Subgroups — C₂×#14558284 #18008727

Order 4736.

1024 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558284	C₂	1	16	yes	maximal, direct product factor
2	C₂×#11924535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11924534	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11924531	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11924531	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11924529	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11924529	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11924527	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11924526	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11924522	C₂	1	1	yes	maximal, characteristic
11	C₂×#11924519	C₂	1	1	yes	maximal, characteristic
12	C₂×#11924518	C₂	1	1	yes	maximal, characteristic
13	C₂×#11924515	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11924514	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#11924512	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂²⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₇₄	C₂²	1	1	yes	characteristic
18	C₂²×Dic₇₄	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₃₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₃₇	C₂²	1	1	yes	characteristic
21	#11924535	C₂²	1	8	yes	complemented
22	#11924534	C₂²	1	8	yes	complemented
23	#11924531	C₂²	1	8	yes	complemented
24	#11924531	C₂²	1	8	yes	complemented
25	#11924529	C₂²	1	8	yes	complemented
26	#11924529	C₂²	1	8	yes	complemented
27	#11924527	C₂²	1	8	yes	complemented
28	#11924526	C₂²	1	8	yes	complemented
29	#11924522	C₂²	1	8	yes	—
30	#11924519	C₂²	1	8	yes	—
31	#11924518	C₂²	1	8	yes	—
32	#11924515	C₂²	1	8	yes	complemented
33	#11924514	C₂²	1	8	yes	complemented
34	#11924512	C₂²	1	8	yes	complemented
35	C₂×C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
39	C₂×#10596936	C₂²	1	1	yes	characteristic
40	C₂×#10596936	C₂²	1	1	yes	characteristic
41	C₂×#10596936	C₂²	1	1	yes	characteristic
42	C₂×#10596936	C₂²	1	1	yes	characteristic
43	C₂×#10596936	C₂²	1	1	yes	characteristic
44	C₂×#10596936	C₂²	1	1	yes	characteristic
45	C₂×#10596936	C₂²	1	1	yes	characteristic
46	C₂×#10596936	C₂²	1	1	yes	characteristic
47	C₂×#10596936	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊Dic₃₇	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊Dic₃₇	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊Dic₃₇	C₂²	1	1	yes	characteristic
51	C₂×#10596938	C₂²	1	1	yes	characteristic
52	C₂×#10596938	C₂²	1	1	yes	characteristic
53	C₂×#10596938	C₂²	1	1	yes	characteristic
54	C₂×#10596938	C₂²	1	1	yes	characteristic
55	C₂×#10596938	C₂²	1	1	yes	characteristic
