Subgroups — #25080449

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145182	C₂	1	1	yes	maximal, characteristic
2	#19144401	C₂	1	2	yes	maximal
3	C₈×Q₈×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#19134056	C₂	1	2	yes	maximal, complemented
5	#19134055	C₂	1	2	yes	maximal, complemented
6	#19133996	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133966	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133965	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133352	C₂	1	1	yes	maximal, characteristic
10	#19133282	C₂	1	2	yes	maximal
11	C₄₃×#1676	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583454	C₂²	1	2	yes	—
13	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
14	#14583279	C₂²	1	1	yes	characteristic
15	#14583251	C₂²	1	2	yes	—
16	#14583205	—	2	2	no	—
17	#14583204	—	2	2	no	—
18	#14583191	C₂²	1	2	yes	—
19	#14583185	C₂²	1	2	yes	—
20	#14583184	C₂²	1	2	yes	—
21	#14583141	—	2	1	no	—
22	#14583141	—	2	1	no	—
23	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₈×Dic₈₆	—	2	1	no	—
25	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
26	#14583023	—	2	1	no	—
27	#14583023	C₂²	1	1	yes	characteristic
28	#14582993	—	2	1	no	—
29	#14582993	—	2	1	no	—
30	#14582940	—	2	2	no	—
31	#14582921	C₂²	1	2	yes	—
32	C₄⋊C₈×D₄₃	—	2	1	no	—
33	C₄⋊C₈×D₄₃	C₂²	1	1	yes	characteristic
34	#14582906	—	2	2	no	—
35	C₄×C₈×D₄₃	—	2	1	no	—
36	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
37	#14582652	C₂²	1	1	yes	characteristic
38	#14582651	C₂²	1	2	yes	—
39	#14582648	C₂²	1	2	yes	—
40	#14582646	C₂²	1	2	yes	—
41	#14582644	C₂²	1	2	yes	—
42	C₄₃×#500	C₂²	1	1	yes	characteristic
43	C₄₃×#477	C₂²	1	2	yes	—
44	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#335	C₂²	1	1	yes	characteristic
46	C₄₃×#333	C₂²	1	2	yes	—
47	C₂×Q₈×D₄₃	D₄	1	1	yes	characteristic
48	C₂×Dic₁₇₂	—	2	1	no	—
49	C₂×Dic₁₇₂	—	2	1	no	—
50	C₂×#10621872	—	2	2	no	—
51	C₂×C₈×D₄₃	—	2	1	no	—
52	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
53	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
54	#13063325	C₂³	1	2	yes	—
55	#13063316	—	2	2	no	—
56	#13063305	—	2	2	no	—
57	#13063301	—	2	2	no	—
58	Q₈×Dic₄₃	—	2	2	no	—
59	Q₈×Dic₄₃	D₄	1	1	yes	characteristic
60	C₄×Dic₈₆	—	2	1	no	—
61	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
62	#13063290	—	2	1	no	—
63	#13063290	—	2	2	no	—
64	#13063290	D₄	1	1	yes	characteristic
65	#13063283	—	2	2	no	—
66	C₄⋊C₄×D₄₃	—	2	1	no	—
67	C₄⋊C₄×D₄₃	D₄	1	1	yes	characteristic
68	C₄²×D₄₃	—	2	1	no	—
69	C₄²×D₄₃	C₂³	1	1	yes	characteristic
70	#13063258	—	2	2	no	—
