Subgroups — #36708695

Order 22784.

718 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152028	C₂	1	2	yes	maximal, complemented
2	#26030680	C₂	1	1	yes	maximal, characteristic, complemented
3	#26022314	C₂	1	2	yes	maximal, complemented
4	#26022307	C₂	1	2	yes	maximal, complemented
5	#26022302	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022297	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022292	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022287	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄⋊#13083549	C₂	1	1	yes	maximal, characteristic, complemented
10	#26021957	C₂	1	2	yes	maximal, complemented
11	C₄×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	—	2	1	no	—
13	C₂×#15668034	C₂²	1	2	yes	—
14	#19152148	—	2	1	no	—
15	#19152028	—	2	8	no	—
16	C₂×#15667958	C₂²	1	2	yes	—
17	C₂×#15667956	C₂²	1	2	yes	—
18	C₂×#15667955	C₂²	1	2	yes	—
19	C₂×#15667953	C₂²	1	2	yes	—
20	C₂²×#13083549	C₂²	1	2	yes	—
21	#19151982	—	2	1	no	—
22	#19151982	C₂²	1	2	yes	—
23	#19151978	C₂²	1	1	yes	characteristic
24	#19151975	C₂²	1	1	yes	characteristic
25	#19151971	—	2	1	no	—
26	C₄⋊#13083549	C₂²	1	1	yes	characteristic
27	C₄⋊#13083549	C₂²	1	1	yes	characteristic
28	C₄⋊#13083549	C₂²	1	2	yes	—
29	#19151401	C₂²	1	2	yes	—
30	#19151401	C₂²	1	2	yes	—
31	#19151398	C₂²	1	2	yes	—
32	#19151398	C₂²	1	2	yes	—
33	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
34	C₄×#41×C₈₉	—	2	1	no	—
35	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
36	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
37	C₄×SD₁₆×C₈₉	—	2	1	no	—
38	C₄×SD₁₆×C₈₉	—	2	1	no	—
39	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
41	#427×C₈₉	C₂²	1	1	yes	characteristic
42	#416×C₈₉	—	2	1	no	—
43	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#13083574	—	2	2	no	—
45	#15668034	—	2	4	no	—
46	#15668034	—	2	4	no	—
47	#15668034	—	4	4	no	—
48	C₂×Dic₃₅₆	—	2	1	no	—
49	C₂×Dic₃₅₆	C₂³	1	2	yes	—
50	C₂×#13083563	—	2	2	no	—
51	C₂×#13083563	—	2	2	no	—
52	C₂×D₇₁₂	—	2	1	no	—
53	C₂×D₇₁₂	C₂³	1	2	yes	—
54	#15668012	—	2	1	no	—
55	#15668009	—	2	1	no	—
56	#15668000	—	2	2	no	—
57	#15667986	—	4	1	no	—
58	#15667986	—	4	1	no	—
59	C₄×D₃₅₆	—	4	1	no	—
60	C₄×D₃₅₆	—	4	1	no	—
61	#15667958	—	2	4	no	—
62	#15667956	—	2	4	no	—
63	#15667955	—	2	4	no	—
64	#15667953	—	2	4	no	—
65	C₂×#13083549	—	2	4	no	—
66	C₂×#13083549	C₂³	1	2	yes	—
67	C₂×#13083549	C₂³	1	2	yes	—
68	C₂×#41×C₈₉	—	2	1	no	—
69	#135×C₈₉	—	2	2	no	—
70	#135×C₈₉	D₄	1	4	yes	complemented
71	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
72	C₂×SD₁₆×C₈₉	—	2	1	no	—
73	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₄×Q₈×C₈₉	—	2	1	no	—
77	C₄×Q₈×C₈₉	—	2	1	no	—
78	C₄×D₄×C₈₉	—	2	1	no	—
79	C₄×D₄×C₈₉	—	2	1	no	—
80	C₄×D₄×C₈₉	—	4	1	no	—
81	C₄×D₄×C₈₉	—	4	1	no	—
82	#117×C₈₉	—	2	1	no	—
83	#117×C₈₉	—	4	1	no	—
84	C₂×C₄²×C₈₉	—	4	1	no	—
85	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
86	#107×C₈₉	C₂³	1	1	yes	characteristic
87	#107×C₈₉	C₂³	1	1	yes	characteristic
88	#106×C₈₉	—	2	1	no	—
89	#103×C₈₉	—	2	1	no	—
90	#103×C₈₉	—	2	1	no	—
91	#102×C₈₉	—	2	1	no	—
92	#102×C₈₉	—	2	1	no	—
93	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
94	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
95	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	#13083574	—	4	4	no	—
