Subgroups — #36446471

Order 22784.

760 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26020272	C₂	1	1	yes	maximal, characteristic
2	C₄×#15667936	C₂	1	1	yes	maximal, characteristic, complemented
3	#26018751	C₂	1	1	yes	maximal, characteristic, complemented
4	#26018707	C₂	1	1	yes	maximal, characteristic, complemented
5	#26018681	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018634	C₂	1	1	yes	maximal, characteristic
7	Q₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic
8	#19151651	C₂²	1	1	yes	characteristic
9	#19151622	C₂²	1	1	yes	characteristic
10	C₂×#15667939	—	2	1	no	—
11	C₂×#15667936	—	2	1	no	—
12	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
13	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
14	#19151360	—	2	1	no	—
15	#19151357	—	2	1	no	—
16	#19151335	—	2	2	no	—
17	Q₈⋊#10623494	—	2	1	no	—
18	Q₈⋊#10623494	—	2	1	no	—
19	Q₈⋊#10623494	—	2	1	no	—
20	Q₈⋊#10623494	—	2	2	no	—
21	D₄⋊#10623494	—	2	1	no	—
22	Q₈²×C₈₉	C₄	1	1	yes	characteristic, complemented
23	#557×C₈₉	—	2	1	no	—
24	#557×C₈₉	C₄	1	1	yes	characteristic, complemented
25	#554×C₈₉	—	2	2	no	—
26	#554×C₈₉	—	2	1	no	—
27	#554×C₈₉	—	2	1	no	—
28	#554×C₈₉	C₄	1	1	yes	characteristic, complemented
29	D₄×Q₈×C₈₉	—	2	1	no	—
30	D₄×Q₈×C₈₉	C₄	1	1	yes	characteristic, complemented
31	#533×C₈₉	—	2	2	no	—
32	#533×C₈₉	—	2	1	no	—
33	#533×C₈₉	—	2	1	no	—
34	#533×C₈₉	C₂²	1	1	yes	characteristic
35	C₄×#41×C₈₉	—	2	1	no	—
36	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
38	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#13083558	—	2	1	no	—
40	C₂²×#10623494	—	2	1	no	—
41	C₂×C₄⋊Dic₈₉	—	2	1	no	—
42	C₂×C₄×Dic₈₉	—	2	1	no	—
43	C₄⋊#10623494	—	2	1	no	—
44	C₄⋊#10623494	—	2	1	no	—
45	C₄⋊#10623494	—	2	1	no	—
46	#15667939	—	4	2	no	—
47	#15667936	—	2	4	no	—
48	C₂²⋊#10623494	—	2	1	no	—
49	C₄×#10623494	—	2	1	no	—
50	C₄×#10623494	—	2	1	no	—
51	C₄×#10623494	—	2	1	no	—
52	#15667919	—	2	1	no	—
53	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
54	C₂²×Q₈×C₈₉	—	2	1	no	—
55	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
56	C₄⋊Q₈×C₈₉	—	2	2	no	—
57	C₄⋊Q₈×C₈₉	—	2	1	no	—
58	C₄⋊Q₈×C₈₉	—	2	2	no	—
59	C₄⋊Q₈×C₈₉	—	2	1	no	—
60	C₄⋊Q₈×C₈₉	—	2	1	no	—
61	C₄⋊Q₈×C₈₉	—	2	1	no	—
62	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
64	#125×C₈₉	—	2	2	no	—
65	#125×C₈₉	—	2	2	no	—
66	#125×C₈₉	—	2	2	no	—
67	#125×C₈₉	—	2	1	no	—
68	#125×C₈₉	—	2	1	no	—
69	#125×C₈₉	—	2	1	no	—
70	C₂²⋊Q₈×C₈₉	—	2	2	no	—
71	C₂²⋊Q₈×C₈₉	—	2	2	no	—
72	C₂²⋊Q₈×C₈₉	—	2	2	no	—
73	C₂²⋊Q₈×C₈₉	—	2	2	no	—
74	C₂²⋊Q₈×C₈₉	—	2	2	no	—
75	C₂²⋊Q₈×C₈₉	—	2	1	no	—
76	C₂²⋊Q₈×C₈₉	—	2	2	no	—
77	C₂²⋊Q₈×C₈₉	—	2	1	no	—
78	C₂²⋊Q₈×C₈₉	—	2	1	no	—
79	C₂²⋊Q₈×C₈₉	—	2	2	no	—
80	C₂²⋊Q₈×C₈₉	D₄	1	2	yes	—
81	C₄×Q₈×C₈₉	—	2	2	no	—
