Subgroups — #62748

Order 256.

3640 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3562	C₂	1	4	yes	maximal, complemented
2	#3561	C₂	1	2	yes	maximal, complemented
3	#3560	C₂	1	4	yes	maximal, complemented
4	#3559	C₂	1	2	yes	maximal, complemented
5	#3558	C₂	1	2	yes	maximal, complemented
6	#3558	C₂	1	2	yes	maximal, complemented
7	#3554	C₂	1	2	yes	maximal, complemented
8	#3552	C₂	1	2	yes	maximal, complemented
9	#3546	C₂	1	2	yes	maximal, complemented
10	#3543	C₂	1	2	yes	maximal, complemented
11	#3537	C₂	1	2	yes	maximal, complemented
12	#3536	C₂	1	2	yes	maximal, complemented
13	#3534	C₂	1	4	yes	maximal, complemented
14	#3529	C₂	1	4	yes	maximal, complemented
15	#3481	C₂	1	4	yes	maximal, complemented
16	#3480	C₂	1	2	yes	maximal, complemented
17	D₄×#41	C₂	1	4	yes	maximal, complemented
18	D₄×#41	C₂	1	2	yes	maximal, complemented
19	#3460	C₂	1	4	yes	maximal, complemented
20	#3459	C₂	1	4	yes	maximal, complemented
21	#3455	C₂	1	2	yes	maximal, complemented
22	#3449	C₂	1	2	yes	maximal, complemented
23	#3444	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#532	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂×#529	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂²×#41	C₂²	1	2	yes	complemented
27	C₂²×#41	C₂²	1	4	yes	complemented
28	#563	C₂²	1	8	yes	complemented
29	#563	C₂²	1	4	yes	complemented
30	#562	C₂²	1	8	yes	complemented
31	#562	C₂²	1	8	yes	complemented
32	#562	C₂²	1	4	yes	complemented
33	#562	C₂²	1	4	yes	complemented
34	H(3,𝔽₄)	C₂²	1	4	yes	complemented
35	#560	C₂²	1	8	yes	complemented
36	#560	C₂²	1	8	yes	complemented
37	#560	C₂²	1	8	yes	complemented
38	#559	C₂²	1	2	yes	complemented
39	#559	C₂²	1	4	yes	complemented
40	#559	C₂²	1	4	yes	complemented
41	#557	C₂²	1	2	yes	complemented
42	#556	C₂²	1	2	yes	complemented
43	#556	C₂²	1	4	yes	complemented
44	#554	C₂²	1	4	yes	complemented
45	#554	C₂²	1	4	yes	complemented
46	#553	C₂²	1	8	yes	complemented
47	#553	C₂²	1	4	yes	complemented
48	#553	C₂²	1	4	yes	complemented
49	#553	C₂²	1	4	yes	complemented
50	#553	C₂²	1	8	yes	complemented
51	#551	C₂²	1	8	yes	complemented
52	#551	C₂²	1	8	yes	complemented
53	#550	C₂²	1	2	yes	complemented
54	#550	C₂²	1	4	yes	complemented
55	#550	C₂²	1	2	yes	complemented
56	D₄×Q₈	C₂²	1	2	yes	complemented
57	D₄×Q₈	C₂²	1	4	yes	complemented
58	#548	C₂²	1	4	yes	complemented
59	#548	C₂²	1	4	yes	complemented
60	#548	C₂²	1	4	yes	complemented
61	#548	C₂²	1	4	yes	complemented
62	#547	C₂²	1	4	yes	complemented
63	#547	C₂²	1	2	yes	complemented
64	#547	C₂²	1	4	yes	complemented
65	#547	C₂²	1	8	yes	complemented
66	#546	C₂²	1	8	yes	complemented
67	#546	C₂²	1	8	yes	complemented
68	#546	C₂²	1	4	yes	complemented
69	#546	C₂²	1	4	yes	complemented
70	#546	C₂²	1	8	yes	complemented
71	#546	C₂²	1	4	yes	complemented
72	#546	C₂²	1	8	yes	complemented
73	#546	C₂²	1	4	yes	complemented
74	#546	C₂²	1	4	yes	complemented
75	D₄²	C₂²	1	8	yes	complemented
76	D₄²	C₂²	1	4	yes	complemented
77	D₄²	C₂²	1	2	yes	complemented
78	D₄²	C₂²	1	4	yes	complemented
79	D₄²	C₂²	1	4	yes	complemented
80	#544	C₂²	1	4	yes	complemented
81	#543	C₂²	1	4	yes	complemented
82	#542	C₂²	1	4	yes	complemented
83	#542	C₂²	1	4	yes	complemented
84	#542	C₂²	1	4	yes	complemented
85	#542	C₂²	1	4	yes	complemented
86	#542	C₂²	1	8	yes	complemented
87	#541	C₂²	1	4	yes	complemented
88	#540	C₂²	1	4	yes	complemented
89	#540	C₂²	1	8	yes	complemented
90	#540	C₂²	1	4	yes	complemented
91	#540	C₂²	1	4	yes	complemented
