Subgroups — #36448610

Order 22784.

546 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26023203	C₂	1	1	yes	maximal, characteristic
2	#26021016	C₂	1	1	yes	maximal, characteristic, complemented
3	#26020411	C₂	1	1	yes	maximal, characteristic, complemented
4	#26020253	C₂	1	1	yes	maximal, characteristic
5	C₂×#19151325	C₂	1	1	yes	maximal, characteristic
6	#26018091	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
9	C₂×#15667970	—	2	1	no	—
10	C₂×#15667945	—	2	2	no	—
11	C₂×#15667944	—	2	1	no	—
12	C₂×#15667934	—	2	1	no	—
13	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
14	#19151499	—	2	1	no	—
15	#19151488	—	2	2	no	—
16	#19151468	C₂²	1	1	yes	characteristic
17	#19151455	—	2	1	no	—
18	C₄⋊C₄×Dic₈₉	—	2	1	no	—
19	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
20	#19151361	—	2	1	no	—
21	#19151361	—	2	1	no	—
22	#19151325	C₄	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
25	#384×C₈₉	C₂²	1	1	yes	characteristic
26	C₂²×D₃₅₆	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₈₉	—	2	1	no	—
28	C₂²×#10623494	—	2	1	no	—
29	C₄×D₃₅₆	—	2	1	no	—
30	C₄×D₃₅₆	—	2	1	no	—
31	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
32	C₄×D₃₅₆	Q₈	1	2	yes	—
33	#15667970	—	4	2	no	—
34	#15667970	—	4	2	no	—
35	C₂×C₄⋊Dic₈₉	—	2	1	no	—
36	C₂×C₄⋊Dic₈₉	—	2	1	no	—
37	C₂×C₄⋊Dic₈₉	—	2	1	no	—
38	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
39	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
41	C₂×#13083551	—	2	2	no	—
42	C₂×#13083551	—	2	2	no	—
43	C₂×#13083551	—	2	1	no	—
44	C₂×C₄×Dic₈₉	—	2	2	no	—
45	C₂×C₄×Dic₈₉	—	2	1	no	—
46	#15667945	—	4	4	no	—
47	#15667944	—	4	2	no	—
48	#15667934	—	4	2	no	—
49	C₄×#10623494	—	2	1	no	—
50	C₄×#10623494	C₂×C₄	1	2	yes	—
51	#15667919	—	2	2	no	—
52	#15667919	—	2	1	no	—
53	C₂²×C₈×C₈₉	—	2	1	no	—
54	C₂²×C₈×C₈₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
58	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₈₉	—	2	1	no	—
60	C₄⋊C₈×C₈₉	—	2	1	no	—
61	C₄⋊C₈×C₈₉	—	2	1	no	—
62	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
63	C₂³×D₈₉	—	2	1	no	—
64	C₂×D₃₅₆	—	2	1	no	—
65	C₂×D₃₅₆	—	2	1	no	—
66	C₂×D₃₅₆	—	2	1	no	—
67	C₂×D₃₅₆	—	2	1	no	—
68	C₂×D₃₅₆	—	2	1	no	—
69	C₂×D₃₅₆	C₄⋊C₄	1	2	yes	—
70	C₂²×Dic₈₉	—	2	1	no	—
71	C₂²×Dic₈₉	—	2	1	no	—
72	C₂²×Dic₈₉	—	2	1	no	—
73	C₂²×Dic₈₉	—	4	1	no	—
74	C₂×C₄×D₈₉	—	2	2	no	—
75	C₂×C₄×D₈₉	—	2	2	no	—
76	C₂×C₄×D₈₉	—	4	1	no	—
77	C₂×C₄×D₈₉	—	4	1	no	—
78	C₂×C₄×D₈₉	—	4	1	no	—
79	C₂×C₄×D₈₉	—	4	1	no	—
80	C₂×#10623494	—	2	2	no	—
