Subgroups — #34440

Order 256.

1041 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542	C₂	1	1	yes	maximal, characteristic
2	#2383	C₂	1	1	yes	maximal, characteristic, complemented
3	#2379	C₂	1	1	yes	maximal, characteristic, complemented
4	#2379	C₂	1	1	yes	maximal, characteristic, complemented
5	#2377	C₂	1	1	yes	maximal, characteristic
6	#2374	C₂	1	1	yes	maximal, characteristic, complemented
7	#2373	C₂	1	1	yes	maximal, characteristic, complemented
8	#2372	C₂	1	1	yes	maximal, characteristic, complemented
9	#2368	C₂	1	1	yes	maximal, characteristic, complemented
10	#2367	C₂	1	1	yes	maximal, characteristic, complemented
11	#2364	C₂	1	1	yes	maximal, characteristic
12	#2362	C₂	1	1	yes	maximal, characteristic, complemented
13	#2359	C₂	1	1	yes	maximal, characteristic, complemented
14	#2356	C₂	1	1	yes	maximal, characteristic, complemented
15	#2355	C₂	1	1	yes	maximal, characteristic, complemented
16	#2346	C₂	1	1	yes	maximal, characteristic, complemented
17	#2343	C₂	1	1	yes	maximal, characteristic, complemented
18	#2337	C₂	1	1	yes	maximal, characteristic, complemented
19	#2335	C₂	1	1	yes	maximal, characteristic, complemented
20	#2334	C₂	1	1	yes	maximal, characteristic, complemented
21	#2334	C₂	1	1	yes	maximal, characteristic, complemented
22	#2332	C₂	1	1	yes	maximal, characteristic, complemented
23	#2332	C₂	1	1	yes	maximal, characteristic, complemented
24	#2331	C₂	1	1	yes	maximal, characteristic, complemented
25	#2329	C₂	1	1	yes	maximal, characteristic, complemented
26	#2327	C₂	1	1	yes	maximal, characteristic, complemented
27	#2326	C₂	1	1	yes	maximal, characteristic, complemented
28	#2318	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#123	C₂	1	1	yes	maximal, characteristic, complemented
31	#2290	C₂	1	1	yes	maximal, characteristic, complemented
32	#542	C₄	1	16	yes	complemented
33	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×#126	C₂²	1	1	yes	characteristic
35	C₂×#126	C₂²	1	1	yes	characteristic
36	C₂×#124	C₂²	1	1	yes	characteristic
37	C₂×#124	C₂²	1	1	yes	characteristic
38	C₂×#124	C₂²	1	1	yes	characteristic
39	C₂×#123	C₂²	1	1	yes	characteristic
40	C₂×#123	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×#121	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
51	C₂×#117	C₂²	1	1	yes	characteristic
52	C₂×#117	C₂²	1	1	yes	characteristic
53	C₂²×C₄²	C₂²	1	1	yes	characteristic
54	#391	C₂²	1	1	yes	characteristic
55	#391	C₂²	1	1	yes	characteristic
56	#391	C₂²	1	1	yes	characteristic
57	#391	C₂²	1	1	yes	characteristic
58	#391	C₂²	1	1	yes	characteristic
59	#391	C₂²	1	1	yes	characteristic
60	#391	C₂²	1	1	yes	characteristic
61	#391	C₂²	1	1	yes	characteristic
62	#391	C₂²	1	1	yes	characteristic
63	#391	C₂²	1	1	yes	characteristic
64	#390	C₂²	1	1	yes	characteristic
65	#390	C₂²	1	1	yes	characteristic
66	#389	C₂²	1	1	yes	characteristic
67	#389	C₂²	1	1	yes	characteristic
68	#389	C₂²	1	1	yes	characteristic
69	#389	C₂²	1	1	yes	characteristic
70	#389	C₂²	1	1	yes	characteristic
