Subgroups — #29698481

Order 15616.

870 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839880	C₂	1	2	yes	maximal
2	C₄×#14519799	C₂	1	1	yes	maximal, characteristic
3	#21454384	C₂	1	2	yes	maximal, complemented
4	#21446567	C₂	1	2	yes	maximal, complemented
5	#21446097	C₂	1	4	yes	maximal, complemented
6	#21445991	C₂	1	1	yes	maximal, characteristic, complemented
7	#21445840	C₂	1	2	yes	maximal, complemented
8	C₈×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14519799	C₂²	1	1	yes	characteristic
10	C₂×#14519783	C₂²	1	4	yes	—
11	C₄×#11758222	C₂²	1	2	yes	—
12	#16839880	—	2	8	no	—
13	C₄×Dic₂₄₄	C₄	1	1	yes	characteristic, complemented
14	C₄×Dic₂₄₄	C₄	1	1	yes	characteristic, complemented
15	C₄×#11758190	C₄	1	2	yes	complemented
16	C₄×#11758190	C₄	1	2	yes	complemented
17	C₄×D₄₈₈	C₄	1	1	yes	characteristic, complemented
18	C₄×D₄₈₈	C₄	1	1	yes	characteristic, complemented
19	C₂×#14519713	C₂²	1	2	yes	—
20	C₂×#14519713	C₂²	1	2	yes	—
21	#16839800	C₂²	1	1	yes	characteristic
22	#16839788	C₂²	1	4	yes	—
23	#16839787	—	2	4	no	—
24	#16839786	C₂²	1	2	yes	—
25	#16839784	—	2	2	no	—
26	C₄⋊C₈×D₆₁	—	2	2	no	—
27	C₂×#14519705	C₂²	1	4	yes	—
28	#16839759	C₂²	1	2	yes	—
29	#16839522	C₂²	1	4	yes	—
30	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#336	C₂²	1	2	yes	—
35	C₂×#11758222	C₂³	1	2	yes	—
36	#14519799	D₄	1	4	yes	—
37	#14519799	Q₈	1	4	yes	—
38	C₂×Dic₂₄₄	C₂×C₄	1	1	yes	characteristic
39	C₂×#11758190	C₂×C₄	1	2	yes	—
40	C₂×D₄₈₈	C₂×C₄	1	1	yes	characteristic
41	#14519783	—	2	8	no	—
42	#14519783	—	4	4	no	—
43	C₂×#11758194	C₂³	1	4	yes	—
44	C₂×#11758189	—	2	4	no	—
45	C₂×C₈×D₆₁	—	2	4	no	—
46	C₄×Dic₁₂₂	C₂×C₄	1	2	yes	—
47	C₄×Dic₁₂₂	C₂×C₄	1	2	yes	—
48	C₄×D₂₄₄	C₂×C₄	1	2	yes	—
49	C₄×D₂₄₄	C₂×C₄	1	2	yes	—
50	C₄×C₂²⋊D₆₁	—	2	2	no	—
51	C₄×C₂²⋊D₆₁	—	2	2	no	—
52	#14519736	C₂³	1	2	yes	—
53	#14519734	—	2	2	no	—
54	C₄²×D₆₁	—	2	2	no	—
55	#14519713	—	2	4	no	—
56	#14519713	—	4	2	no	—
57	#14519711	C₂×C₄	1	1	yes	characteristic
58	#14519711	C₂×C₄	1	1	yes	characteristic
59	#14519709	C₂×C₄	1	2	yes	—
60	C₄⋊#92418	—	2	2	no	—
61	C₄⋊#92418	—	2	2	no	—
62	#14519706	—	2	4	no	—
63	#14519706	—	2	4	no	—
64	#14519705	—	2	8	no	—
65	#14519702	C₂×C₄	1	2	yes	—
66	#14519702	C₂×C₄	1	2	yes	—
67	#14519699	C₂×C₄	1	2	yes	—
68	#14519699	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
73	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₆₁	D₄	1	1	yes	characteristic
76	C₄⋊C₈×C₆₁	D₄	1	1	yes	characteristic
77	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
78	C₄×C₈×C₆₁	—	2	4	no	—
79	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
83	#95×C₆₁	—	2	1	no	—
84	C₂²×C₄×C₆₁	—	2	2	no	—
85	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
86	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
88	C₂×C₂²⋊D₆₁	—	2	2	no	—
89	#11758222	—	2	2	no	—
90	#11758222	—	2	2	no	—
91	#11758222	C₂×D₄	1	4	yes	—
92	#11758222	C₂×Q₈	1	4	yes	—
93	C₂×D₂₄₄	C₂²×C₄	1	2	yes	—
94	C₂×C₄×D₆₁	—	2	2	no	—
95	C₂×C₄×D₆₁	—	2	2	no	—
96	C₂×C₄×D₆₁	—	2	2	no	—
97	C₂×Dic₁₂₂	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₆₁	—	2	2	no	—
