Subgroups — #36572926

Order 22784.

862 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151714	C₂	1	1	yes	maximal, characteristic
2	#26029129	C₂	1	1	yes	maximal, characteristic
3	#26029126	C₂	1	1	yes	maximal, characteristic
4	#26028851	C₂	1	2	yes	maximal, complemented
5	#26021038	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020481	C₂	1	2	yes	maximal, complemented
7	#26020475	C₂	1	2	yes	maximal, complemented
8	#26020410	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020315	C₂	1	2	yes	maximal, complemented
10	#26020132	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1952	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	C₂²	1	1	yes	characteristic
13	C₂×#15668020	C₂²	1	2	yes	—
14	#19152079	C₂²	1	2	yes	—
15	#19152078	C₂²	1	2	yes	—
16	#19151714	C₄	1	8	yes	complemented
17	#19151700	—	2	2	no	—
18	#19151697	—	2	2	no	—
19	C₄×Dic₃₅₆	—	2	1	no	—
20	#19151692	—	2	1	no	—
21	C₄×D₇₁₂	—	2	1	no	—
22	#19151680	—	2	1	no	—
23	C₂×#15667947	C₂²	1	1	yes	characteristic
24	#19151640	C₂²	1	2	yes	—
25	#19151639	—	2	2	no	—
26	#19151637	—	2	2	no	—
27	#19151634	C₂²	1	1	yes	characteristic
28	#19151633	—	2	2	no	—
29	C₂×#15667946	C₂²	1	1	yes	characteristic
30	C₂×#15667945	C₂²	1	2	yes	—
31	#107×D₈₉	—	2	2	no	—
32	C₂×#15667938	C₂²	1	2	yes	—
33	#19151600	C₂²	1	2	yes	—
34	#19151597	C₂²	1	2	yes	—
35	#19151553	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
37	#19151467	C₂²	1	2	yes	—
38	#19151366	C₂²	1	2	yes	—
39	#19151359	C₂²	1	1	yes	characteristic
40	#19151357	C₂²	1	1	yes	characteristic
41	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
42	#428×C₈₉	C₂²	1	2	yes	—
43	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
44	#405×C₈₉	C₂²	1	1	yes	characteristic
45	#343×C₈₉	C₂²	1	2	yes	—
46	C₂×#13083574	C₂³	1	2	yes	—
47	#15668034	C₂×C₄	1	4	yes	—
48	#15668034	Q₈	1	4	yes	—
49	C₂×Dic₃₅₆	D₄	1	1	yes	characteristic
50	C₂×#13083563	D₄	1	2	yes	—
51	C₂×D₇₁₂	D₄	1	1	yes	characteristic
52	#15668020	—	2	4	no	—
53	#15668020	C₂×C₄	1	8	yes	complemented
54	C₂×#13083558	C₂³	1	1	yes	characteristic
55	C₂×#13083557	—	2	2	no	—
56	C₂²×#10623494	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₈₉	—	2	2	no	—
58	C₄×Dic₁₇₈	—	2	2	no	—
59	#15667977	—	2	2	no	—
60	C₄×D₃₅₆	—	2	2	no	—
61	#15667974	—	2	2	no	—
62	C₄×C₂²⋊D₈₉	—	4	2	no	—
63	#15667972	—	4	2	no	—
64	#15667971	C₂³	1	1	yes	characteristic
65	#15667970	—	2	2	no	—
66	#15667970	—	2	2	no	—
67	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
68	C₂×#13083553	—	4	2	no	—
69	C₄⋊C₄×D₈₉	—	2	2	no	—
70	C₄⋊C₄×D₈₉	—	2	2	no	—
71	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
72	#15667947	—	2	2	no	—
73	#15667946	—	2	2	no	—
74	#15667946	—	2	1	no	—
75	#15667946	—	2	1	no	—
76	#15667945	—	2	2	no	—
77	#15667945	—	2	2	no	—
78	#15667945	D₄	1	1	yes	characteristic
79	#15667945	D₄	1	1	yes	characteristic
