Subgroups — #34021817

Order 18688.

926 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626391	C₂	1	1	yes	maximal, characteristic
2	#117×#64408	C₂	1	1	yes	maximal, characteristic
3	#22625995	C₂	1	2	yes	maximal, complemented
4	#22625994	C₂	1	2	yes	maximal, complemented
5	#22625993	C₂	1	2	yes	maximal, complemented
6	#22625992	C₂	1	2	yes	maximal, complemented
7	#22625617	C₂	1	1	yes	maximal, characteristic
8	#22625616	C₂	1	1	yes	maximal, characteristic
9	#22625616	C₂	1	1	yes	maximal, characteristic
10	C₂×#17989452	C₂	1	1	yes	maximal, characteristic
11	#427×D₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×#11924036	C₂²	1	1	yes	characteristic
13	C₂×#14556670	C₂²	1	1	yes	characteristic
14	C₂×#14556670	C₂²	1	1	yes	characteristic
15	C₂²×C₄×#64408	C₂²	1	1	yes	characteristic
16	#17989538	C₂²	1	2	yes	—
17	#17989538	C₂²	1	2	yes	—
18	#17989534	—	2	2	no	—
19	C₄⋊C₄×#64408	C₂²	1	2	yes	—
20	C₄⋊C₄×#64408	C₂²	1	2	yes	—
21	C₄×C₄⋊#64408	—	2	1	no	—
22	C₄×C₄⋊#64408	—	2	1	no	—
23	C₂²⋊C₄×#64408	—	2	2	no	—
24	#17989523	—	2	1	no	—
25	C₄²×#64408	—	2	1	no	—
26	#17989461	C₂²	1	2	yes	—
27	#17989461	C₂²	1	2	yes	—
28	#17989460	C₂²	1	2	yes	—
29	#17989460	C₂²	1	2	yes	—
30	#17989460	C₂²	1	2	yes	—
31	#17989460	C₂²	1	2	yes	—
32	#17989452	C₂²	1	2	yes	—
33	#17989452	C₂²	1	2	yes	—
34	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
35	#117×D₇₃	C₂²	1	1	yes	characteristic
36	#117×D₇₃	C₂²	1	1	yes	characteristic
37	#17988625	C₄	1	1	yes	characteristic, complemented
38	#17988624	C₄	1	1	yes	characteristic, complemented
39	#17988624	C₄	1	1	yes	characteristic, complemented
40	#17988623	C₄	1	1	yes	characteristic, complemented
41	#17988623	C₄	1	1	yes	characteristic, complemented
42	#17988622	C₄	1	1	yes	characteristic, complemented
43	#17988622	C₄	1	1	yes	characteristic, complemented
44	#107×D₇₃	C₂²	1	1	yes	characteristic
45	#107×D₇₃	C₂²	1	1	yes	characteristic
46	#106×D₇₃	C₂²	1	1	yes	characteristic
47	#106×D₇₃	C₂²	1	1	yes	characteristic
48	#427×C₇₃	C₄	1	1	yes	characteristic, complemented
49	C₂³×#64408	D₄	1	2	yes	—
50	C₂×#11924036	—	2	1	no	—
51	C₂×#11924036	—	2	2	no	—
52	C₂×#11924036	—	2	2	no	—
53	C₂×#11924036	C₂³	1	2	yes	—
54	C₂²×#10596833	—	2	1	no	—
55	#14556670	—	2	2	no	—
56	#14556670	—	2	2	no	—
57	#14556670	—	2	2	no	—
58	#14556670	Q₈	1	4	yes	—
59	C₂×C₄⋊#64408	—	2	2	no	—
60	C₂×C₄⋊#64408	—	2	2	no	—
61	C₂×C₄⋊#64408	C₂³	1	2	yes	—
62	C₂×C₄⋊#64408	C₂³	1	2	yes	—
