Subgroups — #62047

Order 256.

930 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	#3521	C₂	1	1	yes	maximal, characteristic, complemented
3	#3401	C₂	1	1	yes	maximal, characteristic, complemented
4	#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	#3370	C₂	1	1	yes	maximal, characteristic, complemented
6	#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	#3326	C₂	1	1	yes	maximal, characteristic, complemented
8	#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	#3323	C₂	1	1	yes	maximal, characteristic, complemented
10	#3318	C₂	1	1	yes	maximal, characteristic, complemented
11	#3313	C₂	1	1	yes	maximal, characteristic, complemented
12	#3296	C₂	1	1	yes	maximal, characteristic, complemented
13	#3280	C₂	1	1	yes	maximal, characteristic, complemented
14	#3275	C₂	1	1	yes	maximal, characteristic, complemented
15	#3273	C₂	1	1	yes	maximal, characteristic, complemented
16	#3272	C₂	1	1	yes	maximal, characteristic, complemented
17	#3269	C₂	1	1	yes	maximal, characteristic, complemented
18	#3264	C₂	1	1	yes	maximal, characteristic, complemented
19	#3262	C₂	1	1	yes	maximal, characteristic, complemented
20	#3258	C₂	1	1	yes	maximal, characteristic, complemented
21	#3251	C₂	1	1	yes	maximal, characteristic, complemented
22	#3224	C₂	1	1	yes	maximal, characteristic, complemented
23	#3222	C₂	1	1	yes	maximal, characteristic, complemented
24	#3211	C₂	1	1	yes	maximal, characteristic, complemented
25	#3125	C₂	1	1	yes	maximal, characteristic, complemented
26	#3118	C₂	1	1	yes	maximal, characteristic, complemented
27	#3106	C₂	1	1	yes	maximal, characteristic, complemented
28	#3045	C₂	1	1	yes	maximal, characteristic, complemented
29	#3041	C₂	1	1	yes	maximal, characteristic, complemented
30	#3040	C₂	1	1	yes	maximal, characteristic, complemented
31	#2993	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137	C₂²	1	1	yes	characteristic, complemented
33	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
34	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
35	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
36	C₂×#135	C₂²	1	1	yes	characteristic, complemented
37	C₂²×D₈	C₂²	1	1	yes	characteristic, complemented
38	#562	—	2	1	no	—
39	H(3,𝔽₄)	—	2	1	no	—
40	#559	C₂²	1	1	yes	characteristic, complemented
41	#559	C₂²	1	1	yes	characteristic, complemented
42	#556	C₂²	1	1	yes	characteristic, complemented
43	#556	C₂²	1	1	yes	characteristic, complemented
44	#554	C₂²	1	1	yes	characteristic, complemented
45	#553	—	2	1	no	—
46	#553	C₂²	1	1	yes	characteristic, complemented
47	#552	—	2	1	no	—
48	#552	C₂²	1	1	yes	characteristic, complemented
49	#551	—	2	1	no	—
50	#551	—	2	1	no	—
51	#548	C₂²	1	1	yes	characteristic
52	#548	C₂²	1	1	yes	characteristic, complemented
53	#547	C₂²	1	1	yes	characteristic, complemented
54	#546	—	2	1	no	—
55	#546	—	2	1	no	—
56	#546	C₂²	1	1	yes	characteristic
57	#546	C₂²	1	1	yes	characteristic
58	#546	C₂²	1	1	yes	characteristic, complemented
59	#546	C₂²	1	1	yes	characteristic, complemented
60	D₄²	C₂²	1	1	yes	characteristic
61	D₄²	C₂²	1	1	yes	characteristic, complemented
62	#542	C₂²	1	1	yes	characteristic
63	#542	C₂²	1	1	yes	characteristic, complemented
64	#542	C₂²	1	1	yes	characteristic, complemented
65	#541	C₂²	1	1	yes	characteristic, complemented
66	#539	—	2	1	no	—
67	#538	—	2	1	no	—
68	#538	—	2	1	no	—
69	#538	—	2	1	no	—
70	#538	—	2	1	no	—
71	#535	C₂²	1	1	yes	characteristic
72	#535	C₂²	1	1	yes	characteristic, complemented
73	#534	—	2	1	no	—
74	#532	C₂²	1	1	yes	characteristic, complemented
75	#529	—	2	1	no	—
76	#529	C₂²	1	1	yes	characteristic
77	#529	C₂²	1	1	yes	characteristic, complemented
78	C₂×#126	—	2	1	no	—
79	C₂×#124	C₂²	1	1	yes	characteristic, complemented
80	#520	C₂²	1	1	yes	characteristic, complemented
