Subgroups — #30652334

Order 16256.

1242 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550609	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550585	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550581	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550576	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550575	C₂	1	2	yes	maximal, complemented
6	#22550574	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550555	C₂	1	2	yes	maximal, complemented
8	#22550552	C₂	1	2	yes	maximal, complemented
9	#22550521	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550520	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550516	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550423	C₂	1	1	yes	maximal, characteristic, complemented
14	#22550410	C₂	1	1	yes	maximal, characteristic, complemented
15	#22550408	C₂	1	1	yes	maximal, characteristic, complemented
16	#22550406	C₂	1	2	yes	maximal, complemented
17	#22550387	C₂	1	2	yes	maximal, complemented
18	#22550385	C₂	1	2	yes	maximal, complemented
19	C₄×#14523248	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#14523247	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×C₂²⋊D₁₂₇	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14523248	C₂²	1	1	yes	characteristic
25	C₂×#14523248	C₂²	1	2	yes	complemented
26	C₂×#14523247	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊D₁₂₇	C₂²	1	2	yes	—
28	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₂₇	C₂²	1	2	yes	complemented
30	#16861208	C₂²	1	1	yes	characteristic, complemented
31	#16861205	C₂²	1	1	yes	characteristic
32	#16861204	C₂²	1	2	yes	complemented
33	#16861203	C₂²	1	2	yes	complemented
34	#16861202	C₂²	1	2	yes	complemented
35	#16861202	C₂²	1	2	yes	complemented
36	#16861201	C₂²	1	1	yes	characteristic, complemented
37	#16861200	C₂²	1	1	yes	characteristic, complemented
38	#16861199	C₂²	1	2	yes	complemented
39	#16861197	C₂²	1	1	yes	characteristic, complemented
40	#16861196	C₂²	1	1	yes	characteristic, complemented
41	#16861195	C₂²	1	2	yes	complemented
42	#16861195	C₂²	1	2	yes	complemented
43	#16861194	C₂²	1	2	yes	complemented
44	#16861193	C₂²	1	2	yes	complemented
45	#16861192	C₂²	1	2	yes	complemented
46	#16861192	C₂²	1	2	yes	complemented
47	#16861192	C₂²	1	2	yes	complemented
48	#16861191	C₂²	1	2	yes	complemented
49	#16861191	C₂²	1	2	yes	complemented
50	#16861190	C₂²	1	2	yes	complemented
51	#16861189	C₂²	1	1	yes	characteristic, complemented
52	#16861188	C₂²	1	2	yes	complemented
53	#16861188	C₂²	1	2	yes	complemented
54	#16861188	C₂²	1	1	yes	characteristic, complemented
55	#16861187	C₂²	1	2	yes	complemented
56	#16861186	C₂²	1	2	yes	complemented
57	#16861186	C₂²	1	2	yes	complemented
58	#16861184	C₂²	1	1	yes	characteristic, complemented
59	#16861183	C₂²	1	1	yes	characteristic
60	#16861183	C₂²	1	2	yes	complemented
61	#16861183	C₂²	1	2	yes	complemented
62	#16861182	C₂²	1	2	yes	complemented
63	#16861182	C₂²	1	2	yes	complemented
64	#16861181	C₂²	1	2	yes	—
65	#16861181	C₂²	1	2	yes	complemented
66	#16861180	C₂²	1	1	yes	characteristic
