Subgroups — #36536839

Order 22784.

628 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030575	C₂	1	1	yes	maximal, characteristic
2	#26030292	C₂	1	1	yes	maximal, characteristic, complemented
3	#26030284	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019711	C₂	1	2	yes	maximal, complemented
6	#26019697	C₂	1	2	yes	maximal, complemented
7	#26019683	C₂	1	2	yes	maximal, complemented
8	#26019669	C₂	1	2	yes	maximal, complemented
9	#26018907	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018899	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152155	C₂²	1	1	yes	characteristic
13	#19152148	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
15	#19151953	—	2	1	no	—
16	#19151953	—	2	1	no	—
17	#19151949	C₂²	1	1	yes	characteristic
18	#19151949	C₂²	1	1	yes	characteristic
19	#19151945	C₂²	1	1	yes	characteristic
20	#19151945	C₂²	1	1	yes	characteristic
21	#19151934	—	2	1	no	—
22	#19151917	—	2	1	no	—
23	#19151894	C₂²	1	2	yes	—
24	#19151884	C₂²	1	2	yes	—
25	#19151809	C₂²	1	2	yes	—
26	#19151799	C₂²	1	2	yes	—
27	#19151756	—	2	1	no	—
28	#19151739	—	2	1	no	—
29	C₈×Dic₁₇₈	—	2	1	no	—
30	C₈×Dic₁₇₈	—	2	1	no	—
31	C₈×Dic₁₇₈	C₂²	1	2	yes	—
32	C₈×Dic₁₇₈	C₂²	1	2	yes	—
33	C₄×Dic₃₅₆	—	2	2	no	—
34	C₄×#13083563	—	2	2	no	—
35	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
36	C₂×#15667941	—	2	1	no	—
37	#19151595	—	2	1	no	—
38	#19151595	—	2	1	no	—
39	C₂×C₈×Dic₈₉	—	2	1	no	—
40	#19151346	C₂²	1	2	yes	—
41	#19151345	C₂²	1	2	yes	—
42	#19151343	C₂²	1	2	yes	—
43	#19151341	C₂²	1	2	yes	—
44	#431×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	C₂×#13083574	—	2	1	no	—
50	C₂²×Dic₁₇₈	D₄	1	1	yes	characteristic
51	C₂×Dic₃₅₆	—	2	2	no	—
52	C₂×#13083563	—	2	2	no	—
53	C₂²×#10623494	—	2	1	no	—
54	#15668012	C₂³	1	1	yes	characteristic
55	#15668012	C₂³	1	1	yes	characteristic
56	#15668012	C₂³	1	1	yes	characteristic
57	#15668009	C₂³	1	1	yes	characteristic
58	#15668004	—	2	1	no	—
59	#15668000	—	2	1	no	—
60	#15667991	—	2	1	no	—
61	#15667991	—	2	1	no	—
62	#15667986	—	2	1	no	—
63	#15667986	—	2	1	no	—
64	C₄×Dic₁₇₈	—	2	1	no	—
65	C₄×Dic₁₇₈	—	2	1	no	—
66	C₄×Dic₁₇₈	—	2	1	no	—
67	C₄×Dic₁₇₈	—	2	1	no	—
68	C₄×Dic₁₇₈	D₄	1	2	yes	—
69	C₄×Dic₁₇₈	C₂³	1	2	yes	—
70	C₄×D₃₅₆	—	2	1	no	—
71	C₄×D₃₅₆	—	2	1	no	—
72	#15667971	—	2	1	no	—
73	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
74	C₂×#13083553	—	2	1	no	—
75	C₂×C₄×Dic₈₉	—	2	1	no	—
76	#15667946	—	2	2	no	—
77	#15667944	—	2	2	no	—
78	C₄⋊#10623494	—	2	1	no	—
79	C₄⋊#10623494	C₂³	1	2	yes	—
80	#15667941	—	2	2	no	—
81	#15667941	—	2	2	no	—
