Subgroups — #26034822

Order 11392.

1032 conjugacy classes of subgroups.

The subgroup lattice has 412 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	#19152342	C₂	1	2	yes	maximal, complemented
3	#19152321	C₂	1	2	yes	maximal, complemented
4	#19152271	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₁₇₈	C₂	1	2	yes	maximal, complemented
6	#19152257	C₂	1	2	yes	maximal, complemented
7	#19152244	C₂	1	2	yes	maximal, complemented
8	#19152223	C₂	1	2	yes	maximal, complemented
9	#19152219	C₂	1	2	yes	maximal, complemented
10	#19152214	C₂	1	4	yes	maximal, complemented
11	#19152185	C₂	1	2	yes	maximal, complemented
12	#19152174	C₂	1	2	yes	maximal, complemented
13	#19152155	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#15668000	C₂	1	1	yes	maximal, characteristic, complemented
15	#529×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083574	C₂²	1	2	yes	—
17	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic
18	C₂²×Dic₁₇₈	C₂²	1	2	yes	complemented
19	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic
20	#15668012	C₂²	1	1	yes	characteristic, complemented
21	#15668012	C₂²	1	1	yes	characteristic, complemented
22	#15668012	C₂²	1	2	yes	complemented
23	#15668011	C₂²	1	4	yes	complemented
24	#15668007	C₂²	1	4	yes	complemented
25	#15668007	C₂²	1	4	yes	complemented
26	#15668007	C₂²	1	4	yes	complemented
27	#15668004	C₂²	1	2	yes	complemented
28	#15668000	C₂²	1	2	yes	—
29	#15668000	C₂²	1	2	yes	—
30	#15668000	C₂²	1	2	yes	—
31	#15668000	C₂²	1	2	yes	—
32	#15668000	C₂²	1	2	yes	—
33	#15667998	C₂²	1	4	yes	complemented
34	#15667998	C₂²	1	4	yes	complemented
35	#15667997	C₂²	1	4	yes	—
36	#15667996	C₂²	1	4	yes	complemented
37	#15667996	C₂²	1	4	yes	complemented
38	#15667994	C₂²	1	4	yes	complemented
39	#15667992	C₂²	1	4	yes	complemented
40	#15667992	C₂²	1	4	yes	complemented
41	#15667991	C₂²	1	2	yes	—
42	#15667991	C₂²	1	2	yes	—
43	#15667991	C₂²	1	2	yes	complemented
44	#15667990	C₂²	1	4	yes	complemented
45	#15667990	C₂²	1	4	yes	complemented
46	#15667989	C₂²	1	4	yes	—
47	#15667989	C₂²	1	4	yes	complemented
48	#15667988	C₂²	1	4	yes	complemented
49	#15667986	C₂²	1	2	yes	—
50	#15667985	C₂²	1	4	yes	—
51	#15667984	C₂²	1	4	yes	complemented
52	#15667980	C₂²	1	4	yes	—
53	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
54	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
55	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
56	C₄×D₃₅₆	C₂²	1	2	yes	—
57	D₄×Dic₈₉	C₂²	1	4	yes	—
58	#15667972	C₂²	1	4	yes	complemented
59	#15667971	C₂²	1	2	yes	—
60	#15667970	C₂²	1	4	yes	complemented
61	C₂×#13083551	C₂²	1	2	yes	—
62	C₂×#13083551	C₂²	1	2	yes	—
63	C₂²⋊C₄×D₈₉	C₂²	1	4	yes	—
64	#126×C₈₉	C₂²	1	2	yes	complemented
65	#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#123×C₈₉	C₂²	1	2	yes	—
68	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
69	#121×C₈₉	C₂²	1	1	yes	characteristic