63	C₂×C₂²⋊#64408	—	2	1	no	—
64	C₂×C₂²⋊#64408	—	2	1	no	—
65	C₂×C₄×#64408	—	2	2	no	—
66	C₂×C₄×#64408	—	2	2	no	—
67	C₂×C₄×#64408	—	2	1	no	—
68	C₂×C₄×#64408	—	2	1	no	—
69	C₂×C₄×#64408	—	2	2	no	—
70	C₂×C₄×#64408	—	2	2	no	—
71	C₂×C₄×#64408	D₄	1	1	yes	characteristic
72	C₂×C₄×#64408	D₄	1	1	yes	characteristic
73	C₂×C₄×#64408	C₂³	1	2	yes	—
74	(C₂×#64408)⋊C₄	—	2	2	no	—
75	(C₂×#64408)⋊C₄	—	2	2	no	—
76	(C₂×#64408)⋊C₄	—	2	2	no	—
77	(C₂×#64408)⋊C₄	—	2	2	no	—
78	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
79	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
80	C₂×C₈×D₇₃	—	2	2	no	—
81	C₂×C₈×D₇₃	—	2	2	no	—
82	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
85	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
86	#14556550	C₂×C₄	1	1	yes	characteristic
87	#14556550	C₂×C₄	1	1	yes	characteristic
88	#14556549	C₂×C₄	1	1	yes	characteristic
89	#14556549	C₂×C₄	1	1	yes	characteristic
90	#14556549	C₂×C₄	1	1	yes	characteristic
91	#14556549	C₂×C₄	1	1	yes	characteristic
92	#14556548	—	2	1	no	—
93	#14556548	—	2	1	no	—
94	#14556547	—	2	1	no	—
95	#14556547	—	2	1	no	—
96	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
100	C₂²⋊C₄×D₇₃	—	2	1	no	—
101	C₂²⋊C₄×D₇₃	—	2	1	no	—
102	C₄²×D₇₃	—	2	1	no	—
103	C₄²×D₇₃	—	2	1	no	—
104	#14556525	C₂×C₄	1	1	yes	characteristic, complemented
105	#14556525	C₂×C₄	1	1	yes	characteristic, complemented
106	#14556524	C₂×C₄	1	1	yes	characteristic, complemented
107	#14556524	C₂×C₄	1	1	yes	characteristic, complemented
108	#14556524	C₂×C₄	1	1	yes	characteristic, complemented
109	#14556524	C₂×C₄	1	1	yes	characteristic, complemented
110	#14556523	C₂×C₄	1	1	yes	characteristic, complemented
111	#14556523	C₂×C₄	1	1	yes	characteristic, complemented
112	#14556522	C₂×C₄	1	1	yes	characteristic, complemented
113	#14556522	C₂×C₄	1	1	yes	characteristic, complemented
114	#14556522	C₂×C₄	1	1	yes	characteristic, complemented
115	#14556522	C₂×C₄	1	1	yes	characteristic, complemented
116	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
117	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
118	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
119	#107×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
120	#107×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
121	#106×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
122	#106×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
123	C₂²×#64408	—	2	4	no	—
