Subgroups — #36524452

Order 22784.

624 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030334	C₂	1	1	yes	maximal, characteristic
2	#26029221	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151722	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019101	C₂	1	2	yes	maximal, complemented
5	#26019094	C₂	1	2	yes	maximal, complemented
6	#26019070	C₂	1	2	yes	maximal, complemented
7	#26019063	C₂	1	2	yes	maximal, complemented
8	#26018698	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018663	C₂	1	1	yes	maximal, characteristic
10	#26018542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1573	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152132	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
14	#19151929	C₄	1	1	yes	characteristic
15	#19151912	C₄	1	1	yes	characteristic
16	#19151906	C₄	1	2	yes	—
17	#19151821	C₄	1	2	yes	—
18	#19151756	C₄	1	1	yes	characteristic
19	#19151739	C₄	1	1	yes	characteristic
20	#19151725	C₂²	1	1	yes	characteristic
21	#19151722	—	2	1	no	—
22	#19151722	—	2	1	no	—
23	#19151722	C₂²	1	2	yes	—
24	#19151722	C₂²	1	2	yes	—
25	#19151722	C₂²	1	1	yes	characteristic
26	C₄×Dic₃₅₆	C₂²	1	2	yes	—
27	C₄×#13083563	C₂²	1	2	yes	—
28	#19151675	C₂²	1	1	yes	characteristic
29	#19151666	—	2	1	no	—
30	#19151663	C₂²	1	1	yes	characteristic
31	#19151661	—	2	1	no	—
32	#19151660	—	2	1	no	—
33	C₂×#15667941	—	2	1	no	—
34	#19151555	—	2	1	no	—
35	C₄×#13083558	C₂²	1	1	yes	characteristic
36	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₈₉	—	2	1	no	—
38	#19151328	C₂²	1	2	yes	—
39	#19151328	C₂²	1	2	yes	—
40	#19151328	C₂²	1	2	yes	—
41	#19151325	C₂²	1	2	yes	—
42	#19151320	C₂²	1	2	yes	—
43	#19151319	C₂²	1	2	yes	—
44	#432×C₈₉	C₂²	1	1	yes	characteristic
45	#431×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
47	#335×C₈₉	C₂²	1	2	yes	—
48	#334×C₈₉	C₂²	1	2	yes	—
49	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
50	C₂×Dic₃₅₆	C₂×C₄	1	2	yes	—
51	C₂×#13083563	C₂×C₄	1	2	yes	—
52	C₂×#13083558	—	2	1	no	—
53	C₂×#13083557	—	2	1	no	—
54	C₂²×#10623494	D₄	1	1	yes	characteristic
55	C₂²×#10623494	D₄	1	1	yes	characteristic
56	C₂×C₈×D₈₉	—	2	1	no	—
57	#15668006	—	2	1	no	—
58	#15668004	C₂×C₄	1	1	yes	characteristic
59	#15668000	C₂×C₄	1	1	yes	characteristic
60	#15667995	—	2	1	no	—
61	#15667991	C₂×C₄	1	1	yes	characteristic
62	#15667986	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₁₇₈	—	2	1	no	—
64	C₄×Dic₁₇₈	—	2	1	no	—
65	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
66	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
67	C₄×Dic₁₇₈	C₂³	1	2	yes	—
68	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
69	C₄×C₂²⋊D₈₉	—	2	1	no	—
70	#15667969	—	2	1	no	—
71	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083553	—	2	1	no	—
73	C₂×C₄×Dic₈₉	—	2	1	no	—
74	#15667946	C₂×C₄	1	2	yes	—
75	#15667944	C₂×C₄	1	2	yes	—
76	#15667941	—	2	2	no	—
77	#15667941	—	2	2	no	—
78	#15667941	—	2	1	no	—
79	#15667941	—	2	1	no	—
80	#15667937	C₂×C₄	1	2	yes	—
81	#15667937	C₂×C₄	1	2	yes	—
82	#15667937	C₂×C₄	1	2	yes	—
83	#15667934	C₂×C₄	1	2	yes	—
84	#15667924	—	2	1	no	—
85	#15667924	—	2	1	no	—
86	#15667923	—	2	1	no	—
87	#15667922	—	2	1	no	—
88	C₄×#10623494	D₄	1	1	yes	characteristic
89	C₄×#10623494	D₄	1	1	yes	characteristic
90	C₄×#10623494	C₂³	1	2	yes	—
91	C₄×#10623494	C₂³	1	1	yes	characteristic
92	C₄×#10623494	C₂³	1	1	yes	characteristic
