Subgroups — #36568335

Order 22784.

796 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030729	C₂	1	1	yes	maximal, characteristic
2	#26029113	C₂	1	1	yes	maximal, characteristic, complemented
3	#26021153	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021151	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020786	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020781	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020779	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020774	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020743	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020736	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020732	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020725	C₂	1	1	yes	maximal, characteristic, complemented
13	#26020377	C₂	1	1	yes	maximal, characteristic, complemented
14	#26020007	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2957	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668042	C₂²	1	1	yes	characteristic
17	C₂×#15668037	C₂²	1	1	yes	characteristic
18	C₂²×#13083563	C₂²	1	1	yes	characteristic
19	#19152169	C₂²	1	1	yes	characteristic
20	#19152162	C₂²	1	1	yes	characteristic
21	#19152075	C₂²	1	1	yes	characteristic
22	#19152072	C₂²	1	1	yes	characteristic
23	#19151991	C₄	1	2	yes	complemented
24	#19151986	C₄	1	2	yes	complemented
25	#19151979	C₄	1	2	yes	complemented
26	#19151969	C₄	1	2	yes	complemented
27	#19151700	—	2	2	no	—
28	C₄×#13083563	—	2	2	no	—
29	#19151636	C₂²	1	1	yes	characteristic
30	#19151615	C₂²	1	1	yes	characteristic
31	#19151615	C₂²	1	1	yes	characteristic
32	#19151608	C₂²	1	1	yes	characteristic
33	#19151608	C₂²	1	1	yes	characteristic
34	#19151604	C₂²	1	1	yes	characteristic
35	#19151604	C₂²	1	1	yes	characteristic
36	C₂×#15667930	C₂²	1	1	yes	characteristic
37	C₂×#15667928	C₂²	1	1	yes	characteristic
38	#19151572	C₂²	1	1	yes	characteristic
39	#19151572	C₂²	1	1	yes	characteristic
40	#19151553	C₂²	1	1	yes	characteristic
41	#19151553	C₂²	1	1	yes	characteristic
42	#19151370	C₂²	1	1	yes	characteristic
43	#19151370	C₂²	1	1	yes	characteristic
44	#19151356	C₂²	1	1	yes	characteristic
45	#19151355	C₂²	1	1	yes	characteristic
46	#19151355	C₂²	1	1	yes	characteristic
47	#19151355	C₂²	1	1	yes	characteristic
48	#19151354	C₂²	1	1	yes	characteristic
49	#19151354	C₂²	1	1	yes	characteristic
50	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
51	#568×C₈₉	C₂²	1	1	yes	characteristic
52	#568×C₈₉	C₂²	1	1	yes	characteristic
53	#444×C₈₉	—	2	2	no	—
54	#443×C₈₉	—	2	2	no	—
