Subgroups — #36538314

Order 22784.

786 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×#19151971	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030067	C₂	1	1	yes	maximal, characteristic, complemented
3	#26029732	C₂	1	1	yes	maximal, characteristic
4	#26019600	C₂	1	4	yes	maximal, complemented
5	#26019593	C₂	1	4	yes	maximal, complemented
6	#26019008	C₂	1	1	yes	maximal, characteristic, complemented
7	#26018936	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018919	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15668037	—	2	1	no	—
11	C₂²×#13083563	—	2	2	no	—
12	C₂×#15668012	C₂²	1	1	yes	characteristic
13	C₂×#15668009	C₂²	1	1	yes	characteristic
14	#19151971	—	2	1	no	—
15	#19151971	—	2	1	no	—
16	#19151971	C₂²	1	4	yes	—
17	#19151893	—	2	1	no	—
18	#19151888	—	2	1	no	—
19	#19151883	C₂²	1	2	yes	complemented
20	#19151878	C₂²	1	2	yes	complemented
21	#19151798	—	2	1	no	—
22	#19151798	C₂²	1	2	yes	—
23	#19151793	—	2	1	no	—
24	#19151793	C₂²	1	2	yes	—
25	#19151641	—	2	1	no	—
26	#19151622	C₂²	1	1	yes	characteristic
27	#19151622	C₂²	1	1	yes	characteristic
28	#19151602	—	2	1	no	—
29	#19151599	—	2	1	no	—
30	#19151349	C₂²	1	4	yes	complemented
31	#19151345	C₂²	1	4	yes	complemented
32	#19151341	C₂²	1	4	yes	—
33	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
34	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
35	C₈×D₄×C₈₉	—	2	2	no	—
36	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
37	#431×C₈₉	—	2	1	no	—
38	#431×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₈₉	—	2	1	no	—
40	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×Dic₁₇₈	—	2	1	no	—
42	C₂²×D₃₅₆	—	2	1	no	—
43	C₂²×D₃₅₆	—	2	1	no	—
44	C₂²×D₃₅₆	—	2	1	no	—
45	#15668037	—	4	4	no	—
46	C₂×#13083563	—	2	4	no	—
47	C₂×#13083563	—	2	4	no	—
48	C₂×#13083563	—	4	8	no	—
49	C₂×#13083561	—	2	2	no	—
50	C₂×#13083559	—	2	2	no	—
51	C₂×#13083558	—	2	1	no	—
52	C₂×#13083558	—	2	1	no	—
53	#15668012	—	2	1	no	—
54	#15668012	—	2	1	no	—
55	#15668012	—	2	1	no	—
56	#15668012	C₂³	1	2	yes	—
57	#15668009	—	2	1	no	—
58	#15668009	—	2	1	no	—
59	#15668009	—	2	1	no	—
60	#15668009	C₂³	1	2	yes	—
61	C₂×C₄⋊Dic₈₉	—	2	1	no	—
62	C₂×C₄⋊Dic₈₉	—	2	1	no	—
63	#15667945	—	2	2	no	—
64	#15667943	—	2	2	no	—
65	C₄⋊#10623494	—	2	1	no	—
66	C₄⋊#10623494	—	2	1	no	—
67	C₄⋊#10623494	C₂³	1	2	yes	—
68	C₄⋊#10623494	C₂³	1	2	yes	—
69	#15667936	—	2	2	no	—
70	#15667933	—	2	2	no	—
71	#15667932	—	2	2	no	—
72	#15667932	—	2	2	no	—
73	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₈₉	—	2	2	no	—
75	C₂²×C₈×C₈₉	D₄	1	2	yes	—
76	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
77	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
78	C₄×D₄×C₈₉	—	2	1	no	—