82	C₄×Q₈×C₈₉	—	2	2	no	—
83	C₄×Q₈×C₈₉	—	2	2	no	—
84	C₄×Q₈×C₈₉	—	2	1	no	—
85	C₄×Q₈×C₈₉	—	2	1	no	—
86	C₄×Q₈×C₈₉	—	2	1	no	—
87	C₄×Q₈×C₈₉	—	2	1	no	—
88	C₄×Q₈×C₈₉	—	2	1	no	—
89	C₄×Q₈×C₈₉	—	2	1	no	—
90	C₄×Q₈×C₈₉	—	2	1	no	—
91	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
92	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
93	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
94	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
96	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₈₉	D₄	1	2	yes	—
98	C₄×D₄×C₈₉	—	2	2	no	—
99	C₄×D₄×C₈₉	—	2	2	no	—
100	C₄×D₄×C₈₉	—	2	1	no	—
101	C₄×D₄×C₈₉	—	2	1	no	—
102	C₄×D₄×C₈₉	—	2	1	no	—
103	C₄×D₄×C₈₉	—	2	1	no	—
104	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
106	#117×C₈₉	—	2	2	no	—
107	#117×C₈₉	—	2	1	no	—
108	#117×C₈₉	—	2	1	no	—
109	#117×C₈₉	D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
111	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₈₉	—	2	2	no	—
115	C₂×C₄²×C₈₉	—	2	1	no	—
116	C₂×C₄²×C₈₉	—	2	1	no	—
117	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
118	C₂²×Dic₈₉	—	4	1	no	—
119	#13083558	—	4	1	no	—
120	#13083558	—	4	1	no	—
121	C₂×#10623494	—	2	2	no	—
122	C₂×#10623494	—	4	1	no	—
123	C₂×#10623494	—	4	1	no	—
124	C₂×#10623494	—	4	1	no	—
125	C₂×#10623494	—	4	1	no	—
126	C₄⋊Dic₈₉	—	2	2	no	—
127	C₄⋊Dic₈₉	—	4	1	no	—
128	C₄×Dic₈₉	—	4	1	no	—
129	C₄×Dic₈₉	—	4	1	no	—
130	#41×C₈₉	—	2	1	no	—
131	#41×C₈₉	—	2	1	no	—
132	#41×C₈₉	SD₁₆	1	2	yes	—
133	#41×C₈₉	Q₁₆	1	2	yes	—
134	C₂×Q₈×C₈₉	—	2	2	no	—
135	C₂×Q₈×C₈₉	—	2	2	no	—
136	C₂×Q₈×C₈₉	—	2	1	no	—
137	C₂×Q₈×C₈₉	—	2	1	no	—
138	C₂×Q₈×C₈₉	—	2	2	no	—
139	C₂×Q₈×C₈₉	—	4	1	no	—
140	C₂×Q₈×C₈₉	—	4	2	no	—
141	C₂×Q₈×C₈₉	—	4	2	no	—
142	C₂×Q₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
143	C₂×Q₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
144	C₂×Q₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
145	C₂×Q₈×C₈₉	C₂²⋊C₄	1	2	yes	—
146	C₂×D₄×C₈₉	—	2	1	no	—
147	C₂×D₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	—	2	1	no	—
149	C₂²×C₄×C₈₉	—	2	2	no	—
150	C₂²×C₄×C₈₉	—	2	1	no	—
151	C₂²×C₄×C₈₉	—	2	2	no	—
152	C₂²×C₄×C₈₉	—	2	1	no	—
153	C₂²×C₄×C₈₉	—	2	1	no	—
154	C₂²×C₄×C₈₉	—	2	1	no	—
155	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₄⋊C₄×C₈₉	—	2	2	no	—
159	C₄⋊C₄×C₈₉	—	2	2	no	—
160	C₄⋊C₄×C₈₉	—	2	2	no	—
161	C₄⋊C₄×C₈₉	—	2	2	no	—
162	C₄⋊C₄×C₈₉	—	2	2	no	—
163	C₄⋊C₄×C₈₉	—	2	2	no	—
164	C₄⋊C₄×C₈₉	—	2	2	no	—
165	C₄⋊C₄×C₈₉	—	2	2	no	—
166	C₄⋊C₄×C₈₉	—	2	1	no	—
167	C₄⋊C₄×C₈₉	—	2	1	no	—
168	C₄⋊C₄×C₈₉	—	2	1	no	—
169	C₄⋊C₄×C₈₉	—	2	1	no	—
170	C₄⋊C₄×C₈₉	—	2	1	no	—
171	C₄⋊C₄×C₈₉	—	2	1	no	—
172	C₄⋊C₄×C₈₉	—	2	1	no	—
173	C₄⋊C₄×C₈₉	—	2	2	no	—
174	C₄⋊C₄×C₈₉	—	2	1	no	—
175	C₄⋊C₄×C₈₉	—	2	1	no	—