67	#16861180	C₂²	1	1	yes	characteristic, complemented
68	#16861179	C₂²	1	2	yes	complemented
69	#16861178	C₂²	1	2	yes	—
70	#16861178	C₂²	1	2	yes	complemented
71	#16861177	C₂²	1	2	yes	—
72	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
73	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
74	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
75	#16861174	C₂²	1	1	yes	characteristic, complemented
76	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
77	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
78	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
79	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
80	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
81	#16861171	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	—
83	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
84	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
89	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
92	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
95	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
96	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
97	#16861168	C₂²	1	1	yes	characteristic, complemented
98	#16861168	C₂²	1	2	yes	complemented
99	#16861167	C₂²	1	1	yes	characteristic, complemented
100	#16861166	C₂²	1	1	yes	characteristic, complemented
101	#16861166	C₂²	1	1	yes	characteristic, complemented
102	#16861166	C₂²	1	2	yes	complemented
103	#16861165	C₂²	1	2	yes	complemented
104	C₂×Dic₁₂₇⋊C₄	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊Dic₁₂₇	C₂²	1	2	yes	complemented
107	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
109	C₂×C₄×Dic₁₂₇	C₂²	1	2	yes	complemented
110	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
112	C₂²×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
113	C₂³×C₄×C₁₂₇	C₂²	1	2	yes	complemented
114	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
115	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
116	C₄×D₄×C₁₂₇	C₂²	1	2	yes	complemented
117	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄×C₁₂₇	C₂²	1	2	yes	complemented
119	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₂²⋊C₄×C₁₂₇	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₂₇	C₂³	1	2	yes	—
124	#14523248	—	2	4	no	—
125	#14523248	—	4	4	no	—
126	#14523247	—	2	4	no	—
127	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
128	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₅₄	C₂³	1	2	yes	—
130	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
131	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
132	C₂×D₅₀₈	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₂₇	—	2	8	no	—
134	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
143	D₄×D₁₂₇	—	2	4	no	—
144	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
145	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
146	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
147	C₂×C₄×D₁₂₇	—	4	4	no	—
148	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
153	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
