Subgroups — #33239182

Order 18688.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989003	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14556531	C₂	1	1	yes	maximal, characteristic, complemented
3	#22618625	C₂	1	1	yes	maximal, characteristic
4	#22611760	C₂	1	2	yes	maximal, complemented
5	#22611759	C₂	1	2	yes	maximal, complemented
6	#22611753	C₂	1	2	yes	maximal, complemented
7	#22611748	C₂	1	2	yes	maximal, complemented
8	#22611689	C₂	1	1	yes	maximal, characteristic, complemented
9	#22611544	C₂	1	1	yes	maximal, characteristic, complemented
10	#22611527	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂²⋊C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556597	C₂²	1	1	yes	characteristic
13	#17989098	C₄	1	1	yes	characteristic
14	#17989003	—	2	4	no	—
15	C₂×#14556531	—	2	4	no	—
16	C₂×#14556531	C₂²	1	2	yes	—
17	C₂×#14556531	C₂²	1	1	yes	characteristic
18	C₂×#14556531	C₂²	1	1	yes	characteristic
19	C₂×#14556530	C₂²	1	2	yes	complemented
20	C₂²×#11924003	C₂²	1	2	yes	—
21	C₂×C₁₆×D₇₃	C₂²	1	2	yes	complemented
22	#17988658	C₄	1	2	yes	—
23	#17988658	C₄	1	2	yes	—
24	C₈×C₂²⋊D₇₃	C₂²	1	2	yes	—
25	C₈×C₂²⋊D₇₃	C₂²	1	2	yes	—
26	#17988613	C₄	1	1	yes	characteristic
27	#17988553	C₄	1	1	yes	characteristic
28	#17988551	C₄	1	1	yes	characteristic
29	#17988542	C₂²	1	1	yes	characteristic
30	#17988405	C₂²	1	2	yes	complemented
31	#17988405	C₂²	1	2	yes	complemented
32	#17988366	C₂²	1	2	yes	complemented
33	#17988366	C₂²	1	2	yes	complemented
34	#17988362	C₂²	1	2	yes	complemented
35	C₁₆×Dic₇₃	C₂²	1	2	yes	complemented
36	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
37	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
38	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
39	C₂²⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic
40	C₂²⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic
41	C₂²⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic
42	C₂²⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×#11924028	C₂×C₄	1	1	yes	characteristic
44	#14556597	—	2	2	no	—
45	#14556597	—	2	2	no	—
46	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
47	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
48	C₂×#11924011	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₇₃	C₂³	1	2	yes	—
50	#14556574	C₈	1	2	yes	—
51	#14556570	C₈	1	1	yes	characteristic
52	#14556570	C₈	1	1	yes	characteristic
53	#14556565	C₈	1	1	yes	characteristic
54	#14556565	C₈	1	1	yes	characteristic
55	#14556560	C₈	1	2	yes	—
56	C₄×C₂²⋊D₇₃	C₂×C₄	1	2	yes	—
57	C₄×C₂²⋊D₇₃	C₂×C₄	1	2	yes	—
58	#14556550	C₂×C₄	1	1	yes	characteristic
59	#14556531	—	2	4	no	—
60	#14556531	—	2	2	no	—
61	#14556531	D₄	1	4	yes	complemented
