Subgroups — #26031869

Order 11392.

556 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668040	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15668036	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152266	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152232	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151973	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151852	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151797	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151792	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151744	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151741	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151733	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151731	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151685	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151674	C₂	1	1	yes	maximal, characteristic, complemented
15	#469×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083574	C₂²	1	1	yes	characteristic, complemented
17	C₂×#13083573	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₈₉	—	2	1	no	—
20	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
21	#15668040	—	2	4	no	—
22	#15668036	—	2	4	no	—
23	C₂×#13083563	C₂²	1	1	yes	characteristic
24	C₂×#13083563	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13083562	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₇₁₂	C₂²	1	1	yes	characteristic
27	C₂×D₇₁₂	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13083559	C₂²	1	1	yes	characteristic
29	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
30	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
31	C₂×#13083557	C₂²	1	1	yes	characteristic, complemented
32	#15668008	—	2	1	no	—
33	#15668008	C₂²	1	1	yes	characteristic
34	#15668008	C₂²	1	1	yes	characteristic, complemented
35	#15667987	C₂²	1	1	yes	characteristic
36	#15667987	C₂²	1	1	yes	characteristic, complemented
37	#15667985	—	2	1	no	—
38	#15667985	—	2	1	no	—
39	#15667984	—	2	1	no	—
40	#15667982	—	2	1	no	—
41	#15667980	—	2	1	no	—
42	#15667977	C₂²	1	1	yes	characteristic, complemented
43	#15667974	C₂²	1	1	yes	characteristic
44	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
45	#15667972	—	2	1	no	—
46	#15667941	C₂²	1	1	yes	characteristic, complemented
47	#15667935	C₂²	1	1	yes	characteristic, complemented
48	#15667932	C₂²	1	1	yes	characteristic
49	#15667932	C₂²	1	1	yes	characteristic, complemented
50	#15667932	C₂²	1	1	yes	characteristic, complemented
51	C₂²⋊#10623494	C₂²	1	1	yes	characteristic, complemented
52	#15667924	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#121×C₈₉	C₂²	1	1	yes	characteristic
57	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₉	—	2	1	no	—
62	C₂³×D₈₉	—	2	1	no	—
63	#13083574	—	2	2	no	—
64	#13083574	—	4	1	no	—
65	#13083573	—	2	2	no	—
66	#13083573	—	4	1	no	—
67	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
68	C₂×D₃₅₆	—	2	2	no	—