81	C₂×#10623494	—	2	2	no	—
82	C₂×#10623494	—	2	2	no	—
83	C₄⋊Dic₈₉	—	2	1	no	—
84	C₄⋊Dic₈₉	—	2	1	no	—
85	C₄⋊Dic₈₉	—	2	1	no	—
86	C₄⋊Dic₈₉	—	2	1	no	—
87	C₄⋊Dic₈₉	—	4	2	no	—
88	C₄⋊Dic₈₉	—	4	1	no	—
89	C₄⋊Dic₈₉	—	4	1	no	—
90	C₄⋊Dic₈₉	—	4	1	no	—
91	C₄⋊Dic₈₉	—	4	1	no	—
92	C₄⋊Dic₈₉	C₄⋊C₄	1	2	yes	—
93	C₄⋊Dic₈₉	D₈	1	2	yes	—
94	#13083551	—	2	2	no	—
95	#13083551	—	2	2	no	—
96	#13083551	—	4	4	no	—
97	#13083551	—	8	2	no	—
98	C₄×Dic₈₉	—	4	4	no	—
99	C₄×Dic₈₉	—	4	1	no	—
100	C₄×Dic₈₉	—	4	1	no	—
101	C₂²×C₄×C₈₉	—	2	2	no	—
102	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₈₉	—	2	2	no	—
106	C₂×C₈×C₈₉	—	4	1	no	—
107	C₂×C₈×C₈₉	—	4	1	no	—
108	C₂×C₈×C₈₉	—	4	1	no	—
109	C₂×C₈×C₈₉	—	4	1	no	—
110	C₂×C₈×C₈₉	—	4	1	no	—
111	C₄⋊C₄×C₈₉	—	4	2	no	—
112	C₄⋊C₄×C₈₉	—	4	1	no	—
113	C₄⋊C₄×C₈₉	—	4	1	no	—
114	C₄⋊C₄×C₈₉	—	4	1	no	—
115	C₄⋊C₄×C₈₉	—	4	1	no	—
116	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
118	C₄²×C₈₉	#41	1	1	yes	characteristic
119	C₄²×C₈₉	#41	1	1	yes	characteristic
120	C₂³×C₈₉	#120	1	1	yes	characteristic
121	C₂²×D₈₉	—	2	2	no	—
122	C₂²×D₈₉	—	4	1	no	—
123	C₂²×D₈₉	—	4	1	no	—
124	C₂²×D₈₉	—	4	1	no	—
125	C₂²×D₈₉	—	4	1	no	—
126	C₂²×D₈₉	—	4	1	no	—
127	C₂²×D₈₉	—	4	1	no	—
128	C₂×C₄×C₈₉	—	2	1	no	—
129	C₂×C₄×C₈₉	—	2	1	no	—
130	C₂×C₄×C₈₉	—	4	2	no	—
131	C₂×C₄×C₈₉	—	4	2	no	—
132	C₂×C₄×C₈₉	—	4	2	no	—
133	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
136	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
137	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
138	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
139	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
140	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
141	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
142	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
143	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
144	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
146	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
147	C₂×Dic₈₉	—	2	2	no	—
148	C₂×Dic₈₉	—	2	2	no	—
149	C₂×Dic₈₉	—	4	1	no	—
150	C₂×Dic₈₉	—	4	1	no	—
151	C₂×Dic₈₉	—	4	1	no	—
152	C₂×Dic₈₉	—	4	1	no	—
153	C₂×Dic₈₉	—	4	1	no	—
154	C₂×Dic₈₉	—	4	1	no	—
155	C₂×Dic₈₉	—	4	1	no	—
156	C₂×Dic₈₉	—	8	1	no	—
157	C₂×Dic₈₉	—	8	1	no	—
158	C₂×Dic₈₉	—	8	1	no	—
159	D₃₅₆	—	2	2	no	—
160	D₃₅₆	—	2	2	no	—
161	D₃₅₆	—	4	1	no	—
162	D₃₅₆	—	4	1	no	—
163	C₄×D₈₉	—	4	2	no	—
164	C₄×D₈₉	—	4	2	no	—
165	C₄×D₈₉	—	4	2	no	—
166	C₄×D₈₉	—	4	2	no	—
167	C₈×C₈₉	—	4	2	no	—
