Subgroups — #36572887

Order 22784.

858 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151721	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151716	C₂	1	1	yes	maximal, characteristic
3	#26029054	C₂	1	1	yes	maximal, characteristic
4	#26028817	C₂	1	2	yes	maximal, complemented
5	#26021005	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021000	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020530	C₂	1	2	yes	maximal, complemented
8	#26020530	C₂	1	2	yes	maximal, complemented
9	#26020427	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020273	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	C₂²	1	1	yes	characteristic
13	C₂×#15668018	C₂²	1	2	yes	—
14	C₂×#15668018	C₂²	1	2	yes	—
15	C₄×#13083574	C₂²	1	2	yes	—
16	#19151721	—	2	4	no	—
17	#19151716	—	2	4	no	—
18	#19151711	C₄	1	2	yes	complemented
19	#19151706	C₄	1	2	yes	complemented
20	#19151700	C₄	1	2	yes	complemented
21	#19151700	C₄	1	2	yes	complemented
22	C₂×#15667948	C₂²	1	1	yes	characteristic
23	C₂×#15667948	C₂²	1	1	yes	characteristic
24	C₂×#15667948	C₂²	1	2	yes	—
25	#19151636	C₂²	1	1	yes	characteristic
26	#19151624	C₂²	1	2	yes	—
27	#19151624	C₂²	1	2	yes	—
28	#19151623	—	2	2	no	—
29	#19151623	—	2	2	no	—
30	#19151622	C₂²	1	2	yes	—
31	#19151620	—	2	2	no	—
32	C₄⋊C₈×D₈₉	—	2	2	no	—
33	C₂×#15667940	C₂²	1	2	yes	—
34	C₂×#15667940	C₂²	1	2	yes	—
35	#19151595	C₂²	1	2	yes	—
36	#19151358	C₂²	1	2	yes	—
37	#19151358	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
43	#336×C₈₉	C₂²	1	1	yes	characteristic
44	#336×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#13083574	C₂³	1	2	yes	—
46	#15668034	D₄	1	4	yes	—
47	#15668034	Q₈	1	4	yes	—
48	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
49	C₂×#13083563	C₂×C₄	1	2	yes	—
50	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
51	#15668018	—	2	4	no	—
52	#15668018	—	2	4	no	—
53	#15668018	—	4	2	no	—
54	#15668018	—	4	2	no	—
55	C₂×#13083558	C₂³	1	2	yes	—
56	C₂×#13083558	C₂³	1	2	yes	—
57	C₂×#13083557	—	2	2	no	—
58	C₂×#13083557	—	2	2	no	—
59	C₂×C₈×D₈₉	—	2	2	no	—
60	C₂×C₈×D₈₉	—	2	2	no	—
61	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
62	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
63	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
64	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
65	C₄×C₂²⋊D₈₉	—	2	2	no	—
66	C₄×C₂²⋊D₈₉	—	2	2	no	—
67	#15667971	C₂³	1	2	yes	—
68	#15667969	—	2	2	no	—
69	C₄²×D₈₉	—	2	2	no	—
70	#15667948	—	2	2	no	—
71	#15667948	—	2	2	no	—
72	#15667948	—	4	2	no	—
73	#15667946	C₂×C₄	1	1	yes	characteristic
74	#15667946	C₂×C₄	1	1	yes	characteristic
75	#15667944	C₂×C₄	1	2	yes	—
76	C₄⋊#10623494	—	2	2	no	—
77	C₄⋊#10623494	—	2	2	no	—
78	#15667941	—	2	2	no	—
79	#15667941	—	2	2	no	—
80	#15667941	—	2	2	no	—
81	#15667941	—	2	2	no	—
82	#15667940	—	2	4	no	—
83	#15667940	—	2	4	no	—
84	#15667937	C₂×C₄	1	2	yes	—
85	#15667937	C₂×C₄	1	2	yes	—
86	#15667934	C₂×C₄	1	2	yes	—
87	#15667934	C₂×C₄	1	2	yes	—
88	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
93	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
97	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
98	#97×C₈₉	—	2	2	no	—
99	#97×C₈₉	C₂×C₄	1	2	yes	—
100	#97×C₈₉	C₂×C₄	1	2	yes	—
101	C₄×C₈×C₈₉	—	2	2	no	—
102	#95×C₈₉	—	2	1	no	—
103	#13083574	—	2	2	no	—
104	#13083574	—	2	2	no	—
105	#13083574	C₂×D₄	1	4	yes	—
106	#13083574	C₂×Q₈	1	4	yes	—
