Subgroups — #36447784

Order 22784.

592 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26020232	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊#10623494	C₂	1	1	yes	maximal, characteristic
3	#26018093	C₂	1	2	yes	maximal, complemented
4	#26018093	C₂	1	2	yes	maximal, complemented
5	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
7	C₂×C₂²⋊#10623494	—	2	1	no	—
8	C₂×C₂²⋊#10623494	—	2	1	no	—
9	C₂×C₄×#10623494	C₂²	1	2	yes	—
10	#19151353	—	2	1	no	—
11	#19151353	—	2	1	no	—
12	C₂×#117×C₈₉	C₄	1	1	yes	characteristic
13	C₂×#117×C₈₉	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
15	C₄×C₄⋊C₄×C₈₉	C₄	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₈₉	C₄	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
20	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
21	#376×C₈₉	—	2	1	no	—
22	C₄³×C₈₉	—	2	1	no	—
23	C₂²×#10623494	—	2	2	no	—
24	C₂²×#10623494	—	2	2	no	—
25	C₄⋊#10623494	—	2	2	no	—
26	C₄⋊#10623494	—	2	2	no	—
27	C₂²⋊#10623494	—	2	4	no	—
28	C₂²⋊#10623494	—	4	2	no	—
29	C₄×#10623494	—	2	2	no	—
30	C₄×#10623494	—	2	2	no	—
31	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
34	#117×C₈₉	—	2	2	no	—
35	#117×C₈₉	—	2	2	no	—
36	#117×C₈₉	—	2	2	no	—
37	#117×C₈₉	C₈	1	4	yes	complemented
38	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
44	C₂×C₄²×C₈₉	—	2	1	no	—
45	C₂×C₄²×C₈₉	—	2	1	no	—
46	C₂×C₄²×C₈₉	—	2	2	no	—
47	C₂×C₄²×C₈₉	—	2	2	no	—
48	C₂×C₄²×C₈₉	—	2	1	no	—
49	C₂×C₄²×C₈₉	—	2	1	no	—
50	C₂×C₄²×C₈₉	—	2	1	no	—
51	C₂×C₄²×C₈₉	—	2	1	no	—
52	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
56	#95×C₈₉	—	2	1	no	—
57	#95×C₈₉	—	2	1	no	—
58	#95×C₈₉	—	2	1	no	—
59	#95×C₈₉	—	2	1	no	—
60	C₂×#10623494	—	2	4	no	—
61	C₂×#10623494	—	4	2	no	—
62	C₂×#10623494	—	4	2	no	—
63	C₂×#10623494	—	4	2	no	—
64	C₂×#10623494	—	4	2	no	—
65	C₂×#10623494	—	4	2	no	—
66	C₂⁴×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₈₉	—	2	1	no	—
68	C₂²×C₄×C₈₉	—	2	1	no	—
69	C₂²×C₄×C₈₉	—	2	1	no	—
70	C₂²×C₄×C₈₉	—	2	1	no	—
71	C₂²×C₄×C₈₉	—	2	1	no	—
72	C₂²×C₄×C₈₉	—	2	1	no	—
73	C₂²×C₄×C₈₉	—	2	1	no	—
74	C₂²×C₄×C₈₉	—	2	1	no	—
75	C₂²×C₄×C₈₉	—	2	2	no	—
76	C₂²×C₄×C₈₉	—	2	2	no	—
77	C₂²×C₄×C₈₉	—	2	2	no	—
78	C₂²×C₄×C₈₉	—	2	2	no	—
79	C₂²×C₄×C₈₉	—	2	1	no	—
80	C₂²×C₄×C₈₉	—	2	1	no	—
81	C₂²×C₄×C₈₉	—	4	1	no	—
82	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₈₉	C₂×C₈	1	2	yes	—
86	C₂²×C₄×C₈₉	M₁₆	1	2	yes	—
87	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
90	C₄⋊C₄×C₈₉	—	2	1	no	—
91	C₄⋊C₄×C₈₉	—	2	1	no	—
92	C₄⋊C₄×C₈₉	—	2	1	no	—
93	C₄⋊C₄×C₈₉	—	2	1	no	—
94	C₄⋊C₄×C₈₉	C₂×C₈	1	2	yes	—
95	C₄⋊C₄×C₈₉	C₂×C₈	1	2	yes	—