168	C₈×C₈₉	—	8	1	no	—
169	#10623494	—	2	4	no	—
170	C₂²×C₈₉	#385	1	1	yes	characteristic
171	C₂²×C₈₉	#447	1	1	yes	characteristic
172	C₂²×C₈₉	#449	1	1	yes	characteristic
173	C₂²×C₈₉	#452	1	1	yes	characteristic
174	C₂²×C₈₉	#452	1	1	yes	characteristic
175	C₂²×C₈₉	#453	1	1	yes	characteristic
176	C₂²×C₈₉	#456	1	1	yes	characteristic
177	C₂×D₈₉	—	4	2	no	—
178	C₂×D₈₉	—	4	2	no	—
179	C₂×D₈₉	—	4	2	no	—
180	C₂×D₈₉	—	8	1	no	—
181	C₂×D₈₉	—	8	1	no	—
182	C₂×D₈₉	—	8	1	no	—
183	C₂×D₈₉	—	8	1	no	—
184	C₄×C₈₉	—	2	1	no	—
185	C₄×C₈₉	—	2	1	no	—
186	C₄×C₈₉	—	8	2	no	—
187	C₄×C₈₉	#427	1	1	yes	characteristic
188	C₄×C₈₉	#428	1	1	yes	characteristic
189	C₄×C₈₉	C₄×D₈	1	1	yes	characteristic
190	C₄×C₈₉	#440	1	1	yes	characteristic
191	C₄×C₈₉	#474	1	1	yes	characteristic
192	C₄×C₈₉	#478	1	1	yes	characteristic
193	C₄×C₈₉	#482	1	1	yes	characteristic
194	C₄×C₈₉	#485	1	1	yes	characteristic
195	Dic₈₉	—	4	2	no	—
196	Dic₈₉	—	4	2	no	—
197	Dic₈₉	—	8	1	no	—
198	Dic₈₉	—	16	1	no	—
199	#8885	—	89	1	no	maximal, Sylow
200	C₂×C₈₉	#1621	1	1	yes	characteristic
201	C₂×C₈₉	#1634	1	1	yes	characteristic
202	C₂×C₈₉	#1647	1	1	yes	characteristic
203	C₂×C₈₉	#1650	1	1	yes	characteristic
204	C₂×C₈₉	#1854	1	1	yes	characteristic
205	C₂×C₈₉	#1859	1	1	yes	characteristic
206	C₂×C₈₉	#1862	1	1	yes	characteristic
207	D₈₉	—	8	2	no	—
208	#2354	—	89	1	no	—
209	#1948	—	89	1	no	—
210	#1845	—	89	1	no	—
211	#1802	—	89	1	no	—
212	C₂×D₄⋊C₈	—	89	1	no	—
213	#1296	D₈₉	1	1	yes	characteristic, complemented
214	#1279	—	89	1	no	—
215	C₈₉	#8885	1	1	yes	characteristic, complemented, Sylow
216	C₂×C₄×D₄	—	89	1	no	—
217	C₂×#117	—	178	1	no	—
218	C₂×#107	—	178	2	no	—
219	C₂×#106	—	178	1	no	—
220	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
222	C₂×#102	—	178	1	no	—
223	C₂×C₄×C₈	—	89	1	no	—
224	#390	—	178	1	no	—
225	#388	—	178	2	no	—
226	#384	—	89	1	no	—
227	#384	C₂×D₈₉	1	1	yes	characteristic
228	#380	—	178	1	no	—
229	C₄×C₄⋊C₄	—	89	1	no	—
230	C₄×C₄⋊C₄	—	178	1	no	—
231	#340	—	178	1	no	—
232	#340	—	178	1	no	—
233	D₄⋊C₈	—	89	4	no	—
234	C₂²×D₄	—	89	1	no	—
235	C₂³×C₄	—	178	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	178	1	no	—
239	C₄×D₄	—	89	2	no	—
240	C₄×D₄	—	89	2	no	—
241	C₄×D₄	—	178	1	no	—
242	C₄×D₄	—	178	1	no	—
243	#117	—	356	2	no	—
244	#117	—	356	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	89	1	no	—
248	C₂×C₄⋊C₄	—	89	1	no	—
249	C₂×C₄⋊C₄	—	89	1	no	—
250	C₂×C₄⋊C₄	—	178	1	no	—
251	C₂×C₄⋊C₄	—	178	1	no	—
252	C₂×C₄⋊C₄	—	178	1	no	—
253	C₂×C₄⋊C₄	D₃₅₆	1	2	yes	—