156	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
157	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
159	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
160	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
163	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
164	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
165	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
166	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
167	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
168	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
169	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
170	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
171	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
173	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
184	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₂₇	C₂³	1	2	yes	—
198	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₂₇	C₂³	1	2	yes	—
201	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₂₇	C₂³	1	2	yes	—
205	C₂⁴×C₁₂₇	C₂³	1	2	yes	—
206	C₂×D₄×C₁₂₇	—	2	4	no	—
207	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
208	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₂₇	—	4	4	no	—
211	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
214	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
215	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
216	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
217	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
218	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
219	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
221	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
226	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
227	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
228	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
229	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
230	C₂²×D₁₂₇	—	2	4	no	—
231	C₂²×D₁₂₇	—	2	4	no	—
232	C₂²×D₁₂₇	—	4	2	no	—
233	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
234	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
236	Dic₂₅₄	—	2	2	no	—
237	Dic₂₅₄	—	2	2	no	—
238	Dic₂₅₄	—	4	2	no	—
239	D₅₀₈	—	2	2	no	—
240	D₅₀₈	—	2	2	no	—
241	D₅₀₈	—	4	2	no	—
242	C₂²⋊D₁₂₇	—	2	4	no	—
243	C₂²⋊D₁₂₇	—	2	4	no	—
244	C₂²⋊D₁₂₇	—	2	4	no	—
245	C₂²⋊D₁₂₇	—	2	2	no	—
246	C₂²⋊D₁₂₇	—	2	4	no	—
247	C₂²⋊D₁₂₇	—	2	4	no	—
248	C₂²⋊D₁₂₇	—	4	2	no	—
249	C₂²⋊D₁₂₇	—	4	2	no	—
250	C₂²⋊D₁₂₇	#41	1	4	yes	complemented
251	C₂×Dic₁₂₇	—	2	4	no	—
252	C₂×Dic₁₂₇	—	2	4	no	—
253	C₂×Dic₁₂₇	—	4	2	no	—
254	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
256	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
258	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
262	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
263	C₄×D₁₂₇	—	2	2	no	—
264	C₄×D₁₂₇	—	2	2	no	—
265	C₄×D₁₂₇	—	2	2	no	—
266	C₄×D₁₂₇	—	2	2	no	—
267	C₄×D₁₂₇	—	2	4	no	—
268	C₄×D₁₂₇	—	2	2	no	—
269	C₄×D₁₂₇	—	2	2	no	—
270	C₄×D₁₂₇	—	4	2	no	—
271	C₄×D₁₂₇	—	4	2	no	—
272	C₂³×C₁₂₇	—	2	4	no	—
