Subgroups — #62265

Order 256.

929 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	#3542	C₂	1	1	yes	maximal, characteristic, complemented
2	#3541	C₂	1	1	yes	maximal, characteristic, complemented
3	#3340	C₂	1	1	yes	maximal, characteristic, complemented
4	#3337	C₂	1	1	yes	maximal, characteristic, complemented
5	#3337	C₂	1	1	yes	maximal, characteristic, complemented
6	#3335	C₂	1	1	yes	maximal, characteristic, complemented
7	#3321	C₂	1	1	yes	maximal, characteristic, complemented
8	#3318	C₂	1	1	yes	maximal, characteristic, complemented
9	#3317	C₂	1	1	yes	maximal, characteristic, complemented
10	#3314	C₂	1	1	yes	maximal, characteristic, complemented
11	#3312	C₂	1	1	yes	maximal, characteristic, complemented
12	#3311	C₂	1	1	yes	maximal, characteristic, complemented
13	#3308	C₂	1	1	yes	maximal, characteristic, complemented
14	#3307	C₂	1	1	yes	maximal, characteristic, complemented
15	#3284	C₂	1	1	yes	maximal, characteristic, complemented
16	#3282	C₂	1	1	yes	maximal, characteristic, complemented
17	#3282	C₂	1	1	yes	maximal, characteristic, complemented
18	D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
19	#3258	C₂	1	1	yes	maximal, characteristic, complemented
20	#3257	C₂	1	1	yes	maximal, characteristic, complemented
21	#3201	C₂	1	1	yes	maximal, characteristic, complemented
22	#3198	C₂	1	1	yes	maximal, characteristic, complemented
23	#3196	C₂	1	1	yes	maximal, characteristic, complemented
24	#3194	C₂	1	1	yes	maximal, characteristic, complemented
25	#3174	C₂	1	1	yes	maximal, characteristic, complemented
26	#3173	C₂	1	1	yes	maximal, characteristic, complemented
27	#3060	C₂	1	1	yes	maximal, characteristic, complemented
28	#3057	C₂	1	1	yes	maximal, characteristic, complemented
29	#3050	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#465	C₂	1	1	yes	maximal, characteristic, complemented
31	#2929	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#135	C₂²	1	1	yes	characteristic, complemented
33	C₂×#135	C₂²	1	1	yes	characteristic, complemented
34	C₂²×SD₁₆	C₂²	1	1	yes	characteristic
35	C₂²×SD₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₂×#131	C₂²	1	1	yes	characteristic, complemented
37	C₂³×C₈	C₂²	1	1	yes	characteristic, complemented
38	#563	—	2	1	no	—
39	#562	—	2	1	no	—
40	#562	—	2	1	no	—
41	#560	—	2	1	no	—
42	#556	C₂²	1	1	yes	characteristic, complemented
43	#555	C₂²	1	1	yes	characteristic
44	#554	—	2	1	no	—
45	#554	C₂²	1	1	yes	characteristic, complemented
46	#553	—	2	1	no	—
47	#553	C₂²	1	1	yes	characteristic
48	#553	C₂²	1	1	yes	characteristic
49	#552	C₂²	1	1	yes	characteristic
50	#552	C₂²	1	1	yes	characteristic, complemented
51	#551	—	2	1	no	—
52	#550	C₂²	1	1	yes	characteristic
53	D₄×Q₈	C₂²	1	1	yes	characteristic
54	#548	C₂²	1	1	yes	characteristic, complemented
55	#548	C₂²	1	1	yes	characteristic, complemented
56	#547	C₂²	1	1	yes	characteristic
57	#547	C₂²	1	1	yes	characteristic, complemented
58	#546	—	2	1	no	—
59	#546	C₂²	1	1	yes	characteristic
60	#546	C₂²	1	1	yes	characteristic
61	D₄²	C₂²	1	1	yes	characteristic
62	#542	—	2	1	no	—
63	#542	C₂²	1	1	yes	characteristic
64	#542	C₂²	1	1	yes	characteristic, complemented
65	#541	C₂²	1	1	yes	characteristic, complemented
66	#540	—	2	1	no	—
67	#540	C₂²	1	1	yes	characteristic
68	#539	—	2	1	no	—
69	#538	—	2	1	no	—
70	#538	—	2	1	no	—
71	#538	—	2	1	no	—
72	#537	C₂²	1	1	yes	characteristic
