Subgroups — #33055331

Order 18688.

592 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22619063	C₂	1	1	yes	maximal, characteristic
2	#22619056	C₂	1	1	yes	maximal, characteristic
3	#22608720	C₂	1	1	yes	maximal, characteristic, complemented
4	#22608720	C₂	1	1	yes	maximal, characteristic, complemented
5	#22608711	C₂	1	2	yes	maximal, complemented
6	#22608702	C₂	1	2	yes	maximal, complemented
7	#22608698	C₂	1	2	yes	maximal, complemented
8	#22608687	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608683	C₂	1	2	yes	maximal, complemented
10	#22608679	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2965	C₂	1	1	yes	maximal, characteristic
12	#17988718	—	2	1	no	—
13	Q₈×#10596831	—	2	1	no	—
14	#17988665	—	2	1	no	—
15	#17988665	—	2	2	no	—
16	#17988659	—	2	2	no	—
17	D₄×#10596831	—	2	1	no	—
18	#17988644	C₂²	1	2	yes	—
19	#17988640	C₂²	1	1	yes	characteristic
20	#17988640	C₂²	1	1	yes	characteristic
21	#17988640	C₂²	1	2	yes	—
22	#17988611	C₂²	1	1	yes	characteristic
23	#17988611	C₂²	1	1	yes	characteristic
24	#17988611	C₂²	1	2	yes	—
25	C₂×C₄⋊#10596831	C₂²	1	2	yes	—
26	#17988340	C₂²	1	1	yes	characteristic
27	#17988340	C₂²	1	1	yes	characteristic
28	#17988340	C₂²	1	2	yes	—
29	#17988340	C₂²	1	2	yes	—
30	#17988338	C₂²	1	1	yes	characteristic
31	#17988338	C₂²	1	1	yes	characteristic
32	#17988338	C₂²	1	2	yes	—
33	#17988338	C₂²	1	2	yes	—
34	#17988338	C₂²	1	2	yes	—
35	#17988338	C₂²	1	2	yes	—
36	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
37	#446×C₇₃	C₄	1	1	yes	characteristic
38	#446×C₇₃	C₄	1	1	yes	characteristic
39	#436×C₇₃	C₄	1	1	yes	characteristic
40	#436×C₇₃	C₄	1	1	yes	characteristic
41	#435×C₇₃	C₄	1	2	yes	—
42	#435×C₇₃	C₄	1	2	yes	—
43	#431×C₇₃	C₂²	1	2	yes	—
44	#431×C₇₃	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₇₃	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#11924012	—	2	1	no	—
48	C₂×#11924012	—	2	2	no	—
49	C₂×#11924012	—	2	1	no	—
50	C₂²×#10596831	—	2	2	no	—
51	C₄⋊#10596831	—	2	2	no	—
52	C₄⋊#10596831	—	2	1	no	—
53	C₄⋊#10596831	—	2	1	no	—
54	C₄⋊#10596831	—	2	2	no	—
55	C₄⋊#10596831	C₂³	1	1	yes	characteristic
56	C₄⋊#10596831	C₂³	1	2	yes	—
57	C₄⋊#10596831	C₂³	1	2	yes	—
58	C₄⋊#10596831	C₂³	1	1	yes	characteristic
59	C₄⋊#10596831	C₂³	1	1	yes	characteristic
60	C₄⋊#10596831	C₂³	1	1	yes	characteristic
61	C₂²⋊#10596831	—	2	1	no	—
62	C₂²⋊#10596831	—	2	2	no	—
63	C₂²⋊#10596831	—	2	1	no	—
64	C₂²⋊#10596831	—	2	2	no	—
65	#14556502	—	2	2	no	—
66	C₄×#10596831	—	2	1	no	—
67	C₄×#10596831	—	2	1	no	—
68	C₄×#10596831	—	2	2	no	—
69	C₂×#41×C₇₃	Q₈	1	1	yes	characteristic
70	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
71	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
74	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
75	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
76	C₄×D₄×C₇₃	C₂×C₄	1	2	yes	—
77	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
78	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
79	C₄×D₄×C₇₃	D₄	1	2	yes	—
80	#117×C₇₃	Q₈	1	1	yes	characteristic
81	#117×C₇₃	Q₈	1	2	yes	—
82	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
85	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
