Subgroups — #108×D₅₂ #15881173

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₆×D₅₂	C₂	1	2	yes	maximal
2	C₂×C₈×D₅₂	C₂	1	1	yes	maximal, characteristic
3	C₂×D₁₃×#108	C₂	1	2	yes	maximal, complemented
4	#13115611	C₂	1	2	yes	maximal, complemented
5	#13115042	C₂	1	4	yes	maximal, complemented
6	#13115008	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114871	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×M₁₆×D₁₃	C₂²	1	4	yes	—
10	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
11	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	#11718787	C₂²	1	4	yes	—
17	C₂×#88062	C₂²	1	4	yes	—
18	C₂×#88060	C₂²	1	2	yes	—
19	C₂×#88059	C₂²	1	2	yes	—
20	C₂×#88059	C₂²	1	2	yes	—
21	#11718585	C₂²	1	2	yes	—
22	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
23	D₁₃×#108	—	2	8	no	—
24	#11718367	—	2	4	no	—
25	#11718349	—	2	2	no	—
26	C₈×D₅₂	—	2	2	no	—
27	C₈×D₅₂	C₄	1	4	yes	—
28	C₈×D₅₂	C₄	1	2	yes	—
29	C₈×D₅₂	C₄	1	2	yes	—
30	C₁₃×#341	C₂²	1	2	yes	—
31	#11718150	C₂²	1	4	yes	—
32	C₂²×D₅₂	Q₈	1	1	yes	characteristic
33	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
34	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
35	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
36	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
38	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
39	C₂×#6103	Q₈	1	2	yes	—
40	C₂×C₄⋊Dic₁₃	Q₈	1	1	yes	characteristic
41	C₂×#6099	C₂³	1	4	yes	—
42	C₂²×#1055	C₂³	1	2	yes	—
43	M₁₆×D₁₃	—	2	8	no	—
44	M₁₆×D₁₃	—	4	4	no	—
45	C₂×#6094	—	2	4	no	—
46	C₂×C₈×D₁₃	—	2	4	no	—
47	C₂×C₈×D₁₃	—	2	4	no	—
48	C₂×C₈×D₁₃	—	2	4	no	—
49	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
50	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
51	C₄×D₅₂	C₂×C₄	1	2	yes	—
52	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
53	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
54	C₄×D₅₂	D₄	1	1	yes	characteristic
55	C₄×D₅₂	D₄	1	1	yes	characteristic
56	C₄×D₅₂	D₄	1	2	yes	—
57	C₁₃×#108	—	2	2	no	—
58	C₁₃×#108	D₄	1	4	yes	complemented
59	C₁₃×#97	—	2	2	no	—
60	C₄×C₈×C₁₃	—	2	2	no	—
61	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
62	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
63	#88062	—	2	8	no	—
64	#88060	—	2	4	no	—
65	#88060	—	2	4	no	—
66	#88060	C₂×C₄	1	4	yes	—
67	#88060	C₂×C₄	1	4	yes	—
68	#88059	—	2	4	no	—
69	#88059	—	4	2	no	—
70	C₄⋊#1055	—	2	2	no	—
71	C₄⋊#1055	—	2	2	no	—
72	C₄⋊#1055	C₂×C₄	1	2	yes	—
73	C₄⋊#1055	C₂×C₄	1	2	yes	—
74	D₄×#108	—	13	1	no	maximal, Sylow
75	C₂³×D₁₃	C₂×Q₈	1	2	yes	—
76	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
79	C₂²×Dic₁₃	C₂×Q₈	1	2	yes	—
80	C₂×D₅₂	—	2	4	no	—
81	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
82	C₂×D₅₂	C₄⋊C₄	1	1	yes	characteristic
83	C₂×D₅₂	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₁₃	—	2	2	no	—
85	C₂×C₄×D₁₃	—	2	2	no	—
86	C₂×C₄×D₁₃	—	2	2	no	—
87	C₂×C₄×D₁₃	—	2	2	no	—
88	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
89	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
90	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
91	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
