Subgroups — #32975554

Order 18688.

818 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988638	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988609	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#22607772	C₂	1	1	yes	maximal, characteristic, complemented
5	#22607771	C₂	1	1	yes	maximal, characteristic, complemented
6	#22607770	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11924011	—	2	1	no	—
9	C₂×C₄⋊C₄×D₇₃	C₄	1	2	yes	—
10	C₂×C₄²×D₇₃	—	2	1	no	—
11	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
12	#17988638	—	2	2	no	—
13	#17988638	C₄	1	4	yes	complemented
14	#17988609	—	2	2	no	—
15	#17988609	C₄	1	4	yes	complemented
16	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
17	C₂×#14556520	—	2	1	no	—
18	C₂×#14556520	—	2	1	no	—
19	C₂×#14556503	—	2	1	no	—
20	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
21	C₄⋊C₄×Dic₇₃	C₄	1	2	yes	—
22	C₄×#11924007	—	2	1	no	—
23	C₄×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
24	#17988438	—	2	1	no	—
25	#95×D₇₃	—	2	1	no	—
26	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₇₃	—	2	2	no	—
30	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
32	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
33	C₂×#11924011	—	2	4	no	—
34	C₂×#11924011	—	4	2	no	—
35	C₂×#11924011	—	4	2	no	—
36	C₂²×#10596831	—	2	1	no	—
37	C₂²×#10596831	—	2	1	no	—
38	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
39	C₂×#11924007	—	2	2	no	—
40	C₄⋊C₄×D₇₃	—	2	4	no	—
41	C₄⋊C₄×D₇₃	—	2	4	no	—
42	C₂×C₄×Dic₇₃	—	2	2	no	—
43	C₂×C₄×Dic₇₃	—	2	1	no	—
44	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
46	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
47	C₄²×D₇₃	—	4	2	no	—
48	C₄²×D₇₃	—	4	2	no	—
49	C₄²×D₇₃	C₂×C₄	1	2	yes	—
50	C₄²×D₇₃	C₂×C₄	1	2	yes	—
51	C₄²×D₇₃	D₄	1	2	yes	—
52	C₄²×D₇₃	Q₈	1	2	yes	—
53	C₄⋊#10596831	—	2	1	no	—
54	C₄⋊#10596831	C₂×C₄	1	2	yes	complemented
55	#14556520	—	2	4	no	—
56	#14556520	—	2	4	no	—
57	#14556503	—	2	4	no	—
58	C₄×#10596831	—	2	1	no	—
59	C₄×#10596831	C₂×C₄	1	2	yes	complemented
60	#14556498	—	2	2	no	—
61	#14556498	—	2	1	no	—
62	C₂²×C₈×C₇₃	—	2	1	no	—
63	C₂²×C₈×C₇₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₇₃	—	2	1	no	—
66	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₇₃	—	2	1	no	—
68	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	complemented
69	C₄×C₈×C₇₃	—	2	1	no	—
70	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
71	#95×C₇₃	—	2	1	no	—
72	C₂³×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×Dic₇₃	—	2	2	no	—