92	#539	C₂²	1	4	yes	complemented
93	#539	C₂²	1	4	yes	complemented
94	#539	C₂²	1	8	yes	complemented
95	#539	C₂²	1	8	yes	complemented
96	#539	C₂²	1	8	yes	complemented
97	#538	C₂²	1	4	yes	complemented
98	#538	C₂²	1	4	yes	complemented
99	#538	C₂²	1	4	yes	complemented
100	#538	C₂²	1	4	yes	complemented
101	#538	C₂²	1	8	yes	complemented
102	#538	C₂²	1	8	yes	complemented
103	#538	C₂²	1	8	yes	complemented
104	#538	C₂²	1	8	yes	complemented
105	#537	C₂²	1	4	yes	complemented
106	#537	C₂²	1	4	yes	complemented
107	#537	C₂²	1	4	yes	complemented
108	#536	C₂²	1	4	yes	complemented
109	#536	C₂²	1	4	yes	complemented
110	#535	C₂²	1	4	yes	complemented
111	#535	C₂²	1	4	yes	complemented
112	#535	C₂²	1	4	yes	complemented
113	#535	C₂²	1	4	yes	complemented
114	#534	C₂²	1	4	yes	complemented
115	#534	C₂²	1	4	yes	complemented
116	#534	C₂²	1	8	yes	complemented
117	#534	C₂²	1	4	yes	complemented
118	#533	C₂²	1	1	yes	characteristic, complemented
119	#533	C₂²	1	1	yes	characteristic, complemented
120	#533	C₂²	1	1	yes	characteristic, complemented
121	#532	C₂²	1	2	yes	complemented
122	#532	C₂²	1	2	yes	complemented
123	#532	C₂²	1	2	yes	complemented
124	#532	C₂²	1	2	yes	complemented
125	#532	C₂²	1	2	yes	complemented
126	#532	C₂²	1	2	yes	complemented
127	#532	C₂²	1	2	yes	complemented
128	#532	C₂²	1	2	yes	complemented
129	#532	C₂²	1	1	yes	characteristic, complemented
130	#532	C₂²	1	1	yes	characteristic, complemented
131	#532	C₂²	1	1	yes	characteristic, complemented
132	#532	C₂²	1	4	yes	complemented
133	#532	C₂²	1	4	yes	complemented
134	#532	C₂²	1	8	yes	complemented
135	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
136	C₂×#127	C₂²	1	1	yes	characteristic, complemented
137	#529	C₂²	1	2	yes	complemented
138	#529	C₂²	1	2	yes	complemented
139	#529	C₂²	1	2	yes	complemented
140	#529	C₂²	1	2	yes	complemented
141	#529	C₂²	1	2	yes	complemented
142	#529	C₂²	1	2	yes	complemented
143	#529	C₂²	1	2	yes	complemented
144	#529	C₂²	1	2	yes	complemented
145	#529	C₂²	1	2	yes	complemented
146	#529	C₂²	1	2	yes	complemented
147	#529	C₂²	1	2	yes	complemented
148	#529	C₂²	1	2	yes	complemented
149	#529	C₂²	1	2	yes	complemented
150	#529	C₂²	1	2	yes	complemented
151	#529	C₂²	1	8	yes	complemented
152	#529	C₂²	1	8	yes	complemented
153	#529	C₂²	1	8	yes	complemented
154	#529	C₂²	1	4	yes	complemented
155	C₂×#126	C₂²	1	2	yes	complemented
156	C₂×#125	C₂²	1	1	yes	characteristic, complemented
157	C₂×#124	C₂²	1	1	yes	characteristic, complemented
158	C₂×#124	C₂²	1	2	yes	complemented
159	#525	C₂²	1	2	yes	complemented
160	#525	C₂²	1	2	yes	complemented
161	#525	C₂²	1	2	yes	complemented
162	#525	C₂²	1	8	yes	complemented
163	#525	C₂²	1	8	yes	complemented
164	#525	C₂²	1	4	yes	complemented
165	#525	C₂²	1	8	yes	complemented
166	#525	C₂²	1	8	yes	complemented
167	#525	C₂²	1	8	yes	complemented
168	C₂×#123	C₂²	1	2	yes	complemented
169	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
170	C₂×#121	C₂²	1	1	yes	characteristic
171	C₂×#121	C₂²	1	2	yes	complemented
172	C₂×#121	C₂²	1	2	yes	complemented
173	C₄×#41	C₂²	1	2	yes	complemented
174	C₄×#41	C₂²	1	2	yes	complemented
175	C₄×#41	C₂²	1	2	yes	complemented
176	C₄×#41	C₂²	1	4	yes	complemented
177	C₄×#41	C₂²	1	4	yes	complemented
178	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
179	C₂×C₄×D₄	C₂²	1	2	yes	complemented
180	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
181	C₂×C₄×D₄	C₂²	1	2	yes	complemented
182	C₂×C₄×D₄	C₂²	1	2	yes	complemented