176	C₄⋊C₄×C₈₉	—	2	1	no	—
177	C₄⋊C₄×C₈₉	—	2	2	no	—
178	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
179	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
180	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
181	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
182	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
183	C₂²⋊C₄×C₈₉	—	2	2	no	—
184	C₂²⋊C₄×C₈₉	—	2	2	no	—
185	C₂²⋊C₄×C₈₉	—	2	2	no	—
186	C₂²⋊C₄×C₈₉	—	2	1	no	—
187	C₂²⋊C₄×C₈₉	—	2	1	no	—
188	C₂²⋊C₄×C₈₉	—	2	1	no	—
189	C₄²×C₈₉	—	2	2	no	—
190	C₄²×C₈₉	—	2	2	no	—
191	C₄²×C₈₉	—	2	1	no	—
192	C₄²×C₈₉	—	2	1	no	—
193	C₄²×C₈₉	—	2	1	no	—
194	C₄²×C₈₉	—	2	1	no	—
195	C₄²×C₈₉	—	2	2	no	—
196	C₄²×C₈₉	—	2	1	no	—
197	C₄²×C₈₉	—	2	1	no	—
198	C₄²×C₈₉	—	2	1	no	—
199	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
203	C₂³×C₈₉	—	2	1	no	—
204	C₂³×C₈₉	#120	1	1	yes	characteristic
205	Q₈×C₈₉	—	2	1	no	—
206	Q₈×C₈₉	—	2	1	no	—
207	Q₈×C₈₉	—	2	1	no	—
208	Q₈×C₈₉	—	2	1	no	—
209	Q₈×C₈₉	—	4	2	no	—
210	Q₈×C₈₉	—	4	2	no	—
211	Q₈×C₈₉	—	4	4	no	—
212	Q₈×C₈₉	—	4	1	no	—
213	Q₈×C₈₉	—	4	1	no	—
214	Q₈×C₈₉	—	8	2	no	—
215	Q₈×C₈₉	#103	1	2	yes	complemented
216	Q₈×C₈₉	#104	1	2	yes	complemented
217	D₄×C₈₉	—	2	2	no	—
218	D₄×C₈₉	—	2	2	no	—
219	D₄×C₈₉	—	2	1	no	—
220	D₄×C₈₉	#103	1	2	yes	complemented
221	C₂×C₄×C₈₉	—	2	1	no	—
222	C₂×C₄×C₈₉	—	2	1	no	—
223	C₂×C₄×C₈₉	—	2	1	no	—
224	C₂×C₄×C₈₉	—	2	1	no	—
225	C₂×C₄×C₈₉	—	2	2	no	—
226	C₂×C₄×C₈₉	—	2	2	no	—
227	C₂×C₄×C₈₉	—	2	1	no	—
228	C₂×C₄×C₈₉	—	2	2	no	—
229	C₂×C₄×C₈₉	—	2	1	no	—
230	C₂×C₄×C₈₉	—	2	1	no	—
231	C₂×C₄×C₈₉	—	2	1	no	—
232	C₂×C₄×C₈₉	—	2	2	no	—
233	C₂×C₄×C₈₉	—	2	1	no	—
234	C₂×C₄×C₈₉	—	4	1	no	—
235	C₂×C₄×C₈₉	—	4	2	no	—
236	C₂×C₄×C₈₉	—	4	4	no	—
237	C₂×C₄×C₈₉	—	4	1	no	—
238	C₂×C₄×C₈₉	—	4	1	no	—
239	C₂×C₄×C₈₉	—	8	1	no	—
240	C₂×C₄×C₈₉	—	8	1	no	—
241	C₂×C₄×C₈₉	—	8	2	no	—
242	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
246	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
247	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
248	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
249	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
250	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
251	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
252	C₂×Dic₈₉	—	4	2	no	—
253	C₂×Dic₈₉	—	8	1	no	—
254	C₂×Dic₈₉	—	8	1	no	—
255	#10623494	—	4	2	no	—
256	#10623494	—	8	1	no	—
257	#10623494	—	8	1	no	—
258	C₂²×C₈₉	—	2	1	no	—
259	C₂²×C₈₉	—	2	1	no	—
260	C₂²×C₈₉	—	2	2	no	—
261	C₂²×C₈₉	—	4	1	no	—
262	C₂²×C₈₉	—	4	1	no	—
263	C₂²×C₈₉	#379	1	1	yes	characteristic
264	C₂²×C₈₉	#448	1	1	yes	characteristic
265	C₂²×C₈₉	#451	1	1	yes	characteristic
266	C₄×C₈₉	—	2	1	no	—
267	C₄×C₈₉	—	2	1	no	—
268	C₄×C₈₉	—	2	2	no	—
269	C₄×C₈₉	—	2	1	no	—
