Subgroups — C₂×#20299302 #28404102

Order 14464.

1200 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299302	C₂	1	16	yes	maximal, direct product factor
2	C₂×#16813620	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16813612	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16813612	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16813600	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16813600	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16813599	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16813599	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16813598	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16813587	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₂²⋊D₁₁₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#16813582	C₂	1	1	yes	maximal, characteristic
13	C₂×#16813582	C₂	1	1	yes	maximal, characteristic
14	C₂²×#14268626	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄⋊C₄×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂²⋊Q₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic
18	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
20	C₂³×Dic₁₁₃	C₂²	1	1	yes	characteristic
21	C₂³×Dic₁₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
25	#16813620	C₂²	1	8	yes	complemented
26	#16813612	C₂²	1	8	yes	complemented
27	#16813612	C₂²	1	8	yes	complemented
28	#16813600	C₂²	1	8	yes	complemented
29	#16813600	C₂²	1	8	yes	complemented
30	#16813599	C₂²	1	8	yes	complemented
31	#16813599	C₂²	1	8	yes	complemented
32	#16813598	C₂²	1	8	yes	complemented
33	#16813587	C₂²	1	8	yes	complemented
34	C₄×C₂²⋊D₁₁₃	C₂²	1	8	yes	—
35	#16813582	C₂²	1	8	yes	—
36	#16813582	C₂²	1	8	yes	—
37	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
39	C₂×#14268626	C₂²	1	1	yes	characteristic
40	C₂×#14268626	C₂²	1	1	yes	characteristic
41	C₂×#14268626	C₂²	1	1	yes	characteristic
42	C₂×#14268626	C₂²	1	1	yes	characteristic
43	C₂×#14268626	C₂²	1	1	yes	characteristic
44	C₂×#14268626	C₂²	1	1	yes	characteristic
45	C₂×#14268626	C₂²	1	1	yes	characteristic
46	C₂×#14268626	C₂²	1	1	yes	characteristic
47	C₂×#14268626	C₂²	1	1	yes	characteristic
48	C₂×#14268626	C₂²	1	1	yes	characteristic
49	C₂×#14268626	C₂²	1	1	yes	characteristic
50	C₂×#14268626	C₂²	1	8	yes	complemented
51	C₄⋊C₄×D₁₁₃	C₂²	1	8	yes	complemented
52	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
53	C₂×#14268624	C₂²	1	1	yes	characteristic
54	C₂×#14268624	C₂²	1	1	yes	characteristic
55	C₂×#14268624	C₂²	1	1	yes	characteristic
56	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
60	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
61	C₂²⋊Q₈×C₁₁₃	C₂²	1	8	yes	complemented
62	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
67	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
68	C₂×Dic₂₂₆	—	2	4	no	—
69	C₂×Dic₂₂₆	—	4	2	no	—
70	C₂×Dic₂₂₆	C₂³	1	4	yes	—
71	C₂×Dic₂₂₆	C₂³	1	4	yes	—
72	C₂×C₂²⋊D₁₁₃	Q₈	1	8	yes	complemented
