Subgroups — #24919033

Order 10624.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14581824	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×C₂²⋊D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128362	C₂	1	1	yes	maximal, characteristic
4	#19128094	C₂	1	1	yes	maximal, characteristic, complemented
5	#19127956	C₂	1	1	yes	maximal, characteristic, complemented
6	#19127930	C₂	1	1	yes	maximal, characteristic, complemented
7	#19127925	C₂	1	1	yes	maximal, characteristic, complemented
8	#19127909	C₂	1	1	yes	maximal, characteristic, complemented
9	#19127862	C₂	1	1	yes	maximal, characteristic, complemented
10	#19127857	C₂	1	1	yes	maximal, characteristic, complemented
11	#19127855	C₂	1	1	yes	maximal, characteristic, complemented
12	#19127840	C₂	1	1	yes	maximal, characteristic, complemented
13	#19127808	C₂	1	1	yes	maximal, characteristic, complemented
14	#19127772	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×Q₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13050591	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₈₃	C₂²	1	1	yes	characteristic
18	#14581824	—	2	4	no	—
19	C₂×#13050580	C₂²	1	1	yes	characteristic
20	C₂×#13050580	C₂²	1	1	yes	characteristic
21	C₂×#13050579	C₂²	1	1	yes	characteristic
22	C₂×#13050577	C₂²	1	1	yes	characteristic
23	C₂×#13050577	C₂²	1	1	yes	characteristic
24	C₂×#13050573	C₂²	1	1	yes	characteristic
25	#14581790	—	2	1	no	—
26	#14581790	C₂²	1	1	yes	characteristic
27	#14581781	—	2	1	no	—
28	#14581781	C₂²	1	1	yes	characteristic
29	#14581771	—	2	1	no	—
30	#14581771	C₂²	1	1	yes	characteristic
31	#14581768	—	2	1	no	—
32	#14581768	—	2	1	no	—
33	#14581768	C₂²	1	1	yes	characteristic
34	#14581768	C₂²	1	1	yes	characteristic
35	#14581766	—	2	1	no	—
36	#14581766	C₂²	1	1	yes	characteristic
37	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic
38	Q₈×Dic₈₃	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₈₃	—	2	1	no	—
40	C₄×C₂²⋊D₈₃	—	2	1	no	—
41	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
42	#14581724	C₂²	1	1	yes	characteristic
43	Dic₈₃⋊C₈	C₂²	1	1	yes	characteristic
44	#14581717	C₂²	1	1	yes	characteristic
45	#14581716	C₂²	1	1	yes	characteristic
46	#14581716	C₂²	1	1	yes	characteristic
47	#14581716	C₂²	1	1	yes	characteristic
48	#14581716	C₂²	1	1	yes	characteristic
49	#14581714	C₂²	1	1	yes	characteristic
50	C₂²⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
51	(C₂×D₈₃)⋊C₈	C₂²	1	1	yes	characteristic
52	#14581702	C₂²	1	1	yes	characteristic
53	C₂²×Q₈×C₈₃	C₂²	1	1	yes	characteristic
54	C₂²×Q₈×C₈₃	C₂²	1	1	yes	characteristic
55	C₂×Q₁₆×C₈₃	—	2	4	no	—
