Subgroups — #25250043

Order 11008.

652 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19147729	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583021	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143395	C₂	1	1	yes	maximal, characteristic, complemented
4	#19136490	C₂	1	4	yes	maximal, complemented
5	#19136483	C₂	1	4	yes	maximal, complemented
6	#19136367	C₂	1	1	yes	maximal, characteristic, complemented
7	#19136345	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14582676	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#2145	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13063347	C₂²	1	1	yes	characteristic
11	C₂×#13063332	—	2	1	no	—
12	#14583367	—	2	1	no	—
13	#14583340	C₄	1	2	yes	complemented
14	#14583339	C₂²	1	2	yes	—
15	#14583335	C₄	1	2	yes	complemented
16	#14583334	C₂²	1	2	yes	—
17	#14583329	C₄	1	4	yes	complemented
18	C₂×#13063265	C₂²	1	1	yes	characteristic
19	#14583021	—	2	2	no	—
20	#14583021	C₂²	1	4	yes	—
21	#14583010	C₂²	1	2	yes	complemented
22	#14583005	C₂²	1	2	yes	complemented
23	#14582998	—	2	2	no	—
24	C₂×#13063261	C₂²	1	1	yes	characteristic
25	C₂×#13063252	—	2	1	no	—
26	#14582893	—	2	1	no	—
27	C₂×#13063235	C₂²	1	1	yes	characteristic
28	#14582721	C₂²	1	4	yes	complemented
29	#14582716	C₂²	1	2	yes	complemented
30	#14582713	C₂²	1	2	yes	complemented
31	#14582676	C₂²	1	4	yes	complemented
32	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
34	C₄₃×#427	C₂²	1	1	yes	characteristic
35	C₄₃×#360	C₂²	1	4	yes	—
36	C₂×#10621898	—	2	1	no	—
37	#13063347	—	2	1	no	—
38	#13063347	—	2	1	no	—
39	#13063347	C₂×C₄	1	2	yes	—
40	#13063347	C₂×C₄	1	2	yes	—
41	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
42	C₂×#10621873	—	2	1	no	—
43	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
44	#13063332	—	2	4	no	—
45	#13063332	—	4	2	no	—
46	C₂×#10621877	—	2	1	no	—
47	C₂×#10621877	—	4	1	no	—
48	C₂²×C₄₃⋊C₈	—	4	1	no	—
49	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
50	#13063290	—	2	2	no	—
51	#13063287	—	2	2	no	—
52	(C₂²⋊D₄₃)⋊C₄	—	4	2	no	—
53	#13063282	—	4	1	no	—
54	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
55	C₄²×D₄₃	—	4	1	no	—
56	#13063271	C₂×C₄	1	4	yes	complemented
57	#13063269	C₂×C₄	1	4	yes	complemented
58	#13063268	C₂×C₄	1	4	yes	complemented
59	#13063266	C₂×C₄	1	4	yes	complemented
60	#13063265	C₂×C₄	1	2	yes	complemented
61	#13063265	C₂³	1	2	yes	—
62	C₂×C₄₃⋊C₁₆	C₂×C₄	1	2	yes	complemented
63	#13063261	—	2	1	no	—
64	#13063261	C₂³	1	2	yes	—
65	#13063252	—	2	4	no	—
66	#13063248	—	2	2	no	—
67	#13063245	—	2	2	no	—
68	#13063235	D₄	1	2	yes	—
69	#13063235	C₂³	1	2	yes	—