56	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
57	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₃₇	C₂²	1	1	yes	characteristic
60	C₂³×C₄×C₃₇	C₂²	1	1	yes	characteristic
61	C₂²⋊Q₈×C₃₇	C₂²	1	8	yes	complemented
62	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
67	C₂⁴×C₃₇	C₂³	1	1	yes	characteristic
68	C₂³×D₃₇	C₂³	1	1	yes	characteristic
69	C₂×Q₈×C₃₇	—	4	2	no	—
70	C₂×Q₈×C₃₇	C₂³	1	4	yes	—
71	C₂²×C₄×C₃₇	—	4	2	no	—
72	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₃₇	C₂³	1	4	yes	—
79	C₂×C₂²⋊D₃₇	—	4	2	no	—
80	C₂×C₂²⋊D₃₇	C₂³	1	4	yes	—
81	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
82	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
83	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
84	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
85	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
86	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
87	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
88	C₂×C₄×D₃₇	—	4	2	no	—
89	C₂×C₄×D₃₇	C₂³	1	4	yes	—
90	C₂×Dic₇₄	—	4	2	no	—
91	C₂×Dic₇₄	—	4	2	no	—
92	C₂×Dic₇₄	C₂³	1	4	yes	—
93	C₂×Dic₇₄	C₂³	1	4	yes	—
94	C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
95	C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
96	C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
97	C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
98	C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
99	C₂²⋊Dic₃₇	C₂³	1	4	yes	—
100	C₂²⋊Dic₃₇	C₂³	1	4	yes	—
101	C₂²⋊Dic₃₇	C₂³	1	4	yes	—
102	#10596938	C₂³	1	4	yes	—
103	#10596938	C₂³	1	4	yes	—
104	#10596938	C₂³	1	4	yes	—
105	#10596938	C₂³	1	4	yes	—
106	#10596938	C₂³	1	4	yes	—
107	C₄⋊Dic₃₇	C₂³	1	4	yes	—
108	C₄⋊Dic₃₇	C₂³	1	4	yes	—
109	C₄⋊Dic₃₇	C₂³	1	4	yes	—
110	C₄⋊Dic₃₇	C₂³	1	4	yes	—
111	#10596936	C₂³	1	4	yes	—
112	#10596936	C₂³	1	4	yes	—
113	#10596936	C₂³	1	4	yes	—
114	#10596936	C₂³	1	4	yes	—
115	#10596936	C₂³	1	4	yes	—
116	#10596936	C₂³	1	4	yes	—
117	#10596936	C₂³	1	4	yes	—
118	#10596936	C₂³	1	4	yes	—
119	#10596936	C₂³	1	4	yes	—
120	C₄×Dic₃₇	C₂³	1	4	yes	—
121	C₄×Dic₃₇	C₂³	1	4	yes	—
122	C₄×Dic₃₇	C₂³	1	4	yes	—
123	C₂³×C₃₇	—	2	2	no	—
124	C₂³×C₃₇	—	2	2	no	—
125	C₂³×C₃₇	—	2	2	no	—
126	C₂³×C₃₇	C₂⁴	1	2	yes	—
127	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
128	C₂²×D₃₇	—	2	2	no	—
129	C₂²×D₃₇	—	2	2	no	—
130	C₂²×D₃₇	—	2	2	no	—
131	C₂²×D₃₇	C₂⁴	1	2	yes	—
132	Q₈×C₃₇	—	4	4	no	—
133	C₂×C₄×C₃₇	—	2	2	no	—
134	C₂×C₄×C₃₇	—	2	2	no	—
135	C₂×C₄×C₃₇	—	2	2	no	—
136	C₂×C₄×C₃₇	—	2	2	no	—
137	C₂×C₄×C₃₇	—	2	2	no	—
138	C₂×C₄×C₃₇	—	2	2	no	—
139	C₂×C₄×C₃₇	—	4	4	no	—
140	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