55	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
56	#421×C₈₉	C₂²	1	1	yes	characteristic
57	#421×C₈₉	C₂²	1	1	yes	characteristic
58	#405×C₈₉	C₂²	1	1	yes	characteristic
59	C₂²×Dic₁₇₈	C₂³	1	1	yes	characteristic
60	C₂²×D₃₅₆	C₂³	1	1	yes	characteristic
61	#15668042	—	4	1	no	—
62	#15668042	—	4	1	no	—
63	#15668037	—	4	1	no	—
64	#15668037	—	4	1	no	—
65	C₂×#13083564	C₂×C₄	1	2	yes	complemented
66	C₂×#13083563	—	2	1	no	—
67	C₂×#13083563	—	2	1	no	—
68	C₂×#13083563	—	2	1	no	—
69	C₂×#13083563	—	2	1	no	—
70	C₂×#13083563	C₂×C₄	1	2	yes	—
71	C₂×#13083563	C₂×C₄	1	2	yes	—
72	C₂×#13083562	C₂×C₄	1	2	yes	complemented
73	C₂×#13083561	C₂×C₄	1	2	yes	—
74	C₂×#13083559	C₂×C₄	1	2	yes	—
75	C₂×#13083558	C₂³	1	1	yes	characteristic
76	C₂×#13083558	C₂³	1	1	yes	characteristic
77	#15668010	C₂×C₄	1	2	yes	complemented
78	#15668008	C₂×C₄	1	2	yes	—
79	#15668001	C₂×C₄	1	2	yes	—
80	#15667999	C₂×C₄	1	2	yes	complemented
81	#15667993	—	4	1	no	—
82	#15667991	—	4	1	no	—
83	#15667986	—	4	1	no	—
84	#15667980	—	4	1	no	—
85	C₄×Dic₁₇₈	—	2	2	no	—
86	#15667977	—	4	1	no	—
87	C₄×D₃₅₆	—	2	2	no	—
88	#15667974	—	4	1	no	—
89	#15667971	C₂³	1	1	yes	characteristic
90	#15667971	C₂³	1	1	yes	characteristic
91	#15667971	C₂³	1	1	yes	characteristic
92	#15667971	C₂³	1	1	yes	characteristic
93	#15667968	—	4	1	no	—
94	C₂²⋊C₄×D₈₉	—	4	1	no	—
95	#15667946	—	2	1	no	—
96	#15667944	—	2	1	no	—
97	#15667939	—	4	1	no	—
98	#15667939	—	4	1	no	—
99	#15667937	—	2	2	no	—
100	#15667937	—	4	1	no	—
101	#15667934	—	2	2	no	—
102	#15667934	—	4	1	no	—
103	#15667930	—	4	1	no	—
104	#15667928	—	4	1	no	—
105	#15667927	—	4	1	no	—
106	#15667927	—	4	1	no	—
107	#15667922	—	2	1	no	—
108	#15667922	C₂×C₄	1	2	yes	complemented
109	C₈×Dic₈₉	—	2	1	no	—
110	C₈×Dic₈₉	C₂×C₄	1	2	yes	complemented
111	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
113	#135×C₈₉	—	2	1	no	—
114	#135×C₈₉	—	2	1	no	—
115	#135×C₈₉	—	2	1	no	—
116	#135×C₈₉	—	2	1	no	—
117	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
118	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
119	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
120	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
121	#131×C₈₉	—	2	2	no	—
122	#131×C₈₉	—	2	2	no	—
123	#131×C₈₉	—	4	1	no	—
124	#131×C₈₉	—	4	1	no	—
125	C₂×M₁₆×C₈₉	—	4	1	no	—
126	C₂×M₁₆×C₈₉	—	4	1	no	—
127	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
129	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
131	#117×C₈₉	C₂³	1	1	yes	characteristic
132	#108×C₈₉	—	2	1	no	—
133	#108×C₈₉	—	2	1	no	—
134	#104×C₈₉	—	2	2	no	—
135	#104×C₈₉	—	2	2	no	—
136	#97×C₈₉	D₄	1	2	yes	complemented