71	#389	C₂²	1	1	yes	characteristic
72	#388	C₂²	1	1	yes	characteristic
73	#388	C₂²	1	1	yes	characteristic
74	#388	C₂²	1	1	yes	characteristic
75	#388	C₂²	1	1	yes	characteristic
76	#388	C₂²	1	1	yes	characteristic
77	#388	C₂²	1	1	yes	characteristic
78	#388	C₂²	1	1	yes	characteristic
79	#388	C₂²	1	1	yes	characteristic
80	#388	C₂²	1	1	yes	characteristic
81	#388	C₂²	1	1	yes	characteristic
82	#388	C₂²	1	1	yes	characteristic
83	#388	C₂²	1	1	yes	characteristic
84	#388	C₂²	1	1	yes	characteristic
85	#388	C₂²	1	1	yes	characteristic
86	#388	C₂²	1	1	yes	characteristic
87	#388	C₂²	1	1	yes	characteristic
88	#388	C₂²	1	1	yes	characteristic
89	#388	C₂²	1	1	yes	characteristic
90	#388	C₂²	1	1	yes	characteristic
91	#388	C₂²	1	1	yes	characteristic
92	#388	C₂²	1	1	yes	characteristic
93	#388	C₂²	1	1	yes	characteristic
94	#388	C₂²	1	1	yes	characteristic
95	#388	C₂²	1	1	yes	characteristic
96	#387	C₂²	1	1	yes	characteristic
97	#387	C₂²	1	1	yes	characteristic
98	#387	C₂²	1	1	yes	characteristic
99	#387	C₂²	1	1	yes	characteristic
100	#387	C₂²	1	1	yes	characteristic
101	#387	C₂²	1	1	yes	characteristic
102	#387	C₂²	1	1	yes	characteristic
103	#387	C₂²	1	1	yes	characteristic
104	#387	C₂²	1	1	yes	characteristic
105	#387	C₂²	1	1	yes	characteristic
106	#387	C₂²	1	1	yes	characteristic
107	#387	C₂²	1	1	yes	characteristic
108	#387	C₂²	1	1	yes	characteristic
109	#387	C₂²	1	1	yes	characteristic
110	#387	C₂²	1	1	yes	characteristic
111	#387	C₂²	1	1	yes	characteristic
112	#387	C₂²	1	1	yes	characteristic
113	#387	C₂²	1	1	yes	characteristic
114	#387	C₂²	1	1	yes	characteristic
115	#387	C₂²	1	1	yes	characteristic
116	#387	C₂²	1	1	yes	characteristic
117	#387	C₂²	1	1	yes	characteristic
118	#387	C₂²	1	1	yes	characteristic
119	#387	C₂²	1	1	yes	characteristic
120	#386	C₂²	1	1	yes	characteristic
121	#386	C₂²	1	1	yes	characteristic
122	#386	C₂²	1	1	yes	characteristic
123	#386	C₂²	1	1	yes	characteristic
124	#386	C₂²	1	1	yes	characteristic
125	#386	C₂²	1	1	yes	characteristic
126	#386	C₂²	1	1	yes	characteristic
127	#386	C₂²	1	1	yes	characteristic
128	#385	C₂²	1	1	yes	characteristic
129	#385	C₂²	1	1	yes	characteristic
130	#385	C₂²	1	1	yes	characteristic
131	#385	C₂²	1	1	yes	characteristic
132	#385	C₂²	1	1	yes	characteristic
133	#385	C₂²	1	1	yes	characteristic
134	#385	C₂²	1	1	yes	characteristic
135	#385	C₂²	1	1	yes	characteristic
136	#385	C₂²	1	1	yes	characteristic
137	#385	C₂²	1	1	yes	characteristic
138	#385	C₂²	1	1	yes	characteristic
139	#385	C₂²	1	1	yes	characteristic
140	#385	C₂²	1	1	yes	characteristic
141	#385	C₂²	1	1	yes	characteristic
142	#384	C₂²	1	1	yes	characteristic
143	#383	C₂²	1	1	yes	characteristic
144	#383	C₂²	1	1	yes	characteristic
145	#382	C₂²	1	1	yes	characteristic
146	#382	C₂²	1	1	yes	characteristic
147	#382	C₂²	1	1	yes	characteristic
148	#382	C₂²	1	1	yes	characteristic
149	#382	C₂²	1	1	yes	characteristic
150	#381	C₂²	1	1	yes	characteristic
151	#381	C₂²	1	1	yes	characteristic
