Subgroups — #35386775

Order 21248.

606 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24917974	C₂	1	1	yes	maximal, characteristic
2	#24917504	C₂	1	2	yes	maximal
3	C₈×Q₈×D₈₃	C₂	1	1	yes	maximal, characteristic
4	#24906864	C₂	1	1	yes	maximal, characteristic, complemented
5	#24906858	C₂	1	1	yes	maximal, characteristic, complemented
6	#24906857	C₂	1	1	yes	maximal, characteristic, complemented
7	#24906848	C₂	1	2	yes	maximal, complemented
8	#24906847	C₂	1	2	yes	maximal, complemented
9	#24906210	C₂	1	1	yes	maximal, characteristic
10	#24906117	C₂	1	2	yes	maximal
11	C₈₃×#1676	C₂	1	1	yes	maximal, characteristic, complemented
12	#19128256	C₂²	1	2	yes	—
13	C₄×Q₈×D₈₃	C₂²	1	1	yes	characteristic
14	#19128106	C₂²	1	1	yes	characteristic
15	#19128102	—	2	1	no	—
16	#19128102	—	2	1	no	—
17	#19128097	C₂²	1	2	yes	—
18	#19128038	—	2	2	no	—
19	#19127993	C₂²	1	2	yes	—
20	#19127912	C₂²	1	2	yes	—
21	#19127911	C₂²	1	2	yes	—
22	#19127858	—	2	2	no	—
23	Q₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₈×Dic₁₆₆	—	2	1	no	—
25	C₈×Dic₁₆₆	C₂²	1	1	yes	characteristic
26	#19127825	—	2	1	no	—
27	#19127825	C₂²	1	1	yes	characteristic
28	#19127795	—	2	2	no	—
29	#19127793	—	2	2	no	—
30	#19127753	C₂²	1	2	yes	—
31	#19127738	—	2	1	no	—
32	#19127738	—	2	1	no	—
33	C₄⋊C₈×D₈₃	—	2	1	no	—
34	C₄⋊C₈×D₈₃	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₈₃	—	2	1	no	—
36	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
37	#19127454	C₂²	1	1	yes	characteristic
38	#19127451	C₂²	1	2	yes	—
39	#19127450	C₂²	1	2	yes	—
40	#19127448	C₂²	1	2	yes	—
41	#19127446	C₂²	1	2	yes	—
42	#500×C₈₃	C₂²	1	1	yes	characteristic
43	#477×C₈₃	C₂²	1	2	yes	—
44	C₈×Q₈×C₈₃	C₂²	1	1	yes	characteristic
45	#335×C₈₃	C₂²	1	1	yes	characteristic
46	#333×C₈₃	C₂²	1	2	yes	—
47	C₂×Q₈×D₈₃	D₄	1	1	yes	characteristic
48	C₂×Dic₃₃₂	—	2	2	no	—
49	C₂×#13050580	—	2	2	no	—
50	C₂×C₈×D₈₃	—	2	1	no	—
51	C₂×C₈×D₈₃	D₄	1	1	yes	characteristic
52	C₂×C₈×D₈₃	D₄	1	1	yes	characteristic
53	#14581792	C₂³	1	2	yes	—
54	#14581783	—	2	2	no	—
55	#14581772	—	2	2	no	—
56	#14581768	—	2	2	no	—
57	Q₈×Dic₈₃	—	2	2	no	—
58	Q₈×Dic₈₃	D₄	1	1	yes	characteristic
59	C₄×Dic₁₆₆	—	2	1	no	—
60	C₄×Dic₁₆₆	C₂³	1	1	yes	characteristic
61	#14581757	—	2	1	no	—
62	#14581757	—	2	2	no	—
63	#14581757	D₄	1	1	yes	characteristic
64	#14581750	—	2	2	no	—
65	C₄⋊C₄×D₈₃	—	2	1	no	—
66	C₄⋊C₄×D₈₃	D₄	1	1	yes	characteristic
67	C₄²×D₈₃	—	2	1	no	—
68	C₄²×D₈₃	C₂³	1	1	yes	characteristic
69	#14581726	—	2	1	no	—
70	#14581726	—	2	1	no	—
71	#14581725	—	2	2	no	—
