Subgroups — #26034742

Order 11392.

910 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152351	C₂	1	4	yes	maximal, complemented
2	Q₈×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152326	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152325	C₂	1	2	yes	maximal, complemented
5	#19152318	C₂	1	2	yes	maximal, complemented
6	#19152318	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152317	C₂	1	2	yes	maximal, complemented
8	#19152305	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152288	C₂	1	2	yes	maximal, complemented
10	#19152226	C₂	1	2	yes	maximal, complemented
11	#19152215	C₂	1	2	yes	maximal
12	#19152210	C₂	1	2	yes	maximal, complemented
13	#19152208	C₂	1	2	yes	maximal, complemented
14	#19152205	C₂	1	4	yes	maximal, complemented
15	#19152155	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152155	C₂	1	1	yes	maximal, characteristic, complemented
17	#529×C₈₉	C₂	1	1	yes	maximal, characteristic
18	#15668012	C₂²	1	1	yes	characteristic
19	#15668012	C₂²	1	1	yes	characteristic
20	#15668012	C₂²	1	1	yes	characteristic
21	#15668012	C₂²	1	1	yes	characteristic
22	#15668012	C₂²	1	2	yes	—
23	#15668011	C₂²	1	4	yes	—
24	#15668011	C₂²	1	2	yes	—
25	#15668011	C₂²	1	4	yes	—
26	#15668010	C₂²	1	2	yes	—
27	#15668005	C₂²	1	4	yes	—
28	#15668005	C₂²	1	4	yes	—
29	#15668005	C₂²	1	4	yes	—
30	#15668005	C₂²	1	4	yes	—
31	#15668005	C₂²	1	4	yes	—
32	#15668005	C₂²	1	4	yes	—
33	#15668004	C₂²	1	2	yes	—
34	#15668004	C₂²	1	2	yes	—
35	#15668004	C₂²	1	2	yes	—
36	#15668003	C₂²	1	4	yes	—
37	#15668003	C₂²	1	2	yes	—
38	#15668002	C₂²	1	4	yes	—
39	#15668002	C₂²	1	4	yes	—
40	#15668002	C₂²	1	4	yes	—
41	#15668002	C₂²	1	4	yes	—
42	#15667999	C₂²	1	2	yes	—
43	#15667999	C₂²	1	4	yes	—
44	#15667993	C₂²	1	4	yes	—
45	#15667991	C₂²	1	2	yes	—
46	#15667991	C₂²	1	1	yes	characteristic
47	#15667991	C₂²	1	1	yes	characteristic
48	#15667991	C₂²	1	2	yes	—
49	#15667991	C₂²	1	2	yes	—
50	#15667991	C₂²	1	2	yes	—
51	#15667991	C₂²	1	2	yes	—
52	#15667989	C₂²	1	4	yes	—
53	#15667989	C₂²	1	4	yes	—
54	#15667989	C₂²	1	4	yes	—
55	Q₈×Dic₈₉	C₂²	1	2	yes	—
56	C₄×Dic₁₇₈	C₂²	1	2	yes	—
57	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
58	C₄×Dic₁₇₈	C₂²	1	2	yes	—
59	C₄×Dic₁₇₈	C₂²	1	2	yes	—
60	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
61	C₄×Dic₁₇₈	C₂²	1	2	yes	—
62	C₄×Dic₁₇₈	C₂²	1	2	yes	—
63	#15667977	C₂²	1	4	yes	—
64	#15667977	C₂²	1	2	yes	—
65	#15667977	C₂²	1	2	yes	—
66	D₄×Dic₈₉	C₂²	1	2	yes	—
67	#15667971	C₂²	1	2	yes	—
68	#15667971	C₂²	1	2	yes	—
69	#15667971	C₂²	1	2	yes	—
70	#15667968	C₂²	1	4	yes	—
71	C₂×C₄⋊Dic₈₉	C₂²	1	2	yes	—
72	#126×C₈₉	C₂²	1	2	yes	—
73	#125×C₈₉	C₂²	1	1	yes	characteristic
74	#124×C₈₉	C₂²	1	1	yes	characteristic
75	#123×C₈₉	C₂²	1	2	yes	—
76	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
77	#121×C₈₉	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
79	C₄×D₄×C₈₉	C₂²	1	2	yes	—
80	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
81	#117×C₈₉	C₂²	1	2	yes	—
82	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic
83	C₂×Dic₁₇₈	C₂³	1	2	yes	—
84	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
85	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
86	C₂×Dic₁₇₈	C₂³	1	4	yes	—
87	C₂×Dic₁₇₈	C₂³	1	2	yes	—
88	C₂×Dic₁₇₈	C₂³	1	2	yes	—
89	C₂²×Dic₈₉	C₂³	1	4	yes	—
