Subgroups — #108×D₁₇₂ #25114851

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₆×D₁₇₂	C₂	1	2	yes	maximal
2	C₂×C₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic
3	C₂×#108×D₄₃	C₂	1	2	yes	maximal, complemented
4	#19135370	C₂	1	2	yes	maximal, complemented
5	#19134801	C₂	1	4	yes	maximal, complemented
6	#19134767	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134630	C₂	1	2	yes	maximal, complemented
8	C₄×#108×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×M₁₆×D₄₃	C₂²	1	4	yes	—
10	C₂²×C₈×D₄₃	C₂²	1	2	yes	—
11	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
12	#14582978	—	2	2	no	—
13	#14582972	—	2	4	no	—
14	C₈×D₁₇₂	—	2	2	no	—
15	C₈×D₁₇₂	C₄	1	4	yes	—
16	C₈×D₁₇₂	C₄	1	2	yes	—
17	C₈×D₁₇₂	C₄	1	2	yes	—
18	C₂×#13063261	C₂²	1	2	yes	—
19	C₂×#13063261	C₂²	1	2	yes	—
20	C₂×#13063260	C₂²	1	4	yes	—
21	#108×D₄₃	—	2	8	no	—
22	#14582923	C₂²	1	2	yes	—
23	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
24	#14582862	C₂²	1	4	yes	—
25	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	2	yes	—
26	#14582663	C₂²	1	4	yes	—
27	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
29	C₄×M₁₆×C₄₃	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₄₃×#341	C₂²	1	2	yes	—
32	C₂²×D₁₇₂	Q₈	1	1	yes	characteristic
33	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
34	C₂×#10621877	C₂³	1	4	yes	—
35	C₂×#10621872	—	2	4	no	—
36	M₁₆×D₄₃	—	2	8	no	—
37	M₁₆×D₄₃	—	4	4	no	—
38	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
39	C₂×C₈×D₄₃	—	2	4	no	—
40	C₂×C₈×D₄₃	—	2	4	no	—
41	C₂×C₈×D₄₃	—	2	4	no	—
42	C₂×C₈×D₄₃	C₂×C₄	1	4	yes	—
43	C₂×C₈×D₄₃	C₂×C₄	1	4	yes	—
44	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
45	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
46	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
47	C₄×D₁₇₂	D₄	1	1	yes	characteristic
48	C₄×D₁₇₂	D₄	1	2	yes	—
49	C₄×D₁₇₂	D₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₃	Q₈	1	1	yes	characteristic
51	C₂×(C₂×D₄₃)⋊C₄	Q₈	1	2	yes	—
52	#13063261	—	2	4	no	—
53	#13063261	—	4	2	no	—
54	#13063260	—	2	8	no	—
55	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
56	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
57	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
58	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
59	(C₂×D₄₃)⋊C₈	—	2	4	no	—
60	(C₂×D₄₃)⋊C₈	—	2	4	no	—
61	(C₂×D₄₃)⋊C₈	C₂×C₄	1	4	yes	—
62	(C₂×D₄₃)⋊C₈	C₂×C₄	1	4	yes	—
63	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
64	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
65	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
68	#108×C₄₃	—	2	2	no	—
69	#108×C₄₃	D₄	1	4	yes	complemented
70	#97×C₄₃	—	2	2	no	—
71	C₄×C₈×C₄₃	—	2	2	no	—
72	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
74	C₂³×D₄₃	C₂×Q₈	1	2	yes	—
75	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
76	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
78	C₂²×Dic₄₃	C₂×Q₈	1	2	yes	—
79	C₂×D₁₇₂	—	2	4	no	—
80	C₂×D₁₇₂	C₄⋊C₄	1	1	yes	characteristic
81	C₂×D₁₇₂	C₄⋊C₄	1	2	yes	—
82	C₂×D₁₇₂	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₄₃	—	2	2	no	—
84	C₂×C₄×D₄₃	—	2	2	no	—
85	C₂×C₄×D₄₃	—	2	2	no	—
86	C₂×C₄×D₄₃	—	2	2	no	—
87	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
88	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
89	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
