Subgroups — #26034582

Order 11392.

1260 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152339	C₂	1	4	yes	maximal, complemented
2	#19152333	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152270	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152269	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152244	C₂	1	2	yes	maximal, complemented
6	#19152239	C₂	1	2	yes	maximal, complemented
7	D₄×D₃₅₆	C₂	1	2	yes	maximal, complemented
8	D₄×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152232	C₂	1	2	yes	maximal, complemented
10	#19152204	C₂	1	2	yes	maximal, complemented
11	#19152203	C₂	1	2	yes	maximal, complemented
12	#19152167	C₂	1	2	yes	maximal, complemented
13	#19152166	C₂	1	2	yes	maximal, complemented
14	#19152159	C₂	1	4	yes	maximal, complemented
15	C₂×#15668009	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152132	C₂	1	1	yes	maximal, characteristic, complemented
17	#529×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13083575	C₂²	1	2	yes	complemented
19	C₂×#13083574	C₂²	1	2	yes	complemented
20	C₂²×D₃₅₆	C₂²	1	2	yes	complemented
21	C₂²×D₃₅₆	C₂²	1	2	yes	complemented
22	C₂²×D₃₅₆	C₂²	1	2	yes	complemented
23	C₂²×D₃₅₆	C₂²	1	2	yes	complemented
24	C₂×D₄×D₈₉	C₂²	1	4	yes	complemented
25	C₂×D₄×D₈₉	C₂²	1	2	yes	complemented
26	#15668009	C₂²	1	1	yes	characteristic
27	#15668009	C₂²	1	2	yes	complemented
28	#15668009	C₂²	1	2	yes	complemented
29	#15668009	C₂²	1	1	yes	characteristic, complemented
30	#15668009	C₂²	1	2	yes	complemented
31	#15668009	C₂²	1	2	yes	complemented
32	#15668008	C₂²	1	2	yes	complemented
33	#15668006	C₂²	1	2	yes	complemented
34	#15668004	C₂²	1	1	yes	characteristic, complemented
35	#15668001	C₂²	1	2	yes	complemented
36	#15668000	C₂²	1	1	yes	characteristic, complemented
37	#15668000	C₂²	1	2	yes	complemented
38	#15667997	C₂²	1	4	yes	complemented
39	#15667997	C₂²	1	4	yes	complemented
40	#15667997	C₂²	1	4	yes	complemented
41	#15667997	C₂²	1	4	yes	complemented
42	#15667995	C₂²	1	2	yes	complemented
43	#15667991	C₂²	1	1	yes	characteristic, complemented
44	#15667987	C₂²	1	4	yes	complemented
45	#15667987	C₂²	1	4	yes	complemented
46	#15667987	C₂²	1	4	yes	complemented
47	#15667987	C₂²	1	2	yes	complemented
48	#15667987	C₂²	1	2	yes	complemented
49	#15667987	C₂²	1	4	yes	complemented
50	#15667986	C₂²	1	1	yes	characteristic
51	#15667986	C₂²	1	2	yes	complemented
52	#15667986	C₂²	1	2	yes	complemented
53	#15667985	C₂²	1	4	yes	complemented
54	#15667985	C₂²	1	4	yes	complemented
55	#15667985	C₂²	1	4	yes	complemented
56	#15667985	C₂²	1	4	yes	complemented
57	#15667982	C₂²	1	4	yes	complemented
58	#15667982	C₂²	1	4	yes	complemented
59	#15667982	C₂²	1	4	yes	complemented
60	#15667982	C₂²	1	4	yes	complemented
61	#15667982	C₂²	1	4	yes	complemented
62	#15667980	C₂²	1	4	yes	complemented
63	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