69	C₂×D₃₅₆	—	2	1	no	—
70	C₂×D₃₅₆	—	2	1	no	—
71	C₂×D₃₅₆	—	2	1	no	—
72	C₂×D₃₅₆	—	4	1	no	—
73	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
74	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
75	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊D₈₉	—	2	1	no	—
77	C₂×C₂²⋊D₈₉	—	2	1	no	—
78	C₂×C₂²⋊D₈₉	—	2	1	no	—
79	C₂×C₂²⋊D₈₉	—	2	1	no	—
80	C₂×C₂²⋊D₈₉	—	2	1	no	—
81	C₂×C₂²⋊D₈₉	—	2	1	no	—
82	C₂×C₂²⋊D₈₉	—	2	1	no	—
83	C₂×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
84	D₄×D₈₉	—	2	2	no	—
85	D₄×D₈₉	—	4	1	no	—
86	D₄×D₈₉	—	4	4	no	—
87	C₂²×Dic₈₉	—	2	1	no	—
88	C₂×C₄×D₈₉	—	2	1	no	—
89	C₂×C₄×D₈₉	—	2	1	no	—
90	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
91	#13083563	—	2	2	no	—
92	#13083563	D₄	1	4	yes	complemented
93	#13083562	—	2	2	no	—
94	D₇₁₂	—	2	2	no	—
95	D₇₁₂	—	2	2	no	—
96	#13083559	—	2	2	no	—
97	#13083559	—	4	1	no	—
98	#13083559	—	4	1	no	—
99	#13083557	—	2	2	no	—
100	C₂×#10623494	C₂³	1	1	yes	characteristic
101	C₂×#10623494	C₂³	1	1	yes	characteristic
102	#13083553	—	2	1	no	—
103	#13083553	D₄	1	1	yes	characteristic
104	C₂²⋊Dic₈₉	D₄	1	1	yes	characteristic
105	#13083551	—	2	1	no	—
106	#13083551	—	2	1	no	—
107	#13083551	—	2	1	no	—
108	#13083551	D₄	1	1	yes	characteristic
109	C₄×Dic₈₉	—	2	1	no	—
110	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
111	C₂×D₄×C₈₉	—	2	1	no	—
112	C₂×D₄×C₈₉	—	2	1	no	—
113	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
116	D₈×C₈₉	—	2	2	no	—
117	M₁₆×C₈₉	—	2	2	no	—
118	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
120	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
121	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
122	C₂²⋊C₄×C₈₉	—	2	1	no	—
123	C₂²⋊C₄×C₈₉	—	2	1	no	—
124	C₂³×C₈₉	—	2	1	no	—
125	C₂³×C₈₉	—	2	1	no	—
126	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×D₈₉	—	2	1	no	—
128	C₂²×D₈₉	—	2	1	no	—
129	C₂²×D₈₉	—	2	1	no	—
130	C₂²×D₈₉	—	4	2	no	—
131	C₂²×D₈₉	—	4	2	no	—
132	C₂²×D₈₉	—	4	2	no	—
133	C₂²×D₈₉	—	4	2	no	—
134	C₂²×D₈₉	—	8	1	no	—
135	C₂²×D₈₉	—	8	1	no	—
136	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
137	D₄×C₈₉	—	2	1	no	—
138	D₄×C₈₉	—	2	1	no	—
139	D₄×C₈₉	—	2	1	no	—
140	D₄×C₈₉	—	2	1	no	—
141	D₄×C₈₉	—	4	2	no	—
142	D₄×C₈₉	—	8	1	no	—
143	C₂×C₄×C₈₉	—	2	1	no	—
144	C₂×C₄×C₈₉	—	2	1	no	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	—	2	1	no	—
147	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
149	C₂²⋊D₈₉	—	2	2	no	—
150	C₂²⋊D₈₉	—	4	2	no	—
151	C₂²⋊D₈₉	—	4	2	no	—
152	C₂²⋊D₈₉	—	4	2	no	—
153	C₂²⋊D₈₉	—	4	2	no	—
154	C₂²⋊D₈₉	—	4	2	no	—
155	C₂²⋊D₈₉	—	8	1	no	—
156	C₂²⋊D₈₉	—	8	1	no	—
157	C₂×Dic₈₉	—	2	1	no	—
158	C₂×Dic₈₉	—	4	2	no	—
159	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
161	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
162	D₃₅₆	—	2	1	no	—
163	D₃₅₆	—	2	1	no	—
164	D₃₅₆	—	2	1	no	—
165	D₃₅₆	—	2	1	no	—
166	D₃₅₆	—	2	1	no	—
167	D₃₅₆	—	4	2	no	—
168	D₃₅₆	—	4	2	no	—
169	D₃₅₆	—	8	1	no	—
170	D₃₅₆	C₂×D₄	1	2	yes	—
171	C₄×D₈₉	—	2	1	no	—
