Subgroups — #61124

Order 256.

1082 conjugacy classes of subgroups.

The subgroup lattice has 605 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	#3305	C₂	1	1	yes	maximal, characteristic, complemented
4	#3304	C₂	1	1	yes	maximal, characteristic, complemented
5	#3303	C₂	1	1	yes	maximal, characteristic, complemented
6	#3302	C₂	1	1	yes	maximal, characteristic, complemented
7	#3301	C₂	1	2	yes	maximal, complemented
8	#3300	C₂	1	2	yes	maximal, complemented
9	#3299	C₂	1	1	yes	maximal, characteristic, complemented
10	#3298	C₂	1	1	yes	maximal, characteristic, complemented
11	#3297	C₂	1	2	yes	maximal, complemented
12	#3296	C₂	1	2	yes	maximal, complemented
13	#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	#3131	C₂	1	1	yes	maximal, characteristic, complemented
16	#3091	C₂	1	2	yes	maximal, complemented
17	#3076	C₂	1	1	yes	maximal, characteristic, complemented
18	#3050	C₂	1	2	yes	maximal, complemented
19	#3035	C₂	1	1	yes	maximal, characteristic, complemented
20	#3002	C₂	1	2	yes	maximal, complemented
21	C₄×#135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#416	C₂	1	2	yes	maximal, complemented
24	C₂²×#41	C₂²	1	2	yes	—
25	C₂×#135	C₂²	1	1	yes	characteristic
26	C₂×#135	C₂²	1	2	yes	complemented
27	C₂³×C₈	C₂²	1	2	yes	complemented
28	#556	C₂²	1	1	yes	characteristic, complemented
29	#555	C₂²	1	1	yes	characteristic, complemented
30	#554	C₂²	1	1	yes	characteristic
31	#553	C₂²	1	2	yes	complemented
32	#552	—	2	1	no	—
33	#552	C₂²	1	2	yes	complemented
34	#551	—	2	2	no	—
35	#550	C₂²	1	1	yes	characteristic
36	D₄×Q₈	C₂²	1	1	yes	characteristic
37	#548	C₂²	1	2	yes	—
38	#547	—	2	1	no	—
39	#547	C₂²	1	1	yes	characteristic
40	#547	C₂²	1	1	yes	characteristic
41	#546	—	2	1	no	—
42	#546	—	2	2	no	—
43	#546	C₂²	1	2	yes	—
44	D₄²	—	2	1	no	—
45	D₄²	C₂²	1	1	yes	characteristic
46	#533	C₂²	1	1	yes	characteristic, complemented
47	#532	—	2	1	no	—
48	#532	C₂²	1	1	yes	characteristic
49	#529	—	2	2	no	—
50	#529	—	2	1	no	—
51	#525	—	2	2	no	—
52	#525	C₂²	1	2	yes	—
53	#525	C₂²	1	2	yes	complemented
54	C₄×#41	—	2	1	no	—
55	C₄×#41	C₂²	1	1	yes	characteristic
56	C₄×#41	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄	—	2	1	no	—
58	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
59	C₂×#117	C₂²	1	2	yes	complemented
60	#488	C₂²	1	2	yes	complemented
61	#488	C₂²	1	2	yes	complemented
62	#487	C₂²	1	1	yes	characteristic, complemented
63	#487	C₂²	1	1	yes	characteristic, complemented
64	#486	C₂²	1	1	yes	characteristic, complemented
65	#486	C₂²	1	1	yes	characteristic, complemented
66	#485	C₂²	1	2	yes	complemented
67	#485	C₂²	1	2	yes	complemented
68	#484	C₂²	1	2	yes	complemented
69	#483	C₂²	1	2	yes	complemented
70	#482	C₂²	1	2	yes	complemented
71	#482	C₂²	1	2	yes	complemented
72	#481	C₂²	1	2	yes	complemented
73	#480	C₂²	1	2	yes	complemented