73	#537	C₂²	1	1	yes	characteristic, complemented
74	#536	C₂²	1	1	yes	characteristic, complemented
75	#535	—	2	1	no	—
76	#535	C₂²	1	1	yes	characteristic
77	#534	—	2	1	no	—
78	#525	C₂²	1	1	yes	characteristic
79	#525	C₂²	1	1	yes	characteristic
80	#525	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
82	C₂×#121	C₂²	1	1	yes	characteristic
83	#499	C₂²	1	1	yes	characteristic, complemented
84	#498	C₂²	1	1	yes	characteristic, complemented
85	#495	C₂²	1	1	yes	characteristic, complemented
86	#492	C₂²	1	1	yes	characteristic, complemented
87	#491	C₂²	1	1	yes	characteristic, complemented
88	#490	C₂²	1	1	yes	characteristic, complemented
89	#489	C₂²	1	1	yes	characteristic, complemented
90	#489	C₂²	1	1	yes	characteristic, complemented
91	#485	C₂²	1	1	yes	characteristic, complemented
92	#485	C₂²	1	1	yes	characteristic, complemented
93	#485	C₂²	1	1	yes	characteristic, complemented
94	#485	C₂²	1	1	yes	characteristic, complemented
95	#484	C₂²	1	1	yes	characteristic, complemented
96	#484	C₂²	1	1	yes	characteristic, complemented
97	#483	C₂²	1	1	yes	characteristic, complemented
98	#483	C₂²	1	1	yes	characteristic, complemented
99	#482	C₂²	1	1	yes	characteristic
100	#482	C₂²	1	1	yes	characteristic, complemented
101	#482	C₂²	1	1	yes	characteristic, complemented
102	#482	C₂²	1	1	yes	characteristic, complemented
103	#481	C₂²	1	1	yes	characteristic
104	#481	C₂²	1	1	yes	characteristic, complemented
105	#480	C₂²	1	1	yes	characteristic, complemented
106	#480	C₂²	1	1	yes	characteristic, complemented
107	#479	C₂²	1	1	yes	characteristic, complemented
108	#479	C₂²	1	1	yes	characteristic, complemented
109	#478	C₂²	1	1	yes	characteristic, complemented
110	#478	C₂²	1	1	yes	characteristic, complemented
111	#477	C₂²	1	1	yes	characteristic, complemented
112	#476	C₂²	1	1	yes	characteristic, complemented
113	#475	C₂²	1	1	yes	characteristic, complemented
114	#474	C₂²	1	1	yes	characteristic, complemented
115	#470	C₂²	1	1	yes	characteristic, complemented
116	#470	C₂²	1	1	yes	characteristic, complemented
117	#470	C₂²	1	1	yes	characteristic, complemented
118	#469	C₂²	1	1	yes	characteristic
119	#469	C₂²	1	1	yes	characteristic, complemented
120	#469	C₂²	1	1	yes	characteristic, complemented
121	#468	C₂²	1	1	yes	characteristic
122	#468	C₂²	1	1	yes	characteristic, complemented
123	#468	C₂²	1	1	yes	characteristic, complemented
124	#468	C₂²	1	1	yes	characteristic, complemented
125	#468	C₂²	1	1	yes	characteristic, complemented
126	#468	C₂²	1	1	yes	characteristic, complemented
127	#467	C₂²	1	1	yes	characteristic, complemented
128	#467	C₂²	1	1	yes	characteristic, complemented
129	#466	C₂²	1	1	yes	characteristic
130	#466	C₂²	1	1	yes	characteristic, complemented
131	#465	C₂²	1	1	yes	characteristic
132	#465	C₂²	1	1	yes	characteristic
133	#465	C₂²	1	1	yes	characteristic
134	#465	C₂²	1	1	yes	characteristic
135	#465	C₂²	1	1	yes	characteristic
136	#465	C₂²	1	1	yes	characteristic, complemented
137	#465	C₂²	1	1	yes	characteristic, complemented
138	#465	C₂²	1	1	yes	characteristic, complemented
139	#465	C₂²	1	1	yes	characteristic, complemented
140	#465	C₂²	1	1	yes	characteristic, complemented
141	#465	C₂²	1	1	yes	characteristic, complemented
142	#465	C₂²	1	1	yes	characteristic, complemented
143	#465	C₂²	1	1	yes	characteristic, complemented
144	#465	C₂²	1	1	yes	characteristic, complemented
