Subgroups — #60976

Order 256.

896 conjugacy classes of subgroups.

The subgroup lattice has 649 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#542	C₂	1	1	yes	maximal, characteristic, complemented
3	#3262	C₂	1	2	yes	maximal, complemented
4	#3257	C₂	1	2	yes	maximal, complemented
5	#3243	C₂	1	2	yes	maximal, complemented
6	#3238	C₂	1	1	yes	maximal, characteristic, complemented
7	#3226	C₂	1	1	yes	maximal, characteristic, complemented
8	#3224	C₂	1	2	yes	maximal, complemented
9	#3213	C₂	1	1	yes	maximal, characteristic, complemented
10	#3211	C₂	1	1	yes	maximal, characteristic, complemented
11	#3194	C₂	1	1	yes	maximal, characteristic, complemented
12	#3193	C₂	1	1	yes	maximal, characteristic, complemented
13	#3190	C₂	1	1	yes	maximal, characteristic, complemented
14	#3186	C₂	1	1	yes	maximal, characteristic, complemented
15	#3179	C₂	1	2	yes	maximal, complemented
16	#3175	C₂	1	2	yes	maximal, complemented
17	#3124	C₂	1	2	yes	maximal, complemented
18	#3118	C₂	1	2	yes	maximal, complemented
19	#3114	C₂	1	1	yes	maximal, characteristic, complemented
20	#3112	C₂	1	1	yes	maximal, characteristic, complemented
21	#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	#3100	C₂	1	1	yes	maximal, characteristic, complemented
23	#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	#555	—	2	1	no	—
25	#553	—	2	1	no	—
26	#553	—	2	1	no	—
27	#551	—	2	1	no	—
28	#551	—	2	1	no	—
29	#547	—	2	1	no	—
30	#546	—	2	1	no	—
31	#546	—	2	1	no	—
32	#544	C₂²	1	1	yes	characteristic, complemented
33	#542	—	2	1	no	—
34	#542	—	2	1	no	—
35	#542	—	2	1	no	—
36	#542	—	2	1	no	—
37	#542	C₂²	1	2	yes	—
38	#542	C₂²	1	2	yes	—
39	#542	C₂²	1	1	yes	characteristic, complemented
40	#542	C₂²	1	2	yes	complemented
41	#542	C₂²	1	2	yes	complemented
42	#542	C₂²	1	1	yes	characteristic, complemented
43	#540	C₂²	1	1	yes	characteristic, complemented
44	#540	C₂²	1	1	yes	characteristic, complemented
45	#535	C₂²	1	1	yes	characteristic, complemented
46	#532	C₂²	1	1	yes	characteristic
47	#532	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	#529	C₂²	1	1	yes	characteristic
50	#529	C₂²	1	1	yes	characteristic
51	C₂×#126	—	2	1	no	—
52	C₂×#124	—	2	1	no	—
53	C₂×#124	C₂²	1	1	yes	characteristic, complemented
54	#525	C₂²	1	1	yes	characteristic
55	C₂×#123	—	2	1	no	—
56	C₂×C₂²⋊Q₈	—	2	1	no	—
57	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×#121	C₂²	1	1	yes	characteristic
59	C₂×#121	C₂²	1	1	yes	characteristic
60	#520	C₂²	1	1	yes	characteristic, complemented
61	#518	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
64	C₂×#117	C₂²	1	1	yes	characteristic
65	#501	C₂²	1	2	yes	complemented