270	C₄×C₈₉	—	2	2	no	—
271	C₄×C₈₉	—	4	1	no	—
272	C₄×C₈₉	—	4	2	no	—
273	C₄×C₈₉	—	4	1	no	—
274	C₄×C₈₉	—	4	1	no	—
275	C₄×C₈₉	—	4	1	no	—
276	C₄×C₈₉	—	4	2	no	—
277	C₄×C₈₉	—	4	1	no	—
278	C₄×C₈₉	C₂×#103	1	1	yes	characteristic
279	C₄×C₈₉	#419	1	1	yes	characteristic
280	C₄×C₈₉	C₂×#104	1	1	yes	characteristic
281	C₄×C₈₉	#421	1	1	yes	characteristic
282	C₄×C₈₉	#448	1	1	yes	characteristic
283	C₄×C₈₉	#451	1	1	yes	characteristic
284	Dic₈₉	—	8	2	no	—
285	#8439	—	89	1	no	maximal, Sylow
286	C₂×C₈₉	—	2	1	no	—
287	C₂×C₈₉	—	2	1	no	—
288	C₂×C₈₉	—	4	2	no	—
289	C₂×C₈₉	#1787	1	1	yes	characteristic
290	C₂×C₈₉	#1789	1	1	yes	characteristic
291	C₂×C₈₉	#1794	1	1	yes	characteristic
292	Q₈×#41	D₈₉	1	1	yes	characteristic
293	#1806	—	89	1	no	—
294	C₄×#103	—	89	1	no	—
295	#1503	—	89	1	no	—
296	#1493	—	89	1	no	—
297	#1487	—	89	1	no	—
298	#1476	—	89	1	no	—
299	C₈₉	#8439	1	1	yes	characteristic, complemented, Sylow
300	Q₈²	Dic₈₉	1	1	yes	characteristic, complemented
301	#557	—	2	1	no	—
302	#557	Dic₈₉	1	1	yes	characteristic, complemented
303	#554	—	2	2	no	—
304	#554	—	2	1	no	—
305	#554	—	2	1	no	—
306	#554	Dic₈₉	1	1	yes	characteristic, complemented
307	D₄×Q₈	—	2	1	no	—
308	D₄×Q₈	Dic₈₉	1	1	yes	characteristic, complemented
309	#533	—	2	2	no	—
310	#533	—	2	1	no	—
311	#533	—	2	1	no	—
312	#533	C₂×D₈₉	1	1	yes	characteristic
313	C₄×#41	—	2	1	no	—
314	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
315	C₂×C₄×Q₈	—	2	1	no	—
316	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
317	#431	—	89	1	no	—
318	#423	—	89	1	no	—
319	C₂×#104	—	178	1	no	—
320	C₂×#103	—	178	1	no	—
321	C₂×C₄×C₈	—	89	1	no	—
322	C₄×C₄⋊C₄	—	89	1	no	—
323	#340	—	178	1	no	—
324	#339	—	178	1	no	—
325	#328	—	178	2	no	—
326	Q₈⋊C₈	—	178	1	no	—
327	Q₈⋊C₈	—	178	1	no	—
328	Q₈⋊C₈	—	178	1	no	—
329	Q₈⋊C₈	—	178	2	no	—
330	D₄⋊C₈	—	178	1	no	—
331	C₂×#41	C₂²⋊D₈₉	1	1	yes	characteristic
332	C₂²×Q₈	—	2	1	no	—
333	C₂²×Q₈	C₂²⋊D₈₉	1	1	yes	characteristic
334	C₂×M₁₆	—	178	1	no	—
335	C₂²×C₈	—	178	1	no	—
336	C₄⋊Q₈	—	2	2	no	—
337	C₄⋊Q₈	—	2	1	no	—
338	C₄⋊Q₈	—	2	2	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	C₄⋊Q₈	—	2	1	no	—
341	C₄⋊Q₈	—	2	1	no	—
342	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
343	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
344	#125	—	2	2	no	—
345	#125	—	2	2	no	—
346	#125	—	2	2	no	—
347	#125	—	2	1	no	—
348	#125	—	2	1	no	—
349	#125	—	2	1	no	—
350	C₂²⋊Q₈	—	2	2	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	2	2	no	—
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	—	2	1	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	1	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	C₂²⋊D₈₉	1	2	yes	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	—	2	1	no	—
