Subgroups — #16017994

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125415	C₂	1	1	yes	maximal, characteristic, complemented
2	#13117027	C₂	1	2	yes	maximal, complemented
3	#13116978	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116973	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116876	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116871	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116759	C₂	1	2	yes	maximal, complemented
8	#13116710	C₂	1	2	yes	maximal, complemented
9	#13116698	C₂	1	2	yes	maximal, complemented
10	#13116639	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×#41	—	2	1	no	—
14	#11719182	—	2	1	no	—
15	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×SD₁₆	—	2	1	no	—
18	C₄×C₁₃×SD₁₆	—	2	1	no	—
19	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₁₃×#427	C₂²	1	1	yes	characteristic
22	C₁₃×#416	—	2	1	no	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×#88068	C₂²	1	2	yes	—
25	C₂×#88066	C₂²	1	2	yes	—
26	#11718776	—	2	1	no	—
27	#11718776	C₂²	1	2	yes	—
28	#11718356	C₂²	1	1	yes	characteristic
29	#11718355	—	2	1	no	—
30	C₄×D₁₀₄	—	2	1	no	—
31	C₄×D₁₀₄	C₂²	1	2	yes	—
32	#11718343	C₂²	1	1	yes	characteristic
33	#11718156	C₂²	1	2	yes	—
34	#11718154	C₂²	1	2	yes	—
35	C₂²⋊#6090	C₂²	1	2	yes	—
36	#11718083	C₂²	1	2	yes	—
37	#11718083	C₂²	1	2	yes	—
38	#11718082	C₂²	1	2	yes	—
39	#11718081	C₂²	1	2	yes	—
40	C₄⋊#6090	C₂²	1	1	yes	characteristic
41	C₄⋊#6090	C₂²	1	1	yes	characteristic
42	#11718053	C₂²	1	2	yes	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×#6127	—	4	1	no	—
45	C₁₃×#135	—	2	2	no	—
46	C₁₃×#135	—	2	2	no	—
47	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×SD₁₆	—	2	1	no	—
49	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	—	2	1	no	—
53	C₄×Q₈×C₁₃	—	2	1	no	—
54	C₄×D₄×C₁₃	—	2	1	no	—
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	—	4	1	no	—
57	C₄×D₄×C₁₃	—	4	1	no	—
58	C₁₃×#117	—	2	1	no	—
59	C₁₃×#117	—	4	1	no	—
60	C₂×C₄²×C₁₃	—	4	1	no	—
61	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
62	#88184	—	2	2	no	—
63	#88184	—	4	1	no	—
64	C₂×D₁₀₄	—	2	1	no	—
65	C₂×D₁₀₄	C₂³	1	2	yes	—
66	#88129	—	4	1	no	—
67	#88128	—	2	1	no	—
68	C₄×D₅₂	—	2	2	no	—
69	C₄×D₅₂	—	4	1	no	—
70	#88123	—	2	1	no	—
71	C₁₃×#107	C₂³	1	1	yes	characteristic
72	C₁₃×#107	C₂³	1	1	yes	characteristic
73	C₁₃×#106	—	2	1	no	—
74	C₁₃×#103	—	2	1	no	—
75	C₁₃×#103	—	2	1	no	—
76	C₁₃×#102	—	2	1	no	—
77	C₁₃×#102	—	2	1	no	—
78	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	#88068	—	2	4	no	—
83	#88066	—	2	4	no	—
84	#88061	—	2	2	no	—
85	#88061	—	2	2	no	—
86	#88058	—	2	1	no	—
87	#88058	C₂³	1	2	yes	—
88	C₂×#6090	C₂³	1	2	yes	—
89	C₂×#6090	C₂³	1	2	yes	—
90	#33675	—	13	1	no	maximal, Sylow
91	C₁₃×#41	—	2	4	no	—
92	C₁₃×#41	—	4	2	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	4	1	no	—
96	C₂²×C₄×C₁₃	—	4	1	no	—
97	C₂²×C₄×C₁₃	—	4	1	no	—
