Subgroups — #63028

Order 256.

3317 conjugacy classes of subgroups.

The subgroup lattice has 703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3566	C₂	1	8	yes	maximal, complemented
2	#3565	C₂	1	4	yes	maximal, complemented
3	#3547	C₂	1	2	yes	maximal, complemented
4	#3545	C₂	1	4	yes	maximal, complemented
5	#3544	C₂	1	1	yes	maximal, characteristic, complemented
6	#3542	C₂	1	4	yes	maximal, complemented
7	#3540	C₂	1	4	yes	maximal, complemented
8	#3524	C₂	1	4	yes	maximal, complemented
9	#3520	C₂	1	2	yes	maximal, complemented
10	#3518	C₂	1	2	yes	maximal, complemented
11	#3510	C₂	1	4	yes	maximal, complemented
12	#3509	C₂	1	1	yes	maximal, characteristic, complemented
13	#3506	C₂	1	2	yes	maximal, complemented
14	#3505	C₂	1	4	yes	maximal, complemented
15	#3495	C₂	1	4	yes	maximal, complemented
16	#3493	C₂	1	4	yes	maximal, complemented
17	#3481	C₂	1	2	yes	maximal, complemented
18	#3475	C₂	1	4	yes	maximal, complemented
19	#3475	C₂	1	2	yes	maximal, complemented
20	C₂×#555	C₂	1	1	yes	maximal, characteristic, complemented
21	#563	C₂²	1	4	yes	complemented
22	#563	C₂²	1	4	yes	complemented
23	#562	C₂²	1	8	yes	complemented
24	#562	C₂²	1	8	yes	complemented
25	H(3,𝔽₄)	C₂²	1	4	yes	complemented
26	#560	C₂²	1	8	yes	complemented
27	#559	C₂²	1	2	yes	complemented
28	#559	C₂²	1	8	yes	complemented
29	#559	C₂²	1	8	yes	complemented
30	Q₈²	C₂²	1	1	yes	characteristic, complemented
31	#557	C₂²	1	4	yes	complemented
32	#556	C₂²	1	4	yes	complemented
33	#556	C₂²	1	2	yes	complemented
34	#556	C₂²	1	4	yes	complemented
35	#556	C₂²	1	8	yes	complemented
36	#556	C₂²	1	4	yes	complemented
37	#556	C₂²	1	4	yes	complemented
38	#556	C₂²	1	8	yes	complemented
39	#555	C₂²	1	1	yes	characteristic
40	#555	C₂²	1	4	yes	complemented
41	#555	C₂²	1	2	yes	complemented
42	#555	C₂²	1	4	yes	complemented
43	#555	C₂²	1	1	yes	characteristic, complemented
44	#555	C₂²	1	4	yes	complemented
45	#555	C₂²	1	4	yes	complemented
46	#555	C₂²	1	4	yes	complemented
47	#555	C₂²	1	4	yes	complemented
48	#555	C₂²	1	1	yes	characteristic, complemented
49	#555	C₂²	1	4	yes	complemented
50	#554	C₂²	1	4	yes	complemented
51	#554	C₂²	1	2	yes	complemented
52	#554	C₂²	1	2	yes	complemented
53	#554	C₂²	1	2	yes	complemented
54	#553	C₂²	1	2	yes	—
55	#553	C₂²	1	4	yes	complemented
56	#553	C₂²	1	4	yes	complemented
57	#553	C₂²	1	2	yes	complemented
58	#553	C₂²	1	4	yes	complemented
59	#553	C₂²	1	4	yes	complemented
60	#553	C₂²	1	8	yes	complemented
61	#553	C₂²	1	4	yes	complemented
62	#553	C₂²	1	8	yes	complemented
63	#552	C₂²	1	4	yes	complemented
64	#552	C₂²	1	4	yes	complemented
65	#552	C₂²	1	4	yes	complemented
66	#552	C₂²	1	4	yes	complemented
67	#552	C₂²	1	8	yes	complemented
68	#552	C₂²	1	8	yes	complemented
69	#552	C₂²	1	4	yes	complemented
70	#552	C₂²	1	4	yes	complemented
71	#552	C₂²	1	4	yes	complemented
72	#552	C₂²	1	8	yes	complemented