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
372	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
373	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
374	C₄×Q₈	C₂²⋊D₈₉	1	1	yes	characteristic
375	C₄×Q₈	C₂²⋊D₈₉	1	1	yes	characteristic
376	C₄×Q₈	C₂²⋊D₈₉	1	1	yes	characteristic
377	C₄×Q₈	C₂²⋊D₈₉	1	2	yes	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
385	C₄×D₄	C₂²⋊D₈₉	1	1	yes	characteristic
386	#117	—	2	2	no	—
387	#117	—	2	1	no	—
388	#117	—	2	1	no	—
389	#117	C₂²⋊D₈₉	1	1	yes	characteristic
390	C₂×C₄⋊C₄	—	2	2	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	178	1	no	—
394	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
395	C₂×C₄²	—	2	2	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	178	1	no	—
399	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
400	C₄⋊C₈	—	178	1	no	—
401	C₄⋊C₈	—	178	1	no	—
402	C₄⋊C₈	—	178	1	no	—
403	#104	—	356	2	no	—
404	#103	—	178	4	no	—
405	C₂²⋊C₈	—	178	1	no	—
406	C₄×C₈	—	178	1	no	—
407	C₄×C₈	—	178	1	no	—
408	C₄×C₈	—	178	1	no	—
409	#95	—	178	1	no	—
410	#41	—	2	1	no	—
411	#41	—	2	1	no	—
412	#41	#13083561	1	2	yes	—
413	#41	#13083564	1	2	yes	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	4	1	no	—
420	C₂×Q₈	—	4	2	no	—
421	C₂×Q₈	—	4	2	no	—
422	C₂×Q₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
423	C₂×Q₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
424	C₂×Q₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
425	C₂×Q₈	C₂²⋊Dic₈₉	1	2	yes	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	356	1	no	—
436	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
439	M₁₆	—	356	1	no	—
440	M₁₆	—	356	1	no	—
441	C₂×C₈	—	356	1	no	—
442	C₂×C₈	—	356	1	no	—
443	C₂×C₈	—	356	1	no	—
444	C₂×C₈	—	356	1	no	—
445	C₂×C₈	—	178	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	356	1	no	—
467	C₄⋊C₄	—	178	2	no	—
468	C₄⋊C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
469	C₄⋊C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
470	C₄⋊C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
471	C₄⋊C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
472	C₄⋊C₄	C₂²⋊Dic₈₉	1	2	yes	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	356	1	no	—
490	C₄²	—	356	1	no	—
491	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
492	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
493	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
494	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
495	C₂³	—	2	1	no	—
496	C₂³	#15667981	1	1	yes	characteristic
497	Q₈	—	2	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	Q₈	—	4	4	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	8	2	no	—
507	Q₈	#15667936	1	2	yes	complemented
508	Q₈	#15667939	1	2	yes	complemented
