Subgroups — #36447117

Order 22784.

588 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic
2	#26020404	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151330	C₂	1	2	yes	maximal
4	#26018092	C₂	1	2	yes	maximal
5	C₄×C₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₇₈	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₁₇₈	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊#10623494	—	2	1	no	—
10	C₂×C₄⋊#10623494	—	2	1	no	—
11	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
12	C₄×#13083553	—	2	1	no	—
13	C₄×#13083553	—	2	1	no	—
14	C₄×#13083553	—	2	1	no	—
15	C₄×C₄⋊Dic₈₉	C₄	1	1	yes	characteristic
16	C₄×C₄⋊Dic₈₉	C₄	1	1	yes	characteristic
17	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
18	C₄²×Dic₈₉	—	2	1	no	—
19	#19151330	—	2	4	no	—
20	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
21	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
22	C₄³×C₈₉	C₂²	1	1	yes	characteristic
23	#336×C₈₉	—	2	1	no	—
24	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
25	C₂²×#10623494	—	2	2	no	—
26	C₄×Dic₁₇₈	—	2	2	no	—
27	C₄×Dic₁₇₈	—	2	2	no	—
28	C₄×Dic₁₇₈	—	2	2	no	—
29	C₄×Dic₁₇₈	—	2	1	no	—
30	C₄×Dic₁₇₈	—	2	1	no	—
31	C₄×Dic₁₇₈	C₈	1	4	yes	complemented
32	C₄×Dic₁₇₈	D₄	1	2	yes	—
33	C₄×Dic₁₇₈	Q₈	1	2	yes	—
34	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
37	C₂×#13083553	—	2	1	no	—
38	C₂×#13083553	—	2	1	no	—
39	C₂×#13083553	—	2	1	no	—
40	C₂×C₄×Dic₈₉	—	2	1	no	—
41	C₂×C₄×Dic₈₉	—	2	1	no	—
42	C₂×C₄×Dic₈₉	—	2	1	no	—
43	C₂×C₄×Dic₈₉	—	2	1	no	—
44	C₂×C₄×Dic₈₉	—	2	1	no	—
45	C₂×C₄×Dic₈₉	—	2	1	no	—
46	C₄⋊#10623494	—	2	2	no	—
47	C₄⋊#10623494	—	2	2	no	—
48	C₄⋊#10623494	—	4	2	no	—
49	C₄⋊#10623494	—	4	2	no	—
50	#15667919	—	2	1	no	—
51	#15667919	—	2	1	no	—
52	#15667919	—	2	1	no	—
53	C₂²×C₈×C₈₉	—	2	2	no	—
54	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₈₉	—	2	4	no	—
62	C₄×C₈×C₈₉	—	2	2	no	—
63	C₄×C₈×C₈₉	—	2	2	no	—
64	C₂×Dic₁₇₈	—	2	1	no	—
65	C₂×Dic₁₇₈	—	2	1	no	—
66	C₂×Dic₁₇₈	—	2	1	no	—
67	C₂×Dic₁₇₈	C₄⋊C₄	1	2	yes	—
68	C₂×Dic₁₇₈	C₂×C₈	1	2	yes	—
69	C₂×Dic₁₇₈	M₁₆	1	2	yes	—
70	C₂²×Dic₈₉	—	2	1	no	—
71	C₂²×Dic₈₉	—	2	1	no	—
72	C₂²×Dic₈₉	—	2	1	no	—
73	C₂²×Dic₈₉	—	2	1	no	—
74	C₂×#10623494	—	4	2	no	—
75	C₂×#10623494	—	4	2	no	—
76	C₂×#10623494	—	4	2	no	—
77	C₄⋊Dic₈₉	—	2	1	no	—
78	C₄⋊Dic₈₉	—	2	1	no	—
79	C₄⋊Dic₈₉	—	2	1	no	—
80	C₄⋊Dic₈₉	C₄⋊C₄	1	2	yes	—
81	C₄⋊Dic₈₉	C₂×C₈	1	2	yes	—