82	#15667937	—	2	2	no	—
83	#15667937	—	2	2	no	—
84	#15667937	—	2	2	no	—
85	#15667937	—	2	1	no	—
86	#15667937	—	2	1	no	—
87	#15667937	—	2	1	no	—
88	#15667937	—	2	1	no	—
89	#15667934	—	2	2	no	—
90	#15667934	—	2	1	no	—
91	#15667934	—	2	1	no	—
92	#15667934	—	2	1	no	—
93	#15667934	—	2	1	no	—
94	C₈×Dic₈₉	—	2	2	no	—
95	C₈×Dic₈₉	—	2	2	no	—
96	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
100	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
101	C₂²⋊C₈×C₈₉	—	2	1	no	—
102	C₂²⋊C₈×C₈₉	—	2	1	no	—
103	C₄×C₈×C₈₉	—	2	1	no	—
104	C₄×C₈×C₈₉	—	2	1	no	—
105	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
106	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	#13083574	—	4	2	no	—
110	#13083574	—	4	2	no	—
111	C₂×Dic₁₇₈	—	2	1	no	—
112	C₂×Dic₁₇₈	—	2	4	no	—
113	C₂×Dic₁₇₈	—	2	1	no	—
114	C₂×Dic₁₇₈	—	2	1	no	—
115	C₂×Dic₁₇₈	—	2	1	no	—
116	C₂×Dic₁₇₈	C₂×D₄	1	2	yes	—
117	C₂×D₃₅₆	—	2	1	no	—
118	C₂×D₃₅₆	—	2	1	no	—
119	C₂×D₃₅₆	—	2	1	no	—
120	C₂×C₂²⋊D₈₉	—	4	1	no	—
121	C₂²×Dic₈₉	—	2	1	no	—
122	C₂²×Dic₈₉	—	2	1	no	—
123	C₂×C₄×D₈₉	—	4	1	no	—
124	Dic₃₅₆	—	4	4	no	—
125	#13083563	—	4	4	no	—
126	C₂×#10623494	—	2	2	no	—
127	C₂×#10623494	—	4	2	no	—
128	C₄⋊Dic₈₉	—	2	1	no	—
129	C₄⋊Dic₈₉	—	2	1	no	—
130	C₄⋊Dic₈₉	—	2	1	no	—
131	C₄⋊Dic₈₉	—	2	1	no	—
132	C₄⋊Dic₈₉	—	2	1	no	—
133	C₄⋊Dic₈₉	—	2	1	no	—
134	C₄⋊Dic₈₉	—	2	1	no	—
135	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
136	#13083553	—	2	2	no	—
137	#13083553	—	2	2	no	—
138	#13083553	—	4	1	no	—
139	#13083553	—	4	1	no	—
140	C₂²⋊Dic₈₉	—	4	1	no	—
141	#13083551	—	4	1	no	—
142	#13083551	—	4	1	no	—
143	C₄×Dic₈₉	—	2	2	no	—
144	C₄×Dic₈₉	—	2	2	no	—
145	C₄×Dic₈₉	—	4	1	no	—
146	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
149	C₂×C₈×C₈₉	—	2	2	no	—
150	C₂×C₈×C₈₉	—	2	2	no	—
151	C₂×C₈×C₈₉	—	2	2	no	—
152	C₂×C₈×C₈₉	—	2	2	no	—
153	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₈₉	#41	1	1	yes	characteristic
160	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
161	C₂³×C₈₉	#121	1	1	yes	characteristic
162	C₂²×D₈₉	—	4	1	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	4	1	no	—
165	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₈₉	#135	1	2	yes	—
169	C₂×C₄×C₈₉	#137	1	2	yes	—
170	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
173	C₂²⋊D₈₉	—	8	2	no	—
174	C₂×Dic₈₉	—	2	4	no	—
175	C₂×Dic₈₉	—	2	2	no	—
176	C₂×Dic₈₉	—	2	2	no	—
177	C₂×Dic₈₉	—	4	2	no	—
178	C₂×Dic₈₉	—	4	1	no	—
179	C₂×Dic₈₉	—	4	1	no	—
180	C₂×Dic₈₉	—	4	1	no	—
181	D₃₅₆	—	4	2	no	—
182	D₃₅₆	—	4	1	no	—
183	D₃₅₆	—	4	1	no	—
184	D₃₅₆	—	8	1	no	—
185	C₄×D₈₉	—	8	2	no	—
