Subgroups — #36525354

Order 22784.

670 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030284	C₂	1	1	yes	maximal, characteristic
2	M₁₆×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028998	C₂	1	1	yes	maximal, characteristic
4	#26019144	C₂	1	2	yes	maximal, complemented
5	#26019097	C₂	1	2	yes	maximal, complemented
6	#26019090	C₂	1	2	yes	maximal, complemented
7	C₈×#13083563	C₂	1	2	yes	maximal, complemented
8	#26019023	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018704	C₂	1	1	yes	maximal, characteristic
10	C₂×#19151330	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668020	—	2	1	no	—
13	#19152148	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
15	#19151917	C₄	1	2	yes	—
16	#19151884	C₄	1	1	yes	characteristic
17	#19151884	C₄	1	1	yes	characteristic
18	#19151799	C₄	1	1	yes	characteristic
19	#19151799	C₄	1	1	yes	characteristic
20	#19151739	C₄	1	2	yes	—
21	#19151728	C₂²	1	2	yes	—
22	#19151726	—	2	2	no	—
23	C₈×Dic₁₇₈	C₂²	1	2	yes	—
24	C₄×#13083563	C₂²	1	2	yes	—
25	C₄×#13083563	C₂²	1	2	yes	—
26	#19151677	C₂²	1	2	yes	—
27	#19151671	—	2	2	no	—
28	C₈×D₃₅₆	C₂²	1	2	yes	—
29	#19151622	C₂²	1	1	yes	characteristic
30	#19151621	—	2	1	no	—
31	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
32	#19151566	—	2	1	no	—
33	M₁₆×Dic₈₉	—	2	1	no	—
34	#19151349	C₂²	1	2	yes	—
35	#19151349	C₂²	1	2	yes	—
36	#19151330	C₂²	1	1	yes	characteristic
37	#19151330	C₂²	1	1	yes	characteristic
38	#19151330	C₂²	1	1	yes	characteristic
39	#19151330	C₂²	1	1	yes	characteristic
40	#19151327	C₂²	1	2	yes	—
41	#19151327	C₂²	1	2	yes	—
42	#431×C₈₉	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#322×C₈₉	C₂²	1	2	yes	—
46	C₈²×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083574	—	2	1	no	—
48	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
49	C₂×#13083563	C₂×C₄	1	2	yes	—
50	C₂×#13083563	C₂×C₄	1	2	yes	—
51	#15668020	—	4	4	no	—
52	C₂×#13083558	—	2	1	no	—
53	C₂×#13083557	—	2	2	no	—
54	C₂²×#10623494	—	2	1	no	—
55	C₂×C₈×D₈₉	—	2	2	no	—
56	#15668012	C₂×C₄	1	1	yes	characteristic
57	#15668009	C₂×C₄	1	1	yes	characteristic
58	#15668000	—	2	1	no	—
59	#15667986	—	2	1	no	—
60	#15667986	C₂×C₄	1	2	yes	—
61	C₄×Dic₁₇₈	—	2	1	no	—
62	C₄×Dic₁₇₈	—	2	1	no	—
63	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
66	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
67	C₄×D₃₅₆	—	2	1	no	—
68	C₄×D₃₅₆	C₂³	1	2	yes	—
69	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083553	—	2	1	no	—
71	C₂×C₄×Dic₈₉	—	2	1	no	—
72	#15667944	C₂×C₄	1	2	yes	—
73	#15667944	C₂×C₄	1	2	yes	—
74	C₄⋊#10623494	—	2	1	no	—
75	C₄⋊#10623494	—	2	1	no	—
76	C₄⋊#10623494	C₂³	1	1	yes	characteristic
77	C₄⋊#10623494	C₂³	1	1	yes	characteristic
78	C₄⋊#10623494	C₂³	1	2	yes	—
