Subgroups — #26031733

Order 11392.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668037	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13083559	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151988	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151849	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151829	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151810	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151793	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151748	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151743	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151732	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151731	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151708	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151670	C₂	1	1	yes	maximal, characteristic, complemented
15	#546×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic
17	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
18	C₂×D₄×D₈₉	—	2	1	no	—
19	#15668037	—	2	4	no	—
20	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083559	—	2	4	no	—
24	C₂×#13083559	C₂²	1	1	yes	characteristic
25	C₂×#13083559	C₂²	1	1	yes	characteristic
26	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
29	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
30	C₂×#13083558	C₂²	1	1	yes	characteristic, complemented
31	C₂²×#10623494	C₂²	1	1	yes	characteristic, complemented
32	#15668009	C₂²	1	1	yes	characteristic, complemented
33	#15667987	—	2	1	no	—
34	#15667986	C₂²	1	1	yes	characteristic
35	#15667986	C₂²	1	1	yes	characteristic, complemented
36	#15667982	—	2	1	no	—
37	#15667982	—	2	1	no	—
38	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
39	#15667943	C₂²	1	1	yes	characteristic, complemented
40	C₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
41	#15667936	C₂²	1	1	yes	characteristic, complemented
42	#15667933	C₂²	1	1	yes	characteristic, complemented
43	#15667933	C₂²	1	1	yes	characteristic, complemented
44	#15667932	C₂²	1	1	yes	characteristic, complemented
45	#15667932	C₂²	1	1	yes	characteristic, complemented
46	#15667932	C₂²	1	1	yes	characteristic, complemented
47	C₂²⋊#10623494	C₂²	1	1	yes	characteristic, complemented
48	C₂²⋊#10623494	C₂²	1	1	yes	characteristic, complemented
49	#15667923	C₂²	1	1	yes	characteristic, complemented
50	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#123×C₈₉	—	2	1	no	—
54	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#121×C₈₉	—	2	1	no	—
56	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#120×C₈₉	—	2	1	no	—
58	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
59	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
61	C₂³×D₈₉	—	2	1	no	—
62	C₂³×D₈₉	—	2	1	no	—
63	C₂×D₃₅₆	—	2	2	no	—
64	C₂×D₃₅₆	—	2	2	no	—
65	C₂×D₃₅₆	—	2	1	no	—
66	C₂×D₃₅₆	—	2	1	no	—
67	C₂×D₃₅₆	—	2	1	no	—
68	C₂×D₃₅₆	—	2	1	no	—
69	C₂×D₃₅₆	—	4	1	no	—
70	C₂×D₃₅₆	—	4	1	no	—
