Subgroups — #36707839

Order 22784.

652 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26033386	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151716	C₂	1	1	yes	maximal, characteristic, complemented
3	#26022136	C₂	1	4	yes	maximal, complemented
4	#26022131	C₂	1	4	yes	maximal, complemented
5	#26022046	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021980	C₂	1	1	yes	maximal, characteristic, complemented
7	#26021979	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#15667952	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#443×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15668034	C₂²	1	1	yes	characteristic
11	C₂×#15668018	—	2	1	no	—
12	#19152039	C₄	1	2	yes	complemented
13	#19152038	C₄	1	2	yes	complemented
14	#19152034	C₄	1	2	yes	complemented
15	#19152033	C₄	1	2	yes	complemented
16	#19152028	C₂²	1	4	yes	—
17	C₂×#15667952	C₂²	1	1	yes	characteristic
18	C₂×#15667952	C₂²	1	1	yes	characteristic
19	#19151716	—	2	1	no	—
20	#19151716	—	2	1	no	—
21	#19151716	C₂²	1	2	yes	complemented
22	#19151716	C₂²	1	2	yes	complemented
23	C₂×#15667948	C₂²	1	1	yes	characteristic
24	C₂×#15667940	—	2	1	no	—
25	#19151427	C₂²	1	4	yes	complemented
26	#19151405	C₂²	1	4	yes	complemented
27	#19151404	C₂²	1	4	yes	complemented
28	#19151374	C₂²	1	2	yes	complemented
29	C₄×#13083549	C₂²	1	2	yes	complemented
30	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#131×C₈₉	—	2	1	no	—
32	#443×C₈₉	—	2	1	no	—
33	#443×C₈₉	—	2	1	no	—
34	#443×C₈₉	C₂²	1	2	yes	complemented
35	#443×C₈₉	C₂²	1	2	yes	complemented
36	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#104×C₈₉	—	2	1	no	—
38	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#13083574	—	2	1	no	—
40	#15668034	—	2	1	no	—
41	#15668034	—	2	1	no	—
42	#15668034	C₂×C₄	1	2	yes	—
43	#15668034	C₂³	1	2	yes	—
44	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
45	C₂×#13083563	—	2	1	no	—
46	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
47	#15668018	—	2	2	no	—
48	#15668018	—	2	2	no	—
49	#15668018	—	4	1	no	—
50	#15668018	—	4	1	no	—
51	C₂×#13083558	—	2	1	no	—
52	C₂×#13083557	—	4	1	no	—
53	C₂×C₈×D₈₉	—	4	1	no	—
54	#15667958	C₂×C₄	1	4	yes	complemented
55	#15667956	C₂×C₄	1	4	yes	complemented
56	#15667955	C₂×C₄	1	4	yes	complemented
57	#15667953	C₂×C₄	1	4	yes	complemented
58	#15667952	—	2	1	no	—
59	#15667952	—	2	1	no	—
60	#15667952	C₂×C₄	1	2	yes	—
61	#15667952	C₂×C₄	1	2	yes	—
62	C₂×#13083549	C₂³	1	2	yes	—
63	C₂×#13083549	C₂³	1	2	yes	—
64	#15667948	—	2	1	no	—
65	#15667948	C₂³	1	2	yes	—
66	#15667940	—	2	2	no	—
67	#15667940	—	2	2	no	—
68	C₂×#41×C₈₉	—	2	1	no	—
69	#135×C₈₉	—	2	1	no	—
70	#135×C₈₉	—	2	1	no	—
71	#135×C₈₉	C₂×C₄	1	2	yes	—
72	#135×C₈₉	C₂³	1	2	yes	—
73	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂×SD₁₆×C₈₉	—	2	1	no	—
75	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
76	#131×C₈₉	—	2	2	no	—
77	#131×C₈₉	—	2	2	no	—
