Subgroups — #36445393

Order 22784.

696 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26022814	C₂	1	1	yes	maximal, characteristic
2	#26020107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₈×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19151341	C₂	1	1	yes	maximal, characteristic
5	C₂×#19151341	C₂	1	1	yes	maximal, characteristic
6	#26018135	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15668009	C₂²	1	1	yes	characteristic
9	C₂×#15667974	—	2	1	no	—
10	C₂×#15667974	—	2	1	no	—
11	C₂×#15667974	C₄	1	2	yes	—
12	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
14	C₂×#15667922	—	2	1	no	—
15	C₂×C₈×Dic₈₉	—	2	1	no	—
16	#19151499	—	2	1	no	—
17	#19151499	—	2	1	no	—
18	#19151499	C₄	1	2	yes	—
19	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
20	#19151352	—	2	1	no	—
21	#19151352	—	2	1	no	—
22	#19151341	C₄	1	4	yes	complemented
23	#19151341	C₄	1	4	yes	complemented
24	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
26	#384×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×D₃₅₆	—	2	1	no	—
28	C₂²×D₃₅₆	—	2	1	no	—
29	C₂²×D₃₅₆	C₂×C₄	1	2	yes	—
30	C₂²×C₄×D₈₉	—	2	2	no	—
31	C₂²×#10623494	—	2	1	no	—
32	C₂²×#10623494	—	2	1	no	—
33	#15668009	—	2	1	no	—
34	#15668009	—	2	1	no	—
35	#15668009	C₂×C₄	1	2	yes	—
36	#15668009	C₂×C₄	1	2	yes	—
37	#15667974	—	4	2	no	—
38	#15667974	—	4	2	no	—
39	#15667974	—	4	4	no	—
40	#15667974	—	4	2	no	—
41	#15667974	—	4	2	no	—
42	C₂×#13083551	—	2	2	no	—
43	C₂×#13083551	—	2	2	no	—
44	C₂×#13083551	—	2	2	no	—
45	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
49	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
51	C₄⋊#10623494	—	2	1	no	—
52	C₄⋊#10623494	—	2	1	no	—
53	C₄⋊#10623494	C₂×C₄	1	2	yes	complemented
54	C₄⋊#10623494	C₂×C₄	1	2	yes	complemented
55	#15667922	—	4	2	no	—
56	C₈×Dic₈₉	—	4	2	no	—
57	C₂²×C₈×C₈₉	—	2	1	no	—
58	C₂²×C₈×C₈₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₈₉	—	2	1	no	—
64	C₄⋊C₈×C₈₉	—	2	1	no	—
65	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	complemented
66	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	complemented
67	C₂³×D₈₉	—	2	2	no	—
68	C₂×D₃₅₆	—	2	2	no	—
69	C₂×D₃₅₆	—	2	2	no	—
70	C₂×D₃₅₆	—	2	2	no	—
71	C₂×D₃₅₆	—	2	2	no	—
72	C₂×D₃₅₆	—	2	2	no	—
73	C₂×D₃₅₆	—	4	2	no	—
74	C₂×D₃₅₆	—	4	2	no	—
75	C₂×D₃₅₆	—	4	1	no	—
76	C₂×D₃₅₆	—	4	1	no	—
77	C₂×D₃₅₆	—	4	1	no	—
78	C₂×D₃₅₆	—	4	1	no	—
79	C₂×D₃₅₆	—	4	1	no	—
80	C₂×D₃₅₆	—	4	1	no	—
81	C₂×D₃₅₆	—	4	1	no	—
82	C₂×D₃₅₆	—	4	1	no	—
83	C₂×D₃₅₆	C₄²	1	4	yes	—