90	C₄⋊Dic₈₉	C₂³	1	2	yes	—
91	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
92	C₄⋊Dic₈₉	C₂³	1	2	yes	—
93	C₄⋊Dic₈₉	C₂³	1	2	yes	—
94	C₄⋊Dic₈₉	C₂³	1	2	yes	—
95	C₄⋊Dic₈₉	C₂³	1	2	yes	—
96	C₄⋊Dic₈₉	C₂³	1	2	yes	—
97	C₄⋊Dic₈₉	C₂³	1	2	yes	—
98	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₈₉	C₂³	1	4	yes	—
100	C₄⋊Dic₈₉	C₂³	1	4	yes	—
101	#13083553	C₂³	1	2	yes	—
102	#13083553	C₂³	1	4	yes	—
103	#13083553	C₂³	1	2	yes	—
104	#13083553	C₂³	1	4	yes	—
105	#13083553	C₂³	1	4	yes	—
106	#13083553	C₂³	1	4	yes	—
107	#13083553	C₂³	1	2	yes	—
108	#13083553	C₂³	1	4	yes	—
109	#13083553	C₂³	1	4	yes	—
110	#13083553	C₂³	1	2	yes	—
111	#13083553	C₂³	1	4	yes	—
112	#13083553	C₂³	1	4	yes	—
113	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
114	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
115	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
116	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
117	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
118	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
119	C₄×Dic₈₉	C₂³	1	4	yes	—
120	C₄×Dic₈₉	C₂³	1	4	yes	—
121	C₄×Dic₈₉	C₂³	1	2	yes	—
122	C₄×Dic₈₉	C₂³	1	4	yes	—
123	C₄×Dic₈₉	C₂³	1	2	yes	—
124	C₄×Dic₈₉	C₂³	1	4	yes	—
125	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₈₉	C₂³	1	2	yes	—
128	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
131	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
133	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
137	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₄²×C₈₉	C₂³	1	1	yes	characteristic
144	C₄²×C₈₉	C₂³	1	1	yes	characteristic
145	C₄²×C₈₉	C₂³	1	2	yes	—
146	C₄²×C₈₉	C₂³	1	1	yes	characteristic
147	C₄²×C₈₉	C₂³	1	1	yes	characteristic
148	C₂³×C₈₉	C₂⁴	1	2	yes	—
149	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
150	Q₈×C₈₉	—	2	2	no	—
151	D₄×C₈₉	—	2	2	no	—
152	D₄×C₈₉	—	4	2	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	4	no	—
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	4	1	no	—
157	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
162	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
163	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
164	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
166	C₂×Dic₈₉	—	4	4	no	—
167	C₂×Dic₈₉	C₂⁴	1	4	yes	—
168	C₂×Dic₈₉	C₂⁴	1	2	yes	—
169	C₂×Dic₈₉	C₂⁴	1	2	yes	—
170	C₂×Dic₈₉	C₂⁴	1	2	yes	—
171	C₂×Dic₈₉	C₂⁴	1	4	yes	—
172	C₂×Dic₈₉	C₂⁴	1	2	yes	—
173	Dic₁₇₈	—	2	2	no	—
174	Dic₁₇₈	—	2	2	no	—
175	Dic₁₇₈	—	2	4	no	—
176	Dic₁₇₈	—	4	4	no	—
177	Dic₁₇₈	—	4	2	no	—
178	Dic₁₇₈	—	4	2	no	—
179	C₂²×C₈₉	—	2	2	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	—	2	2	no	—
183	C₂²×C₈₉	—	2	2	no	—
184	C₂²×C₈₉	—	2	1	no	—
185	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
186	C₄×C₈₉	—	2	1	no	—
187	C₄×C₈₉	—	2	1	no	—
188	C₄×C₈₉	—	2	2	no	—
189	C₄×C₈₉	—	2	2	no	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	—	2	1	no	—
192	C₄×C₈₉	—	2	2	no	—
193	C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
194	C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
195	Dic₈₉	—	2	2	no	—
196	Dic₈₉	—	2	2	no	—
197	Dic₈₉	—	2	4	no	—
198	Dic₈₉	—	2	2	no	—
199	Dic₈₉	—	2	4	no	—
200	Dic₈₉	—	2	2	no	—
201	C₂×C₈₉	—	4	1	no	—
202	C₂×C₈₉	—	4	2	no	—
203	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
