Subgroups — #16860480

Order 3968.

1424 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521885	C₂	1	2	yes	maximal, complemented
2	#14521863	C₂	1	2	yes	maximal, complemented
3	#14521862	C₂	1	2	yes	maximal, complemented
4	#14521856	C₂	1	4	yes	maximal, complemented
5	#14521855	C₂	1	4	yes	maximal, complemented
6	#14521851	C₂	1	2	yes	maximal, complemented
7	#14521850	C₂	1	2	yes	maximal, complemented
8	#14521847	C₂	1	2	yes	maximal, complemented
9	#14521846	C₂	1	4	yes	maximal, complemented
10	C₂×#11758481	C₂	1	1	yes	maximal, characteristic, complemented
11	#135×D₃₁	C₂	1	4	yes	maximal, complemented
12	C₂×#11758478	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#41×C₃₁	C₂²	1	2	yes	complemented
15	#11758567	—	2	2	no	—
16	#11758567	C₂²	1	4	yes	complemented
17	#11758566	—	2	2	no	—
18	#11758566	C₂²	1	4	yes	complemented
19	#41×D₃₁	—	2	4	no	—
20	#41×D₃₁	C₂²	1	8	yes	complemented
21	#11758564	C₂²	1	4	yes	complemented
22	#11758561	—	2	4	no	—
23	#11758561	C₂²	1	4	yes	complemented
24	C₂×#92495	—	2	4	no	—
25	C₂×#92495	C₂²	1	1	yes	characteristic
26	C₂×#92495	C₂²	1	2	yes	complemented
27	C₃₁×#135	C₂²	1	2	yes	complemented
28	C₃₁×#135	C₂²	1	2	yes	complemented
29	C₃₁×#135	C₂²	1	2	yes	complemented
30	C₃₁×#135	C₂²	1	2	yes	complemented
31	C₂×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
33	C₂×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	#11758528	C₂²	1	4	yes	complemented
36	#11758527	C₂²	1	8	yes	complemented
37	#11758526	C₂²	1	4	yes	complemented
38	#11758519	C₂²	1	4	yes	complemented
39	#11758509	C₂²	1	4	yes	complemented
40	C₂×#92474	C₂²	1	1	yes	characteristic, complemented
41	#11758496	C₂²	1	4	yes	complemented
42	#11758495	C₂²	1	8	yes	complemented
43	Q₁₆×D₃₁	C₂²	1	4	yes	complemented
44	#11758493	C₂²	1	8	yes	complemented
45	#11758492	C₂²	1	8	yes	complemented
46	#11758491	C₂²	1	8	yes	complemented
47	SD₁₆×D₃₁	C₂²	1	8	yes	complemented
48	#11758489	C₂²	1	4	yes	complemented
49	#11758488	C₂²	1	8	yes	complemented
50	D₈×D₃₁	C₂²	1	4	yes	complemented
51	C₂×Dic₁₂₄	C₂²	1	1	yes	characteristic, complemented
52	#11758481	C₂²	1	2	yes	complemented
53	#11758481	C₂²	1	2	yes	complemented
54	#11758481	C₂²	1	2	yes	complemented
55	#11758481	C₂²	1	2	yes	complemented
56	C₂×D₂₄₈	C₂²	1	1	yes	characteristic, complemented
57	C₂×#92470	C₂²	1	2	yes	complemented
58	#11758478	C₂²	1	2	yes	complemented
59	#11758478	C₂²	1	2	yes	complemented
60	#11758478	C₂²	1	2	yes	complemented
61	#11758478	C₂²	1	2	yes	complemented