98	C₂²×C₄×C₁₃	—	4	1	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	2	no	—
103	#6127	—	8	4	no	—
104	C₂×D₅₂	—	2	2	no	—
105	C₂×D₅₂	—	4	1	no	—
106	C₂×D₅₂	—	4	1	no	—
107	C₂×C₄×D₁₃	—	4	2	no	—
108	C₂×Dic₂₆	—	4	1	no	—
109	C₁₃×Q₁₆	—	2	1	no	—
110	C₁₃×Q₁₆	#41	1	2	yes	complemented
111	C₁₃×SD₁₆	—	2	4	no	—
112	C₁₃×D₈	—	2	1	no	—
113	C₁₃×D₈	#41	1	2	yes	complemented
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	4	1	no	—
117	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₁₃×C₄⋊C₄	—	2	1	no	—
122	C₁₃×C₄⋊C₄	—	2	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₄⋊C₄	—	4	1	no	—
125	C₁₃×C₂²⋊C₄	—	4	1	no	—
126	C₁₃×C₂²⋊C₄	—	4	1	no	—
127	C₁₃×C₂²⋊C₄	—	4	1	no	—
128	C₄²×C₁₃	—	4	1	no	—
129	C₄²×C₁₃	—	4	1	no	—
130	C₄²×C₁₃	—	4	1	no	—
131	C₄²×C₁₃	D₈	1	1	yes	characteristic
132	C₄²×C₁₃	D₈	1	1	yes	characteristic
133	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
135	#6103	—	4	2	no	—
136	#6103	—	4	2	no	—
137	C₄⋊Dic₁₃	—	2	2	no	—
138	C₄⋊Dic₁₃	—	4	1	no	—
139	D₁₀₄	—	2	2	no	—
140	D₁₀₄	—	2	2	no	—
141	D₁₀₄	—	4	2	no	—
142	#6090	—	2	2	no	—
143	#6090	—	2	2	no	—
144	#3169	—	13	1	no	—
145	C₄×#135	D₁₃	1	1	yes	characteristic, complemented
146	#2234	—	13	2	no	—
147	#2225	—	13	1	no	—
148	#2224	—	13	1	no	—
149	#2207	—	13	1	no	—
150	#2206	—	13	1	no	—
151	#2186	—	13	2	no	—
152	#2177	—	13	2	no	—
153	#2175	—	13	2	no	—
154	#2163	—	13	1	no	—
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
157	C₂²×D₁₃	—	4	2	no	—
158	Q₈×C₁₃	—	2	2	no	—
159	Q₈×C₁₃	—	4	1	no	—
160	D₄×C₁₃	—	2	2	no	—
161	D₄×C₁₃	—	4	4	no	—
162	D₄×C₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	4	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	8	2	no	—
172	C₂×C₄×C₁₃	—	8	2	no	—
173	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	C₂²⋊D₁₃	—	8	4	no	—
180	C₂×Dic₁₃	—	4	2	no	—
181	D₅₂	—	4	2	no	—
182	D₅₂	—	4	2	no	—
183	D₅₂	—	8	2	no	—
184	D₅₂	—	8	2	no	—
185	C₄×D₁₃	—	8	4	no	—
186	Dic₂₆	—	8	2	no	—
187	C₈×C₁₃	—	2	1	no	—
188	C₈×C₁₃	—	2	1	no	—
189	C₈×C₁₃	—	2	1	no	—
190	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
191	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
192	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
193	#532	—	26	1	no	—
194	C₄×#41	—	2	1	no	—
195	C₂×SD₃₂	—	13	2	no	—
196	C₂×D₁₆	—	13	2	no	—
197	#500	—	13	1	no	—
198	#493	—	13	1	no	—
199	#486	—	26	1	no	—
200	#466	—	13	2	no	—
201	#466	—	26	1	no	—
202	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
203	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
204	C₄×SD₁₆	—	2	1	no	—
205	C₄×SD₁₆	—	2	1	no	—
206	C₄×D₈	—	13	2	no	—
207	C₄×D₈	—	26	1	no	—
208	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
209	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
210	#427	C₂×D₁₃	1	1	yes	characteristic
211	#416	—	2	1	no	—
212	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
213	#367	—	13	2	no	—
214	#366	—	13	2	no	—
