Subgroups — #16019696

Order 3328.

652 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13127979	C₂	1	2	yes	maximal, complemented
2	#13126641	C₂	1	1	yes	maximal, characteristic, complemented
3	#13126636	C₂	1	1	yes	maximal, characteristic, complemented
4	#13117092	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116967	C₂	1	2	yes	maximal, complemented
6	#13116917	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116912	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116808	C₂	1	2	yes	maximal, complemented
9	#13116801	C₂	1	2	yes	maximal, complemented
10	#13116674	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2178	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719476	C₂²	1	2	yes	complemented
13	#11719474	C₂²	1	2	yes	—
14	#11719458	—	2	1	no	—
15	#11719457	—	2	1	no	—
16	C₁₃×#508	C₂²	1	1	yes	characteristic
17	C₁₃×#443	C₂²	1	1	yes	characteristic
18	C₁₃×#443	C₂²	1	1	yes	characteristic, complemented
19	#11718856	C₂²	1	2	yes	—
20	#11718854	C₂²	1	2	yes	complemented
21	#11718804	—	2	1	no	—
22	#11718803	—	2	1	no	—
23	#11718579	—	2	2	no	—
24	#11718577	—	2	2	no	—
25	D₁₃×SD₃₂	—	2	2	no	—
26	#11718572	—	2	2	no	—
27	C₂×#88040	C₂²	1	2	yes	complemented
28	C₂×#88040	C₂²	1	2	yes	complemented
29	#11718562	C₂²	1	2	yes	complemented
30	#11718558	C₂²	1	2	yes	—
31	#11718557	C₂²	1	2	yes	complemented
32	#11718487	—	2	2	no	—
33	#11718483	—	2	2	no	—
34	#11718361	C₂²	1	1	yes	characteristic
35	#11718360	C₂²	1	1	yes	characteristic, complemented
36	#11718356	C₂²	1	1	yes	characteristic
37	C₁₃×#368	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#359	C₂²	1	1	yes	characteristic
39	C₁₃×#359	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
41	#11718100	C₂²	1	2	yes	complemented
42	#11718088	C₂²	1	2	yes	complemented
43	#11718087	C₂²	1	2	yes	complemented
44	#11718055	C₂²	1	1	yes	characteristic, complemented
45	#88257	—	2	2	no	—
46	#88256	—	2	2	no	—
47	C₁₃×#135	C₂³	1	1	yes	characteristic
48	C₁₃×#135	C₂³	1	1	yes	characteristic
49	C₁₃×#131	—	2	1	no	—
50	C₁₃×#131	—	2	1	no	—
51	#88205	—	2	2	no	—
52	#88203	—	2	2	no	—
53	#88173	—	2	2	no	—
54	Q₁₆×D₁₃	—	2	2	no	—
55	#88169	—	4	2	no	—
56	#88168	—	4	2	no	—
57	#88166	—	2	2	no	—
58	D₈×D₁₃	—	2	2	no	—
59	#88163	—	2	2	no	—
60	#88163	—	4	2	no	—
61	#88162	—	2	2	no	—
62	#88162	—	4	2	no	—
63	C₂×Dic₅₂	—	2	1	no	—
64	C₂×Dic₅₂	—	4	1	no	—
65	C₂×Dic₅₂	C₂³	1	2	yes	—
66	#88158	—	4	1	no	—
67	#88158	—	4	1	no	—
68	#88158	D₄	1	1	yes	characteristic
69	C₂×D₁₀₄	—	2	1	no	—
70	C₂×D₁₀₄	—	4	1	no	—
71	C₂×D₁₀₄	C₂³	1	2	yes	—
72	#88155	C₂³	1	2	yes	—
73	#88128	—	2	1	no	—
74	#88123	—	2	1	no	—
75	C₁₃×Q₃₂	D₄	1	1	yes	characteristic, complemented
76	C₁₃×SD₃₂	D₄	1	1	yes	characteristic, complemented
