Subgroups — #24918959

Order 10624.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14581817	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13050577	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×D₃₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128091	C₂	1	1	yes	maximal, characteristic, complemented
5	#19127949	C₂	1	1	yes	maximal, characteristic, complemented
6	#19127935	C₂	1	1	yes	maximal, characteristic, complemented
7	#19127913	C₂	1	1	yes	maximal, characteristic, complemented
8	#19127901	C₂	1	1	yes	maximal, characteristic, complemented
9	#19127851	C₂	1	1	yes	maximal, characteristic, complemented
10	#19127846	C₂	1	1	yes	maximal, characteristic, complemented
11	#19127840	C₂	1	1	yes	maximal, characteristic, complemented
12	#19127834	C₂	1	1	yes	maximal, characteristic, complemented
13	#19127799	C₂	1	1	yes	maximal, characteristic, complemented
14	#19127773	C₂	1	1	yes	maximal, characteristic, complemented
15	#548×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₃₃₂	C₂²	1	1	yes	characteristic
17	C₂²×D₃₃₂	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₈₃	—	2	1	no	—
19	#14581817	—	2	4	no	—
20	C₂×#13050577	—	2	4	no	—
21	C₂×#13050577	C₂²	1	1	yes	characteristic
22	C₂×#13050577	C₂²	1	1	yes	characteristic
23	C₂×#13050577	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13050577	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13050577	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13050577	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13050575	C₂²	1	1	yes	characteristic
28	C₂×#13050575	C₂²	1	1	yes	characteristic, complemented
29	C₂×#13050575	C₂²	1	1	yes	characteristic, complemented
30	C₂×#13050574	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	#14581789	C₂²	1	1	yes	characteristic
33	#14581767	—	2	1	no	—
34	#14581766	C₂²	1	1	yes	characteristic
35	#14581766	C₂²	1	1	yes	characteristic
36	#14581762	—	2	1	no	—
37	#14581762	—	2	1	no	—
38	C₄×D₃₃₂	C₂²	1	1	yes	characteristic
39	#14581725	C₂²	1	1	yes	characteristic, complemented
40	C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
41	#14581716	C₂²	1	1	yes	characteristic, complemented
42	#14581716	C₂²	1	1	yes	characteristic, complemented
43	#14581713	C₂²	1	1	yes	characteristic, complemented
44	#14581712	C₂²	1	1	yes	characteristic
45	#14581712	C₂²	1	1	yes	characteristic, complemented
46	#14581712	C₂²	1	1	yes	characteristic, complemented
47	C₂²⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
48	C₂²⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
49	#14581703	C₂²	1	1	yes	characteristic, complemented
50	C₂×#41×C₈₃	C₂²	1	1	yes	characteristic, complemented
51	C₂²×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
52	#124×C₈₃	—	2	1	no	—
53	#124×C₈₃	C₂²	1	1	yes	characteristic, complemented
54	C₂²⋊Q₈×C₈₃	—	2	1	no	—
55	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
56	#121×C₈₃	—	2	1	no	—
57	#121×C₈₃	C₂²	1	1	yes	characteristic, complemented
