Subgroups — #15761702

Order 3328.

582 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88201	C₂	1	1	yes	maximal, characteristic
2	#13114987	C₂	1	1	yes	maximal, characteristic, complemented
3	#13114581	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11718051	C₂	1	1	yes	maximal, characteristic
6	C₂×#11718075	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88201	C₄	1	1	yes	characteristic
10	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	#11718891	C₄	1	1	yes	characteristic
14	C₂×#88054	—	2	2	no	—
15	#11718651	—	2	2	no	—
16	#11718649	C₄	1	1	yes	characteristic
17	#11718638	C₄	1	1	yes	characteristic
18	C₄×#6103	—	2	2	no	—
19	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
21	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
22	C₁₃×Q₈⋊C₈	—	2	2	no	—
23	#11718142	—	2	2	no	—
24	Q₈⋊#1055	—	2	2	no	—
25	#11718075	—	2	2	no	—
26	#11718051	—	2	2	no	—
27	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	—	2	1	no	—
30	C₂²×C₈×C₁₃	—	2	1	no	—
31	C₂²×C₈×C₁₃	—	2	1	no	—
32	C₄×Q₈×C₁₃	—	2	1	no	—
33	C₄×Q₈×C₁₃	—	2	1	no	—
34	C₄×Q₈×C₁₃	—	2	1	no	—
35	C₄×Q₈×C₁₃	—	2	1	no	—
36	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
37	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₃	—	2	1	no	—
39	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
40	#88201	—	2	2	no	—
41	#88201	C₈	1	4	yes	complemented
42	C₂×#6103	—	2	2	no	—
43	C₂×#6103	—	2	1	no	—
44	C₂×#6103	—	2	2	no	—
45	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
49	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
50	C₂²×#1055	—	2	1	no	—
51	C₂²×#1055	—	2	1	no	—
52	C₄×D₅₂	—	2	1	no	—
53	C₄×D₅₂	—	2	1	no	—
54	C₄×D₅₂	—	2	1	no	—
55	C₄×D₅₂	—	2	1	no	—
56	C₁₃×C₄⋊C₈	—	2	1	no	—
57	C₁₃×C₄⋊C₈	—	2	1	no	—
58	C₄×C₈×C₁₃	—	2	1	no	—
59	C₄×C₈×C₁₃	D₄	1	2	yes	—
60	#88071	—	2	2	no	—
61	#88071	—	2	2	no	—
62	#88054	—	4	4	no	—
63	C₄⋊#1055	—	2	1	no	—
64	C₄⋊#1055	—	2	1	no	—
65	C₄×#1055	—	2	1	no	—
66	C₄×#1055	D₄	1	2	yes	—
67	#9640	—	13	1	no	maximal, Sylow
68	C₂³×D₁₃	—	2	1	no	—
69	C₂×Q₈×C₁₃	—	2	1	no	—
70	C₂×Q₈×C₁₃	—	2	1	no	—
71	C₂×Q₈×C₁₃	—	2	1	no	—
72	C₂×Q₈×C₁₃	—	2	1	no	—
73	C₂×Q₈×C₁₃	—	2	1	no	—
74	C₂×Q₈×C₁₃	C₂×C₈	1	2	yes	—
75	C₂²×C₄×C₁₃	—	2	1	no	—
76	C₂²×C₄×C₁₃	—	2	1	no	—
77	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×Dic₁₃	—	2	1	no	—
81	C₂²×Dic₁₃	C₂²⋊C₄	1	2	yes	—
82	C₂²×Dic₁₃	C₂²⋊C₄	1	2	yes	—
83	C₂×D₅₂	—	2	1	no	—
84	C₂×D₅₂	—	2	1	no	—
85	C₂×D₅₂	—	2	1	no	—
86	C₂×D₅₂	—	2	1	no	—
87	C₂×D₅₂	—	2	1	no	—
88	C₂×D₅₂	C₂×C₈	1	2	yes	—
89	C₂×C₄×D₁₃	—	4	1	no	—
90	C₂×C₄×D₁₃	—	4	1	no	—
91	C₂×C₄×D₁₃	—	4	2	no	—
92	C₂×C₄×D₁₃	—	4	2	no	—
93	C₂×C₈×C₁₃	—	2	2	no	—
94	C₂×C₈×C₁₃	—	4	2	no	—
95	C₂×C₈×C₁₃	—	4	1	no	—
96	C₂×C₈×C₁₃	—	4	2	no	—
97	C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₁₃×C₄⋊C₄	—	4	1	no	—
100	C₁₃×C₄⋊C₄	—	4	1	no	—
101	C₄²×C₁₃	—	4	1	no	—
102	C₄²×C₁₃	—	4	1	no	—
