Subgroups — #25250221

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143305	C₂	1	1	yes	maximal, characteristic
2	#19136425	C₂	1	2	yes	maximal, complemented
3	#19136424	C₂	1	2	yes	maximal, complemented
4	C₁₆×C₂²⋊D₄₃	C₂	1	2	yes	maximal, complemented
5	(C₂²⋊D₄₃)⋊C₁₆	C₂	1	2	yes	maximal, complemented
6	#19136391	C₂	1	2	yes	maximal, complemented
7	#19136209	C₂	1	1	yes	maximal, characteristic, complemented
8	#19136207	C₂	1	2	yes	maximal, complemented
9	C₄₃×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13063331	C₂²	1	1	yes	characteristic
11	#14583445	C₄	1	1	yes	characteristic
12	C₂×#13063265	C₂²	1	1	yes	characteristic
13	C₂×#13063264	C₂²	1	2	yes	—
14	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₆×D₄₃	C₂²	1	2	yes	—
16	#14582975	C₄	1	2	yes	—
17	#14582975	C₄	1	2	yes	—
18	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	—
19	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	—
20	#14582922	C₄	1	1	yes	characteristic
21	#14582867	C₄	1	1	yes	characteristic
22	#14582866	C₄	1	1	yes	characteristic
23	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
24	Dic₄₃⋊C₁₆	C₂²	1	2	yes	—
25	Dic₄₃⋊C₁₆	C₂²	1	2	yes	—
26	C₂²⋊(C₄₃⋊C₁₆)	C₂²	1	2	yes	—
27	C₂²⋊(C₄₃⋊C₁₆)	C₂²	1	2	yes	—
28	(C₂×D₄₃)⋊C₁₆	C₂²	1	2	yes	—
29	(C₂×D₄₃)⋊C₁₆	C₂²	1	2	yes	—
30	C₁₆×Dic₄₃	C₂²	1	2	yes	—
31	C₁₆×Dic₄₃	C₂²	1	2	yes	—
32	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
34	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
35	C₄₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
36	C₄₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
37	C₂×#10621898	C₂×C₄	1	1	yes	characteristic
38	#13063331	—	4	1	no	—
39	#13063331	—	4	1	no	—
40	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
41	C₂×#10621872	C₂×C₄	1	2	yes	—
42	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₄₃	C₂³	1	2	yes	—
44	#13063323	C₈	1	1	yes	characteristic
45	#13063321	C₈	1	1	yes	characteristic
46	#13063314	C₈	1	1	yes	characteristic
47	#13063312	C₈	1	1	yes	characteristic
48	#13063297	C₈	1	2	yes	—
49	#13063297	C₈	1	2	yes	—
50	C₄×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
51	C₄×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
52	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
53	#13063265	—	4	1	no	—
54	#13063264	—	4	2	no	—
55	C₂×C₄₃⋊C₁₆	—	4	1	no	—
56	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
57	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
58	C₁₆×D₄₃	—	4	2	no	—
59	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
60	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
61	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
62	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
63	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
64	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
65	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
66	C₈×Dic₄₃	C₂³	1	2	yes	—
67	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
68	#131×C₄₃	—	4	1	no	—
69	#131×C₄₃	—	4	1	no	—
