Subgroups — #33055112

Order 18688.

602 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22619044	C₂	1	1	yes	maximal, characteristic
2	#22619039	C₂	1	1	yes	maximal, characteristic
3	#22618573	C₂	1	1	yes	maximal, characteristic
4	#22608721	C₂	1	2	yes	maximal, complemented
5	#22608715	C₂	1	2	yes	maximal, complemented
6	#22608708	C₂	1	2	yes	maximal, complemented
7	#22608700	C₂	1	2	yes	maximal, complemented
8	#22608684	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608684	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#17988338	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11924028	C₂²	1	1	yes	characteristic
13	#17988717	—	2	1	no	—
14	C₈×Dic₁₄₆	—	2	1	no	—
15	#17988666	—	2	1	no	—
16	#17988655	—	2	2	no	—
17	C₈×D₂₉₂	—	2	1	no	—
18	#17988650	—	2	2	no	—
19	#17988646	C₄	1	2	yes	—
20	#17988646	C₄	1	2	yes	—
21	#17988643	C₂²	1	2	yes	—
22	#17988639	C₂²	1	2	yes	—
23	#17988638	C₂²	1	2	yes	—
24	#17988638	C₂²	1	2	yes	—
25	#17988613	C₄	1	1	yes	characteristic
26	#17988613	C₄	1	1	yes	characteristic
27	#17988609	C₂²	1	2	yes	—
28	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
30	C₄⋊C₈×D₇₃	C₂²	1	2	yes	—
31	#17988553	C₄	1	1	yes	characteristic
32	#17988553	C₄	1	1	yes	characteristic
33	C₄×#11924012	C₂²	1	1	yes	characteristic
34	#17988339	C₂²	1	2	yes	—
35	#17988339	C₂²	1	2	yes	—
36	#17988338	C₂²	1	2	yes	—
37	#17988338	C₂²	1	2	yes	—
38	#17988337	C₂²	1	2	yes	—
39	#17988337	C₂²	1	2	yes	—
40	#431×C₇₃	C₂²	1	1	yes	characteristic
41	#431×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
43	#335×C₇₃	C₂²	1	1	yes	characteristic
44	#335×C₇₃	C₂²	1	1	yes	characteristic
45	#334×C₇₃	C₂²	1	1	yes	characteristic
46	#334×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#11924028	C₂×C₄	1	1	yes	characteristic
48	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
49	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
50	C₂×#11924011	—	2	2	no	—
51	C₂²×#10596831	—	2	1	no	—
52	C₂²×#10596831	—	2	1	no	—
53	C₂×C₈×D₇₃	—	2	2	no	—
54	C₄×Dic₁₄₆	D₄	1	1	yes	characteristic
55	C₄×Dic₁₄₆	Q₈	1	1	yes	characteristic
56	C₄×D₂₉₂	D₄	1	1	yes	characteristic
57	C₄×D₂₉₂	Q₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₇₃	D₄	1	2	yes	—
59	C₄×C₂²⋊D₇₃	Q₈	1	2	yes	—
60	#14556550	C₂×C₄	1	1	yes	characteristic
61	#14556548	C₂×C₄	1	2	yes	—
62	C₄²×D₇₃	C₂³	1	2	yes	—
63	C₄⋊#10596831	—	2	1	no	—
64	C₄⋊#10596831	—	2	1	no	—
65	C₄⋊#10596831	C₂³	1	2	yes	—
66	C₄⋊#10596831	C₂³	1	2	yes	—
67	#14556520	—	2	2	no	—
68	#14556520	—	2	2	no	—
69	#14556520	C₂×C₄	1	2	yes	—
70	#14556520	C₂×C₄	1	2	yes	—
71	#14556520	C₂×C₄	1	2	yes	—
72	#14556520	C₂×C₄	1	2	yes	—
73	#14556503	—	2	2	no	—
74	#14556503	—	2	2	no	—
75	#14556503	C₂×C₄	1	2	yes	—
76	#14556503	C₂×C₄	1	2	yes	—
77	#14556503	C₂×C₄	1	2	yes	—
78	#14556503	C₂×C₄	1	2	yes	—
79	#14556502	C₂×C₄	1	2	yes	—
80	#14556501	—	2	2	no	—
81	C₄×#10596831	C₂³	1	2	yes	—
82	C₈×Dic₇₃	—	2	2	no	—
83	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
90	C₂²⋊C₈×C₇₃	—	2	1	no	—
91	C₂²⋊C₈×C₇₃	—	2	1	no	—
92	C₄×C₈×C₇₃	—	2	1	no	—
93	C₄×C₈×C₇₃	—	2	1	no	—
94	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
