Subgroups — #28404364

Order 14464.

1540 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813670	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16813667	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299256	C₂	1	4	yes	maximal, complemented
4	#20299241	C₂	1	4	yes	maximal, complemented
5	#20299238	C₂	1	8	yes	maximal, complemented
6	#20299172	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299168	C₂	1	2	yes	maximal, complemented
8	#20299166	C₂	1	2	yes	maximal, complemented
9	#20299165	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299148	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299147	C₂	1	2	yes	maximal, complemented
12	#124×D₁₁₃	C₂	1	2	yes	maximal, complemented
13	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#124×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#16813670	—	2	8	no	—
16	#16813667	—	2	8	no	—
17	C₂×#14268648	C₂²	1	2	yes	complemented
18	C₂×#14268648	C₂²	1	2	yes	complemented
19	C₂×#14268647	C₂²	1	1	yes	characteristic
20	C₂×#14268647	C₂²	1	1	yes	characteristic
21	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
22	C₂×#14268647	C₂²	1	4	yes	complemented
23	C₂×#14268646	C₂²	1	2	yes	—
24	C₂×#14268646	C₂²	1	2	yes	—
25	C₂×Q₈×D₁₁₃	C₂²	1	2	yes	complemented
26	C₂×Q₈×D₁₁₃	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
28	C₂×D₄×D₁₁₃	C₂²	1	2	yes	—
29	C₂×D₄×D₁₁₃	C₂²	1	2	yes	—
30	#16813622	C₂²	1	1	yes	characteristic, complemented
31	#16813620	C₂²	1	2	yes	complemented
32	#16813619	C₂²	1	1	yes	characteristic, complemented
33	#16813618	C₂²	1	2	yes	complemented
34	#16813611	C₂²	1	2	yes	complemented
35	#16813610	C₂²	1	1	yes	characteristic, complemented
36	#16813610	C₂²	1	1	yes	characteristic, complemented
37	#16813609	C₂²	1	2	yes	complemented
38	#16813608	C₂²	1	8	yes	complemented
39	#16813605	C₂²	1	4	yes	complemented
40	#16813604	C₂²	1	8	yes	complemented
41	#16813599	C₂²	1	8	yes	complemented
42	#16813598	C₂²	1	4	yes	complemented
43	#16813596	C₂²	1	4	yes	complemented
44	#16813595	C₂²	1	8	yes	complemented
45	#16813595	C₂²	1	8	yes	complemented
46	#16813593	C₂²	1	4	yes	complemented
47	#16813592	C₂²	1	8	yes	complemented
48	#16813591	C₂²	1	4	yes	complemented
49	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
50	C₄×D₄₅₂	C₂²	1	2	yes	complemented
51	C₄×D₄₅₂	C₂²	1	4	yes	complemented
52	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
53	#16813582	C₂²	1	8	yes	complemented
54	#16813581	C₂²	1	1	yes	characteristic, complemented
55	#16813579	C₂²	1	2	yes	complemented
56	C₂²⋊C₄×D₁₁₃	C₂²	1	8	yes	complemented
57	C₄²×D₁₁₃	C₂²	1	2	yes	complemented
58	C₂²×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
59	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
60	#124×C₁₁₃	C₂²	1	2	yes	complemented
61	#124×C₁₁₃	C₂²	1	2	yes	complemented
62	#124×C₁₁₃	C₂²	1	4	yes	complemented
63	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	complemented
64	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
65	C₂³×D₁₁₃	C₂³	1	4	yes	—
66	#14268648	—	2	8	no	—
67	#14268648	—	2	8	no	—
68	#14268647	—	2	4	no	—
69	#14268647	—	2	4	no	—
70	#14268647	—	2	16	no	—
71	#14268647	D₄	1	8	yes	complemented
72	#14268646	—	2	8	no	—
73	#14268646	—	2	8	no	—
74	C₂×Dic₂₂₆	C₂³	1	4	yes	—
