Subgroups — #26034004

Order 11392.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152316	C₂	1	2	yes	maximal, complemented
2	#19152303	C₂	1	2	yes	maximal, complemented
3	#19152287	C₂	1	2	yes	maximal, complemented
4	#19152283	C₂	1	2	yes	maximal, complemented
5	#19152281	C₂	1	4	yes	maximal, complemented
6	#19152274	C₂	1	4	yes	maximal, complemented
7	#19152226	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152219	C₂	1	2	yes	maximal, complemented
9	#19152210	C₂	1	2	yes	maximal, complemented
10	#19152174	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152155	C₂	1	2	yes	maximal, complemented
12	#19152132	C₂	1	2	yes	maximal, complemented
13	#19152109	C₂	1	1	yes	maximal, characteristic
14	C₂×#15667991	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152078	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152075	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13083574	C₂²	1	1	yes	characteristic
19	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic
20	#15668012	C₂²	1	2	yes	complemented
21	#15668012	C₂²	1	2	yes	complemented
22	#15668011	C₂²	1	2	yes	complemented
23	#15668007	C₂²	1	4	yes	complemented
24	#15668006	C₂²	1	4	yes	complemented
25	#15668005	C₂²	1	4	yes	—
26	#15668005	C₂²	1	4	yes	—
27	#15668004	C₂²	1	2	yes	complemented
28	#15668004	C₂²	1	4	yes	complemented
29	#15668003	C₂²	1	2	yes	complemented
30	#15668002	C₂²	1	4	yes	complemented
31	#15668002	C₂²	1	4	yes	complemented
32	#15668000	C₂²	1	2	yes	complemented
33	#15667998	C₂²	1	4	yes	—
34	#15667996	C₂²	1	4	yes	—
35	#15667995	C₂²	1	4	yes	—
36	#15667995	C₂²	1	2	yes	—
37	#15667994	C₂²	1	4	yes	—
38	#15667992	C₂²	1	2	yes	complemented
39	#15667992	C₂²	1	2	yes	complemented
40	#15667991	C₂²	1	2	yes	—
41	#15667991	C₂²	1	1	yes	characteristic
42	#15667991	C₂²	1	4	yes	—
43	#15667991	C₂²	1	1	yes	characteristic
44	#15667991	C₂²	1	2	yes	—
45	#15667991	C₂²	1	2	yes	—
46	#15667991	C₂²	1	2	yes	—
47	#15667990	C₂²	1	4	yes	complemented
48	#15667989	C₂²	1	4	yes	—
49	#15667986	C₂²	1	1	yes	characteristic
50	#15667986	C₂²	1	1	yes	characteristic
51	#15667981	C₂²	1	2	yes	—
52	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
53	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
54	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
55	C₄×Dic₁₇₈	C₂²	1	4	yes	complemented
56	#15667977	C₂²	1	2	yes	complemented
57	#15667977	C₂²	1	2	yes	complemented
58	C₄×D₃₅₆	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₈₉	C₂²	1	4	yes	—
60	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
62	#15667972	C₂²	1	4	yes	—
63	#15667971	C₂²	1	4	yes	—
64	#15667971	C₂²	1	1	yes	characteristic
65	#15667970	C₂²	1	2	yes	complemented
66	#15667969	C₂²	1	4	yes	complemented
67	#15667968	C₂²	1	4	yes	—
68	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
69	C₂×#13083553	C₂²	1	2	yes	—
70	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