186	Dic₁₇₈	—	2	4	no	—
187	Dic₁₇₈	—	2	2	no	—
188	Dic₁₇₈	—	4	2	no	—
189	Dic₁₇₈	—	4	1	no	—
190	Dic₁₇₈	—	4	1	no	—
191	Dic₁₇₈	—	8	1	no	—
192	Dic₁₇₈	#135	1	4	yes	—
193	C₈×C₈₉	—	2	1	no	—
194	C₈×C₈₉	—	2	1	no	—
195	C₈×C₈₉	—	2	1	no	—
196	C₈×C₈₉	—	2	1	no	—
197	C₈×C₈₉	—	4	2	no	—
198	C₈×C₈₉	—	4	2	no	—
199	#10623494	—	4	2	no	—
200	C₂²×C₈₉	—	2	1	no	—
201	C₂²×C₈₉	—	2	1	no	—
202	C₂²×C₈₉	#464	1	2	yes	—
203	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
204	C₂×D₈₉	—	8	1	no	—
205	C₂×D₈₉	—	8	1	no	—
206	C₂×D₈₉	—	8	1	no	—
207	C₄×C₈₉	—	2	1	no	—
208	C₄×C₈₉	—	2	1	no	—
209	C₄×C₈₉	—	2	1	no	—
210	C₄×C₈₉	#464	1	2	yes	—
211	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
212	C₄×C₈₉	C₂×#135	1	2	yes	—
213	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
214	Dic₈₉	—	2	4	no	—
215	Dic₈₉	—	4	2	no	—
216	Dic₈₉	—	8	1	no	—
217	Dic₈₉	—	8	1	no	—
218	Dic₈₉	—	8	1	no	—
219	#19123	—	89	1	no	maximal, Sylow
220	C₂×C₈₉	—	2	2	no	—
221	C₂×C₈₉	C₂×#464	1	1	yes	characteristic
222	C₂×C₈₉	#3050	1	1	yes	characteristic
223	C₂×C₈₉	#3067	1	1	yes	characteristic
224	D₈₉	—	16	1	no	—
225	#3131	—	89	1	no	—
226	#3104	—	89	1	no	—
227	#3103	—	89	1	no	—
228	C₂×C₈×Q₈	—	89	1	no	—
229	#1684	—	89	2	no	—
230	#1682	—	89	2	no	—
231	#1680	—	89	2	no	—
232	#1678	—	89	2	no	—
233	#1564	D₈₉	1	1	yes	characteristic, complemented
234	#1542	—	89	1	no	—
235	#1540	—	89	1	no	—
236	C₈₉	#19123	1	1	yes	characteristic, complemented, Sylow
237	#533	—	89	1	no	—
238	#532	—	89	1	no	—
239	C₂×C₄×Q₈	—	89	1	no	—
240	#488	—	178	1	no	—
241	#488	—	178	1	no	—
242	#487	—	89	1	no	—
243	#487	—	89	1	no	—
244	#486	—	89	1	no	—
245	#486	—	89	1	no	—
246	#484	—	178	1	no	—
247	#481	—	178	1	no	—
248	#477	—	89	2	no	—
249	#475	—	89	2	no	—
250	#462	—	89	2	no	—
251	#460	—	89	2	no	—
252	#451	—	178	1	no	—
253	#448	—	178	1	no	—
254	C₈×Q₈	—	89	2	no	—
255	C₈×Q₈	—	89	2	no	—
256	C₈×Q₈	—	178	1	no	—
257	C₈×Q₈	—	178	1	no	—
258	C₄×Q₁₆	—	178	2	no	—
259	C₄×SD₁₆	—	178	2	no	—
260	#431	C₂×D₈₉	1	1	yes	characteristic
261	#431	C₂×D₈₉	1	1	yes	characteristic
262	C₂×C₄⋊C₈	—	89	1	no	—
263	C₂×C₄⋊C₈	—	178	1	no	—
264	#416	—	178	1	no	—
265	#416	—	178	1	no	—
266	C₂×C₄×C₈	—	178	1	no	—
267	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
268	#335	C₂×D₈₉	1	2	yes	—
269	#334	C₂×D₈₉	1	2	yes	—
270	#333	—	89	2	no	—
271	#332	—	89	2	no	—
272	#332	—	89	2	no	—
273	#331	—	89	2	no	—
274	C₂×#41	—	178	1	no	—
275	C₂²×Q₈	—	89	1	no	—
276	C₂×Q₁₆	—	178	2	no	—
277	C₂×SD₁₆	—	178	2	no	—
278	C₂²×C₈	—	178	1	no	—
279	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
280	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