74	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×D₇₃	—	2	2	no	—
78	C₂×C₄×D₇₃	—	2	2	no	—
79	C₂×C₄×D₇₃	—	2	8	no	—
80	C₂×C₄×D₇₃	—	4	2	no	—
81	C₂×C₄×D₇₃	—	4	4	no	—
82	C₂×C₄×D₇₃	—	4	4	no	—
83	C₂×C₄×D₇₃	C₄²	1	2	yes	—
84	C₂×C₄×D₇₃	C₂²⋊C₄	1	2	yes	—
85	C₂×C₄×D₇₃	C₂²⋊C₄	1	2	yes	—
86	C₂×C₄×D₇₃	C₄⋊C₄	1	2	yes	—
87	C₂×C₄×D₇₃	C₄⋊C₄	1	2	yes	—
88	C₂×C₄×D₇₃	C₄⋊C₄	1	2	yes	—
89	C₂×C₄×D₇₃	D₈	1	2	yes	—
90	C₂×C₄×D₇₃	SD₁₆	1	2	yes	—
91	C₂×C₄×D₇₃	SD₁₆	1	2	yes	—
92	C₂×C₄×D₇₃	Q₁₆	1	2	yes	—
93	#11924011	—	4	8	no	—
94	C₂×#10596831	—	2	2	no	—
95	C₂×#10596831	—	2	2	no	—
96	C₂×#10596831	—	4	2	no	—
97	C₂×#10596831	—	4	1	no	—
98	C₂×#10596831	—	4	1	no	—
99	C₄⋊Dic₇₃	—	2	2	no	—
100	C₄⋊Dic₇₃	M₁₆	1	4	yes	complemented
101	#11924007	—	2	8	no	—
102	C₄×Dic₇₃	—	4	1	no	—
103	C₄×Dic₇₃	—	4	1	no	—
104	C₄×Dic₇₃	—	4	4	no	—
105	C₄×Dic₇₃	C₄²	1	2	yes	—
106	C₄×Dic₇₃	C₂²⋊C₄	1	2	yes	—
107	C₄×Dic₇₃	C₂²⋊C₄	1	2	yes	—
108	C₄×Dic₇₃	C₄⋊C₄	1	2	yes	—
109	C₄×Dic₇₃	C₄⋊C₄	1	2	yes	—
110	C₄×Dic₇₃	C₄⋊C₄	1	2	yes	—
111	C₂²×C₄×C₇₃	—	2	2	no	—
112	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₇₃	—	2	2	no	—
116	C₂×C₈×C₇₃	—	2	2	no	—
117	C₂×C₈×C₇₃	—	4	2	no	—
118	C₂×C₈×C₇₃	—	4	1	no	—
119	C₂×C₈×C₇₃	—	4	1	no	—
120	C₄⋊C₄×C₇₃	—	2	2	no	—
121	C₄⋊C₄×C₇₃	M₁₆	1	4	yes	complemented
122	C₄²×C₇₃	—	4	1	no	—
123	C₄²×C₇₃	—	4	1	no	—
124	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₇₃	C₂×Q₈	1	1	yes	characteristic
128	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×D₇₃	—	2	2	no	—
130	C₂²×D₇₃	—	2	2	no	—
131	C₂²×D₇₃	#95	1	2	yes	—
132	C₂²×D₇₃	#102	1	2	yes	—
133	C₂²×D₇₃	#103	1	2	yes	—
134	C₂×C₄×C₇₃	—	2	2	no	—
135	C₂×C₄×C₇₃	—	2	4	no	—
136	C₂×C₄×C₇₃	—	4	2	no	—
137	C₂×C₄×C₇₃	—	4	2	no	—
138	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
139	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
145	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
146	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
148	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
149	C₂×C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
150	C₂×Dic₇₃	—	2	2	no	—
151	C₂×Dic₇₃	—	2	2	no	—
152	C₂×Dic₇₃	—	2	4	no	—
153	C₂×Dic₇₃	—	4	2	no	—
154	C₂×Dic₇₃	—	4	2	no	—
155	C₂×Dic₇₃	#95	1	2	yes	—
156	C₂×Dic₇₃	#95	1	2	yes	—
157	C₂×Dic₇₃	#95	1	2	yes	—
158	C₂×Dic₇₃	#102	1	2	yes	—
159	C₂×Dic₇₃	#103	1	2	yes	—
160	C₄×D₇₃	—	2	2	no	—
161	C₄×D₇₃	—	2	2	no	—
162	C₄×D₇₃	—	2	4	no	—
163	C₄×D₇₃	—	4	2	no	—
164	C₄×D₇₃	—	4	2	no	—
165	C₄×D₇₃	—	4	16	no	—
166	C₄×D₇₃	#102	1	4	yes	—
167	C₄×D₇₃	#103	1	4	yes	—
168	C₄×D₇₃	#106	1	4	yes	—
169	C₄×D₇₃	#107	1	4	yes	—
170	C₈×C₇₃	—	4	2	no	—
