Subgroups — #61738

Order 256.

879 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3520	C₂	1	1	yes	maximal, characteristic
2	C₂×#552	C₂	1	1	yes	maximal, characteristic, complemented
3	#3352	C₂	1	2	yes	maximal, complemented
4	#3349	C₂	1	2	yes	maximal, complemented
5	#3343	C₂	1	2	yes	maximal, complemented
6	#3336	C₂	1	2	yes	maximal, complemented
7	#3327	C₂	1	2	yes	maximal, complemented
8	#3315	C₂	1	2	yes	maximal, complemented
9	#3312	C₂	1	2	yes	maximal, complemented
10	#3300	C₂	1	2	yes	maximal, complemented
11	#3236	C₂	1	1	yes	maximal, characteristic, complemented
12	#3232	C₂	1	1	yes	maximal, characteristic, complemented
13	#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	#3195	C₂	1	1	yes	maximal, characteristic, complemented
15	#3190	C₂	1	1	yes	maximal, characteristic, complemented
16	#3189	C₂	1	1	yes	maximal, characteristic, complemented
17	#3117	C₂	1	1	yes	maximal, characteristic, complemented
18	#3104	C₂	1	1	yes	maximal, characteristic, complemented
19	#3095	C₂	1	1	yes	maximal, characteristic, complemented
20	#3092	C₂	1	1	yes	maximal, characteristic, complemented
21	#3091	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#484	C₂	1	1	yes	maximal, characteristic, complemented
23	#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	#556	C₂²	1	1	yes	characteristic
25	#554	—	2	1	no	—
26	#552	—	2	1	no	—
27	#552	—	2	1	no	—
28	#552	—	2	1	no	—
29	#552	—	2	1	no	—
30	#552	C₂²	1	1	yes	characteristic
31	#552	C₂²	1	2	yes	—
32	#552	C₂²	1	2	yes	—
33	#552	C₂²	1	2	yes	—
34	#552	C₂²	1	1	yes	characteristic
35	#552	C₂²	1	2	yes	—
36	#551	—	2	1	no	—
37	#551	—	2	1	no	—
38	D₄×Q₈	C₂²	1	1	yes	characteristic
39	#548	C₂²	1	1	yes	characteristic
40	#548	C₂²	1	1	yes	characteristic
41	#547	C₂²	1	1	yes	characteristic
42	#547	C₂²	1	1	yes	characteristic
43	#546	—	2	1	no	—
44	#542	—	2	1	no	—
45	#539	—	2	1	no	—
46	#539	—	2	1	no	—
47	#533	C₂²	1	1	yes	characteristic
48	#529	C₂²	1	1	yes	characteristic
49	C₂×#126	—	2	1	no	—
50	C₂×#125	—	2	1	no	—
51	C₂×#125	C₂²	1	1	yes	characteristic
52	#525	C₂²	1	1	yes	characteristic
53	#525	C₂²	1	1	yes	characteristic
54	C₂×#123	—	2	1	no	—
55	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	#520	—	2	1	no	—
60	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
62	C₂×#117	—	2	1	no	—
63	C₂×#117	C₂²	1	1	yes	characteristic
64	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	#501	C₂²	1	2	yes	complemented
66	#499	C₂²	1	2	yes	complemented
67	#491	C₂²	1	2	yes	complemented
68	#488	C₂²	1	2	yes	complemented
69	#485	C₂²	1	2	yes	complemented
70	#485	C₂²	1	2	yes	complemented
71	#485	C₂²	1	2	yes	complemented
72	#485	C₂²	1	2	yes	complemented
73	#485	C₂²	1	2	yes	complemented
74	#484	C₂²	1	1	yes	characteristic