78	#131×C₈₉	—	4	1	no	—
79	#131×C₈₉	—	4	1	no	—
80	C₂×M₁₆×C₈₉	—	2	1	no	—
81	C₂×M₁₆×C₈₉	—	4	1	no	—
82	C₂²×C₈×C₈₉	—	4	1	no	—
83	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
86	#108×C₈₉	—	2	1	no	—
87	#108×C₈₉	C₂³	1	2	yes	—
88	#104×C₈₉	—	2	2	no	—
89	#104×C₈₉	—	2	2	no	—
90	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
91	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	#13083574	—	2	2	no	—
95	#13083574	—	2	2	no	—
96	#13083574	—	4	1	no	—
97	#13083574	—	4	1	no	—
98	C₂×Dic₁₇₈	—	2	1	no	—
99	C₂×D₃₅₆	—	2	1	no	—
100	C₂×C₂²⋊D₈₉	—	4	1	no	—
101	C₂×C₄×D₈₉	—	4	1	no	—
102	Dic₃₅₆	—	2	1	no	—
103	Dic₃₅₆	C₂²×C₄	1	2	yes	—
104	#13083563	—	2	2	no	—
105	#13083563	—	2	2	no	—
106	D₇₁₂	—	2	1	no	—
107	D₇₁₂	C₂²×C₄	1	2	yes	—
108	#13083558	—	2	2	no	—
109	#13083558	—	4	1	no	—
110	#13083557	—	4	2	no	—
111	#13083557	—	4	2	no	—
112	C₂×#10623494	—	4	1	no	—
113	C₈×D₈₉	—	4	2	no	—
114	C₈×D₈₉	—	4	2	no	—
115	#13083549	—	2	2	no	—
116	#13083549	C₂²×C₄	1	4	yes	—
117	#41×C₈₉	—	2	2	no	—
118	#41×C₈₉	—	2	2	no	—
119	#41×C₈₉	—	4	1	no	—
120	#41×C₈₉	—	4	1	no	—
121	C₂×Q₈×C₈₉	—	2	1	no	—
122	C₂×D₄×C₈₉	—	2	1	no	—
123	C₂×D₄×C₈₉	—	4	1	no	—
124	C₂²×C₄×C₈₉	—	2	1	no	—
125	C₂²×C₄×C₈₉	—	4	1	no	—
126	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
127	Q₁₆×C₈₉	—	2	1	no	—
128	Q₁₆×C₈₉	C₂²×C₄	1	2	yes	—
129	SD₁₆×C₈₉	—	2	2	no	—
130	SD₁₆×C₈₉	—	2	2	no	—
131	D₈×C₈₉	—	2	1	no	—
132	D₈×C₈₉	C₂²×C₄	1	2	yes	—
133	M₁₆×C₈₉	—	2	2	no	—
134	M₁₆×C₈₉	—	4	1	no	—
135	M₁₆×C₈₉	—	4	2	no	—
136	M₁₆×C₈₉	—	4	2	no	—
137	C₂×C₈×C₈₉	—	4	1	no	—
138	C₂×C₈×C₈₉	—	4	2	no	—
139	C₂×C₈×C₈₉	—	4	2	no	—
140	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
141	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
142	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
143	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
144	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
150	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
151	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₄²×C₈₉	—	2	1	no	—
153	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂³×C₈₉	—	4	1	no	—
156	C₂³×C₈₉	#135	1	1	yes	characteristic
157	C₂²×D₈₉	—	4	1	no	—
158	Q₈×C₈₉	—	2	2	no	—
159	Q₈×C₈₉	—	4	1	no	—
160	D₄×C₈₉	—	2	2	no	—
161	D₄×C₈₉	—	4	2	no	—
162	D₄×C₈₉	—	4	2	no	—
163	D₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	4	2	no	—
167	C₂×C₄×C₈₉	—	4	1	no	—
168	C₂×C₄×C₈₉	—	4	2	no	—
169	C₂×C₄×C₈₉	—	4	2	no	—
170	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
176	C₂²⋊D₈₉	—	4	2	no	—
177	C₂²⋊D₈₉	—	4	2	no	—
178	C₂×Dic₈₉	—	4	1	no	—
179	D₃₅₆	—	2	2	no	—
180	D₃₅₆	—	4	1	no	—
181	C₄×D₈₉	—	4	2	no	—
182	C₄×D₈₉	—	4	2	no	—
183	Dic₁₇₈	—	2	2	no	—
184	Dic₁₇₈	—	4	1	no	—
185	C₈×C₈₉	—	4	2	no	—
186	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
187	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
188	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