124	C₂²×#64408	—	2	2	no	—
125	C₂²×#64408	—	2	4	no	—
126	C₂²×#64408	—	2	2	no	—
127	C₂²×#64408	—	4	2	no	—
128	C₂²×#64408	C₂×D₄	1	2	yes	—
129	C₂²×#64408	C₂×D₄	1	2	yes	—
130	#11924036	—	2	2	no	—
131	#11924036	—	2	2	no	—
132	#11924036	—	4	2	no	—
133	C₂×#10596833	—	2	2	no	—
134	C₂×#10596833	—	4	2	no	—
135	C₄⋊#64408	—	2	2	no	—
136	C₄⋊#64408	—	2	2	no	—
137	C₄⋊#64408	—	2	2	no	—
138	C₄⋊#64408	—	4	4	no	—
139	C₄⋊#64408	—	4	4	no	—
140	C₄⋊#64408	C₂×Q₈	1	4	yes	—
141	C₂²⋊#64408	—	2	4	no	—
142	C₂²⋊#64408	—	4	2	no	—
143	C₄×#64408	—	2	4	no	—
144	C₄×#64408	—	2	2	no	—
145	C₄×#64408	—	2	2	no	—
146	C₄×#64408	—	2	2	no	—
147	C₄×#64408	—	2	2	no	—
148	C₄×#64408	—	4	4	no	—
149	C₄×#64408	—	4	4	no	—
150	C₄×#64408	—	4	2	no	—
151	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×Dic₇₃	#41	1	1	yes	characteristic
153	C₂×C₄×D₇₃	—	2	1	no	—
154	C₂×C₄×D₇₃	—	2	1	no	—
155	C₂×C₄×D₇₃	—	2	1	no	—
156	C₂×C₄×D₇₃	—	2	1	no	—
157	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
160	C₂×C₄×D₇₃	#41	1	2	yes	—
161	C₂×C₄×D₇₃	#41	1	2	yes	—
162	C₂×C₄×D₇₃	#41	1	2	yes	—
163	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
164	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
165	C₂×#10596831	—	2	2	no	—
166	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
167	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
168	C₈×D₇₃	—	2	2	no	—
169	C₈×D₇₃	—	2	2	no	—
170	C₈×D₇₃	—	2	1	no	—
171	C₈×D₇₃	—	2	1	no	—
172	C₈×D₇₃	—	2	1	no	—
173	C₈×D₇₃	—	2	1	no	—
174	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
175	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
176	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
177	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
178	#11924007	—	2	1	no	—
179	#11924007	—	2	1	no	—
180	#11924007	—	2	1	no	—
181	#11924007	—	2	1	no	—
182	C₂²⋊Dic₇₃	—	2	1	no	—
183	C₂²⋊Dic₇₃	—	2	1	no	—
184	#11924005	—	2	1	no	—
185	#11924005	—	2	1	no	—
186	#11924005	—	2	1	no	—
187	#11924005	—	2	1	no	—
188	C₄×Dic₇₃	—	2	1	no	—
189	C₄×Dic₇₃	—	2	1	no	—
190	C₄×Dic₇₃	—	2	1	no	—
191	C₄×Dic₇₃	—	2	1	no	—
192	C₄×Dic₇₃	—	2	1	no	—
193	C₄×Dic₇₃	—	2	1	no	—
194	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₈×C₇₃	—	2	2	no	—
196	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
198	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
199	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
201	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
