Subgroups — #137×#10623494 #36523855

Order 22784.

714 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×#10623494	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019071	C₂	1	2	yes	maximal, complemented
4	SD₁₆⋊#10623494	C₂	1	2	yes	maximal, complemented
5	Q₁₆×#10623494	C₂	1	2	yes	maximal, complemented
6	SD₁₆×#10623494	C₂	1	2	yes	maximal, complemented
7	#26019004	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018647	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018639	C₂	1	1	yes	maximal, characteristic
10	M₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#137×C₈₉	C₂	1	1	yes	maximal, characteristic
12	Q₈×#10623494	—	2	1	no	—
13	Q₈×#10623494	—	2	1	no	—
14	Q₈×#10623494	C₂²	1	2	yes	—
15	Q₈×#10623494	C₂²	1	2	yes	—
16	Q₈×#10623494	C₂²	1	1	yes	characteristic
17	Q₈×#10623494	C₂²	1	1	yes	characteristic
18	D₄×#10623494	—	2	1	no	—
19	D₄×#10623494	—	2	1	no	—
20	D₄×#10623494	C₂²	1	1	yes	characteristic
21	D₄×#10623494	C₂²	1	1	yes	characteristic
22	#19151651	—	2	1	no	—
23	#19151651	C₂²	1	1	yes	characteristic
24	#19151651	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊#10623494	—	2	1	no	—
26	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
27	C₂×C₄×#10623494	—	2	1	no	—
28	C₂×C₄×#10623494	—	2	1	no	—
29	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
30	#19151351	C₂²	1	2	yes	—
31	#19151349	C₂²	1	2	yes	—
32	Q₈⋊#10623494	C₂²	1	2	yes	—
33	Q₈⋊#10623494	C₂²	1	2	yes	—
34	Q₈⋊#10623494	C₂²	1	2	yes	—
35	D₄⋊#10623494	C₂²	1	2	yes	—
36	#19151319	C₂²	1	2	yes	—
37	C₈×#10623494	C₂²	1	2	yes	—
38	C₂×#137×C₈₉	C₄	1	1	yes	characteristic
39	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	#441×C₈₉	C₄	1	2	yes	—
42	#440×C₈₉	C₄	1	2	yes	—
43	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
44	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
45	#428×C₈₉	C₄	1	1	yes	characteristic
46	#419×C₈₉	C₄	1	1	yes	characteristic
47	#417×C₈₉	C₄	1	1	yes	characteristic
48	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
49	C₂²×#10623494	—	2	1	no	—
50	C₂²×#10623494	—	2	1	no	—
51	C₂²×#10623494	—	2	1	no	—
52	C₂²×#10623494	D₄	1	1	yes	characteristic
53	C₂²×#10623494	D₄	1	1	yes	characteristic
54	C₄⋊#10623494	—	2	2	no	—
55	C₄⋊#10623494	—	2	2	no	—
56	C₄⋊#10623494	—	2	1	no	—
57	C₄⋊#10623494	—	2	1	no	—
58	C₄⋊#10623494	—	2	1	no	—
59	C₄⋊#10623494	—	2	1	no	—
60	C₄⋊#10623494	C₂³	1	2	yes	—
61	C₄⋊#10623494	C₂³	1	1	yes	characteristic
62	C₄⋊#10623494	C₂³	1	1	yes	characteristic
63	C₂²⋊#10623494	—	2	1	no	—
64	C₂²⋊#10623494	—	2	1	no	—
65	C₂²⋊#10623494	—	2	1	no	—
66	C₂²⋊#10623494	—	2	1	no	—
67	C₄×#10623494	—	2	1	no	—
68	C₄×#10623494	—	2	1	no	—
69	C₄×#10623494	—	2	2	no	—
70	C₄×#10623494	—	2	2	no	—
71	C₄×#10623494	—	2	1	no	—
72	C₄×#10623494	D₄	1	1	yes	characteristic
73	C₄×#10623494	D₄	1	1	yes	characteristic
74	C₄×#10623494	C₂³	1	2	yes	—
75	C₄×#10623494	C₂³	1	1	yes	characteristic
76	C₄×#10623494	C₂³	1	1	yes	characteristic
