Subgroups — #25080056

Order 11008.

584 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145933	C₂	1	2	yes	maximal
2	#19145181	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143570	C₂	1	1	yes	maximal, characteristic
4	#19134114	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134109	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134090	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134085	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134026	C₂	1	2	yes	maximal, complemented
9	#19134019	C₂	1	2	yes	maximal, complemented
10	#19133293	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583456	C₂²	1	2	yes	—
13	#14583433	C₂²	1	1	yes	characteristic
14	#14583304	C₂²	1	1	yes	characteristic
15	#14583279	C₂²	1	1	yes	characteristic
16	#14583250	C₂²	1	2	yes	—
17	#14583207	—	2	2	no	—
18	#14583185	C₂²	1	2	yes	—
19	#14583180	C₂²	1	2	yes	—
20	#14583140	—	2	2	no	—
21	#14583140	—	2	1	no	—
22	#14583140	—	2	1	no	—
23	#14583128	—	2	2	no	—
24	#14583122	—	2	2	no	—
25	#14583110	C₂²	1	2	yes	—
26	#14583105	C₂²	1	2	yes	—
27	#14583029	C₂²	1	1	yes	characteristic
28	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
29	C₄×Dic₁₇₂	—	2	1	no	—
30	C₄×Dic₁₇₂	—	2	1	no	—
31	#14582978	C₂²	1	1	yes	characteristic
32	#14582970	—	2	1	no	—
33	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₄₃	—	2	1	no	—
35	#14582958	—	2	1	no	—
36	#14582956	C₂²	1	1	yes	characteristic
37	#14582853	—	2	1	no	—
38	#14582646	C₂²	1	2	yes	—
39	#14582646	C₂²	1	2	yes	—
40	#14582644	C₂²	1	2	yes	—
41	#14582644	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#334	C₂²	1	2	yes	—
45	C₄₃×#334	C₂²	1	1	yes	characteristic
46	C₄₃×#334	C₂²	1	1	yes	characteristic
47	C₂×Dic₁₇₂	—	2	1	no	—
48	C₂×Dic₁₇₂	—	2	1	no	—
49	C₂×Dic₁₇₂	—	2	2	no	—
50	C₂×#10621873	—	2	2	no	—
51	C₂×#10621872	—	2	1	no	—
52	C₂×C₈×D₄₃	—	2	1	no	—
53	#13063325	C₂³	1	2	yes	—
54	#13063325	C₂³	1	2	yes	—
55	#13063319	—	2	1	no	—
56	#13063317	—	2	2	no	—
57	#13063317	D₄	1	1	yes	characteristic
58	#13063313	D₄	1	1	yes	characteristic
59	#13063308	—	2	1	no	—
60	#13063304	—	2	2	no	—
61	#13063304	—	2	2	no	—
62	#13063304	D₄	1	1	yes	characteristic
63	#13063299	D₄	1	1	yes	characteristic
64	C₄×Dic₈₆	—	2	2	no	—
65	C₄×Dic₈₆	—	2	2	no	—
66	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
67	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
68	C₄×C₂²⋊D₄₃	—	2	1	no	—
69	#13063284	—	2	2	no	—
70	#13063282	—	2	1	no	—
71	#13063259	—	2	1	no	—
72	#13063259	—	2	1	no	—
73	#13063259	—	2	2	no	—
74	#13063257	—	2	2	no	—
75	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
77	Dic₄₃⋊C₈	—	2	1	no	—
78	Dic₄₃⋊C₈	—	2	1	no	—
79	#13063250	—	2	2	no	—
80	#13063250	—	2	2	no	—
81	#13063250	—	2	2	no	—
82	#13063250	—	2	2	no	—
83	#13063250	—	2	2	no	—
84	#13063247	—	2	2	no	—
85	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
86	(C₂×D₄₃)⋊C₈	—	2	1	no	—
87	(C₂×D₄₃)⋊C₈	—	2	1	no	—
88	#13063236	—	2	1	no	—
89	#13063235	—	2	1	no	—
90	C₈×Dic₄₃	—	2	1	no	—
91	C₂²×C₈×C₄₃	—	2	2	no	—
92	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₃	—	2	2	no	—
