Subgroups — #36553005

Order 22784.

1014 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151717	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151712	C₂	1	1	yes	maximal, characteristic
3	#26029050	C₂	1	1	yes	maximal, characteristic
4	#26028681	C₂	1	1	yes	maximal, characteristic, complemented
5	#26028680	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020159	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020135	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020130	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020097	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020093	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020090	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020086	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#15667940	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#15667923	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#104×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668032	C₂²	1	1	yes	characteristic
17	C₂×#15668020	C₂²	1	1	yes	characteristic
18	C₂×#15668020	C₂²	1	1	yes	characteristic
19	C₂×#15668019	C₂²	1	1	yes	characteristic
20	C₂×#15668019	C₂²	1	1	yes	characteristic
21	C₄×#13083574	C₂²	1	1	yes	characteristic
22	#19151717	C₄	1	8	yes	complemented
23	#19151712	C₄	1	8	yes	complemented
24	#19151708	C₄	1	2	yes	complemented
25	#19151703	C₄	1	2	yes	complemented
26	#19151698	C₄	1	2	yes	complemented
27	#19151696	C₄	1	2	yes	complemented
28	C₂×#15667947	C₂²	1	1	yes	characteristic
29	C₂×#15667947	C₂²	1	1	yes	characteristic
30	#19151634	C₂²	1	1	yes	characteristic
31	C₂×#15667940	C₂²	1	1	yes	characteristic
32	C₂×#15667940	C₂²	1	1	yes	characteristic
33	#19151594	C₂²	1	1	yes	characteristic
34	#19151592	C₂²	1	1	yes	characteristic
35	#19151556	C₂²	1	1	yes	characteristic
36	#19151556	C₂²	1	1	yes	characteristic
37	#19151554	—	2	1	no	—
38	#19151554	—	2	1	no	—
39	#19151554	C₂²	1	1	yes	characteristic
40	#19151554	C₂²	1	1	yes	characteristic
41	#19151552	—	2	1	no	—
42	#19151552	—	2	1	no	—
43	C₄×#13083558	—	2	1	no	—
44	C₄×#13083558	C₂²	1	1	yes	characteristic
45	#19151550	—	2	1	no	—
46	C₂×#15667923	—	2	1	no	—
47	C₂×#15667923	C₂²	1	1	yes	characteristic
48	C₂×#15667923	C₂²	1	1	yes	characteristic
49	C₂×#15667923	C₂²	1	1	yes	characteristic
50	C₂×#15667923	C₂²	1	1	yes	characteristic
51	#97×D₈₉	—	2	1	no	—
52	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
53	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
54	#19151362	C₂²	1	1	yes	characteristic
55	#19151362	C₂²	1	1	yes	characteristic
56	#19151358	C₂²	1	1	yes	characteristic
57	#19151358	C₂²	1	1	yes	characteristic
58	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
60	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
61	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
