Subgroups — #387×D₂₂₇ #44402154

Order 29056.

712 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	C₂×C₄⋊C₄×D₂₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×D₂₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×D₂₂₇	C₂	1	1	yes	maximal, characteristic
4	#28408919	C₂	1	1	yes	maximal, characteristic, complemented
5	#28408918	C₂	1	1	yes	maximal, characteristic, complemented
6	#28408917	C₂	1	1	yes	maximal, characteristic, complemented
7	#28408916	C₂	1	1	yes	maximal, characteristic, complemented
8	#28408915	C₂	1	1	yes	maximal, characteristic, complemented
9	#28408914	C₂	1	1	yes	maximal, characteristic, complemented
10	#28408913	C₂	1	1	yes	maximal, characteristic, complemented
11	#95×D₂₂₇	C₂	1	1	yes	maximal, characteristic
12	#95×D₂₂₇	C₂	1	1	yes	maximal, characteristic
13	#95×D₂₂₇	C₂	1	1	yes	maximal, characteristic
14	#95×D₂₂₇	C₂	1	1	yes	maximal, characteristic
15	#387×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₄×D₂₂₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₂₂₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₂₂₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₂₂₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₂₂₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₂₂₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₂₂₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Dic₂₂₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Dic₂₂₇	C₂²	1	1	yes	characteristic
25	C₂×Dic₂₂₇⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×Dic₂₂₇⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×Dic₂₂₇⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×Dic₂₂₇⋊C₄	C₂²	1	1	yes	characteristic
29	C₄⋊C₄×D₂₂₇	—	2	4	no	—
30	C₄⋊C₄×D₂₂₇	C₄	1	8	yes	complemented
31	C₂×C₄×Dic₂₂₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×Dic₂₂₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×Dic₂₂₇	C₂²	1	1	yes	characteristic
34	C₄²×D₂₂₇	—	2	4	no	—
35	C₂₂₇⋊#95	C₂²	1	1	yes	characteristic
36	C₂₂₇⋊#95	C₂²	1	1	yes	characteristic
37	C₂₂₇⋊#95	C₂²	1	1	yes	characteristic
38	C₂₂₇⋊#95	C₂²	1	1	yes	characteristic
39	C₂₂₇⋊#95	C₂²	1	1	yes	characteristic
40	C₂₂₇⋊#95	C₂²	1	1	yes	characteristic