107	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
108	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
109	C₂×C₂²⋊D₈₉	—	2	2	no	—
110	C₂×C₄×D₈₉	—	2	2	no	—
111	C₂×C₄×D₈₉	—	2	2	no	—
112	C₂×C₄×D₈₉	—	2	2	no	—
113	Dic₃₅₆	C₄⋊C₄	1	4	yes	complemented
114	#13083563	C₄⋊C₄	1	8	yes	complemented
115	D₇₁₂	C₄⋊C₄	1	4	yes	complemented
116	#13083558	—	2	2	no	—
117	#13083558	—	2	2	no	—
118	#13083558	—	2	2	no	—
119	#13083558	—	2	2	no	—
120	#13083557	—	4	4	no	—
121	#13083557	—	4	4	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₈×D₈₉	—	4	4	no	—
125	C₈×D₈₉	—	4	4	no	—
126	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
127	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
128	#13083553	—	2	2	no	—
129	#13083553	—	2	2	no	—
130	C₂²⋊Dic₈₉	—	2	2	no	—
131	#13083551	—	2	2	no	—
132	#13083551	—	2	2	no	—
133	C₄×Dic₈₉	—	2	2	no	—
134	C₄×Dic₈₉	—	2	2	no	—
135	C₄×Dic₈₉	—	2	2	no	—
136	C₂²×C₄×C₈₉	—	2	1	no	—
137	C₂²×C₄×C₈₉	—	2	1	no	—
138	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
140	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
141	C₂×C₈×C₈₉	—	2	1	no	—
142	C₂×C₈×C₈₉	—	2	1	no	—
143	C₂×C₈×C₈₉	—	2	1	no	—
144	C₂×C₈×C₈₉	—	2	1	no	—
145	C₂×C₈×C₈₉	—	2	1	no	—
146	C₂×C₈×C₈₉	—	2	1	no	—
147	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
155	C₄⋊C₄×C₈₉	—	4	2	no	—
156	C₄²×C₈₉	—	2	1	no	—
157	C₄²×C₈₉	—	2	1	no	—
158	C₄²×C₈₉	—	2	1	no	—
159	C₄²×C₈₉	—	2	1	no	—
160	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
161	C₄²×C₈₉	C₂×D₄	1	2	yes	—
162	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
163	C₂²×D₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	2	2	no	—
165	C₂×C₄×C₈₉	—	4	1	no	—
166	C₂×C₄×C₈₉	—	4	1	no	—
167	C₂×C₄×C₈₉	—	4	1	no	—
168	C₂×C₄×C₈₉	—	4	1	no	—
169	C₂×C₄×C₈₉	—	4	1	no	—
170	C₂×C₄×C₈₉	—	4	1	no	—
171	C₂×C₄×C₈₉	—	4	1	no	—
172	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
180	C₂²⋊D₈₉	—	2	4	no	—
181	C₂²⋊D₈₉	—	2	4	no	—
182	C₂×Dic₈₉	—	2	2	no	—
183	C₂×Dic₈₉	—	2	2	no	—
184	C₂×Dic₈₉	—	2	2	no	—
185	D₃₅₆	—	2	2	no	—
186	D₃₅₆	C₂×C₄⋊C₄	1	4	yes	—
187	C₄×D₈₉	—	2	4	no	—
188	C₄×D₈₉	—	2	4	no	—
189	C₄×D₈₉	—	4	4	no	—
190	C₄×D₈₉	—	8	2	no	—
191	Dic₁₇₈	—	2	2	no	—
192	Dic₁₇₈	C₂×C₄⋊C₄	1	4	yes	—
193	C₈×C₈₉	—	2	2	no	—
194	C₈×C₈₉	—	2	1	no	—
195	C₈×C₈₉	—	2	2	no	—
196	C₈×C₈₉	—	2	1	no	—
197	C₈×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
198	C₈×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
199	#10623494	—	4	2	no	—
200	#10623494	—	4	2	no	—
201	C₂²×C₈₉	—	2	1	no	—
202	C₂²×C₈₉	—	2	1	no	—
203	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
204	C₂²×C₈₉	#547	1	1	yes	characteristic
205	C₂²×C₈₉	#554	1	1	yes	characteristic
206	C₂×D₈₉	—	2	4	no	—
207	C₂×D₈₉	—	4	2	no	—
208	C₂×D₈₉	—	4	2	no	—
209	C₄×C₈₉	—	2	2	no	—
210	C₄×C₈₉	—	2	2	no	—
211	C₄×C₈₉	—	4	2	no	—
212	C₄×C₈₉	—	8	1	no	—
213	C₄×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
214	C₄×C₈₉	#520	1	1	yes	characteristic
215	C₄×C₈₉	D₄²	1	1	yes	characteristic
216	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
217	Dic₈₉	—	2	4	no	—
218	Dic₈₉	—	4	2	no	—
219	Dic₈₉	—	4	2	no	—
220	#22687	—	89	1	no	maximal, Sylow
221	C₂×C₈₉	—	2	1	no	—
222	C₂×C₈₉	—	2	1	no	—
223	C₂×C₈₉	D₄×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₈₉	#2955	1	1	yes	characteristic
225	C₂×C₈₉	#2956	1	1	yes	characteristic
226	D₈₉	—	4	4	no	—
227	C₂×#444	—	89	1	no	—
228	C₂×#443	—	89	1	no	—