145	#465	C₂²	1	1	yes	characteristic, complemented
146	#465	C₂²	1	1	yes	characteristic, complemented
147	#464	C₂²	1	1	yes	characteristic, complemented
148	#464	C₂²	1	1	yes	characteristic, complemented
149	#463	C₂²	1	1	yes	characteristic, complemented
150	#463	C₂²	1	1	yes	characteristic, complemented
151	#462	C₂²	1	1	yes	characteristic, complemented
152	#461	C₂²	1	1	yes	characteristic, complemented
153	#460	C₂²	1	1	yes	characteristic, complemented
154	#459	C₂²	1	1	yes	characteristic, complemented
155	#452	C₂²	1	1	yes	characteristic, complemented
156	#452	C₂²	1	1	yes	characteristic, complemented
157	#452	C₂²	1	1	yes	characteristic, complemented
158	#452	C₂²	1	1	yes	characteristic, complemented
159	#451	C₂²	1	1	yes	characteristic, complemented
160	#451	C₂²	1	1	yes	characteristic, complemented
161	#450	C₂²	1	1	yes	characteristic
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
168	#448	C₂²	1	1	yes	characteristic, complemented
169	#447	C₂²	1	1	yes	characteristic
170	#447	C₂²	1	1	yes	characteristic, complemented
171	#442	C₂²	1	1	yes	characteristic, complemented
172	#441	C₂²	1	1	yes	characteristic, complemented
173	#440	C₂²	1	1	yes	characteristic, complemented
174	#440	C₂²	1	1	yes	characteristic, complemented
175	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
176	C₄×SD₁₆	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	#435	C₂²	1	1	yes	characteristic
180	#435	C₂²	1	1	yes	characteristic, complemented
181	#435	C₂²	1	1	yes	characteristic, complemented
182	#435	C₂²	1	1	yes	characteristic, complemented
183	C₈×D₄	C₂²	1	1	yes	characteristic
184	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
185	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
186	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
187	#427	C₂²	1	1	yes	characteristic, complemented
188	#427	C₂²	1	1	yes	characteristic, complemented
189	C₂×#106	C₂²	1	1	yes	characteristic, complemented
190	C₂×#106	C₂²	1	1	yes	characteristic, complemented
191	#424	C₂²	1	1	yes	characteristic, complemented
192	#419	C₂²	1	1	yes	characteristic, complemented
193	#418	C₂²	1	1	yes	characteristic, complemented
194	#417	C₂²	1	1	yes	characteristic, complemented
195	#417	C₂²	1	1	yes	characteristic, complemented
196	#416	C₂²	1	1	yes	characteristic, complemented
197	#416	C₂²	1	1	yes	characteristic, complemented
198	C₂×#103	C₂²	1	1	yes	characteristic, complemented
199	C₂×#102	C₂²	1	1	yes	characteristic
200	#408	C₂²	1	1	yes	characteristic, complemented
201	#407	C₂²	1	1	yes	characteristic, complemented
202	#405	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	C₂×#41	C₂³	1	1	yes	characteristic
209	C₂²×Q₈	C₂³	1	1	yes	characteristic
210	C₂²×Q₈	C₂³	1	1	yes	characteristic
211	C₂²×D₄	—	2	1	no	—
212	C₂²×D₄	—	2	1	no	—
213	C₂²×D₄	C₂³	1	1	yes	characteristic
214	C₂²×D₄	C₂³	1	1	yes	characteristic
215	C₂³×C₄	C₂³	1	1	yes	characteristic
216	#135	—	4	2	no	—
217	#135	—	4	2	no	—
218	C₂×Q₁₆	C₂³	1	1	yes	characteristic
219	C₂×Q₁₆	C₂³	1	1	yes	characteristic
220	C₂×Q₁₆	C₂³	1	1	yes	characteristic
221	C₂×SD₁₆	—	4	2	no	—
222	C₂×SD₁₆	—	4	2	no	—
223	C₂×SD₁₆	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×D₈	C₂³	1	1	yes	characteristic
234	C₂×D₈	C₂³	1	1	yes	characteristic
235	C₂×D₈	C₂³	1	1	yes	characteristic
236	#131	—	4	2	no	—
237	C₂×M₁₆	C₂³	1	1	yes	characteristic
238	C₂×M₁₆	C₂³	1	1	yes	characteristic
239	C₂×M₁₆	C₂³	1	1	yes	characteristic
