Subgroups — #26034498

Order 11392.

1014 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152352	C₂	1	2	yes	maximal, complemented
2	#19152350	C₂	1	2	yes	maximal, complemented
3	#19152287	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152286	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152283	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152272	C₂	1	2	yes	maximal, complemented
7	#19152271	C₂	1	2	yes	maximal, complemented
8	Q₈×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152261	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152261	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152228	C₂	1	2	yes	maximal, complemented
13	#19152226	C₂	1	2	yes	maximal, complemented
14	#19152211	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152206	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152192	C₂	1	2	yes	maximal, complemented
17	#19152189	C₂	1	2	yes	maximal, complemented
18	#19152174	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152171	C₂	1	1	yes	maximal, characteristic, complemented
20	#19152107	C₂	1	1	yes	maximal, characteristic
21	C₂×#15667992	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂²⋊Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083574	C₂²	1	1	yes	characteristic
25	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic
26	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
30	#15668012	C₂²	1	2	yes	complemented
31	#15668012	C₂²	1	1	yes	characteristic, complemented
32	#15668012	C₂²	1	2	yes	complemented
33	#15668011	C₂²	1	2	yes	complemented
34	#15668011	C₂²	1	2	yes	complemented
35	#15668011	C₂²	1	2	yes	complemented
36	#15668011	C₂²	1	2	yes	complemented
37	#15668010	C₂²	1	1	yes	characteristic, complemented
38	#15668007	C₂²	1	2	yes	—
39	#15668007	C₂²	1	2	yes	—
40	#15668007	C₂²	1	2	yes	—
41	#15668007	C₂²	1	2	yes	complemented
42	#15668007	C₂²	1	2	yes	complemented
43	#15668006	C₂²	1	2	yes	—
44	#15668005	C₂²	1	2	yes	complemented
45	#15668004	C₂²	1	2	yes	complemented
46	#15668004	C₂²	1	2	yes	complemented
47	#15668003	C₂²	1	2	yes	complemented
48	#15668003	C₂²	1	2	yes	complemented
49	#15668003	C₂²	1	1	yes	characteristic, complemented
50	#15668003	C₂²	1	2	yes	complemented
51	#15668002	C₂²	1	2	yes	complemented
52	#15668002	C₂²	1	2	yes	complemented
53	#15668000	C₂²	1	2	yes	—
54	#15667998	C₂²	1	2	yes	—
55	#15667997	C₂²	1	2	yes	—
56	#15667997	C₂²	1	2	yes	—
57	#15667997	C₂²	1	1	yes	characteristic
58	#15667996	C₂²	1	2	yes	—
59	#15667996	C₂²	1	2	yes	complemented
60	#15667995	C₂²	1	2	yes	—
61	#15667994	C₂²	1	2	yes	—