84	C₂²×Dic₈₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₈₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₈₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₈₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₈₉	—	4	4	no	—
89	C₂×C₄×D₈₉	—	4	4	no	—
90	C₂×C₄×D₈₉	—	4	4	no	—
91	C₂×#10623494	—	2	2	no	—
92	C₂×#10623494	—	2	2	no	—
93	C₂×#10623494	—	4	1	no	—
94	C₂×#10623494	—	4	1	no	—
95	C₂×#10623494	—	4	1	no	—
96	C₂×#10623494	—	4	1	no	—
97	#13083551	—	4	4	no	—
98	#13083551	—	4	4	no	—
99	#13083551	—	4	4	no	—
100	C₄×Dic₈₉	—	2	1	no	—
101	C₄×Dic₈₉	—	2	1	no	—
102	C₄×Dic₈₉	—	2	1	no	—
103	C₄×Dic₈₉	—	2	1	no	—
104	C₄×Dic₈₉	—	2	1	no	—
105	C₄×Dic₈₉	—	2	1	no	—
106	C₄×Dic₈₉	—	2	2	no	—
107	C₄×Dic₈₉	—	4	1	no	—
108	C₄×Dic₈₉	D₈	1	2	yes	—
109	C₄×Dic₈₉	SD₁₆	1	2	yes	—
110	C₂²×C₄×C₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₈₉	—	2	2	no	—
115	C₂×C₈×C₈₉	—	2	2	no	—
116	C₂×C₈×C₈₉	—	4	1	no	—
117	C₂×C₈×C₈₉	—	4	1	no	—
118	C₂×C₈×C₈₉	—	4	1	no	—
119	C₂×C₈×C₈₉	—	4	1	no	—
120	C₄⋊C₄×C₈₉	—	4	2	no	—
121	C₄⋊C₄×C₈₉	—	4	1	no	—
122	C₄⋊C₄×C₈₉	—	4	1	no	—
123	C₄⋊C₄×C₈₉	—	4	1	no	—
124	C₄⋊C₄×C₈₉	—	4	1	no	—
125	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₈₉	#41	1	1	yes	characteristic
128	C₄²×C₈₉	#41	1	1	yes	characteristic
129	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×D₈₉	—	2	4	no	—
131	C₂²×D₈₉	—	4	2	no	—
132	C₂²×D₈₉	—	4	2	no	—
133	C₂²×D₈₉	—	4	2	no	—
134	C₂²×D₈₉	—	4	2	no	—
135	C₂²×D₈₉	—	4	2	no	—
136	C₂²×D₈₉	—	4	2	no	—
137	C₂×C₄×C₈₉	—	2	1	no	—
138	C₂×C₄×C₈₉	—	2	1	no	—
139	C₂×C₄×C₈₉	—	4	2	no	—
140	C₂×C₄×C₈₉	—	4	2	no	—
141	C₂×C₄×C₈₉	—	4	2	no	—
142	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
150	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
151	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
152	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
156	C₂×Dic₈₉	—	2	1	no	—
157	C₂×Dic₈₉	—	2	1	no	—
158	C₂×Dic₈₉	—	2	1	no	—
159	C₂×Dic₈₉	—	2	1	no	—
160	C₂×Dic₈₉	—	2	1	no	—
161	C₂×Dic₈₉	—	2	1	no	—
162	C₂×Dic₈₉	—	2	1	no	—
163	C₂×Dic₈₉	—	2	1	no	—
164	C₂×Dic₈₉	—	2	1	no	—
165	C₂×Dic₈₉	#100	1	2	yes	—
166	C₂×Dic₈₉	#102	1	2	yes	—
167	C₂×Dic₈₉	#102	1	2	yes	—
168	D₃₅₆	—	4	4	no	—
169	D₃₅₆	—	4	4	no	—
170	D₃₅₆	—	4	2	no	—
171	D₃₅₆	—	4	2	no	—
172	D₃₅₆	—	4	2	no	—
173	D₃₅₆	—	4	2	no	—
174	D₃₅₆	—	4	2	no	—
175	D₃₅₆	—	4	2	no	—
176	D₃₅₆	—	4	2	no	—
177	D₃₅₆	—	4	2	no	—
178	C₄×D₈₉	—	8	8	no	—
179	C₈×C₈₉	—	4	2	no	—
180	C₈×C₈₉	—	4	2	no	—
181	#10623494	—	4	2	no	—
182	#10623494	—	4	2	no	—
183	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₈₉	C₂×#100	1	1	yes	characteristic
185	C₂²×C₈₉	#413	1	1	yes	characteristic
186	C₂²×C₈₉	C₂×#102	1	1	yes	characteristic