64	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₃₅₆	C₂²	1	2	yes	complemented
66	C₄×D₃₅₆	C₂²	1	2	yes	complemented
67	#15667974	C₂²	1	2	yes	complemented
68	#15667974	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
70	#15667969	C₂²	1	2	yes	complemented
71	C₂²⋊C₄×D₈₉	C₂²	1	4	yes	complemented
72	#126×C₈₉	C₂²	1	2	yes	complemented
73	#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
74	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	#123×C₈₉	C₂²	1	2	yes	complemented
76	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
77	#121×C₈₉	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
80	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
81	#117×C₈₉	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₈₉	C₂³	1	4	yes	—
84	C₂³×D₈₉	C₂³	1	4	yes	—
85	#13083575	—	4	4	no	—
86	#13083574	—	4	4	no	—
87	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
88	C₂×D₃₅₆	—	4	4	no	—
89	C₂×D₃₅₆	—	4	4	no	—
90	C₂×D₃₅₆	—	4	4	no	—
91	C₂×D₃₅₆	—	4	4	no	—
92	C₂×D₃₅₆	C₂³	1	2	yes	—
93	C₂×D₃₅₆	C₂³	1	2	yes	—
94	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
95	C₂×D₃₅₆	C₂³	1	2	yes	—
96	C₂×D₃₅₆	C₂³	1	2	yes	—
97	C₂×D₃₅₆	C₂³	1	4	yes	—
98	C₂×D₃₅₆	C₂³	1	4	yes	—
99	C₂×D₃₅₆	C₂³	1	2	yes	—
100	C₂×D₃₅₆	C₂³	1	4	yes	—
101	C₂×D₃₅₆	C₂³	1	4	yes	—
102	C₂×D₃₅₆	C₂³	1	4	yes	—
103	C₂×D₃₅₆	C₂³	1	4	yes	—
104	C₂×D₃₅₆	C₂³	1	2	yes	—
105	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
106	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
109	D₄×D₈₉	—	4	4	no	—
110	D₄×D₈₉	—	4	8	no	—
111	C₂×C₄×D₈₉	C₂³	1	2	yes	—
112	C₂×C₄×D₈₉	C₂³	1	4	yes	—
113	C₂×C₄×D₈₉	C₂³	1	4	yes	—
114	C₂×C₄×D₈₉	C₂³	1	4	yes	—
115	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
116	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
117	#13083553	C₂³	1	2	yes	—
118	#13083553	C₂³	1	2	yes	—
119	#13083553	C₂³	1	2	yes	—
120	#13083553	C₂³	1	2	yes	—
121	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
122	#13083551	C₂³	1	2	yes	—
123	#13083551	C₂³	1	2	yes	—
124	#13083551	C₂³	1	2	yes	—
125	#13083551	C₂³	1	4	yes	—
126	#13083551	C₂³	1	4	yes	—
127	#13083551	C₂³	1	4	yes	—
128	#13083551	C₂³	1	4	yes	—
129	#13083551	C₂³	1	2	yes	—
130	#13083551	C₂³	1	4	yes	—
131	#13083551	C₂³	1	4	yes	—
132	C₄×Dic₈₉	C₂³	1	2	yes	—
133	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₈₉	C₂³	1	2	yes	—
135	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
139	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
140	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₄²×C₈₉	C₂³	1	1	yes	characteristic
152	C₄²×C₈₉	C₂³	1	2	yes	—
153	C₄²×C₈₉	C₂³	1	1	yes	characteristic
154	C₄²×C₈₉	C₂³	1	1	yes	characteristic
155	C₄²×C₈₉	C₂³	1	1	yes	characteristic
156	C₂³×C₈₉	C₂⁴	1	2	yes	—
157	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
158	C₂²×D₈₉	—	2	8	no	—
159	C₂²×D₈₉	—	4	4	no	—
160	C₂²×D₈₉	—	4	4	no	—
161	C₂²×D₈₉	—	4	4	no	—
162	C₂²×D₈₉	—	4	4	no	—
163	C₂²×D₈₉	—	4	4	no	—
164	C₂²×D₈₉	C₂⁴	1	2	yes	—