103	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₃	#41	1	1	yes	characteristic
106	C₄²×C₁₃	#41	1	1	yes	characteristic
107	#6103	—	2	8	no	—
108	#6103	—	4	4	no	—
109	#6103	—	4	1	no	—
110	#6103	—	4	1	no	—
111	C₄⋊Dic₁₃	—	2	1	no	—
112	C₄⋊Dic₁₃	—	2	1	no	—
113	C₄×Dic₁₃	—	2	1	no	—
114	C₄×Dic₁₃	—	2	1	no	—
115	C₄×Dic₁₃	—	2	2	no	—
116	C₄×Dic₁₃	—	2	2	no	—
117	C₄×Dic₁₃	—	4	2	no	—
118	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
119	C₄×Dic₁₃	M₁₆	1	2	yes	—
120	C₂×#1055	—	2	2	no	—
121	C₂×#1055	—	4	2	no	—
122	C₂×#1055	—	4	1	no	—
123	C₂×#1055	—	4	2	no	—
124	C₄×#124	—	13	1	no	—
125	#1842	—	13	1	no	—
126	#1744	—	13	1	no	—
127	C₂×Q₈⋊C₈	—	13	1	no	—
128	C₂×Q₈⋊C₈	D₁₃	1	1	yes	characteristic, complemented
129	C₂×D₄⋊C₈	—	13	1	no	—
130	C₂×D₄⋊C₈	—	13	1	no	—
131	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×D₁₃	—	2	2	no	—
133	C₂²×D₁₃	—	4	1	no	—
134	C₂²×D₁₃	—	4	1	no	—
135	C₂²×D₁₃	—	4	2	no	—
136	C₂²×D₁₃	—	4	2	no	—
137	Q₈×C₁₃	—	2	2	no	—
138	Q₈×C₁₃	—	2	2	no	—
139	Q₈×C₁₃	—	4	1	no	—
140	Q₈×C₁₃	—	4	1	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	4	1	no	—
144	C₂×C₄×C₁₃	—	4	1	no	—
145	C₂×C₄×C₁₃	—	4	1	no	—
146	C₂×C₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
152	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
155	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
156	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
157	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
158	C₂×C₄×C₁₃	#137	1	2	yes	—
159	C₂×Dic₁₃	—	2	2	no	—
160	C₂×Dic₁₃	—	2	2	no	—
161	C₂×Dic₁₃	—	2	2	no	—
162	C₂×Dic₁₃	—	2	2	no	—
163	C₂×Dic₁₃	—	2	2	no	—
164	C₂×Dic₁₃	—	4	1	no	—
165	C₂×Dic₁₃	—	4	2	no	—
166	C₂×Dic₁₃	C₂²⋊C₈	1	4	yes	—
167	D₅₂	—	2	2	no	—
168	D₅₂	—	2	2	no	—
169	D₅₂	—	4	1	no	—
170	D₅₂	—	4	1	no	—
171	C₄×D₁₃	—	8	2	no	—
172	C₄×D₁₃	—	8	1	no	—
173	C₄×D₁₃	—	8	1	no	—
174	C₈×C₁₃	—	4	2	no	—
175	C₈×C₁₃	—	8	1	no	—
176	#1055	—	4	2	no	—
177	#1055	—	8	1	no	—
178	C₂×#124	—	13	1	no	—
179	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
180	C₂×C₄×D₄	—	13	1	no	—
181	C₂×C₄⋊C₈	—	13	1	no	—
182	C₂×C₄⋊C₈	—	26	2	no	—
183	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
184	C₂×C₄×C₈	—	13	1	no	—
185	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
186	#391	—	13	1	no	—
187	#390	—	13	1	no	—
188	#388	—	26	2	no	—
189	#382	—	13	1	no	—
190	C₄×C₂²⋊C₄	—	26	2	no	—
191	C₄³	—	13	1	no	—
192	#336	—	26	2	no	—
193	Q₈⋊C₈	—	2	2	no	—
194	Q₈⋊C₈	—	26	2	no	—
195	D₄⋊C₈	—	26	2	no	—
196	D₄⋊C₈	—	26	2	no	—
197	C₂²×C₁₃	#390	1	1	yes	characteristic
198	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
199	C₂²×C₁₃	#408	1	1	yes	characteristic
200	C₂²×C₁₃	#417	1	2	yes	—
201	C₂²×C₁₃	#421	1	2	yes	—
202	C₂×D₁₃	—	4	2	no	—
203	C₂×D₁₃	—	4	4	no	—
204	C₂×D₁₃	—	8	1	no	—
205	C₂×D₁₃	—	8	1	no	—
206	C₂×D₁₃	—	8	2	no	—
207	C₄×C₁₃	—	2	1	no	—
208	C₄×C₁₃	—	2	1	no	—
209	C₄×C₁₃	—	4	2	no	—
210	C₄×C₁₃	—	8	1	no	—