137	C₄×C₈×C₈₉	D₄	1	2	yes	complemented
138	C₂³×D₈₉	—	2	1	no	—
139	C₂×Dic₁₇₈	—	2	1	no	—
140	C₂×Dic₁₇₈	—	2	1	no	—
141	C₂×Dic₁₇₈	—	2	1	no	—
142	C₂×Dic₁₇₈	—	2	1	no	—
143	C₂×Dic₁₇₈	—	2	1	no	—
144	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
145	C₂×D₃₅₆	—	2	1	no	—
146	C₂×D₃₅₆	—	2	1	no	—
147	C₂×D₃₅₆	—	2	1	no	—
148	C₂×D₃₅₆	—	2	1	no	—
149	C₂×D₃₅₆	—	2	1	no	—
150	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
151	C₂×C₂²⋊D₈₉	—	4	2	no	—
152	C₂²×Dic₈₉	—	2	1	no	—
153	C₂×C₄×D₈₉	—	4	2	no	—
154	#13083564	—	4	2	no	—
155	#13083563	—	2	2	no	—
156	#13083563	—	2	2	no	—
157	#13083563	—	2	2	no	—
158	#13083563	—	2	2	no	—
159	#13083562	—	4	2	no	—
160	#13083561	—	4	2	no	—
161	#13083559	—	4	2	no	—
162	#13083558	—	2	1	no	—
163	#13083558	—	2	1	no	—
164	#13083558	—	2	1	no	—
165	#13083558	—	2	1	no	—
166	C₂×#10623494	—	2	1	no	—
167	C₂×#10623494	C₂²×C₄	1	2	yes	—
168	C₄⋊Dic₈₉	—	2	1	no	—
169	C₄⋊Dic₈₉	—	2	1	no	—
170	C₄⋊Dic₈₉	—	2	1	no	—
171	C₄⋊Dic₈₉	—	2	1	no	—
172	#13083553	—	4	2	no	—
173	#13083553	—	4	2	no	—
174	C₂²⋊Dic₈₉	—	2	1	no	—
175	C₂²⋊Dic₈₉	—	2	1	no	—
176	C₂²⋊Dic₈₉	—	2	1	no	—
177	C₂²⋊Dic₈₉	—	2	1	no	—
178	C₂²⋊Dic₈₉	—	4	2	no	—
179	#13083551	—	4	2	no	—
180	#13083551	—	4	2	no	—
181	C₄×Dic₈₉	—	2	1	no	—
182	C₄×Dic₈₉	—	2	1	no	—
183	C₄×Dic₈₉	—	2	1	no	—
184	C₄×Dic₈₉	—	4	2	no	—
185	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
186	#41×C₈₉	—	2	1	no	—
187	#41×C₈₉	—	2	1	no	—
188	#41×C₈₉	—	2	1	no	—
189	#41×C₈₉	—	2	1	no	—
190	#41×C₈₉	—	2	1	no	—
191	#41×C₈₉	—	2	1	no	—
192	#41×C₈₉	—	2	1	no	—
193	#41×C₈₉	—	2	1	no	—
194	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
195	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
196	C₂×D₄×C₈₉	—	2	1	no	—
197	C₂×D₄×C₈₉	—	2	1	no	—
198	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₈₉	—	2	1	no	—
201	C₂²×C₄×C₈₉	—	2	1	no	—
202	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
203	Q₁₆×C₈₉	—	2	1	no	—
204	Q₁₆×C₈₉	—	2	1	no	—
205	SD₁₆×C₈₉	—	2	1	no	—
206	SD₁₆×C₈₉	—	2	1	no	—
207	SD₁₆×C₈₉	—	2	1	no	—
208	SD₁₆×C₈₉	—	2	1	no	—
209	D₈×C₈₉	—	2	1	no	—
210	D₈×C₈₉	—	2	1	no	—
211	M₁₆×C₈₉	—	2	1	no	—
212	M₁₆×C₈₉	—	2	1	no	—
213	M₁₆×C₈₉	—	2	1	no	—
214	M₁₆×C₈₉	—	2	1	no	—
215	M₁₆×C₈₉	—	2	1	no	—
216	M₁₆×C₈₉	—	2	1	no	—
217	M₁₆×C₈₉	—	4	2	no	—
218	M₁₆×C₈₉	—	4	2	no	—
219	C₂×C₈×C₈₉	—	2	1	no	—
220	C₂×C₈×C₈₉	—	2	1	no	—
221	C₂×C₈×C₈₉	—	4	2	no	—
222	C₂×C₈×C₈₉	—	4	2	no	—
223	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
224	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
225	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
226	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