183	C₂×C₄×D₄	C₂²	1	8	yes	complemented
184	C₂×C₄×D₄	C₂²	1	4	yes	complemented
185	C₂×#117	C₂²	1	2	yes	complemented
186	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
187	C₂×#41	—	4	8	no	—
188	C₂×#41	—	4	16	no	—
189	C₂×#41	C₂³	1	2	yes	—
190	C₂×#41	C₂³	1	4	yes	—
191	C₂×#41	C₂³	1	2	yes	—
192	C₂×#41	C₂³	1	2	yes	—
193	C₂×#41	C₂³	1	4	yes	—
194	C₂×#41	C₂³	1	8	yes	—
195	C₂×#41	C₂³	1	4	yes	—
196	C₂×#41	C₂³	1	4	yes	—
197	C₂×#41	C₂³	1	4	yes	—
198	C₂×#41	C₂³	1	4	yes	—
199	C₂×#41	C₂³	1	4	yes	—
200	C₂×#41	C₂³	1	8	yes	—
201	C₂²×Q₈	C₂³	1	1	yes	characteristic
202	C₂²×Q₈	C₂³	1	2	yes	—
203	C₂²×Q₈	C₂³	1	4	yes	—
204	C₂²×D₄	C₂³	1	2	yes	—
205	C₂²×D₄	C₂³	1	1	yes	characteristic
206	C₂²×D₄	C₂³	1	2	yes	—
207	C₂²×D₄	C₂³	1	2	yes	—
208	C₂²×D₄	C₂³	1	8	yes	—
209	C₂²×D₄	C₂³	1	4	yes	—
210	C₂²×D₄	C₂³	1	4	yes	—
211	C₂²×D₄	C₂³	1	2	yes	—
212	C₂²×D₄	C₂³	1	8	yes	—
213	C₂²×D₄	C₂³	1	4	yes	—
214	C₂³×C₄	C₂³	1	2	yes	—
215	C₂³×C₄	C₂³	1	1	yes	characteristic
216	C₂³×C₄	C₂³	1	4	yes	—
217	C₂³×C₄	C₂³	1	8	yes	—
218	C₂³×C₄	C₂³	1	1	yes	characteristic
219	C₂³×C₄	C₂³	1	1	yes	characteristic
220	C₄⋊Q₈	C₂³	1	2	yes	—
221	C₄⋊Q₈	C₂³	1	2	yes	—
222	C₄⋊Q₈	C₂³	1	2	yes	—
223	C₄⋊Q₈	C₂³	1	2	yes	—
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⋊Q₈	C₂³	1	4	yes	—
228	C₄⋊Q₈	C₂³	1	4	yes	—
229	C₄⋊Q₈	C₂³	1	8	yes	—
230	#127	C₂³	1	2	yes	—
231	#127	C₂³	1	2	yes	—
232	#127	C₂³	1	2	yes	—
233	#127	C₂³	1	2	yes	—
234	#127	C₂³	1	1	yes	characteristic
235	#127	C₂³	1	4	yes	—
236	#127	C₂³	1	4	yes	—
237	#127	C₂³	1	8	yes	—
238	#126	C₂³	1	4	yes	—
239	#126	C₂³	1	4	yes	—
240	#126	C₂³	1	4	yes	—
241	#126	C₂³	1	4	yes	—
242	#126	C₂³	1	4	yes	—
243	#126	C₂³	1	4	yes	—
244	#126	C₂³	1	8	yes	—
245	#126	C₂³	1	8	yes	—
246	#126	C₂³	1	8	yes	—
247	#126	C₂³	1	8	yes	—
248	#126	C₂³	1	8	yes	—
249	#126	C₂³	1	8	yes	—
250	#126	C₂³	1	8	yes	—
251	#125	C₂³	1	2	yes	—
252	#125	C₂³	1	2	yes	—
253	#125	C₂³	1	2	yes	—
254	#125	C₂³	1	2	yes	—
255	#125	C₂³	1	2	yes	—
256	#125	C₂³	1	2	yes	—
257	#125	C₂³	1	2	yes	—
258	#125	C₂³	1	8	yes	—
259	#125	C₂³	1	8	yes	—
260	#125	C₂³	1	8	yes	—
261	#125	C₂³	1	4	yes	—
262	#124	C₂³	1	2	yes	—
263	#124	C₂³	1	2	yes	—
264	#124	C₂³	1	2	yes	—
265	#124	C₂³	1	2	yes	—
266	#124	C₂³	1	4	yes	—
267	#124	C₂³	1	4	yes	—
268	#124	C₂³	1	4	yes	—
269	#124	C₂³	1	4	yes	—
270	#124	C₂³	1	2	yes	—
271	#124	C₂³	1	2	yes	—
272	#124	C₂³	1	2	yes	—
273	#124	C₂³	1	8	yes	—
274	#124	C₂³	1	4	yes	—
275	#124	C₂³	1	8	yes	—
276	#124	C₂³	1	8	yes	—
277	#124	C₂³	1	4	yes	—
278	#124	C₂³	1	4	yes	—
279	#124	C₂³	1	8	yes	—
280	#124	C₂³	1	8	yes	—
281	#124	C₂³	1	8	yes	—
282	#123	C₂³	1	4	yes	—
283	#123	C₂³	1	4	yes	—
284	#123	C₂³	1	4	yes	—
285	#123	C₂³	1	4	yes	—
286	#123	C₂³	1	4	yes	—
287	#123	C₂³	1	4	yes	—
288	#123	C₂³	1	4	yes	—
289	#123	C₂³	1	8	yes	—
290	#123	C₂³	1	8	yes	—
291	#123	C₂³	1	8	yes	—
292	#123	C₂³	1	8	yes	—
293	#123	C₂³	1	8	yes	—
294	#123	C₂³	1	8	yes	—
295	#123	C₂³	1	8	yes	—
296	#123	C₂³	1	8	yes	—
297	#123	C₂³	1	8	yes	—
298	#123	C₂³	1	8	yes	—
299	#123	C₂³	1	8	yes	—
300	#123	C₂³	1	8	yes	—
301	#123	C₂³	1	8	yes	—
302	#123	C₂³	1	8	yes	—
303	#123	C₂³	1	8	yes	—
304	#123	C₂³	1	8	yes	—
305	#123	C₂³	1	8	yes	—
306	#123	C₂³	1	8	yes	—
307	C₂²⋊Q₈	C₂³	1	2	yes	—
308	C₂²⋊Q₈	C₂³	1	2	yes	—
309	C₂²⋊Q₈	C₂³	1	2	yes	—
310	C₂²⋊Q₈	C₂³	1	2	yes	—
311	C₂²⋊Q₈	C₂³	1	2	yes	—
312	C₂²⋊Q₈	C₂³	1	2	yes	—
313	C₂²⋊Q₈	C₂³	1	2	yes	—
314	C₂²⋊Q₈	C₂³	1	2	yes	—
315	C₂²⋊Q₈	C₂³	1	2	yes	—
316	C₂²⋊Q₈	C₂³	1	2	yes	—
317	C₂²⋊Q₈	C₂³	1	8	yes	—
318	C₂²⋊Q₈	C₂³	1	8	yes	—
319	C₂²⋊Q₈	C₂³	1	8	yes	—