62	#15667994	C₂²	1	1	yes	characteristic
63	#15667994	C₂²	1	2	yes	complemented
64	#15667992	C₂²	1	1	yes	characteristic
65	#15667992	C₂²	1	1	yes	characteristic
66	#15667992	C₂²	1	1	yes	characteristic
67	#15667992	C₂²	1	2	yes	—
68	#15667992	C₂²	1	2	yes	—
69	#15667992	C₂²	1	1	yes	characteristic
70	#15667992	C₂²	1	1	yes	characteristic
71	#15667992	C₂²	1	2	yes	—
72	#15667992	C₂²	1	1	yes	characteristic, complemented
73	#15667992	C₂²	1	1	yes	characteristic, complemented
74	#15667992	C₂²	1	2	yes	complemented
75	#15667991	C₂²	1	1	yes	characteristic
76	#15667991	C₂²	1	1	yes	characteristic, complemented
77	#15667990	C₂²	1	1	yes	characteristic
78	#15667990	C₂²	1	2	yes	—
79	#15667990	C₂²	1	2	yes	—
80	#15667990	C₂²	1	2	yes	complemented
81	#15667989	C₂²	1	2	yes	—
82	#15667989	C₂²	1	1	yes	characteristic
83	#15667989	C₂²	1	2	yes	—
84	#15667989	C₂²	1	2	yes	—
85	#15667989	C₂²	1	2	yes	complemented
86	#15667989	C₂²	1	2	yes	complemented
87	#15667988	C₂²	1	1	yes	characteristic
88	#15667985	C₂²	1	1	yes	characteristic
89	#15667984	C₂²	1	1	yes	characteristic
90	#15667982	C₂²	1	1	yes	characteristic
91	#15667980	C₂²	1	1	yes	characteristic
92	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
93	#15667977	C₂²	1	1	yes	characteristic, complemented
94	#15667977	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₃₅₆	C₂²	1	2	yes	—
96	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
97	D₄×Dic₈₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
100	#15667972	C₂²	1	2	yes	—
101	#15667972	C₂²	1	2	yes	—
102	#15667971	C₂²	1	2	yes	—
103	#15667970	C₂²	1	2	yes	—
104	#15667970	C₂²	1	1	yes	characteristic, complemented
105	#15667969	C₂²	1	1	yes	characteristic
106	#15667969	C₂²	1	2	yes	—
107	C₂×C₄⋊Dic₈₉	C₂²	1	2	yes	—
108	C₄⋊C₄×D₈₉	C₂²	1	2	yes	—
109	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
110	C₂×#13083551	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
112	#126×C₈₉	C₂²	1	2	yes	complemented
113	#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	#125×C₈₉	C₂²	1	2	yes	complemented
115	#123×C₈₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
120	#117×C₈₉	C₂²	1	2	yes	—
121	#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
123	C₂³×D₈₉	C₂³	1	1	yes	characteristic
124	#13083574	—	4	2	no	—
125	C₂×Dic₁₇₈	—	4	2	no	—
126	C₂×Dic₁₇₈	—	4	2	no	—
127	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₇₈	C₂³	1	2	yes	—
131	C₂×Dic₁₇₈	C₂³	1	2	yes	—
132	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
133	C₂×Dic₁₇₈	C₂³	1	2	yes	—
134	C₂×Dic₁₇₈	C₂³	1	2	yes	—
135	Q₈×D₈₉	—	4	2	no	—
