Subgroups — #16017981

Order 3328.

612 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125406	C₂	1	1	yes	maximal, characteristic, complemented
2	#13117033	C₂	1	1	yes	maximal, characteristic, complemented
3	#13117016	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116993	C₂	1	2	yes	maximal, complemented
5	#13116891	C₂	1	2	yes	maximal, complemented
6	#13116765	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116748	C₂	1	1	yes	maximal, characteristic
8	#13116710	C₂	1	2	yes	maximal, complemented
9	#13116700	C₂	1	2	yes	maximal, complemented
10	#13116639	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	—	2	1	no	—
14	#11719184	—	2	1	no	—
15	C₄×C₁₃×D₈	—	2	1	no	—
16	C₄×C₁₃×D₈	—	2	1	no	—
17	C₄×C₁₃×D₈	C₂²	1	2	yes	—
18	C₄×C₁₃×D₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#102	—	2	1	no	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×#88067	C₂²	1	2	yes	—
23	C₂×#88066	C₂²	1	2	yes	—
24	#11718777	C₂²	1	1	yes	characteristic
25	#11718776	C₂²	1	1	yes	characteristic
26	#11718775	—	2	1	no	—
27	C₄×Dic₅₂	C₂²	1	1	yes	characteristic, complemented
28	#11718358	—	2	1	no	—
29	#11718357	C₂²	1	1	yes	characteristic, complemented
30	C₄×D₁₀₄	C₂²	1	1	yes	characteristic, complemented
31	C₄×#6095	—	2	1	no	—
32	#11718344	C₂²	1	1	yes	characteristic, complemented
33	#11718154	C₂²	1	2	yes	—
34	#11718154	C₂²	1	2	yes	—
35	C₂²⋊#6090	C₂²	1	1	yes	characteristic
36	C₂²⋊#6090	C₂²	1	1	yes	characteristic
37	#11718084	C₂²	1	2	yes	complemented
38	#11718083	C₂²	1	2	yes	complemented
39	#11718082	C₂²	1	2	yes	complemented
40	#11718081	C₂²	1	2	yes	complemented
41	C₄⋊#6090	C₂²	1	2	yes	complemented
42	#11718053	C₂²	1	2	yes	complemented
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂³×C₄×C₁₃	—	4	1	no	—
45	C₂×C₁₃×D₈	—	2	4	no	—
46	C₂×C₁₃×D₈	—	2	1	no	—
47	C₂×C₁₃×D₈	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₄×D₄×C₁₃	—	2	2	no	—
51	C₄×D₄×C₁₃	—	2	2	no	—
52	C₄×D₄×C₁₃	—	4	1	no	—
53	C₄×D₄×C₁₃	—	4	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
56	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
57	#88184	—	2	1	no	—
58	#88183	—	4	1	no	—
59	C₄×C₂²⋊D₁₃	—	4	1	no	—
60	#88178	—	2	1	no	—
61	C₂×Dic₅₂	C₂³	1	1	yes	characteristic
62	C₂×D₁₀₄	C₂³	1	1	yes	characteristic
63	C₂×#6095	—	2	1	no	—
64	#88130	—	4	1	no	—
65	#88129	—	2	1	no	—
66	C₄×D₅₂	—	2	1	no	—
67	#88126	—	4	1	no	—
68	#88124	—	2	1	no	—
69	C₄×Dic₂₆	—	2	1	no	—
70	C₁₃×#107	—	2	1	no	—
71	C₁₃×#107	C₂³	1	2	yes	—
72	C₁₃×#102	—	2	2	no	—
73	C₁₃×#102	—	2	2	no	—
74	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
75	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
76	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	#88067	—	2	4	no	—
79	#88066	—	2	4	no	—
80	#88061	—	2	1	no	—
81	#88061	—	2	1	no	—
82	#88058	C₂³	1	1	yes	characteristic
83	#88058	C₂³	1	1	yes	characteristic
84	#88057	—	2	1	no	—
85	#88056	—	2	1	no	—
86	#88056	—	2	1	no	—
87	C₂×#6090	C₂³	1	2	yes	—
88	C₂×#6090	C₂³	1	2	yes	—
