteristic
268	C₂×D₇₃	C₂²×M₁₆	1	1	yes	characteristic
269	C₂×D₇₃	C₂×#131	1	1	yes	characteristic
270	C₂×D₇₃	#568	1	1	yes	characteristic
271	#64408	—	2	2	no	—
272	#64408	—	2	2	no	—
273	#64408	—	2	2	no	—
274	#64408	—	2	2	no	—
275	#64408	—	4	1	no	—
276	#64408	—	4	1	no	—
277	#64408	—	4	1	no	—
278	#64408	#551	1	2	yes	—
279	#64408	#552	1	2	yes	—
280	C₄×C₇₃	—	2	1	no	—
281	C₄×C₇₃	—	2	1	no	—
282	C₄×C₇₃	—	2	1	no	—
283	C₄×C₇₃	—	2	1	no	—
284	C₄×C₇₃	—	2	1	no	—
285	C₄×C₇₃	—	2	1	no	—
286	Dic₇₃	—	2	1	no	—
287	Dic₇₃	—	2	1	no	—
288	Dic₇₃	—	2	1	no	—
289	Dic₇₃	—	2	1	no	—
290	Dic₇₃	—	2	1	no	—
291	Dic₇₃	—	2	1	no	—
292	#22589	—	73	1	no	maximal, Sylow
293	C₂×C₇₃	—	2	2	no	—
294	C₂×C₇₃	C₂×#431	1	1	yes	characteristic
295	C₂×C₇₃	C₈×#41	1	1	yes	characteristic
296	C₂×C₇₃	#2988	1	1	yes	characteristic
297	D₇₃	—	2	2	no	—
298	D₇₃	#2343	1	1	yes	characteristic
299	D₇₃	#2924	1	1	yes	characteristic
300	D₇₃	#2970	1	1	yes	characteristic
301	D₇₃	#2990	1	1	yes	characteristic
302	C₄×#117	—	73	1	no	—
303	#1916	—	73	2	no	—
304	#1916	—	73	2	no	—
305	#1850	—	73	2	no	—
306	#1839	—	73	1	no	—
307	#1831	—	73	1	no	—
308	#1817	—	73	1	no	—
309	C₄×C₄⋊C₈	—	73	1	no	—
310	C₈×C₂²⋊C₄	—	73	2	no	—
311	#1744	—	73	1	no	—
312	C₂×#336	—	73	1	no	—
313	C₇₃	#22589	1	1	yes	characteristic, complemented, Sylow
314	C₂³×C₈	—	73	2	no	—
315	C₂×#117	—	73	1	no	—
316	C₂×#117	—	73	1	no	—
317	C₂²×C₄²	—	73	1	no	—
318	C₂×C₄⋊C₈	—	73	2	no	—
319	C₂×C₄⋊C₈	—	73	2	no	—
320	C₂×C₂²⋊C₈	—	73	2	no	—
321	C₂×C₄×C₈	—	73	2	no	—
322	C₂×C₄×C₈	—	73	2	no	—
323	C₄×C₄⋊C₄	—	73	1	no	—
324	C₄×C₄⋊C₄	—	73	1	no	—
325	C₄×C₄⋊C₄	—	73	1	no	—
326	C₄×C₄⋊C₄	—	73	1	no	—
327	C₄×C₂²⋊C₄	—	73	1	no	—
328	C₄×C₂²⋊C₄	—	73	1	no	—
329	C₄×C₂²⋊C₄	—	73	1	no	—
330	C₄×C₂²⋊C₄	—	73	1	no	—
331	#376	—	73	1	no	—
332	#376	—	73	1	no	—
333	C₄³	—	73	1	no	—
334	C₄³	—	73	1	no	—
335	#336	—	73	1	no	—
336	#336	—	73	1	no	—
337	#336	—	73	2	no	—
338	#336	—	73	1	no	—
339	#336	—	73	2	no	—
340	#336	—	73	2	no	—
341	#336	—	73	2	no	—
342	#336	—	73	2	no	—
343	#336	—	73	2	no	—
344	#336	—	73	1	no	—
345	C₂³×C₄	—	73	1	no	—
346	C₂³×C₄	—	73	1	no	—
347	C₂³×C₄	—	73	1	no	—
348	C₂²×C₈	—	292	2	no	—
349	C₂²×C₈	—	73	2	no	—
350	C₂²×C₈	—	73	2	no	—
351	C₂²×C₈	—	73	2	no	—
352	C₂²×C₈	—	73	2	no	—
353	C₂²×C₈	—	146	4	no	—
354	C₂²×C₈	—	146	4	no	—
355	#117	—	73	1	no	—
356	#117	—	73	1	no	—
357	#117	—	73	1	no	—
358	#117	—	73	1	no	—
359	#117	—	73	1	no	—
360	#117	—	73	1	no	—
361	#117	—	73	1	no	—
362	#117	—	146	4	no	—
363	#117	#10596842	1	1	yes	characteristic, complemented
364	C₂×C₄⋊C₄	—	73	1	no	—
