Subgroups — #36565059

Order 22784.

704 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028885	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151655	C₂	1	1	yes	maximal, characteristic
3	#26021025	C₂	1	4	yes	maximal, complemented
4	#26020457	C₂	1	4	yes	maximal
5	#26020426	C₂	1	2	yes	maximal, complemented
6	#26020392	C₂	1	2	yes	maximal, complemented
7	C₂×#423×C₈₉	C₂	1	1	yes	maximal, characteristic
8	#19151655	—	2	1	no	—
9	#19151655	—	2	1	no	—
10	#19151655	C₄	1	2	yes	—
11	#19151655	C₄	1	2	yes	—
12	#19151655	C₄	1	2	yes	—
13	#19151655	C₄	1	2	yes	—
14	#19151651	—	2	1	no	—
15	#19151651	—	2	1	no	—
16	C₂×#15667947	C₂²	1	8	yes	—
17	#19151622	C₂²	1	1	yes	characteristic
18	#19151622	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
20	#19151562	C₂²	1	2	yes	—
21	C₂×C₂²⋊#10623494	C₂²	1	2	yes	—
22	C₄×#13083558	C₂²	1	2	yes	—
23	C₂×#15667923	C₂²	1	2	yes	—
24	#19151362	C₂²	1	8	yes	—
25	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
26	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
27	#423×C₈₉	—	2	1	no	—
28	#423×C₈₉	—	2	1	no	—
29	#423×C₈₉	C₂²	1	2	yes	—
30	#423×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
32	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
33	C₂×#13083558	C₂³	1	2	yes	—
34	C₂×#13083558	C₂³	1	2	yes	—
35	C₂²×#10623494	C₂³	1	4	yes	—
36	#15667947	—	4	8	no	—
37	C₄⋊#10623494	—	2	1	no	—
38	C₄⋊#10623494	—	2	1	no	—
39	C₄⋊#10623494	—	2	1	no	—
40	C₄⋊#10623494	—	2	1	no	—
41	C₄⋊#10623494	C₂×C₄	1	4	yes	—
42	C₄⋊#10623494	C₂×C₄	1	4	yes	—
43	C₂²⋊#10623494	—	2	2	no	—
44	C₂²⋊#10623494	—	2	2	no	—
45	C₂²⋊#10623494	C₂×C₄	1	4	yes	—
46	C₂²⋊#10623494	C₂×C₄	1	4	yes	—
47	#15667923	—	2	2	no	—
48	#15667923	C₂×C₄	1	4	yes	—
49	#15667923	C₂×C₄	1	4	yes	—
50	C₄×#10623494	—	2	2	no	—
51	C₂³×C₄×C₈₉	Q₈	1	1	yes	characteristic
52	C₂³×C₄×C₈₉	Q₈	1	1	yes	characteristic
53	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₈₉	—	2	2	no	—
55	C₂×M₁₆×C₈₉	—	4	4	no	—
56	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
57	C₂²×C₈×C₈₉	—	2	2	no	—
58	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₈₉	Q₈	1	1	yes	characteristic
67	C₂×C₄²×C₈₉	Q₈	1	1	yes	characteristic
68	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₈₉	—	2	2	no	—
71	C₄⋊C₈×C₈₉	—	2	2	no	—
72	C₄⋊C₈×C₈₉	—	2	2	no	—
73	C₄⋊C₈×C₈₉	—	2	2	no	—
74	#13083558	—	2	4	no	—
75	#13083558	—	2	4	no	—
76	C₂×#10623494	—	2	4	no	—
77	C₂×#10623494	—	2	4	no	—
78	C₂×#10623494	—	2	2	no	—
79	C₂×#10623494	—	2	2	no	—
80	C₂×#10623494	C₂²×C₄	1	8	yes	—
81	C₂⁴×C₈₉	C₂×Q₈	1	1	yes	characteristic
82	C₂²×C₄×C₈₉	—	2	2	no	—
83	C₂²×C₄×C₈₉	—	2	2	no	—
84	C₂²×C₄×C₈₉	—	4	2	no	—
85	C₂²×C₄×C₈₉	—	4	2	no	—
86	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
104	M₁₆×C₈₉	—	2	8	no	—
105	M₁₆×C₈₉	—	4	4	no	—
106	C₂×C₈×C₈₉	—	2	4	no	—
107	C₂×C₈×C₈₉	—	4	4	no	—
108	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂³×C₈₉	—	2	2	no	—
125	C₂³×C₈₉	—	2	2	no	—
126	C₂³×C₈₉	—	4	1	no	—
127	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂³×C₈₉	C₂²×Q₈	1	1	yes	characteristic
130	C₂×C₄×C₈₉	—	2	2	no	—
131	C₂×C₄×C₈₉	—	2	2	no	—
132	C₂×C₄×C₈₉	—	2	2	no	—
133	C₂×C₄×C₈₉	—	2	2	no	—
134	C₂×C₄×C₈₉	—	2	2	no	—
135	C₂×C₄×C₈₉	—	2	1	no	—
136	C₂×C₄×C₈₉	—	2	1	no	—
137	C₂×C₄×C₈₉	—	2	1	no	—
138	C₂×C₄×C₈₉	—	2	1	no	—
139	C₂×C₄×C₈₉	—	2	2	no	—
140	C₂×C₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	2	2	no	—
142	C₂×C₄×C₈₉	—	4	1	no	—
143	C₂×C₄×C₈₉	—	4	1	no	—
144	C₂×C₄×C₈₉	—	4	1	no	—
145	C₂×C₄×C₈₉	—	4	1	no	—
146	C₂×C₄×C₈₉	—	4	1	no	—
147	C₂×C₄×C₈₉	—	4	1	no	—