165	C₂²×D₈₉	C₂⁴	1	4	yes	—
166	C₂²×D₈₉	C₂⁴	1	4	yes	—
167	Q₈×C₈₉	—	2	2	no	—
168	D₄×C₈₉	—	2	4	no	—
169	D₄×C₈₉	—	2	2	no	—
170	C₂×C₄×C₈₉	—	2	2	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	2	2	no	—
173	C₂×C₄×C₈₉	—	2	4	no	—
174	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
179	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
180	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
181	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
183	C₂²⋊D₈₉	—	2	4	no	—
184	C₂²⋊D₈₉	—	4	4	no	—
185	C₂²⋊D₈₉	—	4	4	no	—
186	C₂²⋊D₈₉	—	4	4	no	—
187	C₂×Dic₈₉	C₂⁴	1	2	yes	—
188	C₂×Dic₈₉	C₂⁴	1	2	yes	—
189	C₂×Dic₈₉	C₂⁴	1	2	yes	—
190	D₃₅₆	—	2	4	no	—
191	D₃₅₆	—	2	2	no	—
192	D₃₅₆	—	2	4	no	—
193	D₃₅₆	—	2	4	no	—
194	D₃₅₆	—	2	4	no	—
195	D₃₅₆	—	4	4	no	—
196	D₃₅₆	—	4	4	no	—
197	D₃₅₆	—	4	4	no	—
198	D₃₅₆	—	4	4	no	—
199	D₃₅₆	—	4	2	no	—
200	D₃₅₆	—	4	4	no	—
201	D₃₅₆	—	4	2	no	—
202	D₃₅₆	—	4	4	no	—
203	C₄×D₈₉	—	2	4	no	—
204	C₄×D₈₉	—	4	4	no	—
205	C₄×D₈₉	—	4	4	no	—
206	C₄×D₈₉	—	4	4	no	—
207	Dic₁₇₈	—	2	2	no	—
208	C₂²×C₈₉	—	2	1	no	—
209	C₂²×C₈₉	—	2	1	no	—
210	C₂²×C₈₉	—	2	2	no	—
211	C₂²×C₈₉	—	2	2	no	—
212	C₂²×C₈₉	—	2	2	no	—
213	C₂²×C₈₉	H(5,𝔽₂)	1	2	yes	—
214	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
215	C₂×D₈₉	—	2	2	no	—
216	C₂×D₈₉	—	2	4	no	—
217	C₂×D₈₉	—	2	4	no	—
218	C₂×D₈₉	—	2	4	no	—
219	C₂×D₈₉	—	2	2	no	—
220	C₂×D₈₉	—	2	4	no	—
221	C₂×D₈₉	—	2	4	no	—
222	C₂×D₈₉	—	2	4	no	—
223	C₂×D₈₉	—	2	2	no	—
224	C₂×D₈₉	—	8	8	no	—
225	C₂×D₈₉	—	8	8	no	—
226	C₄×C₈₉	—	2	2	no	—
227	C₄×C₈₉	—	2	2	no	—
228	C₄×C₈₉	—	2	2	no	—
229	C₄×C₈₉	—	2	1	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	—	2	1	no	—
232	C₄×C₈₉	—	2	1	no	—
233	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
234	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
235	Dic₈₉	—	2	2	no	—
236	Dic₈₉	—	2	2	no	—
237	Dic₈₉	—	2	2	no	—
238	C₂×C₈₉	—	2	2	no	—
239	C₂×C₈₉	—	4	2	no	—
240	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
243	D₈₉	—	4	4	no	—
244	D₈₉	—	4	2	no	—
245	D₈₉	—	4	4	no	—
246	#3543	—	89	1	no	maximal, Sylow
247	C₈₉	#3543	1	1	yes	characteristic, complemented, Sylow
248	#560	—	89	4	no	—
249	#559	—	89	1	no	—
250	#550	—	89	1	no	—
251	#550	—	89	1	no	—
252	#546	—	89	2	no	—
253	#546	—	89	2	no	—
254	D₄²	—	89	2	no	—
255	D₄²	—	89	1	no	—
256	D₄²	—	89	2	no	—
257	#540	—	89	2	no	—
258	#540	—	89	2	no	—
259	#535	—	89	2	no	—
260	#535	—	89	2	no	—
261	#534	—	89	4	no	—
262	C₂×#127	—	89	1	no	—
263	#529	—	89	1	no	—
264	#529	D₈₉	1	1	yes	characteristic, complemented
265	C₂×#41	—	89	2	no	—
266	C₂×#41	—	89	2	no	—
267	C₂²×D₄	—	89	4	no	—
268	C₂²×D₄	—	89	2	no	—
269	C₂²×D₄	—	89	2	no	—
270	C₂²×D₄	—	89	2	no	—
271	C₂²×D₄	—	89	2	no	—
272	C₂²×D₄	—	89	2	no	—
273	#127	—	89	2	no	—
274	#127	—	89	2	no	—
275	#127	—	89	2	no	—
276	#127	—	89	1	no	—
277	#127	—	89	1	no	—
278	#127	—	89	2	no	—
279	#127	—	89	2	no	—
280	#126	—	89	2	no	—
281	#126	C₂×D₈₉	1	2	yes	complemented
282	#125	—	89	1	no	—