77	C₁₃×SD₃₂	D₄	1	1	yes	characteristic, complemented
78	C₁₃×D₁₆	D₄	1	1	yes	characteristic, complemented
79	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
81	C₁₃×#108	C₂³	1	1	yes	characteristic
82	C₁₃×#108	C₂³	1	1	yes	characteristic
83	C₁₃×#104	—	2	1	no	—
84	C₁₃×#104	—	2	1	no	—
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	#88069	—	2	2	no	—
87	#88068	—	2	2	no	—
88	#88067	—	2	2	no	—
89	#88066	—	2	2	no	—
90	#88064	—	2	2	no	—
91	#88063	—	2	2	no	—
92	#88059	D₄	1	1	yes	characteristic
93	#88052	C₂³	1	2	yes	—
94	#88045	D₄	1	2	yes	—
95	#88040	—	2	2	no	—
96	#88040	—	2	2	no	—
97	#88040	—	4	2	no	—
98	#88038	—	2	2	no	—
99	C₁₆×D₁₃	—	2	2	no	—
100	#33856	—	13	1	no	maximal, Sylow
101	C₁₃×#41	—	2	1	no	—
102	C₁₃×#41	—	2	1	no	—
103	#6131	—	4	2	no	—
104	Q₈×D₁₃	—	4	2	no	—
105	#6129	—	4	2	no	—
106	#6129	—	8	2	no	—
107	D₄×D₁₃	—	4	2	no	—
108	D₄×D₁₃	—	8	2	no	—
109	#6127	—	4	2	no	—
110	#6127	—	4	2	no	—
111	#6127	C₂×D₄	1	2	yes	—
112	C₂×D₅₂	—	2	2	no	—
113	C₂×D₅₂	—	4	2	no	—
114	C₂×D₅₂	—	8	1	no	—
115	C₂×Dic₂₆	—	2	2	no	—
116	C₂×Dic₂₆	—	4	2	no	—
117	C₁₃×Q₁₆	C₂×D₄	1	1	yes	characteristic
118	C₁₃×Q₁₆	C₂×D₄	1	1	yes	characteristic
119	C₁₃×SD₁₆	—	2	1	no	—
120	C₁₃×SD₁₆	—	2	1	no	—
121	C₁₃×D₈	C₂×D₄	1	1	yes	characteristic
122	C₁₃×D₈	C₂×D₄	1	1	yes	characteristic
123	C₁₃×M₁₆	—	2	1	no	—
124	C₁₃×M₁₆	—	2	1	no	—
125	C₁₃×M₁₆	—	4	1	no	—
126	C₁₃×M₁₆	—	4	1	no	—
127	C₂×C₈×C₁₃	—	4	1	no	—
128	C₂×C₈×C₁₃	—	4	1	no	—
129	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
132	#6107	—	4	2	no	—
133	#6106	—	4	2	no	—
134	#6105	—	4	2	no	—
135	#6104	—	4	2	no	—
136	C₄⋊Dic₁₃	—	8	1	no	—
137	#6099	C₂×D₄	1	2	yes	—
138	Dic₅₂	—	2	2	no	—
139	Dic₅₂	—	2	2	no	—
140	Dic₅₂	—	4	2	no	—
141	Dic₅₂	—	4	1	no	—
142	Dic₅₂	—	4	1	no	—
143	Dic₅₂	D₈	1	1	yes	characteristic
144	D₁₀₄	—	2	2	no	—
145	D₁₀₄	—	2	2	no	—
146	D₁₀₄	—	4	2	no	—
147	D₁₀₄	—	4	1	no	—
148	D₁₀₄	—	4	1	no	—
149	D₁₀₄	D₈	1	1	yes	characteristic
150	#6095	—	4	2	no	—
151	#6095	—	4	2	no	—
152	#6095	D₈	1	2	yes	—
153	#6094	—	2	2	no	—
154	C₈×D₁₃	—	2	2	no	—
155	C₁₃×C₁₆	—	2	1	no	—
156	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
157	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
158	#6090	—	2	2	no	—
159	#3416	—	13	2	no	—
160	#3293	—	13	1	no	—
161	#3292	—	13	1	no	—
162	#2248	—	13	1	no	—
163	#2223	—	13	2	no	—
164	#2214	—	13	1	no	—
165	#2213	—	13	1	no	—
166	#2194	—	13	2	no	—
167	#2193	—	13	2	no	—
168	#2178	D₁₃	1	1	yes	characteristic, complemented
169	#2170	—	13	1	no	—
170	C₂²×D₁₃	—	4	2	no	—
171	C₂²×D₁₃	—	8	2	no	—
172	Q₈×C₁₃	—	2	1	no	—
173	Q₈×C₁₃	—	2	1	no	—
174	D₄×C₁₃	—	2	1	no	—
175	D₄×C₁₃	—	2	1	no	—
176	D₄×C₁₃	—	4	1	no	—
177	D₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	C₂²⋊D₁₃	—	2	2	no	—