136	Q₈×D₈₉	—	4	2	no	—
137	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
138	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
143	C₂²×Dic₈₉	C₂³	1	2	yes	—
144	C₂²×Dic₈₉	C₂³	1	2	yes	—
145	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₈₉	—	4	2	no	—
147	C₂×C₄×D₈₉	C₂³	1	2	yes	—
148	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₈₉	C₂³	1	2	yes	—
152	C₂×C₄×D₈₉	C₂³	1	2	yes	—
153	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₈₉	C₂³	1	2	yes	—
156	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₈₉	C₂³	1	2	yes	—
158	C₄⋊Dic₈₉	C₂³	1	2	yes	—
159	C₄⋊Dic₈₉	C₂³	1	2	yes	—
160	C₄⋊Dic₈₉	C₂³	1	2	yes	—
161	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₈₉	C₂³	1	2	yes	—
163	C₄⋊Dic₈₉	C₂³	1	2	yes	—
164	C₄⋊Dic₈₉	C₂³	1	2	yes	—
165	C₄⋊Dic₈₉	C₂³	1	2	yes	—
166	C₄⋊Dic₈₉	C₂³	1	2	yes	—
167	#13083553	C₂³	1	1	yes	characteristic
168	#13083553	C₂³	1	1	yes	characteristic
169	#13083553	C₂³	1	2	yes	—
170	#13083553	C₂³	1	2	yes	—
171	#13083553	C₂³	1	2	yes	—
172	#13083553	C₂³	1	2	yes	—
173	#13083553	C₂³	1	1	yes	characteristic
174	#13083553	C₂³	1	1	yes	characteristic
175	#13083553	C₂³	1	2	yes	—
176	#13083553	C₂³	1	2	yes	—
177	#13083553	C₂³	1	2	yes	—
178	#13083553	C₂³	1	2	yes	—
179	#13083553	C₂³	1	2	yes	—
180	#13083553	C₂³	1	2	yes	—
181	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
185	#13083551	C₂³	1	1	yes	characteristic
186	#13083551	C₂³	1	2	yes	—
187	#13083551	C₂³	1	1	yes	characteristic
188	#13083551	C₂³	1	1	yes	characteristic
189	#13083551	C₂³	1	1	yes	characteristic
190	#13083551	C₂³	1	2	yes	—
191	#13083551	C₂³	1	2	yes	—
192	#13083551	C₂³	1	2	yes	—
193	#13083551	C₂³	1	1	yes	characteristic
194	#13083551	C₂³	1	1	yes	characteristic
195	#13083551	C₂³	1	2	yes	—
196	#13083551	C₂³	1	2	yes	—
197	#13083551	C₂³	1	2	yes	—
198	#13083551	C₂³	1	2	yes	—
199	#13083551	C₂³	1	2	yes	—
200	C₄×Dic₈₉	C₂³	1	2	yes	—
201	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₈₉	C₂³	1	2	yes	—
203	C₄×Dic₈₉	C₂³	1	2	yes	—
204	C₄×Dic₈₉	C₂³	1	2	yes	—
205	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
208	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
211	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
218	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
219	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
225	C₄²×C₈₉	C₂³	1	1	yes	characteristic
226	C₄²×C₈₉	C₂³	1	2	yes	—
227	C₄²×C₈₉	C₂³	1	2	yes	—
228	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₈₉	—	2	2	no	—
231	C₂²×D₈₉	—	2	2	no	—
232	C₂²×D₈₉	—	4	1	no	—
233	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