82	C₄⋊Dic₈₉	M₁₆	1	2	yes	—
83	#13083553	—	2	4	no	—
84	#13083553	—	2	4	no	—
85	#13083553	—	2	2	no	—
86	#13083553	—	2	2	no	—
87	C₄×Dic₈₉	—	2	4	no	—
88	C₄×Dic₈₉	—	2	4	no	—
89	C₄×Dic₈₉	—	2	2	no	—
90	C₄×Dic₈₉	—	2	2	no	—
91	C₄×Dic₈₉	—	4	2	no	—
92	C₄×Dic₈₉	—	4	2	no	—
93	C₄×Dic₈₉	—	4	1	no	—
94	C₄×Dic₈₉	—	4	1	no	—
95	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₈₉	—	2	4	no	—
103	C₂×C₈×C₈₉	—	4	2	no	—
104	C₂×C₈×C₈₉	—	4	2	no	—
105	C₄²×C₈₉	—	2	2	no	—
106	C₄²×C₈₉	—	2	1	no	—
107	C₄²×C₈₉	—	2	1	no	—
108	C₄²×C₈₉	—	2	1	no	—
109	C₄²×C₈₉	—	2	1	no	—
110	C₄²×C₈₉	—	4	1	no	—
111	C₄²×C₈₉	C₂×C₈	1	2	yes	—
112	C₄²×C₈₉	M₁₆	1	2	yes	—
113	C₄²×C₈₉	SD₁₆	1	2	yes	—
114	C₄²×C₈₉	Q₁₆	1	2	yes	—
115	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
117	C₄²×C₈₉	#41	1	1	yes	characteristic
118	C₄²×C₈₉	#41	1	1	yes	characteristic
119	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₈₉	—	2	1	no	—
121	C₂×C₄×C₈₉	—	2	1	no	—
122	C₂×C₄×C₈₉	—	2	1	no	—
123	C₂×C₄×C₈₉	—	2	1	no	—
124	C₂×C₄×C₈₉	—	2	1	no	—
125	C₂×C₄×C₈₉	—	2	1	no	—
126	C₂×C₄×C₈₉	—	2	1	no	—
127	C₂×C₄×C₈₉	—	2	1	no	—
128	C₂×C₄×C₈₉	—	2	1	no	—
129	C₂×C₄×C₈₉	C₂²⋊C₈	1	2	yes	—
130	C₂×C₄×C₈₉	C₂²⋊C₈	1	2	yes	—
131	C₂×C₄×C₈₉	#103	1	2	yes	—
132	C₂×C₄×C₈₉	#103	1	2	yes	—
133	C₂×C₄×C₈₉	#104	1	2	yes	—
134	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
136	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
137	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
138	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
139	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
140	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
141	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
146	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
148	C₂×Dic₈₉	—	2	2	no	—
149	C₂×Dic₈₉	—	2	2	no	—
150	C₂×Dic₈₉	—	2	2	no	—
151	C₂×Dic₈₉	—	2	2	no	—
152	C₂×Dic₈₉	—	2	2	no	—
153	C₂×Dic₈₉	—	2	2	no	—
154	C₂×Dic₈₉	—	4	1	no	—
155	C₂×Dic₈₉	—	4	1	no	—
156	C₂×Dic₈₉	—	4	1	no	—
157	C₂×Dic₈₉	—	4	1	no	—
158	C₂×Dic₈₉	—	4	1	no	—
159	C₂×Dic₈₉	—	4	1	no	—
160	Dic₁₇₈	—	2	2	no	—
161	Dic₁₇₈	—	2	2	no	—
162	Dic₁₇₈	—	2	2	no	—
163	Dic₁₇₈	C₄⋊C₈	1	4	yes	complemented
164	C₈×C₈₉	—	4	4	no	—
165	#10623494	—	8	2	no	—
166	C₂²×C₈₉	#380	1	1	yes	characteristic
167	C₂²×C₈₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
168	C₂²×C₈₉	#407	1	1	yes	characteristic