227	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
228	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
229	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
230	C₄⋊C₄×C₈₉	—	2	1	no	—
231	C₂²⋊C₄×C₈₉	—	2	1	no	—
232	C₄²×C₈₉	C₂×D₄	1	2	yes	—
233	C₂³×C₈₉	—	2	1	no	—
234	C₂³×C₈₉	—	2	1	no	—
235	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂²×D₈₉	—	2	2	no	—
237	C₂²×D₈₉	—	4	1	no	—
238	C₂²×D₈₉	—	4	1	no	—
239	C₂²×D₈₉	—	16	1	no	—
240	Q₈×C₈₉	—	2	1	no	—
241	Q₈×C₈₉	—	2	1	no	—
242	Q₈×C₈₉	—	2	1	no	—
243	Q₈×C₈₉	—	2	1	no	—
244	D₄×C₈₉	—	2	1	no	—
245	D₄×C₈₉	—	2	1	no	—
246	D₄×C₈₉	—	2	1	no	—
247	D₄×C₈₉	—	2	1	no	—
248	D₄×C₈₉	—	4	1	no	—
249	D₄×C₈₉	—	4	1	no	—
250	D₄×C₈₉	—	4	1	no	—
251	D₄×C₈₉	—	4	1	no	—
252	C₂×C₄×C₈₉	—	2	1	no	—
253	C₂×C₄×C₈₉	—	2	1	no	—
254	C₂×C₄×C₈₉	—	2	2	no	—
255	C₂×C₄×C₈₉	—	4	1	no	—
256	C₂×C₄×C₈₉	—	4	1	no	—
257	C₂×C₄×C₈₉	—	4	1	no	—
258	C₂×C₄×C₈₉	—	4	1	no	—
259	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
260	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
264	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
265	C₂²⋊D₈₉	—	16	2	no	—
266	C₂×Dic₈₉	—	2	2	no	—
267	C₂×Dic₈₉	—	2	2	no	—
268	C₂×Dic₈₉	—	4	1	no	—
269	C₂×Dic₈₉	—	4	1	no	—
270	C₂×Dic₈₉	—	4	1	no	—
271	C₂×Dic₈₉	—	4	1	no	—
272	C₂×Dic₈₉	—	4	1	no	—
273	D₃₅₆	—	2	2	no	—
274	D₃₅₆	—	2	2	no	—
275	D₃₅₆	—	4	1	no	—
276	D₃₅₆	—	4	1	no	—
277	C₄×D₈₉	—	16	2	no	—
278	Dic₁₇₈	—	2	2	no	—
279	Dic₁₇₈	—	2	2	no	—
280	Dic₁₇₈	—	4	1	no	—
281	Dic₁₇₈	—	4	1	no	—
282	C₈×C₈₉	—	2	2	no	—
283	C₈×C₈₉	—	4	1	no	—
284	C₈×C₈₉	—	4	1	no	—
285	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
286	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
287	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
288	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
289	#10623494	—	2	2	no	—
290	#10623494	—	4	1	no	—
291	C₂²×C₈₉	—	4	1	no	—
292	C₂²×C₈₉	—	4	1	no	—
293	C₂²×C₈₉	—	4	1	no	—
294	C₂²×C₈₉	—	8	1	no	—
295	C₂²×C₈₉	—	8	1	no	—
296	C₂²×C₈₉	#518	1	1	yes	characteristic
297	C₂²×C₈₉	#535	1	1	yes	characteristic
298	C₂²×C₈₉	#540	1	1	yes	characteristic
299	C₂×D₈₉	—	4	2	no	—
300	C₂×D₈₉	—	8	2	no	—
301	C₂×D₈₉	—	8	2	no	—
302	C₂×D₈₉	—	16	1	no	—
303	C₄×C₈₉	—	4	2	no	—
304	C₄×C₈₉	—	4	1	no	—
305	C₄×C₈₉	—	4	1	no	—
306	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
307	C₄×C₈₉	#518	1	1	yes	characteristic
308	C₄×C₈₉	#535	1	1	yes	characteristic
309	C₄×C₈₉	#540	1	1	yes	characteristic
310	Dic₈₉	—	4	2	no	—
311	Dic₈₉	—	4	2	no	—
312	Dic₈₉	—	8	1	no	—
313	Dic₈₉	—	8	1	no	—
314	Dic₈₉	—	8	1	no	—
315	#22284	—	89	1	no	maximal, Sylow
