Subgroups — D₈×#6099 #15834342

Order 3328.

794 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#6099	C₂	1	2	yes	maximal, complemented
2	#13113721	C₂	1	2	yes	maximal, complemented
3	#13113666	C₂	1	4	yes	maximal, complemented
4	D₈×#1055	C₂	1	2	yes	maximal, complemented
5	#13113595	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113261	C₂	1	2	yes	maximal, complemented
7	C₈×#6099	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×D₈	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
11	C₂²×#6099	—	2	2	no	—
12	C₄×C₁₃×D₈	C₄	1	2	yes	—
13	C₄×C₁₃×D₈	C₄	1	1	yes	characteristic
14	C₄×C₁₃×D₈	C₄	1	1	yes	characteristic
15	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×D₈	C₂²	1	2	yes	—
17	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#107	C₄	1	1	yes	characteristic
19	C₂×C₁₃×#102	C₄	1	2	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	#11718868	—	2	2	no	—
22	#11718673	C₂²	1	4	yes	complemented
23	#11718672	—	2	4	no	—
24	D₄×#1055	C₂²	1	4	yes	complemented
25	#11718586	C₂²	1	1	yes	characteristic
26	#11718585	C₂²	1	2	yes	—
27	C₄×#6099	C₂²	1	1	yes	characteristic
28	D₄⋊#1055	C₂²	1	4	yes	complemented
29	D₄⋊#1055	C₂²	1	4	yes	complemented
30	#11718050	C₂²	1	2	yes	complemented
31	#11718050	C₂²	1	2	yes	complemented
32	#11718046	C₂²	1	2	yes	complemented
33	C₈×#1055	C₂²	1	2	yes	complemented
34	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₃	—	2	2	no	—
36	C₂×C₁₃×D₈	—	2	4	no	—
37	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
38	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₄×D₄×C₁₃	—	2	2	no	—
43	C₄×D₄×C₁₃	—	2	2	no	—
44	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
45	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
46	C₄×D₄×C₁₃	C₂³	1	2	yes	—
47	C₄×D₄×C₁₃	C₂³	1	2	yes	—
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×#6099	—	2	2	no	—
52	C₂×#6099	—	2	4	no	—
53	C₂×#6099	—	4	8	no	—
54	C₂×#6099	D₄	1	1	yes	characteristic
55	C₂×#6099	D₄	1	1	yes	characteristic
56	C₂²×#1055	—	2	4	no	—
57	C₁₃×#107	C₂×C₄	1	2	yes	—
58	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
59	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
60	C₁₃×#102	C₂×C₄	1	2	yes	—
61	C₁₃×#102	C₂×C₄	1	2	yes	—
62	C₁₃×#102	C₂×C₄	1	2	yes	—
63	C₁₃×#102	C₂×C₄	1	2	yes	—
64	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
66	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²⋊#1055	—	2	1	no	—
69	C₂²⋊#1055	—	2	4	no	—
70	C₂²⋊#1055	—	2	4	no	—
71	C₄⋊#1055	—	2	2	no	—
72	C₄⋊#1055	—	2	1	no	—
73	C₄⋊#1055	C₂³	1	4	yes	—
74	#88043	D₄	1	2	yes	—
75	C₄×#1055	C₂³	1	2	yes	—
76	C₄×#1055	C₂³	1	2	yes	—
77	M₁₆×D₈	—	13	1	no	maximal, Sylow
78	C₂⁴×C₁₃	—	2	2	no	—
79	C₂×D₄×C₁₃	—	2	4	no	—
80	C₂×D₄×C₁₃	—	2	2	no	—
81	C₂×D₄×C₁₃	—	4	2	no	—
82	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
83	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	4	4	no	—
90	C₂²×C₄×C₁₃	—	4	4	no	—
91	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
94	C₁₃×D₈	—	2	4	no	—
95	C₁₃×D₈	—	2	2	no	—
96	C₁₃×D₈	M₁₆	1	4	yes	complemented
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	4	1	no	—
99	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₁₃×C₄⋊C₄	—	2	2	no	—
104	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
105	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
106	C₁₃×C₂²⋊C₄	—	2	2	no	—
107	C₁₃×C₂²⋊C₄	—	2	2	no	—
108	C₁₃×C₂²⋊C₄	—	2	2	no	—
109	C₁₃×C₂²⋊C₄	—	2	2	no	—
110	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₃	#41	1	1	yes	characteristic
113	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
114	#6099	—	2	2	no	—
115	#6099	—	4	4	no	—
116	#6099	—	4	8	no	—
117	#6099	D₈	1	4	yes	direct product factor
118	C₂×#1055	—	2	4	no	—
119	C₂×#1055	—	2	2	no	—
120	C₂×#1055	—	4	8	no	—
121	C₂×#1055	C₂×D₄	1	2	yes	—
122	C₂×#1055	C₂×D₄	1	2	yes	—
123	C₂×C₄×D₈	D₁₃	1	1	yes	characteristic
124	D₄×M₁₆	—	13	2	no	—