96	C₄⋊C₄×C₈₉	M₁₆	1	2	yes	—
97	C₄⋊C₄×C₈₉	M₁₆	1	2	yes	—
98	C₂²⋊C₄×C₈₉	—	2	4	no	—
99	C₂²⋊C₄×C₈₉	—	2	4	no	—
100	C₄²×C₈₉	—	2	4	no	—
101	C₄²×C₈₉	—	2	4	no	—
102	C₄²×C₈₉	—	2	1	no	—
103	C₄²×C₈₉	—	2	1	no	—
104	C₄²×C₈₉	—	2	2	no	—
105	C₄²×C₈₉	—	2	2	no	—
106	C₄²×C₈₉	—	4	2	no	—
107	C₄²×C₈₉	—	4	2	no	—
108	C₄²×C₈₉	—	4	2	no	—
109	C₄²×C₈₉	—	4	1	no	—
110	C₄²×C₈₉	—	4	1	no	—
111	C₄²×C₈₉	#41	1	2	yes	—
112	C₄²×C₈₉	#41	1	2	yes	—
113	C₂³×C₈₉	—	2	1	no	—
114	C₂³×C₈₉	—	2	1	no	—
115	C₂³×C₈₉	—	2	1	no	—
116	C₂³×C₈₉	—	2	1	no	—
117	C₂³×C₈₉	—	2	1	no	—
118	C₂³×C₈₉	—	2	1	no	—
119	C₂³×C₈₉	C₂²⋊C₈	1	2	yes	—
120	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₈₉	—	2	1	no	—
122	C₂×C₄×C₈₉	—	2	1	no	—
123	C₂×C₄×C₈₉	—	2	1	no	—
124	C₂×C₄×C₈₉	—	2	1	no	—
125	C₂×C₄×C₈₉	—	2	1	no	—
126	C₂×C₄×C₈₉	—	2	1	no	—
127	C₂×C₄×C₈₉	—	2	2	no	—
128	C₂×C₄×C₈₉	—	2	2	no	—
129	C₂×C₄×C₈₉	—	2	2	no	—
130	C₂×C₄×C₈₉	—	2	2	no	—
131	C₂×C₄×C₈₉	—	2	1	no	—
132	C₂×C₄×C₈₉	—	2	2	no	—
133	C₂×C₄×C₈₉	—	2	2	no	—
134	C₂×C₄×C₈₉	—	2	2	no	—
135	C₂×C₄×C₈₉	—	2	2	no	—
136	C₂×C₄×C₈₉	—	2	1	no	—
137	C₂×C₄×C₈₉	—	2	1	no	—
138	C₂×C₄×C₈₉	—	4	4	no	—
139	C₂×C₄×C₈₉	—	4	1	no	—
140	C₂×C₄×C₈₉	—	4	1	no	—
141	C₂×C₄×C₈₉	—	4	1	no	—
142	C₂×C₄×C₈₉	—	4	1	no	—
143	C₂×C₄×C₈₉	—	4	1	no	—
144	C₂×C₄×C₈₉	—	4	1	no	—
145	C₂×C₄×C₈₉	—	4	1	no	—
146	C₂×C₄×C₈₉	—	4	1	no	—
147	C₂×C₄×C₈₉	—	4	2	no	—
148	C₂×C₄×C₈₉	—	4	2	no	—
149	C₂×C₄×C₈₉	C₂²⋊C₈	1	2	yes	—
150	C₂×C₄×C₈₉	#104	1	2	yes	—
151	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
152	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
153	C₂×C₄×C₈₉	#123	1	2	yes	—
154	C₂×C₄×C₈₉	#123	1	2	yes	—
155	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
159	C₂×C₄×C₈₉	#135	1	2	yes	—
160	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
162	#10623494	—	4	4	no	—
163	#10623494	—	8	2	no	—
164	C₂²×C₈₉	—	2	2	no	—
165	C₂²×C₈₉	—	2	2	no	—
166	C₂²×C₈₉	—	2	2	no	—
167	C₂²×C₈₉	—	4	1	no	—
168	C₂²×C₈₉	—	4	1	no	—
169	C₂²×C₈₉	—	4	1	no	—
170	C₂²×C₈₉	—	4	1	no	—
171	C₂²×C₈₉	#381	1	1	yes	characteristic
172	C₂²×C₈₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
173	C₂²×C₈₉	#407	1	1	yes	characteristic
174	C₂²×C₈₉	#416	1	1	yes	characteristic
175	C₂²×C₈₉	#417	1	1	yes	characteristic
176	C₂²×C₈₉	C₂×#104	1	1	yes	characteristic
177	C₂²×C₈₉	#421	1	1	yes	characteristic
178	C₄×C₈₉	—	2	2	no	—
179	C₄×C₈₉	—	2	2	no	—
180	C₄×C₈₉	—	2	2	no	—
181	C₄×C₈₉	—	4	1	no	—
182	C₄×C₈₉	—	4	2	no	—
183	C₄×C₈₉	—	4	2	no	—
184	C₄×C₈₉	—	4	2	no	—
185	C₄×C₈₉	—	4	2	no	—
186	C₄×C₈₉	#431	1	1	yes	characteristic
187	C₄×C₈₉	#431	1	1	yes	characteristic
188	C₄×C₈₉	#432	1	1	yes	characteristic
189	C₄×C₈₉	#432	1	1	yes	characteristic