211	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
212	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
213	C₄×C₁₃	#436	1	1	yes	characteristic
214	C₄×C₁₃	#436	1	1	yes	characteristic
215	C₄×C₁₃	#489	1	2	yes	—
216	C₄×C₁₃	#496	1	1	yes	characteristic
217	C₄×C₁₃	#497	1	1	yes	characteristic
218	Dic₁₃	—	2	4	no	—
219	Dic₁₃	—	4	2	no	—
220	Dic₁₃	—	8	1	no	—
221	C₂²×Q₈	C₄×D₁₃	1	1	yes	characteristic
222	C₂²×D₄	—	13	1	no	—
223	C₂³×C₄	—	26	1	no	—
224	C₂²×C₈	—	2	1	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	—	26	1	no	—
227	C₂²×C₈	—	26	1	no	—
228	#124	—	13	4	no	—
229	#124	—	26	2	no	—
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	—	2	1	no	—
232	C₄×Q₈	—	2	1	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×D₄	—	26	1	no	—
235	C₄×D₄	—	26	1	no	—
236	C₄×D₄	—	26	1	no	—
237	C₄×D₄	—	26	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	13	1	no	—
240	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	—	26	2	no	—
242	C₂×C₂²⋊C₄	—	26	2	no	—
243	C₂×C₂²⋊C₄	—	26	1	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	—	13	1	no	—
246	C₂×C₄²	—	13	1	no	—
247	C₂×C₄²	—	13	2	no	—
248	C₂×C₄²	—	13	2	no	—
249	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
250	C₄⋊C₈	—	2	1	no	—
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	—	26	1	no	—
253	C₄⋊C₈	—	26	1	no	—
254	C₄⋊C₈	—	52	4	no	—
255	C₄×C₈	—	2	1	no	—
256	C₄×C₈	—	13	2	no	—
257	C₄×C₈	—	26	1	no	—
258	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
259	#95	—	26	2	no	—
260	#95	—	26	2	no	—
261	C₂×C₁₃	#1477	1	2	yes	—
262	C₂×C₁₃	#1495	1	2	yes	—
263	C₂×C₁₃	#1954	1	1	yes	characteristic
264	C₂×C₁₃	#1959	1	1	yes	characteristic
265	C₂×C₁₃	#1963	1	1	yes	characteristic
266	D₁₃	—	8	2	no	—
267	C₂⁴	—	26	1	no	—
268	C₂×Q₈	—	2	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	2	1	no	—
273	C₂×Q₈	C₈×D₁₃	1	2	yes	—
274	C₂×D₄	—	13	2	no	—
275	C₂×D₄	—	26	1	no	—
276	C₂×D₄	—	26	1	no	—
277	C₂×D₄	—	26	1	no	—
278	C₂×D₄	—	26	1	no	—
279	C₂×D₄	—	26	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	13	2	no	—
283	C₂²×C₄	—	13	2	no	—
284	C₂²×C₄	—	26	1	no	—
285	C₂²×C₄	—	52	1	no	—
286	C₂²×C₄	—	52	2	no	—
287	C₂²×C₄	—	52	2	no	—
288	C₂²×C₄	—	52	1	no	—
289	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
290	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
291	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	26	2	no	—
297	C₂×C₈	—	52	2	no	—
298	C₂×C₈	—	52	2	no	—
299	C₂×C₈	—	52	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	26	1	no	—
305	C₄⋊C₄	—	26	1	no	—
306	C₂²⋊C₄	—	26	8	no	—
307	C₂²⋊C₄	—	52	4	no	—
308	C₂²⋊C₄	—	52	1	no	—
309	C₂²⋊C₄	—	52	1	no	—
310	C₄²	—	4	1	no	—
311	C₄²	—	4	1	no	—
312	C₄²	—	13	2	no	—
313	C₄²	—	13	2	no	—
314	C₄²	—	26	1	no	—
315	C₄²	—	26	1	no	—
316	C₄²	—	26	2	no	—
317	C₄²	—	26	2	no	—
318	C₄²	—	52	2	no	—
319	C₄²	#6127	1	1	yes	characteristic
320	C₄²	D₄×D₁₃	1	1	yes	characteristic
321	C₄²	#6129	1	1	yes	characteristic