73	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
74	C₂²×Dic₁₁₃	—	2	4	no	—
75	C₂²×Dic₁₁₃	—	4	2	no	—
76	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
77	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
78	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
80	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
81	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
82	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
83	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
84	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄×D₁₁₃	—	2	4	no	—
86	C₂×C₄×D₁₁₃	—	4	2	no	—
87	C₂×C₄×D₁₁₃	—	4	2	no	—
88	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
89	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
90	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
91	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
92	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
93	#14268626	C₂³	1	4	yes	—
94	#14268626	C₂³	1	4	yes	—
95	#14268626	C₂³	1	4	yes	—
96	#14268626	C₂³	1	4	yes	—
97	#14268626	C₂³	1	4	yes	—
98	#14268626	C₂³	1	4	yes	—
99	#14268626	C₂³	1	4	yes	—
100	#14268626	C₂³	1	4	yes	—
101	#14268626	C₂³	1	4	yes	—
102	#14268626	C₂³	1	4	yes	—
103	#14268626	C₂³	1	4	yes	—
104	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
105	#14268624	C₂³	1	4	yes	—
106	#14268624	C₂³	1	4	yes	—
107	#14268624	C₂³	1	4	yes	—
108	C₄×Dic₁₁₃	C₂³	1	4	yes	—
109	C₄×Dic₁₁₃	C₂³	1	4	yes	—
110	C₄×Dic₁₁₃	C₂³	1	4	yes	—
111	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
112	C₂×Q₈×C₁₁₃	—	4	2	no	—
113	C₂×Q₈×C₁₁₃	C₂³	1	4	yes	—
114	C₂²×C₄×C₁₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
122	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
123	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
124	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
125	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
126	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
127	C₂³×C₁₁₃	—	2	2	no	—
128	C₂³×C₁₁₃	—	2	2	no	—
129	C₂³×C₁₁₃	C₂×Q₈	1	4	yes	—
130	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
131	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
132	C₂²×D₁₁₃	—	2	2	no	—
133	C₂²×D₁₁₃	—	2	2	no	—
134	C₂²×D₁₁₃	C₂×Q₈	1	4	yes	—
135	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
136	Q₈×C₁₁₃	—	4	4	no	—
137	C₂×C₄×C₁₁₃	—	2	2	no	—
138	C₂×C₄×C₁₁₃	—	2	2	no	—
139	C₂×C₄×C₁₁₃	—	2	2	no	—
140	C₂×C₄×C₁₁₃	—	2	2	no	—
141	C₂×C₄×C₁₁₃	—	2	2	no	—
142	C₂×C₄×C₁₁₃	—	2	2	no	—
143	C₂×C₄×C₁₁₃	—	4	4	no	—
144	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
145	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
146	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
147	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
148	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
149	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
150	C₂²⋊D₁₁₃	C₂×Q₈	1	16	yes	complemented