56	C₂×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
57	C₂×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
58	C₂×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
59	C₂×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic
60	C₂²×C₈×C₈₃	C₂²	1	1	yes	characteristic
61	#13050591	—	2	2	no	—
62	#13050591	—	4	1	no	—
63	C₂×Dic₁₆₆	—	2	1	no	—
64	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
65	Q₈×D₈₃	—	2	2	no	—
66	Q₈×D₈₃	—	4	1	no	—
67	C₂×D₃₃₂	—	2	1	no	—
68	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊D₈₃	—	2	1	no	—
70	C₂×C₂²⋊D₈₃	D₄	1	1	yes	characteristic
71	C₂×C₄×D₈₃	—	2	1	no	—
72	C₂×C₄×D₈₃	—	2	1	no	—
73	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
74	#13050580	—	2	2	no	—
75	#13050580	—	4	1	no	—
76	#13050579	—	2	2	no	—
77	#13050577	—	2	2	no	—
78	#13050577	—	4	1	no	—
79	#13050573	—	2	2	no	—
80	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₄⋊Dic₈₃	—	2	1	no	—
83	C₄⋊Dic₈₃	—	2	1	no	—
84	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
85	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
86	Dic₈₃⋊C₄	—	2	1	no	—
87	Dic₈₃⋊C₄	—	2	1	no	—
88	Dic₈₃⋊C₄	—	2	1	no	—
89	Dic₈₃⋊C₄	—	2	1	no	—
90	Dic₈₃⋊C₄	—	2	1	no	—
91	Dic₈₃⋊C₄	D₄	1	1	yes	characteristic
92	C₂²⋊Dic₈₃	—	2	1	no	—
93	C₂²⋊Dic₈₃	D₄	1	1	yes	characteristic
94	(C₂×D₈₃)⋊C₄	—	2	1	no	—
95	(C₂×D₈₃)⋊C₄	—	2	1	no	—
96	(C₂×D₈₃)⋊C₄	—	2	1	no	—
97	(C₂×D₈₃)⋊C₄	—	2	1	no	—
98	(C₂×D₈₃)⋊C₄	—	2	1	no	—
99	(C₂×D₈₃)⋊C₄	D₄	1	1	yes	characteristic
100	C₄×Dic₈₃	—	2	1	no	—
101	C₄×Dic₈₃	—	2	1	no	—
102	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
103	C₂×Q₈×C₈₃	—	2	1	no	—
104	C₂×Q₈×C₈₃	—	2	1	no	—
105	C₂×Q₈×C₈₃	—	2	2	no	—
106	C₂×Q₈×C₈₃	—	2	2	no	—
107	C₂×Q₈×C₈₃	—	4	1	no	—
108	C₂×Q₈×C₈₃	—	4	1	no	—
109	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
110	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
111	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
112	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₈₃	—	2	1	no	—
114	C₂²×C₄×C₈₃	—	2	1	no	—
115	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
116	Q₁₆×C₈₃	—	2	2	no	—
117	Q₁₆×C₈₃	—	2	2	no	—
118	Q₁₆×C₈₃	—	2	2	no	—
119	Q₁₆×C₈₃	D₄	1	4	yes	complemented
120	C₂×C₈×C₈₃	—	2	2	no	—
121	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
122	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
123	C₂³×C₈₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×D₈₃	—	2	1	no	—
125	C₂²×D₈₃	C₂×D₄	1	1	yes	characteristic
126	Q₈×C₈₃	—	2	1	no	—
127	Q₈×C₈₃	—	2	1	no	—
128	Q₈×C₈₃	—	2	1	no	—
129	Q₈×C₈₃	—	2	1	no	—
130	Q₈×C₈₃	—	2	1	no	—
131	Q₈×C₈₃	—	2	1	no	—
132	Q₈×C₈₃	—	4	2	no	—
133	Q₈×C₈₃	—	4	2	no	—
134	Q₈×C₈₃	C₂×D₄	1	2	yes	—
