Subgroups — #7624825

Order 512.

1278 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62267	C₂	1	2	yes	maximal, complemented
2	#33909	C₂	1	1	yes	maximal, characteristic, complemented
3	#33906	C₂	1	1	yes	maximal, characteristic, complemented
4	#33905	C₂	1	1	yes	maximal, characteristic, complemented
5	#33903	C₂	1	1	yes	maximal, characteristic, complemented
6	#33887	C₂	1	2	yes	maximal, complemented
7	#33883	C₂	1	2	yes	maximal, complemented
8	#33882	C₂	1	2	yes	maximal, complemented
9	#33880	C₂	1	2	yes	maximal, complemented
10	D₄×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	#33851	C₂	1	1	yes	maximal, characteristic, complemented
12	#33851	C₂	1	1	yes	maximal, characteristic, complemented
13	#33849	C₂	1	1	yes	maximal, characteristic, complemented
14	#33824	C₂	1	2	yes	maximal, complemented
15	#33767	C₂	1	2	yes	maximal, complemented
16	#33762	C₂	1	2	yes	maximal, complemented
17	#33741	C₂	1	1	yes	maximal, characteristic, complemented
18	#33739	C₂	1	1	yes	maximal, characteristic, complemented
19	#33610	C₂	1	1	yes	maximal, characteristic, complemented
20	#33608	C₂	1	1	yes	maximal, characteristic, complemented
21	#33600	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#2216	C₂	1	1	yes	maximal, characteristic, complemented
23	#33432	C₂	1	1	yes	maximal, characteristic, complemented
24	#3541	—	2	2	no	—
25	C₂×#508	C₂²	1	1	yes	characteristic
26	C₂×#508	C₂²	1	1	yes	characteristic, complemented
27	C₂²×Q₃₂	C₂²	1	1	yes	characteristic
28	C₂²×Q₃₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×#504	C₂²	1	1	yes	characteristic
30	C₂³×C₁₆	C₂²	1	1	yes	characteristic
31	#3342	C₂²	1	2	yes	—
32	#3339	C₂²	1	2	yes	—
33	#3338	C₂²	1	2	yes	—
34	#3336	C₂²	1	2	yes	—
35	#3320	—	2	2	no	—
36	#3316	—	2	2	no	—
37	#3315	—	2	2	no	—
38	#3313	—	2	2	no	—
39	D₄×Q₁₆	C₂²	1	2	yes	—
40	#3285	C₂²	1	2	yes	—
41	#3285	C₂²	1	2	yes	—
42	#3283	C₂²	1	2	yes	—
43	#3258	—	2	2	no	—
44	#3201	—	2	2	no	—
45	#3196	—	2	2	no	—
46	#3177	C₂²	1	2	yes	—
47	#3175	C₂²	1	2	yes	—
48	#3061	C₂²	1	2	yes	—
49	#3059	C₂²	1	2	yes	—
50	#3050	C₂²	1	2	yes	—
51	C₂×#467	C₂²	1	2	yes	—
52	#2929	C₂²	1	1	yes	characteristic
53	#2253	C₂²	1	1	yes	characteristic, complemented
54	#2252	C₂²	1	1	yes	characteristic, complemented
55	#2249	C₂²	1	1	yes	characteristic, complemented
56	#2247	C₂²	1	1	yes	characteristic, complemented
57	#2245	C₂²	1	2	yes	complemented
58	#2243	C₂²	1	2	yes	complemented
59	#2237	C₂²	1	2	yes	—
60	#2237	C₂²	1	2	yes	—
61	#2237	C₂²	1	2	yes	complemented
62	#2236	C₂²	1	2	yes	—
63	#2236	C₂²	1	2	yes	complemented
64	#2235	C₂²	1	2	yes	complemented
65	#2234	C₂²	1	2	yes	complemented
66	#2233	C₂²	1	2	yes	—
67	#2229	C₂²	1	2	yes	complemented
68	#2228	C₂²	1	2	yes	complemented
69	#2227	C₂²	1	2	yes	complemented
70	#2225	C₂²	1	2	yes	complemented
71	#2220	C₂²	1	2	yes	—
72	#2220	C₂²	1	2	yes	—
73	#2220	C₂²	1	2	yes	complemented
74	#2219	C₂²	1	2	yes	—
75	#2219	C₂²	1	2	yes	—
76	#2219	C₂²	1	2	yes	complemented