273	C₂³×C₁₂₇	—	2	4	no	—
274	C₂³×C₁₂₇	—	4	2	no	—
275	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
276	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
277	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
278	D₄×C₁₂₇	—	2	4	no	—
279	D₄×C₁₂₇	—	2	2	no	—
280	D₄×C₁₂₇	#41	1	4	yes	complemented
281	C₂×C₄×C₁₂₇	—	2	2	no	—
282	C₂×C₄×C₁₂₇	—	2	2	no	—
283	C₂×C₄×C₁₂₇	—	2	2	no	—
284	C₂×C₄×C₁₂₇	—	2	4	no	—
285	C₂×C₄×C₁₂₇	—	2	4	no	—
286	C₂×C₄×C₁₂₇	—	4	2	no	—
287	C₂×C₄×C₁₂₇	—	4	2	no	—
288	C₂×C₄×C₁₂₇	—	4	2	no	—
289	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
290	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
291	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
292	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
293	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
294	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
295	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
296	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₁₂₇	—	2	1	no	—
298	C₂²×C₁₂₇	—	2	2	no	—
299	C₂²×C₁₂₇	—	2	1	no	—
300	C₂²×C₁₂₇	—	2	2	no	—
301	C₂²×C₁₂₇	—	2	2	no	—
302	C₂²×C₁₂₇	—	2	2	no	—
303	C₂²×C₁₂₇	—	2	2	no	—
304	C₂²×C₁₂₇	—	4	8	no	—
305	C₂²×C₁₂₇	C₂×#41	1	2	yes	—
306	C₂²×C₁₂₇	C₂×#41	1	4	yes	—
307	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
308	C₂×D₁₂₇	—	2	1	no	—
309	C₂×D₁₂₇	—	2	1	no	—
310	C₂×D₁₂₇	—	2	1	no	—
311	C₂×D₁₂₇	—	2	1	no	—
312	C₂×D₁₂₇	—	2	2	no	—
313	C₂×D₁₂₇	—	2	2	no	—
314	C₂×D₁₂₇	—	2	2	no	—
315	C₂×D₁₂₇	—	2	1	no	—
316	C₂×D₁₂₇	—	4	8	no	—
317	C₂×D₁₂₇	C₂×#41	1	2	yes	—
318	C₄×C₁₂₇	—	2	1	no	—
319	C₄×C₁₂₇	—	2	1	no	—
320	C₄×C₁₂₇	—	2	1	no	—
321	C₄×C₁₂₇	—	2	1	no	—
322	C₄×C₁₂₇	—	2	2	no	—
323	C₄×C₁₂₇	—	2	2	no	—
324	C₄×C₁₂₇	C₂×#41	1	2	yes	—
325	C₄×C₁₂₇	H(5,𝔽₂)	1	2	yes	—
326	Dic₁₂₇	—	2	1	no	—
327	Dic₁₂₇	—	2	1	no	—
328	Dic₁₂₇	—	2	1	no	—
329	Dic₁₂₇	—	2	2	no	—
330	Dic₁₂₇	—	2	2	no	—
331	Dic₁₂₇	—	2	1	no	—
332	Dic₁₂₇	—	2	2	no	—
333	Dic₁₂₇	—	2	1	no	—
334	Dic₁₂₇	C₂×#41	1	2	yes	—
335	C₂×C₁₂₇	—	2	4	no	—
336	C₂×C₁₂₇	—	2	2	no	—
337	C₂×C₁₂₇	—	4	2	no	—
338	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
339	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
340	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
341	D₁₂₇	—	2	2	no	—
342	D₁₂₇	—	4	1	no	—
343	D₁₂₇	—	4	2	no	—
344	#3481	—	127	1	no	maximal, Sylow
345	C₁₂₇	#3481	1	1	yes	characteristic, complemented, Sylow
346	#559	—	127	1	no	—
347	#554	—	127	1	no	—
348	#554	—	127	1	no	—
349	#553	—	127	2	no	—
350	#553	—	127	1	no	—
351	#553	—	127	1	no	—
352	#551	—	127	2	no	—
353	#551	—	127	2	no	—
354	#546	—	127	1	no	—
355	#546	—	127	1	no	—
356	#546	—	127	2	no	—
357	D₄²	—	127	1	no	—
358	#532	—	127	1	no	—
359	#529	—	127	2	no	—
360	#529	—	127	1	no	—
361	#529	—	127	1	no	—
362	#525	—	127	2	no	—
363	#525	—	127	2	no	—
364	C₄×#41	—	127	1	no	—
365	C₄×#41	—	127	1	no	—
366	C₂×C₄×D₄	—	127	2	no	—
367	C₂×C₄×D₄	—	127	1	no	—
368	C₂×C₄×D₄	D₁₂₇	1	1	yes	characteristic, complemented
369	C₂×#41	—	127	1	no	—
370	C₂×#41	—	127	2	no	—
371	C₂×#41	—	127	1	no	—
372	C₂²×D₄	—	127	2	no	—
373	C₂²×D₄	—	127	1	no	—
