Subgroups — #496650

Order 512.

492 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20476	C₂	1	1	yes	maximal, characteristic
2	#13121	C₂	1	1	yes	maximal, characteristic
3	#13121	C₂	1	1	yes	maximal, characteristic
4	#13120	C₂	1	1	yes	maximal, characteristic
5	#13120	C₂	1	1	yes	maximal, characteristic
6	#13105	C₂	1	1	yes	maximal, characteristic, complemented
7	#13105	C₂	1	1	yes	maximal, characteristic, complemented
8	#13104	C₂	1	1	yes	maximal, characteristic, complemented
9	#13104	C₂	1	1	yes	maximal, characteristic, complemented
10	#12899	C₂	1	1	yes	maximal, characteristic, complemented
11	#12880	C₂	1	1	yes	maximal, characteristic, complemented
12	#12783	C₂	1	1	yes	maximal, characteristic
13	#12783	C₂	1	1	yes	maximal, characteristic
14	#12654	C₂	1	1	yes	maximal, characteristic, complemented
15	#12654	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#432	C₄	1	1	yes	characteristic
17	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
18	#2283	C₄	1	1	yes	characteristic
19	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
31	C₂×#346	C₂²	1	1	yes	characteristic
32	C₂×#346	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
35	#1770	C₄	1	1	yes	characteristic
36	#1770	C₄	1	1	yes	characteristic
37	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	#1752	C₄	1	1	yes	characteristic
40	#1752	C₄	1	1	yes	characteristic
41	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	#1746	C₄	1	1	yes	characteristic
44	#1746	C₄	1	1	yes	characteristic
45	#1726	C₂²	1	1	yes	characteristic
46	#1726	C₂²	1	1	yes	characteristic
47	#1374	C₂²	1	1	yes	characteristic
48	#1374	C₂²	1	1	yes	characteristic
49	#1374	C₂²	1	1	yes	characteristic
50	#1374	C₂²	1	1	yes	characteristic
51	#1374	C₂²	1	1	yes	characteristic
52	#1374	C₂²	1	1	yes	characteristic
53	#1374	C₂²	1	1	yes	characteristic
54	#1374	C₂²	1	1	yes	characteristic
55	#1374	C₂²	1	1	yes	characteristic
56	#1374	C₂²	1	1	yes	characteristic
57	#1374	C₂²	1	1	yes	characteristic
58	#1374	C₂²	1	1	yes	characteristic
59	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₁₆	C₂³	1	1	yes	characteristic
63	C₂²×C₁₆	C₂³	1	1	yes	characteristic
64	C₂²×C₁₆	C₂³	1	1	yes	characteristic
65	C₂²×C₁₆	C₂³	1	1	yes	characteristic
66	C₂²×C₁₆	C₂³	1	1	yes	characteristic
67	C₂²×C₁₆	C₂³	1	1	yes	characteristic
68	C₂²×C₁₆	C₂³	1	1	yes	characteristic
69	C₂²×C₁₆	C₂³	1	1	yes	characteristic
70	#432	—	2	4	no	—
71	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₂×#97	C₂×C₄	1	1	yes	characteristic
76	C₂×#97	C₂×C₄	1	1	yes	characteristic
77	C₂×#97	C₂×C₄	1	1	yes	characteristic
78	C₂×#97	C₂×C₄	1	1	yes	characteristic
79	C₂×#97	C₂×C₄	1	1	yes	characteristic
80	C₂×#97	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×C₈	—	2	2	no	—
82	C₂×C₄×C₈	—	2	2	no	—
83	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
86	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
87	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
88	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
89	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
90	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
91	#383	C₈	1	1	yes	characteristic
92	#383	C₈	1	1	yes	characteristic
93	#382	C₈	1	1	yes	characteristic
94	#382	C₈	1	1	yes	characteristic
95	#381	C₈	1	1	yes	characteristic
96	#381	C₈	1	1	yes	characteristic
97	#380	C₈	1	1	yes	characteristic
98	#380	C₈	1	1	yes	characteristic
99	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
103	#376	C₂×C₄	1	1	yes	characteristic
104	#376	C₂×C₄	1	1	yes	characteristic
105	C₄⋊C₁₆	—	2	2	no	—
106	C₄⋊C₁₆	—	2	2	no	—
107	C₄⋊C₁₆	—	2	2	no	—
108	C₄⋊C₁₆	—	2	2	no	—
109	C₄⋊C₁₆	—	4	1	no	—
110	C₄⋊C₁₆	—	4	1	no	—
111	C₄⋊C₁₆	—	4	1	no	—