215	C₄⋊C₁₆	—	13	1	no	—
216	C₄⋊C₁₆	—	13	1	no	—
217	#358	—	13	2	no	—
218	#357	—	13	2	no	—
219	#357	—	13	2	no	—
220	#357	—	13	2	no	—
221	C₂²⋊C₁₆	—	13	2	no	—
222	#346	—	13	2	no	—
223	C₂²×C₁₃	—	2	1	no	—
224	C₂²×C₁₃	—	2	1	no	—
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	4	2	no	—
227	C₂²×C₁₃	—	8	1	no	—
228	C₂²×C₁₃	—	8	1	no	—
229	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
230	C₂×D₁₃	—	8	2	no	—
231	C₂×D₁₃	—	8	2	no	—
232	C₂×D₁₃	—	8	2	no	—
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	2	1	no	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	8	1	no	—
239	C₄×C₁₃	—	8	1	no	—
240	C₄×C₁₃	#509	1	2	yes	—
241	C₄×C₁₃	#525	1	1	yes	characteristic
242	C₄×C₁₃	#575	1	1	yes	characteristic
243	Dic₁₃	—	8	2	no	—
244	C₂×#41	—	2	1	no	—
245	C₂×#41	—	52	1	no	—
246	#135	—	2	2	no	—
247	#135	—	2	2	no	—
248	C₂×Q₁₆	C₂²×D₁₃	1	1	yes	characteristic
249	C₂×SD₁₆	—	2	1	no	—
250	C₂×D₈	—	13	2	no	—
251	C₂×D₈	—	26	1	no	—
252	C₂×D₈	C₂²×D₁₃	1	1	yes	characteristic
253	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
254	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
255	C₄⋊Q₈	—	26	1	no	—
256	#127	—	26	1	no	—
257	#124	—	52	1	no	—
258	#121	—	26	2	no	—
259	#121	—	52	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	4	1	no	—
265	C₄×D₄	—	4	1	no	—
266	C₄×D₄	—	26	2	no	—
267	C₄×D₄	—	52	1	no	—
268	#117	—	2	1	no	—
269	#117	—	4	1	no	—
270	C₂×C₄²	—	4	1	no	—
271	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
272	SD₃₂	—	26	4	no	—
273	D₁₆	—	26	4	no	—
274	C₂×C₁₆	—	13	2	no	—
275	C₂×C₁₆	—	13	2	no	—
276	#107	—	13	2	no	—
277	#107	—	26	1	no	—
278	#107	C₂²×D₁₃	1	1	yes	characteristic
279	#107	C₂²×D₁₃	1	1	yes	characteristic
280	#106	—	2	1	no	—
281	#103	—	2	1	no	—
282	#103	—	2	1	no	—
283	#102	—	2	1	no	—
284	#102	—	2	1	no	—
285	#102	—	26	2	no	—
286	#102	—	26	2	no	—
287	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
288	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
289	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
291	C₂×C₁₃	—	4	1	no	—
292	C₂×C₁₃	—	8	2	no	—
293	C₂×C₁₃	#3100	1	1	yes	characteristic
294	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
295	C₂×C₁₃	#3414	1	1	yes	characteristic
296	D₁₃	—	16	2	no	—
297	#41	—	2	4	no	—
298	#41	—	4	2	no	—
299	#41	—	104	4	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	52	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	26	2	no	—
305	C₂×D₄	—	52	2	no	—
306	C₂×D₄	—	52	1	no	—
307	C₂×D₄	—	52	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	52	2	no	—
312	C₂²×C₄	#6104	1	1	yes	characteristic
313	C₂²×C₄	#6104	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
315	Q₁₆	—	2	1	no	—
316	Q₁₆	#6127	1	2	yes	complemented
317	SD₁₆	—	2	4	no	—
318	D₈	—	2	1	no	—
319	D₈	—	26	2	no	—
320	D₈	—	26	2	no	—
321	D₈	—	52	2	no	—
322	D₈	#6127	1	2	yes	complemented
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