374	C₂²×D₄	C₂×D₁₂₇	1	1	yes	characteristic
375	C₂³×C₄	—	127	2	no	—
376	C₂³×C₄	C₂×D₁₂₇	1	2	yes	complemented
377	C₄⋊Q₈	—	127	1	no	—
378	#127	—	127	1	no	—
379	#126	—	127	2	no	—
380	#126	—	127	2	no	—
381	#126	—	127	2	no	—
382	#126	—	127	2	no	—
383	#125	—	127	2	no	—
384	#125	—	127	1	no	—
385	#125	—	127	1	no	—
386	#124	—	127	1	no	—
387	#124	—	127	2	no	—
388	#124	—	127	2	no	—
389	#124	—	127	1	no	—
390	#123	—	127	2	no	—
391	#123	—	127	2	no	—
392	#123	—	127	2	no	—
393	#123	—	127	2	no	—
394	#123	—	127	2	no	—
395	#123	—	127	2	no	—
396	#123	—	127	2	no	—
397	#123	—	127	2	no	—
398	C₂²⋊Q₈	—	127	2	no	—
399	C₂²⋊Q₈	—	127	2	no	—
400	C₂²⋊Q₈	—	127	1	no	—
401	C₂²⋊Q₈	—	127	2	no	—
402	C₂²⋊Q₈	—	127	1	no	—
403	C₂²⋊Q₈	—	127	2	no	—
404	C₂²⋊Q₈	—	127	2	no	—
405	#121	—	127	2	no	—
406	#121	—	127	1	no	—
407	#121	—	127	2	no	—
408	#121	—	127	1	no	—
409	#121	—	127	2	no	—
410	#121	—	127	2	no	—
411	#121	—	127	1	no	—
412	#121	—	127	1	no	—
413	#121	—	127	2	no	—
414	#121	—	127	2	no	—
415	#120	—	127	2	no	—
416	#120	—	127	2	no	—
417	#120	—	127	2	no	—
418	#120	—	127	2	no	—
419	C₄×Q₈	—	127	1	no	—
420	C₄×Q₈	—	127	1	no	—
421	C₄×Q₈	—	127	1	no	—
422	C₄×Q₈	—	127	1	no	—
423	C₄×D₄	—	127	1	no	—
424	C₄×D₄	—	127	1	no	—
425	C₄×D₄	—	127	1	no	—
426	C₄×D₄	—	127	2	no	—
427	C₄×D₄	—	127	2	no	—
428	C₄×D₄	—	127	2	no	—
429	C₄×D₄	—	127	2	no	—
430	C₄×D₄	—	127	2	no	—
431	C₄×D₄	—	127	2	no	—
432	C₄×D₄	—	127	2	no	—
433	C₄×D₄	—	127	2	no	—
434	C₄×D₄	—	127	2	no	—
435	C₄×D₄	—	127	1	no	—
436	C₄×D₄	—	127	1	no	—
437	C₄×D₄	—	127	1	no	—
438	C₄×D₄	—	127	1	no	—
439	C₄×D₄	—	127	2	no	—
440	C₄×D₄	—	127	2	no	—
441	C₄×D₄	—	127	1	no	—
442	C₄×D₄	—	127	1	no	—
443	C₄×D₄	—	127	1	no	—
444	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
445	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
446	C₄×D₄	C₂×D₁₂₇	1	2	yes	complemented
447	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
448	C₄×D₄	C₂×D₁₂₇	1	2	yes	complemented
449	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
450	#117	—	127	1	no	—
451	#117	—	127	2	no	—
452	#117	—	127	1	no	—
453	#117	—	127	2	no	—
454	#117	—	127	1	no	—
455	#117	—	127	1	no	—
456	#117	—	127	2	no	—
457	C₂×C₄⋊C₄	—	127	2	no	—
458	C₂×C₄⋊C₄	—	127	1	no	—
459	C₂×C₄⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
460	C₂×C₂²⋊C₄	—	127	2	no	—
461	C₂×C₂²⋊C₄	—	127	2	no	—
462	C₂×C₂²⋊C₄	—	127	2	no	—
463	C₂×C₂²⋊C₄	C₂×D₁₂₇	1	2	yes	complemented
464	C₂×C₄²	—	127	2	no	—
465	C₂×C₄²	—	127	1	no	—
466	C₂×C₄²	—	127	1	no	—
467	C₂×C₄²	C₂×D₁₂₇	1	1	yes	characteristic, complemented
468	C₂⁴	—	127	2	no	—
469	C₂⁴	C₂²×D₁₂₇	1	2	yes	—
470	#41	—	508	4	no	—
471	#41	—	254	4	no	—
472	#41	—	254	4	no	—
473	C₂×Q₈	—	127	2	no	—
474	C₂×Q₈	—	127	1	no	—
475	C₂×Q₈	—	127	1	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	127	1	no	—
478	C₂×D₄	—	127	2	no	—
479	C₂×D₄	—	127	2	no	—
480	C₂×D₄	—	127	1	no	—
481	C₂×D₄	—	127	2	no	—
482	C₂×D₄	—	127	2	no	—
483	C₂×D₄	—	127	2	no	—
484	C₂×D₄	—	127	2	no	—
485	C₂×D₄	—	127	2	no	—
486	C₂×D₄	—	127	2	no	—
487	C₂×D₄	—	127	1	no	—
488	C₂×D₄	—	127	1	no	—
489	C₂×D₄	—	254	8	no	—
490	C₂×D₄	—	254	4	no	—
