Subgroups — #26034072

Order 11392.

988 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152326	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152325	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152325	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152323	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152307	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152307	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152306	C₂	1	2	yes	maximal, complemented
8	#19152305	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152303	C₂	1	2	yes	maximal, complemented
10	#19152302	C₂	1	2	yes	maximal, complemented
11	#19152302	C₂	1	2	yes	maximal, complemented
12	#19152228	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152227	C₂	1	2	yes	maximal, complemented
14	#19152227	C₂	1	2	yes	maximal, complemented
15	#19152225	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152152	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152150	C₂	1	2	yes	maximal, complemented
18	C₂×#15668002	C₂	1	2	yes	maximal, complemented
19	#125×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#19152077	C₂	1	1	yes	maximal, characteristic
21	#19152077	C₂	1	1	yes	maximal, characteristic
22	C₄×#13083573	C₂	1	1	yes	maximal, characteristic
23	#554×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083573	C₂²	1	1	yes	characteristic
25	#15668012	C₂²	1	1	yes	characteristic
26	#15668011	C₂²	1	2	yes	—
27	#15668011	C₂²	1	1	yes	characteristic
28	#15668011	C₂²	1	1	yes	characteristic
29	#15668011	C₂²	1	2	yes	—
30	#15668011	C₂²	1	2	yes	—
31	#15668011	C₂²	1	1	yes	characteristic
32	#15668010	C₂²	1	2	yes	—
33	#15668010	C₂²	1	1	yes	characteristic
34	#15668010	C₂²	1	2	yes	—
35	#15668010	C₂²	1	2	yes	—
36	#15668004	C₂²	1	1	yes	characteristic
37	#15668004	C₂²	1	1	yes	characteristic
38	#15668003	C₂²	1	1	yes	characteristic
39	#15668003	C₂²	1	1	yes	characteristic
40	#15668003	C₂²	1	1	yes	characteristic
41	#15668003	C₂²	1	1	yes	characteristic
42	#15668002	C₂²	1	1	yes	characteristic
43	#15668002	C₂²	1	2	yes	—
44	#15668002	C₂²	1	1	yes	characteristic
45	#15668002	C₂²	1	2	yes	—
46	#15668002	C₂²	1	2	yes	—
47	#15668002	C₂²	1	2	yes	—
48	#15668002	C₂²	1	2	yes	—
49	#15668002	C₂²	1	2	yes	—
50	#15668002	C₂²	1	2	yes	—
51	#15668002	C₂²	1	2	yes	—
52	#15668002	C₂²	1	2	yes	—
53	#15668002	C₂²	1	2	yes	—
54	#15668002	C₂²	1	2	yes	—
55	#15668002	C₂²	1	2	yes	—
56	#15667992	C₂²	1	1	yes	characteristic
57	#15667992	C₂²	1	2	yes	—
58	#15667991	C₂²	1	2	yes	—
59	#15667991	C₂²	1	2	yes	—
60	#15667991	C₂²	1	2	yes	—
61	#15667990	C₂²	1	1	yes	characteristic
62	#15667990	C₂²	1	1	yes	characteristic
63	#15667990	C₂²	1	2	yes	—
64	#15667990	C₂²	1	2	yes	—
65	#15667989	C₂²	1	2	yes	—
66	#15667989	C₂²	1	2	yes	—
67	#15667989	C₂²	1	2	yes	—
68	#15667989	C₂²	1	2	yes	—
69	#15667989	C₂²	1	2	yes	—
70	#15667989	C₂²	1	2	yes	—
71	#15667988	C₂²	1	1	yes	characteristic
72	#15667988	C₂²	1	2	yes	—
73	Q₈×Dic₈₉	C₂²	1	2	yes	—