204	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
205	C₂×C₈₉	#585	1	1	yes	characteristic
206	#3555	—	89	1	no	maximal, Sylow
207	C₈₉	#3555	1	1	yes	characteristic, complemented, Sylow
208	#563	—	89	4	no	—
209	Q₈²	—	89	1	no	—
210	#557	—	89	2	no	—
211	#557	—	89	1	no	—
212	#556	—	89	2	no	—
213	#556	—	89	2	no	—
214	#556	—	89	1	no	—
215	#554	—	89	1	no	—
216	#552	—	89	2	no	—
217	#544	—	89	2	no	—
218	#542	—	89	2	no	—
219	#541	—	89	4	no	—
220	#541	—	89	2	no	—
221	#541	—	89	2	no	—
222	#533	—	89	1	no	—
223	#533	—	89	1	no	—
224	#529	D₈₉	1	1	yes	characteristic
225	C₄⋊Q₈	—	89	2	no	—
226	C₄⋊Q₈	—	89	4	no	—
227	C₄⋊Q₈	—	89	2	no	—
228	C₄⋊Q₈	—	89	4	no	—
229	C₄⋊Q₈	—	89	1	no	—
230	C₄⋊Q₈	—	89	1	no	—
231	C₄⋊Q₈	—	89	1	no	—
232	C₄⋊Q₈	—	89	1	no	—
233	C₄⋊Q₈	—	89	2	no	—
234	#126	—	89	4	no	—
235	#126	—	89	4	no	—
236	#126	—	89	4	no	—
237	#126	—	89	4	no	—
238	#126	—	89	4	no	—
239	#126	—	89	4	no	—
240	#126	C₂×D₈₉	1	2	yes	—
241	#125	—	89	4	no	—
242	#125	—	89	4	no	—
243	#125	—	89	4	no	—
244	#125	—	89	4	no	—
245	#125	—	89	4	no	—
246	#125	—	89	2	no	—
247	#125	—	89	2	no	—
248	#125	—	89	2	no	—
249	#125	—	89	2	no	—
250	#125	C₂×D₈₉	1	1	yes	characteristic
251	#124	—	89	2	no	—
252	#124	—	89	4	no	—
253	#124	C₂×D₈₉	1	1	yes	characteristic
254	#123	—	89	4	no	—
255	#123	C₂×D₈₉	1	2	yes	—
256	C₂²⋊Q₈	—	89	2	no	—
257	C₂²⋊Q₈	—	89	1	no	—
258	C₂²⋊Q₈	—	89	1	no	—
259	C₂²⋊Q₈	—	89	2	no	—
260	C₂²⋊Q₈	—	89	2	no	—
261	C₂²⋊Q₈	—	89	2	no	—
262	C₂²⋊Q₈	—	89	2	no	—
263	C₂²⋊Q₈	—	89	4	no	—
264	C₂²⋊Q₈	—	89	4	no	—
265	C₂²⋊Q₈	—	89	4	no	—
266	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
267	#121	C₂×D₈₉	1	1	yes	characteristic
268	C₄×Q₈	—	89	2	no	—
269	C₄×Q₈	—	89	4	no	—
270	C₄×Q₈	—	89	2	no	—
271	C₄×Q₈	—	89	2	no	—
272	C₄×Q₈	—	89	2	no	—
273	C₄×Q₈	—	89	1	no	—
274	C₄×Q₈	—	89	2	no	—
275	C₄×Q₈	—	89	2	no	—
276	C₄×Q₈	—	89	1	no	—
277	C₄×Q₈	—	89	2	no	—
278	C₄×Q₈	—	89	2	no	—
279	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
280	C₄×D₄	—	89	2	no	—
281	C₄×D₄	C₂×D₈₉	1	2	yes	—
282	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
283	#117	—	89	2	no	—
284	#117	—	89	2	no	—
285	#117	—	89	2	no	—
286	#117	—	89	4	no	—
287	#117	C₂×D₈₉	1	2	yes	—
288	C₂×C₄⋊C₄	—	89	2	no	—
289	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic
290	C₂×Q₈	—	89	2	no	—
291	C₂×Q₈	—	89	2	no	—
292	C₂×Q₈	—	89	4	no	—
293	C₂×Q₈	—	89	1	no	—
294	C₂×Q₈	—	89	1	no	—
295	C₂×Q₈	—	89	2	no	—
296	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
297	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
298	C₂×D₄	C₂²×D₈₉	1	2	yes	—
299	C₂²×C₄	—	89	4	no	—
300	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
301	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
303	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
304	C₄⋊C₄	—	89	1	no	—
305	C₄⋊C₄	—	89	2	no	—
306	C₄⋊C₄	—	89	4	no	—
307	C₄⋊C₄	—	89	2	no	—
308	C₄⋊C₄	—	89	2	no	—
309	C₄⋊C₄	—	89	1	no	—
310	C₄⋊C₄	—	89	2	no	—
311	C₄⋊C₄	—	89	4	no	—
312	C₄⋊C₄	—	89	2	no	—
313	C₄⋊C₄	—	89	2	no	—
314	C₄⋊C₄	—	89	2	no	—
315	C₄⋊C₄	—	89	2	no	—
316	C₄⋊C₄	—	89	4	no	—
317	C₄⋊C₄	—	89	4	no	—
318	C₄⋊C₄	—	89	4	no	—
319	C₄⋊C₄	—	89	4	no	—
320	C₄⋊C₄	—	89	4	no	—
321	C₄⋊C₄	—	89	2	no	—
322	C₄⋊C₄	—	89	2	no	—
323	C₄⋊C₄	—	89	2	no	—
324	C₄⋊C₄	—	89	4	no	—
325	C₄⋊C₄	—	89	4	no	—
326	C₄⋊C₄	—	89	4	no	—