169	C₂²×C₈₉	C₂×#103	1	1	yes	characteristic
170	C₂²×C₈₉	#417	1	1	yes	characteristic
171	C₂²×C₈₉	C₂×#104	1	1	yes	characteristic
172	C₂²×C₈₉	#421	1	1	yes	characteristic
173	C₄×C₈₉	—	2	1	no	—
174	C₄×C₈₉	—	2	1	no	—
175	C₄×C₈₉	—	2	2	no	—
176	C₄×C₈₉	—	2	2	no	—
177	C₄×C₈₉	—	4	1	no	—
178	C₄×C₈₉	Q₈⋊C₈	1	4	yes	complemented
179	C₄×C₈₉	C₂×C₄⋊C₈	1	1	yes	characteristic
180	C₄×C₈₉	#423	1	1	yes	characteristic
181	C₄×C₈₉	#431	1	1	yes	characteristic
182	C₄×C₈₉	#432	1	1	yes	characteristic
183	C₄×C₈₉	#460	1	1	yes	characteristic
184	C₄×C₈₉	#462	1	1	yes	characteristic
185	C₄×C₈₉	#475	1	1	yes	characteristic
186	C₄×C₈₉	#477	1	1	yes	characteristic
187	Dic₈₉	—	2	4	no	—
188	Dic₈₉	—	4	2	no	—
189	Dic₈₉	—	4	2	no	—
190	Dic₈₉	—	4	2	no	—
191	#8564	—	89	1	no	maximal, Sylow
192	C₂×C₈₉	C₂×Q₈⋊C₈	1	1	yes	characteristic
193	C₂×C₈₉	#1477	1	1	yes	characteristic
194	C₂×C₈₉	#1487	1	1	yes	characteristic
195	C₂×C₈₉	#1489	1	1	yes	characteristic
196	C₂×C₈₉	#1797	1	1	yes	characteristic
197	C₂×C₈₉	#1803	1	1	yes	characteristic
198	C₂×C₈₉	#1806	1	1	yes	characteristic
199	C₄²×Q₈	—	89	1	no	—
200	#1842	—	89	1	no	—
201	C₄×C₄⋊C₈	D₈₉	1	1	yes	characteristic
202	C₂×Q₈⋊C₈	—	89	2	no	—
203	#1279	—	89	2	no	—
204	C₈₉	#8564	1	1	yes	characteristic, complemented, Sylow
205	C₂×C₄×Q₈	—	89	1	no	—
206	C₂×C₄×Q₈	—	89	1	no	—
207	C₂×C₄×Q₈	—	89	1	no	—
208	C₂×C₄⋊C₈	—	2	1	no	—
209	C₂×C₄⋊C₈	—	89	2	no	—
210	C₂×C₄⋊C₈	—	178	1	no	—
211	C₂×C₄⋊C₈	—	178	1	no	—
212	C₂×C₄×C₈	C₂×D₈₉	1	2	yes	—
213	C₄×C₄⋊C₄	—	89	1	no	—
214	C₄×C₄⋊C₄	—	89	1	no	—
215	C₄×C₄⋊C₄	—	89	1	no	—
216	C₄×C₄⋊C₄	—	178	1	no	—
217	C₄×C₄⋊C₄	—	178	1	no	—
218	C₄×C₄⋊C₄	—	178	1	no	—
219	C₄³	—	178	1	no	—
220	C₄³	C₂×D₈₉	1	1	yes	characteristic
221	#336	—	2	1	no	—
222	Q₈⋊C₈	—	178	4	no	—
223	C₂²×Q₈	—	89	1	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	—	178	2	no	—
226	C₄×Q₈	—	89	4	no	—
227	C₄×Q₈	—	89	2	no	—
228	C₄×Q₈	—	89	2	no	—
229	C₄×Q₈	—	178	2	no	—
230	C₄×Q₈	—	178	2	no	—
231	C₄×Q₈	—	178	2	no	—
232	C₄×Q₈	—	178	1	no	—
233	C₄×Q₈	—	178	1	no	—
234	C₂×C₄⋊C₄	—	89	1	no	—
235	C₂×C₄⋊C₄	—	89	1	no	—
236	C₂×C₄⋊C₄	—	89	1	no	—
237	C₂×C₄⋊C₄	—	178	1	no	—
238	C₂×C₄⋊C₄	—	178	1	no	—
239	C₂×C₄⋊C₄	—	178	1	no	—
240	C₂×C₄²	—	178	1	no	—
241	C₂×C₄²	—	178	1	no	—
242	C₂×C₄²	—	178	1	no	—
243	C₂×C₄²	—	178	1	no	—
244	C₂×C₄²	—	178	1	no	—
245	C₂×C₄²	—	178	1	no	—
246	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