71	C₂×C₂²⋊Dic₈₉	C₂²	1	2	yes	—
72	C₂³×C₄×C₈₉	C₂²	1	1	yes	characteristic
73	#117×C₈₉	C₂²	1	1	yes	characteristic
74	#117×C₈₉	C₂²	1	2	yes	—
75	#117×C₈₉	C₂²	1	2	yes	—
76	#117×C₈₉	C₂²	1	1	yes	characteristic
77	#117×C₈₉	C₂²	1	1	yes	characteristic
78	#117×C₈₉	C₂²	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
82	C₂×C₄²×C₈₉	C₂²	1	2	yes	—
83	#13083574	—	2	4	no	—
84	C₂×Dic₁₇₈	—	2	4	no	—
85	C₂×Dic₁₇₈	C₂³	1	2	yes	—
86	C₂×Dic₁₇₈	C₂³	1	2	yes	—
87	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
88	C₂×Dic₁₇₈	C₂³	1	4	yes	—
89	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
93	C₂²×Dic₈₉	C₂³	1	2	yes	—
94	C₂²×Dic₈₉	C₂³	1	2	yes	—
95	C₂×C₄×D₈₉	C₂³	1	2	yes	—
96	C₂×C₄×D₈₉	C₂³	1	4	yes	—
97	C₄⋊Dic₈₉	C₂³	1	2	yes	—
98	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
100	C₄⋊Dic₈₉	C₂³	1	4	yes	—
101	C₄⋊Dic₈₉	C₂³	1	4	yes	—
102	C₄⋊Dic₈₉	C₂³	1	2	yes	—
103	C₄⋊Dic₈₉	C₂³	1	4	yes	—
104	#13083553	C₂³	1	4	yes	—
105	#13083553	C₂³	1	4	yes	—
106	#13083553	C₂³	1	4	yes	—
107	#13083553	C₂³	1	4	yes	—
108	#13083553	C₂³	1	4	yes	—
109	#13083553	C₂³	1	2	yes	—
110	#13083553	C₂³	1	4	yes	—
111	#13083553	C₂³	1	2	yes	—
112	#13083553	C₂³	1	4	yes	—
113	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
114	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
115	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
116	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
117	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
118	#13083551	C₂³	1	2	yes	—
119	#13083551	C₂³	1	4	yes	—
120	#13083551	C₂³	1	4	yes	—
121	#13083551	C₂³	1	2	yes	—
122	#13083551	C₂³	1	4	yes	—
123	C₄×Dic₈₉	C₂³	1	4	yes	—
124	C₄×Dic₈₉	C₂³	1	4	yes	—
125	C₄×Dic₈₉	C₂³	1	4	yes	—
126	C₄×Dic₈₉	C₂³	1	2	yes	—
127	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	—	2	4	no	—
129	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
130	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
136	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₄²×C₈₉	C₂³	1	2	yes	—
148	C₄²×C₈₉	C₂³	1	2	yes	—
149	C₄²×C₈₉	C₂³	1	2	yes	—
150	C₄²×C₈₉	C₂³	1	2	yes	—
151	C₂³×C₈₉	—	2	2	no	—
152	C₂³×C₈₉	—	2	2	no	—
153	C₂³×C₈₉	—	4	1	no	—
154	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
155	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
156	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
157	C₂²×D₈₉	C₂⁴	1	2	yes	—
158	C₂×C₄×C₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	—	2	4	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	4	2	no	—
165	C₂×C₄×C₈₉	#41	1	4	yes	—
166	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
168	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
169	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
170	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
171	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
174	C₂²⋊D₈₉	—	2	4	no	—
175	C₂²⋊D₈₉	—	2	4	no	—