58	C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
59	C₄×D₄×C₈₃	—	2	1	no	—
60	C₄×D₄×C₈₃	C₂²	1	1	yes	characteristic
61	C₂³×D₈₃	—	2	1	no	—
62	C₂³×D₈₃	—	2	1	no	—
63	C₂×D₃₃₂	—	2	2	no	—
64	C₂×D₃₃₂	—	2	2	no	—
65	C₂×D₃₃₂	—	2	1	no	—
66	C₂×D₃₃₂	—	2	1	no	—
67	C₂×D₃₃₂	—	2	1	no	—
68	C₂×D₃₃₂	—	2	1	no	—
69	C₂×D₃₃₂	—	4	1	no	—
70	C₂×D₃₃₂	—	4	1	no	—
71	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
72	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
73	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊D₈₃	—	2	1	no	—
75	C₂×C₂²⋊D₈₃	—	2	1	no	—
76	D₄×D₈₃	—	4	4	no	—
77	C₂×C₄×D₈₃	—	2	1	no	—
78	#13050577	—	2	2	no	—
79	#13050577	—	2	2	no	—
80	#13050577	—	2	2	no	—
81	#13050577	—	2	2	no	—
82	#13050577	—	4	1	no	—
83	#13050577	D₄	1	4	yes	complemented
84	#13050575	—	2	2	no	—
85	#13050575	—	2	2	no	—
86	#13050575	—	4	1	no	—
87	#13050574	—	2	2	no	—
88	C₂×C₈₃⋊C₈	—	2	2	no	—
89	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
90	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
91	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
92	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
93	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
94	(C₂×D₈₃)⋊C₄	—	2	1	no	—
95	(C₂×D₈₃)⋊C₄	—	2	1	no	—
96	(C₂×D₈₃)⋊C₄	—	2	1	no	—
97	#41×C₈₃	—	2	2	no	—
98	#41×C₈₃	—	4	1	no	—
99	C₂×Q₈×C₈₃	—	2	1	no	—
100	C₂×Q₈×C₈₃	—	2	2	no	—
101	C₂×Q₈×C₈₃	—	4	1	no	—
102	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
103	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
104	C₂×D₄×C₈₃	—	2	1	no	—
105	C₂×D₄×C₈₃	—	2	1	no	—
106	C₂×D₄×C₈₃	D₄	1	1	yes	characteristic
107	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
108	C₂²×C₄×C₈₃	—	2	1	no	—
109	C₂²×C₄×C₈₃	—	2	1	no	—
110	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
112	C₄⋊C₄×C₈₃	—	2	1	no	—
113	C₄⋊C₄×C₈₃	—	2	1	no	—
114	C₄⋊C₄×C₈₃	D₄	1	1	yes	characteristic
115	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
116	C₂²⋊C₄×C₈₃	—	2	1	no	—
117	C₂²⋊C₄×C₈₃	—	2	1	no	—
118	C₂²⋊C₄×C₈₃	—	2	1	no	—
119	C₂²⋊C₄×C₈₃	—	2	1	no	—
120	C₂²⋊C₄×C₈₃	D₄	1	1	yes	characteristic
121	C₂²⋊C₄×C₈₃	D₄	1	1	yes	characteristic
122	C₄²×C₈₃	—	2	1	no	—
123	C₄²×C₈₃	C₂³	1	1	yes	characteristic
124	C₂³×C₈₃	—	2	1	no	—
125	C₂³×C₈₃	C₂×D₄	1	1	yes	characteristic
126	C₂³×C₈₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×D₈₃	—	2	1	no	—
128	C₂²×D₈₃	—	2	1	no	—
129	C₂²×D₈₃	—	2	1	no	—
130	C₂²×D₈₃	—	4	2	no	—
131	C₂²×D₈₃	—	4	2	no	—
132	C₂²×D₈₃	—	4	2	no	—
133	C₂²×D₈₃	—	4	2	no	—
134	C₂²×D₈₃	—	8	1	no	—
135	C₂²×D₈₃	—	8	1	no	—
136	Q₈×C₈₃	—	2	1	no	—
137	Q₈×C₈₃	—	2	1	no	—
138	Q₈×C₈₃	—	2	1	no	—
139	Q₈×C₈₃	—	4	2	no	—
140	Q₈×C₈₃	C₂×D₄	1	2	yes	complemented
141	D₄×C₈₃	—	2	2	no	—
142	D₄×C₈₃	—	2	1	no	—
143	D₄×C₈₃	—	2	1	no	—
144	D₄×C₈₃	—	4	2	no	—
145	D₄×C₈₃	—	4	2	no	—
146	C₂×C₄×C₈₃	—	2	1	no	—
147	C₂×C₄×C₈₃	—	2	1	no	—
148	C₂×C₄×C₈₃	—	2	1	no	—
149	C₂×C₄×C₈₃	—	2	1	no	—
150	C₂×C₄×C₈₃	—	2	1	no	—
151	C₂×C₄×C₈₃	—	2	1	no	—