80	#15667944	—	2	2	no	—
81	#15667943	D₄	1	1	yes	characteristic
82	#15667943	D₄	1	1	yes	characteristic
83	#15667938	C₂×C₄	1	8	yes	complemented
84	#15667937	—	2	2	no	—
85	#15667935	—	2	2	no	—
86	#15667934	—	2	2	no	—
87	#15667932	—	2	2	no	—
88	#15667922	—	2	1	no	—
89	C₈×Dic₈₉	—	2	1	no	—
90	C₈×Dic₈₉	C₂×C₄	1	4	yes	complemented
91	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
93	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	#117×C₈₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
96	#108×C₈₉	C₂×C₄	1	4	yes	complemented
97	#107×C₈₉	—	2	1	no	—
98	#107×C₈₉	—	2	1	no	—
99	#107×C₈₉	—	2	2	no	—
100	#106×C₈₉	—	2	2	no	—
101	#97×C₈₉	—	2	1	no	—
102	C₄×C₈×C₈₉	—	2	1	no	—
103	#13083574	—	2	2	no	—
104	#13083574	—	2	2	no	—
105	#13083574	C₂²×C₄	1	4	yes	—
106	#13083574	C₂×Q₈	1	4	yes	—
107	C₂×Dic₁₇₈	C₂×D₄	1	2	yes	—
108	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
109	C₂×C₂²⋊D₈₉	—	2	2	no	—
110	C₂²×Dic₈₉	—	2	1	no	—
111	C₂²×Dic₈₉	—	2	2	no	—
112	C₂×C₄×D₈₉	—	2	2	no	—
113	C₂×C₄×D₈₉	—	4	2	no	—
114	C₂×C₄×D₈₉	—	4	2	no	—
115	Dic₃₅₆	C₄⋊C₄	1	4	yes	complemented
116	#13083563	C₄⋊C₄	1	8	yes	complemented
117	D₇₁₂	C₄⋊C₄	1	4	yes	complemented
118	#13083558	—	2	1	no	—
119	#13083558	—	2	1	no	—
120	#13083557	—	2	8	no	—
121	C₂×#10623494	—	2	1	no	—
122	C₂×#10623494	C₂²×C₄	1	2	yes	—
123	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
124	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
125	C₂×#10623494	#41	1	2	yes	—
126	C₈×D₈₉	—	2	8	no	—
127	C₄⋊Dic₈₉	—	2	2	no	—
128	C₄⋊Dic₈₉	—	2	2	no	—
129	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
130	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
131	#13083553	—	4	2	no	—
132	#13083553	—	4	2	no	—
133	#13083553	—	8	4	no	—
134	C₂²⋊Dic₈₉	—	2	1	no	—
135	#13083551	—	4	2	no	—
136	#13083551	—	4	2	no	—
137	C₄×Dic₈₉	—	2	1	no	—
138	C₄×Dic₈₉	—	2	1	no	—
139	C₄×Dic₈₉	—	4	2	no	—
140	C₄×Dic₈₉	—	4	2	no	—
141	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₈₉	—	2	2	no	—
143	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
144	M₁₆×C₈₉	—	2	2	no	—
145	M₁₆×C₈₉	—	2	1	no	—
146	M₁₆×C₈₉	—	2	1	no	—
147	M₁₆×C₈₉	C₂²×C₄	1	4	yes	—
148	C₂×C₈×C₈₉	—	2	2	no	—
149	C₂×C₈×C₈₉	—	2	1	no	—
150	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
154	C₄⋊C₄×C₈₉	—	2	2	no	—
155	C₄⋊C₄×C₈₉	—	2	2	no	—
156	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂²⋊C₄×C₈₉	—	2	1	no	—
159	C₄²×C₈₉	—	2	1	no	—
160	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	4	2	no	—
165	C₂×C₄×C₈₉	—	8	2	no	—
166	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂²⋊D₈₉	—	2	4	no	—
173	C₂²⋊D₈₉	—	2	4	no	—
174	C₂×Dic₈₉	—	2	2	no	—
175	C₂×Dic₈₉	—	2	2	no	—
176	C₂×Dic₈₉	—	2	2	no	—
177	C₂×Dic₈₉	—	2	2	no	—
178	C₂×Dic₈₉	—	2	1	no	—
179	C₂×Dic₈₉	—	2	1	no	—
180	C₂×Dic₈₉	—	4	2	no	—
181	C₂×Dic₈₉	—	8	2	no	—