316	C₂×C₈₉	—	2	1	no	—
317	C₂×C₈₉	—	2	1	no	—
318	C₂×C₈₉	—	2	1	no	—
319	C₂×C₈₉	—	8	1	no	—
320	C₂×C₈₉	—	8	1	no	—
321	C₂×C₈₉	#2328	1	1	yes	characteristic
322	D₈₉	—	8	2	no	—
323	#3154	—	89	1	no	—
324	#2957	D₈₉	1	1	yes	characteristic, complemented
325	#2949	—	89	1	no	—
326	#1977	—	89	1	no	—
327	#1976	—	89	1	no	—
328	#1912	—	89	1	no	—
329	#1911	—	89	1	no	—
330	#1910	—	89	1	no	—
331	#1909	—	89	1	no	—
332	#1905	—	89	1	no	—
333	#1904	—	89	1	no	—
334	#1903	—	89	1	no	—
335	#1902	—	89	1	no	—
336	#1833	—	89	1	no	—
337	#1747	—	89	1	no	—
338	C₈₉	#22284	1	1	yes	characteristic, complemented, Sylow
339	C₂×#137	—	89	1	no	—
340	C₂×AGL(1,ℤ/8)	—	89	1	no	—
341	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
342	C₂²×SD₁₆	—	89	1	no	—
343	#568	C₂×D₈₉	1	1	yes	characteristic
344	#568	C₂×D₈₉	1	1	yes	characteristic
345	#536	—	89	1	no	—
346	#535	—	89	1	no	—
347	#519	—	89	1	no	—
348	#518	—	89	1	no	—
349	#497	—	89	2	no	—
350	#496	—	89	2	no	—
351	#495	—	89	2	no	—
352	#492	—	89	2	no	—
353	#444	—	2	2	no	—
354	#443	—	2	2	no	—
355	#440	—	178	2	no	—
356	C₄×SD₁₆	—	178	2	no	—
357	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
358	#427	—	89	1	no	—
359	#421	—	89	1	no	—
360	#421	—	89	1	no	—
361	#421	C₂×D₈₉	1	1	yes	characteristic
362	#421	C₂×D₈₉	1	1	yes	characteristic
363	#419	—	89	1	no	—
364	#419	—	89	1	no	—
365	#418	—	89	1	no	—
366	#418	—	89	1	no	—
367	C₂×#101	—	89	1	no	—
368	C₂×#100	—	89	1	no	—
369	#410	—	89	1	no	—
370	#410	—	89	1	no	—
371	#405	—	89	1	no	—
372	#405	—	89	1	no	—
373	#405	C₂×D₈₉	1	1	yes	characteristic
374	#344	—	89	1	no	—
375	#344	—	89	1	no	—
376	#338	—	89	1	no	—
377	H(3,ℤ/4)	—	89	1	no	—
378	H(3,ℤ/4)	—	89	1	no	—
379	H(3,ℤ/4)	—	89	1	no	—
380	H(3,ℤ/4)	—	89	1	no	—
381	H(3,ℤ/4)	—	89	1	no	—
382	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
383	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
384	C₂²×Q₈	—	89	1	no	—
385	C₂²×D₄	—	89	1	no	—
386	#137	—	356	1	no	—
387	#137	—	356	1	no	—
388	AGL(1,ℤ/8)	—	356	1	no	—
389	AGL(1,ℤ/8)	—	356	1	no	—
390	#135	—	2	1	no	—
391	#135	—	2	1	no	—
392	#135	—	2	1	no	—
393	#135	—	2	1	no	—
394	C₂×Q₁₆	—	89	2	no	—
395	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic, complemented
396	C₂×SD₁₆	—	89	2	no	—
397	C₂×SD₁₆	—	89	2	no	—
398	C₂×SD₁₆	—	89	2	no	—
399	C₂×SD₁₆	—	89	2	no	—
400	C₂×SD₁₆	—	178	1	no	—
401	C₂×SD₁₆	—	178	1	no	—
402	C₂×SD₁₆	—	178	1	no	—
403	C₂×SD₁₆	—	178	1	no	—
404	C₂×SD₁₆	C₄×D₈₉	1	1	yes	characteristic, complemented
405	C₂×SD₁₆	C₄×D₈₉	1	1	yes	characteristic, complemented
406	C₂×D₈	—	89	2	no	—
407	C₂×D₈	C₄×D₈₉	1	1	yes	characteristic, complemented