247	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
248	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
249	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
250	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
251	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
252	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
253	C₄⋊C₈	—	2	4	no	—
254	C₄⋊C₈	—	356	2	no	—
255	C₄⋊C₈	—	356	2	no	—
256	C₄⋊C₈	—	178	2	no	—
257	C₄⋊C₈	—	178	2	no	—
258	C₄×C₈	—	2	2	no	—
259	C₄×C₈	—	2	2	no	—
260	#95	—	178	1	no	—
261	#95	—	178	1	no	—
262	#95	—	178	1	no	—
263	C₂×Q₈	—	89	2	no	—
264	C₂×Q₈	—	89	2	no	—
265	C₂×Q₈	—	89	2	no	—
266	C₂×Q₈	—	178	1	no	—
267	C₂×Q₈	—	178	1	no	—
268	C₂×Q₈	—	178	1	no	—
269	C₂²×C₄	—	178	1	no	—
270	C₂²×C₄	—	178	1	no	—
271	C₂²×C₄	—	178	1	no	—
272	C₂²×C₄	—	178	1	no	—
273	C₂²×C₄	#13083551	1	1	yes	characteristic
274	C₂²×C₄	#13083551	1	1	yes	characteristic
275	C₂²×C₄	#13083551	1	1	yes	characteristic
276	C₂²×C₄	#13083551	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	4	2	no	—
282	C₂×C₈	—	4	2	no	—
283	C₂×C₈	—	356	2	no	—
284	C₂×C₈	—	356	2	no	—
285	C₂×C₈	—	356	2	no	—
286	C₄⋊C₄	—	89	2	no	—
287	C₄⋊C₄	—	89	2	no	—
288	C₄⋊C₄	—	89	2	no	—
289	C₄⋊C₄	—	178	4	no	—
290	C₄⋊C₄	—	178	1	no	—
291	C₄⋊C₄	—	178	2	no	—
292	C₄⋊C₄	—	178	2	no	—
293	C₄⋊C₄	—	178	1	no	—
294	C₄⋊C₄	—	178	1	no	—
295	C₄⋊C₄	—	178	4	no	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	4	1	no	—
302	C₄²	—	356	2	no	—
303	C₄²	—	356	1	no	—
304	C₄²	—	356	1	no	—
305	C₄²	—	356	2	no	—
306	C₄²	—	178	4	no	—
307	C₄²	—	178	2	no	—
308	C₄²	—	178	2	no	—
309	C₄²	—	178	4	no	—
310	C₄²	C₈×D₈₉	1	2	yes	—
311	C₄²	#13083557	1	2	yes	—
312	C₄²	#13083563	1	2	yes	—
313	C₄²	Dic₃₅₆	1	2	yes	—
314	C₄²	D₄×D₈₉	1	1	yes	characteristic
315	C₄²	Q₈×D₈₉	1	1	yes	characteristic
316	C₄²	#13083573	1	1	yes	characteristic
317	C₄²	#13083575	1	1	yes	characteristic
318	C₂³	C₂×#13083551	1	1	yes	characteristic
319	Q₈	—	89	4	no	—
320	Q₈	—	178	2	no	—
321	Q₈	—	178	2	no	—
322	Q₈	—	178	2	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	356	1	no	—
333	C₂×C₄	—	356	1	no	—
334	C₂×C₄	—	356	1	no	—
335	C₂×C₄	—	356	1	no	—
336	C₂×C₄	—	356	1	no	—
337	C₂×C₄	—	356	1	no	—
338	C₂×C₄	—	178	2	no	—
339	C₂×C₄	—	178	2	no	—
340	C₂×C₄	—	178	2	no	—
341	C₂×C₄	—	178	2	no	—
342	C₂×C₄	—	178	2	no	—
343	C₂×C₄	—	178	2	no	—
344	C₂×C₄	#15667924	1	2	yes	—
345	C₂×C₄	#15667924	1	2	yes	—