75	#484	C₂²	1	1	yes	characteristic
76	#484	C₂²	1	1	yes	characteristic
77	#484	C₂²	1	1	yes	characteristic
78	#484	C₂²	1	1	yes	characteristic
79	#484	C₂²	1	1	yes	characteristic
80	#484	C₂²	1	2	yes	complemented
81	#484	C₂²	1	2	yes	complemented
82	#484	C₂²	1	2	yes	complemented
83	#483	C₂²	1	1	yes	characteristic
84	#483	C₂²	1	1	yes	characteristic
85	#483	C₂²	1	1	yes	characteristic
86	#483	C₂²	1	2	yes	complemented
87	#483	C₂²	1	2	yes	complemented
88	#482	C₂²	1	2	yes	complemented
89	#481	C₂²	1	1	yes	characteristic
90	#481	C₂²	1	1	yes	characteristic
91	#480	C₂²	1	1	yes	characteristic
92	#480	C₂²	1	2	yes	complemented
93	#479	C₂²	1	2	yes	complemented
94	#479	C₂²	1	2	yes	complemented
95	#479	C₂²	1	2	yes	complemented
96	#479	C₂²	1	2	yes	complemented
97	#478	C₂²	1	2	yes	complemented
98	#477	C₂²	1	2	yes	complemented
99	#470	C₂²	1	2	yes	complemented
100	#470	C₂²	1	2	yes	complemented
101	#470	C₂²	1	2	yes	complemented
102	#468	C₂²	1	2	yes	complemented
103	#467	C₂²	1	2	yes	complemented
104	#467	C₂²	1	2	yes	complemented
105	#467	C₂²	1	2	yes	complemented
106	#465	C₂²	1	2	yes	complemented
107	#464	C₂²	1	2	yes	complemented
108	#462	C₂²	1	2	yes	complemented
109	#452	C₂²	1	2	yes	complemented
110	#452	C₂²	1	2	yes	complemented
111	#451	C₂²	1	1	yes	characteristic
112	#451	C₂²	1	1	yes	characteristic
113	#451	C₂²	1	1	yes	characteristic
114	#451	C₂²	1	2	yes	complemented
115	#451	C₂²	1	2	yes	complemented
116	#448	C₂²	1	1	yes	characteristic
117	#441	C₂²	1	2	yes	complemented
118	#440	C₂²	1	2	yes	complemented
119	C₄×Q₁₆	C₂²	1	2	yes	complemented
120	C₄×Q₁₆	C₂²	1	2	yes	complemented
121	#436	C₂²	1	2	yes	—
122	#435	C₂²	1	2	yes	—
123	#435	C₂²	1	2	yes	—
124	C₈×D₄	C₂²	1	2	yes	—
125	#432	C₂²	1	1	yes	characteristic
126	#431	C₂²	1	1	yes	characteristic
127	#428	C₂²	1	2	yes	complemented
128	#428	C₂²	1	2	yes	complemented
129	#427	C₂²	1	2	yes	complemented
130	C₂×#107	C₂²	1	2	yes	complemented
131	#419	C₂²	1	2	yes	complemented
132	#417	C₂²	1	2	yes	complemented
133	#416	C₂²	1	2	yes	complemented
134	C₂×#103	C₂²	1	2	yes	complemented
135	#407	C₂²	1	1	yes	characteristic
136	#407	C₂²	1	1	yes	characteristic
137	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
138	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
139	C₂×#41	—	2	1	no	—
140	C₂×#41	C₂³	1	1	yes	characteristic
141	C₂×#41	C₂³	1	1	yes	characteristic
142	C₂²×Q₈	C₂³	1	1	yes	characteristic
143	C₂²×Q₈	C₂³	1	1	yes	characteristic
144	C₂²×Q₈	C₂³	1	1	yes	characteristic
145	C₂²×D₄	D₄	1	1	yes	characteristic
146	C₂³×C₄	—	2	1	no	—
147	C₂³×C₄	C₂³	1	1	yes	characteristic
148	C₂³×C₄	C₂³	1	1	yes	characteristic
149	C₂×Q₁₆	C₂³	1	2	yes	—
150	C₂×Q₁₆	C₂³	1	2	yes	—
151	C₂×Q₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×M₁₆	C₂³	1	2	yes	—