491	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
492	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
493	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
494	C₂²×C₄	—	4	4	no	—
495	C₂²×C₄	—	127	2	no	—
496	C₂²×C₄	—	127	2	no	—
497	C₂²×C₄	—	127	2	no	—
498	C₂²×C₄	—	127	2	no	—
499	C₂²×C₄	—	127	2	no	—
500	C₂²×C₄	—	127	1	no	—
501	C₂²×C₄	—	127	1	no	—
502	C₂²×C₄	—	127	1	no	—
503	C₂²×C₄	—	127	1	no	—
504	C₂²×C₄	—	127	1	no	—
505	C₂²×C₄	—	127	1	no	—
506	C₂²×C₄	—	127	2	no	—
507	C₂²×C₄	—	508	4	no	—
508	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
509	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
510	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
511	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
513	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
514	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
515	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
516	C₄⋊C₄	—	127	1	no	—
517	C₄⋊C₄	—	127	2	no	—
518	C₄⋊C₄	—	127	2	no	—
519	C₄⋊C₄	—	127	2	no	—
520	C₄⋊C₄	—	127	2	no	—
521	C₄⋊C₄	—	127	1	no	—
522	C₄⋊C₄	—	127	2	no	—
523	C₄⋊C₄	—	127	1	no	—
524	C₄⋊C₄	—	127	1	no	—
525	C₄⋊C₄	—	127	2	no	—
526	C₄⋊C₄	—	127	2	no	—
527	C₄⋊C₄	—	127	2	no	—
528	C₄⋊C₄	—	127	1	no	—
529	C₄⋊C₄	—	127	1	no	—
530	C₄⋊C₄	—	127	1	no	—
531	C₄⋊C₄	—	127	1	no	—
532	C₄⋊C₄	—	127	2	no	—
533	C₄⋊C₄	—	127	2	no	—
534	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
537	C₂²⋊C₄	—	127	1	no	—
538	C₂²⋊C₄	—	127	2	no	—
539	C₂²⋊C₄	—	127	2	no	—
540	C₂²⋊C₄	—	127	2	no	—
541	C₂²⋊C₄	—	127	2	no	—
542	C₂²⋊C₄	—	127	1	no	—
543	C₂²⋊C₄	—	127	2	no	—
544	C₂²⋊C₄	—	127	2	no	—
545	C₂²⋊C₄	—	127	2	no	—
546	C₂²⋊C₄	—	127	1	no	—
547	C₂²⋊C₄	—	127	2	no	—
548	C₂²⋊C₄	—	127	2	no	—
549	C₂²⋊C₄	—	127	2	no	—
550	C₂²⋊C₄	—	127	2	no	—
551	C₂²⋊C₄	—	127	2	no	—
552	C₂²⋊C₄	—	127	1	no	—
553	C₂²⋊C₄	—	127	2	no	—
554	C₂²⋊C₄	—	127	1	no	—
555	C₂²⋊C₄	—	127	1	no	—
556	C₂²⋊C₄	—	127	2	no	—
557	C₂²⋊C₄	—	127	2	no	—
558	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
562	C₄²	—	127	1	no	—
563	C₄²	—	127	2	no	—
564	C₄²	—	127	1	no	—
565	C₄²	—	127	2	no	—
566	C₄²	—	127	1	no	—
567	C₄²	—	127	1	no	—
568	C₄²	—	127	1	no	—
569	C₄²	—	127	1	no	—
570	C₄²	—	127	2	no	—
571	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
572	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
573	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
574	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
575	C₂³	—	2	4	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	127	1	no	—
579	C₂³	—	127	2	no	—
580	C₂³	—	127	1	no	—
581	C₂³	—	508	2	no	—
582	C₂³	—	254	4	no	—
583	C₂³	—	254	4	no	—
584	C₂³	C₂³×D₁₂₇	1	2	yes	—
585	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
586	C₂³	C₂³×D₁₂₇	1	2	yes	—
587	Q₈	—	508	2	no	—
588	Q₈	—	254	2	no	—
589	Q₈	—	254	2	no	—
590	D₄	—	2	4	no	—
591	D₄	—	2	2	no	—
592	D₄	—	127	4	no	—
593	D₄	—	508	2	no	—
594	D₄	—	508	2	no	—
595	D₄	—	508	2	no	—
596	D₄	—	254	2	no	—
597	D₄	—	254	4	no	—
598	D₄	—	254	4	no	—
599	D₄	—	254	4	no	—
600	D₄	—	254	2	no	—
601	D₄	—	254	4	no	—
602	D₄	—	254	4	no	—
603	D₄	—	254	2	no	—