74	#479	C₂²	1	2	yes	complemented
75	#478	C₂²	1	2	yes	complemented
76	#477	C₂²	1	1	yes	characteristic, complemented
77	#476	C₂²	1	1	yes	characteristic, complemented
78	#475	C₂²	1	1	yes	characteristic, complemented
79	#474	C₂²	1	1	yes	characteristic, complemented
80	#467	C₂²	1	2	yes	complemented
81	#467	C₂²	1	2	yes	complemented
82	#466	C₂²	1	2	yes	complemented
83	#466	C₂²	1	2	yes	complemented
84	#465	C₂²	1	2	yes	complemented
85	#465	C₂²	1	2	yes	complemented
86	#465	C₂²	1	2	yes	complemented
87	#465	C₂²	1	2	yes	complemented
88	#464	C₂²	1	2	yes	complemented
89	#463	C₂²	1	2	yes	complemented
90	#462	C₂²	1	1	yes	characteristic, complemented
91	#461	C₂²	1	1	yes	characteristic, complemented
92	#460	C₂²	1	1	yes	characteristic, complemented
93	#459	C₂²	1	1	yes	characteristic, complemented
94	#452	C₂²	1	2	yes	complemented
95	#452	C₂²	1	2	yes	complemented
96	#451	C₂²	1	2	yes	complemented
97	#450	C₂²	1	2	yes	complemented
98	#449	C₂²	1	2	yes	complemented
99	#449	C₂²	1	2	yes	complemented
100	#448	C₂²	1	2	yes	complemented
101	#447	C₂²	1	2	yes	complemented
102	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
103	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
104	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
105	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
106	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
107	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
110	C₈×D₄	C₂²	1	1	yes	characteristic
111	C₈×D₄	C₂²	1	1	yes	characteristic
112	C₈×D₄	C₂²	1	2	yes	complemented
113	C₈×D₄	C₂²	1	2	yes	complemented
114	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
115	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
116	#427	C₂²	1	2	yes	complemented
117	#427	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	#416	C₂²	1	2	yes	—
120	#416	C₂²	1	1	yes	characteristic
121	#416	C₂²	1	2	yes	complemented
122	#416	C₂²	1	2	yes	complemented
123	#416	C₂²	1	2	yes	complemented
124	#416	C₂²	1	2	yes	complemented
125	#416	C₂²	1	2	yes	complemented
126	#416	C₂²	1	2	yes	complemented
127	#416	C₂²	1	2	yes	complemented
128	#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×#103	C₂²	1	2	yes	complemented
130	C₂×#103	C₂²	1	2	yes	complemented
131	C₂×#102	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₈	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	2	no	—
137	C₂×#41	—	2	2	no	—
138	C₂×#41	—	2	8	no	—
139	C₂×#41	—	4	4	no	—
140	C₂×#41	C₂³	1	1	yes	characteristic
141	C₂×#41	C₂³	1	2	yes	—
142	C₂×#41	C₂³	1	2	yes	—
143	C₂×#41	C₂³	1	2	yes	—
144	C₂×#41	C₂³	1	1	yes	characteristic
145	C₂²×Q₈	C₂³	1	2	yes	—
146	C₂²×D₄	—	2	2	no	—
147	C₂²×D₄	—	2	1	no	—
148	C₂²×D₄	D₄	1	1	yes	characteristic
149	C₂²×D₄	C₂³	1	2	yes	—
150	C₂³×C₄	—	2	2	no	—
151	C₂³×C₄	C₂³	1	2	yes	—
152	#135	—	2	4	no	—
153	#135	—	4	4	no	—