75	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
76	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
77	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
78	Q₈×D₁₁₃	—	2	8	no	—
79	Q₈×D₁₁₃	—	2	8	no	—
80	C₂×D₄₅₂	C₂³	1	4	yes	—
81	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
82	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
83	C₂×D₄₅₂	C₂³	1	4	yes	—
84	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
85	C₂×C₂²⋊D₁₁₃	—	2	16	no	—
86	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
87	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
90	C₂×C₂²⋊D₁₁₃	C₂³	1	8	yes	—
91	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
92	D₄×D₁₁₃	—	2	8	no	—
93	D₄×D₁₁₃	—	2	8	no	—
94	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
95	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
96	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
97	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
98	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
99	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
100	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
101	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
102	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
103	#14268626	C₂³	1	4	yes	—
104	#14268626	C₂³	1	8	yes	—
105	C₂²⋊Dic₁₁₃	C₂³	1	8	yes	—
106	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
107	#14268624	C₂³	1	4	yes	—
108	#14268624	C₂³	1	8	yes	—
109	#14268624	C₂³	1	4	yes	—
110	#14268624	C₂³	1	4	yes	—
111	C₄×Dic₁₁₃	C₂³	1	2	yes	—
112	C₄×Dic₁₁₃	C₂³	1	4	yes	—
113	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
114	C₂×Q₈×C₁₁₃	—	2	4	no	—
115	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
116	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
117	C₂×D₄×C₁₁₃	—	2	4	no	—
118	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
119	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
120	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
121	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
122	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
123	C₂²⋊C₄×C₁₁₃	C₂³	1	8	yes	—
124	C₂²⋊C₄×C₁₁₃	C₂³	1	8	yes	—
125	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
126	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
127	C₄²×C₁₁₃	C₂³	1	2	yes	—
128	C₂³×C₁₁₃	—	2	4	no	—
129	C₂³×C₁₁₃	—	4	4	no	—
130	C₂³×C₁₁₃	C₂⁴	1	4	yes	—
131	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
132	C₂²×D₁₁₃	—	2	8	no	—
133	C₂²×D₁₁₃	—	4	8	no	—
134	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
135	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
136	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
137	Q₈×C₁₁₃	—	2	4	no	—
138	Q₈×C₁₁₃	—	2	4	no	—
139	D₄×C₁₁₃	—	2	4	no	—
140	D₄×C₁₁₃	—	2	4	no	—
141	C₂×C₄×C₁₁₃	—	2	4	no	—
142	C₂×C₄×C₁₁₃	—	4	2	no	—
143	C₂×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
144	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
145	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
146	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
147	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
148	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
149	C₂²⋊D₁₁₃	—	2	4	no	—