70	C₂×#41×C₄₃	—	2	1	no	—
71	#135×C₄₃	—	2	1	no	—
72	#135×C₄₃	—	2	1	no	—
73	#135×C₄₃	C₂×C₄	1	2	yes	complemented
74	#135×C₄₃	C₂³	1	2	yes	—
75	C₂×Q₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic, complemented
76	C₂×SD₁₆×C₄₃	—	2	1	no	—
77	C₂×D₈×C₄₃	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
79	#117×C₄₃	—	2	1	no	—
80	M₃₂×C₄₃	—	2	1	no	—
81	M₃₂×C₄₃	C₂³	1	2	yes	—
82	C₂×C₁₆×C₄₃	—	2	1	no	—
83	#107×C₄₃	—	2	1	no	—
84	#106×C₄₃	C₂³	1	2	yes	—
85	#41×C₄₃	—	2	2	no	—
86	#41×C₄₃	—	2	2	no	—
87	#41×C₄₃	—	4	1	no	—
88	#41×C₄₃	—	4	1	no	—
89	C₂×Q₈×C₄₃	—	2	1	no	—
90	C₂×D₄×C₄₃	—	2	1	no	—
91	C₂×D₄×C₄₃	—	4	1	no	—
92	C₂²×C₄×C₄₃	—	4	1	no	—
93	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
94	C₂×C₂²⋊D₄₃	—	4	1	no	—
95	C₂²×Dic₄₃	—	2	1	no	—
96	#10621898	—	2	2	no	—
97	#10621898	—	2	2	no	—
98	#10621898	—	4	1	no	—
99	#10621898	—	4	1	no	—
100	C₂×D₁₇₂	—	2	1	no	—
101	C₂×C₄×D₄₃	—	4	1	no	—
102	C₂×C₄×D₄₃	—	4	2	no	—
103	C₂×Dic₈₆	—	2	1	no	—
104	Q₁₆×C₄₃	—	2	1	no	—
105	Q₁₆×C₄₃	C₂²×C₄	1	2	yes	—
106	SD₁₆×C₄₃	—	2	2	no	—
107	SD₁₆×C₄₃	—	2	2	no	—
108	D₈×C₄₃	—	2	1	no	—
109	D₈×C₄₃	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
114	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
115	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
116	C₄⋊C₄×C₄₃	—	2	2	no	—
117	C₂²⋊C₄×C₄₃	—	4	1	no	—
118	C₄²×C₄₃	—	4	1	no	—
119	(C₂×D₄₃)⋊C₄	—	4	2	no	—
120	Dic₄₃⋊C₄	—	4	2	no	—
121	C₄×Dic₄₃	—	2	1	no	—
122	C₄×Dic₄₃	—	4	2	no	—
123	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
124	#10621877	—	2	2	no	—
125	#10621877	—	4	4	no	—
126	#10621877	—	4	1	no	—
127	C₂×C₄₃⋊C₈	—	2	1	no	—
128	C₂×C₄₃⋊C₈	—	2	1	no	—
129	C₂×C₄₃⋊C₈	—	4	4	no	—
130	C₂×C₄₃⋊C₈	—	4	1	no	—
131	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
132	Dic₁₇₂	—	2	1	no	—
133	Dic₁₇₂	C₂²×C₄	1	2	yes	—
134	D₃₄₄	—	2	1	no	—
135	D₃₄₄	C₂²×C₄	1	2	yes	—
136	#10621873	—	2	2	no	—
137	#10621873	—	2	2	no	—
138	C₁₆×C₄₃	—	2	2	no	—
139	C₄₃⋊C₁₆	C₂²×C₄	1	4	yes	—
140	C₂³×C₄₃	—	4	1	no	—
141	C₂³×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
142	C₂²×D₄₃	—	4	1	no	—
143	Q₈×C₄₃	—	2	2	no	—
144	Q₈×C₄₃	—	4	1	no	—
145	D₄×C₄₃	—	2	2	no	—
146	D₄×C₄₃	—	4	2	no	—
147	D₄×C₄₃	—	4	2	no	—
148	D₄×C₄₃	—	4	1	no	—
149	C₂×C₄×C₄₃	—	4	1	no	—
150	C₂×C₄×C₄₃	—	4	2	no	—
151	C₂×C₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
159	C₂²⋊D₄₃	—	4	2	no	—
160	C₂²⋊D₄₃	—	4	2	no	—
161	C₂×Dic₄₃	—	2	2	no	—
162	C₂×Dic₄₃	—	4	1	no	—
163	C₂×Dic₄₃	—	8	1	no	—
164	D₁₇₂	—	2	2	no	—
165	D₁₇₂	—	4	1	no	—
166	C₄×D₄₃	—	4	2	no	—
167	C₄×D₄₃	—	4	2	no	—
168	C₄×D₄₃	—	8	4	no	—
169	Dic₈₆	—	2	2	no	—
170	Dic₈₆	—	4	1	no	—