81	#518	C₂²	1	1	yes	characteristic, complemented
82	C₄×#41	C₂²	1	1	yes	characteristic, complemented
83	#497	C₂²	1	1	yes	characteristic, complemented
84	#496	C₂²	1	1	yes	characteristic
85	#495	C₂²	1	1	yes	characteristic, complemented
86	#495	C₂²	1	1	yes	characteristic, complemented
87	#495	C₂²	1	1	yes	characteristic, complemented
88	#492	C₂²	1	1	yes	characteristic, complemented
89	#490	C₂²	1	1	yes	characteristic, complemented
90	#489	C₂²	1	1	yes	characteristic, complemented
91	#488	C₂²	1	1	yes	characteristic, complemented
92	#488	C₂²	1	1	yes	characteristic, complemented
93	#488	C₂²	1	1	yes	characteristic, complemented
94	#486	C₂²	1	1	yes	characteristic, complemented
95	#485	C₂²	1	1	yes	characteristic, complemented
96	#483	C₂²	1	1	yes	characteristic, complemented
97	#482	C₂²	1	1	yes	characteristic
98	#482	C₂²	1	1	yes	characteristic, complemented
99	#482	C₂²	1	1	yes	characteristic, complemented
100	#481	C₂²	1	1	yes	characteristic, complemented
101	#479	C₂²	1	1	yes	characteristic, complemented
102	#478	C₂²	1	1	yes	characteristic, complemented
103	#478	C₂²	1	1	yes	characteristic, complemented
104	#478	C₂²	1	1	yes	characteristic, complemented
105	#477	C₂²	1	1	yes	characteristic, complemented
106	#477	C₂²	1	1	yes	characteristic, complemented
107	#476	C₂²	1	1	yes	characteristic, complemented
108	#475	C₂²	1	1	yes	characteristic, complemented
109	#474	C₂²	1	1	yes	characteristic, complemented
110	#474	C₂²	1	1	yes	characteristic, complemented
111	#470	C₂²	1	1	yes	characteristic, complemented
112	#469	C₂²	1	1	yes	characteristic, complemented
113	#469	C₂²	1	1	yes	characteristic, complemented
114	#468	C₂²	1	1	yes	characteristic
115	#468	C₂²	1	1	yes	characteristic, complemented
116	#468	C₂²	1	1	yes	characteristic, complemented
117	#468	C₂²	1	1	yes	characteristic, complemented
118	#468	C₂²	1	1	yes	characteristic, complemented
119	#467	C₂²	1	1	yes	characteristic, complemented
120	#467	C₂²	1	1	yes	characteristic, complemented
121	#466	C₂²	1	1	yes	characteristic
122	#465	C₂²	1	1	yes	characteristic
123	#464	C₂²	1	1	yes	characteristic, complemented
124	#464	C₂²	1	1	yes	characteristic, complemented
125	#464	C₂²	1	1	yes	characteristic, complemented
126	#464	C₂²	1	1	yes	characteristic, complemented
127	#464	C₂²	1	1	yes	characteristic, complemented
128	#464	C₂²	1	1	yes	characteristic, complemented
129	#464	C₂²	1	1	yes	characteristic, complemented
130	#464	C₂²	1	1	yes	characteristic, complemented
131	#463	C₂²	1	1	yes	characteristic, complemented
132	#463	C₂²	1	1	yes	characteristic, complemented
133	#463	C₂²	1	1	yes	characteristic, complemented
134	#463	C₂²	1	1	yes	characteristic, complemented
135	#463	C₂²	1	1	yes	characteristic, complemented
136	#463	C₂²	1	1	yes	characteristic, complemented
137	#463	C₂²	1	1	yes	characteristic, complemented
138	#463	C₂²	1	1	yes	characteristic, complemented
139	#463	C₂²	1	1	yes	characteristic, complemented
140	#463	C₂²	1	1	yes	characteristic, complemented
141	#463	C₂²	1	1	yes	characteristic, complemented
142	#463	C₂²	1	1	yes	characteristic, complemented
143	#462	C₂²	1	1	yes	characteristic, complemented
144	#461	C₂²	1	1	yes	characteristic, complemented
145	#460	C₂²	1	1	yes	characteristic, complemented
146	#460	C₂²	1	1	yes	characteristic, complemented
147	#460	C₂²	1	1	yes	characteristic, complemented
148	#459	C₂²	1	1	yes	characteristic
149	#459	C₂²	1	1	yes	characteristic
150	#459	C₂²	1	1	yes	characteristic
151	#459	C₂²	1	1	yes	characteristic, complemented
152	#459	C₂²	1	1	yes	characteristic, complemented
153	#452	C₂²	1	1	yes	characteristic, complemented
154	#452	C₂²	1	1	yes	characteristic, complemented
155	#452	C₂²	1	1	yes	characteristic, complemented
156	#452	C₂²	1	1	yes	characteristic, complemented