96	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
97	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
98	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
105	C₂×C₂²⋊D₄₃	—	2	1	no	—
106	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₄₃	—	2	1	no	—
108	C₂×Dic₈₆	—	2	2	no	—
109	C₂×Dic₈₆	—	2	2	no	—
110	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₄₃	—	2	2	no	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	4	1	no	—
115	C₂×C₈×C₄₃	—	8	2	no	—
116	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₃	#41	1	1	yes	characteristic
123	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
124	C₂²⋊Dic₄₃	—	2	1	no	—
125	C₂²⋊Dic₄₃	—	4	2	no	—
126	(C₂×D₄₃)⋊C₄	—	2	1	no	—
127	(C₂×D₄₃)⋊C₄	—	2	1	no	—
128	(C₂×D₄₃)⋊C₄	—	2	1	no	—
129	(C₂×D₄₃)⋊C₄	—	2	1	no	—
130	C₄⋊Dic₄₃	—	2	2	no	—
131	C₄⋊Dic₄₃	—	2	2	no	—
132	C₄⋊Dic₄₃	—	2	2	no	—
133	C₄⋊Dic₄₃	—	2	2	no	—
134	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
135	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
136	Dic₄₃⋊C₄	—	2	1	no	—
137	Dic₄₃⋊C₄	—	2	1	no	—
138	Dic₄₃⋊C₄	—	2	1	no	—
139	Dic₄₃⋊C₄	—	2	1	no	—
140	Dic₄₃⋊C₄	—	4	2	no	—
141	Dic₄₃⋊C₄	—	4	2	no	—
142	C₄×Dic₄₃	—	2	1	no	—
143	C₄×Dic₄₃	—	4	2	no	—
144	C₂×C₄₃⋊C₈	—	2	1	no	—
145	C₂×C₄₃⋊C₈	—	2	1	no	—
146	Dic₁₇₂	—	4	2	no	—
147	Dic₁₇₂	—	4	2	no	—
148	Dic₁₇₂	—	8	2	no	—
149	#10621873	—	8	2	no	—
150	#10621872	—	4	2	no	—
151	C₈×D₄₃	—	4	2	no	—
152	C₂³×C₄₃	#121	1	1	yes	characteristic
153	C₂²×D₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	1	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
159	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
164	C₂²⋊D₄₃	—	4	2	no	—
165	C₂×Dic₄₃	—	2	1	no	—
166	C₂×Dic₄₃	—	2	1	no	—
167	C₂×Dic₄₃	—	2	1	no	—
168	C₂×Dic₄₃	—	4	2	no	—
169	C₂×Dic₄₃	—	4	2	no	—
170	D₁₇₂	—	2	2	no	—
171	C₄×D₄₃	—	4	1	no	—
172	C₄×D₄₃	—	4	1	no	—
173	Dic₈₆	—	2	2	no	—
174	Dic₈₆	—	4	2	no	—
175	Dic₈₆	—	4	2	no	—
176	Dic₈₆	—	4	2	no	—
177	Dic₈₆	—	4	2	no	—
178	C₈×C₄₃	—	2	1	no	—
179	C₈×C₄₃	—	2	1	no	—
180	C₈×C₄₃	—	2	1	no	—
181	C₈×C₄₃	—	4	2	no	—
182	C₈×C₄₃	—	4	2	no	—
183	C₈×C₄₃	#135	1	2	yes	—
184	C₄₃⋊C₈	—	4	1	no	—
185	C₄₃⋊C₈	—	4	1	no	—
186	#19228	—	43	1	no	maximal, Sylow
187	C₂²×C₄₃	—	2	1	no	—
188	C₂²×C₄₃	—	2	1	no	—
189	C₂²×C₄₃	#473	1	2	yes	—
190	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
191	C₂×D₄₃	—	4	1	no	—
192	C₂×D₄₃	—	4	1	no	—
193	C₂×D₄₃	—	4	1	no	—
194	C₄×C₄₃	—	2	1	no	—
195	C₄×C₄₃	—	2	1	no	—
196	C₄×C₄₃	—	2	1	no	—
197	C₄×C₄₃	—	2	1	no	—
198	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
199	C₄×C₄₃	#575	1	1	yes	characteristic
200	C₄×C₄₃	#577	1	2	yes	—
201	Dic₄₃	—	4	1	no	—
202	Dic₄₃	—	4	1	no	—
203	Dic₄₃	—	4	1	no	—
204	Dic₄₃	—	8	2	no	—
205	Dic₄₃	—	8	2	no	—
206	#3248	—	43	2	no	—
207	#3170	—	43	1	no	—
208	#2966	—	43	1	no	—
209	#1694	—	43	1	no	—
210	#1693	—	43	1	no	—
211	#1690	—	43	1	no	—
212	#1689	—	43	1	no	—
213	#1680	—	43	2	no	—
214	#1679	—	43	2	no	—
215	C₂×#334	D₄₃	1	1	yes	characteristic, complemented
216	#1552	—	43	2	no	—
217	C₂×C₄₃	—	2	2	no	—
218	C₂×C₄₃	#3035	1	1	yes	characteristic
219	C₂×C₄₃	#3060	1	1	yes	characteristic