152	#380	C₂²	1	1	yes	characteristic
153	#380	C₂²	1	1	yes	characteristic
154	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
155	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
156	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
157	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
158	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
159	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
160	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
161	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
162	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
163	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
164	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
165	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
166	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
167	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
168	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
169	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
170	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
171	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
172	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
173	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
176	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
182	#376	C₂²	1	1	yes	characteristic
183	#376	C₂²	1	1	yes	characteristic
184	#376	C₂²	1	1	yes	characteristic
185	#376	C₂²	1	1	yes	characteristic
186	C₂×#95	C₂²	1	1	yes	characteristic
187	C₂×#95	C₂²	1	1	yes	characteristic
188	C₂²×Q₈	C₂³	1	1	yes	characteristic
189	C₂²×Q₈	C₂³	1	1	yes	characteristic
190	C₂²×Q₈	C₂³	1	1	yes	characteristic
191	C₂²×D₄	C₂³	1	1	yes	characteristic
192	C₂²×D₄	C₂³	1	1	yes	characteristic
193	C₂²×D₄	C₂³	1	1	yes	characteristic
194	C₂³×C₄	C₂³	1	1	yes	characteristic
195	C₂³×C₄	C₂³	1	1	yes	characteristic
196	C₂³×C₄	C₂³	1	1	yes	characteristic
197	C₂³×C₄	C₂³	1	1	yes	characteristic
198	C₂³×C₄	C₂³	1	1	yes	characteristic
199	C₂³×C₄	C₂³	1	1	yes	characteristic
200	C₂³×C₄	C₂³	1	1	yes	characteristic
201	C₂³×C₄	C₂³	1	1	yes	characteristic
202	C₂³×C₄	C₂³	1	1	yes	characteristic
203	C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
204	#126	C₂×C₄	1	8	yes	complemented
205	#126	C₂×C₄	1	8	yes	complemented
206	#124	C₂×C₄	1	8	yes	complemented
207	#124	C₂×C₄	1	8	yes	complemented
208	#124	C₂×C₄	1	8	yes	complemented
209	#123	C₂×C₄	1	8	yes	complemented
210	#123	C₂×C₄	1	8	yes	complemented
211	C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
212	C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
213	C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
214	#121	C₂×C₄	1	8	yes	—
215	C₄×Q₈	—	4	2	no	—
216	C₄×Q₈	—	4	2	no	—
217	C₄×Q₈	C₂×C₄	1	8	yes	complemented
218	C₄×D₄	—	4	2	no	—
219	C₄×D₄	—	4	2	no	—
220	C₄×D₄	C₂×C₄	1	8	yes	complemented
221	#117	—	4	2	no	—
222	#117	C₂×C₄	1	8	yes	complemented
223	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₄²	—	4	2	no	—
286	C₂×C₄²	C₂³	1	1	yes	characteristic