346	C₂×C₄	#15667937	1	2	yes	—
347	C₂×C₄	#15667937	1	2	yes	—
348	C₂×C₄	#15667940	1	2	yes	—
349	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
350	C₂×C₄	#15667970	1	1	yes	characteristic
351	C₂×C₄	#15667983	1	1	yes	characteristic
352	C₂×C₄	#15667987	1	1	yes	characteristic
353	C₂×C₄	#15667988	1	1	yes	characteristic
354	C₂×C₄	#15667992	1	1	yes	characteristic
355	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
356	C₂×C₄	M₁₆×D₈₉	1	1	yes	characteristic
357	C₂×C₄	M₁₆×D₈₉	1	1	yes	characteristic
358	C₂×C₄	C₂×#13083557	1	1	yes	characteristic
359	C₂×C₄	C₂×#13083563	1	1	yes	characteristic
360	C₂×C₄	C₂×Dic₃₅₆	1	1	yes	characteristic
361	C₂×C₄	#15668040	1	1	yes	characteristic
362	C₂×C₄	#15668045	1	1	yes	characteristic
363	C₈	—	4	4	no	—
364	C₈	—	712	2	no	—
365	C₂²	#19151455	1	1	yes	characteristic
366	C₂²	C₂×#15667924	1	1	yes	characteristic
367	C₂²	#19151561	1	1	yes	characteristic
368	C₂²	C₂×#15667937	1	1	yes	characteristic
369	C₂²	#19151600	1	1	yes	characteristic
370	C₂²	C₂×#15667940	1	1	yes	characteristic
371	C₂²	#19151616	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	1	no	—
377	C₄	—	356	2	no	—
378	C₄	—	356	2	no	—
379	C₄	—	356	2	no	—
380	C₄	—	178	4	no	—
381	C₄	#19151330	1	4	yes	complemented
382	C₄	C₄⋊C₈×D₈₉	1	1	yes	characteristic
383	C₄	#19151620	1	1	yes	characteristic
384	C₄	#19151650	1	1	yes	characteristic
385	C₄	#19151654	1	1	yes	characteristic
386	C₄	#19151799	1	1	yes	characteristic
387	C₄	#19151809	1	1	yes	characteristic
388	C₄	#19151884	1	1	yes	characteristic
389	C₄	#19151894	1	1	yes	characteristic
390	C₂	C₂×#19151330	1	1	yes	characteristic
391	C₂	#26018640	1	1	yes	characteristic
392	C₂	#26018682	1	1	yes	characteristic
393	C₂	#26018692	1	1	yes	characteristic
394	C₂	#26020229	1	1	yes	characteristic
395	C₂	#26020258	1	1	yes	characteristic
396	C₂	#26020273	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₄×C₄⋊C₈×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₄×C₄⋊C₈	D₈₉
hypocenter	C₈₉	#8564
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
31. C₄×Dic₁₇₈	C₈	semidirect
163. Dic₁₇₈	C₄⋊C₈	semidirect
178. C₄×C₈₉	Q₈⋊C₈	semidirect
204. C₈₉	#8564	semidirect
381. C₄	#19151330	semidirect

Maximal subgroups

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

subgroup	index
C₄²×Dic₁₇₈	2
#26020404	2
C₂×#19151330	2
#26018092	2
C₄×C₄⋊C₈×C₈₉	2
#8564	89