62	C₂×#92469	C₂²	1	2	yes	complemented
63	C₂×C₈×D₃₁	C₂²	1	2	yes	complemented
64	#41×C₃₁	—	2	2	no	—
65	#41×C₃₁	—	2	2	no	—
66	#41×C₃₁	C₂³	1	4	yes	—
67	#41×C₃₁	C₂³	1	4	yes	—
68	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
69	C₂×D₄×C₃₁	—	2	2	no	—
70	C₂×D₄×C₃₁	C₂³	1	2	yes	—
71	C₂²×C₄×C₃₁	—	2	2	no	—
72	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊D₃₁	—	2	2	no	—
74	C₂×C₂²⋊D₃₁	—	2	8	no	—
75	C₂×C₂²⋊D₃₁	D₄	1	2	yes	—
76	#92499	—	2	4	no	—
77	#92499	C₂³	1	8	yes	—
78	Q₈×D₃₁	—	2	4	no	—
79	Q₈×D₃₁	C₂³	1	8	yes	—
80	#92497	—	2	8	no	—
81	#92497	—	2	8	no	—
82	#92497	—	2	4	no	—
83	#92497	C₂³	1	8	yes	—
84	D₄×D₃₁	—	2	8	no	—
85	D₄×D₃₁	—	2	8	no	—
86	D₄×D₃₁	—	2	4	no	—
87	D₄×D₃₁	C₂³	1	8	yes	—
88	#92495	—	2	2	no	—
89	#92495	—	2	2	no	—
90	#92495	—	2	8	no	—
91	#92495	—	2	4	no	—
92	#92495	—	2	8	no	—
93	#92495	—	2	4	no	—
94	#92495	D₄	1	2	yes	—
95	#92495	D₄	1	2	yes	—
96	#92495	C₂³	1	2	yes	—
97	#92495	C₂³	1	2	yes	—
98	#92495	C₂³	1	4	yes	—
99	#92495	C₂³	1	4	yes	—
100	C₂×D₁₂₄	—	2	4	no	—
101	C₂×D₁₂₄	D₄	1	1	yes	characteristic
102	C₂×D₁₂₄	C₂³	1	2	yes	—
103	C₂×C₄×D₃₁	—	2	2	no	—
104	C₂×C₄×D₃₁	—	2	8	no	—
105	C₂×C₄×D₃₁	C₂³	1	2	yes	—
106	C₂×Dic₆₂	—	2	4	no	—
107	C₂×Dic₆₂	D₄	1	1	yes	characteristic
108	C₂×Dic₆₂	C₂³	1	2	yes	—
109	Q₁₆×C₃₁	C₂³	1	2	yes	—
110	Q₁₆×C₃₁	C₂³	1	2	yes	—
111	SD₁₆×C₃₁	C₂³	1	4	yes	—
112	SD₁₆×C₃₁	C₂³	1	4	yes	—
113	D₈×C₃₁	C₂³	1	2	yes	—
114	D₈×C₃₁	C₂³	1	2	yes	—
115	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
116	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
117	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
118	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
119	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
121	#92482	C₂³	1	8	yes	—
122	#92481	C₂³	1	8	yes	—
123	#92480	C₂³	1	8	yes	—
124	#92479	C₂³	1	8	yes	—
125	#92474	C₂³	1	2	yes	—
126	#92474	C₂³	1	2	yes	—
127	C₂×C₃₁⋊C₈	C₂³	1	2	yes	—
128	Dic₁₂₄	C₂³	1	2	yes	—
129	Dic₁₂₄	C₂³	1	2	yes	—
130	D₂₄₈	C₂³	1	2	yes	—
131	D₂₄₈	C₂³	1	2	yes	—
132	#92470	C₂³	1	4	yes	—
133	#92470	C₂³	1	4	yes	—
134	#92469	C₂³	1	4	yes	—
135	#92469	C₂³	1	4	yes	—
136	C₈×D₃₁	C₂³	1	4	yes	—
137	C₈×D₃₁	C₂³	1	4	yes	—
138	C₂³×C₃₁	—	2	2	no	—
139	C₂³×C₃₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×D₃₁	—	2	2	no	—
141	C₂²×D₃₁	—	2	8	no	—
142	C₂²×D₃₁	C₂×D₄	1	2	yes	—
143	Q₈×C₃₁	—	2	2	no	—
144	Q₈×C₃₁	C₂⁴	1	4	yes	—
145	D₄×C₃₁	—	2	4	no	—
146	D₄×C₃₁	—	2	4	no	—
147	D₄×C₃₁	—	2	2	no	—
148	D₄×C₃₁	C₂⁴	1	4	yes	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	2	4	no	—