176	C₂²⋊D₈₉	—	4	2	no	—
177	C₂×Dic₈₉	—	2	4	no	—
178	C₂×Dic₈₉	—	4	2	no	—
179	C₂×Dic₈₉	C₂⁴	1	2	yes	—
180	C₂×Dic₈₉	C₂⁴	1	2	yes	—
181	C₂×Dic₈₉	C₂⁴	1	4	yes	—
182	C₂×Dic₈₉	C₂⁴	1	2	yes	—
183	C₂×Dic₈₉	C₂⁴	1	4	yes	—
184	D₃₅₆	—	2	2	no	—
185	C₄×D₈₉	—	2	4	no	—
186	C₄×D₈₉	—	4	4	no	—
187	Dic₁₇₈	—	2	4	no	—
188	Dic₁₇₈	—	2	4	no	—
189	Dic₁₇₈	—	2	2	no	—
190	Dic₁₇₈	—	4	4	no	—
191	C₂²×C₈₉	—	2	1	no	—
192	C₂²×C₈₉	—	2	1	no	—
193	C₂²×C₈₉	—	2	1	no	—
194	C₂²×C₈₉	—	2	1	no	—
195	C₂²×C₈₉	—	2	1	no	—
196	C₂²×C₈₉	—	2	1	no	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	—	4	4	no	—
199	C₂²×C₈₉	C₂×#41	1	2	yes	—
200	C₂²×C₈₉	2₋¹⁺⁴	1	2	yes	—
201	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
202	C₂×D₈₉	—	2	2	no	—
203	C₂×D₈₉	—	2	2	no	—
204	C₂×D₈₉	—	2	2	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	2	2	no	—
208	C₄×C₈₉	—	2	2	no	—
209	C₄×C₈₉	—	2	2	no	—
210	C₄×C₈₉	—	2	2	no	—
211	C₄×C₈₉	C₂×#41	1	2	yes	—
212	C₄×C₈₉	C₂×#41	1	2	yes	—
213	Dic₈₉	—	2	4	no	—
214	Dic₈₉	—	2	2	no	—
215	Dic₈₉	—	2	2	no	—
216	Dic₈₉	—	2	2	no	—
217	Dic₈₉	—	2	4	no	—
218	C₂×C₈₉	—	2	2	no	—
219	C₂×C₈₉	—	2	2	no	—
220	C₂×C₈₉	—	4	1	no	—
221	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
222	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
223	C₂×C₈₉	#585	1	1	yes	characteristic
224	D₈₉	—	4	2	no	—
225	#3495	—	89	1	no	maximal, Sylow
226	C₈₉	#3495	1	1	yes	characteristic, complemented, Sylow
227	#556	—	89	2	no	—
228	#554	—	89	2	no	—
229	#552	—	89	4	no	—
230	#552	—	89	2	no	—
231	#552	—	89	2	no	—
232	#551	—	89	4	no	—
233	#544	—	89	1	no	—
234	#542	—	89	2	no	—
235	#541	—	89	2	no	—
236	#536	—	89	1	no	—
237	#533	—	89	2	no	—
238	#529	—	89	2	no	—
239	#525	—	89	1	no	—
240	C₂×C₂²⋊Q₈	—	89	1	no	—
241	#520	—	89	1	no	—
242	#519	—	89	1	no	—
243	C₂×#117	D₈₉	1	1	yes	characteristic, complemented
244	C₂×#41	—	89	1	no	—
245	C₂²×Q₈	—	89	1	no	—
246	C₂³×C₄	C₂×D₈₉	1	1	yes	characteristic
247	C₄⋊Q₈	—	89	2	no	—
248	C₄⋊Q₈	—	89	2	no	—
249	C₄⋊Q₈	—	89	2	no	—
250	#126	—	89	4	no	—
251	#126	—	89	4	no	—
252	#126	—	89	4	no	—
253	#126	—	89	4	no	—
254	#125	—	89	4	no	—
255	#125	—	89	4	no	—
256	#125	—	89	2	no	—
257	#125	—	89	2	no	—
258	#125	—	89	4	no	—
259	#124	—	89	4	no	—
260	#124	—	89	2	no	—
261	#123	—	89	2	no	—
262	#123	—	89	4	no	—
263	#123	—	89	4	no	—
264	#123	—	89	4	no	—
265	C₂²⋊Q₈	—	89	2	no	—
266	C₂²⋊Q₈	—	89	2	no	—
267	C₂²⋊Q₈	—	89	2	no	—
268	C₂²⋊Q₈	—	89	2	no	—
269	C₂²⋊Q₈	—	89	1	no	—
270	C₂²⋊Q₈	—	89	1	no	—
271	C₂²⋊Q₈	—	89	4	no	—
272	C₂²⋊Q₈	—	89	4	no	—
273	C₂²⋊Q₈	—	89	2	no	—
274	C₂²⋊Q₈	—	89	2	no	—
275	C₂²⋊Q₈	—	89	4	no	—
276	#121	—	89	1	no	—
277	#121	—	89	1	no	—
278	#120	—	89	2	no	—
279	C₄×Q₈	—	89	2	no	—
280	C₄×Q₈	—	89	2	no	—
281	C₄×Q₈	—	89	2	no	—
282	C₄×Q₈	—	89	2	no	—
283	C₄×Q₈	—	89	2	no	—
284	C₄×Q₈	—	89	4	no	—
285	C₄×D₄	—	89	2	no	—
286	C₄×D₄	—	89	2	no	—
287	C₄×D₄	—	89	4	no	—
288	C₄×D₄	—	89	4	no	—
289	C₄×D₄	—	89	2	no	—
290	#117	—	89	1	no	—