171	C₈×C₇₃	—	4	2	no	—
172	#10596831	—	4	2	no	—
173	#10596831	—	4	2	no	—
174	C₂²×C₇₃	C₂×#95	1	1	yes	characteristic
175	C₂²×C₇₃	#407	1	2	yes	—
176	C₂²×C₇₃	C₂×#102	1	1	yes	characteristic
177	C₂²×C₇₃	C₂×#103	1	1	yes	characteristic
178	C₂²×C₇₃	#421	1	2	yes	—
179	C₂×D₇₃	—	2	2	no	—
180	C₂×D₇₃	—	2	2	no	—
181	C₂×D₇₃	—	2	4	no	—
182	C₂×D₇₃	—	2	4	no	—
183	C₂×D₇₃	#340	1	4	yes	—
184	C₄×C₇₃	—	2	1	no	—
185	C₄×C₇₃	—	2	1	no	—
186	C₄×C₇₃	—	4	4	no	—
187	C₄×C₇₃	C₄×M₁₆	1	1	yes	characteristic
188	C₄×C₇₃	C₄×M₁₆	1	1	yes	characteristic
189	C₄×C₇₃	C₂×#102	1	1	yes	characteristic
190	C₄×C₇₃	C₂×#103	1	1	yes	characteristic
191	C₄×C₇₃	#423	1	2	yes	—
192	C₄×C₇₃	C₂×#106	1	1	yes	characteristic
193	C₄×C₇₃	C₂×#107	1	1	yes	characteristic
194	Dic₇₃	—	2	2	no	—
195	Dic₇₃	—	2	2	no	—
196	Dic₇₃	—	4	4	no	—
197	Dic₇₃	#340	1	4	yes	—
198	#7901	—	73	1	no	maximal, Sylow
199	C₂×C₇₃	#1486	1	2	yes	—
200	C₂×C₇₃	#1487	1	2	yes	—
201	C₂×C₇₃	#1728	1	1	yes	characteristic
202	C₂×C₇₃	#1733	1	1	yes	characteristic
203	C₂×C₇₃	C₂×#340	1	1	yes	characteristic
204	D₇₃	—	2	4	no	—
205	C₂×#431	—	73	1	no	—
206	C₂×#423	—	73	1	no	—
207	C₂×C₄×C₄⋊C₄	—	73	1	no	—
208	#1279	—	73	1	no	—
209	#1279	—	73	1	no	—
210	#1279	—	73	1	no	—
211	#1279	D₇₃	1	1	yes	characteristic, complemented
212	C₇₃	#7901	1	1	yes	characteristic, complemented, Sylow
213	C₂²×M₁₆	—	146	1	no	—
214	C₂²×C₄⋊C₄	—	73	2	no	—
215	C₂²×C₄²	—	73	1	no	—
216	C₂²×C₄²	—	146	1	no	—
217	#431	—	73	4	no	—
218	#431	—	146	2	no	—
219	#423	—	73	4	no	—
220	#423	—	146	2	no	—
221	C₂×C₄⋊C₈	—	73	1	no	—
222	C₂×C₄⋊C₈	—	146	1	no	—
223	C₂×C₄⋊C₈	—	146	1	no	—
224	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
225	C₂×C₂²⋊C₈	—	146	1	no	—
226	C₂×C₄×C₈	—	73	1	no	—
227	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
228	C₄×C₄⋊C₄	—	73	2	no	—
229	C₄×C₄⋊C₄	—	73	1	no	—
230	C₄×C₄⋊C₄	—	146	1	no	—
231	C₄×C₄⋊C₄	—	146	1	no	—
232	C₄×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
233	C₂×#95	—	146	1	no	—
234	C₂³×C₄	—	73	1	no	—
235	C₂³×C₄	—	73	1	no	—
236	C₂³×C₄	—	73	1	no	—
237	C₂³×C₄	—	146	2	no	—
238	C₂×M₁₆	—	292	2	no	—
239	C₂×M₁₆	—	292	2	no	—
240	C₂×M₁₆	—	146	4	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	146	1	no	—
244	C₂²×C₈	—	146	1	no	—
245	C₂×C₄⋊C₄	—	73	2	no	—
246	C₂×C₄⋊C₄	—	146	4	no	—
247	C₂×C₄⋊C₄	—	146	2	no	—
248	C₂×C₄⋊C₄	—	146	4	no	—
249	C₂×C₄⋊C₄	C₄×D₇₃	1	2	yes	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	292	2	no	—
252	C₂×C₄²	—	292	2	no	—
253	C₂×C₄²	—	73	1	no	—
254	C₂×C₄²	—	73	1	no	—
255	C₂×C₄²	—	73	1	no	—
256	C₂×C₄²	—	73	2	no	—