151	C₂×C₄×C₃₁	—	2	4	no	—
152	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
157	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
158	C₂²⋊D₃₁	—	2	4	no	—
159	C₂²⋊D₃₁	—	2	4	no	—
160	C₂²⋊D₃₁	—	2	8	no	—
161	C₂²⋊D₃₁	—	2	8	no	—
162	C₂²⋊D₃₁	C₂×D₄	1	4	yes	—
163	C₂²⋊D₃₁	C₂×D₄	1	4	yes	—
164	C₂×Dic₃₁	—	2	2	no	—
165	C₂×Dic₃₁	—	2	8	no	—
166	C₂×Dic₃₁	C₂×D₄	1	2	yes	—
167	D₁₂₄	—	2	8	no	—
168	D₁₂₄	—	2	2	no	—
169	D₁₂₄	C₂×D₄	1	2	yes	—
170	D₁₂₄	C₂×D₄	1	2	yes	—
171	D₁₂₄	C₂⁴	1	4	yes	—
172	C₄×D₃₁	—	2	8	no	—
173	C₄×D₃₁	—	2	4	no	—
174	C₄×D₃₁	—	2	4	no	—
175	C₄×D₃₁	—	2	8	no	—
176	C₄×D₃₁	C₂×D₄	1	4	yes	—
177	C₄×D₃₁	C₂⁴	1	4	yes	—
178	Dic₆₂	—	2	2	no	—
179	Dic₆₂	—	2	8	no	—
180	Dic₆₂	C₂×D₄	1	2	yes	—
181	Dic₆₂	C₂×D₄	1	2	yes	—
182	Dic₆₂	C₂⁴	1	4	yes	—
183	C₈×C₃₁	C₂⁴	1	1	yes	characteristic
184	C₈×C₃₁	C₂⁴	1	1	yes	characteristic
185	C₈×C₃₁	C₂⁴	1	1	yes	characteristic
186	C₈×C₃₁	C₂⁴	1	1	yes	characteristic
187	C₃₁⋊C₈	C₂⁴	1	4	yes	—
188	#3584	—	31	1	no	maximal, Sylow
189	C₂²×C₃₁	—	2	4	no	—
190	C₂²×C₃₁	—	4	1	no	—
191	C₂²×C₃₁	—	8	2	no	—
192	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
193	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
194	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×D₃₁	—	2	4	no	—
196	C₂×D₃₁	—	4	2	no	—
197	C₂×D₃₁	—	8	8	no	—
198	C₂×D₃₁	—	8	2	no	—
199	C₂×D₃₁	C₂²×D₄	1	4	yes	—
200	C₄×C₃₁	—	2	4	no	—
201	C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
202	C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
203	C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
204	C₄×C₃₁	C₂⁵	1	1	yes	characteristic
205	Dic₃₁	—	2	4	no	—
206	Dic₃₁	C₂²×D₄	1	4	yes	—
207	#585	—	31	2	no	—
208	#578	—	31	2	no	—
209	#578	—	31	2	no	—
210	#577	—	31	4	no	—
211	#577	—	31	4	no	—
212	#576	—	31	2	no	—
213	#576	—	31	2	no	—
214	#575	—	31	2	no	—
215	#575	—	31	4	no	—
216	C₂×#135	—	31	4	no	—
217	C₂×#135	—	31	1	no	—
218	C₂×#135	D₃₁	1	1	yes	characteristic, complemented
219	C₂×#131	—	31	1	no	—
220	C₂×C₃₁	—	2	1	no	—
221	C₂×C₃₁	—	2	1	no	—
222	C₂×C₃₁	—	2	1	no	—
223	C₂×C₃₁	—	4	4	no	—
224	C₂×C₃₁	C₂³×D₄	1	1	yes	characteristic
225	D₃₁	—	2	4	no	—
226	D₃₁	—	4	4	no	—
227	2₋¹⁺⁴	—	31	4	no	—
228	2₋¹⁺⁴	—	31	4	no	—
229	2₋¹⁺⁴	—	62	2	no	—
230	H(5,𝔽₂)	—	31	4	no	—
231	H(5,𝔽₂)	—	31	4	no	—
232	H(5,𝔽₂)	—	62	4	no	—
233	H(5,𝔽₂)	—	62	2	no	—
234	C₂×#41	—	31	1	no	—
235	C₂×#41	—	31	8	no	—
236	C₂×#41	—	31	2	no	—
237	C₂×#41	—	62	4	no	—
238	C₂×#41	—	62	4	no	—
239	C₂×#41	C₂×D₃₁	1	2	yes	complemented
240	#137	—	31	4	no	—