509	D₄	—	2	2	no	—
510	D₄	—	2	2	no	—
511	D₄	—	2	1	no	—
512	D₄	#15667936	1	2	yes	complemented
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	8	1	no	—
532	C₂×C₄	—	8	1	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	—	356	2	no	—
535	C₂×C₄	—	712	1	no	—
536	C₂×C₄	—	712	1	no	—
537	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
538	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
539	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
540	C₂×C₄	#15667981	1	1	yes	characteristic
541	C₂×C₄	#15667981	1	1	yes	characteristic
542	C₂×C₄	#15667981	1	1	yes	characteristic
543	C₂×C₄	C₂×#13083561	1	1	yes	characteristic
544	C₂×C₄	C₂×#13083564	1	1	yes	characteristic
545	C₂×C₄	#15668043	1	1	yes	characteristic
546	C₂×C₄	#15668043	1	1	yes	characteristic
547	C₈	—	356	2	no	—
548	C₈	—	712	1	no	—
549	C₈	—	712	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	#19151454	1	1	yes	characteristic
556	C₂²	#19151737	1	1	yes	characteristic
557	C₂²	#19151754	1	1	yes	characteristic
558	C₄	—	2	2	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	2	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	712	2	no	—
571	C₄	C₂×#15667936	1	1	yes	characteristic
572	C₄	#19151607	1	1	yes	characteristic
573	C₄	C₂×#15667939	1	1	yes	characteristic
574	C₄	#19151615	1	1	yes	characteristic
575	C₄	#19151737	1	1	yes	characteristic
576	C₄	#19151754	1	1	yes	characteristic
577	C₂	—	2	1	no	—
578	C₂	—	2	1	no	—
579	C₂	—	4	2	no	—
580	C₂	#26020187	1	1	yes	characteristic
581	C₂	#26020196	1	1	yes	characteristic
582	C₂	#26020216	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667981
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	Q₈×#41×C₈₉	C₂
socle	C₂²×C₈₉	#379
prime radical	C₂×#41×C₈₉	D₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	Q₈×#41	D₈₉
hypocenter	C₈₉	#8439
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ Q₈×#41

Complements

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

N	H ≅ G/N	type
2. C₄×#15667936	C₂	semidirect
3. #26018751	C₂	semidirect
4. #26018707	C₂	semidirect
5. #26018681	C₂	semidirect
22. Q₈²×C₈₉	C₄	semidirect
24. #557×C₈₉	C₄	semidirect
28. #554×C₈₉	C₄	semidirect
30. D₄×Q₈×C₈₉	C₄	semidirect
215. Q₈×C₈₉	#103	semidirect
216. Q₈×C₈₉	#104	semidirect
220. D₄×C₈₉	#103	semidirect
299. C₈₉	#8439	semidirect
300. Q₈²	Dic₈₉	semidirect
302. #557	Dic₈₉	semidirect
306. #554	Dic₈₉	semidirect
308. D₄×Q₈	Dic₈₉	semidirect
507. Q₈	#15667936	semidirect
508. Q₈	#15667939	semidirect
512. D₄	#15667936	semidirect

Maximal subgroups

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

subgroup	index
#26020272	2
C₄×#15667936	2
#26018751	2
#26018707	2
#26018681	2
#26018634	2
Q₈×#41×C₈₉	2
#8439	89