183	C₂²⋊D₁₃	—	8	2	no	—
184	C₂²⋊D₁₃	—	8	2	no	—
185	C₂×Dic₁₃	—	4	2	no	—
186	C₂×Dic₁₃	—	8	2	no	—
187	D₅₂	—	4	2	no	—
188	D₅₂	—	4	2	no	—
189	D₅₂	—	8	2	no	—
190	D₅₂	—	16	2	no	—
191	D₅₂	C₂×D₈	1	2	yes	—
192	C₄×D₁₃	—	2	2	no	—
193	C₄×D₁₃	—	8	2	no	—
194	C₄×D₁₃	—	8	2	no	—
195	Dic₂₆	—	4	2	no	—
196	Dic₂₆	—	4	2	no	—
197	Dic₂₆	—	8	2	no	—
198	Dic₂₆	C₂×D₈	1	2	yes	—
199	C₈×C₁₃	—	4	1	no	—
200	C₈×C₁₃	—	4	1	no	—
201	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
202	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
203	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
205	#1055	—	2	2	no	—
206	#578	—	13	2	no	—
207	#578	—	26	1	no	—
208	#576	—	13	2	no	—
209	#576	—	26	1	no	—
210	#510	—	13	2	no	—
211	#510	—	26	2	no	—
212	#509	—	13	2	no	—
213	#509	—	26	2	no	—
214	#508	—	26	2	no	—
215	#508	C₂×D₁₃	1	1	yes	characteristic
216	C₂×SD₃₂	—	13	2	no	—
217	C₂×SD₃₂	—	13	2	no	—
218	C₂×SD₃₂	—	26	2	no	—
219	#504	—	13	2	no	—
220	#494	—	13	1	no	—
221	#493	—	13	1	no	—
222	#473	—	13	2	no	—
223	#473	—	26	1	no	—
224	#472	—	13	2	no	—
225	#472	—	26	1	no	—
226	#456	—	26	2	no	—
227	#453	—	26	2	no	—
228	#443	—	13	1	no	—
229	#443	C₂×D₁₃	1	1	yes	characteristic
230	#443	C₂×D₁₃	1	1	yes	characteristic, complemented
231	#368	C₂×D₁₃	1	1	yes	characteristic, complemented
232	#364	—	13	1	no	—
233	#362	—	13	2	no	—
234	#361	—	13	2	no	—
235	#359	C₂×D₁₃	1	1	yes	characteristic
236	#359	C₂×D₁₃	1	1	yes	characteristic, complemented
237	#350	—	13	2	no	—
238	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
239	C₂²×C₁₃	—	4	1	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	#576	1	1	yes	characteristic
242	C₂×D₁₃	—	2	2	no	—
243	C₂×D₁₃	—	8	2	no	—
244	C₂×D₁₃	—	16	2	no	—
245	C₂×D₁₃	—	32	2	no	—
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	—	4	1	no	—
248	C₄×C₁₃	—	4	1	no	—
249	C₄×C₁₃	D₄²	1	1	yes	characteristic
250	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
251	Dic₁₃	—	2	2	no	—
252	Dic₁₃	—	8	2	no	—
253	2₋¹⁺⁴	—	26	2	no	—
254	H(5,𝔽₂)	—	26	2	no	—
255	#137	—	26	2	no	—
256	#137	—	26	2	no	—
257	#137	—	52	2	no	—
258	#137	—	52	2	no	—
259	AGL(1,ℤ/8)	—	26	2	no	—
260	AGL(1,ℤ/8)	—	26	2	no	—
261	AGL(1,ℤ/8)	—	52	2	no	—
262	AGL(1,ℤ/8)	—	52	2	no	—
263	#135	—	13	1	no	—
264	#135	—	26	2	no	—
265	#135	—	26	2	no	—
266	#135	—	52	1	no	—
267	#135	—	52	1	no	—
268	#135	C₂²×D₁₃	1	1	yes	characteristic
269	#135	C₂²×D₁₃	1	1	yes	characteristic
270	C₂×Q₁₆	—	13	2	no	—
271	C₂×Q₁₆	—	26	2	no	—
272	C₂×Q₁₆	—	26	1	no	—
273	C₂×Q₁₆	—	52	1	no	—
274	C₂×D₈	—	13	2	no	—
275	C₂×D₈	—	26	2	no	—
276	C₂×D₈	—	26	1	no	—
277	C₂×D₈	—	52	1	no	—
278	#131	—	2	1	no	—
279	#131	—	2	1	no	—
280	#131	—	13	2	no	—
281	C₄⋊Q₈	—	26	1	no	—
282	#127	—	26	1	no	—