151	C₂×Dic₁₁₃	—	2	2	no	—
152	C₂×Dic₁₁₃	—	2	2	no	—
153	C₂×Dic₁₁₃	—	2	2	no	—
154	C₂×Dic₁₁₃	—	2	2	no	—
155	C₂×Dic₁₁₃	—	2	2	no	—
156	C₂×Dic₁₁₃	—	2	8	no	—
157	C₂×Dic₁₁₃	—	4	4	no	—
158	C₂×Dic₁₁₃	C₂×Q₈	1	4	yes	—
159	C₂×Dic₁₁₃	#41	1	4	yes	—
160	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
161	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
162	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
163	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
164	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
165	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
166	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
167	C₄×D₁₁₃	—	2	8	no	—
168	C₄×D₁₁₃	—	4	4	no	—
169	C₄×D₁₁₃	—	4	4	no	—
170	Dic₂₂₆	—	2	8	no	—
171	Dic₂₂₆	—	4	4	no	—
172	C₂²×C₁₁₃	—	2	8	no	—
173	C₂²×C₁₁₃	—	2	2	no	—
174	C₂²×C₁₁₃	—	2	2	no	—
175	C₂²×C₁₁₃	C₂²×Q₈	1	4	yes	—
176	C₂²×C₁₁₃	C₂²×Q₈	1	2	yes	—
177	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
178	C₂²×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
179	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
180	C₂×D₁₁₃	—	2	8	no	—
181	C₂×D₁₁₃	—	2	2	no	—
182	C₂×D₁₁₃	—	2	2	no	—
183	C₂×D₁₁₃	C₂²×Q₈	1	4	yes	—
184	C₄×C₁₁₃	—	2	2	no	—
185	C₄×C₁₁₃	—	2	2	no	—
186	C₄×C₁₁₃	—	2	2	no	—
187	C₄×C₁₁₃	—	2	2	no	—
188	C₄×C₁₁₃	—	2	2	no	—
189	C₄×C₁₁₃	—	2	2	no	—
190	Dic₁₁₃	—	2	2	no	—
191	Dic₁₁₃	—	2	2	no	—
192	Dic₁₁₃	—	2	2	no	—
193	Dic₁₁₃	—	2	2	no	—
194	Dic₁₁₃	—	2	2	no	—
195	Dic₁₁₃	C₂²×Q₈	1	4	yes	—
196	Dic₁₁₃	C₂×#41	1	4	yes	—
197	C₂×C₁₁₃	—	2	4	no	—
198	C₂×C₁₁₃	#554	1	4	yes	complemented
199	C₂×C₁₁₃	C₂³×Q₈	1	1	yes	characteristic
200	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
201	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
202	D₁₁₃	—	2	4	no	—
203	C₂×#554	—	113	1	no	maximal, Sylow
204	C₁₁₃	C₂×#554	1	1	yes	characteristic, complemented, Sylow
205	#554	—	113	16	no	—
206	C₂×C₄⋊Q₈	—	113	1	no	—
207	C₂×#125	—	113	1	no	—
208	C₂×#125	—	113	1	no	—
209	C₂×C₂²⋊Q₈	—	113	1	no	—
210	C₂×C₂²⋊Q₈	—	113	1	no	—
211	C₂×C₂²⋊Q₈	—	113	1	no	—
212	C₂×C₂²⋊Q₈	—	113	1	no	—
213	C₂×C₂²⋊Q₈	—	113	1	no	—
214	C₂×C₂²⋊Q₈	D₁₁₃	1	1	yes	characteristic, complemented
215	C₂×C₄×Q₈	—	113	1	no	—
216	C₂×C₄×D₄	—	113	1	no	—
217	C₂×C₄×D₄	—	113	1	no	—
218	C₂×C₄×D₄	—	113	1	no	—
219	C₂²×C₄⋊C₄	—	113	1	no	—
220	C₂²×C₄⋊C₄	—	113	1	no	—
221	C₂²×Q₈	—	113	1	no	—
222	C₂²×Q₈	—	113	1	no	—
223	C₂²×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
224	C₂²×D₄	—	113	1	no	—
225	C₂³×C₄	—	113	1	no	—
226	C₂³×C₄	—	113	1	no	—
227	C₂³×C₄	—	113	1	no	—
228	C₂³×C₄	—	113	1	no	—
229	C₂³×C₄	—	113	1	no	—
230	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic
231	C₄⋊Q₈	—	113	8	no	—
232	#125	—	113	8	no	—
233	#125	—	113	8	no	—
234	C₂²⋊Q₈	—	113	8	no	—
235	C₂²⋊Q₈	—	113	8	no	—
236	C₂²⋊Q₈	—	113	8	no	—
237	C₂²⋊Q₈	—	113	8	no	—
238	C₂²⋊Q₈	—	113	8	no	—
239	C₂²⋊Q₈	C₂×D₁₁₃	1	8	yes	complemented
240	C₄×Q₈	—	113	8	no	—
241	C₄×D₄	—	113	8	no	—
242	C₄×D₄	—	113	8	no	—