41	C₂₂₇⋊#95	C₂²	1	1	yes	characteristic
42	C₂₂₇⋊#95	C₂²	1	1	yes	characteristic
43	C₂₂₇⋊#95	C₂²	1	1	yes	characteristic
44	C₂₂₇⋊#95	C₂²	1	1	yes	characteristic
45	C₂₂₇⋊#95	C₂²	1	1	yes	characteristic
46	C₂₂₇⋊#95	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₂₂₇	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₂₂₇	C₂²	1	1	yes	characteristic
49	C₂×C₄²×C₂₂₇	C₂²	1	1	yes	characteristic
50	#95×C₂₂₇	C₂²	1	1	yes	characteristic
51	#95×C₂₂₇	C₂²	1	1	yes	characteristic
52	#95×C₂₂₇	C₂²	1	1	yes	characteristic
53	#95×C₂₂₇	C₂²	1	1	yes	characteristic
54	C₂³×D₂₂₇	C₂³	1	1	yes	characteristic
55	C₂²×Dic₂₂₇	C₂³	1	1	yes	characteristic
56	C₂²×Dic₂₂₇	C₂³	1	1	yes	characteristic
57	C₂²×Dic₂₂₇	C₂³	1	1	yes	characteristic
58	C₂²×Dic₂₂₇	C₂³	1	1	yes	characteristic
59	C₂²×Dic₂₂₇	C₂³	1	1	yes	characteristic
60	C₂²×Dic₂₂₇	C₂³	1	1	yes	characteristic
61	C₂²×Dic₂₂₇	C₂³	1	1	yes	characteristic
62	C₂×C₄×D₂₂₇	—	2	2	no	—
63	C₂×C₄×D₂₂₇	—	2	2	no	—
64	C₂×C₄×D₂₂₇	—	2	2	no	—
65	C₂×C₄×D₂₂₇	—	2	2	no	—
66	C₂×C₄×D₂₂₇	—	2	2	no	—
67	C₂×C₄×D₂₂₇	—	2	2	no	—
68	C₂×C₄×D₂₂₇	—	2	2	no	—
69	C₂×C₄×D₂₂₇	—	2	2	no	—
70	C₂×C₄×D₂₂₇	—	2	2	no	—
71	C₂×C₄×D₂₂₇	—	2	2	no	—
72	C₂×C₄×D₂₂₇	—	2	2	no	—
73	C₂×C₄×D₂₂₇	—	2	2	no	—
74	C₂×C₄×D₂₂₇	—	2	2	no	—
75	C₂×C₄×D₂₂₇	—	2	2	no	—
76	C₂×C₄×D₂₂₇	—	2	2	no	—
77	C₂×C₄×D₂₂₇	—	2	2	no	—
78	C₂×C₄×D₂₂₇	C₂×C₄	1	4	yes	—
79	C₂×C₄×D₂₂₇	C₂×C₄	1	4	yes	—
80	C₂×C₄×D₂₂₇	C₂×C₄	1	4	yes	—
81	C₂×C₄×D₂₂₇	D₄	1	4	yes	—
82	C₂×C₄×D₂₂₇	Q₈	1	4	yes	—
83	C₄⋊Dic₂₂₇	—	2	2	no	—
84	C₄⋊Dic₂₂₇	C₂×C₄	1	4	yes	complemented
85	Dic₂₂₇⋊C₄	—	2	2	no	—
86	Dic₂₂₇⋊C₄	—	2	2	no	—
87	Dic₂₂₇⋊C₄	C₂×C₄	1	4	yes	complemented
88	Dic₂₂₇⋊C₄	C₂×C₄	1	4	yes	complemented
89	C₄×Dic₂₂₇	—	2	2	no	—
90	C₄×Dic₂₂₇	—	2	2	no	—
91	C₄×Dic₂₂₇	—	2	2	no	—
92	C₂²×C₄×C₂₂₇	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₂₂₇	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₂₂₇	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₂₂₇	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₂₂₇	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₂₂₇	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₂₂₇	C₂³	1	1	yes	characteristic
99	C₄⋊C₄×C₂₂₇	—	2	2	no	—
100	C₄⋊C₄×C₂₂₇	C₂×C₄	1	4	yes	complemented
101	C₄²×C₂₂₇	—	2	2	no	—