408	#131	—	2	2	no	—
409	#131	—	2	2	no	—
410	#131	—	4	1	no	—
411	#131	—	4	1	no	—
412	C₂×M₁₆	—	4	1	no	—
413	C₂×M₁₆	—	4	1	no	—
414	C₂×M₁₆	—	89	1	no	—
415	C₂×M₁₆	—	89	1	no	—
416	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
417	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
418	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
419	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
420	C₄⋊Q₈	—	89	2	no	—
421	#127	—	89	2	no	—
422	#124	—	89	2	no	—
423	#124	—	89	2	no	—
424	#123	—	356	1	no	—
425	C₂²⋊Q₈	—	356	1	no	—
426	#121	—	356	1	no	—
427	#120	—	356	1	no	—
428	C₄×Q₈	—	356	1	no	—
429	C₄×Q₈	—	178	2	no	—
430	C₄×D₄	—	356	1	no	—
431	C₄×D₄	—	178	2	no	—
432	#117	—	89	1	no	—
433	#117	—	89	1	no	—
434	#117	—	89	1	no	—
435	#117	—	89	1	no	—
436	#117	—	356	1	no	—
437	#117	C₂²×D₈₉	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	—	356	1	no	—
439	#108	—	2	1	no	—
440	#108	—	2	1	no	—
441	#107	—	178	1	no	—
442	#106	—	178	1	no	—
443	#104	—	2	2	no	—
444	#104	—	2	2	no	—
445	#104	—	356	1	no	—
446	#104	—	356	1	no	—
447	#103	—	356	1	no	—
448	#103	—	178	2	no	—
449	#102	—	356	1	no	—
450	#102	—	178	2	no	—
451	#101	—	356	1	no	—
452	#100	—	356	1	no	—
453	#99	—	356	1	no	—
454	#99	—	356	1	no	—
455	#97	—	89	2	no	—
456	#97	—	178	1	no	—
457	#97	C₂²⋊D₈₉	1	2	yes	complemented
458	C₄×C₈	—	89	2	no	—
459	C₄×C₈	—	178	1	no	—
460	C₄×C₈	C₂²⋊D₈₉	1	2	yes	complemented
461	C₂⁴	—	178	1	no	—
462	#41	—	2	1	no	—
463	#41	—	2	1	no	—
464	#41	—	2	1	no	—
465	#41	—	2	1	no	—
466	#41	—	2	1	no	—
467	#41	—	2	1	no	—
468	#41	—	2	1	no	—
469	#41	—	2	1	no	—
470	C₂×Q₈	—	89	2	no	—
471	C₂×Q₈	—	178	1	no	—
472	C₂×Q₈	—	178	1	no	—
473	C₂×Q₈	—	178	1	no	—
474	C₂×Q₈	—	178	1	no	—
475	C₂×Q₈	—	178	1	no	—
476	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
477	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	89	2	no	—
481	C₂×D₄	—	356	2	no	—
482	C₂×D₄	—	178	1	no	—
483	C₂×D₄	—	178	1	no	—
484	C₂×D₄	—	178	1	no	—
485	C₂×D₄	—	178	1	no	—
486	C₂×D₄	—	178	1	no	—
487	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
488	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	356	2	no	—
492	C₂²×C₄	—	178	1	no	—
493	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
494	Q₁₆	—	2	1	no	—
495	Q₁₆	—	2	1	no	—
496	Q₁₆	—	356	2	no	—
497	SD₁₆	—	2	1	no	—
498	SD₁₆	—	2	1	no	—
499	SD₁₆	—	2	1	no	—
500	SD₁₆	—	2	1	no	—
501	SD₁₆	—	356	2	no	—
502	SD₁₆	—	356	2	no	—
503	SD₁₆	—	178	2	no	—
504	SD₁₆	—	178	2	no	—
505	SD₁₆	—	178	2	no	—
506	SD₁₆	—	178	2	no	—
507	D₈	—	2	1	no	—
508	D₈	—	2	1	no	—
509	D₈	—	356	2	no	—
510	M₁₆	—	2	1	no	—
511	M₁₆	—	2	1	no	—