86	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
87	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
90	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
91	#97×C₇₃	C₂×C₄	1	2	yes	—
92	#97×C₇₃	C₂×C₄	1	2	yes	—
93	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
94	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₇₃	C₂³	1	2	yes	—
98	#11924012	—	8	1	no	—
99	#11924012	—	8	2	no	—
100	#11924012	—	8	1	no	—
101	C₂×#10596831	—	2	1	no	—
102	C₂×#10596831	—	2	1	no	—
103	C₂×#10596831	—	2	1	no	—
104	C₂×#10596831	—	2	1	no	—
105	C₂×#10596831	—	2	2	no	—
106	C₂×#10596831	—	2	2	no	—
107	C₂×#10596831	—	8	2	no	—
108	#41×C₇₃	—	4	2	no	—
109	C₂×Q₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
110	C₂×D₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂×D₄×C₇₃	C₄⋊C₄	1	2	yes	—
112	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₄×C₇₃	C₂×Q₈	1	2	yes	—
118	M₁₆×C₇₃	—	2	4	no	—
119	M₁₆×C₇₃	—	4	2	no	—
120	C₂×C₈×C₇₃	—	2	2	no	—
121	C₂×C₈×C₇₃	—	4	1	no	—
122	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
128	C₄⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
129	C₄⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
131	C₄⋊C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
132	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
133	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
134	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
135	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
137	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₇₃	C₂×D₄	1	2	yes	—
139	C₄²×C₇₃	C₂×Q₈	1	2	yes	—
140	C₄²×C₇₃	C₂×Q₈	1	1	yes	characteristic
141	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
142	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂³×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
144	Q₈×C₇₃	—	2	2	no	—
145	D₄×C₇₃	—	2	2	no	—
146	D₄×C₇₃	—	4	2	no	—
147	C₂×C₄×C₇₃	—	2	1	no	—
148	C₂×C₄×C₇₃	—	2	2	no	—
149	C₂×C₄×C₇₃	—	2	1	no	—
150	C₂×C₄×C₇₃	—	2	2	no	—
151	C₂×C₄×C₇₃	—	2	2	no	—
152	C₂×C₄×C₇₃	—	2	2	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	—	4	2	no	—
157	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
166	C₈×C₇₃	—	2	1	no	—
167	C₈×C₇₃	—	2	2	no	—
168	C₈×C₇₃	—	2	1	no	—
169	C₈×C₇₃	—	2	1	no	—
170	C₈×C₇₃	—	2	2	no	—
171	C₈×C₇₃	#131	1	2	yes	—
172	#10596831	—	4	1	no	—
173	#10596831	—	4	1	no	—
174	#10596831	—	4	1	no	—
175	#10596831	—	4	2	no	—
176	#10596831	—	4	1	no	—
177	#10596831	—	4	2	no	—
178	C₂²×C₇₃	—	2	1	no	—
179	C₂²×C₇₃	—	2	2	no	—
180	C₂²×C₇₃	—	2	2	no	—
181	C₂²×C₇₃	—	2	1	no	—
182	C₂²×C₇₃	—	2	1	no	—
183	C₂²×C₇₃	—	2	2	no	—
184	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₄×C₇₃	—	2	1	no	—
186	C₄×C₇₃	—	2	2	no	—
187	C₄×C₇₃	—	2	2	no	—
188	C₄×C₇₃	—	2	1	no	—
189	C₄×C₇₃	—	2	1	no	—
190	C₄×C₇₃	—	2	2	no	—
191	C₄×C₇₃	#430	1	2	yes	—
192	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
193	C₄×C₇₃	#568	1	1	yes	characteristic
194	C₄×C₇₃	#577	1	1	yes	characteristic
195	C₄×C₇₃	#577	1	1	yes	characteristic
196	#17841	—	73	1	no	maximal, Sylow
197	C₂×C₇₃	—	4	1	no	—
198	C₂×C₇₃	—	4	2	no	—
199	C₂×C₇₃	#2906	1	1	yes	characteristic
200	C₂×C₇₃	#2912	1	1	yes	characteristic
201	C₂×C₇₃	C₂×#430	1	1	yes	characteristic