99	C₂×C₈×C₆₁	—	2	1	no	—
100	C₂×C₈×C₆₁	—	2	2	no	—
101	C₂×C₈×C₆₁	—	2	1	no	—
102	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₆₁	C₂×Q₈	1	2	yes	—
110	C₄⋊C₄×C₆₁	—	2	4	no	—
111	C₄²×C₆₁	—	2	2	no	—
112	C₄²×C₆₁	—	2	2	no	—
113	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
117	C₂²⋊Dic₆₁	—	2	2	no	—
118	#11758198	—	2	2	no	—
119	#11758198	—	2	2	no	—
120	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
121	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
122	#11758196	—	2	2	no	—
123	#11758196	—	2	2	no	—
124	C₄×Dic₆₁	—	2	2	no	—
125	C₄×Dic₆₁	—	2	2	no	—
126	C₄×Dic₆₁	—	2	2	no	—
127	#11758194	—	2	4	no	—
128	#11758194	—	2	4	no	—
129	C₂×#92418	—	2	4	no	—
130	Dic₂₄₄	C₄⋊C₄	1	4	yes	complemented
131	D₄₈₈	C₄⋊C₄	1	4	yes	complemented
132	#11758190	C₄⋊C₄	1	8	yes	complemented
133	#11758189	—	4	8	no	—
134	C₈×D₆₁	—	4	8	no	—
135	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
136	C₂²×D₆₁	—	2	2	no	—
137	C₂×C₄×C₆₁	—	2	2	no	—
138	C₂×C₄×C₆₁	—	2	4	no	—
139	C₂×C₄×C₆₁	—	4	1	no	—
140	C₂×C₄×C₆₁	—	4	2	no	—
141	C₂×C₄×C₆₁	—	4	2	no	—
142	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
151	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
152	C₂²⋊D₆₁	—	2	4	no	—
153	C₂²⋊D₆₁	—	2	4	no	—
154	C₂×Dic₆₁	—	2	2	no	—
155	C₂×Dic₆₁	—	2	2	no	—
156	C₂×Dic₆₁	—	2	2	no	—
157	D₂₄₄	—	2	2	no	—
158	D₂₄₄	C₂×C₄⋊C₄	1	4	yes	—
159	C₄×D₆₁	—	2	4	no	—
160	C₄×D₆₁	—	2	4	no	—
161	C₄×D₆₁	—	4	4	no	—
162	C₄×D₆₁	—	8	2	no	—
163	Dic₁₂₂	—	2	2	no	—
164	Dic₁₂₂	C₂×C₄⋊C₄	1	4	yes	—
165	C₈×C₆₁	—	2	1	no	—
166	C₈×C₆₁	—	2	1	no	—
167	C₈×C₆₁	—	2	2	no	—
168	C₈×C₆₁	—	2	2	no	—
169	C₈×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
170	C₈×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
171	#92418	—	4	4	no	—
172	#22688	—	61	1	no	maximal, Sylow
173	C₂²×C₆₁	—	2	1	no	—
174	C₂²×C₆₁	—	2	1	no	—
175	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
176	C₂²×C₆₁	#547	1	1	yes	characteristic
177	C₂²×C₆₁	#554	1	1	yes	characteristic
178	C₂×D₆₁	—	2	4	no	—
179	C₂×D₆₁	—	4	2	no	—
180	C₂×D₆₁	—	4	2	no	—
181	C₄×C₆₁	—	2	1	no	—
182	C₄×C₆₁	—	2	1	no	—
183	C₄×C₆₁	—	2	1	no	—
184	C₄×C₆₁	—	4	4	no	—
185	C₄×C₆₁	#443	1	2	yes	complemented
186	C₄×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₄×C₆₁	#520	1	1	yes	characteristic
188	C₄×C₆₁	D₄²	1	1	yes	characteristic
189	C₄×C₆₁	D₄×Q₈	1	1	yes	characteristic
190	Dic₆₁	—	2	4	no	—
191	Dic₆₁	—	4	2	no	—
192	Dic₆₁	—	4	2	no	—
193	C₂×#443	—	61	2	no	—
194	C₄×#135	—	61	1	no	—
195	#2906	—	61	2	no	—
196	#1945	—	61	2	no	—
197	#1866	—	61	4	no	—
198	#1848	—	61	1	no	—
199	#1806	—	61	2	no	—
200	C₈×C₄⋊C₄	D₆₁	1	1	yes	characteristic, complemented
201	C₂×C₆₁	—	2	1	no	—
202	C₂×C₆₁	—	2	1	no	—
203	C₂×C₆₁	D₄×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₆₁	C₂×#443	1	1	yes	characteristic
205	C₂×C₆₁	#2957	1	1	yes	characteristic
206	D₆₁	—	4	4	no	—
207	C₂×#135	—	61	1	no	—
208	C₂×#131	—	61	4	no	—
209	C₄×#41	—	61	2	no	—
210	#443	—	122	8	no	—
211	C₄×Q₁₆	—	61	1	no	—
212	C₄×Q₁₆	—	61	1	no	—
213	C₄×SD₁₆	—	61	2	no	—
214	C₄×SD₁₆	—	61	2	no	—
215	C₄×D₈	—	61	1	no	—
216	C₄×D₈	—	61	1	no	—