220	C₂×C₄₃	C₂×#473	1	1	yes	characteristic
221	D₄₃	—	8	1	no	—
222	#533	—	43	2	no	—
223	#529	—	43	1	no	—
224	#500	—	43	1	no	—
225	#494	—	43	1	no	—
226	#487	—	43	2	no	—
227	#479	—	86	2	no	—
228	#475	—	43	2	no	—
229	#474	—	43	2	no	—
230	#467	—	86	2	no	—
231	#467	—	86	1	no	—
232	#467	—	86	1	no	—
233	#465	—	86	2	no	—
234	#464	—	86	2	no	—
235	#462	—	43	2	no	—
236	#461	—	43	2	no	—
237	#446	—	43	1	no	—
238	C₈×Q₈	—	43	1	no	—
239	C₄×Q₁₆	—	86	1	no	—
240	C₄×Q₁₆	—	86	1	no	—
241	#436	—	43	1	no	—
242	#435	—	86	1	no	—
243	C₈×D₄	—	43	1	no	—
244	C₈×D₄	—	86	1	no	—
245	#433	—	86	1	no	—
246	#432	—	43	1	no	—
247	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
248	#405	—	86	1	no	—
249	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
250	#334	C₂×D₄₃	1	2	yes	—
251	#334	C₂×D₄₃	1	1	yes	characteristic
252	#334	C₂×D₄₃	1	1	yes	characteristic
253	#332	—	43	2	no	—
254	#332	—	43	2	no	—
255	#332	—	43	2	no	—
256	#332	—	43	2	no	—
257	C₄₃	#19228	1	1	yes	characteristic, complemented, Sylow
258	C₂×Q₁₆	—	86	2	no	—
259	C₂×Q₁₆	—	86	1	no	—
260	C₂×Q₁₆	—	86	1	no	—
261	C₂×SD₁₆	—	86	2	no	—
262	C₂×M₁₆	—	86	1	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	86	1	no	—
265	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
266	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
267	C₄⋊Q₈	—	43	2	no	—
268	C₄⋊Q₈	—	43	2	no	—
269	#126	—	86	1	no	—
270	#125	—	43	1	no	—
271	#125	—	86	2	no	—
272	#124	—	43	1	no	—
273	#123	—	86	1	no	—
274	C₂²⋊Q₈	—	43	1	no	—
275	C₂²⋊Q₈	—	86	2	no	—
276	C₂²⋊Q₈	—	86	2	no	—
277	#121	—	43	1	no	—
278	C₄×Q₈	—	43	1	no	—
279	C₄×Q₈	—	86	2	no	—
280	C₄×Q₈	—	86	2	no	—
281	C₄×D₄	—	43	1	no	—
282	C₄×D₄	—	86	1	no	—
283	#117	—	86	1	no	—
284	#117	—	86	2	no	—
285	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
286	#107	—	86	2	no	—
287	#107	—	86	1	no	—
288	#107	—	86	1	no	—
289	#106	—	86	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	—	43	1	no	—
292	C₄⋊C₈	—	43	1	no	—
293	C₄⋊C₈	—	86	1	no	—
294	C₄⋊C₈	—	86	1	no	—
295	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
296	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
297	#103	—	86	2	no	—
298	#103	—	86	2	no	—
299	#103	—	86	2	no	—
300	#103	—	86	2	no	—
301	#103	—	86	2	no	—
302	#102	—	86	2	no	—
303	C₂²⋊C₈	—	86	1	no	—
304	C₂²⋊C₈	—	86	1	no	—
305	C₂²⋊C₈	—	86	1	no	—
306	#97	—	86	1	no	—
307	#97	—	86	1	no	—
308	C₄×C₈	—	86	1	no	—
309	C₄×C₈	D₁₇₂	1	1	yes	characteristic
310	C₄×C₈	D₁₇₂	1	1	yes	characteristic
311	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
313	C₂×Q₈	—	43	1	no	—
314	C₂×Q₈	—	86	2	no	—
315	C₂×Q₈	—	86	2	no	—
316	C₂×D₄	—	43	1	no	—
317	C₂×D₄	—	86	1	no	—
318	C₂²×C₄	—	86	1	no	—
319	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
320	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
321	C₂²×C₄	#10621902	1	1	yes	characteristic
322	Q₁₆	—	344	2	no	—
323	Q₁₆	—	172	2	no	—
324	Q₁₆	—	172	2	no	—
325	SD₁₆	—	344	2	no	—
326	M₁₆	—	172	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	8	2	no	—
332	C₂×C₈	—	86	1	no	—
333	C₂×C₈	—	86	1	no	—
334	C₂×C₈	—	172	2	no	—
335	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