102	C₂²×D₂₂₇	C₂²×C₄	1	2	yes	—
103	C₂²×D₂₂₇	C₂×D₄	1	2	yes	—
104	C₂²×D₂₂₇	C₂×Q₈	1	2	yes	—
105	C₂²×D₂₂₇	#41	1	2	yes	—
106	C₂²×D₂₂₇	#41	1	2	yes	—
107	C₂²×D₂₂₇	#41	1	2	yes	—
108	C₂²×D₂₂₇	#41	1	2	yes	—
109	C₂×Dic₂₂₇	—	2	1	no	—
110	C₂×Dic₂₂₇	—	2	1	no	—
111	C₂×Dic₂₂₇	—	2	1	no	—
112	C₂×Dic₂₂₇	—	2	1	no	—
113	C₂×Dic₂₂₇	—	2	1	no	—
114	C₂×Dic₂₂₇	—	2	1	no	—
115	C₂×Dic₂₂₇	—	2	1	no	—
116	C₂×Dic₂₂₇	—	2	1	no	—
117	C₂×Dic₂₂₇	—	2	1	no	—
118	C₂×Dic₂₂₇	—	2	1	no	—
119	C₂×Dic₂₂₇	—	2	1	no	—
120	C₂×Dic₂₂₇	—	2	1	no	—
121	C₂×Dic₂₂₇	—	2	1	no	—
122	C₂×Dic₂₂₇	—	2	1	no	—
123	C₂×Dic₂₂₇	—	2	1	no	—
124	C₂×Dic₂₂₇	—	2	1	no	—
125	C₂×Dic₂₂₇	C₂²×C₄	1	2	yes	—
126	C₂×Dic₂₂₇	C₂²×C₄	1	2	yes	—
127	C₂×Dic₂₂₇	C₂²×C₄	1	2	yes	—
128	C₂×Dic₂₂₇	C₂×D₄	1	2	yes	—
129	C₂×Dic₂₂₇	C₂×Q₈	1	2	yes	—
130	C₄×D₂₂₇	—	2	8	no	—
131	C₄×D₂₂₇	—	2	8	no	—
132	C₄×D₂₂₇	—	2	8	no	—
133	C₄×D₂₂₇	—	2	8	no	—
134	C₄×D₂₂₇	—	2	8	no	—
135	C₄×D₂₂₇	—	4	4	no	—
136	C₄×D₂₂₇	—	4	4	no	—
137	C₂³×C₂₂₇	C₂⁴	1	1	yes	characteristic
138	C₂×C₄×C₂₂₇	—	2	1	no	—
139	C₂×C₄×C₂₂₇	—	2	1	no	—
140	C₂×C₄×C₂₂₇	—	2	1	no	—
141	C₂×C₄×C₂₂₇	—	2	1	no	—
142	C₂×C₄×C₂₂₇	—	2	1	no	—
143	C₂×C₄×C₂₂₇	—	2	1	no	—
144	C₂×C₄×C₂₂₇	—	2	1	no	—
145	C₂×C₄×C₂₂₇	—	2	1	no	—
146	C₂×C₄×C₂₂₇	—	2	1	no	—
147	C₂×C₄×C₂₂₇	—	2	1	no	—
148	C₂×C₄×C₂₂₇	—	2	1	no	—
149	C₂×C₄×C₂₂₇	—	2	1	no	—
150	C₂×C₄×C₂₂₇	—	2	1	no	—
151	C₂×C₄×C₂₂₇	—	2	1	no	—
152	C₂×C₄×C₂₂₇	—	2	1	no	—
153	C₂×C₄×C₂₂₇	—	2	1	no	—
154	C₂×C₄×C₂₂₇	C₂²×C₄	1	2	yes	—
155	C₂×C₄×C₂₂₇	C₂²×C₄	1	2	yes	—
156	C₂×C₄×C₂₂₇	C₂²×C₄	1	2	yes	—
157	C₂×C₄×C₂₂₇	C₂×D₄	1	2	yes	—
158	C₂×C₄×C₂₂₇	C₂×Q₈	1	2	yes	—
159	C₂²×C₂₂₇	C₂³×C₄	1	1	yes	characteristic
160	C₂²×C₂₂₇	C₂²×D₄	1	1	yes	characteristic
161	C₂²×C₂₂₇	C₂²×Q₈	1	1	yes	characteristic
162	C₂²×C₂₂₇	C₂×#41	1	1	yes	characteristic
163	C₂²×C₂₂₇	C₂×#41	1	1	yes	characteristic
164	C₂²×C₂₂₇	C₂×#41	1	1	yes	characteristic
165	C₂²×C₂₂₇	C₂×#41	1	1	yes	characteristic
166	C₂×D₂₂₇	#117	1	4	yes	—
167	C₂×D₂₂₇	C₄×D₄	1	4	yes	—
168	C₂×D₂₂₇	C₄×Q₈	1	4	yes	—
169	C₂×D₂₂₇	C₂²⋊Q₈	1	4	yes	—
170	C₂×D₂₂₇	#123	1	4	yes	—
171	C₂×D₂₂₇	#125	1	4	yes	—
172	C₂×D₂₂₇	#126	1	4	yes	—
173	C₄×C₂₂₇	—	2	2	no	—
174	C₄×C₂₂₇	—	2	2	no	—
175	C₄×C₂₂₇	—	2	2	no	—
176	C₄×C₂₂₇	—	2	2	no	—
177	C₄×C₂₂₇	—	2	2	no	—