202	C₂²⋊C₄×C₇₃	—	2	1	no	—
203	C₂²⋊C₄×C₇₃	—	2	1	no	—
204	C₄²×C₇₃	—	2	1	no	—
205	C₄²×C₇₃	—	2	1	no	—
206	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
207	C₂²×D₇₃	—	2	2	no	—
208	C₂²×D₇₃	—	2	2	no	—
209	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
210	C₂²×D₇₃	C₂²⋊Q₈	1	2	yes	—
211	C₂²×D₇₃	#123	1	2	yes	—
212	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×#64408	—	2	2	no	—
214	C₂×#64408	—	2	2	no	—
215	C₂×#64408	—	2	4	no	—
216	C₂×#64408	—	2	2	no	—
217	C₂×#64408	—	2	2	no	—
218	C₂×#64408	—	2	2	no	—
219	C₂×#64408	—	4	8	no	—
220	C₂×#64408	—	4	2	no	—
221	C₂×#64408	—	4	2	no	—
222	C₂×#64408	—	4	2	no	—
223	C₂×#64408	—	4	2	no	—
224	C₂×#64408	—	4	2	no	—
225	C₂×#64408	#135	1	4	yes	—
226	C₂×C₄×C₇₃	—	2	1	no	—
227	C₂×C₄×C₇₃	—	2	1	no	—
228	C₂×C₄×C₇₃	—	2	1	no	—
229	C₂×C₄×C₇₃	—	2	1	no	—
230	C₂×C₄×C₇₃	#117	1	2	yes	—
231	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₇₃	C₄×Q₈	1	2	yes	—
233	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
234	C₂×Dic₇₃	—	2	1	no	—
235	C₂×Dic₇₃	—	2	1	no	—
236	C₂×Dic₇₃	—	2	1	no	—
237	C₂×Dic₇₃	—	2	1	no	—
238	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
239	C₂×Dic₇₃	#125	1	2	yes	—
240	C₂×Dic₇₃	#126	1	2	yes	—
241	C₂×Dic₇₃	C₂×#41	1	1	yes	characteristic
242	C₄×D₇₃	—	4	2	no	—
243	C₄×D₇₃	—	4	2	no	—
244	C₄×D₇₃	—	4	2	no	—
245	C₄×D₇₃	—	4	2	no	—
246	C₄×D₇₃	#117	1	2	yes	—
247	C₄×D₇₃	C₄×Q₈	1	2	yes	—
248	C₄×D₇₃	C₂²⋊Q₈	1	2	yes	—
249	C₄×D₇₃	#123	1	2	yes	—
250	C₄×D₇₃	#125	1	2	yes	—
251	C₄×D₇₃	#126	1	2	yes	—
252	C₄×D₇₃	C₂²×Q₈	1	1	yes	characteristic
253	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
254	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
255	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
256	#10596833	—	4	2	no	—
257	C₈×C₇₃	—	2	1	no	—
258	C₈×C₇₃	—	2	1	no	—
259	#10596831	—	2	1	no	—
260	#10596831	—	2	1	no	—
261	C₂²×C₇₃	—	2	1	no	—
262	C₂²×C₇₃	—	2	1	no	—
263	C₂²×C₇₃	#387	1	2	yes	—
264	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
265	C₂×D₇₃	—	2	1	no	—
266	C₂×D₇₃	—	2	1	no	—
267	C₂×D₇₃	—	2	4	no	—
268	C₂×D₇₃	—	2	4	no	—
269	C₂×D₇₃	#387	1	2	yes	—
270	C₂×D₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×D₇₃	C₂×#123	1	1	yes	characteristic
272	C₂×D₇₃	C₂×#135	1	2	yes	—
273	C₂×D₇₃	#575	1	2	yes	—
274	#64408	—	2	4	no	—
275	#64408	—	4	4	no	—
276	#64408	—	4	2	no	—
277	#64408	—	8	2	no	—
278	C₄×C₇₃	—	4	1	no	—
279	C₄×C₇₃	—	4	1	no	—
280	C₄×C₇₃	—	4	1	no	—
281	C₄×C₇₃	—	4	1	no	—