291	#117	—	89	4	no	—
292	#117	—	89	2	no	—
293	#117	—	89	4	no	—
294	#117	—	89	4	no	—
295	#117	C₂×D₈₉	1	1	yes	characteristic
296	#117	C₂×D₈₉	1	1	yes	characteristic
297	#117	C₂×D₈₉	1	2	yes	—
298	#117	C₂×D₈₉	1	1	yes	characteristic
299	#117	C₂×D₈₉	1	2	yes	—
300	#117	C₂×D₈₉	1	1	yes	characteristic
301	C₂×C₄⋊C₄	—	89	1	no	—
302	C₂×C₄⋊C₄	—	89	2	no	—
303	C₂×C₄⋊C₄	—	89	2	no	—
304	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	89	2	no	—
307	C₂×C₂²⋊C₄	C₂×D₈₉	1	2	yes	—
308	C₂×C₄²	C₂×D₈₉	1	2	yes	—
309	C₂⁴	C₂²×D₈₉	1	1	yes	characteristic
310	#41	—	178	4	no	—
311	C₂×Q₈	—	89	4	no	—
312	C₂×Q₈	—	89	2	no	—
313	C₂×Q₈	—	89	2	no	—
314	C₂×Q₈	—	89	1	no	—
315	C₂×Q₈	—	178	4	no	—
316	C₂×D₄	—	89	2	no	—
317	C₂×D₄	—	89	2	no	—
318	C₂×D₄	—	89	2	no	—
319	C₂×D₄	—	89	1	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	89	2	no	—
322	C₂²×C₄	—	89	2	no	—
323	C₂²×C₄	—	89	4	no	—
324	C₂²×C₄	—	89	2	no	—
325	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
327	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
328	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
329	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
330	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
331	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
332	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
333	C₄⋊C₄	—	89	2	no	—
334	C₄⋊C₄	—	89	4	no	—
335	C₄⋊C₄	—	89	2	no	—
336	C₄⋊C₄	—	89	4	no	—
337	C₄⋊C₄	—	89	4	no	—
338	C₄⋊C₄	—	89	1	no	—
339	C₄⋊C₄	—	89	1	no	—
340	C₄⋊C₄	—	89	4	no	—
341	C₄⋊C₄	—	89	4	no	—
342	C₄⋊C₄	—	89	4	no	—
343	C₄⋊C₄	—	89	4	no	—
344	C₄⋊C₄	—	89	4	no	—
345	C₄⋊C₄	—	89	2	no	—
346	C₄⋊C₄	—	89	2	no	—
347	C₄⋊C₄	—	89	4	no	—
348	C₄⋊C₄	—	89	4	no	—
349	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
350	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
351	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
352	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
353	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
354	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
355	C₂²⋊C₄	—	89	4	no	—
356	C₂²⋊C₄	—	89	4	no	—
357	C₂²⋊C₄	—	89	2	no	—
358	C₂²⋊C₄	—	89	2	no	—
359	C₂²⋊C₄	—	89	2	no	—
360	C₂²⋊C₄	—	89	2	no	—
361	C₂²⋊C₄	—	89	4	no	—
362	C₂²⋊C₄	—	89	4	no	—
363	C₂²⋊C₄	—	89	2	no	—
364	C₂²⋊C₄	—	89	4	no	—
365	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
366	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
367	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
368	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
369	C₄²	—	89	4	no	—
370	C₄²	—	89	4	no	—
371	C₄²	—	89	4	no	—
372	C₄²	—	89	2	no	—
373	C₄²	C₂²×D₈₉	1	2	yes	—
374	C₄²	C₂²×D₈₉	1	2	yes	—
375	C₄²	C₂²×D₈₉	1	2	yes	—
376	C₄²	C₂²×D₈₉	1	2	yes	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	89	2	no	—
381	C₂³	C₂³×D₈₉	1	1	yes	characteristic
382	C₂³	C₂³×D₈₉	1	1	yes	characteristic
383	C₂³	C₂³×D₈₉	1	1	yes	characteristic