79	C₄×D₄×C₈₉	—	2	1	no	—
80	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
81	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
82	#117×C₈₉	—	2	1	no	—
83	#117×C₈₉	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₈₉	—	2	1	no	—
85	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₈₉	—	2	2	no	—
87	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
88	C₂²⋊C₈×C₈₉	—	2	1	no	—
89	C₂²⋊C₈×C₈₉	—	2	2	no	—
90	C₄×C₈×C₈₉	—	2	2	no	—
91	C₄×C₈×C₈₉	—	2	1	no	—
92	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
93	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
94	C₄×C₈×C₈₉	C₂³	1	2	yes	—
95	C₂³×D₈₉	—	4	1	no	—
96	C₂×Dic₁₇₈	—	2	2	no	—
97	C₂×Dic₁₇₈	—	4	4	no	—
98	C₂×Dic₁₇₈	—	4	1	no	—
99	C₂×D₃₅₆	—	2	2	no	—
100	C₂×D₃₅₆	—	2	2	no	—
101	C₂×D₃₅₆	—	2	2	no	—
102	C₂×D₃₅₆	—	4	4	no	—
103	C₂×D₃₅₆	—	4	2	no	—
104	C₂×D₃₅₆	—	4	2	no	—
105	C₂×D₃₅₆	—	4	1	no	—
106	C₂×D₃₅₆	—	4	1	no	—
107	C₂×D₃₅₆	—	4	1	no	—
108	C₂×D₃₅₆	—	8	2	no	—
109	C₂²×Dic₈₉	—	4	1	no	—
110	#13083563	—	4	8	no	—
111	#13083563	—	4	8	no	—
112	#13083561	—	4	4	no	—
113	#13083559	—	4	4	no	—
114	#13083558	—	4	2	no	—
115	#13083558	—	4	2	no	—
116	C₂×#10623494	—	2	2	no	—
117	C₂×#10623494	—	2	2	no	—
118	C₄⋊Dic₈₉	—	2	2	no	—
119	C₄⋊Dic₈₉	—	2	2	no	—
120	C₄⋊Dic₈₉	—	4	1	no	—
121	C₄⋊Dic₈₉	—	4	1	no	—
122	#41×C₈₉	—	2	2	no	—
123	#41×C₈₉	SD₁₆	1	4	yes	complemented
124	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂×D₄×C₈₉	—	2	1	no	—
126	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	—	2	1	no	—
128	C₂²×C₄×C₈₉	—	2	1	no	—
129	C₂²×C₄×C₈₉	—	2	1	no	—
130	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
133	C₂×C₈×C₈₉	—	2	4	no	—
134	C₂×C₈×C₈₉	—	2	2	no	—
135	C₂×C₈×C₈₉	—	4	4	no	—
136	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₈₉	—	2	1	no	—
139	C₄⋊C₄×C₈₉	—	2	1	no	—
140	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂²⋊C₄×C₈₉	—	2	1	no	—
143	C₂²⋊C₄×C₈₉	—	2	1	no	—
144	C₂²⋊C₄×C₈₉	—	2	1	no	—
145	C₄²×C₈₉	—	2	1	no	—
146	C₄²×C₈₉	—	2	1	no	—
147	C₄²×C₈₉	—	2	1	no	—
148	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₈₉	#41	1	1	yes	characteristic
151	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₂³×C₈₉	—	2	1	no	—
153	C₂³×C₈₉	#121	1	1	yes	characteristic
154	C₂²×D₈₉	—	4	2	no	—
155	C₂²×D₈₉	—	8	2	no	—
156	C₂²×D₈₉	—	8	2	no	—
157	C₂²×D₈₉	—	8	2	no	—
158	Q₈×C₈₉	—	2	1	no	—
159	Q₈×C₈₉	C₂×SD₁₆	1	2	yes	complemented
160	D₄×C₈₉	—	2	4	no	—
161	D₄×C₈₉	—	2	1	no	—
162	D₄×C₈₉	C₂×SD₁₆	1	2	yes	complemented
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	2	no	—
165	C₂×C₄×C₈₉	—	2	4	no	—
166	C₂×C₄×C₈₉	—	2	2	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	4	2	no	—
170	C₂×C₄×C₈₉	—	4	2	no	—
171	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