171	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
172	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
173	C₈×C₄₃	C₂³×C₄	1	1	yes	characteristic
174	C₈×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₄₃⋊C₈	—	2	2	no	—
176	C₄₃⋊C₈	—	4	2	no	—
177	#33468	—	43	1	no	maximal, Sylow
178	C₂²×C₄₃	—	4	1	no	—
179	C₂²×C₄₃	—	4	2	no	—
180	C₂²×C₄₃	—	8	2	no	—
181	C₂²×C₄₃	#442	1	1	yes	characteristic
182	C₂²×C₄₃	#442	1	1	yes	characteristic
183	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂×D₄₃	—	4	2	no	—
185	C₂×D₄₃	—	8	2	no	—
186	C₄×C₄₃	—	4	2	no	—
187	C₄×C₄₃	—	8	2	no	—
188	C₄×C₄₃	#442	1	1	yes	characteristic
189	C₄×C₄₃	#442	1	1	yes	characteristic
190	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
191	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
192	Dic₄₃	—	4	2	no	—
193	Dic₄₃	—	4	2	no	—
194	#3414	—	43	1	no	—
195	C₂×#444	—	43	1	no	—
196	#2943	—	43	1	no	—
197	AGL(1,ℤ/16)	—	43	4	no	—
198	#2180	—	43	4	no	—
199	#2155	—	43	1	no	—
200	#2148	—	43	1	no	—
201	#2145	D₄₃	1	1	yes	characteristic, complemented
202	C₂×#347	—	43	1	no	—
203	C₂×C₄₃	—	2	1	no	—
204	C₂×C₄₃	—	2	1	no	—
205	C₂×C₄₃	—	2	1	no	—
206	C₂×C₄₃	—	8	2	no	—
207	C₂×C₄₃	C₂×#442	1	1	yes	characteristic
208	D₄₃	—	8	2	no	—
209	C₂×#135	—	43	1	no	—
210	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
211	C₂×#131	—	86	1	no	—
212	C₄×#41	—	86	1	no	—
213	#510	—	43	2	no	—
214	#510	—	43	2	no	—
215	#509	—	43	2	no	—
216	#509	—	43	2	no	—
217	#508	—	43	4	no	—
218	C₂×M₃₂	—	43	1	no	—
219	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
220	#444	—	43	4	no	—
221	#444	—	86	2	no	—
222	#442	—	43	2	no	—
223	#441	—	43	2	no	—
224	#440	—	86	2	no	—
225	C₂×#108	—	43	1	no	—
226	#427	C₂×D₄₃	1	1	yes	characteristic
227	C₂×#104	—	86	1	no	—
228	#416	—	86	1	no	—
229	C₂×#97	—	43	1	no	—
230	#365	—	43	4	no	—
231	#362	—	43	2	no	—
232	#361	—	43	2	no	—
233	#360	C₂×D₄₃	1	4	yes	—
234	#347	—	43	4	no	—
235	C₄₃	#33468	1	1	yes	characteristic, complemented, Sylow
236	C₂×#41	—	2	1	no	—
237	C₂×#41	—	86	1	no	—
238	#135	—	2	1	no	—
239	#135	—	2	1	no	—
240	#135	—	43	2	no	—
241	#135	—	43	2	no	—
242	#135	—	86	1	no	—
243	#135	—	86	1	no	—
244	#135	C₄×D₄₃	1	2	yes	complemented
245	#135	C₂²×D₄₃	1	2	yes	—
246	C₂×Q₁₆	—	43	1	no	—
247	C₂×Q₁₆	C₄×D₄₃	1	1	yes	characteristic, complemented
248	C₂×SD₁₆	—	2	1	no	—
249	C₂×SD₁₆	—	86	1	no	—
250	C₂×D₈	—	43	1	no	—
251	C₂×D₈	C₄×D₄₃	1	1	yes	characteristic, complemented
252	#131	—	86	4	no	—
253	#131	—	172	2	no	—
254	C₂×M₁₆	—	86	1	no	—
255	C₂×M₁₆	—	172	1	no	—
256	C₂²×C₈	—	43	1	no	—
257	C₂²×C₈	—	172	1	no	—
258	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
