Subgroups — C₄×#19152002 #36563161

Order 22784.

878 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152002	C₂	1	1	yes	maximal, characteristic
2	C₄×#15668011	C₂	1	2	yes	maximal
3	#26021211	C₂	1	2	yes	maximal
4	#26020986	C₂	1	1	yes	maximal, characteristic
5	#26020984	C₂	1	2	yes	maximal
6	#26020983	C₂	1	1	yes	maximal, characteristic
7	#26020410	C₂	1	1	yes	maximal, characteristic
8	C₄×#15667945	C₂	1	2	yes	maximal
9	C₄×#15667946	C₂	1	1	yes	maximal, characteristic
10	C₄×C₈×Dic₈₉	C₂	1	1	yes	maximal, characteristic
11	C₄×#107×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668011	C₂²	1	2	yes	—
13	C₂×C₄×Dic₁₇₈	—	2	2	no	—
14	#19152002	C₄	1	8	yes	direct product factor
15	C₂×#15667946	C₂²	1	1	yes	characteristic
16	C₂×#15667946	C₂²	1	1	yes	characteristic
17	C₂×#15667945	C₂²	1	2	yes	—
18	C₂×#15667945	C₂²	1	2	yes	—
19	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
24	#19151502	—	2	2	no	—
25	#19151497	C₂²	1	2	yes	—
26	#19151495	—	2	2	no	—
27	#19151494	C₂²	1	2	yes	—
28	#19151467	C₂²	1	2	yes	—
29	C₄×#13083553	—	2	2	no	—
30	C₄×C₄⋊Dic₈₉	C₂²	1	2	yes	—
31	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
32	#19151361	C₂²	1	2	yes	—
33	#19151360	C₂²	1	2	yes	—
34	#19151360	C₂²	1	2	yes	—
35	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
39	#340×C₈₉	C₂²	1	2	yes	—
40	C₂²×Dic₁₇₈	—	2	2	no	—
41	C₂²×#10623494	C₂³	1	1	yes	characteristic
42	C₂²×#10623494	C₂³	1	1	yes	characteristic
43	#15668011	—	2	4	no	—
44	#15668011	C₂×C₄	1	8	yes	—
45	C₄×Dic₁₇₈	—	4	8	no	—
46	C₂×C₄⋊Dic₈₉	—	2	2	no	—
47	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
49	C₂×#13083553	—	2	2	no	—
50	C₂×#13083553	—	2	2	no	—
51	C₂×#13083553	—	2	2	no	—
52	C₂×#13083553	—	2	2	no	—
53	C₂×C₄×Dic₈₉	—	2	2	no	—
54	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
57	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
58	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
60	#15667946	—	2	2	no	—
61	#15667946	C₂×C₄	1	4	yes	—
62	#15667945	—	2	4	no	—
63	#15667945	C₂×C₄	1	8	yes	—
64	C₄×#10623494	Q₈	1	4	yes	complemented
65	C₈×Dic₈₉	—	2	2	no	—
66	C₈×Dic₈₉	—	2	2	no	—
67	C₈×Dic₈₉	—	2	2	no	—
68	C₈×Dic₈₉	C₂×C₄	1	4	yes	—
69	#15667919	—	2	2	no	—
70	#15667919	—	2	2	no	—
71	#15667919	—	2	2	no	—
72	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
76	C₂×C₄²×C₈₉	—	2	2	no	—
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	#107×C₈₉	—	2	2	no	—
79	#107×C₈₉	C₂×C₄	1	4	yes	—
80	C₄×C₈×C₈₉	Q₈	1	4	yes	complemented
81	#95×C₈₉	—	2	2	no	—
82	C₂×Dic₁₇₈	—	2	8	no	—
83	C₂×Dic₁₇₈	—	4	4	no	—
84	C₂×Dic₁₇₈	—	4	4	no	—
85	C₂²×Dic₈₉	—	2	2	no	—