234	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
235	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
236	Q₈×C₈₉	—	2	2	no	—
237	D₄×C₈₉	—	2	2	no	—
238	C₂×C₄×C₈₉	—	2	4	no	—
239	C₂×C₄×C₈₉	—	2	2	no	—
240	C₂×C₄×C₈₉	—	2	2	no	—
241	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
243	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
245	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
246	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
248	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂²⋊D₈₉	—	2	2	no	—
251	C₂²⋊D₈₉	—	2	2	no	—
252	C₂²⋊D₈₉	—	4	1	no	—
253	C₂²⋊D₈₉	—	4	1	no	—
254	C₂×Dic₈₉	—	4	1	no	—
255	C₂×Dic₈₉	—	4	2	no	—
256	C₂×Dic₈₉	—	4	2	no	—
257	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₈₉	C₂⁴	1	2	yes	—
260	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₈₉	C₂⁴	1	2	yes	—
262	C₂×Dic₈₉	C₂⁴	1	2	yes	—
263	C₂×Dic₈₉	C₂⁴	1	2	yes	—
264	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
266	D₃₅₆	—	2	2	no	—
267	D₃₅₆	—	4	1	no	—
268	C₄×D₈₉	—	2	4	no	—
269	C₄×D₈₉	—	2	2	no	—
270	C₄×D₈₉	—	2	2	no	—
271	C₄×D₈₉	—	2	2	no	—
272	C₄×D₈₉	—	4	1	no	—
273	C₄×D₈₉	—	4	1	no	—
274	C₄×D₈₉	—	4	2	no	—
275	C₄×D₈₉	—	4	2	no	—
276	Dic₁₇₈	—	2	2	no	—
277	Dic₁₇₈	—	2	2	no	—
278	Dic₁₇₈	—	2	2	no	—
279	Dic₁₇₈	—	4	2	no	—
280	Dic₁₇₈	—	4	2	no	—
281	Dic₁₇₈	—	4	2	no	—
282	Dic₁₇₈	—	4	2	no	—
283	Dic₁₇₈	—	4	1	no	—
284	C₂²×C₈₉	—	2	1	no	—
285	C₂²×C₈₉	—	2	1	no	—
286	C₂²×C₈₉	—	2	1	no	—
287	C₂²×C₈₉	—	2	1	no	—
288	C₂²×C₈₉	—	2	1	no	—
289	C₂²×C₈₉	2₋¹⁺⁴	1	2	yes	—
290	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
291	C₂×D₈₉	—	2	1	no	—
292	C₂×D₈₉	—	2	1	no	—
293	C₂×D₈₉	—	2	1	no	—
294	C₂×D₈₉	—	2	1	no	—
295	C₂×D₈₉	—	2	1	no	—
296	C₂×D₈₉	—	2	1	no	—
297	C₂×D₈₉	—	2	1	no	—
298	C₂×D₈₉	—	2	1	no	—
299	C₂×D₈₉	—	4	4	no	—
300	C₂×D₈₉	2₋¹⁺⁴	1	2	yes	—
301	C₄×C₈₉	—	2	1	no	—
302	C₄×C₈₉	—	2	1	no	—
303	C₄×C₈₉	—	2	2	no	—
304	C₄×C₈₉	—	2	2	no	—
305	C₄×C₈₉	—	2	1	no	—
306	C₄×C₈₉	—	2	2	no	—
307	C₄×C₈₉	—	2	2	no	—
308	C₄×C₈₉	—	2	1	no	—
309	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
310	Dic₈₉	—	2	2	no	—
311	Dic₈₉	—	2	2	no	—
312	Dic₈₉	—	2	2	no	—
313	Dic₈₉	—	2	1	no	—
314	Dic₈₉	—	2	1	no	—
315	Dic₈₉	—	2	1	no	—
316	Dic₈₉	—	2	2	no	—
317	Dic₈₉	—	2	1	no	—
318	Dic₈₉	—	2	1	no	—
319	C₂×C₈₉	—	2	2	no	—
320	C₂×C₈₉	—	4	1	no	—
321	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
323	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
324	D₈₉	—	2	2	no	—
325	D₈₉	—	4	1	no	—
326	D₈₉	—	4	1	no	—
327	#3538	—	89	1	no	maximal, Sylow
328	C₈₉	#3538	1	1	yes	characteristic, complemented, Sylow