241	#137	—	31	4	no	—
242	#137	—	31	8	no	—
243	#137	—	31	8	no	—
244	AGL(1,ℤ/8)	—	31	4	no	—
245	AGL(1,ℤ/8)	—	31	4	no	—
246	AGL(1,ℤ/8)	—	31	8	no	—
247	AGL(1,ℤ/8)	—	31	8	no	—
248	#135	—	31	8	no	—
249	#135	—	31	4	no	—
250	#135	—	31	8	no	—
251	#135	—	31	4	no	—
252	#135	—	31	2	no	—
253	#135	—	31	2	no	—
254	#135	—	31	2	no	—
255	#135	—	31	2	no	—
256	#135	C₂×D₃₁	1	2	yes	complemented
257	#135	C₂×D₃₁	1	2	yes	complemented
258	#135	C₂×D₃₁	1	2	yes	complemented
259	#135	C₂×D₃₁	1	2	yes	complemented
260	C₂×Q₁₆	—	31	4	no	—
261	C₂×Q₁₆	—	31	1	no	—
262	C₂×Q₁₆	C₂×D₃₁	1	1	yes	characteristic, complemented
263	C₂×SD₁₆	—	31	8	no	—
264	C₂×SD₁₆	—	31	2	no	—
265	C₂×SD₁₆	C₂×D₃₁	1	2	yes	complemented
266	C₂×D₈	—	31	4	no	—
267	C₂×D₈	—	31	1	no	—
268	C₂×D₈	C₂×D₃₁	1	1	yes	characteristic, complemented
269	#131	—	31	2	no	—
270	#131	—	31	2	no	—
271	#131	—	31	2	no	—
272	#131	—	31	2	no	—
273	C₂×M₁₆	—	31	1	no	—
274	C₂×M₁₆	—	31	2	no	—
275	C₂²×C₈	—	31	2	no	—
276	C₂²×C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
277	C₃₁	#3584	1	1	yes	characteristic, complemented, Sylow
278	#41	—	2	2	no	—
279	#41	—	2	2	no	—
280	#41	—	31	2	no	—
281	#41	—	31	2	no	—
282	#41	—	31	2	no	—
283	#41	—	31	2	no	—
284	#41	—	31	8	no	—
285	#41	—	31	8	no	—
286	#41	—	31	4	no	—
287	#41	—	31	4	no	—
288	#41	—	62	8	no	—
289	#41	—	62	8	no	—
290	#41	—	62	4	no	—
291	#41	—	62	4	no	—
292	#41	—	62	8	no	—
293	#41	—	62	8	no	—
294	#41	—	62	4	no	—
295	#41	—	62	4	no	—
296	#41	—	62	2	no	—
297	#41	—	62	2	no	—
298	#41	C₂²×D₃₁	1	4	yes	—
299	#41	C₂²×D₃₁	1	4	yes	—
300	C₂×Q₈	—	31	1	no	—
301	C₂×Q₈	—	31	8	no	—
302	C₂×Q₈	—	31	2	no	—
303	C₂×Q₈	—	62	4	no	—
304	C₂×Q₈	—	62	4	no	—
305	C₂×Q₈	C₂²×D₃₁	1	2	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	31	2	no	—
308	C₂×D₄	—	31	8	no	—
309	C₂×D₄	—	31	1	no	—
310	C₂×D₄	—	31	2	no	—
311	C₂×D₄	—	62	4	no	—
312	C₂×D₄	—	62	8	no	—
313	C₂×D₄	—	62	4	no	—
314	C₂×D₄	—	62	8	no	—
315	C₂×D₄	—	62	8	no	—
316	C₂×D₄	—	62	2	no	—
317	C₂×D₄	C₂²×D₃₁	1	2	yes	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	31	2	no	—
320	C₂²×C₄	—	62	8	no	—
321	C₂²×C₄	—	62	2	no	—
322	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
323	Q₁₆	—	31	8	no	—
324	Q₁₆	—	31	2	no	—
325	Q₁₆	—	31	2	no	—
326	Q₁₆	C₂²×D₃₁	1	2	yes	—
327	Q₁₆	C₂²×D₃₁	1	2	yes	—
328	SD₁₆	—	31	8	no	—
329	SD₁₆	—	31	8	no	—
330	SD₁₆	—	31	4	no	—
331	SD₁₆	—	31	4	no	—
332	SD₁₆	C₂²×D₃₁	1	4	yes	—
333	SD₁₆	C₂²×D₃₁	1	4	yes	—
334	D₈	—	31	8	no	—
335	D₈	—	31	2	no	—
336	D₈	—	31	2	no	—
337	D₈	C₂²×D₃₁	1	2	yes	—