90	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
91	M₁₆×C₄₃	—	2	2	no	—
92	M₁₆×C₄₃	—	2	2	no	—
93	M₁₆×C₄₃	—	2	2	no	—
94	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
95	C₂×C₈×C₄₃	—	2	2	no	—
96	C₂×C₈×C₄₃	—	2	1	no	—
97	C₂×C₈×C₄₃	—	2	1	no	—
98	C₂×C₈×C₄₃	—	2	2	no	—
99	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₄₃	#41	1	2	yes	—
103	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
107	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	2	yes	—
108	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	2	yes	—
109	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	2	yes	—
110	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	2	yes	—
111	C₄⋊Dic₄₃	C₄⋊C₄	1	2	yes	—
112	C₄⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
113	C₄⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
114	#10621877	—	2	4	no	—
115	#10621877	—	2	4	no	—
116	C₂×C₄₃⋊C₈	—	2	2	no	—
117	C₂×C₄₃⋊C₈	—	2	2	no	—
118	C₂×C₄₃⋊C₈	—	2	4	no	—
119	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
120	#10621872	—	4	8	no	—
121	C₈×D₄₃	—	2	8	no	—
122	C₈×D₄₃	—	2	8	no	—
123	C₈×D₄₃	—	4	8	no	—
124	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
125	C₂²×D₄₃	—	2	2	no	—
126	C₂²×D₄₃	—	2	2	no	—
127	C₂²×D₄₃	—	2	4	no	—
128	C₂²×D₄₃	—	4	2	no	—
129	C₂²×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
130	C₂²×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×C₄×C₄₃	—	2	2	no	—
132	C₂×C₄×C₄₃	—	4	1	no	—
133	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
138	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
139	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
140	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
141	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
142	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
143	C₂×Dic₄₃	—	2	2	no	—
144	C₂×Dic₄₃	—	2	2	no	—
145	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
146	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
147	D₁₇₂	—	2	4	no	—
148	D₁₇₂	—	2	2	no	—
149	D₁₇₂	#108	1	4	yes	direct product factor
150	C₄×D₄₃	—	2	2	no	—
151	C₄×D₄₃	—	2	2	no	—
152	C₄×D₄₃	—	2	2	no	—
153	C₄×D₄₃	—	2	2	no	—
154	C₄×D₄₃	—	2	2	no	—
155	C₄×D₄₃	—	2	2	no	—
156	C₄×D₄₃	—	2	2	no	—
157	C₄×D₄₃	—	2	2	no	—
158	C₈×C₄₃	—	2	2	no	—
159	C₈×C₄₃	—	2	4	no	—
160	C₈×C₄₃	—	4	2	no	—
161	C₈×C₄₃	C₄×D₄	1	4	yes	—
162	C₄₃⋊C₈	—	2	4	no	—
163	C₄₃⋊C₈	—	4	4	no	—
164	D₄×#108	—	43	1	no	maximal, Sylow
165	C₂²×C₄₃	—	2	1	no	—
166	C₂²×C₄₃	—	2	1	no	—
167	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
168	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
169	C₂²×C₄₃	#554	1	1	yes	characteristic
170	C₂×D₄₃	—	2	2	no	—
171	C₂×D₄₃	—	2	2	no	—
172	C₂×D₄₃	—	2	2	no	—
173	C₂×D₄₃	—	2	2	no	—
174	C₂×D₄₃	—	2	2	no	—
175	C₂×D₄₃	—	4	4	no	—
176	C₂×D₄₃	—	4	4	no	—
177	C₂×D₄₃	C₂×#108	1	4	yes	complemented
178	C₄×C₄₃	—	2	1	no	—
179	C₄×C₄₃	—	2	1	no	—
180	C₄×C₄₃	—	2	1	no	—
181	C₄×C₄₃	C₂×#108	1	2	yes	complemented
182	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
183	C₄×C₄₃	#520	1	1	yes	characteristic
184	C₄×C₄₃	D₄²	1	1	yes	characteristic
185	C₄×C₄₃	#547	1	1	yes	characteristic
186	Dic₄₃	—	2	2	no	—
187	Dic₄₃	—	2	2	no	—
188	D₄×M₁₆	—	43	2	no	—
189	C₂×C₈×D₄	—	43	1	no	—
190	C₂²×#108	—	43	2	no	—
191	#1950	—	43	2	no	—
192	#1855	—	43	4	no	—
193	#1848	—	43	1	no	—