182	D₃₅₆	—	2	2	no	—
183	D₃₅₆	C₂×C₄⋊C₄	1	4	yes	—
184	C₄×D₈₉	—	2	4	no	—
185	C₄×D₈₉	—	2	4	no	—
186	C₄×D₈₉	—	16	2	no	—
187	C₄×D₈₉	—	16	2	no	—
188	Dic₁₇₈	—	2	2	no	—
189	Dic₁₇₈	C₂×C₄⋊C₄	1	4	yes	—
190	C₈×C₈₉	—	2	4	no	—
191	C₈×C₈₉	—	4	1	no	—
192	C₈×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
193	C₈×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
194	#10623494	—	4	1	no	—
195	#10623494	C₄×D₄	1	2	yes	—
196	#10623494	C₄×D₄	1	2	yes	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	—	2	1	no	—
199	C₂²×C₈₉	#520	1	1	yes	characteristic
200	C₂²×C₈₉	D₄²	1	1	yes	characteristic
201	C₂²×C₈₉	#554	1	1	yes	characteristic
202	C₂×D₈₉	—	2	4	no	—
203	C₂×D₈₉	—	4	2	no	—
204	C₂×D₈₉	—	4	2	no	—
205	C₄×C₈₉	—	4	1	no	—
206	C₄×C₈₉	—	4	1	no	—
207	C₄×C₈₉	—	8	2	no	—
208	C₄×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
209	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
210	C₄×C₈₉	#547	1	1	yes	characteristic
211	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
212	Dic₈₉	—	2	4	no	—
213	Dic₈₉	—	2	4	no	—
214	Dic₈₉	—	4	1	no	—
215	Dic₈₉	—	4	1	no	—
216	Dic₈₉	—	8	2	no	—
217	#22692	—	89	1	no	maximal, Sylow
218	C₂×C₈₉	—	2	1	no	—
219	C₂×C₈₉	—	2	1	no	—
220	C₂×C₈₉	D₄×C₄⋊C₄	1	1	yes	characteristic
221	C₂×C₈₉	#3292	1	1	yes	characteristic
222	C₂×C₈₉	#3293	1	1	yes	characteristic
223	D₈₉	—	4	4	no	—
224	C₂×#443	—	89	1	no	—
225	#2951	—	89	1	no	—
226	#2951	—	89	1	no	—
227	#2913	—	89	2	no	—
228	#1952	—	89	1	no	—
229	#1952	D₈₉	1	1	yes	characteristic, complemented
230	#1859	—	89	2	no	—
231	#1859	—	89	2	no	—
232	#1845	—	89	1	no	—
233	#1816	—	89	2	no	—
234	#1772	—	89	1	no	—
235	C₈₉	#22692	1	1	yes	characteristic, complemented, Sylow
236	C₂×#135	—	89	1	no	—
237	C₂×#131	—	89	2	no	—
238	#520	—	89	2	no	—
239	#520	—	89	2	no	—
240	#443	—	89	8	no	—
241	#440	—	178	2	no	—
242	#440	—	178	2	no	—
243	C₄×Q₁₆	—	178	1	no	—
244	C₄×Q₁₆	—	178	1	no	—
245	C₄×D₈	—	178	1	no	—
246	C₄×D₈	—	178	1	no	—
247	C₂×#108	—	89	1	no	—
248	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
249	#428	—	89	2	no	—
250	#428	—	178	2	no	—
251	#428	—	178	2	no	—
252	#428	C₂×D₈₉	1	2	yes	—
253	#427	—	89	1	no	—
254	#427	—	178	2	no	—
255	C₂×#107	—	89	1	no	—
256	C₂×#107	—	89	2	no	—
257	C₂×#107	—	178	2	no	—
258	C₂×#107	C₂×D₈₉	1	1	yes	characteristic
259	C₂×#104	—	89	2	no	—
260	#417	—	89	2	no	—
261	#417	—	89	2	no	—
262	#405	—	89	1	no	—
263	#405	C₂×D₈₉	1	1	yes	characteristic
264	C₂×C₄×C₈	—	89	1	no	—
265	#384	—	89	2	no	—
266	#343	—	89	2	no	—
267	#343	C₂×D₈₉	1	2	yes	—
268	#339	—	89	1	no	—
269	#339	—	89	1	no	—
270	C₂×#41	—	89	2	no	—
271	#135	—	89	4	no	—
272	#135	—	89	4	no	—
273	C₂×Q₁₆	—	89	1	no	—
274	C₂×SD₁₆	—	89	2	no	—
275	C₂×D₈	—	89	1	no	—
276	#131	—	89	8	no	—
277	#131	—	178	4	no	—
278	C₂×M₁₆	—	89	1	no	—
279	C₂×M₁₆	—	178	2	no	—
280	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