157	#451	C₂²	1	1	yes	characteristic, complemented
158	#450	C₂²	1	1	yes	characteristic, complemented
159	#450	C₂²	1	1	yes	characteristic, complemented
160	#450	C₂²	1	1	yes	characteristic, complemented
161	#450	C₂²	1	1	yes	characteristic, complemented
162	#450	C₂²	1	1	yes	characteristic, complemented
163	#449	C₂²	1	1	yes	characteristic
164	#449	C₂²	1	1	yes	characteristic, complemented
165	#449	C₂²	1	1	yes	characteristic, complemented
166	#449	C₂²	1	1	yes	characteristic, complemented
167	#448	C₂²	1	1	yes	characteristic, complemented
168	#447	C₂²	1	1	yes	characteristic
169	#447	C₂²	1	1	yes	characteristic
170	#447	C₂²	1	1	yes	characteristic, complemented
171	#446	C₂²	1	1	yes	characteristic, complemented
172	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
173	#442	C₂²	1	1	yes	characteristic, complemented
174	#442	C₂²	1	1	yes	characteristic, complemented
175	#441	C₂²	1	1	yes	characteristic, complemented
176	#440	C₂²	1	1	yes	characteristic, complemented
177	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
178	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
179	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
180	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
181	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
185	#436	C₂²	1	1	yes	characteristic, complemented
186	#436	C₂²	1	1	yes	characteristic, complemented
187	#436	C₂²	1	1	yes	characteristic, complemented
188	#435	C₂²	1	1	yes	characteristic, complemented
189	#435	C₂²	1	1	yes	characteristic, complemented
190	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
191	#433	C₂²	1	1	yes	characteristic, complemented
192	#433	C₂²	1	1	yes	characteristic, complemented
193	#431	C₂²	1	1	yes	characteristic, complemented
194	#424	C₂²	1	1	yes	characteristic, complemented
195	#424	C₂²	1	1	yes	characteristic, complemented
196	#423	C₂²	1	1	yes	characteristic, complemented
197	#419	C₂²	1	1	yes	characteristic, complemented
198	#418	C₂²	1	1	yes	characteristic, complemented
199	#418	C₂²	1	1	yes	characteristic, complemented
200	#417	C₂²	1	1	yes	characteristic, complemented
201	#416	C₂²	1	1	yes	characteristic, complemented
202	C₂×#102	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41	—	2	1	no	—
204	C₂×#41	C₂³	1	1	yes	characteristic
205	C₂×#41	C₂³	1	1	yes	characteristic
206	C₂×#41	C₂³	1	1	yes	characteristic
207	C₂×#41	C₂³	1	1	yes	characteristic
208	C₂²×Q₈	C₂³	1	1	yes	characteristic
209	C₂²×D₄	—	2	1	no	—
210	C₂²×D₄	—	2	1	no	—
211	C₂²×D₄	C₂³	1	1	yes	characteristic
212	C₂²×D₄	C₂³	1	1	yes	characteristic
213	C₂²×D₄	C₂³	1	1	yes	characteristic
214	C₂²×D₄	C₂³	1	1	yes	characteristic
215	#137	—	4	2	no	—
216	AGL(1,ℤ/8)	—	4	2	no	—
217	AGL(1,ℤ/8)	—	4	2	no	—
218	AGL(1,ℤ/8)	—	4	2	no	—
219	#135	—	4	2	no	—
220	C₂×Q₁₆	C₂³	1	1	yes	characteristic
221	C₂×Q₁₆	C₂³	1	1	yes	characteristic
222	C₂×Q₁₆	C₂³	1	1	yes	characteristic
223	C₂×Q₁₆	C₂³	1	1	yes	characteristic
224	C₂×SD₁₆	C₂³	1	1	yes	characteristic
225	C₂×SD₁₆	C₂³	1	1	yes	characteristic
226	C₂×SD₁₆	C₂³	1	1	yes	characteristic
227	C₂×SD₁₆	C₂³	1	1	yes	characteristic
228	C₂×SD₁₆	C₂³	1	1	yes	characteristic
229	C₂×SD₁₆	C₂³	1	1	yes	characteristic
230	C₂×SD₁₆	C₂³	1	1	yes	characteristic
231	C₂×SD₁₆	C₂³	1	1	yes	characteristic
232	C₂×SD₁₆	C₂³	1	1	yes	characteristic
233	C₂×SD₁₆	C₂³	1	1	yes	characteristic
234	C₂×SD₁₆	C₂³	1	1	yes	characteristic
235	C₂×SD₁₆	C₂³	1	1	yes	characteristic
236	C₂×D₈	—	4	2	no	—
237	C₂×D₈	C₂³	1	1	yes	characteristic
238	C₂×D₈	C₂³	1	1	yes	characteristic
239	C₂×D₈	C₂³	1	1	yes	characteristic
240	C₂×D₈	C₂³	1	1	yes	characteristic
241	C₂×D₈	C₂³	1	1	yes	characteristic
242	C₂×D₈	C₂³	1	1	yes	characteristic
243	C₂×D₈	C₂³	1	1	yes	characteristic
244	C₂×D₈	C₂³	1	1	yes	characteristic
245	C₂×M₁₆	C₂³	1	1	yes	characteristic