229	#2943	—	89	1	no	—
230	#2906	—	89	2	no	—
231	#1946	—	89	1	no	—
232	#1945	—	89	1	no	—
233	#1866	—	89	2	no	—
234	#1866	—	89	2	no	—
235	#1849	—	89	1	no	—
236	#1806	—	89	2	no	—
237	#1771	D₈₉	1	1	yes	characteristic, complemented
238	C₈₉	#22687	1	1	yes	characteristic, complemented, Sylow
239	C₂×#135	—	89	1	no	—
240	C₂×#131	—	89	2	no	—
241	C₂×#131	—	89	2	no	—
242	C₄×#41	—	89	2	no	—
243	#444	—	178	4	no	—
244	#443	—	178	4	no	—
245	#442	—	89	2	no	—
246	#441	—	89	2	no	—
247	#440	—	89	2	no	—
248	#440	—	89	2	no	—
249	C₂×#108	—	89	2	no	—
250	C₂×#108	—	89	1	no	—
251	C₂×#108	—	89	1	no	—
252	#427	—	89	1	no	—
253	#424	—	89	2	no	—
254	#424	—	89	2	no	—
255	#424	—	178	2	no	—
256	#424	—	178	2	no	—
257	#423	—	89	2	no	—
258	#423	—	178	2	no	—
259	C₂×C₄⋊C₈	—	178	2	no	—
260	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
261	C₂×#104	—	89	2	no	—
262	C₂×#104	—	89	2	no	—
263	#416	—	89	2	no	—
264	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
265	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
266	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
267	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
268	#339	—	89	2	no	—
269	#339	—	89	2	no	—
270	#336	C₂×D₈₉	1	1	yes	characteristic
271	#336	C₂×D₈₉	1	1	yes	characteristic
272	C₂×#41	—	89	2	no	—
273	#135	—	89	4	no	—
274	#135	—	89	4	no	—
275	C₂×Q₁₆	—	89	1	no	—
276	C₂×SD₁₆	—	89	2	no	—
277	C₂×D₈	—	89	1	no	—
278	#131	—	356	2	no	—
279	#131	—	356	2	no	—
280	#131	—	178	4	no	—
281	#131	—	178	4	no	—
282	C₂×M₁₆	—	89	2	no	—
283	C₂×M₁₆	—	89	2	no	—
284	C₂×M₁₆	—	178	2	no	—
285	C₂×M₁₆	—	178	2	no	—
286	C₂²×C₈	—	178	2	no	—
287	C₂²×C₈	—	178	2	no	—
288	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
290	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
291	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
292	C₄×Q₈	—	89	2	no	—
293	C₄×Q₈	—	89	2	no	—
294	C₄×D₄	—	89	2	no	—
295	C₄×D₄	—	89	2	no	—
296	C₄×D₄	—	178	2	no	—
297	C₄×D₄	—	178	2	no	—
298	#117	—	89	2	no	—
299	#117	—	178	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄²	—	178	2	no	—
302	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
303	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
304	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
305	#108	—	356	2	no	—
306	#108	—	178	2	no	—
307	#108	—	178	2	no	—
308	#107	—	89	1	no	—
309	#107	—	89	1	no	—
310	#106	—	89	2	no	—
311	C₄⋊C₈	—	178	2	no	—
312	C₄⋊C₈	—	178	2	no	—
313	C₄⋊C₈	—	178	2	no	—
314	C₄⋊C₈	—	178	2	no	—
315	C₄⋊C₈	—	178	2	no	—
316	C₄⋊C₈	—	178	2	no	—
317	C₄⋊C₈	D₃₅₆	1	2	yes	—
318	C₄⋊C₈	D₃₅₆	1	2	yes	—
319	#104	—	178	4	no	—
320	#104	—	178	4	no	—
321	#103	—	89	2	no	—
322	#103	—	89	2	no	—
323	#102	—	89	2	no	—
324	#102	—	89	2	no	—
325	#97	—	2	2	no	—
326	#97	C₄×D₈₉	1	2	yes	—
327	#97	C₄×D₈₉	1	2	yes	—
328	C₄×C₈	—	2	2	no	—
329	#95	—	2	1	no	—
330	#41	—	89	4	no	—
331	#41	—	89	4	no	—
332	#41	—	178	2	no	—
333	#41	—	178	2	no	—
334	C₂×Q₈	—	89	2	no	—
335	C₂×D₄	—	89	2	no	—
336	C₂×D₄	—	178	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	178	2	no	—
340	C₂²×C₄	—	178	2	no	—
341	C₂²×C₄	—	178	2	no	—
342	C₂²×C₄	#13083574	1	1	yes	characteristic
343	C₂²×C₄	#13083574	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
345	Q₁₆	—	89	4	no	—
346	SD₁₆	—	89	8	no	—
347	D₈	—	89	4	no	—
348	M₁₆	—	356	4	no	—
349	M₁₆	—	356	4	no	—
350	M₁₆	—	178	2	no	—
351	M₁₆	—	178	2	no	—
352	M₁₆	—	178	2	no	—