329	#563	—	89	2	no	—
330	#563	—	89	2	no	—
331	#552	—	89	1	no	—
332	#552	—	89	1	no	—
333	#552	—	89	1	no	—
334	#552	D₈₉	1	1	yes	characteristic, complemented
335	#551	—	89	2	no	—
336	#551	—	89	2	no	—
337	D₄×Q₈	—	89	1	no	—
338	D₄×Q₈	—	89	1	no	—
339	D₄×Q₈	—	89	1	no	—
340	D₄×Q₈	—	89	1	no	—
341	#544	—	89	2	no	—
342	#544	—	89	2	no	—
343	#541	—	89	1	no	—
344	#541	—	89	1	no	—
345	#539	—	89	2	no	—
346	#539	—	89	2	no	—
347	#536	—	89	1	no	—
348	#536	—	89	1	no	—
349	#525	—	89	1	no	—
350	C₂×C₂²⋊Q₈	—	89	1	no	—
351	C₂×C₂²⋊Q₈	—	89	1	no	—
352	C₂×#41	—	89	1	no	—
353	C₂²×Q₈	—	89	1	no	—
354	C₂²×Q₈	—	89	1	no	—
355	C₂²×Q₈	—	89	1	no	—
356	C₂²×Q₈	—	89	1	no	—
357	C₂³×C₄	—	89	1	no	—
358	C₄⋊Q₈	—	89	1	no	—
359	C₄⋊Q₈	—	89	2	no	—
360	C₄⋊Q₈	—	89	2	no	—
361	C₄⋊Q₈	—	89	2	no	—
362	C₄⋊Q₈	—	89	2	no	—
363	C₄⋊Q₈	—	89	2	no	—
364	C₄⋊Q₈	—	89	1	no	—
365	C₄⋊Q₈	—	89	2	no	—
366	#126	—	89	2	no	—
367	#126	—	89	2	no	—
368	#126	—	89	2	no	—
369	#126	—	89	2	no	—
370	#126	—	89	2	no	—
371	#126	—	89	2	no	—
372	#126	—	89	2	no	—
373	#126	C₂×D₈₉	1	2	yes	complemented
374	#125	—	89	2	no	—
375	#125	—	89	2	no	—
376	#125	—	89	2	no	—
377	#125	—	89	1	no	—
378	#125	—	89	2	no	—
379	#125	—	89	2	no	—
380	#125	—	89	2	no	—
381	#125	—	89	2	no	—
382	#125	C₂×D₈₉	1	1	yes	characteristic, complemented
383	#125	C₂×D₈₉	1	2	yes	complemented
384	#124	—	89	2	no	—
385	#124	—	89	2	no	—
386	#123	—	89	2	no	—
387	#123	—	89	1	no	—
388	#123	—	89	2	no	—
389	#123	—	89	2	no	—
390	#123	—	89	1	no	—
391	#123	—	89	2	no	—
392	#123	—	89	2	no	—
393	#123	—	89	2	no	—
394	#123	—	89	2	no	—
395	#123	C₂×D₈₉	1	2	yes	—
396	C₂²⋊Q₈	—	89	1	no	—
397	C₂²⋊Q₈	—	89	1	no	—
398	C₂²⋊Q₈	—	89	1	no	—
399	C₂²⋊Q₈	—	89	2	no	—
400	C₂²⋊Q₈	—	89	1	no	—
401	C₂²⋊Q₈	—	89	1	no	—
402	C₂²⋊Q₈	—	89	1	no	—
403	C₂²⋊Q₈	—	89	2	no	—
404	C₂²⋊Q₈	—	89	1	no	—
405	C₂²⋊Q₈	—	89	1	no	—
406	C₂²⋊Q₈	—	89	2	no	—
407	C₂²⋊Q₈	—	89	1	no	—
408	C₂²⋊Q₈	—	89	2	no	—
409	C₂²⋊Q₈	—	89	2	no	—
410	C₂²⋊Q₈	—	89	1	no	—
411	C₂²⋊Q₈	—	89	1	no	—
412	C₂²⋊Q₈	—	89	2	no	—
413	C₂²⋊Q₈	—	89	2	no	—
414	C₂²⋊Q₈	—	89	2	no	—
415	C₂²⋊Q₈	—	89	1	no	—
416	C₂²⋊Q₈	—	89	2	no	—
417	C₂²⋊Q₈	—	89	2	no	—
418	C₂²⋊Q₈	—	89	2	no	—
419	C₂²⋊Q₈	—	89	2	no	—
420	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
421	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
422	#121	—	89	1	no	—
423	#121	—	89	1	no	—
424	#120	—	89	1	no	—
425	#120	—	89	1	no	—
426	C₄×Q₈	—	89	1	no	—
427	C₄×Q₈	—	89	1	no	—
428	C₄×Q₈	—	89	1	no	—
429	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
430	C₄×D₄	—	89	2	no	—
431	C₄×D₄	—	89	1	no	—
432	C₄×D₄	—	89	1	no	—
433	C₄×D₄	—	89	2	no	—
434	C₄×D₄	—	89	2	no	—