512	M₁₆	—	2	1	no	—
513	M₁₆	—	2	1	no	—
514	M₁₆	—	2	1	no	—
515	M₁₆	—	2	1	no	—
516	M₁₆	—	4	2	no	—
517	M₁₆	—	4	2	no	—
518	M₁₆	—	178	1	no	—
519	M₁₆	—	178	1	no	—
520	M₁₆	—	178	1	no	—
521	M₁₆	—	178	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	4	2	no	—
525	C₂×C₈	—	4	2	no	—
526	C₂×C₈	—	89	2	no	—
527	C₂×C₈	—	178	1	no	—
528	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
529	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
530	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
531	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
532	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
533	C₂×C₈	#13083574	1	1	yes	characteristic
534	C₂×C₈	#13083574	1	1	yes	characteristic
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	356	2	no	—
537	C₄⋊C₄	—	356	2	no	—
538	C₄⋊C₄	—	178	1	no	—
539	C₄⋊C₄	—	178	1	no	—
540	C₄⋊C₄	—	178	1	no	—
541	C₄⋊C₄	—	178	1	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	356	2	no	—
544	C₂²⋊C₄	—	356	2	no	—
545	C₂²⋊C₄	—	356	2	no	—
546	C₂²⋊C₄	—	178	1	no	—
547	C₂²⋊C₄	—	178	1	no	—
548	C₂²⋊C₄	—	178	1	no	—
549	C₂²⋊C₄	—	178	1	no	—
550	C₄²	—	89	2	no	—
551	C₄²	—	356	2	no	—
552	C₄²	—	178	1	no	—
553	C₄²	—	178	1	no	—
554	C₄²	—	178	1	no	—
555	C₄²	C₂×C₂²⋊D₈₉	1	2	yes	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	356	1	no	—
559	C₂³	—	356	1	no	—
560	C₂³	—	1424	1	no	—
561	C₂³	—	178	2	no	—
562	C₂³	#15668058	1	1	yes	characteristic
563	Q₈	—	2	1	no	—
564	Q₈	—	2	1	no	—
565	Q₈	—	2	1	no	—
566	Q₈	—	2	1	no	—
567	Q₈	—	356	1	no	—
568	Q₈	—	356	1	no	—
569	Q₈	—	178	2	no	—
570	Q₈	—	178	2	no	—
571	D₄	—	2	1	no	—
572	D₄	—	2	1	no	—
573	D₄	—	2	1	no	—
574	D₄	—	2	1	no	—
575	D₄	—	4	1	no	—
576	D₄	—	4	1	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	D₄	—	356	1	no	—
580	D₄	—	356	1	no	—
581	D₄	—	1424	2	no	—
582	D₄	—	178	2	no	—
583	D₄	—	178	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	356	1	no	—
592	C₂×C₄	—	356	1	no	—
593	C₂×C₄	—	356	1	no	—
594	C₂×C₄	—	356	1	no	—
595	C₂×C₄	—	356	1	no	—
596	C₂×C₄	—	1424	2	no	—
597	C₂×C₄	—	178	2	no	—
598	C₂×C₄	—	178	2	no	—
599	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
600	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
601	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
602	C₂×C₄	#15668057	1	1	yes	characteristic
603	C₂×C₄	#15668057	1	1	yes	characteristic
604	C₂×C₄	#15668058	1	1	yes	characteristic
605	C₈	—	2	2	no	—
606	C₈	—	4	1	no	—
607	C₈	—	4	1	no	—
608	C₈	—	356	1	no	—
609	C₈	—	178	2	no	—
610	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
611	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