365	C₂×C₄⋊C₄	—	73	1	no	—
366	C₂×C₄⋊C₄	—	73	1	no	—
367	C₂×C₄⋊C₄	—	73	1	no	—
368	C₂×C₂²⋊C₄	—	73	1	no	—
369	C₂×C₂²⋊C₄	—	73	1	no	—
370	C₂×C₂²⋊C₄	—	73	1	no	—
371	C₂×C₂²⋊C₄	—	73	1	no	—
372	C₂×C₄²	—	73	1	no	—
373	C₂×C₄²	—	73	1	no	—
374	C₂×C₄²	—	73	1	no	—
375	C₂×C₄²	—	73	1	no	—
376	C₂×C₄²	—	73	1	no	—
377	C₂×C₄²	—	73	1	no	—
378	C₂×C₄²	—	73	1	no	—
379	C₂×C₄²	—	73	1	no	—
380	C₂×C₄²	—	73	1	no	—
381	C₂×C₄²	—	73	1	no	—
382	C₂×C₄²	—	73	1	no	—
383	C₂×C₄²	—	73	1	no	—
384	C₂×C₄²	—	73	1	no	—
385	C₂×C₄²	—	73	1	no	—
386	C₂×C₄²	—	73	1	no	—
387	C₂×C₄²	—	73	1	no	—
388	C₂×C₄²	—	146	4	no	—
389	C₄⋊C₈	—	292	2	no	—
390	C₄⋊C₈	—	146	4	no	—
391	C₂²⋊C₈	—	146	4	no	—
392	C₄×C₈	—	292	2	no	—
393	C₄×C₈	—	146	4	no	—
394	#95	—	73	1	no	—
395	#95	—	73	1	no	—
396	#95	—	73	1	no	—
397	#95	—	73	1	no	—
398	#95	—	73	1	no	—
399	#95	—	73	1	no	—
400	#95	—	73	1	no	—
401	#95	—	73	1	no	—
402	C₂⁴	—	73	1	no	—
403	C₂²×C₄	—	292	1	no	—
404	C₂²×C₄	—	73	1	no	—
405	C₂²×C₄	—	73	1	no	—
406	C₂²×C₄	—	73	1	no	—
407	C₂²×C₄	—	73	1	no	—
408	C₂²×C₄	—	73	1	no	—
409	C₂²×C₄	—	73	4	no	—
410	C₂²×C₄	—	73	1	no	—
411	C₂²×C₄	—	73	1	no	—
412	C₂²×C₄	—	73	1	no	—
413	C₂²×C₄	—	73	1	no	—
414	C₂²×C₄	—	73	1	no	—
415	C₂²×C₄	—	73	1	no	—
416	C₂²×C₄	—	73	1	no	—
417	C₂²×C₄	—	73	1	no	—
418	C₂²×C₄	—	73	1	no	—
419	C₂²×C₄	—	73	1	no	—
420	C₂²×C₄	—	73	1	no	—
421	C₂²×C₄	—	73	1	no	—
422	C₂²×C₄	—	146	2	no	—
423	C₂²×C₄	—	146	2	no	—
424	C₂²×C₄	—	146	2	no	—
425	C₂²×C₄	—	146	2	no	—
426	C₂²×C₄	—	146	1	no	—
427	C₂²×C₄	—	146	2	no	—
428	C₂²×C₄	—	146	1	no	—
429	C₂²×C₄	C₂×#10596842	1	1	yes	characteristic
430	C₂×C₈	—	292	8	no	—
431	C₂×C₈	—	73	4	no	—
432	C₂×C₈	—	146	2	no	—
433	C₂×C₈	—	146	2	no	—
434	C₂×C₈	—	146	2	no	—
435	C₂×C₈	—	146	2	no	—
436	C₂×C₈	—	146	2	no	—
437	C₂×C₈	—	146	2	no	—
438	C₂×C₈	—	146	2	no	—
439	C₂×C₈	—	146	2	no	—
440	C₂×C₈	—	146	2	no	—
441	C₂×C₈	—	146	2	no	—
442	C₂×C₈	—	146	2	no	—
443	C₄⋊C₄	—	73	1	no	—
444	C₄⋊C₄	—	73	1	no	—
445	C₄⋊C₄	—	73	1	no	—
446	C₄⋊C₄	—	73	1	no	—
447	C₄⋊C₄	—	73	1	no	—
448	C₄⋊C₄	—	73	1	no	—
449	C₄⋊C₄	—	146	2	no	—
450	C₄⋊C₄	—	146	2	no	—
451	C₄⋊C₄	C₂×#10596842	1	1	yes	characteristic, complemented
452	C₄⋊C₄	C₂×#10596842	1	1	yes	characteristic, complemented
453	C₂²⋊C₄	—	73	4	no	—
454	C₂²⋊C₄	—	73	1	no	—
455	C₂²⋊C₄	—	73	1	no	—
456	C₂²⋊C₄	—	73	1	no	—
457	C₂²⋊C₄	—	73	1	no	—
458	C₂²⋊C₄	—	73	1	no	—
459	C₂²⋊C₄	—	73	1	no	—
460	C₂²⋊C₄	—	146	2	no	—
461	C₂²⋊C₄	C₂×#10596842	1	1	yes	characteristic
462	C₂²⋊C₄	C₂×#10596842	1	1	yes	characteristic
463	C₄²	—	292	1	no	—
464	C₄²	—	292	1	no	—
465	C₄²	—	73	1	no	—
