Subgroups — #36525427

Order 22784.

594 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#13083558	C₂	1	1	yes	maximal, characteristic
2	#26029201	C₂	1	1	yes	maximal, characteristic
3	#26019161	C₂	1	2	yes	maximal, complemented
4	#26019124	C₂	1	2	yes	maximal, complemented
5	#26019124	C₂	1	2	yes	maximal, complemented
6	#26019071	C₂	1	2	yes	maximal, complemented
7	#26019023	C₂	1	1	yes	maximal, characteristic
8	#26018707	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈⋊#10623494	C₂	1	1	yes	maximal, characteristic
10	#26018542	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#3104	C₂	1	1	yes	maximal, characteristic
12	#19151729	—	2	2	no	—
13	#19151729	—	2	2	no	—
14	#19151729	C₂²	1	2	yes	—
15	#19151729	C₂²	1	2	yes	—
16	Q₈×#10623494	C₂²	1	2	yes	—
17	Q₈×#10623494	C₂²	1	2	yes	—
18	#19151625	—	2	1	no	—
19	#19151622	—	2	1	no	—
20	#19151622	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
22	#19151554	—	2	1	no	—
23	C₄×#13083558	—	2	1	no	—
24	C₄×#13083558	C₂²	1	1	yes	characteristic
25	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
26	#19151349	C₂²	1	2	yes	—
27	#19151349	C₂²	1	2	yes	—
28	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
29	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
30	Q₈⋊#10623494	C₂²	1	2	yes	—
31	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
32	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
33	Q₈⋊#10623494	C₂²	1	2	yes	—
34	#19151320	C₂²	1	2	yes	—
35	#19151319	C₂²	1	2	yes	—
36	#533×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
38	#484×C₈₉	C₄	1	2	yes	—
39	#477×C₈₉	C₄	1	1	yes	characteristic
40	#477×C₈₉	C₄	1	1	yes	characteristic
41	#462×C₈₉	C₄	1	1	yes	characteristic
42	#462×C₈₉	C₄	1	1	yes	characteristic
43	#451×C₈₉	C₄	1	2	yes	—
44	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
45	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
46	#431×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083558	—	2	1	no	—
48	C₂×#13083558	D₄	1	1	yes	characteristic
49	C₂×#13083558	D₄	1	1	yes	characteristic
50	C₂²×#10623494	—	2	1	no	—
51	C₂²×#10623494	—	2	1	no	—
52	C₄⋊#10623494	—	2	2	no	—
53	C₄⋊#10623494	—	2	2	no	—
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	C₂³	1	1	yes	characteristic
59	C₄⋊#10623494	C₂³	1	1	yes	characteristic
60	C₄⋊#10623494	C₂³	1	2	yes	—
61	#15667923	—	2	2	no	—
62	#15667923	—	2	2	no	—
63	#15667923	D₄	1	2	yes	—
64	C₄×#10623494	—	2	2	no	—
65	C₄×#10623494	—	2	2	no	—
66	C₄×#10623494	—	2	1	no	—
67	C₄×#10623494	C₂³	1	1	yes	characteristic
68	C₄×#10623494	C₂³	1	1	yes	characteristic
69	C₄×#10623494	C₂³	1	2	yes	—
70	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
71	C₂×Q₁₆×C₈₉	C₂×C₄	1	2	yes	—
72	C₂×Q₁₆×C₈₉	C₂×C₄	1	2	yes	—
73	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
74	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
75	#125×C₈₉	—	2	1	no	—
76	C₂²⋊Q₈×C₈₉	—	2	1	no	—
77	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
78	C₄×Q₈×C₈₉	—	2	1	no	—
79	C₄×Q₈×C₈₉	—	2	1	no	—
80	C₄×Q₈×C₈₉	—	2	1	no	—
81	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
82	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
