Subgroups — #26034051

Order 11392.

1100 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152308	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152307	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152307	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152304	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152304	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152303	C₂	1	2	yes	maximal, complemented
7	#19152302	C₂	1	2	yes	maximal, complemented
8	#19152302	C₂	1	2	yes	maximal, complemented
9	D₄×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152263	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152261	C₂	1	2	yes	maximal, complemented
12	#19152228	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152225	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152223	C₂	1	2	yes	maximal, complemented
15	#19152223	C₂	1	2	yes	maximal, complemented
16	#19152154	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152152	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#15667990	C₂	1	2	yes	maximal, complemented
19	C₂²⋊Q₈×D₈₉	C₂	1	2	yes	maximal, complemented
20	#19152070	C₂	1	1	yes	maximal, characteristic
21	#19152070	C₂	1	1	yes	maximal, characteristic
22	C₄×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic
23	#554×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×Dic₁₇₈	C₂²	1	2	yes	complemented
25	C₂×Q₈×D₈₉	C₂²	1	2	yes	complemented
26	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₈₉	C₂²	1	2	yes	—
28	#15668012	C₂²	1	1	yes	characteristic, complemented
29	#15668011	C₂²	1	1	yes	characteristic, complemented
30	#15668011	C₂²	1	1	yes	characteristic, complemented
31	#15668011	C₂²	1	1	yes	characteristic, complemented
32	#15668011	C₂²	1	1	yes	characteristic, complemented
33	#15668011	C₂²	1	2	yes	complemented
34	#15668011	C₂²	1	1	yes	characteristic, complemented
35	#15668010	C₂²	1	1	yes	characteristic, complemented
36	#15668010	C₂²	1	2	yes	complemented
37	#15668004	C₂²	1	1	yes	characteristic, complemented
38	#15668004	C₂²	1	1	yes	characteristic, complemented
39	#15668003	C₂²	1	1	yes	characteristic, complemented
40	#15668003	C₂²	1	1	yes	characteristic, complemented
41	#15668002	C₂²	1	1	yes	characteristic, complemented
42	#15668002	C₂²	1	1	yes	characteristic, complemented
43	#15668002	C₂²	1	2	yes	complemented
44	#15668002	C₂²	1	2	yes	complemented
45	#15667992	C₂²	1	1	yes	characteristic
46	#15667992	C₂²	1	2	yes	—
47	#15667992	C₂²	1	2	yes	complemented
48	#15667992	C₂²	1	2	yes	complemented
49	#15667991	C₂²	1	2	yes	complemented