353	M₁₆	—	178	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	356	4	no	—
361	C₂×C₈	—	356	4	no	—
362	C₂×C₈	—	178	2	no	—
363	C₂×C₈	—	178	2	no	—
364	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
365	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
367	C₂×C₈	D₄×D₈₉	1	2	yes	—
368	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
369	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
370	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
371	C₂×C₈	Q₈×D₈₉	1	2	yes	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	89	2	no	—
374	C₄⋊C₄	—	89	2	no	—
375	C₄⋊C₄	—	178	2	no	—
376	C₄⋊C₄	—	178	2	no	—
377	C₂²⋊C₄	—	178	2	no	—
378	C₂²⋊C₄	—	178	2	no	—
379	C₂²⋊C₄	—	178	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	178	2	no	—
385	C₄²	—	178	2	no	—
386	C₄²	—	178	2	no	—
387	C₄²	C₂×C₄×D₈₉	1	2	yes	—
388	C₄²	C₂×D₃₅₆	1	2	yes	—
389	C₂³	—	178	2	no	—
390	C₂³	C₂×#13083574	1	1	yes	characteristic
391	Q₈	—	89	4	no	—
392	Q₈	—	178	2	no	—
393	D₄	—	89	4	no	—
394	D₄	—	178	4	no	—
395	D₄	—	178	4	no	—
396	D₄	—	178	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	356	4	no	—
406	C₂×C₄	—	178	2	no	—
407	C₂×C₄	—	178	2	no	—
408	C₂×C₄	—	178	2	no	—
409	C₂×C₄	—	178	4	no	—
410	C₂×C₄	—	178	4	no	—
411	C₂×C₄	—	712	2	no	—
412	C₂×C₄	C₄×D₃₅₆	1	2	yes	—
413	C₂×C₄	C₄×D₃₅₆	1	2	yes	—
414	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
417	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
418	C₂×C₄	#15668058	1	1	yes	characteristic
419	C₂×C₄	#15668059	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	2	2	no	—
422	C₈	—	2	1	no	—
423	C₈	—	2	2	no	—
424	C₈	—	356	2	no	—
425	C₈	—	356	2	no	—
426	C₈	C₄⋊C₄×D₈₉	1	2	yes	—
427	C₈	C₄⋊C₄×D₈₉	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	356	2	no	—
431	C₂²	—	356	2	no	—
432	C₂²	—	178	4	no	—
433	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
434	C₂²	#19152253	1	1	yes	characteristic
435	C₂²	#19152308	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	8	1	no	—
440	C₄	—	356	2	no	—
441	C₄	—	356	2	no	—
442	C₄	—	178	4	no	—
443	C₄	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
444	C₄	#19152078	1	1	yes	characteristic
445	C₄	D₄×D₃₅₆	1	1	yes	characteristic
446	C₄	Q₈×D₃₅₆	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	356	4	no	—
450	C₂	C₄⋊C₄×D₃₅₆	1	1	yes	characteristic
451	C₂	#26029156	1	1	yes	characteristic
452	C₂	#26029163	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1771	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668034	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1771	D₈₉
hypocenter	C₈₉	#22687
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #1771

Complements

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

N	H ≅ G/N	type
4. #26028817	C₂	semidirect
5. #26021005	C₂	semidirect
6. #26021000	C₂	semidirect
7. #26020530	C₂	semidirect
8. #26020530	C₂	semidirect
9. #26020427	C₂	semidirect
10. #26020273	C₂	semidirect
11. C₈₉×#1771	C₂	semidirect
18. #19151711	C₄	semidirect
19. #19151706	C₄	semidirect
20. #19151700	C₄	semidirect
21. #19151700	C₄	semidirect
113. Dic₃₅₆	C₄⋊C₄	semidirect
114. #13083563	C₄⋊C₄	semidirect
115. D₇₁₂	C₄⋊C₄	semidirect
237. #1771	D₈₉	semidirect
238. C₈₉	#22687	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151721	2
C₂×#19151716	2
#26029054	2
#26028817	2
#26021005	2
#26021000	2
#26020530	2
#26020427	2
#26020273	2
C₈₉×#1771	2
#22687	89