74	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
75	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
76	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
77	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
78	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
79	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
80	#15667977	C₂²	1	2	yes	—
81	#15667977	C₂²	1	2	yes	—
82	#15667977	C₂²	1	2	yes	—
83	#15667977	C₂²	1	1	yes	characteristic
84	#15667977	C₂²	1	1	yes	characteristic
85	#15667977	C₂²	1	1	yes	characteristic
86	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
87	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
88	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
90	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
92	#15667972	C₂²	1	2	yes	—
93	#15667972	C₂²	1	2	yes	—
94	#15667972	C₂²	1	2	yes	—
95	#15667970	C₂²	1	1	yes	characteristic
96	#15667969	C₂²	1	1	yes	characteristic
97	#15667969	C₂²	1	1	yes	characteristic
98	#15667968	C₂²	1	2	yes	—
99	#15667968	C₂²	1	2	yes	—
100	#15667968	C₂²	1	2	yes	—
101	C₂×C₄⋊Dic₈₉	C₂²	1	2	yes	—
102	C₂×#13083553	C₂²	1	2	yes	—
103	C₂×#13083553	C₂²	1	2	yes	—
104	C₂×#13083553	C₂²	1	2	yes	—
105	C₂×#13083553	C₂²	1	2	yes	—
106	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₈₉	C₂²	1	2	yes	—
109	C₄⋊C₄×D₈₉	C₂²	1	2	yes	—
110	C₂×C₄×Dic₈₉	C₂²	1	2	yes	—
111	C₄²×D₈₉	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
113	#125×C₈₉	C₂²	1	1	yes	characteristic
114	#125×C₈₉	C₂²	1	1	yes	characteristic
115	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
117	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
118	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
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	—
123	#13083573	Q₈	1	8	yes	complemented
124	C₂×Dic₁₇₈	C₂³	1	2	yes	—
125	C₂×Dic₁₇₈	C₂³	1	2	yes	—
126	C₂×Dic₁₇₈	C₂³	1	2	yes	—
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	1	yes	characteristic
131	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
132	C₂²×Dic₈₉	C₂³	1	2	yes	—
133	C₂²×Dic₈₉	C₂³	1	2	yes	—
134	C₂²×Dic₈₉	C₂³	1	2	yes	—
135	C₂²×Dic₈₉	C₂³	1	2	yes	—
136	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₈₉	C₂³	1	2	yes	—
138	C₂×C₄×D₈₉	C₂³	1	2	yes	—
139	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₈₉	C₂³	1	2	yes	—
148	C₄⋊Dic₈₉	C₂³	1	2	yes	—
149	C₄⋊Dic₈₉	C₂³	1	2	yes	—
150	C₄⋊Dic₈₉	C₂³	1	2	yes	—
151	C₄⋊Dic₈₉	C₂³	1	2	yes	—
152	#13083553	C₂³	1	1	yes	characteristic
153	#13083553	C₂³	1	1	yes	characteristic
154	#13083553	C₂³	1	2	yes	—
155	#13083553	C₂³	1	2	yes	—
156	#13083553	C₂³	1	2	yes	—
157	#13083553	C₂³	1	2	yes	—
158	#13083553	C₂³	1	1	yes	characteristic
159	#13083553	C₂³	1	1	yes	characteristic
160	#13083553	C₂³	1	2	yes	—
161	#13083553	C₂³	1	2	yes	—
162	#13083553	C₂³	1	2	yes	—
163	#13083553	C₂³	1	2	yes	—
164	#13083553	C₂³	1	1	yes	characteristic
165	#13083553	C₂³	1	1	yes	characteristic
166	#13083553	C₂³	1	2	yes	—
167	#13083553	C₂³	1	2	yes	—
168	#13083553	C₂³	1	2	yes	—