175	C₂×C₄×C₈₉	#135	1	2	yes	—
176	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
179	C₂×Dic₈₉	—	4	2	no	—
180	C₂×Dic₈₉	—	8	2	no	—
181	D₃₅₆	—	4	2	no	—
182	D₃₅₆	—	4	2	no	—
183	D₃₅₆	—	4	4	no	—
184	D₃₅₆	—	8	2	no	—
185	D₃₅₆	—	8	2	no	—
186	D₃₅₆	—	8	2	no	—
187	D₃₅₆	—	8	2	no	—
188	Dic₁₇₈	—	4	4	no	—
189	Dic₁₇₈	—	8	2	no	—
190	C₈×C₈₉	—	2	2	no	—
191	C₈×C₈₉	—	4	2	no	—
192	C₈×C₈₉	AGL(1,ℤ/8)	1	4	yes	complemented
193	#10623494	—	4	2	no	—
194	#10623494	—	4	2	no	—
195	C₂²×C₈₉	—	2	1	no	—
196	C₂²×C₈₉	—	2	1	no	—
197	C₂²×C₈₉	—	2	2	no	—
198	C₂²×C₈₉	—	4	1	no	—
199	C₂²×C₈₉	—	4	1	no	—
200	C₂²×C₈₉	#465	1	2	yes	—
201	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
202	C₂×D₈₉	—	8	2	no	—
203	C₂×D₈₉	—	8	2	no	—
204	C₂×D₈₉	—	8	2	no	—
205	C₂×D₈₉	—	16	4	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	2	2	no	—
208	C₄×C₈₉	—	2	1	no	—
209	C₄×C₈₉	—	4	1	no	—
210	C₄×C₈₉	—	4	1	no	—
211	C₄×C₈₉	#465	1	2	yes	—
212	C₄×C₈₉	#471	1	2	yes	—
213	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
214	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
215	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
216	Dic₈₉	—	8	2	no	—
217	#19266	—	89	1	no	maximal, Sylow
218	C₂×C₈₉	—	2	2	no	—
219	C₂×C₈₉	—	4	2	no	—
220	C₂×C₈₉	#3038	1	1	yes	characteristic
221	C₂×C₈₉	C₂×#465	1	1	yes	characteristic
222	C₂×C₈₉	C₂×#471	1	1	yes	characteristic
223	D₈₉	—	16	2	no	—
224	C₂×#492	—	89	1	no	—
225	#3079	—	89	1	no	—
226	#3038	—	89	1	no	—
227	C₈×#41	D₈₉	1	1	yes	characteristic, complemented
228	#1666	—	89	4	no	—
229	#1665	—	89	4	no	—
230	#1566	—	89	1	no	—
231	#1549	—	89	1	no	—
232	#1545	—	89	1	no	—
233	C₈₉	#19266	1	1	yes	characteristic, complemented, Sylow
234	C₂×AGL(1,ℤ/8)	—	178	1	no	—
235	C₂²×SD₁₆	—	178	2	no	—
236	C₂×C₄⋊Q₈	—	89	1	no	—
237	C₂×#127	—	89	1	no	—
238	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
239	#492	—	89	4	no	—
240	#492	—	178	1	no	—
241	#492	—	178	1	no	—
242	#477	—	178	1	no	—
243	#476	—	178	1	no	—
244	#475	—	89	2	no	—
245	#474	—	89	2	no	—
246	#460	—	89	2	no	—
247	#460	—	178	1	no	—
248	#459	—	89	2	no	—
249	#459	—	178	1	no	—
250	C₈×Q₈	C₂×D₈₉	1	2	yes	complemented
251	C₈×D₄	—	2	2	no	—
252	C₈×D₄	C₂×D₈₉	1	2	yes	complemented
253	#431	—	2	1	no	—
254	#431	C₂×D₈₉	1	1	yes	characteristic
255	#428	—	178	1	no	—
256	#423	—	89	1	no	—
257	#423	—	89	1	no	—
258	#418	—	178	1	no	—
259	#417	—	178	1	no	—
260	C₂×C₄×C₈	—	2	1	no	—
261	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
262	#334	—	89	4	no	—
263	#332	—	89	4	no	—
264	#331	—	89	4	no	—
265	C₂×#41	D₃₅₆	1	1	yes	characteristic
266	C₂²×Q₈	—	178	1	no	—
267	C₂²×D₄	—	178	1	no	—
268	C₂²×D₄	—	178	1	no	—
269	C₂²×D₄	—	178	1	no	—
270	AGL(1,ℤ/8)	—	356	4	no	—
271	C₂×SD₁₆	—	356	8	no	—