77	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
78	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
79	#137×C₈₉	C₈	1	8	yes	complemented
80	C₂×Q₁₆×C₈₉	C₂×C₄	1	2	yes	—
81	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
82	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
83	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
84	C₄×Q₈×C₈₉	—	2	1	no	—
85	C₄×Q₈×C₈₉	—	2	1	no	—
86	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
87	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
89	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₄×D₄×C₈₉	—	2	1	no	—
91	C₄×D₄×C₈₉	—	2	1	no	—
92	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
93	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
94	#117×C₈₉	—	2	1	no	—
95	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₈₉	—	2	1	no	—
99	C₂×C₄²×C₈₉	—	2	1	no	—
100	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
101	#107×C₈₉	C₂×C₄	1	2	yes	—
102	#106×C₈₉	C₂×C₄	1	2	yes	—
103	#103×C₈₉	C₂×C₄	1	2	yes	—
104	#103×C₈₉	C₂×C₄	1	2	yes	—
105	#103×C₈₉	C₂×C₄	1	2	yes	—
106	#102×C₈₉	C₂×C₄	1	2	yes	—
107	#97×C₈₉	C₂×C₄	1	2	yes	—
108	C₄×C₈×C₈₉	C₂³	1	2	yes	—
109	C₂×#10623494	—	2	2	no	—
110	C₂×#10623494	—	2	1	no	—
111	C₂×#10623494	—	2	1	no	—
112	C₂×#10623494	—	2	2	no	—
113	C₂×#10623494	—	2	2	no	—
114	C₂×#10623494	—	4	1	no	—
115	C₂×#10623494	—	4	2	no	—
116	C₂×#10623494	—	4	2	no	—
117	C₂×#10623494	—	4	2	no	—
118	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
119	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
120	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
121	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
122	#41×C₈₉	—	2	2	no	—
123	#41×C₈₉	C₂×C₈	1	4	yes	—
124	C₂×Q₈×C₈₉	—	2	1	no	—
125	C₂×Q₈×C₈₉	—	2	2	no	—
126	C₂×Q₈×C₈₉	C₂×C₈	1	4	yes	complemented
127	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
128	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₂×D₄×C₈₉	—	2	1	no	—
130	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	—	2	1	no	—
132	C₂²×C₄×C₈₉	—	2	1	no	—
133	C₂²×C₄×C₈₉	—	2	1	no	—
134	C₂²×C₄×C₈₉	—	2	1	no	—
135	C₂²×C₄×C₈₉	—	2	1	no	—
136	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
139	Q₁₆×C₈₉	C₂×C₈	1	8	yes	complemented
140	SD₁₆×C₈₉	C₂×C₈	1	8	yes	complemented
141	M₁₆×C₈₉	—	2	2	no	—
142	M₁₆×C₈₉	C₂×C₈	1	4	yes	complemented
143	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
145	C₄⋊C₄×C₈₉	—	2	2	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₄⋊C₄×C₈₉	—	2	2	no	—
149	C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
151	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²⋊C₄×C₈₉	—	2	1	no	—
154	C₂²⋊C₄×C₈₉	—	2	1	no	—
155	C₂²⋊C₄×C₈₉	—	2	1	no	—
156	C₄²×C₈₉	—	2	1	no	—
157	C₄²×C₈₉	—	2	1	no	—
158	C₄²×C₈₉	—	2	2	no	—
159	C₄²×C₈₉	—	2	1	no	—
160	C₄²×C₈₉	—	2	2	no	—
161	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₈₉	#41	1	1	yes	characteristic
164	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
165	C₂³×C₈₉	—	2	1	no	—