125	#1589	—	13	2	no	—
126	#1581	—	13	4	no	—
127	C₈×D₈	—	13	2	no	—
128	#1567	—	13	1	no	—
129	#1486	—	13	2	no	—
130	C₈×M₁₆	—	13	1	no	—
131	C₂³×C₁₃	—	2	2	no	—
132	C₂³×C₁₃	—	2	2	no	—
133	C₂³×C₁₃	—	4	4	no	—
134	C₂³×C₁₃	—	4	4	no	—
135	C₂³×C₁₃	—	8	2	no	—
136	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
137	D₄×C₁₃	—	2	2	no	—
138	D₄×C₁₃	—	2	2	no	—
139	D₄×C₁₃	—	2	2	no	—
140	D₄×C₁₃	—	4	4	no	—
141	D₄×C₁₃	C₂×M₁₆	1	4	yes	complemented
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	4	1	no	—
147	C₂×C₄×C₁₃	—	4	4	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	4	2	no	—
152	C₂×C₄×C₁₃	—	4	4	no	—
153	C₂×C₄×C₁₃	—	4	4	no	—
154	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
158	C₂×C₄×C₁₃	#135	1	2	yes	—
159	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
162	C₈×C₁₃	—	2	1	no	—
163	C₈×C₁₃	—	2	1	no	—
164	C₈×C₁₃	—	2	1	no	—
165	C₈×C₁₃	C₂×M₁₆	1	2	yes	complemented
166	#1055	—	2	2	no	—
167	#1055	—	4	2	no	—
168	#1055	—	4	4	no	—
169	#1055	C₂×D₈	1	4	yes	complemented
170	C₂²×D₈	Dic₁₃	1	1	yes	characteristic
171	C₂²×M₁₆	—	26	2	no	—
172	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
173	C₄×D₈	Dic₁₃	1	2	yes	—
174	C₄×D₈	Dic₁₃	1	1	yes	characteristic
175	C₄×D₈	Dic₁₃	1	1	yes	characteristic
176	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
177	C₄×D₈	C₂×D₁₃	1	2	yes	—
178	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
179	#436	—	13	4	no	—
180	#435	—	26	4	no	—
181	C₈×D₄	—	13	4	no	—
182	#431	—	13	1	no	—
183	C₂×#107	Dic₁₃	1	1	yes	characteristic
184	#423	—	13	2	no	—
185	C₂×#102	Dic₁₃	1	2	yes	—
186	#407	—	26	2	no	—
187	C₄×M₁₆	—	13	1	no	—
188	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
189	#335	—	13	2	no	—
190	#335	—	13	2	no	—
191	D₄⋊C₈	—	13	4	no	—
192	D₄⋊C₈	—	13	4	no	—
193	#322	—	13	2	no	—
194	C₈²	—	13	2	no	—
195	C₂²×C₁₃	—	2	1	no	—
196	C₂²×C₁₃	—	2	1	no	—
197	C₂²×C₁₃	—	2	4	no	—
198	C₂²×C₁₃	—	4	2	no	—
199	C₂²×C₁₃	—	4	2	no	—
200	C₂²×C₁₃	—	4	2	no	—
201	C₂²×C₁₃	—	4	2	no	—
202	C₂²×C₁₃	—	4	2	no	—
203	C₂²×C₁₃	—	8	8	no	—
204	C₂²×C₁₃	C₄×D₈	1	2	yes	—
205	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₁₃	—	2	1	no	—
207	C₄×C₁₃	—	2	1	no	—
208	C₄×C₁₃	—	2	1	no	—
209	C₄×C₁₃	—	4	2	no	—
210	C₄×C₁₃	—	4	2	no	—
211	C₄×C₁₃	C₄×D₈	1	2	yes	—
212	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
213	C₄×C₁₃	#568	1	1	yes	characteristic
214	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
215	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
216	C₂²×D₄	C₂×Dic₁₃	1	2	yes	—
217	C₂³×C₄	—	2	2	no	—
218	C₂×D₈	—	2	4	no	—
219	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
220	C₂×D₈	C₂×Dic₁₃	1	1	yes	characteristic
221	C₂×D₈	C₂×Dic₁₃	1	1	yes	characteristic
222	C₂×M₁₆	—	13	1	no	—
223	C₂×M₁₆	—	13	1	no	—
224	C₂×M₁₆	—	26	4	no	—
225	C₂×M₁₆	—	26	2	no	—
226	C₂×M₁₆	—	52	8	no	—
227	C₂²×C₈	—	26	4	no	—
228	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
229	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
233	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
234	C₄×D₄	C₂²×D₁₃	1	2	yes	—
235	C₄×D₄	C₂²×D₁₃	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
239	#107	C₂×Dic₁₃	1	2	yes	—
240	#107	C₂×Dic₁₃	1	1	yes	characteristic
241	#107	C₂×Dic₁₃	1	1	yes	characteristic
242	C₄⋊C₈	—	13	4	no	—
243	C₄⋊C₈	—	26	2	no	—
244	C₄⋊C₈	—	26	1	no	—
245	#102	C₂×Dic₁₃	1	2	yes	—
246	#102	C₂×Dic₁₃	1	2	yes	—
247	#102	C₂×Dic₁₃	1	2	yes	—
248	#102	C₂×Dic₁₃	1	2	yes	—
249	C₂²⋊C₈	—	26	4	no	—
250	C₂²⋊C₈	—	26	4	no	—
251	C₂²⋊C₈	—	26	1	no	—
252	#97	—	13	2	no	—
253	C₄×C₈	—	13	2	no	—
254	C₄×C₈	—	13	2	no	—
255	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
256	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
257	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
258	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
259	C₂×C₁₃	—	2	2	no	—
260	C₂×C₁₃	—	4	4	no	—
261	C₂×C₁₃	—	8	2	no	—