604	D₄	#14523248	1	4	yes	complemented
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	127	1	no	—
614	C₂×C₄	—	127	1	no	—
615	C₂×C₄	—	127	1	no	—
616	C₂×C₄	—	127	2	no	—
617	C₂×C₄	—	127	2	no	—
618	C₂×C₄	—	127	1	no	—
619	C₂×C₄	—	127	1	no	—
620	C₂×C₄	—	127	1	no	—
621	C₂×C₄	—	127	2	no	—
622	C₂×C₄	—	508	2	no	—
623	C₂×C₄	—	508	2	no	—
624	C₂×C₄	—	508	2	no	—
625	C₂×C₄	—	254	2	no	—
626	C₂×C₄	—	254	2	no	—
627	C₂×C₄	—	254	4	no	—
628	C₂×C₄	—	254	4	no	—
629	C₂×C₄	—	254	2	no	—
630	C₂×C₄	—	254	2	no	—
631	C₂×C₄	—	254	2	no	—
632	C₂×C₄	—	254	4	no	—
633	C₂×C₄	—	254	2	no	—
634	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
636	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
640	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
641	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	4	8	no	—
650	C₂²	—	127	2	no	—
651	C₂²	—	508	8	no	—
652	C₂²	—	254	1	no	—
653	C₂²	—	254	2	no	—
654	C₂²	—	254	1	no	—
655	C₂²	—	254	2	no	—
656	C₂²	—	254	2	no	—
657	C₂²	—	254	1	no	—
658	C₂²	—	254	1	no	—
659	C₂²	—	254	1	no	—
660	C₂²	#41×D₁₂₇	1	2	yes	—
661	C₂²	C₂×#14523248	1	4	yes	—
662	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	127	2	no	—
670	C₄	—	254	2	no	—
671	C₄	—	254	1	no	—
672	C₄	—	254	1	no	—
673	C₄	—	254	1	no	—
674	C₄	—	254	2	no	—
675	C₄	—	254	1	no	—
676	C₄	—	254	2	no	—
677	C₄	—	254	1	no	—
678	C₄	C₂×#14523248	1	2	yes	—
679	C₄	#16861254	1	2	yes	—
680	C₂	—	2	2	no	—
681	C₂	—	2	4	no	—
682	C₂	—	4	2	no	—
683	C₂	—	508	2	no	—
684	C₂	—	508	1	no	—
685	C₂	—	254	2	no	—
686	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
687	C₂	C₂²×#14523248	1	1	yes	characteristic
688	C₂	C₂×#16861254	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Frattini	C₂²	C₂⁴×D₁₂₇
Fitting	C₂×C₄×D₄×C₁₂₇	C₂
hypercenter	C₂×C₄×D₄	D₁₂₇
hypocenter	C₁₂₇	#3481
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #22550609	C₂	semidirect
2. #22550585	C₂	semidirect
3. #22550581	C₂	semidirect
4. #22550576	C₂	semidirect
5. #22550575	C₂	semidirect
6. #22550574	C₂	semidirect
7. #22550555	C₂	semidirect
8. #22550552	C₂	semidirect
9. #22550521	C₂	semidirect
10. #22550520	C₂	semidirect
11. #22550516	C₂	semidirect
12. D₄×C₂²⋊D₁₂₇	C₂	semidirect
13. #22550423	C₂	semidirect
14. #22550410	C₂	semidirect
15. #22550408	C₂	semidirect
16. #22550406	C₂	semidirect
17. #22550387	C₂	semidirect
18. #22550385	C₂	semidirect
19. C₄×#14523248	C₂	semidirect
20. C₄×#14523247	C₂	semidirect
21. C₂×C₄×C₂²⋊D₁₂₇	C₂	semidirect
22. C₄×D₄×D₁₂₇	C₂	semidirect
23. C₂×C₄×D₄×C₁₂₇	C₂	semidirect
25. C₂×#14523248	C₂²	semidirect
29. C₂²×C₄×D₁₂₇	C₂²	semidirect
30. #16861208	C₂²	semidirect
32. #16861204	C₂²	semidirect
33. #16861203	C₂²	semidirect
34. #16861202	C₂²	semidirect
35. #16861202	C₂²	semidirect
36. #16861201	C₂²	semidirect
37. #16861200	C₂²	semidirect
38. #16861199	C₂²	semidirect
39. #16861197	C₂²	semidirect
40. #16861196	C₂²	semidirect
41. #16861195	C₂²	semidirect
42. #16861195	C₂²	semidirect
43. #16861194	C₂²	semidirect
44. #16861193	C₂²	semidirect
45. #16861192	C₂²	semidirect
46. #16861192	C₂²	semidirect
47. #16861192	C₂²	semidirect