384	Q₈	—	356	4	no	—
385	Q₈	—	178	4	no	—
386	Q₈	—	178	4	no	—
387	Q₈	—	178	2	no	—
388	D₄	—	356	2	no	—
389	D₄	—	178	4	no	—
390	D₄	—	178	4	no	—
391	D₄	—	178	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	89	2	no	—
400	C₂×C₄	—	89	2	no	—
401	C₂×C₄	—	89	4	no	—
402	C₂×C₄	—	89	2	no	—
403	C₂×C₄	—	89	4	no	—
404	C₂×C₄	—	356	4	no	—
405	C₂×C₄	—	356	2	no	—
406	C₂×C₄	—	178	4	no	—
407	C₂×C₄	—	178	4	no	—
408	C₂×C₄	#13083574	1	4	yes	—
409	C₂×C₄	C₂³×D₈₉	1	2	yes	—
410	C₂×C₄	C₂³×D₈₉	1	2	yes	—
411	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₈₉	1	2	yes	—
413	C₂×C₄	C₂³×D₈₉	1	2	yes	—
414	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	178	2	no	—
426	C₂²	—	178	2	no	—
427	C₂²	—	178	2	no	—
428	C₂²	C₂×#13083574	1	2	yes	—
429	C₂²	#15668059	1	2	yes	—
430	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	178	2	no	—
438	C₄	—	178	4	no	—
439	C₄	—	178	2	no	—
440	C₄	—	178	4	no	—
441	C₄	—	178	2	no	—
442	C₄	C₂×#13083574	1	2	yes	—
443	C₄	C₂×#13083574	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	2	2	no	—
446	C₂	—	4	1	no	—
447	C₂	—	356	2	no	—
448	C₂	C₂²×#13083574	1	1	yes	characteristic
449	C₂	C₂×#15668059	1	1	yes	characteristic
450	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	C₂×#117×C₈₉	C₂
prime radical	#19152109	C₂
hypercenter	C₂×#117	D₈₉
hypocenter	C₈₉	#3495
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
1. #19152316	C₂	semidirect
2. #19152303	C₂	semidirect
3. #19152287	C₂	semidirect
4. #19152283	C₂	semidirect
5. #19152281	C₂	semidirect
6. #19152274	C₂	semidirect
7. #19152226	C₂	semidirect
8. #19152219	C₂	semidirect
9. #19152210	C₂	semidirect
10. #19152174	C₂	semidirect
11. #19152155	C₂	semidirect
12. #19152132	C₂	semidirect
14. C₂×#15667991	C₂	semidirect
15. #19152078	C₂	semidirect
16. #19152075	C₂	semidirect
17. C₂×#117×C₈₉	C₂	semidirect
20. #15668012	C₂²	semidirect
21. #15668012	C₂²	semidirect
22. #15668011	C₂²	semidirect
23. #15668007	C₂²	semidirect
24. #15668006	C₂²	semidirect
27. #15668004	C₂²	semidirect
28. #15668004	C₂²	semidirect
29. #15668003	C₂²	semidirect
30. #15668002	C₂²	semidirect
31. #15668002	C₂²	semidirect
32. #15668000	C₂²	semidirect
38. #15667992	C₂²	semidirect
39. #15667992	C₂²	semidirect
47. #15667990	C₂²	semidirect
52. C₄×Dic₁₇₈	C₂²	semidirect
53. C₄×Dic₁₇₈	C₂²	semidirect
54. C₄×Dic₁₇₈	C₂²	semidirect
55. C₄×Dic₁₇₈	C₂²	semidirect
56. #15667977	C₂²	semidirect
57. #15667977	C₂²	semidirect
58. C₄×D₃₅₆	C₂²	semidirect
65. #15667970	C₂²	semidirect
66. #15667969	C₂²	semidirect
70. C₄⋊C₄×D₈₉	C₂²	semidirect
226. C₈₉	#3495	semidirect
243. C₂×#117	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152316	2
#19152303	2
#19152287	2
#19152283	2
#19152281	2
#19152274	2
#19152226	2
#19152219	2
#19152210	2
#19152174	2
#19152155	2
#19152132	2
#19152109	2
C₂×#15667991	2
#19152078	2
#19152075	2
C₂×#117×C₈₉	2
#3495	89