194	#1810	—	43	2	no	—
195	C₄×#108	D₄₃	1	1	yes	characteristic, complemented
196	C₂×C₄₃	—	2	1	no	—
197	C₂×C₄₃	—	2	1	no	—
198	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
199	C₂×C₄₃	C₂²×#108	1	1	yes	characteristic
200	C₂×C₄₃	#2916	1	1	yes	characteristic
201	D₄₃	—	2	4	no	—
202	D₄₃	—	4	2	no	—
203	C₂²×M₁₆	—	43	4	no	—
204	C₂³×C₈	—	43	2	no	—
205	C₂×C₄×D₄	—	43	1	no	—
206	#436	—	86	2	no	—
207	#435	—	86	4	no	—
208	C₈×D₄	—	43	2	no	—
209	C₈×D₄	—	43	4	no	—
210	C₈×D₄	—	43	2	no	—
211	C₈×D₄	—	86	2	no	—
212	C₂×#108	—	43	4	no	—
213	C₂×#108	—	43	2	no	—
214	C₂×#108	—	43	2	no	—
215	C₂×#108	—	86	8	no	—
216	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
217	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
218	#423	—	43	2	no	—
219	C₂×C₄⋊C₈	—	43	1	no	—
220	#407	—	43	4	no	—
221	C₂×C₂²⋊C₈	—	43	2	no	—
222	C₄×M₁₆	C₂×D₄₃	1	2	yes	—
223	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
224	#341	—	43	4	no	—
225	#341	C₂×D₄₃	1	2	yes	—
226	C₄₃	D₄×#108	1	1	yes	characteristic, complemented, Sylow
227	C₂²×D₄	—	43	1	no	—
228	C₂³×C₄	—	43	2	no	—
229	C₂×M₁₆	—	43	4	no	—
230	C₂×M₁₆	—	86	4	no	—
231	C₂×M₁₆	—	86	8	no	—
232	C₂×M₁₆	—	172	4	no	—
233	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
234	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
235	C₂²×C₈	—	43	2	no	—
236	C₂²×C₈	—	43	4	no	—
237	C₂²×C₈	—	43	4	no	—
238	C₂²×C₈	—	86	4	no	—
239	C₂²×C₈	—	86	4	no	—
240	C₂²×C₈	—	86	4	no	—
241	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
242	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
243	C₄×D₄	—	43	1	no	—
244	C₄×D₄	—	43	2	no	—
245	C₄×D₄	—	43	1	no	—
246	C₄×D₄	—	43	1	no	—
247	C₄×D₄	—	43	2	no	—
248	C₄×D₄	—	43	1	no	—
249	C₂×C₄⋊C₄	—	43	1	no	—
250	C₂×C₂²⋊C₄	—	43	2	no	—
251	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
252	#108	—	2	2	no	—
253	#108	—	86	8	no	—
254	#108	—	86	4	no	—
255	#108	—	172	2	no	—
256	#108	D₁₇₂	1	4	yes	direct product factor
257	C₄⋊C₈	—	43	2	no	—
258	C₄⋊C₈	—	43	2	no	—
259	C₄⋊C₈	—	86	2	no	—
260	C₄⋊C₈	—	86	2	no	—
261	C₂²⋊C₈	—	43	4	no	—
262	C₂²⋊C₈	—	43	4	no	—
263	C₂²⋊C₈	—	86	4	no	—
264	C₂²⋊C₈	—	86	4	no	—
265	#97	—	2	2	no	—
266	C₄×C₈	—	2	2	no	—
267	C₄×C₈	C₄×D₄₃	1	2	yes	—
268	C₄×C₈	C₄×D₄₃	1	2	yes	—
269	C₂⁴	—	43	2	no	—
270	C₂×D₄	—	43	1	no	—
271	C₂×D₄	—	43	2	no	—
272	C₂×D₄	—	43	1	no	—
273	C₂×D₄	—	86	4	no	—
274	C₂²×C₄	—	43	2	no	—
275	C₂²×C₄	—	43	2	no	—
276	C₂²×C₄	—	43	2	no	—
277	C₂²×C₄	—	43	2	no	—
278	C₂²×C₄	—	43	2	no	—
279	C₂²×C₄	—	86	2	no	—
280	C₂²×C₄	—	86	2	no	—
281	C₂²×C₄	—	86	2	no	—
282	C₂²×C₄	—	86	2	no	—
283	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
284	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
285	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
286	M₁₆	—	2	2	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	2	2	no	—
289	M₁₆	—	86	4	no	—
290	M₁₆	—	86	4	no	—
291	M₁₆	—	172	8	no	—
292	M₁₆	C₂×D₁₇₂	1	4	yes	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	43	4	no	—
298	C₂×C₈	—	86	2	no	—
299	C₂×C₈	—	86	2	no	—
300	C₂×C₈	—	86	8	no	—
301	C₂×C₈	—	86	8	no	—
302	C₂×C₈	—	86	4	no	—
303	C₂×C₈	—	172	8	no	—
304	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
305	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
306	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
307	C₂×C₈	#10621898	1	2	yes	—
308	C₄⋊C₄	—	43	2	no	—
309	C₄⋊C₄	—	43	1	no	—
