Subgroups — #26031846

Order 11392.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668036	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152247	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151969	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151844	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151841	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151801	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151791	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151749	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151747	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151743	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151740	C₂	1	1	yes	maximal, characteristic, complemented
13	D₈×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151674	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083573	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₈₉	—	2	1	no	—
18	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
19	#15668036	—	2	4	no	—
20	C₂×#13083563	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13083562	C₂²	1	1	yes	characteristic
22	C₂×#13083562	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13083557	C₂²	1	1	yes	characteristic, complemented
26	#15668010	C₂²	1	1	yes	characteristic, complemented
27	#15668008	C₂²	1	1	yes	characteristic
28	#15667995	—	2	1	no	—
29	#15667993	—	2	1	no	—
30	#15667991	C₂²	1	1	yes	characteristic, complemented
31	#15667988	C₂²	1	1	yes	characteristic, complemented
32	#15667986	C₂²	1	1	yes	characteristic
33	#15667984	—	2	1	no	—
34	#15667984	—	2	1	no	—
35	#15667983	C₂²	1	1	yes	characteristic
36	#15667981	—	2	1	no	—
37	#15667980	—	2	1	no	—
38	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
39	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
41	C₂×#13083553	—	2	1	no	—
42	#15667946	C₂²	1	1	yes	characteristic, complemented
43	#15667941	C₂²	1	1	yes	characteristic, complemented
44	#15667937	C₂²	1	1	yes	characteristic, complemented
45	#15667936	C₂²	1	1	yes	characteristic, complemented
46	#15667934	C₂²	1	1	yes	characteristic, complemented
47	#15667933	C₂²	1	1	yes	characteristic
48	#15667933	C₂²	1	1	yes	characteristic, complemented
49	#15667933	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊#10623494	C₂²	1	1	yes	characteristic, complemented
51	#15667924	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
55	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
56	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₉	—	2	1	no	—
62	#13083573	—	2	2	no	—
63	#13083573	—	4	1	no	—
64	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
65	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₈₉	—	2	1	no	—
67	C₂×C₂²⋊D₈₉	—	2	1	no	—
68	C₂×C₂²⋊D₈₉	—	2	1	no	—
