Subgroups — #72317445

Order 1024.

At least 6626 conjugacy classes of subgroups; only the 707 normal subgroups are shown.

The subgroup lattice has 407 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10586342	C₂	1	1	yes	maximal, characteristic
2	#493625	C₂	1	1	yes	maximal, characteristic, complemented
3	#493605	C₂	1	1	yes	maximal, characteristic, complemented
4	#493590	C₂	1	2	yes	maximal, complemented
5	C₂×#12765	C₂	1	1	yes	maximal, characteristic, complemented
6	#493577	C₂	1	1	yes	maximal, characteristic, complemented
7	#493561	C₂	1	2	yes	maximal, complemented
8	#493419	C₂	1	1	yes	maximal, characteristic, complemented
9	#493410	C₂	1	2	yes	maximal, complemented
10	#359673	C₂	1	1	yes	maximal, characteristic, complemented
11	#359649	C₂	1	2	yes	maximal, complemented
12	#63022	C₄	1	1	yes	characteristic, complemented
13	#63021	C₄	1	1	yes	characteristic, complemented
14	#63020	C₄	1	2	yes	complemented
15	#63017	C₄	1	2	yes	complemented
16	#63016	C₄	1	1	yes	characteristic, complemented
17	#63011	C₄	1	1	yes	characteristic, complemented
18	#62812	C₂²	1	1	yes	characteristic
19	#62811	C₂²	1	2	yes	—
20	#62759	C₂²	1	1	yes	characteristic
21	#62729	C₂²	1	2	yes	—
22	C₂×#3481	C₂²	1	1	yes	characteristic
23	#60093	C₂²	1	1	yes	characteristic, complemented
24	#33369	C₂²	1	2	yes	complemented
25	C₂×#2132	C₂²	1	1	yes	characteristic, complemented
26	#33358	C₂²	1	2	yes	complemented
27	C₂×#2126	C₂²	1	1	yes	characteristic, complemented
28	#33347	C₂²	1	2	yes	complemented
29	C₂×#2120	C₂²	1	2	yes	complemented
30	C₂×#2120	C₂²	1	2	yes	complemented
31	#21014	C₂²	1	1	yes	characteristic, complemented
32	#21012	C₂²	1	2	yes	complemented
33	#20964	C₂²	1	1	yes	characteristic, complemented
34	C₂×#1891	C₂²	1	2	yes	complemented
35	#20959	C₂²	1	2	yes	complemented
36	#20952	C₂²	1	1	yes	characteristic, complemented
37	#20947	C₂²	1	2	yes	complemented
38	C₂×#1884	C₂²	1	1	yes	characteristic, complemented
39	#20623	C₂²	1	1	yes	characteristic, complemented
40	#20623	C₂²	1	2	yes	complemented
41	C₂×#585	D₄	1	1	yes	characteristic
42	C₂×#585	C₂³	1	1	yes	characteristic
43	C₂³×#41	D₄	1	2	yes	—
44	C₂×#568	C₂³	1	1	yes	characteristic, complemented
45	#3551	C₂×C₄	1	2	yes	—
46	#3550	C₂×C₄	1	1	yes	characteristic
47	#3549	C₂×C₄	1	1	yes	characteristic
48	#3545	D₄	1	2	yes	—
49	#3544	D₄	1	2	yes	—
50	#3540	C₂×C₄	1	2	yes	—
51	#3540	C₂×C₄	1	2	yes	—
52	#3538	C₂×C₄	1	2	yes	—
53	#3537	C₂×C₄	1	2	yes	—
54	#3533	D₄	1	4	yes	—
55	#3532	D₄	1	4	yes	—
56	#3529	D₄	1	2	yes	—
57	#3529	D₄	1	4	yes	—
58	#3500	C₂×C₄	1	1	yes	characteristic