169	#13083553	C₂³	1	2	yes	—
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	2	yes	—
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	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
183	#13083551	C₂³	1	1	yes	characteristic
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	2	yes	—
188	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
189	C₄×Dic₈₉	C₂³	1	2	yes	—
190	C₄×Dic₈₉	C₂³	1	2	yes	—
191	C₄×Dic₈₉	C₂³	1	2	yes	—
192	C₄×Dic₈₉	C₂³	1	2	yes	—
193	C₄×Dic₈₉	C₂³	1	2	yes	—
194	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₈₉	C₂³	1	2	yes	—
197	C₄×Dic₈₉	C₂³	1	2	yes	—
198	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
200	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
201	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
202	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
203	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
204	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
205	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
206	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
209	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
210	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
217	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
220	C₄²×C₈₉	C₂³	1	1	yes	characteristic
221	C₄²×C₈₉	C₂³	1	1	yes	characteristic
222	C₄²×C₈₉	C₂³	1	1	yes	characteristic
223	C₂³×C₈₉	C₂⁴	1	2	yes	—
224	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
225	Q₈×C₈₉	—	4	1	no	—
226	Q₈×C₈₉	—	4	2	no	—
227	D₄×C₈₉	C₂×Q₈	1	4	yes	—
228	C₂×C₄×C₈₉	—	4	2	no	—
229	C₂×C₄×C₈₉	—	4	2	no	—
230	C₂×C₄×C₈₉	—	4	2	no	—
231	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
238	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
239	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
240	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂²⋊D₈₉	C₂×Q₈	1	8	yes	—
242	C₂×Dic₈₉	—	4	2	no	—
243	C₂×Dic₈₉	—	4	2	no	—
244	C₂×Dic₈₉	—	4	2	no	—
245	C₂×Dic₈₉	C₂×Q₈	1	8	yes	—
246	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₈₉	C₂⁴	1	2	yes	—
250	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₈₉	C₂⁴	1	2	yes	—
254	C₂×Dic₈₉	C₂⁴	1	2	yes	—
255	C₂×Dic₈₉	C₂⁴	1	2	yes	—
256	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
257	C₄×D₈₉	—	4	1	no	—
258	C₄×D₈₉	—	4	2	no	—
259	C₄×D₈₉	—	4	2	no	—
260	C₄×D₈₉	—	4	1	no	—
261	C₄×D₈₉	C₂×Q₈	1	4	yes	—
262	Dic₁₇₈	—	4	1	no	—
263	Dic₁₇₈	—	4	2	no	—
264	Dic₁₇₈	—	4	2	no	—
265	Dic₁₇₈	—	4	1	no	—
266	Dic₁₇₈	—	4	1	no	—
267	Dic₁₇₈	—	4	2	no	—
268	Dic₁₇₈	C₂×Q₈	1	4	yes	—
269	C₂²×C₈₉	—	2	2	no	—
270	C₂²×C₈₉	—	2	2	no	—
271	C₂²×C₈₉	C₂²×Q₈	1	4	yes	—
272	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
273	C₂×D₈₉	—	2	1	no	—
274	C₂×D₈₉	—	2	1	no	—
275	C₂×D₈₉	C₂²×Q₈	1	2	yes	—
276	C₄×C₈₉	—	2	1	no	—
277	C₄×C₈₉	—	2	2	no	—
278	C₄×C₈₉	—	2	1	no	—
279	C₄×C₈₉	—	2	1	no	—
280	C₄×C₈₉	—	2	2	no	—
281	C₄×C₈₉	—	2	1	no	—
282	C₄×C₈₉	—	2	1	no	—
283	C₄×C₈₉	—	2	2	no	—
284	C₄×C₈₉	—	2	1	no	—
285	C₄×C₈₉	C₂²×Q₈	1	2	yes	—
286	Dic₈₉	—	2	1	no	—