92	C₁₃×M₁₆	—	2	2	no	—
93	C₁₃×M₁₆	—	2	2	no	—
94	C₁₃×M₁₆	—	2	2	no	—
95	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	—	2	1	no	—
98	C₂×C₈×C₁₃	—	2	1	no	—
99	C₂×C₈×C₁₃	—	2	2	no	—
100	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₁₃	#41	1	2	yes	—
104	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
108	#6103	C₄⋊C₄	1	2	yes	—
109	#6103	C₄⋊C₄	1	2	yes	—
110	#6103	C₄⋊C₄	1	2	yes	—
111	#6103	C₄⋊C₄	1	2	yes	—
112	C₄⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
113	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
114	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
115	#6099	—	2	4	no	—
116	#6099	—	2	4	no	—
117	C₂×#1055	—	2	2	no	—
118	C₂×#1055	—	2	2	no	—
119	C₂×#1055	—	2	4	no	—
120	C₂×#1055	C₂²×C₄	1	4	yes	—
121	#6094	—	4	8	no	—
122	C₈×D₁₃	—	2	8	no	—
123	C₈×D₁₃	—	2	8	no	—
124	C₈×D₁₃	—	4	8	no	—
125	D₄×M₁₆	—	13	2	no	—
126	C₂×C₈×D₄	—	13	1	no	—
127	C₂²×#108	—	13	2	no	—
128	#1950	—	13	2	no	—
129	#1855	—	13	4	no	—
130	#1848	—	13	1	no	—
131	#1810	—	13	2	no	—
132	C₄×#108	D₁₃	1	1	yes	characteristic, complemented
133	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
134	C₂²×D₁₃	—	2	2	no	—
135	C₂²×D₁₃	—	2	2	no	—
136	C₂²×D₁₃	—	2	4	no	—
137	C₂²×D₁₃	—	4	2	no	—
138	C₂²×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
139	C₂²×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	4	1	no	—
142	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
151	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
152	C₂×Dic₁₃	—	2	2	no	—
153	C₂×Dic₁₃	—	2	2	no	—
154	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
155	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
156	D₅₂	—	2	4	no	—
157	D₅₂	—	2	2	no	—
158	D₅₂	#108	1	4	yes	direct product factor
159	C₄×D₁₃	—	2	2	no	—
160	C₄×D₁₃	—	2	2	no	—
161	C₄×D₁₃	—	2	2	no	—
162	C₄×D₁₃	—	2	2	no	—
163	C₄×D₁₃	—	2	2	no	—
164	C₄×D₁₃	—	2	2	no	—
165	C₄×D₁₃	—	2	2	no	—
166	C₄×D₁₃	—	2	2	no	—
167	C₈×C₁₃	—	2	2	no	—
168	C₈×C₁₃	—	2	4	no	—
169	C₈×C₁₃	—	4	2	no	—
170	C₈×C₁₃	C₄×D₄	1	4	yes	—
171	#1055	—	2	4	no	—
172	#1055	—	4	4	no	—
173	C₂²×M₁₆	—	13	4	no	—
174	C₂³×C₈	—	13	2	no	—
175	C₂×C₄×D₄	—	13	1	no	—
176	#436	—	26	2	no	—
177	#435	—	26	4	no	—
178	C₈×D₄	—	13	2	no	—
179	C₈×D₄	—	13	4	no	—
180	C₈×D₄	—	13	2	no	—
181	C₈×D₄	—	26	2	no	—
182	C₂×#108	—	13	4	no	—
183	C₂×#108	—	13	2	no	—
184	C₂×#108	—	13	2	no	—
185	C₂×#108	—	26	8	no	—
186	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
187	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
188	#423	—	13	2	no	—
189	C₂×C₄⋊C₈	—	13	1	no	—
190	#407	—	13	4	no	—
191	C₂×C₂²⋊C₈	—	13	2	no	—
192	C₄×M₁₆	C₂×D₁₃	1	2	yes	—
193	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
194	#341	—	13	4	no	—
195	#341	C₂×D₁₃	1	2	yes	—
196	C₂²×C₁₃	—	2	1	no	—
197	C₂²×C₁₃	—	2	1	no	—
198	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
199	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
200	C₂²×C₁₃	#554	1	1	yes	characteristic
201	C₂×D₁₃	—	2	2	no	—
202	C₂×D₁₃	—	2	2	no	—
203	C₂×D₁₃	—	2	2	no	—
204	C₂×D₁₃	—	2	2	no	—
205	C₂×D₁₃	—	2	2	no	—
206	C₂×D₁₃	—	4	4	no	—
207	C₂×D₁₃	—	4	4	no	—
208	C₂×D₁₃	C₂×#108	1	4	yes	complemented