69	C₂×C₂²⋊D₈₉	—	2	1	no	—
70	C₂×C₂²⋊D₈₉	—	2	1	no	—
71	C₂×C₂²⋊D₈₉	—	2	1	no	—
72	C₂×C₂²⋊D₈₉	—	4	4	no	—
73	C₂×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
74	D₄×D₈₉	—	2	2	no	—
75	D₄×D₈₉	—	4	1	no	—
76	C₂²×Dic₈₉	—	2	1	no	—
77	C₂²×Dic₈₉	—	2	1	no	—
78	C₂²×Dic₈₉	—	2	1	no	—
79	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
80	#13083563	—	2	2	no	—
81	#13083562	—	2	2	no	—
82	#13083562	—	4	1	no	—
83	#13083561	—	4	1	no	—
84	#13083559	—	2	2	no	—
85	#13083557	—	2	2	no	—
86	C₂×#10623494	C₂³	1	1	yes	characteristic
87	C₂×#10623494	C₂³	1	1	yes	characteristic
88	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
89	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
90	#13083553	—	2	1	no	—
91	#13083553	—	2	1	no	—
92	#13083553	—	2	1	no	—
93	#13083553	—	2	1	no	—
94	#13083553	D₄	1	1	yes	characteristic
95	C₂²⋊Dic₈₉	—	2	1	no	—
96	C₂²⋊Dic₈₉	—	2	1	no	—
97	C₂²⋊Dic₈₉	—	2	1	no	—
98	C₂²⋊Dic₈₉	—	2	1	no	—
99	C₂²⋊Dic₈₉	D₄	1	1	yes	characteristic
100	#13083551	—	2	1	no	—
101	#13083551	—	2	1	no	—
102	#13083551	D₄	1	1	yes	characteristic
103	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
104	C₂⁴×C₈₉	—	2	1	no	—
105	#41×C₈₉	—	2	2	no	—
106	#41×C₈₉	—	4	1	no	—
107	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₈₉	—	2	2	no	—
109	C₂×D₄×C₈₉	—	2	1	no	—
110	C₂×D₄×C₈₉	—	2	1	no	—
111	C₂×D₄×C₈₉	—	4	1	no	—
112	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	—	2	1	no	—
116	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
117	SD₁₆×C₈₉	—	2	2	no	—
118	SD₁₆×C₈₉	—	2	2	no	—
119	D₈×C₈₉	—	2	2	no	—
120	D₈×C₈₉	D₄	1	4	yes	complemented
121	M₁₆×C₈₉	—	2	2	no	—
122	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₂³×C₈₉	—	2	1	no	—
125	C₂³×C₈₉	—	2	1	no	—
126	C₂³×C₈₉	—	2	1	no	—
127	C₂³×C₈₉	—	4	2	no	—
128	C₂³×C₈₉	—	4	2	no	—
129	C₂³×C₈₉	—	8	1	no	—
130	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×D₈₉	—	2	1	no	—
132	C₂²×D₈₉	—	4	2	no	—
133	C₂²×D₈₉	—	4	2	no	—
134	C₂²×D₈₉	—	8	1	no	—
135	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₈₉	—	2	1	no	—
137	Q₈×C₈₉	—	2	1	no	—
138	D₄×C₈₉	—	2	1	no	—
139	D₄×C₈₉	—	2	1	no	—
140	D₄×C₈₉	—	2	1	no	—
141	D₄×C₈₉	—	2	1	no	—
142	D₄×C₈₉	—	4	2	no	—
143	D₄×C₈₉	—	4	2	no	—
144	D₄×C₈₉	C₂×D₄	1	2	yes	—
145	D₄×C₈₉	C₂×D₄	1	2	yes	complemented
146	C₂×C₄×C₈₉	—	2	1	no	—
147	C₂×C₄×C₈₉	—	2	1	no	—
148	C₂×C₄×C₈₉	—	2	1	no	—
149	C₂×C₄×C₈₉	—	4	2	no	—
150	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₂²⋊D₈₉	—	2	2	no	—
153	C₂²⋊D₈₉	—	4	2	no	—
154	C₂²⋊D₈₉	—	4	2	no	—
155	C₂²⋊D₈₉	—	4	2	no	—
156	C₂²⋊D₈₉	—	4	2	no	—
157	C₂²⋊D₈₉	—	4	2	no	—
158	C₂²⋊D₈₉	—	8	1	no	—
159	C₂×Dic₈₉	—	2	1	no	—
160	C₂×Dic₈₉	—	2	1	no	—
161	C₂×Dic₈₉	—	2	1	no	—
162	C₂×Dic₈₉	—	4	2	no	—
163	C₂×Dic₈₉	—	4	2	no	—
164	C₂×Dic₈₉	—	4	2	no	—
165	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
166	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