141	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
142	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
143	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
144	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
145	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
146	C₂²⋊D₃₇	—	4	4	no	—
147	C₂×Dic₃₇	—	2	2	no	—
148	C₂×Dic₃₇	—	2	2	no	—
149	C₂×Dic₃₇	—	2	2	no	—
150	C₂×Dic₃₇	—	2	2	no	—
151	C₂×Dic₃₇	—	2	2	no	—
152	C₂×Dic₃₇	—	2	2	no	—
153	C₂×Dic₃₇	—	2	2	no	—
154	C₂×Dic₃₇	C₂⁴	1	2	yes	—
155	C₂×Dic₃₇	C₂⁴	1	2	yes	—
156	C₂×Dic₃₇	C₂⁴	1	2	yes	—
157	C₂×Dic₃₇	C₂⁴	1	2	yes	—
158	C₂×Dic₃₇	C₂⁴	1	2	yes	—
159	C₂×Dic₃₇	C₂⁴	1	2	yes	—
160	C₂×Dic₃₇	C₂⁴	1	2	yes	—
161	C₄×D₃₇	—	4	4	no	—
162	Dic₇₄	—	4	4	no	—
163	Dic₇₄	—	4	4	no	—
164	C₂²×C₃₇	—	2	2	no	—
165	C₂²×C₃₇	—	2	2	no	—
166	C₂²×C₃₇	—	2	2	no	—
167	C₂²×C₃₇	—	4	4	no	—
168	C₂²×C₃₇	H(5,𝔽₂)	1	2	yes	—
169	C₂²×C₃₇	2₋¹⁺⁴	1	2	yes	—
170	C₂²×C₃₇	2₋¹⁺⁴	1	2	yes	—
171	C₂²×C₃₇	C₂⁵	1	1	yes	characteristic
172	C₂×D₃₇	—	2	2	no	—
173	C₂×D₃₇	—	2	2	no	—
174	C₂×D₃₇	—	2	2	no	—
175	C₂×D₃₇	—	4	4	no	—
176	C₄×C₃₇	—	2	2	no	—
177	C₄×C₃₇	—	2	2	no	—
178	C₄×C₃₇	—	2	2	no	—
179	C₄×C₃₇	—	2	2	no	—
180	C₄×C₃₇	—	2	2	no	—
181	C₄×C₃₇	—	2	2	no	—
182	Dic₃₇	—	2	2	no	—
183	Dic₃₇	—	2	2	no	—
184	Dic₃₇	—	2	2	no	—
185	Dic₃₇	—	2	2	no	—
186	Dic₃₇	—	2	2	no	—
187	Dic₃₇	—	2	2	no	—
188	Dic₃₇	—	2	2	no	—
189	C₂×#563	—	37	1	no	maximal, Sylow
190	C₂×C₃₇	—	4	2	no	—
191	C₂×C₃₇	#563	1	4	yes	complemented
192	C₂×C₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×C₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
194	C₂×C₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
195	D₃₇	—	4	2	no	—
196	#563	—	37	16	no	—
197	C₂×C₄⋊Q₈	—	37	1	no	—
198	C₂×C₄⋊Q₈	—	37	1	no	—
199	C₂×#126	—	37	1	no	—
200	C₂×#126	—	37	1	no	—
201	C₂×#126	—	37	1	no	—
202	C₂×#126	—	37	1	no	—
203	C₂×#125	—	37	1	no	—
204	C₂×#125	—	37	1	no	—
205	C₂×#124	—	37	1	no	—
206	C₂×#123	—	37	1	no	—
207	C₂×#123	—	37	1	no	—
208	C₂×C₂²⋊Q₈	—	37	1	no	—
209	C₂×C₂²⋊Q₈	—	37	1	no	—
210	C₂×C₂²⋊Q₈	—	37	1	no	—
211	C₂×C₂²⋊Q₈	D₃₇	1	1	yes	characteristic, complemented
212	C₃₇	C₂×#563	1	1	yes	characteristic, complemented, Sylow
213	C₂²×Q₈	—	37	1	no	—
214	C₂²×Q₈	—	37	1	no	—
215	C₂²×Q₈	C₂×D₃₇	1	1	yes	characteristic
216	C₂²×D₄	—	37	1	no	—
217	C₂³×C₄	—	37	1	no	—
218	C₂³×C₄	C₂×D₃₇	1	1	yes	characteristic
219	C₄⋊Q₈	—	37	8	no	—
220	C₄⋊Q₈	—	37	8	no	—
221	#126	—	37	8	no	—
222	#126	—	37	8	no	—
223	#126	—	37	8	no	—
224	#126	—	37	8	no	—
225	#125	—	37	8	no	—
226	#125	—	37	8	no	—
227	#124	—	37	8	no	—
228	#123	—	37	8	no	—
229	#123	—	37	8	no	—
230	C₂²⋊Q₈	—	37	8	no	—
231	C₂²⋊Q₈	—	37	8	no	—
232	C₂²⋊Q₈	—	37	8	no	—
233	C₂²⋊Q₈	C₂×D₃₇	1	8	yes	complemented