336	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
337	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
338	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
339	C₄⋊C₄	—	43	1	no	—
340	C₄⋊C₄	—	43	1	no	—
341	C₄⋊C₄	—	86	1	no	—
342	C₄⋊C₄	—	86	1	no	—
343	C₄⋊C₄	—	86	1	no	—
344	C₄⋊C₄	—	86	1	no	—
345	C₄⋊C₄	—	86	2	no	—
346	C₄⋊C₄	—	86	2	no	—
347	C₄⋊C₄	—	86	2	no	—
348	C₄⋊C₄	—	86	2	no	—
349	C₄⋊C₄	—	172	2	no	—
350	C₄⋊C₄	—	172	2	no	—
351	C₂²⋊C₄	—	86	1	no	—
352	C₂²⋊C₄	—	86	1	no	—
353	C₂²⋊C₄	—	86	1	no	—
354	C₂²⋊C₄	—	86	1	no	—
355	C₂²⋊C₄	—	86	1	no	—
356	C₂²⋊C₄	—	172	2	no	—
357	C₄²	—	86	1	no	—
358	C₄²	—	172	2	no	—
359	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
360	C₄²	D₄×D₄₃	1	1	yes	characteristic
361	C₄²	#10621902	1	1	yes	characteristic
362	C₄²	C₂³×D₄₃	1	1	yes	characteristic
363	C₂³	—	86	1	no	—
364	C₂³	#13063300	1	1	yes	characteristic
365	Q₈	—	86	2	no	—
366	Q₈	—	172	2	no	—
367	Q₈	—	172	2	no	—
368	Q₈	—	172	2	no	—
369	Q₈	—	172	2	no	—
370	D₄	—	86	2	no	—
371	D₄	—	172	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	86	1	no	—
377	C₂×C₄	—	86	1	no	—
378	C₂×C₄	—	86	1	no	—
379	C₂×C₄	—	172	2	no	—
380	C₂×C₄	—	172	2	no	—
381	C₂×C₄	—	172	1	no	—
382	C₂×C₄	—	172	1	no	—
383	C₂×C₄	#13063300	1	1	yes	characteristic
384	C₂×C₄	#13063300	1	1	yes	characteristic
385	C₂×C₄	#13063300	1	1	yes	characteristic
386	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
388	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
389	C₈	—	2	1	no	—
390	C₈	—	2	1	no	—
391	C₈	—	2	1	no	—
392	C₈	—	4	2	no	—
393	C₈	—	4	2	no	—
394	C₈	—	172	1	no	—
395	C₈	—	172	1	no	—
396	C₈	#13063347	1	2	yes	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	172	1	no	—
400	C₂²	—	172	1	no	—
401	C₂²	—	172	1	no	—
402	C₂²	#14583175	1	2	yes	—
403	C₂²	C₂×#13063300	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	344	2	no	—
409	C₄	—	344	2	no	—
410	C₄	—	172	1	no	—
411	C₄	—	172	1	no	—
412	C₄	—	172	1	no	—
413	C₄	C₂×#13063347	1	1	yes	characteristic
414	C₄	#14583699	1	1	yes	characteristic
415	C₄	#14583705	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	344	1	no	—
418	C₂	#19144052	1	1	yes	characteristic
419	C₂	#19144258	1	1	yes	characteristic
420	C₂	C₂×#14583175	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063300
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#334	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#13063299	D₄
hypercenter	C₂×#334	D₄₃
hypocenter	C₄₃	#19228
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
2. #19145181	C₂	semidirect
4. #19134114	C₂	semidirect
5. #19134109	C₂	semidirect
6. #19134090	C₂	semidirect
7. #19134085	C₂	semidirect
8. #19134026	C₂	semidirect
9. #19134019	C₂	semidirect
10. #19133293	C₂	semidirect
11. C₂×C₄₃×#334	C₂	semidirect
215. C₂×#334	D₄₃	semidirect
257. C₄₃	#19228	semidirect

Maximal subgroups

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

subgroup	index
#19145933	2
#19145181	2
#19143570	2
#19134114	2
#19134109	2
#19134090	2
#19134085	2
#19134026	2
#19134019	2
#19133293	2
C₂×C₄₃×#334	2
#19228	43