283	Q₃₂	—	26	2	no	—
284	Q₃₂	D₅₂	1	1	yes	characteristic, complemented
285	SD₃₂	—	26	2	no	—
286	SD₃₂	—	26	2	no	—
287	SD₃₂	—	26	2	no	—
288	SD₃₂	—	26	2	no	—
289	SD₃₂	—	52	2	no	—
290	SD₃₂	D₅₂	1	1	yes	characteristic, complemented
291	SD₃₂	D₅₂	1	1	yes	characteristic, complemented
292	D₁₆	—	26	2	no	—
293	D₁₆	D₅₂	1	1	yes	characteristic, complemented
294	M₃₂	—	13	2	no	—
295	M₃₂	—	26	2	no	—
296	C₂×C₁₆	—	26	2	no	—
297	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
298	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
299	#108	—	13	1	no	—
300	#108	C₂²×D₁₃	1	1	yes	characteristic
301	#108	C₂²×D₁₃	1	1	yes	characteristic
302	#104	—	2	1	no	—
303	#104	—	2	1	no	—
304	#104	—	13	2	no	—
305	#101	—	26	2	no	—
306	#100	—	26	2	no	—
307	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
308	C₂×C₁₃	—	2	1	no	—
309	C₂×C₁₃	—	8	1	no	—
310	C₂×C₁₃	—	8	1	no	—
311	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
312	D₁₃	—	4	2	no	—
313	D₁₃	—	16	2	no	—
314	#41	—	2	1	no	—
315	#41	—	2	1	no	—
316	#41	—	13	2	no	—
317	#41	—	52	2	no	—
318	#41	—	52	2	no	—
319	#41	—	52	2	no	—
320	#41	—	52	2	no	—
321	#41	—	104	2	no	—
322	C₂×Q₈	—	26	2	no	—
323	C₂×Q₈	—	52	2	no	—
324	C₂×Q₈	—	52	2	no	—
325	C₂×D₄	—	26	2	no	—
326	C₂×D₄	—	52	2	no	—
327	C₂×D₄	—	52	2	no	—
328	C₂×D₄	—	104	1	no	—
329	C₂×D₄	—	104	2	no	—
330	Q₁₆	—	13	1	no	—
331	Q₁₆	—	26	2	no	—
332	Q₁₆	—	26	2	no	—
333	Q₁₆	—	52	2	no	—
334	Q₁₆	—	52	2	no	—
335	Q₁₆	—	52	1	no	—
336	Q₁₆	—	52	1	no	—
337	Q₁₆	C₂×D₅₂	1	1	yes	characteristic
338	Q₁₆	C₂×D₅₂	1	1	yes	characteristic
339	SD₁₆	—	2	1	no	—
340	SD₁₆	—	2	1	no	—
341	SD₁₆	—	13	2	no	—
342	SD₁₆	—	52	2	no	—
343	SD₁₆	—	52	2	no	—
344	SD₁₆	—	52	2	no	—
345	SD₁₆	—	52	2	no	—
346	D₈	—	13	1	no	—
347	D₈	—	26	2	no	—
348	D₈	—	26	2	no	—
349	D₈	—	52	2	no	—
350	D₈	—	52	2	no	—
351	D₈	—	52	1	no	—
352	D₈	—	52	1	no	—
353	D₈	C₂×D₅₂	1	1	yes	characteristic
354	D₈	C₂×D₅₂	1	1	yes	characteristic
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	1	no	—
357	M₁₆	—	4	1	no	—
358	M₁₆	—	4	1	no	—
359	M₁₆	—	13	2	no	—
360	M₁₆	—	26	2	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	26	2	no	—
364	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
365	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
366	C₄⋊C₄	—	104	1	no	—
367	C₄²	D₄×D₁₃	1	1	yes	characteristic
368	C₁₆	—	2	1	no	—
369	C₁₆	—	26	2	no	—
370	C₁₆	C₂×D₅₂	1	1	yes	characteristic
371	C₁₆	C₂×D₅₂	1	1	yes	characteristic
372	C₁₃	#33856	1	1	yes	characteristic, complemented, Sylow
373	C₂³	—	52	2	no	—
374	C₂³	—	104	2	no	—
375	Q₈	—	2	1	no	—
376	Q₈	—	2	1	no	—
377	Q₈	—	13	2	no	—
378	Q₈	—	52	2	no	—
379	Q₈	—	52	2	no	—
380	Q₈	—	104	2	no	—
381	D₄	—	2	1	no	—
382	D₄	—	2	1	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	13	2	no	—