150	C₂²⋊D₁₁₃	—	2	4	no	—
151	C₂²⋊D₁₁₃	—	2	8	no	—
152	C₂²⋊D₁₁₃	—	2	8	no	—
153	C₂²⋊D₁₁₃	—	4	8	no	—
154	C₂²⋊D₁₁₃	C₂×D₄	1	8	yes	—
155	C₂×Dic₁₁₃	—	2	8	no	—
156	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
157	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
158	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
159	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
160	D₄₅₂	—	2	8	no	—
161	D₄₅₂	—	2	2	no	—
162	D₄₅₂	—	2	2	no	—
163	D₄₅₂	—	4	4	no	—
164	D₄₅₂	C₂×D₄	1	4	yes	—
165	C₄×D₁₁₃	—	2	8	no	—
166	C₄×D₁₁₃	—	2	4	no	—
167	C₄×D₁₁₃	—	2	4	no	—
168	C₄×D₁₁₃	—	2	8	no	—
169	C₄×D₁₁₃	—	4	4	no	—
170	C₄×D₁₁₃	C₂×D₄	1	8	yes	—
171	Dic₂₂₆	—	2	2	no	—
172	Dic₂₂₆	—	2	2	no	—
173	Dic₂₂₆	—	2	8	no	—
174	Dic₂₂₆	C₂×D₄	1	4	yes	—
175	C₂²×C₁₁₃	—	2	2	no	—
176	C₂²×C₁₁₃	—	2	4	no	—
177	C₂²×C₁₁₃	—	2	8	no	—
178	C₂²×C₁₁₃	—	8	4	no	—
179	C₂²×C₁₁₃	C₂²×D₄	1	2	yes	—
180	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
181	C₂×D₁₁₃	—	2	4	no	—
182	C₂×D₁₁₃	—	2	2	no	—
183	C₂×D₁₁₃	—	2	2	no	—
184	C₂×D₁₁₃	—	2	4	no	—
185	C₂×D₁₁₃	—	2	4	no	—
186	C₂×D₁₁₃	—	8	8	no	—
187	C₂×D₁₁₃	C₂²×D₄	1	4	yes	—
188	C₄×C₁₁₃	—	2	4	no	—
189	C₄×C₁₁₃	—	2	2	no	—
190	C₄×C₁₁₃	—	2	2	no	—
191	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
192	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
193	Dic₁₁₃	—	2	2	no	—
194	Dic₁₁₃	—	2	2	no	—
195	Dic₁₁₃	—	2	4	no	—
196	Dic₁₁₃	C₂²×D₄	1	4	yes	—
197	C₂×C₁₁₃	—	2	2	no	—
198	C₂×C₁₁₃	—	4	4	no	—
199	C₂×C₁₁₃	C₂³×D₄	1	1	yes	characteristic
200	C₂×C₁₁₃	#585	1	2	yes	—
201	D₁₁₃	—	2	4	no	—
202	D₁₁₃	—	4	2	no	—
203	D₁₁₃	—	4	2	no	—
204	#3500	—	113	1	no	maximal, Sylow
205	C₁₁₃	#3500	1	1	yes	characteristic, complemented, Sylow
206	C₂×2₋¹⁺⁴	—	113	1	no	—
207	C₂×H(5,𝔽₂)	—	113	1	no	—
208	#548	—	113	4	no	—
209	#546	—	113	4	no	—
210	#546	—	113	8	no	—
211	#536	—	113	1	no	—
212	#536	—	113	2	no	—
213	#535	—	113	1	no	—
214	#535	—	113	2	no	—
215	#532	—	113	2	no	—
216	#532	—	113	1	no	—
217	C₂×#124	—	113	2	no	—
218	C₂×#124	D₁₁₃	1	1	yes	characteristic, complemented
219	C₄×#41	—	113	1	no	—
220	2₋¹⁺⁴	—	226	8	no	—
221	H(5,𝔽₂)	—	226	8	no	—
222	C₂×#41	—	113	2	no	—
223	C₂×#41	—	113	2	no	—
224	C₂×#41	—	113	2	no	—
225	C₂×#41	—	113	2	no	—
226	C₂×#41	—	113	1	no	—
227	C₂×#41	—	113	1	no	—
228	C₂×#41	—	113	1	no	—
229	C₂×#41	—	113	4	no	—
230	C₂²×Q₈	—	113	2	no	—
231	C₂²×Q₈	—	113	2	no	—
232	C₂²×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
233	C₂²×D₄	—	113	4	no	—
234	C₂²×D₄	—	113	2	no	—
235	C₂²×D₄	—	113	2	no	—
236	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic
237	C₄⋊Q₈	—	113	2	no	—
238	C₄⋊Q₈	—	113	1	no	—
239	#127	—	113	2	no	—
240	#127	—	113	1	no	—
241	#124	—	113	2	no	—
242	#124	—	113	2	no	—
243	#124	—	113	8	no	—
244	#124	—	113	1	no	—
245	#124	—	113	1	no	—
246	#124	C₂×D₁₁₃	1	2	yes	complemented
247	#124	C₂×D₁₁₃	1	2	yes	complemented
248	#124	C₂×D₁₁₃	1	4	yes	complemented
249	#123	—	113	4	no	—
250	#123	—	113	8	no	—
251	C₂²⋊Q₈	—	113	4	no	—
252	C₂²⋊Q₈	—	113	8	no	—
253	#121	—	113	4	no	—
254	#121	—	113	4	no	—
255	#121	—	113	8	no	—
256	#121	—	113	8	no	—
257	#120	—	113	4	no	—
258	#120	—	113	8	no	—
259	C₄×Q₈	—	113	2	no	—
260	C₄×D₄	—	113	4	no	—
261	C₄×D₄	—	113	8	no	—
262	C₄×D₄	—	113	2	no	—
263	C₄×D₄	—	113	4	no	—
264	#117	—	113	1	no	—
265	#117	—	113	2	no	—