72	#14581723	—	2	2	no	—
73	#14581723	—	2	2	no	—
74	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
75	C₄⋊(C₈₃⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₈₃⋊C₈)	C₂³	1	2	yes	—
77	Dic₈₃⋊C₈	—	2	1	no	—
78	Dic₈₃⋊C₈	—	2	1	no	—
79	Dic₈₃⋊C₈	—	2	1	no	—
80	#14581717	—	2	2	no	—
81	#14581715	—	2	2	no	—
82	#14581715	—	2	2	no	—
83	(C₂×D₈₃)⋊C₈	—	2	2	no	—
84	C₄×C₈₃⋊C₈	—	2	1	no	—
85	C₄×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₈×Dic₈₃	—	2	1	no	—
87	C₈×Dic₈₃	—	2	2	no	—
88	C₈×Dic₈₃	—	2	1	no	—
89	C₈×Dic₈₃	D₄	1	1	yes	characteristic
90	C₈×Dic₈₃	D₄	1	1	yes	characteristic
91	C₄⋊Q₈×C₈₃	C₂³	1	2	yes	—
92	C₄×Q₈×C₈₃	C₂³	1	1	yes	characteristic
93	#107×C₈₃	—	2	1	no	—
94	#107×C₈₃	—	2	1	no	—
95	#107×C₈₃	—	2	2	no	—
96	C₄⋊C₈×C₈₃	—	2	1	no	—
97	C₄⋊C₈×C₈₃	C₂³	1	2	yes	—
98	C₄⋊C₈×C₈₃	C₂³	1	1	yes	characteristic
99	#103×C₈₃	—	2	2	no	—
100	C₄×C₈×C₈₃	—	2	1	no	—
101	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
102	C₂×Dic₁₆₆	—	2	1	no	—
103	C₂×Dic₁₆₆	—	2	2	no	—
104	C₂×Dic₁₆₆	C₂×D₄	1	1	yes	characteristic
105	Q₈×D₈₃	—	2	2	no	—
106	Q₈×D₈₃	—	2	2	no	—
107	C₂×C₄×D₈₃	—	2	1	no	—
108	C₂×C₄×D₈₃	—	2	1	no	—
109	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₈₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₈₃	#41	1	1	yes	characteristic
112	Dic₃₃₂	—	4	4	no	—
113	#13050580	—	4	4	no	—
114	C₂×C₈₃⋊C₈	—	2	1	no	—
115	C₂×C₈₃⋊C₈	—	2	2	no	—
116	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
118	C₈×D₈₃	—	2	2	no	—
119	C₈×D₈₃	—	4	2	no	—
120	C₈×D₈₃	Q₁₆	1	4	yes	complemented
121	C₄⋊Dic₈₃	—	2	1	no	—
122	C₄⋊Dic₈₃	—	2	2	no	—
123	C₄⋊Dic₈₃	—	2	2	no	—
124	C₄⋊Dic₈₃	—	4	2	no	—
125	C₄⋊Dic₈₃	C₂×D₄	1	1	yes	characteristic
126	Dic₈₃⋊C₄	—	2	1	no	—
127	Dic₈₃⋊C₄	—	2	1	no	—
128	Dic₈₃⋊C₄	—	2	1	no	—
129	Dic₈₃⋊C₄	—	4	2	no	—
130	(C₂×D₈₃)⋊C₄	—	4	2	no	—
131	C₄×Dic₈₃	—	2	1	no	—
132	C₄×Dic₈₃	—	2	1	no	—
133	C₄×Dic₈₃	—	2	1	no	—
134	C₄×Dic₈₃	—	4	2	no	—
135	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
136	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₈₃	#41	1	1	yes	characteristic
138	C₂×Q₈×C₈₃	—	2	2	no	—
139	C₂×Q₈×C₈₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₈₃	—	2	1	no	—
141	C₂×C₈×C₈₃	—	2	2	no	—
142	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
144	C₄⋊C₄×C₈₃	—	2	1	no	—
145	C₄⋊C₄×C₈₃	—	2	2	no	—
146	C₄⋊C₄×C₈₃	—	2	2	no	—
147	C₄⋊C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₈₃	—	2	1	no	—
149	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
150	C₂²×D₈₃	#121	1	1	yes	characteristic
151	Q₈×C₈₃	—	2	1	no	—
152	Q₈×C₈₃	—	8	2	no	—