77	#2217	C₂²	1	2	yes	—
78	#2217	C₂²	1	2	yes	—
79	#2216	C₂²	1	2	yes	—
80	#2216	C₂²	1	1	yes	characteristic
81	#2216	C₂²	1	1	yes	characteristic
82	#2216	C₂²	1	1	yes	characteristic
83	#2216	C₂²	1	1	yes	characteristic
84	#2216	C₂²	1	1	yes	characteristic
85	#2216	C₂²	1	2	yes	—
86	#2216	C₂²	1	1	yes	characteristic
87	#2216	C₂²	1	1	yes	characteristic, complemented
88	#2216	C₂²	1	1	yes	characteristic, complemented
89	#2216	C₂²	1	1	yes	characteristic, complemented
90	#2215	C₂²	1	1	yes	characteristic
91	#2215	C₂²	1	1	yes	characteristic
92	#2215	C₂²	1	1	yes	characteristic, complemented
93	#2211	C₂²	1	2	yes	complemented
94	#2211	C₂²	1	2	yes	complemented
95	#2209	C₂²	1	2	yes	complemented
96	#2208	C₂²	1	2	yes	complemented
97	#2189	C₂²	1	2	yes	—
98	#2189	C₂²	1	2	yes	—
99	#2189	C₂²	1	2	yes	complemented
100	#2189	C₂²	1	2	yes	complemented
101	#2188	C₂²	1	2	yes	—
102	#2188	C₂²	1	2	yes	complemented
103	#2185	C₂²	1	2	yes	—
104	#2185	C₂²	1	2	yes	complemented
105	#2176	C₂²	1	2	yes	complemented
106	#2175	C₂²	1	2	yes	complemented
107	C₄×Q₃₂	C₂²	1	1	yes	characteristic, complemented
108	C₄×Q₃₂	C₂²	1	1	yes	characteristic, complemented
109	C₄×Q₃₂	C₂²	1	1	yes	characteristic, complemented
110	C₄×D₁₆	C₂²	1	1	yes	characteristic, complemented
111	#2168	C₂²	1	1	yes	characteristic
112	#2168	C₂²	1	1	yes	characteristic
113	#2168	C₂²	1	1	yes	characteristic
114	#2168	C₂²	1	1	yes	characteristic
115	D₄×C₁₆	C₂²	1	1	yes	characteristic
116	D₄×C₁₆	C₂²	1	1	yes	characteristic
117	D₄×C₁₆	C₂²	1	1	yes	characteristic
118	D₄×C₁₆	C₂²	1	1	yes	characteristic
119	#2158	C₂²	1	1	yes	characteristic
120	#2158	C₂²	1	1	yes	characteristic, complemented
121	C₂×#366	C₂²	1	1	yes	characteristic
122	C₂×#366	C₂²	1	1	yes	characteristic, complemented
123	#2151	C₂²	1	1	yes	characteristic
124	#2141	C₂²	1	2	yes	complemented
125	#2139	C₂²	1	2	yes	complemented
126	#2138	C₂²	1	2	yes	—
127	C₂×#358	C₂²	1	2	yes	—
128	#2113	C₂²	1	1	yes	characteristic
129	#2112	C₂²	1	1	yes	characteristic
130	#2108	C₂²	1	1	yes	characteristic
131	C₂×#135	C₂³	1	2	yes	—
132	C₂×#135	C₂³	1	2	yes	—
133	C₂²×Q₁₆	C₂³	1	2	yes	—
134	C₂²×Q₁₆	C₂³	1	2	yes	—
135	C₂×#131	C₂³	1	1	yes	characteristic
136	C₂³×C₈	C₂³	1	1	yes	characteristic
137	#563	—	4	2	no	—
138	#562	—	4	2	no	—
139	#556	—	2	2	no	—
140	#554	—	2	2	no	—
141	#554	—	4	2	no	—
142	#553	—	2	2	no	—
143	#553	—	4	2	no	—
144	#552	—	2	2	no	—
145	D₄×Q₈	—	2	2	no	—
146	#548	—	2	2	no	—
147	#548	—	2	2	no	—
148	#547	—	2	2	no	—
149	#542	—	2	2	no	—
150	#542	—	4	2	no	—
151	#541	—	2	2	no	—
152	#539	—	4	2	no	—
153	#538	—	4	2	no	—
154	#538	—	4	2	no	—
155	#537	—	2	2	no	—
156	#536	—	2	2	no	—
157	#525	—	2	2	no	—
158	#525	D₄	1	1	yes	characteristic
159	C₂×C₂²⋊Q₈	—	2	2	no	—
160	#508	—	4	2	no	—
161	#508	—	4	2	no	—
162	C₂×Q₃₂	—	4	2	no	—
163	C₂×Q₃₂	—	4	2	no	—
164	C₂×Q₃₂	C₂³	1	1	yes	characteristic
165	C₂×Q₃₂	C₂³	1	1	yes	characteristic
166	C₂×Q₃₂	C₂³	1	1	yes	characteristic
167	C₂×Q₃₂	C₂³	1	2	yes	—
168	C₂×Q₃₂	C₂³	1	2	yes	—
