Subgroups — #24921806

Order 10624.

1004 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128455	C₂	1	2	yes	maximal, complemented
2	#19128452	C₂	1	2	yes	maximal, complemented
3	#19128431	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128414	C₂	1	1	yes	maximal, characteristic, complemented
5	#19128407	C₂	1	1	yes	maximal, characteristic, complemented
6	#19128406	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128390	C₂	1	1	yes	maximal, characteristic, complemented
8	#19128389	C₂	1	1	yes	maximal, characteristic, complemented
9	#19128383	C₂	1	2	yes	maximal, complemented
10	#19128354	C₂	1	1	yes	maximal, characteristic, complemented
11	#19128353	C₂	1	2	yes	maximal, complemented
12	#19128352	C₂	1	1	yes	maximal, characteristic, complemented
13	#19128331	C₂	1	1	yes	maximal, characteristic, complemented
14	#19128328	C₂	1	2	yes	maximal, complemented
15	#19128325	C₂	1	1	yes	maximal, characteristic, complemented
16	#19128322	C₂	1	1	yes	maximal, characteristic, complemented
17	#19128321	C₂	1	2	yes	maximal, complemented
18	#19128276	C₂	1	2	yes	maximal, complemented
19	#19128274	C₂	1	2	yes	maximal, complemented
20	C₄⋊Q₈×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#19128236	C₂	1	1	yes	maximal, characteristic, complemented
22	#19128229	C₂	1	1	yes	maximal, characteristic, complemented
23	#544×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13050591	C₂²	1	2	yes	—
25	C₂×#13050590	C₂²	1	2	yes	—
26	C₂×Q₈×D₈₃	C₂²	1	2	yes	—
27	#14581792	C₂²	1	1	yes	characteristic
28	#14581791	C₂²	1	2	yes	—
29	#14581791	C₂²	1	1	yes	characteristic
30	#14581791	C₂²	1	1	yes	characteristic
31	#14581791	C₂²	1	1	yes	characteristic
32	#14581791	C₂²	1	2	yes	—
33	#14581791	C₂²	1	2	yes	—
34	#14581790	C₂²	1	2	yes	—
35	#14581790	C₂²	1	2	yes	—
36	#14581790	C₂²	1	2	yes	—
37	#14581787	C₂²	1	2	yes	—
38	#14581787	C₂²	1	2	yes	—
39	#14581787	C₂²	1	2	yes	—
40	#14581787	C₂²	1	2	yes	—
41	#14581787	C₂²	1	1	yes	characteristic
42	#14581785	C₂²	1	2	yes	—
43	#14581785	C₂²	1	1	yes	characteristic
44	#14581784	C₂²	1	2	yes	—
45	#14581783	C₂²	1	2	yes	—
46	#14581783	C₂²	1	1	yes	characteristic
47	#14581782	C₂²	1	1	yes	characteristic
48	#14581782	C₂²	1	2	yes	—
49	#14581782	C₂²	1	2	yes	—
50	#14581781	C₂²	1	2	yes	—
51	#14581780	C₂²	1	1	yes	characteristic
52	#14581780	C₂²	1	2	yes	—
53	#14581778	C₂²	1	1	yes	characteristic
54	#14581778	C₂²	1	2	yes	—
55	#14581778	C₂²	1	2	yes	—
56	#14581777	C₂²	1	2	yes	—
57	#14581777	C₂²	1	2	yes	—
58	#14581777	C₂²	1	2	yes	—
59	#14581777	C₂²	1	2	yes	—
60	#14581777	C₂²	1	2	yes	—
61	#14581777	C₂²	1	1	yes	characteristic
62	#14581777	C₂²	1	2	yes	—
63	#14581775	C₂²	1	2	yes	—
64	#14581774	C₂²	1	2	yes	—
65	#14581774	C₂²	1	2	yes	—
66	#14581774	C₂²	1	1	yes	characteristic
67	#14581772	C₂²	1	1	yes	characteristic
68	#14581772	C₂²	1	2	yes	—
69	#14581772	C₂²	1	1	yes	characteristic
70	#14581772	C₂²	1	2	yes	—
71	#14581771	C₂²	1	1	yes	characteristic
72	#14581771	C₂²	1	2	yes	—
73	#14581770	C₂²	1	2	yes	—
74	#14581770	C₂²	1	2	yes	—
75	#14581770	C₂²	1	2	yes	—
76	#14581770	C₂²	1	2	yes	—
77	#14581770	C₂²	1	1	yes	characteristic
78	#14581770	C₂²	1	2	yes	—
79	#14581770	C₂²	1	2	yes	—
80	#14581768	C₂²	1	2	yes	—
81	#14581768	C₂²	1	2	yes	—
82	#14581767	C₂²	1	1	yes	characteristic
83	#14581767	C₂²	1	1	yes	characteristic
84	#14581766	C₂²	1	1	yes	characteristic
85	#14581765	C₂²	1	2	yes	—
86	#14581765	C₂²	1	1	yes	characteristic
87	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
88	C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
89	#14581757	C₂²	1	2	yes	—
90	#14581757	C₂²	1	1	yes	characteristic