59	#3500	C₂×C₄	1	1	yes	characteristic
60	#3500	D₄	1	1	yes	characteristic
61	#3500	D₄	1	1	yes	characteristic
62	#3499	C₂×C₄	1	1	yes	characteristic
63	#3499	D₄	1	1	yes	characteristic
64	#3498	C₂×C₄	1	1	yes	characteristic
65	#3498	D₄	1	1	yes	characteristic
66	#3487	C₂×C₄	1	2	yes	—
67	#3487	D₄	1	2	yes	—
68	#3486	C₂×C₄	1	2	yes	—
69	#3486	D₄	1	2	yes	—
70	#3485	C₂×C₄	1	2	yes	—
71	#3485	D₄	1	2	yes	—
72	#3484	C₂×C₄	1	2	yes	—
73	#3484	D₄	1	2	yes	—
74	#3483	D₄	1	2	yes	—
75	#3481	C₂×C₄	1	1	yes	characteristic
76	#3481	C₂×C₄	1	2	yes	—
77	#3481	C₂×C₄	1	1	yes	characteristic
78	#3481	D₄	1	2	yes	—
79	#3481	D₄	1	1	yes	characteristic
80	#3481	D₄	1	1	yes	characteristic
81	#3481	D₄	1	4	yes	—
82	C₂×#559	D₄	1	1	yes	characteristic
83	C₂×#551	D₄	1	2	yes	—
84	C₂×D₄²	D₄	1	1	yes	characteristic
85	#3449	D₄	1	1	yes	characteristic
86	#3449	D₄	1	2	yes	—
87	#3449	C₂³	1	2	yes	—
88	#3449	C₂³	1	1	yes	characteristic
89	C₂×#532	D₄	1	1	yes	characteristic
90	C₂×#532	C₂³	1	1	yes	characteristic
91	C₂×#525	D₄	1	2	yes	—
92	C₂×#525	C₂³	1	2	yes	—
93	#3428	D₄	1	2	yes	—
94	#3428	C₂³	1	1	yes	characteristic, complemented
95	C₂×C₄×#41	D₄	1	1	yes	characteristic
96	C₂×#413	C₂³	1	2	yes	complemented
97	C₂×#413	C₂³	1	1	yes	characteristic, complemented
98	C₂×#410	C₂³	1	1	yes	characteristic, complemented
99	C₂×#410	C₂³	1	2	yes	complemented
100	C₂×2₋¹⁺⁴	C₂²⋊C₄	1	1	yes	characteristic, complemented
101	C₂×2₋¹⁺⁴	C₂²⋊C₄	1	1	yes	characteristic, complemented
102	C₂×2₋¹⁺⁴	C₂²×C₄	1	1	yes	characteristic
103	C₂×2₋¹⁺⁴	C₂×D₄	1	2	yes	—
104	C₂×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
105	C₂×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic, complemented
106	C₂×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic, complemented
107	C₂×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
108	C₂×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
109	C₂×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
110	C₂²×#41	C₂²⋊C₄	1	2	yes	complemented
111	C₂²×#41	C₂²⋊C₄	1	2	yes	complemented
112	C₂²×#41	C₂×D₄	1	2	yes	—
113	C₂²×#41	C₂×D₄	1	2	yes	—
114	C₂²×#41	C₂×D₄	1	1	yes	characteristic
115	C₂²×#41	C₂×D₄	1	1	yes	characteristic
116	C₂²×#41	C₂×D₄	1	1	yes	characteristic
117	C₂²×#41	C₂×D₄	1	2	yes	—
118	C₂²×#41	C₂×D₄	1	1	yes	characteristic
119	C₂²×#41	C₂⁴	1	1	yes	characteristic
120	C₂³×Q₈	C₂²⋊C₄	1	2	yes	complemented
121	C₂³×D₄	C₂²⋊C₄	1	2	yes	complemented
122	C₂⁴×C₄	C₂×D₄	1	2	yes	—
123	#563	C₂²⋊C₄	1	2	yes	complemented
124	#563	C₂²⋊C₄	1	4	yes	complemented
125	#563	C₂²⋊C₄	1	4	yes	complemented