62	C₄³×C₈₉	C₂²	1	1	yes	characteristic
63	#339×C₈₉	C₂²	1	1	yes	characteristic
64	#339×C₈₉	C₂²	1	1	yes	characteristic
65	C₂×#13083574	C₂³	1	1	yes	characteristic
66	#15668032	C₂×C₄	1	4	yes	—
67	#15668032	C₂×C₄	1	4	yes	—
68	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
72	#15668020	—	2	2	no	—
73	#15668020	—	2	2	no	—
74	#15668020	C₂×C₄	1	4	yes	complemented
75	#15668020	C₂×C₄	1	4	yes	complemented
76	#15668019	—	2	2	no	—
77	#15668019	—	2	2	no	—
78	#15668019	C₂×C₄	1	4	yes	complemented
79	#15668019	C₂×C₄	1	4	yes	complemented
80	C₂×#13083558	—	2	1	no	—
81	C₂×#13083558	—	2	1	no	—
82	C₂×#13083558	C₂³	1	1	yes	characteristic
83	C₂×#13083558	C₂³	1	1	yes	characteristic
84	C₂×#13083557	—	2	1	no	—
85	C₂×#13083557	—	2	1	no	—
86	C₂²×#10623494	—	2	1	no	—
87	C₂²×#10623494	—	2	1	no	—
88	C₂²×#10623494	C₂³	1	1	yes	characteristic
89	C₂²×#10623494	C₂³	1	1	yes	characteristic
90	C₂²×#10623494	C₂³	1	1	yes	characteristic
91	C₂²×#10623494	C₂³	1	1	yes	characteristic
92	C₂×C₈×D₈₉	—	2	1	no	—
93	C₂×C₈×D₈₉	—	2	1	no	—
94	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
95	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
96	C₄×C₂²⋊D₈₉	—	2	2	no	—
97	#15667971	C₂³	1	1	yes	characteristic
98	#15667969	—	2	1	no	—
99	C₄²×D₈₉	—	2	1	no	—
100	#15667947	C₂×C₄	1	4	yes	complemented
101	#15667947	C₂×C₄	1	4	yes	complemented
102	#15667945	C₂×C₄	1	2	yes	—
103	#15667943	C₂×C₄	1	2	yes	—
104	#15667940	C₂×C₄	1	4	yes	complemented
105	#15667940	C₂×C₄	1	4	yes	complemented
106	#15667936	C₂×C₄	1	2	yes	—
107	#15667935	C₂×C₄	1	2	yes	—
108	#15667933	C₂×C₄	1	2	yes	—
109	#15667932	C₂×C₄	1	2	yes	—
110	#15667923	—	2	1	no	—
111	#15667923	—	2	1	no	—
112	#15667923	—	2	2	no	—
113	#15667923	—	2	1	no	—
114	#15667923	C₂×C₄	1	2	yes	—
115	#15667923	C₂×C₄	1	2	yes	—
116	#15667923	C₂×C₄	1	4	yes	complemented
117	#15667923	D₄	1	1	yes	characteristic
118	#15667923	D₄	1	1	yes	characteristic
119	#15667923	D₄	1	1	yes	characteristic
120	#15667923	D₄	1	1	yes	characteristic
121	#15667922	—	2	1	no	—
122	#15667922	—	2	1	no	—
123	C₄×#10623494	—	2	1	no	—
124	C₄×#10623494	—	2	1	no	—
125	C₄×#10623494	—	2	2	no	—
126	C₄×#10623494	—	2	1	no	—
127	C₄×#10623494	C₂×C₄	1	4	yes	complemented
128	C₈×Dic₈₉	—	2	1	no	—
129	C₈×Dic₈₉	—	2	1	no	—
130	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
133	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
134	C₄×D₄×C₈₉	—	2	2	no	—
135	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
136	#117×C₈₉	—	2	1	no	—
137	#117×C₈₉	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₈₉	—	2	1	no	—
139	C₂×C₄²×C₈₉	—	2	2	no	—
140	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
143	#104×C₈₉	C₂×C₄	1	4	yes	complemented
144	#104×C₈₉	C₂×C₄	1	4	yes	complemented
145	#97×C₈₉	—	2	1	no	—
146	C₄×C₈×C₈₉	—	2	1	no	—
147	#13083574	—	2	1	no	—
148	#13083574	—	2	1	no	—
149	#13083574	C₂²×C₄	1	2	yes	—