172	C₄×D₈₉	—	2	1	no	—
173	C₄×D₈₉	—	4	2	no	—
174	C₄×D₈₉	—	4	2	no	—
175	Dic₁₇₈	—	2	1	no	—
176	Dic₁₇₈	C₂×D₄	1	2	yes	complemented
177	C₈×C₈₉	—	2	1	no	—
178	C₈×C₈₉	C₂×D₄	1	2	yes	complemented
179	#10623494	—	2	1	no	—
180	#10623494	—	2	1	no	—
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	—	2	1	no	—
183	C₂²×C₈₉	—	2	1	no	—
184	C₂²×C₈₉	—	4	1	no	—
185	C₂²×C₈₉	—	4	1	no	—
186	C₂²×C₈₉	—	4	1	no	—
187	C₂²×C₈₉	—	4	1	no	—
188	C₂²×C₈₉	—	4	1	no	—
189	C₂²×C₈₉	—	4	1	no	—
190	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×D₈₉	—	2	1	no	—
192	C₂×D₈₉	—	2	2	no	—
193	C₂×D₈₉	—	2	1	no	—
194	C₂×D₈₉	—	2	1	no	—
195	C₂×D₈₉	—	4	1	no	—
196	C₂×D₈₉	—	4	1	no	—
197	C₂×D₈₉	—	4	1	no	—
198	C₂×D₈₉	—	4	1	no	—
199	C₂×D₈₉	—	4	1	no	—
200	C₂×D₈₉	—	4	1	no	—
201	C₂×D₈₉	—	4	1	no	—
202	C₂×D₈₉	—	4	1	no	—
203	C₂×D₈₉	—	8	4	no	—
204	C₂×D₈₉	—	8	4	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	4	1	no	—
207	C₄×C₈₉	—	4	1	no	—
208	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
209	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
210	Dic₈₉	—	2	2	no	—
211	Dic₈₉	—	2	1	no	—
212	Dic₈₉	—	2	1	no	—
213	Dic₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
214	C₂×C₈₉	—	4	1	no	—
215	C₂×C₈₉	—	8	1	no	—
216	C₂×C₈₉	—	8	1	no	—
217	C₂×C₈₉	D₄²	1	1	yes	characteristic
218	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₂×C₈₉	#576	1	1	yes	characteristic
220	D₈₉	—	4	1	no	—
221	D₈₉	—	4	2	no	—
222	D₈₉	—	8	1	no	—
223	D₈₉	—	8	1	no	—
224	#3274	—	89	1	no	maximal, Sylow
225	C₈₉	#3274	1	1	yes	characteristic, complemented, Sylow
226	C₂×AGL(1,ℤ/8)	—	89	1	no	—
227	C₂×AGL(1,ℤ/8)	—	89	1	no	—
228	#550	—	89	1	no	—
229	D₄²	—	89	1	no	—
230	#493	—	89	1	no	—
231	#469	—	89	1	no	—
232	#469	D₈₉	1	1	yes	characteristic, complemented
233	#460	—	89	1	no	—
234	#459	—	89	1	no	—
235	#449	—	89	1	no	—
236	#449	—	89	1	no	—
237	#447	—	89	1	no	—
238	#447	—	89	1	no	—
239	C₄×SD₁₆	—	89	1	no	—
240	#436	—	89	1	no	—
241	C₂×#41	—	89	1	no	—
242	C₂×#41	—	89	1	no	—
243	C₂²×D₄	—	89	1	no	—
244	C₂²×D₄	—	89	1	no	—
245	C₂²×D₄	—	178	1	no	—
246	AGL(1,ℤ/8)	—	178	4	no	—
247	AGL(1,ℤ/8)	—	178	4	no	—
248	C₂×SD₁₆	—	89	1	no	—
249	C₂×SD₁₆	—	89	1	no	—
250	C₂×SD₁₆	—	89	1	no	—
251	C₂×D₈	—	89	1	no	—
252	C₂×D₈	—	89	1	no	—
253	C₂×D₈	—	89	1	no	—
254	C₂×D₈	—	89	1	no	—
255	C₂×D₈	—	89	1	no	—
256	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic, complemented
257	C₂×M₁₆	—	89	1	no	—
258	C₂×M₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
259	#127	—	89	1	no	—
260	#127	—	89	1	no	—
261	#127	—	178	1	no	—
262	#121	—	89	1	no	—
263	#121	—	89	1	no	—
264	#121	—	178	1	no	—
265	#121	—	178	1	no	—
266	#121	—	178	1	no	—
267	#121	C₂×D₈₉	1	1	yes	characteristic
268	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
269	#120	—	178	1	no	—
270	#120	—	178	1	no	—
271	C₄×Q₈	—	89	1	no	—
272	C₄×D₄	—	89	1	no	—
273	C₄×D₄	—	89	1	no	—
274	C₄×D₄	—	178	1	no	—
275	#106	C₂×D₈₉	1	1	yes	characteristic, complemented
276	C₄⋊C₈	—	89	1	no	—
277	#103	—	89	1	no	—
278	#102	—	89	1	no	—