287	C₂×C₄²	C₂³	1	1	yes	characteristic
288	C₂×C₄²	C₂³	1	1	yes	characteristic
289	C₂×C₄²	C₂³	1	1	yes	characteristic
290	C₂×C₄²	C₂³	1	1	yes	characteristic
291	C₂×C₄²	C₂³	1	1	yes	characteristic
292	C₂×C₄²	C₂³	1	1	yes	characteristic
293	C₂×C₄²	C₂³	1	1	yes	characteristic
294	C₂×C₄²	C₂³	1	1	yes	characteristic
295	C₂×C₄²	C₂³	1	1	yes	characteristic
296	C₂×C₄²	C₂³	1	1	yes	characteristic
297	C₂×C₄²	C₂³	1	1	yes	characteristic
298	C₂×C₄²	C₂³	1	1	yes	characteristic
299	C₂×C₄²	C₂³	1	1	yes	characteristic
300	C₂×C₄²	C₂³	1	1	yes	characteristic
301	C₂×C₄²	C₂³	1	1	yes	characteristic
302	C₂×C₄²	C₂³	1	1	yes	characteristic
303	C₂×C₄²	C₂³	1	1	yes	characteristic
304	C₂×C₄²	C₂³	1	1	yes	characteristic
305	C₂×C₄²	C₂³	1	1	yes	characteristic
306	C₂×C₄²	C₂³	1	1	yes	characteristic
307	C₂×C₄²	C₂³	1	1	yes	characteristic
308	C₂×C₄²	C₂³	1	1	yes	characteristic
309	C₂×C₄²	C₂³	1	1	yes	characteristic
310	C₂×C₄²	C₂³	1	1	yes	characteristic
311	C₂×C₄²	C₂³	1	1	yes	characteristic
312	#95	C₂³	1	1	yes	characteristic
313	#95	C₂³	1	1	yes	characteristic
314	#95	C₂³	1	1	yes	characteristic
315	#95	C₂³	1	1	yes	characteristic
316	#95	C₂³	1	1	yes	characteristic
317	#95	C₂³	1	1	yes	characteristic
318	#95	C₂³	1	1	yes	characteristic
319	#95	C₂³	1	1	yes	characteristic
320	#95	C₂³	1	1	yes	characteristic
321	#95	C₂³	1	1	yes	characteristic
322	#95	C₂³	1	1	yes	characteristic
323	#95	C₂³	1	1	yes	characteristic
324	#95	C₂³	1	1	yes	characteristic
325	#95	C₂³	1	1	yes	characteristic
326	#95	C₂³	1	1	yes	characteristic
327	#95	C₂³	1	1	yes	characteristic
328	#95	C₂³	1	1	yes	characteristic
329	#95	C₂³	1	1	yes	characteristic
330	#95	C₂³	1	1	yes	characteristic
331	#95	C₂³	1	1	yes	characteristic
332	#95	C₂³	1	1	yes	characteristic
333	#95	C₂³	1	1	yes	characteristic
334	#95	C₂³	1	1	yes	characteristic
335	#95	C₂³	1	1	yes	characteristic
336	#95	C₂³	1	1	yes	characteristic
337	#95	C₂³	1	1	yes	characteristic
338	#95	C₂³	1	1	yes	characteristic
339	#95	C₂³	1	1	yes	characteristic
340	#95	C₂³	1	1	yes	characteristic
341	#95	C₂³	1	1	yes	characteristic
342	#95	C₂³	1	1	yes	characteristic
343	#95	C₂³	1	1	yes	characteristic
344	#95	C₂³	1	1	yes	characteristic
345	#95	C₂³	1	1	yes	characteristic
346	#95	C₂³	1	1	yes	characteristic
347	#95	C₂³	1	1	yes	characteristic
348	#95	C₂³	1	1	yes	characteristic
349	#95	C₂³	1	1	yes	characteristic
350	#95	C₂³	1	1	yes	characteristic
351	#95	C₂³	1	1	yes	characteristic
352	#95	C₂³	1	1	yes	characteristic
353	#95	C₂³	1	1	yes	characteristic
354	#95	C₂³	1	1	yes	characteristic
355	#95	C₂³	1	1	yes	characteristic
356	#95	C₂³	1	1	yes	characteristic
357	#95	C₂³	1	1	yes	characteristic
358	#95	C₂³	1	1	yes	characteristic
359	#95	C₂³	1	1	yes	characteristic
360	#95	C₂³	1	1	yes	characteristic
361	#95	C₂³	1	1	yes	characteristic
362	#95	C₂³	1	1	yes	characteristic
363	#95	C₂³	1	1	yes	characteristic
364	C₂⁴	C₂⁴	1	1	yes	characteristic
365	C₂⁴	C₂⁴	1	1	yes	characteristic
366	C₂⁴	C₂⁴	1	1	yes	characteristic
367	C₂×Q₈	—	4	1	no	—
368	C₂×Q₈	—	4	1	no	—
