Subgroups — #24917552

Order 10624.

488 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128248	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₄×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128021	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128018	C₂	1	1	yes	maximal, characteristic, complemented
5	#19127990	C₂	1	1	yes	maximal, characteristic, complemented
6	#19127989	C₂	1	1	yes	maximal, characteristic, complemented
7	#19127895	C₂	1	1	yes	maximal, characteristic, complemented
8	#19127894	C₂	1	1	yes	maximal, characteristic, complemented
9	#19127836	C₂	1	1	yes	maximal, characteristic, complemented
10	#19127833	C₂	1	1	yes	maximal, characteristic, complemented
11	#19127814	C₂	1	1	yes	maximal, characteristic, complemented
12	#19127811	C₂	1	1	yes	maximal, characteristic, complemented
13	#19127811	C₂	1	1	yes	maximal, characteristic, complemented
14	#19127756	C₂	1	1	yes	maximal, characteristic, complemented
15	#442×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13050590	—	2	1	no	—
17	C₂×D₄×D₈₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₈₃	—	2	1	no	—
19	C₂×D₆₆₄	C₂²	1	1	yes	characteristic
20	C₂×#13050575	C₂²	1	1	yes	characteristic
21	C₂×#13050575	C₂²	1	1	yes	characteristic
22	#14581791	C₂²	1	1	yes	characteristic, complemented
23	#14581788	C₂²	1	1	yes	characteristic, complemented
24	#14581778	—	2	1	no	—
25	#14581767	C₂²	1	1	yes	characteristic
26	#14581765	—	2	1	no	—
27	#14581763	C₂²	1	1	yes	characteristic
28	C₄×D₃₃₂	C₂²	1	1	yes	characteristic
29	C₄×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
30	D₄×Dic₈₃	C₂²	1	1	yes	characteristic
31	#14581754	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊D₈₃	—	2	1	no	—
33	C₄×C₂²⋊D₈₃	—	2	1	no	—
34	(C₂²⋊D₈₃)⋊C₄	—	2	1	no	—
35	C₄⋊C₄×D₈₃	C₂²	1	1	yes	characteristic
36	C₂²⋊C₄×D₈₃	—	2	1	no	—
37	C₄²×D₈₃	C₂²	1	1	yes	characteristic
38	#14581724	C₂²	1	1	yes	characteristic, complemented
39	#14581723	C₂²	1	1	yes	characteristic, complemented
40	#14581723	C₂²	1	1	yes	characteristic, complemented
41	Dic₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	Dic₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	#14581714	C₂²	1	1	yes	characteristic
44	#14581714	C₂²	1	1	yes	characteristic, complemented
45	#14581713	C₂²	1	1	yes	characteristic
46	#14581713	C₂²	1	1	yes	characteristic, complemented
47	#14581712	C₂²	1	1	yes	characteristic
48	#14581712	C₂²	1	1	yes	characteristic, complemented
49	(C₂×D₈₃)⋊C₈	C₂²	1	1	yes	characteristic
50	(C₂×D₈₃)⋊C₈	C₂²	1	1	yes	characteristic
51	#14581703	C₂²	1	1	yes	characteristic, complemented
52	C₂×D₈×C₈₃	C₂²	1	1	yes	characteristic