152	C₂×C₄×C₈₃	—	2	1	no	—
153	C₂×C₄×C₈₃	—	4	2	no	—
154	C₂×C₄×C₈₃	—	4	2	no	—
155	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
160	C₂²⋊D₈₃	—	4	2	no	—
161	C₂²⋊D₈₃	—	4	2	no	—
162	C₂×Dic₈₃	—	2	1	no	—
163	D₃₃₂	—	2	1	no	—
164	D₃₃₂	—	2	1	no	—
165	D₃₃₂	—	2	1	no	—
166	D₃₃₂	—	2	1	no	—
167	D₃₃₂	—	2	1	no	—
168	D₃₃₂	—	4	2	no	—
169	D₃₃₂	—	4	2	no	—
170	D₃₃₂	—	4	2	no	—
171	D₃₃₂	—	8	1	no	—
172	D₃₃₂	C₂×D₄	1	2	yes	—
173	C₄×D₈₃	—	4	2	no	—
174	C₈₃⋊C₈	—	2	1	no	—
175	C₈₃⋊C₈	—	2	1	no	—
176	C₈₃⋊C₈	—	2	1	no	—
177	C₈₃⋊C₈	C₂×D₄	1	2	yes	complemented
178	C₂²×C₈₃	—	2	1	no	—
179	C₂²×C₈₃	—	2	1	no	—
180	C₂²×C₈₃	—	2	1	no	—
181	C₂²×C₈₃	—	2	1	no	—
182	C₂²×C₈₃	—	2	1	no	—
183	C₂²×C₈₃	—	4	1	no	—
184	C₂²×C₈₃	—	4	1	no	—
185	C₂²×C₈₃	—	4	1	no	—
186	C₂²×C₈₃	AGL(1,ℤ/8)	1	2	yes	complemented
187	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×D₈₃	—	2	2	no	—
189	C₂×D₈₃	—	4	1	no	—
190	C₂×D₈₃	—	4	1	no	—
191	C₂×D₈₃	—	4	1	no	—
192	C₂×D₈₃	—	4	1	no	—
193	C₂×D₈₃	—	4	1	no	—
194	C₂×D₈₃	—	4	1	no	—
195	C₂×D₈₃	—	4	1	no	—
196	C₂×D₈₃	—	4	1	no	—
197	C₂×D₈₃	—	8	4	no	—
198	C₂×D₈₃	—	8	4	no	—
199	C₄×C₈₃	—	2	1	no	—
200	C₄×C₈₃	—	2	1	no	—
201	C₄×C₈₃	—	2	2	no	—
202	C₄×C₈₃	—	2	1	no	—
203	C₄×C₈₃	—	2	1	no	—
204	C₄×C₈₃	—	4	1	no	—
205	C₄×C₈₃	—	4	1	no	—
206	C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
207	C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
208	Dic₈₃	—	4	1	no	—
209	C₂×C₈₃	—	2	2	no	—
210	C₂×C₈₃	—	4	1	no	—
211	C₂×C₈₃	—	8	1	no	—
212	C₂×C₈₃	D₄²	1	1	yes	characteristic
213	C₂×C₈₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂×C₈₃	#577	1	1	yes	characteristic
215	D₈₃	—	4	2	no	—
216	D₈₃	—	8	1	no	—
217	D₈₃	—	8	1	no	—
218	#3265	—	83	1	no	maximal, Sylow
219	C₈₃	#3265	1	1	yes	characteristic, complemented, Sylow
220	C₂×AGL(1,ℤ/8)	—	83	1	no	—
221	C₂²×SD₁₆	—	83	1	no	—
222	#548	D₈₃	1	1	yes	characteristic, complemented
223	D₄²	—	83	1	no	—
224	#496	—	83	1	no	—
225	#468	—	83	1	no	—
226	#466	—	83	1	no	—
227	#463	—	83	1	no	—
228	#460	—	83	1	no	—
229	#450	—	83	1	no	—
230	#449	—	83	1	no	—
231	#448	—	83	1	no	—
232	#447	—	83	1	no	—
233	#440	—	83	1	no	—
234	#435	—	83	1	no	—
235	C₂×#41	C₂×D₈₃	1	1	yes	characteristic, complemented
236	C₂²×Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
237	C₂²×D₄	—	83	1	no	—
238	C₂²×D₄	—	83	1	no	—
239	C₂²×D₄	—	166	1	no	—
240	AGL(1,ℤ/8)	—	166	4	no	—
241	C₂×SD₁₆	—	83	1	no	—
242	C₂×SD₁₆	—	83	1	no	—
243	C₂×SD₁₆	—	83	1	no	—
244	C₂×SD₁₆	—	83	1	no	—
245	C₂×SD₁₆	—	83	1	no	—
246	C₂×SD₁₆	—	83	1	no	—
247	C₂×SD₁₆	—	166	4	no	—
248	C₂×D₈	—	83	1	no	—
249	C₂×D₈	—	83	1	no	—
250	C₂×D₈	—	83	1	no	—
251	C₂×M₁₆	—	83	1	no	—
252	C₂²×C₈	—	83	1	no	—
253	#127	—	83	1	no	—
254	#124	—	2	1	no	—
255	#124	C₂×D₈₃	1	1	yes	characteristic, complemented
256	C₂²⋊Q₈	—	2	1	no	—
257	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
258	#121	—	2	1	no	—
259	#121	—	83	1	no	—
260	#121	—	83	1	no	—
261	#121	—	166	1	no	—
262	#121	C₂×D₈₃	1	1	yes	characteristic, complemented
263	#120	—	166	1	no	—