153	Q₈×C₈₃	#135	1	2	yes	—
154	C₂×C₄×C₈₃	—	2	1	no	—
155	C₂×C₄×C₈₃	—	2	1	no	—
156	C₂×C₄×C₈₃	—	4	2	no	—
157	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
160	C₂×Dic₈₃	—	2	1	no	—
161	C₂×Dic₈₃	—	2	1	no	—
162	C₂×Dic₈₃	—	4	2	no	—
163	C₂×Dic₈₃	#121	1	1	yes	characteristic
164	C₂×Dic₈₃	#121	1	1	yes	characteristic
165	C₂×Dic₈₃	#121	1	1	yes	characteristic
166	C₄×D₈₃	—	2	4	no	—
167	C₄×D₈₃	—	2	1	no	—
168	C₄×D₈₃	—	2	1	no	—
169	C₄×D₈₃	—	4	1	no	—
170	C₄×D₈₃	—	4	2	no	—
171	C₄×D₈₃	C₂×Q₁₆	1	2	yes	—
172	C₄×D₈₃	#137	1	2	yes	—
173	Dic₁₆₆	—	2	4	no	—
174	Dic₁₆₆	—	2	1	no	—
175	Dic₁₆₆	—	4	2	no	—
176	Dic₁₆₆	—	4	2	no	—
177	Dic₁₆₆	#135	1	2	yes	—
178	C₈×C₈₃	—	2	1	no	—
179	C₈×C₈₃	—	4	2	no	—
180	C₈×C₈₃	—	4	1	no	—
181	C₈×C₈₃	C₂×Q₁₆	1	2	yes	—
182	C₈₃⋊C₈	—	2	1	no	—
183	C₈₃⋊C₈	—	4	2	no	—
184	C₈₃⋊C₈	—	4	1	no	—
185	C₈₃⋊C₈	C₂×Q₁₆	1	2	yes	—
186	C₂²×C₈₃	C₂×#121	1	1	yes	characteristic
187	C₂×D₈₃	—	2	1	no	—
188	C₂×D₈₃	—	2	1	no	—
189	C₂×D₈₃	#462	1	2	yes	—
190	C₄×C₈₃	—	2	2	no	—
191	C₄×C₈₃	—	2	1	no	—
192	C₄×C₈₃	—	4	1	no	—
193	C₄×C₈₃	—	8	2	no	—
194	C₄×C₈₃	C₂²×Q₁₆	1	1	yes	characteristic
195	C₄×C₈₃	C₂×#135	1	1	yes	characteristic
196	C₄×C₈₃	C₂×#135	1	1	yes	characteristic
197	C₄×C₈₃	C₂×#137	1	1	yes	characteristic
198	Dic₈₃	—	2	1	no	—
199	Dic₈₃	—	2	2	no	—
200	Dic₈₃	—	2	1	no	—
201	Dic₈₃	—	4	1	no	—
202	Dic₈₃	—	8	2	no	—
203	Dic₈₃	#462	1	2	yes	—
204	#19118	—	83	1	no	maximal, Sylow
205	C₂×C₈₃	C₂×#462	1	1	yes	characteristic
206	C₂×C₈₃	#3050	1	1	yes	characteristic
207	C₂×C₈₃	#3067	1	1	yes	characteristic
208	D₈₃	—	2	2	no	—
209	#3160	—	83	1	no	—
210	#3104	—	83	2	no	—
211	C₂×C₈×Q₈	—	83	1	no	—
212	#1676	—	83	1	no	—
213	#1676	D₈₃	1	1	yes	characteristic, complemented
214	#1674	—	83	1	no	—
215	#1674	—	83	1	no	—
216	#1672	—	83	2	no	—
217	#1672	—	83	2	no	—
218	#1564	—	83	1	no	—
219	#1542	—	83	2	no	—
220	C₈₃	#19118	1	1	yes	characteristic, complemented, Sylow
221	#533	—	83	2	no	—
222	C₂×C₄×Q₈	—	83	1	no	—
223	#500	—	83	1	no	—
224	#500	C₂×D₈₃	1	1	yes	characteristic
225	#499	—	166	1	no	—
226	#499	—	166	1	no	—
227	#498	—	83	2	no	—
228	#484	—	166	2	no	—
229	#477	—	83	2	no	—
230	#477	C₂×D₈₃	1	2	yes	—
231	#462	—	83	2	no	—
232	#462	—	83	2	no	—
233	#451	—	166	2	no	—
234	C₈×Q₈	—	83	1	no	—
235	C₈×Q₈	—	83	1	no	—
236	C₈×Q₈	—	83	1	no	—
237	C₈×Q₈	—	166	1	no	—
238	C₈×Q₈	—	166	1	no	—
239	C₈×Q₈	C₂×D₈₃	1	1	yes	characteristic
240	C₄×Q₁₆	—	166	2	no	—
241	C₄×Q₁₆	—	166	2	no	—
242	#431	—	83	2	no	—
243	#427	—	166	1	no	—
244	#427	—	166	1	no	—
245	C₂×C₄⋊C₈	—	83	1	no	—
246	C₂×C₄⋊C₈	—	166	1	no	—
247	C₂×C₄×C₈	—	83	1	no	—