282	C₄×C₇₃	#387	1	2	yes	—
283	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
284	C₄×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
285	Dic₇₃	—	4	1	no	—
286	Dic₇₃	—	4	1	no	—
287	Dic₇₃	—	4	1	no	—
288	Dic₇₃	—	4	1	no	—
289	Dic₇₃	#387	1	2	yes	—
290	Dic₇₃	C₂×#125	1	1	yes	characteristic
291	Dic₇₃	C₂×#126	1	1	yes	characteristic
292	#21032	—	73	1	no	maximal, Sylow
293	C₂×C₇₃	—	2	2	no	—
294	C₂×C₇₃	C₂×#387	1	1	yes	characteristic
295	C₂×C₇₃	C₄×#135	1	1	yes	characteristic
296	C₂×C₇₃	#2943	1	1	yes	characteristic
297	D₇₃	—	2	2	no	—
298	D₇₃	#3076	1	2	yes	—
299	D₇₃	#3091	1	2	yes	—
300	C₂×#427	—	73	1	no	—
301	#2296	—	73	1	no	—
302	C₄×#117	—	73	1	no	—
303	#1921	—	73	2	no	—
304	#1920	—	73	2	no	—
305	#1919	—	73	2	no	—
306	#1918	—	73	2	no	—
307	#1735	—	73	1	no	—
308	#1735	—	73	1	no	—
309	#1735	—	73	1	no	—
310	C₂×#336	—	73	1	no	—
311	C₇₃	#21032	1	1	yes	characteristic, complemented, Sylow
312	C₂³×C₈	—	73	1	no	—
313	C₂³×C₈	—	73	1	no	—
314	C₂×#117	—	73	1	no	—
315	C₂×#117	—	73	1	no	—
316	C₂×#117	—	73	1	no	—
317	C₂×#117	—	73	1	no	—
318	C₂²×C₄²	—	73	1	no	—
319	#427	—	73	1	no	—
320	#427	—	73	1	no	—
321	#427	—	73	1	no	—
322	#427	—	73	1	no	—
323	#427	—	73	1	no	—
324	#427	—	73	1	no	—
325	#427	—	73	1	no	—
326	#427	#64408	1	1	yes	characteristic, complemented
327	C₂×#107	—	73	1	no	—
328	C₂×#107	—	73	1	no	—
329	C₂×#106	—	73	1	no	—
330	C₂×#106	—	73	1	no	—
331	#389	—	73	2	no	—
332	#389	—	73	2	no	—
333	#385	—	146	2	no	—
334	C₄×C₄⋊C₄	—	73	2	no	—
335	C₄×C₄⋊C₄	—	73	2	no	—
336	C₄×C₄⋊C₄	—	146	1	no	—
337	C₄×C₄⋊C₄	—	146	1	no	—
338	C₄×C₂²⋊C₄	—	146	2	no	—
339	#376	—	146	1	no	—
340	C₄³	—	146	1	no	—
341	#340	—	73	2	no	—
342	#340	—	73	2	no	—
343	#340	—	73	2	no	—
344	#340	—	73	2	no	—
345	#340	—	73	2	no	—
346	#340	—	73	2	no	—
347	#336	—	73	2	no	—
348	#336	—	73	2	no	—
349	C₂³×C₄	—	73	2	no	—
350	C₂³×C₄	—	73	1	no	—
351	C₂²×C₈	—	73	1	no	—
352	C₂²×C₈	—	73	1	no	—
353	C₂²×C₈	—	73	1	no	—
354	C₂²×C₈	—	73	1	no	—
355	C₂²×C₈	—	73	1	no	—
356	C₂²×C₈	—	73	2	no	—
357	C₂²×C₈	—	146	2	no	—
358	C₂²×C₈	—	146	2	no	—
359	C₂²×C₈	—	146	1	no	—
360	C₂²×C₈	—	146	2	no	—
361	C₂²×C₈	—	146	2	no	—
362	C₂²×C₈	—	146	1	no	—
363	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
364	#117	—	73	4	no	—
365	#117	—	73	1	no	—
366	#117	—	73	1	no	—
367	#117	—	73	1	no	—
368	#117	—	73	1	no	—
369	#117	—	73	1	no	—
370	#117	—	73	1	no	—
371	#117	—	146	1	no	—
372	#117	—	146	1	no	—
373	#117	—	146	2	no	—