93	C₈×Dic₈₉	—	2	1	no	—
94	C₈×Dic₈₉	—	2	2	no	—
95	C₈×Dic₈₉	—	2	2	no	—
96	C₂²×C₈×C₈₉	—	2	1	no	—
97	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	—	2	1	no	—
99	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
100	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
102	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²⋊C₈×C₈₉	—	2	1	no	—
104	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
106	#97×C₈₉	—	2	1	no	—
107	C₄×C₈×C₈₉	C₂³	1	2	yes	—
108	C₂×Dic₁₇₈	—	2	1	no	—
109	C₂×Dic₁₇₈	—	2	4	no	—
110	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
111	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
112	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊D₈₉	—	2	1	no	—
114	C₂²×Dic₈₉	—	2	1	no	—
115	C₂²×Dic₈₉	—	2	1	no	—
116	C₂×C₄×D₈₉	—	2	1	no	—
117	Dic₃₅₆	—	2	4	no	—
118	#13083563	—	2	4	no	—
119	#13083558	—	4	2	no	—
120	#13083557	—	4	2	no	—
121	C₂×#10623494	—	2	2	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	—	4	1	no	—
124	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
125	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
126	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
127	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
128	C₈×D₈₉	—	4	2	no	—
129	C₄⋊Dic₈₉	—	2	1	no	—
130	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
132	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
133	#13083553	—	2	1	no	—
134	#13083553	—	2	1	no	—
135	#13083553	—	2	1	no	—
136	#13083553	—	2	2	no	—
137	#13083553	—	2	2	no	—
138	#13083553	—	2	1	no	—
139	C₂²⋊Dic₈₉	—	2	1	no	—
140	#13083551	—	2	1	no	—
141	#13083551	—	2	1	no	—
142	#13083551	—	2	1	no	—
143	#13083551	—	2	1	no	—
144	C₄×Dic₈₉	—	2	2	no	—
145	C₄×Dic₈₉	—	2	1	no	—
146	C₄×Dic₈₉	—	2	2	no	—
147	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
150	C₂×C₈×C₈₉	—	2	1	no	—
151	C₂×C₈×C₈₉	—	2	1	no	—
152	C₂×C₈×C₈₉	—	2	2	no	—
153	C₂×C₈×C₈₉	—	4	2	no	—
154	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
156	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₈₉	#41	1	1	yes	characteristic
159	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
160	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
172	C₂²⋊D₈₉	—	4	2	no	—
173	C₂×Dic₈₉	—	2	4	no	—
174	C₂×Dic₈₉	—	2	2	no	—
175	C₂×Dic₈₉	—	2	2	no	—
176	C₂×Dic₈₉	—	2	1	no	—
177	C₂×Dic₈₉	—	2	1	no	—
178	C₂×Dic₈₉	—	2	1	no	—
179	C₂×Dic₈₉	—	4	2	no	—
180	D₃₅₆	—	2	2	no	—
181	C₄×D₈₉	—	4	1	no	—
182	C₄×D₈₉	—	4	1	no	—
183	Dic₁₇₈	—	2	4	no	—
184	Dic₁₇₈	—	2	2	no	—
185	Dic₁₇₈	—	2	2	no	—
186	Dic₁₇₈	#131	1	4	yes	—
187	C₈×C₈₉	—	2	2	no	—
188	C₈×C₈₉	—	2	2	no	—
189	C₈×C₈₉	—	4	1	no	—
190	C₈×C₈₉	—	4	2	no	—
191	C₈×C₈₉	—	4	1	no	—
192	#10623494	—	2	1	no	—
193	#10623494	—	2	1	no	—
194	#10623494	—	2	1	no	—
195	#10623494	—	4	2	no	—
196	#10623494	#137	1	2	yes	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	—	2	1	no	—
199	C₂²×C₈₉	#444	1	2	yes	—
200	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂×D₈₉	—	4	1	no	—
202	C₂×D₈₉	—	4	1	no	—
203	C₂×D₈₉	—	4	1	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	2	1	no	—
208	C₄×C₈₉	C₂×#131	1	2	yes	—
209	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
210	C₄×C₈₉	#575	1	1	yes	characteristic
211	Dic₈₉	—	2	4	no	—
212	Dic₈₉	—	4	1	no	—
213	Dic₈₉	—	4	1	no	—
214	Dic₈₉	—	4	2	no	—
215	Dic₈₉	—	4	1	no	—
216	#17915	—	89	1	no	maximal, Sylow
217	C₂×C₈₉	—	2	2	no	—
218	C₂×C₈₉	#2929	1	1	yes	characteristic