338	D₈	C₂²×D₃₁	1	2	yes	—
339	M₁₆	—	31	2	no	—
340	M₁₆	—	31	2	no	—
341	M₁₆	—	31	4	no	—
342	M₁₆	—	31	4	no	—
343	C₂×C₈	—	31	2	no	—
344	C₂×C₈	—	31	4	no	—
345	C₂×C₈	—	31	4	no	—
346	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
347	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
348	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
349	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
350	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
351	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
352	C₂³	—	2	2	no	—
353	C₂³	—	31	2	no	—
354	C₂³	—	62	8	no	—
355	C₂³	—	62	2	no	—
356	C₂³	D₄×D₃₁	1	1	yes	characteristic
357	Q₈	—	2	2	no	—
358	Q₈	—	31	2	no	—
359	Q₈	—	31	2	no	—
360	Q₈	—	31	4	no	—
361	Q₈	—	62	8	no	—
362	Q₈	—	62	2	no	—
363	Q₈	C₂³×D₃₁	1	4	yes	—
364	D₄	—	2	4	no	—
365	D₄	—	2	4	no	—
366	D₄	—	2	2	no	—
367	D₄	—	31	4	no	—
368	D₄	—	31	4	no	—
369	D₄	—	31	2	no	—
370	D₄	—	31	2	no	—
371	D₄	—	31	4	no	—
372	D₄	—	62	8	no	—
373	D₄	—	62	8	no	—
374	D₄	—	62	8	no	—
375	D₄	—	62	4	no	—
376	D₄	—	62	4	no	—
377	D₄	—	62	2	no	—
378	D₄	C₂³×D₃₁	1	4	yes	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	31	2	no	—
383	C₂×C₄	—	31	4	no	—
384	C₂×C₄	—	31	4	no	—
385	C₂×C₄	—	62	8	no	—
386	C₂×C₄	—	62	8	no	—
387	C₂×C₄	—	62	8	no	—
388	C₂×C₄	—	62	2	no	—
389	C₂×C₄	—	62	4	no	—
390	C₂×C₄	—	62	4	no	—
391	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
392	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
393	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
395	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
396	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
397	C₈	—	31	4	no	—
398	C₈	C₂³×D₃₁	1	1	yes	characteristic
399	C₈	C₂³×D₃₁	1	1	yes	characteristic
400	C₈	C₂³×D₃₁	1	1	yes	characteristic
401	C₈	C₂³×D₃₁	1	1	yes	characteristic
402	C₂²	—	2	4	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	31	4	no	—
406	C₂²	—	62	4	no	—
407	C₂²	—	124	2	no	—
408	C₂²	—	248	2	no	—
409	C₂²	—	248	8	no	—
410	C₂²	C₂×D₄×D₃₁	1	1	yes	characteristic
411	C₂²	C₂×D₄×D₃₁	1	1	yes	characteristic
412	C₂²	C₂×D₄×D₃₁	1	1	yes	characteristic
413	C₄	—	2	4	no	—
414	C₄	—	31	4	no	—
415	C₄	—	62	4	no	—
416	C₄	C₂×D₄×D₃₁	1	1	yes	characteristic
417	C₄	C₂×D₄×D₃₁	1	1	yes	characteristic
418	C₄	C₂×D₄×D₃₁	1	1	yes	characteristic
419	C₄	C₂⁴×D₃₁	1	1	yes	characteristic
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	4	4	no	—
424	C₂	—	62	4	no	—
425	C₂	—	124	4	no	—
426	C₂	C₂²×D₄×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×D₃₁