248	C₂×C₄×C₈	—	166	1	no	—
249	#335	—	83	1	no	—
250	#335	C₂×D₈₃	1	1	yes	characteristic
251	#334	—	83	2	no	—
252	#333	—	83	2	no	—
253	#333	C₂×D₈₃	1	2	yes	—
254	#332	—	83	2	no	—
255	#332	—	83	2	no	—
256	C₂²×Q₈	—	83	1	no	—
257	C₂×Q₁₆	—	166	2	no	—
258	C₂×Q₁₆	—	166	2	no	—
259	C₂²×C₈	—	83	1	no	—
260	C₂²×C₈	—	83	1	no	—
261	C₂²×C₈	—	166	1	no	—
262	C₄⋊Q₈	—	83	2	no	—
263	C₄⋊Q₈	C₂²×D₈₃	1	2	yes	—
264	#125	—	166	2	no	—
265	C₂²⋊Q₈	—	166	2	no	—
266	C₂²⋊Q₈	—	166	2	no	—
267	C₄×Q₈	—	83	1	no	—
268	C₄×Q₈	—	83	1	no	—
269	C₄×Q₈	—	83	1	no	—
270	C₄×Q₈	—	166	1	no	—
271	C₄×Q₈	—	166	2	no	—
272	C₄×Q₈	—	166	2	no	—
273	C₄×Q₈	—	166	1	no	—
274	C₄×Q₈	C₂²×D₈₃	1	1	yes	characteristic
275	#117	—	166	2	no	—
276	C₂×C₄⋊C₄	—	83	1	no	—
277	C₂×C₄⋊C₄	—	166	1	no	—
278	C₂×C₄²	—	83	1	no	—
279	C₂×C₄²	—	166	1	no	—
280	#107	—	2	1	no	—
281	#107	—	2	1	no	—
282	#107	—	2	2	no	—
283	#107	—	166	2	no	—
284	#107	—	166	1	no	—
285	#107	—	166	1	no	—
286	#106	—	166	2	no	—
287	#106	—	166	2	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	83	1	no	—
290	C₄⋊C₈	—	83	2	no	—
291	C₄⋊C₈	—	166	1	no	—
292	C₄⋊C₈	—	166	1	no	—
293	C₄⋊C₈	—	166	1	no	—
294	C₄⋊C₈	—	166	1	no	—
295	C₄⋊C₈	C₂²×D₈₃	1	1	yes	characteristic
296	C₄⋊C₈	C₂²×D₈₃	1	2	yes	—
297	#103	—	2	2	no	—
298	#103	—	166	2	no	—
299	#103	—	166	2	no	—
300	#103	—	166	2	no	—
301	C₂²⋊C₈	—	166	2	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	—	83	1	no	—
304	C₄×C₈	—	83	1	no	—
305	C₄×C₈	—	83	1	no	—
306	C₄×C₈	—	166	1	no	—
307	C₄×C₈	—	166	2	no	—
308	C₄×C₈	—	166	1	no	—
309	C₄×C₈	—	166	1	no	—
310	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	83	1	no	—
313	C₂×Q₈	—	166	1	no	—
314	C₂×Q₈	—	166	2	no	—
315	C₂×Q₈	—	166	2	no	—
316	C₂×Q₈	—	166	2	no	—
317	C₂×Q₈	D₄×D₈₃	1	1	yes	characteristic
318	C₂²×C₄	—	83	1	no	—
319	C₂²×C₄	—	83	1	no	—
320	C₂²×C₄	—	83	1	no	—
321	C₂²×C₄	—	166	1	no	—
322	C₂²×C₄	—	166	1	no	—
323	Q₁₆	—	332	4	no	—
324	Q₁₆	—	332	4	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	332	2	no	—
328	C₂×C₈	—	83	1	no	—
329	C₂×C₈	—	83	4	no	—
330	C₂×C₈	—	83	1	no	—
331	C₂×C₈	—	166	2	no	—
332	C₂×C₈	—	166	1	no	—
333	C₂×C₈	—	166	2	no	—
334	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
335	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	332	2	no	—
340	C₄⋊C₄	—	332	2	no	—
341	C₄⋊C₄	—	83	1	no	—
342	C₄⋊C₄	—	166	1	no	—
343	C₄⋊C₄	—	166	1	no	—
344	C₄⋊C₄	—	166	1	no	—
345	C₄⋊C₄	—	166	2	no	—
346	C₄⋊C₄	—	166	2	no	—
347	C₄⋊C₄	—	166	1	no	—
348	C₄⋊C₄	D₄×D₈₃	1	1	yes	characteristic
349	C₂²⋊C₄	—	332	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	332	2	no	—