246	C₂×M₁₆	C₂³	1	1	yes	characteristic
247	C₂×M₁₆	C₂³	1	1	yes	characteristic
248	C₂×M₁₆	C₂³	1	1	yes	characteristic
249	C₂²×C₈	C₂³	1	1	yes	characteristic
250	C₂²×C₈	C₂³	1	1	yes	characteristic
251	C₄⋊Q₈	C₂³	1	1	yes	characteristic
252	C₄⋊Q₈	C₂³	1	1	yes	characteristic
253	C₄⋊Q₈	C₂³	1	1	yes	characteristic
254	#127	C₂³	1	1	yes	characteristic
255	#127	C₂³	1	1	yes	characteristic
256	#127	C₂³	1	1	yes	characteristic
257	#126	—	2	1	no	—
258	#126	—	2	1	no	—
259	#126	—	2	1	no	—
260	#126	—	2	1	no	—
261	#126	—	2	1	no	—
262	#126	—	2	1	no	—
263	#126	—	2	1	no	—
264	#126	—	2	1	no	—
265	#126	—	2	1	no	—
266	#126	—	2	1	no	—
267	#126	—	2	1	no	—
268	#126	—	2	1	no	—
269	#126	D₄	1	1	yes	characteristic
270	#126	D₄	1	1	yes	characteristic
271	#125	—	2	1	no	—
272	#125	—	2	1	no	—
273	#125	—	2	1	no	—
274	#125	D₄	1	1	yes	characteristic
275	#125	C₂³	1	1	yes	characteristic
276	#125	C₂³	1	1	yes	characteristic
277	#124	—	2	1	no	—
278	#124	—	2	1	no	—
279	#124	—	2	1	no	—
280	#124	—	2	1	no	—
281	#124	—	2	1	no	—
282	#124	—	2	1	no	—
283	#124	—	2	1	no	—
284	#124	—	2	1	no	—
285	#124	—	2	1	no	—
286	#124	—	2	1	no	—
287	#124	—	2	1	no	—
288	#124	D₄	1	1	yes	characteristic
289	#124	C₂³	1	1	yes	characteristic
290	#124	C₂³	1	1	yes	characteristic
291	#124	C₂³	1	1	yes	characteristic
292	#124	C₂³	1	1	yes	characteristic
293	#124	C₂³	1	1	yes	characteristic
294	#124	C₂³	1	1	yes	characteristic
295	#124	C₂³	1	1	yes	characteristic
296	#124	C₂³	1	1	yes	characteristic
297	#123	—	2	1	no	—
298	#123	—	2	1	no	—
299	#123	—	2	1	no	—
300	#123	—	2	1	no	—
301	#123	—	2	1	no	—
302	#123	—	2	1	no	—
303	#123	—	2	1	no	—
304	#123	—	2	1	no	—
305	#123	—	2	1	no	—
306	#123	—	2	1	no	—
307	#123	—	2	1	no	—
308	#123	—	2	1	no	—
309	#123	—	2	1	no	—
310	#123	—	2	1	no	—
311	#123	—	2	1	no	—
312	#123	—	2	1	no	—
313	#123	D₄	1	1	yes	characteristic
314	#123	D₄	1	1	yes	characteristic
315	C₂²⋊Q₈	—	2	1	no	—
316	C₂²⋊Q₈	—	2	1	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₂²⋊Q₈	—	2	1	no	—
319	C₂²⋊Q₈	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₂²⋊Q₈	—	2	1	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	D₄	1	1	yes	characteristic
325	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
326	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
327	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
328	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
329	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
330	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
331	#121	—	2	1	no	—
332	#121	—	2	1	no	—
333	#121	—	2	1	no	—
334	#121	—	2	1	no	—
335	#121	—	2	1	no	—
336	#121	—	2	1	no	—
337	#121	—	2	1	no	—
338	#121	—	2	1	no	—
339	#121	—	2	1	no	—
340	#121	—	2	1	no	—
341	#121	—	2	1	no	—
342	#121	—	2	1	no	—
343	#121	—	2	1	no	—
344	#121	—	2	1	no	—
345	#121	—	2	1	no	—
346	#121	D₄	1	1	yes	characteristic
347	#121	C₂³	1	1	yes	characteristic
348	#121	C₂³	1	1	yes	characteristic
349	#121	C₂³	1	1	yes	characteristic
350	#121	C₂³	1	1	yes	characteristic
351	#121	C₂³	1	1	yes	characteristic
352	#121	C₂³	1	1	yes	characteristic
353	#120	—	2	1	no	—
354	#120	—	2	1	no	—
355	#120	—	2	1	no	—
356	#120	—	2	1	no	—
357	#120	—	2	1	no	—
358	#120	—	2	1	no	—
359	#120	—	2	1	no	—
360	#120	—	2	1	no	—
361	#120	—	2	1	no	—
362	#120	—	2	1	no	—
363	#120	—	2	1	no	—
364	#120	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	C₂³	1	1	yes	characteristic
367	C₄×Q₈	C₂³	1	1	yes	characteristic
368	C₄×Q₈	C₂³	1	1	yes	characteristic
369	C₄×Q₈	C₂³	1	1	yes	characteristic
370	C₄×Q₈	C₂³	1	1	yes	characteristic
371	C₄×Q₈	C₂³	1	1	yes	characteristic
372	C₄×Q₈	C₂³	1	1	yes	characteristic
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	C₂³	1	1	yes	characteristic
387	C₄×D₄	C₂³	1	1	yes	characteristic
388	C₄×D₄	C₂³	1	1	yes	characteristic
