Subgroups — #33055798

Order 18688.

636 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22619049	C₂	1	1	yes	maximal, characteristic
2	#22619016	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14556622	C₂	1	1	yes	maximal, characteristic
4	#22608837	C₂	1	2	yes	maximal, complemented
5	#22608836	C₂	1	2	yes	maximal, complemented
6	#22608825	C₂	1	2	yes	maximal, complemented
7	#22608818	C₂	1	2	yes	maximal, complemented
8	#22608681	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608314	C₂	1	1	yes	maximal, characteristic
10	C₈×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×Q₈⋊C₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556622	C₄	1	1	yes	characteristic
13	C₄×#11924028	C₂²	1	1	yes	characteristic
14	#17988718	—	2	1	no	—
15	#17988718	—	2	1	no	—
16	#17988718	C₂²	1	2	yes	—
17	#17988718	C₂²	1	2	yes	—
18	#17988714	C₂²	1	2	yes	—
19	#17988692	C₄	1	2	yes	—
20	#17988685	C₄	1	2	yes	—
21	C₄×#11924018	C₂²	1	2	yes	—
22	C₄×#11924015	C₂²	1	2	yes	—
23	#17988664	C₂²	1	2	yes	—
24	#17988658	—	2	2	no	—
25	#17988644	—	2	2	no	—
26	#17988643	—	2	1	no	—
27	#17988640	C₂²	1	1	yes	characteristic
28	#17988640	C₂²	1	1	yes	characteristic
29	#17988627	C₄	1	1	yes	characteristic
30	#17988609	—	2	1	no	—
31	#17988596	C₄	1	1	yes	characteristic
32	#17988586	C₄	1	1	yes	characteristic
33	C₄×#11924012	C₂²	1	1	yes	characteristic
34	#17988339	C₂²	1	2	yes	—
35	#17988337	C₂²	1	2	yes	—
36	#17988319	C₂²	1	1	yes	characteristic
37	#17988319	C₂²	1	1	yes	characteristic
38	#17988316	C₂²	1	1	yes	characteristic
39	#17988316	C₂²	1	1	yes	characteristic
40	#17988309	C₂²	1	2	yes	—
41	C₈×#10596831	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
45	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	—
46	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	—
47	C₂×#11924028	C₂×C₄	1	1	yes	characteristic
48	#14556622	—	2	4	no	—
49	C₂×#11924018	C₂×C₄	1	2	yes	—
50	C₂×#11924015	C₂×C₄	1	2	yes	—
51	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
52	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
53	C₂×#11924011	—	2	2	no	—
54	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
56	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
57	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
58	C₄×C₂²⋊D₇₃	—	2	1	no	—
59	C₄×C₂²⋊D₇₃	—	2	1	no	—
60	#14556550	C₂×C₄	1	1	yes	characteristic
61	#14556548	—	2	1	no	—
62	C₄²×D₇₃	—	2	1	no	—
63	#14556524	C₂×C₄	1	2	yes	—
64	#14556522	C₂×C₄	1	2	yes	—
65	C₄⋊#10596831	—	2	2	no	—
66	C₄⋊#10596831	—	2	2	no	—
67	C₄⋊#10596831	D₄	1	1	yes	characteristic
68	C₄⋊#10596831	D₄	1	1	yes	characteristic
69	C₄⋊#10596831	C₂³	1	1	yes	characteristic
70	C₄⋊#10596831	C₂³	1	1	yes	characteristic
71	#14556520	—	2	2	no	—
72	#14556515	C₂×C₄	1	2	yes	—
73	#14556515	C₂×C₄	1	2	yes	—
74	#14556514	C₂×C₄	1	2	yes	—
75	#14556511	C₂×C₄	1	2	yes	—
76	C₂²⋊#10596831	—	2	1	no	—
77	C₂²⋊#10596831	D₄	1	2	yes	—
78	#14556503	—	2	2	no	—
79	#14556502	—	2	2	no	—
80	#14556502	—	2	2	no	—
81	#14556502	C₂×C₄	1	2	yes	—
82	#14556501	—	2	2	no	—
83	C₄×#10596831	—	2	1	no	—
84	C₄×#10596831	C₂³	1	2	yes	—
85	C₄×#10596831	C₂³	1	2	yes	—
86	C₂²×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₇₃	—	2	1	no	—
88	C₂²×C₈×C₇₃	—	2	1	no	—
89	C₄×Q₈×C₇₃	—	2	1	no	—
90	C₄×Q₈×C₇₃	—	2	1	no	—
91	C₄×Q₈×C₇₃	C₂×C₄	1	2	yes	—
92	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₇₃	—	2	1	no	—