374	#117	—	146	2	no	—
375	#117	—	146	1	no	—
376	#117	—	146	1	no	—
377	#117	—	146	2	no	—
378	#117	C₂×#64408	1	1	yes	characteristic
379	#117	C₂×#64408	1	1	yes	characteristic
380	C₂×C₄⋊C₄	—	73	2	no	—
381	C₂×C₄⋊C₄	—	73	1	no	—
382	C₂×C₄⋊C₄	—	73	1	no	—
383	C₂×C₄⋊C₄	—	73	1	no	—
384	C₂×C₄⋊C₄	—	73	1	no	—
385	C₂×C₄⋊C₄	—	73	2	no	—
386	C₂×C₄⋊C₄	—	146	2	no	—
387	C₂×C₄⋊C₄	—	146	2	no	—
388	C₂×C₂²⋊C₄	—	146	1	no	—
389	C₂×C₂²⋊C₄	—	146	1	no	—
390	C₂×C₂²⋊C₄	—	146	1	no	—
391	C₂×C₂²⋊C₄	—	146	1	no	—
392	C₂×C₄²	—	73	2	no	—
393	C₂×C₄²	—	73	1	no	—
394	C₂×C₄²	—	73	1	no	—
395	C₂×C₄²	—	146	1	no	—
396	C₂×C₄²	—	146	1	no	—
397	C₂×C₄²	—	146	1	no	—
398	C₂×C₄²	—	146	2	no	—
399	C₂×C₄²	—	146	2	no	—
400	C₂×C₄²	—	146	1	no	—
401	C₂×C₄²	—	146	2	no	—
402	C₂×C₄²	—	146	2	no	—
403	#107	—	73	1	no	—
404	#107	—	73	1	no	—
405	#107	—	73	1	no	—
406	#107	—	73	1	no	—
407	#107	—	73	1	no	—
408	#107	—	73	1	no	—
409	#107	C₂×#64408	1	1	yes	characteristic, complemented
410	#107	C₂×#64408	1	1	yes	characteristic, complemented
411	#106	—	73	1	no	—
412	#106	—	73	1	no	—
413	#106	—	73	1	no	—
414	#106	—	73	1	no	—
415	#106	—	73	1	no	—
416	#106	—	73	1	no	—
417	#106	C₂×#64408	1	1	yes	characteristic, complemented
418	#106	C₂×#64408	1	1	yes	characteristic, complemented
419	#95	—	146	2	no	—
420	#95	—	146	2	no	—
421	#95	—	146	2	no	—
422	#95	—	146	2	no	—
423	C₂⁴	—	73	1	no	—
424	C₂²×C₄	—	292	2	no	—
425	C₂²×C₄	—	73	1	no	—
426	C₂²×C₄	—	73	2	no	—
427	C₂²×C₄	—	73	2	no	—
428	C₂²×C₄	—	73	1	no	—
429	C₂²×C₄	—	73	1	no	—
430	C₂²×C₄	—	73	2	no	—
431	C₂²×C₄	—	73	2	no	—
432	C₂²×C₄	—	73	1	no	—
433	C₂²×C₄	—	73	1	no	—
434	C₂²×C₄	—	73	2	no	—
435	C₂²×C₄	—	73	2	no	—
436	C₂²×C₄	—	146	1	no	—
437	C₂²×C₄	—	146	1	no	—
438	C₂²×C₄	—	146	1	no	—
439	C₂²×C₄	—	146	1	no	—
440	C₂²×C₄	—	146	2	no	—
441	C₂²×C₄	—	146	4	no	—
442	C₂²×C₄	—	146	2	no	—
443	C₂²×C₄	—	146	4	no	—
444	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	292	2	no	—
447	C₂×C₈	—	292	2	no	—
448	C₂×C₈	—	73	1	no	—
449	C₂×C₈	—	73	1	no	—
450	C₂×C₈	—	146	1	no	—
451	C₂×C₈	—	146	1	no	—
452	C₂×C₈	—	146	1	no	—
453	C₂×C₈	—	146	1	no	—
454	C₂×C₈	—	146	2	no	—
455	C₂×C₈	—	146	2	no	—
456	C₂×C₈	—	146	2	no	—
457	C₂×C₈	—	146	2	no	—
458	C₂×C₈	—	146	2	no	—
459	C₂×C₈	—	146	2	no	—
460	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
461	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
462	C₄⋊C₄	—	292	4	no	—
463	C₄⋊C₄	—	292	4	no	—
464	C₄⋊C₄	—	73	4	no	—
465	C₄⋊C₄	—	73	1	no	—