126	H(3,𝔽₄)	C₂²⋊C₄	1	2	yes	complemented
127	H(3,𝔽₄)	C₂²⋊C₄	1	4	yes	complemented
128	#560	C₂²⋊C₄	1	4	yes	complemented
129	#560	C₂²⋊C₄	1	4	yes	complemented
130	#559	C₂²⋊C₄	1	1	yes	characteristic
131	#559	C₂²⋊C₄	1	2	yes	—
132	#559	C₂²⋊C₄	1	1	yes	characteristic
133	#559	C₂²⋊C₄	1	4	yes	complemented
134	Q₈²	C₂²⋊C₄	1	2	yes	complemented
135	#555	C₂²⋊C₄	1	4	yes	complemented
136	#555	C₂²⋊C₄	1	2	yes	complemented
137	#551	C₂²⋊C₄	1	2	yes	—
138	#551	C₂²⋊C₄	1	2	yes	—
139	#551	C₂²⋊C₄	1	2	yes	—
140	#551	C₂²⋊C₄	1	2	yes	—
141	#551	C₂²⋊C₄	1	4	yes	complemented
142	#551	C₂²⋊C₄	1	4	yes	complemented
143	D₄²	C₂²⋊C₄	1	1	yes	characteristic
144	D₄²	C₂²⋊C₄	1	2	yes	—
145	D₄²	C₂²⋊C₄	1	1	yes	characteristic
146	D₄²	C₂²⋊C₄	1	4	yes	complemented
147	#536	C₂²⋊C₄	1	2	yes	complemented
148	#536	C₂²⋊C₄	1	2	yes	complemented
149	#536	C₂²⋊C₄	1	1	yes	characteristic, complemented
150	#536	C₂²⋊C₄	1	1	yes	characteristic, complemented
151	#536	C₂²×C₄	1	2	yes	—
152	#536	C₂²×C₄	1	1	yes	characteristic
153	#536	C₂×D₄	1	2	yes	—
154	#536	C₂×D₄	1	1	yes	characteristic
155	#536	C₂×D₄	1	4	yes	—
156	#535	C₂²⋊C₄	1	2	yes	complemented
157	#535	C₂²⋊C₄	1	2	yes	complemented
158	#535	C₂²⋊C₄	1	1	yes	characteristic, complemented
159	#535	C₂²⋊C₄	1	1	yes	characteristic, complemented
160	#535	C₂²×C₄	1	2	yes	—
161	#535	C₂²×C₄	1	1	yes	characteristic
162	#535	C₂×D₄	1	2	yes	—
163	#535	C₂×D₄	1	1	yes	characteristic
164	#535	C₂×D₄	1	4	yes	—
165	#534	C₂×D₄	1	4	yes	—
166	#532	C₂²×C₄	1	1	yes	characteristic
167	#532	C₂²×C₄	1	1	yes	characteristic
168	#532	C₂×D₄	1	1	yes	characteristic
169	#532	C₂×D₄	1	1	yes	characteristic
170	#532	C₂×D₄	1	1	yes	characteristic
171	#532	C₂×D₄	1	1	yes	characteristic
172	#532	C₂×D₄	1	4	yes	—
173	#532	C₂×D₄	1	1	yes	characteristic
174	#532	C₂×D₄	1	1	yes	characteristic
175	#532	C₂×D₄	1	4	yes	—
176	C₂×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic, complemented
177	C₂×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
178	C₂×#127	C₂²⋊C₄	1	1	yes	characteristic, complemented
179	C₂×#127	C₂×D₄	1	1	yes	characteristic
180	C₂×#124	C₂²⋊C₄	1	1	yes	characteristic, complemented
181	C₂×#124	C₂²⋊C₄	1	1	yes	characteristic, complemented
182	C₂×#124	C₂×D₄	1	1	yes	characteristic
183	C₂×#124	C₂×D₄	1	1	yes	characteristic
184	#525	C₂²⋊C₄	1	2	yes	complemented
185	#525	C₂²⋊C₄	1	2	yes	complemented
186	#525	C₂²⋊C₄	1	2	yes	complemented
187	#525	C₂²⋊C₄	1	2	yes	complemented
188	#525	C₂²×C₄	1	2	yes	—
189	#525	C₂²×C₄	1	2	yes	—
190	#525	C₂×D₄	1	2	yes	—
191	#525	C₂×D₄	1	2	yes	—
192	#525	C₂×D₄	1	2	yes	—
193	#525	C₂×D₄	1	2	yes	—