70	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	C₄×D₄×C₈₉	C₂²	1	2	yes	—
72	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
73	#117×C₈₉	C₂²	1	2	yes	complemented
74	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic
75	C₂³×D₈₉	C₂³	1	2	yes	—
76	#13083574	—	4	4	no	—
77	C₂×Dic₁₇₈	—	4	2	no	—
78	C₂×Dic₁₇₈	—	4	4	no	—
79	C₂×Dic₁₇₈	C₂³	1	2	yes	—
80	C₂×Dic₁₇₈	C₂³	1	2	yes	—
81	C₂×Dic₁₇₈	C₂³	1	2	yes	—
82	C₂×Dic₁₇₈	C₂³	1	4	yes	—
83	C₂×Dic₁₇₈	C₂³	1	2	yes	—
84	C₂×D₃₅₆	—	4	2	no	—
85	C₂×D₃₅₆	C₂³	1	2	yes	—
86	C₂×D₃₅₆	C₂³	1	2	yes	—
87	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
89	C₂²×Dic₈₉	C₂³	1	4	yes	—
90	C₂²×Dic₈₉	C₂³	1	2	yes	—
91	C₂×C₄×D₈₉	C₂³	1	4	yes	—
92	C₂×C₄×D₈₉	C₂³	1	4	yes	—
93	C₄⋊Dic₈₉	C₂³	1	4	yes	—
94	C₄⋊Dic₈₉	C₂³	1	2	yes	—
95	C₄⋊Dic₈₉	C₂³	1	2	yes	—
96	C₄⋊Dic₈₉	C₂³	1	4	yes	—
97	C₄⋊Dic₈₉	C₂³	1	2	yes	—
98	C₄⋊Dic₈₉	C₂³	1	2	yes	—
99	#13083553	C₂³	1	4	yes	—
100	#13083553	C₂³	1	4	yes	—
101	#13083553	C₂³	1	4	yes	—
102	#13083553	C₂³	1	4	yes	—
103	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
104	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
105	#13083551	C₂³	1	4	yes	—
106	#13083551	C₂³	1	4	yes	—
107	#13083551	C₂³	1	4	yes	—
108	#13083551	C₂³	1	4	yes	—
109	#13083551	C₂³	1	4	yes	—
110	#13083551	C₂³	1	4	yes	—
111	#13083551	C₂³	1	4	yes	—
112	#13083551	C₂³	1	4	yes	—
113	C₄×Dic₈₉	C₂³	1	4	yes	—
114	C₄×Dic₈₉	C₂³	1	4	yes	—
115	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×D₄×C₈₉	C₂³	1	2	yes	—
117	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
120	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
123	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
124	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
125	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
126	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
127	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
129	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
130	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
131	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
132	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
133	C₄²×C₈₉	C₂³	1	2	yes	—
134	C₄²×C₈₉	C₂³	1	1	yes	characteristic
135	C₄²×C₈₉	C₂³	1	1	yes	characteristic
136	C₄²×C₈₉	C₂³	1	1	yes	characteristic
137	C₄²×C₈₉	C₂³	1	1	yes	characteristic
138	C₂³×C₈₉	C₂⁴	1	2	yes	—
139	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
140	C₂²×D₈₉	—	2	4	no	—
141	C₂²×D₈₉	—	4	2	no	—
142	C₂²×D₈₉	—	4	2	no	—
143	C₂²×D₈₉	C₂⁴	1	4	yes	—
144	Q₈×C₈₉	—	4	1	no	—
145	D₄×C₈₉	—	2	4	no	—
146	D₄×C₈₉	—	4	1	no	—
147	C₂×C₄×C₈₉	—	2	2	no	—
148	C₂×C₄×C₈₉	—	2	2	no	—
149	C₂×C₄×C₈₉	—	2	4	no	—
150	C₂×C₄×C₈₉	—	4	1	no	—
151	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
157	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
158	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