240	C₂×M₁₆	C₂³	1	1	yes	characteristic
241	C₂²×C₈	—	4	2	no	—
242	C₂²×C₈	C₂³	1	1	yes	characteristic
243	C₂²×C₈	C₂³	1	1	yes	characteristic
244	C₂²×C₈	C₂³	1	1	yes	characteristic
245	C₂²×C₈	C₂³	1	1	yes	characteristic
246	C₂²×C₈	C₂³	1	1	yes	characteristic
247	C₂²×C₈	C₂³	1	1	yes	characteristic
248	C₂²×C₈	C₂³	1	1	yes	characteristic
249	C₂²×C₈	C₂³	1	1	yes	characteristic
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	C₂³	1	1	yes	characteristic
253	C₄⋊Q₈	C₂³	1	1	yes	characteristic
254	C₄⋊Q₈	C₂³	1	1	yes	characteristic
255	#127	—	2	1	no	—
256	#127	—	2	1	no	—
257	#127	C₂³	1	1	yes	characteristic
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	#125	—	2	1	no	—
269	#125	—	2	1	no	—
270	#125	—	2	1	no	—
271	#125	—	2	1	no	—
272	#125	—	2	1	no	—
273	#125	C₂³	1	1	yes	characteristic
274	#125	C₂³	1	1	yes	characteristic
275	#124	—	2	1	no	—
276	#124	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
285	#124	C₂³	1	1	yes	characteristic
286	#123	—	2	1	no	—
287	#123	—	2	1	no	—
288	#123	—	2	1	no	—
289	#123	—	2	1	no	—
290	#123	—	2	1	no	—
291	#123	—	2	1	no	—
292	#123	—	2	1	no	—
293	#123	—	2	1	no	—
294	#123	—	2	1	no	—
295	#123	—	2	1	no	—
296	#123	—	2	1	no	—
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	D₄	1	1	yes	characteristic
305	#123	D₄	1	1	yes	characteristic
306	C₂²⋊Q₈	—	2	1	no	—
307	C₂²⋊Q₈	—	2	1	no	—
308	C₂²⋊Q₈	—	2	1	no	—
309	C₂²⋊Q₈	—	2	1	no	—
310	C₂²⋊Q₈	—	2	1	no	—
311	C₂²⋊Q₈	—	2	1	no	—
312	C₂²⋊Q₈	—	2	1	no	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	—	2	1	no	—
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	D₄	1	1	yes	characteristic
320	C₂²⋊Q₈	D₄	1	1	yes	characteristic
321	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
322	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
323	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
324	C₂²⋊Q₈	C₂³	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	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
332	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
347	#121	—	2	1	no	—
348	#121	—	2	1	no	—
349	#121	—	2	1	no	—
350	#121	—	2	1	no	—
351	#121	—	2	1	no	—
352	#121	—	2	1	no	—
353	#121	—	2	1	no	—
354	#121	D₄	1	1	yes	characteristic
355	#121	D₄	1	1	yes	characteristic
356	#121	C₂³	1	1	yes	characteristic
357	#121	C₂³	1	1	yes	characteristic
358	#121	C₂³	1	1	yes	characteristic
359	#121	C₂³	1	1	yes	characteristic
360	#121	C₂³	1	1	yes	characteristic
361	#121	C₂³	1	1	yes	characteristic
362	#121	C₂³	1	1	yes	characteristic
363	#121	C₂³	1	1	yes	characteristic
364	#121	C₂³	1	1	yes	characteristic
365	#121	C₂³	1	1	yes	characteristic
366	#121	C₂³	1	1	yes	characteristic
367	#121	C₂³	1	1	yes	characteristic
368	#120	—	2	1	no	—
369	#120	—	2	1	no	—
370	#120	—	2	1	no	—
371	#120	—	2	1	no	—
372	#120	—	2	1	no	—
373	#120	—	2	1	no	—
374	#120	—	2	1	no	—
375	#120	—	2	1	no	—
376	#120	D₄	1	1	yes	characteristic
377	#120	D₄	1	1	yes	characteristic
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	C₂³	1	1	yes	characteristic
380	C₄×Q₈	C₂³	1	1	yes	characteristic
381	C₄×Q₈	C₂³	1	1	yes	characteristic
382	C₄×Q₈	C₂³	1	1	yes	characteristic
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
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	C₄×D₄	C₂³	1	1	yes	characteristic
400	C₄×D₄	C₂³	1	1	yes	characteristic
401	C₄×D₄	C₂³	1	1	yes	characteristic
402	#117	—	2	1	no	—