287	Dic₈₉	—	2	1	no	—
288	Dic₈₉	—	2	1	no	—
289	Dic₈₉	—	2	2	no	—
290	Dic₈₉	—	2	2	no	—
291	Dic₈₉	—	2	2	no	—
292	Dic₈₉	—	2	1	no	—
293	Dic₈₉	—	2	1	no	—
294	Dic₈₉	—	2	1	no	—
295	Dic₈₉	C₂²×Q₈	1	4	yes	—
296	Dic₈₉	C₂²×Q₈	1	2	yes	—
297	C₂×C₈₉	—	2	4	no	—
298	C₂×C₈₉	C₂³×Q₈	1	1	yes	characteristic
299	C₂×C₈₉	#585	1	1	yes	characteristic
300	C₂×C₈₉	#585	1	1	yes	characteristic
301	D₈₉	—	2	2	no	—
302	#3504	—	89	1	no	maximal, Sylow
303	C₈₉	#3504	1	1	yes	characteristic, complemented, Sylow
304	#557	—	89	1	no	—
305	#557	—	89	1	no	—
306	#557	—	89	1	no	—
307	#557	—	89	1	no	—
308	#554	—	89	2	no	—
309	#554	—	89	2	no	—
310	#554	—	89	2	no	—
311	#554	—	89	1	no	—
312	#554	—	89	1	no	—
313	#554	—	89	1	no	—
314	#554	—	89	2	no	—
315	#554	D₈₉	1	1	yes	characteristic, complemented
316	#544	—	89	1	no	—
317	#544	—	89	1	no	—
318	#544	—	89	2	no	—
319	#544	—	89	2	no	—
320	#533	—	89	2	no	—
321	#533	—	89	1	no	—
322	C₂×#125	—	89	1	no	—
323	C₂×#125	—	89	2	no	—
324	#520	—	89	1	no	—
325	#520	—	89	1	no	—
326	C₄×#41	—	89	1	no	—
327	C₂×#41	—	89	1	no	—
328	C₄⋊Q₈	—	89	2	no	—
329	C₄⋊Q₈	—	89	1	no	—
330	C₄⋊Q₈	—	89	2	no	—
331	C₄⋊Q₈	—	89	2	no	—
332	C₄⋊Q₈	—	89	2	no	—
333	C₄⋊Q₈	—	89	1	no	—
334	C₄⋊Q₈	—	89	2	no	—
335	C₄⋊Q₈	—	89	2	no	—
336	C₄⋊Q₈	—	89	1	no	—
337	C₄⋊Q₈	—	89	1	no	—
338	C₄⋊Q₈	—	89	1	no	—
339	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
340	#125	—	89	2	no	—
341	#125	—	89	1	no	—
342	#125	—	89	2	no	—
343	#125	—	89	2	no	—
344	#125	—	89	2	no	—
345	#125	—	89	2	no	—
346	#125	—	89	2	no	—
347	#125	—	89	2	no	—
348	#125	—	89	2	no	—
349	#125	—	89	1	no	—
350	#125	—	89	1	no	—
351	#125	—	89	1	no	—
352	#125	—	89	2	no	—
353	#125	—	89	2	no	—
354	#125	—	89	2	no	—
355	#125	—	89	2	no	—
356	#125	—	89	1	no	—
357	#125	—	89	1	no	—
358	#125	—	89	1	no	—
359	#125	—	89	1	no	—
360	#125	C₂×D₈₉	1	1	yes	characteristic
361	#125	C₂×D₈₉	1	1	yes	characteristic
362	C₂²⋊Q₈	—	89	1	no	—
363	C₂²⋊Q₈	—	89	2	no	—
364	C₂²⋊Q₈	—	89	2	no	—
365	C₂²⋊Q₈	—	89	2	no	—
366	C₂²⋊Q₈	—	89	2	no	—
367	C₂²⋊Q₈	—	89	1	no	—
368	C₂²⋊Q₈	—	89	1	no	—
369	C₂²⋊Q₈	—	89	1	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	2	no	—
375	C₂²⋊Q₈	—	89	2	no	—
376	C₂²⋊Q₈	—	89	2	no	—
377	C₂²⋊Q₈	—	89	2	no	—
378	C₂²⋊Q₈	—	89	2	no	—
379	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	—
380	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	—
381	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	—
382	C₄×Q₈	—	89	2	no	—
383	C₄×Q₈	—	89	1	no	—
384	C₄×Q₈	—	89	1	no	—
385	C₄×Q₈	—	89	1	no	—
386	C₄×Q₈	—	89	2	no	—
387	C₄×Q₈	—	89	2	no	—
388	C₄×Q₈	—	89	2	no	—
389	C₄×Q₈	—	89	1	no	—
390	C₄×Q₈	—	89	1	no	—
391	C₄×Q₈	—	89	1	no	—
392	C₄×Q₈	—	89	1	no	—
393	C₄×Q₈	—	89	1	no	—
394	C₄×Q₈	—	89	1	no	—
395	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
396	C₄×D₄	—	89	1	no	—
397	C₄×D₄	—	89	1	no	—
398	C₄×D₄	—	89	1	no	—
399	C₄×D₄	—	89	2	no	—
400	C₄×D₄	—	89	2	no	—
401	C₄×D₄	—	89	2	no	—
402	C₄×D₄	—	89	2	no	—
403	C₄×D₄	—	89	2	no	—
404	C₄×D₄	—	89	2	no	—
405	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