209	C₄×C₁₃	—	2	1	no	—
210	C₄×C₁₃	—	2	1	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	C₂×#108	1	2	yes	complemented
213	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
214	C₄×C₁₃	#520	1	1	yes	characteristic
215	C₄×C₁₃	D₄²	1	1	yes	characteristic
216	C₄×C₁₃	#547	1	1	yes	characteristic
217	Dic₁₃	—	2	2	no	—
218	Dic₁₃	—	2	2	no	—
219	C₂²×D₄	—	13	1	no	—
220	C₂³×C₄	—	13	2	no	—
221	C₂×M₁₆	—	13	4	no	—
222	C₂×M₁₆	—	26	4	no	—
223	C₂×M₁₆	—	26	8	no	—
224	C₂×M₁₆	—	52	4	no	—
225	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
226	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
227	C₂²×C₈	—	13	2	no	—
228	C₂²×C₈	—	13	4	no	—
229	C₂²×C₈	—	13	4	no	—
230	C₂²×C₈	—	26	4	no	—
231	C₂²×C₈	—	26	4	no	—
232	C₂²×C₈	—	26	4	no	—
233	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
234	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
235	C₄×D₄	—	13	1	no	—
236	C₄×D₄	—	13	2	no	—
237	C₄×D₄	—	13	1	no	—
238	C₄×D₄	—	13	1	no	—
239	C₄×D₄	—	13	2	no	—
240	C₄×D₄	—	13	1	no	—
241	C₂×C₄⋊C₄	—	13	1	no	—
242	C₂×C₂²⋊C₄	—	13	2	no	—
243	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
244	#108	—	2	2	no	—
245	#108	—	26	8	no	—
246	#108	—	26	4	no	—
247	#108	—	52	2	no	—
248	#108	D₅₂	1	4	yes	direct product factor
249	C₄⋊C₈	—	13	2	no	—
250	C₄⋊C₈	—	13	2	no	—
251	C₄⋊C₈	—	26	2	no	—
252	C₄⋊C₈	—	26	2	no	—
253	C₂²⋊C₈	—	13	4	no	—
254	C₂²⋊C₈	—	13	4	no	—
255	C₂²⋊C₈	—	26	4	no	—
256	C₂²⋊C₈	—	26	4	no	—
257	#97	—	2	2	no	—
258	C₄×C₈	—	2	2	no	—
259	C₄×C₈	C₄×D₁₃	1	2	yes	—
260	C₄×C₈	C₄×D₁₃	1	2	yes	—
261	C₂×C₁₃	—	2	1	no	—
262	C₂×C₁₃	—	2	1	no	—
263	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
264	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
265	C₂×C₁₃	#2916	1	1	yes	characteristic
266	D₁₃	—	2	4	no	—
267	D₁₃	—	4	2	no	—
268	C₂⁴	—	13	2	no	—
269	C₂×D₄	—	13	1	no	—
270	C₂×D₄	—	13	2	no	—
271	C₂×D₄	—	13	1	no	—
272	C₂×D₄	—	26	4	no	—
273	C₂²×C₄	—	13	2	no	—
274	C₂²×C₄	—	13	2	no	—
275	C₂²×C₄	—	13	2	no	—
276	C₂²×C₄	—	13	2	no	—
277	C₂²×C₄	—	13	2	no	—
278	C₂²×C₄	—	26	2	no	—
279	C₂²×C₄	—	26	2	no	—
280	C₂²×C₄	—	26	2	no	—
281	C₂²×C₄	—	26	2	no	—
282	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
283	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
285	M₁₆	—	2	2	no	—
286	M₁₆	—	2	2	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	26	4	no	—
289	M₁₆	—	26	4	no	—
290	M₁₆	—	52	8	no	—
291	M₁₆	C₂×D₅₂	1	4	yes	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	13	4	no	—
297	C₂×C₈	—	26	2	no	—
298	C₂×C₈	—	26	2	no	—
299	C₂×C₈	—	26	8	no	—
300	C₂×C₈	—	26	8	no	—
301	C₂×C₈	—	26	4	no	—
302	C₂×C₈	—	52	8	no	—
303	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
304	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
305	C₂×C₈	C₂×D₅₂	1	2	yes	—
306	C₂×C₈	#6127	1	2	yes	—
307	C₄⋊C₄	—	13	2	no	—
308	C₄⋊C₄	—	13	1	no	—
309	C₄⋊C₄	—	13	1	no	—
310	C₂²⋊C₄	—	13	2	no	—
311	C₂²⋊C₄	—	13	2	no	—
312	C₂²⋊C₄	—	13	2	no	—
313	C₂²⋊C₄	—	13	2	no	—
314	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
315	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
316	C₄²	D₄×D₁₃	1	1	yes	characteristic