79	#15667941	—	2	2	no	—
80	#15667941	—	2	2	no	—
81	#15667937	C₂×C₄	1	2	yes	—
82	#15667937	C₂×C₄	1	2	yes	—
83	#15667934	C₂×C₄	1	2	yes	—
84	#15667934	C₂×C₄	1	2	yes	—
85	#15667924	—	2	2	no	—
86	#15667924	—	2	2	no	—
87	#15667922	—	2	2	no	—
88	C₈×Dic₈₉	—	2	2	no	—
89	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
90	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
91	C₂²×C₈×C₈₉	—	2	1	no	—
92	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
94	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
96	#97×C₈₉	D₄	1	2	yes	—
97	C₄×C₈×C₈₉	—	2	1	no	—
98	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₈₉	C₂³	1	2	yes	—
101	C₄×C₈×C₈₉	C₂³	1	2	yes	—
102	#13083574	—	4	2	no	—
103	#13083574	—	4	2	no	—
104	C₂×Dic₁₇₈	—	2	2	no	—
105	C₂×Dic₁₇₈	—	2	1	no	—
106	C₂×Dic₁₇₈	—	2	1	no	—
107	C₂×Dic₁₇₈	—	4	1	no	—
108	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
109	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
110	C₂×D₃₅₆	—	2	1	no	—
111	C₂×D₃₅₆	—	2	1	no	—
112	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
113	C₂×C₂²⋊D₈₉	—	2	2	no	—
114	C₂²×Dic₈₉	—	2	1	no	—
115	C₂²×Dic₈₉	—	2	1	no	—
116	C₂×C₄×D₈₉	—	2	2	no	—
117	#13083563	—	2	4	no	—
118	#13083563	—	4	2	no	—
119	#13083558	—	4	2	no	—
120	#13083557	—	4	4	no	—
121	C₂×#10623494	—	2	1	no	—
122	C₂×#10623494	—	2	1	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₂×#10623494	—	4	2	no	—
125	C₈×D₈₉	—	4	4	no	—
126	C₄⋊Dic₈₉	—	2	1	no	—
127	C₄⋊Dic₈₉	—	2	1	no	—
128	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
129	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
131	#13083553	—	2	1	no	—
132	#13083553	—	2	1	no	—
133	#13083553	—	2	1	no	—
134	#13083553	—	2	1	no	—
135	#13083551	—	2	2	no	—
136	#13083551	—	2	2	no	—
137	C₄×Dic₈₉	—	2	1	no	—
138	C₄×Dic₈₉	—	2	1	no	—
139	C₄×Dic₈₉	—	2	1	no	—
140	C₄×Dic₈₉	—	2	1	no	—
141	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
144	M₁₆×C₈₉	—	2	2	no	—
145	M₁₆×C₈₉	SD₁₆	1	4	yes	complemented
146	C₂×C₈×C₈₉	—	2	1	no	—
147	C₂×C₈×C₈₉	—	2	1	no	—
148	C₂×C₈×C₈₉	—	4	2	no	—
149	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
153	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₈₉	#41	1	1	yes	characteristic
156	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
157	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
158	C₂²×D₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	4	1	no	—
162	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
166	C₂×C₄×C₈₉	#135	1	2	yes	—
167	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
170	C₂²⋊D₈₉	—	4	4	no	—
171	C₂×Dic₈₉	—	2	1	no	—
172	C₂×Dic₈₉	—	2	1	no	—
173	C₂×Dic₈₉	—	2	1	no	—
174	C₂×Dic₈₉	—	2	1	no	—
175	C₂×Dic₈₉	—	2	2	no	—
176	C₂×Dic₈₉	—	4	2	no	—
177	C₂×Dic₈₉	—	8	1	no	—