73	#551	C₂²	1	8	yes	complemented
74	#551	C₂²	1	8	yes	complemented
75	#551	C₂²	1	8	yes	complemented
76	#551	C₂²	1	4	yes	complemented
77	#551	C₂²	1	4	yes	complemented
78	#551	C₂²	1	8	yes	complemented
79	#551	C₂²	1	8	yes	complemented
80	#551	C₂²	1	8	yes	complemented
81	#550	C₂²	1	4	yes	complemented
82	D₄×Q₈	C₂²	1	2	yes	complemented
83	#548	C₂²	1	4	yes	complemented
84	#548	C₂²	1	4	yes	complemented
85	#548	C₂²	1	4	yes	complemented
86	#547	C₂²	1	2	yes	complemented
87	#547	C₂²	1	4	yes	complemented
88	#547	C₂²	1	2	yes	complemented
89	#546	C₂²	1	2	yes	—
90	#546	C₂²	1	4	yes	—
91	#546	C₂²	1	4	yes	complemented
92	#546	C₂²	1	8	yes	complemented
93	#546	C₂²	1	2	yes	complemented
94	#546	C₂²	1	4	yes	complemented
95	D₄²	C₂²	1	2	yes	complemented
96	#544	C₂²	1	4	yes	complemented
97	#544	C₂²	1	4	yes	complemented
98	#542	C₂²	1	8	yes	complemented
99	#542	C₂²	1	8	yes	complemented
100	#542	C₂²	1	8	yes	complemented
101	#542	C₂²	1	4	yes	complemented
102	#542	C₂²	1	8	yes	complemented
103	#542	C₂²	1	4	yes	complemented
104	#542	C₂²	1	4	yes	complemented
105	#542	C₂²	1	8	yes	complemented
106	#541	C₂²	1	8	yes	complemented
107	#541	C₂²	1	4	yes	complemented
108	#540	C₂²	1	4	yes	complemented
109	#540	C₂²	1	8	yes	complemented
110	#539	C₂²	1	8	yes	complemented
111	#539	C₂²	1	8	yes	complemented
112	#538	C₂²	1	8	yes	complemented
113	#538	C₂²	1	8	yes	complemented
114	#538	C₂²	1	8	yes	complemented
115	#538	C₂²	1	8	yes	complemented
116	#537	C₂²	1	4	yes	complemented
117	#536	C₂²	1	2	yes	—
118	#536	C₂²	1	4	yes	complemented
119	#536	C₂²	1	4	yes	complemented
120	#535	C₂²	1	4	yes	—
121	#535	C₂²	1	4	yes	complemented
122	#534	C₂²	1	8	yes	complemented
123	#533	C₂²	1	2	yes	complemented
124	#533	C₂²	1	4	yes	complemented
125	#533	C₂²	1	4	yes	complemented
126	#533	C₂²	1	2	yes	complemented
127	#533	C₂²	1	1	yes	characteristic, complemented
128	#532	C₂²	1	2	yes	complemented
129	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
130	#529	C₂²	1	8	yes	complemented
131	#529	C₂²	1	8	yes	complemented
132	#529	C₂²	1	4	yes	complemented
133	#529	C₂²	1	8	yes	complemented
134	#529	C₂²	1	8	yes	complemented
135	#529	C₂²	1	2	yes	complemented
136	#529	C₂²	1	2	yes	complemented
137	#529	C₂²	1	4	yes	complemented
138	#529	C₂²	1	8	yes	complemented
139	#529	C₂²	1	4	yes	complemented
140	C₂×#124	C₂²	1	4	yes	complemented
141	#525	C₂²	1	4	yes	—
142	#525	C₂²	1	4	yes	complemented
143	#525	C₂²	1	4	yes	complemented
144	#525	C₂²	1	4	yes	complemented
145	#525	C₂²	1	4	yes	complemented
146	#525	C₂²	1	4	yes	complemented
147	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
148	C₂×#121	C₂²	1	4	yes	complemented
149	#520	C₂²	1	4	yes	complemented
150	#520	C₂²	1	4	yes	complemented
151	#519	C₂²	1	4	yes	complemented
152	#519	C₂²	1	2	yes	complemented
153	#518	C₂²	1	4	yes	complemented
154	C₄×#41	C₂²	1	1	yes	characteristic