466	C₄⋊C₄	—	73	1	no	—
467	C₄⋊C₄	—	73	1	no	—
468	C₄⋊C₄	—	73	1	no	—
469	C₄⋊C₄	—	146	1	no	—
470	C₄⋊C₄	—	146	1	no	—
471	C₄⋊C₄	—	146	1	no	—
472	C₄⋊C₄	—	146	1	no	—
473	C₄⋊C₄	—	146	2	no	—
474	C₄⋊C₄	—	146	2	no	—
475	C₄⋊C₄	—	146	2	no	—
476	C₄⋊C₄	C₂²×#64408	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×#64408	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×#64408	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×#64408	1	1	yes	characteristic
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	292	2	no	—
483	C₂²⋊C₄	—	146	1	no	—
484	C₂²⋊C₄	—	146	1	no	—
485	C₂²⋊C₄	—	146	1	no	—
486	C₂²⋊C₄	—	146	1	no	—
487	C₂²⋊C₄	—	146	4	no	—
488	C₂²⋊C₄	—	146	1	no	—
489	C₂²⋊C₄	—	146	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	292	4	no	—
493	C₄²	—	292	2	no	—
494	C₄²	—	292	4	no	—
495	C₄²	—	146	1	no	—
496	C₄²	—	146	1	no	—
497	C₄²	—	146	1	no	—
498	C₄²	—	146	1	no	—
499	C₄²	—	146	2	no	—
500	C₄²	—	146	2	no	—
501	C₄²	—	146	2	no	—
502	C₄²	—	146	2	no	—
503	C₄²	—	146	4	no	—
504	C₄²	—	146	1	no	—
505	C₄²	—	146	1	no	—
506	C₂³	—	73	1	no	—
507	C₂³	—	73	1	no	—
508	C₂³	—	73	2	no	—
509	C₂³	—	73	2	no	—
510	C₂³	—	146	2	no	—
511	C₂³	—	146	2	no	—
512	C₂³	D₄×#64408	1	1	yes	characteristic
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	292	2	no	—
518	C₂×C₄	—	292	2	no	—
519	C₂×C₄	—	292	2	no	—
520	C₂×C₄	—	292	2	no	—
521	C₂×C₄	—	292	2	no	—
522	C₂×C₄	—	292	2	no	—
523	C₂×C₄	—	292	8	no	—
524	C₂×C₄	—	292	2	no	—
525	C₂×C₄	—	292	2	no	—
526	C₂×C₄	—	292	2	no	—
527	C₂×C₄	—	73	1	no	—
528	C₂×C₄	—	73	1	no	—
529	C₂×C₄	—	73	2	no	—
530	C₂×C₄	—	73	2	no	—
531	C₂×C₄	—	73	1	no	—
532	C₂×C₄	—	73	1	no	—
533	C₂×C₄	—	73	2	no	—
534	C₂×C₄	—	73	1	no	—
535	C₂×C₄	—	73	1	no	—
536	C₂×C₄	—	73	2	no	—
537	C₂×C₄	—	73	2	no	—
538	C₂×C₄	—	73	2	no	—
539	C₂×C₄	—	73	2	no	—
540	C₂×C₄	—	73	2	no	—
541	C₂×C₄	—	73	4	no	—
542	C₂×C₄	—	146	2	no	—
543	C₂×C₄	—	146	4	no	—
544	C₂×C₄	—	146	2	no	—
545	C₂×C₄	—	146	2	no	—
546	C₂×C₄	—	146	1	no	—
547	C₂×C₄	—	146	1	no	—
548	C₂×C₄	—	146	1	no	—
549	C₂×C₄	—	146	1	no	—
550	C₂×C₄	—	146	2	no	—
551	C₂×C₄	—	146	2	no	—
552	C₂×C₄	#14556670	1	2	yes	—
553	C₂×C₄	D₄×#64408	1	1	yes	characteristic
554	C₂×C₄	Q₈×#64408	1	2	yes	—
555	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	292	2	no	—
559	C₈	—	146	1	no	—
560	C₈	—	146	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	73	1	no	—
564	C₂²	—	73	1	no	—
565	C₂²	—	73	2	no	—
566	C₂²	—	73	2	no	—
567	C₂²	—	73	2	no	—