194	#525	C₂×D₄	1	2	yes	—
195	#525	C₂×D₄	1	2	yes	—
196	#525	C₂×D₄	1	4	yes	—
197	C₂×#123	C₂×D₄	1	2	yes	—
198	C₂×#123	C₂×D₄	1	2	yes	—
199	C₂×#120	C₂×D₄	1	2	yes	—
200	C₂×#120	C₂×D₄	1	2	yes	—
201	#519	C₂²⋊C₄	1	2	yes	complemented
202	#519	C₂²⋊C₄	1	2	yes	complemented
203	#518	C₂²⋊C₄	1	2	yes	complemented
204	#518	C₂²⋊C₄	1	2	yes	complemented
205	C₄×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
206	C₄×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
207	C₄×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
208	C₄×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
209	C₂×#117	C₂×D₄	1	1	yes	characteristic
210	C₂×#117	C₂×D₄	1	2	yes	—
211	C₂×#117	C₂×D₄	1	2	yes	—
212	C₂²×C₄²	C₂×D₄	1	1	yes	characteristic
213	C₂⁵	#120	1	2	yes	—
214	C₂×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×#41	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×#41	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂×#41	#120	1	2	yes	—
221	C₂×#41	#120	1	2	yes	—
222	C₂×#41	#120	1	1	yes	characteristic
223	C₂×#41	#120	1	4	yes	—
224	C₂×#41	#120	1	1	yes	characteristic
225	C₂×#41	#120	1	2	yes	—
226	C₂×#41	#120	1	4	yes	—
227	C₂×#41	#120	1	2	yes	—
228	C₂×#41	#120	1	1	yes	characteristic
229	C₂×#41	#120	1	1	yes	characteristic
230	C₂×#41	C₂³×C₄	1	1	yes	characteristic
231	C₂×#41	C₂²×D₄	1	1	yes	characteristic
232	C₂×#41	C₂²×D₄	1	2	yes	—
233	C₂×#41	C₂²×D₄	1	2	yes	—
234	C₂×#41	C₂²×D₄	1	1	yes	characteristic
235	C₂×#41	C₂²×D₄	1	1	yes	characteristic
236	C₂²×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
237	C₂²×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂²×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
239	C₂²×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×Q₈	#120	1	1	yes	characteristic
241	C₂²×Q₈	#120	1	1	yes	characteristic
242	C₂²×Q₈	#120	1	2	yes	—
243	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
244	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
245	C₂²×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂²×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
248	C₂²×D₄	#120	1	1	yes	characteristic
249	C₂²×D₄	#120	1	1	yes	characteristic
250	C₂²×D₄	#120	1	2	yes	—
251	C₂²×D₄	#120	1	2	yes	—
252	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
253	C₂²×D₄	C₂²×D₄	1	2	yes	—
254	C₂³×C₄	C₂×C₂²⋊C₄	1	2	yes	—
255	C₂³×C₄	C₂×C₂²⋊C₄	1	2	yes	—
256	C₂³×C₄	#120	1	2	yes	—
257	C₂³×C₄	#120	1	2	yes	—
258	C₂³×C₄	#120	1	2	yes	—
259	C₂³×C₄	#120	1	2	yes	—
260	C₂³×C₄	C₂²×D₄	1	2	yes	—
261	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