50	#15667991	C₂²	1	2	yes	complemented
51	#15667991	C₂²	1	2	yes	complemented
52	#15667990	C₂²	1	1	yes	characteristic
53	#15667990	C₂²	1	1	yes	characteristic
54	#15667990	C₂²	1	2	yes	—
55	#15667990	C₂²	1	2	yes	—
56	#15667990	C₂²	1	2	yes	—
57	#15667990	C₂²	1	2	yes	—
58	#15667990	C₂²	1	2	yes	complemented
59	#15667990	C₂²	1	2	yes	complemented
60	#15667990	C₂²	1	2	yes	complemented
61	#15667990	C₂²	1	2	yes	complemented
62	#15667990	C₂²	1	2	yes	complemented
63	#15667990	C₂²	1	2	yes	complemented
64	#15667990	C₂²	1	2	yes	complemented
65	#15667990	C₂²	1	2	yes	complemented
66	#15667989	C₂²	1	2	yes	complemented
67	#15667989	C₂²	1	2	yes	complemented
68	#15667989	C₂²	1	2	yes	complemented
69	#15667989	C₂²	1	2	yes	complemented
70	#15667989	C₂²	1	2	yes	complemented
71	#15667989	C₂²	1	2	yes	complemented
72	#15667988	C₂²	1	1	yes	characteristic
73	#15667988	C₂²	1	2	yes	—
74	#15667988	C₂²	1	2	yes	complemented
75	#15667988	C₂²	1	2	yes	complemented
76	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
78	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
79	#15667977	C₂²	1	2	yes	complemented
80	#15667977	C₂²	1	2	yes	complemented
81	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
82	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
83	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
84	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
85	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
86	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
87	#15667974	C₂²	1	1	yes	characteristic
88	#15667974	C₂²	1	1	yes	characteristic
89	#15667974	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
92	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
93	#15667972	C₂²	1	2	yes	—
94	#15667972	C₂²	1	2	yes	—
95	#15667972	C₂²	1	2	yes	—
96	#15667970	C₂²	1	1	yes	characteristic
97	#15667970	C₂²	1	1	yes	characteristic
98	#15667969	C₂²	1	1	yes	characteristic
99	#15667969	C₂²	1	1	yes	characteristic
100	C₂×#13083553	C₂²	1	2	yes	complemented
101	C₂×#13083553	C₂²	1	2	yes	complemented
102	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
103	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
106	C₂×#13083551	C₂²	1	2	yes	—
107	C₂×#13083551	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
111	C₄²×D₈₉	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
118	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
123	C₂³×D₈₉	C₂³	1	2	yes	—
124	C₂×Dic₁₇₈	—	4	4	no	—
125	C₂×Dic₁₇₈	C₂³	1	2	yes	—
126	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₇₈	C₂³	1	2	yes	—
