Subgroups — #33104783

Order 18688.

760 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988714	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₁₄₆	C₂	1	1	yes	maximal, characteristic
3	#22612405	C₂	1	1	yes	maximal, characteristic
4	#22610651	C₂	1	2	yes	maximal
5	#22610650	C₂	1	1	yes	maximal, characteristic
6	#22610648	C₂	1	2	yes	maximal
7	#22610084	C₂	1	2	yes	maximal
8	#22610082	C₂	1	1	yes	maximal, characteristic
9	#22609787	C₂	1	2	yes	maximal
10	C₄×#14556520	C₂	1	1	yes	maximal, characteristic
11	C₇₃×#1939	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
13	#17988714	—	2	4	no	—
14	C₈×Dic₁₄₆	—	2	4	no	—
15	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊#10596831	C₂²	1	2	yes	—
17	C₂×#14556520	C₂²	1	1	yes	characteristic
18	C₂×#14556520	C₂²	1	2	yes	—
19	C₂×#14556520	C₂²	1	2	yes	—
20	C₂×#14556520	C₂²	1	2	yes	—
21	C₂×#14556520	C₂²	1	2	yes	—
22	C₂×#14556520	C₂²	1	1	yes	characteristic
23	C₂×#14556501	C₂²	1	2	yes	—
24	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₇₃	C₂²	1	2	yes	—
26	#17988492	C₄	1	1	yes	characteristic
27	#17988492	C₄	1	1	yes	characteristic
28	#17988483	C₄	1	1	yes	characteristic
29	#17988483	C₄	1	1	yes	characteristic
30	#17988469	C₄	1	2	yes	—
31	#17988469	C₄	1	2	yes	—
32	C₄×#11924007	C₂²	1	2	yes	—
33	#17988433	C₂²	1	2	yes	—
34	C₄²×Dic₇₃	C₂²	1	1	yes	characteristic
35	#17988342	C₂²	1	2	yes	—
36	#17988341	C₂²	1	1	yes	characteristic
37	#17988341	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
42	#336×C₇₃	C₂²	1	2	yes	—
43	C₂²×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
44	C₂²×#10596831	C₂³	1	2	yes	—
45	C₂²×#10596831	C₂³	1	1	yes	characteristic
46	C₂²×#10596831	C₂³	1	1	yes	characteristic
47	C₄×Dic₁₄₆	D₄	1	4	yes	—
48	C₄×Dic₁₄₆	Q₈	1	4	yes	—
49	C₂×C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
50	C₂×#11924007	C₂×C₄	1	2	yes	—
51	C₂×#11924007	C₂×C₄	1	2	yes	—
52	C₂×#11924007	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
59	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
60	C₄⋊#10596831	—	2	2	no	—
61	C₄⋊#10596831	—	4	2	no	—
62	#14556520	—	2	4	no	—
63	#14556520	—	2	4	no	—
64	#14556520	—	2	2	no	—
65	#14556520	—	2	4	no	—
66	#14556520	—	4	2	no	—
67	#14556520	Q₈	1	4	yes	complemented
68	#14556501	—	2	4	no	—
69	C₄×#10596831	—	2	2	no	—
70	C₈×Dic₇₃	—	2	4	no	—
71	#14556498	C₂×C₄	1	2	yes	—
72	#14556498	C₂×C₄	1	2	yes	—
73	#14556498	C₂×C₄	1	2	yes	—
74	#14556498	C₂×C₄	1	2	yes	—
75	#14556498	C₂×C₄	1	2	yes	—
76	#14556498	C₂×C₄	1	2	yes	—
77	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
79	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₇₃	—	2	2	no	—
85	C₄⋊C₈×C₇₃	—	4	2	no	—
86	C₄×C₈×C₇₃	—	2	2	no	—
87	#95×C₇₃	C₂×C₄	1	2	yes	—
88	C₂×Dic₁₄₆	—	2	2	no	—
89	C₂×Dic₁₄₆	—	2	2	no	—
90	C₂×Dic₁₄₆	C₄⋊C₄	1	4	yes	—
91	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
93	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
94	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×#10596831	—	2	1	no	—
98	C₂×#10596831	—	2	1	no	—
99	C₂×#10596831	—	2	2	no	—
100	C₂×#10596831	—	2	1	no	—