155	C₄×#41	C₂²	1	4	yes	complemented
156	C₄×#41	C₂²	1	4	yes	complemented
157	C₄×#41	C₂²	1	2	yes	complemented
158	C₂×C₄×D₄	C₂²	1	2	yes	complemented
159	C₂×C₄×D₄	C₂²	1	4	yes	complemented
160	C₂×C₄×D₄	C₂²	1	2	yes	complemented
161	C₂×#117	C₂²	1	4	yes	complemented
162	C₂×#117	C₂²	1	4	yes	complemented
163	C₂×#41	C₂³	1	1	yes	characteristic
164	C₂×#41	C₂³	1	2	yes	—
165	C₂×#41	C₂³	1	4	yes	—
166	C₂×#41	C₂³	1	4	yes	—
167	C₂×#41	C₂³	1	4	yes	—
168	C₂×#41	C₂³	1	4	yes	—
169	C₂²×Q₈	C₂³	1	4	yes	—
170	C₂²×Q₈	C₂³	1	2	yes	—
171	C₂²×D₄	C₂³	1	2	yes	—
172	C₂²×D₄	C₂³	1	4	yes	—
173	C₂²×D₄	C₂³	1	2	yes	—
174	C₂²×D₄	C₂³	1	4	yes	—
175	C₂³×C₄	C₂³	1	4	yes	—
176	C₂³×C₄	C₂³	1	4	yes	—
177	C₄⋊Q₈	C₂³	1	1	yes	characteristic
178	C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈	C₂³	1	2	yes	—
180	C₄⋊Q₈	C₂³	1	4	yes	—
181	C₄⋊Q₈	C₂³	1	2	yes	—
182	C₄⋊Q₈	C₂³	1	2	yes	—
183	C₄⋊Q₈	C₂³	1	8	yes	—
184	C₄⋊Q₈	C₂³	1	4	yes	—
185	C₄⋊Q₈	C₂³	1	4	yes	—
186	C₄⋊Q₈	C₂³	1	4	yes	—
187	C₄⋊Q₈	C₂³	1	4	yes	—
188	C₄⋊Q₈	C₂³	1	4	yes	—
189	#127	C₂³	1	2	yes	—
190	#127	C₂³	1	8	yes	—
191	#126	C₂³	1	4	yes	—
192	#126	C₂³	1	8	yes	—
193	#126	C₂³	1	4	yes	—
194	#126	C₂³	1	8	yes	—
195	#126	C₂³	1	8	yes	—
196	#126	C₂³	1	8	yes	—
197	#126	C₂³	1	8	yes	—
198	#126	C₂³	1	4	yes	—
199	#126	C₂³	1	8	yes	—
200	#126	C₂³	1	8	yes	—
201	#126	C₂³	1	8	yes	—
202	#126	C₂³	1	4	yes	—
203	#126	C₂³	1	8	yes	—
204	#126	C₂³	1	8	yes	—
205	#126	C₂³	1	8	yes	—
206	#126	C₂³	1	8	yes	—
207	#126	C₂³	1	8	yes	—
208	#125	C₂³	1	8	yes	—
209	#125	C₂³	1	2	yes	—
210	#125	C₂³	1	4	yes	—
211	#125	C₂³	1	8	yes	—
212	#125	C₂³	1	8	yes	—
213	#125	C₂³	1	4	yes	—
214	#125	C₂³	1	8	yes	—
215	#125	C₂³	1	4	yes	—
216	#125	C₂³	1	2	yes	—
217	#125	C₂³	1	2	yes	—
218	#125	C₂³	1	4	yes	—
219	#125	C₂³	1	8	yes	—
220	#125	C₂³	1	8	yes	—
221	#124	C₂³	1	4	yes	—
222	#124	C₂³	1	4	yes	—
223	#124	C₂³	1	8	yes	—
224	#124	C₂³	1	8	yes	—
225	#124	C₂³	1	4	yes	—
226	#124	C₂³	1	4	yes	—
227	#124	C₂³	1	2	yes	—
228	#124	C₂³	1	8	yes	—
229	#124	C₂³	1	8	yes	—
230	#124	C₂³	1	8	yes	—
231	#124	C₂³	1	4	yes	—
232	#124	C₂³	1	4	yes	—
233	#124	C₂³	1	2	yes	—
234	#124	C₂³	1	4	yes	—
235	#124	C₂³	1	8	yes	—
236	#124	C₂³	1	8	yes	—
237	#124	C₂³	1	4	yes	—
238	#124	C₂³	1	4	yes	—
239	#124	C₂³	1	4	yes	—
240	#124	C₂³	1	8	yes	—
241	#124	C₂³	1	8	yes	—
242	#123	C₂³	1	4	yes	—
243	#123	C₂³	1	4	yes	—
244	#123	C₂³	1	4	yes	—
245	#123	C₂³	1	8	yes	—
246	#123	C₂³	1	4	yes	—
247	#123	C₂³	1	8	yes	—
248	#123	C₂³	1	8	yes	—
249	#123	C₂³	1	8	yes	—
250	#123	C₂³	1	8	yes	—
251	#123	C₂³	1	8	yes	—
252	#123	C₂³	1	8	yes	—
253	#123	C₂³	1	8	yes	—
254	#123	C₂³	1	4	yes	—
255	#123	C₂³	1	8	yes	—
256	#123	C₂³	1	4	yes	—
257	#123	C₂³	1	8	yes	—
258	#123	C₂³	1	8	yes	—
259	#123	C₂³	1	8	yes	—
260	#123	C₂³	1	4	yes	—
261	#123	C₂³	1	4	yes	—
262	#123	C₂³	1	8	yes	—
263	#123	C₂³	1	8	yes	—
264	#123	C₂³	1	8	yes	—
265	#123	C₂³	1	8	yes	—
266	C₂²⋊Q₈	C₂³	1	2	yes	—
267	C₂²⋊Q₈	C₂³	1	4	yes	—