86	C₂²×Dic₈₉	—	2	2	no	—
87	C₂²×Dic₈₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×Dic₈₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×Dic₈₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×Dic₈₉	C₂×D₄	1	1	yes	characteristic
91	C₂×#10623494	—	2	1	no	—
92	C₂×#10623494	—	2	1	no	—
93	C₂×#10623494	C₂²×C₄	1	2	yes	—
94	C₂×#10623494	C₂×Q₈	1	2	yes	—
95	C₂×#10623494	C₂×Q₈	1	2	yes	—
96	C₂×#10623494	#41	1	2	yes	—
97	C₄⋊Dic₈₉	—	2	2	no	—
98	C₄⋊Dic₈₉	—	2	2	no	—
99	C₄⋊Dic₈₉	—	2	2	no	—
100	C₄⋊Dic₈₉	—	4	4	no	—
101	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
102	#13083553	—	2	8	no	—
103	#13083553	—	4	4	no	—
104	#13083553	—	4	4	no	—
105	#13083553	—	4	4	no	—
106	C₄×Dic₈₉	—	2	1	no	—
107	C₄×Dic₈₉	—	2	1	no	—
108	C₄×Dic₈₉	—	2	2	no	—
109	C₄×Dic₈₉	—	2	2	no	—
110	C₄×Dic₈₉	—	4	4	no	—
111	C₄×Dic₈₉	D₈	1	4	yes	—
112	C₄×Dic₈₉	Q₁₆	1	4	yes	—
113	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
114	C₄×Dic₈₉	#41	1	2	yes	—
115	C₂²×C₄×C₈₉	—	2	2	no	—
116	C₂²×C₄×C₈₉	—	2	2	no	—
117	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₈₉	—	2	1	no	—
121	C₂×C₈×C₈₉	—	2	1	no	—
122	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
124	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
125	C₂×C₈×C₈₉	#41	1	2	yes	—
126	C₄⋊C₄×C₈₉	—	2	2	no	—
127	C₄⋊C₄×C₈₉	—	2	2	no	—
128	C₄⋊C₄×C₈₉	—	2	2	no	—
129	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
130	C₄²×C₈₉	—	4	4	no	—
131	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
132	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
133	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₈₉	—	2	1	no	—
135	C₂×C₄×C₈₉	—	2	1	no	—
136	C₂×C₄×C₈₉	—	2	4	no	—
137	C₂×C₄×C₈₉	—	4	2	no	—
138	C₂×C₄×C₈₉	—	4	2	no	—
139	C₂×C₄×C₈₉	—	4	2	no	—
140	C₂×C₄×C₈₉	—	4	2	no	—
141	C₂×C₄×C₈₉	—	4	2	no	—
142	C₂×C₄×C₈₉	C₄⋊Q₈	1	2	yes	—
143	C₂×C₄×C₈₉	C₄⋊Q₈	1	2	yes	—
144	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
145	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
146	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
152	C₂×Dic₈₉	—	2	1	no	—
153	C₂×Dic₈₉	—	2	1	no	—
154	C₂×Dic₈₉	—	2	1	no	—
155	C₂×Dic₈₉	—	2	1	no	—
156	C₂×Dic₈₉	—	2	4	no	—
157	C₂×Dic₈₉	—	4	2	no	—
158	C₂×Dic₈₉	—	4	2	no	—
159	C₂×Dic₈₉	—	4	2	no	—
160	C₂×Dic₈₉	—	4	2	no	—
161	C₂×Dic₈₉	—	4	2	no	—
162	C₂×Dic₈₉	C₄×D₄	1	2	yes	—
163	C₂×Dic₈₉	C₄×D₄	1	2	yes	—
164	C₂×Dic₈₉	C₂×D₈	1	2	yes	—
165	C₂×Dic₈₉	C₂×D₈	1	2	yes	—
166	C₂×Dic₈₉	C₂×Q₁₆	1	2	yes	—
167	C₂×Dic₈₉	C₂×Q₁₆	1	2	yes	—
168	C₂×Dic₈₉	#135	1	2	yes	—
169	C₂×Dic₈₉	#135	1	2	yes	—
170	Dic₁₇₈	—	4	16	no	—
171	C₈×C₈₉	—	2	2	no	—
172	C₈×C₈₉	C₄×Q₈	1	4	yes	complemented