234	C₂×C₄⋊C₄	—	37	1	no	—
235	C₂×C₄⋊C₄	—	37	1	no	—
236	C₂×C₄⋊C₄	—	37	1	no	—
237	C₂×C₄⋊C₄	—	37	1	no	—
238	C₂×C₄⋊C₄	—	37	1	no	—
239	C₂×C₄⋊C₄	—	37	1	no	—
240	C₂×C₄⋊C₄	—	37	1	no	—
241	C₂×C₄⋊C₄	—	37	1	no	—
242	C₂×C₄⋊C₄	—	37	1	no	—
243	C₂×C₄⋊C₄	—	37	1	no	—
244	C₂×C₄⋊C₄	—	37	1	no	—
245	C₂×C₄⋊C₄	—	37	1	no	—
246	C₂×C₄⋊C₄	—	37	1	no	—
247	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	—	37	1	no	—
251	C₂×C₂²⋊C₄	—	37	1	no	—
252	C₂×C₂²⋊C₄	—	37	1	no	—
253	C₂×C₂²⋊C₄	—	37	1	no	—
254	C₂×C₂²⋊C₄	—	37	1	no	—
255	C₂×C₂²⋊C₄	—	37	1	no	—
256	C₂×C₂²⋊C₄	—	37	1	no	—
257	C₂×C₂²⋊C₄	—	37	1	no	—
258	C₂×C₂²⋊C₄	C₂×D₃₇	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂×D₃₇	1	1	yes	characteristic
260	C₂×C₄²	—	37	1	no	—
261	C₂×C₄²	—	37	1	no	—
262	C₂×C₄²	—	37	1	no	—
263	C₂⁴	—	37	1	no	—
264	C₂⁴	C₂²×D₃₇	1	1	yes	characteristic
265	C₂×Q₈	—	4	2	no	—
266	C₂×Q₈	—	37	4	no	—
267	C₂×Q₈	—	37	4	no	—
268	C₂×Q₈	—	148	2	no	—
269	C₂×Q₈	—	148	2	no	—
270	C₂×Q₈	C₂²×D₃₇	1	4	yes	—
271	C₂×D₄	—	37	4	no	—
272	C₂×D₄	—	148	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	37	1	no	—
275	C₂²×C₄	—	37	1	no	—
276	C₂²×C₄	—	37	1	no	—
277	C₂²×C₄	—	37	1	no	—
278	C₂²×C₄	—	37	1	no	—
279	C₂²×C₄	—	37	1	no	—
280	C₂²×C₄	—	37	1	no	—
281	C₂²×C₄	—	37	4	no	—
282	C₂²×C₄	—	148	2	no	—
283	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
284	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
287	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
288	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
289	C₂²×C₄	C₂²×D₃₇	1	4	yes	—
290	C₄⋊C₄	—	37	4	no	—
291	C₄⋊C₄	—	37	4	no	—
292	C₄⋊C₄	—	37	4	no	—
293	C₄⋊C₄	—	37	4	no	—
294	C₄⋊C₄	—	37	4	no	—
295	C₄⋊C₄	—	37	4	no	—
296	C₄⋊C₄	—	37	4	no	—
297	C₄⋊C₄	—	37	4	no	—
298	C₄⋊C₄	—	37	4	no	—
299	C₄⋊C₄	—	37	4	no	—
300	C₄⋊C₄	—	37	4	no	—
301	C₄⋊C₄	—	37	4	no	—
302	C₄⋊C₄	—	37	4	no	—
303	C₄⋊C₄	C₂²×D₃₇	1	4	yes	—
304	C₄⋊C₄	C₂²×D₃₇	1	4	yes	—
305	C₄⋊C₄	C₂²×D₃₇	1	4	yes	—
306	C₂²⋊C₄	—	37	4	no	—
307	C₂²⋊C₄	—	37	4	no	—
308	C₂²⋊C₄	—	37	4	no	—
309	C₂²⋊C₄	—	37	4	no	—
310	C₂²⋊C₄	—	37	4	no	—
311	C₂²⋊C₄	—	37	4	no	—
312	C₂²⋊C₄	—	37	4	no	—
313	C₂²⋊C₄	—	37	4	no	—
314	C₂²⋊C₄	C₂²×D₃₇	1	4	yes	—
315	C₂²⋊C₄	C₂²×D₃₇	1	4	yes	—
316	C₄²	—	37	4	no	—
317	C₄²	—	37	4	no	—
318	C₄²	—	37	4	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	37	2	no	—
323	C₂³	—	74	2	no	—
324	C₂³	—	74	2	no	—
325	C₂³	—	74	2	no	—
326	C₂³	C₂³×D₃₇	1	2	yes	—
327	C₂³	C₂³×D₃₇	1	1	yes	characteristic
328	Q₈	—	4	4	no	—
329	Q₈	—	148	4	no	—
330	Q₈	—	148	4	no	—
331	D₄	—	148	4	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	37	2	no	—
340	C₂×C₄	—	37	2	no	—
341	C₂×C₄	—	37	2	no	—
342	C₂×C₄	—	37	2	no	—
343	C₂×C₄	—	37	2	no	—