268	C₂²⋊Q₈	C₂³	1	4	yes	—
269	C₂²⋊Q₈	C₂³	1	4	yes	—
270	C₂²⋊Q₈	C₂³	1	8	yes	—
271	C₂²⋊Q₈	C₂³	1	8	yes	—
272	C₂²⋊Q₈	C₂³	1	4	yes	—
273	C₂²⋊Q₈	C₂³	1	4	yes	—
274	C₂²⋊Q₈	C₂³	1	4	yes	—
275	C₂²⋊Q₈	C₂³	1	4	yes	—
276	C₂²⋊Q₈	C₂³	1	4	yes	—
277	C₂²⋊Q₈	C₂³	1	4	yes	—
278	C₂²⋊Q₈	C₂³	1	4	yes	—
279	C₂²⋊Q₈	C₂³	1	4	yes	—
280	C₂²⋊Q₈	C₂³	1	2	yes	—
281	C₂²⋊Q₈	C₂³	1	8	yes	—
282	C₂²⋊Q₈	C₂³	1	8	yes	—
283	C₂²⋊Q₈	C₂³	1	8	yes	—
284	C₂²⋊Q₈	C₂³	1	8	yes	—
285	C₂²⋊Q₈	C₂³	1	4	yes	—
286	C₂²⋊Q₈	C₂³	1	4	yes	—
287	C₂²⋊Q₈	C₂³	1	4	yes	—
288	C₂²⋊Q₈	C₂³	1	4	yes	—
289	C₂²⋊Q₈	C₂³	1	8	yes	—
290	C₂²⋊Q₈	C₂³	1	8	yes	—
291	C₂²⋊Q₈	C₂³	1	8	yes	—
292	C₂²⋊Q₈	C₂³	1	8	yes	—
293	C₂²⋊Q₈	C₂³	1	8	yes	—
294	#121	C₂³	1	4	yes	—
295	#121	C₂³	1	4	yes	—
296	#121	C₂³	1	4	yes	—
297	#121	C₂³	1	4	yes	—
298	#121	C₂³	1	8	yes	—
299	#121	C₂³	1	8	yes	—
300	#121	C₂³	1	4	yes	—
301	#121	C₂³	1	4	yes	—
302	#121	C₂³	1	2	yes	—
303	#121	C₂³	1	2	yes	—
304	#121	C₂³	1	2	yes	—
305	#121	C₂³	1	4	yes	—
306	#121	C₂³	1	4	yes	—
307	#121	C₂³	1	4	yes	—
308	#121	C₂³	1	4	yes	—
309	#121	C₂³	1	4	yes	—
310	#121	C₂³	1	8	yes	—
311	#121	C₂³	1	8	yes	—
312	#121	C₂³	1	2	yes	—
313	#121	C₂³	1	8	yes	—
314	#121	C₂³	1	8	yes	—
315	#121	C₂³	1	4	yes	—
316	#121	C₂³	1	4	yes	—
317	#121	C₂³	1	8	yes	—
318	#121	C₂³	1	8	yes	—
319	#121	C₂³	1	8	yes	—
320	#121	C₂³	1	8	yes	—
321	#121	C₂³	1	8	yes	—
322	#120	C₂³	1	4	yes	—
323	#120	C₂³	1	4	yes	—
324	#120	C₂³	1	8	yes	—
325	#120	C₂³	1	8	yes	—
326	#120	C₂³	1	8	yes	—
327	#120	C₂³	1	8	yes	—
328	#120	C₂³	1	4	yes	—
329	#120	C₂³	1	4	yes	—
330	C₄×Q₈	C₂³	1	2	yes	—
331	C₄×Q₈	C₂³	1	2	yes	—
332	C₄×Q₈	C₂³	1	4	yes	—
333	C₄×Q₈	C₂³	1	2	yes	—
334	C₄×Q₈	C₂³	1	4	yes	—
335	C₄×Q₈	C₂³	1	8	yes	—
336	C₄×Q₈	C₂³	1	4	yes	—
337	C₄×Q₈	C₂³	1	8	yes	—
338	C₄×Q₈	C₂³	1	4	yes	—
339	C₄×Q₈	C₂³	1	8	yes	—
340	C₄×Q₈	C₂³	1	4	yes	—
341	C₄×Q₈	C₂³	1	4	yes	—
342	C₄×Q₈	C₂³	1	8	yes	—
343	C₄×Q₈	C₂³	1	8	yes	—
344	C₄×Q₈	C₂³	1	4	yes	—
345	C₄×D₄	C₂³	1	2	yes	—
346	C₄×D₄	C₂³	1	2	yes	—
347	C₄×D₄	C₂³	1	4	yes	—
348	C₄×D₄	C₂³	1	2	yes	—
349	C₄×D₄	C₂³	1	2	yes	—
350	C₄×D₄	C₂³	1	4	yes	—
351	C₄×D₄	C₂³	1	4	yes	—
352	C₄×D₄	C₂³	1	4	yes	—
353	C₄×D₄	C₂³	1	4	yes	—
354	C₄×D₄	C₂³	1	4	yes	—
355	C₄×D₄	C₂³	1	2	yes	—
356	C₄×D₄	C₂³	1	4	yes	—
357	C₄×D₄	C₂³	1	4	yes	—
358	C₄×D₄	C₂³	1	4	yes	—
359	C₄×D₄	C₂³	1	2	yes	—
360	C₄×D₄	C₂³	1	2	yes	—
361	C₄×D₄	C₂³	1	4	yes	—
362	C₄×D₄	C₂³	1	4	yes	—
363	C₄×D₄	C₂³	1	2	yes	—
364	C₄×D₄	C₂³	1	2	yes	—
365	C₄×D₄	C₂³	1	2	yes	—
366	C₄×D₄	C₂³	1	4	yes	—
367	C₄×D₄	C₂³	1	8	yes	—
368	C₄×D₄	C₂³	1	8	yes	—
369	C₄×D₄	C₂³	1	8	yes	—
370	C₄×D₄	C₂³	1	4	yes	—
371	C₄×D₄	C₂³	1	8	yes	—
372	C₄×D₄	C₂³	1	2	yes	—
373	C₄×D₄	C₂³	1	4	yes	—
374	C₄×D₄	C₂³	1	8	yes	—
375	C₄×D₄	C₂³	1	8	yes	—
376	C₄×D₄	C₂³	1	8	yes	—
377	C₄×D₄	C₂³	1	8	yes	—
378	C₄×D₄	C₂³	1	8	yes	—
379	C₄×D₄	C₂³	1	8	yes	—
380	C₄×D₄	C₂³	1	8	yes	—
381	C₄×D₄	C₂³	1	8	yes	—
382	C₄×D₄	C₂³	1	8	yes	—
383	C₄×D₄	C₂³	1	4	yes	—
384	#117	C₂³	1	4	yes	—