148	C₂×C₄×C₈₉	—	4	1	no	—
149	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
162	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
163	C₈×C₈₉	—	4	4	no	—
164	#10623494	—	2	8	no	—
165	#10623494	—	4	2	no	—
166	#10623494	—	4	2	no	—
167	C₂²×C₈₉	—	2	1	no	—
168	C₂²×C₈₉	—	2	1	no	—
169	C₂²×C₈₉	—	2	1	no	—
170	C₂²×C₈₉	—	2	1	no	—
171	C₂²×C₈₉	—	2	1	no	—
172	C₂²×C₈₉	—	2	1	no	—
173	C₂²×C₈₉	—	2	1	no	—
174	C₂²×C₈₉	—	4	4	no	—
175	C₂²×C₈₉	#430	1	2	yes	—
176	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
177	C₂²×C₈₉	#544	1	2	yes	—
178	C₄×C₈₉	—	2	1	no	—
179	C₄×C₈₉	—	2	1	no	—
180	C₄×C₈₉	—	2	1	no	—
181	C₄×C₈₉	—	2	1	no	—
182	C₄×C₈₉	—	2	1	no	—
183	C₄×C₈₉	—	2	1	no	—
184	C₄×C₈₉	—	2	1	no	—
185	C₄×C₈₉	—	2	1	no	—
186	C₄×C₈₉	—	2	1	no	—
187	C₄×C₈₉	#430	1	2	yes	—
188	C₄×C₈₉	#520	1	2	yes	—
189	C₄×C₈₉	#535	1	1	yes	characteristic
190	C₄×C₈₉	#536	1	1	yes	characteristic
191	#21994	—	89	1	no	maximal, Sylow
192	C₂×C₈₉	—	2	2	no	—
193	C₂×C₈₉	—	2	2	no	—
194	C₂×C₈₉	—	4	1	no	—
195	C₂×C₈₉	#2317	1	1	yes	characteristic
196	C₂×C₈₉	C₂×#430	1	1	yes	characteristic
197	C₂×C₈₉	C₂×#430	1	1	yes	characteristic
198	#2920	—	89	1	no	—
199	C₂×#432	—	89	1	no	—
200	C₂×#423	D₈₉	1	1	yes	characteristic
201	#1950	—	89	4	no	—
202	#1855	—	89	4	no	—
203	#1849	—	89	2	no	—
204	#1838	—	89	2	no	—
205	C₈₉	#21994	1	1	yes	characteristic, complemented, Sylow
206	C₂²×M₁₆	C₂×D₈₉	1	2	yes	—
207	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
208	#432	—	89	2	no	—
209	#432	—	89	2	no	—
210	#432	—	89	2	no	—
211	#432	—	89	2	no	—
212	#432	—	178	1	no	—
213	#432	—	178	1	no	—
214	#431	—	178	1	no	—
215	#431	—	178	1	no	—
216	C₂×#108	—	89	8	no	—
217	#423	—	2	1	no	—
218	#423	—	2	1	no	—
219	#423	—	89	1	no	—
220	#423	—	89	1	no	—
221	#423	C₂×D₈₉	1	2	yes	—
222	#423	C₂×D₈₉	1	2	yes	—
223	C₂×C₄⋊C₈	—	2	1	no	—
224	C₂×C₄⋊C₈	—	2	1	no	—
225	C₂×C₄⋊C₈	—	89	2	no	—
226	#407	—	89	2	no	—
227	C₂×C₂²⋊C₈	—	89	2	no	—
228	C₄×M₁₆	—	89	2	no	—
229	C₂×#97	—	89	2	no	—
230	#341	—	89	8	no	—
231	C₂³×C₄	Dic₁₇₈	1	1	yes	characteristic
232	C₂³×C₄	Dic₁₇₈	1	1	yes	characteristic
233	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	4	4	no	—
236	C₂×M₁₆	—	89	2	no	—
237	C₂×M₁₆	—	89	2	no	—
238	C₂×M₁₆	C₂²×D₈₉	1	4	yes	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	89	4	no	—
241	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
242	C₂×C₄²	Dic₁₇₈	1	1	yes	characteristic
243	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
244	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
245	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
246	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
247	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
248	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
249	C₂×C₄²	C₂²⋊D₈₉	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	#108	—	356	8	no	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	89	4	no	—
259	C₄⋊C₈	—	89	4	no	—
260	C₄⋊C₈	—	178	1	no	—
261	C₄⋊C₈	—	178	1	no	—
262	C₄⋊C₈	—	178	1	no	—
263	C₄⋊C₈	—	178	1	no	—
264	C₂²⋊C₈	—	89	4	no	—
265	C₂²⋊C₈	—	89	4	no	—
266	C₂²⋊C₈	—	178	2	no	—
267	C₂²⋊C₈	—	178	2	no	—
268	#97	—	89	4	no	—
269	#97	—	89	4	no	—
270	#97	—	178	2	no	—
271	C₄×C₈	—	178	2	no	—
272	C₂⁴	C₂×Dic₁₇₈	1	1	yes	characteristic
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	#13083553	1	1	yes	characteristic
278	C₂²×C₄	#13083553	1	1	yes	characteristic
279	C₂²×C₄	#13083553	1	1	yes	characteristic
280	C₂²×C₄	#13083553	1	1	yes	characteristic
281	C₂²×C₄	#13083553	1	1	yes	characteristic