89	#33674	—	13	1	no	maximal, Sylow
90	C₂⁴×C₁₃	—	4	1	no	—
91	C₂×D₄×C₁₃	—	2	4	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	4	2	no	—
94	C₂×D₄×C₁₃	—	4	1	no	—
95	C₂²×C₄×C₁₃	—	4	1	no	—
96	C₂²×C₄×C₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₃	—	4	2	no	—
98	C₂²×C₄×C₁₃	—	8	4	no	—
99	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₂²⋊D₁₃	—	4	1	no	—
103	C₂×D₅₂	—	2	1	no	—
104	C₂×C₄×D₁₃	—	4	1	no	—
105	C₂×Dic₂₆	—	2	1	no	—
106	C₁₃×D₈	—	2	4	no	—
107	C₁₃×D₈	—	2	2	no	—
108	C₁₃×D₈	#41	1	4	yes	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	4	1	no	—
111	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	4	1	no	—
117	C₁₃×C₂²⋊C₄	—	4	2	no	—
118	C₁₃×C₂²⋊C₄	—	4	2	no	—
119	C₄²×C₁₃	D₈	1	1	yes	characteristic
120	C₄²×C₁₃	D₈	1	1	yes	characteristic
121	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²⋊Dic₁₃	—	4	1	no	—
124	#6103	—	4	1	no	—
125	#6103	—	4	1	no	—
126	#6103	—	4	1	no	—
127	#6103	—	4	1	no	—
128	C₄⋊Dic₁₃	—	2	1	no	—
129	C₄⋊Dic₁₃	—	2	1	no	—
130	#6101	—	4	1	no	—
131	#6101	—	4	1	no	—
132	#6101	—	4	1	no	—
133	#6101	—	4	1	no	—
134	C₄×Dic₁₃	—	4	1	no	—
135	Dic₅₂	—	2	2	no	—
136	D₁₀₄	—	2	2	no	—
137	#6095	—	4	2	no	—
138	#6090	—	2	2	no	—
139	#6090	—	2	2	no	—
140	#3168	—	13	1	no	—
141	C₂×C₄×D₈	D₁₃	1	1	yes	characteristic, complemented
142	#2235	—	13	1	no	—
143	#2232	—	13	1	no	—
144	#2228	—	13	2	no	—
145	#2210	—	13	2	no	—
146	#2187	—	13	1	no	—
147	#2184	—	13	1	no	—
148	#2177	—	13	2	no	—
149	#2175	—	13	2	no	—
150	#2163	—	13	1	no	—
151	C₂³×C₁₃	—	4	4	no	—
152	C₂³×C₁₃	—	4	2	no	—
153	C₂³×C₁₃	—	8	2	no	—
154	C₂³×C₁₃	—	8	2	no	—
155	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
156	C₂²×D₁₃	—	4	1	no	—
157	D₄×C₁₃	—	2	4	no	—
158	D₄×C₁₃	—	4	4	no	—
159	D₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	8	4	no	—
166	C₂×C₄×C₁₃	—	8	4	no	—
167	C₂×C₄×C₁₃	—	8	2	no	—
168	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₂²⋊D₁₃	—	8	2	no	—
175	C₂×Dic₁₃	—	4	1	no	—
176	C₂×Dic₁₃	—	4	1	no	—
177	C₂×Dic₁₃	—	4	1	no	—
178	D₅₂	—	4	1	no	—
179	D₅₂	—	4	1	no	—
180	C₄×D₁₃	—	8	2	no	—
181	Dic₂₆	—	4	1	no	—
182	Dic₂₆	—	4	1	no	—
183	C₈×C₁₃	—	2	1	no	—
184	C₈×C₁₃	—	2	1	no	—
185	C₈×C₁₃	—	2	1	no	—
186	C₈×C₁₃	C₂×#41	1	2	yes	—
187	C₂²×D₈	C₂×D₁₃	1	1	yes	characteristic
188	#529	—	26	1	no	—
189	C₂×C₄×D₄	—	2	1	no	—
190	C₂×SD₃₂	—	13	2	no	—
191	C₂×D₁₆	—	13	2	no	—
192	#499	—	13	1	no	—
193	#495	—	13	1	no	—
194	#488	—	26	1	no	—
195	#467	—	13	1	no	—
196	#466	—	13	1	no	—
197	#465	—	26	1	no	—
198	C₄×Q₁₆	—	13	1	no	—
199	C₄×SD₁₆	—	26	1	no	—
200	C₄×D₈	—	2	1	no	—
201	C₄×D₈	—	2	1	no	—
202	C₄×D₈	—	13	1	no	—
203	C₄×D₈	C₂×D₁₃	1	2	yes	—
204	C₄×D₈	C₂×D₁₃	1	2	yes	—
205	C₂×#107	C₂×D₁₃	1	1	yes	characteristic
206	C₂×#102	—	2	1	no	—
207	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
208	#367	—	13	2	no	—
209	#366	—	13	2	no	—
210	C₄⋊C₁₆	—	13	2	no	—
211	#358	—	13	2	no	—
212	#357	—	13	2	no	—
213	#357	—	13	2	no	—
214	#357	—	13	2	no	—
215	C₂²⋊C₁₆	—	13	1	no	—