352	C₄²	—	83	1	no	—
353	C₄²	—	83	1	no	—
354	C₄²	—	83	1	no	—
355	C₄²	—	166	1	no	—
356	C₄²	—	166	1	no	—
357	C₄²	—	166	1	no	—
358	C₄²	C₂³×D₈₃	1	1	yes	characteristic
359	C₂³	—	83	1	no	—
360	Q₈	—	2	1	no	—
361	Q₈	—	8	2	no	—
362	Q₈	—	332	2	no	—
363	Q₈	—	332	2	no	—
364	Q₈	—	83	2	no	—
365	Q₈	—	166	4	no	—
366	Q₈	—	166	1	no	—
367	Q₈	#14581815	1	2	yes	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	332	1	no	—
372	C₂×C₄	—	332	2	no	—
373	C₂×C₄	—	332	2	no	—
374	C₂×C₄	—	83	1	no	—
375	C₂×C₄	—	83	2	no	—
376	C₂×C₄	—	83	2	no	—
377	C₂×C₄	—	83	1	no	—
378	C₂×C₄	—	83	1	no	—
379	C₂×C₄	—	166	4	no	—
380	C₂×C₄	—	166	1	no	—
381	C₂×C₄	—	166	1	no	—
382	C₂×C₄	—	166	1	no	—
383	C₂×C₄	—	166	1	no	—
384	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
385	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
386	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
387	C₈	—	2	1	no	—
388	C₈	—	4	2	no	—
389	C₈	—	4	1	no	—
390	C₈	—	332	2	no	—
391	C₈	—	332	1	no	—
392	C₈	—	83	2	no	—
393	C₈	—	166	1	no	—
394	C₈	Q₁₆×D₈₃	1	2	yes	—
395	C₂²	—	83	2	no	—
396	C₂²	—	166	1	no	—
397	C₂²	—	166	1	no	—
398	C₂²	#121×D₈₃	1	1	yes	characteristic
399	C₄	—	2	2	no	—
400	C₄	—	2	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	332	1	no	—
404	C₄	—	83	2	no	—
405	C₄	—	664	2	no	—
406	C₄	—	166	1	no	—
407	C₄	—	166	2	no	—
408	C₄	—	166	1	no	—
409	C₄	C₂×Q₁₆×D₈₃	1	1	yes	characteristic
410	C₄	#135×D₈₃	1	1	yes	characteristic
411	C₄	C₂×#14581815	1	1	yes	characteristic
412	C₄	#137×D₈₃	1	1	yes	characteristic
413	C₂	—	166	2	no	—
414	C₂	#462×D₈₃	1	1	yes	characteristic
415	C₂	#24917046	1	1	yes	characteristic
416	C₂	#24917181	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₈₃
commutator, cosocle	C₄²×C₈₃	C₂⁴
Frattini	C₄²	C₂³×D₈₃
Fitting	C₈₃×#1676	C₂
socle	C₂²×C₈₃	C₂×#121
prime radical	C₂²×D₈₃	#121
hypercenter	#1676	D₈₃
hypocenter	C₈₃	#19118
LCS	G ▷ C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1676

Complements

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

N	H ≅ G/N	type
4. #24906864	C₂	semidirect
5. #24906858	C₂	semidirect
6. #24906857	C₂	semidirect
7. #24906848	C₂	semidirect
8. #24906847	C₂	semidirect
11. C₈₃×#1676	C₂	semidirect
120. C₈×D₈₃	Q₁₆	semidirect
213. #1676	D₈₃	semidirect
220. C₈₃	#19118	semidirect

Maximal subgroups

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

subgroup	index
#24917974	2
#24917504	2
C₈×Q₈×D₈₃	2
#24906864	2
#24906858	2
#24906857	2
#24906848	2
#24906847	2
#24906210	2
#24906117	2
C₈₃×#1676	2
#19118	83