259	C₄×Q₈	—	86	2	no	—
260	C₄×D₄	—	86	2	no	—
261	C₄×D₄	—	172	2	no	—
262	#117	—	2	1	no	—
263	#117	—	172	1	no	—
264	C₂×C₄²	—	43	1	no	—
265	C₂×C₄²	—	172	1	no	—
266	Q₃₂	—	43	4	no	—
267	SD₃₂	—	43	4	no	—
268	SD₃₂	—	43	4	no	—
269	D₁₆	—	43	4	no	—
270	M₃₂	—	2	1	no	—
271	M₃₂	—	43	2	no	—
272	M₃₂	—	43	2	no	—
273	M₃₂	C₂²×D₄₃	1	2	yes	—
274	C₂×C₁₆	—	2	1	no	—
275	C₂×C₁₆	—	43	2	no	—
276	#108	—	43	2	no	—
277	#108	—	86	1	no	—
278	#107	—	2	1	no	—
279	#106	C₂²×D₄₃	1	2	yes	—
280	#104	—	86	4	no	—
281	#103	—	86	2	no	—
282	#102	—	86	2	no	—
283	#97	—	43	2	no	—
284	#97	—	43	2	no	—
285	#41	—	2	2	no	—
286	#41	—	2	2	no	—
287	#41	—	4	1	no	—
288	#41	—	4	1	no	—
289	#41	—	86	2	no	—
290	#41	—	86	2	no	—
291	#41	—	172	1	no	—
292	#41	—	172	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	86	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	86	1	no	—
298	C₂×D₄	—	172	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	86	1	no	—
301	C₂²×C₄	—	172	2	no	—
302	C₂²×C₄	—	172	1	no	—
303	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
304	Q₁₆	—	2	1	no	—
305	Q₁₆	—	43	2	no	—
306	Q₁₆	—	86	1	no	—
307	Q₁₆	C₂×C₄×D₄₃	1	2	yes	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	2	2	no	—
310	SD₁₆	—	86	2	no	—
311	SD₁₆	—	86	2	no	—
312	D₈	—	2	1	no	—
313	D₈	—	43	2	no	—
314	D₈	—	86	1	no	—
315	D₈	C₂×C₄×D₄₃	1	2	yes	—
316	M₁₆	—	86	2	no	—
317	M₁₆	—	172	4	no	—
318	M₁₆	—	172	1	no	—
319	C₂×C₈	—	43	2	no	—
320	C₂×C₈	—	86	1	no	—
321	C₂×C₈	—	86	1	no	—
322	C₂×C₈	—	172	4	no	—
323	C₂×C₈	—	172	1	no	—
324	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
325	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
326	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
327	C₂×C₈	#10621900	1	1	yes	characteristic
328	C₂×C₈	#10621900	1	1	yes	characteristic
329	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	172	2	no	—
332	C₂²⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	172	2	no	—
334	C₄²	—	4	1	no	—
335	C₄²	—	43	2	no	—
336	C₄²	—	86	1	no	—
337	C₄²	—	172	2	no	—
338	C₁₆	—	2	2	no	—
339	C₁₆	—	43	4	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	172	1	no	—
342	C₂³	#13063349	1	1	yes	characteristic
343	Q₈	—	2	2	no	—
344	Q₈	—	4	1	no	—
345	Q₈	—	86	2	no	—
346	Q₈	—	172	1	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	1	no	—
351	D₄	—	86	2	no	—
352	D₄	—	172	2	no	—
353	D₄	—	172	2	no	—
354	D₄	—	172	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	86	2	no	—
360	C₂×C₄	—	344	4	no	—
361	C₂×C₄	—	344	1	no	—
362	C₂×C₄	—	172	1	no	—
363	C₂×C₄	—	172	2	no	—
364	C₂×C₄	—	172	2	no	—
365	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