62	#14556530	—	2	4	no	—
63	C₂×#11924003	—	2	4	no	—
64	C₂×#11924003	C₂³	1	2	yes	—
65	C₂×#11924003	C₂³	1	2	yes	—
66	C₁₆×D₇₃	—	2	4	no	—
67	#14556520	C₂×C₄	1	2	yes	—
68	#14556520	C₂×C₄	1	2	yes	—
69	C₂²⋊#10596831	C₂×C₄	1	2	yes	—
70	C₂²⋊#10596831	C₂×C₄	1	2	yes	—
71	#14556503	C₂×C₄	1	2	yes	—
72	#14556503	C₂×C₄	1	2	yes	—
73	#14556501	C₂×C₄	1	2	yes	—
74	C₈×Dic₇₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₇₃	—	2	2	no	—
77	C₂²×C₈×C₇₃	—	2	2	no	—
78	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
84	C₂×C₁₆×C₇₃	—	2	2	no	—
85	C₂×C₁₆×C₇₃	—	2	2	no	—
86	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
87	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
88	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
89	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
90	#11924028	—	2	2	no	—
91	#11924028	—	2	2	no	—
92	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
93	C₂×D₂₉₂	C₂×C₈	1	1	yes	characteristic
94	C₂×C₂²⋊D₇₃	C₂×C₈	1	2	yes	—
95	C₂×C₂²⋊D₇₃	C₂×C₈	1	2	yes	—
96	C₂×C₂²⋊D₇₃	C₂×C₈	1	2	yes	—
97	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
98	#11924012	—	2	2	no	—
99	#11924012	—	2	2	no	—
100	#11924011	—	2	4	no	—
101	C₂×#10596831	C₂²×C₄	1	2	yes	—
102	C₂×#10596831	C₂²×C₄	1	2	yes	—
103	C₈×D₇₃	—	2	2	no	—
104	C₈×D₇₃	—	2	2	no	—
105	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
106	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
107	#11924007	C₂×C₈	1	2	yes	—
108	#11924007	C₂×C₈	1	2	yes	—
109	C₂²⋊Dic₇₃	C₂×C₈	1	2	yes	—
110	C₂²⋊Dic₇₃	C₂×C₈	1	2	yes	—
111	C₂²⋊Dic₇₃	C₂×C₈	1	2	yes	—
112	#11924005	C₂×C₈	1	2	yes	—
113	#11924005	C₂×C₈	1	2	yes	—
114	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
115	#11924003	—	2	2	no	—
116	#11924003	C₂×D₄	1	4	yes	—
117	C₂⁴×C₇₃	C₂×C₈	1	1	yes	characteristic
118	C₂²×C₄×C₇₃	—	2	2	no	—
119	C₂²×C₄×C₇₃	—	2	2	no	—
120	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
121	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
122	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
123	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₇₃	—	2	2	no	—
127	C₂×C₈×C₇₃	—	2	2	no	—
128	C₂×C₈×C₇₃	—	2	2	no	—
129	C₂×C₈×C₇₃	—	2	1	no	—
130	C₂×C₈×C₇₃	—	2	1	no	—
131	C₂×C₈×C₇₃	—	2	1	no	—
132	C₂×C₈×C₇₃	—	2	1	no	—
133	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₇₃	#41	1	2	yes	—
138	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
139	C₁₆×C₇₃	—	2	1	no	—
140	C₁₆×C₇₃	—	2	1	no	—
141	C₁₆×C₇₃	—	2	1	no	—
142	C₁₆×C₇₃	—	2	1	no	—
143	C₂³×C₇₃	—	2	2	no	—
144	C₂³×C₇₃	—	2	2	no	—
145	C₂³×C₇₃	—	4	1	no	—
146	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
147	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
148	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₇₃	C₂²×C₈	1	2	yes	—