219	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
220	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
221	D₈₉	—	8	1	no	—
222	#3108	—	89	1	no	—
223	#2966	—	89	1	no	—
224	C₂×C₈×Q₈	—	89	1	no	—
225	#1584	—	89	2	no	—
226	#1583	—	89	2	no	—
227	#1579	—	89	2	no	—
228	SD₁₆⋊C₈	—	89	2	no	—
229	#1573	D₈₉	1	1	yes	characteristic, complemented
230	#1491	—	89	1	no	—
231	#1483	—	89	1	no	—
232	#1451	—	89	1	no	—
233	C₈₉	#17915	1	1	yes	characteristic, complemented, Sylow
234	#529	—	89	1	no	—
235	C₂×C₄×Q₈	—	89	1	no	—
236	#483	—	89	1	no	—
237	#480	—	89	1	no	—
238	#479	—	89	2	no	—
239	#464	—	89	2	no	—
240	#451	—	89	1	no	—
241	#448	—	89	1	no	—
242	#446	—	89	1	no	—
243	C₈×Q₈	—	89	2	no	—
244	C₈×Q₈	—	89	1	no	—
245	C₈×Q₈	—	89	2	no	—
246	C₈×Q₈	—	178	1	no	—
247	C₈×Q₈	—	178	1	no	—
248	C₄×Q₁₆	—	89	2	no	—
249	C₄×SD₁₆	—	89	2	no	—
250	#436	—	89	1	no	—
251	#435	—	178	1	no	—
252	C₈×D₄	—	89	1	no	—
253	C₈×D₄	—	178	1	no	—
254	#433	—	178	1	no	—
255	#432	C₂×D₈₉	1	1	yes	characteristic
256	#431	C₂×D₈₉	1	1	yes	characteristic
257	C₂×C₄⋊C₈	—	178	1	no	—
258	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
259	#405	—	178	1	no	—
260	C₄×M₁₆	—	89	1	no	—
261	C₂×C₄×C₈	—	89	1	no	—
262	C₂×C₄×C₈	—	178	1	no	—
263	#335	C₂×D₈₉	1	2	yes	—
264	#334	C₂×D₈₉	1	2	yes	—
265	Q₈⋊C₈	—	89	2	no	—
266	Q₈⋊C₈	—	89	2	no	—
267	Q₈⋊C₈	—	89	2	no	—
268	D₄⋊C₈	—	89	2	no	—
269	#322	—	89	2	no	—
270	#322	—	89	2	no	—
271	C₂²×Q₈	—	89	1	no	—
272	C₂×Q₁₆	—	89	2	no	—
273	C₂×SD₁₆	—	89	2	no	—
274	C₂×M₁₆	—	178	1	no	—
275	C₂×M₁₆	—	178	1	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	89	1	no	—
278	C₂²×C₈	—	89	1	no	—
279	C₂²×C₈	—	178	1	no	—
280	#126	—	178	1	no	—
281	#125	—	89	1	no	—
282	#124	—	89	1	no	—
283	#123	—	178	1	no	—
284	C₂²⋊Q₈	—	89	1	no	—
285	#121	—	89	1	no	—
286	C₄×Q₈	—	89	2	no	—
287	C₄×Q₈	—	89	2	no	—
288	C₄×Q₈	—	89	1	no	—
289	C₄×Q₈	—	178	1	no	—
290	C₄×Q₈	—	178	1	no	—
291	C₄×D₄	—	89	1	no	—
292	C₄×D₄	—	178	1	no	—
293	#117	—	178	1	no	—
294	C₂×C₄⋊C₄	—	89	1	no	—
295	C₂×C₄⋊C₄	—	178	1	no	—
296	C₂×C₄²	—	178	1	no	—
297	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
298	#107	—	89	2	no	—
299	#106	—	89	2	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	178	2	no	—
302	C₄⋊C₈	—	178	2	no	—
303	C₄⋊C₈	—	178	1	no	—
304	C₄⋊C₈	—	178	1	no	—
305	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
306	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
307	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
308	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
309	#103	—	89	2	no	—
310	#103	—	89	2	no	—
311	#103	—	89	2	no	—
312	#102	—	89	2	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	178	1	no	—
315	C₂²⋊C₈	—	178	1	no	—
316	C₂²⋊C₈	C₄×D₈₉	1	1	yes	characteristic
317	C₂²⋊C₈	C₄×D₈₉	1	1	yes	characteristic
318	#97	—	2	1	no	—
319	#97	—	178	1	no	—
320	#97	—	178	1	no	—
321	C₄×C₈	—	89	1	no	—
322	C₄×C₈	—	89	1	no	—
323	C₄×C₈	—	89	1	no	—
324	C₄×C₈	—	89	1	no	—
325	C₄×C₈	—	89	2	no	—
326	C₄×C₈	—	178	2	no	—
327	C₄×C₈	—	178	2	no	—
328	C₄×C₈	—	178	1	no	—
329	C₄×C₈	C₂²×D₈₉	1	2	yes	—
330	C₂×Q₈	—	89	2	no	—
331	C₂×Q₈	—	89	1	no	—
332	C₂×Q₈	—	178	4	no	—
333	C₂×Q₈	—	178	1	no	—
334	C₂×D₄	—	89	1	no	—
335	C₂×D₄	—	178	1	no	—
336	C₂²×C₄	—	178	1	no	—
337	C₂²×C₄	—	178	1	no	—
338	C₂²×C₄	—	178	1	no	—
339	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
340	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