91	#14581757	C₂²	1	1	yes	characteristic
92	C₄×D₃₃₂	C₂²	1	1	yes	characteristic
93	C₄×D₃₃₂	C₂²	1	1	yes	characteristic
94	#14581754	C₂²	1	1	yes	characteristic
95	#14581754	C₂²	1	2	yes	—
96	#14581754	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₈₃	C₂²	1	2	yes	—
98	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
100	#14581750	C₂²	1	2	yes	—
101	#14581750	C₂²	1	1	yes	characteristic
102	#14581750	C₂²	1	2	yes	—
103	#14581749	C₂²	1	1	yes	characteristic
104	#14581749	C₂²	1	2	yes	—
105	#14581749	C₂²	1	2	yes	—
106	C₄⋊C₄×D₈₃	C₂²	1	2	yes	—
107	C₄⋊C₄×D₈₃	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₈₃	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₈₃	C₂²	1	2	yes	—
110	C₄⋊C₄×D₈₃	C₂²	1	1	yes	characteristic
111	C₄²×D₈₃	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
113	C₄⋊Q₈×C₈₃	C₂²	1	2	yes	—
114	C₄⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic
115	#125×C₈₃	C₂²	1	1	yes	characteristic
116	#125×C₈₃	C₂²	1	2	yes	—
117	#125×C₈₃	C₂²	1	1	yes	characteristic
118	C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	—
119	C₂²⋊Q₈×C₈₃	C₂²	1	2	yes	—
120	#117×C₈₃	C₂²	1	1	yes	characteristic
121	#117×C₈₃	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
123	#13050591	—	4	4	no	—
124	#13050590	—	4	4	no	—
125	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
126	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₆₆	C₂³	1	2	yes	—
128	C₂×Dic₁₆₆	C₂³	1	2	yes	—
129	C₂×Dic₁₆₆	C₂³	1	2	yes	—
130	C₂×Dic₁₆₆	C₂³	1	2	yes	—
131	Q₈×D₈₃	—	4	4	no	—
132	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
133	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
134	C₂×D₃₃₂	C₂³	1	2	yes	—
135	C₂×D₃₃₂	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₈₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₈₃	C₂³	1	2	yes	—
139	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₈₃	C₂³	1	2	yes	—
141	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₈₃	C₂³	1	2	yes	—
145	C₂×C₄×D₈₃	C₂³	1	2	yes	—
146	C₂×C₄×D₈₃	C₂³	1	2	yes	—
147	C₂×C₄×D₈₃	C₂³	1	2	yes	—
148	C₂×C₄×D₈₃	C₂³	1	2	yes	—
149	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₈₃	C₂³	1	2	yes	—
152	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₈₃	C₂³	1	2	yes	—
154	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₈₃	C₂³	1	2	yes	—
156	C₄⋊Dic₈₃	C₂³	1	2	yes	—
157	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
158	Dic₈₃⋊C₄	C₂³	1	2	yes	—
159	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
160	Dic₈₃⋊C₄	C₂³	1	2	yes	—
161	Dic₈₃⋊C₄	C₂³	1	2	yes	—
162	Dic₈₃⋊C₄	C₂³	1	2	yes	—
163	Dic₈₃⋊C₄	C₂³	1	2	yes	—
164	Dic₈₃⋊C₄	C₂³	1	2	yes	—
165	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₈₃⋊C₄	C₂³	1	2	yes	—
168	Dic₈₃⋊C₄	C₂³	1	2	yes	—
169	Dic₈₃⋊C₄	C₂³	1	2	yes	—
170	Dic₈₃⋊C₄	C₂³	1	2	yes	—
171	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₈₃⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₈₃⋊C₄	C₂³	1	2	yes	—
174	C₂²⋊Dic₈₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₈₃	C₂³	1	1	yes	characteristic
177	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₈₃)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₈₃)⋊C₄	C₂³	1	1	yes	characteristic
194	C₄×Dic₈₃	C₂³	1	2	yes	—
195	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
196	C₄×Dic₈₃	C₂³	1	2	yes	—
197	C₄×Dic₈₃	C₂³	1	2	yes	—
198	C₄×Dic₈₃	C₂³	1	2	yes	—
199	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
201	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
202	C₂×Q₈×C₈₃	C₂³	1	2	yes	—
203	C₂×Q₈×C₈₃	C₂³	1	2	yes	—
204	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