169	C₂×Q₃₂	C₂³	1	2	yes	—
170	C₂×SD₃₂	C₂³	1	2	yes	—
171	C₂×SD₃₂	C₂³	1	2	yes	—
172	C₂×SD₃₂	C₂³	1	2	yes	—
173	C₂×D₁₆	C₂³	1	1	yes	characteristic
174	#504	—	4	2	no	—
175	C₂×M₃₂	C₂³	1	1	yes	characteristic
176	C₂×M₃₂	C₂³	1	1	yes	characteristic
177	C₂×M₃₂	C₂³	1	1	yes	characteristic
178	C₂×M₃₂	C₂³	1	1	yes	characteristic
179	C₂²×C₁₆	—	4	2	no	—
180	C₂²×C₁₆	C₂³	1	1	yes	characteristic
181	C₂²×C₁₆	C₂³	1	1	yes	characteristic
182	C₂²×C₁₆	C₂³	1	1	yes	characteristic
183	C₂²×C₁₆	C₂³	1	1	yes	characteristic
184	C₂²×C₁₆	C₂³	1	1	yes	characteristic
185	C₂²×C₁₆	C₂³	1	1	yes	characteristic
186	C₂²×C₁₆	C₂³	1	1	yes	characteristic
187	C₂²×C₁₆	C₂³	1	1	yes	characteristic
188	#500	C₂³	1	2	yes	—
189	#499	C₂³	1	2	yes	—
190	#495	C₂³	1	2	yes	—
191	#494	C₂³	1	2	yes	—
192	#491	—	2	2	no	—
193	#489	—	2	2	no	—
194	#485	—	2	2	no	—
195	#485	—	2	2	no	—
196	#485	—	2	2	no	—
197	#484	—	2	2	no	—
198	#484	—	2	2	no	—
199	#483	—	2	2	no	—
200	#482	—	2	2	no	—
201	#481	—	2	2	no	—
202	#479	—	2	2	no	—
203	#478	—	2	2	no	—
204	#477	—	2	2	no	—
205	#475	—	2	2	no	—
206	#470	—	2	2	no	—
207	#470	—	2	2	no	—
208	#470	—	2	2	no	—
209	#468	—	2	2	no	—
210	#468	—	2	2	no	—
211	#468	—	2	2	no	—
212	#467	—	2	2	no	—
213	#467	—	2	2	no	—
214	#467	C₂³	1	2	yes	—
215	#467	C₂³	1	2	yes	—
216	#467	C₂³	1	2	yes	—
217	#467	C₂³	1	2	yes	—
218	#467	C₂³	1	2	yes	—
219	#467	C₂³	1	2	yes	—
220	#467	C₂³	1	2	yes	—
221	#467	C₂³	1	2	yes	—
222	#467	C₂³	1	2	yes	—
223	#466	C₂³	1	2	yes	—
224	#466	C₂³	1	2	yes	—
225	#466	C₂³	1	2	yes	—
226	#465	—	2	2	no	—
227	#465	—	2	2	no	—
228	#464	—	2	2	no	—
229	#464	—	2	2	no	—
230	#462	—	2	2	no	—
231	#461	—	2	2	no	—
232	#452	—	2	2	no	—
233	#452	—	2	2	no	—
234	#452	—	2	2	no	—
235	#452	—	2	2	no	—
236	#451	—	2	2	no	—
237	#451	—	2	2	no	—
238	#448	—	2	2	no	—
239	#448	—	2	2	no	—
240	#441	—	2	2	no	—
241	#440	—	2	2	no	—
242	C₄×Q₁₆	C₂³	1	2	yes	—
243	C₄×Q₁₆	C₂³	1	2	yes	—
244	C₄×Q₁₆	C₂³	1	2	yes	—
245	C₄×D₈	C₂³	1	2	yes	—
246	#435	D₄	1	1	yes	characteristic
247	#435	D₄	1	1	yes	characteristic
248	#435	D₄	1	1	yes	characteristic
249	#435	D₄	1	1	yes	characteristic
250	C₈×D₄	C₂³	1	1	yes	characteristic
251	C₈×D₄	C₂³	1	1	yes	characteristic
252	C₈×D₄	C₂³	1	1	yes	characteristic
253	C₈×D₄	C₂³	1	1	yes	characteristic
254	#427	C₂³	1	2	yes	—
255	#427	C₂³	1	2	yes	—
256	C₂×#107	C₂³	1	2	yes	—
257	C₂×#107	C₂³	1	2	yes	—
258	#424	D₄	1	1	yes	characteristic
259	#419	—	2	2	no	—
260	#417	—	2	2	no	—
261	#416	—	2	2	no	—
262	C₂×#103	—	2	2	no	—
263	#408	D₄	1	1	yes	characteristic
264	#407	D₄	1	1	yes	characteristic
265	#405	C₂³	1	1	yes	characteristic
266	#367	C₂³	1	2	yes	—
267	#367	C₂³	1	2	yes	—
268	#367	C₂³	1	2	yes	—
269	#366	C₂³	1	1	yes	characteristic
270	#366	C₂³	1	1	yes	characteristic
271	#366	C₂³	1	2	yes	—
272	#366	C₂³	1	1	yes	characteristic
273	#366	C₂³	1	2	yes	—
274	#366	C₂³	1	1	yes	characteristic
275	#366	C₂³	1	2	yes	—
276	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
277	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