254	C₂×C₂²⋊C₄	—	178	2	no	—
255	C₂×C₂²⋊C₄	—	178	1	no	—
256	C₂×C₂²⋊C₄	—	178	2	no	—
257	C₂×C₄²	—	178	2	no	—
258	C₂×C₄²	—	178	1	no	—
259	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
260	#107	—	356	4	no	—
261	#106	—	356	2	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
266	#102	—	356	2	no	—
267	C₄×C₈	—	89	2	no	—
268	C₄×C₈	—	178	1	no	—
269	#95	—	178	2	no	—
270	#95	—	178	1	no	—
271	C₂⁴	—	178	1	no	—
272	C₂×D₄	—	89	2	no	—
273	C₂×D₄	—	178	1	no	—
274	C₂×D₄	—	178	1	no	—
275	C₂×D₄	—	178	1	no	—
276	C₂×D₄	—	178	1	no	—
277	C₂×D₄	—	178	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	356	1	no	—
280	C₂²×C₄	—	356	1	no	—
281	C₂²×C₄	—	356	1	no	—
282	C₂²×C₄	—	356	1	no	—
283	C₂²×C₄	—	356	1	no	—
284	C₂²×C₄	—	178	1	no	—
285	C₂²×C₄	—	178	1	no	—
286	C₂²×C₄	—	178	1	no	—
287	C₂²×C₄	—	178	2	no	—
288	C₂²×C₄	—	178	2	no	—
289	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
290	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	178	2	no	—
299	C₂×C₈	—	178	2	no	—
300	C₂×C₈	—	178	2	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	89	2	no	—
307	C₄⋊C₄	—	89	2	no	—
308	C₄⋊C₄	—	356	2	no	—
309	C₄⋊C₄	—	356	1	no	—
310	C₄⋊C₄	—	356	1	no	—
311	C₄⋊C₄	—	356	1	no	—
312	C₄⋊C₄	—	356	1	no	—
313	C₄⋊C₄	—	178	1	no	—
314	C₄⋊C₄	—	178	1	no	—
315	C₄⋊C₄	—	178	1	no	—
316	C₄⋊C₄	—	178	1	no	—
317	C₂²⋊C₄	—	356	4	no	—
318	C₂²⋊C₄	—	178	2	no	—
319	C₂²⋊C₄	—	178	2	no	—
320	C₂²⋊C₄	—	712	2	no	—
321	C₄²	—	356	4	no	—
322	C₄²	—	356	1	no	—
323	C₄²	—	356	1	no	—
324	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
325	C₄²	Q₈×D₈₉	1	1	yes	characteristic
326	C₄²	#13083573	1	1	yes	characteristic
327	C₄²	#13083574	1	1	yes	characteristic
328	C₂³	—	356	1	no	—
329	C₂³	—	356	1	no	—
330	C₂³	—	356	1	no	—
331	C₂³	—	356	1	no	—
332	C₂³	—	356	1	no	—
333	C₂³	—	356	1	no	—
334	C₂³	—	178	2	no	—
335	C₂³	#15667982	1	1	yes	characteristic
336	D₄	—	356	1	no	—
337	D₄	—	356	1	no	—
338	D₄	—	178	2	no	—
339	D₄	—	178	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	356	1	no	—
346	C₂×C₄	—	356	1	no	—
347	C₂×C₄	—	356	1	no	—
348	C₂×C₄	—	356	1	no	—
349	C₂×C₄	—	356	2	no	—
350	C₂×C₄	—	356	2	no	—
351	C₂×C₄	—	356	2	no	—
352	C₂×C₄	—	356	2	no	—
353	C₂×C₄	—	356	1	no	—
354	C₂×C₄	—	356	1	no	—
355	C₂×C₄	—	356	1	no	—
356	C₂×C₄	—	178	2	no	—
357	C₂×C₄	—	178	2	no	—
358	C₂×C₄	—	712	1	no	—
359	C₂×C₄	—	712	1	no	—
360	C₂×C₄	—	712	1	no	—
361	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
362	C₂×C₄	#15667972	1	1	yes	characteristic