366	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
367	C₂×C₄	#13063349	1	1	yes	characteristic
368	C₂×C₄	#13063352	1	1	yes	characteristic
369	C₂×C₄	#13063352	1	1	yes	characteristic
370	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
371	C₈	—	86	2	no	—
372	C₈	—	172	2	no	—
373	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
374	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
375	C₈	C₂²×C₄×D₄₃	1	1	yes	characteristic
376	C₈	C₂×#10621900	1	1	yes	characteristic
377	C₂²	—	4	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	344	2	no	—
381	C₂²	—	172	2	no	—
382	C₂²	#14583008	1	1	yes	characteristic
383	C₂²	#14583008	1	1	yes	characteristic
384	C₂²	C₂×#13063349	1	1	yes	characteristic
385	C₄	—	4	2	no	—
386	C₄	—	8	2	no	—
387	C₄	—	172	2	no	—
388	C₄	—	172	2	no	—
389	C₄	#14583008	1	1	yes	characteristic
390	C₄	#14583008	1	1	yes	characteristic
391	C₄	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
392	C₄	C₂×#13063352	1	1	yes	characteristic
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	—	8	2	no	—
397	C₂	—	344	2	no	—
398	C₂	C₂×#14583008	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14583008
commutator	C₈×C₄₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₄₃×#2145	C₂
socle	C₂×C₄₃	C₂×#442
prime radical	#19147729	C₂
cosocle	C₂×C₈×C₄₃	C₂⁴
hypercenter	#2145	D₄₃
hypocenter	C₄₃	#33468
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2145

Complements

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

N	H ≅ G/N	type
2. C₂×#14583021	C₂	semidirect
3. #19143395	C₂	semidirect
4. #19136490	C₂	semidirect
5. #19136483	C₂	semidirect
6. #19136367	C₂	semidirect
7. #19136345	C₂	semidirect
8. C₂×#14582676	C₂	semidirect
9. C₄₃×#2145	C₂	semidirect
13. #14583340	C₄	semidirect
15. #14583335	C₄	semidirect
17. #14583329	C₄	semidirect
21. #14583010	C₂²	semidirect
22. #14583005	C₂²	semidirect
28. #14582721	C₂²	semidirect
29. #14582716	C₂²	semidirect
30. #14582713	C₂²	semidirect
31. #14582676	C₂²	semidirect
56. #13063271	C₂×C₄	semidirect
57. #13063269	C₂×C₄	semidirect
58. #13063268	C₂×C₄	semidirect
59. #13063266	C₂×C₄	semidirect
60. #13063265	C₂×C₄	semidirect
62. C₂×C₄₃⋊C₁₆	C₂×C₄	semidirect
73. #135×C₄₃	C₂×C₄	semidirect
75. C₂×Q₁₆×C₄₃	C₂×C₄	semidirect
77. C₂×D₈×C₄₃	C₂×C₄	semidirect
201. #2145	D₄₃	semidirect
235. C₄₃	#33468	semidirect
244. #135	C₄×D₄₃	semidirect
247. C₂×Q₁₆	C₄×D₄₃	semidirect
251. C₂×D₈	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19147729	2
C₂×#14583021	2
#19143395	2
#19136490	2
#19136483	2
#19136367	2
#19136345	2
C₂×#14582676	2
C₄₃×#2145	2
#33468	43