281	C₄⋊Q₈	—	89	1	no	—
282	C₄⋊Q₈	—	89	1	no	—
283	C₄⋊Q₈	—	89	1	no	—
284	#127	—	89	1	no	—
285	#125	—	178	1	no	—
286	#124	—	178	1	no	—
287	C₂²⋊Q₈	—	178	1	no	—
288	C₂²⋊Q₈	—	178	1	no	—
289	#121	—	178	1	no	—
290	#121	—	178	1	no	—
291	C₄×Q₈	—	89	2	no	—
292	C₄×Q₈	—	89	2	no	—
293	C₄×Q₈	—	178	1	no	—
294	C₄×Q₈	—	178	1	no	—
295	C₄×Q₈	—	178	1	no	—
296	C₄×Q₈	—	178	1	no	—
297	C₄×D₄	—	178	1	no	—
298	C₄×D₄	—	178	1	no	—
299	#117	—	178	1	no	—
300	C₂×C₄⋊C₄	—	89	1	no	—
301	C₂×C₄⋊C₄	—	178	1	no	—
302	C₂×C₄²	—	178	1	no	—
303	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
304	#107	—	178	2	no	—
305	#106	—	178	2	no	—
306	C₄⋊C₈	—	89	2	no	—
307	C₄⋊C₈	—	178	2	no	—
308	C₄⋊C₈	—	178	2	no	—
309	C₄⋊C₈	—	178	1	no	—
310	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
311	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
312	#103	—	178	2	no	—
313	#103	—	178	2	no	—
314	#103	—	178	2	no	—
315	#103	—	178	1	no	—
316	#103	—	178	1	no	—
317	#103	—	178	1	no	—
318	#103	—	178	1	no	—
319	#102	—	178	2	no	—
320	#102	—	178	1	no	—
321	#102	—	178	1	no	—
322	#102	—	178	1	no	—
323	#102	—	178	1	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₄×C₈	—	2	1	no	—
327	C₄×C₈	—	2	1	no	—
328	C₄×C₈	—	178	2	no	—
329	C₄×C₈	—	178	2	no	—
330	C₄×C₈	D₃₅₆	1	1	yes	characteristic
331	C₄×C₈	D₃₅₆	1	1	yes	characteristic
332	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
334	#41	—	356	2	no	—
335	#41	—	356	2	no	—
336	C₂×Q₈	—	89	2	no	—
337	C₂×Q₈	—	178	4	no	—
338	C₂×Q₈	—	178	1	no	—
339	C₂×Q₈	—	178	1	no	—
340	C₂×Q₈	—	178	1	no	—
341	C₂×Q₈	—	178	1	no	—
342	C₂×D₄	—	356	1	no	—
343	C₂×D₄	—	178	1	no	—
344	C₂×D₄	—	178	1	no	—
345	C₂×D₄	—	178	1	no	—
346	C₂²×C₄	—	356	1	no	—
347	C₂²×C₄	—	178	1	no	—
348	C₂²×C₄	—	178	1	no	—
349	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
351	C₂²×C₄	#13083575	1	1	yes	characteristic
352	Q₁₆	—	356	4	no	—
353	SD₁₆	—	356	4	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	356	2	no	—
359	C₂×C₈	—	178	2	no	—
360	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
361	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
362	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
363	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
364	C₄⋊C₄	—	89	2	no	—
365	C₄⋊C₄	—	356	1	no	—
366	C₄⋊C₄	—	356	1	no	—
367	C₄⋊C₄	—	178	1	no	—
368	C₄⋊C₄	—	178	1	no	—
369	C₄⋊C₄	—	178	1	no	—
370	C₄⋊C₄	—	178	1	no	—
371	C₄⋊C₄	—	178	1	no	—
372	C₄⋊C₄	—	178	1	no	—
373	C₄⋊C₄	—	178	1	no	—
374	C₄⋊C₄	—	178	2	no	—
375	C₄⋊C₄	—	178	2	no	—
376	C₂²⋊C₄	—	356	1	no	—
377	C₂²⋊C₄	—	356	1	no	—