363	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
364	C₂×C₄	#15667990	1	1	yes	characteristic
365	C₂×C₄	#15667992	1	1	yes	characteristic
366	C₂×C₄	#15667994	1	1	yes	characteristic
367	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
368	C₂×C₄	#15668033	1	1	yes	characteristic
369	C₂×C₄	#15668033	1	1	yes	characteristic
370	C₂×C₄	#15668033	1	1	yes	characteristic
371	C₂×C₄	#15668036	1	1	yes	characteristic
372	C₂×C₄	#15668039	1	1	yes	characteristic
373	C₂×C₄	#15668044	1	1	yes	characteristic
374	C₂×C₄	#15668044	1	1	yes	characteristic
375	C₈	—	4	2	no	—
376	C₈	—	8	1	no	—
377	C₈	—	178	4	no	—
378	C₂²	—	356	2	no	—
379	C₂²	—	356	2	no	—
380	C₂²	—	356	2	no	—
381	C₂²	—	712	1	no	—
382	C₂²	—	712	1	no	—
383	C₂²	—	712	1	no	—
384	C₂²	—	712	1	no	—
385	C₂²	#19151472	1	1	yes	characteristic
386	C₂²	#19151733	1	1	yes	characteristic
387	C₂²	#19151744	1	1	yes	characteristic
388	C₂²	#19151763	1	1	yes	characteristic
389	C₂²	#19151763	1	1	yes	characteristic
390	C₂²	#19151768	1	1	yes	characteristic
391	C₂²	#19151783	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	8	2	no	—
395	C₄	—	356	2	no	—
396	C₄	—	356	2	no	—
397	C₄	—	1424	1	no	—
398	C₄	—	712	1	no	—
399	C₄	#19151633	1	1	yes	characteristic
400	C₄	#19151639	1	1	yes	characteristic
401	C₄	#19151678	1	1	yes	characteristic
402	C₄	#19151701	1	1	yes	characteristic
403	C₄	#19151877	1	1	yes	characteristic
404	C₄	#19151897	1	1	yes	characteristic
405	C₄	#19151921	1	1	yes	characteristic
406	C₄	#19151937	1	1	yes	characteristic
407	C₂	—	712	2	no	—
408	C₂	#26019318	1	1	yes	characteristic
409	C₂	#26019398	1	1	yes	characteristic
410	C₂	#26019488	1	1	yes	characteristic
411	C₂	#26019509	1	1	yes	characteristic
412	C₂	#26020452	1	1	yes	characteristic
413	C₂	#26020481	1	1	yes	characteristic
414	C₂	#26020500	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#15667982
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1296	C₂
socle	C₂³×C₈₉	#120
prime radical	C₂²×D₃₅₆	D₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1296	D₈₉
hypocenter	C₈₉	#8885
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
2. #26021016	C₂	semidirect
3. #26020411	C₂	semidirect
6. #26018091	C₂	semidirect
7. C₈₉×#1296	C₂	semidirect
22. #19151325	C₄	semidirect
213. #1296	D₈₉	semidirect
215. C₈₉	#8885	semidirect

Maximal subgroups

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

subgroup	index
#26023203	2
#26021016	2
#26020411	2
#26020253	2
C₂×#19151325	2
#26018091	2
C₈₉×#1296	2
#8885	89