53	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
55	#106×C₈₃	C₂²	1	1	yes	characteristic, complemented
56	#102×C₈₃	C₂²	1	1	yes	characteristic
57	#102×C₈₃	C₂²	1	1	yes	characteristic, complemented
58	#97×C₈₃	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₈₃	—	2	1	no	—
60	#13050590	—	4	4	no	—
61	C₂×Dic₁₆₆	—	2	1	no	—
62	C₂×D₃₃₂	—	2	1	no	—
63	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
64	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₈₃	—	2	1	no	—
66	C₂×C₂²⋊D₈₃	—	2	1	no	—
67	C₂×C₂²⋊D₈₃	—	2	1	no	—
68	C₂×C₂²⋊D₈₃	—	2	1	no	—
69	D₄×D₈₃	—	2	2	no	—
70	D₄×D₈₃	—	2	2	no	—
71	C₂²×Dic₈₃	—	2	1	no	—
72	C₂×C₄×D₈₃	—	2	1	no	—
73	C₂×C₄×D₈₃	—	2	1	no	—
74	C₂×C₄×D₈₃	—	2	1	no	—
75	C₂×C₄×D₈₃	—	2	1	no	—
76	C₂×C₄×D₈₃	—	4	4	no	—
77	C₂×C₄×D₈₃	D₄	1	1	yes	characteristic
78	C₂×C₄×D₈₃	D₄	1	1	yes	characteristic
79	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
80	D₆₆₄	—	2	2	no	—
81	#13050575	—	2	2	no	—
82	#13050575	—	2	2	no	—
83	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
86	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
87	Dic₈₃⋊C₄	—	2	1	no	—
88	Dic₈₃⋊C₄	—	2	1	no	—
89	C₂²⋊Dic₈₃	—	2	1	no	—
90	C₂²⋊Dic₈₃	—	2	1	no	—
91	(C₂×D₈₃)⋊C₄	—	2	1	no	—
92	(C₂×D₈₃)⋊C₄	—	2	1	no	—
93	(C₂×D₈₃)⋊C₄	—	2	1	no	—
94	(C₂×D₈₃)⋊C₄	—	2	1	no	—
95	C₄×Dic₈₃	D₄	1	1	yes	characteristic
96	C₄×Dic₈₃	D₄	1	1	yes	characteristic
97	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
98	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
99	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₈₃	—	2	1	no	—
101	C₂²×C₄×C₈₃	—	2	1	no	—
102	D₈×C₈₃	—	2	2	no	—
103	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
104	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
105	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
106	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
107	C₂²⋊C₄×C₈₃	—	2	1	no	—
108	C₂²⋊C₄×C₈₃	—	2	1	no	—
109	C₄²×C₈₃	C₂³	1	1	yes	characteristic
110	C₂³×C₈₃	—	2	1	no	—
111	C₂³×C₈₃	—	2	1	no	—
112	C₂²×D₈₃	—	2	4	no	—
113	C₂²×D₈₃	—	2	1	no	—
114	C₂²×D₈₃	—	2	1	no	—
115	C₂²×D₈₃	—	4	2	no	—
116	C₂²×D₈₃	—	4	2	no	—
117	C₂²×D₈₃	C₂×D₄	1	1	yes	characteristic
118	D₄×C₈₃	—	2	1	no	—
119	D₄×C₈₃	—	2	1	no	—
120	D₄×C₈₃	—	2	1	no	—
121	D₄×C₈₃	#41	1	2	yes	complemented
122	C₂×C₄×C₈₃	—	2	1	no	—
123	C₂×C₄×C₈₃	—	2	1	no	—
124	C₂×C₄×C₈₃	—	4	2	no	—
125	C₂×C₄×C₈₃	—	4	2	no	—
126	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
129	C₂²⋊D₈₃	—	2	4	no	—
130	C₂²⋊D₈₃	—	4	2	no	—
131	C₂²⋊D₈₃	—	4	2	no	—
132	C₂²⋊D₈₃	—	4	2	no	—
133	C₂×Dic₈₃	—	2	1	no	—
134	C₂×Dic₈₃	—	2	1	no	—
135	C₂×Dic₈₃	—	4	2	no	—
136	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
139	D₃₃₂	—	2	1	no	—
140	D₃₃₂	—	2	1	no	—