378	C₂²⋊C₄	—	356	1	no	—
379	C₄²	—	356	1	no	—
380	C₄²	—	178	2	no	—
381	C₄²	—	178	2	no	—
382	C₄²	D₄×D₈₉	1	1	yes	characteristic
383	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
384	C₄²	#13083575	1	1	yes	characteristic
385	C₄²	C₂³×D₈₉	1	1	yes	characteristic
386	C₂³	—	356	1	no	—
387	C₂³	#15667987	1	1	yes	characteristic
388	Q₈	—	89	4	no	—
389	Q₈	—	356	1	no	—
390	Q₈	—	356	2	no	—
391	Q₈	—	356	1	no	—
392	Q₈	—	178	4	no	—
393	Q₈	—	178	2	no	—
394	Q₈	—	712	1	no	—
395	D₄	—	356	1	no	—
396	D₄	—	356	2	no	—
397	D₄	—	356	1	no	—
398	D₄	—	712	1	no	—
399	D₄	—	712	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	356	2	no	—
403	C₂×C₄	—	356	1	no	—
404	C₂×C₄	—	356	1	no	—
405	C₂×C₄	—	356	1	no	—
406	C₂×C₄	—	178	2	no	—
407	C₂×C₄	—	178	4	no	—
408	C₂×C₄	—	178	2	no	—
409	C₂×C₄	—	712	2	no	—
410	C₂×C₄	#15667987	1	1	yes	characteristic
411	C₂×C₄	#15667987	1	1	yes	characteristic
412	C₂×C₄	#15667987	1	1	yes	characteristic
413	C₂×C₄	#15668034	1	2	yes	—
414	C₂×C₄	#15668045	1	2	yes	—
415	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
417	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	4	2	no	—
423	C₈	—	4	2	no	—
424	C₈	—	356	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	712	1	no	—
428	C₂²	—	712	1	no	—
429	C₂²	—	712	1	no	—
430	C₂²	#19151821	1	2	yes	—
431	C₂²	C₂×#15667987	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	356	2	no	—
436	C₄	—	178	4	no	—
437	C₄	—	712	1	no	—
438	C₄	—	712	1	no	—
439	C₄	—	712	1	no	—
440	C₄	#19151821	1	2	yes	—
441	C₄	#135×D₈₉	1	2	yes	—
442	C₄	C₂×#15668034	1	1	yes	characteristic
443	C₄	C₂×#15668045	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	1424	1	no	—
446	C₂	C₂×#19151821	1	1	yes	characteristic
447	C₂	#26029834	1	1	yes	characteristic
448	C₂	#26029973	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667987
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1564	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#19152148	C₂²
hypercenter	#1564	D₈₉
hypocenter	C₈₉	#19123
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
2. #26030292	C₂	semidirect
4. C₂×C₈×Dic₁₇₈	C₂	semidirect
5. #26019711	C₂	semidirect
6. #26019697	C₂	semidirect
7. #26019683	C₂	semidirect
8. #26019669	C₂	semidirect
9. #26018907	C₂	semidirect
11. C₈₉×#1564	C₂	semidirect
233. #1564	D₈₉	semidirect
236. C₈₉	#19123	semidirect

Maximal subgroups

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

subgroup	index
#26030575	2
#26030292	2
#26030284	2
C₂×C₈×Dic₁₇₈	2
#26019711	2
#26019697	2
#26019683	2
#26019669	2
#26018907	2
#26018899	2
C₈₉×#1564	2
#19123	89