320	C₂²⋊Q₈	C₂³	1	8	yes	—
321	C₂²⋊Q₈	C₂³	1	8	yes	—
322	C₂²⋊Q₈	C₂³	1	8	yes	—
323	C₂²⋊Q₈	C₂³	1	8	yes	—
324	C₂²⋊Q₈	C₂³	1	8	yes	—
325	C₂²⋊Q₈	C₂³	1	8	yes	—
326	C₂²⋊Q₈	C₂³	1	4	yes	—
327	C₂²⋊Q₈	C₂³	1	4	yes	—
328	C₂²⋊Q₈	C₂³	1	8	yes	—
329	C₂²⋊Q₈	C₂³	1	8	yes	—
330	C₂²⋊Q₈	C₂³	1	4	yes	—
331	C₂²⋊Q₈	C₂³	1	8	yes	—
332	C₂²⋊Q₈	C₂³	1	8	yes	—
333	#121	C₂³	1	2	yes	—
334	#121	C₂³	1	2	yes	—
335	#121	C₂³	1	2	yes	—
336	#121	C₂³	1	2	yes	—
337	#121	C₂³	1	4	yes	—
338	#121	C₂³	1	4	yes	—
339	#121	C₂³	1	4	yes	—
340	#121	C₂³	1	4	yes	—
341	#121	C₂³	1	4	yes	—
342	#121	C₂³	1	4	yes	—
343	#121	C₂³	1	4	yes	—
344	#121	C₂³	1	4	yes	—
345	#121	C₂³	1	2	yes	—
346	#121	C₂³	1	2	yes	—
347	#121	C₂³	1	2	yes	—
348	#121	C₂³	1	2	yes	—
349	#121	C₂³	1	2	yes	—
350	#121	C₂³	1	2	yes	—
351	#121	C₂³	1	8	yes	—
352	#121	C₂³	1	8	yes	—
353	#121	C₂³	1	8	yes	—
354	#121	C₂³	1	8	yes	—
355	#121	C₂³	1	8	yes	—
356	#121	C₂³	1	8	yes	—
357	#121	C₂³	1	8	yes	—
358	#121	C₂³	1	8	yes	—
359	#121	C₂³	1	8	yes	—
360	#121	C₂³	1	8	yes	—
361	#121	C₂³	1	4	yes	—
362	#121	C₂³	1	4	yes	—
363	#121	C₂³	1	8	yes	—
364	#121	C₂³	1	8	yes	—
365	#121	C₂³	1	4	yes	—
366	#121	C₂³	1	8	yes	—
367	#121	C₂³	1	8	yes	—
368	#121	C₂³	1	8	yes	—
369	#121	C₂³	1	4	yes	—
370	#121	C₂³	1	8	yes	—
371	#121	C₂³	1	4	yes	—
372	#121	C₂³	1	8	yes	—
373	#121	C₂³	1	8	yes	—
374	#121	C₂³	1	8	yes	—
375	#121	C₂³	1	8	yes	—
376	#120	C₂³	1	4	yes	—
377	#120	C₂³	1	8	yes	—
378	#120	C₂³	1	8	yes	—
379	#120	C₂³	1	8	yes	—
380	#120	C₂³	1	8	yes	—
381	#120	C₂³	1	8	yes	—
382	#120	C₂³	1	8	yes	—
383	#120	C₂³	1	8	yes	—
384	#120	C₂³	1	8	yes	—
385	#120	C₂³	1	8	yes	—
386	#120	C₂³	1	8	yes	—
387	#120	C₂³	1	8	yes	—
388	C₄×Q₈	C₂³	1	2	yes	—
389	C₄×Q₈	C₂³	1	2	yes	—
390	C₄×Q₈	C₂³	1	2	yes	—
391	C₄×Q₈	C₂³	1	2	yes	—
392	C₄×Q₈	C₂³	1	2	yes	—
393	C₄×Q₈	C₂³	1	2	yes	—
394	C₄×Q₈	C₂³	1	2	yes	—
395	C₄×Q₈	C₂³	1	2	yes	—
396	C₄×Q₈	C₂³	1	2	yes	—
397	C₄×Q₈	C₂³	1	2	yes	—
398	C₄×Q₈	C₂³	1	4	yes	—
399	C₄×Q₈	C₂³	1	4	yes	—
400	C₄×Q₈	C₂³	1	4	yes	—
401	C₄×D₄	C₂³	1	4	yes	—
402	C₄×D₄	C₂³	1	2	yes	—
403	C₄×D₄	C₂³	1	4	yes	—
404	C₄×D₄	C₂³	1	4	yes	—
405	C₄×D₄	C₂³	1	2	yes	—
406	C₄×D₄	C₂³	1	8	yes	—
407	C₄×D₄	C₂³	1	8	yes	—
408	C₄×D₄	C₂³	1	4	yes	—
409	C₄×D₄	C₂³	1	4	yes	—
410	C₄×D₄	C₂³	1	4	yes	—
411	C₄×D₄	C₂³	1	4	yes	—
412	C₄×D₄	C₂³	1	8	yes	—
413	C₄×D₄	C₂³	1	4	yes	—
414	C₄×D₄	C₂³	1	2	yes	—
415	C₄×D₄	C₂³	1	2	yes	—
416	C₄×D₄	C₂³	1	4	yes	—
417	C₄×D₄	C₂³	1	4	yes	—
418	C₄×D₄	C₂³	1	4	yes	—
419	C₄×D₄	C₂³	1	4	yes	—
420	C₄×D₄	C₂³	1	4	yes	—
421	C₄×D₄	C₂³	1	8	yes	—
422	C₄×D₄	C₂³	1	8	yes	—
423	C₄×D₄	C₂³	1	8	yes	—
424	C₄×D₄	C₂³	1	8	yes	—
425	C₄×D₄	C₂³	1	4	yes	—
426	C₄×D₄	C₂³	1	4	yes	—
427	C₄×D₄	C₂³	1	8	yes	—
428	C₄×D₄	C₂³	1	2	yes	—
429	C₄×D₄	C₂³	1	2	yes	—
430	C₄×D₄	C₂³	1	8	yes	—
431	C₄×D₄	C₂³	1	4	yes	—
432	C₄×D₄	C₂³	1	4	yes	—
433	C₄×D₄	C₂³	1	4	yes	—
434	C₄×D₄	C₂³	1	4	yes	—
435	C₄×D₄	C₂³	1	4	yes	—
436	C₄×D₄	C₂³	1	2	yes	—
437	C₄×D₄	C₂³	1	2	yes	—
438	C₄×D₄	C₂³	1	2	yes	—
439	C₄×D₄	C₂³	1	2	yes	—
440	C₄×D₄	C₂³	1	8	yes	—
441	C₄×D₄	C₂³	1	8	yes	—
442	C₄×D₄	C₂³	1	8	yes	—
443	C₄×D₄	C₂³	1	4	yes	—
444	C₄×D₄	C₂³	1	4	yes	—
445	C₄×D₄	C₂³	1	4	yes	—
446	#117	C₂³	1	4	yes	—
447	#117	C₂³	1	4	yes	—
448	#117	C₂³	1	4	yes	—
449	#117	C₂³	1	4	yes	—
450	#117	C₂³	1	2	yes	—
451	#117	C₂³	1	4	yes	—
452	#117	C₂³	1	8	yes	—
453	#117	C₂³	1	2	yes	—
454	#117	C₂³	1	2	yes	—
455	#117	C₂³	1	4	yes	—
456	#117	C₂³	1	4	yes	—
457	#117	C₂³	1	4	yes	—
458	#117	C₂³	1	8	yes	—
459	C₂×C₄⋊C₄	C₂³	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³	1	8	yes	—