150	#13083574	C₂²×C₄	1	2	yes	—
151	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₂²⋊D₈₉	—	2	1	no	—
154	C₂×C₄×D₈₉	—	2	1	no	—
155	C₂×C₄×D₈₉	—	2	2	no	—
156	#13083564	C₄²	1	4	yes	complemented
157	#13083562	C₄²	1	4	yes	complemented
158	#13083561	C₄²	1	4	yes	complemented
159	#13083559	C₄²	1	4	yes	complemented
160	#13083558	—	2	1	no	—
161	#13083558	—	2	1	no	—
162	#13083558	—	2	4	no	—
163	#13083558	—	2	4	no	—
164	#13083558	C₂²×C₄	1	2	yes	—
165	#13083558	C₂²×C₄	1	2	yes	—
166	#13083557	—	2	4	no	—
167	#13083557	—	2	4	no	—
168	C₂×#10623494	—	2	1	no	—
169	C₂×#10623494	—	2	1	no	—
170	C₂×#10623494	—	2	1	no	—
171	C₂×#10623494	—	2	1	no	—
172	C₂×#10623494	—	2	4	no	—
173	C₂×#10623494	—	2	4	no	—
174	C₂×#10623494	C₂²×C₄	1	2	yes	—
175	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
176	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
177	C₂×#10623494	C₂²×C₄	1	2	yes	—
178	C₂×#10623494	C₂²×C₄	1	2	yes	—
179	C₂×#10623494	C₂²×C₄	1	2	yes	—
180	C₂×#10623494	C₂²×C₄	1	2	yes	—
181	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
182	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
183	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
184	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
185	C₂×#10623494	#41	1	2	yes	—
186	C₂×#10623494	#41	1	2	yes	—
187	C₈×D₈₉	—	2	4	no	—
188	C₈×D₈₉	—	2	4	no	—
189	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
190	#13083553	—	2	2	no	—
191	C₂²⋊Dic₈₉	—	2	1	no	—
192	#13083551	—	2	2	no	—
193	C₄×Dic₈₉	—	2	2	no	—
194	C₄×Dic₈₉	—	2	1	no	—
195	#41×C₈₉	—	2	1	no	—
196	#41×C₈₉	—	2	1	no	—
197	#41×C₈₉	C₂²×C₄	1	2	yes	—
198	#41×C₈₉	C₂²×C₄	1	2	yes	—
199	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₂×D₄×C₈₉	—	2	1	no	—
201	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₈₉	—	2	1	no	—
203	C₂²×C₄×C₈₉	—	2	1	no	—
204	C₂²×C₄×C₈₉	—	2	1	no	—
205	C₂²×C₄×C₈₉	—	2	2	no	—
206	C₂²×C₄×C₈₉	#41	1	2	yes	—
207	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
208	M₁₆×C₈₉	—	2	1	no	—
209	M₁₆×C₈₉	—	2	1	no	—
210	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
211	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
212	C₂×C₈×C₈₉	—	2	1	no	—
213	C₂×C₈×C₈₉	—	2	1	no	—
214	C₄⋊C₄×C₈₉	—	2	2	no	—
215	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
216	C₂²⋊C₄×C₈₉	—	2	1	no	—
217	C₂²⋊C₄×C₈₉	—	2	2	no	—
218	C₄²×C₈₉	—	2	2	no	—
219	C₄²×C₈₉	—	2	1	no	—
220	C₄²×C₈₉	—	2	1	no	—
221	C₄²×C₈₉	—	2	1	no	—
222	C₄²×C₈₉	—	4	4	no	—
223	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
224	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
225	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
226	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
228	C₂³×C₈₉	—	2	1	no	—
229	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
230	C₂²×D₈₉	—	2	1	no	—
231	Q₈×C₈₉	—	2	1	no	—
232	Q₈×C₈₉	C₂×C₄²	1	2	yes	—