112	C₄⋊C₁₆	—	4	1	no	—
113	C₂²⋊C₁₆	—	4	1	no	—
114	C₂²⋊C₁₆	—	4	1	no	—
115	C₂²⋊C₁₆	—	4	1	no	—
116	C₂²⋊C₁₆	—	4	1	no	—
117	#346	—	4	1	no	—
118	#346	—	4	1	no	—
119	C₄×C₁₆	—	4	1	no	—
120	C₄×C₁₆	—	4	1	no	—
121	#336	C₂×C₄	1	1	yes	characteristic
122	#336	C₂×C₄	1	1	yes	characteristic
123	#336	C₂×C₄	1	1	yes	characteristic
124	#336	C₂×C₄	1	1	yes	characteristic
125	#336	C₂×C₄	1	1	yes	characteristic
126	#336	C₂×C₄	1	1	yes	characteristic
127	#336	C₂×C₄	1	1	yes	characteristic
128	#336	C₂×C₄	1	1	yes	characteristic
129	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
130	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
131	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₈	—	2	2	no	—
133	C₂²×C₈	—	2	1	no	—
134	C₂²×C₈	—	2	1	no	—
135	C₂²×C₈	—	2	1	no	—
136	C₂²×C₈	—	2	1	no	—
137	C₂²×C₈	—	2	1	no	—
138	C₂²×C₈	—	2	1	no	—
139	C₂²×C₈	—	4	1	no	—
140	C₂²×C₈	—	4	1	no	—
141	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₈	C₂⁴	1	1	yes	characteristic
149	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
150	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
151	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
152	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
153	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
154	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
155	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
156	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
157	C₂×C₄²	—	2	2	no	—
158	C₂×C₄²	—	2	2	no	—
159	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
160	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
161	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₁₆	—	2	1	no	—
168	C₂×C₁₆	—	2	1	no	—
169	C₂×C₁₆	—	2	1	no	—
170	C₂×C₁₆	—	2	1	no	—
171	C₂×C₁₆	—	2	1	no	—
172	C₂×C₁₆	—	2	1	no	—
173	C₂×C₁₆	—	2	1	no	—
174	C₂×C₁₆	—	2	1	no	—
175	C₂×C₁₆	—	2	1	no	—
176	C₂×C₁₆	—	2	1	no	—
177	C₂×C₁₆	—	2	1	no	—
178	C₂×C₁₆	—	2	1	no	—
179	C₂×C₁₆	—	2	1	no	—
180	C₂×C₁₆	—	2	1	no	—
181	C₂×C₁₆	—	2	1	no	—
182	C₂×C₁₆	—	2	1	no	—
183	C₂×C₁₆	—	2	1	no	—
184	C₂×C₁₆	—	2	1	no	—
185	C₂×C₁₆	—	2	1	no	—
186	C₂×C₁₆	—	2	1	no	—
187	C₂×C₁₆	—	2	1	no	—
188	C₂×C₁₆	—	2	1	no	—
189	C₂×C₁₆	—	2	1	no	—
190	C₂×C₁₆	—	2	1	no	—
191	C₄⋊C₈	—	2	2	no	—
192	C₄⋊C₈	—	2	2	no	—
193	C₂²⋊C₈	—	2	2	no	—
194	C₂²⋊C₈	—	2	2	no	—
195	#97	—	2	2	no	—
196	#97	—	4	1	no	—
197	#97	—	4	1	no	—
198	#97	—	4	1	no	—
199	#97	—	4	1	no	—
200	#97	M₁₆	1	4	yes	—
201	C₄×C₈	—	2	2	no	—
202	C₄×C₈	—	2	1	no	—
203	C₄×C₈	—	2	1	no	—
204	C₄×C₈	—	2	1	no	—
205	C₄×C₈	—	2	1	no	—
206	C₄×C₈	—	2	1	no	—
207	C₄×C₈	—	2	1	no	—
208	C₄×C₈	—	2	1	no	—
209	C₄×C₈	—	2	1	no	—
210	C₄×C₈	—	2	1	no	—
211	C₄×C₈	—	2	1	no	—
212	C₄×C₈	—	2	2	no	—
213	C₄×C₈	#41	1	2	yes	—
214	C₄×C₈	#41	1	2	yes	—
215	#95	C₂×C₈	1	1	yes	characteristic
216	#95	C₂×C₈	1	1	yes	characteristic
217	#95	C₂×C₈	1	1	yes	characteristic
218	#95	C₂×C₈	1	1	yes	characteristic
219	#95	C₂×C₈	1	1	yes	characteristic
220	#95	C₂×C₈	1	1	yes	characteristic
221	#95	C₂×C₈	1	1	yes	characteristic
222	#95	C₂×C₈	1	1	yes	characteristic
223	#95	C₂×C₈	1	1	yes	characteristic
224	#95	C₂×C₈	1	1	yes	characteristic
225	#95	C₂×C₈	1	1	yes	characteristic
226	#95	C₂×C₈	1	1	yes	characteristic
227	#95	C₂×C₈	1	1	yes	characteristic
228	#95	C₂×C₈	1	1	yes	characteristic
229	#95	C₂×C₈	1	1	yes	characteristic
230	#95	C₂×C₈	1	1	yes	characteristic
231	C₂⁴	C₂²×C₈	1	1	yes	characteristic
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	1	no	—
234	C₂²×C₄	—	2	1	no	—
235	C₂²×C₄	—	2	1	no	—
236	C₂²×C₄	—	2	1	no	—
237	C₂²×C₄	—	2	1	no	—
238	C₂²×C₄	—	2	1	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	4	1	no	—
243	C₂²×C₄	—	4	1	no	—
244	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