243	C₄×D₄	—	113	8	no	—
244	C₂×C₄⋊C₄	—	113	1	no	—
245	C₂×C₄⋊C₄	—	113	1	no	—
246	C₂×C₄⋊C₄	—	113	1	no	—
247	C₂×C₄⋊C₄	—	113	1	no	—
248	C₂×C₄⋊C₄	—	113	1	no	—
249	C₂×C₄⋊C₄	—	113	8	no	—
250	C₂×C₄⋊C₄	—	113	1	no	—
251	C₂×C₄⋊C₄	—	113	1	no	—
252	C₂×C₄⋊C₄	—	113	1	no	—
253	C₂×C₄⋊C₄	—	113	1	no	—
254	C₂×C₄⋊C₄	—	113	1	no	—
255	C₂×C₄⋊C₄	—	113	1	no	—
256	C₂×C₄⋊C₄	—	113	1	no	—
257	C₂×C₄⋊C₄	—	113	1	no	—
258	C₂×C₄⋊C₄	—	113	8	no	—
259	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	113	1	no	—
263	C₂×C₂²⋊C₄	—	113	1	no	—
264	C₂×C₂²⋊C₄	—	113	1	no	—
265	C₂×C₂²⋊C₄	—	113	1	no	—
266	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
268	C₂×C₄²	—	113	1	no	—
269	C₂×C₄²	—	113	1	no	—
270	C₂×C₄²	—	113	1	no	—
271	C₂⁴	—	113	1	no	—
272	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
273	C₂×Q₈	—	4	2	no	—
274	C₂×Q₈	—	113	4	no	—
275	C₂×Q₈	—	113	4	no	—
276	C₂×Q₈	—	452	2	no	—
277	C₂×Q₈	—	226	4	no	—
278	C₂×Q₈	C₂²×D₁₁₃	1	4	yes	—
279	C₂×D₄	—	113	8	no	—
280	C₂×D₄	—	113	4	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	113	1	no	—
283	C₂²×C₄	—	113	1	no	—
284	C₂²×C₄	—	113	4	no	—
285	C₂²×C₄	—	113	4	no	—
286	C₂²×C₄	—	113	1	no	—
287	C₂²×C₄	—	113	1	no	—
288	C₂²×C₄	—	113	1	no	—
289	C₂²×C₄	—	113	1	no	—
290	C₂²×C₄	—	113	1	no	—
291	C₂²×C₄	—	113	4	no	—
292	C₂²×C₄	—	113	4	no	—
293	C₂²×C₄	—	113	4	no	—
294	C₂²×C₄	—	452	2	no	—
295	C₂²×C₄	—	452	2	no	—
296	C₂²×C₄	—	452	2	no	—
297	C₂²×C₄	—	226	4	no	—
298	C₂²×C₄	—	226	4	no	—
299	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
306	C₄⋊C₄	—	113	4	no	—
307	C₄⋊C₄	—	113	4	no	—
308	C₄⋊C₄	—	113	4	no	—
309	C₄⋊C₄	—	113	4	no	—
310	C₄⋊C₄	—	113	4	no	—
311	C₄⋊C₄	—	113	4	no	—
312	C₄⋊C₄	—	113	4	no	—
313	C₄⋊C₄	—	113	4	no	—
314	C₄⋊C₄	—	113	4	no	—
315	C₄⋊C₄	—	113	4	no	—
316	C₄⋊C₄	—	113	4	no	—
317	C₄⋊C₄	—	113	4	no	—
318	C₄⋊C₄	—	113	4	no	—
319	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
320	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
321	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
322	C₂²⋊C₄	—	113	4	no	—
323	C₂²⋊C₄	—	113	4	no	—
324	C₂²⋊C₄	—	113	4	no	—
325	C₂²⋊C₄	—	113	4	no	—
326	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
327	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
328	C₄²	—	113	4	no	—
329	C₄²	—	113	4	no	—
330	C₄²	—	113	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	113	4	no	—
334	C₂³	—	113	2	no	—
335	C₂³	—	226	2	no	—
336	C₂³	—	226	2	no	—
337	C₂³	Q₈×D₁₁₃	1	4	yes	—
338	C₂³	C₂³×D₁₁₃	1	2	yes	—
339	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
340	Q₈	—	4	4	no	—
341	Q₈	—	452	4	no	—
342	Q₈	—	226	8	no	—
343	D₄	—	113	16	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	113	4	no	—
352	C₂×C₄	—	113	4	no	—
353	C₂×C₄	—	113	2	no	—
354	C₂×C₄	—	113	2	no	—
355	C₂×C₄	—	113	2	no	—
356	C₂×C₄	—	113	2	no	—
357	C₂×C₄	—	113	2	no	—
358	C₂×C₄	—	113	2	no	—
359	C₂×C₄	—	113	2	no	—
360	C₂×C₄	—	452	4	no	—
361	C₂×C₄	—	452	4	no	—
362	C₂×C₄	—	452	4	no	—