283	#125	C₂×D₈₉	1	1	yes	characteristic, complemented
284	#124	—	89	2	no	—
285	#124	—	89	1	no	—
286	#124	—	89	2	no	—
287	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
288	#123	—	89	2	no	—
289	#123	—	89	4	no	—
290	#123	—	89	4	no	—
291	#123	—	89	4	no	—
292	#123	—	89	4	no	—
293	#123	C₂×D₈₉	1	2	yes	complemented
294	C₂²⋊Q₈	—	89	1	no	—
295	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
296	#121	—	89	1	no	—
297	#121	—	89	2	no	—
298	#121	—	89	2	no	—
299	#121	—	89	4	no	—
300	#121	—	89	4	no	—
301	#121	—	89	4	no	—
302	#121	—	89	2	no	—
303	#121	—	89	2	no	—
304	#121	—	89	4	no	—
305	#121	—	89	4	no	—
306	#121	—	89	4	no	—
307	#121	—	89	4	no	—
308	#121	—	89	4	no	—
309	#121	C₂×D₈₉	1	1	yes	characteristic
310	#120	—	89	4	no	—
311	#120	—	89	4	no	—
312	#120	—	89	4	no	—
313	#120	—	89	4	no	—
314	#120	—	89	4	no	—
315	#120	—	89	4	no	—
316	C₄×Q₈	—	89	1	no	—
317	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
318	C₄×D₄	—	89	2	no	—
319	C₄×D₄	—	89	2	no	—
320	C₄×D₄	—	89	2	no	—
321	C₄×D₄	—	89	1	no	—
322	C₄×D₄	—	89	2	no	—
323	C₄×D₄	—	89	2	no	—
324	C₄×D₄	C₂×D₈₉	1	2	yes	complemented
325	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
326	#117	—	89	2	no	—
327	#117	C₂×D₈₉	1	2	yes	complemented
328	C₂×C₂²⋊C₄	—	89	4	no	—
329	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic, complemented
330	C₂⁴	—	89	4	no	—
331	C₂⁴	—	89	4	no	—
332	#41	—	356	4	no	—
333	#41	—	356	4	no	—
334	C₂×Q₈	—	89	1	no	—
335	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
336	C₂×D₄	—	89	4	no	—
337	C₂×D₄	—	89	4	no	—
338	C₂×D₄	—	89	4	no	—
339	C₂×D₄	—	89	2	no	—
340	C₂×D₄	—	89	4	no	—
341	C₂×D₄	—	89	4	no	—
342	C₂×D₄	—	89	2	no	—
343	C₂×D₄	—	89	4	no	—
344	C₂×D₄	—	89	4	no	—
345	C₂×D₄	—	89	4	no	—
346	C₂×D₄	—	89	4	no	—
347	C₂×D₄	—	89	2	no	—
348	C₂×D₄	—	89	2	no	—
349	C₂×D₄	—	89	1	no	—
350	C₂×D₄	—	89	2	no	—
351	C₂×D₄	—	89	2	no	—
352	C₂×D₄	—	89	2	no	—
353	C₂×D₄	—	356	4	no	—
354	C₂×D₄	—	356	4	no	—
355	C₂×D₄	—	356	4	no	—
356	C₂×D₄	—	356	4	no	—
357	C₂×D₄	—	356	8	no	—
358	C₂×D₄	—	356	4	no	—
359	C₂×D₄	C₂²×D₈₉	1	2	yes	—
360	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
361	C₂²×C₄	—	89	4	no	—
362	C₂²×C₄	—	89	4	no	—
363	C₂²×C₄	—	89	4	no	—
364	C₂²×C₄	—	89	2	no	—
365	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
366	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
367	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
368	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
369	C₄⋊C₄	—	89	2	no	—
370	C₄⋊C₄	—	89	2	no	—
371	C₄⋊C₄	—	89	1	no	—
372	C₄⋊C₄	—	89	1	no	—
373	C₄⋊C₄	—	89	2	no	—
374	C₄⋊C₄	—	89	2	no	—
375	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
376	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
377	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
378	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
379	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