71	#13063257	—	2	2	no	—
72	#13063256	—	2	2	no	—
73	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
74	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
75	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
76	Dic₄₃⋊C₈	—	2	1	no	—
77	Dic₄₃⋊C₈	—	2	1	no	—
78	Dic₄₃⋊C₈	—	2	2	no	—
79	Dic₄₃⋊C₈	—	2	1	no	—
80	#13063250	—	2	2	no	—
81	#13063249	—	2	2	no	—
82	#13063248	—	2	2	no	—
83	#13063248	—	2	2	no	—
84	#13063248	—	2	2	no	—
85	C₄×C₄₃⋊C₈	—	2	1	no	—
86	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
87	C₈×Dic₄₃	—	2	1	no	—
88	C₈×Dic₄₃	—	2	1	no	—
89	C₈×Dic₄₃	D₄	1	1	yes	characteristic
90	C₈×Dic₄₃	D₄	1	1	yes	characteristic
91	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
92	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
93	#107×C₄₃	—	2	1	no	—
94	#107×C₄₃	—	2	1	no	—
95	#107×C₄₃	—	2	2	no	—
96	C₄⋊C₈×C₄₃	—	2	1	no	—
97	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
99	#103×C₄₃	—	2	2	no	—
100	C₄×C₈×C₄₃	—	2	1	no	—
101	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₄₃	—	2	2	no	—
103	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
104	Q₈×D₄₃	—	2	2	no	—
105	Q₈×D₄₃	Q₁₆	1	4	yes	complemented
106	C₂×C₄×D₄₃	—	2	1	no	—
107	C₂×C₄×D₄₃	—	2	1	no	—
108	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₄₃	#41	1	1	yes	characteristic
111	C₂×Dic₈₆	—	2	1	no	—
112	C₂×Dic₈₆	—	2	2	no	—
113	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₄₃	—	2	1	no	—
115	C₂×C₈×C₄₃	—	2	2	no	—
116	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₄⋊C₄×C₄₃	—	2	1	no	—
119	C₄⋊C₄×C₄₃	—	2	2	no	—
120	C₄⋊C₄×C₄₃	—	2	2	no	—
121	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₃	—	2	1	no	—
123	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
124	(C₂×D₄₃)⋊C₄	—	4	2	no	—
125	C₄⋊Dic₄₃	—	2	1	no	—
126	C₄⋊Dic₄₃	—	2	2	no	—
127	C₄⋊Dic₄₃	—	2	2	no	—
128	C₄⋊Dic₄₃	—	4	2	no	—
129	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
130	Dic₄₃⋊C₄	—	2	1	no	—
131	Dic₄₃⋊C₄	—	2	1	no	—
132	Dic₄₃⋊C₄	—	2	1	no	—
133	Dic₄₃⋊C₄	—	4	2	no	—
134	C₄×Dic₄₃	—	2	1	no	—
135	C₄×Dic₄₃	—	2	1	no	—
136	C₄×Dic₄₃	—	2	1	no	—
137	C₄×Dic₄₃	—	4	2	no	—
138	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
140	C₄×Dic₄₃	#41	1	1	yes	characteristic
141	C₂×C₄₃⋊C₈	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	2	2	no	—
143	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
145	Dic₁₇₂	—	4	2	no	—
146	Dic₁₇₂	—	4	2	no	—
147	#10621872	—	4	4	no	—
148	C₈×D₄₃	—	2	2	no	—
149	C₈×D₄₃	—	4	1	no	—
150	C₈×D₄₃	—	4	2	no	—
151	C₂²×D₄₃	#121	1	1	yes	characteristic
152	Q₈×C₄₃	—	2	1	no	—
153	Q₈×C₄₃	—	8	2	no	—