154	C₂×M₁₆	C₂³	1	2	yes	—
155	C₂²×C₈	C₂³	1	2	yes	—
156	C₂²×C₈	C₂³	1	2	yes	—
157	C₄⋊Q₈	—	2	1	no	—
158	C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	#126	—	2	2	no	—
161	#126	—	2	2	no	—
162	#126	—	2	2	no	—
163	#126	—	2	2	no	—
164	#126	—	2	1	no	—
165	#126	—	2	1	no	—
166	#126	—	2	1	no	—
167	#126	—	2	1	no	—
168	#126	—	2	1	no	—
169	#125	—	2	2	no	—
170	#125	—	2	2	no	—
171	#125	—	2	2	no	—
172	#125	—	2	2	no	—
173	#125	—	2	1	no	—
174	#125	—	2	1	no	—
175	#125	—	2	1	no	—
176	#125	—	2	1	no	—
177	#125	—	2	1	no	—
178	#125	C₂³	1	2	yes	—
179	#125	C₂³	1	2	yes	—
180	#125	C₂³	1	1	yes	characteristic
181	#124	—	2	1	no	—
182	#124	—	2	1	no	—
183	#124	—	2	1	no	—
184	#124	C₂³	1	1	yes	characteristic
185	#123	—	2	2	no	—
186	#123	—	2	2	no	—
187	#123	—	2	2	no	—
188	#123	—	2	2	no	—
189	#123	—	2	1	no	—
190	#123	—	2	1	no	—
191	#123	—	2	1	no	—
192	#123	—	2	1	no	—
193	#123	—	2	1	no	—
194	#123	—	2	1	no	—
195	#123	—	2	1	no	—
196	#123	—	2	1	no	—
197	#123	—	2	1	no	—
198	C₂²⋊Q₈	—	2	1	no	—
199	C₂²⋊Q₈	—	2	1	no	—
200	C₂²⋊Q₈	—	2	1	no	—
201	C₂²⋊Q₈	—	2	1	no	—
202	C₂²⋊Q₈	—	2	1	no	—
203	C₂²⋊Q₈	—	2	1	no	—
204	C₂²⋊Q₈	—	2	1	no	—
205	C₂²⋊Q₈	—	2	1	no	—
206	C₂²⋊Q₈	—	2	1	no	—
207	C₂²⋊Q₈	—	2	1	no	—
208	C₂²⋊Q₈	—	2	1	no	—
209	C₂²⋊Q₈	—	2	1	no	—
210	C₂²⋊Q₈	—	2	1	no	—
211	C₂²⋊Q₈	—	2	1	no	—
212	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	#121	—	2	1	no	—
226	#121	—	2	1	no	—
227	#121	—	2	1	no	—
228	#121	C₂³	1	1	yes	characteristic
229	#121	C₂³	1	1	yes	characteristic
230	#121	C₂³	1	1	yes	characteristic
231	#120	—	2	1	no	—
232	#120	—	2	1	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×Q₈	—	2	1	no	—
236	C₄×Q₈	—	2	1	no	—
237	C₄×Q₈	C₂³	1	2	yes	—
238	C₄×Q₈	C₂³	1	2	yes	—
239	C₄×Q₈	C₂³	1	1	yes	characteristic
240	C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	D₄	1	1	yes	characteristic
251	C₄×D₄	D₄	1	1	yes	characteristic
252	C₄×D₄	D₄	1	1	yes	characteristic
253	C₄×D₄	D₄	1	1	yes	characteristic
254	C₄×D₄	C₂³	1	1	yes	characteristic
255	C₄×D₄	C₂³	1	1	yes	characteristic
256	C₄×D₄	C₂³	1	1	yes	characteristic
257	C₄×D₄	C₂³	1	1	yes	characteristic
258	C₄×D₄	C₂³	1	1	yes	characteristic
259	#117	—	2	1	no	—
260	#117	—	2	1	no	—
261	#117	—	2	1	no	—
262	#117	—	2	2	no	—
263	#117	—	2	2	no	—
264	#117	—	2	2	no	—
265	#117	—	2	2	no	—
266	#117	—	2	1	no	—
267	#117	—	2	1	no	—
268	#117	—	2	1	no	—
269	#117	C₂³	1	2	yes	—
270	#117	C₂³	1	2	yes	—
271	#117	C₂³	1	1	yes	characteristic
272	#117	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	C₂³	1	1	yes	characteristic
302	#107	C₂³	1	2	yes	—
303	#107	C₂³	1	2	yes	—
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	#106	C₂³	1	2	yes	—
310	#106	C₂³	1	2	yes	—
311	#106	C₂³	1	2	yes	—
312	#106	C₂³	1	2	yes	—