98	#11924028	—	2	2	no	—
99	#11924028	—	2	2	no	—
100	C₂×Dic₁₄₆	C₄⋊C₄	1	1	yes	characteristic
101	C₂×D₂₉₂	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₂²⋊D₇₃	C₄⋊C₄	1	2	yes	—
103	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
105	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
106	#11924012	—	2	2	no	—
107	#11924012	—	2	2	no	—
108	#11924011	—	8	2	no	—
109	C₂×#10596831	—	2	2	no	—
110	C₂×#10596831	—	2	2	no	—
111	C₂×#10596831	—	8	1	no	—
112	C₂×#10596831	—	8	1	no	—
113	C₂×#10596831	C₂²×C₄	1	2	yes	—
114	C₂×#10596831	C₂²×C₄	1	2	yes	—
115	C₈×D₇₃	—	8	2	no	—
116	C₄⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
117	C₄⋊Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
118	#11924007	C₄⋊C₄	1	2	yes	—
119	#11924007	C₄⋊C₄	1	2	yes	—
120	C₂²⋊Dic₇₃	C₄⋊C₄	1	2	yes	—
121	#11924005	C₄⋊C₄	1	2	yes	—
122	#11924005	C₄⋊C₄	1	2	yes	—
123	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
124	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
125	C₄×Dic₇₃	C₂×Q₈	1	2	yes	—
126	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
129	C₂×C₈×C₇₃	—	2	2	no	—
130	C₂×C₈×C₇₃	—	2	2	no	—
131	C₂×C₈×C₇₃	—	2	1	no	—
132	C₂×C₈×C₇₃	—	2	1	no	—
133	C₂×C₈×C₇₃	—	2	1	no	—
134	C₂×C₈×C₇₃	—	2	1	no	—
135	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₇₃	C₂×Q₈	1	1	yes	characteristic
142	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
143	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂²×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₇₃	—	2	1	no	—
146	C₂×C₄×C₇₃	—	2	1	no	—
147	C₂×C₄×C₇₃	—	4	1	no	—
148	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₇₃	#131	1	2	yes	—
152	C₂×C₄×C₇₃	#131	1	2	yes	—
153	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
156	C₂²⋊D₇₃	—	2	4	no	—
157	C₂×Dic₇₃	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×Dic₇₃	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×Dic₇₃	C₂×C₄⋊C₄	1	2	yes	—
160	D₂₉₂	—	2	2	no	—
161	C₄×D₇₃	—	2	2	no	—
162	C₄×D₇₃	—	2	2	no	—
163	C₄×D₇₃	—	2	2	no	—
164	C₄×D₇₃	—	2	2	no	—
165	C₄×D₇₃	—	4	2	no	—
166	Dic₁₄₆	—	2	2	no	—
167	C₈×C₇₃	—	2	1	no	—
168	C₈×C₇₃	—	2	1	no	—
169	C₈×C₇₃	—	2	1	no	—
170	C₈×C₇₃	—	2	1	no	—
171	C₈×C₇₃	—	4	1	no	—
172	C₈×C₇₃	—	4	1	no	—
173	C₈×C₇₃	—	4	1	no	—
174	C₈×C₇₃	—	4	1	no	—
175	#10596831	—	2	2	no	—
176	#10596831	—	2	2	no	—
177	#10596831	—	4	2	no	—
178	#10596831	—	4	2	no	—
179	C₂²×C₇₃	—	2	1	no	—
180	C₂²×C₇₃	—	2	1	no	—
181	C₂²×C₇₃	#424	1	2	yes	—
182	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂×D₇₃	—	2	2	no	—
184	C₂×D₇₃	—	2	2	no	—
185	C₂×D₇₃	—	2	2	no	—
186	C₄×C₇₃	—	2	1	no	—
187	C₄×C₇₃	—	2	1	no	—
188	C₄×C₇₃	—	2	1	no	—
189	C₄×C₇₃	#424	1	2	yes	—
190	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
191	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
192	C₄×C₇₃	#577	1	1	yes	characteristic
193	C₄×C₇₃	#577	1	1	yes	characteristic
194	Dic₇₃	—	2	2	no	—
195	Dic₇₃	—	2	2	no	—
196	Dic₇₃	—	2	2	no	—
197	#17811	—	73	1	no	maximal, Sylow
198	C₂×C₇₃	—	2	2	no	—
199	C₂×C₇₃	C₂×#424	1	1	yes	characteristic
200	C₂×C₇₃	#2912	1	1	yes	characteristic