467	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
477	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
478	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
479	C₂×C₄²	C₂³	1	1	yes	characteristic
480	C₂×C₄²	C₂³	1	2	yes	—
481	C₂×C₄²	C₂³	1	1	yes	characteristic
482	C₂×C₄²	C₂³	1	1	yes	characteristic
483	C₂×C₄²	C₂³	1	1	yes	characteristic
484	C₂×C₄²	C₂³	1	4	yes	—
485	C₂×C₄²	C₂³	1	8	yes	—
486	C₂×C₄²	C₂³	1	1	yes	characteristic
487	C₂×C₄²	C₂³	1	1	yes	characteristic
488	C₂×C₄²	C₂³	1	1	yes	characteristic
489	C₂×C₄²	C₂³	1	1	yes	characteristic
490	C₂×C₄²	C₂³	1	1	yes	characteristic
491	C₂×C₄²	C₂³	1	1	yes	characteristic
492	C₂×C₄²	C₂³	1	1	yes	characteristic
493	C₂×C₄²	C₂³	1	1	yes	characteristic
494	C₂⁴	C₂⁴	1	1	yes	characteristic
495	C₂⁴	C₂⁴	1	2	yes	—
496	C₂⁴	C₂⁴	1	4	yes	—
497	C₂⁴	C₂⁴	1	8	yes	—
498	#41	—	2	16	no	—
499	#41	—	2	8	no	—
500	#41	—	4	16	no	—
501	#41	—	4	8	no	—
502	#41	—	4	4	no	—
503	#41	—	4	8	no	—
504	#41	—	4	16	no	—
505	#41	—	4	4	no	—
506	#41	—	4	8	no	—
507	#41	—	4	8	no	—
508	#41	—	4	8	no	—
509	#41	—	4	8	no	—
510	C₂×Q₈	—	4	2	no	—
511	C₂×Q₈	—	4	4	no	—
512	C₂×Q₈	—	4	8	no	—
513	C₂×Q₈	C₂⁴	1	2	yes	—
514	C₂×Q₈	C₂⁴	1	2	yes	—
515	C₂×Q₈	C₂⁴	1	4	yes	—
516	C₂×Q₈	C₂⁴	1	2	yes	—
517	C₂×Q₈	C₂⁴	1	2	yes	—
518	C₂×Q₈	C₂⁴	1	2	yes	—
519	C₂×Q₈	C₂⁴	1	8	yes	—
520	C₂×Q₈	C₂⁴	1	4	yes	—
521	C₂×D₄	—	4	4	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	—	4	8	no	—
524	C₂×D₄	—	4	4	no	—
525	C₂×D₄	—	4	8	no	—
526	C₂×D₄	—	4	4	no	—
527	C₂×D₄	—	4	4	no	—
528	C₂×D₄	—	4	16	no	—
529	C₂×D₄	—	4	8	no	—
530	C₂×D₄	—	4	16	no	—
531	C₂×D₄	C₂⁴	1	4	yes	—
532	C₂×D₄	C₂⁴	1	4	yes	—
533	C₂×D₄	C₂⁴	1	2	yes	—
534	C₂×D₄	C₂⁴	1	4	yes	—
535	C₂×D₄	C₂⁴	1	4	yes	—
536	C₂×D₄	C₂⁴	1	8	yes	—
537	C₂×D₄	C₂⁴	1	2	yes	—
538	C₂×D₄	C₂⁴	1	4	yes	—
539	C₂×D₄	C₂⁴	1	2	yes	—
540	C₂×D₄	C₂⁴	1	2	yes	—
541	C₂×D₄	C₂⁴	1	2	yes	—
542	C₂×D₄	C₂⁴	1	8	yes	—
543	C₂×D₄	C₂⁴	1	8	yes	—
544	C₂×D₄	C₂⁴	1	8	yes	—
545	C₂×D₄	C₂⁴	1	4	yes	—
546	C₂×D₄	C₂⁴	1	4	yes	—
547	C₂×D₄	C₂⁴	1	4	yes	—
548	C₂×D₄	C₂⁴	1	4	yes	—
549	C₂×D₄	C₂⁴	1	4	yes	—
550	C₂×D₄	C₂⁴	1	8	yes	—
551	C₂×D₄	C₂⁴	1	8	yes	—
552	C₂×D₄	C₂⁴	1	8	yes	—
553	C₂×D₄	C₂⁴	1	8	yes	—
554	C₂×D₄	C₂⁴	1	4	yes	—
555	C₂×D₄	C₂⁴	1	8	yes	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	8	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	4	8	no	—
560	C₂²×C₄	—	4	16	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	C₂⁴	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴	1	1	yes	characteristic
568	C₂²×C₄	C₂⁴	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴	1	4	yes	—
571	C₂²×C₄	C₂⁴	1	2	yes	—
572	C₂²×C₄	C₂⁴	1	4	yes	—
573	C₂²×C₄	C₂⁴	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴	1	4	yes	—
576	C₂²×C₄	C₂⁴	1	8	yes	—
577	C₂²×C₄	C₂⁴	1	4	yes	—
578	C₂²×C₄	C₂⁴	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴	1	2	yes	—
586	C₂²×C₄	C₂⁴	1	4	yes	—
587	C₂²×C₄	C₂⁴	1	8	yes	—
588	C₂²×C₄	C₂⁴	1	2	yes	—
589	C₂²×C₄	C₂⁴	1	8	yes	—
590	C₂²×C₄	C₂⁴	1	4	yes	—
591	C₂²×C₄	C₂⁴	1	8	yes	—
592	C₂²×C₄	C₂⁴	1	8	yes	—
593	C₂²×C₄	C₂⁴	1	8	yes	—
594	C₂²×C₄	C₂⁴	1	8	yes	—
595	C₂²×C₄	C₂⁴	1	1	yes	characteristic
596	C₄⋊C₄	C₂⁴	1	2	yes	—
597	C₄⋊C₄	C₂⁴	1	4	yes	—
598	C₄⋊C₄	C₂⁴	1	4	yes	—
599	C₄⋊C₄	C₂⁴	1	4	yes	—
600	C₄⋊C₄	C₂⁴	1	2	yes	—
601	C₄⋊C₄	C₂⁴	1	4	yes	—
602	C₄⋊C₄	C₂⁴	1	4	yes	—
603	C₄⋊C₄	C₂⁴	1	4	yes	—
604	C₄⋊C₄	C₂⁴	1	4	yes	—
605	C₄⋊C₄	C₂⁴	1	4	yes	—
606	C₄⋊C₄	C₂⁴	1	4	yes	—
607	C₄⋊C₄	C₂⁴	1	4	yes	—
608	C₄⋊C₄	C₂⁴	1	4	yes	—
609	C₄⋊C₄	C₂⁴	1	4	yes	—
610	C₄⋊C₄	C₂⁴	1	8	yes	—
611	C₄⋊C₄	C₂⁴	1	8	yes	—