84	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
85	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
86	#117×C₈₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₈₉	—	2	1	no	—
90	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
91	#107×C₈₉	C₂×C₄	1	2	yes	—
92	#107×C₈₉	C₂×C₄	1	2	yes	—
93	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
94	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
95	#103×C₈₉	C₂×C₄	1	2	yes	—
96	#103×C₈₉	C₂×C₄	1	2	yes	—
97	#103×C₈₉	C₂×C₄	1	2	yes	—
98	#103×C₈₉	C₂×C₄	1	2	yes	—
99	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
100	C₄×C₈×C₈₉	C₂³	1	2	yes	—
101	#13083558	—	2	2	no	—
102	#13083558	—	2	2	no	—
103	#13083558	—	4	2	no	—
104	C₂×#10623494	—	2	1	no	—
105	C₂×#10623494	—	2	1	no	—
106	C₂×#10623494	—	2	1	no	—
107	C₂×#10623494	—	2	2	no	—
108	C₂×#10623494	—	2	1	no	—
109	C₂×#10623494	—	4	2	no	—
110	C₂×#10623494	—	4	2	no	—
111	C₂×#10623494	C₂×D₄	1	2	yes	—
112	C₂×#10623494	C₂×D₄	1	2	yes	—
113	C₂×Q₈×C₈₉	—	2	1	no	—
114	C₂×Q₈×C₈₉	—	2	1	no	—
115	C₂×Q₈×C₈₉	—	2	2	no	—
116	C₂×Q₈×C₈₉	—	4	1	no	—
117	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
119	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	—	2	1	no	—
121	C₂²×C₄×C₈₉	—	2	1	no	—
122	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
125	Q₁₆×C₈₉	—	2	4	no	—
126	Q₁₆×C₈₉	—	4	2	no	—
127	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
129	C₄⋊C₄×C₈₉	—	2	1	no	—
130	C₄⋊C₄×C₈₉	—	2	1	no	—
131	C₄⋊C₄×C₈₉	—	2	1	no	—
132	C₄⋊C₄×C₈₉	—	2	1	no	—
133	C₄⋊C₄×C₈₉	—	2	1	no	—
134	C₄⋊C₄×C₈₉	—	2	1	no	—
135	C₄⋊C₄×C₈₉	—	2	2	no	—
136	C₄⋊C₄×C₈₉	—	2	1	no	—
137	C₄⋊C₄×C₈₉	—	2	1	no	—
138	C₄⋊C₄×C₈₉	—	2	2	no	—
139	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
142	C₂²⋊C₄×C₈₉	—	2	2	no	—
143	C₄²×C₈₉	—	2	1	no	—
144	C₄²×C₈₉	—	2	1	no	—
145	C₄²×C₈₉	—	2	1	no	—
146	C₄²×C₈₉	—	2	1	no	—
147	C₄²×C₈₉	—	2	2	no	—
148	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₈₉	#41	1	1	yes	characteristic
151	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
153	Q₈×C₈₉	—	2	1	no	—
154	Q₈×C₈₉	—	2	2	no	—
155	Q₈×C₈₉	—	2	1	no	—
156	Q₈×C₈₉	—	2	1	no	—
157	Q₈×C₈₉	—	2	2	no	—
158	Q₈×C₈₉	—	4	2	no	—
159	Q₈×C₈₉	—	8	1	no	—
160	Q₈×C₈₉	#131	1	2	yes	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	2	no	—
168	C₂×C₄×C₈₉	—	2	2	no	—
169	C₂×C₄×C₈₉	—	4	1	no	—
170	C₂×C₄×C₈₉	—	4	2	no	—
171	C₂×C₄×C₈₉	—	8	1	no	—
172	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	#137	1	2	yes	—
176	C₂×C₄×C₈₉	#137	1	2	yes	—
177	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
180	C₈×C₈₉	—	2	2	no	—
181	C₈×C₈₉	—	2	2	no	—
182	#10623494	—	2	2	no	—
183	#10623494	—	2	2	no	—
184	#10623494	—	2	2	no	—
185	#10623494	—	4	1	no	—
186	#10623494	—	4	1	no	—
187	#10623494	—	4	1	no	—
188	#10623494	—	4	2	no	—
189	C₂²×C₈₉	—	2	1	no	—
190	C₂²×C₈₉	—	2	1	no	—
191	C₂²×C₈₉	#441	1	2	yes	—
192	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₈₉	—	2	1	no	—
194	C₄×C₈₉	—	2	2	no	—
195	C₄×C₈₉	—	2	1	no	—
196	C₄×C₈₉	—	2	1	no	—
197	C₄×C₈₉	—	4	1	no	—
198	C₄×C₈₉	—	4	2	no	—
199	C₄×C₈₉	—	4	1	no	—
200	C₄×C₈₉	—	4	1	no	—
201	C₄×C₈₉	—	4	2	no	—
202	C₄×C₈₉	#441	1	2	yes	—