154	Q₈×C₄₃	C₂×Q₁₆	1	2	yes	—
155	C₂×C₄×C₄₃	—	2	1	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	4	2	no	—
158	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
161	C₂×Dic₄₃	—	2	1	no	—
162	C₂×Dic₄₃	—	2	1	no	—
163	C₂×Dic₄₃	—	4	2	no	—
164	C₂×Dic₄₃	#121	1	1	yes	characteristic
165	C₂×Dic₄₃	#121	1	1	yes	characteristic
166	C₂×Dic₄₃	#121	1	1	yes	characteristic
167	C₄×D₄₃	—	2	4	no	—
168	C₄×D₄₃	—	2	1	no	—
169	C₄×D₄₃	—	2	1	no	—
170	C₄×D₄₃	—	4	1	no	—
171	C₄×D₄₃	—	4	2	no	—
172	C₄×D₄₃	C₂×Q₁₆	1	2	yes	—
173	C₄×D₄₃	#135	1	2	yes	—
174	Dic₈₆	—	2	1	no	—
175	Dic₈₆	—	2	4	no	—
176	Dic₈₆	—	4	2	no	—
177	Dic₈₆	—	4	2	no	—
178	Dic₈₆	C₂×Q₁₆	1	2	yes	—
179	C₈×C₄₃	—	2	1	no	—
180	C₈×C₄₃	—	4	2	no	—
181	C₈×C₄₃	—	4	1	no	—
182	C₈×C₄₃	#137	1	2	yes	—
183	C₄₃⋊C₈	—	2	1	no	—
184	C₄₃⋊C₈	—	2	1	no	—
185	C₄₃⋊C₈	—	4	2	no	—
186	C₄₃⋊C₈	—	4	1	no	—
187	#19262	—	43	1	no	maximal, Sylow
188	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
189	C₂×D₄₃	—	2	1	no	—
190	C₂×D₄₃	—	2	1	no	—
191	C₂×D₄₃	#467	1	2	yes	—
192	C₄×C₄₃	—	2	2	no	—
193	C₄×C₄₃	—	2	1	no	—
194	C₄×C₄₃	—	4	1	no	—
195	C₄×C₄₃	—	8	2	no	—
196	C₄×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
197	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
198	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
199	C₄×C₄₃	#575	1	1	yes	characteristic
200	Dic₄₃	—	2	1	no	—
201	Dic₄₃	—	2	2	no	—
202	Dic₄₃	—	2	1	no	—
203	Dic₄₃	—	4	1	no	—
204	Dic₄₃	—	8	2	no	—
205	Dic₄₃	#467	1	2	yes	—
206	#3170	—	43	1	no	—
207	#3078	—	43	2	no	—
208	C₂×C₈×Q₈	—	43	1	no	—
209	#1684	—	43	2	no	—
210	#1684	—	43	2	no	—
211	#1676	—	43	1	no	—
212	#1676	D₄₃	1	1	yes	characteristic, complemented
213	#1670	—	43	1	no	—
214	#1670	—	43	1	no	—
215	#1567	—	43	1	no	—
216	#1550	—	43	2	no	—
217	C₂×C₄₃	#3037	1	1	yes	characteristic
218	C₂×C₄₃	C₂×#467	1	1	yes	characteristic
219	C₂×C₄₃	#3067	1	1	yes	characteristic
220	D₄₃	—	2	2	no	—
221	#533	—	43	2	no	—
222	C₂×C₄×Q₈	—	43	1	no	—
223	#500	C₂×D₄₃	1	1	yes	characteristic
224	#494	—	43	1	no	—
225	#487	—	43	2	no	—
226	#479	—	86	2	no	—
227	#479	—	86	2	no	—
228	#477	—	43	2	no	—
229	#477	C₂×D₄₃	1	2	yes	—
230	#475	—	43	2	no	—
231	#475	—	43	2	no	—
232	#467	—	86	1	no	—
233	#467	—	86	1	no	—
234	C₈×Q₈	—	43	1	no	—
235	C₈×Q₈	—	43	1	no	—
236	C₈×Q₈	—	43	1	no	—
237	C₈×Q₈	—	86	1	no	—
238	C₈×Q₈	—	86	1	no	—
239	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic
240	C₄×Q₁₆	—	86	1	no	—
241	C₄×Q₁₆	—	86	1	no	—
242	#428	—	86	2	no	—
243	#423	—	43	2	no	—
244	C₂×C₄⋊C₈	—	43	1	no	—
245	C₂×C₄⋊C₈	—	86	1	no	—
246	#419	—	86	2	no	—
247	C₂×C₄×C₈	—	43	1	no	—