266	C₂×C₂²⋊C₄	—	113	8	no	—
267	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	4	yes	complemented
268	C₂×C₄²	—	113	2	no	—
269	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic, complemented
270	C₂⁴	—	113	4	no	—
271	C₂⁴	C₂²×D₁₁₃	1	2	yes	—
272	#41	—	113	8	no	—
273	#41	—	226	16	no	—
274	#41	—	226	8	no	—
275	#41	—	226	8	no	—
276	#41	—	226	8	no	—
277	#41	—	226	8	no	—
278	#41	—	226	4	no	—
279	#41	—	226	4	no	—
280	C₂×Q₈	—	2	4	no	—
281	C₂×Q₈	—	113	1	no	—
282	C₂×Q₈	—	113	4	no	—
283	C₂×Q₈	—	113	1	no	—
284	C₂×Q₈	—	113	1	no	—
285	C₂×Q₈	—	226	8	no	—
286	C₂×Q₈	—	226	8	no	—
287	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
288	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	113	2	no	—
291	C₂×D₄	—	113	8	no	—
292	C₂×D₄	—	113	2	no	—
293	C₂×D₄	—	113	4	no	—
294	C₂×D₄	—	113	2	no	—
295	C₂×D₄	—	113	4	no	—
296	C₂×D₄	—	113	1	no	—
297	C₂×D₄	—	113	4	no	—
298	C₂×D₄	—	113	4	no	—
299	C₂×D₄	—	113	1	no	—
300	C₂×D₄	—	113	1	no	—
301	C₂×D₄	—	226	8	no	—
302	C₂×D₄	—	226	8	no	—
303	C₂×D₄	—	226	16	no	—
304	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
305	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
306	C₂²×C₄	—	113	2	no	—
307	C₂²×C₄	—	113	4	no	—
308	C₂²×C₄	—	113	4	no	—
309	C₂²×C₄	—	113	4	no	—
310	C₂²×C₄	—	113	4	no	—
311	C₂²×C₄	—	113	2	no	—
312	C₂²×C₄	—	113	2	no	—
313	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
314	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
315	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
316	C₄⋊C₄	—	113	4	no	—
317	C₄⋊C₄	—	113	2	no	—
318	C₄⋊C₄	—	113	8	no	—
319	C₄⋊C₄	—	113	4	no	—
320	C₂²⋊C₄	—	113	8	no	—
321	C₂²⋊C₄	—	113	2	no	—
322	C₂²⋊C₄	—	113	4	no	—
323	C₂²⋊C₄	—	113	8	no	—
324	C₂²⋊C₄	—	113	4	no	—
325	C₂²⋊C₄	—	113	4	no	—
326	C₂²⋊C₄	C₂²×D₁₁₃	1	8	yes	—
327	C₂²⋊C₄	C₂²×D₁₁₃	1	8	yes	—
328	C₄²	—	113	2	no	—
329	C₄²	—	113	4	no	—
330	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
331	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
332	C₄²	C₂²×D₁₁₃	1	2	yes	—
333	C₂³	—	2	4	no	—
334	C₂³	—	4	4	no	—
335	C₂³	—	113	2	no	—
336	C₂³	—	113	2	no	—
337	C₂³	—	113	2	no	—
338	C₂³	—	452	8	no	—
339	C₂³	—	226	8	no	—
340	C₂³	C₂³×D₁₁₃	1	4	yes	—
341	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
342	Q₈	—	2	4	no	—
343	Q₈	—	2	4	no	—
344	Q₈	—	113	4	no	—
345	Q₈	—	226	8	no	—
346	Q₈	—	226	2	no	—
347	Q₈	—	226	2	no	—
348	D₄	—	2	4	no	—
349	D₄	—	2	4	no	—
350	D₄	—	113	8	no	—
351	D₄	—	113	4	no	—
352	D₄	—	452	4	no	—
353	D₄	—	452	8	no	—
354	D₄	—	226	8	no	—
355	D₄	—	226	8	no	—
356	D₄	—	226	8	no	—
357	D₄	—	226	4	no	—
358	D₄	—	226	4	no	—
359	D₄	—	226	2	no	—
360	D₄	—	226	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	113	2	no	—
364	C₂×C₄	—	113	8	no	—
365	C₂×C₄	—	113	4	no	—
366	C₂×C₄	—	113	2	no	—
367	C₂×C₄	—	113	2	no	—
368	C₂×C₄	—	452	4	no	—
369	C₂×C₄	—	226	8	no	—
370	C₂×C₄	—	226	8	no	—
371	C₂×C₄	—	226	8	no	—
372	C₂×C₄	—	226	4	no	—
373	C₂×C₄	—	226	4	no	—
374	C₂×C₄	D₄×D₁₁₃	1	4	yes	—
375	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
376	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
377	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
378	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
379	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