178	D₃₅₆	—	2	2	no	—
179	D₃₅₆	—	2	2	no	—
180	D₃₅₆	—	4	2	no	—
181	D₃₅₆	—	8	1	no	—
182	C₄×D₈₉	—	4	2	no	—
183	C₄×D₈₉	—	4	2	no	—
184	Dic₁₇₈	—	2	1	no	—
185	Dic₁₇₈	—	2	1	no	—
186	Dic₁₇₈	—	2	1	no	—
187	Dic₁₇₈	—	4	2	no	—
188	Dic₁₇₈	—	4	2	no	—
189	Dic₁₇₈	#131	1	2	yes	complemented
190	C₈×C₈₉	—	2	2	no	—
191	C₈×C₈₉	—	2	2	no	—
192	C₈×C₈₉	—	2	2	no	—
193	C₈×C₈₉	—	2	2	no	—
194	C₈×C₈₉	—	4	1	no	—
195	C₈×C₈₉	C₂×SD₁₆	1	4	yes	—
196	#10623494	—	4	1	no	—
197	#10623494	—	4	1	no	—
198	#10623494	—	4	2	no	—
199	C₂²×C₈₉	—	2	1	no	—
200	C₂²×C₈₉	—	2	1	no	—
201	C₂²×C₈₉	C₄×SD₁₆	1	2	yes	—
202	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂×D₈₉	—	4	2	no	—
204	C₂×D₈₉	—	4	2	no	—
205	C₂×D₈₉	—	4	2	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	2	1	no	—
208	C₄×C₈₉	—	2	1	no	—
209	C₄×C₈₉	C₄×SD₁₆	1	2	yes	—
210	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
211	C₄×C₈₉	#568	1	1	yes	characteristic
212	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
213	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
214	Dic₈₉	—	2	2	no	—
215	Dic₈₉	—	4	1	no	—
216	Dic₈₉	—	4	2	no	—
217	Dic₈₉	—	4	1	no	—
218	Dic₈₉	—	4	1	no	—
219	#17997	—	89	1	no	maximal, Sylow
220	C₂×C₈₉	—	2	2	no	—
221	C₂×C₈₉	#2933	1	1	yes	characteristic
222	C₂×C₈₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
223	C₂×C₈₉	#2956	1	1	yes	characteristic
224	D₈₉	—	8	2	no	—
225	#3103	—	89	1	no	—
226	Q₈×M₁₆	—	89	1	no	—
227	#2935	—	89	1	no	—
228	#1590	—	89	2	no	—
229	#1583	—	89	2	no	—
230	#1582	—	89	2	no	—
231	C₈×SD₁₆	—	89	2	no	—
232	#1570	—	89	1	no	—
233	#1492	—	89	1	no	—
234	C₂×Q₈⋊C₈	—	89	1	no	—
235	C₈×M₁₆	D₈₉	1	1	yes	characteristic, complemented
236	C₈₉	#17997	1	1	yes	characteristic, complemented, Sylow
237	C₂×#131	—	178	1	no	—
238	#532	—	89	1	no	—
239	C₂×C₄×Q₈	—	89	1	no	—
240	#481	—	89	2	no	—
241	#475	—	89	1	no	—
242	#475	—	89	1	no	—
243	#460	—	89	1	no	—
244	#460	—	89	1	no	—
245	#448	—	89	2	no	—
246	#446	—	89	2	no	—
247	#446	—	178	2	no	—
248	C₈×Q₈	—	89	2	no	—
249	C₄×SD₁₆	—	89	2	no	—
250	C₄×SD₁₆	—	89	2	no	—
251	#436	—	89	2	no	—
252	#435	—	178	2	no	—
253	C₈×D₄	—	89	2	no	—
254	#431	C₂×D₈₉	1	1	yes	characteristic
255	#423	—	89	1	no	—
256	#423	—	178	1	no	—
257	C₂×C₄⋊C₈	—	89	1	no	—
258	#408	—	178	1	no	—
259	C₄×M₁₆	—	178	1	no	—
260	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
262	#334	—	89	2	no	—
263	#334	—	89	2	no	—
264	Q₈⋊C₈	—	89	1	no	—
265	Q₈⋊C₈	—	89	1	no	—
266	Q₈⋊C₈	—	89	1	no	—
267	Q₈⋊C₈	—	89	1	no	—
268	D₄⋊C₈	—	89	2	no	—
269	D₄⋊C₈	—	89	2	no	—
270	#322	C₂×D₈₉	1	2	yes	—
271	C₈²	C₂×D₈₉	1	2	yes	—
272	C₂×#41	—	178	1	no	—
273	C₂²×Q₈	—	89	1	no	—
274	C₂×SD₁₆	—	89	2	no	—
275	C₂×SD₁₆	—	89	2	no	—
276	#131	—	356	4	no	—
277	C₂×M₁₆	—	178	1	no	—
278	C₂×M₁₆	—	178	2	no	—