380	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
381	C₂²⋊C₄	—	89	2	no	—
382	C₂²⋊C₄	—	89	4	no	—
383	C₂²⋊C₄	—	89	4	no	—
384	C₂²⋊C₄	—	89	2	no	—
385	C₂²⋊C₄	—	89	2	no	—
386	C₂²⋊C₄	—	89	2	no	—
387	C₂²⋊C₄	—	89	2	no	—
388	C₂²⋊C₄	—	89	4	no	—
389	C₂²⋊C₄	—	89	4	no	—
390	C₂²⋊C₄	—	89	4	no	—
391	C₂²⋊C₄	—	89	4	no	—
392	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
393	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
394	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
395	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
396	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
397	C₄²	—	89	2	no	—
398	C₄²	C₂²×D₈₉	1	1	yes	characteristic
399	C₄²	C₂²×D₈₉	1	1	yes	characteristic
400	C₄²	C₂²×D₈₉	1	1	yes	characteristic
401	C₄²	C₂²×D₈₉	1	1	yes	characteristic
402	C₄²	C₂²×D₈₉	1	2	yes	—
403	C₂³	—	89	4	no	—
404	C₂³	—	89	2	no	—
405	C₂³	—	89	4	no	—
406	C₂³	—	356	4	no	—
407	C₂³	—	356	4	no	—
408	C₂³	—	356	4	no	—
409	C₂³	—	356	4	no	—
410	C₂³	—	356	4	no	—
411	C₂³	—	178	8	no	—
412	C₂³	C₂³×D₈₉	1	2	yes	—
413	C₂³	C₂³×D₈₉	1	1	yes	characteristic
414	Q₈	—	2	2	no	—
415	Q₈	—	178	2	no	—
416	D₄	—	2	4	no	—
417	D₄	—	2	2	no	—
418	D₄	—	356	4	no	—
419	D₄	—	356	4	no	—
420	D₄	—	356	4	no	—
421	D₄	—	356	2	no	—
422	D₄	—	356	4	no	—
423	D₄	—	356	2	no	—
424	D₄	—	356	4	no	—
425	D₄	—	356	4	no	—
426	D₄	—	356	4	no	—
427	D₄	—	356	4	no	—
428	D₄	—	356	4	no	—
429	D₄	—	178	4	no	—
430	D₄	—	178	2	no	—
431	D₄	—	178	4	no	—
432	D₄	—	178	4	no	—
433	D₄	—	178	4	no	—
434	D₄	—	178	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	89	2	no	—
440	C₂×C₄	—	89	2	no	—
441	C₂×C₄	—	89	2	no	—
442	C₂×C₄	—	356	4	no	—
443	C₂×C₄	—	356	4	no	—
444	C₂×C₄	—	356	4	no	—
445	C₂×C₄	—	178	4	no	—
446	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
447	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
448	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
449	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₈₉	1	2	yes	—
451	C₂×C₄	C₂³×D₈₉	1	2	yes	—
452	C₂×C₄	C₂³×D₈₉	1	2	yes	—
453	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
454	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	178	4	no	—
461	C₂²	—	178	4	no	—
462	C₂²	—	178	4	no	—
463	C₂²	—	178	2	no	—
464	C₂²	—	178	4	no	—
465	C₂²	—	178	2	no	—
466	C₂²	—	178	4	no	—
467	C₂²	—	178	2	no	—
468	C₂²	—	178	4	no	—
469	C₂²	—	712	8	no	—
470	C₂²	—	712	8	no	—
471	C₂²	#15668058	1	2	yes	—
472	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	178	2	no	—
481	C₄	—	178	2	no	—
482	C₄	—	178	2	no	—
483	C₄	#15668058	1	2	yes	—
484	C₄	#15668058	1	2	yes	—
485	C₂	—	2	2	no	—
486	C₂	—	4	2	no	—
487	C₂	—	356	4	no	—
488	C₂	—	356	4	no	—
489	C₂	—	356	2	no	—
490	C₂	C₂×#15668058	1	1	yes	characteristic
491	C₂	C₂×#15668058	1	1	yes	characteristic
492	C₂	C₂×#15668058	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#529×C₈₉	C₂
hypercenter	#529	D₈₉
hypocenter	C₈₉	#3543
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #19152339	C₂	semidirect