327	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
328	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
329	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	26	2	no	—
335	C₄⋊C₄	—	52	1	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	52	2	no	—
340	C₂²⋊C₄	—	52	2	no	—
341	C₄²	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	4	1	no	—
344	C₄²	#6104	1	1	yes	characteristic
345	C₄²	#6104	1	1	yes	characteristic
346	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
347	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
348	C₁₆	—	26	2	no	—
349	C₁₆	—	26	2	no	—
350	C₁₃	#33675	1	1	yes	characteristic, complemented, Sylow
351	C₂³	—	4	1	no	—
352	C₂³	—	52	2	no	—
353	C₂³	C₂×#6104	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	104	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	1	no	—
360	D₄	—	52	2	no	—
361	D₄	—	52	2	no	—
362	D₄	—	104	2	no	—
363	D₄	—	104	4	no	—
364	D₄	—	104	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	8	2	no	—
375	C₂×C₄	—	52	2	no	—
376	C₂×C₄	—	104	4	no	—
377	C₂×C₄	C₂×#6104	1	1	yes	characteristic
378	C₂×C₄	C₂×#6104	1	1	yes	characteristic
379	C₂×C₄	C₂×#6104	1	1	yes	characteristic
380	C₂×C₄	C₂×#6104	1	1	yes	characteristic
381	C₂×C₄	C₂×#6104	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	2	1	no	—
386	C₈	C₂×#6127	1	1	yes	characteristic
387	C₈	C₂×#6127	1	1	yes	characteristic
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	8	1	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	104	2	no	—
395	C₂²	—	104	2	no	—
396	C₂²	—	104	2	no	—
397	C₂²	C₂²×#6104	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	4	2	no	—
403	C₄	—	8	1	no	—
404	C₄	—	8	1	no	—
405	C₄	—	104	2	no	—
406	C₄	#11718854	1	2	yes	—
407	C₄	#11719496	1	1	yes	characteristic
408	C₄	#11719527	1	1	yes	characteristic
409	C₂	—	4	1	no	—
410	C₂	—	8	2	no	—
411	C₂	—	208	2	no	—
412	C₂	#13124836	1	1	yes	characteristic
413	C₂	C₂×#11718854	1	1	yes	characteristic
414	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	C₄×C₁₃×#135	C₂
socle	C₂²×C₁₃	C₂²×D₈
hypercenter	C₄×#135	D₁₃
hypocenter	C₁₃	#33675
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #13125415	C₂	semidirect
2. #13117027	C₂	semidirect
3. #13116978	C₂	semidirect
4. #13116973	C₂	semidirect
5. #13116876	C₂	semidirect
6. #13116871	C₂	semidirect
7. #13116759	C₂	semidirect
8. #13116710	C₂	semidirect
9. #13116698	C₂	semidirect
10. #13116639	C₂	semidirect
11. C₄×C₁₃×#135	C₂	semidirect
110. C₁₃×Q₁₆	#41	semidirect
113. C₁₃×D₈	#41	semidirect
145. C₄×#135	D₁₃	semidirect
316. Q₁₆	#6127	semidirect
322. D₈	#6127	semidirect
350. C₁₃	#33675	semidirect

Maximal subgroups

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

subgroup	index
#13125415	2
#13117027	2
#13116978	2
#13116973	2
#13116876	2
#13116871	2
#13116759	2
#13116710	2
#13116698	2
#13116639	2
C₄×C₁₃×#135	2
#33675	13