264	#120	—	166	1	no	—
265	C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	83	1	no	—
268	C₄×D₄	C₂×D₈₃	1	1	yes	characteristic
269	#107	—	83	1	no	—
270	C₄⋊C₈	—	83	1	no	—
271	#103	—	83	1	no	—
272	#103	—	83	1	no	—
273	#102	—	83	1	no	—
274	#102	—	83	1	no	—
275	#102	—	83	1	no	—
276	#102	—	83	1	no	—
277	C₂²⋊C₈	—	83	1	no	—
278	C₂²⋊C₈	—	83	1	no	—
279	#97	—	83	1	no	—
280	C₂⁴	—	166	1	no	—
281	C₂⁴	—	166	1	no	—
282	#41	—	2	2	no	—
283	#41	—	4	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
288	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	332	1	no	—
292	C₂×D₄	—	332	1	no	—
293	C₂×D₄	—	332	4	no	—
294	C₂×D₄	—	83	1	no	—
295	C₂×D₄	—	83	1	no	—
296	C₂×D₄	—	83	1	no	—
297	C₂×D₄	—	166	2	no	—
298	C₂×D₄	—	166	2	no	—
299	C₂×D₄	—	166	1	no	—
300	C₂×D₄	—	166	1	no	—
301	C₂×D₄	—	166	1	no	—
302	C₂×D₄	—	166	1	no	—
303	C₂×D₄	—	166	1	no	—
304	C₂×D₄	—	166	1	no	—
305	C₂×D₄	C₂²⋊D₈₃	1	1	yes	characteristic
306	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	166	1	no	—
310	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
311	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
312	SD₁₆	—	332	1	no	—
313	SD₁₆	—	83	4	no	—
314	SD₁₆	—	166	2	no	—
315	SD₁₆	—	166	2	no	—
316	SD₁₆	—	166	2	no	—
317	SD₁₆	—	166	2	no	—
318	D₈	—	332	1	no	—
319	D₈	—	166	2	no	—
320	D₈	—	166	2	no	—
321	M₁₆	—	166	2	no	—
322	C₂×C₈	—	83	1	no	—
323	C₂×C₈	—	83	1	no	—
324	C₂×C₈	—	83	1	no	—
325	C₂×C₈	—	83	1	no	—
326	C₂×C₈	—	166	2	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	83	1	no	—
330	C₄⋊C₄	C₂²⋊D₈₃	1	1	yes	characteristic
331	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	166	1	no	—
337	C₂²⋊C₄	—	166	1	no	—
338	C₂²⋊C₄	—	166	1	no	—
339	C₂²⋊C₄	C₂²⋊D₈₃	1	1	yes	characteristic
340	C₂²⋊C₄	C₂²⋊D₈₃	1	1	yes	characteristic
341	C₄²	—	2	1	no	—
342	C₄²	C₂²×D₈₃	1	1	yes	characteristic
343	C₂³	—	2	1	no	—
344	C₂³	—	332	2	no	—
345	C₂³	—	332	2	no	—
346	C₂³	—	332	2	no	—
347	C₂³	—	332	2	no	—
348	C₂³	—	664	1	no	—
349	C₂³	—	664	1	no	—
350	C₂³	—	166	1	no	—
351	C₂³	—	166	1	no	—
352	C₂³	—	166	1	no	—
353	C₂³	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
354	C₂³	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	2	1	no	—
358	Q₈	—	4	2	no	—
359	Q₈	D₄×D₈₃	1	2	yes	complemented
360	D₄	—	2	2	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	332	2	no	—
366	D₄	—	332	2	no	—
367	D₄	—	332	2	no	—
368	D₄	—	332	2	no	—
369	D₄	—	332	2	no	—
370	D₄	—	83	2	no	—
371	D₄	—	664	1	no	—
372	D₄	—	166	1	no	—
373	D₄	—	166	1	no	—
374	D₄	—	166	1	no	—
375	D₄	—	166	1	no	—
376	D₄	—	166	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	332	2	no	—
387	C₂×C₄	—	166	1	no	—
388	C₂×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
389	C₂×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
390	C₂×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
391	C₂×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
393	C₈	—	83	2	no	—
394	C₈	—	166	1	no	—
395	C₈	—	166	1	no	—