66	#500	C₂²	1	2	yes	complemented
67	#496	C₂²	1	2	yes	complemented
68	#495	C₂²	1	2	yes	complemented
69	#489	C₂²	1	2	yes	complemented
70	#489	C₂²	1	2	yes	complemented
71	#488	C₂²	1	2	yes	complemented
72	#486	C₂²	1	2	yes	complemented
73	#485	C₂²	1	2	yes	complemented
74	#484	C₂²	1	2	yes	complemented
75	#483	C₂²	1	1	yes	characteristic, complemented
76	#483	C₂²	1	1	yes	characteristic, complemented
77	#482	C₂²	1	2	yes	—
78	#480	C₂²	1	1	yes	characteristic
79	#480	C₂²	1	1	yes	characteristic
80	#480	C₂²	1	1	yes	characteristic
81	#480	C₂²	1	1	yes	characteristic
82	#480	C₂²	1	2	yes	—
83	#480	C₂²	1	1	yes	characteristic, complemented
84	#480	C₂²	1	1	yes	characteristic, complemented
85	#479	C₂²	1	2	yes	complemented
86	#478	C₂²	1	2	yes	complemented
87	#477	C₂²	1	2	yes	complemented
88	#477	C₂²	1	2	yes	complemented
89	#476	C₂²	1	2	yes	complemented
90	#474	C₂²	1	2	yes	complemented
91	#474	C₂²	1	2	yes	complemented
92	#474	C₂²	1	2	yes	complemented
93	#469	C₂²	1	2	yes	complemented
94	#468	C₂²	1	2	yes	complemented
95	#468	C₂²	1	2	yes	complemented
96	#468	C₂²	1	2	yes	complemented
97	#467	C₂²	1	2	yes	complemented
98	#466	C₂²	1	2	yes	—
99	#466	C₂²	1	2	yes	—
100	#465	C₂²	1	2	yes	complemented
101	#464	C₂²	1	2	yes	complemented
102	#464	C₂²	1	2	yes	complemented
103	#463	C₂²	1	2	yes	complemented
104	#463	C₂²	1	2	yes	complemented
105	#463	C₂²	1	2	yes	complemented
106	#463	C₂²	1	2	yes	complemented
107	#460	C₂²	1	2	yes	complemented
108	#459	C₂²	1	2	yes	complemented
109	#452	C₂²	1	2	yes	complemented
110	#451	C₂²	1	1	yes	characteristic, complemented
111	#450	C₂²	1	1	yes	characteristic, complemented
112	#450	C₂²	1	2	yes	complemented
113	#449	C₂²	1	2	yes	—
114	#448	C₂²	1	1	yes	characteristic
115	#448	C₂²	1	1	yes	characteristic
116	#448	C₂²	1	1	yes	characteristic, complemented
117	#447	C₂²	1	1	yes	characteristic
118	#447	C₂²	1	1	yes	characteristic
119	#447	C₂²	1	2	yes	—
120	#447	C₂²	1	1	yes	characteristic, complemented
121	#442	C₂²	1	2	yes	complemented
122	#440	C₂²	1	2	yes	complemented
123	#440	C₂²	1	2	yes	complemented
124	#440	C₂²	1	2	yes	complemented
125	C₄×Q₁₆	C₂²	1	2	yes	complemented
126	C₄×SD₁₆	C₂²	1	2	yes	complemented
127	C₄×D₈	C₂²	1	2	yes	complemented
128	C₄×D₈	C₂²	1	2	yes	complemented
129	#433	C₂²	1	2	yes	complemented
130	#433	C₂²	1	2	yes	complemented
131	#432	C₂²	1	1	yes	characteristic, complemented
132	#432	C₂²	1	1	yes	characteristic, complemented
133	#431	C₂²	1	1	yes	characteristic, complemented
134	#431	C₂²	1	1	yes	characteristic, complemented
135	#424	C₂²	1	2	yes	complemented
136	#407	C₂²	1	1	yes	characteristic