70	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
71	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
72	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
76	M₃₂×C₄₃	—	4	1	no	—
77	C₂×C₁₆×C₄₃	—	4	1	no	—
78	C₂×C₁₆×C₄₃	C₂³	1	2	yes	—
79	C₂×C₁₆×C₄₃	C₂³	1	2	yes	—
80	#41×C₄₃	—	4	1	no	—
81	#41×C₄₃	—	4	1	no	—
82	C₂×Q₈×C₄₃	C₂×C₈	1	1	yes	characteristic
83	C₂×D₄×C₄₃	C₂×C₈	1	1	yes	characteristic
84	C₂×D₄×C₄₃	C₂×C₈	1	1	yes	characteristic
85	C₂×D₄×C₄₃	C₂×C₈	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₂²⋊D₄₃	C₂×C₈	1	2	yes	—
90	C₂×C₂²⋊D₄₃	C₂×C₈	1	2	yes	—
91	C₂×C₂²⋊D₄₃	C₂×C₈	1	2	yes	—
92	C₂²×Dic₄₃	C₂×C₈	1	2	yes	—
93	#10621898	—	4	1	no	—
94	#10621898	—	4	1	no	—
95	C₂×D₁₇₂	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
97	C₂×Dic₈₆	C₂×C₈	1	1	yes	characteristic
98	M₁₆×C₄₃	—	4	1	no	—
99	M₁₆×C₄₃	—	4	1	no	—
100	M₁₆×C₄₃	—	4	1	no	—
101	C₂×C₈×C₄₃	—	2	1	no	—
102	C₂×C₈×C₄₃	—	2	1	no	—
103	C₂×C₈×C₄₃	—	2	1	no	—
104	C₂×C₈×C₄₃	—	2	1	no	—
105	C₂×C₈×C₄₃	—	2	1	no	—
106	C₂×C₈×C₄₃	—	2	1	no	—
107	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
111	C₂²⋊Dic₄₃	C₂×C₈	1	2	yes	—
112	C₂²⋊Dic₄₃	C₂×C₈	1	2	yes	—
113	(C₂×D₄₃)⋊C₄	C₂×C₈	1	2	yes	—
114	(C₂×D₄₃)⋊C₄	C₂×C₈	1	2	yes	—
115	Dic₄₃⋊C₄	C₂×C₈	1	2	yes	—
116	Dic₄₃⋊C₄	C₂×C₈	1	2	yes	—
117	C₄×Dic₄₃	C₂×C₈	1	1	yes	characteristic
118	C₄×Dic₄₃	C₂×C₈	1	1	yes	characteristic
119	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
120	#10621877	—	4	1	no	—
121	C₂×C₄₃⋊C₈	—	4	1	no	—
122	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
123	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
124	#10621872	—	4	2	no	—
125	C₈×D₄₃	—	2	2	no	—
126	C₈×D₄₃	—	2	2	no	—
127	C₁₆×C₄₃	—	2	2	no	—
128	C₁₆×C₄₃	—	2	2	no	—
129	C₄₃⋊C₁₆	—	2	2	no	—
130	C₄₃⋊C₁₆	—	2	2	no	—
131	C₂³×C₄₃	C₂²×C₈	1	1	yes	characteristic
132	C₂³×C₄₃	C₂²×C₈	1	1	yes	characteristic
133	C₂³×C₄₃	C₂²×C₈	1	1	yes	characteristic
134	C₂²×D₄₃	C₂²×C₈	1	2	yes	—
135	Q₈×C₄₃	—	4	1	no	—
136	D₄×C₄₃	—	4	1	no	—
137	D₄×C₄₃	—	4	1	no	—
138	D₄×C₄₃	—	4	1	no	—
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	—	2	1	no	—
141	C₂×C₄×C₄₃	—	2	1	no	—
142	C₂×C₄×C₄₃	—	2	1	no	—
143	C₂×C₄×C₄₃	—	2	1	no	—
144	C₂×C₄×C₄₃	—	2	1	no	—
145	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
147	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
148	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
149	C₂²⋊D₄₃	—	2	4	no	—
150	C₂²⋊D₄₃	—	2	4	no	—
151	C₂²⋊D₄₃	—	4	2	no	—
152	C₂×Dic₄₃	—	2	4	no	—
153	C₂×Dic₄₃	C₂²×C₈	1	2	yes	—
154	C₂×Dic₄₃	C₂²×C₈	1	2	yes	—
155	C₂×Dic₄₃	C₂²×C₈	1	2	yes	—
156	D₁₇₂	—	4	1	no	—
157	C₄×D₄₃	—	2	2	no	—
158	C₄×D₄₃	—	2	2	no	—
159	Dic₈₆	—	4	1	no	—
160	C₈×C₄₃	—	2	1	no	—
161	C₈×C₄₃	—	2	1	no	—
162	C₈×C₄₃	—	2	1	no	—
163	C₈×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
164	C₈×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
165	C₄₃⋊C₈	—	2	2	no	—
166	C₄₃⋊C₈	—	2	2	no	—
167	#33493	—	43	1	no	maximal, Sylow
168	C₂²×C₄₃	—	2	2	no	—
169	C₂²×C₄₃	—	2	2	no	—
170	C₂²×C₄₃	—	2	2	no	—
171	C₂²×C₄₃	—	2	1	no	—
172	C₂²×C₄₃	—	2	1	no	—
173	C₂²×C₄₃	—	2	1	no	—