612	C₄⋊C₄	C₂⁴	1	8	yes	—
613	C₄⋊C₄	C₂⁴	1	2	yes	—
614	C₄⋊C₄	C₂⁴	1	2	yes	—
615	C₄⋊C₄	C₂⁴	1	4	yes	—
616	C₄⋊C₄	C₂⁴	1	2	yes	—
617	C₄⋊C₄	C₂⁴	1	2	yes	—
618	C₄⋊C₄	C₂⁴	1	4	yes	—
619	C₄⋊C₄	C₂⁴	1	8	yes	—
620	C₄⋊C₄	C₂⁴	1	4	yes	—
621	C₄⋊C₄	C₂⁴	1	8	yes	—
622	C₄⋊C₄	C₂⁴	1	4	yes	—
623	C₄⋊C₄	C₂⁴	1	4	yes	—
624	C₄⋊C₄	C₂⁴	1	4	yes	—
625	C₄⋊C₄	C₂⁴	1	2	yes	—
626	C₄⋊C₄	C₂⁴	1	2	yes	—
627	C₄⋊C₄	C₂⁴	1	8	yes	—
628	C₄⋊C₄	C₂⁴	1	2	yes	—
629	C₄⋊C₄	C₂⁴	1	2	yes	—
630	C₂²⋊C₄	C₂⁴	1	4	yes	—
631	C₂²⋊C₄	C₂⁴	1	4	yes	—
632	C₂²⋊C₄	C₂⁴	1	4	yes	—
633	C₂²⋊C₄	C₂⁴	1	4	yes	—
634	C₂²⋊C₄	C₂⁴	1	4	yes	—
635	C₂²⋊C₄	C₂⁴	1	8	yes	—
636	C₂²⋊C₄	C₂⁴	1	4	yes	—
637	C₂²⋊C₄	C₂⁴	1	4	yes	—
638	C₂²⋊C₄	C₂⁴	1	4	yes	—
639	C₂²⋊C₄	C₂⁴	1	4	yes	—
640	C₂²⋊C₄	C₂⁴	1	4	yes	—
641	C₂²⋊C₄	C₂⁴	1	8	yes	—
642	C₂²⋊C₄	C₂⁴	1	8	yes	—
643	C₂²⋊C₄	C₂⁴	1	4	yes	—
644	C₂²⋊C₄	C₂⁴	1	8	yes	—
645	C₂²⋊C₄	C₂⁴	1	8	yes	—
646	C₂²⋊C₄	C₂⁴	1	8	yes	—
647	C₂²⋊C₄	C₂⁴	1	8	yes	—
648	C₂²⋊C₄	C₂⁴	1	8	yes	—
649	C₂²⋊C₄	C₂⁴	1	8	yes	—
650	C₂²⋊C₄	C₂⁴	1	8	yes	—
651	C₂²⋊C₄	C₂⁴	1	4	yes	—
652	C₂²⋊C₄	C₂⁴	1	4	yes	—
653	C₂²⋊C₄	C₂⁴	1	4	yes	—
654	C₂²⋊C₄	C₂⁴	1	4	yes	—
655	C₂²⋊C₄	C₂⁴	1	8	yes	—
656	C₂²⋊C₄	C₂⁴	1	8	yes	—
657	C₂²⋊C₄	C₂⁴	1	4	yes	—
658	C₂²⋊C₄	C₂⁴	1	4	yes	—
659	C₂²⋊C₄	C₂⁴	1	8	yes	—
660	C₂²⋊C₄	C₂⁴	1	4	yes	—
661	C₂²⋊C₄	C₂⁴	1	8	yes	—
662	C₂²⋊C₄	C₂⁴	1	4	yes	—
663	C₄²	C₂⁴	1	1	yes	characteristic
664	C₄²	C₂⁴	1	1	yes	characteristic
665	C₄²	C₂⁴	1	1	yes	characteristic
666	C₄²	C₂⁴	1	1	yes	characteristic
667	C₄²	C₂⁴	1	1	yes	characteristic
668	C₄²	C₂⁴	1	1	yes	characteristic
669	C₄²	C₂⁴	1	1	yes	characteristic
670	C₄²	C₂⁴	1	1	yes	characteristic
671	C₄²	C₂⁴	1	1	yes	characteristic
672	C₄²	C₂⁴	1	1	yes	characteristic
673	C₄²	C₂⁴	1	1	yes	characteristic
674	C₄²	C₂⁴	1	1	yes	characteristic
675	C₄²	C₂⁴	1	4	yes	—
676	C₄²	C₂⁴	1	4	yes	—
677	C₄²	C₂⁴	1	4	yes	—
678	C₄²	C₂⁴	1	8	yes	—
679	C₄²	C₂⁴	1	8	yes	—
680	C₄²	C₂⁴	1	1	yes	characteristic
681	C₄²	C₂⁴	1	1	yes	characteristic
682	C₄²	C₂⁴	1	1	yes	characteristic
683	C₄²	C₂⁴	1	4	yes	—
684	C₄²	C₂⁴	1	1	yes	characteristic
685	C₄²	C₂⁴	1	4	yes	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	4	no	—
689	C₂³	—	2	8	no	—
690	C₂³	—	4	1	no	—
691	C₂³	—	4	4	no	—
692	C₂³	—	4	8	no	—
693	C₂³	—	4	2	no	—
694	C₂³	—	4	4	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	8	no	—
697	C₂³	—	4	8	no	—
698	C₂³	C₂⁵	1	4	yes	—
699	C₂³	C₂⁵	1	4	yes	—
700	C₂³	C₂⁵	1	8	yes	—
701	C₂³	C₂⁵	1	1	yes	characteristic
702	C₂³	C₂⁵	1	1	yes	characteristic
703	C₂³	C₂⁵	1	1	yes	characteristic
704	Q₈	—	2	8	no	—
705	Q₈	—	2	4	no	—
706	Q₈	—	2	4	no	—
707	Q₈	—	4	2	no	—
708	Q₈	—	4	8	no	—
709	Q₈	—	4	4	no	—
710	Q₈	—	4	2	no	—
711	Q₈	—	4	2	no	—
712	D₄	—	2	16	no	—
713	D₄	—	2	8	no	—
714	D₄	—	2	8	no	—
715	D₄	—	2	8	no	—
716	D₄	—	2	8	no	—
717	D₄	—	2	4	no	—
718	D₄	—	2	4	no	—
719	D₄	—	2	8	no	—
720	D₄	—	4	4	no	—
721	D₄	—	4	4	no	—
722	D₄	—	4	4	no	—
723	D₄	—	4	8	no	—
724	D₄	—	4	2	no	—
725	D₄	—	4	4	no	—
726	D₄	—	4	8	no	—
727	D₄	—	4	8	no	—
728	D₄	—	4	8	no	—
729	D₄	—	4	4	no	—
730	D₄	—	4	8	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	8	no	—
733	D₄	—	4	4	no	—
734	D₄	—	4	2	no	—
735	D₄	—	4	2	no	—
736	D₄	—	4	8	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	8	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	8	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	16	no	—
748	C₂×C₄	—	2	8	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	8	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	4	no	—
761	C₂×C₄	—	4	8	no	—
762	C₂×C₄	—	4	8	no	—
763	C₂×C₄	—	4	8	no	—