137	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
138	#405	C₂²	1	2	yes	complemented
139	C₂×#41	—	2	1	no	—
140	C₂×#41	—	2	1	no	—
141	C₂×#41	C₂³	1	1	yes	characteristic
142	C₂²×Q₈	—	2	1	no	—
143	C₂²×Q₈	C₂³	1	1	yes	characteristic
144	C₂²×D₄	—	2	1	no	—
145	C₂²×D₄	—	2	1	no	—
146	C₂²×D₄	C₂³	1	1	yes	characteristic
147	C₂²×D₄	C₂³	1	1	yes	characteristic
148	C₂³×C₄	—	2	1	no	—
149	C₂³×C₄	C₂³	1	1	yes	characteristic
150	C₂×Q₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×SD₁₆	C₂³	1	2	yes	—
155	C₂×D₈	C₂³	1	2	yes	—
156	C₂×D₈	C₂³	1	2	yes	—
157	C₂×D₈	C₂³	1	2	yes	—
158	C₂×M₁₆	C₂³	1	2	yes	—
159	C₂²×C₈	C₂³	1	2	yes	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	—	2	1	no	—
162	C₄⋊Q₈	—	2	1	no	—
163	C₄⋊Q₈	C₂³	1	2	yes	—
164	C₄⋊Q₈	C₂³	1	2	yes	—
165	C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	#127	C₂³	1	1	yes	characteristic
168	#127	C₂³	1	1	yes	characteristic
169	#126	—	2	2	no	—
170	#126	—	2	2	no	—
171	#126	—	2	2	no	—
172	#126	—	2	2	no	—
173	#126	—	2	1	no	—
174	#126	—	2	1	no	—
175	#126	—	2	1	no	—
176	#126	—	2	1	no	—
177	#125	—	2	1	no	—
178	#125	C₂³	1	1	yes	characteristic
179	#125	C₂³	1	1	yes	characteristic
180	#124	—	2	2	no	—
181	#124	—	2	2	no	—
182	#124	—	2	2	no	—
183	#124	—	2	2	no	—
184	#124	—	2	1	no	—
185	#124	—	2	1	no	—
186	#124	—	2	1	no	—
187	#124	—	2	1	no	—
188	#124	—	2	1	no	—
189	#124	—	2	1	no	—
190	#124	C₂³	1	2	yes	—
191	#124	C₂³	1	2	yes	—
192	#124	C₂³	1	1	yes	characteristic
193	#124	C₂³	1	1	yes	characteristic
194	#123	—	2	1	no	—
195	#123	—	2	1	no	—
196	#123	—	2	1	no	—
197	#123	—	2	1	no	—
198	#123	—	2	1	no	—
199	#123	—	2	1	no	—
200	#123	—	2	1	no	—
201	#123	—	2	2	no	—
202	#123	—	2	2	no	—
203	#123	—	2	2	no	—
204	#123	—	2	2	no	—
205	#123	—	2	1	no	—
206	#123	—	2	1	no	—
207	C₂²⋊Q₈	—	2	1	no	—
208	C₂²⋊Q₈	—	2	1	no	—
209	C₂²⋊Q₈	—	2	2	no	—
210	C₂²⋊Q₈	—	2	2	no	—
211	C₂²⋊Q₈	—	2	2	no	—
212	C₂²⋊Q₈	—	2	2	no	—
213	C₂²⋊Q₈	—	2	1	no	—
214	C₂²⋊Q₈	—	2	1	no	—
215	C₂²⋊Q₈	—	2	1	no	—
216	C₂²⋊Q₈	—	2	1	no	—
217	C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	#121	—	2	1	no	—
222	#121	—	2	1	no	—
223	#121	—	2	1	no	—
224	#121	—	2	1	no	—
225	#121	—	2	1	no	—
226	#121	—	2	1	no	—
227	#121	—	2	1	no	—
228	#121	—	2	1	no	—
229	#121	—	2	1	no	—
230	#121	—	2	1	no	—
231	#121	—	2	1	no	—
232	#121	—	2	1	no	—
233	#121	C₂³	1	1	yes	characteristic
234	#121	C₂³	1	1	yes	characteristic
235	#121	C₂³	1	1	yes	characteristic
236	#121	C₂³	1	1	yes	characteristic
237	#121	C₂³	1	2	yes	—
238	#121	C₂³	1	2	yes	—
239	#121	C₂³	1	1	yes	characteristic
240	#121	C₂³	1	1	yes	characteristic
241	#120	—	2	1	no	—
242	#120	—	2	1	no	—
243	#120	—	2	1	no	—
244	C₄×Q₈	—	2	1	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	C₂³	1	2	yes	—