396	C₈	—	166	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	332	1	no	—
406	C₂²	—	332	1	no	—
407	C₂²	—	332	1	no	—
408	C₂²	—	332	1	no	—
409	C₂²	—	332	1	no	—
410	C₂²	—	332	1	no	—
411	C₂²	—	332	1	no	—
412	C₂²	—	332	1	no	—
413	C₂²	—	664	4	no	—
414	C₂²	—	664	4	no	—
415	C₂²	—	166	2	no	—
416	C₂²	#14581817	1	2	yes	complemented
417	C₂²	C₂²×C₂²⋊D₈₃	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	332	1	no	—
426	C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
427	C₄	#14581837	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	4	1	no	—
430	C₂	—	8	1	no	—
431	C₂	—	332	2	no	—
432	C₂	—	664	1	no	—
433	C₂	—	664	1	no	—
434	C₂	D₄×C₂²⋊D₈₃	1	1	yes	characteristic
435	C₂	C₂×#14581817	1	1	yes	characteristic
436	C₂	#19128509	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₈₃
commutator, cosocle	C₂×C₄×C₈₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₃
Fitting	#548×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×D₄
hypercenter	#548	D₈₃
hypocenter	C₈₃	#3265
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #548

Complements

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

N	H ≅ G/N	type
1. C₂×#14581817	C₂	semidirect
2. C₂²×#13050577	C₂	semidirect
3. D₄×D₃₃₂	C₂	semidirect
4. #19128091	C₂	semidirect
5. #19127949	C₂	semidirect
6. #19127935	C₂	semidirect
7. #19127913	C₂	semidirect
8. #19127901	C₂	semidirect
9. #19127851	C₂	semidirect
10. #19127846	C₂	semidirect
11. #19127840	C₂	semidirect
12. #19127834	C₂	semidirect
13. #19127799	C₂	semidirect
14. #19127773	C₂	semidirect
15. #548×C₈₃	C₂	semidirect
23. C₂×#13050577	C₂²	semidirect
24. C₂×#13050577	C₂²	semidirect
25. C₂×#13050577	C₂²	semidirect
26. C₂×#13050577	C₂²	semidirect
28. C₂×#13050575	C₂²	semidirect
29. C₂×#13050575	C₂²	semidirect
30. C₂×#13050574	C₂²	semidirect
31. C₂²×C₈₃⋊C₈	C₂²	semidirect
39. #14581725	C₂²	semidirect
40. C₄⋊(C₈₃⋊C₈)	C₂²	semidirect
41. #14581716	C₂²	semidirect
42. #14581716	C₂²	semidirect
43. #14581713	C₂²	semidirect
45. #14581712	C₂²	semidirect
46. #14581712	C₂²	semidirect
47. C₂²⋊(C₈₃⋊C₈)	C₂²	semidirect
48. C₂²⋊(C₈₃⋊C₈)	C₂²	semidirect
49. #14581703	C₂²	semidirect
50. C₂×#41×C₈₃	C₂²	semidirect
51. C₂²×Q₈×C₈₃	C₂²	semidirect
53. #124×C₈₃	C₂²	semidirect
55. C₂²⋊Q₈×C₈₃	C₂²	semidirect
57. #121×C₈₃	C₂²	semidirect
58. C₄×Q₈×C₈₃	C₂²	semidirect
83. #13050577	D₄	semidirect
140. Q₈×C₈₃	C₂×D₄	semidirect
177. C₈₃⋊C₈	C₂×D₄	semidirect
186. C₂²×C₈₃	AGL(1,ℤ/8)	semidirect
219. C₈₃	#3265	semidirect
222. #548	D₈₃	semidirect
235. C₂×#41	C₂×D₈₃	semidirect
236. C₂²×Q₈	C₂×D₈₃	semidirect
255. #124	C₂×D₈₃	semidirect
257. C₂²⋊Q₈	C₂×D₈₃	semidirect
262. #121	C₂×D₈₃	semidirect
265. C₄×Q₈	C₂×D₈₃	semidirect
359. Q₈	D₄×D₈₃	semidirect
416. C₂²	#14581817	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14581817	2
C₂²×#13050577	2
D₄×D₃₃₂	2
#19128091	2
#19127949	2
#19127935	2
#19127913	2
#19127901	2
#19127851	2
#19127846	2
#19127840	2
#19127834	2
#19127799	2
#19127773	2
#548×C₈₃	2
#3265	83