71	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
72	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
73	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊D₈₉	—	2	1	no	—
75	C₂×C₂²⋊D₈₉	—	2	1	no	—
76	D₄×D₈₉	—	4	4	no	—
77	C₂×C₄×D₈₉	—	2	1	no	—
78	#13083561	—	2	2	no	—
79	#13083561	—	2	2	no	—
80	#13083561	—	4	1	no	—
81	#13083559	—	2	2	no	—
82	#13083559	—	2	2	no	—
83	#13083559	—	2	2	no	—
84	#13083559	—	2	2	no	—
85	#13083559	—	4	1	no	—
86	#13083559	D₄	1	4	yes	complemented
87	#13083558	—	2	2	no	—
88	C₂×#10623494	—	2	2	no	—
89	C₂×#10623494	C₂³	1	1	yes	characteristic
90	C₂×#10623494	C₂³	1	1	yes	characteristic
91	C₂×#10623494	C₂³	1	1	yes	characteristic
92	C₂×#10623494	C₂³	1	1	yes	characteristic
93	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
94	#13083551	—	2	1	no	—
95	#13083551	—	2	1	no	—
96	#13083551	—	2	1	no	—
97	C₂⁴×C₈₉	—	2	1	no	—
98	#41×C₈₉	—	2	2	no	—
99	#41×C₈₉	—	4	1	no	—
100	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×D₄×C₈₉	—	2	2	no	—
102	C₂×D₄×C₈₉	—	2	1	no	—
103	C₂×D₄×C₈₉	—	2	1	no	—
104	C₂×D₄×C₈₉	—	2	1	no	—
105	C₂×D₄×C₈₉	—	4	1	no	—
106	C₂×D₄×C₈₉	D₄	1	1	yes	characteristic
107	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₈₉	—	2	1	no	—
110	C₂²×C₄×C₈₉	—	2	1	no	—
111	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₈₉	—	2	1	no	—
114	C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
115	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂²⋊C₄×C₈₉	—	2	1	no	—
117	C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₂²⋊C₄×C₈₉	—	2	1	no	—
119	C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂²⋊C₄×C₈₉	—	2	1	no	—
121	C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
122	C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
123	C₄²×C₈₉	C₂³	1	1	yes	characteristic
124	C₂³×C₈₉	—	2	1	no	—
125	C₂³×C₈₉	—	2	1	no	—
126	C₂³×C₈₉	—	4	2	no	—
127	C₂³×C₈₉	—	4	2	no	—
128	C₂³×C₈₉	—	8	1	no	—
129	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×D₈₉	—	2	1	no	—
132	C₂²×D₈₉	—	2	1	no	—
133	C₂²×D₈₉	—	2	1	no	—
134	C₂²×D₈₉	—	4	2	no	—
135	C₂²×D₈₉	—	4	2	no	—
136	C₂²×D₈₉	—	4	2	no	—
137	C₂²×D₈₉	—	4	2	no	—
138	C₂²×D₈₉	—	8	1	no	—
139	C₂²×D₈₉	—	8	1	no	—
140	Q₈×C₈₉	—	2	1	no	—
141	Q₈×C₈₉	—	2	1	no	—
142	D₄×C₈₉	—	2	2	no	—
143	D₄×C₈₉	—	2	1	no	—
144	D₄×C₈₉	—	2	1	no	—
145	D₄×C₈₉	—	2	1	no	—
146	D₄×C₈₉	—	4	2	no	—
147	D₄×C₈₉	—	4	2	no	—
148	D₄×C₈₉	—	8	1	no	—
149	D₄×C₈₉	C₂×D₄	1	2	yes	complemented
150	C₂×C₄×C₈₉	—	2	1	no	—
151	C₂×C₄×C₈₉	—	2	1	no	—
152	C₂×C₄×C₈₉	—	2	1	no	—
153	C₂×C₄×C₈₉	—	2	1	no	—
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	4	2	no	—
157	C₂×C₄×C₈₉	—	8	1	no	—
158	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
163	C₂²⋊D₈₉	—	4	2	no	—
164	C₂²⋊D₈₉	—	4	2	no	—
165	C₂×Dic₈₉	—	2	1	no	—
166	D₃₅₆	—	2	1	no	—
167	D₃₅₆	—	2	1	no	—
168	D₃₅₆	—	2	1	no	—
169	D₃₅₆	—	2	1	no	—
170	D₃₅₆	—	2	1	no	—
171	D₃₅₆	—	4	2	no	—
172	D₃₅₆	—	4	2	no	—
173	D₃₅₆	—	4	2	no	—
174	D₃₅₆	—	8	1	no	—