389	C₄×D₄	C₂³	1	1	yes	characteristic
390	C₄×D₄	C₂³	1	1	yes	characteristic
391	C₄×D₄	C₂³	1	1	yes	characteristic
392	C₄×D₄	C₂³	1	1	yes	characteristic
393	C₄×D₄	C₂³	1	1	yes	characteristic
394	C₄×D₄	C₂³	1	1	yes	characteristic
395	C₄×D₄	C₂³	1	1	yes	characteristic
396	C₄×D₄	C₂³	1	1	yes	characteristic
397	C₄×D₄	C₂³	1	1	yes	characteristic
398	C₄×D₄	C₂³	1	1	yes	characteristic
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	#117	—	2	1	no	—
402	#117	—	2	1	no	—
403	#117	—	2	1	no	—
404	#117	C₂³	1	1	yes	characteristic
405	#117	C₂³	1	1	yes	characteristic
406	#117	C₂³	1	1	yes	characteristic
407	#117	C₂³	1	1	yes	characteristic
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	C₂³	1	1	yes	characteristic
422	#107	C₂³	1	1	yes	characteristic
423	#107	C₂³	1	1	yes	characteristic
424	#107	C₂³	1	1	yes	characteristic
425	#107	C₂³	1	1	yes	characteristic
426	#106	C₂³	1	1	yes	characteristic
427	#106	C₂³	1	1	yes	characteristic
428	#106	C₂³	1	1	yes	characteristic
429	#106	C₂³	1	1	yes	characteristic
430	C₄⋊C₈	C₂³	1	1	yes	characteristic
431	C₄⋊C₈	C₂³	1	1	yes	characteristic
432	C₄⋊C₈	C₂³	1	1	yes	characteristic
433	C₄⋊C₈	C₂³	1	1	yes	characteristic
434	C₄⋊C₈	C₂³	1	1	yes	characteristic
435	C₄⋊C₈	C₂³	1	1	yes	characteristic
436	C₄⋊C₈	C₂³	1	1	yes	characteristic
437	C₄⋊C₈	C₂³	1	1	yes	characteristic
438	C₄⋊C₈	C₂³	1	1	yes	characteristic
439	C₄⋊C₈	C₂³	1	1	yes	characteristic
440	#103	C₂³	1	1	yes	characteristic
441	#103	C₂³	1	1	yes	characteristic
442	#103	C₂³	1	1	yes	characteristic
443	#103	C₂³	1	1	yes	characteristic
444	#103	C₂³	1	1	yes	characteristic
445	#103	C₂³	1	1	yes	characteristic
446	#103	C₂³	1	1	yes	characteristic
447	#103	C₂³	1	1	yes	characteristic
448	#103	C₂³	1	1	yes	characteristic
449	#103	C₂³	1	1	yes	characteristic
450	#103	C₂³	1	1	yes	characteristic
451	#103	C₂³	1	1	yes	characteristic
452	#102	C₂³	1	1	yes	characteristic
453	#102	C₂³	1	1	yes	characteristic
454	#102	C₂³	1	1	yes	characteristic
455	#102	C₂³	1	1	yes	characteristic
456	#102	C₂³	1	1	yes	characteristic
457	#102	C₂³	1	1	yes	characteristic
458	#102	C₂³	1	1	yes	characteristic
459	#102	C₂³	1	1	yes	characteristic
460	#102	C₂³	1	1	yes	characteristic
461	#102	C₂³	1	1	yes	characteristic
462	#102	C₂³	1	1	yes	characteristic
463	#102	C₂³	1	1	yes	characteristic
464	#102	C₂³	1	1	yes	characteristic
465	#102	C₂³	1	1	yes	characteristic
466	#102	C₂³	1	1	yes	characteristic
467	#102	C₂³	1	1	yes	characteristic
468	#102	C₂³	1	1	yes	characteristic
469	#102	C₂³	1	1	yes	characteristic
470	#102	C₂³	1	1	yes	characteristic
471	#102	C₂³	1	1	yes	characteristic
472	C₂²⋊C₈	C₂³	1	1	yes	characteristic
473	C₂²⋊C₈	C₂³	1	1	yes	characteristic
474	C₂²⋊C₈	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈	C₂³	1	1	yes	characteristic
478	#97	C₂³	1	1	yes	characteristic
479	#97	C₂³	1	1	yes	characteristic
480	C₄×C₈	C₂³	1	1	yes	characteristic
481	C₄×C₈	C₂³	1	1	yes	characteristic
482	C₄×C₈	C₂³	1	1	yes	characteristic
483	C₄×C₈	C₂³	1	1	yes	characteristic
484	C₂⁴	—	2	1	no	—
485	C₂⁴	—	2	1	no	—
486	C₂⁴	—	2	1	no	—
487	C₂⁴	—	2	1	no	—
488	#41	—	2	2	no	—
489	#41	—	2	2	no	—
490	#41	—	4	1	no	—
491	#41	—	4	1	no	—
492	#41	—	4	1	no	—
493	#41	—	4	1	no	—
494	#41	—	4	1	no	—
495	#41	—	4	1	no	—
496	#41	—	8	2	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	4	1	no	—
501	C₂×Q₈	—	4	1	no	—
502	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
503	C₂×Q₈	C₂⁴	1	1	yes	characteristic
504	C₂×Q₈	C₂⁴	1	1	yes	characteristic
505	C₂×Q₈	C₂⁴	1	1	yes	characteristic
506	C₂×Q₈	C₂⁴	1	1	yes	characteristic
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	4	1	no	—
529	C₂×D₄	—	4	1	no	—
530	C₂×D₄	—	4	1	no	—
531	C₂×D₄	—	4	1	no	—
532	C₂×D₄	—	4	1	no	—
533	C₂×D₄	—	4	1	no	—
534	C₂×D₄	—	4	1	no	—
535	C₂×D₄	—	8	2	no	—
536	C₂×D₄	—	8	2	no	—