369	C₂×Q₈	—	4	1	no	—
370	C₂×Q₈	—	4	1	no	—
371	C₂×Q₈	—	4	1	no	—
372	C₂×Q₈	—	4	1	no	—
373	C₂×Q₈	C₂²×C₄	1	4	yes	—
374	C₂×Q₈	C₂²×C₄	1	4	yes	—
375	C₂×Q₈	C₂²×C₄	1	4	yes	—
376	C₂×D₄	—	4	1	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	—	4	1	no	—
379	C₂×D₄	—	4	1	no	—
380	C₂×D₄	—	4	1	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	C₂²×C₄	1	4	yes	—
383	C₂×D₄	C₂²×C₄	1	4	yes	—
384	C₂×D₄	C₂²×C₄	1	4	yes	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	—	4	1	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	—	4	1	no	—
397	C₂²×C₄	—	4	1	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	—	4	1	no	—
402	C₂²×C₄	—	4	1	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	—	4	1	no	—
405	C₂²×C₄	—	4	1	no	—
406	C₂²×C₄	—	4	1	no	—
407	C₂²×C₄	—	4	1	no	—
408	C₂²×C₄	—	4	1	no	—
409	C₂²×C₄	C₂²×C₄	1	4	yes	—
410	C₂²×C₄	C₂²×C₄	1	4	yes	—
411	C₂²×C₄	C₂²×C₄	1	4	yes	—
412	C₂²×C₄	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	4	1	no	—
444	C₄⋊C₄	—	4	1	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₄⋊C₄	—	4	1	no	—
447	C₄⋊C₄	—	4	1	no	—
448	C₄⋊C₄	—	4	1	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₄⋊C₄	—	4	1	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	C₂²×C₄	1	4	yes	—
463	C₄⋊C₄	C₂²×C₄	1	4	yes	—
464	C₄⋊C₄	C₂²×C₄	1	4	yes	—
465	C₄⋊C₄	C₂²×C₄	1	4	yes	—
466	C₄⋊C₄	C₂²×C₄	1	4	yes	—
467	C₄⋊C₄	C₂²×C₄	1	4	yes	—
468	C₄⋊C₄	C₂²×C₄	1	4	yes	—
469	C₄⋊C₄	C₂²×C₄	1	4	yes	—
470	C₄⋊C₄	C₂²×C₄	1	4	yes	—
471	C₄⋊C₄	C₂²×C₄	1	4	yes	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₂²⋊C₄	—	4	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
491	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
492	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
493	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
494	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
495	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
496	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
497	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
498	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
499	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
500	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
501	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	2	2	no	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	4	1	no	—
508	C₄²	—	4	1	no	—
509	C₄²	—	4	1	no	—
510	C₄²	—	4	1	no	—
511	C₄²	—	4	1	no	—
512	C₄²	—	4	1	no	—
513	C₄²	—	4	1	no	—
514	C₄²	—	4	1	no	—
515	C₄²	—	4	1	no	—
516	C₄²	—	4	1	no	—
517	C₄²	—	4	1	no	—
518	C₄²	—	4	1	no	—
519	C₄²	—	4	1	no	—
520	C₄²	—	4	1	no	—
521	C₄²	—	4	1	no	—
522	C₄²	—	4	1	no	—
523	C₄²	—	4	1	no	—
524	C₄²	C₂²×C₄	1	4	yes	—
525	C₄²	C₂²×C₄	1	4	yes	—
526	C₄²	C₂²×C₄	1	4	yes	—
527	C₄²	C₂²×C₄	1	4	yes	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	C₂³×C₄	1	2	yes	—
547	C₂³	C₂³×C₄	1	2	yes	—
548	C₂³	C₂³×C₄	1	2	yes	—
549	C₂³	C₂⁵	1	1	yes	characteristic
550	Q₈	—	4	4	no	—
551	Q₈	—	4	4	no	—
552	Q₈	—	4	4	no	—
553	D₄	—	4	4	no	—