167	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
168	D₃₅₆	—	2	1	no	—
169	D₃₅₆	—	2	1	no	—
170	C₄×D₈₉	—	2	1	no	—
171	C₄×D₈₉	—	2	1	no	—
172	Dic₁₇₈	—	2	1	no	—
173	Dic₁₇₈	—	2	1	no	—
174	C₈×C₈₉	—	2	1	no	—
175	C₈×C₈₉	C₂×D₄	1	2	yes	complemented
176	#10623494	—	2	1	no	—
177	#10623494	—	2	1	no	—
178	C₂²×C₈₉	—	2	2	no	—
179	C₂²×C₈₉	—	2	2	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	—	2	1	no	—
183	C₂²×C₈₉	—	4	1	no	—
184	C₂²×C₈₉	—	4	1	no	—
185	C₂²×C₈₉	—	4	1	no	—
186	C₂²×C₈₉	—	4	1	no	—
187	C₂²×C₈₉	—	4	1	no	—
188	C₂²×C₈₉	—	4	1	no	—
189	C₂²×C₈₉	—	4	1	no	—
190	C₂²×C₈₉	—	8	4	no	—
191	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×D₈₉	—	2	1	no	—
193	C₂×D₈₉	—	2	1	no	—
194	C₂×D₈₉	—	2	1	no	—
195	C₂×D₈₉	—	4	1	no	—
196	C₂×D₈₉	—	4	1	no	—
197	C₂×D₈₉	—	4	1	no	—
198	C₂×D₈₉	—	8	4	no	—
199	C₄×C₈₉	—	2	1	no	—
200	C₄×C₈₉	—	4	1	no	—
201	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
202	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
203	Dic₈₉	—	2	1	no	—
204	Dic₈₉	—	2	1	no	—
205	Dic₈₉	—	4	1	no	—
206	Dic₈₉	—	4	1	no	—
207	Dic₈₉	—	4	1	no	—
208	Dic₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
209	C₂×C₈₉	—	4	2	no	—
210	C₂×C₈₉	—	4	1	no	—
211	C₂×C₈₉	—	4	2	no	—
212	C₂×C₈₉	—	8	1	no	—
213	C₂×C₈₉	D₄²	1	1	yes	characteristic
214	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂×C₈₉	#577	1	1	yes	characteristic
216	D₈₉	—	4	1	no	—
217	D₈₉	—	8	1	no	—
218	#3272	—	89	1	no	maximal, Sylow
219	C₈₉	#3272	1	1	yes	characteristic, complemented, Sylow
220	C₂×AGL(1,ℤ/8)	—	89	1	no	—
221	C₂×AGL(1,ℤ/8)	D₈₉	1	1	yes	characteristic, complemented
222	#547	—	89	1	no	—
223	D₄²	—	89	1	no	—
224	#492	—	89	1	no	—
225	#468	—	89	1	no	—
226	#468	—	89	1	no	—
227	#461	—	89	1	no	—
228	#459	—	89	1	no	—
229	#450	—	89	1	no	—
230	#450	—	89	1	no	—
231	#449	—	89	1	no	—
232	#449	—	89	1	no	—
233	C₄×D₈	—	89	1	no	—
234	#436	—	89	1	no	—
235	C₂×#41	—	89	1	no	—
236	C₂×#41	C₂×D₈₉	1	1	yes	characteristic, complemented
237	C₂²×D₄	—	89	1	no	—
238	C₂²×D₄	—	178	1	no	—
239	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic
240	AGL(1,ℤ/8)	—	2	4	no	—
241	AGL(1,ℤ/8)	—	178	4	no	—
242	C₂×SD₁₆	—	89	1	no	—
243	C₂×SD₁₆	—	89	1	no	—
244	C₂×SD₁₆	—	89	1	no	—
245	C₂×SD₁₆	—	89	1	no	—
246	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
247	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
248	C₂×D₈	—	89	1	no	—
249	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic
250	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic, complemented
251	C₂×M₁₆	—	89	1	no	—
252	C₂×M₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
253	C₄⋊Q₈	—	89	1	no	—
254	#127	—	89	1	no	—
255	#123	—	178	1	no	—
256	#123	—	178	1	no	—
257	C₂²⋊Q₈	—	89	1	no	—
258	C₂²⋊Q₈	—	89	1	no	—
259	#121	—	89	1	no	—
260	#121	—	89	1	no	—