313	#106	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	#103	C₂³	1	2	yes	—
323	#103	C₂³	1	2	yes	—
324	#103	C₂³	1	2	yes	—
325	#103	C₂³	1	2	yes	—
326	#103	C₂³	1	2	yes	—
327	#103	C₂³	1	2	yes	—
328	#103	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	1	yes	characteristic
335	C₂²⋊C₈	C₂³	1	2	yes	—
336	C₂²⋊C₈	C₂³	1	2	yes	—
337	C₂²⋊C₈	C₂³	1	1	yes	characteristic
338	C₂²⋊C₈	C₂³	1	2	yes	—
339	C₂²⋊C₈	C₂³	1	2	yes	—
340	#97	C₂³	1	2	yes	—
341	C₄×C₈	C₂³	1	2	yes	—
342	C₂⁴	C₂×D₄	1	1	yes	characteristic
343	C₂⁴	C₂×D₄	1	1	yes	characteristic
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	#41	—	4	4	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	—	4	2	no	—
353	C₂×Q₈	—	4	2	no	—
354	C₂×Q₈	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈	C₂⁴	1	2	yes	—
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	—	4	2	no	—
364	C₂×D₄	C₂×D₄	1	1	yes	characteristic
365	C₂×D₄	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄	C₂×D₄	1	1	yes	characteristic
368	C₂×D₄	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴	1	1	yes	characteristic
398	Q₁₆	—	4	2	no	—
399	Q₁₆	—	4	2	no	—
400	Q₁₆	—	4	2	no	—
401	SD₁₆	—	4	2	no	—
402	M₁₆	—	4	2	no	—
403	M₁₆	—	4	2	no	—
404	C₂×C₈	—	4	2	no	—
405	C₂×C₈	—	4	2	no	—
406	C₂×C₈	C₂⁴	1	2	yes	—
407	C₂×C₈	C₂⁴	1	2	yes	—
408	C₂×C₈	C₂⁴	1	2	yes	—
409	C₂×C₈	C₂⁴	1	2	yes	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	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	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄	C₂⁴	1	2	yes	—
449	C₄⋊C₄	C₂⁴	1	2	yes	—
450	C₄⋊C₄	C₂⁴	1	2	yes	—
451	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	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	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₄²	—	2	2	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	2	no	—
489	C₄²	—	2	2	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	C₂×D₄	1	1	yes	characteristic
496	C₄²	C₂×D₄	1	1	yes	characteristic
497	C₄²	C₂⁴	1	1	yes	characteristic
498	C₄²	C₂⁴	1	1	yes	characteristic
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	4	1	no	—
506	C₂³	C₂²×D₄	1	1	yes	characteristic
507	C₂³	C₂²×D₄	1	1	yes	characteristic
508	C₂³	C₂²×D₄	1	1	yes	characteristic
509	C₂³	C₂²×D₄	1	1	yes	characteristic
510	C₂³	C₂²×D₄	1	1	yes	characteristic
511	Q₈	—	2	2	no	—
512	Q₈	—	2	2	no	—
513	Q₈	—	2	2	no	—
514	Q₈	—	2	2	no	—
515	Q₈	—	2	2	no	—
516	Q₈	—	4	2	no	—
517	Q₈	—	4	2	no	—
518	Q₈	—	8	1	no	—
519	Q₈	—	8	1	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	2	no	—
522	D₄	—	2	2	no	—
523	D₄	—	4	1	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	8	1	no	—
529	D₄	—	8	1	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	8	1	no	—
564	C₂×C₄	—	8	1	no	—
565	C₂×C₄	—	8	1	no	—
566	C₂×C₄	—	8	1	no	—