435	C₄×D₄	—	89	1	no	—
436	C₄×D₄	—	89	2	no	—
437	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
438	#117	—	89	2	no	—
439	#117	—	89	2	no	—
440	#117	—	89	1	no	—
441	#117	—	89	1	no	—
442	#117	—	89	2	no	—
443	#117	C₂×D₈₉	1	2	yes	—
444	#117	C₂×D₈₉	1	1	yes	characteristic, complemented
445	C₂×C₄⋊C₄	—	89	2	no	—
446	C₂×C₄⋊C₄	—	89	2	no	—
447	C₂×C₄⋊C₄	—	89	1	no	—
448	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	—	89	2	no	—
450	C₂×C₂²⋊C₄	—	89	2	no	—
451	C₂⁴	—	89	1	no	—
452	#41	—	356	2	no	—
453	C₂×Q₈	—	89	2	no	—
454	C₂×Q₈	—	89	2	no	—
455	C₂×Q₈	—	89	2	no	—
456	C₂×Q₈	—	89	2	no	—
457	C₂×Q₈	—	89	1	no	—
458	C₂×Q₈	—	89	1	no	—
459	C₂×Q₈	—	89	1	no	—
460	C₂×Q₈	—	89	1	no	—
461	C₂×Q₈	—	356	2	no	—
462	C₂×Q₈	—	356	2	no	—
463	C₂×Q₈	—	356	2	no	—
464	C₂×Q₈	—	356	2	no	—
465	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
466	C₂×D₄	—	89	1	no	—
467	C₂×D₄	—	89	1	no	—
468	C₂×D₄	—	89	1	no	—
469	C₂×D₄	—	89	1	no	—
470	C₂×D₄	—	89	1	no	—
471	C₂×D₄	—	89	1	no	—
472	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
473	C₂²×C₄	—	89	2	no	—
474	C₂²×C₄	—	89	1	no	—
475	C₂²×C₄	—	89	2	no	—
476	C₂²×C₄	—	89	2	no	—
477	C₂²×C₄	—	89	1	no	—
478	C₂²×C₄	—	89	2	no	—
479	C₂²×C₄	—	89	1	no	—
480	C₂²×C₄	—	89	2	no	—
481	C₂²×C₄	—	89	1	no	—
482	C₂²×C₄	—	89	1	no	—
483	C₂²×C₄	—	89	1	no	—
484	C₂²×C₄	—	356	2	no	—
485	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
486	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
488	C₄⋊C₄	—	89	1	no	—
489	C₄⋊C₄	—	89	2	no	—
490	C₄⋊C₄	—	89	2	no	—
491	C₄⋊C₄	—	89	2	no	—
492	C₄⋊C₄	—	89	2	no	—
493	C₄⋊C₄	—	89	2	no	—
494	C₄⋊C₄	—	89	2	no	—
495	C₄⋊C₄	—	89	2	no	—
496	C₄⋊C₄	—	89	2	no	—
497	C₄⋊C₄	—	89	1	no	—
498	C₄⋊C₄	—	89	1	no	—
499	C₄⋊C₄	—	89	2	no	—
500	C₄⋊C₄	—	89	2	no	—
501	C₄⋊C₄	—	89	2	no	—
502	C₄⋊C₄	—	89	2	no	—
503	C₄⋊C₄	—	89	2	no	—
504	C₄⋊C₄	—	89	2	no	—
505	C₄⋊C₄	—	89	2	no	—
506	C₄⋊C₄	—	89	2	no	—
507	C₄⋊C₄	—	89	2	no	—
508	C₄⋊C₄	—	89	1	no	—
509	C₄⋊C₄	—	89	1	no	—
510	C₄⋊C₄	—	89	1	no	—
511	C₄⋊C₄	—	89	2	no	—
512	C₄⋊C₄	—	89	2	no	—
513	C₄⋊C₄	—	89	2	no	—
514	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
516	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
519	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
520	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
521	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
522	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
524	C₂²⋊C₄	—	89	2	no	—
525	C₂²⋊C₄	—	89	1	no	—
526	C₂²⋊C₄	—	89	1	no	—
527	C₂²⋊C₄	—	89	2	no	—
528	C₂²⋊C₄	—	89	2	no	—
529	C₂²⋊C₄	—	89	2	no	—
530	C₂²⋊C₄	—	89	2	no	—
531	C₂²⋊C₄	—	89	2	no	—