257	C₂×C₄²	—	73	2	no	—
258	C₂×C₄²	—	73	2	no	—
259	C₂×C₄²	—	73	2	no	—
260	C₂×C₄²	—	146	2	no	—
261	C₂×C₄²	—	146	1	no	—
262	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	73	2	no	—
265	C₄⋊C₈	—	146	4	no	—
266	C₄⋊C₈	—	146	4	no	—
267	C₄⋊C₈	—	146	1	no	—
268	C₄⋊C₈	C₄×D₇₃	1	2	yes	complemented
269	C₂²⋊C₈	—	146	4	no	—
270	C₄×C₈	—	2	1	no	—
271	C₄×C₈	—	73	2	no	—
272	C₄×C₈	—	146	1	no	—
273	C₄×C₈	C₄×D₇₃	1	2	yes	complemented
274	#95	—	2	1	no	—
275	#95	—	146	2	no	—
276	#95	—	146	1	no	—
277	C₂⁴	—	73	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	292	2	no	—
280	C₂²×C₄	—	292	4	no	—
281	C₂²×C₄	—	292	4	no	—
282	C₂²×C₄	—	73	2	no	—
283	C₂²×C₄	—	73	2	no	—
284	C₂²×C₄	—	73	1	no	—
285	C₂²×C₄	—	73	2	no	—
286	C₂²×C₄	—	73	2	no	—
287	C₂²×C₄	—	73	2	no	—
288	C₂²×C₄	—	73	2	no	—
289	C₂²×C₄	—	73	2	no	—
290	C₂²×C₄	—	73	2	no	—
291	C₂²×C₄	—	73	1	no	—
292	C₂²×C₄	—	73	1	no	—
293	C₂²×C₄	—	73	2	no	—
294	C₂²×C₄	—	73	2	no	—
295	C₂²×C₄	—	146	8	no	—
296	C₂²×C₄	—	146	2	no	—
297	C₂²×C₄	—	146	2	no	—
298	C₂²×C₄	—	146	2	no	—
299	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
300	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
301	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
302	M₁₆	—	292	8	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	4	2	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	292	2	no	—
309	C₂×C₈	—	292	1	no	—
310	C₂×C₈	—	292	1	no	—
311	C₂×C₈	—	146	2	no	—
312	C₂×C₈	—	146	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	73	4	no	—
315	C₄⋊C₄	—	146	8	no	—
316	C₄⋊C₄	—	146	2	no	—
317	C₄⋊C₄	#11924011	1	4	yes	complemented
318	C₄²	—	4	1	no	—
319	C₄²	—	4	1	no	—
320	C₄²	—	292	4	no	—
321	C₄²	—	292	1	no	—
322	C₄²	—	292	1	no	—
323	C₄²	—	73	2	no	—
324	C₄²	—	73	2	no	—
325	C₄²	—	73	2	no	—
326	C₄²	—	73	2	no	—
327	C₄²	—	73	2	no	—
328	C₄²	—	73	2	no	—
329	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
330	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
331	C₄²	D₄×D₇₃	1	1	yes	characteristic
332	C₄²	Q₈×D₇₃	1	1	yes	characteristic
333	C₂³	—	73	2	no	—
334	C₂³	—	73	2	no	—
335	C₂³	—	73	2	no	—
336	C₂³	—	146	2	no	—
337	C₂³	—	146	2	no	—
338	C₂³	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	292	2	no	—
344	C₂×C₄	—	292	2	no	—
345	C₂×C₄	—	292	16	no	—
346	C₂×C₄	—	292	2	no	—
347	C₂×C₄	—	292	2	no	—
348	C₂×C₄	—	73	2	no	—
349	C₂×C₄	—	73	2	no	—
350	C₂×C₄	—	73	2	no	—
351	C₂×C₄	—	73	4	no	—
352	C₂×C₄	—	73	4	no	—
353	C₂×C₄	—	73	4	no	—
354	C₂×C₄	—	73	4	no	—
355	C₂×C₄	—	73	2	no	—
356	C₂×C₄	—	73	2	no	—
357	C₂×C₄	—	146	4	no	—
358	C₂×C₄	—	146	2	no	—
359	C₂×C₄	—	146	2	no	—