261	#121	—	178	1	no	—
262	#121	—	178	1	no	—
263	#120	—	178	1	no	—
264	#120	—	178	1	no	—
265	C₄×D₄	—	89	1	no	—
266	C₄×D₄	—	89	1	no	—
267	C₄×D₄	—	89	1	no	—
268	C₂×C₄⋊C₄	—	178	1	no	—
269	#107	—	89	1	no	—
270	C₄⋊C₈	—	89	1	no	—
271	#103	—	89	1	no	—
272	#103	—	89	1	no	—
273	#102	—	89	1	no	—
274	#102	—	89	1	no	—
275	#102	—	89	1	no	—
276	#102	—	89	1	no	—
277	C₂²⋊C₈	—	89	1	no	—
278	C₂²⋊C₈	—	89	1	no	—
279	C₄×C₈	—	89	1	no	—
280	C₂⁴	—	2	1	no	—
281	C₂⁴	—	178	1	no	—
282	#41	—	2	2	no	—
283	#41	—	4	1	no	—
284	#41	—	356	1	no	—
285	#41	—	178	2	no	—
286	C₂×Q₈	—	89	1	no	—
287	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	89	1	no	—
293	C₂×D₄	—	89	1	no	—
294	C₂×D₄	—	356	4	no	—
295	C₂×D₄	—	356	1	no	—
296	C₂×D₄	—	178	1	no	—
297	C₂×D₄	—	178	1	no	—
298	C₂×D₄	—	178	1	no	—
299	C₂×D₄	—	178	1	no	—
300	C₂×D₄	—	178	1	no	—
301	C₂×D₄	—	178	1	no	—
302	C₂×D₄	—	178	2	no	—
303	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
304	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
305	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	89	1	no	—
308	C₂²×C₄	—	178	1	no	—
309	C₂²×C₄	—	178	1	no	—
310	C₂²×C₄	—	178	1	no	—
311	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	2	2	no	—
314	SD₁₆	—	356	1	no	—
315	SD₁₆	—	356	1	no	—
316	SD₁₆	—	178	2	no	—
317	SD₁₆	—	178	2	no	—
318	D₈	—	2	2	no	—
319	D₈	—	178	2	no	—
320	D₈	C₂²⋊D₈₉	1	4	yes	complemented
321	M₁₆	—	2	2	no	—
322	M₁₆	—	178	2	no	—
323	C₂×C₈	—	89	1	no	—
324	C₂×C₈	—	89	1	no	—
325	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
327	C₄⋊C₄	—	89	1	no	—
328	C₄⋊C₄	—	89	1	no	—
329	C₄⋊C₄	—	89	1	no	—
330	C₄⋊C₄	—	178	1	no	—
331	C₄⋊C₄	—	178	1	no	—
332	C₄⋊C₄	—	178	1	no	—
333	C₄⋊C₄	—	178	1	no	—
334	C₂²⋊C₄	—	89	1	no	—
335	C₂²⋊C₄	—	89	1	no	—
336	C₂²⋊C₄	—	178	1	no	—
337	C₂²⋊C₄	—	178	1	no	—
338	C₂²⋊C₄	—	178	1	no	—
339	C₂²⋊C₄	—	178	1	no	—
340	C₂²⋊C₄	—	178	1	no	—
341	C₂²⋊C₄	—	178	1	no	—
342	C₄²	—	89	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	89	1	no	—
350	C₂³	—	356	2	no	—
351	C₂³	—	356	2	no	—
352	C₂³	—	178	1	no	—
353	C₂³	—	712	1	no	—
354	C₂³	D₄×D₈₉	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	178	1	no	—
358	Q₈	—	178	1	no	—
359	D₄	—	2	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	356	2	no	—
366	D₄	—	356	2	no	—
367	D₄	—	356	2	no	—
368	D₄	—	356	2	no	—
369	D₄	—	356	2	no	—
370	D₄	—	178	2	no	—
371	D₄	—	178	1	no	—
372	D₄	—	178	1	no	—
373	D₄	—	712	1	no	—
374	D₄	C₂×C₂²⋊D₈₉	1	2	yes	—
375	D₄	C₂×C₂²⋊D₈₉	1	2	yes	complemented
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	89	1	no	—
381	C₂×C₄	—	89	1	no	—
382	C₂×C₄	—	89	1	no	—
383	C₂×C₄	—	356	2	no	—
384	C₂×C₄	—	356	2	no	—
385	C₂×C₄	—	356	2	no	—
386	C₂×C₄	—	178	1	no	—
387	C₂×C₄	—	178	1	no	—
388	C₂×C₄	—	178	1	no	—
389	C₂×C₄	—	178	1	no	—
390	C₂×C₄	—	178	1	no	—