141	D₃₃₂	—	2	1	no	—
142	D₃₃₂	—	4	2	no	—
143	D₃₃₂	#41	1	2	yes	complemented
144	C₄×D₈₃	—	2	2	no	—
145	C₄×D₈₃	—	2	1	no	—
146	C₄×D₈₃	—	2	1	no	—
147	C₄×D₈₃	—	2	2	no	—
148	C₄×D₈₃	—	4	2	no	—
149	C₄×D₈₃	—	4	2	no	—
150	C₄×D₈₃	—	4	2	no	—
151	C₄×D₈₃	—	4	2	no	—
152	Dic₁₆₆	—	4	2	no	—
153	C₈×C₈₃	—	2	1	no	—
154	C₈×C₈₃	—	2	1	no	—
155	C₈₃⋊C₈	—	2	1	no	—
156	C₈₃⋊C₈	—	2	1	no	—
157	C₂²×C₈₃	—	2	2	no	—
158	C₂²×C₈₃	—	4	1	no	—
159	C₂²×C₈₃	—	4	1	no	—
160	C₂²×C₈₃	—	4	1	no	—
161	C₂²×C₈₃	—	4	1	no	—
162	C₂²×C₈₃	—	4	1	no	—
163	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×D₈₃	—	2	1	no	—
165	C₂×D₈₃	—	2	1	no	—
166	C₂×D₈₃	—	2	2	no	—
167	C₂×D₈₃	—	4	8	no	—
168	C₂×D₈₃	—	4	1	no	—
169	C₂×D₈₃	—	4	1	no	—
170	C₂×D₈₃	—	4	1	no	—
171	C₂×D₈₃	—	4	1	no	—
172	C₂×D₈₃	—	4	1	no	—
173	C₂×D₈₃	AGL(1,ℤ/8)	1	2	yes	—
174	C₄×C₈₃	—	2	1	no	—
175	C₄×C₈₃	—	2	1	no	—
176	C₄×C₈₃	—	4	1	no	—
177	C₄×C₈₃	—	4	1	no	—
178	C₄×C₈₃	C₂×#41	1	1	yes	characteristic
179	C₄×C₈₃	C₂×#41	1	1	yes	characteristic
180	Dic₈₃	—	2	1	no	—
181	Dic₈₃	—	2	1	no	—
182	Dic₈₃	—	4	1	no	—
183	Dic₈₃	—	4	1	no	—
184	Dic₈₃	AGL(1,ℤ/8)	1	2	yes	—
185	C₂×C₈₃	—	4	2	no	—
186	C₂×C₈₃	—	8	1	no	—
187	C₂×C₈₃	#525	1	1	yes	characteristic
188	C₂×C₈₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂×C₈₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
190	D₈₃	—	2	2	no	—
191	D₈₃	—	4	2	no	—
192	D₈₃	—	8	1	no	—
193	#3109	—	83	1	no	maximal, Sylow
194	C₈₃	#3109	1	1	yes	characteristic, complemented, Sylow
195	#532	—	83	1	no	—
196	C₂×C₄×D₄	—	83	1	no	—
197	#481	—	83	1	no	—
198	#481	—	83	1	no	—
199	#476	—	83	1	no	—
200	#476	—	83	1	no	—
201	#459	—	83	1	no	—
202	#459	—	83	1	no	—
203	#447	—	83	1	no	—
204	#447	—	83	1	no	—
205	#442	—	83	1	no	—
206	#442	—	83	1	no	—
207	#442	—	83	1	no	—
208	#442	D₈₃	1	1	yes	characteristic, complemented
209	#432	—	83	1	no	—
210	C₂×#41	—	166	1	no	—
211	C₂²×D₄	—	83	1	no	—
212	C₂³×C₄	—	166	1	no	—
213	C₂×D₈	—	83	1	no	—
214	C₂×D₈	—	83	1	no	—
215	C₂×D₈	—	83	1	no	—
216	C₂×D₈	C₂×D₈₃	1	1	yes	characteristic
217	C₄⋊Q₈	—	83	1	no	—
218	#127	—	83	1	no	—
219	#124	—	166	1	no	—
220	#121	—	83	1	no	—
221	#121	—	83	1	no	—
222	#121	—	166	1	no	—
223	C₄×D₄	—	83	1	no	—
224	C₄×D₄	—	83	1	no	—
225	C₄×D₄	—	83	1	no	—
226	C₄×D₄	—	83	1	no	—
227	C₄×D₄	—	166	1	no	—
228	C₄×D₄	—	166	1	no	—
229	C₄×D₄	—	166	1	no	—
230	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic
231	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic, complemented
232	C₂×C₄⋊C₄	—	83	1	no	—
233	C₂×C₂²⋊C₄	—	166	1	no	—
234	C₂×C₄²	—	83	1	no	—
235	#106	—	83	1	no	—
236	#106	—	83	1	no	—
237	#106	—	83	1	no	—
238	#106	C₂×D₈₃	1	1	yes	characteristic, complemented
239	C₄⋊C₈	—	83	1	no	—