101	C₂×#10596831	—	2	2	no	—
102	C₂×#10596831	—	2	1	no	—
103	C₂×#10596831	—	2	2	no	—
104	C₂×#10596831	—	2	1	no	—
105	C₂×#10596831	C₂×Q₈	1	2	yes	—
106	C₄⋊Dic₇₃	C₄⋊C₄	1	4	yes	—
107	#11924007	—	2	4	no	—
108	#11924007	—	4	2	no	—
109	#11924007	C₄⋊C₄	1	8	yes	—
110	C₄×Dic₇₃	—	2	2	no	—
111	C₄×Dic₇₃	—	2	2	no	—
112	C₄×Dic₇₃	—	2	1	no	—
113	C₄×Dic₇₃	—	2	1	no	—
114	C₄×Dic₇₃	—	2	2	no	—
115	C₄×Dic₇₃	—	4	1	no	—
116	C₄×Dic₇₃	C₂×D₄	1	4	yes	—
117	C₄×Dic₇₃	C₂×Q₈	1	4	yes	—
118	C₄×Dic₇₃	C₂×Q₈	1	2	yes	—
119	C₄×Dic₇₃	#41	1	2	yes	—
120	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₇₃	—	2	1	no	—
126	C₂×C₈×C₇₃	—	2	1	no	—
127	C₂×C₈×C₇₃	—	2	1	no	—
128	C₂×C₈×C₇₃	—	2	2	no	—
129	C₂×C₈×C₇₃	—	2	1	no	—
130	C₂×C₈×C₇₃	—	2	2	no	—
131	C₂×C₈×C₇₃	—	2	1	no	—
132	C₂×C₈×C₇₃	—	2	2	no	—
133	C₂×C₈×C₇₃	C₂×Q₈	1	2	yes	—
134	C₄⋊C₄×C₇₃	—	2	2	no	—
135	C₄⋊C₄×C₇₃	—	2	2	no	—
136	C₄²×C₇₃	—	2	2	no	—
137	C₄²×C₇₃	—	2	2	no	—
138	C₄²×C₇₃	C₂×D₄	1	2	yes	—
139	C₄²×C₇₃	C₂×Q₈	1	2	yes	—
140	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₇₃	—	2	1	no	—
142	C₂×C₄×C₇₃	—	2	1	no	—
143	C₂×C₄×C₇₃	—	2	2	no	—
144	C₂×C₄×C₇₃	—	2	2	no	—
145	C₂×C₄×C₇₃	—	2	2	no	—
146	C₂×C₄×C₇₃	—	2	2	no	—
147	C₂×C₄×C₇₃	—	2	2	no	—
148	C₂×C₄×C₇₃	—	2	2	no	—
149	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
151	C₂×C₄×C₇₃	#131	1	2	yes	—
152	C₂×C₄×C₇₃	#131	1	2	yes	—
153	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
159	C₂×Dic₇₃	—	2	1	no	—
160	C₂×Dic₇₃	—	2	1	no	—
161	C₂×Dic₇₃	—	2	1	no	—
162	C₂×Dic₇₃	—	2	1	no	—
163	C₂×Dic₇₃	—	2	1	no	—
164	C₂×Dic₇₃	—	2	2	no	—
165	C₂×Dic₇₃	—	2	2	no	—
166	C₂×Dic₇₃	—	2	2	no	—
167	C₂×Dic₇₃	—	2	1	no	—
168	C₂×Dic₇₃	—	2	2	no	—
169	C₂×Dic₇₃	—	2	1	no	—
170	C₂×Dic₇₃	—	2	1	no	—
171	C₂×Dic₇₃	—	2	1	no	—
172	C₂×Dic₇₃	C₂×C₄⋊C₄	1	4	yes	—
173	C₂×Dic₇₃	C₂×C₄⋊C₄	1	4	yes	—
174	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
175	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
176	C₂×Dic₇₃	#131	1	2	yes	—
177	Dic₁₄₆	—	2	8	no	—
178	C₈×C₇₃	—	2	2	no	—
179	C₈×C₇₃	—	4	1	no	—
180	C₈×C₇₃	—	4	2	no	—
181	#10596831	—	2	2	no	—
182	#10596831	—	4	2	no	—
183	#10596831	—	4	1	no	—
184	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
186	C₂²×C₇₃	#520	1	1	yes	characteristic
187	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
188	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
189	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
190	C₂²×C₇₃	#568	1	1	yes	characteristic
191	C₄×C₇₃	—	2	2	no	—
192	C₄×C₇₃	—	4	2	no	—
193	C₄×C₇₃	—	4	2	no	—
194	C₄×C₇₃	#424	1	4	yes	—
195	C₄×C₇₃	D₄×Q₈	1	1	yes	characteristic
196	C₄×C₇₃	#550	1	1	yes	characteristic
197	C₄×C₇₃	#557	1	1	yes	characteristic
198	C₄×C₇₃	Q₈²	1	1	yes	characteristic
199	Dic₇₃	—	2	4	no	—
200	Dic₇₃	—	2	4	no	—
201	Dic₇₃	—	2	2	no	—
202	Dic₇₃	—	2	2	no	—
203	Dic₇₃	—	2	2	no	—
204	Dic₇₃	—	4	1	no	—
205	#22721	—	73	1	no	maximal, Sylow
206	C₂×C₇₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₇₃	C₂×#424	1	1	yes	characteristic
208	C₂×C₇₃	#2906	1	1	yes	characteristic
209	C₂×C₇₃	#2960	1	1	yes	characteristic
210	C₂×C₇₃	#2962	1	1	yes	characteristic