380	C₂²	—	2	2	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	8	no	—
383	C₂²	—	8	4	no	—
384	C₂²	—	113	4	no	—
385	C₂²	—	904	8	no	—
386	C₂²	—	226	2	no	—
387	C₂²	—	226	2	no	—
388	C₂²	—	226	4	no	—
389	C₂²	—	226	4	no	—
390	C₂²	—	226	4	no	—
391	C₂²	C₂×D₄×D₁₁₃	1	2	yes	—
392	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
393	C₄	—	2	4	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	113	4	no	—
397	C₄	—	226	2	no	—
398	C₄	—	226	2	no	—
399	C₄	—	226	4	no	—
400	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
401	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
402	C₂	—	2	2	no	—
403	C₂	—	4	4	no	—
404	C₂	—	452	2	no	—
405	C₂	—	452	2	no	—
406	C₂	—	226	4	no	—
407	C₂	C₂²×D₄×D₁₁₃	1	1	yes	characteristic
408	C₂	#20299434	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	C₂×#124×C₁₁₃	C₂
hypercenter	C₂×#124	D₁₁₃
hypocenter	C₁₁₃	#3500
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×#124

Complements

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

N	H ≅ G/N	type
1. C₂×#16813670	C₂	semidirect
2. C₂×#16813667	C₂	semidirect
3. #20299256	C₂	semidirect
4. #20299241	C₂	semidirect
5. #20299238	C₂	semidirect
6. #20299172	C₂	semidirect
7. #20299168	C₂	semidirect
8. #20299166	C₂	semidirect
9. #20299165	C₂	semidirect
10. #20299148	C₂	semidirect
11. #20299147	C₂	semidirect
12. #124×D₁₁₃	C₂	semidirect
13. C₄×#14268647	C₂	semidirect
14. C₂×#124×C₁₁₃	C₂	semidirect
17. C₂×#14268648	C₂²	semidirect
18. C₂×#14268648	C₂²	semidirect
21. C₂×#14268647	C₂²	semidirect
22. C₂×#14268647	C₂²	semidirect
25. C₂×Q₈×D₁₁₃	C₂²	semidirect
26. C₂×Q₈×D₁₁₃	C₂²	semidirect
30. #16813622	C₂²	semidirect
31. #16813620	C₂²	semidirect
32. #16813619	C₂²	semidirect
33. #16813618	C₂²	semidirect
34. #16813611	C₂²	semidirect
35. #16813610	C₂²	semidirect
36. #16813610	C₂²	semidirect
37. #16813609	C₂²	semidirect
38. #16813608	C₂²	semidirect
39. #16813605	C₂²	semidirect
40. #16813604	C₂²	semidirect
41. #16813599	C₂²	semidirect
42. #16813598	C₂²	semidirect
43. #16813596	C₂²	semidirect
44. #16813595	C₂²	semidirect
45. #16813595	C₂²	semidirect
46. #16813593	C₂²	semidirect
47. #16813592	C₂²	semidirect
48. #16813591	C₂²	semidirect
49. C₄×Dic₂₂₆	C₂²	semidirect
50. C₄×D₄₅₂	C₂²	semidirect
51. C₄×D₄₅₂	C₂²	semidirect
52. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
53. #16813582	C₂²	semidirect
54. #16813581	C₂²	semidirect
55. #16813579	C₂²	semidirect
56. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
57. C₄²×D₁₁₃	C₂²	semidirect
58. C₂²×Q₈×C₁₁₃	C₂²	semidirect
60. #124×C₁₁₃	C₂²	semidirect
61. #124×C₁₁₃	C₂²	semidirect
62. #124×C₁₁₃	C₂²	semidirect
63. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
64. C₂×C₄²×C₁₁₃	C₂²	semidirect
71. #14268647	D₄	semidirect
205. C₁₁₃	#3500	semidirect
218. C₂×#124	D₁₁₃	semidirect
232. C₂²×Q₈	C₂×D₁₁₃	semidirect
246. #124	C₂×D₁₁₃	semidirect
247. #124	C₂×D₁₁₃	semidirect
248. #124	C₂×D₁₁₃	semidirect
267. C₂×C₂²⋊C₄	C₂×D₁₁₃	semidirect
269. C₂×C₄²	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16813670	2
C₂×#16813667	2
#20299256	2
#20299241	2
#20299238	2
#20299172	2
#20299168	2
#20299166	2
#20299165	2
#20299148	2
#20299147	2
#124×D₁₁₃	2
C₄×#14268647	2
C₂×#124×C₁₁₃	2
#3500	113