612	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
613	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	356	2	no	—
620	C₂²	—	1424	1	no	—
621	C₂²	—	712	2	no	—
622	C₂²	—	712	2	no	—
623	C₂²	#19152070	1	1	yes	characteristic
624	C₂²	#19152162	1	1	yes	characteristic
625	C₂²	#19152199	1	1	yes	characteristic
626	C₄	—	4	2	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	356	2	no	—
630	C₄	—	356	2	no	—
631	C₄	—	712	1	no	—
632	C₄	—	712	1	no	—
633	C₄	—	712	1	no	—
634	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
635	C₄	#19152070	1	1	yes	characteristic
636	C₄	#19152165	1	1	yes	characteristic
637	C₄	#19152199	1	1	yes	characteristic
638	C₂	—	2	1	no	—
639	C₂	—	2	1	no	—
640	C₂	—	2	1	no	—
641	C₂	—	8	1	no	—
642	C₂	—	8	1	no	—
643	C₂	—	712	2	no	—
644	C₂	#26022974	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26022974
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2957	C₂
socle	C₂×C₈₉	#2328
prime radical	#26030729	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#2957	D₈₉
hypocenter	C₈₉	#22284
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2957

Complements

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

N	H ≅ G/N	type
2. #26029113	C₂	semidirect
3. #26021153	C₂	semidirect
4. #26021151	C₂	semidirect
5. #26020786	C₂	semidirect
6. #26020781	C₂	semidirect
7. #26020779	C₂	semidirect
8. #26020774	C₂	semidirect
9. #26020743	C₂	semidirect
10. #26020736	C₂	semidirect
11. #26020732	C₂	semidirect
12. #26020725	C₂	semidirect
13. #26020377	C₂	semidirect
14. #26020007	C₂	semidirect
15. C₈₉×#2957	C₂	semidirect
23. #19151991	C₄	semidirect
24. #19151986	C₄	semidirect
25. #19151979	C₄	semidirect
26. #19151969	C₄	semidirect
65. C₂×#13083564	C₂×C₄	semidirect
72. C₂×#13083562	C₂×C₄	semidirect
77. #15668010	C₂×C₄	semidirect
80. #15667999	C₂×C₄	semidirect
108. #15667922	C₂×C₄	semidirect
110. C₈×Dic₈₉	C₂×C₄	semidirect
117. C₂×Q₁₆×C₈₉	C₂×C₄	semidirect
118. C₂×SD₁₆×C₈₉	C₂×C₄	semidirect
119. C₂×SD₁₆×C₈₉	C₂×C₄	semidirect
120. C₂×D₈×C₈₉	C₂×C₄	semidirect
136. #97×C₈₉	D₄	semidirect
137. C₄×C₈×C₈₉	D₄	semidirect
324. #2957	D₈₉	semidirect
338. C₈₉	#22284	semidirect
395. C₂×Q₁₆	C₄×D₈₉	semidirect
404. C₂×SD₁₆	C₄×D₈₉	semidirect
405. C₂×SD₁₆	C₄×D₈₉	semidirect
407. C₂×D₈	C₄×D₈₉	semidirect
457. #97	C₂²⋊D₈₉	semidirect
460. C₄×C₈	C₂²⋊D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26030729	2
#26029113	2
#26021153	2
#26021151	2
#26020786	2
#26020781	2
#26020779	2
#26020774	2
#26020743	2
#26020736	2
#26020732	2
#26020725	2
#26020377	2
#26020007	2
C₈₉×#2957	2
#22284	89