537	C₂×D₄	C₂×D₄	1	1	yes	characteristic
538	C₂×D₄	C₂×D₄	1	1	yes	characteristic
539	C₂×D₄	C₂×D₄	1	1	yes	characteristic
540	C₂×D₄	C₂⁴	1	1	yes	characteristic
541	C₂×D₄	C₂⁴	1	1	yes	characteristic
542	C₂×D₄	C₂⁴	1	1	yes	characteristic
543	C₂×D₄	C₂⁴	1	1	yes	characteristic
544	C₂×D₄	C₂⁴	1	1	yes	characteristic
545	C₂×D₄	C₂⁴	1	1	yes	characteristic
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄	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	Q₁₆	—	4	1	no	—
568	Q₁₆	—	4	1	no	—
569	Q₁₆	—	4	1	no	—
570	Q₁₆	—	4	1	no	—
571	SD₁₆	—	2	2	no	—
572	SD₁₆	—	2	2	no	—
573	SD₁₆	—	4	1	no	—
574	SD₁₆	—	4	1	no	—
575	SD₁₆	—	4	1	no	—
576	SD₁₆	—	4	1	no	—
577	SD₁₆	—	4	1	no	—
578	SD₁₆	—	4	1	no	—
579	SD₁₆	—	4	1	no	—
580	SD₁₆	—	4	1	no	—
581	SD₁₆	—	4	1	no	—
582	SD₁₆	—	4	1	no	—
583	D₈	—	2	2	no	—
584	D₈	—	2	2	no	—
585	D₈	—	2	2	no	—
586	D₈	—	2	2	no	—
587	D₈	—	4	1	no	—
588	D₈	—	4	1	no	—
589	D₈	—	4	1	no	—
590	D₈	—	4	1	no	—
591	M₁₆	—	4	1	no	—
592	M₁₆	—	4	1	no	—
593	M₁₆	—	4	1	no	—
594	M₁₆	—	4	1	no	—
595	C₂×C₈	—	4	1	no	—
596	C₂×C₈	—	4	1	no	—
597	C₂×C₈	C₂⁴	1	1	yes	characteristic
598	C₂×C₈	C₂⁴	1	1	yes	characteristic
599	C₂×C₈	C₂⁴	1	1	yes	characteristic
600	C₂×C₈	C₂⁴	1	1	yes	characteristic
601	C₂×C₈	C₂⁴	1	1	yes	characteristic
602	C₂×C₈	C₂⁴	1	1	yes	characteristic
603	C₂×C₈	C₂⁴	1	1	yes	characteristic
604	C₂×C₈	C₂⁴	1	1	yes	characteristic
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
627	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
628	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
629	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
630	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
631	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
632	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
633	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
634	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
635	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
636	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
637	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
638	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
639	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
640	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
641	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	2	1	no	—
655	C₂²⋊C₄	—	2	1	no	—
656	C₂²⋊C₄	—	2	1	no	—
657	C₂²⋊C₄	—	2	1	no	—
658	C₂²⋊C₄	—	2	1	no	—
659	C₂²⋊C₄	—	2	1	no	—
660	C₂²⋊C₄	—	2	1	no	—
661	C₂²⋊C₄	—	2	1	no	—
662	C₂²⋊C₄	—	2	1	no	—
663	C₂²⋊C₄	—	2	1	no	—
664	C₂²⋊C₄	—	2	1	no	—
665	C₂²⋊C₄	—	2	1	no	—
666	C₂²⋊C₄	—	2	1	no	—
667	C₂²⋊C₄	—	2	1	no	—
668	C₂²⋊C₄	—	2	1	no	—
669	C₂²⋊C₄	—	2	1	no	—
670	C₂²⋊C₄	—	2	1	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	2	1	no	—
676	C₂²⋊C₄	—	2	1	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	1	no	—
679	C₂²⋊C₄	—	2	1	no	—
680	C₂²⋊C₄	—	2	1	no	—
681	C₂²⋊C₄	—	2	1	no	—
682	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
683	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
684	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
685	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
686	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
687	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
688	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
689	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
690	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
691	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
692	C₄²	—	2	1	no	—
693	C₄²	—	2	1	no	—
694	C₄²	—	2	1	no	—
695	C₄²	—	2	1	no	—
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₄²	C₂×D₄	1	1	yes	characteristic
701	C₄²	C₂×D₄	1	1	yes	characteristic
702	C₄²	C₂⁴	1	1	yes	characteristic
703	C₄²	C₂⁴	1	1	yes	characteristic