279	#102	—	89	1	no	—
280	#102	—	89	1	no	—
281	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
282	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
283	C₂²⋊C₈	—	89	1	no	—
284	C₂²⋊C₈	—	89	1	no	—
285	C₄×C₈	—	89	1	no	—
286	C₂⁴	—	178	1	no	—
287	C₂⁴	—	178	1	no	—
288	#41	—	356	1	no	—
289	#41	—	356	1	no	—
290	#41	—	178	2	no	—
291	#41	—	178	2	no	—
292	C₂×Q₈	—	89	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	89	1	no	—
296	C₂×D₄	—	89	1	no	—
297	C₂×D₄	—	89	1	no	—
298	C₂×D₄	—	89	1	no	—
299	C₂×D₄	—	356	1	no	—
300	C₂×D₄	—	356	4	no	—
301	C₂×D₄	—	356	1	no	—
302	C₂×D₄	—	178	2	no	—
303	C₂×D₄	—	178	1	no	—
304	C₂×D₄	—	178	1	no	—
305	C₂×D₄	—	178	1	no	—
306	C₂×D₄	—	178	1	no	—
307	C₂×D₄	—	178	1	no	—
308	C₂×D₄	—	178	1	no	—
309	C₂×D₄	—	178	1	no	—
310	C₂×D₄	—	178	2	no	—
311	C₂×D₄	—	178	1	no	—
312	C₂×D₄	—	178	1	no	—
313	C₂×D₄	—	178	1	no	—
314	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
315	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
316	C₂²×C₄	—	89	1	no	—
317	C₂²×C₄	—	178	1	no	—
318	C₂²×C₄	—	178	1	no	—
319	C₂²×C₄	—	178	1	no	—
320	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
321	SD₁₆	—	89	4	no	—
322	SD₁₆	—	178	2	no	—
323	SD₁₆	—	178	2	no	—
324	D₈	—	2	2	no	—
325	D₈	—	356	1	no	—
326	D₈	—	356	1	no	—
327	D₈	—	178	2	no	—
328	D₈	—	178	2	no	—
329	D₈	—	178	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	178	2	no	—
332	C₂×C₈	—	89	1	no	—
333	C₂×C₈	—	89	1	no	—
334	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
335	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
336	C₄⋊C₄	—	89	1	no	—
337	C₄⋊C₄	—	178	1	no	—
338	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
339	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	89	1	no	—
343	C₂²⋊C₄	—	89	1	no	—
344	C₂²⋊C₄	—	178	1	no	—
345	C₂²⋊C₄	—	178	1	no	—
346	C₂²⋊C₄	—	178	1	no	—
347	C₄²	—	89	1	no	—
348	C₄²	—	178	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	89	1	no	—
352	C₂³	—	356	2	no	—
353	C₂³	—	356	2	no	—
354	C₂³	—	356	2	no	—
355	C₂³	—	356	2	no	—
356	C₂³	—	178	1	no	—
357	C₂³	—	178	1	no	—
358	C₂³	—	178	1	no	—
359	C₂³	—	712	1	no	—
360	C₂³	—	712	1	no	—
361	C₂³	D₄×D₈₉	1	1	yes	characteristic
362	Q₈	—	89	2	no	—
363	Q₈	—	178	1	no	—
364	D₄	—	2	1	no	—
365	D₄	—	2	1	no	—
366	D₄	—	2	1	no	—
367	D₄	—	2	1	no	—
368	D₄	—	4	2	no	—
369	D₄	—	8	1	no	—
370	D₄	—	89	2	no	—
371	D₄	—	356	2	no	—
372	D₄	—	356	2	no	—
373	D₄	—	356	2	no	—
374	D₄	—	356	2	no	—
375	D₄	—	356	2	no	—
376	D₄	—	356	2	no	—
377	D₄	—	356	2	no	—
378	D₄	—	178	2	no	—
379	D₄	—	178	1	no	—
380	D₄	—	178	1	no	—
381	D₄	—	178	1	no	—
382	D₄	—	178	1	no	—
383	D₄	—	178	1	no	—
384	D₄	—	712	1	no	—
385	D₄	—	712	1	no	—
386	D₄	—	712	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	89	1	no	—
392	C₂×C₄	—	89	1	no	—
393	C₂×C₄	—	89	1	no	—
394	C₂×C₄	—	356	2	no	—
395	C₂×C₄	—	356	2	no	—
396	C₂×C₄	—	356	2	no	—
397	C₂×C₄	—	178	1	no	—
398	C₂×C₄	—	178	1	no	—
399	C₂×C₄	—	178	1	no	—
400	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	178	1	no	—