211	C₂×C₇₃	#2993	1	1	yes	characteristic
212	C₂×C₇₃	#2994	1	1	yes	characteristic
213	C₂×#446	—	73	1	no	—
214	C₂×C₈×Q₈	—	73	1	no	—
215	#2295	—	73	1	no	—
216	#1940	—	73	2	no	—
217	#1939	—	73	1	no	—
218	#1939	—	73	2	no	—
219	#1939	D₇₃	1	1	yes	characteristic
220	#1843	—	73	2	no	—
221	#1842	—	73	1	no	—
222	#1768	—	73	2	no	—
223	C₄×C₄⋊C₈	—	73	1	no	—
224	C₇₃	#22721	1	1	yes	characteristic, complemented, Sylow
225	C₂×C₄×Q₈	—	73	1	no	—
226	#446	—	146	4	no	—
227	C₈×Q₈	—	146	4	no	—
228	C₂×C₄⋊C₈	—	73	2	no	—
229	C₂×C₄⋊C₈	—	73	2	no	—
230	C₂×C₄⋊C₈	—	73	1	no	—
231	C₂×C₄⋊C₈	—	73	2	no	—
232	C₂×C₄⋊C₈	—	73	1	no	—
233	C₂×C₄⋊C₈	—	73	2	no	—
234	C₂×C₄⋊C₈	—	73	2	no	—
235	C₂×C₄⋊C₈	—	73	1	no	—
236	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂×D₇₃	1	2	yes	—
238	C₂×#97	—	73	2	no	—
239	C₂×C₄×C₈	—	73	2	no	—
240	C₂×C₄×C₈	—	73	1	no	—
241	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
242	#391	—	73	1	no	—
243	#391	—	73	1	no	—
244	#389	—	73	1	no	—
245	#389	—	73	1	no	—
246	#387	—	73	2	no	—
247	#387	—	73	2	no	—
248	C₄×C₄⋊C₄	—	73	2	no	—
249	C₄×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
250	#376	—	73	2	no	—
251	C₄³	—	73	1	no	—
252	#336	—	73	1	no	—
253	#336	—	73	1	no	—
254	#336	—	73	2	no	—
255	#336	C₂×D₇₃	1	2	yes	—
256	C₂²×Q₈	—	73	1	no	—
257	C₂²×C₈	—	73	1	no	—
258	C₂²×C₈	—	73	1	no	—
259	C₂²×C₈	—	73	2	no	—
260	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
261	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
262	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
263	C₄×Q₈	—	73	4	no	—
264	C₄×Q₈	—	73	4	no	—
265	C₂×C₄⋊C₄	—	73	2	no	—
266	C₂×C₄⋊C₄	—	73	2	no	—
267	C₂×C₄⋊C₄	—	73	1	no	—
268	C₂×C₄⋊C₄	—	73	2	no	—
269	C₂×C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
271	C₂×C₄²	—	73	1	no	—
272	C₂×C₄²	—	73	2	no	—
273	C₂×C₄²	—	73	1	no	—
274	C₂×C₄²	—	73	1	no	—
275	C₂×C₄²	—	73	1	no	—
276	C₂×C₄²	—	73	1	no	—
277	C₂×C₄²	—	73	1	no	—
278	C₂×C₄²	C₂²×D₇₃	1	2	yes	—
279	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
280	C₄⋊C₈	—	2	2	no	—
281	C₄⋊C₈	—	4	2	no	—
282	C₄⋊C₈	—	292	2	no	—
283	C₄⋊C₈	—	292	2	no	—
284	C₄⋊C₈	—	73	4	no	—
285	C₄⋊C₈	—	146	4	no	—
286	C₄⋊C₈	—	146	2	no	—
287	C₄⋊C₈	—	146	4	no	—
288	C₄⋊C₈	—	146	4	no	—
289	C₄⋊C₈	—	146	2	no	—
290	#97	—	146	4	no	—
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	—	146	4	no	—
293	C₄×C₈	—	146	2	no	—
294	#95	—	73	2	no	—
295	#95	—	73	2	no	—
296	#95	—	73	2	no	—
297	#95	—	73	2	no	—
298	#95	—	73	2	no	—
299	#95	—	73	2	no	—
300	#95	C₄×D₇₃	1	2	yes	—
301	C₂×Q₈	—	73	4	no	—
302	C₂×Q₈	—	146	2	no	—
303	C₂×Q₈	—	146	2	no	—
304	C₂²×C₄	—	73	1	no	—
305	C₂²×C₄	—	73	1	no	—
306	C₂²×C₄	—	73	2	no	—
307	C₂²×C₄	—	73	1	no	—
308	C₂²×C₄	—	73	2	no	—
309	C₂²×C₄	—	73	1	no	—
310	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
311	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
312	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
314	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	73	2	no	—
324	C₂×C₈	—	146	2	no	—
325	C₂×C₈	—	146	1	no	—
326	C₂×C₈	—	146	2	no	—
327	C₂×C₈	—	146	1	no	—
328	C₂×C₈	—	146	2	no	—