278	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
279	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
280	#358	C₂³	1	2	yes	—
281	#358	C₂³	1	2	yes	—
282	#358	C₂³	1	2	yes	—
283	#358	C₂³	1	2	yes	—
284	#358	C₂³	1	2	yes	—
285	#358	C₂³	1	2	yes	—
286	#358	C₂³	1	2	yes	—
287	#358	C₂³	1	2	yes	—
288	#358	C₂³	1	2	yes	—
289	#358	C₂³	1	2	yes	—
290	#358	C₂³	1	2	yes	—
291	#358	C₂³	1	2	yes	—
292	#357	C₂³	1	2	yes	—
293	#357	C₂³	1	2	yes	—
294	#357	C₂³	1	2	yes	—
295	#357	C₂³	1	2	yes	—
296	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
297	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
298	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
299	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
300	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
301	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
302	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
303	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
304	#346	C₂³	1	1	yes	characteristic
305	#346	C₂³	1	1	yes	characteristic
306	C₄×C₁₆	C₂³	1	1	yes	characteristic
307	C₄×C₁₆	C₂³	1	1	yes	characteristic
308	C₂×#41	—	2	2	no	—
309	C₂×#41	—	2	2	no	—
310	C₂×#41	C₂×D₄	1	1	yes	characteristic
311	C₂²×Q₈	—	2	2	no	—
312	C₂²×Q₈	—	2	2	no	—
313	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
314	#135	—	4	2	no	—
315	#135	—	4	2	no	—
316	#135	—	4	2	no	—
317	#135	—	4	2	no	—
318	C₂×Q₁₆	—	2	2	no	—
319	C₂×Q₁₆	—	2	2	no	—
320	C₂×Q₁₆	—	2	2	no	—
321	C₂×Q₁₆	—	4	2	no	—
322	C₂×Q₁₆	—	4	2	no	—
323	C₂×Q₁₆	—	4	2	no	—
324	C₂×Q₁₆	—	4	2	no	—
325	C₂×Q₁₆	C₂⁴	1	2	yes	—
326	C₂×Q₁₆	C₂⁴	1	2	yes	—
327	C₂×Q₁₆	C₂⁴	1	2	yes	—
328	C₂×SD₁₆	—	2	2	no	—
329	C₂×SD₁₆	—	2	2	no	—
330	C₂×SD₁₆	—	2	2	no	—
331	C₂×D₈	C₂⁴	1	2	yes	—
332	#131	—	4	1	no	—
333	#131	—	4	1	no	—
334	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
335	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
336	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
337	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₈	—	4	1	no	—
339	C₂²×C₈	—	4	1	no	—
340	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₈	C₂⁴	1	1	yes	characteristic
344	C₂²×C₈	C₂⁴	1	1	yes	characteristic
345	C₂²×C₈	C₂⁴	1	1	yes	characteristic
346	C₂²×C₈	C₂⁴	1	1	yes	characteristic
347	C₂²×C₈	C₂⁴	1	1	yes	characteristic
348	C₄⋊Q₈	—	2	2	no	—
349	C₄⋊Q₈	—	2	2	no	—
350	C₄⋊Q₈	—	4	2	no	—
351	C₄⋊Q₈	—	4	2	no	—
352	#126	—	4	2	no	—
353	#126	—	4	2	no	—
354	#126	—	4	2	no	—
355	#126	—	4	2	no	—
356	#126	—	4	2	no	—
357	#126	—	4	2	no	—
358	#126	—	4	2	no	—
359	#125	—	2	2	no	—
360	#125	—	4	2	no	—
361	#125	—	4	2	no	—
362	#125	—	4	2	no	—
363	#125	—	4	2	no	—
364	#124	—	2	2	no	—
365	#124	—	4	2	no	—
366	#124	—	4	2	no	—
367	#124	—	4	2	no	—
368	#124	—	4	2	no	—
369	#124	—	4	2	no	—
370	#123	—	4	2	no	—
371	#123	—	4	2	no	—
372	#123	—	4	2	no	—
373	#123	—	4	2	no	—
374	#123	—	4	2	no	—
375	#123	—	4	2	no	—
376	#123	—	4	2	no	—
377	#123	—	4	2	no	—
378	#123	D₈	1	1	yes	characteristic