281	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
282	C₂²×C₈	—	89	1	no	—
283	C₂²×C₈	—	178	2	no	—
284	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
285	C₄×Q₈	—	178	2	no	—
286	C₄×Q₈	—	178	2	no	—
287	C₄×D₄	—	356	2	no	—
288	C₄×D₄	—	356	2	no	—
289	C₄×D₄	—	178	2	no	—
290	C₄×D₄	—	178	2	no	—
291	#117	—	89	1	no	—
292	#117	—	178	2	no	—
293	#117	—	178	2	no	—
294	#117	C₂²×D₈₉	1	1	yes	characteristic
295	C₂×C₄⋊C₄	—	89	2	no	—
296	C₂×C₄⋊C₄	—	356	2	no	—
297	C₂×C₄⋊C₄	—	178	2	no	—
298	C₂×C₄⋊C₄	—	178	2	no	—
299	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
300	C₂×C₄²	—	89	1	no	—
301	#108	—	178	2	no	—
302	#108	C₄×D₈₉	1	4	yes	complemented
303	#107	—	2	1	no	—
304	#107	—	2	1	no	—
305	#107	—	2	2	no	—
306	#107	—	89	1	no	—
307	#107	—	89	1	no	—
308	#107	—	178	2	no	—
309	#107	—	178	2	no	—
310	#107	—	178	2	no	—
311	#107	—	178	1	no	—
312	#107	—	178	1	no	—
313	#106	—	2	2	no	—
314	#106	—	89	1	no	—
315	#106	—	89	1	no	—
316	#106	—	178	2	no	—
317	#104	—	89	8	no	—
318	#103	—	178	2	no	—
319	#103	—	178	2	no	—
320	#102	—	178	2	no	—
321	#102	—	178	2	no	—
322	#97	—	2	1	no	—
323	#97	—	178	1	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	89	4	no	—
326	C₄×C₈	—	178	1	no	—
327	#41	—	89	4	no	—
328	#41	—	89	4	no	—
329	#41	—	178	2	no	—
330	#41	—	178	2	no	—
331	C₂×Q₈	—	89	2	no	—
332	C₂×D₄	—	89	2	no	—
333	C₂×D₄	—	178	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	356	2	no	—
336	C₂²×C₄	—	356	2	no	—
337	C₂²×C₄	—	178	2	no	—
338	C₂²×C₄	—	178	1	no	—
339	C₂²×C₄	—	178	2	no	—
340	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
341	Q₁₆	—	89	4	no	—
342	SD₁₆	—	89	8	no	—
343	D₈	—	89	4	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	1	no	—
346	M₁₆	—	2	1	no	—
347	M₁₆	—	178	8	no	—
348	M₁₆	—	178	1	no	—
349	M₁₆	—	178	1	no	—
350	M₁₆	C₂×C₄×D₈₉	1	4	yes	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	89	2	no	—
354	C₂×C₈	—	89	1	no	—
355	C₂×C₈	—	89	1	no	—
356	C₂×C₈	—	89	2	no	—
357	C₂×C₈	—	178	8	no	—
358	C₂×C₈	—	178	1	no	—
359	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
360	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
361	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
362	C₂×C₈	Q₈×D₈₉	1	2	yes	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	89	1	no	—
366	C₄⋊C₄	—	89	1	no	—
367	C₄⋊C₄	—	356	2	no	—
368	C₄⋊C₄	—	356	2	no	—
369	C₄⋊C₄	—	178	2	no	—
370	C₄⋊C₄	—	178	2	no	—
371	C₄⋊C₄	—	712	4	no	—
372	C₄⋊C₄	D₄×D₈₉	1	1	yes	characteristic
373	C₄⋊C₄	D₄×D₈₉	1	1	yes	characteristic
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	356	2	no	—
376	C₂²⋊C₄	—	356	2	no	—
377	C₂²⋊C₄	—	178	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	89	2	no	—
380	C₄²	—	356	2	no	—
381	C₄²	—	356	2	no	—
382	C₄²	—	178	1	no	—
383	C₄²	—	178	1	no	—
384	C₂³	—	178	2	no	—
385	C₂³	#15668058	1	1	yes	characteristic
386	Q₈	—	89	4	no	—