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	2	yes	—
133	Q₈×D₈₉	—	4	4	no	—
134	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
136	D₄×D₈₉	Q₈	1	8	yes	complemented
137	C₂²×Dic₈₉	C₂³	1	2	yes	—
138	C₂²×Dic₈₉	C₂³	1	2	yes	—
139	C₂²×Dic₈₉	C₂³	1	2	yes	—
140	C₂×C₄×D₈₉	—	4	4	no	—
141	C₂×C₄×D₈₉	C₂³	1	2	yes	—
142	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₈₉	C₂³	1	2	yes	—
144	C₂×C₄×D₈₉	C₂³	1	2	yes	—
145	C₂×C₄×D₈₉	C₂³	1	2	yes	—
146	C₂×C₄×D₈₉	C₂³	1	2	yes	—
147	C₂×C₄×D₈₉	C₂³	1	2	yes	—
148	C₂×C₄×D₈₉	C₂³	1	2	yes	—
149	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
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	#13083553	C₂³	1	1	yes	characteristic
161	#13083553	C₂³	1	1	yes	characteristic
162	#13083553	C₂³	1	1	yes	characteristic
163	#13083553	C₂³	1	1	yes	characteristic
164	#13083553	C₂³	1	2	yes	—
165	#13083553	C₂³	1	2	yes	—
166	#13083553	C₂³	1	2	yes	—
167	#13083553	C₂³	1	2	yes	—
168	#13083553	C₂³	1	2	yes	—
169	#13083553	C₂³	1	1	yes	characteristic
170	#13083553	C₂³	1	1	yes	characteristic
171	#13083553	C₂³	1	1	yes	characteristic
172	#13083553	C₂³	1	1	yes	characteristic
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	2	yes	—
182	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
184	#13083551	C₂³	1	1	yes	characteristic
185	#13083551	C₂³	1	1	yes	characteristic
186	#13083551	C₂³	1	1	yes	characteristic
187	#13083551	C₂³	1	1	yes	characteristic
188	#13083551	C₂³	1	2	yes	—
189	#13083551	C₂³	1	2	yes	—
190	#13083551	C₂³	1	2	yes	—
191	#13083551	C₂³	1	2	yes	—
192	#13083551	C₂³	1	2	yes	—
193	#13083551	C₂³	1	2	yes	—
194	#13083551	C₂³	1	2	yes	—
195	#13083551	C₂³	1	2	yes	—
196	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
198	C₄×Dic₈₉	C₂³	1	2	yes	—
199	C₄×Dic₈₉	C₂³	1	2	yes	—
200	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
204	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
205	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
207	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
208	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
209	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
213	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
217	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
223	C₄²×C₈₉	C₂³	1	1	yes	characteristic
224	C₄²×C₈₉	C₂³	1	1	yes	characteristic
225	C₄²×C₈₉	C₂³	1	1	yes	characteristic
226	C₂³×C₈₉	C₂⁴	1	2	yes	—
227	C₂²×D₈₉	—	4	2	no	—
228	C₂²×D₈₉	—	4	2	no	—
229	C₂²×D₈₉	C₂×Q₈	1	8	yes	complemented
230	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₈₉	C₂⁴	1	2	yes	—
232	Q₈×C₈₉	—	4	1	no	—
233	Q₈×C₈₉	—	4	2	no	—