379	#123	D₈	1	1	yes	characteristic
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	—	2	2	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	—	4	2	no	—
390	C₂²⋊Q₈	—	4	2	no	—
391	C₂²⋊Q₈	—	4	2	no	—
392	C₂²⋊Q₈	—	4	2	no	—
393	C₂²⋊Q₈	—	4	2	no	—
394	C₂²⋊Q₈	—	4	2	no	—
395	C₂²⋊Q₈	—	4	2	no	—
396	C₂²⋊Q₈	—	4	2	no	—
397	C₂²⋊Q₈	—	4	2	no	—
398	C₂²⋊Q₈	—	4	2	no	—
399	C₂²⋊Q₈	D₈	1	1	yes	characteristic
400	C₂²⋊Q₈	D₈	1	1	yes	characteristic
401	#121	—	2	2	no	—
402	#121	—	2	2	no	—
403	#121	—	2	2	no	—
404	#121	—	4	2	no	—
405	#121	—	4	2	no	—
406	#121	—	4	2	no	—
407	#121	—	4	2	no	—
408	#121	—	4	2	no	—
409	#121	—	4	2	no	—
410	#121	—	4	2	no	—
411	#121	D₈	1	1	yes	characteristic
412	#121	D₈	1	1	yes	characteristic
413	#120	—	4	2	no	—
414	#120	D₈	1	1	yes	characteristic
415	#120	D₈	1	1	yes	characteristic
416	C₄×Q₈	—	2	2	no	—
417	C₄×Q₈	—	2	2	no	—
418	C₄×Q₈	—	2	2	no	—
419	C₄×Q₈	—	4	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	4	2	no	—
422	C₄×D₄	—	4	2	no	—
423	C₄×D₄	—	4	2	no	—
424	C₄×D₄	—	4	2	no	—
425	C₄×D₄	—	4	2	no	—
426	C₄×D₄	—	4	2	no	—
427	C₄×D₄	—	4	2	no	—
428	C₄×D₄	C₂×D₄	1	1	yes	characteristic
429	C₄×D₄	C₂×D₄	1	1	yes	characteristic
430	C₄×D₄	C₂×D₄	1	1	yes	characteristic
431	C₄×D₄	C₂×D₄	1	1	yes	characteristic
432	#117	—	2	2	no	—
433	#117	—	2	2	no	—
434	#117	—	4	2	no	—
435	#117	C₂×D₄	1	1	yes	characteristic
436	C₂×C₄⋊C₄	—	2	2	no	—
437	C₂×C₄⋊C₄	—	2	2	no	—
438	C₂×C₄⋊C₄	—	4	2	no	—
439	C₂×C₄⋊C₄	—	4	2	no	—
440	C₂×C₂²⋊C₄	—	4	2	no	—
441	Q₃₂	—	2	2	no	—
442	Q₃₂	—	2	2	no	—
443	Q₃₂	—	2	2	no	—
444	Q₃₂	—	4	2	no	—
445	Q₃₂	—	4	2	no	—
446	Q₃₂	—	4	2	no	—
447	SD₃₂	—	4	2	no	—
448	SD₃₂	—	4	2	no	—
449	SD₃₂	—	4	2	no	—
450	D₁₆	—	2	2	no	—
451	M₃₂	—	4	1	no	—
452	M₃₂	—	4	1	no	—
453	M₃₂	—	4	1	no	—
454	M₃₂	—	4	1	no	—
455	C₂×C₁₆	—	2	2	no	—
456	C₂×C₁₆	—	2	2	no	—
457	C₂×C₁₆	—	2	2	no	—
458	C₂×C₁₆	—	2	2	no	—
459	C₂×C₁₆	—	2	2	no	—
460	C₂×C₁₆	—	4	1	no	—
461	C₂×C₁₆	—	4	1	no	—
462	C₂×C₁₆	—	4	1	no	—
463	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
464	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
465	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
466	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
467	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
468	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
469	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
470	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
471	#107	—	2	2	no	—
472	#107	—	2	2	no	—
473	#107	—	2	2	no	—
474	#107	C₂⁴	1	2	yes	—
475	#107	C₂⁴	1	2	yes	—
476	#107	C₂⁴	1	2	yes	—
477	#107	C₂⁴	1	2	yes	—
478	#106	—	2	2	no	—
479	#106	—	2	2	no	—
480	#106	—	2	2	no	—
481	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
482	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
483	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
484	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
485	#103	—	2	2	no	—
486	#103	—	2	2	no	—
487	#103	—	2	2	no	—
488	#103	—	2	2	no	—
489	#103	—	2	2	no	—
490	#103	—	2	2	no	—