248	C₂×C₄×C₈	—	86	1	no	—
249	#335	—	43	2	no	—
250	#335	—	43	1	no	—
251	#335	C₂×D₄₃	1	1	yes	characteristic
252	#333	—	43	2	no	—
253	#333	C₂×D₄₃	1	2	yes	—
254	#332	—	43	2	no	—
255	#332	—	43	2	no	—
256	C₄₃	#19262	1	1	yes	characteristic, complemented, Sylow
257	C₂²×Q₈	—	43	1	no	—
258	C₂×Q₁₆	—	86	1	no	—
259	C₂×Q₁₆	—	86	1	no	—
260	C₂×M₁₆	—	86	2	no	—
261	C₂²×C₈	—	43	1	no	—
262	C₂²×C₈	—	43	1	no	—
263	C₂²×C₈	—	86	1	no	—
264	C₄⋊Q₈	—	43	2	no	—
265	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
266	#125	—	86	2	no	—
267	C₂²⋊Q₈	—	86	2	no	—
268	C₂²⋊Q₈	—	86	2	no	—
269	C₄×Q₈	—	43	1	no	—
270	C₄×Q₈	—	43	1	no	—
271	C₄×Q₈	—	43	1	no	—
272	C₄×Q₈	—	86	1	no	—
273	C₄×Q₈	—	86	1	no	—
274	C₄×Q₈	—	86	2	no	—
275	C₄×Q₈	—	86	2	no	—
276	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
277	#117	—	86	2	no	—
278	C₂×C₄⋊C₄	—	43	1	no	—
279	C₂×C₄⋊C₄	—	86	1	no	—
280	C₂×C₄²	—	43	1	no	—
281	C₂×C₄²	—	86	1	no	—
282	#107	—	2	1	no	—
283	#107	—	2	1	no	—
284	#107	—	2	2	no	—
285	#107	—	86	2	no	—
286	#106	—	86	2	no	—
287	#106	—	86	2	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	43	1	no	—
290	C₄⋊C₈	—	43	2	no	—
291	C₄⋊C₈	—	86	1	no	—
292	C₄⋊C₈	—	86	1	no	—
293	C₄⋊C₈	—	86	2	no	—
294	C₄⋊C₈	—	86	1	no	—
295	C₄⋊C₈	—	86	1	no	—
296	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
298	#103	—	2	2	no	—
299	#103	—	86	2	no	—
300	#103	—	86	2	no	—
301	#103	—	86	2	no	—
302	#103	—	86	2	no	—
303	#103	—	86	2	no	—
304	C₄×C₈	—	2	1	no	—
305	C₄×C₈	—	43	1	no	—
306	C₄×C₈	—	43	1	no	—
307	C₄×C₈	—	43	1	no	—
308	C₄×C₈	—	86	1	no	—
309	C₄×C₈	—	86	1	no	—
310	C₄×C₈	—	86	1	no	—
311	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	43	4	no	—
314	C₂×Q₈	—	43	1	no	—
315	C₂×Q₈	—	86	1	no	—
316	C₂×Q₈	—	86	2	no	—
317	C₂×Q₈	—	86	2	no	—
318	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
319	C₂²×C₄	—	43	1	no	—
320	C₂²×C₄	—	43	1	no	—
321	C₂²×C₄	—	43	1	no	—
322	C₂²×C₄	—	86	1	no	—
323	C₂²×C₄	—	86	1	no	—
324	Q₁₆	—	172	2	no	—
325	Q₁₆	—	172	2	no	—
326	M₁₆	—	172	4	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	43	1	no	—
330	C₂×C₈	—	43	1	no	—
331	C₂×C₈	—	86	2	no	—
332	C₂×C₈	—	86	1	no	—
333	C₂×C₈	—	86	2	no	—
334	C₂×C₈	—	172	1	no	—
335	C₂×C₈	—	172	2	no	—
336	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
337	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	43	1	no	—
342	C₄⋊C₄	—	86	1	no	—
343	C₄⋊C₄	—	86	1	no	—
344	C₄⋊C₄	—	86	1	no	—
345	C₄⋊C₄	—	86	1	no	—
346	C₄⋊C₄	—	86	2	no	—
347	C₄⋊C₄	—	86	2	no	—
348	C₄⋊C₄	—	172	2	no	—
349	C₄⋊C₄	—	172	2	no	—
350	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