173	#10623494	—	2	2	no	—
174	#10623494	C₄×Q₈	1	4	yes	complemented
175	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
176	C₂²×C₈₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
177	C₂²×C₈₉	#532	1	1	yes	characteristic
178	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
179	C₂²×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
180	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
181	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
182	C₄×C₈₉	—	2	2	no	—
183	C₄×C₈₉	—	4	4	no	—
184	C₄×C₈₉	—	8	2	no	—
185	C₄×C₈₉	#500	1	4	yes	complemented
186	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
187	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
188	C₄×C₈₉	#533	1	1	yes	characteristic
189	C₄×C₈₉	#533	1	1	yes	characteristic
190	Dic₈₉	—	2	2	no	—
191	Dic₈₉	—	2	2	no	—
192	Dic₈₉	—	4	4	no	—
193	Dic₈₉	—	8	2	no	—
194	Dic₈₉	C₄×D₈	1	4	yes	—
195	Dic₈₉	C₄×Q₁₆	1	4	yes	—
196	C₄×#500	—	89	1	no	maximal, Sylow
197	C₂×C₈₉	C₄×C₄⋊Q₈	1	1	yes	characteristic
198	C₂×C₈₉	C₂×C₄×D₈	1	1	yes	characteristic
199	C₂×C₈₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
200	C₂×C₈₉	C₂×#500	1	1	yes	characteristic
201	C₂×C₈₉	#3160	1	1	yes	characteristic
202	C₂×C₈₉	#3169	1	1	yes	characteristic
203	C₂×C₈₉	#3170	1	1	yes	characteristic
204	C₂×#500	—	89	1	no	—
205	C₄×C₄⋊Q₈	—	89	2	no	—
206	#1990	—	89	2	no	—
207	#1942	—	89	1	no	—
208	#1942	—	89	1	no	—
209	#1942	—	89	2	no	—
210	#1845	—	89	1	no	—
211	C₄×#107	—	89	1	no	—
212	C₄×#107	—	89	2	no	—
213	C₄×#107	D₈₉	1	1	yes	characteristic
214	C₄²×C₈	—	89	1	no	—
215	C₈₉	C₄×#500	1	1	yes	characteristic, complemented, Sylow
216	C₂×C₄⋊Q₈	—	89	2	no	—
217	C₂×C₄×Q₈	—	178	2	no	—
218	#500	—	89	8	no	—
219	C₂×#107	—	89	1	no	—
220	C₂×#107	—	89	2	no	—
221	C₂×#107	—	89	1	no	—
222	C₂×#107	—	89	2	no	—
223	C₂×#107	C₂×D₈₉	1	1	yes	characteristic
224	C₂×#107	C₂×D₈₉	1	1	yes	characteristic
225	C₂×C₄×C₈	—	89	1	no	—
226	C₂×C₄×C₈	—	89	1	no	—
227	C₂×C₄×C₈	—	89	1	no	—
228	C₂×C₄×C₈	—	89	1	no	—
229	C₂×C₄×C₈	—	89	1	no	—
230	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
231	#391	—	178	2	no	—
232	#389	—	89	2	no	—
233	#389	—	89	2	no	—
234	#389	—	178	2	no	—
235	#384	—	89	2	no	—
236	C₄×C₄⋊C₄	—	89	2	no	—
237	C₄×C₄⋊C₄	—	178	2	no	—
238	C₄×C₄⋊C₄	C₂×D₈₉	1	2	yes	—
239	C₄³	—	89	1	no	—
240	#340	—	89	2	no	—
241	#340	—	89	2	no	—
242	#340	—	89	2	no	—
243	#340	C₂×D₈₉	1	2	yes	—
244	C₂²×Q₈	—	178	2	no	—
245	C₂²×C₈	—	89	1	no	—
246	C₂²×C₈	—	89	1	no	—
247	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
248	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
249	C₄⋊Q₈	—	89	8	no	—