491	#103	—	2	2	no	—
492	#103	—	2	2	no	—
493	#103	—	2	2	no	—
494	#103	—	2	2	no	—
495	#103	—	2	2	no	—
496	#103	—	2	2	no	—
497	#102	—	2	2	no	—
498	#102	—	2	2	no	—
499	#102	—	2	2	no	—
500	#102	—	2	2	no	—
501	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
502	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
503	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
504	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
505	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
506	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
507	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
508	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
509	#97	C₂×D₄	1	1	yes	characteristic
510	#97	C₂×D₄	1	1	yes	characteristic
511	C₄×C₈	C₂⁴	1	1	yes	characteristic
512	C₄×C₈	C₂⁴	1	1	yes	characteristic
513	C₂⁴	C₂×D₈	1	1	yes	characteristic
514	#41	—	4	1	no	—
515	#41	—	4	1	no	—
516	#41	—	8	2	no	—
517	#41	—	8	2	no	—
518	#41	—	8	2	no	—
519	#41	—	8	2	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	4	2	no	—
524	C₂×Q₈	—	4	2	no	—
525	C₂×Q₈	—	4	2	no	—
526	C₂×Q₈	—	8	2	no	—
527	C₂×Q₈	—	8	2	no	—
528	C₂×Q₈	—	8	2	no	—
529	C₂×Q₈	—	8	2	no	—
530	C₂×Q₈	C₂×D₈	1	1	yes	characteristic
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	4	2	no	—
533	C₂×D₄	—	4	2	no	—
534	C₂×D₄	—	4	2	no	—
535	C₂×D₄	—	4	2	no	—
536	C₂×D₄	—	4	2	no	—
537	C₂×D₄	C₂×D₈	1	1	yes	characteristic
538	C₂×D₄	C₂×D₈	1	1	yes	characteristic
539	C₂×D₄	C₂×D₈	1	1	yes	characteristic
540	C₂×D₄	C₂×D₈	1	1	yes	characteristic
541	C₂×D₄	C₂×D₈	1	1	yes	characteristic
542	C₂×D₄	C₂×D₈	1	1	yes	characteristic
543	C₂×D₄	C₂×D₈	1	1	yes	characteristic
544	C₂²×C₄	—	4	1	no	—
545	C₂²×C₄	—	4	1	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	—	4	2	no	—
550	C₂²×C₄	—	4	2	no	—
551	C₂²×C₄	—	4	2	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
556	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
557	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
558	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
559	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
560	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
561	Q₁₆	—	2	2	no	—
562	Q₁₆	—	2	2	no	—
563	Q₁₆	—	2	2	no	—
564	Q₁₆	—	2	2	no	—
565	Q₁₆	—	2	2	no	—
566	Q₁₆	—	2	2	no	—
567	Q₁₆	—	8	2	no	—
568	Q₁₆	—	8	2	no	—
569	Q₁₆	—	8	2	no	—
570	SD₁₆	—	8	2	no	—
571	SD₁₆	—	8	2	no	—
572	SD₁₆	—	8	2	no	—
573	D₈	—	2	2	no	—
574	D₈	—	2	2	no	—
575	M₁₆	—	4	1	no	—
576	M₁₆	—	4	1	no	—
577	M₁₆	—	4	1	no	—
578	M₁₆	—	4	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	4	1	no	—
590	C₂×C₈	—	4	1	no	—
591	C₂×C₈	—	4	1	no	—
592	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
595	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
597	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
598	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
599	C₂×C₈	C₂⁵	1	1	yes	characteristic
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	4	2	no	—