386	D₄	—	26	2	no	—
387	D₄	—	52	2	no	—
388	D₄	—	52	2	no	—
389	D₄	—	104	2	no	—
390	D₄	—	104	2	no	—
391	D₄	—	104	2	no	—
392	D₄	—	208	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	26	2	no	—
397	C₂×C₄	—	52	2	no	—
398	C₂×C₄	—	104	2	no	—
399	C₂×C₄	—	104	2	no	—
400	C₂×C₄	—	104	2	no	—
401	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
402	C₈	—	4	1	no	—
403	C₈	—	4	1	no	—
404	C₈	—	26	2	no	—
405	C₈	D₈×D₁₃	1	1	yes	characteristic
406	C₈	D₈×D₁₃	1	1	yes	characteristic
407	C₈	C₂²×D₅₂	1	1	yes	characteristic
408	C₈	#88256	1	1	yes	characteristic
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	26	2	no	—
412	C₂²	—	104	2	no	—
413	C₂²	—	416	2	no	—
414	C₂²	—	208	2	no	—
415	C₂²	#11719474	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	26	2	no	—
420	C₄	—	104	2	no	—
421	C₄	D₄×D₅₂	1	1	yes	characteristic
422	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	8	1	no	—
425	C₂	—	8	1	no	—
426	C₂	—	52	2	no	—
427	C₂	—	208	2	no	—
428	C₂	D₈×D₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₅₂
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2178	C₂
socle	C₂×C₁₃	D₄×D₈
hypercenter	#2178	D₁₃
hypocenter	C₁₃	#33856
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2178

Complements

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

N	H ≅ G/N	type
1. #13127979	C₂	semidirect
2. #13126641	C₂	semidirect
3. #13126636	C₂	semidirect
4. #13117092	C₂	semidirect
5. #13116967	C₂	semidirect
6. #13116917	C₂	semidirect
7. #13116912	C₂	semidirect
8. #13116808	C₂	semidirect
9. #13116801	C₂	semidirect
10. #13116674	C₂	semidirect
11. C₁₃×#2178	C₂	semidirect
12. #11719476	C₂²	semidirect
18. C₁₃×#443	C₂²	semidirect
20. #11718854	C₂²	semidirect
27. C₂×#88040	C₂²	semidirect
28. C₂×#88040	C₂²	semidirect
29. #11718562	C₂²	semidirect
31. #11718557	C₂²	semidirect
35. #11718360	C₂²	semidirect
37. C₁₃×#368	C₂²	semidirect
39. C₁₃×#359	C₂²	semidirect
40. C₄×C₁₃×C₁₆	C₂²	semidirect
41. #11718100	C₂²	semidirect
42. #11718088	C₂²	semidirect
43. #11718087	C₂²	semidirect
44. #11718055	C₂²	semidirect
75. C₁₃×Q₃₂	D₄	semidirect
76. C₁₃×SD₃₂	D₄	semidirect
77. C₁₃×SD₃₂	D₄	semidirect
78. C₁₃×D₁₆	D₄	semidirect
168. #2178	D₁₃	semidirect
230. #443	C₂×D₁₃	semidirect
231. #368	C₂×D₁₃	semidirect
236. #359	C₂×D₁₃	semidirect
238. C₄×C₁₆	C₂×D₁₃	semidirect
284. Q₃₂	D₅₂	semidirect
290. SD₃₂	D₅₂	semidirect
291. SD₃₂	D₅₂	semidirect
293. D₁₆	D₅₂	semidirect
372. C₁₃	#33856	semidirect

Maximal subgroups

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

subgroup	index
#13127979	2
#13126641	2
#13126636	2
#13117092	2
#13116967	2
#13116917	2
#13116912	2
#13116808	2
#13116801	2
#13116674	2
C₁₃×#2178	2
#33856	13