178	C₄×C₂₂₇	—	4	1	no	—
179	C₄×C₂₂₇	—	4	1	no	—
180	Dic₂₂₇	—	2	2	no	—
181	Dic₂₂₇	—	2	2	no	—
182	Dic₂₂₇	—	2	2	no	—
183	Dic₂₂₇	—	2	2	no	—
184	Dic₂₂₇	—	2	2	no	—
185	Dic₂₂₇	—	4	1	no	—
186	Dic₂₂₇	—	4	1	no	—
187	C₂×C₂₂₇	C₂×#117	1	1	yes	characteristic
188	C₂×C₂₂₇	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂×C₂₂₇	C₂×C₄×Q₈	1	1	yes	characteristic
190	C₂×C₂₂₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
191	C₂×C₂₂₇	C₂×#123	1	1	yes	characteristic
192	C₂×C₂₂₇	C₂×#125	1	1	yes	characteristic
193	C₂×C₂₂₇	C₂×#126	1	1	yes	characteristic
194	D₂₂₇	#387	1	8	yes	direct product factor
195	C₂₂₇	C₂×#387	1	1	yes	characteristic, complemented, Sylow
196	C₂×#387	—	227	1	no	maximal, Sylow
197	C₂²×C₄⋊C₄	—	227	1	no	—
198	C₂²×C₄⋊C₄	—	227	1	no	—
199	C₂²×C₄²	—	227	1	no	—
200	#387	—	227	1	no	—
201	#387	—	227	1	no	—
202	#387	—	227	1	no	—
203	#387	—	227	1	no	—
204	#387	—	227	1	no	—
205	#387	—	227	1	no	—
206	#387	—	227	1	no	—
207	#387	D₂₂₇	1	1	yes	characteristic, direct product factor
208	C₂×#95	—	227	1	no	—
209	C₂×#95	—	227	1	no	—
210	C₂×#95	—	227	1	no	—
211	C₂×#95	—	227	1	no	—
212	C₂³×C₄	—	227	1	no	—
213	C₂³×C₄	—	227	1	no	—
214	C₂³×C₄	—	227	1	no	—
215	C₂³×C₄	—	227	1	no	—
216	C₂³×C₄	—	227	1	no	—
217	C₂³×C₄	—	227	1	no	—
218	C₂³×C₄	—	227	1	no	—
219	C₂×C₄⋊C₄	—	454	4	no	—
220	C₂×C₄⋊C₄	—	227	1	no	—
221	C₂×C₄⋊C₄	—	227	1	no	—
222	C₂×C₄⋊C₄	—	227	1	no	—
223	C₂×C₄⋊C₄	—	227	1	no	—
224	C₂×C₄⋊C₄	—	227	1	no	—
225	C₂×C₄⋊C₄	—	227	1	no	—
226	C₂×C₄⋊C₄	—	227	8	no	—
227	C₂×C₄⋊C₄	C₂×D₂₂₇	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×D₂₂₇	1	1	yes	characteristic
229	C₂×C₄²	—	454	4	no	—
230	C₂×C₄²	—	227	1	no	—
231	C₂×C₄²	—	227	1	no	—
232	C₂×C₄²	—	227	1	no	—
233	C₂×C₄²	C₂×D₂₂₇	1	1	yes	characteristic
234	#95	—	227	1	no	—
235	#95	—	227	1	no	—
236	#95	—	227	1	no	—
237	#95	—	227	1	no	—
238	#95	—	227	1	no	—
239	#95	—	227	1	no	—
240	#95	—	227	1	no	—
241	#95	—	227	1	no	—
242	#95	—	227	1	no	—
243	#95	—	227	1	no	—
244	#95	—	227	1	no	—
245	#95	—	227	1	no	—
246	#95	C₂×D₂₂₇	1	1	yes	characteristic
247	#95	C₂×D₂₂₇	1	1	yes	characteristic
248	#95	C₂×D₂₂₇	1	1	yes	characteristic
249	#95	C₂×D₂₂₇	1	1	yes	characteristic
250	C₂⁴	—	227	1	no	—
251	C₂²×C₄	—	454	2	no	—
252	C₂²×C₄	—	454	2	no	—