2. #19152333	C₂	semidirect
3. #19152270	C₂	semidirect
4. #19152269	C₂	semidirect
5. #19152244	C₂	semidirect
6. #19152239	C₂	semidirect
7. D₄×D₃₅₆	C₂	semidirect
8. D₄×D₃₅₆	C₂	semidirect
9. #19152232	C₂	semidirect
10. #19152204	C₂	semidirect
11. #19152203	C₂	semidirect
12. #19152167	C₂	semidirect
13. #19152166	C₂	semidirect
14. #19152159	C₂	semidirect
15. C₂×#15668009	C₂	semidirect
16. #19152132	C₂	semidirect
17. #529×C₈₉	C₂	semidirect
18. C₂×#13083575	C₂²	semidirect
19. C₂×#13083574	C₂²	semidirect
20. C₂²×D₃₅₆	C₂²	semidirect
21. C₂²×D₃₅₆	C₂²	semidirect
22. C₂²×D₃₅₆	C₂²	semidirect
23. C₂²×D₃₅₆	C₂²	semidirect
24. C₂×D₄×D₈₉	C₂²	semidirect
25. C₂×D₄×D₈₉	C₂²	semidirect
27. #15668009	C₂²	semidirect
28. #15668009	C₂²	semidirect
29. #15668009	C₂²	semidirect
30. #15668009	C₂²	semidirect
31. #15668009	C₂²	semidirect
32. #15668008	C₂²	semidirect
33. #15668006	C₂²	semidirect
34. #15668004	C₂²	semidirect
35. #15668001	C₂²	semidirect
36. #15668000	C₂²	semidirect
37. #15668000	C₂²	semidirect
38. #15667997	C₂²	semidirect
39. #15667997	C₂²	semidirect
40. #15667997	C₂²	semidirect
41. #15667997	C₂²	semidirect
42. #15667995	C₂²	semidirect
43. #15667991	C₂²	semidirect
44. #15667987	C₂²	semidirect
45. #15667987	C₂²	semidirect
46. #15667987	C₂²	semidirect
47. #15667987	C₂²	semidirect
48. #15667987	C₂²	semidirect
49. #15667987	C₂²	semidirect
51. #15667986	C₂²	semidirect
52. #15667986	C₂²	semidirect
53. #15667985	C₂²	semidirect
54. #15667985	C₂²	semidirect
55. #15667985	C₂²	semidirect
56. #15667985	C₂²	semidirect
57. #15667982	C₂²	semidirect
58. #15667982	C₂²	semidirect
59. #15667982	C₂²	semidirect
60. #15667982	C₂²	semidirect
61. #15667982	C₂²	semidirect
62. #15667980	C₂²	semidirect
63. C₄×Dic₁₇₈	C₂²	semidirect
64. C₄×D₃₅₆	C₂²	semidirect
65. C₄×D₃₅₆	C₂²	semidirect
66. C₄×D₃₅₆	C₂²	semidirect
67. #15667974	C₂²	semidirect
68. #15667974	C₂²	semidirect
69. C₄×C₂²⋊D₈₉	C₂²	semidirect
70. #15667969	C₂²	semidirect
71. C₂²⋊C₄×D₈₉	C₂²	semidirect
72. #126×C₈₉	C₂²	semidirect
73. #125×C₈₉	C₂²	semidirect
74. #124×C₈₉	C₂²	semidirect
75. #123×C₈₉	C₂²	semidirect
76. C₂²⋊Q₈×C₈₉	C₂²	semidirect
78. C₄×Q₈×C₈₉	C₂²	semidirect
79. C₄×D₄×C₈₉	C₂²	semidirect
80. C₄×D₄×C₈₉	C₂²	semidirect
81. #117×C₈₉	C₂²	semidirect
82. C₂×C₄²×C₈₉	C₂²	semidirect
247. C₈₉	#3543	semidirect
264. #529	D₈₉	semidirect
281. #126	C₂×D₈₉	semidirect
283. #125	C₂×D₈₉	semidirect
287. #124	C₂×D₈₉	semidirect
293. #123	C₂×D₈₉	semidirect
295. C₂²⋊Q₈	C₂×D₈₉	semidirect
317. C₄×Q₈	C₂×D₈₉	semidirect
324. C₄×D₄	C₂×D₈₉	semidirect
325. C₄×D₄	C₂×D₈₉	semidirect
327. #117	C₂×D₈₉	semidirect
329. C₂×C₄²	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152339	2
#19152333	2
#19152270	2
#19152269	2
#19152244	2
#19152239	2
D₄×D₃₅₆	2
#19152232	2
#19152204	2
#19152203	2
#19152167	2
#19152166	2
#19152159	2
C₂×#15668009	2
#19152132	2
#529×C₈₉	2
#3543	89