764	C₂×C₄	—	4	8	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	—	4	8	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	—	4	8	no	—
770	C₂×C₄	H(5,𝔽₂)	1	4	yes	—
771	C₂×C₄	C₂⁵	1	1	yes	characteristic
772	C₂×C₄	C₂⁵	1	1	yes	characteristic
773	C₂×C₄	C₂⁵	1	1	yes	characteristic
774	C₂×C₄	C₂⁵	1	1	yes	characteristic
775	C₂×C₄	C₂⁵	1	4	yes	—
776	C₂×C₄	C₂⁵	1	4	yes	—
777	C₂×C₄	C₂⁵	1	4	yes	—
778	C₂×C₄	C₂⁵	1	1	yes	characteristic
779	C₂×C₄	C₂⁵	1	1	yes	characteristic
780	C₂×C₄	C₂⁵	1	1	yes	characteristic
781	C₂×C₄	C₂⁵	1	4	yes	—
782	C₂×C₄	C₂⁵	1	1	yes	characteristic
783	C₂×C₄	C₂⁵	1	1	yes	characteristic
784	C₂×C₄	C₂⁵	1	4	yes	—
785	C₂×C₄	C₂⁵	1	8	yes	—
786	C₂×C₄	C₂⁵	1	4	yes	—
787	C₂×C₄	C₂⁵	1	1	yes	characteristic
788	C₂×C₄	C₂⁵	1	1	yes	characteristic
789	C₂×C₄	C₂⁵	1	1	yes	characteristic
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	2	8	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	4	no	—
802	C₂²	—	2	8	no	—
803	C₂²	—	2	8	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	4	4	no	—
807	C₂²	—	8	8	no	—
808	C₂²	—	8	4	no	—
809	C₂²	—	8	16	no	—
810	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
811	C₂²	#585	1	2	yes	—
812	C₂²	C₂⁶	1	1	yes	characteristic
813	C₄	—	2	1	no	—
814	C₄	—	2	4	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	8	no	—
817	C₄	—	2	4	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	4	no	—
823	C₄	—	2	1	no	—
824	C₄	—	2	1	no	—
825	C₄	—	2	1	no	—
826	C₄	—	2	4	no	—
827	C₄	—	2	4	no	—
828	C₄	—	2	4	no	—
829	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
830	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
831	C₄	#585	1	2	yes	—
832	C₂	—	2	2	no	—
833	C₂	—	2	2	no	—
834	C₂	—	4	1	no	—
835	C₂	—	4	4	no	—
836	C₂	—	4	8	no	—
837	C₂	—	4	4	no	—
838	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
839	C₂	C₂×#585	1	1	yes	characteristic
840	C₂	C₂×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁵
commutator, Frattini, socle, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3562	C₂	semidirect
2. #3561	C₂	semidirect
3. #3560	C₂	semidirect
4. #3559	C₂	semidirect
5. #3558	C₂	semidirect
6. #3558	C₂	semidirect
7. #3554	C₂	semidirect
8. #3552	C₂	semidirect
9. #3546	C₂	semidirect
10. #3543	C₂	semidirect
11. #3537	C₂	semidirect
12. #3536	C₂	semidirect
13. #3534	C₂	semidirect
14. #3529	C₂	semidirect
15. #3481	C₂	semidirect
16. #3480	C₂	semidirect
17. D₄×#41	C₂	semidirect
18. D₄×#41	C₂	semidirect
19. #3460	C₂	semidirect
20. #3459	C₂	semidirect
21. #3455	C₂	semidirect
22. #3449	C₂	semidirect
23. #3444	C₂	semidirect
24. C₂×#532	C₂	semidirect
25. C₂×#529	C₂	semidirect
26. C₂²×#41	C₂²	semidirect
27. C₂²×#41	C₂²	semidirect
28. #563	C₂²	semidirect
29. #563	C₂²	semidirect
30. #562	C₂²	semidirect
31. #562	C₂²	semidirect
32. #562	C₂²	semidirect
33. #562	C₂²	semidirect
34. H(3,𝔽₄)	C₂²	semidirect
35. #560	C₂²	semidirect
36. #560	C₂²	semidirect
37. #560	C₂²	semidirect
38. #559	C₂²	semidirect
39. #559	C₂²	semidirect
40. #559	C₂²	semidirect
41. #557	C₂²	semidirect
42. #556	C₂²	semidirect
43. #556	C₂²	semidirect
44. #554	C₂²	semidirect
45. #554	C₂²	semidirect
46. #553	C₂²	semidirect
47. #553	C₂²	semidirect
48. #553	C₂²	semidirect
49. #553	C₂²	semidirect
50. #553	C₂²	semidirect
51. #551	C₂²	semidirect
52. #551	C₂²	semidirect
53. #550	C₂²	semidirect
54. #550	C₂²	semidirect
55. #550	C₂²	semidirect
56. D₄×Q₈	C₂²	semidirect
57. D₄×Q₈	C₂²	semidirect
58. #548	C₂²	semidirect
59. #548	C₂²	semidirect
60. #548	C₂²	semidirect