310	C₄⋊C₄	—	43	1	no	—
311	C₂²⋊C₄	—	43	2	no	—
312	C₂²⋊C₄	—	43	2	no	—
313	C₂²⋊C₄	—	43	2	no	—
314	C₂²⋊C₄	—	43	2	no	—
315	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
316	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
317	C₄²	D₄×D₄₃	1	1	yes	characteristic
318	C₄²	D₄×D₄₃	1	1	yes	characteristic
319	C₂³	—	43	2	no	—
320	C₂³	—	43	2	no	—
321	C₂³	—	86	4	no	—
322	C₂³	—	86	2	no	—
323	C₂³	—	86	2	no	—
324	C₂³	—	172	2	no	—
325	C₂³	C₂×Q₈×D₄₃	1	1	yes	characteristic
326	D₄	—	43	4	no	—
327	D₄	—	86	4	no	—
328	D₄	—	86	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	43	2	no	—
332	C₂×C₄	—	43	2	no	—
333	C₂×C₄	—	86	2	no	—
334	C₂×C₄	—	86	2	no	—
335	C₂×C₄	—	86	2	no	—
336	C₂×C₄	—	86	2	no	—
337	C₂×C₄	—	86	2	no	—
338	C₂×C₄	—	86	2	no	—
339	C₂×C₄	—	86	2	no	—
340	C₂×C₄	—	86	2	no	—
341	C₂×C₄	—	86	2	no	—
342	C₂×C₄	—	86	2	no	—
343	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
344	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
345	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
346	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
347	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
348	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
350	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
351	C₂×C₄	#13063371	1	1	yes	characteristic
352	C₂×C₄	#13063372	1	1	yes	characteristic
353	C₈	—	2	2	no	—
354	C₈	—	2	4	no	—
355	C₈	—	4	2	no	—
356	C₈	—	86	4	no	—
357	C₈	—	172	4	no	—
358	C₈	C₄×D₁₇₂	1	4	yes	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	43	4	no	—
362	C₂²	—	86	2	no	—
363	C₂²	—	86	2	no	—
364	C₂²	—	86	2	no	—
365	C₂²	—	86	2	no	—
366	C₂²	—	86	2	no	—
367	C₂²	—	172	4	no	—
368	C₂²	—	172	4	no	—
369	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
370	C₂²	Q₈×D₁₇₂	1	1	yes	characteristic
371	C₂²	#14583609	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	86	2	no	—
376	C₄	—	86	2	no	—
377	C₄	#108×D₄₃	1	2	yes	complemented
378	C₄	C₂×C₄×D₁₇₂	1	1	yes	characteristic
379	C₄	#14583379	1	1	yes	characteristic
380	C₄	D₄×D₁₇₂	1	1	yes	characteristic
381	C₄	#14583554	1	1	yes	characteristic
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	86	4	no	—
385	C₂	—	172	2	no	—
386	C₂	C₄⋊C₄×D₁₇₂	1	1	yes	characteristic
387	C₂	C₂×#108×D₄₃	1	1	yes	characteristic
388	C₂	#19143203	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×#108×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×C₄⋊C₄
prime radical	C₂²×D₁₇₂	Q₈
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×#108	D₄₃
hypocenter	C₄₃	D₄×#108
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#108

Complements

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

N	H ≅ G/N	type
3. C₂×#108×D₄₃	C₂	semidirect
4. #19135370	C₂	semidirect
5. #19134801	C₂	semidirect
6. #19134767	C₂	semidirect
7. #19134630	C₂	semidirect
8. C₄×#108×C₄₃	C₂	semidirect
69. #108×C₄₃	D₄	semidirect
149. D₁₇₂	#108	direct (N × H)
177. C₂×D₄₃	C₂×#108	semidirect
181. C₄×C₄₃	C₂×#108	semidirect
195. C₄×#108	D₄₃	semidirect
226. C₄₃	D₄×#108	semidirect
256. #108	D₁₇₂	direct (N × H)
377. C₄	#108×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
M₁₆×D₁₇₂	2
C₂×C₈×D₁₇₂	2
C₂×#108×D₄₃	2
#19135370	2
#19134801	2
#19134767	2
#19134630	2
C₄×#108×C₄₃	2
D₄×#108	43

Subgroups — #108×D172 #25114851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #108×D₁₇₂ #25114851