187	C₂²×C₈₉	#416	1	1	yes	characteristic
188	C₂²×C₈₉	#417	1	1	yes	characteristic
189	C₂²×C₈₉	#418	1	1	yes	characteristic
190	C₂×D₈₉	—	4	4	no	—
191	C₂×D₈₉	—	4	4	no	—
192	C₂×D₈₉	—	4	4	no	—
193	C₂×D₈₉	—	8	2	no	—
194	C₂×D₈₉	—	8	2	no	—
195	C₂×D₈₉	—	8	2	no	—
196	C₂×D₈₉	—	8	2	no	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	—	2	1	no	—
199	C₄×C₈₉	—	8	2	no	—
200	C₄×C₈₉	C₄×D₈	1	1	yes	characteristic
201	C₄×C₈₉	C₄×D₈	1	1	yes	characteristic
202	C₄×C₈₉	C₄×SD₁₆	1	1	yes	characteristic
203	C₄×C₈₉	C₄×SD₁₆	1	1	yes	characteristic
204	C₄×C₈₉	#440	1	1	yes	characteristic
205	C₄×C₈₉	#440	1	1	yes	characteristic
206	C₄×C₈₉	#442	1	1	yes	characteristic
207	C₄×C₈₉	#442	1	1	yes	characteristic
208	Dic₈₉	—	2	2	no	—
209	Dic₈₉	—	2	2	no	—
210	Dic₈₉	—	2	2	no	—
211	Dic₈₉	—	4	1	no	—
212	#8234	—	89	1	no	maximal, Sylow
213	C₂×C₈₉	#1545	1	1	yes	characteristic
214	C₂×C₈₉	#1547	1	1	yes	characteristic
215	C₂×C₈₉	#1551	1	1	yes	characteristic
216	C₂×C₈₉	#1553	1	1	yes	characteristic
217	C₂×C₈₉	C₄×#100	1	1	yes	characteristic
218	C₂×C₈₉	C₄×#102	1	1	yes	characteristic
219	C₂×C₈₉	#1762	1	1	yes	characteristic
220	D₈₉	—	8	4	no	—
221	C₄×#127	—	89	1	no	—
222	#1767	—	89	1	no	—
223	C₄×C₄⋊C₈	—	89	1	no	—
224	C₂×#331	—	89	1	no	—
225	C₂×#331	—	89	1	no	—
226	#1296	—	89	1	no	—
227	#1296	D₈₉	1	1	yes	characteristic, complemented
228	C₈₉	#8234	1	1	yes	characteristic, complemented, Sylow
229	C₂×#127	—	89	1	no	—
230	C₂×C₄×D₄	—	89	2	no	—
231	C₂×C₄×D₄	—	178	1	no	—
232	C₂×C₄×D₄	—	178	1	no	—
233	C₂×C₄⋊C₈	—	89	1	no	—
234	C₂×C₄⋊C₈	—	89	1	no	—
235	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
237	C₂×#97	—	178	1	no	—
238	C₂×C₄×C₈	—	178	1	no	—
239	#390	—	89	2	no	—
240	#390	—	178	1	no	—
241	#390	—	178	1	no	—
242	#384	C₂×D₈₉	1	1	yes	characteristic
243	C₄³	—	89	1	no	—
244	#336	—	178	1	no	—
245	#336	—	178	1	no	—
246	#331	—	89	4	no	—
247	#331	—	89	4	no	—
248	C₂²×D₄	—	89	2	no	—
249	C₂²×D₄	—	178	1	no	—
250	C₂²×D₄	—	178	1	no	—
251	C₂³×C₄	—	178	2	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	178	1	no	—
255	C₂²×C₈	—	178	1	no	—
256	#127	—	89	2	no	—
257	#127	—	89	2	no	—
258	#127	—	178	1	no	—
259	#127	—	178	1	no	—
260	C₄×D₄	—	356	2	no	—
261	C₄×D₄	—	356	2	no	—
262	C₄×D₄	—	356	2	no	—
263	C₄×D₄	—	356	2	no	—
264	C₄×D₄	—	356	4	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	C₄×D₈₉	1	2	yes	—
268	C₂×C₂²⋊C₄	—	178	2	no	—
269	C₂×C₂²⋊C₄	—	178	2	no	—
270	C₂×C₂²⋊C₄	—	178	2	no	—
271	C₂×C₄²	—	89	1	no	—
272	C₂×C₄²	—	89	1	no	—
273	C₂×C₄²	—	89	1	no	—
274	C₂×C₄²	—	89	1	no	—
275	C₂×C₄²	—	89	1	no	—
276	C₂×C₄²	—	89	1	no	—