605	C₄⋊C₄	—	4	2	no	—
606	C₄⋊C₄	—	4	2	no	—
607	C₄⋊C₄	—	4	2	no	—
608	C₄⋊C₄	—	4	2	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	2	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
624	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
625	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
626	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
627	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
628	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
629	C₂²⋊C₄	—	4	2	no	—
630	C₂²⋊C₄	—	4	2	no	—
631	C₂²⋊C₄	—	4	2	no	—
632	C₂²⋊C₄	—	4	2	no	—
633	C₂²⋊C₄	—	4	2	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
647	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
648	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
649	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
650	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
651	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
652	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
653	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
654	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
655	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
656	C₄²	—	4	2	no	—
657	C₄²	—	4	2	no	—
658	C₄²	—	4	2	no	—
659	C₄²	—	4	2	no	—
660	C₄²	—	4	2	no	—
661	C₄²	C₂²×D₄	1	1	yes	characteristic
662	C₄²	C₂²×D₄	1	1	yes	characteristic
663	C₁₆	—	2	1	no	—
664	C₁₆	—	2	1	no	—
665	C₁₆	—	2	1	no	—
666	C₁₆	—	2	1	no	—
667	C₁₆	—	2	1	no	—
668	C₁₆	—	2	1	no	—
669	C₁₆	—	2	1	no	—
670	C₁₆	H(5,𝔽₂)	1	2	yes	—
671	C₂³	—	2	2	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	2	no	—
675	C₂³	C₂²×D₈	1	1	yes	characteristic
676	C₂³	C₂²×D₈	1	1	yes	characteristic
677	C₂³	C₂²×D₈	1	1	yes	characteristic
678	C₂³	C₂²×D₈	1	1	yes	characteristic
679	C₂³	C₂²×D₈	1	1	yes	characteristic
680	Q₈	—	4	1	no	—
681	Q₈	—	4	2	no	—
682	Q₈	—	4	2	no	—
683	Q₈	—	4	2	no	—
684	Q₈	—	4	2	no	—
685	Q₈	—	4	2	no	—
686	Q₈	—	4	2	no	—
687	Q₈	—	16	2	no	—
688	Q₈	—	16	2	no	—
689	Q₈	—	16	2	no	—
690	D₄	—	2	2	no	—
691	D₄	—	2	2	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	—	4	1	no	—
695	D₄	—	4	1	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	2	no	—
699	D₄	—	8	4	no	—
700	D₄	—	16	2	no	—
701	D₄	—	16	2	no	—
702	D₄	—	16	2	no	—
703	D₄	—	16	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	16	2	no	—
725	C₂×C₄	—	16	2	no	—
726	C₂×C₄	—	16	2	no	—
727	C₂×C₄	—	16	2	no	—
728	C₂×C₄	—	16	2	no	—
729	C₂×C₄	—	16	2	no	—
730	C₂×C₄	—	16	2	no	—
731	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
735	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
736	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
738	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
739	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
740	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
741	C₈	—	2	1	no	—
742	C₈	—	2	1	no	—
743	C₈	—	2	1	no	—
744	C₈	—	2	1	no	—
745	C₈	—	2	1	no	—
746	C₈	—	2	1	no	—
747	C₈	—	2	1	no	—