174	C₂²×C₄₃	C₂³×C₈	1	1	yes	characteristic
175	C₂×D₄₃	—	2	2	no	—
176	C₂×D₄₃	—	2	2	no	—
177	C₂×D₄₃	—	2	2	no	—
178	C₄×C₄₃	—	2	1	no	—
179	C₄×C₄₃	—	2	1	no	—
180	C₄×C₄₃	—	2	1	no	—
181	C₄×C₄₃	#518	1	1	yes	characteristic
182	C₄×C₄₃	#568	1	1	yes	characteristic
183	Dic₄₃	—	2	2	no	—
184	Dic₄₃	—	2	2	no	—
185	Dic₄₃	#504	1	4	yes	—
186	#2931	—	43	1	no	—
187	#2169	—	43	2	no	—
188	#2169	—	43	2	no	—
189	D₄×C₁₆	—	43	2	no	—
190	D₄×C₁₆	—	43	2	no	—
191	#2162	—	43	2	no	—
192	#2113	—	43	2	no	—
193	#2113	—	43	1	no	—
194	#2113	D₄₃	1	1	yes	characteristic, complemented
195	C₂×C₄₃	—	4	1	no	—
196	C₂×C₄₃	—	4	1	no	—
197	C₂×C₄₃	—	4	1	no	—
198	C₂×C₄₃	#2972	1	1	yes	characteristic
199	C₂×C₄₃	C₂×#504	1	2	yes	—
200	D₄₃	—	4	2	no	—
201	C₂×#131	—	43	1	no	—
202	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
203	#532	—	43	1	no	—
204	C₂×M₃₂	—	43	1	no	—
205	C₂×M₃₂	—	43	2	no	—
206	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
207	C₂²×C₁₆	—	43	1	no	—
208	C₂²×C₁₆	—	43	2	no	—
209	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
210	#436	—	43	2	no	—
211	#436	—	43	2	no	—
212	C₈×D₄	—	43	2	no	—
213	C₈×D₄	—	43	2	no	—
214	#423	—	43	1	no	—
215	#408	—	43	1	no	—
216	#408	—	43	1	no	—
217	C₂×C₄×C₈	—	43	1	no	—
218	C₄⋊C₁₆	—	43	2	no	—
219	C₄⋊C₁₆	—	43	2	no	—
220	C₂²⋊C₁₆	—	43	2	no	—
221	C₂²⋊C₁₆	—	43	2	no	—
222	C₂²⋊C₁₆	—	43	2	no	—
223	C₂²⋊C₁₆	—	43	2	no	—
224	C₂²⋊C₁₆	C₂×D₄₃	1	2	yes	—
225	C₂²⋊C₁₆	C₂×D₄₃	1	2	yes	—
226	C₄×C₁₆	—	43	2	no	—
227	C₄×C₁₆	—	43	2	no	—
228	C₄₃	#33493	1	1	yes	characteristic, complemented, Sylow
229	C₂×#41	—	43	1	no	—
230	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
231	#131	—	4	1	no	—
232	#131	—	4	1	no	—
233	#131	—	172	1	no	—
234	#131	—	172	1	no	—
235	C₂×M₁₆	—	43	1	no	—
236	C₂×M₁₆	—	43	2	no	—
237	C₂×M₁₆	C₄×D₄₃	1	1	yes	characteristic
238	C₂×M₁₆	C₄×D₄₃	1	1	yes	characteristic
239	C₂×M₁₆	C₄×D₄₃	1	1	yes	characteristic
240	C₂²×C₈	—	43	1	no	—
241	C₂²×C₈	—	43	2	no	—
242	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
243	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
244	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
245	C₄⋊Q₈	—	43	1	no	—
246	#127	—	43	1	no	—
247	#124	—	43	1	no	—
248	#124	—	43	1	no	—
249	#121	—	43	2	no	—
250	#121	—	43	2	no	—
251	C₄×D₄	—	43	2	no	—
252	C₄×D₄	—	43	2	no	—
253	C₂×C₄²	—	43	1	no	—
254	M₃₂	—	4	1	no	—
255	M₃₂	—	172	2	no	—
256	M₃₂	—	172	1	no	—
257	C₂×C₁₆	—	4	1	no	—
258	C₂×C₁₆	—	43	2	no	—
259	C₂×C₁₆	—	43	2	no	—
260	C₂×C₁₆	—	172	2	no	—
261	C₂×C₁₆	—	172	1	no	—
262	C₂×C₁₆	C₂²×D₄₃	1	2	yes	—
263	C₂×C₁₆	C₂²×D₄₃	1	2	yes	—
264	C₄⋊C₈	—	43	2	no	—
265	C₄⋊C₈	—	43	2	no	—
266	C₂²⋊C₈	—	43	2	no	—
267	C₂²⋊C₈	—	43	2	no	—
268	C₂²⋊C₈	—	43	2	no	—
269	C₂²⋊C₈	—	43	2	no	—
270	C₄×C₈	—	43	2	no	—
271	C₄×C₈	—	43	2	no	—
272	#41	—	4	1	no	—
273	#41	—	4	1	no	—
274	#41	—	172	1	no	—
275	#41	—	172	1	no	—
276	C₂×Q₈	—	43	1	no	—
277	C₂×Q₈	C₈×D₄₃	1	1	yes	characteristic
278	C₂×D₄	—	43	2	no	—
279	C₂×D₄	—	43	2	no	—
280	C₂×D₄	—	43	2	no	—
281	C₂×D₄	—	43	1	no	—
282	C₂×D₄	C₈×D₄₃	1	1	yes	characteristic
283	C₂×D₄	C₈×D₄₃	1	1	yes	characteristic