135	Q₈×C₈₃	C₂×D₄	1	2	yes	—
136	C₂×C₄×C₈₃	—	2	1	no	—
137	C₂×C₄×C₈₃	—	2	1	no	—
138	C₂×C₄×C₈₃	—	2	1	no	—
139	C₂×C₄×C₈₃	—	2	1	no	—
140	C₂×C₄×C₈₃	—	2	1	no	—
141	C₂×C₄×C₈₃	—	2	1	no	—
142	C₂×C₄×C₈₃	—	4	2	no	—
143	C₂×C₄×C₈₃	—	4	2	no	—
144	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
146	C₂²⋊D₈₃	—	2	2	no	—
147	C₂²⋊D₈₃	—	4	2	no	—
148	C₂×Dic₈₃	—	2	1	no	—
149	C₂×Dic₈₃	—	2	1	no	—
150	C₂×Dic₈₃	—	2	1	no	—
151	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
152	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
153	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
154	D₃₃₂	—	2	1	no	—
155	D₃₃₂	—	2	1	no	—
156	D₃₃₂	—	4	2	no	—
157	C₄×D₈₃	—	2	1	no	—
158	C₄×D₈₃	—	2	1	no	—
159	C₄×D₈₃	—	4	2	no	—
160	C₄×D₈₃	—	4	2	no	—
161	Dic₁₆₆	—	2	1	no	—
162	Dic₁₆₆	—	2	1	no	—
163	Dic₁₆₆	—	4	2	no	—
164	C₈×C₈₃	—	2	1	no	—
165	C₈×C₈₃	C₂×D₄	1	2	yes	—
166	C₈₃⋊C₈	—	2	1	no	—
167	C₈₃⋊C₈	—	2	1	no	—
168	C₂²×C₈₃	—	2	1	no	—
169	C₂²×C₈₃	—	2	1	no	—
170	C₂²×C₈₃	#137	1	2	yes	complemented
171	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×D₈₃	—	2	1	no	—
173	C₂×D₈₃	—	2	1	no	—
174	C₂×D₈₃	—	2	1	no	—
175	C₂×D₈₃	—	4	1	no	—
176	C₂×D₈₃	—	4	1	no	—
177	C₂×D₈₃	—	4	1	no	—
178	C₄×C₈₃	—	2	2	no	—
179	C₄×C₈₃	—	2	2	no	—
180	C₄×C₈₃	—	2	1	no	—
181	C₄×C₈₃	—	4	1	no	—
182	C₄×C₈₃	—	4	1	no	—
183	C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
184	C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
185	Dic₈₃	—	2	1	no	—
186	Dic₈₃	—	2	1	no	—
187	Dic₈₃	—	2	1	no	—
188	Dic₈₃	—	4	1	no	—
189	Dic₈₃	—	4	1	no	—
190	Dic₈₃	—	4	1	no	—
191	C₂×C₈₃	—	2	2	no	—
192	C₂×C₈₃	D₄²	1	1	yes	characteristic
193	C₂×C₈₃	C₂×#137	1	1	yes	characteristic
194	C₂×C₈₃	#578	1	1	yes	characteristic
195	D₈₃	—	4	1	no	—
196	D₈₃	—	8	1	no	—
197	#3270	—	83	1	no	maximal, Sylow
198	C₈₃	#3270	1	1	yes	characteristic, complemented, Sylow
199	C₂×#137	—	83	1	no	—
200	C₂²×Q₁₆	D₈₃	1	1	yes	characteristic, complemented
201	D₄×Q₈	—	83	1	no	—
202	#548	—	83	1	no	—
203	#497	—	83	1	no	—
204	#470	—	83	1	no	—
205	#465	—	83	1	no	—
206	#464	—	83	1	no	—
207	#462	—	83	1	no	—
208	#452	—	83	1	no	—
209	#451	—	83	1	no	—
210	#451	—	83	1	no	—
211	#448	—	83	1	no	—
212	#441	—	83	1	no	—
213	#435	—	83	1	no	—
214	C₂×#41	—	83	1	no	—
215	C₂²×Q₈	—	83	1	no	—
216	C₂²×Q₈	C₂×D₈₃	1	1	yes	characteristic
217	C₂²×Q₈	C₂×D₈₃	1	1	yes	characteristic
218	#137	—	166	4	no	—
219	C₂×Q₁₆	—	2	4	no	—
220	C₂×Q₁₆	—	83	1	no	—
221	C₂×Q₁₆	—	83	1	no	—
222	C₂×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
223	C₂×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
224	C₂×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
225	C₂×Q₁₆	C₂×D₈₃	1	1	yes	characteristic