317	C₄²	D₄×D₁₃	1	1	yes	characteristic
318	C₁₃	D₄×#108	1	1	yes	characteristic, complemented, Sylow
319	C₂³	—	13	2	no	—
320	C₂³	—	13	2	no	—
321	C₂³	—	26	4	no	—
322	C₂³	—	26	2	no	—
323	C₂³	—	26	2	no	—
324	C₂³	—	52	2	no	—
325	C₂³	C₂×Q₈×D₁₃	1	1	yes	characteristic
326	D₄	—	13	4	no	—
327	D₄	—	26	4	no	—
328	D₄	—	26	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	13	2	no	—
332	C₂×C₄	—	13	2	no	—
333	C₂×C₄	—	26	2	no	—
334	C₂×C₄	—	26	2	no	—
335	C₂×C₄	—	26	2	no	—
336	C₂×C₄	—	26	2	no	—
337	C₂×C₄	—	26	2	no	—
338	C₂×C₄	—	26	2	no	—
339	C₂×C₄	—	26	2	no	—
340	C₂×C₄	—	26	2	no	—
341	C₂×C₄	—	26	2	no	—
342	C₂×C₄	—	26	2	no	—
343	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
344	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
345	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
346	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
347	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
349	C₂×C₄	C₂×#6127	1	1	yes	characteristic
350	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
351	C₂×C₄	#88256	1	1	yes	characteristic
352	C₂×C₄	#88257	1	1	yes	characteristic
353	C₈	—	2	2	no	—
354	C₈	—	2	4	no	—
355	C₈	—	4	2	no	—
356	C₈	—	26	4	no	—
357	C₈	—	52	4	no	—
358	C₈	C₄×D₅₂	1	4	yes	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	13	4	no	—
362	C₂²	—	26	2	no	—
363	C₂²	—	26	2	no	—
364	C₂²	—	26	2	no	—
365	C₂²	—	26	2	no	—
366	C₂²	—	26	2	no	—
367	C₂²	—	52	4	no	—
368	C₂²	—	52	4	no	—
369	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
370	C₂²	Q₈×D₅₂	1	1	yes	characteristic
371	C₂²	#11719284	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	26	2	no	—
376	C₄	—	26	2	no	—
377	C₄	D₁₃×#108	1	2	yes	complemented
378	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
379	C₄	#11719228	1	1	yes	characteristic
380	C₄	D₄×D₅₂	1	1	yes	characteristic
381	C₄	#11719256	1	1	yes	characteristic
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	26	4	no	—
385	C₂	—	52	2	no	—
386	C₂	C₄⋊C₄×D₅₂	1	1	yes	characteristic
387	C₂	C₂×D₁₃×#108	1	1	yes	characteristic
388	C₂	#13123444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₄×C₁₃×#108	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂²×D₅₂	Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#108	D₁₃
hypocenter	C₁₃	D₄×#108
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#108

Complements

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

N	H ≅ G/N	type
3. C₂×D₁₃×#108	C₂	semidirect
4. #13115611	C₂	semidirect
5. #13115042	C₂	semidirect
6. #13115008	C₂	semidirect
7. #13114871	C₂	semidirect
8. C₄×C₁₃×#108	C₂	semidirect
58. C₁₃×#108	D₄	semidirect
132. C₄×#108	D₁₃	semidirect
158. D₅₂	#108	direct (N × H)
208. C₂×D₁₃	C₂×#108	semidirect
212. C₄×C₁₃	C₂×#108	semidirect
248. #108	D₅₂	direct (N × H)
318. C₁₃	D₄×#108	semidirect
377. C₄	D₁₃×#108	semidirect

Maximal subgroups

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

subgroup	index
M₁₆×D₅₂	2
C₂×C₈×D₅₂	2
C₂×D₁₃×#108	2
#13115611	2
#13115042	2
#13115008	2
#13114871	2
C₄×C₁₃×#108	2
D₄×#108	13

Subgroups — #108×D52 #15881173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #108×D₅₂ #15881173