61. #548	C₂²	semidirect
62. #547	C₂²	semidirect
63. #547	C₂²	semidirect
64. #547	C₂²	semidirect
65. #547	C₂²	semidirect
66. #546	C₂²	semidirect
67. #546	C₂²	semidirect
68. #546	C₂²	semidirect
69. #546	C₂²	semidirect
70. #546	C₂²	semidirect
71. #546	C₂²	semidirect
72. #546	C₂²	semidirect
73. #546	C₂²	semidirect
74. #546	C₂²	semidirect
75. D₄²	C₂²	semidirect
76. D₄²	C₂²	semidirect
77. D₄²	C₂²	semidirect
78. D₄²	C₂²	semidirect
79. D₄²	C₂²	semidirect
80. #544	C₂²	semidirect
81. #543	C₂²	semidirect
82. #542	C₂²	semidirect
83. #542	C₂²	semidirect
84. #542	C₂²	semidirect
85. #542	C₂²	semidirect
86. #542	C₂²	semidirect
87. #541	C₂²	semidirect
88. #540	C₂²	semidirect
89. #540	C₂²	semidirect
90. #540	C₂²	semidirect
91. #540	C₂²	semidirect
92. #539	C₂²	semidirect
93. #539	C₂²	semidirect
94. #539	C₂²	semidirect
95. #539	C₂²	semidirect
96. #539	C₂²	semidirect
97. #538	C₂²	semidirect
98. #538	C₂²	semidirect
99. #538	C₂²	semidirect
100. #538	C₂²	semidirect
101. #538	C₂²	semidirect
102. #538	C₂²	semidirect
103. #538	C₂²	semidirect
104. #538	C₂²	semidirect
105. #537	C₂²	semidirect
106. #537	C₂²	semidirect
107. #537	C₂²	semidirect
108. #536	C₂²	semidirect
109. #536	C₂²	semidirect
110. #535	C₂²	semidirect
111. #535	C₂²	semidirect
112. #535	C₂²	semidirect
113. #535	C₂²	semidirect
114. #534	C₂²	semidirect
115. #534	C₂²	semidirect
116. #534	C₂²	semidirect
117. #534	C₂²	semidirect
118. #533	C₂²	semidirect
119. #533	C₂²	semidirect
120. #533	C₂²	semidirect
121. #532	C₂²	semidirect
122. #532	C₂²	semidirect
123. #532	C₂²	semidirect
124. #532	C₂²	semidirect
125. #532	C₂²	semidirect
126. #532	C₂²	semidirect
127. #532	C₂²	semidirect
128. #532	C₂²	semidirect
129. #532	C₂²	semidirect
130. #532	C₂²	semidirect
131. #532	C₂²	semidirect
132. #532	C₂²	semidirect
133. #532	C₂²	semidirect
134. #532	C₂²	semidirect
135. C₂×C₄⋊Q₈	C₂²	semidirect
136. C₂×#127	C₂²	semidirect
137. #529	C₂²	semidirect
138. #529	C₂²	semidirect
139. #529	C₂²	semidirect
140. #529	C₂²	semidirect
141. #529	C₂²	semidirect
142. #529	C₂²	semidirect
143. #529	C₂²	semidirect
144. #529	C₂²	semidirect
145. #529	C₂²	semidirect
146. #529	C₂²	semidirect
147. #529	C₂²	semidirect
148. #529	C₂²	semidirect
149. #529	C₂²	semidirect
150. #529	C₂²	semidirect
151. #529	C₂²	semidirect
152. #529	C₂²	semidirect
153. #529	C₂²	semidirect
154. #529	C₂²	semidirect
155. C₂×#126	C₂²	semidirect
156. C₂×#125	C₂²	semidirect
157. C₂×#124	C₂²	semidirect
158. C₂×#124	C₂²	semidirect
159. #525	C₂²	semidirect
160. #525	C₂²	semidirect
161. #525	C₂²	semidirect
162. #525	C₂²	semidirect
163. #525	C₂²	semidirect
164. #525	C₂²	semidirect
165. #525	C₂²	semidirect
166. #525	C₂²	semidirect
167. #525	C₂²	semidirect
168. C₂×#123	C₂²	semidirect
169. C₂×C₂²⋊Q₈	C₂²	semidirect
171. C₂×#121	C₂²	semidirect
172. C₂×#121	C₂²	semidirect
173. C₄×#41	C₂²	semidirect
174. C₄×#41	C₂²	semidirect
175. C₄×#41	C₂²	semidirect
176. C₄×#41	C₂²	semidirect
177. C₄×#41	C₂²	semidirect
178. C₂×C₄×Q₈	C₂²	semidirect
179. C₂×C₄×D₄	C₂²	semidirect
180. C₂×C₄×D₄	C₂²	semidirect
181. C₂×C₄×D₄	C₂²	semidirect
182. C₂×C₄×D₄	C₂²	semidirect
183. C₂×C₄×D₄	C₂²	semidirect
184. C₂×C₄×D₄	C₂²	semidirect
185. C₂×#117	C₂²	semidirect
186. C₂²×C₄²	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3562	2
#3561	2
#3560	2
#3559	2
#3558	2
#3554	2
#3552	2
#3546	2
#3543	2
#3537	2
#3536	2
#3534	2
#3529	2
#3481	2
#3480	2
D₄×#41	2
#3460	2
#3459	2
#3455	2
#3449	2
#3444	2
C₂×#532	2
C₂×#529	2