203	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
204	C₄×C₈₉	#568	1	1	yes	characteristic
205	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
206	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
207	#18003	—	89	1	no	maximal, Sylow
208	C₂×C₈₉	—	2	2	no	—
209	C₂×C₈₉	#2933	1	1	yes	characteristic
210	C₂×C₈₉	C₂×#441	1	1	yes	characteristic
211	C₂×C₈₉	#2956	1	1	yes	characteristic
212	#3104	D₈₉	1	1	yes	characteristic
213	Q₈×M₁₆	—	89	1	no	—
214	#2962	—	89	1	no	—
215	#1593	—	89	2	no	—
216	#1587	—	89	2	no	—
217	#1587	—	89	2	no	—
218	#1579	—	89	2	no	—
219	#1570	—	89	1	no	—
220	#1493	—	89	1	no	—
221	C₂×Q₈⋊C₈	—	89	1	no	—
222	#1451	—	89	1	no	—
223	C₈₉	#18003	1	1	yes	characteristic, complemented, Sylow
224	#533	C₂×D₈₉	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
226	#484	Dic₈₉	1	2	yes	—
227	#477	Dic₈₉	1	1	yes	characteristic
228	#477	Dic₈₉	1	1	yes	characteristic
229	#462	Dic₈₉	1	1	yes	characteristic
230	#462	Dic₈₉	1	1	yes	characteristic
231	#451	Dic₈₉	1	2	yes	—
232	#446	—	89	2	no	—
233	#446	—	89	2	no	—
234	#446	—	178	2	no	—
235	#446	—	178	2	no	—
236	C₈×Q₈	—	89	2	no	—
237	C₈×Q₈	—	89	2	no	—
238	C₄×Q₁₆	C₂×D₈₉	1	2	yes	—
239	C₄×Q₁₆	C₂×D₈₉	1	2	yes	—
240	#431	C₂×D₈₉	1	1	yes	characteristic
241	#424	—	178	1	no	—
242	#423	—	89	1	no	—
243	#423	—	178	1	no	—
244	C₂×C₄⋊C₈	—	89	1	no	—
245	#405	—	178	1	no	—
246	C₄×M₁₆	—	89	1	no	—
247	C₄×M₁₆	—	178	1	no	—
248	C₂×C₄×C₈	—	89	1	no	—
249	#334	—	89	2	no	—
250	#334	—	89	2	no	—
251	Q₈⋊C₈	—	89	1	no	—
252	Q₈⋊C₈	—	89	2	no	—
253	Q₈⋊C₈	—	89	1	no	—
254	Q₈⋊C₈	—	89	1	no	—
255	Q₈⋊C₈	—	89	2	no	—
256	Q₈⋊C₈	—	89	1	no	—
257	#322	—	89	2	no	—
258	#322	—	89	2	no	—
259	C₂²×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
260	C₂×Q₁₆	C₂×Dic₈₉	1	2	yes	—
261	C₂×Q₁₆	C₂×Dic₈₉	1	2	yes	—
262	C₂×M₁₆	—	89	1	no	—
263	C₂×M₁₆	—	89	1	no	—
264	C₂×M₁₆	—	178	1	no	—
265	C₂²×C₈	—	178	1	no	—
266	C₂²×C₈	—	178	1	no	—
267	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
268	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
269	#125	—	2	1	no	—
270	C₂²⋊Q₈	—	2	1	no	—
271	C₂²⋊Q₈	C₂×Dic₈₉	1	2	yes	—
272	C₄×Q₈	—	2	1	no	—
273	C₄×Q₈	—	2	1	no	—
274	C₄×Q₈	—	2	1	no	—
275	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
276	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
277	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
278	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
279	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
280	#117	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
285	#107	C₂×Dic₈₉	1	2	yes	—
286	#107	C₂×Dic₈₉	1	2	yes	—
287	C₄⋊C₈	—	89	1	no	—
288	C₄⋊C₈	—	89	1	no	—
289	C₄⋊C₈	—	89	2	no	—
290	C₄⋊C₈	—	178	2	no	—
291	C₄⋊C₈	—	178	2	no	—
292	C₄⋊C₈	—	178	2	no	—
293	C₄⋊C₈	—	178	2	no	—
294	C₄⋊C₈	—	178	1	no	—
295	C₄⋊C₈	—	178	1	no	—
296	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
297	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
298	#103	C₂×Dic₈₉	1	2	yes	—
299	#103	C₂×Dic₈₉	1	2	yes	—
300	#103	C₂×Dic₈₉	1	2	yes	—
301	#103	C₂×Dic₈₉	1	2	yes	—
302	C₂²⋊C₈	C₂×Dic₈₉	1	2	yes	—
303	#97	—	89	2	no	—
304	#97	—	178	2	no	—
305	#97	—	178	2	no	—
306	C₄×C₈	—	89	2	no	—