247	C₄×Q₈	C₂³	1	2	yes	—
248	C₄×Q₈	C₂³	1	1	yes	characteristic
249	C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	C₂³	1	2	yes	—
263	C₄×D₄	C₂³	1	2	yes	—
264	C₄×D₄	C₂³	1	1	yes	characteristic
265	C₄×D₄	C₂³	1	1	yes	characteristic
266	C₄×D₄	C₂³	1	1	yes	characteristic
267	C₄×D₄	C₂³	1	1	yes	characteristic
268	C₄×D₄	C₂³	1	1	yes	characteristic
269	C₄×D₄	C₂³	1	1	yes	characteristic
270	#117	—	2	1	no	—
271	#117	—	2	1	no	—
272	#117	—	2	1	no	—
273	#117	D₄	1	1	yes	characteristic
274	#117	D₄	1	1	yes	characteristic
275	#117	D₄	1	1	yes	characteristic
276	#117	D₄	1	1	yes	characteristic
277	#117	C₂³	1	1	yes	characteristic
278	#117	C₂³	1	1	yes	characteristic
279	#117	C₂³	1	1	yes	characteristic
280	#117	C₂³	1	1	yes	characteristic
281	#117	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
287	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂³	1	1	yes	characteristic
303	C₂×C₄²	C₂³	1	1	yes	characteristic
304	#107	C₂³	1	2	yes	—
305	#107	C₂³	1	2	yes	—
306	#107	C₂³	1	2	yes	—
307	#107	C₂³	1	2	yes	—
308	#107	C₂³	1	2	yes	—
309	#107	C₂³	1	2	yes	—
310	#106	C₂³	1	2	yes	—
311	#106	C₂³	1	2	yes	—
312	C₄⋊C₈	C₂³	1	2	yes	—
313	C₄⋊C₈	C₂³	1	2	yes	—
314	C₄⋊C₈	C₂³	1	2	yes	—
315	C₄⋊C₈	C₂³	1	2	yes	—
316	#103	C₂³	1	2	yes	—
317	#103	C₂³	1	2	yes	—
318	#103	C₂³	1	2	yes	—
319	#103	C₂³	1	2	yes	—
320	#103	C₂³	1	2	yes	—
321	#103	C₂³	1	2	yes	—
322	#102	C₂³	1	2	yes	—
323	#102	C₂³	1	2	yes	—
324	#102	C₂³	1	2	yes	—
325	#102	C₂³	1	2	yes	—
326	#102	C₂³	1	2	yes	—
327	#102	C₂³	1	2	yes	—
328	#102	C₂³	1	2	yes	—
329	#102	C₂³	1	2	yes	—
330	#102	C₂³	1	2	yes	—
331	#102	C₂³	1	2	yes	—
332	C₂²⋊C₈	C₂³	1	1	yes	characteristic
333	C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₂²⋊C₈	C₂³	1	2	yes	—
335	C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₂²⋊C₈	C₂³	1	1	yes	characteristic
337	C₂²⋊C₈	C₂³	1	2	yes	—
338	#97	C₂³	1	2	yes	—
339	#97	C₂³	1	2	yes	—
340	C₄×C₈	C₂³	1	2	yes	—
341	C₄×C₈	C₂³	1	2	yes	—
342	C₂⁴	—	2	1	no	—
343	C₂⁴	—	2	1	no	—
344	C₂⁴	C₂×D₄	1	1	yes	characteristic
345	#41	—	4	2	no	—
346	#41	—	8	2	no	—
347	#41	—	8	2	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	4	2	no	—
354	C₂×Q₈	—	8	2	no	—
355	C₂×Q₈	C₂⁴	1	2	yes	—
356	C₂×Q₈	C₂⁴	1	1	yes	characteristic
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	—	8	2	no	—
375	C₂×D₄	—	8	2	no	—
376	C₂×D₄	C₂⁴	1	2	yes	—
377	C₂×D₄	C₂⁴	1	1	yes	characteristic
378	C₂×D₄	C₂⁴	1	1	yes	characteristic
379	C₂×D₄	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	8	2	no	—
395	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴	1	1	yes	characteristic
405	Q₁₆	—	4	2	no	—