262	C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₄⋊Q₈	C₂×C₂²⋊C₄	1	4	yes	—
265	C₄⋊Q₈	#120	1	1	yes	characteristic
266	C₄⋊Q₈	#120	1	1	yes	characteristic
267	C₄⋊Q₈	#120	1	4	yes	—
268	#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	#127	C₂×C₂²⋊C₄	1	4	yes	—
271	#127	#120	1	1	yes	characteristic
272	#127	#120	1	1	yes	characteristic
273	#127	#120	1	4	yes	—
274	#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	#124	C₂×C₂²⋊C₄	1	4	yes	—
277	#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	#124	C₂×C₂²⋊C₄	1	4	yes	—
280	#124	#120	1	1	yes	characteristic
281	#124	#120	1	1	yes	characteristic
282	#124	#120	1	4	yes	—
283	#124	#120	1	1	yes	characteristic
284	#124	#120	1	1	yes	characteristic
285	#124	#120	1	4	yes	—
286	#123	C₂×C₂²⋊C₄	1	2	yes	—
287	#123	C₂×C₂²⋊C₄	1	2	yes	—
288	#123	C₂×C₂²⋊C₄	1	2	yes	—
289	#123	C₂×C₂²⋊C₄	1	2	yes	—
290	#123	C₂×C₂²⋊C₄	1	4	yes	—
291	#123	#120	1	2	yes	—
292	#123	#120	1	2	yes	—
293	#123	#120	1	2	yes	—
294	#123	#120	1	2	yes	—
295	#123	#120	1	4	yes	—
296	#120	C₂×C₂²⋊C₄	1	2	yes	—
297	#120	C₂×C₂²⋊C₄	1	2	yes	—
298	#120	C₂×C₂²⋊C₄	1	2	yes	—
299	#120	C₂×C₂²⋊C₄	1	2	yes	—
300	#120	C₂×C₂²⋊C₄	1	4	yes	—
301	#120	#120	1	2	yes	—
302	#120	#120	1	2	yes	—
303	#120	#120	1	2	yes	—
304	#120	#120	1	2	yes	—
305	#120	#120	1	4	yes	—
306	#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	#117	C₂×C₂²⋊C₄	1	2	yes	—
309	#117	C₂×C₂²⋊C₄	1	2	yes	—
310	#117	C₂×C₂²⋊C₄	1	2	yes	—
311	#117	C₂×C₂²⋊C₄	1	2	yes	—
312	#117	#120	1	2	yes	—
313	#117	#120	1	2	yes	—
314	#117	#120	1	2	yes	—
315	#117	#120	1	4	yes	—
316	C₂×C₂²⋊C₄	#120	1	2	yes	—
317	C₂×C₂²⋊C₄	#120	1	2	yes	—
318	C₂×C₂²⋊C₄	#120	1	2	yes	—
319	C₂×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
320	C₂×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
321	C₂×C₄²	#120	1	1	yes	characteristic
322	C₂×C₄²	#120	1	1	yes	characteristic
323	C₂×C₄²	#120	1	4	yes	—
324	C₂×C₄²	#120	1	1	yes	characteristic
325	C₂×C₄²	#120	1	1	yes	characteristic
326	C₂⁴	#379	1	2	yes	—
327	C₂⁴	#379	1	2	yes	—
328	C₂⁴	#379	1	2	yes	—
329	C₂⁴	C₂×#120	1	2	yes	—
330	C₂⁴	C₂×#120	1	1	yes	characteristic
331	#41	B(4,𝔽₂)	1	2	yes	—
332	#41	#458	1	2	yes	—
333	C₂×Q₈	#379	1	2	yes	—
334	C₂×Q₈	#379	1	1	yes	characteristic
335	C₂×Q₈	#379	1	1	yes	characteristic
336	C₂×Q₈	#379	1	1	yes	characteristic
337	C₂×Q₈	#379	1	4	yes	—
338	C₂×Q₈	#379	1	1	yes	characteristic
339	C₂×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
340	C₂×Q₈	C₂×#120	1	2	yes	—
341	C₂×Q₈	C₂×#120	1	1	yes	characteristic
342	C₂×D₄	#379	1	2	yes	—
343	C₂×D₄	#379	1	1	yes	characteristic