226	C₂×SD₁₆	—	83	1	no	—
227	C₂×SD₁₆	—	83	1	no	—
228	C₂×SD₁₆	—	83	1	no	—
229	C₂×M₁₆	—	83	1	no	—
230	C₂²×C₈	C₂×D₈₃	1	1	yes	characteristic
231	C₄⋊Q₈	—	83	1	no	—
232	C₄⋊Q₈	—	166	1	no	—
233	#124	—	83	1	no	—
234	#124	—	166	1	no	—
235	C₂²⋊Q₈	—	83	1	no	—
236	C₂²⋊Q₈	—	83	1	no	—
237	C₂²⋊Q₈	—	83	1	no	—
238	C₂²⋊Q₈	—	166	1	no	—
239	C₂²⋊Q₈	—	166	1	no	—
240	C₂²⋊Q₈	—	166	1	no	—
241	#121	—	83	1	no	—
242	#121	—	166	1	no	—
243	C₄×Q₈	—	83	1	no	—
244	C₄×Q₈	—	83	1	no	—
245	C₄×D₄	—	83	1	no	—
246	C₄×D₄	—	166	1	no	—
247	C₄×D₄	—	166	1	no	—
248	#106	—	83	1	no	—
249	C₄⋊C₈	—	83	1	no	—
250	#103	—	83	1	no	—
251	#103	—	83	1	no	—
252	#103	—	83	1	no	—
253	#103	—	83	1	no	—
254	#103	—	83	1	no	—
255	#102	—	83	1	no	—
256	C₂²⋊C₈	—	83	1	no	—
257	C₂²⋊C₈	—	83	1	no	—
258	#97	—	83	1	no	—
259	#41	—	332	1	no	—
260	#41	—	166	2	no	—
261	C₂×Q₈	—	2	1	no	—
262	C₂×Q₈	—	2	1	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	4	1	no	—
266	C₂×Q₈	—	4	1	no	—
267	C₂×Q₈	—	332	1	no	—
268	C₂×Q₈	—	83	1	no	—
269	C₂×Q₈	—	166	1	no	—
270	C₂×Q₈	—	166	2	no	—
271	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
272	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
273	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
274	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
275	C₂×D₄	—	83	1	no	—
276	C₂×D₄	—	83	1	no	—
277	C₂×D₄	—	166	1	no	—
278	C₂×D₄	—	166	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	83	1	no	—
282	C₂²×C₄	—	166	1	no	—
283	C₂²×C₄	—	166	1	no	—
284	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
285	Q₁₆	—	2	2	no	—
286	Q₁₆	—	2	2	no	—
287	Q₁₆	—	2	2	no	—
288	Q₁₆	—	332	1	no	—
289	Q₁₆	—	166	2	no	—
290	Q₁₆	C₂²⋊D₈₃	1	4	yes	complemented
291	SD₁₆	—	332	1	no	—
292	SD₁₆	—	166	2	no	—
293	SD₁₆	—	166	2	no	—
294	M₁₆	—	166	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	83	1	no	—
297	C₂×C₈	—	83	1	no	—
298	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
299	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
300	C₄⋊C₄	—	83	1	no	—
301	C₄⋊C₄	—	83	1	no	—
302	C₄⋊C₄	—	83	1	no	—
303	C₄⋊C₄	—	166	1	no	—
304	C₄⋊C₄	—	166	1	no	—
305	C₄⋊C₄	—	166	1	no	—
306	C₄⋊C₄	—	166	1	no	—
307	C₄⋊C₄	—	166	1	no	—
308	C₄⋊C₄	—	166	1	no	—
309	C₄⋊C₄	—	166	1	no	—
310	C₂²⋊C₄	—	83	1	no	—
311	C₂²⋊C₄	—	83	1	no	—
312	C₂²⋊C₄	—	166	1	no	—
313	C₂²⋊C₄	—	166	1	no	—
314	C₂²⋊C₄	—	166	1	no	—
315	C₂²⋊C₄	—	166	1	no	—
316	C₂²⋊C₄	—	166	1	no	—
317	C₂²⋊C₄	—	166	1	no	—
318	C₄²	—	83	1	no	—
319	C₄²	—	166	1	no	—
320	C₄²	—	166	1	no	—
321	C₂³	—	83	1	no	—
322	C₂³	—	166	1	no	—
323	C₂³	D₄×D₈₃	1	1	yes	characteristic
324	Q₈	—	2	1	no	—
325	Q₈	—	2	1	no	—
326	Q₈	—	2	1	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	2	1	no	—