704	C₄²	C₂⁴	1	1	yes	characteristic
705	C₄²	C₂⁴	1	1	yes	characteristic
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	4	2	no	—
713	C₂³	—	4	2	no	—
714	C₂³	—	8	1	no	—
715	C₂³	—	8	1	no	—
716	C₂³	—	8	1	no	—
717	C₂³	—	8	1	no	—
718	C₂³	—	8	1	no	—
719	C₂³	—	8	1	no	—
720	C₂³	—	8	1	no	—
721	C₂³	—	8	1	no	—
722	C₂³	—	8	1	no	—
723	C₂³	—	8	1	no	—
724	C₂³	C₂²×D₄	1	1	yes	characteristic
725	C₂³	C₂²×D₄	1	1	yes	characteristic
726	C₂³	C₂²×D₄	1	1	yes	characteristic
727	Q₈	—	2	1	no	—
728	Q₈	—	2	1	no	—
729	Q₈	—	2	1	no	—
730	Q₈	—	2	1	no	—
731	Q₈	—	2	1	no	—
732	Q₈	—	2	1	no	—
733	Q₈	—	2	1	no	—
734	Q₈	—	2	1	no	—
735	Q₈	—	4	1	no	—
736	Q₈	—	8	1	no	—
737	Q₈	—	8	1	no	—
738	Q₈	—	8	1	no	—
739	D₄	—	2	1	no	—
740	D₄	—	2	1	no	—
741	D₄	—	2	1	no	—
742	D₄	—	2	1	no	—
743	D₄	—	2	1	no	—
744	D₄	—	2	1	no	—
745	D₄	—	2	1	no	—
746	D₄	—	2	1	no	—
747	D₄	—	2	1	no	—
748	D₄	—	2	1	no	—
749	D₄	—	2	1	no	—
750	D₄	—	4	1	no	—
751	D₄	—	4	1	no	—
752	D₄	—	4	1	no	—
753	D₄	—	4	2	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	2	no	—
756	D₄	—	4	2	no	—
757	D₄	—	4	2	no	—
758	D₄	—	8	1	no	—
759	D₄	—	8	1	no	—
760	D₄	—	8	1	no	—
761	D₄	—	8	1	no	—
762	D₄	—	8	1	no	—
763	D₄	—	8	1	no	—
764	D₄	—	8	1	no	—
765	D₄	—	8	1	no	—
766	D₄	—	8	1	no	—
767	D₄	—	8	1	no	—
768	D₄	—	8	1	no	—
769	D₄	—	8	1	no	—
770	D₄	—	8	1	no	—
771	D₄	—	8	1	no	—
772	D₄	—	8	1	no	—
773	D₄	H(5,𝔽₂)	1	2	yes	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	8	1	no	—
795	C₂×C₄	—	8	1	no	—
796	C₂×C₄	—	8	1	no	—
797	C₂×C₄	—	8	1	no	—
798	C₂×C₄	—	8	1	no	—
799	C₂×C₄	—	8	1	no	—
800	C₂×C₄	—	8	1	no	—
801	C₂×C₄	—	8	1	no	—
802	C₂×C₄	—	8	1	no	—
803	C₂×C₄	—	8	1	no	—
804	C₂×C₄	—	8	1	no	—
805	C₂×C₄	—	8	1	no	—
806	C₂×C₄	—	8	1	no	—
807	C₂×C₄	—	8	1	no	—
808	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
810	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
811	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
819	C₂×C₄	C₂⁵	1	1	yes	characteristic
820	C₈	—	2	1	no	—
821	C₈	—	2	1	no	—
822	C₈	—	2	1	no	—
823	C₈	—	2	1	no	—
824	C₈	—	2	1	no	—
825	C₈	—	2	1	no	—
826	C₈	—	2	1	no	—
827	C₈	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	1	no	—
853	C₂²	—	4	1	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	16	2	no	—
856	C₂²	—	16	2	no	—
857	C₂²	—	16	2	no	—
858	C₂²	—	16	2	no	—
859	C₂²	C₂³×D₄	1	1	yes	characteristic
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	2	1	no	—
863	C₄	—	2	1	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	1	no	—
866	C₄	—	2	1	no	—
867	C₄	—	2	1	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	1	no	—
881	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
882	C₄	#585	1	1	yes	characteristic
883	C₂	—	4	1	no	—
884	C₂	—	4	1	no	—
885	C₂	—	4	1	no	—
886	C₂	—	4	2	no	—
887	C₂	—	8	1	no	—
888	C₂	—	8	1	no	—
889	C₂	—	8	1	no	—
890	C₂	—	8	1	no	—
891	C₂	—	8	1	no	—
892	C₂	#3488	1	1	yes	characteristic
893	C₂	#3584	1	1	yes	characteristic
894	C₂	#3585	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 ◁ #529 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3558	C₂	semidirect
2. #3521	C₂	semidirect
3. #3401	C₂	semidirect
4. #3394	C₂	semidirect
5. #3370	C₂	semidirect
6. #3361	C₂	semidirect
7. #3326	C₂	semidirect
8. #3324	C₂	semidirect
9. #3323	C₂	semidirect
10. #3318	C₂	semidirect
11. #3313	C₂	semidirect
12. #3296	C₂	semidirect
13. #3280	C₂	semidirect
14. #3275	C₂	semidirect
15. #3273	C₂	semidirect
16. #3272	C₂	semidirect
17. #3269	C₂	semidirect
18. #3264	C₂	semidirect
19. #3262	C₂	semidirect
20. #3258	C₂	semidirect
21. #3251	C₂	semidirect
22. #3224	C₂	semidirect
23. #3222	C₂	semidirect
24. #3211	C₂	semidirect
25. #3125	C₂	semidirect
26. #3118	C₂	semidirect
27. #3106	C₂	semidirect
28. #3045	C₂	semidirect
29. #3041	C₂	semidirect
30. #3040	C₂	semidirect
31. #2993	C₂	semidirect
32. C₂×#137	C₂²	semidirect