360	C₂×C₄	—	146	4	no	—
361	C₂×C₄	—	146	2	no	—
362	C₂×C₄	—	146	2	no	—
363	C₂×C₄	C₄²×D₇₃	1	1	yes	characteristic
364	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
365	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
366	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
367	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
368	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
369	C₂×C₄	M₁₆×D₇₃	1	2	yes	—
370	C₂×C₄	C₂×#11924011	1	2	yes	—
371	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
372	C₂×C₄	SD₁₆×D₇₃	1	1	yes	characteristic
373	C₂×C₄	SD₁₆×D₇₃	1	1	yes	characteristic
374	C₂×C₄	Q₁₆×D₇₃	1	1	yes	characteristic
375	C₈	—	4	2	no	—
376	C₈	—	4	2	no	—
377	C₈	—	292	2	no	—
378	C₈	—	292	2	no	—
379	C₂²	—	73	4	no	—
380	C₂²	—	146	2	no	—
381	C₂²	—	146	4	no	—
382	C₂²	—	146	4	no	—
383	C₂²	—	146	2	no	—
384	C₂²	#95×D₇₃	1	1	yes	characteristic
385	C₂²	#17988549	1	2	yes	—
386	C₂²	#102×D₇₃	1	1	yes	characteristic
387	C₂²	#103×D₇₃	1	1	yes	characteristic
388	C₂²	#17988602	1	2	yes	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	4	4	no	—
392	C₄	—	292	4	no	—
393	C₄	—	73	4	no	—
394	C₄	—	146	2	no	—
395	C₄	—	146	2	no	—
396	C₄	C₄×#11924011	1	1	yes	characteristic
397	C₄	#17988539	1	1	yes	characteristic
398	C₄	#102×D₇₃	1	1	yes	characteristic
399	C₄	#103×D₇₃	1	1	yes	characteristic
400	C₄	#17988609	1	2	yes	—
401	C₄	#106×D₇₃	1	1	yes	characteristic
402	C₄	#107×D₇₃	1	1	yes	characteristic
403	C₂	—	146	4	no	—
404	C₂	#22608354	1	2	yes	—
405	C₂	#22608358	1	2	yes	—
406	C₂	#22609623	1	1	yes	characteristic
407	C₂	#22609639	1	1	yes	characteristic
408	C₂	#340×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1279	C₂
socle	C₂³×C₇₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₇₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1279	D₇₃
hypocenter	C₇₃	#7901
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. #22607772	C₂	semidirect
5. #22607771	C₂	semidirect
6. #22607770	C₂	semidirect
7. C₇₃×#1279	C₂	semidirect
13. #17988638	C₄	semidirect
15. #17988609	C₄	semidirect
54. C₄⋊#10596831	C₂×C₄	semidirect
59. C₄×#10596831	C₂×C₄	semidirect
68. C₄⋊C₈×C₇₃	C₂×C₄	semidirect
70. C₄×C₈×C₇₃	C₂×C₄	semidirect
100. C₄⋊Dic₇₃	M₁₆	semidirect
121. C₄⋊C₄×C₇₃	M₁₆	semidirect
211. #1279	D₇₃	semidirect
212. C₇₃	#7901	semidirect
268. C₄⋊C₈	C₄×D₇₃	semidirect
273. C₄×C₈	C₄×D₇₃	semidirect
317. C₄⋊C₄	#11924011	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988638	2
C₂×#17988609	2
C₄×C₄⋊C₄×D₇₃	2
#22607772	2
#22607771	2
#22607770	2
C₇₃×#1279	2
#7901	73