532	C₂²⋊C₄	—	89	2	no	—
533	C₂²⋊C₄	—	89	2	no	—
534	C₂²⋊C₄	—	89	1	no	—
535	C₂²⋊C₄	—	89	1	no	—
536	C₂²⋊C₄	—	89	1	no	—
537	C₂²⋊C₄	—	89	1	no	—
538	C₂²⋊C₄	—	89	2	no	—
539	C₂²⋊C₄	—	89	1	no	—
540	C₂²⋊C₄	—	89	1	no	—
541	C₂²⋊C₄	—	89	2	no	—
542	C₂²⋊C₄	—	89	2	no	—
543	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
548	C₄²	—	89	2	no	—
549	C₄²	—	89	1	no	—
550	C₄²	—	89	2	no	—
551	C₄²	—	89	2	no	—
552	C₄²	—	89	2	no	—
553	C₄²	C₂²×D₈₉	1	2	yes	—
554	C₄²	C₂²×D₈₉	1	1	yes	characteristic
555	C₄²	C₂²×D₈₉	1	2	yes	—
556	C₂³	—	89	1	no	—
557	C₂³	—	89	1	no	—
558	C₂³	—	89	1	no	—
559	C₂³	—	356	1	no	—
560	C₂³	—	178	2	no	—
561	C₂³	—	178	2	no	—
562	C₂³	C₂³×D₈₉	1	1	yes	characteristic
563	C₂³	C₂³×D₈₉	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	356	2	no	—
566	Q₈	—	356	2	no	—
567	Q₈	—	356	2	no	—
568	Q₈	—	356	2	no	—
569	Q₈	—	356	1	no	—
570	Q₈	—	178	2	no	—
571	Q₈	—	178	2	no	—
572	Q₈	—	178	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	356	1	no	—
575	D₄	—	356	1	no	—
576	D₄	—	356	1	no	—
577	D₄	—	178	2	no	—
578	D₄	—	178	2	no	—
579	D₄	—	178	2	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	89	1	no	—
584	C₂×C₄	—	89	1	no	—
585	C₂×C₄	—	89	2	no	—
586	C₂×C₄	—	89	1	no	—
587	C₂×C₄	—	89	2	no	—
588	C₂×C₄	—	89	2	no	—
589	C₂×C₄	—	89	2	no	—
590	C₂×C₄	—	89	1	no	—
591	C₂×C₄	—	89	1	no	—
592	C₂×C₄	—	356	1	no	—
593	C₂×C₄	—	356	1	no	—
594	C₂×C₄	—	356	2	no	—
595	C₂×C₄	—	356	2	no	—
596	C₂×C₄	—	356	1	no	—
597	C₂×C₄	—	356	2	no	—
598	C₂×C₄	—	356	2	no	—
599	C₂×C₄	—	178	4	no	—
600	C₂×C₄	—	178	2	no	—
601	C₂×C₄	—	178	2	no	—
602	C₂×C₄	—	178	2	no	—
603	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₈₉	1	2	yes	—
605	C₂×C₄	C₂³×D₈₉	1	2	yes	—
606	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₈₉	1	2	yes	—
608	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₈₉	1	2	yes	—
610	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	89	2	no	—
618	C₂²	—	356	4	no	—
619	C₂²	—	178	1	no	—
620	C₂²	—	178	1	no	—
621	C₂²	—	178	1	no	—
622	C₂²	—	178	1	no	—
623	C₂²	—	178	1	no	—
624	C₂²	—	178	1	no	—
625	C₂²	—	178	1	no	—
626	C₂²	—	178	1	no	—
627	C₂²	#15668059	1	2	yes	—
628	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	178	1	no	—
638	C₄	—	178	1	no	—
639	C₄	—	178	2	no	—
640	C₄	—	178	2	no	—
641	C₄	—	178	2	no	—
642	C₄	—	178	1	no	—
643	C₄	—	178	2	no	—
644	C₄	—	178	1	no	—
645	C₄	—	178	1	no	—
646	C₄	#15668058	1	2	yes	—
647	C₂	—	2	2	no	—
648	C₂	—	4	1	no	—
649	C₂	—	356	1	no	—
650	C₂	—	356	1	no	—
651	C₂	—	178	2	no	—
652	C₂	C₂×#15668058	1	1	yes	characteristic
653	C₂	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