279	C₂×M₁₆	D₃₅₆	1	1	yes	characteristic
280	C₂×M₁₆	D₃₅₆	1	1	yes	characteristic
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	178	1	no	—
283	C₂²×C₈	—	178	2	no	—
284	C₄⋊Q₈	—	89	1	no	—
285	#127	—	89	1	no	—
286	#124	—	178	1	no	—
287	#121	—	89	2	no	—
288	#121	—	178	1	no	—
289	C₄×Q₈	—	89	1	no	—
290	C₄×Q₈	—	89	1	no	—
291	C₄×Q₈	—	89	1	no	—
292	C₄×Q₈	—	89	1	no	—
293	C₄×Q₈	—	178	1	no	—
294	C₄×Q₈	—	178	1	no	—
295	C₄×D₄	—	89	2	no	—
296	C₄×D₄	—	178	1	no	—
297	C₂×C₄⋊C₄	—	89	1	no	—
298	C₂×C₄⋊C₄	—	178	1	no	—
299	C₂×C₄²	—	178	1	no	—
300	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
301	#106	—	89	2	no	—
302	#106	—	89	2	no	—
303	C₄⋊C₈	—	89	2	no	—
304	C₄⋊C₈	—	89	1	no	—
305	C₄⋊C₈	—	89	1	no	—
306	C₄⋊C₈	—	178	2	no	—
307	C₄⋊C₈	—	178	2	no	—
308	C₄⋊C₈	—	178	1	no	—
309	C₄⋊C₈	—	178	1	no	—
310	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
311	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
312	#103	—	89	2	no	—
313	#103	—	89	2	no	—
314	#102	—	89	2	no	—
315	#102	—	89	2	no	—
316	C₂²⋊C₈	—	178	2	no	—
317	C₂²⋊C₈	—	178	2	no	—
318	C₂²⋊C₈	C₄×D₈₉	1	2	yes	—
319	#97	—	178	2	no	—
320	#97	D₃₅₆	1	2	yes	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	178	2	no	—
323	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
324	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
325	C₄×C₈	C₂²×D₈₉	1	2	yes	—
326	C₄×C₈	C₂²×D₈₉	1	2	yes	—
327	#41	—	356	2	no	—
328	#41	—	356	2	no	—
329	C₂×Q₈	—	89	1	no	—
330	C₂×Q₈	—	89	1	no	—
331	C₂×Q₈	—	356	1	no	—
332	C₂×Q₈	—	178	2	no	—
333	C₂×Q₈	—	178	1	no	—
334	C₂×Q₈	—	178	1	no	—
335	C₂×D₄	—	89	2	no	—
336	C₂×D₄	—	178	2	no	—
337	C₂×D₄	—	178	1	no	—
338	C₂×D₄	—	178	1	no	—
339	C₂²×C₄	—	178	1	no	—
340	C₂²×C₄	—	178	2	no	—
341	C₂²×C₄	—	178	1	no	—
342	C₂²×C₄	C₂×C₄×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	2	no	—
346	SD₁₆	—	178	4	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	356	2	no	—
349	M₁₆	—	356	4	no	—
350	M₁₆	#13083563	1	4	yes	complemented
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	4	2	no	—
354	C₂×C₈	—	356	2	no	—
355	C₂×C₈	—	356	4	no	—
356	C₂×C₈	—	178	2	no	—
357	C₂×C₈	—	178	1	no	—
358	C₂×C₈	—	178	1	no	—
359	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
360	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
361	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
362	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
363	C₄⋊C₄	—	89	1	no	—
364	C₄⋊C₄	—	89	1	no	—
365	C₄⋊C₄	—	89	2	no	—
366	C₄⋊C₄	—	178	1	no	—
367	C₄⋊C₄	—	178	1	no	—
368	C₄⋊C₄	—	178	1	no	—
369	C₄⋊C₄	—	178	1	no	—
370	C₄⋊C₄	—	178	1	no	—
371	C₄⋊C₄	—	178	1	no	—
372	C₂²⋊C₄	—	178	2	no	—
373	C₂²⋊C₄	—	178	2	no	—
374	C₄²	—	178	1	no	—
375	C₄²	—	178	1	no	—
376	C₄²	—	178	1	no	—
377	C₄²	—	178	1	no	—