233	D₄×C₈₉	—	2	2	no	—
234	D₄×C₈₉	—	2	2	no	—
235	D₄×C₈₉	—	2	1	no	—
236	D₄×C₈₉	C₂×C₄²	1	2	yes	—
237	C₂×C₄×C₈₉	—	2	4	no	—
238	C₂×C₄×C₈₉	—	2	1	no	—
239	C₂×C₄×C₈₉	—	2	2	no	—
240	C₂×C₄×C₈₉	—	2	2	no	—
241	C₂×C₄×C₈₉	—	2	2	no	—
242	C₂×C₄×C₈₉	—	2	2	no	—
243	C₂×C₄×C₈₉	—	2	2	no	—
244	C₂×C₄×C₈₉	—	4	2	no	—
245	C₂×C₄×C₈₉	—	4	2	no	—
246	C₂×C₄×C₈₉	—	8	2	no	—
247	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
248	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
249	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
250	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
252	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
255	C₂²⋊D₈₉	—	2	2	no	—
256	C₂²⋊D₈₉	—	2	2	no	—
257	C₂×Dic₈₉	—	2	1	no	—
258	C₂×Dic₈₉	—	2	2	no	—
259	D₃₅₆	—	2	1	no	—
260	D₃₅₆	C₂×C₄²	1	2	yes	—
261	C₄×D₈₉	—	2	2	no	—
262	C₄×D₈₉	—	2	2	no	—
263	C₄×D₈₉	—	8	2	no	—
264	Dic₁₇₈	—	2	1	no	—
265	Dic₁₇₈	C₂×C₄²	1	2	yes	—
266	C₈×C₈₉	—	2	2	no	—
267	C₈×C₈₉	—	2	2	no	—
268	#10623494	—	2	2	no	—
269	#10623494	—	2	2	no	—
270	#10623494	—	2	2	no	—
271	#10623494	C₂×C₄²	1	2	yes	—
272	#10623494	C₂×C₄²	1	2	yes	—
273	#10623494	C₄×D₄	1	2	yes	—
274	#10623494	C₄×D₄	1	2	yes	—
275	#10623494	C₄×D₄	1	2	yes	—
276	#10623494	C₄×D₄	1	2	yes	—
277	C₂²×C₈₉	—	2	2	no	—
278	C₂²×C₈₉	—	2	2	no	—
279	C₂²×C₈₉	—	4	2	no	—
280	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
281	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
282	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
283	C₂×D₈₉	—	2	2	no	—
284	C₂×D₈₉	—	4	2	no	—
285	C₄×C₈₉	—	2	4	no	—
286	C₄×C₈₉	—	2	2	no	—
287	C₄×C₈₉	—	2	2	no	—
288	C₄×C₈₉	—	2	2	no	—
289	C₄×C₈₉	—	4	2	no	—
290	C₄×C₈₉	—	4	2	no	—
291	C₄×C₈₉	C₂²×C₄²	1	1	yes	characteristic
292	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
293	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
294	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
295	Dic₈₉	—	2	2	no	—
296	Dic₈₉	—	4	2	no	—
297	#20512	—	89	1	no	maximal, Sylow
298	C₂×C₈₉	—	2	1	no	—
299	C₂×C₈₉	—	2	1	no	—
300	C₂×C₈₉	—	4	2	no	—
301	C₂×C₈₉	C₄²×D₄	1	1	yes	characteristic
302	C₂×C₈₉	#2956	1	2	yes	—
303	D₈₉	—	4	2	no	—
304	C₂×#444	—	89	1	no	—
305	C₂×#443	—	89	1	no	—
306	#2943	—	89	1	no	—
307	#2875	—	89	1	no	—
308	#2875	—	89	1	no	—
309	#1778	—	89	1	no	—
310	#1773	—	89	1	no	—
311	#1772	—	89	1	no	—
312	#1765	—	89	1	no	—
313	#1765	—	89	1	no	—
314	#1764	—	89	1	no	—
315	#1764	—	89	1	no	—
316	C₄×#104	—	89	1	no	—
317	C₄×#104	D₈₉	1	1	yes	characteristic, complemented
318	C₄×#97	—	89	1	no	—
319	C₈₉	#20512	1	1	yes	characteristic, complemented, Sylow
320	C₂×#135	—	89	1	no	—
321	C₂×#131	—	89	1	no	—
322	C₂×#131	—	89	1	no	—
323	C₂×#131	—	89	1	no	—
324	C₂×#131	—	89	1	no	—
325	C₄×#41	—	89	1	no	—
326	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
327	#444	—	89	8	no	—
328	#443	—	89	8	no	—
329	#442	—	89	2	no	—
330	#441	—	89	2	no	—