466	C₄²	—	73	1	no	—
467	C₄²	—	73	1	no	—
468	C₄²	—	73	1	no	—
469	C₄²	—	73	1	no	—
470	C₄²	—	73	1	no	—
471	C₄²	—	146	1	no	—
472	C₄²	—	146	2	no	—
473	C₄²	—	146	1	no	—
474	C₄²	—	146	2	no	—
475	C₄²	—	146	1	no	—
476	C₄²	—	146	1	no	—
477	C₄²	—	146	2	no	—
478	C₄²	—	146	2	no	—
479	C₄²	—	146	2	no	—
480	C₄²	—	146	2	no	—
481	C₄²	—	146	2	no	—
482	C₄²	—	146	2	no	—
483	C₄²	—	146	2	no	—
484	C₄²	—	146	2	no	—
485	C₄²	C₂×#10596842	1	1	yes	characteristic, complemented
486	C₄²	C₂×#10596842	1	1	yes	characteristic, complemented
487	C₂³	—	73	1	no	—
488	C₂³	—	73	2	no	—
489	C₂³	—	73	2	no	—
490	C₂³	—	73	1	no	—
491	C₂³	—	146	1	no	—
492	C₂³	—	146	1	no	—
493	C₂³	—	146	1	no	—
494	C₂³	—	146	1	no	—
495	C₂³	C₂²×#10596842	1	1	yes	characteristic
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	292	4	no	—
498	C₂×C₄	—	73	2	no	—
499	C₂×C₄	—	73	1	no	—
500	C₂×C₄	—	73	2	no	—
501	C₂×C₄	—	73	1	no	—
502	C₂×C₄	—	73	2	no	—
503	C₂×C₄	—	73	2	no	—
504	C₂×C₄	—	73	2	no	—
505	C₂×C₄	—	73	2	no	—
506	C₂×C₄	—	73	1	no	—
507	C₂×C₄	—	73	1	no	—
508	C₂×C₄	—	73	1	no	—
509	C₂×C₄	—	73	1	no	—
510	C₂×C₄	—	73	1	no	—
511	C₂×C₄	—	73	1	no	—
512	C₂×C₄	—	146	1	no	—
513	C₂×C₄	—	146	1	no	—
514	C₂×C₄	—	146	1	no	—
515	C₂×C₄	—	146	1	no	—
516	C₂×C₄	—	146	1	no	—
517	C₂×C₄	—	146	1	no	—
518	C₂×C₄	—	146	1	no	—
519	C₂×C₄	—	146	1	no	—
520	C₂×C₄	—	146	1	no	—
521	C₂×C₄	—	146	1	no	—
522	C₂×C₄	—	146	1	no	—
523	C₂×C₄	—	146	1	no	—
524	C₂×C₄	—	146	2	no	—
525	C₂×C₄	—	146	2	no	—
526	C₂×C₄	—	146	1	no	—
527	C₂×C₄	—	146	1	no	—
528	C₂×C₄	—	146	1	no	—
529	C₂×C₄	—	146	1	no	—
530	C₂×C₄	—	146	1	no	—
531	C₂×C₄	—	146	1	no	—
532	C₂×C₄	—	146	1	no	—
533	C₂×C₄	—	146	1	no	—
534	C₂×C₄	—	146	1	no	—
535	C₂×C₄	—	146	4	no	—
536	C₂×C₄	—	146	4	no	—
537	C₂×C₄	—	146	1	no	—
538	C₂×C₄	—	146	1	no	—
539	C₂×C₄	—	146	1	no	—
540	C₂×C₄	—	146	1	no	—
541	C₂×C₄	—	146	1	no	—
542	C₂×C₄	—	146	1	no	—
543	C₂×C₄	—	146	1	no	—
544	C₂×C₄	—	146	1	no	—
545	C₂×C₄	—	146	2	no	—
546	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
547	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
548	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
549	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
550	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
551	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
552	C₈	—	292	2	no	—
553	C₈	—	292	2	no	—
554	C₈	—	292	2	no	—
555	C₈	—	146	4	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	73	1	no	—
559	C₂²	—	73	1	no	—
560	C₂²	—	73	1	no	—
561	C₂²	—	73	1	no	—
562	C₂²	—	73	1	no	—
563	C₂²	—	73	1	no	—