748	C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
749	C₈	#585	1	1	yes	characteristic
750	C₂²	—	2	1	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	1	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	4	4	no	—
765	C₂²	—	8	2	no	—
766	C₂²	—	8	2	no	—
767	C₂²	—	8	2	no	—
768	C₂²	#3417	1	2	yes	—
769	C₂²	C₂³×D₈	1	1	yes	characteristic
770	C₄	—	2	1	no	—
771	C₄	—	2	1	no	—
772	C₄	—	2	1	no	—
773	C₄	—	2	1	no	—
774	C₄	—	2	1	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	1	no	—
778	C₄	—	2	1	no	—
779	C₄	—	8	2	no	—
780	C₄	—	8	2	no	—
781	C₄	—	8	2	no	—
782	C₄	—	8	2	no	—
783	C₄	—	8	2	no	—
784	C₄	—	8	2	no	—
785	C₄	—	8	2	no	—
786	C₄	#3496	1	1	yes	characteristic
787	C₄	#3584	1	1	yes	characteristic
788	C₂	—	2	2	no	—
789	C₂	—	4	1	no	—
790	C₂	—	4	1	no	—
791	C₂	—	4	1	no	—
792	C₂	—	4	1	no	—
793	C₂	—	16	2	no	—
794	C₂	#62245	1	1	yes	characteristic
795	C₂	C₂×#3417	1	1	yes	characteristic
796	C₂	#62635	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁵
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #525 ◁ #2929 ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #62267	C₂	semidirect
2. #33909	C₂	semidirect
3. #33906	C₂	semidirect
4. #33905	C₂	semidirect
5. #33903	C₂	semidirect
6. #33887	C₂	semidirect
7. #33883	C₂	semidirect
8. #33882	C₂	semidirect
9. #33880	C₂	semidirect
10. D₄×Q₃₂	C₂	semidirect
11. #33851	C₂	semidirect
12. #33851	C₂	semidirect
13. #33849	C₂	semidirect
14. #33824	C₂	semidirect
15. #33767	C₂	semidirect
16. #33762	C₂	semidirect
17. #33741	C₂	semidirect
18. #33739	C₂	semidirect
19. #33610	C₂	semidirect
20. #33608	C₂	semidirect
21. #33600	C₂	semidirect
22. C₂×#2216	C₂	semidirect
23. #33432	C₂	semidirect
26. C₂×#508	C₂²	semidirect
28. C₂²×Q₃₂	C₂²	semidirect
53. #2253	C₂²	semidirect
54. #2252	C₂²	semidirect
55. #2249	C₂²	semidirect
56. #2247	C₂²	semidirect
57. #2245	C₂²	semidirect
58. #2243	C₂²	semidirect
61. #2237	C₂²	semidirect
63. #2236	C₂²	semidirect
64. #2235	C₂²	semidirect
65. #2234	C₂²	semidirect
67. #2229	C₂²	semidirect
68. #2228	C₂²	semidirect
69. #2227	C₂²	semidirect
70. #2225	C₂²	semidirect
73. #2220	C₂²	semidirect
76. #2219	C₂²	semidirect
87. #2216	C₂²	semidirect
88. #2216	C₂²	semidirect
89. #2216	C₂²	semidirect
92. #2215	C₂²	semidirect
93. #2211	C₂²	semidirect
94. #2211	C₂²	semidirect
95. #2209	C₂²	semidirect
96. #2208	C₂²	semidirect
99. #2189	C₂²	semidirect
100. #2189	C₂²	semidirect
102. #2188	C₂²	semidirect
104. #2185	C₂²	semidirect
105. #2176	C₂²	semidirect
106. #2175	C₂²	semidirect
107. C₄×Q₃₂	C₂²	semidirect
108. C₄×Q₃₂	C₂²	semidirect
109. C₄×Q₃₂	C₂²	semidirect
110. C₄×D₁₆	C₂²	semidirect
120. #2158	C₂²	semidirect
122. C₂×#366	C₂²	semidirect
124. #2141	C₂²	semidirect
125. #2139	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#62267	2
#33909	2
#33906	2
#33905	2
#33903	2
#33887	2
#33883	2
#33882	2
#33880	2
D₄×Q₃₂	2
#33851	2
#33849	2
#33824	2
#33767	2
#33762	2
#33741	2
#33739	2
#33610	2
#33608	2
#33600	2
C₂×#2216	2
#33432	2