331	#440	—	89	2	no	—
332	#440	—	89	2	no	—
333	C₂×#108	—	89	1	no	—
334	C₂×#108	—	89	1	no	—
335	#427	—	89	1	no	—
336	C₂×#104	—	89	1	no	—
337	C₂×#104	—	89	1	no	—
338	C₂×#104	C₂×D₈₉	1	1	yes	characteristic
339	C₂×#104	C₂×D₈₉	1	1	yes	characteristic
340	#416	—	89	1	no	—
341	#416	—	89	1	no	—
342	#405	—	89	1	no	—
343	#405	—	89	1	no	—
344	#405	—	89	1	no	—
345	#405	—	89	1	no	—
346	#405	—	178	1	no	—
347	#405	—	178	1	no	—
348	#405	—	178	1	no	—
349	#405	—	178	1	no	—
350	C₄×M₁₆	—	89	1	no	—
351	C₄×M₁₆	—	178	1	no	—
352	C₄×M₁₆	—	178	1	no	—
353	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
354	C₂×#97	—	89	1	no	—
355	C₂×#97	—	89	1	no	—
356	C₂×#97	—	89	1	no	—
357	C₂×#97	—	89	1	no	—
358	C₂×#97	—	178	1	no	—
359	C₂×#97	—	178	1	no	—
360	C₂×C₄×C₈	—	89	1	no	—
361	C₂×C₄×C₈	—	89	1	no	—
362	C₄³	C₂×D₈₉	1	1	yes	characteristic
363	#341	—	89	1	no	—
364	#341	—	89	1	no	—
365	#339	—	89	1	no	—
366	#339	—	89	1	no	—
367	#339	C₂×D₈₉	1	1	yes	characteristic
368	#339	C₂×D₈₉	1	1	yes	characteristic
369	C₂×#41	—	89	1	no	—
370	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
371	#135	—	89	4	no	—
372	#135	—	89	4	no	—
373	C₂×Q₁₆	—	89	1	no	—
374	C₂×SD₁₆	—	89	1	no	—
375	C₂×SD₁₆	—	89	1	no	—
376	C₂×D₈	—	89	1	no	—
377	#131	—	89	4	no	—
378	#131	—	89	4	no	—
379	#131	—	89	4	no	—
380	#131	—	89	4	no	—
381	#131	—	178	2	no	—
382	#131	—	178	2	no	—
383	#131	—	178	2	no	—
384	#131	—	178	2	no	—
385	C₂×M₁₆	—	89	1	no	—
386	C₂×M₁₆	—	89	1	no	—
387	C₂×M₁₆	—	178	1	no	—
388	C₂×M₁₆	—	178	1	no	—
389	C₂×M₁₆	—	178	1	no	—
390	C₂×M₁₆	—	178	1	no	—
391	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
392	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
393	C₂²×C₈	—	89	1	no	—
394	C₂²×C₈	—	89	1	no	—
395	C₂²×C₈	—	89	1	no	—
396	C₂²×C₈	—	89	1	no	—
397	C₂²×C₈	—	178	1	no	—
398	C₂²×C₈	—	178	1	no	—
399	C₂²×C₈	—	178	1	no	—
400	C₂²×C₈	—	178	1	no	—
401	C₄×Q₈	—	89	2	no	—
402	C₄×Q₈	C₄×D₈₉	1	2	yes	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	89	2	no	—
405	C₄×D₄	—	178	2	no	—
406	C₄×D₄	C₄×D₈₉	1	2	yes	—
407	#117	—	2	1	no	—
408	#117	—	89	1	no	—
409	#117	—	178	1	no	—
410	#117	C₂²×D₈₉	1	1	yes	characteristic
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	—	2	2	no	—
413	C₂×C₄²	—	178	1	no	—
414	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
415	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
416	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
417	#108	—	89	4	no	—
418	#108	—	89	4	no	—
419	#107	—	89	2	no	—
420	#106	—	89	2	no	—
421	#104	—	89	4	no	—
422	#104	—	89	4	no	—
423	#104	C₄×D₈₉	1	4	yes	complemented
424	#104	C₄×D₈₉	1	4	yes	complemented
425	#103	—	89	2	no	—
426	#103	—	89	2	no	—
427	#102	—	89	2	no	—
428	#102	—	89	2	no	—
429	#97	—	2	1	no	—
430	#97	—	89	2	no	—
431	#97	—	89	2	no	—
432	#97	—	89	4	no	—
433	#97	—	89	1	no	—
434	#97	—	89	1	no	—
435	#97	—	89	1	no	—