189	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
190	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
191	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
192	C₈×C₈₉	C₂³×C₄	1	1	yes	characteristic
193	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
194	#10623494	—	4	2	no	—
195	C₂²×C₈₉	—	4	1	no	—
196	C₂²×C₈₉	—	4	2	no	—
197	C₂²×C₈₉	—	8	2	no	—
198	C₂²×C₈₉	C₄×D₈	1	1	yes	characteristic
199	C₂²×C₈₉	C₄×D₈	1	1	yes	characteristic
200	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
201	C₂×D₈₉	—	4	2	no	—
202	C₂×D₈₉	—	8	2	no	—
203	C₄×C₈₉	—	2	2	no	—
204	C₄×C₈₉	—	4	1	no	—
205	C₄×C₈₉	—	4	2	no	—
206	C₄×C₈₉	C₄×D₈	1	1	yes	characteristic
207	C₄×C₈₉	C₄×D₈	1	1	yes	characteristic
208	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
209	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
210	Dic₈₉	—	4	2	no	—
211	#33463	—	89	1	no	maximal, Sylow
212	C₂×C₈₉	—	2	1	no	—
213	C₂×C₈₉	—	2	1	no	—
214	C₂×C₈₉	—	2	1	no	—
215	C₂×C₈₉	—	8	2	no	—
216	C₂×C₈₉	C₂×C₄×D₈	1	1	yes	characteristic
217	D₈₉	—	8	2	no	—
218	#3414	—	89	1	no	—
219	C₂×#443	—	89	1	no	—
220	C₂×#443	D₈₉	1	1	yes	characteristic, complemented
221	#2179	—	89	4	no	—
222	#2178	—	89	4	no	—
223	#2161	—	89	1	no	—
224	#2143	—	89	1	no	—
225	#2143	—	89	1	no	—
226	C₄×M₃₂	—	89	1	no	—
227	C₈₉	#33463	1	1	yes	characteristic, complemented, Sylow
228	C₂×#135	—	89	1	no	—
229	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
230	C₂×#131	—	2	1	no	—
231	C₂×#131	—	178	1	no	—
232	#510	—	89	2	no	—
233	#510	—	89	2	no	—
234	#509	—	89	2	no	—
235	#509	—	89	2	no	—
236	#508	—	89	4	no	—
237	C₂×M₃₂	—	89	1	no	—
238	C₂×M₃₂	—	89	1	no	—
239	#443	—	2	1	no	—
240	#443	—	2	1	no	—
241	#443	—	89	2	no	—
242	#443	—	89	2	no	—
243	#443	—	178	1	no	—
244	#443	—	178	1	no	—
245	#443	C₂×D₈₉	1	2	yes	complemented
246	#443	C₂×D₈₉	1	2	yes	complemented
247	C₂×#108	—	89	1	no	—
248	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
249	C₂×#104	—	2	1	no	—
250	C₂×#104	—	178	1	no	—
251	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
252	#368	—	89	4	no	—
253	#359	—	89	4	no	—
254	#359	—	89	4	no	—
255	#346	—	89	2	no	—
256	C₄×C₁₆	—	89	2	no	—
257	C₂×#41	—	2	1	no	—
258	C₂×#41	—	178	1	no	—
259	#135	—	2	1	no	—
260	#135	—	2	1	no	—
261	#135	—	89	2	no	—
262	#135	—	89	2	no	—
263	#135	—	178	1	no	—
264	#135	—	178	1	no	—
265	#135	C₄×D₈₉	1	2	yes	—
266	#135	C₂²×D₈₉	1	2	yes	—
267	C₂×Q₁₆	—	89	1	no	—
268	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic
269	C₂×SD₁₆	—	2	1	no	—
270	C₂×SD₁₆	—	178	1	no	—
271	C₂×D₈	—	89	1	no	—
272	C₂×D₈	C₄×D₈₉	1	1	yes	characteristic
273	#131	—	2	2	no	—
274	#131	—	2	2	no	—
275	#131	—	4	1	no	—
276	#131	—	4	1	no	—
277	#131	—	356	1	no	—
278	#131	—	356	1	no	—
279	#131	—	178	2	no	—
280	#131	—	178	2	no	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	—	4	1	no	—
283	C₂×M₁₆	—	356	1	no	—
284	C₂×M₁₆	—	178	1	no	—
285	C₂²×C₈	—	4	1	no	—
286	C₂²×C₈	—	356	1	no	—