272	C₂×SD₁₆	—	178	2	no	—
273	C₂×SD₁₆	—	178	4	no	—
274	C₂×SD₁₆	—	178	4	no	—
275	C₂×D₈	—	178	2	no	—
276	C₂×M₁₆	—	178	1	no	—
277	C₂×M₁₆	—	178	1	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	C₂²⋊D₈₉	1	2	yes	—
280	C₄⋊Q₈	—	89	2	no	—
281	C₄⋊Q₈	—	178	1	no	—
282	C₄⋊Q₈	—	178	1	no	—
283	C₄⋊Q₈	—	178	1	no	—
284	#127	—	89	2	no	—
285	#127	—	178	1	no	—
286	#127	—	178	1	no	—
287	#127	—	178	1	no	—
288	C₄×Q₈	D₃₅₆	1	1	yes	characteristic
289	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	D₃₅₆	1	1	yes	characteristic
293	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
294	#117	—	2	1	no	—
295	#117	D₃₅₆	1	1	yes	characteristic
296	C₂×C₄⋊C₄	—	178	1	no	—
297	C₂×C₄⋊C₄	—	178	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
300	#107	—	178	2	no	—
301	#106	—	178	2	no	—
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	89	2	no	—
304	C₄⋊C₈	—	89	2	no	—
305	C₄⋊C₈	—	178	1	no	—
306	C₄⋊C₈	—	178	1	no	—
307	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
308	#103	—	178	2	no	—
309	#102	—	178	2	no	—
310	#102	—	178	2	no	—
311	#102	—	178	2	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
317	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₈₉	1	2	yes	—
319	C₂⁴	—	356	1	no	—
320	#41	—	2	2	no	—
321	#41	#13083563	1	4	yes	complemented
322	C₂×Q₈	—	356	4	no	—
323	C₂×Q₈	—	356	1	no	—
324	C₂×Q₈	—	178	2	no	—
325	C₂×Q₈	C₂×D₃₅₆	1	1	yes	characteristic
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	356	4	no	—
328	C₂×D₄	—	356	1	no	—
329	C₂×D₄	—	356	1	no	—
330	C₂×D₄	—	356	1	no	—
331	C₂×D₄	—	356	2	no	—
332	C₂×D₄	—	356	2	no	—
333	C₂×D₄	—	178	2	no	—
334	C₂×D₄	—	178	2	no	—
335	C₂×D₄	—	178	2	no	—
336	C₂×D₄	—	712	2	no	—
337	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	356	1	no	—
342	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
344	C₂²×C₄	#13083574	1	1	yes	characteristic
345	SD₁₆	—	356	8	no	—
346	SD₁₆	—	356	4	no	—
347	SD₁₆	—	356	8	no	—
348	D₈	—	356	4	no	—
349	M₁₆	—	356	2	no	—
350	M₁₆	—	356	2	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	4	no	—
354	C₂×C₈	—	178	2	no	—
355	C₂×C₈	—	178	2	no	—
356	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
357	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	356	1	no	—
361	C₄⋊C₄	—	356	1	no	—
362	C₄⋊C₄	—	178	2	no	—
363	C₄⋊C₄	—	178	2	no	—
364	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
365	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
373	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
374	C₄²	#13083574	1	1	yes	characteristic
375	C₄²	C₂³×D₈₉	1	1	yes	characteristic
376	C₂³	—	2	1	no	—
377	C₂³	—	356	2	no	—
378	C₂³	—	712	2	no	—
379	C₂³	—	712	2	no	—
380	C₂³	—	712	2	no	—
381	C₂³	#15667986	1	1	yes	characteristic