154	C₂×Q₁₆	C₂³	1	1	yes	characteristic
155	C₂×Q₁₆	C₂³	1	2	yes	—
156	C₂×SD₁₆	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆	C₂³	1	2	yes	—
159	C₂×SD₁₆	C₂³	1	2	yes	—
160	C₂×D₈	C₂³	1	1	yes	characteristic
161	C₂×D₈	C₂³	1	2	yes	—
162	C₂²×C₈	—	4	4	no	—
163	C₂²×C₈	C₂³	1	1	yes	characteristic
164	C₂²×C₈	C₂³	1	2	yes	—
165	C₂²×C₈	C₂³	1	1	yes	characteristic
166	C₂²×C₈	C₂³	1	2	yes	—
167	C₂²×C₈	C₂³	1	2	yes	—
168	C₂²×C₈	C₂³	1	2	yes	—
169	C₂²×C₈	C₂³	1	2	yes	—
170	C₄⋊Q₈	—	2	1	no	—
171	C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	C₄⋊Q₈	C₂³	1	1	yes	characteristic
174	#127	—	2	1	no	—
175	#127	C₂³	1	1	yes	characteristic
176	#126	—	2	2	no	—
177	#126	—	2	2	no	—
178	#126	—	2	2	no	—
179	#125	—	2	2	no	—
180	#125	—	2	1	no	—
181	#125	C₂³	1	2	yes	—
182	#124	—	2	1	no	—
183	#124	—	2	2	no	—
184	#124	—	2	2	no	—
185	#124	C₂³	1	2	yes	—
186	#123	—	2	2	no	—
187	#123	—	2	2	no	—
188	#123	—	2	2	no	—
189	#123	—	2	2	no	—
190	#123	—	2	2	no	—
191	#123	—	2	2	no	—
192	#123	—	2	2	no	—
193	C₂²⋊Q₈	—	2	1	no	—
194	C₂²⋊Q₈	—	2	1	no	—
195	C₂²⋊Q₈	—	2	2	no	—
196	C₂²⋊Q₈	—	2	1	no	—
197	C₂²⋊Q₈	—	2	2	no	—
198	C₂²⋊Q₈	—	2	2	no	—
199	C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₂²⋊Q₈	C₂³	1	2	yes	—
203	#121	—	2	2	no	—
204	#121	—	2	2	no	—
205	#121	—	2	1	no	—
206	#121	—	2	1	no	—
207	#121	—	2	1	no	—
208	#121	—	2	1	no	—
209	#121	—	2	1	no	—
210	#121	—	2	2	no	—
211	#121	—	2	2	no	—
212	#121	C₂³	1	2	yes	—
213	#121	C₂³	1	2	yes	—
214	#121	C₂³	1	2	yes	—
215	#121	C₂³	1	2	yes	—
216	#120	—	2	2	no	—
217	#120	—	2	2	no	—
218	#120	—	2	2	no	—
219	#120	—	2	2	no	—
220	C₄×Q₈	—	2	1	no	—
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	—	2	1	no	—
223	C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₄×D₄	—	2	1	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	—	2	2	no	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	D₄	1	1	yes	characteristic
243	C₄×D₄	D₄	1	2	yes	—
244	C₄×D₄	D₄	1	1	yes	characteristic
245	C₄×D₄	C₂³	1	1	yes	characteristic
246	C₄×D₄	C₂³	1	1	yes	characteristic
247	C₄×D₄	C₂³	1	1	yes	characteristic
248	C₄×D₄	C₂³	1	1	yes	characteristic
249	C₄×D₄	C₂³	1	1	yes	characteristic
250	C₄×D₄	C₂³	1	2	yes	—
251	C₄×D₄	C₂³	1	1	yes	characteristic
252	#117	—	2	2	no	—
253	#117	—	2	2	no	—
254	#117	—	2	1	no	—
255	#117	—	2	2	no	—
256	#117	—	2	1	no	—
257	#117	—	2	1	no	—
258	#117	C₂³	1	1	yes	characteristic
259	#117	C₂³	1	2	yes	—
260	#117	C₂³	1	2	yes	—
261	#117	C₂³	1	2	yes	—
262	#117	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³	1	2	yes	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	D₄	1	2	yes	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂³	1	1	yes	characteristic
274	#107	C₂³	1	1	yes	characteristic
275	#107	C₂³	1	1	yes	characteristic
276	#107	C₂³	1	2	yes	—
277	#107	C₂³	1	2	yes	—
278	#106	C₂³	1	1	yes	characteristic