287	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
288	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
289	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
290	Q₃₂	—	89	4	no	—
291	SD₃₂	—	89	4	no	—
292	SD₃₂	—	89	4	no	—
293	D₁₆	—	89	4	no	—
294	M₃₂	—	89	2	no	—
295	M₃₂	—	89	2	no	—
296	M₃₂	—	178	1	no	—
297	M₃₂	—	178	1	no	—
298	C₂×C₁₆	—	89	2	no	—
299	C₂×C₁₆	—	89	2	no	—
300	#108	—	2	1	no	—
301	#108	—	89	2	no	—
302	#108	—	178	1	no	—
303	#108	C₂²×D₈₉	1	2	yes	—
304	#104	—	2	2	no	—
305	#104	—	2	2	no	—
306	#104	—	178	2	no	—
307	#104	—	178	2	no	—
308	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
309	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
311	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
312	#41	—	2	2	no	—
313	#41	—	2	2	no	—
314	#41	—	4	1	no	—
315	#41	—	4	1	no	—
316	#41	—	356	1	no	—
317	#41	—	356	1	no	—
318	#41	—	178	2	no	—
319	#41	—	178	2	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	178	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	356	1	no	—
325	C₂×D₄	—	178	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	356	1	no	—
329	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
330	Q₁₆	—	2	1	no	—
331	Q₁₆	—	89	2	no	—
332	Q₁₆	—	178	1	no	—
333	Q₁₆	C₂×C₄×D₈₉	1	2	yes	—
334	SD₁₆	—	2	2	no	—
335	SD₁₆	—	2	2	no	—
336	SD₁₆	—	178	2	no	—
337	SD₁₆	—	178	2	no	—
338	D₈	—	2	1	no	—
339	D₈	—	89	2	no	—
340	D₈	—	178	1	no	—
341	D₈	C₂×C₄×D₈₉	1	2	yes	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	4	1	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	4	2	no	—
346	M₁₆	—	356	1	no	—
347	M₁₆	—	356	2	no	—
348	M₁₆	—	356	2	no	—
349	M₁₆	—	178	2	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	2	no	—
352	C₂×C₈	—	4	2	no	—
353	C₂×C₈	—	356	1	no	—
354	C₂×C₈	—	356	2	no	—
355	C₂×C₈	—	356	2	no	—
356	C₂×C₈	#13083559	1	1	yes	characteristic
357	C₂×C₈	#13083559	1	1	yes	characteristic
358	C₂×C₈	#13083559	1	1	yes	characteristic
359	C₂×C₈	#13083559	1	1	yes	characteristic
360	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
361	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
362	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
363	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
364	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
365	C₂×C₈	#13083574	1	1	yes	characteristic
366	C₂×C₈	#13083574	1	1	yes	characteristic
367	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
368	C₄²	—	2	1	no	—
369	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
370	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
371	C₁₆	—	89	4	no	—
372	C₁₆	—	178	2	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	356	1	no	—
375	C₂³	#15668032	1	1	yes	characteristic
376	Q₈	—	2	2	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	356	1	no	—
379	Q₈	—	178	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	1	no	—
384	D₄	—	356	2	no	—
385	D₄	—	356	2	no	—