217	C₂×#108	—	61	2	no	—
218	C₂×#108	—	61	2	no	—
219	#427	—	61	1	no	—
220	#424	—	61	4	no	—
221	#424	—	122	4	no	—
222	#423	—	61	2	no	—
223	#423	—	122	2	no	—
224	C₂×C₄⋊C₈	—	122	2	no	—
225	C₂×C₄⋊C₈	C₂×D₆₁	1	1	yes	characteristic
226	C₂×#104	—	61	4	no	—
227	#416	—	61	2	no	—
228	C₂×C₄×C₈	C₂×D₆₁	1	2	yes	—
229	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
230	C₄×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
231	#339	—	61	4	no	—
232	#336	C₂×D₆₁	1	2	yes	—
233	C₆₁	#22688	1	1	yes	characteristic, complemented, Sylow
234	C₂×#41	—	61	2	no	—
235	#135	—	61	4	no	—
236	#135	—	61	4	no	—
237	C₂×Q₁₆	—	61	1	no	—
238	C₂×SD₁₆	—	61	2	no	—
239	C₂×D₈	—	61	1	no	—
240	#131	—	122	8	no	—
241	#131	—	244	4	no	—
242	C₂×M₁₆	—	61	4	no	—
243	C₂×M₁₆	—	122	4	no	—
244	C₂²×C₈	—	122	4	no	—
245	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
246	C₂²×C₈	C₂²×D₆₁	1	2	yes	—
247	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
248	C₄×Q₈	—	61	2	no	—
249	C₄×Q₈	—	61	2	no	—
250	C₄×D₄	—	61	2	no	—
251	C₄×D₄	—	61	2	no	—
252	C₄×D₄	—	122	2	no	—
253	C₄×D₄	—	122	2	no	—
254	#117	—	61	2	no	—
255	#117	—	122	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄²	—	122	2	no	—
258	C₂×C₄²	C₂²×D₆₁	1	2	yes	—
259	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
260	#108	—	122	4	no	—
261	#108	—	244	2	no	—
262	#107	—	61	1	no	—
263	#107	—	61	1	no	—
264	#106	—	61	2	no	—
265	C₄⋊C₈	—	122	4	no	—
266	C₄⋊C₈	—	122	4	no	—
267	C₄⋊C₈	—	122	2	no	—
268	C₄⋊C₈	—	122	2	no	—
269	C₄⋊C₈	D₂₄₄	1	1	yes	characteristic
270	C₄⋊C₈	D₂₄₄	1	1	yes	characteristic
271	C₄⋊C₈	D₂₄₄	1	2	yes	—
272	#104	—	122	8	no	—
273	#103	—	61	2	no	—
274	#103	—	61	2	no	—
275	#102	—	61	2	no	—
276	#102	—	61	2	no	—
277	C₄×C₈	—	2	4	no	—
278	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
279	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
280	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
281	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
282	#95	—	2	1	no	—
283	#41	—	61	4	no	—
284	#41	—	61	4	no	—
285	#41	—	122	2	no	—
286	#41	—	122	2	no	—
287	C₂×Q₈	—	61	2	no	—
288	C₂×D₄	—	61	2	no	—
289	C₂×D₄	—	122	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	122	2	no	—
292	C₂²×C₄	—	122	2	no	—
293	C₂²×C₄	—	122	2	no	—
294	C₂²×C₄	#11758222	1	1	yes	characteristic
295	C₂²×C₄	#11758222	1	1	yes	characteristic
296	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
297	Q₁₆	—	61	4	no	—
298	SD₁₆	—	61	8	no	—
299	D₈	—	61	4	no	—
300	M₁₆	—	122	4	no	—
301	M₁₆	—	122	4	no	—
302	M₁₆	—	244	8	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	122	4	no	—
308	C₂×C₈	—	244	8	no	—
309	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
310	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
311	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
312	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
313	C₂×C₈	C₂×D₂₄₄	1	2	yes	—
314	C₂×C₈	C₂×D₂₄₄	1	2	yes	—
315	C₂×C₈	D₄×D₆₁	1	2	yes	—
316	C₂×C₈	Q₈×D₆₁	1	2	yes	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	61	2	no	—
319	C₄⋊C₄	—	61	2	no	—
320	C₄⋊C₄	—	122	2	no	—