245	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
246	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
247	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
248	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
251	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
257	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
258	C₂×C₈	—	2	1	no	—
259	C₂×C₈	—	2	1	no	—
260	C₂×C₈	—	2	1	no	—
261	C₂×C₈	—	2	1	no	—
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	—	2	1	no	—
264	C₂×C₈	—	2	1	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	—	2	1	no	—
267	C₂×C₈	—	2	1	no	—
268	C₂×C₈	—	2	1	no	—
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	—	2	1	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	1	no	—
276	C₂×C₈	—	4	4	no	—
277	C₂×C₈	—	4	1	no	—
278	C₂×C₈	—	4	1	no	—
279	C₂×C₈	—	4	1	no	—
280	C₂×C₈	—	4	1	no	—
281	C₂×C₈	#117	1	2	yes	—
282	C₂×C₈	C₂×M₁₆	1	2	yes	—
283	C₂×C₈	C₂×M₁₆	1	2	yes	—
284	C₂×C₈	C₂×#41	1	1	yes	characteristic
285	C₂×C₈	C₂×#41	1	1	yes	characteristic
286	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
287	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
289	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	4	1	no	—
293	C₄⋊C₄	—	4	1	no	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	4	1	no	—
297	C₂²⋊C₄	—	4	1	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	2	1	no	—
301	C₄²	—	2	1	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	#117	1	2	yes	—
311	C₄²	C₂×M₁₆	1	2	yes	—
312	C₁₆	—	4	1	no	—
313	C₁₆	—	4	1	no	—
314	C₁₆	—	4	1	no	—
315	C₁₆	—	4	1	no	—
316	C₁₆	—	4	1	no	—
317	C₁₆	—	4	1	no	—
318	C₁₆	—	4	1	no	—
319	C₁₆	—	4	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	#504	1	2	yes	—
327	C₂³	C₂³×C₈	1	1	yes	characteristic
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	#431	1	2	yes	—
371	C₂×C₄	#431	1	2	yes	—
372	C₂×C₄	#504	1	2	yes	—
373	C₂×C₄	C₂×#117	1	1	yes	characteristic
374	C₂×C₄	#520	1	1	yes	characteristic
375	C₂×C₄	#520	1	1	yes	characteristic
376	C₂×C₄	C₂²×M₁₆	1	1	yes	characteristic
377	C₂×C₄	#568	1	1	yes	characteristic
378	C₂×C₄	#568	1	1	yes	characteristic
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	2	2	no	—
382	C₈	—	4	1	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	#540	1	1	yes	characteristic
387	C₈	#541	1	1	yes	characteristic
388	C₈	#542	1	1	yes	characteristic
389	C₈	#542	1	1	yes	characteristic
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	C₂×#431	1	1	yes	characteristic
398	C₂²	#2988	1	1	yes	characteristic
399	C₂²	#2988	1	1	yes	characteristic
400	C₂²	C₂×#504	1	1	yes	characteristic
401	C₂²	C₂×#504	1	1	yes	characteristic
402	C₂²	#3407	1	1	yes	characteristic
403	C₂²	#3407	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	1	no	—
417	C₄	#2314	1	1	yes	characteristic
418	C₄	#2921	1	1	yes	characteristic
419	C₄	#2989	1	1	yes	characteristic
420	C₄	#2989	1	1	yes	characteristic
421	C₂	—	4	2	no	—
422	C₂	#21922	1	1	yes	characteristic
423	C₂	#33422	1	1	yes	characteristic
424	C₂	#33422	1	1	yes	characteristic
425	C₂	#33506	1	1	yes	characteristic
426	C₂	#33507	1	1	yes	characteristic
427	C₂	#33508	1	1	yes	characteristic
428	C₂	#33509	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₈	C₂⁴
commutator, socle	C₂³	C₂³×C₈
prime radical	C₂⁴	C₂²×C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
6. #13105	C₂	semidirect
7. #13105	C₂	semidirect
8. #13104	C₂	semidirect
9. #13104	C₂	semidirect
10. #12899	C₂	semidirect
11. #12880	C₂	semidirect
14. #12654	C₂	semidirect
15. #12654	C₂	semidirect

Maximal subgroups

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

subgroup	index
#20476	2
#13121	2
#13120	2
#13105	2
#13104	2
#12899	2
#12880	2
#12783	2
#12654	2