253	C₂²×C₄	—	454	2	no	—
254	C₂²×C₄	—	454	2	no	—
255	C₂²×C₄	—	454	2	no	—
256	C₂²×C₄	—	454	2	no	—
257	C₂²×C₄	—	454	2	no	—
258	C₂²×C₄	—	454	2	no	—
259	C₂²×C₄	—	454	2	no	—
260	C₂²×C₄	—	454	2	no	—
261	C₂²×C₄	—	454	2	no	—
262	C₂²×C₄	—	454	2	no	—
263	C₂²×C₄	—	454	2	no	—
264	C₂²×C₄	—	454	2	no	—
265	C₂²×C₄	—	454	2	no	—
266	C₂²×C₄	—	454	2	no	—
267	C₂²×C₄	—	227	1	no	—
268	C₂²×C₄	—	227	1	no	—
269	C₂²×C₄	—	227	1	no	—
270	C₂²×C₄	—	227	1	no	—
271	C₂²×C₄	—	227	1	no	—
272	C₂²×C₄	—	227	1	no	—
273	C₂²×C₄	—	227	1	no	—
274	C₂²×C₄	—	227	4	no	—
275	C₂²×C₄	—	227	4	no	—
276	C₂²×C₄	—	227	4	no	—
277	C₂²×C₄	—	227	4	no	—
278	C₂²×C₄	—	227	4	no	—
279	C₂²×C₄	C₂²×D₂₂₇	1	1	yes	characteristic
280	C₂²×C₄	C₂²×D₂₂₇	1	1	yes	characteristic
281	C₂²×C₄	C₂²×D₂₂₇	1	1	yes	characteristic
282	C₂²×C₄	C₂²×D₂₂₇	1	1	yes	characteristic
283	C₂²×C₄	C₂²×D₂₂₇	1	1	yes	characteristic
284	C₂²×C₄	C₂²×D₂₂₇	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₂₂₇	1	1	yes	characteristic
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	454	2	no	—
288	C₄⋊C₄	—	454	2	no	—
289	C₄⋊C₄	—	454	2	no	—
290	C₄⋊C₄	—	227	4	no	—
291	C₄⋊C₄	—	227	4	no	—
292	C₄⋊C₄	—	227	4	no	—
293	C₄⋊C₄	C₄×D₂₂₇	1	4	yes	complemented
294	C₄²	—	2	2	no	—
295	C₄²	—	454	2	no	—
296	C₄²	—	454	2	no	—
297	C₄²	—	454	2	no	—
298	C₂³	—	227	2	no	—
299	C₂³	—	227	2	no	—
300	C₂³	—	227	2	no	—
301	C₂³	—	227	2	no	—
302	C₂³	—	227	2	no	—
303	C₂³	—	227	2	no	—
304	C₂³	—	227	2	no	—
305	C₂³	C₂³×D₂₂₇	1	1	yes	characteristic
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	908	4	no	—
323	C₂×C₄	—	908	4	no	—
324	C₂×C₄	—	454	8	no	—
325	C₂×C₄	—	454	8	no	—
326	C₂×C₄	—	454	8	no	—
327	C₂×C₄	—	454	8	no	—
328	C₂×C₄	—	454	8	no	—
329	C₂×C₄	—	454	1	no	—
330	C₂×C₄	—	454	1	no	—
331	C₂×C₄	—	454	1	no	—
332	C₂×C₄	—	454	1	no	—
333	C₂×C₄	—	454	1	no	—
334	C₂×C₄	—	454	1	no	—
335	C₂×C₄	—	454	1	no	—
336	C₂×C₄	—	454	1	no	—
337	C₂×C₄	—	454	1	no	—
338	C₂×C₄	—	454	1	no	—
339	C₂×C₄	—	454	1	no	—
340	C₂×C₄	—	454	1	no	—
341	C₂×C₄	—	454	1	no	—
342	C₂×C₄	—	454	1	no	—
343	C₂×C₄	—	454	1	no	—
344	C₂×C₄	—	454	1	no	—
345	C₂×C₄	—	227	2	no	—
346	C₂×C₄	—	227	2	no	—
347	C₂×C₄	—	227	2	no	—
348	C₂×C₄	—	227	2	no	—
349	C₂×C₄	—	227	2	no	—
350	C₂×C₄	C₂×C₄×D₂₂₇	1	2	yes	—