150	C₂×C₄×C₇₃	—	2	2	no	—
151	C₂×C₄×C₇₃	—	2	1	no	—
152	C₂×C₄×C₇₃	—	2	1	no	—
153	C₂×C₄×C₇₃	—	2	1	no	—
154	C₂×C₄×C₇₃	—	2	1	no	—
155	C₂×C₄×C₇₃	—	2	2	no	—
156	C₂×C₄×C₇₃	—	2	2	no	—
157	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
160	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₇₃	#131	1	2	yes	—
162	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
163	C₂²⋊D₇₃	—	2	4	no	—
164	C₂²⋊D₇₃	—	2	4	no	—
165	C₂²⋊D₇₃	—	4	2	no	—
166	C₂×Dic₇₃	C₂²×C₈	1	2	yes	—
167	C₂×Dic₇₃	C₂²×C₈	1	2	yes	—
168	C₂×Dic₇₃	C₂²×C₈	1	2	yes	—
169	D₂₉₂	—	2	2	no	—
170	C₄×D₇₃	—	2	2	no	—
171	C₄×D₇₃	—	2	2	no	—
172	Dic₁₄₆	—	2	2	no	—
173	C₈×C₇₃	—	2	1	no	—
174	C₈×C₇₃	—	2	1	no	—
175	C₈×C₇₃	C₄×D₄	1	2	yes	—
176	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
177	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
178	#10596831	—	2	2	no	—
179	#10596831	—	2	2	no	—
180	C₂²×C₇₃	—	2	1	no	—
181	C₂²×C₇₃	—	2	1	no	—
182	C₂²×C₇₃	—	2	1	no	—
183	C₂²×C₇₃	—	2	1	no	—
184	C₂²×C₇₃	—	2	1	no	—
185	C₂²×C₇₃	—	2	1	no	—
186	C₂²×C₇₃	—	2	1	no	—
187	C₂²×C₇₃	—	4	4	no	—
188	C₂²×C₇₃	C₈×D₄	1	2	yes	—
189	C₂²×C₇₃	#504	1	2	yes	complemented
190	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
191	C₂×D₇₃	—	2	2	no	—
192	C₂×D₇₃	—	2	2	no	—
193	C₂×D₇₃	—	2	2	no	—
194	C₄×C₇₃	—	2	1	no	—
195	C₄×C₇₃	—	2	1	no	—
196	C₄×C₇₃	C₈×D₄	1	2	yes	—
197	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
198	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
199	Dic₇₃	—	2	2	no	—
200	Dic₇₃	—	2	2	no	—
201	Dic₇₃	—	2	2	no	—
202	#33436	—	73	1	no	maximal, Sylow
203	C₂×C₇₃	—	2	2	no	—
204	C₂×C₇₃	—	2	2	no	—
205	C₂×C₇₃	—	4	1	no	—
206	C₂×C₇₃	C₂×C₈×D₄	1	1	yes	characteristic
207	C₂×C₇₃	C₂×#504	1	1	yes	characteristic
208	C₂×C₇₃	#3407	1	1	yes	characteristic
209	D₇₃	—	4	2	no	—
210	C₂×#504	—	73	1	no	—
211	C₂²×M₃₂	—	73	1	no	—
212	#2929	—	73	1	no	—
213	#2169	—	73	2	no	—
214	#2168	—	73	2	no	—
215	#2168	—	73	2	no	—
216	D₄×C₁₆	—	73	2	no	—
217	#2151	—	73	1	no	—
218	#2113	—	73	1	no	—
219	C₂×C₂²⋊C₁₆	D₇₃	1	1	yes	characteristic, complemented
220	#2108	—	73	1	no	—
221	C₇₃	#33436	1	1	yes	characteristic, complemented, Sylow
222	C₂×#131	—	73	1	no	—
223	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic
224	#525	—	73	1	no	—
225	#504	—	146	4	no	—
226	C₂×M₃₂	—	73	1	no	—
227	C₂×M₃₂	—	73	1	no	—
228	C₂×M₃₂	—	73	2	no	—
229	C₂×M₃₂	—	73	2	no	—
230	C₂×M₃₂	—	146	4	no	—
231	C₂²×C₁₆	—	73	2	no	—
232	C₂²×C₁₆	—	73	2	no	—
233	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
234	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
235	#435	—	73	2	no	—
236	#435	—	73	2	no	—
237	C₈×D₄	—	73	2	no	—
238	C₈×D₄	—	73	2	no	—
239	#424	—	73	1	no	—
240	#408	—	73	1	no	—