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	#117	C₂³	1	1	yes	characteristic
406	#117	C₂³	1	1	yes	characteristic
407	#117	C₂³	1	1	yes	characteristic
408	#117	C₂³	1	1	yes	characteristic
409	#117	C₂³	1	1	yes	characteristic
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	#107	C₂³	1	1	yes	characteristic
421	#107	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	#106	C₂³	1	1	yes	characteristic
431	#106	C₂³	1	1	yes	characteristic
432	#106	C₂³	1	1	yes	characteristic
433	#106	C₂³	1	1	yes	characteristic
434	#106	C₂³	1	1	yes	characteristic
435	#106	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	#103	C₂³	1	1	yes	characteristic
453	#103	C₂³	1	1	yes	characteristic
454	#103	C₂³	1	1	yes	characteristic
455	#103	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	C₂²⋊C₈	C₂³	1	1	yes	characteristic
479	C₂²⋊C₈	C₂³	1	1	yes	characteristic
480	#97	C₂³	1	1	yes	characteristic
481	#97	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	C₂×D₄	1	1	yes	characteristic
487	#41	—	4	1	no	—
488	#41	—	4	1	no	—
489	#41	—	4	1	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	—	4	1	no	—
497	#41	—	8	2	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	4	1	no	—
503	C₂×Q₈	—	4	1	no	—
504	C₂×Q₈	—	4	1	no	—
505	C₂×Q₈	—	4	1	no	—
506	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
507	C₂×Q₈	C₂⁴	1	1	yes	characteristic
508	C₂×Q₈	C₂⁴	1	1	yes	characteristic
509	C₂×Q₈	C₂⁴	1	1	yes	characteristic
510	C₂×Q₈	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	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	C₂×D₄	1	1	yes	characteristic
541	C₂×D₄	C₂×D₄	1	1	yes	characteristic
542	C₂×D₄	C₂×D₄	1	1	yes	characteristic
543	C₂×D₄	C₂×D₄	1	1	yes	characteristic
544	C₂×D₄	C₂⁴	1	1	yes	characteristic
545	C₂×D₄	C₂⁴	1	1	yes	characteristic
546	C₂×D₄	C₂⁴	1	1	yes	characteristic
547	C₂×D₄	C₂⁴	1	1	yes	characteristic
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	—	4	1	no	—
563	C₂²×C₄	—	4	1	no	—
564	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₄	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	1	yes	characteristic
571	C₂²×C₄	C₂⁴	1	1	yes	characteristic
572	Q₁₆	—	4	1	no	—
573	Q₁₆	—	4	1	no	—
574	Q₁₆	—	4	1	no	—
575	SD₁₆	—	2	2	no	—
576	SD₁₆	—	2	2	no	—
577	SD₁₆	—	2	2	no	—
578	SD₁₆	—	2	2	no	—
579	SD₁₆	—	4	1	no	—
580	SD₁₆	—	4	1	no	—
581	SD₁₆	—	4	1	no	—
582	SD₁₆	—	4	1	no	—
583	SD₁₆	—	4	1	no	—
584	SD₁₆	—	4	1	no	—
585	D₈	—	4	1	no	—
586	D₈	—	4	1	no	—
587	D₈	—	4	1	no	—
588	M₁₆	—	4	1	no	—
589	M₁₆	—	4	1	no	—
590	M₁₆	—	4	1	no	—
591	M₁₆	—	4	1	no	—
592	C₂×C₈	—	2	2	no	—
593	C₂×C₈	—	2	2	no	—
594	C₂×C₈	—	2	2	no	—
595	C₂×C₈	—	2	2	no	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	—	4	1	no	—
598	C₂×C₈	—	4	1	no	—
599	C₂×C₈	—	4	1	no	—
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	C₂×C₈	C₂⁴	1	1	yes	characteristic
606	C₂×C₈	C₂⁴	1	1	yes	characteristic
607	C₂×C₈	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
637	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
638	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
639	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
640	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
641	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
642	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
643	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
644	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
645	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