363	C₂×C₄	—	226	8	no	—
364	C₂×C₄	—	226	8	no	—
365	C₂×C₄	—	226	2	no	—
366	C₂×C₄	—	226	2	no	—
367	C₂×C₄	—	226	2	no	—
368	C₂×C₄	—	226	2	no	—
369	C₂×C₄	—	226	2	no	—
370	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
371	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
372	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
373	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
374	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
375	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
376	C₂²	—	2	8	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	113	4	no	—
380	C₂²	—	226	8	no	—
381	C₂²	—	226	2	no	—
382	C₂²	—	226	2	no	—
383	C₂²	C₂×Q₈×D₁₁₃	1	4	yes	—
384	C₂²	C₂×Q₈×D₁₁₃	1	2	yes	—
385	C₂²	#41×D₁₁₃	1	2	yes	—
386	C₂²	#16813667	1	2	yes	—
387	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	113	4	no	—
395	C₄	—	113	4	no	—
396	C₄	—	226	2	no	—
397	C₄	—	226	2	no	—
398	C₄	—	226	2	no	—
399	C₄	—	226	2	no	—
400	C₄	—	226	2	no	—
401	C₂	—	2	4	no	—
402	C₂	—	226	4	no	—
403	C₂	#20299302	1	4	yes	direct product factor
404	C₂	C₂²×Q₈×D₁₁₃	1	1	yes	characteristic
405	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
406	C₂	C₂×#16813667	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₁₃
commutator, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	C₂×C₂²⋊Q₈×C₁₁₃	C₂
socle	C₂³×C₁₁₃	C₂⁴
prime radical	C₂²×C₂²⋊D₁₁₃	C₂²
hypercenter	C₂×C₂²⋊Q₈	D₁₁₃
hypocenter	C₁₁₃	C₂×#554
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #20299302	C₂	direct (N × H)
2. C₂×#16813620	C₂	semidirect
3. C₂×#16813612	C₂	semidirect
4. C₂×#16813612	C₂	semidirect
5. C₂×#16813600	C₂	semidirect
6. C₂×#16813600	C₂	semidirect
7. C₂×#16813599	C₂	semidirect
8. C₂×#16813599	C₂	semidirect
9. C₂×#16813598	C₂	semidirect
10. C₂×#16813587	C₂	semidirect
14. C₂²×#14268626	C₂	semidirect
15. C₂×C₄⋊C₄×D₁₁₃	C₂	semidirect
16. C₂×C₂²⋊Q₈×C₁₁₃	C₂	semidirect
25. #16813620	C₂²	semidirect
26. #16813612	C₂²	semidirect
27. #16813612	C₂²	semidirect
28. #16813600	C₂²	semidirect
29. #16813600	C₂²	semidirect
30. #16813599	C₂²	semidirect
31. #16813599	C₂²	semidirect
32. #16813598	C₂²	semidirect
33. #16813587	C₂²	semidirect
50. C₂×#14268626	C₂²	semidirect
51. C₄⋊C₄×D₁₁₃	C₂²	semidirect
61. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
72. C₂×C₂²⋊D₁₁₃	Q₈	semidirect
150. C₂²⋊D₁₁₃	C₂×Q₈	semidirect
198. C₂×C₁₁₃	#554	semidirect
204. C₁₁₃	C₂×#554	semidirect
214. C₂×C₂²⋊Q₈	D₁₁₃	semidirect
239. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
403. C₂	#20299302	direct (N × H)

Maximal subgroups

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

subgroup	index
#20299302	2
C₂×#16813620	2
C₂×#16813612	2
C₂×#16813600	2
C₂×#16813599	2
C₂×#16813598	2
C₂×#16813587	2
C₂×C₄×C₂²⋊D₁₁₃	2
C₂×#16813582	2
C₂²×#14268626	2
C₂×C₄⋊C₄×D₁₁₃	2
C₂×C₂²⋊Q₈×C₁₁₃	2
C₂×#554	113

Subgroups — C2×#20299302 #28404102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20299302 #28404102