96	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₇₃	—	2	1	no	—
98	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
99	C₄×C₈×C₇₃	—	2	1	no	—
100	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
102	#11924028	—	2	2	no	—
103	#11924028	—	2	2	no	—
104	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
105	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₇₃	—	2	1	no	—
107	C₂×C₄×D₇₃	—	2	1	no	—
108	C₂×C₄×D₇₃	—	2	1	no	—
109	C₂×C₄×D₇₃	—	2	1	no	—
110	#11924018	—	2	4	no	—
111	#11924015	—	2	4	no	—
112	#11924012	—	2	2	no	—
113	#11924012	M₁₆	1	4	yes	complemented
114	#11924011	—	8	2	no	—
115	C₂×#10596831	—	2	1	no	—
116	C₂×#10596831	—	2	1	no	—
117	C₂×#10596831	C₂²×C₄	1	2	yes	—
118	C₂×#10596831	C₂²×C₄	1	2	yes	—
119	C₂×#10596831	C₂×D₄	1	2	yes	—
120	C₂×#10596831	C₂×D₄	1	2	yes	—
121	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
122	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
123	#11924007	—	2	1	no	—
124	#11924007	—	2	1	no	—
125	C₂²⋊Dic₇₃	—	2	1	no	—
126	#11924005	—	2	1	no	—
127	#11924005	—	2	1	no	—
128	C₄×Dic₇₃	—	2	1	no	—
129	C₄×Dic₇₃	—	2	1	no	—
130	C₄×Dic₇₃	—	2	1	no	—
131	C₂×Q₈×C₇₃	—	2	1	no	—
132	C₂×Q₈×C₇₃	—	2	2	no	—
133	C₂×Q₈×C₇₃	—	2	2	no	—
134	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₇₃	—	2	1	no	—
136	C₂²×C₄×C₇₃	—	2	1	no	—
137	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
140	C₂×C₈×C₇₃	—	2	1	no	—
141	C₂×C₈×C₇₃	—	2	2	no	—
142	C₂×C₈×C₇₃	—	2	1	no	—
143	C₂×C₈×C₇₃	—	4	2	no	—
144	C₂×C₈×C₇₃	—	8	1	no	—
145	C₄⋊C₄×C₇₃	—	2	2	no	—
146	C₄⋊C₄×C₇₃	—	2	1	no	—
147	C₄⋊C₄×C₇₃	—	2	2	no	—
148	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
149	C₄²×C₇₃	—	2	2	no	—
150	C₄²×C₇₃	—	2	2	no	—
151	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₇₃	#41	1	1	yes	characteristic
154	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
155	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
156	C₂²×D₇₃	—	2	1	no	—
157	Q₈×C₇₃	—	2	2	no	—
158	Q₈×C₇₃	—	2	2	no	—
159	Q₈×C₇₃	—	4	2	no	—
160	C₂×C₄×C₇₃	—	2	1	no	—
161	C₂×C₄×C₇₃	—	2	1	no	—
162	C₂×C₄×C₇₃	—	2	2	no	—
163	C₂×C₄×C₇₃	—	2	2	no	—
164	C₂×C₄×C₇₃	—	4	1	no	—
165	C₂×C₄×C₇₃	—	4	2	no	—
166	C₂×C₄×C₇₃	—	8	1	no	—
167	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
171	C₂×C₄×C₇₃	#131	1	2	yes	—
172	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
175	C₂²⋊D₇₃	—	4	2	no	—
176	C₂×Dic₇₃	—	2	1	no	—
177	C₂×Dic₇₃	—	2	1	no	—
178	C₂×Dic₇₃	—	2	1	no	—
179	D₂₉₂	—	2	1	no	—
180	D₂₉₂	—	2	1	no	—
181	C₄×D₇₃	—	4	1	no	—
182	C₄×D₇₃	—	4	1	no	—
183	C₄×D₇₃	—	4	2	no	—
184	C₄×D₇₃	—	8	1	no	—
185	Dic₁₄₆	—	2	1	no	—
186	Dic₁₄₆	—	2	1	no	—
187	C₈×C₇₃	—	2	2	no	—
188	C₈×C₇₃	—	4	1	no	—
189	C₈×C₇₃	—	4	2	no	—
190	#10596831	—	2	2	no	—
191	#10596831	—	2	2	no	—
192	#10596831	—	2	2	no	—
193	#10596831	—	4	1	no	—
194	#10596831	—	4	1	no	—
195	#10596831	C₂×M₁₆	1	4	yes	—
196	C₂²×C₇₃	—	2	1	no	—
197	C₂²×C₇₃	—	2	1	no	—
198	C₂²×C₇₃	#436	1	2	yes	—
199	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
200	C₂×D₇₃	—	4	1	no	—
201	C₂×D₇₃	—	4	1	no	—
202	C₂×D₇₃	—	4	1	no	—
203	C₄×C₇₃	—	2	1	no	—
204	C₄×C₇₃	—	2	1	no	—
205	C₄×C₇₃	—	2	1	no	—
206	C₄×C₇₃	—	4	2	no	—
207	C₄×C₇₃	—	4	2	no	—
208	C₄×C₇₃	#436	1	2	yes	—
209	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
210	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
211	C₄×C₇₃	#577	1	1	yes	characteristic