307	C₄×C₈	—	89	1	no	—
308	C₄×C₈	—	89	1	no	—
309	C₄×C₈	—	178	2	no	—
310	C₄×C₈	—	178	2	no	—
311	C₄×C₈	—	178	1	no	—
312	C₄×C₈	C₂²×D₈₉	1	2	yes	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	4	1	no	—
317	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
318	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
319	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
324	C₂²×C₄	#13083573	1	1	yes	characteristic
325	Q₁₆	—	2	4	no	—
326	Q₁₆	—	4	2	no	—
327	M₁₆	—	356	2	no	—
328	M₁₆	—	178	2	no	—
329	M₁₆	—	178	2	no	—
330	C₂×C₈	—	89	2	no	—
331	C₂×C₈	—	89	2	no	—
332	C₂×C₈	—	356	2	no	—
333	C₂×C₈	—	356	2	no	—
334	C₂×C₈	—	178	1	no	—
335	C₂×C₈	—	178	2	no	—
336	C₂×C₈	—	178	1	no	—
337	C₂×C₈	—	178	1	no	—
338	C₂×C₈	—	178	1	no	—
339	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
340	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
352	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
353	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
361	C₄²	D₄×D₈₉	1	1	yes	characteristic
362	C₄²	#13083573	1	1	yes	characteristic
363	C₄²	C₂³×D₈₉	1	1	yes	characteristic
364	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
365	Q₈	—	2	1	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	2	1	no	—
368	Q₈	—	2	1	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	8	1	no	—
372	Q₈	#15668019	1	2	yes	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
385	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
386	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
387	C₂×C₄	#15668044	1	2	yes	—
388	C₂×C₄	#15668044	1	2	yes	—
389	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
390	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
391	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
392	C₈	—	2	2	no	—
393	C₈	—	2	2	no	—
394	C₈	—	356	1	no	—
395	C₈	—	356	1	no	—
396	C₈	—	356	1	no	—
397	C₈	—	356	2	no	—
398	C₈	—	178	2	no	—
399	C₈	—	178	2	no	—
400	C₈	—	178	2	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	#19151705	1	2	yes	—
404	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	2	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	2	no	—
414	C₄	#19151705	1	2	yes	—
415	C₄	C₂×#15668019	1	1	yes	characteristic
416	C₄	#19152365	1	1	yes	characteristic
417	C₄	C₂×#15668044	1	1	yes	characteristic
418	C₄	C₂×#15668044	1	1	yes	characteristic
419	C₂	—	2	2	no	—
420	C₂	#26028979	1	1	yes	characteristic
421	C₂	C₂×#19151705	1	1	yes	characteristic
422	C₂	#26029162	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#3104	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂³×C₈₉	C₄×D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#3104	D₈₉
hypocenter	C₈₉	#18003
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3104

Complements

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

N	H ≅ G/N	type
3. #26019161	C₂	semidirect
4. #26019124	C₂	semidirect
5. #26019124	C₂	semidirect
6. #26019071	C₂	semidirect
223. C₈₉	#18003	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#13083558	2
#26029201	2
#26019161	2
#26019124	2
#26019071	2
#26019023	2
#26018707	2
C₂×Q₈⋊#10623494	2
#26018542	2
C₈₉×#3104	2
#18003	89