406	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
407	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
408	#117	—	89	1	no	—
409	#117	—	89	2	no	—
410	#117	—	89	2	no	—
411	#117	—	89	2	no	—
412	#117	—	89	1	no	—
413	#117	—	89	1	no	—
414	C₂×C₄⋊C₄	—	89	2	no	—
415	C₂×C₄⋊C₄	—	89	2	no	—
416	C₂×C₄⋊C₄	—	89	2	no	—
417	C₂×C₄⋊C₄	—	89	2	no	—
418	C₂×C₄⋊C₄	—	89	2	no	—
419	C₂×C₄⋊C₄	—	89	1	no	—
420	C₂×C₄⋊C₄	—	89	1	no	—
421	C₂×C₄⋊C₄	—	89	2	no	—
422	C₂×C₄⋊C₄	—	89	2	no	—
423	C₂×C₄⋊C₄	C₂×D₈₉	1	2	yes	—
424	C₂×C₄²	—	89	2	no	—
425	C₂×C₄²	—	89	1	no	—
426	#41	—	89	8	no	—
427	C₂×Q₈	—	89	1	no	—
428	C₂×Q₈	—	89	2	no	—
429	C₂×Q₈	—	89	1	no	—
430	C₂×Q₈	—	89	2	no	—
431	C₂×Q₈	—	89	1	no	—
432	C₂×Q₈	—	89	1	no	—
433	C₂×Q₈	—	89	2	no	—
434	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
435	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
436	C₂×D₄	—	89	2	no	—
437	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
438	C₂²×C₄	—	89	2	no	—
439	C₂²×C₄	—	89	1	no	—
440	C₂²×C₄	—	89	2	no	—
441	C₂²×C₄	—	89	2	no	—
442	C₂²×C₄	—	89	2	no	—
443	C₂²×C₄	—	89	1	no	—
444	C₂²×C₄	—	89	1	no	—
445	C₂²×C₄	—	89	2	no	—
446	C₂²×C₄	—	89	2	no	—
447	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
448	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
449	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
450	C₄⋊C₄	—	89	2	no	—
451	C₄⋊C₄	—	89	2	no	—
452	C₄⋊C₄	—	89	1	no	—
453	C₄⋊C₄	—	89	1	no	—
454	C₄⋊C₄	—	89	2	no	—
455	C₄⋊C₄	—	89	1	no	—
456	C₄⋊C₄	—	89	1	no	—
457	C₄⋊C₄	—	89	2	no	—
458	C₄⋊C₄	—	89	2	no	—
459	C₄⋊C₄	—	89	1	no	—
460	C₄⋊C₄	—	89	2	no	—
461	C₄⋊C₄	—	89	2	no	—
462	C₄⋊C₄	—	89	2	no	—
463	C₄⋊C₄	—	89	2	no	—
464	C₄⋊C₄	—	89	1	no	—
465	C₄⋊C₄	—	89	1	no	—
466	C₄⋊C₄	—	89	2	no	—
467	C₄⋊C₄	—	89	2	no	—
468	C₄⋊C₄	—	89	2	no	—
469	C₄⋊C₄	—	89	2	no	—
470	C₄⋊C₄	—	89	2	no	—
471	C₄⋊C₄	—	89	2	no	—
472	C₄⋊C₄	—	89	2	no	—
473	C₄⋊C₄	—	89	2	no	—
474	C₄⋊C₄	—	89	2	no	—
475	C₄⋊C₄	—	89	1	no	—
476	C₄⋊C₄	—	89	1	no	—
477	C₄⋊C₄	—	89	2	no	—
478	C₄⋊C₄	—	89	2	no	—
479	C₄⋊C₄	—	89	1	no	—
480	C₄⋊C₄	—	89	1	no	—
481	C₄⋊C₄	—	89	1	no	—
482	C₄⋊C₄	—	89	1	no	—
483	C₄⋊C₄	—	89	2	no	—
484	C₄⋊C₄	—	89	1	no	—
485	C₄⋊C₄	—	89	2	no	—
486	C₄⋊C₄	—	89	1	no	—
487	C₄⋊C₄	—	89	2	no	—
488	C₄⋊C₄	—	89	1	no	—
489	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
490	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
493	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
495	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
496	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
499	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
500	C₂²⋊C₄	—	89	2	no	—
501	C₂²⋊C₄	—	89	2	no	—
502	C₂²⋊C₄	—	89	2	no	—
503	C₂²⋊C₄	—	89	1	no	—
504	C₂²⋊C₄	—	89	1	no	—
505	C₂²⋊C₄	—	89	2	no	—
506	C₂²⋊C₄	—	89	1	no	—
507	C₂²⋊C₄	—	89	1	no	—
508	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
510	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
511	C₄²	—	89	1	no	—
512	C₄²	—	89	2	no	—
513	C₄²	—	89	1	no	—
514	C₄²	—	89	2	no	—
515	C₄²	—	89	2	no	—