159	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
160	C₂²⋊D₈₉	—	4	4	no	—
161	C₂²⋊D₈₉	—	4	4	no	—
162	C₂×Dic₈₉	—	4	2	no	—
163	C₂×Dic₈₉	—	4	4	no	—
164	C₂×Dic₈₉	C₂⁴	1	4	yes	—
165	C₂×Dic₈₉	C₂⁴	1	4	yes	—
166	C₂×Dic₈₉	C₂⁴	1	4	yes	—
167	D₃₅₆	—	2	4	no	—
168	D₃₅₆	—	4	2	no	—
169	C₄×D₈₉	—	4	4	no	—
170	C₄×D₈₉	—	4	4	no	—
171	Dic₁₇₈	—	2	4	no	—
172	Dic₁₇₈	—	2	4	no	—
173	Dic₁₇₈	—	4	2	no	—
174	Dic₁₇₈	—	4	4	no	—
175	Dic₁₇₈	—	4	2	no	—
176	C₂²×C₈₉	—	2	1	no	—
177	C₂²×C₈₉	—	2	1	no	—
178	C₂²×C₈₉	—	2	2	no	—
179	C₂²×C₈₉	—	2	2	no	—
180	C₂²×C₈₉	—	2	2	no	—
181	C₂²×C₈₉	2₋¹⁺⁴	1	2	yes	—
182	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
183	C₂×D₈₉	—	2	4	no	—
184	C₂×D₈₉	—	2	4	no	—
185	C₂×D₈₉	—	2	4	no	—
186	C₂×D₈₉	—	8	4	no	—
187	C₄×C₈₉	—	2	2	no	—
188	C₄×C₈₉	—	2	1	no	—
189	C₄×C₈₉	—	2	1	no	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	—	2	2	no	—
192	C₄×C₈₉	—	2	1	no	—
193	C₄×C₈₉	—	2	2	no	—
194	C₄×C₈₉	—	2	1	no	—
195	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
196	Dic₈₉	—	2	4	no	—
197	Dic₈₉	—	2	4	no	—
198	Dic₈₉	—	2	4	no	—
199	C₂×C₈₉	—	2	2	no	—
200	C₂×C₈₉	—	4	2	no	—
201	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₈₉	#585	1	1	yes	characteristic
204	D₈₉	—	4	4	no	—
205	#3561	—	89	1	no	maximal, Sylow
206	C₈₉	#3561	1	1	yes	characteristic, complemented, Sylow
207	#563	—	89	2	no	—
208	#562	—	89	2	no	—
209	#556	—	89	2	no	—
210	#551	—	89	4	no	—
211	D₄×Q₈	—	89	2	no	—
212	#548	—	89	2	no	—
213	#546	—	89	2	no	—
214	#543	—	89	2	no	—
215	#542	—	89	4	no	—
216	#542	—	89	2	no	—
217	#538	—	89	2	no	—
218	#536	—	89	2	no	—
219	#533	—	89	1	no	—
220	#529	D₈₉	1	1	yes	characteristic, complemented
221	C₂×#124	—	89	1	no	—
222	C₂×#41	—	89	2	no	—
223	C₂²×Q₈	—	89	1	no	—
224	C₂²×Q₈	—	89	2	no	—
225	C₂²×D₄	—	89	1	no	—
226	C₄⋊Q₈	—	89	4	no	—
227	C₄⋊Q₈	—	89	1	no	—
228	C₄⋊Q₈	—	89	1	no	—
229	C₄⋊Q₈	—	89	2	no	—
230	#126	—	89	4	no	—
231	#126	—	89	4	no	—
232	#126	—	89	4	no	—
233	#126	C₂×D₈₉	1	2	yes	complemented
234	#125	—	89	2	no	—
235	#125	C₂×D₈₉	1	1	yes	characteristic, complemented
236	#124	—	89	4	no	—
237	#124	—	89	4	no	—
238	#124	—	89	2	no	—
239	#124	—	89	2	no	—
240	#124	—	89	2	no	—
241	#124	—	89	2	no	—
242	#124	—	89	2	no	—
243	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
244	#123	—	89	4	no	—
245	#123	—	89	4	no	—
246	#123	—	89	4	no	—
247	#123	—	89	4	no	—
248	#123	C₂×D₈₉	1	2	yes	—
249	C₂²⋊Q₈	—	89	4	no	—
250	C₂²⋊Q₈	—	89	2	no	—
251	C₂²⋊Q₈	—	89	2	no	—
252	C₂²⋊Q₈	—	89	2	no	—
253	C₂²⋊Q₈	—	89	4	no	—
254	C₂²⋊Q₈	—	89	4	no	—
255	C₂²⋊Q₈	—	89	4	no	—
256	C₂²⋊Q₈	—	89	4	no	—
257	C₂²⋊Q₈	—	89	4	no	—
258	C₂²⋊Q₈	—	89	4	no	—
259	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
260	#121	—	89	4	no	—
261	#121	—	89	2	no	—
262	#121	—	89	4	no	—
263	#121	C₂×D₈₉	1	1	yes	characteristic
264	#120	—	89	4	no	—
265	C₄×Q₈	—	89	2	no	—
266	C₄×Q₈	—	89	2	no	—
267	C₄×Q₈	—	89	2	no	—
268	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