216	C₂²⋊C₁₆	—	13	1	no	—
217	#346	—	13	2	no	—
218	C₂²×C₁₃	—	2	1	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	—	4	4	no	—
221	C₂²×C₁₃	—	8	8	no	—
222	C₂²×C₁₃	—	8	2	no	—
223	C₂²×C₁₃	—	8	2	no	—
224	C₂²×C₁₃	#509	1	2	yes	—
225	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
226	C₂×D₁₃	—	8	1	no	—
227	C₂×D₁₃	—	8	1	no	—
228	C₂×D₁₃	—	8	1	no	—
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	—	2	1	no	—
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	8	2	no	—
235	C₄×C₁₃	#525	1	1	yes	characteristic
236	C₄×C₁₃	#575	1	1	yes	characteristic
237	Dic₁₃	—	8	1	no	—
238	Dic₁₃	—	8	1	no	—
239	Dic₁₃	—	8	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂³×C₄	—	4	1	no	—
242	C₂×Q₁₆	—	13	1	no	—
243	C₂×SD₁₆	—	26	1	no	—
244	C₂×D₈	—	2	4	no	—
245	C₂×D₈	—	2	1	no	—
246	C₂×D₈	—	13	1	no	—
247	C₂×D₈	C₂²×D₁₃	1	2	yes	—
248	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
249	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
250	#126	—	52	1	no	—
251	#125	—	26	1	no	—
252	#124	—	26	1	no	—
253	#123	—	52	1	no	—
254	C₂²⋊Q₈	—	26	1	no	—
255	#121	—	26	1	no	—
256	C₄×Q₈	—	26	1	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	4	1	no	—
260	C₄×D₄	—	4	1	no	—
261	C₄×D₄	—	26	1	no	—
262	C₄×D₄	—	52	1	no	—
263	#117	—	52	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	4	1	no	—
266	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
267	SD₃₂	—	26	4	no	—
268	D₁₆	—	26	4	no	—
269	C₂×C₁₆	—	13	2	no	—
270	C₂×C₁₆	—	13	2	no	—
271	#107	—	2	1	no	—
272	#107	—	13	1	no	—
273	#107	—	13	1	no	—
274	#107	C₂²×D₁₃	1	2	yes	—
275	#106	—	26	1	no	—
276	#103	—	26	1	no	—
277	#103	—	26	1	no	—
278	#102	—	2	2	no	—
279	#102	—	2	2	no	—
280	#102	—	26	1	no	—
281	#102	—	26	1	no	—
282	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
283	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
284	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
285	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
286	C₂×C₁₃	—	2	2	no	—
287	C₂×C₁₃	—	8	4	no	—
288	C₂×C₁₃	#3100	1	1	yes	characteristic
289	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
290	C₂×C₁₃	#3414	1	1	yes	characteristic
291	D₁₃	—	16	1	no	—
292	C₂⁴	—	4	1	no	—
293	C₂×Q₈	—	26	1	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	26	1	no	—
299	C₂×D₄	—	52	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	8	4	no	—
304	C₂²×C₄	—	52	1	no	—
305	C₂²×C₄	#6104	1	1	yes	characteristic
306	C₂²×C₄	#6104	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
308	Q₁₆	—	26	2	no	—
309	SD₁₆	—	52	2	no	—
310	D₈	—	2	4	no	—
311	D₈	—	2	2	no	—
312	D₈	—	26	2	no	—
313	D₈	#6127	1	4	yes	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
317	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
318	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
319	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	26	1	no	—
323	C₄⋊C₄	—	26	1	no	—
324	C₄⋊C₄	—	52	1	no	—
325	C₄⋊C₄	—	52	1	no	—
326	C₄⋊C₄	—	52	1	no	—