382	Q₈	—	2	1	no	—
383	Q₈	—	356	4	no	—
384	Q₈	—	712	2	no	—
385	Q₈	C₂×#13083563	1	2	yes	complemented
386	D₄	—	2	4	no	—
387	D₄	—	2	1	no	—
388	D₄	—	356	4	no	—
389	D₄	—	356	2	no	—
390	D₄	—	356	2	no	—
391	D₄	—	712	2	no	—
392	D₄	—	712	2	no	—
393	D₄	—	712	2	no	—
394	D₄	—	712	2	no	—
395	D₄	C₂×#13083563	1	2	yes	complemented
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	356	2	no	—
405	C₂×C₄	—	712	2	no	—
406	C₂×C₄	#15667986	1	1	yes	characteristic
407	C₂×C₄	#15667986	1	1	yes	characteristic
408	C₂×C₄	#15667986	1	1	yes	characteristic
409	C₂×C₄	C₂×#13083563	1	2	yes	—
410	C₂×C₄	#15668034	1	2	yes	—
411	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
413	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	4	2	no	—
416	C₈	—	356	2	no	—
417	C₈	—	356	2	no	—
418	C₈	#15668037	1	4	yes	complemented
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	1424	4	no	—
425	C₂²	—	712	2	no	—
426	C₂²	—	712	2	no	—
427	C₂²	—	712	2	no	—
428	C₂²	#19151827	1	2	yes	—
429	C₂²	C₂×#15667986	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	2	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	712	2	no	—
436	C₄	#19151827	1	2	yes	—
437	C₄	#19151861	1	2	yes	—
438	C₄	C₂²×#13083563	1	1	yes	characteristic
439	C₄	C₂×#15668034	1	1	yes	characteristic
440	C₄	C₂×#15668037	1	2	yes	—
441	C₂	—	2	2	no	—
442	C₂	—	4	2	no	—
443	C₂	—	1424	2	no	—
444	C₂	#26029732	1	1	yes	characteristic
445	C₂	C₂×#19151827	1	1	yes	characteristic
446	C₂	C₂×#19151861	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667986
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×#41×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#26029732	C₂
hypercenter	C₈×#41	D₈₉
hypocenter	C₈₉	#19266
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#19151971	C₂	semidirect
2. #26030067	C₂	semidirect
4. #26019600	C₂	semidirect
5. #26019593	C₂	semidirect
6. #26019008	C₂	semidirect
7. #26018936	C₂	semidirect
8. #26018919	C₂	semidirect
9. C₈×#41×C₈₉	C₂	semidirect
19. #19151883	C₂²	semidirect
20. #19151878	C₂²	semidirect
30. #19151349	C₂²	semidirect
31. #19151345	C₂²	semidirect
34. C₈×Q₈×C₈₉	C₂²	semidirect
36. C₈×D₄×C₈₉	C₂²	semidirect
123. #41×C₈₉	SD₁₆	semidirect
159. Q₈×C₈₉	C₂×SD₁₆	semidirect
162. D₄×C₈₉	C₂×SD₁₆	semidirect
192. C₈×C₈₉	AGL(1,ℤ/8)	semidirect
227. C₈×#41	D₈₉	semidirect
233. C₈₉	#19266	semidirect
250. C₈×Q₈	C₂×D₈₉	semidirect
252. C₈×D₄	C₂×D₈₉	semidirect
321. #41	#13083563	semidirect
385. Q₈	C₂×#13083563	semidirect
395. D₄	C₂×#13083563	semidirect
418. C₈	#15668037	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151971	2
#26030067	2
#26029732	2
#26019600	2
#26019593	2
#26019008	2
#26018936	2
#26018919	2
C₈×#41×C₈₉	2
#19266	89