48. #16861191	C₂²	semidirect
49. #16861191	C₂²	semidirect
50. #16861190	C₂²	semidirect
51. #16861189	C₂²	semidirect
52. #16861188	C₂²	semidirect
53. #16861188	C₂²	semidirect
54. #16861188	C₂²	semidirect
55. #16861187	C₂²	semidirect
56. #16861186	C₂²	semidirect
57. #16861186	C₂²	semidirect
58. #16861184	C₂²	semidirect
60. #16861183	C₂²	semidirect
61. #16861183	C₂²	semidirect
62. #16861182	C₂²	semidirect
63. #16861182	C₂²	semidirect
65. #16861181	C₂²	semidirect
67. #16861180	C₂²	semidirect
68. #16861179	C₂²	semidirect
70. #16861178	C₂²	semidirect
72. C₄×Dic₂₅₄	C₂²	semidirect
73. C₄×Dic₂₅₄	C₂²	semidirect
74. C₄×Dic₂₅₄	C₂²	semidirect
75. #16861174	C₂²	semidirect
76. C₄×D₅₀₈	C₂²	semidirect
77. C₄×D₅₀₈	C₂²	semidirect
78. C₄×D₅₀₈	C₂²	semidirect
81. #16861171	C₂²	semidirect
85. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
86. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
87. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
88. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
89. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
90. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
91. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
92. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
93. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
94. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
95. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
96. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
97. #16861168	C₂²	semidirect
98. #16861168	C₂²	semidirect
99. #16861167	C₂²	semidirect
100. #16861166	C₂²	semidirect
101. #16861166	C₂²	semidirect
102. #16861166	C₂²	semidirect
103. #16861165	C₂²	semidirect
104. C₂×Dic₁₂₇⋊C₄	C₂²	semidirect
105. C₄⋊C₄×D₁₂₇	C₂²	semidirect
106. C₂×C₂²⋊Dic₁₂₇	C₂²	semidirect
107. C₂×(C₂×D₁₂₇)⋊C₄	C₂²	semidirect
108. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
109. C₂×C₄×Dic₁₂₇	C₂²	semidirect
110. C₄²×D₁₂₇	C₂²	semidirect
111. C₄²×D₁₂₇	C₂²	semidirect
113. C₂³×C₄×C₁₂₇	C₂²	semidirect
116. C₄×D₄×C₁₂₇	C₂²	semidirect
117. C₄×D₄×C₁₂₇	C₂²	semidirect
118. C₄×D₄×C₁₂₇	C₂²	semidirect
119. C₄×D₄×C₁₂₇	C₂²	semidirect
120. C₂×C₄⋊C₄×C₁₂₇	C₂²	semidirect
121. C₂×C₂²⋊C₄×C₁₂₇	C₂²	semidirect
122. C₂×C₄²×C₁₂₇	C₂²	semidirect
250. C₂²⋊D₁₂₇	#41	semidirect
280. D₄×C₁₂₇	#41	semidirect
345. C₁₂₇	#3481	semidirect
368. C₂×C₄×D₄	D₁₂₇	semidirect
376. C₂³×C₄	C₂×D₁₂₇	semidirect
446. C₄×D₄	C₂×D₁₂₇	semidirect
447. C₄×D₄	C₂×D₁₂₇	semidirect
448. C₄×D₄	C₂×D₁₂₇	semidirect
449. C₄×D₄	C₂×D₁₂₇	semidirect
459. C₂×C₄⋊C₄	C₂×D₁₂₇	semidirect
463. C₂×C₂²⋊C₄	C₂×D₁₂₇	semidirect
467. C₂×C₄²	C₂×D₁₂₇	semidirect
604. D₄	#14523248	semidirect

Maximal subgroups

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

subgroup	index
#22550609	2
#22550585	2
#22550581	2
#22550576	2
#22550575	2
#22550574	2
#22550555	2
#22550552	2
#22550521	2
#22550520	2
#22550516	2
D₄×C₂²⋊D₁₂₇	2
#22550423	2
#22550410	2
#22550408	2
#22550406	2
#22550387	2
#22550385	2
C₄×#14523248	2
C₄×#14523247	2
C₂×C₄×C₂²⋊D₁₂₇	2
C₄×D₄×D₁₂₇	2
C₂×C₄×D₄×C₁₂₇	2
#3481	127