327	C₄⋊C₄	—	52	1	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	52	1	no	—
331	C₂²⋊C₄	—	52	1	no	—
332	C₂²⋊C₄	—	52	1	no	—
333	C₂²⋊C₄	—	52	1	no	—
334	C₂²⋊C₄	—	52	1	no	—
335	C₄²	—	52	1	no	—
336	C₄²	#6104	1	1	yes	characteristic
337	C₄²	#6104	1	1	yes	characteristic
338	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
339	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
340	C₁₆	—	26	2	no	—
341	C₁₆	—	26	2	no	—
342	C₁₃	#33674	1	1	yes	characteristic, complemented, Sylow
343	C₂³	—	4	4	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	2	no	—
346	C₂³	—	8	2	no	—
347	C₂³	—	52	1	no	—
348	C₂³	C₂×#6104	1	1	yes	characteristic
349	Q₈	—	52	1	no	—
350	Q₈	—	52	1	no	—
351	D₄	—	2	4	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	2	no	—
354	D₄	—	52	1	no	—
355	D₄	—	52	1	no	—
356	D₄	—	104	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	8	4	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	52	1	no	—
366	C₂×C₄	—	52	1	no	—
367	C₂×C₄	—	52	1	no	—
368	C₂×C₄	—	104	2	no	—
369	C₂×C₄	C₂×#6104	1	1	yes	characteristic
370	C₂×C₄	C₂×#6104	1	1	yes	characteristic
371	C₂×C₄	C₂×#6104	1	1	yes	characteristic
372	C₂×C₄	C₂×#6104	1	1	yes	characteristic
373	C₂×C₄	C₂×#6104	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	C₂×#6127	1	2	yes	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	8	8	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	104	1	no	—
386	C₂²	—	104	1	no	—
387	C₂²	—	104	1	no	—
388	C₂²	#11718808	1	2	yes	—
389	C₂²	C₂²×#6104	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	8	2	no	—
396	C₄	—	104	1	no	—
397	C₄	—	104	1	no	—
398	C₄	—	104	1	no	—
399	C₄	#11719496	1	1	yes	characteristic
400	C₄	#11719527	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	8	4	no	—
403	C₂	—	208	1	no	—
404	C₂	#13124836	1	1	yes	characteristic
405	C₂	C₂×#11718808	1	1	yes	characteristic
406	C₂	#13127970	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×D₈	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	#13116748	C₂
hypercenter	C₂×C₄×D₈	D₁₃
hypocenter	C₁₃	#33674
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. #13125406	C₂	semidirect
2. #13117033	C₂	semidirect
3. #13117016	C₂	semidirect
4. #13116993	C₂	semidirect
5. #13116891	C₂	semidirect
6. #13116765	C₂	semidirect
8. #13116710	C₂	semidirect
9. #13116700	C₂	semidirect
10. #13116639	C₂	semidirect
11. C₂×C₄×C₁₃×D₈	C₂	semidirect
27. C₄×Dic₅₂	C₂²	semidirect
29. #11718357	C₂²	semidirect
30. C₄×D₁₀₄	C₂²	semidirect
32. #11718344	C₂²	semidirect
37. #11718084	C₂²	semidirect
38. #11718083	C₂²	semidirect
39. #11718082	C₂²	semidirect
40. #11718081	C₂²	semidirect
41. C₄⋊#6090	C₂²	semidirect
42. #11718053	C₂²	semidirect
141. C₂×C₄×D₈	D₁₃	semidirect
342. C₁₃	#33674	semidirect

Maximal subgroups

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

subgroup	index
#13125406	2
#13117033	2
#13117016	2
#13116993	2
#13116891	2
#13116765	2
#13116748	2
#13116710	2
#13116700	2
#13116639	2
C₂×C₄×C₁₃×D₈	2
#33674	13