250	C₄⋊Q₈	—	178	4	no	—
251	C₄×Q₈	—	356	8	no	—
252	C₂×C₄⋊C₄	—	89	2	no	—
253	C₂×C₄⋊C₄	—	89	2	no	—
254	C₂×C₄⋊C₄	—	178	2	no	—
255	C₂×C₄⋊C₄	—	178	2	no	—
256	C₂×C₄⋊C₄	—	178	2	no	—
257	C₂×C₄⋊C₄	—	178	2	no	—
258	C₂×C₄⋊C₄	—	178	2	no	—
259	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
260	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	89	1	no	—
263	C₂×C₄²	—	89	1	no	—
264	C₂×C₄²	—	89	1	no	—
265	C₂×C₄²	—	89	1	no	—
266	C₂×C₄²	—	89	1	no	—
267	C₂×C₄²	—	89	1	no	—
268	C₂×C₄²	—	178	2	no	—
269	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
270	#107	—	2	2	no	—
271	#107	—	89	4	no	—
272	#107	—	89	8	no	—
273	#107	—	178	4	no	—
274	#107	—	178	2	no	—
275	#107	C₄×D₈₉	1	4	yes	—
276	C₄×C₈	—	89	4	no	—
277	C₄×C₈	—	89	4	no	—
278	C₄×C₈	—	178	2	no	—
279	C₄×C₈	—	178	2	no	—
280	C₄×C₈	—	178	2	no	—
281	C₄×C₈	Dic₁₇₈	1	4	yes	complemented
282	#95	—	2	2	no	—
283	#95	—	178	2	no	—
284	#95	—	178	2	no	—
285	#95	—	178	2	no	—
286	C₂×Q₈	—	356	4	no	—
287	C₂×Q₈	—	356	4	no	—
288	C₂×Q₈	—	178	8	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	89	1	no	—
292	C₂²×C₄	—	89	1	no	—
293	C₂²×C₄	—	89	1	no	—
294	C₂²×C₄	—	89	1	no	—
295	C₂²×C₄	—	178	2	no	—
296	C₂²×C₄	—	178	2	no	—
297	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
298	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
299	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	89	2	no	—
303	C₂×C₈	—	89	2	no	—
304	C₂×C₈	—	89	2	no	—
305	C₂×C₈	—	89	2	no	—
306	C₂×C₈	—	178	1	no	—
307	C₂×C₈	—	178	1	no	—
308	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
309	C₂×C₈	C₂×Dic₁₇₈	1	2	yes	—
310	C₂×C₈	C₂×Dic₁₇₈	1	2	yes	—
311	C₂×C₈	#13083574	1	2	yes	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	89	4	no	—
316	C₄⋊C₄	—	356	4	no	—
317	C₄⋊C₄	—	356	4	no	—
318	C₄⋊C₄	—	356	4	no	—
319	C₄⋊C₄	—	356	4	no	—
320	C₄⋊C₄	—	178	8	no	—
321	C₄⋊C₄	—	178	2	no	—
322	C₄⋊C₄	—	178	2	no	—
323	C₄⋊C₄	—	178	2	no	—
324	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
325	C₄²	—	4	4	no	—
326	C₄²	—	89	4	no	—
327	C₄²	—	89	4	no	—
328	C₄²	—	89	2	no	—
329	C₄²	—	89	2	no	—
330	C₄²	—	356	4	no	—
331	C₄²	—	178	2	no	—
332	C₄²	—	178	2	no	—
333	C₄²	—	178	1	no	—
334	C₄²	—	178	1	no	—
335	C₄²	Q₈×D₈₉	1	2	yes	—
336	C₄²	C₂×Dic₁₇₈	1	2	yes	—
337	C₂³	C₂×D₄×D₈₉	1	1	yes	characteristic
338	Q₈	—	356	16	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	89	2	no	—
348	C₂×C₄	—	89	2	no	—
349	C₂×C₄	—	89	2	no	—
350	C₂×C₄	—	89	2	no	—
351	C₂×C₄	—	89	2	no	—
352	C₂×C₄	—	89	2	no	—
353	C₂×C₄	—	89	2	no	—
354	C₂×C₄	—	89	2	no	—
355	C₂×C₄	—	356	2	no	—
356	C₂×C₄	—	356	2	no	—
357	C₂×C₄	—	356	2	no	—