241	#407	—	73	1	no	—
242	#405	—	73	1	no	—
243	C₄⋊C₁₆	—	73	2	no	—
244	C₄⋊C₁₆	—	73	2	no	—
245	C₂²⋊C₁₆	—	73	2	no	—
246	C₂²⋊C₁₆	—	73	2	no	—
247	C₂²⋊C₁₆	C₂×D₇₃	1	1	yes	characteristic
248	C₂²⋊C₁₆	C₂×D₇₃	1	1	yes	characteristic
249	C₂²⋊C₁₆	C₂×D₇₃	1	1	yes	characteristic
250	C₂²⋊C₁₆	C₂×D₇₃	1	1	yes	characteristic
251	#346	—	73	2	no	—
252	C₄×C₁₆	—	73	2	no	—
253	C₂×#41	—	73	1	no	—
254	C₂³×C₄	C₄×D₇₃	1	1	yes	characteristic
255	#131	—	146	2	no	—
256	#131	—	146	2	no	—
257	C₂×M₁₆	—	73	1	no	—
258	C₂×M₁₆	—	73	1	no	—
259	C₂×M₁₆	—	73	2	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	73	2	no	—
263	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
264	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
265	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
269	#123	—	73	2	no	—
270	C₂²⋊Q₈	—	73	1	no	—
271	C₂²⋊Q₈	—	73	1	no	—
272	#121	—	73	1	no	—
273	#121	—	73	1	no	—
274	#120	—	73	2	no	—
275	C₄×D₄	—	73	2	no	—
276	C₄×D₄	—	73	2	no	—
277	#117	—	73	1	no	—
278	M₃₂	—	73	4	no	—
279	M₃₂	—	146	4	no	—
280	M₃₂	—	146	4	no	—
281	M₃₂	—	146	2	no	—
282	C₂×C₁₆	—	2	2	no	—
283	C₂×C₁₆	—	2	2	no	—
284	C₂×C₁₆	—	73	2	no	—
285	C₂×C₁₆	—	73	2	no	—
286	C₂×C₁₆	—	146	4	no	—
287	C₂×C₁₆	—	146	4	no	—
288	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
289	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
290	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
291	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
292	C₄⋊C₈	—	73	2	no	—
293	C₄⋊C₈	—	73	2	no	—
294	C₂²⋊C₈	—	73	2	no	—
295	C₂²⋊C₈	—	73	2	no	—
296	C₂²⋊C₈	—	73	2	no	—
297	C₂²⋊C₈	—	73	2	no	—
298	#97	—	73	2	no	—
299	C₄×C₈	—	73	2	no	—
300	C₂⁴	C₈×D₇₃	1	1	yes	characteristic
301	#41	—	146	2	no	—
302	#41	—	146	2	no	—
303	C₂×Q₈	—	73	1	no	—
304	C₂×D₄	—	73	2	no	—
305	C₂×D₄	—	73	2	no	—
306	C₂×D₄	—	73	2	no	—
307	C₂×D₄	—	73	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	73	2	no	—
311	C₂²×C₄	C₈×D₇₃	1	1	yes	characteristic
312	C₂²×C₄	C₈×D₇₃	1	1	yes	characteristic
313	C₂²×C₄	C₈×D₇₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
317	M₁₆	—	146	2	no	—
318	M₁₆	—	146	2	no	—
319	M₁₆	—	146	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	73	2	no	—
328	C₂×C₈	—	73	2	no	—
329	C₂×C₈	—	146	2	no	—
330	C₂×C₈	—	146	2	no	—
331	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
332	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
334	C₂×C₈	D₄×D₇₃	1	2	yes	—
335	C₂×C₈	#11924027	1	2	yes	—
336	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
337	C₄⋊C₄	—	73	2	no	—
338	C₄⋊C₄	—	73	2	no	—
339	C₄⋊C₄	—	73	1	no	—
340	C₄⋊C₄	—	73	1	no	—
341	C₂²⋊C₄	—	73	2	no	—
342	C₂²⋊C₄	—	73	2	no	—
343	C₂²⋊C₄	—	73	2	no	—
344	C₂²⋊C₄	—	73	2	no	—
345	C₂²⋊C₄	—	73	2	no	—
346	C₄²	—	73	2	no	—
347	C₁₆	—	2	1	no	—