202	#2991	—	73	1	no	—
203	#2990	—	73	1	no	—
204	#2965	D₇₃	1	1	yes	characteristic
205	#1574	—	73	1	no	—
206	#1574	—	73	1	no	—
207	#1572	—	73	2	no	—
208	#1570	—	73	2	no	—
209	#1569	—	73	2	no	—
210	#1566	—	73	1	no	—
211	#1565	—	73	2	no	—
212	#1564	—	73	1	no	—
213	C₇₃	#17841	1	1	yes	characteristic, complemented, Sylow
214	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
215	#446	—	146	1	no	—
216	#446	Dic₇₃	1	1	yes	characteristic
217	#446	Dic₇₃	1	1	yes	characteristic
218	C₈×Q₈	—	146	1	no	—
219	#436	—	146	1	no	—
220	#436	—	146	2	no	—
221	#436	Dic₇₃	1	1	yes	characteristic
222	#436	Dic₇₃	1	1	yes	characteristic
223	#435	—	146	2	no	—
224	#435	Dic₇₃	1	2	yes	—
225	#435	Dic₇₃	1	2	yes	—
226	C₈×D₄	—	146	1	no	—
227	#432	—	73	2	no	—
228	#431	—	73	1	no	—
229	#431	—	73	1	no	—
230	#431	—	73	2	no	—
231	#431	C₂×D₇₃	1	2	yes	—
232	#431	C₂×D₇₃	1	1	yes	characteristic
233	#423	—	73	1	no	—
234	#423	—	73	1	no	—
235	#423	—	73	2	no	—
236	C₂×C₄⋊C₈	—	73	2	no	—
237	C₄×M₁₆	C₂×D₇₃	1	2	yes	—
238	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
239	#335	—	73	1	no	—
240	#335	—	73	1	no	—
241	#335	—	73	2	no	—
242	#335	—	73	2	no	—
243	#334	—	73	1	no	—
244	#334	—	73	1	no	—
245	#334	—	73	2	no	—
246	#334	—	73	2	no	—
247	#334	—	73	2	no	—
248	#334	—	73	2	no	—
249	C₂×#41	Dic₁₄₆	1	1	yes	characteristic
250	C₂×M₁₆	—	146	1	no	—
251	C₂×M₁₆	—	146	2	no	—
252	C₂×M₁₆	—	146	1	no	—
253	C₂×M₁₆	C₂×Dic₇₃	1	2	yes	—
254	C₂×M₁₆	C₂×Dic₇₃	1	2	yes	—
255	C₂²×C₈	—	146	2	no	—
256	C₂²×C₈	C₂×Dic₇₃	1	1	yes	characteristic
257	C₂²×C₈	C₂×Dic₇₃	1	1	yes	characteristic
258	C₄×Q₈	D₂₉₂	1	1	yes	characteristic
259	C₄×Q₈	C₂×Dic₇₃	1	1	yes	characteristic
260	C₄×D₄	D₂₉₂	1	1	yes	characteristic
261	C₄×D₄	D₂₉₂	1	2	yes	—
262	C₄×D₄	C₂×Dic₇₃	1	2	yes	—
263	C₄×D₄	C₂×Dic₇₃	1	1	yes	characteristic
264	#117	Dic₁₄₆	1	1	yes	characteristic
265	#117	Dic₁₄₆	1	2	yes	—
266	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
267	C₂×C₄²	C₂²×D₇₃	1	2	yes	—
268	C₄⋊C₈	—	73	1	no	—
269	C₄⋊C₈	—	73	2	no	—
270	C₄⋊C₈	—	73	1	no	—
271	C₄⋊C₈	—	73	2	no	—
272	C₄⋊C₈	—	73	1	no	—
273	C₄⋊C₈	—	73	1	no	—
274	C₄⋊C₈	—	146	2	no	—
275	C₄⋊C₈	—	146	1	no	—
276	C₄⋊C₈	—	146	1	no	—
277	C₄⋊C₈	—	146	2	no	—
278	C₄⋊C₈	C₂×Dic₇₃	1	2	yes	—
279	C₄⋊C₈	C₂×Dic₇₃	1	2	yes	—
280	C₄⋊C₈	C₂×Dic₇₃	1	1	yes	characteristic
281	C₄⋊C₈	C₂×Dic₇₃	1	1	yes	characteristic
282	C₂²⋊C₈	—	146	1	no	—
283	C₂²⋊C₈	—	146	2	no	—
284	C₂²⋊C₈	—	146	1	no	—
285	C₂²⋊C₈	—	146	2	no	—
286	C₂²⋊C₈	C₂×Dic₇₃	1	2	yes	—
287	C₂²⋊C₈	C₂×Dic₇₃	1	2	yes	—
288	C₂²⋊C₈	C₂×Dic₇₃	1	2	yes	—
289	#97	—	146	2	no	—
290	#97	C₂×Dic₇₃	1	2	yes	—
291	#97	C₂×Dic₇₃	1	2	yes	—
292	C₄×C₈	—	146	1	no	—
293	C₄×C₈	—	146	1	no	—
294	C₄×C₈	—	146	2	no	—
295	C₄×C₈	C₂×Dic₇₃	1	1	yes	characteristic
296	C₄×C₈	C₂×Dic₇₃	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₇₃	1	2	yes	—
300	#41	—	4	2	no	—
301	C₂×Q₈	C₄⋊Dic₇₃	1	1	yes	characteristic
302	C₂×D₄	C₄⋊Dic₇₃	1	1	yes	characteristic
303	C₂×D₄	C₄⋊Dic₇₃	1	2	yes	—
304	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
305	C₂²×C₄	C₂²×Dic₇₃	1	2	yes	—
306	C₂²×C₄	C₂×D₂₉₂	1	2	yes	—
307	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
308	C₂²×C₄	C₂×Dic₁₄₆	1	1	yes	characteristic
309	C₂²×C₄	C₂×Dic₁₄₆	1	2	yes	—