190	C₄×C₈₉	#482	1	2	yes	—
191	C₄×C₈₉	#485	1	2	yes	—
192	#8708	—	89	1	no	maximal, Sylow
193	C₂×C₈₉	—	4	2	no	—
194	C₂×C₈₉	#1476	1	1	yes	characteristic
195	C₂×C₈₉	#1477	1	1	yes	characteristic
196	C₂×C₈₉	#1488	1	1	yes	characteristic
197	C₂×C₈₉	#1489	1	1	yes	characteristic
198	C₂×C₈₉	#1817	1	1	yes	characteristic
199	C₂×C₈₉	#1825	1	1	yes	characteristic
200	C₂×C₈₉	#1826	1	1	yes	characteristic
201	C₄×#117	D₈₉	1	1	yes	characteristic
202	#1797	—	89	1	no	—
203	C₄×C₂²⋊C₈	—	89	1	no	—
204	#1279	—	89	2	no	—
205	#1279	—	89	2	no	—
206	C₈₉	#8708	1	1	yes	characteristic, complemented, Sylow
207	C₂×#117	Dic₈₉	1	1	yes	characteristic
208	C₂×#117	Dic₈₉	1	1	yes	characteristic
209	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
210	C₂×C₄⋊C₈	—	89	2	no	—
211	C₂×C₂²⋊C₈	—	178	1	no	—
212	C₂×C₂²⋊C₈	—	178	1	no	—
213	C₂×C₄×C₈	—	89	2	no	—
214	C₄×C₄⋊C₄	Dic₈₉	1	1	yes	characteristic
215	C₄×C₄⋊C₄	Dic₈₉	1	1	yes	characteristic
216	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
217	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
218	C₄×C₂²⋊C₄	—	2	1	no	—
219	C₄×C₂²⋊C₄	—	2	1	no	—
220	#376	—	2	1	no	—
221	C₄³	—	2	1	no	—
222	#336	—	178	1	no	—
223	#336	—	178	1	no	—
224	C₂³×C₄	C₂×Dic₈₉	1	1	yes	characteristic
225	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
226	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
227	C₂²×C₈	—	178	2	no	—
228	C₂²×C₈	—	178	2	no	—
229	#117	—	2	2	no	—
230	#117	—	2	2	no	—
231	#117	—	2	2	no	—
232	#117	#10623494	1	4	yes	complemented
233	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
237	C₂×C₂²⋊C₄	—	2	1	no	—
238	C₂×C₂²⋊C₄	—	2	1	no	—
239	C₂×C₄²	—	2	1	no	—
240	C₂×C₄²	—	2	1	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	—	2	1	no	—
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
248	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
249	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
250	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
251	C₄⋊C₈	—	178	2	no	—
252	C₄⋊C₈	—	178	2	no	—
253	C₂²⋊C₈	—	356	2	no	—
254	C₂²⋊C₈	—	178	4	no	—
255	C₄×C₈	—	178	2	no	—
256	C₄×C₈	—	178	2	no	—
257	#95	—	2	1	no	—
258	#95	—	2	1	no	—
259	#95	—	2	1	no	—
260	#95	—	2	1	no	—
261	C₂⁴	C₂²⋊Dic₈₉	1	1	yes	characteristic
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
278	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊Dic₈₉	1	1	yes	characteristic
280	C₂²×C₄	C₂×#10623494	1	2	yes	—
281	C₂²×C₄	#13083558	1	2	yes	—
282	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
285	C₂×C₈	—	356	2	no	—
286	C₂×C₈	—	356	2	no	—
287	C₂×C₈	—	356	2	no	—
288	C₂×C₈	—	356	2	no	—