554	D₄	—	4	4	no	—
555	D₄	—	4	4	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	4	4	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	4	4	no	—
631	C₂×C₄	—	8	2	no	—
632	C₂×C₄	—	8	2	no	—
633	C₂×C₄	—	8	2	no	—
634	C₂×C₄	—	8	2	no	—
635	C₂×C₄	C₂³×C₄	1	2	yes	—
636	C₂×C₄	C₂³×C₄	1	2	yes	—
637	C₂×C₄	C₂³×C₄	1	2	yes	—
638	C₂×C₄	C₂³×C₄	1	2	yes	—
639	C₂×C₄	C₂³×C₄	1	2	yes	—
640	C₂×C₄	C₂³×C₄	1	2	yes	—
641	C₂×C₄	C₂³×C₄	1	2	yes	—
642	C₂×C₄	C₂³×C₄	1	2	yes	—
643	C₂×C₄	C₂³×C₄	1	2	yes	—
644	C₂×C₄	C₂³×C₄	1	2	yes	—
645	C₂×C₄	C₂³×C₄	1	2	yes	—
646	C₂×C₄	C₂³×C₄	1	2	yes	—
647	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
648	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	C₂⁴×C₄	1	1	yes	characteristic
671	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
672	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
673	C₂²	#585	1	1	yes	characteristic
674	C₂²	#585	1	1	yes	characteristic
675	C₂²	#585	1	1	yes	characteristic
676	C₂²	#585	1	1	yes	characteristic
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	2	no	—
690	C₄	—	2	2	no	—
691	C₄	—	4	1	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	1	no	—
705	C₂	—	4	2	no	—
706	C₂	—	4	2	no	—
707	C₂	—	4	2	no	—
708	C₂	#3428	1	1	yes	characteristic
709	C₂	C₄×H(5,𝔽₂)	1	1	yes	characteristic
710	C₂	C₄×2₋¹⁺⁴	1	1	yes	characteristic
711	C₂	#3535	1	1	yes	characteristic
712	C₂	#3540	1	1	yes	characteristic
713	C₂	#3565	1	1	yes	characteristic
714	C₂	#3566	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle, cosocle	C₂³	C₂⁵
commutator	C₂²	C₂⁴×C₄
prime radical	C₂×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #2383	C₂	semidirect
3. #2379	C₂	semidirect
4. #2379	C₂	semidirect
6. #2374	C₂	semidirect
7. #2373	C₂	semidirect
8. #2372	C₂	semidirect
9. #2368	C₂	semidirect
10. #2367	C₂	semidirect
12. #2362	C₂	semidirect
13. #2359	C₂	semidirect
14. #2356	C₂	semidirect
15. #2355	C₂	semidirect
16. #2346	C₂	semidirect
17. #2343	C₂	semidirect
18. #2337	C₂	semidirect
19. #2335	C₂	semidirect
20. #2334	C₂	semidirect
21. #2334	C₂	semidirect
22. #2332	C₂	semidirect
23. #2332	C₂	semidirect
24. #2331	C₂	semidirect
25. #2329	C₂	semidirect
26. #2327	C₂	semidirect
27. #2326	C₂	semidirect
28. #2318	C₂	semidirect
29. C₄×C₂²⋊Q₈	C₂	semidirect
30. C₄×#123	C₂	semidirect
31. #2290	C₂	semidirect
32. #542	C₄	semidirect
203. C₄⋊Q₈	C₂×C₄	semidirect
204. #126	C₂×C₄	semidirect
205. #126	C₂×C₄	semidirect
206. #124	C₂×C₄	semidirect
207. #124	C₂×C₄	semidirect
208. #124	C₂×C₄	semidirect
209. #123	C₂×C₄	semidirect
210. #123	C₂×C₄	semidirect
211. C₂²⋊Q₈	C₂×C₄	semidirect
212. C₂²⋊Q₈	C₂×C₄	semidirect
213. C₂²⋊Q₈	C₂×C₄	semidirect
217. C₄×Q₈	C₂×C₄	semidirect
220. C₄×D₄	C₂×C₄	semidirect
222. #117	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#542	2
#2383	2
#2379	2
#2377	2
#2374	2
#2373	2
#2372	2
#2368	2
#2367	2
#2364	2
#2362	2
#2359	2
#2356	2
#2355	2
#2346	2
#2343	2
#2337	2
#2335	2
#2334	2
#2332	2
#2331	2
#2329	2
#2327	2
#2326	2
#2318	2
C₄×C₂²⋊Q₈	2
C₄×#123	2
#2290	2