234	D₄×C₈₉	C₂×Q₈	1	4	yes	complemented
235	C₂×C₄×C₈₉	—	4	2	no	—
236	C₂×C₄×C₈₉	—	4	2	no	—
237	C₂×C₄×C₈₉	—	4	2	no	—
238	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
247	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂²⋊D₈₉	C₂×Q₈	1	8	yes	complemented
249	C₂×Dic₈₉	—	2	4	no	—
250	C₂×Dic₈₉	—	4	2	no	—
251	C₂×Dic₈₉	—	4	2	no	—
252	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₈₉	C₂⁴	1	2	yes	—
256	C₂×Dic₈₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
262	D₃₅₆	C₂×Q₈	1	4	yes	complemented
263	C₄×D₈₉	—	2	2	no	—
264	C₄×D₈₉	—	2	4	no	—
265	C₄×D₈₉	—	4	2	no	—
266	C₄×D₈₉	—	4	2	no	—
267	C₄×D₈₉	—	4	1	no	—
268	C₄×D₈₉	—	4	2	no	—
269	C₄×D₈₉	—	4	2	no	—
270	C₄×D₈₉	—	4	2	no	—
271	C₄×D₈₉	—	4	2	no	—
272	C₄×D₈₉	C₂×Q₈	1	4	yes	complemented
273	Dic₁₇₈	—	2	2	no	—
274	Dic₁₇₈	—	2	4	no	—
275	Dic₁₇₈	—	2	2	no	—
276	Dic₁₇₈	—	4	2	no	—
277	Dic₁₇₈	—	4	2	no	—
278	Dic₁₇₈	—	4	2	no	—
279	Dic₁₇₈	—	4	2	no	—
280	Dic₁₇₈	—	4	1	no	—
281	C₂²×C₈₉	—	2	2	no	—
282	C₂²×C₈₉	—	2	2	no	—
283	C₂²×C₈₉	C₂²×Q₈	1	4	yes	—
284	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
285	C₂×D₈₉	—	2	2	no	—
286	C₂×D₈₉	—	2	1	no	—
287	C₂×D₈₉	—	2	2	no	—
288	C₂×D₈₉	—	2	1	no	—
289	C₂×D₈₉	—	4	8	no	—
290	C₂×D₈₉	C₂²×Q₈	1	2	yes	—
291	C₂×D₈₉	C₂²×Q₈	1	4	yes	—
292	C₄×C₈₉	—	2	1	no	—
293	C₄×C₈₉	—	2	2	no	—
294	C₄×C₈₉	—	2	1	no	—
295	C₄×C₈₉	—	2	2	no	—
296	C₄×C₈₉	—	2	1	no	—
297	C₄×C₈₉	—	2	2	no	—
298	C₄×C₈₉	—	2	1	no	—
299	C₄×C₈₉	—	2	1	no	—
300	C₄×C₈₉	—	2	1	no	—
301	C₄×C₈₉	C₂²×Q₈	1	2	yes	—
302	Dic₈₉	—	2	1	no	—
303	Dic₈₉	—	2	2	no	—
304	Dic₈₉	—	2	1	no	—
305	Dic₈₉	—	2	2	no	—
306	Dic₈₉	—	2	1	no	—
307	Dic₈₉	—	2	1	no	—
308	Dic₈₉	—	2	2	no	—
309	Dic₈₉	—	2	1	no	—
310	Dic₈₉	C₂²×Q₈	1	2	yes	—
311	Dic₈₉	H(5,𝔽₂)	1	2	yes	—
312	C₂×C₈₉	—	2	4	no	—
313	C₂×C₈₉	C₂³×Q₈	1	1	yes	characteristic
314	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×C₈₉	#585	1	1	yes	characteristic
316	D₈₉	—	2	2	no	—
317	D₈₉	—	2	4	no	—
318	#3501	—	89	1	no	maximal, Sylow
319	C₈₉	#3501	1	1	yes	characteristic, complemented, Sylow
320	#554	—	89	1	no	—
321	#554	—	89	1	no	—
322	#554	—	89	2	no	—
323	#554	—	89	2	no	—
324	#554	—	89	1	no	—
325	#554	—	89	1	no	—
326	#554	—	89	1	no	—
327	#554	—	89	2	no	—
328	#554	D₈₉	1	1	yes	characteristic, complemented
329	D₄×Q₈	—	89	1	no	—
330	D₄×Q₈	—	89	2	no	—
331	D₄×Q₈	—	89	1	no	—
332	#544	—	89	1	no	—
333	#544	—	89	1	no	—
334	#543	—	89	2	no	—
335	#543	—	89	2	no	—
336	#533	—	89	1	no	—
337	#533	—	89	1	no	—
338	C₂×C₂²⋊Q₈	—	89	2	no	—
339	C₂×C₂²⋊Q₈	—	89	2	no	—
340	#518	—	89	1	no	—
341	#518	—	89	1	no	—
342	C₂×C₄×D₄	—	89	1	no	—
343	C₂²×Q₈	—	89	2	no	—
344	C₂²×Q₈	—	89	2	no	—