289	C₂×C₈	—	356	2	no	—
290	C₂×C₈	—	178	4	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	C₂×#10623494	1	2	yes	—
296	C₄⋊C₄	C₂×#10623494	1	2	yes	—
297	C₄⋊C₄	#13083558	1	2	yes	—
298	C₄⋊C₄	#13083558	1	2	yes	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	4	no	—
307	C₄²	—	4	2	no	—
308	C₄²	—	4	2	no	—
309	C₄²	—	4	1	no	—
310	C₄²	—	4	1	no	—
311	C₄²	—	4	2	no	—
312	C₄²	#13083574	1	2	yes	—
313	C₄²	#13083574	1	2	yes	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	C₂²⋊#10623494	1	2	yes	—
321	C₂³	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	C₂²⋊#10623494	1	2	yes	—
351	C₂×C₄	#15667939	1	2	yes	—
352	C₂×C₄	#15667971	1	1	yes	characteristic
353	C₂×C₄	#15667971	1	1	yes	characteristic
354	C₂×C₄	#15667995	1	2	yes	—
355	C₂×C₄	#15667995	1	2	yes	—
356	C₂×C₄	C₂²×#10623494	1	1	yes	characteristic
357	C₂×C₄	C₂×#13083558	1	1	yes	characteristic
358	C₂×C₄	C₂×#13083558	1	1	yes	characteristic
359	C₂×C₄	C₂×#13083558	1	1	yes	characteristic
360	C₂×C₄	#15668032	1	2	yes	—
361	C₂×C₄	#15668037	1	1	yes	characteristic
362	C₂×C₄	#15668042	1	1	yes	characteristic
363	C₈	—	356	4	no	—
364	C₈	—	712	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	#19151461	1	1	yes	characteristic
373	C₂²	C₂×C₂²⋊#10623494	1	1	yes	characteristic
374	C₂²	#19151562	1	1	yes	characteristic
375	C₂²	#19151594	1	1	yes	characteristic
376	C₂²	#19151599	1	1	yes	characteristic
377	C₂²	C₂×#15667939	1	1	yes	characteristic
378	C₂²	#19151615	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	1	no	—
387	C₄	#19151651	1	1	yes	characteristic
388	C₄	#19151651	1	1	yes	characteristic
389	C₄	#19151655	1	1	yes	characteristic
390	C₄	#19151655	1	1	yes	characteristic
391	C₄	#19151922	1	2	yes	—
392	C₄	#19151939	1	2	yes	—
393	C₂	—	4	2	no	—
394	C₂	#26018634	1	1	yes	characteristic
395	C₂	#26018639	1	1	yes	characteristic
396	C₂	#26018686	1	1	yes	characteristic
397	C₂	#26018691	1	1	yes	characteristic
398	C₂	#26020320	1	1	yes	characteristic
399	C₂	#26020347	1	1	yes	characteristic
400	C₂	#26020351	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₄×#117×C₈₉	C₂
socle	C₂³×C₈₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₈₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₄×#117	D₈₉
hypocenter	C₈₉	#8708
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
3. #26018093	C₂	semidirect
4. #26018093	C₂	semidirect
37. #117×C₈₉	C₈	semidirect
206. C₈₉	#8708	semidirect
232. #117	#10623494	semidirect

Maximal subgroups

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

subgroup	index
#26020232	2
C₄×C₂²⋊#10623494	2
#26018093	2
C₄×#117×C₈₉	2
#8708	89