262	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
263	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
264	C₂×C₁₃	#2957	1	1	yes	characteristic
265	C₂⁴	—	2	2	no	—
266	C₂×D₄	—	2	4	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
270	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
279	C₂²×C₄	#6129	1	1	yes	characteristic
280	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
281	D₈	—	2	4	no	—
282	D₈	—	2	2	no	—
283	D₈	#6099	1	4	yes	direct product factor
284	M₁₆	—	13	4	no	—
285	M₁₆	—	26	2	no	—
286	M₁₆	—	52	8	no	—
287	M₁₆	—	52	4	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	—	13	2	no	—
291	C₂×C₈	—	13	2	no	—
292	C₂×C₈	—	26	4	no	—
293	C₂×C₈	—	26	2	no	—
294	C₂×C₈	—	52	8	no	—
295	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
296	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
297	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
298	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
301	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₄²	D₄×D₁₃	1	1	yes	characteristic
307	C₄²	#6129	1	1	yes	characteristic
308	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
309	C₄²	C₂³×D₁₃	1	1	yes	characteristic
310	C₁₃	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	4	4	no	—
314	C₂³	—	4	4	no	—
315	C₂³	—	8	2	no	—
316	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
317	D₄	—	2	2	no	—
318	D₄	—	2	2	no	—
319	D₄	—	2	2	no	—
320	D₄	—	4	4	no	—
321	D₄	C₂×#6099	1	4	yes	complemented
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	D₈×D₁₃	1	2	yes	—
335	C₂×C₄	#88166	1	2	yes	—
336	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
337	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
338	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
339	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
340	C₂×C₄	C₂×#6129	1	1	yes	characteristic
341	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
342	C₈	—	2	1	no	—
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	—	13	4	no	—
346	C₈	—	26	2	no	—
347	C₈	—	52	2	no	—
348	C₈	—	52	4	no	—
349	C₈	C₂×#6099	1	2	yes	complemented
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	8	8	no	—
359	C₂²	D₈×Dic₁₃	1	2	yes	—
360	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	D₈×Dic₁₃	1	2	yes	—
367	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
368	C₄	C₂×#88166	1	1	yes	characteristic
369	C₄	C₂²×#6099	1	1	yes	characteristic
370	C₄	#11719524	1	1	yes	characteristic
371	C₂	—	2	2	no	—
372	C₂	—	4	4	no	—
373	C₂	—	8	2	no	—
374	C₂	D₄×#6099	1	1	yes	characteristic
375	C₂	C₂×D₈×Dic₁₃	1	1	yes	characteristic
376	C₂	#13123753	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×D₈	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×C₁₃×D₈	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×C₄×D₈	D₁₃
hypocenter	C₁₃	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. D₄×#6099	C₂	semidirect
2. #13113721	C₂	semidirect
3. #13113666	C₂	semidirect
4. D₈×#1055	C₂	semidirect
5. #13113595	C₂	semidirect
6. #13113261	C₂	semidirect
7. C₈×#6099	C₂	semidirect
22. #11718673	C₂²	semidirect
24. D₄×#1055	C₂²	semidirect
28. D₄⋊#1055	C₂²	semidirect
29. D₄⋊#1055	C₂²	semidirect
30. #11718050	C₂²	semidirect
31. #11718050	C₂²	semidirect
32. #11718046	C₂²	semidirect
33. C₈×#1055	C₂²	semidirect
96. C₁₃×D₈	M₁₆	semidirect
117. #6099	D₈	direct (N × H)
141. D₄×C₁₃	C₂×M₁₆	semidirect
165. C₈×C₁₃	C₂×M₁₆	semidirect
169. #1055	C₂×D₈	semidirect
283. D₈	#6099	direct (N × H)
310. C₁₃	M₁₆×D₈	semidirect
321. D₄	C₂×#6099	semidirect
349. C₈	C₂×#6099	semidirect

Maximal subgroups

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

subgroup	index
D₄×#6099	2
#13113721	2
#13113666	2
D₈×#1055	2
#13113595	2
#13113261	2
C₈×#6099	2
C₂×C₄×C₁₃×D₈	2
M₁₆×D₈	13

Subgroups — D8×#6099 #15834342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×#6099 #15834342