406	SD₁₆	—	4	2	no	—
407	SD₁₆	—	4	2	no	—
408	SD₁₆	—	4	2	no	—
409	SD₁₆	—	4	2	no	—
410	D₈	—	4	2	no	—
411	D₈	—	4	2	no	—
412	D₈	—	4	2	no	—
413	M₁₆	—	4	2	no	—
414	C₂×C₈	—	4	2	no	—
415	C₂×C₈	C₂⁴	1	2	yes	—
416	C₂×C₈	C₂⁴	1	2	yes	—
417	C₂×C₈	C₂⁴	1	2	yes	—
418	C₂×C₈	C₂⁴	1	2	yes	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄	C₂⁴	1	2	yes	—
447	C₄⋊C₄	C₂⁴	1	2	yes	—
448	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
486	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
487	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
488	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
489	C₄²	—	2	2	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	C₂×D₄	1	1	yes	characteristic
495	C₄²	C₂×D₄	1	1	yes	characteristic
496	C₄²	C₂×D₄	1	1	yes	characteristic
497	C₄²	C₂×D₄	1	1	yes	characteristic
498	C₄²	C₂⁴	1	1	yes	characteristic
499	C₄²	C₂⁴	1	1	yes	characteristic
500	C₄²	C₂⁴	1	1	yes	characteristic
501	C₄²	C₂⁴	1	1	yes	characteristic
502	C₂³	—	2	2	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	4	1	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	8	1	no	—
514	C₂³	—	8	1	no	—
515	C₂³	C₂²×D₄	1	1	yes	characteristic
516	C₂³	C₂²×D₄	1	1	yes	characteristic
517	C₂³	C₂²×D₄	1	1	yes	characteristic
518	Q₈	—	2	2	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	4	2	no	—
522	Q₈	—	8	2	no	—
523	Q₈	—	8	2	no	—
524	Q₈	—	8	1	no	—
525	Q₈	—	8	1	no	—
526	D₄	—	2	2	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	2	2	no	—
530	D₄	—	2	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	8	1	no	—
538	D₄	—	8	1	no	—
539	D₄	—	8	1	no	—
540	D₄	—	8	1	no	—
541	D₄	—	8	1	no	—
542	D₄	—	8	2	no	—
543	D₄	—	8	2	no	—
544	D₄	—	8	1	no	—
545	D₄	—	8	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	8	1	no	—
569	C₂×C₄	—	8	1	no	—
570	C₂×C₄	—	8	2	no	—
571	C₂×C₄	—	8	2	no	—
572	C₂×C₄	—	8	1	no	—
573	C₂×C₄	—	8	1	no	—
574	C₂×C₄	—	8	1	no	—
575	C₂×C₄	—	8	1	no	—
576	C₂×C₄	—	8	1	no	—
577	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄	C₂⁵	1	1	yes	characteristic
589	C₈	—	2	2	no	—
590	C₈	—	2	2	no	—
591	C₈	—	2	2	no	—
592	C₈	—	2	2	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	8	2	no	—
614	C₂²	—	8	4	no	—
615	C₂²	—	16	2	no	—
616	C₂²	#576	1	2	yes	—
617	C₂²	C₂³×D₄	1	1	yes	characteristic
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	2	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	1	no	—
637	C₄	#585	1	2	yes	—
638	C₂	—	2	2	no	—
639	C₂	—	4	1	no	—
640	C₂	—	4	1	no	—
641	C₂	—	8	1	no	—
642	C₂	—	8	2	no	—
643	C₂	—	8	1	no	—
644	C₂	—	8	1	no	—
645	C₂	#3449	1	1	yes	characteristic
646	C₂	C₂×#576	1	1	yes	characteristic
647	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3494	C₂	semidirect