175	D₃₅₆	C₂×D₄	1	2	yes	—
176	C₄×D₈₉	—	4	2	no	—
177	#10623494	—	2	1	no	—
178	#10623494	—	2	1	no	—
179	#10623494	—	2	1	no	—
180	#10623494	C₂×D₄	1	2	yes	complemented
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	—	2	1	no	—
183	C₂²×C₈₉	—	2	1	no	—
184	C₂²×C₈₉	—	2	2	no	—
185	C₂²×C₈₉	—	2	1	no	—
186	C₂²×C₈₉	—	2	1	no	—
187	C₂²×C₈₉	—	4	1	no	—
188	C₂²×C₈₉	—	4	1	no	—
189	C₂²×C₈₉	—	4	1	no	—
190	C₂²×C₈₉	—	4	1	no	—
191	C₂²×C₈₉	—	4	1	no	—
192	C₂²×C₈₉	—	8	4	no	—
193	C₂²×C₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
194	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×D₈₉	—	2	2	no	—
196	C₂×D₈₉	—	4	1	no	—
197	C₂×D₈₉	—	4	1	no	—
198	C₂×D₈₉	—	4	1	no	—
199	C₂×D₈₉	—	4	1	no	—
200	C₂×D₈₉	—	4	1	no	—
201	C₂×D₈₉	—	4	1	no	—
202	C₂×D₈₉	—	4	1	no	—
203	C₂×D₈₉	—	4	1	no	—
204	C₂×D₈₉	—	8	4	no	—
205	C₂×D₈₉	—	8	4	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	2	1	no	—
208	C₄×C₈₉	—	2	1	no	—
209	C₄×C₈₉	—	2	1	no	—
210	C₄×C₈₉	—	4	1	no	—
211	C₄×C₈₉	—	4	1	no	—
212	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
213	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
214	Dic₈₉	—	4	1	no	—
215	C₂×C₈₉	—	2	2	no	—
216	C₂×C₈₉	—	4	1	no	—
217	C₂×C₈₉	—	4	2	no	—
218	C₂×C₈₉	—	8	1	no	—
219	C₂×C₈₉	D₄²	1	1	yes	characteristic
220	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₂×C₈₉	#576	1	1	yes	characteristic
222	D₈₉	—	4	2	no	—
223	D₈₉	—	8	1	no	—
224	D₈₉	—	8	1	no	—
225	#3264	—	89	1	no	maximal, Sylow
226	C₈₉	#3264	1	1	yes	characteristic, complemented, Sylow
227	C₂×AGL(1,ℤ/8)	—	89	1	no	—
228	C₂²×D₈	—	89	1	no	—
229	#546	D₈₉	1	1	yes	characteristic, complemented
230	D₄²	—	89	1	no	—
231	#496	—	89	1	no	—
232	#469	—	89	1	no	—
233	#465	—	89	1	no	—
234	#463	—	89	1	no	—
235	#459	—	89	1	no	—
236	#450	—	89	1	no	—
237	#449	—	89	1	no	—
238	#447	—	89	1	no	—
239	#447	—	89	1	no	—
240	#442	—	89	1	no	—
241	#435	—	89	1	no	—
242	C₂×#41	C₂×D₈₉	1	1	yes	characteristic, complemented
243	C₂²×D₄	—	89	1	no	—
244	C₂²×D₄	—	89	1	no	—
245	C₂²×D₄	—	178	1	no	—
246	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
247	AGL(1,ℤ/8)	—	178	4	no	—
248	C₂×SD₁₆	—	89	1	no	—
249	C₂×SD₁₆	—	89	1	no	—
250	C₂×SD₁₆	—	89	1	no	—
251	C₂×D₈	—	89	1	no	—
252	C₂×D₈	—	89	1	no	—
253	C₂×D₈	—	89	1	no	—
254	C₂×D₈	—	89	1	no	—
255	C₂×D₈	—	89	1	no	—
256	C₂×D₈	—	89	1	no	—
257	C₂×D₈	—	178	4	no	—
258	C₂×M₁₆	—	89	1	no	—
259	C₂²×C₈	—	89	1	no	—
260	#127	—	89	1	no	—
261	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
262	#123	—	2	1	no	—
263	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
264	#121	—	2	1	no	—
265	#121	—	89	1	no	—
266	#121	—	89	1	no	—
267	#121	—	178	1	no	—
268	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
269	#120	—	2	1	no	—
270	#120	—	178	1	no	—
271	#120	—	178	1	no	—
272	C₄×D₄	—	89	1	no	—
273	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
274	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	#106	—	89	1	no	—
277	C₄⋊C₈	—	89	1	no	—
278	#103	—	89	1	no	—