351	C₂²⋊C₄	—	172	2	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	43	1	no	—
354	C₄²	—	43	1	no	—
355	C₄²	—	43	1	no	—
356	C₄²	—	86	1	no	—
357	C₄²	—	86	1	no	—
358	C₄²	—	86	1	no	—
359	C₄²	—	172	2	no	—
360	C₄²	C₂³×D₄₃	1	1	yes	characteristic
361	C₂³	—	43	1	no	—
362	Q₈	—	2	1	no	—
363	Q₈	—	8	2	no	—
364	Q₈	—	43	2	no	—
365	Q₈	—	86	4	no	—
366	Q₈	—	86	1	no	—
367	Q₈	—	172	2	no	—
368	Q₈	—	172	2	no	—
369	Q₈	Q₁₆×D₄₃	1	2	yes	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	43	1	no	—
374	C₂×C₄	—	43	2	no	—
375	C₂×C₄	—	43	2	no	—
376	C₂×C₄	—	43	1	no	—
377	C₂×C₄	—	43	1	no	—
378	C₂×C₄	—	86	4	no	—
379	C₂×C₄	—	86	1	no	—
380	C₂×C₄	—	86	1	no	—
381	C₂×C₄	—	86	1	no	—
382	C₂×C₄	—	86	1	no	—
383	C₂×C₄	—	172	1	no	—
384	C₂×C₄	—	172	2	no	—
385	C₂×C₄	—	172	2	no	—
386	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
387	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
388	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
389	C₈	—	2	1	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	1	no	—
392	C₈	—	86	1	no	—
393	C₈	—	86	1	no	—
394	C₈	—	172	2	no	—
395	C₈	—	172	1	no	—
396	C₈	#13063357	1	2	yes	—
397	C₂²	—	43	2	no	—
398	C₂²	—	86	1	no	—
399	C₂²	—	86	1	no	—
400	C₂²	#121×D₄₃	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	2	no	—
403	C₄	—	4	1	no	—
404	C₄	—	8	2	no	—
405	C₄	—	43	2	no	—
406	C₄	—	86	1	no	—
407	C₄	—	86	1	no	—
408	C₄	—	86	2	no	—
409	C₄	—	344	2	no	—
410	C₄	—	172	1	no	—
411	C₄	C₂×Q₁₆×D₄₃	1	1	yes	characteristic
412	C₄	#135×D₄₃	1	1	yes	characteristic
413	C₄	C₂×#13063357	1	1	yes	characteristic
414	C₄	#14583698	1	1	yes	characteristic
415	C₂	—	86	2	no	—
416	C₂	#19144068	1	1	yes	characteristic
417	C₂	#467×D₄₃	1	1	yes	characteristic
418	C₂	#19144313	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₄₃
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1676	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂²×D₄₃	#121
hypercenter	#1676	D₄₃
hypocenter	C₄₃	#19262
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1676

Complements

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

N	H ≅ G/N	type
4. #19134056	C₂	semidirect
5. #19134055	C₂	semidirect
6. #19133996	C₂	semidirect
7. #19133966	C₂	semidirect
8. #19133965	C₂	semidirect
11. C₄₃×#1676	C₂	semidirect
105. Q₈×D₄₃	Q₁₆	semidirect
212. #1676	D₄₃	semidirect
256. C₄₃	#19262	semidirect

Maximal subgroups

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

subgroup	index
#19145182	2
#19144401	2
C₈×Q₈×D₄₃	2
#19134056	2
#19134055	2
#19133996	2
#19133966	2
#19133965	2
#19133352	2
#19133282	2
C₄₃×#1676	2
#19262	43