345	C₂²×D₄	—	89	1	no	—
346	C₂³×C₄	—	89	2	no	—
347	C₄⋊Q₈	—	89	1	no	—
348	C₄⋊Q₈	—	89	2	no	—
349	C₄⋊Q₈	—	89	1	no	—
350	C₄⋊Q₈	—	89	1	no	—
351	C₄⋊Q₈	—	89	1	no	—
352	C₄⋊Q₈	—	89	2	no	—
353	C₄⋊Q₈	—	89	1	no	—
354	C₄⋊Q₈	—	89	1	no	—
355	C₄⋊Q₈	—	89	1	no	—
356	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
357	#125	—	89	1	no	—
358	#125	—	89	1	no	—
359	#125	—	89	2	no	—
360	#125	—	89	2	no	—
361	#125	—	89	1	no	—
362	#125	—	89	1	no	—
363	#125	—	89	1	no	—
364	#125	—	89	1	no	—
365	#125	C₂×D₈₉	1	1	yes	characteristic, complemented
366	#125	C₂×D₈₉	1	1	yes	characteristic, complemented
367	C₂²⋊Q₈	—	89	2	no	—
368	C₂²⋊Q₈	—	89	1	no	—
369	C₂²⋊Q₈	—	89	2	no	—
370	C₂²⋊Q₈	—	89	2	no	—
371	C₂²⋊Q₈	—	89	2	no	—
372	C₂²⋊Q₈	—	89	2	no	—
373	C₂²⋊Q₈	—	89	2	no	—
374	C₂²⋊Q₈	—	89	1	no	—
375	C₂²⋊Q₈	—	89	2	no	—
376	C₂²⋊Q₈	—	89	1	no	—
377	C₂²⋊Q₈	—	89	2	no	—
378	C₂²⋊Q₈	—	89	2	no	—
379	C₂²⋊Q₈	—	89	2	no	—
380	C₂²⋊Q₈	—	89	2	no	—
381	C₂²⋊Q₈	—	89	2	no	—
382	C₂²⋊Q₈	—	89	2	no	—
383	C₂²⋊Q₈	—	89	2	no	—
384	C₂²⋊Q₈	—	89	2	no	—
385	C₂²⋊Q₈	—	89	1	no	—
386	C₂²⋊Q₈	—	89	2	no	—
387	C₂²⋊Q₈	—	89	2	no	—
388	C₂²⋊Q₈	—	89	2	no	—
389	C₂²⋊Q₈	—	89	2	no	—
390	C₂²⋊Q₈	—	89	2	no	—
391	C₂²⋊Q₈	—	89	2	no	—
392	C₂²⋊Q₈	—	89	2	no	—
393	C₂²⋊Q₈	—	89	2	no	—
394	C₂²⋊Q₈	—	89	2	no	—
395	C₂²⋊Q₈	—	89	2	no	—
396	C₂²⋊Q₈	—	89	2	no	—
397	C₂²⋊Q₈	—	89	2	no	—
398	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
399	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
400	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
401	C₄×Q₈	—	89	2	no	—
402	C₄×Q₈	—	89	2	no	—
403	C₄×Q₈	—	89	1	no	—
404	C₄×Q₈	—	89	1	no	—
405	C₄×Q₈	—	89	1	no	—
406	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
407	C₄×D₄	—	89	1	no	—
408	C₄×D₄	—	89	1	no	—
409	C₄×D₄	—	89	1	no	—
410	C₄×D₄	—	89	2	no	—
411	C₄×D₄	—	89	2	no	—
412	C₄×D₄	—	89	2	no	—
413	C₄×D₄	—	89	1	no	—
414	C₄×D₄	—	89	1	no	—
415	C₄×D₄	—	89	1	no	—
416	C₄×D₄	—	89	2	no	—
417	C₄×D₄	—	89	2	no	—
418	C₄×D₄	—	89	2	no	—
419	C₄×D₄	—	89	1	no	—
420	C₄×D₄	—	89	1	no	—
421	C₄×D₄	—	89	1	no	—
422	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
423	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
424	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
425	#117	—	89	1	no	—
426	#117	—	89	1	no	—
427	#117	—	89	1	no	—
428	#117	—	89	1	no	—
429	C₂×C₄⋊C₄	—	89	2	no	—
430	C₂×C₄⋊C₄	—	89	2	no	—
431	C₂×C₄⋊C₄	—	89	1	no	—
432	C₂×C₄⋊C₄	—	89	2	no	—
433	C₂×C₄⋊C₄	—	89	2	no	—
434	C₂×C₄⋊C₄	—	89	2	no	—
435	C₂×C₄⋊C₄	C₂×D₈₉	1	2	yes	complemented
436	C₂×C₂²⋊C₄	—	89	2	no	—
437	C₂×C₂²⋊C₄	—	89	2	no	—
438	C₂×C₂²⋊C₄	—	89	2	no	—
439	C₂×C₂²⋊C₄	—	89	2	no	—