516	C₄²	—	89	1	no	—
517	C₄²	—	89	2	no	—
518	C₄²	—	89	2	no	—
519	C₄²	—	89	2	no	—
520	C₄²	—	89	2	no	—
521	C₄²	—	89	1	no	—
522	C₄²	—	89	1	no	—
523	C₄²	C₂²×D₈₉	1	1	yes	characteristic
524	C₄²	C₂²×D₈₉	1	1	yes	characteristic
525	C₄²	C₂²×D₈₉	1	1	yes	characteristic
526	C₂³	—	89	1	no	—
527	C₂³	C₂³×D₈₉	1	2	yes	—
528	Q₈	—	4	2	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	89	4	no	—
531	Q₈	—	356	1	no	—
532	Q₈	—	356	2	no	—
533	Q₈	—	356	1	no	—
534	Q₈	—	356	2	no	—
535	Q₈	—	356	1	no	—
536	Q₈	—	356	2	no	—
537	D₄	—	89	8	no	—
538	D₄	Q₈×D₈₉	1	4	yes	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	89	8	no	—
543	C₂×C₄	—	89	2	no	—
544	C₂×C₄	—	89	1	no	—
545	C₂×C₄	—	89	4	no	—
546	C₂×C₄	—	89	1	no	—
547	C₂×C₄	—	89	1	no	—
548	C₂×C₄	—	89	1	no	—
549	C₂×C₄	—	89	1	no	—
550	C₂×C₄	—	89	2	no	—
551	C₂×C₄	—	89	1	no	—
552	C₂×C₄	—	89	2	no	—
553	C₂×C₄	—	89	1	no	—
554	C₂×C₄	—	89	2	no	—
555	C₂×C₄	—	356	1	no	—
556	C₂×C₄	—	356	2	no	—
557	C₂×C₄	—	356	2	no	—
558	C₂×C₄	—	356	1	no	—
559	C₂×C₄	—	356	2	no	—
560	C₂×C₄	—	356	2	no	—
561	C₂×C₄	—	356	2	no	—
562	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
563	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
564	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₈₉	1	2	yes	—
566	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₈₉	1	2	yes	—
568	C₂×C₄	C₂³×D₈₉	1	2	yes	—
569	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	89	2	no	—
575	C₂²	—	178	1	no	—
576	C₂²	—	178	1	no	—
577	C₂²	C₂×Q₈×D₈₉	1	4	yes	—
578	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	89	2	no	—
589	C₄	—	89	4	no	—
590	C₄	—	178	2	no	—
591	C₄	—	178	1	no	—
592	C₄	—	178	1	no	—
593	C₄	—	178	1	no	—
594	C₄	—	178	1	no	—
595	C₄	—	178	2	no	—
596	C₄	—	178	1	no	—
597	C₄	—	178	2	no	—
598	C₄	—	178	1	no	—
599	C₄	C₂×Q₈×D₈₉	1	2	yes	—
600	C₂	—	2	4	no	—
601	C₂	—	178	2	no	—
602	C₂	C₂²×Q₈×D₈₉	1	1	yes	characteristic
603	C₂	#19152433	1	1	yes	characteristic
604	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×#13083573	C₂²
hypercenter	#554	D₈₉
hypocenter	C₈₉	#3504
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. #19152326	C₂	semidirect
2. #19152325	C₂	semidirect
3. #19152325	C₂	semidirect
4. #19152323	C₂	semidirect
5. #19152307	C₂	semidirect
6. #19152307	C₂	semidirect
7. #19152306	C₂	semidirect
8. #19152305	C₂	semidirect
9. #19152303	C₂	semidirect
10. #19152302	C₂	semidirect
11. #19152302	C₂	semidirect
12. #19152228	C₂	semidirect
13. #19152227	C₂	semidirect
14. #19152227	C₂	semidirect
15. #19152225	C₂	semidirect
16. #19152152	C₂	semidirect
17. #19152150	C₂	semidirect
18. C₂×#15668002	C₂	semidirect
19. #125×D₈₉	C₂	semidirect
23. #554×C₈₉	C₂	semidirect
123. #13083573	Q₈	semidirect
303. C₈₉	#3504	semidirect
315. #554	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152326	2
#19152325	2
#19152323	2
#19152307	2
#19152306	2
#19152305	2
#19152303	2
#19152302	2
#19152228	2
#19152227	2
#19152225	2
#19152152	2
#19152150	2
C₂×#15668002	2
#125×D₈₉	2
#19152077	2
C₄×#13083573	2
#554×C₈₉	2
#3504	89