385	#117	C₂³	1	2	yes	—
386	#117	C₂³	1	4	yes	—
387	#117	C₂³	1	4	yes	—
388	#117	C₂³	1	4	yes	—
389	#117	C₂³	1	4	yes	—
390	#117	C₂³	1	8	yes	—
391	#117	C₂³	1	8	yes	—
392	#117	C₂³	1	8	yes	—
393	#117	C₂³	1	4	yes	—
394	#117	C₂³	1	8	yes	—
395	#117	C₂³	1	1	yes	characteristic
396	#117	C₂³	1	2	yes	—
397	#117	C₂³	1	4	yes	—
398	#117	C₂³	1	4	yes	—
399	#117	C₂³	1	8	yes	—
400	#117	C₂³	1	8	yes	—
401	#117	C₂³	1	4	yes	—
402	#117	C₂³	1	4	yes	—
403	#117	C₂³	1	8	yes	—
404	#117	C₂³	1	8	yes	—
405	#117	C₂³	1	4	yes	—
406	#117	C₂³	1	2	yes	—
407	#117	C₂³	1	4	yes	—
408	#117	C₂³	1	4	yes	—
409	#117	C₂³	1	8	yes	—
410	#117	C₂³	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³	1	4	yes	—
415	C₂×C₄⋊C₄	C₂³	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³	1	8	yes	—
418	C₂×C₄⋊C₄	C₂³	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
420	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
421	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
426	C₂×C₄²	C₂³	1	4	yes	—
427	C₂×C₄²	C₂³	1	8	yes	—
428	C₂×C₄²	C₂³	1	1	yes	characteristic
429	C₂×C₄²	C₂³	1	2	yes	—
430	C₂×C₄²	C₂³	1	4	yes	—
431	C₂⁴	C₂⁴	1	4	yes	—
432	C₂⁴	C₂⁴	1	4	yes	—
433	#41	—	4	8	no	—
434	#41	—	4	8	no	—
435	#41	—	4	2	no	—
436	#41	—	4	4	no	—
437	#41	—	4	8	no	—
438	#41	—	4	8	no	—
439	C₂×Q₈	—	4	4	no	—
440	C₂×Q₈	—	4	8	no	—
441	C₂×Q₈	C₂⁴	1	2	yes	—
442	C₂×Q₈	C₂⁴	1	4	yes	—
443	C₂×Q₈	C₂⁴	1	2	yes	—
444	C₂×Q₈	C₂⁴	1	8	yes	—
445	C₂×Q₈	C₂⁴	1	4	yes	—
446	C₂×Q₈	C₂⁴	1	1	yes	characteristic
447	C₂×Q₈	C₂⁴	1	4	yes	—
448	C₂×Q₈	C₂⁴	1	4	yes	—
449	C₂×Q₈	C₂⁴	1	2	yes	—
450	C₂×D₄	—	4	4	no	—
451	C₂×D₄	—	4	4	no	—
452	C₂×D₄	—	4	8	no	—
453	C₂×D₄	—	4	8	no	—
454	C₂×D₄	C₂⁴	1	4	yes	—
455	C₂×D₄	C₂⁴	1	2	yes	—
456	C₂×D₄	C₂⁴	1	2	yes	—
457	C₂×D₄	C₂⁴	1	2	yes	—
458	C₂×D₄	C₂⁴	1	2	yes	—
459	C₂×D₄	C₂⁴	1	4	yes	—
460	C₂×D₄	C₂⁴	1	1	yes	characteristic
461	C₂×D₄	C₂⁴	1	4	yes	—
462	C₂×D₄	C₂⁴	1	4	yes	—
463	C₂×D₄	C₂⁴	1	8	yes	—
464	C₂×D₄	C₂⁴	1	4	yes	—
465	C₂×D₄	C₂⁴	1	8	yes	—
466	C₂×D₄	C₂⁴	1	4	yes	—
467	C₂×D₄	C₂⁴	1	4	yes	—
468	C₂×D₄	C₂⁴	1	4	yes	—
469	C₂×D₄	C₂⁴	1	4	yes	—
470	C₂×D₄	C₂⁴	1	8	yes	—
471	C₂×D₄	C₂⁴	1	4	yes	—
472	C₂×D₄	C₂⁴	1	4	yes	—
473	C₂×D₄	C₂⁴	1	4	yes	—
474	C₂²×C₄	—	4	8	no	—
475	C₂²×C₄	—	4	8	no	—
476	C₂²×C₄	C₂⁴	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴	1	4	yes	—
478	C₂²×C₄	C₂⁴	1	2	yes	—
479	C₂²×C₄	C₂⁴	1	2	yes	—
480	C₂²×C₄	C₂⁴	1	2	yes	—
481	C₂²×C₄	C₂⁴	1	4	yes	—
482	C₂²×C₄	C₂⁴	1	4	yes	—
483	C₂²×C₄	C₂⁴	1	4	yes	—
484	C₂²×C₄	C₂⁴	1	4	yes	—
485	C₂²×C₄	C₂⁴	1	4	yes	—
486	C₂²×C₄	C₂⁴	1	4	yes	—
487	C₂²×C₄	C₂⁴	1	2	yes	—
488	C₂²×C₄	C₂⁴	1	8	yes	—
489	C₂²×C₄	C₂⁴	1	8	yes	—
490	C₂²×C₄	C₂⁴	1	4	yes	—
491	C₂²×C₄	C₂⁴	1	8	yes	—
492	C₂²×C₄	C₂⁴	1	4	yes	—
493	C₂²×C₄	C₂⁴	1	4	yes	—
494	C₂²×C₄	C₂⁴	1	8	yes	—
495	C₂²×C₄	C₂⁴	1	4	yes	—
496	C₂²×C₄	C₂⁴	1	4	yes	—
497	C₄⋊C₄	C₂⁴	1	2	yes	—
498	C₄⋊C₄	C₂⁴	1	2	yes	—
499	C₄⋊C₄	C₂⁴	1	4	yes	—
500	C₄⋊C₄	C₂⁴	1	4	yes	—