387	Q₈	—	178	2	no	—
388	D₄	—	89	4	no	—
389	D₄	—	178	4	no	—
390	D₄	—	178	4	no	—
391	D₄	—	178	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	—	356	2	no	—
397	C₂×C₄	—	1424	2	no	—
398	C₂×C₄	—	1424	2	no	—
399	C₂×C₄	—	178	1	no	—
400	C₂×C₄	—	178	1	no	—
401	C₂×C₄	—	178	2	no	—
402	C₂×C₄	—	178	2	no	—
403	C₂×C₄	—	178	2	no	—
404	C₂×C₄	—	178	2	no	—
405	C₂×C₄	—	178	4	no	—
406	C₂×C₄	—	178	4	no	—
407	C₂×C₄	—	712	2	no	—
408	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
409	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
410	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
411	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
412	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
413	C₂×C₄	#15668060	1	1	yes	characteristic
414	C₈	—	2	4	no	—
415	C₈	—	4	1	no	—
416	C₈	—	89	2	no	—
417	C₈	—	89	2	no	—
418	C₈	—	356	1	no	—
419	C₈	C₄⋊C₄×D₈₉	1	2	yes	—
420	C₈	C₄⋊C₄×D₈₉	1	2	yes	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	356	2	no	—
424	C₂²	—	356	2	no	—
425	C₂²	—	178	4	no	—
426	C₂²	#19152080	1	1	yes	characteristic
427	C₂²	#19152232	1	1	yes	characteristic
428	C₂²	#19152304	1	1	yes	characteristic
429	C₄	—	4	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	8	2	no	—
432	C₄	—	356	1	no	—
433	C₄	—	356	1	no	—
434	C₄	—	178	4	no	—
435	C₄	—	178	4	no	—
436	C₄	—	712	2	no	—
437	C₄	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
438	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
439	C₄	#19152250	1	1	yes	characteristic
440	C₄	#19152263	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	356	4	no	—
444	C₂	#26023153	1	1	yes	characteristic
445	C₂	#26032050	1	1	yes	characteristic
446	C₂	#26032055	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19152232
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1952	C₂
socle	C₂²×C₈₉	D₄²
prime radical	C₂×#15668034	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1952	D₈₉
hypocenter	C₈₉	#22692
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1952

Complements

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

N	H ≅ G/N	type
4. #26028851	C₂	semidirect
5. #26021038	C₂	semidirect
6. #26020481	C₂	semidirect
7. #26020475	C₂	semidirect
8. #26020410	C₂	semidirect
9. #26020315	C₂	semidirect
10. #26020132	C₂	semidirect
11. C₈₉×#1952	C₂	semidirect
16. #19151714	C₄	semidirect
53. #15668020	C₂×C₄	semidirect
83. #15667938	C₂×C₄	semidirect
90. C₈×Dic₈₉	C₂×C₄	semidirect
96. #108×C₈₉	C₂×C₄	semidirect
115. Dic₃₅₆	C₄⋊C₄	semidirect
116. #13083563	C₄⋊C₄	semidirect
117. D₇₁₂	C₄⋊C₄	semidirect
229. #1952	D₈₉	semidirect
235. C₈₉	#22692	semidirect
302. #108	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151714	2
#26029129	2
#26029126	2
#26028851	2
#26021038	2
#26020481	2
#26020475	2
#26020410	2
#26020315	2
#26020132	2
C₈₉×#1952	2
#22692	89