310	M₁₆	—	2	4	no	—
311	M₁₆	—	4	2	no	—
312	M₁₆	—	584	1	no	—
313	M₁₆	—	584	2	no	—
314	M₁₆	—	584	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	584	2	no	—
318	C₂×C₈	—	146	1	no	—
319	C₂×C₈	—	146	1	no	—
320	C₂×C₈	—	146	1	no	—
321	C₂×C₈	—	146	1	no	—
322	C₂×C₈	—	146	2	no	—
323	C₂×C₈	—	146	2	no	—
324	C₂×C₈	C₂²×Dic₇₃	1	1	yes	characteristic
325	C₂×C₈	C₂²×Dic₇₃	1	1	yes	characteristic
326	C₂×C₈	C₂²×Dic₇₃	1	1	yes	characteristic
327	C₂×C₈	C₂²×Dic₇₃	1	2	yes	—
328	C₂×C₈	C₂²×Dic₇₃	1	2	yes	—
329	C₂×C₈	C₂²×Dic₇₃	1	1	yes	characteristic
330	C₄⋊C₄	C₄⋊Dic₇₃	1	2	yes	—
331	C₄⋊C₄	C₄⋊Dic₇₃	1	1	yes	characteristic
332	C₄⋊C₄	C₄⋊Dic₇₃	1	2	yes	—
333	C₄⋊C₄	C₄⋊Dic₇₃	1	1	yes	characteristic
334	C₂²⋊C₄	C₄⋊Dic₇₃	1	2	yes	—
335	C₂²⋊C₄	C₄⋊Dic₇₃	1	2	yes	—
336	C₂²⋊C₄	C₄⋊Dic₇₃	1	2	yes	—
337	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
338	C₄²	C₂²×Dic₇₃	1	2	yes	—
339	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
340	C₄²	C₂×D₂₉₂	1	2	yes	—
341	C₄²	C₂×Dic₁₄₆	1	1	yes	characteristic
342	C₄²	C₂×Dic₁₄₆	1	2	yes	—
343	C₄²	C₂³×D₇₃	1	1	yes	characteristic
344	C₂³	C₂×C₄⋊Dic₇₃	1	1	yes	characteristic
345	C₂³	C₂×C₄⋊Dic₇₃	1	2	yes	—
346	Q₈	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₂×C₄⋊Dic₇₃	1	2	yes	—
360	C₂×C₄	C₂×C₄⋊Dic₇₃	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄⋊Dic₇₃	1	2	yes	—
362	C₂×C₄	C₂×C₄⋊Dic₇₃	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄⋊Dic₇₃	1	2	yes	—
364	C₂×C₄	C₂×C₄⋊Dic₇₃	1	1	yes	characteristic
365	C₂×C₄	C₂³×Dic₇₃	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
367	C₂×C₄	C₂²×Dic₁₄₆	1	1	yes	characteristic
368	C₈	—	2	1	no	—
369	C₈	—	2	2	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	2	no	—
373	C₈	—	292	1	no	—
374	C₈	—	292	2	no	—
375	C₈	—	292	1	no	—
376	C₈	—	292	2	no	—
377	C₈	—	292	1	no	—
378	C₈	—	292	1	no	—
379	C₈	#14556598	1	2	yes	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	C₂²×C₄⋊Dic₇₃	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	#17988636	1	2	yes	—
394	C₄	C₂×#14556598	1	1	yes	characteristic
395	C₄	#17989354	1	1	yes	characteristic
396	C₄	#17989399	1	1	yes	characteristic
397	C₄	#17989399	1	1	yes	characteristic
398	C₂	—	4	1	no	—
399	C₂	—	4	2	no	—
400	C₂	#22618499	1	1	yes	characteristic
401	C₂	#22618526	1	1	yes	characteristic
402	C₂	C₂×#17988636	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₉₂
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#2965	C₂
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₇₃	Q₈
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#2965	D₇₃
hypocenter	C₇₃	#17841
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2965

Complements

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

N	H ≅ G/N	type
3. #22608720	C₂	semidirect
4. #22608720	C₂	semidirect
5. #22608711	C₂	semidirect
6. #22608702	C₂	semidirect
7. #22608698	C₂	semidirect
8. #22608687	C₂	semidirect
9. #22608683	C₂	semidirect
10. #22608679	C₂	semidirect
213. C₇₃	#17841	semidirect

Maximal subgroups

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

subgroup	index
#22619063	2
#22619056	2
#22608720	2
#22608711	2
#22608702	2
#22608698	2
#22608687	2
#22608683	2
#22608679	2
C₇₃×#2965	2
#17841	73