201	C₂×C₇₃	#2916	1	1	yes	characteristic
202	D₇₃	—	4	2	no	—
203	#2989	—	73	1	no	—
204	#2988	—	73	1	no	—
205	#2922	—	73	1	no	—
206	#1574	—	73	2	no	—
207	#1573	—	73	2	no	—
208	#1572	—	73	2	no	—
209	#1570	—	73	2	no	—
210	#1565	—	73	1	no	—
211	#1565	—	73	1	no	—
212	#1564	D₇₃	1	1	yes	characteristic, complemented
213	C₂×#334	—	73	1	no	—
214	C₇₃	#17811	1	1	yes	characteristic, complemented, Sylow
215	C₄×#41	—	73	1	no	—
216	#446	—	146	1	no	—
217	C₈×Q₈	—	146	1	no	—
218	#436	—	146	1	no	—
219	#435	—	146	2	no	—
220	C₈×D₄	—	146	1	no	—
221	C₈×D₄	—	146	2	no	—
222	#433	—	73	2	no	—
223	#433	—	73	2	no	—
224	#432	—	73	2	no	—
225	#431	—	73	2	no	—
226	#431	—	73	2	no	—
227	#431	—	73	2	no	—
228	#431	C₂×D₇₃	1	1	yes	characteristic
229	#431	C₂×D₇₃	1	1	yes	characteristic
230	#424	—	73	1	no	—
231	#424	—	73	1	no	—
232	#423	—	73	2	no	—
233	C₂×C₄⋊C₈	—	73	1	no	—
234	C₂×C₄⋊C₈	—	73	1	no	—
235	C₂×C₄⋊C₈	—	73	2	no	—
236	#408	—	73	1	no	—
237	#408	—	73	1	no	—
238	C₄×M₁₆	—	73	1	no	—
239	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
240	#335	—	73	2	no	—
241	#335	—	73	2	no	—
242	#335	C₂×D₇₃	1	1	yes	characteristic
243	#335	C₂×D₇₃	1	1	yes	characteristic
244	#334	—	73	2	no	—
245	#334	—	73	2	no	—
246	#334	—	73	2	no	—
247	#334	—	73	2	no	—
248	#334	C₂×D₇₃	1	1	yes	characteristic
249	#334	C₂×D₇₃	1	1	yes	characteristic
250	C₂×#41	—	73	1	no	—
251	C₂×M₁₆	—	73	1	no	—
252	C₂×M₁₆	—	73	1	no	—
253	C₂×M₁₆	—	146	2	no	—
254	C₂²×C₈	—	146	2	no	—
255	C₂²×C₈	—	146	1	no	—
256	C₂²×C₈	—	146	1	no	—
257	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
258	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
259	C₄×Q₈	—	73	1	no	—
260	C₄×Q₈	—	73	1	no	—
261	C₄×D₄	—	73	2	no	—
262	C₄×D₄	—	73	2	no	—
263	C₄×D₄	—	73	1	no	—
264	C₄×D₄	—	73	1	no	—
265	#117	—	73	1	no	—
266	#117	—	73	2	no	—
267	C₂×C₄²	—	73	2	no	—
268	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
269	C₄⋊C₈	—	73	2	no	—
270	C₄⋊C₈	—	73	2	no	—
271	C₄⋊C₈	—	73	2	no	—
272	C₄⋊C₈	—	73	2	no	—
273	C₄⋊C₈	—	73	2	no	—
274	C₄⋊C₈	—	73	2	no	—
275	C₄⋊C₈	—	146	2	no	—
276	C₄⋊C₈	—	146	2	no	—
277	C₄⋊C₈	—	146	1	no	—
278	C₄⋊C₈	—	146	1	no	—
279	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
280	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
281	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
282	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	2	1	no	—
285	C₂²⋊C₈	—	73	2	no	—
286	C₂²⋊C₈	—	73	2	no	—
287	C₂²⋊C₈	—	73	2	no	—
288	C₂²⋊C₈	—	73	2	no	—
289	C₂²⋊C₈	—	146	2	no	—
290	C₂²⋊C₈	—	146	2	no	—
291	#97	—	73	2	no	—
292	#97	—	146	2	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	73	2	no	—
296	C₄×C₈	—	146	2	no	—
297	C₄×C₈	C₄×D₇₃	1	1	yes	characteristic
298	C₄×C₈	C₄×D₇₃	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
300	C₄×C₈	C₂²×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	1	no	—
306	C₂²×C₄	—	73	2	no	—
307	C₂²×C₄	—	73	2	no	—
308	C₂²×C₄	—	73	2	no	—
309	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
310	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
311	C₂²×C₄	Q₈×D₇₃	1	1	yes	characteristic
312	M₁₆	—	584	2	no	—
313	M₁₆	—	146	2	no	—