269	C₄×D₄	—	89	4	no	—
270	C₄×D₄	—	89	4	no	—
271	C₄×D₄	—	89	2	no	—
272	C₄×D₄	C₂×D₈₉	1	2	yes	—
273	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
274	#117	—	89	2	no	—
275	#117	—	89	4	no	—
276	#117	C₂×D₈₉	1	2	yes	complemented
277	C₂×C₂²⋊C₄	—	89	2	no	—
278	C₂×C₂²⋊C₄	—	89	2	no	—
279	C₂×C₂²⋊C₄	—	89	4	no	—
280	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic
281	C₂⁴	—	89	2	no	—
282	#41	—	356	4	no	—
283	C₂×Q₈	—	89	2	no	—
284	C₂×Q₈	—	89	4	no	—
285	C₂×Q₈	—	89	2	no	—
286	C₂×Q₈	—	89	2	no	—
287	C₂×Q₈	—	89	2	no	—
288	C₂×Q₈	—	356	2	no	—
289	C₂×Q₈	—	356	4	no	—
290	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
291	C₂×D₄	—	89	4	no	—
292	C₂×D₄	—	89	4	no	—
293	C₂×D₄	—	89	2	no	—
294	C₂×D₄	—	89	2	no	—
295	C₂×D₄	—	356	2	no	—
296	C₂×D₄	C₂²×D₈₉	1	2	yes	—
297	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
298	C₂²×C₄	—	89	2	no	—
299	C₂²×C₄	—	89	4	no	—
300	C₂²×C₄	—	89	4	no	—
301	C₂²×C₄	—	89	4	no	—
302	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
305	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
306	C₄⋊C₄	—	89	4	no	—
307	C₄⋊C₄	—	89	2	no	—
308	C₄⋊C₄	—	89	2	no	—
309	C₄⋊C₄	—	89	2	no	—
310	C₄⋊C₄	—	89	4	no	—
311	C₄⋊C₄	—	89	4	no	—
312	C₄⋊C₄	—	89	4	no	—
313	C₄⋊C₄	—	89	4	no	—
314	C₄⋊C₄	—	89	4	no	—
315	C₄⋊C₄	—	89	2	no	—
316	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
317	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
318	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
319	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
320	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
321	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
322	C₂²⋊C₄	—	89	4	no	—
323	C₂²⋊C₄	—	89	4	no	—
324	C₂²⋊C₄	—	89	4	no	—
325	C₂²⋊C₄	—	89	4	no	—
326	C₂²⋊C₄	—	89	4	no	—
327	C₂²⋊C₄	—	89	4	no	—
328	C₂²⋊C₄	—	89	4	no	—
329	C₂²⋊C₄	—	89	4	no	—
330	C₂²⋊C₄	—	89	4	no	—
331	C₂²⋊C₄	—	89	4	no	—
332	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
333	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
334	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
335	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
336	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
337	C₄²	—	89	4	no	—
338	C₄²	—	89	4	no	—
339	C₄²	C₂²×D₈₉	1	1	yes	characteristic
340	C₄²	C₂²×D₈₉	1	1	yes	characteristic
341	C₄²	C₂²×D₈₉	1	1	yes	characteristic
342	C₄²	C₂²×D₈₉	1	1	yes	characteristic
343	C₄²	C₂²×D₈₉	1	2	yes	—
344	C₂³	—	89	4	no	—
345	C₂³	—	356	2	no	—
346	C₂³	—	356	2	no	—
347	C₂³	—	178	4	no	—
348	C₂³	C₂³×D₈₉	1	2	yes	—
349	C₂³	C₂³×D₈₉	1	1	yes	characteristic
350	Q₈	—	4	1	no	—
351	Q₈	—	356	2	no	—
352	Q₈	—	356	4	no	—
353	Q₈	—	356	2	no	—
354	Q₈	—	178	4	no	—
355	Q₈	—	178	4	no	—
356	D₄	—	2	4	no	—
357	D₄	—	4	1	no	—
358	D₄	—	356	2	no	—
359	D₄	—	356	4	no	—
360	D₄	—	356	4	no	—
361	D₄	—	178	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	89	4	no	—