436	#97	—	89	1	no	—
437	#97	—	178	2	no	—
438	#97	—	178	1	no	—
439	#97	—	178	1	no	—
440	#97	—	178	1	no	—
441	#97	—	178	1	no	—
442	#97	—	178	1	no	—
443	C₄×C₈	—	2	1	no	—
444	C₄×C₈	—	89	4	no	—
445	C₄×C₈	—	178	2	no	—
446	C₄×C₈	—	178	1	no	—
447	C₄×C₈	—	178	1	no	—
448	C₄×C₈	—	178	1	no	—
449	C₄×C₈	—	178	1	no	—
450	C₄×C₈	—	178	1	no	—
451	#41	—	2	1	no	—
452	#41	—	2	1	no	—
453	#41	—	89	2	no	—
454	#41	—	89	2	no	—
455	#41	—	178	1	no	—
456	#41	—	178	1	no	—
457	#41	C₂×C₄×D₈₉	1	2	yes	—
458	#41	C₂×C₄×D₈₉	1	2	yes	—
459	C₂×Q₈	—	89	1	no	—
460	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	89	1	no	—
463	C₂×D₄	—	178	1	no	—
464	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	178	1	no	—
470	C₂²×C₄	—	178	2	no	—
471	C₂²×C₄	#13083573	1	2	yes	—
472	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
473	Q₁₆	—	89	4	no	—
474	SD₁₆	—	89	4	no	—
475	SD₁₆	—	89	4	no	—
476	D₈	—	89	4	no	—
477	M₁₆	—	2	1	no	—
478	M₁₆	—	2	1	no	—
479	M₁₆	—	89	2	no	—
480	M₁₆	—	89	2	no	—
481	M₁₆	—	178	4	no	—
482	M₁₆	—	178	4	no	—
483	M₁₆	—	178	4	no	—
484	M₁₆	—	178	4	no	—
485	M₁₆	—	178	1	no	—
486	M₁₆	—	178	1	no	—
487	M₁₆	C₂×C₄×D₈₉	1	2	yes	—
488	M₁₆	C₂×C₄×D₈₉	1	2	yes	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	89	2	no	—
492	C₂×C₈	—	89	2	no	—
493	C₂×C₈	—	89	1	no	—
494	C₂×C₈	—	89	1	no	—
495	C₂×C₈	—	89	2	no	—
496	C₂×C₈	—	89	2	no	—
497	C₂×C₈	—	89	1	no	—
498	C₂×C₈	—	89	1	no	—
499	C₂×C₈	—	89	1	no	—
500	C₂×C₈	—	89	1	no	—
501	C₂×C₈	—	89	2	no	—
502	C₂×C₈	—	89	2	no	—
503	C₂×C₈	—	89	2	no	—
504	C₂×C₈	—	178	4	no	—
505	C₂×C₈	—	178	4	no	—
506	C₂×C₈	—	178	4	no	—
507	C₂×C₈	—	178	4	no	—
508	C₂×C₈	—	178	1	no	—
509	C₂×C₈	—	178	1	no	—
510	C₂×C₈	—	178	1	no	—
511	C₂×C₈	—	178	1	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	89	2	no	—
514	C₄⋊C₄	—	178	2	no	—
515	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	178	1	no	—
519	C₂²⋊C₄	—	178	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	4	4	no	—
525	C₄²	—	178	2	no	—
526	C₄²	—	178	1	no	—
527	C₄²	C₂×C₄×D₈₉	1	2	yes	—
528	C₄²	C₂×C₄×D₈₉	1	2	yes	—
529	C₄²	C₂×C₄×D₈₉	1	2	yes	—
530	C₄²	D₄×D₈₉	1	1	yes	characteristic
531	C₄²	D₄×D₈₉	1	1	yes	characteristic
532	C₂³	—	2	1	no	—
533	C₂³	—	178	1	no	—
534	C₂³	C₂×#13083573	1	1	yes	characteristic
535	Q₈	—	2	1	no	—
536	Q₈	—	89	2	no	—
537	Q₈	—	178	1	no	—
538	Q₈	C₄²×D₈₉	1	2	yes	—
539	D₄	—	2	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	1	no	—
542	D₄	—	89	2	no	—
543	D₄	—	178	2	no	—
544	D₄	—	178	2	no	—
545	D₄	—	178	1	no	—
546	D₄	C₄²×D₈₉	1	2	yes	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	8	2	no	—
557	C₂×C₄	—	178	2	no	—
558	C₂×C₄	—	178	1	no	—
559	C₂×C₄	—	178	2	no	—
560	C₂×C₄	—	178	2	no	—
561	C₂×C₄	—	712	2	no	—
562	C₂×C₄	#15667972	1	2	yes	—
563	C₂×C₄	#15667972	1	2	yes	—
564	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
565	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