212	C₄×C₇₃	#578	1	1	yes	characteristic
213	Dic₇₃	—	4	1	no	—
214	Dic₇₃	—	4	1	no	—
215	Dic₇₃	—	4	1	no	—
216	#17894	—	73	1	no	maximal, Sylow
217	C₂×C₇₃	—	2	2	no	—
218	C₂×C₇₃	C₂×#436	1	1	yes	characteristic
219	C₂×C₇₃	#2947	1	1	yes	characteristic
220	C₂×C₇₃	#2956	1	1	yes	characteristic
221	D₇₃	—	8	1	no	—
222	#2989	—	73	1	no	—
223	#2983	—	73	1	no	—
224	C₄×#137	—	73	1	no	—
225	#1593	—	73	2	no	—
226	#1592	—	73	2	no	—
227	#1591	—	73	2	no	—
228	#1590	—	73	2	no	—
229	#1565	—	73	1	no	—
230	#1476	—	73	1	no	—
231	C₂×Q₈⋊C₈	D₇₃	1	1	yes	characteristic, complemented
232	C₈×M₁₆	—	73	1	no	—
233	C₇₃	#17894	1	1	yes	characteristic, complemented, Sylow
234	C₂×#137	—	73	1	no	—
235	C₄×#41	—	73	1	no	—
236	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
237	#446	—	73	2	no	—
238	#446	—	73	2	no	—
239	#446	—	73	2	no	—
240	#446	—	146	1	no	—
241	#446	—	146	1	no	—
242	#441	—	73	2	no	—
243	#440	—	73	2	no	—
244	C₄×Q₁₆	—	73	2	no	—
245	C₄×SD₁₆	—	73	2	no	—
246	#436	—	73	2	no	—
247	#435	—	146	2	no	—
248	#432	—	146	2	no	—
249	#432	—	146	1	no	—
250	#431	—	73	1	no	—
251	#431	—	73	1	no	—
252	#428	—	73	1	no	—
253	#423	—	146	1	no	—
254	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
255	#419	—	73	1	no	—
256	#417	—	73	1	no	—
257	C₄×M₁₆	—	73	1	no	—
258	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
259	#335	—	73	2	no	—
260	#334	—	73	2	no	—
261	Q₈⋊C₈	—	73	1	no	—
262	Q₈⋊C₈	—	73	1	no	—
263	Q₈⋊C₈	C₂×D₇₃	1	2	yes	—
264	Q₈⋊C₈	C₂×D₇₃	1	2	yes	—
265	D₄⋊C₈	—	73	1	no	—
266	D₄⋊C₈	—	73	1	no	—
267	#322	—	73	2	no	—
268	C₈²	—	73	2	no	—
269	C₂×#41	—	73	1	no	—
270	C₂²×Q₈	C₄×D₇₃	1	1	yes	characteristic
271	#137	—	146	4	no	—
272	C₂×Q₁₆	—	73	2	no	—
273	C₂×SD₁₆	—	73	2	no	—
274	C₂×M₁₆	—	73	1	no	—
275	C₂×M₁₆	—	73	1	no	—
276	C₂×M₁₆	—	146	2	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₄×Q₈	—	2	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	73	1	no	—
282	C₄×Q₈	—	73	1	no	—
283	C₄×Q₈	C₄×D₇₃	1	2	yes	—
284	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
285	C₄×D₄	—	73	1	no	—
286	C₄×D₄	—	73	1	no	—
287	C₄×D₄	—	146	1	no	—
288	C₄×D₄	—	146	1	no	—
289	#117	—	73	1	no	—
290	#117	—	146	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	146	1	no	—
295	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
296	#107	—	73	2	no	—
297	#106	—	73	2	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	73	1	no	—
300	C₄⋊C₈	—	73	1	no	—
301	C₄⋊C₈	—	73	1	no	—
302	C₄⋊C₈	—	73	1	no	—
303	C₄⋊C₈	—	146	2	no	—
304	C₄⋊C₈	—	146	2	no	—
305	C₄⋊C₈	—	146	2	no	—
306	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
307	#103	—	73	2	no	—
308	#103	—	73	2	no	—
309	#103	—	73	2	no	—
310	#102	—	73	2	no	—
311	C₂²⋊C₈	—	73	2	no	—
312	C₂²⋊C₈	—	146	2	no	—
313	C₂²⋊C₈	—	146	1	no	—
314	#97	—	73	2	no	—
315	#97	—	146	2	no	—
316	#97	—	146	2	no	—
317	#97	—	146	2	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	73	2	no	—
320	C₄×C₈	—	73	2	no	—
321	C₄×C₈	—	146	1	no	—
322	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
323	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
324	#41	—	146	2	no	—
325	#41	—	146	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	73	1	no	—
330	C₂×Q₈	C₂×C₄×D₇₃	1	2	yes	—
331	C₂×D₄	—	73	1	no	—
332	C₂×D₄	—	146	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	146	1	no	—
336	C₂²×C₄	—	146	1	no	—
337	C₂²×C₄	—	146	1	no	—