348	C₁₆	—	2	1	no	—
349	C₁₆	—	2	1	no	—
350	C₁₆	—	2	1	no	—
351	C₁₆	—	73	4	no	—
352	C₁₆	—	146	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	73	2	no	—
357	C₂³	C₂×C₈×D₇₃	1	1	yes	characteristic
358	C₂³	C₂×C₈×D₇₃	1	1	yes	characteristic
359	C₂³	C₂×C₈×D₇₃	1	1	yes	characteristic
360	Q₈	—	146	2	no	—
361	D₄	—	292	2	no	—
362	D₄	—	146	4	no	—
363	D₄	—	146	4	no	—
364	D₄	—	146	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	73	2	no	—
373	C₂×C₄	—	73	2	no	—
374	C₂×C₄	—	73	2	no	—
375	C₂×C₄	—	146	2	no	—
376	C₂×C₄	—	146	2	no	—
377	C₂×C₄	#14556551	1	2	yes	—
378	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
379	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
380	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
381	C₂×C₄	#14556599	1	2	yes	—
382	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	146	2	no	—
386	C₈	—	146	2	no	—
387	C₈	#14556551	1	2	yes	—
388	C₈	C₂×D₄×D₇₃	1	1	yes	characteristic
389	C₈	C₂×#11924027	1	1	yes	characteristic
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	146	2	no	—
399	C₂²	—	146	2	no	—
400	C₂²	—	146	2	no	—
401	C₂²	#17988650	1	2	yes	—
402	C₂²	#17989003	1	2	yes	complemented
403	C₂²	C₂²×C₈×D₇₃	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	146	2	no	—
407	C₄	—	146	2	no	—
408	C₄	—	146	2	no	—
409	C₄	#17988650	1	2	yes	—
410	C₄	C₂×#14556551	1	1	yes	characteristic
411	C₄	C₂×#14556599	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	292	2	no	—
416	C₂	C₂×#17988650	1	1	yes	characteristic
417	C₂	C₂×#17989003	1	1	yes	characteristic
418	C₂	#22623033	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₇₃
commutator, socle	C₂²×C₇₃	C₂³×C₈
Fitting	C₂×C₂²⋊C₁₆×C₇₃	C₂
prime radical	#17989098	C₄
cosocle	C₂×C₈×C₇₃	C₂⁴
hypercenter	C₂×C₂²⋊C₁₆	D₇₃
hypocenter	C₇₃	#33436
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#17989003	C₂	semidirect
2. C₂²×#14556531	C₂	semidirect
4. #22611760	C₂	semidirect
5. #22611759	C₂	semidirect
6. #22611753	C₂	semidirect
7. #22611748	C₂	semidirect
8. #22611689	C₂	semidirect
9. #22611544	C₂	semidirect
10. #22611527	C₂	semidirect
11. C₂×C₂²⋊C₁₆×C₇₃	C₂	semidirect
19. C₂×#14556530	C₂²	semidirect
21. C₂×C₁₆×D₇₃	C₂²	semidirect
30. #17988405	C₂²	semidirect
31. #17988405	C₂²	semidirect
32. #17988366	C₂²	semidirect
33. #17988366	C₂²	semidirect
34. #17988362	C₂²	semidirect
35. C₁₆×Dic₇₃	C₂²	semidirect
61. #14556531	D₄	semidirect
189. C₂²×C₇₃	#504	semidirect
219. C₂×C₂²⋊C₁₆	D₇₃	semidirect
221. C₇₃	#33436	semidirect
402. C₂²	#17989003	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989003	2
C₂²×#14556531	2
#22618625	2
#22611760	2
#22611759	2
#22611753	2
#22611748	2
#22611689	2
#22611544	2
#22611527	2
C₂×C₂²⋊C₁₆×C₇₃	2
#33436	73