646	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
647	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
648	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
649	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
683	C₂²⋊C₄	—	2	1	no	—
684	C₂²⋊C₄	—	2	1	no	—
685	C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
693	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
694	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
695	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₄²	—	2	1	no	—
701	C₄²	—	2	1	no	—
702	C₄²	—	2	1	no	—
703	C₄²	—	2	1	no	—
704	C₄²	C₂⁴	1	1	yes	characteristic
705	C₄²	C₂⁴	1	1	yes	characteristic
706	C₂³	—	2	2	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
720	C₂³	C₂²×D₄	1	1	yes	characteristic
721	C₂³	C₂²×D₄	1	1	yes	characteristic
722	C₂³	C₂²×D₄	1	1	yes	characteristic
723	C₂³	C₂²×D₄	1	1	yes	characteristic
724	Q₈	—	2	1	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	2	1	no	—
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	—	4	1	no	—
733	Q₈	—	8	1	no	—
734	Q₈	—	8	1	no	—
735	Q₈	—	8	1	no	—
736	Q₈	—	8	1	no	—
737	D₄	—	2	2	no	—
738	D₄	—	2	2	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	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	4	1	no	—
751	D₄	—	4	1	no	—
752	D₄	—	4	2	no	—
753	D₄	—	4	2	no	—
754	D₄	—	8	1	no	—
755	D₄	—	8	1	no	—
756	D₄	—	8	1	no	—
757	D₄	—	8	1	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	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
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	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	2	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	—	8	1	no	—
809	C₂×C₄	—	8	1	no	—
810	C₂×C₄	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
820	C₂×C₄	C₂⁵	1	1	yes	characteristic
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	C₈	H(5,𝔽₂)	1	2	yes	—
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	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	4	4	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	—	4	1	no	—
856	C₂²	—	16	2	no	—
857	C₂²	—	16	2	no	—
858	C₂²	#577	1	2	yes	—
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	—	4	1	no	—
870	C₄	—	4	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	—	2	2	no	—
884	C₂	—	4	1	no	—
885	C₂	—	4	1	no	—
886	C₂	—	4	1	no	—
887	C₂	—	4	1	no	—
888	C₂	—	8	1	no	—
889	C₂	—	8	1	no	—
890	C₂	—	8	1	no	—
891	C₂	—	8	1	no	—
892	C₂	#3496	1	1	yes	characteristic
893	C₂	C₂×#577	1	1	yes	characteristic
894	C₂	#3584	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 ◁ #525 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3542	C₂	semidirect
2. #3541	C₂	semidirect
3. #3340	C₂	semidirect
4. #3337	C₂	semidirect
5. #3337	C₂	semidirect
6. #3335	C₂	semidirect
7. #3321	C₂	semidirect
8. #3318	C₂	semidirect
9. #3317	C₂	semidirect
10. #3314	C₂	semidirect
11. #3312	C₂	semidirect
12. #3311	C₂	semidirect
13. #3308	C₂	semidirect
14. #3307	C₂	semidirect
15. #3284	C₂	semidirect
16. #3282	C₂	semidirect
17. #3282	C₂	semidirect
18. D₄×SD₁₆	C₂	semidirect
19. #3258	C₂	semidirect
20. #3257	C₂	semidirect
21. #3201	C₂	semidirect
22. #3198	C₂	semidirect
23. #3196	C₂	semidirect
24. #3194	C₂	semidirect
25. #3174	C₂	semidirect
26. #3173	C₂	semidirect
27. #3060	C₂	semidirect
28. #3057	C₂	semidirect
29. #3050	C₂	semidirect
30. C₂×#465	C₂	semidirect