344	C₂×D₄	#379	1	1	yes	characteristic
345	C₂×D₄	#379	1	1	yes	characteristic
346	C₂×D₄	#379	1	4	yes	—
347	C₂×D₄	#379	1	1	yes	characteristic
348	C₂×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
349	C₂×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
350	C₂×D₄	C₂×#120	1	2	yes	—
351	C₂×D₄	C₂×#120	1	2	yes	—
352	C₂×D₄	C₂×#120	1	2	yes	—
353	C₂×D₄	C₂×#120	1	1	yes	characteristic
354	C₂×D₄	C₂×#120	1	2	yes	—
355	C₂²×C₄	#379	1	2	yes	—
356	C₂²×C₄	#379	1	2	yes	—
357	C₂²×C₄	#379	1	2	yes	—
358	C₂²×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
359	C₂²×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
360	C₂²×C₄	C₂×#120	1	1	yes	characteristic
361	C₂²×C₄	C₂×#120	1	2	yes	—
362	C₂²×C₄	C₂×#120	1	1	yes	characteristic
363	C₂²×C₄	C₂×#120	1	1	yes	characteristic
364	C₂²×C₄	C₂×#120	1	1	yes	characteristic
365	C₂²×C₄	C₂×#120	1	2	yes	—
366	C₂²×C₄	C₂×#120	1	2	yes	—
367	C₂²×C₄	C₂×#120	1	2	yes	—
368	C₂²×C₄	C₂×#120	1	1	yes	characteristic
369	C₂²⋊C₄	#379	1	2	yes	—
370	C₂²⋊C₄	#379	1	2	yes	—
371	C₂²⋊C₄	#379	1	2	yes	—
372	C₂²⋊C₄	#379	1	2	yes	—
373	C₂²⋊C₄	#379	1	2	yes	—
374	C₂²⋊C₄	#379	1	2	yes	—
375	C₄²	#379	1	1	yes	characteristic
376	C₄²	#379	1	1	yes	characteristic
377	C₄²	#379	1	1	yes	characteristic
378	C₄²	#379	1	1	yes	characteristic
379	C₄²	#379	1	4	yes	—
380	C₄²	#379	1	4	yes	—
381	C₂³	C₂×#379	1	2	yes	—
382	C₂³	C₂×#379	1	1	yes	characteristic
383	C₂³	#2846	1	2	yes	—
384	C₂³	#2846	1	1	yes	characteristic
385	C₂³	#2846	1	1	yes	characteristic
386	Q₈	#1790	1	2	yes	—
387	D₄	#1790	1	2	yes	—
388	C₂×C₄	C₂×#379	1	1	yes	characteristic
389	C₂×C₄	C₂×#379	1	2	yes	—
390	C₂×C₄	C₂×#379	1	1	yes	characteristic
391	C₂×C₄	#2846	1	1	yes	characteristic
392	C₂×C₄	#2846	1	2	yes	—
393	C₂×C₄	#2846	1	1	yes	characteristic
394	C₂×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
395	C₂×C₄	C₂×#458	1	1	yes	characteristic
396	C₂×C₄	#3026	1	1	yes	characteristic
397	C₂×C₄	#3026	1	1	yes	characteristic
398	C₂²	#14679	1	1	yes	characteristic
399	C₂²	#32898	1	1	yes	characteristic
400	C₂²	#32900	1	1	yes	characteristic
401	C₄	C₂×#1790	1	1	yes	characteristic
402	C₄	#20609	1	1	yes	characteristic
403	C₄	#32898	1	1	yes	characteristic
404	C₄	#32900	1	1	yes	characteristic
405	C₂	#392125	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#32898
commutator	C₂×#41	C₂³×C₄
Frattini, cosocle	C₂²×#41	C₂⁴
socle	C₂	#392125
prime radical	#10586342	C₂
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#585 ◁ G
LECS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #493625	C₂	semidirect
3. #493605	C₂	semidirect