322	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
323	C₁₃	#9640	1	1	yes	characteristic, complemented, Sylow
324	C₂³	—	26	2	no	—
325	C₂³	—	52	2	no	—
326	C₂³	—	52	2	no	—
327	C₂³	—	52	1	no	—
328	C₂³	—	52	1	no	—
329	C₂³	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
330	Q₈	—	2	2	no	—
331	Q₈	—	2	2	no	—
332	Q₈	—	4	1	no	—
333	Q₈	—	4	1	no	—
334	D₄	—	26	2	no	—
335	D₄	—	26	2	no	—
336	D₄	—	52	1	no	—
337	D₄	—	52	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	13	4	no	—
345	C₂×C₄	—	26	2	no	—
346	C₂×C₄	—	26	2	no	—
347	C₂×C₄	—	26	2	no	—
348	C₂×C₄	—	26	2	no	—
349	C₂×C₄	—	26	2	no	—
350	C₂×C₄	—	52	2	no	—
351	C₂×C₄	—	52	1	no	—
352	C₂×C₄	—	104	2	no	—
353	C₂×C₄	—	104	1	no	—
354	C₂×C₄	—	104	1	no	—
355	C₂×C₄	#88135	1	1	yes	characteristic
356	C₂×C₄	#88138	1	1	yes	characteristic
357	C₂×C₄	#88139	1	1	yes	characteristic
358	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
359	C₂×C₄	#88155	1	1	yes	characteristic
360	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
361	C₂×C₄	#88161	1	1	yes	characteristic
362	C₂×C₄	#88168	1	2	yes	—
363	C₂×C₄	#88172	1	2	yes	—
364	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
365	C₂×C₄	#88193	1	1	yes	characteristic
366	C₂×C₄	#88194	1	1	yes	characteristic
367	C₈	—	4	2	no	—
368	C₈	—	8	1	no	—
369	C₈	—	52	2	no	—
370	C₈	—	104	1	no	—
371	C₂²	—	52	4	no	—
372	C₂²	—	52	2	no	—
373	C₂²	—	104	1	no	—
374	C₂²	—	104	1	no	—
375	C₂²	—	104	2	no	—
376	C₂²	D₁₃×C₂²⋊C₈	1	1	yes	characteristic
377	C₂²	#11718388	1	1	yes	characteristic
378	C₂²	#11718464	1	2	yes	—
379	C₂²	#11718482	1	2	yes	—
380	C₂²	#11718618	1	1	yes	characteristic
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	1	no	—
385	C₄	—	26	4	no	—
386	C₄	—	52	2	no	—
387	C₄	—	104	1	no	—
388	C₄	#11718386	1	1	yes	characteristic
389	C₄	#11718390	1	1	yes	characteristic
390	C₄	#11718456	1	2	yes	—
391	C₄	C₈×C₂²⋊D₁₃	1	1	yes	characteristic
392	C₄	#11718789	1	1	yes	characteristic
393	C₄	#11718837	1	1	yes	characteristic
394	C₄	#11718851	1	1	yes	characteristic
395	C₂	—	104	2	no	—
396	C₂	#13113222	1	2	yes	—
397	C₂	#13113300	1	2	yes	—
398	C₂	#13115628	1	1	yes	characteristic
399	C₂	#13115649	1	1	yes	characteristic
400	C₂	#13115666	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×Q₈⋊C₈	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₅₂	C₂×C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×Q₈⋊C₈	D₁₃
hypocenter	C₁₃	#9640
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. #13114987	C₂	semidirect
3. #13114581	C₂	semidirect
4. C₂×Q₈⋊#1055	C₂	semidirect
7. C₂×C₁₃×Q₈⋊C₈	C₂	semidirect
41. #88201	C₈	semidirect
128. C₂×Q₈⋊C₈	D₁₃	semidirect
323. C₁₃	#9640	semidirect

Maximal subgroups

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

subgroup	index
C₄×#88201	2
#13114987	2
#13114581	2
C₂×Q₈⋊#1055	2
C₂×#11718051	2
C₂×#11718075	2
C₂×C₁₃×Q₈⋊C₈	2
#9640	13