284	C₂×D₄	C₈×D₄₃	1	1	yes	characteristic
285	C₂²×C₄	—	43	2	no	—
286	C₂²×C₄	—	43	2	no	—
287	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
290	M₁₆	—	4	1	no	—
291	M₁₆	—	4	1	no	—
292	M₁₆	—	4	1	no	—
293	M₁₆	—	172	2	no	—
294	M₁₆	—	172	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	43	2	no	—
302	C₂×C₈	—	43	2	no	—
303	C₂×C₈	—	86	2	no	—
304	C₂×C₈	—	86	2	no	—
305	C₂×C₈	—	172	1	no	—
306	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
307	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
308	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
309	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
310	C₄⋊C₄	—	43	2	no	—
311	C₄⋊C₄	—	43	2	no	—
312	C₂²⋊C₄	—	43	2	no	—
313	C₂²⋊C₄	—	43	2	no	—
314	C₂²⋊C₄	—	43	2	no	—
315	C₂²⋊C₄	—	43	2	no	—
316	C₄²	—	43	1	no	—
317	C₄²	—	43	1	no	—
318	C₄²	—	43	2	no	—
319	C₁₆	—	2	2	no	—
320	C₁₆	—	2	2	no	—
321	C₁₆	—	86	2	no	—
322	C₁₆	—	86	2	no	—
323	C₂³	—	43	2	no	—
324	C₂³	C₂×C₈×D₄₃	1	1	yes	characteristic
325	C₂³	C₂×C₈×D₄₃	1	1	yes	characteristic
326	C₂³	C₂×C₈×D₄₃	1	1	yes	characteristic
327	Q₈	—	4	1	no	—
328	Q₈	—	172	1	no	—
329	D₄	—	4	1	no	—
330	D₄	—	4	1	no	—
331	D₄	—	4	1	no	—
332	D₄	—	86	4	no	—
333	D₄	—	86	4	no	—
334	D₄	—	172	1	no	—
335	D₄	—	172	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	43	2	no	—
343	C₂×C₄	—	43	2	no	—
344	C₂×C₄	—	43	2	no	—
345	C₂×C₄	—	86	4	no	—
346	C₂×C₄	—	86	2	no	—
347	C₂×C₄	—	86	2	no	—
348	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
349	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
350	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
351	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	86	2	no	—
356	C₈	—	86	2	no	—
357	C₈	#13063370	1	1	yes	characteristic
358	C₈	#13063370	1	1	yes	characteristic
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	86	2	no	—
366	C₂²	—	86	2	no	—
367	C₂²	—	86	2	no	—
368	C₂²	C₂²×C₈×D₄₃	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	43	4	no	—
373	C₄	—	86	2	no	—
374	C₄	—	86	2	no	—
375	C₄	#14583372	1	1	yes	characteristic
376	C₄	#14583665	1	1	yes	characteristic
377	C₂	—	4	1	no	—
378	C₂	—	4	1	no	—
379	C₂	—	4	1	no	—
380	C₂	—	172	2	no	—
381	C₂	#19143617	1	1	yes	characteristic
382	C₂	#504×D₄₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₈
Fitting	C₄₃×#2113	C₂
prime radical	#14583445	C₄
cosocle	C₂×C₈×C₄₃	C₂⁴
hypercenter	#2113	D₄₃
hypocenter	C₄₃	#33493
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ #2113

Complements

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

N	H ≅ G/N	type
2. #19136425	C₂	semidirect
3. #19136424	C₂	semidirect
4. C₁₆×C₂²⋊D₄₃	C₂	semidirect
5. (C₂²⋊D₄₃)⋊C₁₆	C₂	semidirect
6. #19136391	C₂	semidirect
7. #19136209	C₂	semidirect
8. #19136207	C₂	semidirect
9. C₄₃×#2113	C₂	semidirect
194. #2113	D₄₃	semidirect
228. C₄₃	#33493	semidirect

Maximal subgroups

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

subgroup	index
#19143305	2
#19136425	2
#19136424	2
C₁₆×C₂²⋊D₄₃	2
(C₂²⋊D₄₃)⋊C₁₆	2
#19136391	2
#19136209	2
#19136207	2
C₄₃×#2113	2
#33493	43