378	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
379	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
380	C₄²	#13083574	1	1	yes	characteristic
381	C₄²	C₂³×D₈₉	1	1	yes	characteristic
382	C₂³	—	178	2	no	—
383	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
384	Q₈	—	89	2	no	—
385	Q₈	—	356	2	no	—
386	Q₈	—	356	2	no	—
387	Q₈	—	178	1	no	—
388	Q₈	—	178	1	no	—
389	Q₈	—	178	1	no	—
390	D₄	—	356	4	no	—
391	D₄	—	356	2	no	—
392	D₄	—	178	2	no	—
393	D₄	—	178	2	no	—
394	D₄	—	712	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	356	2	no	—
399	C₂×C₄	—	356	2	no	—
400	C₂×C₄	—	356	2	no	—
401	C₂×C₄	—	178	1	no	—
402	C₂×C₄	—	178	1	no	—
403	C₂×C₄	—	178	1	no	—
404	C₂×C₄	—	178	2	no	—
405	C₂×C₄	—	178	1	no	—
406	C₂×C₄	—	712	1	no	—
407	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
408	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
409	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
410	C₂×C₄	C₂×#13083563	1	2	yes	—
411	C₂×C₄	#15668034	1	2	yes	—
412	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
414	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	4	1	no	—
420	C₈	—	356	1	no	—
421	C₈	—	356	1	no	—
422	C₈	—	356	2	no	—
423	C₈	C₂×#13083563	1	4	yes	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	356	2	no	—
427	C₂²	—	356	2	no	—
428	C₂²	—	356	2	no	—
429	C₂²	C₄×#13083563	1	2	yes	—
430	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	356	1	no	—
435	C₄	—	356	1	no	—
436	C₄	—	356	1	no	—
437	C₄	—	356	2	no	—
438	C₄	—	178	2	no	—
439	C₄	C₄×#13083563	1	2	yes	—
440	C₄	#131×D₈₉	1	1	yes	characteristic
441	C₄	#19152363	1	1	yes	characteristic
442	C₄	C₂²×#13083563	1	1	yes	characteristic
443	C₄	C₂×#15668034	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	712	2	no	—
446	C₂	#26028980	1	1	yes	characteristic
447	C₂	C₂×C₄×#13083563	1	1	yes	characteristic
448	C₂	#26029163	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×M₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#19152148	C₂²
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×M₁₆	D₈₉
hypocenter	C₈₉	#17997
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. M₁₆×Dic₁₇₈	C₂	semidirect
4. #26019144	C₂	semidirect
5. #26019097	C₂	semidirect
6. #26019090	C₂	semidirect
7. C₈×#13083563	C₂	semidirect
8. #26019023	C₂	semidirect
10. C₂×#19151330	C₂	semidirect
11. C₈×M₁₆×C₈₉	C₂	semidirect
145. M₁₆×C₈₉	SD₁₆	semidirect
189. Dic₁₇₈	#131	semidirect
235. C₈×M₁₆	D₈₉	semidirect
236. C₈₉	#17997	semidirect
350. M₁₆	#13083563	semidirect

Maximal subgroups

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

subgroup	index
#26030284	2
M₁₆×Dic₁₇₈	2
#26028998	2
#26019144	2
#26019097	2
#26019090	2
C₈×#13083563	2
#26019023	2
#26018704	2
C₂×#19151330	2
C₈×M₁₆×C₈₉	2
#17997	89