501	C₄⋊C₄	C₂⁴	1	2	yes	—
502	C₄⋊C₄	C₂⁴	1	8	yes	—
503	C₄⋊C₄	C₂⁴	1	2	yes	—
504	C₄⋊C₄	C₂⁴	1	4	yes	—
505	C₄⋊C₄	C₂⁴	1	2	yes	—
506	C₄⋊C₄	C₂⁴	1	4	yes	—
507	C₄⋊C₄	C₂⁴	1	4	yes	—
508	C₄⋊C₄	C₂⁴	1	4	yes	—
509	C₄⋊C₄	C₂⁴	1	8	yes	—
510	C₄⋊C₄	C₂⁴	1	8	yes	—
511	C₄⋊C₄	C₂⁴	1	8	yes	—
512	C₄⋊C₄	C₂⁴	1	4	yes	—
513	C₄⋊C₄	C₂⁴	1	4	yes	—
514	C₄⋊C₄	C₂⁴	1	4	yes	—
515	C₄⋊C₄	C₂⁴	1	8	yes	—
516	C₄⋊C₄	C₂⁴	1	8	yes	—
517	C₄⋊C₄	C₂⁴	1	4	yes	—
518	C₄⋊C₄	C₂⁴	1	4	yes	—
519	C₄⋊C₄	C₂⁴	1	8	yes	—
520	C₄⋊C₄	C₂⁴	1	8	yes	—
521	C₄⋊C₄	C₂⁴	1	2	yes	—
522	C₄⋊C₄	C₂⁴	1	2	yes	—
523	C₄⋊C₄	C₂⁴	1	8	yes	—
524	C₄⋊C₄	C₂⁴	1	8	yes	—
525	C₄⋊C₄	C₂⁴	1	4	yes	—
526	C₄⋊C₄	C₂⁴	1	8	yes	—
527	C₄⋊C₄	C₂⁴	1	8	yes	—
528	C₄⋊C₄	C₂⁴	1	4	yes	—
529	C₄⋊C₄	C₂⁴	1	8	yes	—
530	C₄⋊C₄	C₂⁴	1	4	yes	—
531	C₄⋊C₄	C₂⁴	1	4	yes	—
532	C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
533	C₂²⋊C₄	C₂⁴	1	4	yes	—
534	C₂²⋊C₄	C₂⁴	1	4	yes	—
535	C₂²⋊C₄	C₂⁴	1	8	yes	—
536	C₂²⋊C₄	C₂⁴	1	4	yes	—
537	C₂²⋊C₄	C₂⁴	1	2	yes	—
538	C₂²⋊C₄	C₂⁴	1	4	yes	—
539	C₂²⋊C₄	C₂⁴	1	8	yes	—
540	C₂²⋊C₄	C₂⁴	1	4	yes	—
541	C₂²⋊C₄	C₂⁴	1	4	yes	—
542	C₂²⋊C₄	C₂⁴	1	4	yes	—
543	C₂²⋊C₄	C₂⁴	1	8	yes	—
544	C₂²⋊C₄	C₂⁴	1	8	yes	—
545	C₂²⋊C₄	C₂⁴	1	8	yes	—
546	C₂²⋊C₄	C₂⁴	1	8	yes	—
547	C₂²⋊C₄	C₂⁴	1	4	yes	—
548	C₂²⋊C₄	C₂⁴	1	4	yes	—
549	C₂²⋊C₄	C₂⁴	1	4	yes	—
550	C₂²⋊C₄	C₂⁴	1	8	yes	—
551	C₂²⋊C₄	C₂⁴	1	8	yes	—
552	C₂²⋊C₄	C₂⁴	1	4	yes	—
553	C₂²⋊C₄	C₂⁴	1	4	yes	—
554	C₂²⋊C₄	C₂⁴	1	4	yes	—
555	C₂²⋊C₄	C₂⁴	1	4	yes	—
556	C₂²⋊C₄	C₂⁴	1	4	yes	—
557	C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
558	C₂²⋊C₄	C₂⁴	1	4	yes	—
559	C₂²⋊C₄	C₂⁴	1	4	yes	—
560	C₂²⋊C₄	C₂⁴	1	2	yes	—
561	C₂²⋊C₄	C₂⁴	1	4	yes	—
562	C₂²⋊C₄	C₂⁴	1	8	yes	—
563	C₂²⋊C₄	C₂⁴	1	4	yes	—
564	C₂²⋊C₄	C₂⁴	1	8	yes	—
565	C₂²⋊C₄	C₂⁴	1	8	yes	—
566	C₂²⋊C₄	C₂⁴	1	8	yes	—
567	C₂²⋊C₄	C₂⁴	1	8	yes	—
568	C₂²⋊C₄	C₂⁴	1	4	yes	—
569	C₄²	C₂⁴	1	4	yes	—
570	C₄²	C₂⁴	1	4	yes	—
571	C₄²	C₂⁴	1	1	yes	characteristic
572	C₄²	C₂⁴	1	2	yes	—
573	C₄²	C₂⁴	1	4	yes	—
574	C₄²	C₂⁴	1	4	yes	—
575	C₄²	C₂⁴	1	8	yes	—
576	C₄²	C₂⁴	1	8	yes	—
577	C₄²	C₂⁴	1	8	yes	—
578	C₄²	C₂⁴	1	2	yes	—
579	C₄²	C₂⁴	1	2	yes	—
580	C₄²	C₂⁴	1	4	yes	—
581	C₄²	C₂⁴	1	2	yes	—
582	C₄²	C₂⁴	1	1	yes	characteristic
583	C₄²	C₂⁴	1	4	yes	—
584	C₄²	C₂⁴	1	4	yes	—
585	C₄²	C₂⁴	1	4	yes	—
586	C₄²	C₂⁴	1	8	yes	—
587	C₂³	—	2	8	no	—
588	C₂³	—	4	4	no	—
589	C₂³	—	4	4	no	—
590	C₂³	—	4	4	no	—
591	C₂³	—	4	4	no	—
592	C₂³	—	4	4	no	—
593	C₂³	C₂⁵	1	2	yes	—
594	C₂³	C₂⁵	1	4	yes	—
595	C₂³	C₂⁵	1	4	yes	—
596	C₂³	C₂⁵	1	4	yes	—
597	C₂³	C₂⁵	1	1	yes	characteristic
598	Q₈	—	2	4	no	—
599	Q₈	—	2	8	no	—
600	Q₈	—	4	2	no	—
601	Q₈	—	4	4	no	—
602	Q₈	—	4	8	no	—
603	Q₈	—	4	2	no	—
604	Q₈	—	4	4	no	—
605	Q₈	—	4	4	no	—
606	Q₈	—	4	1	no	—
607	D₄	—	2	4	no	—
608	D₄	—	2	8	no	—
609	D₄	—	2	4	no	—
610	D₄	—	2	4	no	—
611	D₄	—	2	4	no	—
612	D₄	—	4	4	no	—
613	D₄	—	4	4	no	—
614	D₄	—	4	4	no	—
615	D₄	—	4	4	no	—
616	D₄	—	4	8	no	—
617	D₄	—	4	4	no	—
618	D₄	—	4	4	no	—
619	D₄	—	4	4	no	—