4. #493590	C₂	semidirect
5. C₂×#12765	C₂	semidirect
6. #493577	C₂	semidirect
7. #493561	C₂	semidirect
8. #493419	C₂	semidirect
9. #493410	C₂	semidirect
10. #359673	C₂	semidirect
11. #359649	C₂	semidirect
12. #63022	C₄	semidirect
13. #63021	C₄	semidirect
14. #63020	C₄	semidirect
15. #63017	C₄	semidirect
16. #63016	C₄	semidirect
17. #63011	C₄	semidirect
23. #60093	C₂²	semidirect
24. #33369	C₂²	semidirect
25. C₂×#2132	C₂²	semidirect
26. #33358	C₂²	semidirect
27. C₂×#2126	C₂²	semidirect
28. #33347	C₂²	semidirect
29. C₂×#2120	C₂²	semidirect
30. C₂×#2120	C₂²	semidirect
31. #21014	C₂²	semidirect
32. #21012	C₂²	semidirect
33. #20964	C₂²	semidirect
34. C₂×#1891	C₂²	semidirect
35. #20959	C₂²	semidirect
36. #20952	C₂²	semidirect
37. #20947	C₂²	semidirect
38. C₂×#1884	C₂²	semidirect
39. #20623	C₂²	semidirect
40. #20623	C₂²	semidirect
44. C₂×#568	C₂³	semidirect
94. #3428	C₂³	semidirect
96. C₂×#413	C₂³	semidirect
97. C₂×#413	C₂³	semidirect
98. C₂×#410	C₂³	semidirect
99. C₂×#410	C₂³	semidirect
100. C₂×2₋¹⁺⁴	C₂²⋊C₄	semidirect
101. C₂×2₋¹⁺⁴	C₂²⋊C₄	semidirect
105. C₂×H(5,𝔽₂)	C₂²⋊C₄	semidirect
106. C₂×H(5,𝔽₂)	C₂²⋊C₄	semidirect
110. C₂²×#41	C₂²⋊C₄	semidirect
111. C₂²×#41	C₂²⋊C₄	semidirect
120. C₂³×Q₈	C₂²⋊C₄	semidirect
121. C₂³×D₄	C₂²⋊C₄	semidirect
123. #563	C₂²⋊C₄	semidirect
124. #563	C₂²⋊C₄	semidirect
125. #563	C₂²⋊C₄	semidirect
126. H(3,𝔽₄)	C₂²⋊C₄	semidirect
127. H(3,𝔽₄)	C₂²⋊C₄	semidirect
128. #560	C₂²⋊C₄	semidirect
129. #560	C₂²⋊C₄	semidirect
133. #559	C₂²⋊C₄	semidirect
134. Q₈²	C₂²⋊C₄	semidirect
135. #555	C₂²⋊C₄	semidirect
136. #555	C₂²⋊C₄	semidirect
141. #551	C₂²⋊C₄	semidirect
142. #551	C₂²⋊C₄	semidirect
146. D₄²	C₂²⋊C₄	semidirect
147. #536	C₂²⋊C₄	semidirect
148. #536	C₂²⋊C₄	semidirect
149. #536	C₂²⋊C₄	semidirect
150. #536	C₂²⋊C₄	semidirect
156. #535	C₂²⋊C₄	semidirect
157. #535	C₂²⋊C₄	semidirect
158. #535	C₂²⋊C₄	semidirect
159. #535	C₂²⋊C₄	semidirect
176. C₂×C₄⋊Q₈	C₂²⋊C₄	semidirect
178. C₂×#127	C₂²⋊C₄	semidirect
180. C₂×#124	C₂²⋊C₄	semidirect
181. C₂×#124	C₂²⋊C₄	semidirect
184. #525	C₂²⋊C₄	semidirect
185. #525	C₂²⋊C₄	semidirect
186. #525	C₂²⋊C₄	semidirect
187. #525	C₂²⋊C₄	semidirect
201. #519	C₂²⋊C₄	semidirect
202. #519	C₂²⋊C₄	semidirect
203. #518	C₂²⋊C₄	semidirect
204. #518	C₂²⋊C₄	semidirect
205. C₄×#41	C₂²⋊C₄	semidirect
206. C₄×#41	C₂²⋊C₄	semidirect
207. C₄×#41	C₂²⋊C₄	semidirect
208. C₄×#41	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#10586342	2
#493625	2
#493605	2
#493590	2
C₂×#12765	2
#493577	2
#493561	2
#493419	2
#493410	2
#359673	2
#359649	2