240	C₄⋊C₈	—	83	1	no	—
241	#102	—	83	1	no	—
242	#102	—	83	1	no	—
243	#102	—	83	1	no	—
244	#102	—	83	1	no	—
245	#102	—	83	1	no	—
246	#102	—	83	1	no	—
247	#102	C₂×D₈₃	1	1	yes	characteristic
248	#102	C₂×D₈₃	1	1	yes	characteristic, complemented
249	C₂²⋊C₈	—	83	1	no	—
250	C₂²⋊C₈	—	83	1	no	—
251	#97	—	83	1	no	—
252	#97	C₂×D₈₃	1	1	yes	characteristic, complemented
253	C₂⁴	—	166	1	no	—
254	#41	—	332	4	no	—
255	C₂×Q₈	—	166	1	no	—
256	C₂×D₄	—	83	1	no	—
257	C₂×D₄	—	83	1	no	—
258	C₂×D₄	—	166	1	no	—
259	C₂×D₄	—	166	1	no	—
260	C₂×D₄	—	166	1	no	—
261	C₂×D₄	—	166	1	no	—
262	C₂×D₄	—	166	2	no	—
263	C₂×D₄	—	166	1	no	—
264	C₂×D₄	—	166	2	no	—
265	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
266	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	332	4	no	—
270	C₂²×C₄	—	83	1	no	—
271	C₂²×C₄	—	83	1	no	—
272	C₂²×C₄	—	83	1	no	—
273	C₂²×C₄	—	166	1	no	—
274	C₂²×C₄	—	166	1	no	—
275	C₂²×C₄	—	166	1	no	—
276	C₂²×C₄	—	166	1	no	—
277	C₂²×C₄	—	166	1	no	—
278	D₈	—	2	2	no	—
279	D₈	—	166	2	no	—
280	D₈	—	166	2	no	—
281	D₈	—	166	2	no	—
282	C₂×C₈	—	83	1	no	—
283	C₂×C₈	—	83	1	no	—
284	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
285	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
286	C₄⋊C₄	—	83	1	no	—
287	C₄⋊C₄	—	83	1	no	—
288	C₄⋊C₄	—	166	1	no	—
289	C₄⋊C₄	—	166	1	no	—
290	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
291	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₂²⋊C₄	—	166	1	no	—
295	C₂²⋊C₄	—	166	1	no	—
296	C₂²⋊C₄	—	166	1	no	—
297	C₂²⋊C₄	—	166	1	no	—
298	C₂²⋊C₄	—	166	1	no	—
299	C₂²⋊C₄	—	166	1	no	—
300	C₄²	—	83	1	no	—
301	C₄²	—	83	1	no	—
302	C₄²	—	83	1	no	—
303	C₄²	C₂²×D₈₃	1	1	yes	characteristic
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	332	2	no	—
307	C₂³	—	332	2	no	—
308	C₂³	—	83	1	no	—
309	C₂³	—	166	4	no	—
310	C₂³	—	166	1	no	—
311	C₂³	—	166	1	no	—
312	Q₈	—	332	2	no	—
313	D₄	—	2	1	no	—
314	D₄	—	2	1	no	—
315	D₄	—	2	1	no	—
316	D₄	—	332	2	no	—
317	D₄	—	332	2	no	—
318	D₄	—	332	2	no	—
319	D₄	—	332	2	no	—
320	D₄	—	83	2	no	—
321	D₄	—	166	4	no	—
322	D₄	—	166	1	no	—
323	D₄	—	166	1	no	—
324	D₄	—	166	1	no	—
325	D₄	#13050590	1	2	yes	complemented
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	332	2	no	—
331	C₂×C₄	—	332	2	no	—
332	C₂×C₄	—	332	2	no	—
333	C₂×C₄	—	332	2	no	—
334	C₂×C₄	—	332	2	no	—
335	C₂×C₄	—	83	1	no	—
336	C₂×C₄	—	83	1	no	—
337	C₂×C₄	—	83	1	no	—
338	C₂×C₄	—	166	2	no	—
339	C₂×C₄	—	166	2	no	—
340	C₂×C₄	—	166	1	no	—
341	C₂×C₄	—	166	1	no	—
342	C₂×C₄	—	166	1	no	—
343	C₂×C₄	—	166	1	no	—
344	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
345	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