351	C₂×C₄	C₂×C₄×D₂₂₇	1	2	yes	—
352	C₂×C₄	C₂×C₄×D₂₂₇	1	2	yes	—
353	C₂×C₄	D₄×D₂₂₇	1	2	yes	—
354	C₂×C₄	Q₈×D₂₂₇	1	2	yes	—
355	C₂²	—	227	4	no	—
356	C₂²	—	227	4	no	—
357	C₂²	—	227	4	no	—
358	C₂²	—	227	4	no	—
359	C₂²	—	227	4	no	—
360	C₂²	—	227	4	no	—
361	C₂²	—	227	4	no	—
362	C₂²	C₂²×C₄×D₂₂₇	1	1	yes	characteristic
363	C₂²	C₂×D₄×D₂₂₇	1	1	yes	characteristic
364	C₂²	C₂×Q₈×D₂₂₇	1	1	yes	characteristic
365	C₂²	#41×D₂₂₇	1	1	yes	characteristic
366	C₂²	#41×D₂₂₇	1	1	yes	characteristic
367	C₂²	#41×D₂₂₇	1	1	yes	characteristic
368	C₂²	#41×D₂₂₇	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	4	1	no	—
375	C₄	—	4	1	no	—
376	C₄	—	908	1	no	—
377	C₄	—	908	1	no	—
378	C₄	—	454	2	no	—
379	C₄	—	454	2	no	—
380	C₄	—	454	2	no	—
381	C₄	—	454	2	no	—
382	C₄	—	454	2	no	—
383	C₂	—	227	8	no	—
384	C₂	#117×D₂₂₇	1	1	yes	characteristic
385	C₂	C₄×D₄×D₂₂₇	1	1	yes	characteristic
386	C₂	C₄×Q₈×D₂₂₇	1	1	yes	characteristic
387	C₂	C₂²⋊Q₈×D₂₂₇	1	1	yes	characteristic
388	C₂	#123×D₂₂₇	1	1	yes	characteristic
389	C₂	#125×D₂₂₇	1	1	yes	characteristic
390	C₂	#126×D₂₂₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₂₇
commutator	C₂²×C₂₂₇	C₂³×C₄
Fitting	#387×C₂₂₇	C₂
socle, cosocle	C₂³×C₂₂₇	C₂⁴
prime radical	C₂³×D₂₂₇	C₂³
hypercenter	#387	D₂₂₇
hypocenter	C₂₂₇	C₂×#387
LCS	G ▷ C₂²×C₂₂₇ ▷ C₂₂₇
UCS	C₁ ◁ C₂³ ◁ #387

Complements

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

N	H ≅ G/N	type
4. #28408919	C₂	semidirect
5. #28408918	C₂	semidirect
6. #28408917	C₂	semidirect
7. #28408916	C₂	semidirect
8. #28408915	C₂	semidirect
9. #28408914	C₂	semidirect
10. #28408913	C₂	semidirect
15. #387×C₂₂₇	C₂	semidirect
30. C₄⋊C₄×D₂₂₇	C₄	semidirect
84. C₄⋊Dic₂₂₇	C₂×C₄	semidirect
87. Dic₂₂₇⋊C₄	C₂×C₄	semidirect
88. Dic₂₂₇⋊C₄	C₂×C₄	semidirect
100. C₄⋊C₄×C₂₂₇	C₂×C₄	semidirect
194. D₂₂₇	#387	direct (N × H)
195. C₂₂₇	C₂×#387	semidirect
207. #387	D₂₂₇	direct (N × H)
293. C₄⋊C₄	C₄×D₂₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×D₂₂₇	2
C₂×C₄²×D₂₂₇	2
#28408919	2
#28408918	2
#28408917	2
#28408916	2
#28408915	2
#28408914	2
#28408913	2
#95×D₂₂₇	2
#387×C₂₂₇	2
C₂×#387	227

Subgroups — #387×D227 #44402154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #387×D₂₂₇ #44402154