277	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	89	2	no	—
281	C₄⋊C₈	—	89	2	no	—
282	C₄⋊C₈	—	178	1	no	—
283	C₄⋊C₈	—	178	1	no	—
284	C₄⋊C₈	C₄×D₈₉	1	2	yes	complemented
285	C₄⋊C₈	C₄×D₈₉	1	2	yes	complemented
286	#97	—	356	2	no	—
287	C₄×C₈	—	356	2	no	—
288	C₂⁴	—	178	2	no	—
289	C₂×D₄	—	89	4	no	—
290	C₂×D₄	—	356	2	no	—
291	C₂×D₄	—	356	2	no	—
292	C₂×D₄	—	356	1	no	—
293	C₂×D₄	—	356	1	no	—
294	C₂×D₄	—	356	1	no	—
295	C₂×D₄	—	356	1	no	—
296	C₂×D₄	—	356	1	no	—
297	C₂×D₄	—	356	1	no	—
298	C₂×D₄	—	356	1	no	—
299	C₂×D₄	—	356	1	no	—
300	C₂×D₄	—	178	2	no	—
301	C₂×D₄	—	178	2	no	—
302	C₂×D₄	—	178	2	no	—
303	C₂×D₄	—	178	2	no	—
304	C₂×D₄	—	178	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	89	1	no	—
307	C₂²×C₄	—	89	1	no	—
308	C₂²×C₄	—	89	1	no	—
309	C₂²×C₄	—	89	1	no	—
310	C₂²×C₄	—	356	4	no	—
311	C₂²×C₄	—	356	4	no	—
312	C₂²×C₄	—	356	4	no	—
313	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
314	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
315	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	356	1	no	—
323	C₂×C₈	—	356	1	no	—
324	C₂×C₈	—	356	1	no	—
325	C₂×C₈	—	356	1	no	—
326	C₂×C₈	—	178	2	no	—
327	C₂×C₈	—	178	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	356	4	no	—
334	C₂²⋊C₄	—	356	4	no	—
335	C₂²⋊C₄	—	356	4	no	—
336	C₄²	—	89	2	no	—
337	C₄²	—	89	2	no	—
338	C₄²	—	356	1	no	—
339	C₄²	—	178	2	no	—
340	C₄²	—	178	1	no	—
341	C₄²	—	178	1	no	—
342	C₄²	—	178	1	no	—
343	C₄²	—	178	1	no	—
344	C₄²	—	178	1	no	—
345	C₄²	—	178	1	no	—
346	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
347	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
348	C₄²	#13083573	1	1	yes	characteristic
349	C₄²	#13083575	1	1	yes	characteristic
350	C₂³	—	356	2	no	—
351	C₂³	—	356	2	no	—
352	C₂³	—	356	2	no	—
353	C₂³	—	356	2	no	—
354	C₂³	—	356	2	no	—
355	C₂³	—	356	2	no	—
356	C₂³	—	178	4	no	—
357	C₂³	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
358	D₄	—	356	4	no	—
359	D₄	—	356	4	no	—
360	D₄	—	356	2	no	—
361	D₄	—	356	2	no	—
362	D₄	—	356	2	no	—
363	D₄	—	356	2	no	—
364	D₄	—	356	2	no	—
365	D₄	—	356	2	no	—
366	D₄	—	356	2	no	—
367	D₄	—	356	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	89	2	no	—
374	C₂×C₄	—	89	2	no	—
375	C₂×C₄	—	89	2	no	—
376	C₂×C₄	—	178	1	no	—
377	C₂×C₄	—	178	1	no	—
378	C₂×C₄	—	178	1	no	—
379	C₂×C₄	—	178	1	no	—
380	C₂×C₄	—	178	1	no	—
381	C₂×C₄	—	178	1	no	—
382	C₂×C₄	—	178	1	no	—
383	C₂×C₄	—	178	1	no	—
384	C₂×C₄	—	178	1	no	—
385	C₂×C₄	—	712	8	no	—
386	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
387	C₂×C₄	#15667970	1	1	yes	characteristic
388	C₂×C₄	#15667972	1	1	yes	characteristic