329	Q₈	—	2	1	no	—
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	332	2	no	—
333	Q₈	—	166	1	no	—
334	Q₈	—	166	1	no	—
335	Q₈	C₂×C₂²⋊D₈₃	1	2	yes	—
336	Q₈	C₂×C₂²⋊D₈₃	1	2	yes	—
337	D₄	—	332	2	no	—
338	D₄	—	332	2	no	—
339	D₄	—	166	2	no	—
340	D₄	—	166	1	no	—
341	D₄	—	166	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	332	2	no	—
351	C₂×C₄	—	332	2	no	—
352	C₂×C₄	—	83	1	no	—
353	C₂×C₄	—	83	1	no	—
354	C₂×C₄	—	83	1	no	—
355	C₂×C₄	—	166	1	no	—
356	C₂×C₄	—	166	1	no	—
357	C₂×C₄	—	166	1	no	—
358	C₂×C₄	—	166	1	no	—
359	C₂×C₄	—	166	1	no	—
360	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
361	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	166	1	no	—
364	C₈	—	166	1	no	—
365	C₈	C₂×C₂²⋊D₈₃	1	2	yes	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	332	1	no	—
369	C₂²	—	332	1	no	—
370	C₂²	—	332	1	no	—
371	C₂²	—	166	1	no	—
372	C₂²	—	166	1	no	—
373	C₂²	—	166	1	no	—
374	C₂²	#14581824	1	2	yes	complemented
375	C₂²	C₂×D₄×D₈₃	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	4	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	332	1	no	—
382	C₄	—	332	1	no	—
383	C₄	—	332	1	no	—
384	C₄	—	166	1	no	—
385	C₄	—	166	1	no	—
386	C₄	—	166	1	no	—
387	C₄	C₂²×C₂²⋊D₈₃	1	1	yes	characteristic
388	C₄	#14581837	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	332	1	no	—
391	C₂	—	664	1	no	—
392	C₂	D₄×C₂²⋊D₈₃	1	1	yes	characteristic
393	C₂	C₂×#14581824	1	1	yes	characteristic
394	C₂	#19128514	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₃
commutator, cosocle	C₂×C₄×C₈₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₃
Fitting	C₂²×Q₁₆×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×D₄
prime radical	#19128362	C₂
hypercenter	C₂²×Q₁₆	D₈₃
hypocenter	C₈₃	#3270
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#14581824	C₂	semidirect
2. Q₈×C₂²⋊D₈₃	C₂	semidirect
4. #19128094	C₂	semidirect
5. #19127956	C₂	semidirect
6. #19127930	C₂	semidirect
7. #19127925	C₂	semidirect
8. #19127909	C₂	semidirect
9. #19127862	C₂	semidirect
10. #19127857	C₂	semidirect
11. #19127855	C₂	semidirect
12. #19127840	C₂	semidirect
13. #19127808	C₂	semidirect
14. #19127772	C₂	semidirect
15. C₂²×Q₁₆×C₈₃	C₂	semidirect
119. Q₁₆×C₈₃	D₄	semidirect
170. C₂²×C₈₃	#137	semidirect
198. C₈₃	#3270	semidirect
200. C₂²×Q₁₆	D₈₃	semidirect
290. Q₁₆	C₂²⋊D₈₃	semidirect
374. C₂²	#14581824	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14581824	2
Q₈×C₂²⋊D₈₃	2
#19128362	2
#19128094	2
#19127956	2
#19127930	2
#19127925	2
#19127909	2
#19127862	2
#19127857	2
#19127855	2
#19127840	2
#19127808	2
#19127772	2
C₂²×Q₁₆×C₈₃	2
#3270	83