279	#102	—	89	1	no	—
280	#102	—	89	1	no	—
281	#102	—	89	1	no	—
282	#102	—	89	1	no	—
283	#102	—	89	1	no	—
284	C₂²⋊C₈	—	89	1	no	—
285	C₂²⋊C₈	—	89	1	no	—
286	#97	—	89	1	no	—
287	C₂⁴	—	2	1	no	—
288	C₂⁴	—	178	1	no	—
289	C₂⁴	—	178	1	no	—
290	#41	—	2	2	no	—
291	#41	—	4	1	no	—
292	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	89	1	no	—
299	C₂×D₄	—	89	1	no	—
300	C₂×D₄	—	89	1	no	—
301	C₂×D₄	—	356	1	no	—
302	C₂×D₄	—	356	1	no	—
303	C₂×D₄	—	356	4	no	—
304	C₂×D₄	—	178	2	no	—
305	C₂×D₄	—	178	2	no	—
306	C₂×D₄	—	178	1	no	—
307	C₂×D₄	—	178	1	no	—
308	C₂×D₄	—	178	1	no	—
309	C₂×D₄	—	178	1	no	—
310	C₂×D₄	—	178	1	no	—
311	C₂×D₄	—	178	1	no	—
312	C₂×D₄	C₂²⋊D₈₉	1	1	yes	characteristic
313	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
314	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	178	1	no	—
318	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
320	SD₁₆	—	356	1	no	—
321	SD₁₆	—	178	2	no	—
322	SD₁₆	—	178	2	no	—
323	D₈	—	89	4	no	—
324	D₈	—	356	1	no	—
325	D₈	—	178	2	no	—
326	D₈	—	178	2	no	—
327	D₈	—	178	2	no	—
328	D₈	—	178	2	no	—
329	M₁₆	—	178	2	no	—
330	C₂×C₈	—	89	1	no	—
331	C₂×C₈	—	89	1	no	—
332	C₂×C₈	—	89	1	no	—
333	C₂×C₈	—	89	1	no	—
334	C₂×C₈	—	178	2	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	89	1	no	—
337	C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
338	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	178	1	no	—
345	C₂²⋊C₄	—	178	1	no	—
346	C₂²⋊C₄	—	178	1	no	—
347	C₂²⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
348	C₂²⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
349	C₄²	C₂²×D₈₉	1	1	yes	characteristic
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	8	1	no	—
355	C₂³	—	356	2	no	—
356	C₂³	—	356	2	no	—
357	C₂³	—	356	2	no	—
358	C₂³	—	356	2	no	—
359	C₂³	—	178	1	no	—
360	C₂³	—	178	1	no	—
361	C₂³	—	178	1	no	—
362	C₂³	—	712	1	no	—
363	C₂³	—	712	1	no	—
364	C₂³	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
365	C₂³	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
366	Q₈	—	2	1	no	—
367	Q₈	—	2	1	no	—
368	D₄	—	2	2	no	—
369	D₄	—	2	1	no	—
370	D₄	—	2	1	no	—
371	D₄	—	2	1	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	8	1	no	—
375	D₄	—	89	2	no	—
376	D₄	—	356	2	no	—
377	D₄	—	356	2	no	—
378	D₄	—	356	2	no	—
379	D₄	—	356	2	no	—
380	D₄	—	356	2	no	—
381	D₄	—	178	1	no	—
382	D₄	—	178	1	no	—
383	D₄	—	178	1	no	—
384	D₄	—	178	1	no	—
385	D₄	—	178	1	no	—
386	D₄	—	712	1	no	—
387	D₄	D₄×D₈₉	1	2	yes	complemented
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	1	no	—
396	C₂×C₄	—	356	2	no	—
397	C₂×C₄	—	178	1	no	—
398	C₂×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
399	C₂×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
400	C₂×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
401	C₂×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
403	C₈	—	89	2	no	—
404	C₈	—	178	1	no	—
405	C₈	—	178	1	no	—
406	C₈	—	178	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	8	4	no	—