98	#13083574	—	4	4	no	—
99	C₂×Dic₁₇₈	—	2	2	no	—
100	C₂×D₃₅₆	—	2	2	no	—
101	C₂×D₃₅₆	—	4	1	no	—
102	C₂×D₃₅₆	—	4	1	no	—
103	C₂×C₂²⋊D₈₉	—	4	2	no	—
104	C₂×C₄×D₈₉	—	4	2	no	—
105	Dic₃₅₆	—	2	2	no	—
106	Dic₃₅₆	—	2	2	no	—
107	Dic₃₅₆	—	4	2	no	—
108	#13083563	—	4	4	no	—
109	#13083563	—	4	4	no	—
110	D₇₁₂	—	2	2	no	—
111	D₇₁₂	—	2	2	no	—
112	D₇₁₂	—	4	2	no	—
113	C₄⋊Dic₈₉	—	4	1	no	—
114	C₄⋊Dic₈₉	—	4	1	no	—
115	#13083551	—	4	2	no	—
116	#13083551	—	4	2	no	—
117	#13083549	—	2	2	no	—
118	#13083549	—	2	2	no	—
119	#41×C₈₉	—	2	4	no	—
120	#41×C₈₉	—	4	2	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	—	4	1	no	—
125	C₂²×C₄×C₈₉	—	4	1	no	—
126	C₂²×C₄×C₈₉	—	4	1	no	—
127	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
130	Q₁₆×C₈₉	—	2	1	no	—
131	Q₁₆×C₈₉	C₂×D₄	1	2	yes	—
132	SD₁₆×C₈₉	—	2	4	no	—
133	D₈×C₈₉	—	2	1	no	—
134	D₈×C₈₉	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₈₉	—	2	2	no	—
136	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₈₉	#41	1	2	yes	—
141	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
142	C₄⋊C₄×C₈₉	—	2	1	no	—
143	C₄⋊C₄×C₈₉	—	2	1	no	—
144	C₄⋊C₄×C₈₉	—	4	1	no	—
145	C₄⋊C₄×C₈₉	—	4	1	no	—
146	C₂²⋊C₄×C₈₉	—	4	1	no	—
147	C₂²⋊C₄×C₈₉	—	4	1	no	—
148	C₂²⋊C₄×C₈₉	—	4	1	no	—
149	C₄²×C₈₉	—	4	1	no	—
150	C₄²×C₈₉	—	4	1	no	—
151	C₄²×C₈₉	—	4	1	no	—
152	C₄²×C₈₉	D₈	1	1	yes	characteristic
153	C₄²×C₈₉	D₈	1	1	yes	characteristic
154	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂³×C₈₉	—	4	1	no	—
157	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
158	C₂²×D₈₉	—	4	2	no	—
159	Q₈×C₈₉	—	2	2	no	—
160	Q₈×C₈₉	—	4	1	no	—
161	D₄×C₈₉	—	2	2	no	—
162	D₄×C₈₉	—	4	4	no	—
163	D₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	—	2	2	no	—
165	C₂×C₄×C₈₉	—	4	1	no	—
166	C₂×C₄×C₈₉	—	4	1	no	—
167	C₂×C₄×C₈₉	—	4	4	no	—
168	C₂×C₄×C₈₉	—	4	1	no	—
169	C₂×C₄×C₈₉	—	4	1	no	—
170	C₂×C₄×C₈₉	—	8	2	no	—
171	C₂×C₄×C₈₉	—	8	2	no	—
172	C₂×C₄×C₈₉	#121	1	2	yes	—
173	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
179	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
180	C₂²⋊D₈₉	—	8	4	no	—
181	C₂×Dic₈₉	—	4	2	no	—
182	D₃₅₆	—	4	2	no	—
183	D₃₅₆	—	4	2	no	—
184	D₃₅₆	—	8	2	no	—
185	D₃₅₆	—	8	2	no	—
186	C₄×D₈₉	—	8	4	no	—
187	Dic₁₇₈	—	4	2	no	—
188	Dic₁₇₈	—	4	2	no	—
189	C₈×C₈₉	—	2	1	no	—
190	C₈×C₈₉	—	2	1	no	—
191	C₈×C₈₉	#121	1	2	yes	—
192	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
194	C₂²×C₈₉	—	2	1	no	—
195	C₂²×C₈₉	—	2	1	no	—
196	C₂²×C₈₉	—	4	2	no	—
197	C₂²×C₈₉	—	8	1	no	—
198	C₂²×C₈₉	—	8	1	no	—
199	C₂²×C₈₉	#459	1	2	yes	—
200	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
201	C₂×D₈₉	—	8	2	no	—
202	C₂×D₈₉	—	8	2	no	—
203	C₂×D₈₉	—	8	2	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	4	2	no	—
208	C₄×C₈₉	—	8	1	no	—
209	C₄×C₈₉	—	8	1	no	—
210	C₄×C₈₉	#459	1	2	yes	—
211	C₄×C₈₉	#508	1	2	yes	complemented
212	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
213	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	Dic₈₉	—	8	2	no	—
215	#33579	—	89	1	no	maximal, Sylow
216	C₂×C₈₉	—	2	2	no	—
217	C₂×C₈₉	—	8	2	no	—
218	C₂×C₈₉	C₂×#459	1	1	yes	characteristic
219	C₂×C₈₉	C₂×#508	1	1	yes	characteristic
220	C₂×C₈₉	#3414	1	1	yes	characteristic
221	D₈₉	—	16	2	no	—
222	C₂×#508	—	89	2	no	—
223	#3147	—	89	1	no	—