567	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄	C₂⁵	1	1	yes	characteristic
577	C₈	—	2	2	no	—
578	C₈	—	2	2	no	—
579	C₈	—	2	2	no	—
580	C₈	—	2	2	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	8	2	no	—
599	C₂²	#575	1	2	yes	—
600	C₂²	#578	1	2	yes	—
601	C₂²	C₂³×D₄	1	1	yes	characteristic
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	4	2	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	1	no	—
622	C₄	#585	1	2	yes	—
623	C₂	—	2	2	no	—
624	C₂	—	2	2	no	—
625	C₂	—	4	1	no	—
626	C₂	—	4	1	no	—
627	C₂	—	4	1	no	—
628	C₂	—	8	1	no	—
629	C₂	#3485	1	1	yes	characteristic
630	C₂	C₂×#575	1	1	yes	characteristic
631	C₂	C₂×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3520	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂×#552	C₂	semidirect
3. #3352	C₂	semidirect
4. #3349	C₂	semidirect
5. #3343	C₂	semidirect
6. #3336	C₂	semidirect
7. #3327	C₂	semidirect
8. #3315	C₂	semidirect
9. #3312	C₂	semidirect
10. #3300	C₂	semidirect
11. #3236	C₂	semidirect
12. #3232	C₂	semidirect
13. #3196	C₂	semidirect
14. #3195	C₂	semidirect
15. #3190	C₂	semidirect
16. #3189	C₂	semidirect
17. #3117	C₂	semidirect
18. #3104	C₂	semidirect
19. #3095	C₂	semidirect
20. #3092	C₂	semidirect
21. #3091	C₂	semidirect
22. C₂×#484	C₂	semidirect
23. #2974	C₂	semidirect
65. #501	C₂²	semidirect
66. #499	C₂²	semidirect
67. #491	C₂²	semidirect
68. #488	C₂²	semidirect
69. #485	C₂²	semidirect
70. #485	C₂²	semidirect
71. #485	C₂²	semidirect
72. #485	C₂²	semidirect
73. #485	C₂²	semidirect
80. #484	C₂²	semidirect
81. #484	C₂²	semidirect
82. #484	C₂²	semidirect
86. #483	C₂²	semidirect
87. #483	C₂²	semidirect
88. #482	C₂²	semidirect
92. #480	C₂²	semidirect
93. #479	C₂²	semidirect
94. #479	C₂²	semidirect
95. #479	C₂²	semidirect
96. #479	C₂²	semidirect
97. #478	C₂²	semidirect
98. #477	C₂²	semidirect
99. #470	C₂²	semidirect
100. #470	C₂²	semidirect
101. #470	C₂²	semidirect
102. #468	C₂²	semidirect
103. #467	C₂²	semidirect
104. #467	C₂²	semidirect
105. #467	C₂²	semidirect
106. #465	C₂²	semidirect
107. #464	C₂²	semidirect
108. #462	C₂²	semidirect
109. #452	C₂²	semidirect
110. #452	C₂²	semidirect
114. #451	C₂²	semidirect
115. #451	C₂²	semidirect
117. #441	C₂²	semidirect
118. #440	C₂²	semidirect
119. C₄×Q₁₆	C₂²	semidirect
120. C₄×Q₁₆	C₂²	semidirect
127. #428	C₂²	semidirect
128. #428	C₂²	semidirect
129. #427	C₂²	semidirect
130. C₂×#107	C₂²	semidirect
131. #419	C₂²	semidirect
132. #417	C₂²	semidirect
133. #416	C₂²	semidirect
134. C₂×#103	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3520	2
C₂×#552	2
#3352	2
#3349	2
#3343	2
#3336	2
#3327	2
#3315	2
#3312	2
#3300	2
#3236	2
#3232	2
#3196	2
#3195	2
#3190	2
#3189	2
#3117	2
#3104	2
#3095	2
#3092	2
#3091	2
C₂×#484	2
#2974	2