404	C₈	—	178	1	no	—
405	C₈	D₄×D₈₉	1	2	yes	complemented
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	356	1	no	—
416	C₂²	—	356	1	no	—
417	C₂²	—	356	1	no	—
418	C₂²	—	356	1	no	—
419	C₂²	—	356	1	no	—
420	C₂²	—	356	1	no	—
421	C₂²	—	356	1	no	—
422	C₂²	—	356	1	no	—
423	C₂²	—	178	1	no	—
424	C₂²	—	178	1	no	—
425	C₂²	—	178	2	no	—
426	C₂²	—	178	1	no	—
427	C₂²	—	712	4	no	—
428	C₂²	—	712	4	no	—
429	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	89	2	no	—
434	C₄	—	178	1	no	—
435	C₄	—	178	1	no	—
436	C₄	—	178	2	no	—
437	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
438	C₄	#15668058	1	1	yes	characteristic
439	C₂	—	4	1	no	—
440	C₂	—	8	1	no	—
441	C₂	—	8	1	no	—
442	C₂	—	356	2	no	—
443	C₂	—	356	1	no	—
444	C₂	—	712	1	no	—
445	C₂	—	712	1	no	—
446	C₂	#19152232	1	1	yes	characteristic
447	C₂	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
448	C₂	#19152402	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#469×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	#469	D₈₉
hypocenter	C₈₉	#3274
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #469

Complements

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

N	H ≅ G/N	type
1. C₂×#15668040	C₂	semidirect
2. C₂×#15668036	C₂	semidirect
3. #19152266	C₂	semidirect
4. #19152232	C₂	semidirect
5. #19151973	C₂	semidirect
6. #19151852	C₂	semidirect
7. #19151797	C₂	semidirect
8. #19151792	C₂	semidirect
9. #19151744	C₂	semidirect
10. #19151741	C₂	semidirect
11. #19151733	C₂	semidirect
12. #19151731	C₂	semidirect
13. #19151685	C₂	semidirect
14. #19151674	C₂	semidirect
15. #469×C₈₉	C₂	semidirect
16. C₂×#13083574	C₂²	semidirect
17. C₂×#13083573	C₂²	semidirect
24. C₂×#13083563	C₂²	semidirect
25. C₂×#13083562	C₂²	semidirect
27. C₂×D₇₁₂	C₂²	semidirect
29. C₂×#13083559	C₂²	semidirect
30. C₂×#13083559	C₂²	semidirect
31. C₂×#13083557	C₂²	semidirect
34. #15668008	C₂²	semidirect
36. #15667987	C₂²	semidirect
42. #15667977	C₂²	semidirect
46. #15667941	C₂²	semidirect
47. #15667935	C₂²	semidirect
49. #15667932	C₂²	semidirect
50. #15667932	C₂²	semidirect
51. C₂²⋊#10623494	C₂²	semidirect
52. #15667924	C₂²	semidirect
53. C₈×Dic₈₉	C₂²	semidirect
54. C₂×D₈×C₈₉	C₂²	semidirect
55. C₂×M₁₆×C₈₉	C₂²	semidirect
57. #121×C₈₉	C₂²	semidirect
58. #106×C₈₉	C₂²	semidirect
59. #102×C₈₉	C₂²	semidirect
60. #102×C₈₉	C₂²	semidirect
92. #13083563	D₄	semidirect
176. Dic₁₇₈	C₂×D₄	semidirect
178. C₈×C₈₉	C₂×D₄	semidirect
213. Dic₈₉	AGL(1,ℤ/8)	semidirect
225. C₈₉	#3274	semidirect
232. #469	D₈₉	semidirect
256. C₂×D₈	C₂×D₈₉	semidirect
258. C₂×M₁₆	C₂×D₈₉	semidirect
268. #121	C₂×D₈₉	semidirect
275. #106	C₂×D₈₉	semidirect
281. #102	C₂×D₈₉	semidirect
282. #102	C₂×D₈₉	semidirect
405. C₈	D₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15668040	2
C₂×#15668036	2
#19152266	2
#19152232	2
#19151973	2
#19151852	2
#19151797	2
#19151792	2
#19151744	2
#19151741	2
#19151733	2
#19151731	2
#19151685	2
#19151674	2
#469×C₈₉	2
#3274	89