321	C₄⋊C₄	—	122	2	no	—
322	C₂²⋊C₄	—	122	2	no	—
323	C₂²⋊C₄	—	122	2	no	—
324	C₂²⋊C₄	—	122	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	122	2	no	—
328	C₄²	—	122	2	no	—
329	C₄²	—	122	2	no	—
330	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
331	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
332	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
333	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
334	C₂³	—	122	2	no	—
335	C₂³	C₂×#11758222	1	1	yes	characteristic
336	Q₈	—	61	4	no	—
337	Q₈	—	122	2	no	—
338	D₄	—	61	4	no	—
339	D₄	—	122	4	no	—
340	D₄	—	122	4	no	—
341	D₄	—	122	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	122	2	no	—
348	C₂×C₄	—	122	4	no	—
349	C₂×C₄	—	122	4	no	—
350	C₂×C₄	—	122	2	no	—
351	C₂×C₄	—	122	2	no	—
352	C₂×C₄	—	488	2	no	—
353	C₂×C₄	—	244	4	no	—
354	C₂×C₄	C₄×D₂₄₄	1	1	yes	characteristic
355	C₂×C₄	C₄×D₂₄₄	1	1	yes	characteristic
356	C₂×C₄	C₄×D₂₄₄	1	1	yes	characteristic
357	C₂×C₄	C₄×D₂₄₄	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₂₄₄	1	1	yes	characteristic
361	C₂×C₄	C₂×Q₈×D₆₁	1	1	yes	characteristic
362	C₂×C₄	#14519823	1	1	yes	characteristic
363	C₂×C₄	#14519824	1	1	yes	characteristic
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	2	2	no	—
367	C₈	—	2	2	no	—
368	C₈	—	244	4	no	—
369	C₈	C₄⋊C₄×D₆₁	1	2	yes	—
370	C₈	C₄⋊C₄×D₆₁	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	122	4	no	—
374	C₂²	—	244	2	no	—
375	C₂²	—	244	2	no	—
376	C₂²	C₂×C₄×D₂₄₄	1	1	yes	characteristic
377	C₂²	#16840417	1	1	yes	characteristic
378	C₂²	#16840472	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	4	no	—
383	C₄	—	122	4	no	—
384	C₄	—	244	2	no	—
385	C₄	—	244	2	no	—
386	C₄	#16839880	1	2	yes	complemented
387	C₄	C₂×C₄⋊C₄×D₆₁	1	1	yes	characteristic
388	C₄	#16840242	1	1	yes	characteristic
389	C₄	D₄×D₂₄₄	1	1	yes	characteristic
390	C₄	Q₈×D₂₄₄	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	244	4	no	—
394	C₂	C₄⋊C₄×D₂₄₄	1	1	yes	characteristic
395	C₂	C₂×#16839880	1	1	yes	characteristic
396	C₂	#21454737	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₄₄
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₁
Fitting	C₈×C₄⋊C₄×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	C₂×#14519799	C₂²
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₆₁
hypocenter	C₆₁	#22688
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #21454384	C₂	semidirect
4. #21446567	C₂	semidirect
5. #21446097	C₂	semidirect
6. #21445991	C₂	semidirect
7. #21445840	C₂	semidirect
8. C₈×C₄⋊C₄×C₆₁	C₂	semidirect
13. C₄×Dic₂₄₄	C₄	semidirect
14. C₄×Dic₂₄₄	C₄	semidirect
15. C₄×#11758190	C₄	semidirect
16. C₄×#11758190	C₄	semidirect
17. C₄×D₄₈₈	C₄	semidirect
18. C₄×D₄₈₈	C₄	semidirect
130. Dic₂₄₄	C₄⋊C₄	semidirect
131. D₄₈₈	C₄⋊C₄	semidirect
132. #11758190	C₄⋊C₄	semidirect
185. C₄×C₆₁	#443	semidirect
200. C₈×C₄⋊C₄	D₆₁	semidirect
233. C₆₁	#22688	semidirect
386. C₄	#16839880	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16839880	2
C₄×#14519799	2
#21454384	2
#21446567	2
#21446097	2
#21445991	2
#21445840	2
C₈×C₄⋊C₄×C₆₁	2
#22688	61