commutator, cosocle	C₄×C₃₁	C₂⁵
Frattini	C₄	C₂⁴×D₃₁
Fitting	C₂×C₃₁×#135	C₂
socle	C₂×C₃₁	C₂³×D₄
hypercenter	C₂×#135	D₃₁
hypocenter	C₃₁	#3584
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. #14521885	C₂	semidirect
2. #14521863	C₂	semidirect
3. #14521862	C₂	semidirect
4. #14521856	C₂	semidirect
5. #14521855	C₂	semidirect
6. #14521851	C₂	semidirect
7. #14521850	C₂	semidirect
8. #14521847	C₂	semidirect
9. #14521846	C₂	semidirect
10. C₂×#11758481	C₂	semidirect
11. #135×D₃₁	C₂	semidirect
12. C₂×#11758478	C₂	semidirect
13. C₂×C₃₁×#135	C₂	semidirect
14. C₂×#41×C₃₁	C₂²	semidirect
16. #11758567	C₂²	semidirect
18. #11758566	C₂²	semidirect
20. #41×D₃₁	C₂²	semidirect
21. #11758564	C₂²	semidirect
23. #11758561	C₂²	semidirect
26. C₂×#92495	C₂²	semidirect
27. C₃₁×#135	C₂²	semidirect
28. C₃₁×#135	C₂²	semidirect
29. C₃₁×#135	C₂²	semidirect
30. C₃₁×#135	C₂²	semidirect
31. C₂×Q₁₆×C₃₁	C₂²	semidirect
32. C₂×SD₁₆×C₃₁	C₂²	semidirect
33. C₂×D₈×C₃₁	C₂²	semidirect
34. C₂²×C₈×C₃₁	C₂²	semidirect
35. #11758528	C₂²	semidirect
36. #11758527	C₂²	semidirect
37. #11758526	C₂²	semidirect
38. #11758519	C₂²	semidirect
39. #11758509	C₂²	semidirect
40. C₂×#92474	C₂²	semidirect
41. #11758496	C₂²	semidirect
42. #11758495	C₂²	semidirect
43. Q₁₆×D₃₁	C₂²	semidirect
44. #11758493	C₂²	semidirect
45. #11758492	C₂²	semidirect
46. #11758491	C₂²	semidirect
47. SD₁₆×D₃₁	C₂²	semidirect
48. #11758489	C₂²	semidirect
49. #11758488	C₂²	semidirect
50. D₈×D₃₁	C₂²	semidirect
51. C₂×Dic₁₂₄	C₂²	semidirect
52. #11758481	C₂²	semidirect
53. #11758481	C₂²	semidirect
54. #11758481	C₂²	semidirect
55. #11758481	C₂²	semidirect
56. C₂×D₂₄₈	C₂²	semidirect
57. C₂×#92470	C₂²	semidirect
58. #11758478	C₂²	semidirect
59. #11758478	C₂²	semidirect
60. #11758478	C₂²	semidirect
61. #11758478	C₂²	semidirect
62. C₂×#92469	C₂²	semidirect
63. C₂×C₈×D₃₁	C₂²	semidirect
218. C₂×#135	D₃₁	semidirect
239. C₂×#41	C₂×D₃₁	semidirect
256. #135	C₂×D₃₁	semidirect
257. #135	C₂×D₃₁	semidirect
258. #135	C₂×D₃₁	semidirect
259. #135	C₂×D₃₁	semidirect
262. C₂×Q₁₆	C₂×D₃₁	semidirect
265. C₂×SD₁₆	C₂×D₃₁	semidirect
268. C₂×D₈	C₂×D₃₁	semidirect
276. C₂²×C₈	C₂×D₃₁	semidirect
277. C₃₁	#3584	semidirect

Maximal subgroups

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

subgroup	index
#14521885	2
#14521863	2
#14521862	2
#14521856	2
#14521855	2
#14521851	2
#14521850	2
#14521847	2
#14521846	2
C₂×#11758481	2
#135×D₃₁	2
C₂×#11758478	2
C₂×C₃₁×#135	2
#3584	31