224	C₄×#135	D₈₉	1	1	yes	characteristic, complemented
225	#2211	—	89	2	no	—
226	#2210	—	89	2	no	—
227	#2209	—	89	1	no	—
228	#2208	—	89	1	no	—
229	#2207	—	89	1	no	—
230	#2206	—	89	1	no	—
231	C₂×C₄⋊C₁₆	—	89	1	no	—
232	#2138	—	89	2	no	—
233	C₈₉	#33579	1	1	yes	characteristic, complemented, Sylow
234	C₂×#135	—	89	2	no	—
235	C₂×#135	—	178	1	no	—
236	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
237	#532	—	178	1	no	—
238	C₄×#41	—	2	1	no	—
239	#508	—	178	8	no	—
240	C₂×Q₃₂	—	89	2	no	—
241	C₂×SD₃₂	—	89	2	no	—
242	C₂×SD₃₂	—	89	2	no	—
243	C₂×D₁₆	—	89	2	no	—
244	C₂²×C₁₆	—	89	2	no	—
245	#495	—	89	2	no	—
246	#495	—	178	1	no	—
247	#494	—	89	1	no	—
248	#493	—	89	1	no	—
249	#492	—	178	1	no	—
250	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
251	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
252	C₄×SD₁₆	—	2	1	no	—
253	C₄×SD₁₆	—	2	1	no	—
254	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
255	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
256	#427	C₂×D₈₉	1	1	yes	characteristic
257	#416	—	2	1	no	—
258	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
259	C₄⋊C₁₆	—	89	1	no	—
260	C₄⋊C₁₆	—	89	1	no	—
261	C₄⋊C₁₆	—	89	2	no	—
262	#358	—	89	2	no	—
263	#358	—	89	2	no	—
264	#357	—	89	2	no	—
265	#357	—	89	2	no	—
266	C₂×#41	—	2	1	no	—
267	C₂×#41	—	178	2	no	—
268	#135	—	2	2	no	—
269	#135	—	356	4	no	—
270	#135	—	178	4	no	—
271	#135	—	178	4	no	—
272	#135	D₃₅₆	1	4	yes	complemented
273	C₂×Q₁₆	—	89	2	no	—
274	C₂×Q₁₆	—	178	1	no	—
275	C₂×Q₁₆	C₂²×D₈₉	1	1	yes	characteristic
276	C₂×SD₁₆	—	2	1	no	—
277	C₂×SD₁₆	—	178	2	no	—
278	C₂×SD₁₆	—	178	2	no	—
279	C₂×D₈	—	89	2	no	—
280	C₂×D₈	—	178	1	no	—
281	C₂×D₈	C₂²×D₈₉	1	1	yes	characteristic
282	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
284	C₄⋊Q₈	—	178	1	no	—
285	#127	—	178	1	no	—
286	#124	—	178	2	no	—
287	#121	—	356	1	no	—
288	#121	—	356	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	4	1	no	—
294	C₄×D₄	—	4	1	no	—
295	C₄×D₄	—	356	1	no	—
296	C₄×D₄	—	356	1	no	—
297	#117	—	2	1	no	—
298	#117	—	4	1	no	—
299	C₂×C₄²	—	4	1	no	—
300	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
301	Q₃₂	—	178	4	no	—
302	SD₃₂	—	178	4	no	—
303	SD₃₂	—	178	4	no	—
304	D₁₆	—	178	4	no	—
305	C₂×C₁₆	—	89	2	no	—
306	C₂×C₁₆	—	89	2	no	—
307	C₂×C₁₆	—	178	4	no	—
308	#107	C₂²×D₈₉	1	1	yes	characteristic
309	#107	C₂²×D₈₉	1	1	yes	characteristic
310	#106	—	2	1	no	—
311	#103	—	2	1	no	—
312	#103	—	2	1	no	—
313	#102	—	2	1	no	—
314	#102	—	2	1	no	—
315	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
316	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
319	#41	—	2	4	no	—
320	#41	—	4	2	no	—
321	#41	—	356	4	no	—
322	#41	—	356	4	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	178	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	356	2	no	—
328	C₂×D₄	—	356	1	no	—
329	C₂×D₄	—	356	1	no	—
330	C₂×D₄	—	178	2	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	356	2	no	—
335	C₂²×C₄	#13083559	1	1	yes	characteristic
336	C₂²×C₄	#13083559	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
338	Q₁₆	—	2	1	no	—
339	Q₁₆	—	356	2	no	—
340	Q₁₆	—	178	2	no	—
341	Q₁₆	—	178	2	no	—
342	Q₁₆	C₂×D₃₅₆	1	2	yes	—
343	SD₁₆	—	2	4	no	—
344	SD₁₆	—	356	4	no	—
345	SD₁₆	—	356	4	no	—
346	D₈	—	2	1	no	—
347	D₈	—	356	2	no	—
348	D₈	—	178	2	no	—