166	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
167	Q₈×C₈₉	—	2	2	no	—
168	Q₈×C₈₉	—	2	1	no	—
169	Q₈×C₈₉	—	2	4	no	—
170	Q₈×C₈₉	C₂²×C₈	1	4	yes	—
171	Q₈×C₈₉	C₂²×C₈	1	2	yes	—
172	D₄×C₈₉	—	2	4	no	—
173	D₄×C₈₉	—	2	1	no	—
174	D₄×C₈₉	C₂²×C₈	1	2	yes	—
175	C₂×C₄×C₈₉	—	2	1	no	—
176	C₂×C₄×C₈₉	—	2	2	no	—
177	C₂×C₄×C₈₉	—	2	4	no	—
178	C₂×C₄×C₈₉	—	2	1	no	—
179	C₂×C₄×C₈₉	—	2	1	no	—
180	C₂×C₄×C₈₉	—	2	4	no	—
181	C₂×C₄×C₈₉	—	2	1	no	—
182	C₂×C₄×C₈₉	—	2	1	no	—
183	C₂×C₄×C₈₉	—	2	2	no	—
184	C₂×C₄×C₈₉	—	4	1	no	—
185	C₂×C₄×C₈₉	—	4	2	no	—
186	C₂×C₄×C₈₉	—	4	2	no	—
187	C₂×C₄×C₈₉	—	4	1	no	—
188	C₂×C₄×C₈₉	—	4	1	no	—
189	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
193	C₂×C₄×C₈₉	#131	1	2	yes	—
194	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
197	C₈×C₈₉	—	2	2	no	—
198	C₈×C₈₉	C₂²×C₈	1	4	yes	—
199	#10623494	—	2	1	no	—
200	#10623494	—	2	1	no	—
201	#10623494	—	2	1	no	—
202	#10623494	—	4	2	no	—
203	#10623494	—	4	1	no	—
204	#10623494	—	4	1	no	—
205	#10623494	—	4	2	no	—
206	#10623494	#137	1	2	yes	direct product factor
207	C₂²×C₈₉	—	2	1	no	—
208	C₂²×C₈₉	—	2	1	no	—
209	C₂²×C₈₉	—	2	2	no	—
210	C₂²×C₈₉	—	4	1	no	—
211	C₂²×C₈₉	—	4	1	no	—
212	C₂²×C₈₉	C₈×D₄	1	2	yes	—
213	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
214	C₄×C₈₉	—	2	2	no	—
215	C₄×C₈₉	—	2	4	no	—
216	C₄×C₈₉	—	2	1	no	—
217	C₄×C₈₉	—	2	1	no	—
218	C₄×C₈₉	—	2	1	no	—
219	C₄×C₈₉	—	4	1	no	—
220	C₄×C₈₉	—	4	1	no	—
221	C₄×C₈₉	—	4	2	no	—
222	C₄×C₈₉	C₈×D₄	1	2	yes	—
223	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
224	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
225	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
226	C₄×C₈₉	#575	1	1	yes	characteristic
227	C₈×#137	—	89	1	no	maximal, Sylow
228	C₂×C₈₉	—	2	2	no	—
229	C₂×C₈₉	—	4	2	no	—
230	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
231	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
232	C₂×C₈₉	#2955	1	1	yes	characteristic
233	C₈×#41	—	89	1	no	—
234	C₂×C₈×Q₈	—	89	1	no	—
235	C₄×#137	D₈₉	1	1	yes	characteristic
236	#1579	—	89	2	no	—
237	SD₁₆⋊C₈	—	89	2	no	—
238	C₈×Q₁₆	—	89	2	no	—
239	C₈×SD₁₆	—	89	2	no	—
240	#1565	—	89	1	no	—
241	#1479	—	89	1	no	—
242	#1477	—	89	1	no	—
243	C₈×M₁₆	—	89	1	no	—
244	C₈₉	C₈×#137	1	1	yes	characteristic, complemented, Sylow
245	C₂×#137	Dic₈₉	1	1	yes	characteristic
246	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
248	C₈×Q₈	—	89	2	no	—
249	C₈×Q₈	—	89	1	no	—
250	C₈×Q₈	—	89	2	no	—
251	C₈×Q₈	—	89	1	no	—
252	C₈×Q₈	—	178	1	no	—
253	C₈×Q₈	—	178	1	no	—
254	#441	Dic₈₉	1	2	yes	—
255	#440	Dic₈₉	1	2	yes	—
256	C₄×Q₁₆	C₂×D₈₉	1	2	yes	—
257	C₄×SD₁₆	C₂×D₈₉	1	2	yes	—
258	C₈×D₄	—	89	1	no	—
259	C₈×D₄	—	89	1	no	—
260	C₈×D₄	—	178	1	no	—
261	C₈×D₄	—	178	1	no	—
262	#431	—	89	1	no	—
263	#431	—	89	1	no	—
264	#431	—	178	1	no	—
265	#428	Dic₈₉	1	1	yes	characteristic
266	C₂×C₄⋊C₈	—	89	1	no	—
267	C₂×C₄⋊C₈	—	178	1	no	—
268	#419	Dic₈₉	1	1	yes	characteristic
269	#417	Dic₈₉	1	1	yes	characteristic
270	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