386	D₄	—	356	1	no	—
387	D₄	—	178	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	356	1	no	—
395	C₂×C₄	—	356	2	no	—
396	C₂×C₄	—	356	2	no	—
397	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
398	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
399	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
400	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
401	C₂×C₄	#15668032	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
403	C₈	—	4	2	no	—
404	C₈	—	356	2	no	—
405	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
406	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
407	C₈	C₂×#13083559	1	1	yes	characteristic
408	C₈	C₂×#13083559	1	1	yes	characteristic
409	C₈	C₂×#13083559	1	1	yes	characteristic
410	C₈	C₂×#13083559	1	1	yes	characteristic
411	C₈	C₂²×C₄×D₈₉	1	1	yes	characteristic
412	C₈	C₂×#13083574	1	1	yes	characteristic
413	C₂²	—	4	1	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	356	2	no	—
417	C₂²	—	712	2	no	—
418	C₂²	C₄×#13083559	1	1	yes	characteristic
419	C₂²	C₄×#13083559	1	1	yes	characteristic
420	C₂²	C₂×#15668032	1	1	yes	characteristic
421	C₄	—	2	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	2	no	—
424	C₄	—	356	2	no	—
425	C₄	C₄×#13083559	1	1	yes	characteristic
426	C₄	C₄×#13083559	1	1	yes	characteristic
427	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
428	C₄	C₂²×#13083559	1	1	yes	characteristic
429	C₂	—	2	1	no	—
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	8	2	no	—
433	C₂	—	712	2	no	—
434	C₂	C₂×C₄×#13083559	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×#13083559
commutator	C₈×C₈₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₂×#443×C₈₉	C₂
socle	C₂×C₈₉	C₂×C₄×D₈
prime radical	#26033386	C₂
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	C₂×#443	D₈₉
hypocenter	C₈₉	#33463
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. C₂×#19151716	C₂	semidirect
3. #26022136	C₂	semidirect
4. #26022131	C₂	semidirect
5. #26022046	C₂	semidirect
6. #26021980	C₂	semidirect
7. #26021979	C₂	semidirect
8. C₄×#15667952	C₂	semidirect
9. C₂×#443×C₈₉	C₂	semidirect
12. #19152039	C₄	semidirect
13. #19152038	C₄	semidirect
14. #19152034	C₄	semidirect
15. #19152033	C₄	semidirect
21. #19151716	C₂²	semidirect
22. #19151716	C₂²	semidirect
25. #19151427	C₂²	semidirect
26. #19151405	C₂²	semidirect
27. #19151404	C₂²	semidirect
28. #19151374	C₂²	semidirect
29. C₄×#13083549	C₂²	semidirect
34. #443×C₈₉	C₂²	semidirect
35. #443×C₈₉	C₂²	semidirect
54. #15667958	C₂×C₄	semidirect
55. #15667956	C₂×C₄	semidirect
56. #15667955	C₂×C₄	semidirect
57. #15667953	C₂×C₄	semidirect
220. C₂×#443	D₈₉	semidirect
227. C₈₉	#33463	semidirect
245. #443	C₂×D₈₉	semidirect
246. #443	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26033386	2
C₂×#19151716	2
#26022136	2
#26022131	2
#26022046	2
#26021980	2
#26021979	2
C₄×#15667952	2
C₂×#443×C₈₉	2
#33463	89