567	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
568	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
569	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	2	2	no	—
572	C₈	—	89	2	no	—
573	C₈	—	89	2	no	—
574	C₈	—	89	2	no	—
575	C₈	—	89	2	no	—
576	C₈	—	89	2	no	—
577	C₈	—	89	2	no	—
578	C₈	—	178	2	no	—
579	C₈	—	178	2	no	—
580	C₈	—	178	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	356	2	no	—
585	C₂²	—	178	2	no	—
586	C₂²	C₂×#15667972	1	1	yes	characteristic
587	C₂²	C₄×#13083573	1	1	yes	characteristic
588	C₂²	C₄×#13083573	1	1	yes	characteristic
589	C₄	—	2	4	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	2	no	—
595	C₄	—	356	2	no	—
596	C₄	—	178	2	no	—
597	C₄	C₂×C₄²×D₈₉	1	1	yes	characteristic
598	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
599	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
600	C₄	#19152066	1	1	yes	characteristic
601	C₂	—	2	1	no	—
602	C₂	—	2	1	no	—
603	C₂	—	4	2	no	—
604	C₂	—	356	2	no	—
605	C₂	C₄×#15667972	1	1	yes	characteristic
606	C₂	#26029158	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₄×C₈₉	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₄×#104×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668032	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×#104	D₈₉
hypocenter	C₈₉	#20512
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#104

Complements

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

N	H ≅ G/N	type
4. #26028681	C₂	semidirect
5. #26028680	C₂	semidirect
6. #26020159	C₂	semidirect
7. #26020135	C₂	semidirect
8. #26020130	C₂	semidirect
9. #26020097	C₂	semidirect
10. #26020093	C₂	semidirect
11. #26020090	C₂	semidirect
12. #26020086	C₂	semidirect
13. C₄×#15667940	C₂	semidirect
14. C₄×#15667923	C₂	semidirect
15. C₄×#104×C₈₉	C₂	semidirect
22. #19151717	C₄	semidirect
23. #19151712	C₄	semidirect
24. #19151708	C₄	semidirect
25. #19151703	C₄	semidirect
26. #19151698	C₄	semidirect
27. #19151696	C₄	semidirect
74. #15668020	C₂×C₄	semidirect
75. #15668020	C₂×C₄	semidirect
78. #15668019	C₂×C₄	semidirect
79. #15668019	C₂×C₄	semidirect
100. #15667947	C₂×C₄	semidirect
101. #15667947	C₂×C₄	semidirect
104. #15667940	C₂×C₄	semidirect
105. #15667940	C₂×C₄	semidirect
116. #15667923	C₂×C₄	semidirect
127. C₄×#10623494	C₂×C₄	semidirect
143. #104×C₈₉	C₂×C₄	semidirect
144. #104×C₈₉	C₂×C₄	semidirect
156. #13083564	C₄²	semidirect
157. #13083562	C₄²	semidirect
158. #13083561	C₄²	semidirect
159. #13083559	C₄²	semidirect
317. C₄×#104	D₈₉	semidirect
319. C₈₉	#20512	semidirect
423. #104	C₄×D₈₉	semidirect
424. #104	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151717	2
C₂×#19151712	2
#26029050	2
#26028681	2
#26028680	2
#26020159	2
#26020135	2
#26020130	2
#26020097	2
#26020093	2
#26020090	2
#26020086	2
C₄×#15667940	2
C₄×#15667923	2
C₄×#104×C₈₉	2
#20512	89