440	C₂×C₂²⋊C₄	—	89	2	no	—
441	C₂×C₄²	—	89	1	no	—
442	C₂⁴	—	89	2	no	—
443	C₂×Q₈	—	89	2	no	—
444	C₂×Q₈	—	89	1	no	—
445	C₂×Q₈	—	89	2	no	—
446	C₂×Q₈	—	89	2	no	—
447	C₂×Q₈	—	89	2	no	—
448	C₂×Q₈	—	89	2	no	—
449	C₂×Q₈	—	89	1	no	—
450	C₂×Q₈	—	89	1	no	—
451	C₂×Q₈	—	356	4	no	—
452	C₂×Q₈	—	356	4	no	—
453	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
454	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
455	C₂×D₄	—	89	2	no	—
456	C₂×D₄	—	89	8	no	—
457	C₂×D₄	—	89	1	no	—
458	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
459	C₂²×C₄	—	89	1	no	—
460	C₂²×C₄	—	89	2	no	—
461	C₂²×C₄	—	89	2	no	—
462	C₂²×C₄	—	89	2	no	—
463	C₂²×C₄	—	89	1	no	—
464	C₂²×C₄	—	89	2	no	—
465	C₂²×C₄	—	89	2	no	—
466	C₂²×C₄	—	89	2	no	—
467	C₂²×C₄	—	89	2	no	—
468	C₂²×C₄	—	89	2	no	—
469	C₂²×C₄	—	89	2	no	—
470	C₂²×C₄	—	89	1	no	—
471	C₂²×C₄	—	89	2	no	—
472	C₂²×C₄	—	356	4	no	—
473	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
474	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
475	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
476	C₄⋊C₄	—	89	1	no	—
477	C₄⋊C₄	—	89	2	no	—
478	C₄⋊C₄	—	89	1	no	—
479	C₄⋊C₄	—	89	2	no	—
480	C₄⋊C₄	—	89	1	no	—
481	C₄⋊C₄	—	89	1	no	—
482	C₄⋊C₄	—	89	2	no	—
483	C₄⋊C₄	—	89	1	no	—
484	C₄⋊C₄	—	89	2	no	—
485	C₄⋊C₄	—	89	2	no	—
486	C₄⋊C₄	—	89	2	no	—
487	C₄⋊C₄	—	89	2	no	—
488	C₄⋊C₄	—	89	2	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	1	no	—
494	C₄⋊C₄	—	89	1	no	—
495	C₄⋊C₄	—	89	1	no	—
496	C₄⋊C₄	—	89	1	no	—
497	C₄⋊C₄	—	89	1	no	—
498	C₄⋊C₄	—	89	1	no	—
499	C₄⋊C₄	—	89	1	no	—
500	C₄⋊C₄	—	89	1	no	—
501	C₄⋊C₄	—	89	2	no	—
502	C₄⋊C₄	—	89	1	no	—
503	C₄⋊C₄	—	89	1	no	—
504	C₄⋊C₄	—	89	2	no	—
505	C₄⋊C₄	—	89	1	no	—
506	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
508	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
510	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
512	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
513	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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	C₂²⋊C₄	—	89	2	no	—
518	C₂²⋊C₄	—	89	2	no	—
519	C₂²⋊C₄	—	89	2	no	—
520	C₂²⋊C₄	—	89	2	no	—
521	C₂²⋊C₄	—	89	1	no	—
522	C₂²⋊C₄	—	89	1	no	—
523	C₂²⋊C₄	—	89	2	no	—
524	C₂²⋊C₄	—	89	1	no	—
525	C₂²⋊C₄	—	89	1	no	—
526	C₂²⋊C₄	—	89	2	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	C₂²×D₈₉	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
535	C₄²	—	89	1	no	—
536	C₄²	—	89	1	no	—
537	C₄²	—	89	1	no	—
538	C₄²	—	89	2	no	—
539	C₄²	—	89	2	no	—
540	C₄²	—	89	1	no	—
541	C₄²	—	89	1	no	—
542	C₄²	C₂²×D₈₉	1	1	yes	characteristic
543	C₄²	C₂²×D₈₉	1	1	yes	characteristic