349	D₈	—	178	2	no	—
350	D₈	C₂×D₃₅₆	1	2	yes	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
353	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
354	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
355	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
356	C₂×C₈	#13083574	1	2	yes	—
357	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	356	1	no	—
363	C₄⋊C₄	—	356	1	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	356	2	no	—
368	C₂²⋊C₄	—	356	2	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	4	1	no	—
371	C₄²	—	4	1	no	—
372	C₄²	#13083559	1	1	yes	characteristic
373	C₄²	#13083559	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
375	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
376	C₁₆	—	178	2	no	—
377	C₁₆	—	178	2	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	356	2	no	—
380	C₂³	C₂×#13083559	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	356	2	no	—
384	Q₈	—	356	2	no	—
385	D₄	—	2	2	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	1	no	—
388	D₄	—	356	2	no	—
389	D₄	—	356	2	no	—
390	D₄	—	712	2	no	—
391	D₄	—	712	4	no	—
392	D₄	—	712	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	—	356	2	no	—
402	C₂×C₄	—	712	4	no	—
403	C₂×C₄	#15667986	1	2	yes	—
404	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
405	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
406	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
407	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
408	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
409	C₂×C₄	#15668037	1	2	yes	—
410	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	#15667986	1	2	yes	—
414	C₈	C₂²×D₃₅₆	1	1	yes	characteristic
415	C₈	C₂×#13083574	1	1	yes	characteristic
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	712	2	no	—
422	C₂²	—	712	2	no	—
423	C₂²	—	712	2	no	—
424	C₂²	#19151793	1	2	yes	—
425	C₂²	C₂²×#13083559	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	1	no	—
432	C₄	—	712	2	no	—
433	C₄	#19151793	1	2	yes	—
434	C₄	#19152028	1	2	yes	complemented
435	C₄	C₂×#15667986	1	1	yes	characteristic
436	C₄	C₂×#15668037	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	8	2	no	—
439	C₂	—	1424	2	no	—
440	C₂	C₂×#19151793	1	1	yes	characteristic
441	C₂	C₂×#19152028	1	1	yes	characteristic
442	C₂	#26033386	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#13083559
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₄×#135×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₈
hypercenter	C₄×#135	D₈₉
hypocenter	C₈₉	#33579
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#19152028	C₂	semidirect
2. #26030680	C₂	semidirect
3. #26022314	C₂	semidirect
4. #26022307	C₂	semidirect
5. #26022302	C₂	semidirect
6. #26022297	C₂	semidirect
7. #26022292	C₂	semidirect
8. #26022287	C₂	semidirect
9. C₂×C₄⋊#13083549	C₂	semidirect
10. #26021957	C₂	semidirect
11. C₄×#135×C₈₉	C₂	semidirect
70. #135×C₈₉	D₄	semidirect
211. C₄×C₈₉	#508	semidirect
224. C₄×#135	D₈₉	semidirect
233. C₈₉	#33579	semidirect
272. #135	D₃₅₆	semidirect
434. C₄	#19152028	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152028	2
#26030680	2
#26022314	2
#26022307	2
#26022302	2
#26022297	2
#26022292	2
#26022287	2
C₂×C₄⋊#13083549	2
#26021957	2
C₄×#135×C₈₉	2
#33579	89