391	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	178	1	no	—
395	C₈	—	178	1	no	—
396	C₈	C₂×C₂²⋊D₈₉	1	2	yes	complemented
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	8	4	no	—
410	C₂²	—	356	1	no	—
411	C₂²	—	356	1	no	—
412	C₂²	—	356	1	no	—
413	C₂²	—	178	1	no	—
414	C₂²	—	178	1	no	—
415	C₂²	—	178	1	no	—
416	C₂²	—	712	4	no	—
417	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	89	2	no	—
421	C₄	—	356	1	no	—
422	C₄	—	356	1	no	—
423	C₄	—	356	1	no	—
424	C₄	—	178	1	no	—
425	C₄	—	178	1	no	—
426	C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
427	C₄	#15668057	1	1	yes	characteristic
428	C₂	—	4	1	no	—
429	C₂	—	4	2	no	—
430	C₂	—	4	2	no	—
431	C₂	—	8	1	no	—
432	C₂	—	356	1	no	—
433	C₂	—	712	1	no	—
434	C₂	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
436	C₂	#19152408	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	C₂×AGL(1,ℤ/8)×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₈₉
hypocenter	C₈₉	#3272
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×#15668036	C₂	semidirect
2. #19152247	C₂	semidirect
3. D₄×C₂²⋊D₈₉	C₂	semidirect
4. #19151969	C₂	semidirect
5. #19151844	C₂	semidirect
6. #19151841	C₂	semidirect
7. #19151801	C₂	semidirect
8. #19151791	C₂	semidirect
9. #19151749	C₂	semidirect
10. #19151747	C₂	semidirect
11. #19151743	C₂	semidirect
12. #19151740	C₂	semidirect
13. D₈×Dic₈₉	C₂	semidirect
14. #19151674	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
16. C₂×#13083573	C₂²	semidirect
20. C₂×#13083563	C₂²	semidirect
22. C₂×#13083562	C₂²	semidirect
23. C₂×#13083561	C₂²	semidirect
24. C₂×#13083559	C₂²	semidirect
25. C₂×#13083557	C₂²	semidirect
26. #15668010	C₂²	semidirect
30. #15667991	C₂²	semidirect
31. #15667988	C₂²	semidirect
39. D₄×Dic₈₉	C₂²	semidirect
42. #15667946	C₂²	semidirect
43. #15667941	C₂²	semidirect
44. #15667937	C₂²	semidirect
45. #15667936	C₂²	semidirect
46. #15667934	C₂²	semidirect
48. #15667933	C₂²	semidirect
49. #15667933	C₂²	semidirect
50. C₂²⋊#10623494	C₂²	semidirect
51. #15667924	C₂²	semidirect
52. C₈×Dic₈₉	C₂²	semidirect
53. C₂×#41×C₈₉	C₂²	semidirect
57. C₂×SD₁₆×C₈₉	C₂²	semidirect
59. C₂×D₈×C₈₉	C₂²	semidirect
60. C₂×M₁₆×C₈₉	C₂²	semidirect
120. D₈×C₈₉	D₄	semidirect
145. D₄×C₈₉	C₂×D₄	semidirect
175. C₈×C₈₉	C₂×D₄	semidirect
208. Dic₈₉	AGL(1,ℤ/8)	semidirect
219. C₈₉	#3272	semidirect
221. C₂×AGL(1,ℤ/8)	D₈₉	semidirect
236. C₂×#41	C₂×D₈₉	semidirect
247. C₂×SD₁₆	C₂×D₈₉	semidirect
250. C₂×D₈	C₂×D₈₉	semidirect
252. C₂×M₁₆	C₂×D₈₉	semidirect
320. D₈	C₂²⋊D₈₉	semidirect
375. D₄	C₂×C₂²⋊D₈₉	semidirect
396. C₈	C₂×C₂²⋊D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15668036	2
#19152247	2
D₄×C₂²⋊D₈₉	2
#19151969	2
#19151844	2
#19151841	2
#19151801	2
#19151791	2
#19151749	2
#19151747	2
#19151743	2
#19151740	2
D₈×Dic₈₉	2
#19151674	2
C₂×AGL(1,ℤ/8)×C₈₉	2
#3272	89