282	C₂²×C₄	#13083553	1	1	yes	characteristic
283	C₂²×C₄	#13083553	1	1	yes	characteristic
284	C₂²×C₄	#13083553	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
290	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
291	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
292	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
293	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
294	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
295	M₁₆	—	2	8	no	—
296	M₁₆	—	4	4	no	—
297	M₁₆	—	178	4	no	—
298	M₁₆	—	178	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	4	4	no	—
301	C₂×C₈	—	89	8	no	—
302	C₂×C₈	—	178	2	no	—
303	C₂×C₈	—	178	2	no	—
304	C₂×C₈	—	178	4	no	—
305	C₂×C₈	—	178	4	no	—
306	C₄²	#13083553	1	1	yes	characteristic
307	C₄²	#13083553	1	1	yes	characteristic
308	C₄²	#13083553	1	1	yes	characteristic
309	C₄²	#13083553	1	1	yes	characteristic
310	C₄²	#13083553	1	1	yes	characteristic
311	C₄²	#13083553	1	1	yes	characteristic
312	C₄²	#13083553	1	1	yes	characteristic
313	C₄²	#13083553	1	1	yes	characteristic
314	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
315	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
316	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
317	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
318	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
319	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
320	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
321	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	4	1	no	—
325	C₂³	C₂×#13083553	1	1	yes	characteristic
326	C₂³	C₂×#13083553	1	1	yes	characteristic
327	C₂³	C₂²×Dic₁₇₈	1	1	yes	characteristic
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
348	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
349	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
350	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
351	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
352	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
353	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
354	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
355	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
356	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
359	C₂×C₄	#15668057	1	2	yes	—
360	C₂×C₄	#15668060	1	2	yes	—
361	C₈	—	4	4	no	—
362	C₈	—	356	2	no	—
363	C₈	—	356	2	no	—
364	C₈	—	178	8	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	4	4	no	—
373	C₂²	#19151646	1	2	yes	—
374	C₂²	C₂²×#13083553	1	1	yes	characteristic
375	C₂²	#19152229	1	2	yes	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	#19151646	1	2	yes	—
386	C₄	#19152079	1	2	yes	—
387	C₄	#19152165	1	1	yes	characteristic
388	C₄	#19152172	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	2	2	no	—
391	C₂	—	4	1	no	—
392	C₂	#26022876	1	1	yes	characteristic
393	C₂	C₂×#19151646	1	1	yes	characteristic
394	C₂	C₂×#19151646	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₂×#423×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₈₉	C₂×Q₈
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₂×#423	D₈₉
hypocenter	C₈₉	#21994
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #26021025	C₂	semidirect
5. #26020426	C₂	semidirect
6. #26020392	C₂	semidirect
205. C₈₉	#21994	semidirect

Maximal subgroups

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

subgroup	index
#26028885	2
C₂×#19151655	2
#26021025	2
#26020457	2
#26020426	2
#26020392	2
C₂×#423×C₈₉	2
#21994	89