358	C₂×C₄	—	356	2	no	—
359	C₂×C₄	—	356	2	no	—
360	C₂×C₄	—	178	4	no	—
361	C₂×C₄	—	178	1	no	—
362	C₂×C₄	—	178	1	no	—
363	C₂×C₄	—	178	1	no	—
364	C₂×C₄	—	178	1	no	—
365	C₂×C₄	#15668011	1	2	yes	—
366	C₂×C₄	#15668011	1	2	yes	—
367	C₂×C₄	D₈×D₈₉	1	2	yes	—
368	C₂×C₄	Q₁₆×D₈₉	1	2	yes	—
369	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
370	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
371	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
372	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
373	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
374	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	89	4	no	—
377	C₈	—	178	2	no	—
378	C₈	C₄×Dic₁₇₈	1	4	yes	complemented
379	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
380	C₂²	C₂×#15668011	1	1	yes	characteristic
381	C₂²	#19152145	1	1	yes	characteristic
382	C₂²	C₂×D₈×D₈₉	1	1	yes	characteristic
383	C₂²	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
384	C₂²	#135×D₈₉	1	1	yes	characteristic
385	C₂²	#135×D₈₉	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	4	4	no	—
388	C₄	—	8	2	no	—
389	C₄	—	89	4	no	—
390	C₄	—	89	4	no	—
391	C₄	—	356	4	no	—
392	C₄	—	178	2	no	—
393	C₄	—	178	2	no	—
394	C₄	—	712	2	no	—
395	C₄	#19152002	1	4	yes	direct product factor
396	C₄	C₄×Q₈×D₈₉	1	1	yes	characteristic
397	C₄	C₂×C₄×Dic₁₇₈	1	1	yes	characteristic
398	C₄	#19152151	1	1	yes	characteristic
399	C₄	#19152152	1	1	yes	characteristic
400	C₂	C₄×#15668011	1	1	yes	characteristic
401	C₂	C₄×D₈×D₈₉	1	1	yes	characteristic
402	C₂	C₄×Q₁₆×D₈₉	1	1	yes	characteristic
403	C₂	C₂×#19152002	1	1	yes	characteristic
404	C₂	#26030764	1	1	yes	characteristic
405	C₂	#26030828	1	1	yes	characteristic
406	C₂	#26030835	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₄×#107×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	C₂²×D₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×#107	D₈₉
hypocenter	C₈₉	C₄×#500
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
14. #19152002	C₄	direct (N × H)
64. C₄×#10623494	Q₈	semidirect
80. C₄×C₈×C₈₉	Q₈	semidirect
172. C₈×C₈₉	C₄×Q₈	semidirect
174. #10623494	C₄×Q₈	semidirect
185. C₄×C₈₉	#500	semidirect
215. C₈₉	C₄×#500	semidirect
281. C₄×C₈	Dic₁₇₈	semidirect
378. C₈	C₄×Dic₁₇₈	semidirect
395. C₄	#19152002	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19152002	2
C₄×#15668011	2
#26021211	2
#26020986	2
#26020984	2
#26020983	2
#26020410	2
C₄×#15667945	2
C₄×#15667946	2
C₄×C₈×Dic₈₉	2
C₄×#107×C₈₉	2
C₄×#500	89

Subgroups — C4×#19152002 #36563161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19152002 #36563161