31. #2929	C₂	semidirect
32. C₂×#135	C₂²	semidirect
33. C₂×#135	C₂²	semidirect
35. C₂²×SD₁₆	C₂²	semidirect
36. C₂×#131	C₂²	semidirect
37. C₂³×C₈	C₂²	semidirect
42. #556	C₂²	semidirect
45. #554	C₂²	semidirect
50. #552	C₂²	semidirect
54. #548	C₂²	semidirect
55. #548	C₂²	semidirect
57. #547	C₂²	semidirect
64. #542	C₂²	semidirect
65. #541	C₂²	semidirect
73. #537	C₂²	semidirect
74. #536	C₂²	semidirect
80. #525	C₂²	semidirect
81. C₂×C₂²⋊Q₈	C₂²	semidirect
83. #499	C₂²	semidirect
84. #498	C₂²	semidirect
85. #495	C₂²	semidirect
86. #492	C₂²	semidirect
87. #491	C₂²	semidirect
88. #490	C₂²	semidirect
89. #489	C₂²	semidirect
90. #489	C₂²	semidirect
91. #485	C₂²	semidirect
92. #485	C₂²	semidirect
93. #485	C₂²	semidirect
94. #485	C₂²	semidirect
95. #484	C₂²	semidirect
96. #484	C₂²	semidirect
97. #483	C₂²	semidirect
98. #483	C₂²	semidirect
100. #482	C₂²	semidirect
101. #482	C₂²	semidirect
102. #482	C₂²	semidirect
104. #481	C₂²	semidirect
105. #480	C₂²	semidirect
106. #480	C₂²	semidirect
107. #479	C₂²	semidirect
108. #479	C₂²	semidirect
109. #478	C₂²	semidirect
110. #478	C₂²	semidirect
111. #477	C₂²	semidirect
112. #476	C₂²	semidirect
113. #475	C₂²	semidirect
114. #474	C₂²	semidirect
115. #470	C₂²	semidirect
116. #470	C₂²	semidirect
117. #470	C₂²	semidirect
119. #469	C₂²	semidirect
120. #469	C₂²	semidirect
122. #468	C₂²	semidirect
123. #468	C₂²	semidirect
124. #468	C₂²	semidirect
125. #468	C₂²	semidirect
126. #468	C₂²	semidirect
127. #467	C₂²	semidirect
128. #467	C₂²	semidirect
130. #466	C₂²	semidirect
136. #465	C₂²	semidirect
137. #465	C₂²	semidirect
138. #465	C₂²	semidirect
139. #465	C₂²	semidirect
140. #465	C₂²	semidirect
141. #465	C₂²	semidirect
142. #465	C₂²	semidirect
143. #465	C₂²	semidirect
144. #465	C₂²	semidirect
145. #465	C₂²	semidirect
146. #465	C₂²	semidirect
147. #464	C₂²	semidirect
148. #464	C₂²	semidirect
149. #463	C₂²	semidirect
150. #463	C₂²	semidirect
151. #462	C₂²	semidirect
152. #461	C₂²	semidirect
153. #460	C₂²	semidirect
154. #459	C₂²	semidirect
155. #452	C₂²	semidirect
156. #452	C₂²	semidirect
157. #452	C₂²	semidirect
158. #452	C₂²	semidirect
159. #451	C₂²	semidirect
160. #451	C₂²	semidirect
162. #450	C₂²	semidirect
164. #449	C₂²	semidirect
165. #449	C₂²	semidirect
166. #449	C₂²	semidirect
168. #448	C₂²	semidirect
170. #447	C₂²	semidirect
171. #442	C₂²	semidirect
172. #441	C₂²	semidirect
173. #440	C₂²	semidirect
174. #440	C₂²	semidirect
175. C₄×SD₁₆	C₂²	semidirect
176. C₄×SD₁₆	C₂²	semidirect
177. C₄×SD₁₆	C₂²	semidirect
178. C₄×SD₁₆	C₂²	semidirect
180. #435	C₂²	semidirect
181. #435	C₂²	semidirect
182. #435	C₂²	semidirect
184. C₈×D₄	C₂²	semidirect
185. C₈×D₄	C₂²	semidirect
186. C₈×D₄	C₂²	semidirect
187. #427	C₂²	semidirect
188. #427	C₂²	semidirect
189. C₂×#106	C₂²	semidirect
190. C₂×#106	C₂²	semidirect
191. #424	C₂²	semidirect
192. #419	C₂²	semidirect
193. #418	C₂²	semidirect
194. #417	C₂²	semidirect
195. #417	C₂²	semidirect
196. #416	C₂²	semidirect
197. #416	C₂²	semidirect
198. C₂×#103	C₂²	semidirect
200. #408	C₂²	semidirect
201. #407	C₂²	semidirect
202. #405	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3542	2
#3541	2
#3340	2
#3337	2
#3335	2
#3321	2
#3318	2
#3317	2
#3314	2
#3312	2
#3311	2
#3308	2
#3307	2
#3284	2
#3282	2
D₄×SD₁₆	2
#3258	2
#3257	2
#3201	2
#3198	2
#3196	2
#3194	2
#3174	2
#3173	2
#3060	2
#3057	2
#3050	2
C₂×#465	2
#2929	2