279	#106	C₂³	1	1	yes	characteristic
280	#106	C₂³	1	2	yes	—
281	#106	C₂³	1	2	yes	—
282	C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₄⋊C₈	C₂³	1	2	yes	—
285	#103	C₂³	1	1	yes	characteristic
286	#103	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	2	yes	—
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	1	yes	characteristic
295	#103	C₂³	1	2	yes	—
296	#103	C₂³	1	2	yes	—
297	#102	C₂³	1	1	yes	characteristic
298	#102	C₂³	1	1	yes	characteristic
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	2	yes	—
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	1	yes	characteristic
306	#102	C₂³	1	1	yes	characteristic
307	#102	C₂³	1	2	yes	—
308	#102	C₂³	1	2	yes	—
309	C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂²⋊C₈	C₂³	1	2	yes	—
313	C₄×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₈	C₂³	1	1	yes	characteristic
315	C₄×C₈	C₂³	1	1	yes	characteristic
316	C₄×C₈	C₂³	1	1	yes	characteristic
317	C₂⁴	—	2	2	no	—
318	C₂⁴	C₂×D₄	1	2	yes	—
319	#41	—	2	2	no	—
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	2	2	no	—
323	#41	—	2	4	no	—
324	#41	—	2	2	no	—
325	#41	—	2	4	no	—
326	#41	—	4	8	no	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	#41	—	4	8	no	—
330	#41	—	4	4	no	—
331	#41	#41	1	4	yes	complemented
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	4	2	no	—
337	C₂×Q₈	C₂⁴	1	2	yes	—
338	C₂×Q₈	C₂⁴	1	1	yes	characteristic
339	C₂×Q₈	C₂⁴	1	1	yes	characteristic
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	4	2	no	—
355	C₂×D₄	—	4	8	no	—
356	C₂×D₄	—	4	4	no	—
357	C₂×D₄	C₂×D₄	1	2	yes	—
358	C₂×D₄	C₂×D₄	1	1	yes	characteristic
359	C₂×D₄	C₂×D₄	1	1	yes	characteristic
360	C₂×D₄	C₂⁴	1	2	yes	—
361	C₂×D₄	C₂⁴	1	1	yes	characteristic
362	C₂×D₄	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	4	8	no	—
378	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄	1	2	yes	—
380	C₂²×C₄	C₂×D₄	1	2	yes	—
381	C₂²×C₄	C₂×D₄	1	2	yes	—
382	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴	1	2	yes	—
384	C₂²×C₄	C₂⁴	1	2	yes	—
385	C₂²×C₄	C₂⁴	1	1	yes	characteristic
386	Q₁₆	—	2	2	no	—
387	Q₁₆	—	4	2	no	—
388	SD₁₆	—	2	2	no	—
389	SD₁₆	—	2	2	no	—
390	SD₁₆	—	4	2	no	—
391	SD₁₆	—	4	2	no	—
392	D₈	—	2	2	no	—
393	D₈	—	4	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	4	no	—
397	C₂×C₈	—	4	2	no	—
398	C₂×C₈	—	4	2	no	—
399	C₂×C₈	—	4	2	no	—
400	C₂×C₈	—	4	2	no	—
401	C₂×C₈	C₂⁴	1	1	yes	characteristic
402	C₂×C₈	C₂⁴	1	1	yes	characteristic
403	C₂×C₈	C₂⁴	1	1	yes	characteristic
404	C₂×C₈	C₂⁴	1	1	yes	characteristic
405	C₂×C₈	C₂⁴	1	2	yes	—
406	C₂×C₈	C₂⁴	1	2	yes	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	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	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
424	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
425	C₄⋊C₄	C₂×D₄	1	2	yes	—