327	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
328	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
329	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
330	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
331	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
332	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
333	C₂²⋊C₄	—	89	2	no	—
334	C₂²⋊C₄	—	89	4	no	—
335	C₂²⋊C₄	—	89	2	no	—
336	C₂²⋊C₄	—	89	4	no	—
337	C₂²⋊C₄	—	89	4	no	—
338	C₂²⋊C₄	—	89	4	no	—
339	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
340	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
341	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
342	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
343	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
344	C₄²	—	89	4	no	—
345	C₄²	—	89	2	no	—
346	C₄²	—	89	2	no	—
347	C₄²	—	89	4	no	—
348	C₄²	—	89	4	no	—
349	C₄²	—	89	4	no	—
350	C₄²	C₂²×D₈₉	1	1	yes	characteristic
351	C₄²	C₂²×D₈₉	1	1	yes	characteristic
352	C₄²	C₂²×D₈₉	1	1	yes	characteristic
353	C₄²	C₂²×D₈₉	1	1	yes	characteristic
354	C₄²	C₂²×D₈₉	1	2	yes	—
355	C₂³	C₂³×D₈₉	1	1	yes	characteristic
356	C₂³	C₂³×D₈₉	1	2	yes	—
357	Q₈	—	2	2	no	—
358	Q₈	—	356	2	no	—
359	Q₈	—	356	2	no	—
360	Q₈	—	356	4	no	—
361	Q₈	—	178	2	no	—
362	Q₈	—	178	2	no	—
363	Q₈	—	178	4	no	—
364	D₄	—	2	2	no	—
365	D₄	—	4	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	89	4	no	—
371	C₂×C₄	—	89	2	no	—
372	C₂×C₄	—	89	2	no	—
373	C₂×C₄	—	89	2	no	—
374	C₂×C₄	—	89	4	no	—
375	C₂×C₄	—	89	2	no	—
376	C₂×C₄	—	356	4	no	—
377	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₈₉	1	2	yes	—
379	C₂×C₄	C₂³×D₈₉	1	2	yes	—
380	C₂×C₄	C₂³×D₈₉	1	2	yes	—
381	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
382	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
383	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
384	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
385	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	2	no	—
392	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	178	2	no	—
401	C₄	—	178	2	no	—
402	C₄	—	178	4	no	—
403	C₄	—	178	2	no	—
404	C₄	—	178	4	no	—
405	C₄	—	178	2	no	—
406	C₄	#15668059	1	2	yes	—
407	C₄	#15668059	1	2	yes	—
408	C₂	—	4	1	no	—
409	C₂	—	4	2	no	—
410	C₂	C₂×#15668059	1	1	yes	characteristic
411	C₂	C₂×#15668059	1	1	yes	characteristic
412	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#529×C₈₉	C₂
prime radical	#121×C₈₉	C₂²
hypercenter	#529	D₈₉
hypocenter	C₈₉	#3555
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #19152351	C₂	semidirect
2. Q₈×Dic₁₇₈	C₂	semidirect
3. #19152326	C₂	semidirect
4. #19152325	C₂	semidirect
5. #19152318	C₂	semidirect
6. #19152318	C₂	semidirect
7. #19152317	C₂	semidirect
8. #19152305	C₂	semidirect
9. #19152288	C₂	semidirect
10. #19152226	C₂	semidirect
12. #19152210	C₂	semidirect
13. #19152208	C₂	semidirect
14. #19152205	C₂	semidirect
15. #19152155	C₂	semidirect
16. #19152155	C₂	semidirect
207. C₈₉	#3555	semidirect

Maximal subgroups

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

subgroup	index
#19152351	2
Q₈×Dic₁₇₈	2
#19152326	2
#19152325	2
#19152318	2
#19152317	2
#19152305	2
#19152288	2
#19152226	2
#19152215	2
#19152210	2
#19152208	2
#19152205	2
#19152155	2
#529×C₈₉	2
#3555	89