564	C₂²	—	73	2	no	—
565	C₂²	—	146	2	no	—
566	C₂²	—	146	2	no	—
567	C₂²	—	146	2	no	—
568	C₂²	—	146	2	no	—
569	C₂²	—	146	1	no	—
570	C₂²	—	146	1	no	—
571	C₂²	#17989700	1	2	yes	—
572	C₂²	C₂³×#10596842	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	292	1	no	—
580	C₄	—	292	1	no	—
581	C₄	—	292	1	no	—
582	C₄	—	73	2	no	—
583	C₄	—	73	2	no	—
584	C₄	—	146	2	no	—
585	C₄	—	146	2	no	—
586	C₄	—	146	2	no	—
587	C₄	—	146	2	no	—
588	C₄	—	146	1	no	—
589	C₄	—	146	1	no	—
590	C₄	—	146	1	no	—
591	C₄	—	146	1	no	—
592	C₄	—	146	1	no	—
593	C₄	—	146	1	no	—
594	C₂	—	2	2	no	—
595	C₂	—	73	1	no	—
596	C₂	—	73	1	no	—
597	C₂	—	73	1	no	—
598	C₂	—	73	1	no	—
599	C₂	—	146	2	no	—
600	C₂	C₂×#17989700	1	1	yes	characteristic
601	C₂	#41×#10596842	1	1	yes	characteristic
602	C₂	#22627175	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#10596842
commutator, socle	C₂²×C₇₃	C₂³×C₈
Fitting	#117×C₇₃	C₈
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂²×#64408	C₂⁴
hypercenter	#117	#10596842
hypocenter	C₇₃	#22589
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117

Complements

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

N	H ≅ G/N	type
1. #22627078	C₂	semidirect
2. #22627078	C₂	semidirect
4. #22627074	C₂	semidirect
5. #22627073	C₂	semidirect
7. C₄×C₄⋊#10596842	C₂	semidirect
9. #22627065	C₂	semidirect
86. #14556550	C₈	semidirect
87. #14556549	C₈	semidirect
88. #14556549	C₈	semidirect
89. #14556548	C₈	semidirect
90. #14556548	C₈	semidirect
91. #14556547	C₈	semidirect
92. #14556547	C₈	semidirect
99. #117×C₇₃	C₈	semidirect
160. C₄⋊Dic₇₃	C₂×C₈	semidirect
161. C₄⋊Dic₇₃	C₂×C₈	semidirect
162. #11924007	C₂×C₈	semidirect
163. #11924007	C₂×C₈	semidirect
164. #11924007	C₂×C₈	semidirect
165. #11924007	C₂×C₈	semidirect
172. C₄×Dic₇₃	C₂×C₈	semidirect
173. C₄×Dic₇₃	C₂×C₈	semidirect
174. C₄×Dic₇₃	C₂×C₈	semidirect
175. C₄×Dic₇₃	C₂×C₈	semidirect
176. C₄×Dic₇₃	C₂×C₈	semidirect
177. C₄×Dic₇₃	C₂×C₈	semidirect
179. C₄⋊C₄×C₇₃	C₂×C₈	semidirect
180. C₄⋊C₄×C₇₃	C₂×C₈	semidirect
183. C₄²×C₇₃	C₂×C₈	semidirect
184. C₄²×C₇₃	C₂×C₈	semidirect
313. C₇₃	#22589	semidirect
363. #117	#10596842	semidirect
451. C₄⋊C₄	C₂×#10596842	semidirect
452. C₄⋊C₄	C₂×#10596842	semidirect
485. C₄²	C₂×#10596842	semidirect
486. C₄²	C₂×#10596842	semidirect

Maximal subgroups

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

subgroup	index
#22627078	2
#22627076	2
#22627074	2
#22627073	2
#22627072	2
C₄×C₄⋊#10596842	2
C₂²⋊C₄×#10596842	2
#22627065	2
C₂×(C₂×#10596842)⋊C₄	2
#117×#64408	2
#22589	73