568	C₂²	—	146	4	no	—
569	C₂²	—	146	4	no	—
570	C₂²	—	146	1	no	—
571	C₂²	—	146	1	no	—
572	C₂²	#17989536	1	2	yes	—
573	C₂²	C₂×D₄×#64408	1	1	yes	characteristic
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	292	2	no	—
579	C₄	—	292	4	no	—
580	C₄	—	292	1	no	—
581	C₄	—	292	1	no	—
582	C₄	—	292	1	no	—
583	C₄	—	292	1	no	—
584	C₄	—	584	2	no	—
585	C₄	—	73	1	no	—
586	C₄	—	73	1	no	—
587	C₄	—	73	2	no	—
588	C₄	—	146	4	no	—
589	C₄	#17989536	1	2	yes	—
590	C₄	C₂×#14556670	1	1	yes	characteristic
591	C₄	C₂×Q₈×#64408	1	1	yes	characteristic
592	C₂	—	2	2	no	—
593	C₂	—	73	2	no	—
594	C₂	—	73	2	no	—
595	C₂	—	146	2	no	—
596	C₂	C₂×#17989536	1	1	yes	characteristic
597	C₂	#135×#64408	1	1	yes	characteristic
598	C₂	#22626685	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#64408
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#64408
Fitting	#427×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂³×D₇₃	C₂×D₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#427	#64408
hypocenter	C₇₃	#21032
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

Complements

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

N	H ≅ G/N	type
3. #22625995	C₂	semidirect
4. #22625994	C₂	semidirect
5. #22625993	C₂	semidirect
6. #22625992	C₂	semidirect
37. #17988625	C₄	semidirect
38. #17988624	C₄	semidirect
39. #17988624	C₄	semidirect
40. #17988623	C₄	semidirect
41. #17988623	C₄	semidirect
42. #17988622	C₄	semidirect
43. #17988622	C₄	semidirect
48. #427×C₇₃	C₄	semidirect
104. #14556525	C₂×C₄	semidirect
105. #14556525	C₂×C₄	semidirect
106. #14556524	C₂×C₄	semidirect
107. #14556524	C₂×C₄	semidirect
108. #14556524	C₂×C₄	semidirect
109. #14556524	C₂×C₄	semidirect
110. #14556523	C₂×C₄	semidirect
111. #14556523	C₂×C₄	semidirect
112. #14556522	C₂×C₄	semidirect
113. #14556522	C₂×C₄	semidirect
114. #14556522	C₂×C₄	semidirect
115. #14556522	C₂×C₄	semidirect
119. #107×C₇₃	C₂×C₄	semidirect
120. #107×C₇₃	C₂×C₄	semidirect
121. #106×C₇₃	C₂×C₄	semidirect
122. #106×C₇₃	C₂×C₄	semidirect
311. C₇₃	#21032	semidirect
326. #427	#64408	semidirect
409. #107	C₂×#64408	semidirect
410. #107	C₂×#64408	semidirect
417. #106	C₂×#64408	semidirect
418. #106	C₂×#64408	semidirect

Maximal subgroups

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

subgroup	index
#22626391	2
#117×#64408	2
#22625995	2
#22625994	2
#22625993	2
#22625992	2
#22625617	2
#22625616	2
C₂×#17989452	2
#427×D₇₃	2
#21032	73