344	C₂×C₄	—	37	2	no	—
345	C₂×C₄	—	37	2	no	—
346	C₂×C₄	—	74	2	no	—
347	C₂×C₄	—	74	2	no	—
348	C₂×C₄	—	74	2	no	—
349	C₂×C₄	—	74	2	no	—
350	C₂×C₄	—	74	2	no	—
351	C₂×C₄	—	74	2	no	—
352	C₂×C₄	—	74	2	no	—
353	C₂×C₄	—	148	4	no	—
354	C₂×C₄	C₂³×D₃₇	1	2	yes	—
355	C₂×C₄	C₂³×D₃₇	1	2	yes	—
356	C₂×C₄	C₂³×D₃₇	1	2	yes	—
357	C₂×C₄	C₂³×D₃₇	1	2	yes	—
358	C₂×C₄	C₂³×D₃₇	1	2	yes	—
359	C₂×C₄	C₂³×D₃₇	1	2	yes	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	74	2	no	—
365	C₂²	—	74	2	no	—
366	C₂²	—	74	2	no	—
367	C₂²	—	148	4	no	—
368	C₂²	#11924581	1	2	yes	—
369	C₂²	#11924583	1	2	yes	—
370	C₂²	#11924584	1	2	yes	—
371	C₂²	C₂⁴×D₃₇	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	74	2	no	—
379	C₄	—	74	2	no	—
380	C₄	—	74	2	no	—
381	C₄	—	74	2	no	—
382	C₄	—	74	2	no	—
383	C₄	—	74	2	no	—
384	C₄	—	74	2	no	—
385	C₂	—	4	2	no	—
386	C₂	—	148	2	no	—
387	C₂	#14558284	1	4	yes	direct product factor
388	C₂	C₂×#11924581	1	1	yes	characteristic
389	C₂	C₂×#11924583	1	1	yes	characteristic
390	C₂	C₂×#11924584	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₃₇
commutator, cosocle	C₂²×C₃₇	C₂⁵
Frattini	C₂²	C₂⁴×D₃₇
Fitting	C₂×C₂²⋊Q₈×C₃₇	C₂
socle	C₂³×C₃₇	C₂⁴
prime radical	C₂²×C₂²⋊D₃₇	C₂²
hypercenter	C₂×C₂²⋊Q₈	D₃₇
hypocenter	C₃₇	C₂×#563
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #14558284	C₂	direct (N × H)
2. C₂×#11924535	C₂	semidirect
3. C₂×#11924534	C₂	semidirect
4. C₂×#11924531	C₂	semidirect
5. C₂×#11924531	C₂	semidirect
6. C₂×#11924529	C₂	semidirect
7. C₂×#11924529	C₂	semidirect
8. C₂×#11924527	C₂	semidirect
9. C₂×#11924526	C₂	semidirect
13. C₂×#11924515	C₂	semidirect
14. C₂×#11924514	C₂	semidirect
15. C₂×#11924512	C₂	semidirect
16. C₂×C₂²⋊Q₈×C₃₇	C₂	semidirect
21. #11924535	C₂²	semidirect
22. #11924534	C₂²	semidirect
23. #11924531	C₂²	semidirect
24. #11924531	C₂²	semidirect
25. #11924529	C₂²	semidirect
26. #11924529	C₂²	semidirect
27. #11924527	C₂²	semidirect
28. #11924526	C₂²	semidirect
32. #11924515	C₂²	semidirect
33. #11924514	C₂²	semidirect
34. #11924512	C₂²	semidirect
61. C₂²⋊Q₈×C₃₇	C₂²	semidirect
191. C₂×C₃₇	#563	semidirect
211. C₂×C₂²⋊Q₈	D₃₇	semidirect
212. C₃₇	C₂×#563	semidirect
233. C₂²⋊Q₈	C₂×D₃₇	semidirect
387. C₂	#14558284	direct (N × H)

Maximal subgroups

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

subgroup	index
#14558284	2
C₂×#11924535	2
C₂×#11924534	2
C₂×#11924531	2
C₂×#11924529	2
C₂×#11924527	2
C₂×#11924526	2
C₂×#11924522	2
C₂×#11924519	2
C₂×#11924518	2
C₂×#11924515	2
C₂×#11924514	2
C₂×#11924512	2
C₂×C₂²⋊Q₈×C₃₇	2
C₂×#563	37

Subgroups — C2×#14558284 #18008727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14558284 #18008727