620	D₄	—	4	4	no	—
621	D₄	—	4	4	no	—
622	D₄	—	4	4	no	—
623	D₄	—	4	1	no	—
624	D₄	—	4	8	no	—
625	D₄	—	4	8	no	—
626	D₄	—	4	4	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	8	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	8	no	—
633	C₂×C₄	—	2	8	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	4	4	no	—
636	C₂×C₄	—	4	4	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	8	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	4	no	—
645	C₂×C₄	—	4	8	no	—
646	C₂×C₄	—	4	8	no	—
647	C₂×C₄	—	4	2	no	—
648	C₂×C₄	C₂⁵	1	4	yes	—
649	C₂×C₄	C₂⁵	1	2	yes	—
650	C₂×C₄	C₂⁵	1	1	yes	characteristic
651	C₂×C₄	C₂⁵	1	4	yes	—
652	C₂×C₄	C₂⁵	1	2	yes	—
653	C₂×C₄	C₂⁵	1	1	yes	characteristic
654	C₂×C₄	C₂⁵	1	4	yes	—
655	C₂×C₄	C₂⁵	1	4	yes	—
656	C₂×C₄	C₂⁵	1	4	yes	—
657	C₂×C₄	C₂⁵	1	4	yes	—
658	C₂×C₄	C₂⁵	1	8	yes	—
659	C₂×C₄	C₂⁵	1	2	yes	—
660	C₂×C₄	C₂⁵	1	4	yes	—
661	C₂×C₄	C₂⁵	1	2	yes	—
662	C₂×C₄	C₂⁵	1	2	yes	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	4	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	4	no	—
674	C₂²	—	2	4	no	—
675	C₂²	—	2	4	no	—
676	C₂²	—	8	8	no	—
677	C₂²	—	8	8	no	—
678	C₂²	#585	1	2	yes	—
679	C₂²	C₂⁶	1	1	yes	characteristic
680	C₄	—	2	2	no	—
681	C₄	—	2	4	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	4	no	—
684	C₄	—	2	4	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	1	no	—
690	C₄	—	2	2	no	—
691	C₄	—	2	4	no	—
692	C₄	—	2	8	no	—
693	C₄	—	2	4	no	—
694	C₄	#585	1	4	yes	—
695	C₂	—	2	2	no	—
696	C₂	—	4	4	no	—
697	C₂	—	4	4	no	—
698	C₂	—	4	2	no	—
699	C₂	—	4	4	no	—
700	C₂	C₂×#585	1	1	yes	characteristic
701	C₂	C₂×#585	1	2	yes	—

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3566	C₂	semidirect
2. #3565	C₂	semidirect
3. #3547	C₂	semidirect
4. #3545	C₂	semidirect
5. #3544	C₂	semidirect
6. #3542	C₂	semidirect
7. #3540	C₂	semidirect
8. #3524	C₂	semidirect
9. #3520	C₂	semidirect
10. #3518	C₂	semidirect
11. #3510	C₂	semidirect
12. #3509	C₂	semidirect
13. #3506	C₂	semidirect
14. #3505	C₂	semidirect
15. #3495	C₂	semidirect
16. #3493	C₂	semidirect
17. #3481	C₂	semidirect
18. #3475	C₂	semidirect
19. #3475	C₂	semidirect
20. C₂×#555	C₂	semidirect
21. #563	C₂²	semidirect
22. #563	C₂²	semidirect
23. #562	C₂²	semidirect
24. #562	C₂²	semidirect
25. H(3,𝔽₄)	C₂²	semidirect
26. #560	C₂²	semidirect
27. #559	C₂²	semidirect
28. #559	C₂²	semidirect
29. #559	C₂²	semidirect
30. Q₈²	C₂²	semidirect
31. #557	C₂²	semidirect
32. #556	C₂²	semidirect
33. #556	C₂²	semidirect
34. #556	C₂²	semidirect
35. #556	C₂²	semidirect
36. #556	C₂²	semidirect
37. #556	C₂²	semidirect
38. #556	C₂²	semidirect
40. #555	C₂²	semidirect
41. #555	C₂²	semidirect
42. #555	C₂²	semidirect
43. #555	C₂²	semidirect
44. #555	C₂²	semidirect
45. #555	C₂²	semidirect
46. #555	C₂²	semidirect
47. #555	C₂²	semidirect
48. #555	C₂²	semidirect
49. #555	C₂²	semidirect
50. #554	C₂²	semidirect
51. #554	C₂²	semidirect