389	C₂×C₄	#15667972	1	1	yes	characteristic
390	C₂×C₄	#15667974	1	1	yes	characteristic
391	C₂×C₄	#15667974	1	1	yes	characteristic
392	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
393	C₂×C₄	SD₁₆×D₈₉	1	1	yes	characteristic
394	C₂×C₄	#15668033	1	1	yes	characteristic
395	C₂×C₄	#15668035	1	1	yes	characteristic
396	C₂×C₄	#15668036	1	1	yes	characteristic
397	C₂×C₄	#15668039	1	1	yes	characteristic
398	C₂×C₄	#15668039	1	1	yes	characteristic
399	C₂×C₄	#15668044	1	1	yes	characteristic
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₈	—	356	2	no	—
403	C₈	—	356	2	no	—
404	C₂²	—	356	4	no	—
405	C₂²	—	356	4	no	—
406	C₂²	—	356	4	no	—
407	C₂²	—	712	2	no	—
408	C₂²	—	712	2	no	—
409	C₂²	—	712	2	no	—
410	C₂²	—	712	2	no	—
411	C₂²	#19151445	1	1	yes	characteristic
412	C₂²	#100×D₈₉	1	1	yes	characteristic
413	C₂²	#19151581	1	1	yes	characteristic
414	C₂²	#102×D₈₉	1	1	yes	characteristic
415	C₂²	#19151593	1	1	yes	characteristic
416	C₂²	#19151598	1	1	yes	characteristic
417	C₂²	#19151601	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	8	2	no	—
421	C₄	—	356	1	no	—
422	C₄	—	178	2	no	—
423	C₄	—	178	2	no	—
424	C₄	—	178	2	no	—
425	C₄	#19151678	1	1	yes	characteristic
426	C₄	#19151680	1	1	yes	characteristic
427	C₄	#19151683	1	1	yes	characteristic
428	C₄	#19151685	1	1	yes	characteristic
429	C₄	#19151697	1	1	yes	characteristic
430	C₄	#19151701	1	1	yes	characteristic
431	C₄	#19151707	1	1	yes	characteristic
432	C₄	#19151709	1	1	yes	characteristic
433	C₂	—	712	4	no	—
434	C₂	#26018918	1	1	yes	characteristic
435	C₂	#26018928	1	1	yes	characteristic
436	C₂	#26018946	1	1	yes	characteristic
437	C₂	#26018956	1	1	yes	characteristic
438	C₂	#26020043	1	1	yes	characteristic
439	C₂	#26020066	1	1	yes	characteristic
440	C₂	#26020076	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1296	C₂
socle	C₂³×C₈₉	C₂×C₂²⋊C₄
prime radical	C₂×#15668009	C₂²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1296	D₈₉
hypocenter	C₈₉	#8234
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
2. #26020107	C₂	semidirect
3. C₄⋊C₈×Dic₈₉	C₂	semidirect
6. #26018135	C₂	semidirect
7. C₈₉×#1296	C₂	semidirect
22. #19151341	C₄	semidirect
23. #19151341	C₄	semidirect
53. C₄⋊#10623494	C₂×C₄	semidirect
54. C₄⋊#10623494	C₂×C₄	semidirect
65. C₄⋊C₈×C₈₉	C₂×C₄	semidirect
66. C₄⋊C₈×C₈₉	C₂×C₄	semidirect
227. #1296	D₈₉	semidirect
228. C₈₉	#8234	semidirect
284. C₄⋊C₈	C₄×D₈₉	semidirect
285. C₄⋊C₈	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26022814	2
#26020107	2
C₄⋊C₈×Dic₈₉	2
C₂×#19151341	2
#26018135	2
C₈₉×#1296	2
#8234	89