346	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
347	C₈	—	2	1	no	—
348	C₈	—	2	1	no	—
349	C₈	—	166	1	no	—
350	C₈	—	166	1	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	332	8	no	—
358	C₂²	—	332	1	no	—
359	C₂²	—	332	1	no	—
360	C₂²	—	332	1	no	—
361	C₂²	—	332	1	no	—
362	C₂²	—	332	1	no	—
363	C₂²	—	83	2	no	—
364	C₂²	—	166	2	no	—
365	C₂²	—	166	1	no	—
366	C₂²	—	166	1	no	—
367	C₂²	C₂×D₄×D₈₃	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	1	no	—
372	C₄	—	332	1	no	—
373	C₄	—	332	1	no	—
374	C₄	—	83	2	no	—
375	C₄	—	166	1	no	—
376	C₄	—	166	1	no	—
377	C₄	#41×D₈₃	1	1	yes	characteristic
378	C₄	C₂×#13050590	1	1	yes	characteristic
379	C₂	—	4	2	no	—
380	C₂	—	8	1	no	—
381	C₂	—	332	2	no	—
382	C₂	—	664	1	no	—
383	C₂	—	166	2	no	—
384	C₂	#19128210	1	1	yes	characteristic
385	C₂	AGL(1,ℤ/8)×D₈₃	1	1	yes	characteristic
386	C₂	AGL(1,ℤ/8)×D₈₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₃
commutator, cosocle	C₂×C₄×C₈₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₃
Fitting	#442×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×D₄
hypercenter	#442	D₈₃
hypocenter	C₈₃	#3109
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #442

Complements

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

N	H ≅ G/N	type
1. #19128248	C₂	semidirect
2. C₄×D₄×D₈₃	C₂	semidirect
3. #19128021	C₂	semidirect
4. #19128018	C₂	semidirect
5. #19127990	C₂	semidirect
6. #19127989	C₂	semidirect
7. #19127895	C₂	semidirect
8. #19127894	C₂	semidirect
9. #19127836	C₂	semidirect
10. #19127833	C₂	semidirect
11. #19127814	C₂	semidirect
12. #19127811	C₂	semidirect
13. #19127811	C₂	semidirect
14. #19127756	C₂	semidirect
15. #442×C₈₃	C₂	semidirect
22. #14581791	C₂²	semidirect
23. #14581788	C₂²	semidirect
29. C₄×D₃₃₂	C₂²	semidirect
38. #14581724	C₂²	semidirect
39. #14581723	C₂²	semidirect
40. #14581723	C₂²	semidirect
41. Dic₈₃⋊C₈	C₂²	semidirect
42. Dic₈₃⋊C₈	C₂²	semidirect
44. #14581714	C₂²	semidirect
46. #14581713	C₂²	semidirect
48. #14581712	C₂²	semidirect
51. #14581703	C₂²	semidirect
54. C₄×D₄×C₈₃	C₂²	semidirect
55. #106×C₈₃	C₂²	semidirect
57. #102×C₈₃	C₂²	semidirect
58. #97×C₈₃	C₂²	semidirect
121. D₄×C₈₃	#41	semidirect
143. D₃₃₂	#41	semidirect
194. C₈₃	#3109	semidirect
208. #442	D₈₃	semidirect
231. C₄×D₄	C₂×D₈₃	semidirect
238. #106	C₂×D₈₃	semidirect
248. #102	C₂×D₈₃	semidirect
252. #97	C₂×D₈₃	semidirect
325. D₄	#13050590	semidirect

Maximal subgroups

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

subgroup	index
#19128248	2
C₄×D₄×D₈₃	2
#19128021	2
#19128018	2
#19127990	2
#19127989	2
#19127895	2
#19127894	2
#19127836	2
#19127833	2
#19127814	2
#19127811	2
#19127756	2
#442×C₈₃	2
#3109	83