426	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄	C₂⁴	1	2	yes	—
429	C₄⋊C₄	C₂⁴	1	2	yes	—
430	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	2	1	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄	C₂×D₄	1	2	yes	—
453	C₂²⋊C₄	C₂×D₄	1	2	yes	—
454	C₂²⋊C₄	C₂×D₄	1	2	yes	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	2	no	—
464	C₄²	C₂×D₄	1	1	yes	characteristic
465	C₄²	C₂×D₄	1	1	yes	characteristic
466	C₄²	C₂⁴	1	1	yes	characteristic
467	C₄²	C₂⁴	1	1	yes	characteristic
468	C₂³	—	2	4	no	—
469	C₂³	—	2	4	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	4	4	no	—
476	C₂³	—	8	2	no	—
477	C₂³	C₂²×D₄	1	2	yes	—
478	C₂³	C₂²×D₄	1	1	yes	characteristic
479	C₂³	C₂²×D₄	1	2	yes	—
480	Q₈	—	2	1	no	—
481	Q₈	—	2	1	no	—
482	Q₈	—	2	2	no	—
483	Q₈	—	2	1	no	—
484	Q₈	—	2	2	no	—
485	Q₈	—	4	4	no	—
486	Q₈	—	4	2	no	—
487	Q₈	—	8	1	no	—
488	Q₈	C₂×#41	1	2	yes	—
489	D₄	—	2	4	no	—
490	D₄	—	2	4	no	—
491	D₄	—	2	2	no	—
492	D₄	—	2	1	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	1	no	—
495	D₄	—	2	1	no	—
496	D₄	—	2	2	no	—
497	D₄	—	4	4	no	—
498	D₄	—	4	4	no	—
499	D₄	—	4	4	no	—
500	D₄	—	4	4	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	4	no	—
503	D₄	—	4	4	no	—
504	D₄	—	4	2	no	—
505	D₄	—	8	1	no	—
506	D₄	—	8	2	no	—
507	D₄	—	8	2	no	—
508	D₄	#135	1	4	yes	complemented
509	D₄	C₂×#41	1	2	yes	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	4	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	8	1	no	—
538	C₂×C₄	—	8	1	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄	1	2	yes	—
542	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄	1	2	yes	—
545	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄	C₂×#41	1	2	yes	—
548	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
549	C₂×C₄	C₂⁵	1	1	yes	characteristic
550	C₈	—	2	1	no	—
551	C₈	—	2	1	no	—
552	C₈	—	2	1	no	—
553	C₈	—	2	1	no	—
554	C₈	—	2	2	no	—
555	C₈	—	2	2	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	4	8	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	8	8	no	—
574	C₂²	#546	1	2	yes	—
575	C₂²	C₂×#135	1	4	yes	—
576	C₂²	C₂³×D₄	1	1	yes	characteristic
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	2	no	—
591	C₄	#546	1	2	yes	—
592	C₄	C₂×#135	1	2	yes	—
593	C₄	C₂²×#41	1	1	yes	characteristic
594	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
595	C₂	—	2	2	no	—
596	C₂	—	2	4	no	—
597	C₂	—	4	2	no	—
598	C₂	—	4	2	no	—
599	C₂	—	8	1	no	—
600	C₂	—	8	2	no	—
601	C₂	C₂×#546	1	1	yes	characteristic
602	C₂	C₂²×#135	1	1	yes	characteristic
603	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
socle	C₂²	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ 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
1. #3475	C₂	semidirect
2. D₄×#41	C₂	semidirect
3. #3305	C₂	semidirect
4. #3304	C₂	semidirect
5. #3303	C₂	semidirect
6. #3302	C₂	semidirect
7. #3301	C₂	semidirect