341	C₂²×C₄	#13083575	1	1	yes	characteristic
342	Q₁₆	—	178	4	no	—
343	SD₁₆	—	178	4	no	—
344	M₁₆	—	356	2	no	—
345	M₁₆	—	356	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	—	89	1	no	—
351	C₂×C₈	—	89	1	no	—
352	C₂×C₈	—	89	1	no	—
353	C₂×C₈	—	89	1	no	—
354	C₂×C₈	—	356	2	no	—
355	C₂×C₈	—	356	1	no	—
356	C₂×C₈	—	178	2	no	—
357	C₂×C₈	—	178	2	no	—
358	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
359	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
360	C₄⋊C₄	—	89	2	no	—
361	C₄⋊C₄	—	89	1	no	—
362	C₄⋊C₄	—	89	1	no	—
363	C₄⋊C₄	—	178	1	no	—
364	C₄⋊C₄	—	178	2	no	—
365	C₄⋊C₄	—	178	1	no	—
366	C₄⋊C₄	—	178	1	no	—
367	C₄⋊C₄	—	178	1	no	—
368	C₄⋊C₄	—	178	2	no	—
369	C₄⋊C₄	—	178	1	no	—
370	C₂²⋊C₄	—	178	1	no	—
371	C₂²⋊C₄	—	178	1	no	—
372	C₂²⋊C₄	—	178	1	no	—
373	C₂²⋊C₄	—	178	1	no	—
374	C₂²⋊C₄	—	178	1	no	—
375	C₄²	—	178	2	no	—
376	C₄²	—	178	2	no	—
377	C₄²	—	178	1	no	—
378	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
379	C₄²	D₄×D₈₉	1	1	yes	characteristic
380	C₄²	#13083575	1	1	yes	characteristic
381	C₄²	C₂³×D₈₉	1	1	yes	characteristic
382	C₂³	—	178	1	no	—
383	C₂³	#15667974	1	1	yes	characteristic
384	Q₈	—	89	4	no	—
385	Q₈	—	178	4	no	—
386	Q₈	—	178	2	no	—
387	Q₈	—	178	2	no	—
388	D₄	—	356	2	no	—
389	D₄	—	178	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	356	2	no	—
395	C₂×C₄	—	356	1	no	—
396	C₂×C₄	—	356	1	no	—
397	C₂×C₄	—	178	2	no	—
398	C₂×C₄	—	178	1	no	—
399	C₂×C₄	—	178	1	no	—
400	C₂×C₄	—	178	1	no	—
401	C₂×C₄	—	178	4	no	—
402	C₂×C₄	—	178	2	no	—
403	C₂×C₄	#15667974	1	1	yes	characteristic
404	C₂×C₄	#15667974	1	1	yes	characteristic
405	C₂×C₄	#15667974	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
407	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
408	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	2	no	—
413	C₈	—	4	1	no	—
414	C₈	—	89	2	no	—
415	C₈	—	356	2	no	—
416	C₈	—	178	1	no	—
417	C₈	—	178	1	no	—
418	C₈	—	178	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	356	1	no	—
422	C₂²	—	356	1	no	—
423	C₂²	—	356	1	no	—
424	C₂²	#19151719	1	2	yes	—
425	C₂²	C₂×#15667974	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	356	1	no	—
431	C₄	—	356	2	no	—
432	C₄	—	356	1	no	—
433	C₄	—	356	1	no	—
434	C₄	—	178	4	no	—
435	C₄	#131×D₈₉	1	2	yes	—
436	C₄	#137×D₈₉	1	1	yes	characteristic
437	C₄	#19152394	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	712	1	no	—
440	C₂	#26028945	1	1	yes	characteristic
441	C₂	#26029070	1	1	yes	characteristic
442	C₂	C₂×#19151719	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×#1573	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#15667986	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1573	D₈₉
hypocenter	C₈₉	#17915
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1573

Complements

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

N	H ≅ G/N	type
3. C₂×#19151722	C₂	semidirect
4. #26019101	C₂	semidirect
5. #26019094	C₂	semidirect
6. #26019070	C₂	semidirect
7. #26019063	C₂	semidirect
8. #26018698	C₂	semidirect
10. #26018542	C₂	semidirect
11. C₈₉×#1573	C₂	semidirect
229. #1573	D₈₉	semidirect
233. C₈₉	#17915	semidirect

Maximal subgroups

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

subgroup	index
#26030334	2
#26029221	2
C₂×#19151722	2
#26019101	2
#26019094	2
#26019070	2
#26019063	2
#26018698	2
#26018663	2
#26018542	2
C₈₉×#1573	2
#17915	89