34. C₂×AGL(1,ℤ/8)	C₂²	semidirect
35. C₂×AGL(1,ℤ/8)	C₂²	semidirect
36. C₂×#135	C₂²	semidirect
37. C₂²×D₈	C₂²	semidirect
40. #559	C₂²	semidirect
41. #559	C₂²	semidirect
42. #556	C₂²	semidirect
43. #556	C₂²	semidirect
44. #554	C₂²	semidirect
46. #553	C₂²	semidirect
48. #552	C₂²	semidirect
52. #548	C₂²	semidirect
53. #547	C₂²	semidirect
58. #546	C₂²	semidirect
59. #546	C₂²	semidirect
61. D₄²	C₂²	semidirect
63. #542	C₂²	semidirect
64. #542	C₂²	semidirect
65. #541	C₂²	semidirect
72. #535	C₂²	semidirect
74. #532	C₂²	semidirect
77. #529	C₂²	semidirect
79. C₂×#124	C₂²	semidirect
80. #520	C₂²	semidirect
81. #518	C₂²	semidirect
82. C₄×#41	C₂²	semidirect
83. #497	C₂²	semidirect
85. #495	C₂²	semidirect
86. #495	C₂²	semidirect
87. #495	C₂²	semidirect
88. #492	C₂²	semidirect
89. #490	C₂²	semidirect
90. #489	C₂²	semidirect
91. #488	C₂²	semidirect
92. #488	C₂²	semidirect
93. #488	C₂²	semidirect
94. #486	C₂²	semidirect
95. #485	C₂²	semidirect
96. #483	C₂²	semidirect
98. #482	C₂²	semidirect
99. #482	C₂²	semidirect
100. #481	C₂²	semidirect
101. #479	C₂²	semidirect
102. #478	C₂²	semidirect
103. #478	C₂²	semidirect
104. #478	C₂²	semidirect
105. #477	C₂²	semidirect
106. #477	C₂²	semidirect
107. #476	C₂²	semidirect
108. #475	C₂²	semidirect
109. #474	C₂²	semidirect
110. #474	C₂²	semidirect
111. #470	C₂²	semidirect
112. #469	C₂²	semidirect
113. #469	C₂²	semidirect
115. #468	C₂²	semidirect
116. #468	C₂²	semidirect
117. #468	C₂²	semidirect
118. #468	C₂²	semidirect
119. #467	C₂²	semidirect
120. #467	C₂²	semidirect
123. #464	C₂²	semidirect
124. #464	C₂²	semidirect
125. #464	C₂²	semidirect
126. #464	C₂²	semidirect
127. #464	C₂²	semidirect
128. #464	C₂²	semidirect
129. #464	C₂²	semidirect
130. #464	C₂²	semidirect
131. #463	C₂²	semidirect
132. #463	C₂²	semidirect
133. #463	C₂²	semidirect
134. #463	C₂²	semidirect
135. #463	C₂²	semidirect
136. #463	C₂²	semidirect
137. #463	C₂²	semidirect
138. #463	C₂²	semidirect
139. #463	C₂²	semidirect
140. #463	C₂²	semidirect
141. #463	C₂²	semidirect
142. #463	C₂²	semidirect
143. #462	C₂²	semidirect
144. #461	C₂²	semidirect
145. #460	C₂²	semidirect
146. #460	C₂²	semidirect
147. #460	C₂²	semidirect
151. #459	C₂²	semidirect
152. #459	C₂²	semidirect
153. #452	C₂²	semidirect
154. #452	C₂²	semidirect
155. #452	C₂²	semidirect
156. #452	C₂²	semidirect
157. #451	C₂²	semidirect
158. #450	C₂²	semidirect
159. #450	C₂²	semidirect
160. #450	C₂²	semidirect
161. #450	C₂²	semidirect
162. #450	C₂²	semidirect
164. #449	C₂²	semidirect
165. #449	C₂²	semidirect
166. #449	C₂²	semidirect
167. #448	C₂²	semidirect
170. #447	C₂²	semidirect
171. #446	C₂²	semidirect
172. C₈×Q₈	C₂²	semidirect
173. #442	C₂²	semidirect
174. #442	C₂²	semidirect
175. #441	C₂²	semidirect
176. #440	C₂²	semidirect
177. C₄×SD₁₆	C₂²	semidirect
178. C₄×SD₁₆	C₂²	semidirect
179. C₄×SD₁₆	C₂²	semidirect
180. C₄×SD₁₆	C₂²	semidirect
181. C₄×SD₁₆	C₂²	semidirect
182. C₄×D₈	C₂²	semidirect
183. C₄×D₈	C₂²	semidirect
184. C₄×D₈	C₂²	semidirect
185. #436	C₂²	semidirect
186. #436	C₂²	semidirect
187. #436	C₂²	semidirect
188. #435	C₂²	semidirect
189. #435	C₂²	semidirect
190. C₈×D₄	C₂²	semidirect
191. #433	C₂²	semidirect
192. #433	C₂²	semidirect
193. #431	C₂²	semidirect
194. #424	C₂²	semidirect
195. #424	C₂²	semidirect
196. #423	C₂²	semidirect
197. #419	C₂²	semidirect
198. #418	C₂²	semidirect
199. #418	C₂²	semidirect
200. #417	C₂²	semidirect
201. #416	C₂²	semidirect
202. C₂×#102	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3558	2
#3521	2
#3401	2
#3394	2
#3370	2
#3361	2
#3326	2
#3324	2
#3323	2
#3318	2
#3313	2
#3296	2
#3280	2
#3275	2
#3273	2
#3272	2
#3269	2
#3264	2
#3262	2
#3258	2
#3251	2
#3224	2
#3222	2
#3211	2
#3125	2
#3118	2
#3106	2
#3045	2
#3041	2
#3040	2
#2993	2