8. #3300	C₂	semidirect
9. #3299	C₂	semidirect
10. #3298	C₂	semidirect
11. #3297	C₂	semidirect
12. #3296	C₂	semidirect
13. #3295	C₂	semidirect
14. #3294	C₂	semidirect
15. #3131	C₂	semidirect
16. #3091	C₂	semidirect
17. #3076	C₂	semidirect
18. #3050	C₂	semidirect
19. #3035	C₂	semidirect
20. #3002	C₂	semidirect
21. C₄×#135	C₂	semidirect
22. C₂×C₈×D₄	C₂	semidirect
23. C₂×#416	C₂	semidirect
26. C₂×#135	C₂²	semidirect
27. C₂³×C₈	C₂²	semidirect
28. #556	C₂²	semidirect
29. #555	C₂²	semidirect
31. #553	C₂²	semidirect
33. #552	C₂²	semidirect
46. #533	C₂²	semidirect
53. #525	C₂²	semidirect
56. C₄×#41	C₂²	semidirect
59. C₂×#117	C₂²	semidirect
60. #488	C₂²	semidirect
61. #488	C₂²	semidirect
62. #487	C₂²	semidirect
63. #487	C₂²	semidirect
64. #486	C₂²	semidirect
65. #486	C₂²	semidirect
66. #485	C₂²	semidirect
67. #485	C₂²	semidirect
68. #484	C₂²	semidirect
69. #483	C₂²	semidirect
70. #482	C₂²	semidirect
71. #482	C₂²	semidirect
72. #481	C₂²	semidirect
73. #480	C₂²	semidirect
74. #479	C₂²	semidirect
75. #478	C₂²	semidirect
76. #477	C₂²	semidirect
77. #476	C₂²	semidirect
78. #475	C₂²	semidirect
79. #474	C₂²	semidirect
80. #467	C₂²	semidirect
81. #467	C₂²	semidirect
82. #466	C₂²	semidirect
83. #466	C₂²	semidirect
84. #465	C₂²	semidirect
85. #465	C₂²	semidirect
86. #465	C₂²	semidirect
87. #465	C₂²	semidirect
88. #464	C₂²	semidirect
89. #463	C₂²	semidirect
90. #462	C₂²	semidirect
91. #461	C₂²	semidirect
92. #460	C₂²	semidirect
93. #459	C₂²	semidirect
94. #452	C₂²	semidirect
95. #452	C₂²	semidirect
96. #451	C₂²	semidirect
97. #450	C₂²	semidirect
98. #449	C₂²	semidirect
99. #449	C₂²	semidirect
100. #448	C₂²	semidirect
101. #447	C₂²	semidirect
102. C₄×Q₁₆	C₂²	semidirect
103. C₄×Q₁₆	C₂²	semidirect
104. C₄×SD₁₆	C₂²	semidirect
105. C₄×SD₁₆	C₂²	semidirect
106. C₄×SD₁₆	C₂²	semidirect
107. C₄×SD₁₆	C₂²	semidirect
108. C₄×D₈	C₂²	semidirect
109. C₄×D₈	C₂²	semidirect
112. C₈×D₄	C₂²	semidirect
113. C₈×D₄	C₂²	semidirect
114. C₈×D₄	C₂²	semidirect
115. C₈×D₄	C₂²	semidirect
116. #427	C₂²	semidirect
117. #427	C₂²	semidirect
118. C₂×C₄⋊C₈	C₂²	semidirect
121. #416	C₂²	semidirect
122. #416	C₂²	semidirect
123. #416	C₂²	semidirect
124. #416	C₂²	semidirect
125. #416	C₂²	semidirect
126. #416	C₂²	semidirect
127. #416	C₂²	semidirect
128. #416	C₂²	semidirect
129. C₂×#103	C₂²	semidirect
130. C₂×#103	C₂²	semidirect
131. C₂×#102	C₂²	semidirect
132. C₂×#102	C₂²	semidirect
133. C₂×C₂²⋊C₈	C₂²	semidirect
134. C₂×C₄×C₈	C₂²	semidirect
331. #41	#41	semidirect
508. D₄	#135	semidirect

Maximal subgroups

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

subgroup	index
#3475	2
D₄×#41	2
#3305	2
#3304	2
#3303	2
#3302	2
#3301	2
#3300	2
#3299	2
#3298	2
#3297	2
#3296	2
#3295	2
#3294	2
#3131	2
#3091	2
#3076	2
#3050	2
#3035	2
#3002	2
C₄×#135	2
C₂×C₈×D₄	2
C₂×#416	2