544	C₄²	C₂²×D₈₉	1	1	yes	characteristic
545	C₂³	—	89	8	no	—
546	C₂³	—	89	1	no	—
547	C₂³	—	89	2	no	—
548	C₂³	—	356	2	no	—
549	C₂³	—	356	2	no	—
550	C₂³	C₂³×D₈₉	1	2	yes	—
551	Q₈	—	4	2	no	—
552	Q₈	—	4	1	no	—
553	Q₈	—	356	2	no	—
554	Q₈	—	356	1	no	—
555	Q₈	—	356	2	no	—
556	Q₈	—	356	2	no	—
557	Q₈	—	356	2	no	—
558	Q₈	—	178	2	no	—
559	Q₈	—	178	4	no	—
560	Q₈	—	178	2	no	—
561	D₄	—	89	8	no	—
562	D₄	—	89	4	no	—
563	D₄	Q₈×D₈₉	1	4	yes	complemented
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	89	1	no	—
568	C₂×C₄	—	89	1	no	—
569	C₂×C₄	—	89	4	no	—
570	C₂×C₄	—	89	1	no	—
571	C₂×C₄	—	89	1	no	—
572	C₂×C₄	—	89	2	no	—
573	C₂×C₄	—	89	1	no	—
574	C₂×C₄	—	89	1	no	—
575	C₂×C₄	—	89	2	no	—
576	C₂×C₄	—	89	1	no	—
577	C₂×C₄	—	89	2	no	—
578	C₂×C₄	—	356	2	no	—
579	C₂×C₄	—	356	2	no	—
580	C₂×C₄	—	356	1	no	—
581	C₂×C₄	—	356	2	no	—
582	C₂×C₄	—	356	2	no	—
583	C₂×C₄	—	356	2	no	—
584	C₂×C₄	—	356	2	no	—
585	C₂×C₄	—	356	2	no	—
586	C₂×C₄	—	356	2	no	—
587	C₂×C₄	—	178	2	no	—
588	C₂×C₄	—	178	4	no	—
589	C₂×C₄	—	178	4	no	—
590	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₈₉	1	2	yes	—
593	C₂×C₄	C₂³×D₈₉	1	2	yes	—
594	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₈₉	1	2	yes	—
599	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	89	2	no	—
603	C₂²	—	89	4	no	—
604	C₂²	—	356	8	no	—
605	C₂²	—	178	2	no	—
606	C₂²	—	178	1	no	—
607	C₂²	—	178	2	no	—
608	C₂²	—	178	1	no	—
609	C₂²	C₂×Q₈×D₈₉	1	4	yes	—
610	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	89	2	no	—
621	C₄	—	89	2	no	—
622	C₄	—	178	2	no	—
623	C₄	—	178	1	no	—
624	C₄	—	178	2	no	—
625	C₄	—	178	1	no	—
626	C₄	—	178	1	no	—
627	C₄	—	178	2	no	—
628	C₄	—	178	1	no	—
629	C₄	—	178	1	no	—
630	C₄	C₂×Q₈×D₈₉	1	2	yes	—
631	C₂	—	2	4	no	—
632	C₂	—	178	2	no	—
633	C₂	—	178	4	no	—
634	C₂	C₂²×Q₈×D₈₉	1	1	yes	characteristic
635	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
636	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#554×C₈₉	C₂
prime radical	C₂×D₄×D₈₉	C₂²
hypercenter	#554	D₈₉
hypocenter	C₈₉	#3501
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #19152308	C₂	semidirect
2. #19152307	C₂	semidirect
3. #19152307	C₂	semidirect
4. #19152304	C₂	semidirect
5. #19152304	C₂	semidirect
6. #19152303	C₂	semidirect
7. #19152302	C₂	semidirect
8. #19152302	C₂	semidirect
9. D₄×Dic₁₇₈	C₂	semidirect
10. #19152263	C₂	semidirect
11. #19152261	C₂	semidirect
12. #19152228	C₂	semidirect
13. #19152225	C₂	semidirect
14. #19152223	C₂	semidirect
15. #19152223	C₂	semidirect
16. #19152154	C₂	semidirect
17. #19152152	C₂	semidirect
18. C₂×#15667990	C₂	semidirect