367	C₂×C₄	—	89	4	no	—
368	C₂×C₄	—	89	4	no	—
369	C₂×C₄	—	356	4	no	—
370	C₂×C₄	—	356	4	no	—
371	C₂×C₄	—	356	4	no	—
372	C₂×C₄	—	356	2	no	—
373	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
374	C₂×C₄	C₂³×D₈₉	1	2	yes	—
375	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
376	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
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	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	178	4	no	—
388	C₂²	—	178	4	no	—
389	C₂²	—	178	4	no	—
390	C₂²	—	712	4	no	—
391	C₂²	#15668059	1	2	yes	—
392	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	—	178	4	no	—
402	C₄	—	178	4	no	—
403	C₄	—	178	4	no	—
404	C₄	#15668058	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	4	2	no	—
407	C₂	—	356	4	no	—
408	C₂	C₂×#15668058	1	1	yes	characteristic
409	C₂	C₂×#15668059	1	1	yes	characteristic
410	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#529×C₈₉	C₂
hypercenter	#529	D₈₉
hypocenter	C₈₉	#3561
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. #19152352	C₂	semidirect
2. #19152342	C₂	semidirect
3. #19152321	C₂	semidirect
4. #19152271	C₂	semidirect
5. D₄×Dic₁₇₈	C₂	semidirect
6. #19152257	C₂	semidirect
7. #19152244	C₂	semidirect
8. #19152223	C₂	semidirect
9. #19152219	C₂	semidirect
10. #19152214	C₂	semidirect
11. #19152185	C₂	semidirect
12. #19152174	C₂	semidirect
13. #19152155	C₂	semidirect
14. C₂×#15668000	C₂	semidirect
15. #529×C₈₉	C₂	semidirect
18. C₂²×Dic₁₇₈	C₂²	semidirect
20. #15668012	C₂²	semidirect
21. #15668012	C₂²	semidirect
22. #15668012	C₂²	semidirect
23. #15668011	C₂²	semidirect
24. #15668007	C₂²	semidirect
25. #15668007	C₂²	semidirect
26. #15668007	C₂²	semidirect
27. #15668004	C₂²	semidirect
33. #15667998	C₂²	semidirect
34. #15667998	C₂²	semidirect
36. #15667996	C₂²	semidirect
37. #15667996	C₂²	semidirect
38. #15667994	C₂²	semidirect
39. #15667992	C₂²	semidirect
40. #15667992	C₂²	semidirect
43. #15667991	C₂²	semidirect
44. #15667990	C₂²	semidirect
45. #15667990	C₂²	semidirect
47. #15667989	C₂²	semidirect
48. #15667988	C₂²	semidirect
51. #15667984	C₂²	semidirect
53. C₄×Dic₁₇₈	C₂²	semidirect
54. C₄×Dic₁₇₈	C₂²	semidirect
55. C₄×Dic₁₇₈	C₂²	semidirect
58. #15667972	C₂²	semidirect
60. #15667970	C₂²	semidirect
64. #126×C₈₉	C₂²	semidirect
65. #125×C₈₉	C₂²	semidirect
66. #124×C₈₉	C₂²	semidirect
70. C₄×Q₈×C₈₉	C₂²	semidirect
72. C₄×D₄×C₈₉	C₂²	semidirect
73. #117×C₈₉	C₂²	semidirect
206. C₈₉	#3561	semidirect
220. #529	D₈₉	semidirect
233. #126	C₂×D₈₉	semidirect
235. #125	C₂×D₈₉	semidirect
243. #124	C₂×D₈₉	semidirect
268. C₄×Q₈	C₂×D₈₉	semidirect
273. C₄×D₄	C₂×D₈₉	semidirect
276. #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
#19152342	2
#19152321	2
#19152271	2
D₄×Dic₁₇₈	2
#19152257	2
#19152244	2
#19152223	2
#19152219	2
#19152214	2
#19152185	2
#19152174	2
#19152155	2
C₂×#15668000	2
#529×C₈₉	2
#3561	89