271	C₂×C₄×C₈	—	89	1	no	—
272	C₂×C₄×C₈	—	178	1	no	—
273	C₂×C₄×C₈	—	178	1	no	—
274	#335	—	89	2	no	—
275	#334	—	89	2	no	—
276	Q₈⋊C₈	—	89	2	no	—
277	Q₈⋊C₈	—	89	2	no	—
278	Q₈⋊C₈	—	89	2	no	—
279	D₄⋊C₈	—	89	2	no	—
280	#322	—	89	2	no	—
281	C₈²	—	89	2	no	—
282	C₂×#41	C₂×Dic₈₉	1	1	yes	characteristic
283	C₂²×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
284	#137	#10623494	1	8	yes	direct product factor
285	C₂×Q₁₆	C₂×Dic₈₉	1	2	yes	—
286	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
287	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
288	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
289	C₂²×C₈	—	89	1	no	—
290	C₂²×C₈	—	89	1	no	—
291	C₂²×C₈	—	178	1	no	—
292	C₂²×C₈	—	178	1	no	—
293	C₂²×C₈	—	178	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×Q₈	C₂×Dic₈₉	1	2	yes	—
297	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
298	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
299	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
303	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	#117	C₂×Dic₈₉	1	1	yes	characteristic
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
311	#107	C₂×Dic₈₉	1	2	yes	—
312	#106	C₂×Dic₈₉	1	2	yes	—
313	C₄⋊C₈	—	89	2	no	—
314	C₄⋊C₈	—	89	1	no	—
315	C₄⋊C₈	—	89	1	no	—
316	C₄⋊C₈	—	178	2	no	—
317	C₄⋊C₈	—	178	2	no	—
318	C₄⋊C₈	—	178	1	no	—
319	C₄⋊C₈	—	178	1	no	—
320	C₄⋊C₈	—	178	1	no	—
321	C₄⋊C₈	—	178	1	no	—
322	#103	C₂×Dic₈₉	1	2	yes	—
323	#103	C₂×Dic₈₉	1	2	yes	—
324	#103	C₂×Dic₈₉	1	2	yes	—
325	#102	C₂×Dic₈₉	1	2	yes	—
326	C₂²⋊C₈	—	178	1	no	—
327	C₂²⋊C₈	—	178	1	no	—
328	C₂²⋊C₈	—	178	1	no	—
329	C₂²⋊C₈	—	178	1	no	—
330	#97	C₂×Dic₈₉	1	2	yes	—
331	C₄×C₈	—	89	1	no	—
332	C₄×C₈	—	89	1	no	—
333	C₄×C₈	—	89	1	no	—
334	C₄×C₈	—	89	1	no	—
335	C₄×C₈	—	89	2	no	—
336	C₄×C₈	—	178	1	no	—
337	C₄×C₈	—	178	1	no	—
338	C₄×C₈	—	178	2	no	—
339	C₄×C₈	—	178	2	no	—
340	C₄×C₈	—	178	1	no	—
341	C₄×C₈	C₂²×D₈₉	1	2	yes	—
342	#41	—	2	2	no	—
343	#41	C₂×#10623494	1	4	yes	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	C₂×#10623494	1	4	yes	complemented
347	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
348	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
357	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
358	C₂²×C₄	#13083573	1	1	yes	characteristic
359	Q₁₆	C₂×#10623494	1	8	yes	complemented
360	SD₁₆	C₂×#10623494	1	8	yes	complemented
361	M₁₆	—	2	2	no	—
362	M₁₆	C₂×#10623494	1	4	yes	complemented
363	C₂×C₈	—	89	1	no	—
364	C₂×C₈	—	89	1	no	—
365	C₂×C₈	—	89	1	no	—
366	C₂×C₈	—	89	1	no	—
367	C₂×C₈	—	356	2	no	—
368	C₂×C₈	—	356	2	no	—
369	C₂×C₈	—	356	2	no	—
370	C₂×C₈	—	356	1	no	—
371	C₂×C₈	—	178	2	no	—
372	C₂×C₈	—	178	1	no	—
373	C₂×C₈	—	178	1	no	—
374	C₂×C₈	—	178	2	no	—
375	C₂×C₈	—	178	2	no	—
376	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
377	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
384	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