314	M₁₆	—	146	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	584	2	no	—
322	C₂×C₈	—	584	1	no	—
323	C₂×C₈	—	584	1	no	—
324	C₂×C₈	—	73	2	no	—
325	C₂×C₈	—	73	2	no	—
326	C₂×C₈	—	146	2	no	—
327	C₂×C₈	—	146	2	no	—
328	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
329	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
330	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
331	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
332	C₄⋊C₄	—	73	2	no	—
333	C₄⋊C₄	—	73	2	no	—
334	C₄⋊C₄	—	73	1	no	—
335	C₄⋊C₄	—	73	1	no	—
336	C₂²⋊C₄	—	73	2	no	—
337	C₂²⋊C₄	—	73	2	no	—
338	C₂²⋊C₄	—	73	2	no	—
339	C₄²	—	73	2	no	—
340	C₄²	—	73	2	no	—
341	C₄²	—	73	2	no	—
342	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
343	C₄²	D₄×D₇₃	1	1	yes	characteristic
344	C₄²	Q₈×D₇₃	1	1	yes	characteristic
345	C₄²	C₂³×D₇₃	1	1	yes	characteristic
346	C₂³	—	73	2	no	—
347	C₂³	C₄⋊C₄×D₇₃	1	1	yes	characteristic
348	Q₈	—	146	2	no	—
349	D₄	—	146	4	no	—
350	D₄	—	146	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	292	2	no	—
355	C₂×C₄	—	73	2	no	—
356	C₂×C₄	—	73	2	no	—
357	C₂×C₄	—	73	2	no	—
358	C₂×C₄	—	146	2	no	—
359	C₂×C₄	—	146	2	no	—
360	C₂×C₄	—	146	2	no	—
361	C₂×C₄	—	146	2	no	—
362	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
363	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
364	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
365	C₂×C₄	#14556597	1	2	yes	—
366	C₂×C₄	#14556599	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
369	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	2	1	no	—
374	C₈	—	4	1	no	—
375	C₈	—	4	1	no	—
376	C₈	—	4	1	no	—
377	C₈	—	4	1	no	—
378	C₈	—	292	2	no	—
379	C₈	—	292	2	no	—
380	C₈	—	146	2	no	—
381	C₈	—	146	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	146	2	no	—
385	C₂²	—	146	2	no	—
386	C₂²	—	146	2	no	—
387	C₂²	#17988612	1	2	yes	—
388	C₂²	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	146	2	no	—
393	C₄	—	146	2	no	—
394	C₄	—	146	2	no	—
395	C₄	#17988612	1	2	yes	—
396	C₄	C₂×#14556597	1	1	yes	characteristic
397	C₄	C₂×#14556599	1	1	yes	characteristic
398	C₄	#17989394	1	1	yes	characteristic
399	C₄	#17989394	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	292	2	no	—
402	C₂	C₂×#17988612	1	1	yes	characteristic
403	C₂	#22618523	1	1	yes	characteristic
404	C₂	#22618539	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1564	C₂
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂×#11924028	C₂×C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#1564	D₇₃
hypocenter	C₇₃	#17811
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
4. #22608721	C₂	semidirect
5. #22608715	C₂	semidirect
6. #22608708	C₂	semidirect
7. #22608700	C₂	semidirect
8. #22608684	C₂	semidirect
9. #22608684	C₂	semidirect
10. C₂×#17988338	C₂	semidirect
11. C₇₃×#1564	C₂	semidirect
212. #1564	D₇₃	semidirect
214. C₇₃	#17811	semidirect

Maximal subgroups

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

subgroup	index
#22619044	2
#22619039	2
#22618573	2
#22608721	2
#22608715	2
#22608708	2
#22608700	2
#22608684	2
C₂×#17988338	2
C₇₃×#1564	2
#17811	73