329	C₂×C₈	—	146	1	no	—
330	C₂×C₈	—	146	1	no	—
331	C₂×C₈	—	146	1	no	—
332	C₂×C₈	Q₈×D₇₃	1	2	yes	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	292	2	no	—
336	C₄⋊C₄	—	73	8	no	—
337	C₄⋊C₄	—	73	4	no	—
338	C₄⋊C₄	—	146	4	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	292	1	no	—
342	C₄²	—	73	4	no	—
343	C₄²	—	73	2	no	—
344	C₄²	—	73	4	no	—
345	C₄²	—	73	2	no	—
346	C₄²	—	146	2	no	—
347	C₄²	—	146	2	no	—
348	C₄²	—	146	2	no	—
349	C₄²	—	146	1	no	—
350	C₄²	—	146	1	no	—
351	C₄²	D₄×D₇₃	1	2	yes	—
352	C₄²	Q₈×D₇₃	1	2	yes	—
353	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
354	Q₈	—	146	8	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	73	4	no	—
364	C₂×C₄	—	73	4	no	—
365	C₂×C₄	—	73	2	no	—
366	C₂×C₄	—	73	2	no	—
367	C₂×C₄	—	73	2	no	—
368	C₂×C₄	—	146	1	no	—
369	C₂×C₄	—	146	1	no	—
370	C₂×C₄	—	146	1	no	—
371	C₂×C₄	—	146	1	no	—
372	C₂×C₄	—	146	1	no	—
373	C₂×C₄	—	146	2	no	—
374	C₂×C₄	—	146	1	no	—
375	C₂×C₄	—	146	2	no	—
376	C₂×C₄	—	146	1	no	—
377	C₂×C₄	—	146	1	no	—
378	C₂×C₄	—	146	2	no	—
379	C₂×C₄	—	146	1	no	—
380	C₂×C₄	—	146	2	no	—
381	C₂×C₄	C₄⋊C₄×D₇₃	1	2	yes	—
382	C₂×C₄	C₄⋊C₄×D₇₃	1	2	yes	—
383	C₂×C₄	#14556597	1	2	yes	—
384	C₂×C₄	#14556599	1	2	yes	—
385	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
386	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
387	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
388	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
389	C₂×C₄	#14556636	1	1	yes	characteristic
390	C₂×C₄	#14556638	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	2	no	—
394	C₈	—	292	2	no	—
395	C₈	—	292	1	no	—
396	C₈	—	146	2	no	—
397	C₂²	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
398	C₂²	C₄×Q₈×D₇₃	1	1	yes	characteristic
399	C₂²	#17989066	1	1	yes	characteristic
400	C₂²	#131×D₇₃	1	1	yes	characteristic
401	C₂²	C₂×#14556597	1	1	yes	characteristic
402	C₂²	C₂×#14556599	1	1	yes	characteristic
403	C₂²	#17989352	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	292	1	no	—
408	C₄	—	146	4	no	—
409	C₄	—	146	4	no	—
410	C₄	—	146	2	no	—
411	C₄	—	146	2	no	—
412	C₄	—	146	2	no	—
413	C₄	#17988612	1	4	yes	—
414	C₄	#17989250	1	1	yes	characteristic
415	C₄	#17989255	1	1	yes	characteristic
416	C₄	#17989314	1	1	yes	characteristic
417	C₄	#17989317	1	1	yes	characteristic
418	C₂	#22612845	1	1	yes	characteristic
419	C₂	C₂×#17988612	1	1	yes	characteristic
420	C₂	#22618498	1	1	yes	characteristic
421	C₂	#22618860	1	1	yes	characteristic
422	C₂	#22618879	1	1	yes	characteristic
423	C₂	#22619081	1	1	yes	characteristic
424	C₂	#22619092	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₃
commutator, socle, prime radical	C₂³×C₇₃	C₂³×C₄
Fitting	C₇₃×#1939	C₂
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1939	D₇₃
hypocenter	C₇₃	#22721
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
67. #14556520	Q₈	semidirect
224. C₇₃	#22721	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988714	2
C₂×C₈×Dic₁₄₆	2
#22612405	2
#22610651	2
#22610650	2
#22610648	2
#22610084	2
#22610082	2
#22609787	2
C₄×#14556520	2
C₇₃×#1939	2
#22721	73