385	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
386	C₂²⋊C₄	—	2	1	no	—
387	C₂²⋊C₄	—	2	1	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	2	no	—
394	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
395	C₄²	D₄×D₈₉	1	1	yes	characteristic
396	C₄²	#13083573	1	1	yes	characteristic
397	C₄²	C₂³×D₈₉	1	1	yes	characteristic
398	C₂³	—	2	1	no	—
399	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
400	Q₈	—	2	4	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	2	1	no	—
403	Q₈	C₂²×#10623494	1	4	yes	—
404	Q₈	C₂²×#10623494	1	2	yes	—
405	D₄	—	2	4	no	—
406	D₄	—	2	1	no	—
407	D₄	C₂²×#10623494	1	2	yes	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
423	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
424	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
425	C₂×C₄	C₂²×#10623494	1	2	yes	—
426	C₂×C₄	#15668019	1	2	yes	—
427	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
429	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	89	2	no	—
432	C₈	—	356	2	no	—
433	C₈	—	356	1	no	—
434	C₈	—	356	2	no	—
435	C₈	—	356	1	no	—
436	C₈	—	178	1	no	—
437	C₈	—	178	1	no	—
438	C₈	—	178	1	no	—
439	C₈	C₂²×#10623494	1	4	yes	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	D₄×#10623494	1	2	yes	—
446	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	4	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	2	no	—
455	C₄	D₄×#10623494	1	2	yes	—
456	C₄	C₂³×#10623494	1	1	yes	characteristic
457	C₄	C₂×#15668019	1	1	yes	characteristic
458	C₄	#137×D₈₉	1	1	yes	characteristic
459	C₄	#19152397	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	4	2	no	—
462	C₂	C₂×D₄×#10623494	1	1	yes	characteristic
463	C₂	#137×Dic₈₉	1	1	yes	characteristic
464	C₂	#26029155	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₄²	C₂³×D₈₉
Fitting	C₄×#137×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#41×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₄×#137	D₈₉
hypocenter	C₈₉	C₈×#137
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#137

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈×#10623494	C₂	semidirect
3. #26019071	C₂	semidirect
4. SD₁₆⋊#10623494	C₂	semidirect
5. Q₁₆×#10623494	C₂	semidirect
6. SD₁₆×#10623494	C₂	semidirect
7. #26019004	C₂	semidirect
8. #26018647	C₂	semidirect
10. M₁₆×#10623494	C₂	semidirect
79. #137×C₈₉	C₈	semidirect
126. C₂×Q₈×C₈₉	C₂×C₈	semidirect
139. Q₁₆×C₈₉	C₂×C₈	semidirect
140. SD₁₆×C₈₉	C₂×C₈	semidirect
142. M₁₆×C₈₉	C₂×C₈	semidirect
206. #10623494	#137	direct (N × H)
244. C₈₉	C₈×#137	semidirect
284. #137	#10623494	direct (N × H)
346. C₂×Q₈	C₂×#10623494	semidirect
359. Q₁₆	C₂×#10623494	semidirect
360. SD₁₆	C₂×#10623494	semidirect
362. M₁₆	C₂×#10623494	semidirect

Maximal subgroups

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

subgroup	index
#41×#10623494	2
C₂×Q₈×#10623494	2
#26019071	2
SD₁₆⋊#10623494	2
Q₁₆×#10623494	2
SD₁₆×#10623494	2
#26019004	2
#26018647	2
#26018639	2
M₁₆×#10623494	2
C₄×#137×C₈₉	2
C₈×#137	89