52. #554	C₂²	semidirect
53. #554	C₂²	semidirect
55. #553	C₂²	semidirect
56. #553	C₂²	semidirect
57. #553	C₂²	semidirect
58. #553	C₂²	semidirect
59. #553	C₂²	semidirect
60. #553	C₂²	semidirect
61. #553	C₂²	semidirect
62. #553	C₂²	semidirect
63. #552	C₂²	semidirect
64. #552	C₂²	semidirect
65. #552	C₂²	semidirect
66. #552	C₂²	semidirect
67. #552	C₂²	semidirect
68. #552	C₂²	semidirect
69. #552	C₂²	semidirect
70. #552	C₂²	semidirect
71. #552	C₂²	semidirect
72. #552	C₂²	semidirect
73. #551	C₂²	semidirect
74. #551	C₂²	semidirect
75. #551	C₂²	semidirect
76. #551	C₂²	semidirect
77. #551	C₂²	semidirect
78. #551	C₂²	semidirect
79. #551	C₂²	semidirect
80. #551	C₂²	semidirect
81. #550	C₂²	semidirect
82. D₄×Q₈	C₂²	semidirect
83. #548	C₂²	semidirect
84. #548	C₂²	semidirect
85. #548	C₂²	semidirect
86. #547	C₂²	semidirect
87. #547	C₂²	semidirect
88. #547	C₂²	semidirect
91. #546	C₂²	semidirect
92. #546	C₂²	semidirect
93. #546	C₂²	semidirect
94. #546	C₂²	semidirect
95. D₄²	C₂²	semidirect
96. #544	C₂²	semidirect
97. #544	C₂²	semidirect
98. #542	C₂²	semidirect
99. #542	C₂²	semidirect
100. #542	C₂²	semidirect
101. #542	C₂²	semidirect
102. #542	C₂²	semidirect
103. #542	C₂²	semidirect
104. #542	C₂²	semidirect
105. #542	C₂²	semidirect
106. #541	C₂²	semidirect
107. #541	C₂²	semidirect
108. #540	C₂²	semidirect
109. #540	C₂²	semidirect
110. #539	C₂²	semidirect
111. #539	C₂²	semidirect
112. #538	C₂²	semidirect
113. #538	C₂²	semidirect
114. #538	C₂²	semidirect
115. #538	C₂²	semidirect
116. #537	C₂²	semidirect
118. #536	C₂²	semidirect
119. #536	C₂²	semidirect
121. #535	C₂²	semidirect
122. #534	C₂²	semidirect
123. #533	C₂²	semidirect
124. #533	C₂²	semidirect
125. #533	C₂²	semidirect
126. #533	C₂²	semidirect
127. #533	C₂²	semidirect
128. #532	C₂²	semidirect
129. C₂×C₄⋊Q₈	C₂²	semidirect
130. #529	C₂²	semidirect
131. #529	C₂²	semidirect
132. #529	C₂²	semidirect
133. #529	C₂²	semidirect
134. #529	C₂²	semidirect
135. #529	C₂²	semidirect
136. #529	C₂²	semidirect
137. #529	C₂²	semidirect
138. #529	C₂²	semidirect
139. #529	C₂²	semidirect
140. C₂×#124	C₂²	semidirect
142. #525	C₂²	semidirect
143. #525	C₂²	semidirect
144. #525	C₂²	semidirect
145. #525	C₂²	semidirect
146. #525	C₂²	semidirect
147. C₂×C₂²⋊Q₈	C₂²	semidirect
148. C₂×#121	C₂²	semidirect
149. #520	C₂²	semidirect
150. #520	C₂²	semidirect
151. #519	C₂²	semidirect
152. #519	C₂²	semidirect
153. #518	C₂²	semidirect
155. C₄×#41	C₂²	semidirect
156. C₄×#41	C₂²	semidirect
157. C₄×#41	C₂²	semidirect
158. C₂×C₄×D₄	C₂²	semidirect
159. C₂×C₄×D₄	C₂²	semidirect
160. C₂×C₄×D₄	C₂²	semidirect
161. C₂×#117	C₂²	semidirect
162. C₂×#117	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3566	2
#3565	2
#3547	2
#3545	2
#3544	2
#3542	2
#3540	2
#3524	2
#3520	2
#3518	2
#3510	2
#3509	2
#3506	2
#3505	2
#3495	2
#3493	2
#3481	2
#3475	2
C₂×#555	2