2. C₂×#542	C₂	semidirect
3. #3262	C₂	semidirect
4. #3257	C₂	semidirect
5. #3243	C₂	semidirect
6. #3238	C₂	semidirect
7. #3226	C₂	semidirect
8. #3224	C₂	semidirect
9. #3213	C₂	semidirect
10. #3211	C₂	semidirect
11. #3194	C₂	semidirect
12. #3193	C₂	semidirect
13. #3190	C₂	semidirect
14. #3186	C₂	semidirect
15. #3179	C₂	semidirect
16. #3175	C₂	semidirect
17. #3124	C₂	semidirect
18. #3118	C₂	semidirect
19. #3114	C₂	semidirect
20. #3112	C₂	semidirect
21. #3108	C₂	semidirect
22. #3100	C₂	semidirect
23. #2924	C₂	semidirect
32. #544	C₂²	semidirect
39. #542	C₂²	semidirect
40. #542	C₂²	semidirect
41. #542	C₂²	semidirect
42. #542	C₂²	semidirect
43. #540	C₂²	semidirect
44. #540	C₂²	semidirect
45. #535	C₂²	semidirect
48. C₂×C₄⋊Q₈	C₂²	semidirect
53. C₂×#124	C₂²	semidirect
60. #520	C₂²	semidirect
61. #518	C₂²	semidirect
62. C₂×C₄×Q₈	C₂²	semidirect
63. C₂×C₄×D₄	C₂²	semidirect
65. #501	C₂²	semidirect
66. #500	C₂²	semidirect
67. #496	C₂²	semidirect
68. #495	C₂²	semidirect
69. #489	C₂²	semidirect
70. #489	C₂²	semidirect
71. #488	C₂²	semidirect
72. #486	C₂²	semidirect
73. #485	C₂²	semidirect
74. #484	C₂²	semidirect
75. #483	C₂²	semidirect
76. #483	C₂²	semidirect
83. #480	C₂²	semidirect
84. #480	C₂²	semidirect
85. #479	C₂²	semidirect
86. #478	C₂²	semidirect
87. #477	C₂²	semidirect
88. #477	C₂²	semidirect
89. #476	C₂²	semidirect
90. #474	C₂²	semidirect
91. #474	C₂²	semidirect
92. #474	C₂²	semidirect
93. #469	C₂²	semidirect
94. #468	C₂²	semidirect
95. #468	C₂²	semidirect
96. #468	C₂²	semidirect
97. #467	C₂²	semidirect
100. #465	C₂²	semidirect
101. #464	C₂²	semidirect
102. #464	C₂²	semidirect
103. #463	C₂²	semidirect
104. #463	C₂²	semidirect
105. #463	C₂²	semidirect
106. #463	C₂²	semidirect
107. #460	C₂²	semidirect
108. #459	C₂²	semidirect
109. #452	C₂²	semidirect
110. #451	C₂²	semidirect
111. #450	C₂²	semidirect
112. #450	C₂²	semidirect
116. #448	C₂²	semidirect
120. #447	C₂²	semidirect
121. #442	C₂²	semidirect
122. #440	C₂²	semidirect
123. #440	C₂²	semidirect
124. #440	C₂²	semidirect
125. C₄×Q₁₆	C₂²	semidirect
126. C₄×SD₁₆	C₂²	semidirect
127. C₄×D₈	C₂²	semidirect
128. C₄×D₈	C₂²	semidirect
129. #433	C₂²	semidirect
130. #433	C₂²	semidirect
131. #432	C₂²	semidirect
132. #432	C₂²	semidirect
133. #431	C₂²	semidirect
134. #431	C₂²	semidirect
135. #424	C₂²	semidirect
138. #405	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3494	2
C₂×#542	2
#3262	2
#3257	2
#3243	2
#3238	2
#3226	2
#3224	2
#3213	2
#3211	2
#3194	2
#3193	2
#3190	2
#3186	2
#3179	2
#3175	2
#3124	2
#3118	2
#3114	2
#3112	2
#3108	2
#3100	2
#2924	2