419	C₂²	—	356	1	no	—
420	C₂²	—	356	1	no	—
421	C₂²	—	356	1	no	—
422	C₂²	—	356	1	no	—
423	C₂²	—	356	1	no	—
424	C₂²	—	356	1	no	—
425	C₂²	—	356	1	no	—
426	C₂²	—	356	1	no	—
427	C₂²	—	178	2	no	—
428	C₂²	—	712	4	no	—
429	C₂²	—	712	4	no	—
430	C₂²	#15668037	1	2	yes	complemented
431	C₂²	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	356	1	no	—
439	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
440	C₄	#15668057	1	1	yes	characteristic
441	C₂	—	2	2	no	—
442	C₂	—	4	1	no	—
443	C₂	—	4	2	no	—
444	C₂	—	8	1	no	—
445	C₂	—	356	2	no	—
446	C₂	—	712	1	no	—
447	C₂	—	712	1	no	—
448	C₂	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
449	C₂	C₂×#15668037	1	1	yes	characteristic
450	C₂	#19152401	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#546×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	#546	D₈₉
hypocenter	C₈₉	#3264
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₂×#15668037	C₂	semidirect
2. C₂²×#13083559	C₂	semidirect
3. D₄×D₃₅₆	C₂	semidirect
4. #19151988	C₂	semidirect
5. #19151849	C₂	semidirect
6. #19151829	C₂	semidirect
7. #19151810	C₂	semidirect
8. #19151793	C₂	semidirect
9. #19151748	C₂	semidirect
10. #19151743	C₂	semidirect
11. #19151732	C₂	semidirect
12. #19151731	C₂	semidirect
13. #19151708	C₂	semidirect
14. #19151670	C₂	semidirect
15. #546×C₈₉	C₂	semidirect
17. C₂²×D₃₅₆	C₂²	semidirect
20. C₂×#13083561	C₂²	semidirect
21. C₂×#13083561	C₂²	semidirect
22. C₂×#13083561	C₂²	semidirect
26. C₂×#13083559	C₂²	semidirect
27. C₂×#13083559	C₂²	semidirect
28. C₂×#13083559	C₂²	semidirect
29. C₂×#13083559	C₂²	semidirect
30. C₂×#13083558	C₂²	semidirect
31. C₂²×#10623494	C₂²	semidirect
32. #15668009	C₂²	semidirect
35. #15667986	C₂²	semidirect
38. C₄×D₃₅₆	C₂²	semidirect
39. #15667943	C₂²	semidirect
40. C₄⋊#10623494	C₂²	semidirect
41. #15667936	C₂²	semidirect
42. #15667933	C₂²	semidirect
43. #15667933	C₂²	semidirect
44. #15667932	C₂²	semidirect
45. #15667932	C₂²	semidirect
46. #15667932	C₂²	semidirect
47. C₂²⋊#10623494	C₂²	semidirect
48. C₂²⋊#10623494	C₂²	semidirect
49. #15667923	C₂²	semidirect
50. C₂×#41×C₈₉	C₂²	semidirect
51. C₂²×D₄×C₈₉	C₂²	semidirect
52. #124×C₈₉	C₂²	semidirect
54. C₂²⋊Q₈×C₈₉	C₂²	semidirect
56. #121×C₈₉	C₂²	semidirect
59. C₄×D₄×C₈₉	C₂²	semidirect
86. #13083559	D₄	semidirect
149. D₄×C₈₉	C₂×D₄	semidirect
180. #10623494	C₂×D₄	semidirect
193. C₂²×C₈₉	AGL(1,ℤ/8)	semidirect
226. C₈₉	#3264	semidirect
229. #546	D₈₉	semidirect
242. C₂×#41	C₂×D₈₉	semidirect
246. C₂²×D₄	C₂×D₈₉	semidirect
261. #124	C₂×D₈₉	semidirect
263. C₂²⋊Q₈	C₂×D₈₉	semidirect
268. #121	C₂×D₈₉	semidirect
274. C₄×D₄	C₂×D₈₉	semidirect
387. D₄	D₄×D₈₉	semidirect
430. C₂²	#15668037	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15668037	2
C₂²×#13083559	2
D₄×D₃₅₆	2
#19151988	2
#19151849	2
#19151829	2
#19151810	2
#19151793	2
#19151748	2
#19151743	2
#19151732	2
#19151731	2
#19151708	2
#19151670	2
#546×C₈₉	2
#3264	89