19. C₂²⋊Q₈×D₈₉	C₂	semidirect
23. #554×C₈₉	C₂	semidirect
24. C₂²×Dic₁₇₈	C₂²	semidirect
25. C₂×Q₈×D₈₉	C₂²	semidirect
28. #15668012	C₂²	semidirect
29. #15668011	C₂²	semidirect
30. #15668011	C₂²	semidirect
31. #15668011	C₂²	semidirect
32. #15668011	C₂²	semidirect
33. #15668011	C₂²	semidirect
34. #15668011	C₂²	semidirect
35. #15668010	C₂²	semidirect
36. #15668010	C₂²	semidirect
37. #15668004	C₂²	semidirect
38. #15668004	C₂²	semidirect
39. #15668003	C₂²	semidirect
40. #15668003	C₂²	semidirect
41. #15668002	C₂²	semidirect
42. #15668002	C₂²	semidirect
43. #15668002	C₂²	semidirect
44. #15668002	C₂²	semidirect
47. #15667992	C₂²	semidirect
48. #15667992	C₂²	semidirect
49. #15667991	C₂²	semidirect
50. #15667991	C₂²	semidirect
51. #15667991	C₂²	semidirect
58. #15667990	C₂²	semidirect
59. #15667990	C₂²	semidirect
60. #15667990	C₂²	semidirect
61. #15667990	C₂²	semidirect
62. #15667990	C₂²	semidirect
63. #15667990	C₂²	semidirect
64. #15667990	C₂²	semidirect
65. #15667990	C₂²	semidirect
66. #15667989	C₂²	semidirect
67. #15667989	C₂²	semidirect
68. #15667989	C₂²	semidirect
69. #15667989	C₂²	semidirect
70. #15667989	C₂²	semidirect
71. #15667989	C₂²	semidirect
74. #15667988	C₂²	semidirect
75. #15667988	C₂²	semidirect
76. C₄×Dic₁₇₈	C₂²	semidirect
77. C₄×Dic₁₇₈	C₂²	semidirect
78. C₄×Dic₁₇₈	C₂²	semidirect
79. #15667977	C₂²	semidirect
80. #15667977	C₂²	semidirect
100. C₂×#13083553	C₂²	semidirect
101. C₂×#13083553	C₂²	semidirect
103. C₄⋊C₄×D₈₉	C₂²	semidirect
104. C₄⋊C₄×D₈₉	C₂²	semidirect
105. C₄⋊C₄×D₈₉	C₂²	semidirect
112. C₄⋊Q₈×C₈₉	C₂²	semidirect
113. #125×C₈₉	C₂²	semidirect
114. #125×C₈₉	C₂²	semidirect
115. C₂²⋊Q₈×C₈₉	C₂²	semidirect
116. C₂²⋊Q₈×C₈₉	C₂²	semidirect
117. C₂²⋊Q₈×C₈₉	C₂²	semidirect
118. C₄×Q₈×C₈₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
136. D₄×D₈₉	Q₈	semidirect
229. C₂²×D₈₉	C₂×Q₈	semidirect
234. D₄×C₈₉	C₂×Q₈	semidirect
248. C₂²⋊D₈₉	C₂×Q₈	semidirect
262. D₃₅₆	C₂×Q₈	semidirect
272. C₄×D₈₉	C₂×Q₈	semidirect
319. C₈₉	#3501	semidirect
328. #554	D₈₉	semidirect
356. C₄⋊Q₈	C₂×D₈₉	semidirect
365. #125	C₂×D₈₉	semidirect
366. #125	C₂×D₈₉	semidirect
398. C₂²⋊Q₈	C₂×D₈₉	semidirect
399. C₂²⋊Q₈	C₂×D₈₉	semidirect
400. C₂²⋊Q₈	C₂×D₈₉	semidirect
406. C₄×Q₈	C₂×D₈₉	semidirect
435. C₂×C₄⋊C₄	C₂×D₈₉	semidirect
563. D₄	Q₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152308	2
#19152307	2
#19152304	2
#19152303	2
#19152302	2
D₄×Dic₁₇₈	2
#19152263	2
#19152261	2
#19152228	2
#19152225	2
#19152223	2
#19152154	2
#19152152	2
C₂×#15667990	2
C₂²⋊Q₈×D₈₉	2
#19152070	2
C₄×D₄×D₈₉	2
#554×C₈₉	2
#3501	89