338	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
340	C₂²×C₄	#11924027	1	1	yes	characteristic
341	Q₁₆	—	146	4	no	—
342	SD₁₆	—	146	4	no	—
343	M₁₆	—	584	2	no	—
344	M₁₆	—	73	4	no	—
345	M₁₆	—	146	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	—	8	1	no	—
351	C₂×C₈	—	73	2	no	—
352	C₂×C₈	—	73	2	no	—
353	C₂×C₈	—	73	2	no	—
354	C₂×C₈	—	73	2	no	—
355	C₂×C₈	—	146	1	no	—
356	C₂×C₈	—	146	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	73	1	no	—
361	C₄⋊C₄	—	73	1	no	—
362	C₄⋊C₄	—	146	1	no	—
363	C₄⋊C₄	—	146	1	no	—
364	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
365	C₂²⋊C₄	—	146	1	no	—
366	C₂²⋊C₄	—	146	1	no	—
367	C₂²⋊C₄	—	146	1	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	146	1	no	—
371	C₄²	—	146	1	no	—
372	C₄²	—	146	1	no	—
373	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
374	C₄²	D₄×D₇₃	1	1	yes	characteristic
375	C₄²	#11924027	1	1	yes	characteristic
376	C₄²	C₂³×D₇₃	1	1	yes	characteristic
377	C₂³	—	146	1	no	—
378	C₂³	#14556551	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	—	2	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	146	1	no	—
383	Q₈	—	146	1	no	—
384	D₄	—	292	2	no	—
385	D₄	—	146	1	no	—
386	D₄	—	146	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	292	1	no	—
395	C₂×C₄	—	292	1	no	—
396	C₂×C₄	—	292	2	no	—
397	C₂×C₄	—	584	1	no	—
398	C₂×C₄	—	146	1	no	—
399	C₂×C₄	—	146	1	no	—
400	C₂×C₄	—	146	1	no	—
401	C₂×C₄	#14556551	1	1	yes	characteristic
402	C₂×C₄	#14556551	1	1	yes	characteristic
403	C₂×C₄	#14556551	1	1	yes	characteristic
404	C₂×C₄	M₁₆×D₇₃	1	2	yes	—
405	C₂×C₄	#14556597	1	2	yes	—
406	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
407	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
408	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	2	no	—
412	C₈	—	292	1	no	—
413	C₈	—	292	1	no	—
414	C₈	—	73	4	no	—
415	C₈	—	146	2	no	—
416	C₈	—	146	2	no	—
417	C₈	—	146	2	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	292	1	no	—
421	C₂²	—	292	1	no	—
422	C₂²	—	292	1	no	—
423	C₂²	#17988662	1	2	yes	—
424	C₂²	C₂×#14556551	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	292	1	no	—
431	C₄	—	292	1	no	—
432	C₄	—	292	1	no	—
433	C₄	#17988662	1	2	yes	—
434	C₄	C₂×M₁₆×D₇₃	1	1	yes	characteristic
435	C₄	C₂×#14556597	1	1	yes	characteristic
436	C₄	#17989393	1	1	yes	characteristic
437	C₄	#17989400	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	584	1	no	—
440	C₂	C₂×#17988662	1	1	yes	characteristic
441	C₂	#22618768	1	1	yes	characteristic
442	C₂	#22618837	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₂×Q₈⋊C₈×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×#11924028	C₂×C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	C₂×Q₈⋊C₈	D₇₃
hypocenter	C₇₃	#17894
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. #22619016	C₂	semidirect
4. #22608837	C₂	semidirect
5. #22608836	C₂	semidirect
6. #22608825	C₂	semidirect
7. #22608818	C₂	semidirect
8. #22608681	C₂	semidirect
10. C₈×#11924012	C₂	semidirect
11. C₂×Q₈⋊C₈×C₇₃	C₂	semidirect
113. #11924012	M₁₆	semidirect
231. C₂×Q₈⋊C₈	D₇₃	semidirect
233. C₇₃	#17894	semidirect

Maximal subgroups

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

subgroup	index
#22619049	2
#22619016	2
C₄×#14556622	2
#22608837	2
#22608836	2
#22608825	2
#22608818	2
#22608681	2
#22608314	2
C₈×#11924012	2
C₂×Q₈⋊C₈×C₇₃	2
#17894	73