654	C₂	C₂×#15668059	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#552×C₈₉	C₂
prime radical	#19152107	C₂
hypercenter	#552	D₈₉
hypocenter	C₈₉	#3538
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #19152352	C₂	semidirect
2. #19152350	C₂	semidirect
3. #19152287	C₂	semidirect
4. #19152286	C₂	semidirect
5. #19152283	C₂	semidirect
6. #19152272	C₂	semidirect
7. #19152271	C₂	semidirect
8. Q₈×D₃₅₆	C₂	semidirect
9. D₄×Dic₁₇₈	C₂	semidirect
10. #19152261	C₂	semidirect
11. #19152261	C₂	semidirect
12. #19152228	C₂	semidirect
13. #19152226	C₂	semidirect
14. #19152211	C₂	semidirect
15. #19152206	C₂	semidirect
16. #19152192	C₂	semidirect
17. #19152189	C₂	semidirect
18. #19152174	C₂	semidirect
19. #19152171	C₂	semidirect
21. C₂×#15667992	C₂	semidirect
22. C₂²⋊Q₈×D₈₉	C₂	semidirect
23. #552×C₈₉	C₂	semidirect
26. C₂²×Dic₁₇₈	C₂²	semidirect
28. C₂×Q₈×D₈₉	C₂²	semidirect
30. #15668012	C₂²	semidirect
31. #15668012	C₂²	semidirect
32. #15668012	C₂²	semidirect
33. #15668011	C₂²	semidirect
34. #15668011	C₂²	semidirect
35. #15668011	C₂²	semidirect
36. #15668011	C₂²	semidirect
37. #15668010	C₂²	semidirect
41. #15668007	C₂²	semidirect
42. #15668007	C₂²	semidirect
44. #15668005	C₂²	semidirect
45. #15668004	C₂²	semidirect
46. #15668004	C₂²	semidirect
47. #15668003	C₂²	semidirect
48. #15668003	C₂²	semidirect
49. #15668003	C₂²	semidirect
50. #15668003	C₂²	semidirect
51. #15668002	C₂²	semidirect
52. #15668002	C₂²	semidirect
59. #15667996	C₂²	semidirect
63. #15667994	C₂²	semidirect
72. #15667992	C₂²	semidirect
73. #15667992	C₂²	semidirect
74. #15667992	C₂²	semidirect
76. #15667991	C₂²	semidirect
80. #15667990	C₂²	semidirect
85. #15667989	C₂²	semidirect
86. #15667989	C₂²	semidirect
92. C₄×Dic₁₇₈	C₂²	semidirect
93. #15667977	C₂²	semidirect
94. #15667977	C₂²	semidirect
104. #15667970	C₂²	semidirect
112. #126×C₈₉	C₂²	semidirect
113. #125×C₈₉	C₂²	semidirect
114. #125×C₈₉	C₂²	semidirect
117. C₂²⋊Q₈×C₈₉	C₂²	semidirect
118. C₄×Q₈×C₈₉	C₂²	semidirect
121. #117×C₈₉	C₂²	semidirect
328. C₈₉	#3538	semidirect
334. #552	D₈₉	semidirect
373. #126	C₂×D₈₉	semidirect
382. #125	C₂×D₈₉	semidirect
383. #125	C₂×D₈₉	semidirect
421. C₂²⋊Q₈	C₂×D₈₉	semidirect
429. C₄×Q₈	C₂×D₈₉	semidirect
444. #117	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152352	2
#19152350	2
#19152287	2
#19152286	2
#19152283	2
#19152272	2
#19152271	2
Q₈×D₃₅₆	2
D₄×Dic₁₇₈	2
#19152261	2
#19152228	2
#19152226	2
#19152211	2
#19152206	2
#19152192	2
#19152189	2
#19152174	2
#19152171	2
#19152107	2
C₂×#15667992	2
C₂²⋊Q₈×D₈₉	2
#552×C₈₉	2
#3538	89