206	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
209	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
211	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
212	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
213	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
215	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
218	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₈₃	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
222	C₄²×C₈₃	C₂³	1	2	yes	—
223	C₄²×C₈₃	C₂³	1	1	yes	characteristic
224	C₄²×C₈₃	C₂³	1	1	yes	characteristic
225	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
226	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
227	C₂²×D₈₃	C₂⁴	1	2	yes	—
228	C₂²×D₈₃	C₂⁴	1	1	yes	characteristic
229	Q₈×C₈₃	—	4	2	no	—
230	Q₈×C₈₃	—	4	2	no	—
231	C₂×C₄×C₈₃	—	2	2	no	—
232	C₂×C₄×C₈₃	—	4	2	no	—
233	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
236	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
239	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
241	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
242	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
243	C₂²⋊D₈₃	—	2	2	no	—
244	C₂²⋊D₈₃	—	2	2	no	—
245	C₂²⋊D₈₃	—	4	2	no	—
246	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₈₃	C₂⁴	1	2	yes	—
248	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₈₃	C₂⁴	1	2	yes	—
252	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₈₃	C₂⁴	1	2	yes	—
254	C₂×Dic₈₃	C₂⁴	1	1	yes	characteristic
255	D₃₃₂	—	2	4	no	—
256	D₃₃₂	—	2	2	no	—
257	D₃₃₂	—	2	2	no	—
258	D₃₃₂	—	4	2	no	—
259	C₄×D₈₃	—	2	2	no	—
260	C₄×D₈₃	—	2	4	no	—
261	C₄×D₈₃	—	2	4	no	—
262	C₄×D₈₃	—	2	2	no	—
263	C₄×D₈₃	—	2	2	no	—
264	C₄×D₈₃	—	2	2	no	—
265	C₄×D₈₃	—	2	4	no	—
266	C₄×D₈₃	—	4	2	no	—
267	C₄×D₈₃	—	4	2	no	—
268	C₄×D₈₃	—	4	2	no	—
269	Dic₁₆₆	—	2	2	no	—
270	Dic₁₆₆	—	2	2	no	—
271	Dic₁₆₆	—	4	2	no	—
272	Dic₁₆₆	—	4	2	no	—
273	Dic₁₆₆	—	4	2	no	—
274	Dic₁₆₆	—	4	2	no	—
275	C₂²×C₈₃	—	2	1	no	—
276	C₂²×C₈₃	—	2	1	no	—
277	C₂²×C₈₃	—	2	1	no	—
278	C₂²×C₈₃	C₂⁵	1	1	yes	characteristic
279	C₂×D₈₃	—	2	1	no	—
280	C₂×D₈₃	—	2	1	no	—
281	C₂×D₈₃	—	2	1	no	—
282	C₂×D₈₃	—	2	2	no	—
283	C₂×D₈₃	—	2	2	no	—
284	C₂×D₈₃	—	2	1	no	—
285	C₂×D₈₃	—	2	2	no	—
286	C₂×D₈₃	—	2	1	no	—
287	C₂×D₈₃	H(5,𝔽₂)	1	2	yes	—
288	C₄×C₈₃	—	2	1	no	—
289	C₄×C₈₃	—	2	2	no	—
290	C₄×C₈₃	—	2	2	no	—
291	C₄×C₈₃	—	2	2	no	—
292	C₄×C₈₃	—	2	1	no	—
293	C₄×C₈₃	—	2	1	no	—
294	C₄×C₈₃	—	2	1	no	—
295	C₄×C₈₃	—	2	2	no	—
296	C₄×C₈₃	—	2	1	no	—
297	C₄×C₈₃	2₋¹⁺⁴	1	2	yes	—
298	Dic₈₃	—	2	1	no	—
299	Dic₈₃	—	2	2	no	—
300	Dic₈₃	—	2	2	no	—
301	Dic₈₃	—	2	1	no	—
302	Dic₈₃	—	2	1	no	—
303	Dic₈₃	—	2	2	no	—
304	Dic₈₃	—	2	1	no	—
305	Dic₈₃	—	2	1	no	—
306	Dic₈₃	2₋¹⁺⁴	1	2	yes	—
307	C₂×C₈₃	—	4	1	no	—
308	C₂×C₈₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	C₂×C₈₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
311	D₈₃	—	2	2	no	—
312	D₈₃	—	4	1	no	—
313	D₈₃	—	4	2	no	—
314	#3544	—	83	1	no	maximal, Sylow
315	C₈₃	#3544	1	1	yes	characteristic, complemented, Sylow
316	#563	—	83	2	no	—
317	#563	—	83	2	no	—
318	Q₈²	—	83	1	no	—
319	#555	—	83	1	no	—
320	#554	—	83	1	no	—
321	#554	—	83	1	no	—
322	#552	—	83	2	no	—
323	#552	—	83	1	no	—
324	#552	—	83	1	no	—
325	#547	—	83	1	no	—
326	#547	—	83	2	no	—
327	#547	—	83	1	no	—
328	#544	—	83	2	no	—
329	#544	—	83	1	no	—
330	#544	D₈₃	1	1	yes	characteristic, complemented
331	#542	—	83	1	no	—
332	#542	—	83	2	no	—
333	#542	—	83	1	no	—
334	#536	—	83	2	no	—
335	#536	—	83	2	no	—
336	C₂×C₄⋊Q₈	—	83	1	no	—
337	#529	—	83	1	no	—
338	#529	—	83	1	no	—
339	C₂×#41	—	83	2	no	—
340	C₂×#41	—	83	2	no	—
341	C₂²×Q₈	—	83	2	no	—
342	C₄⋊Q₈	—	83	2	no	—
343	C₄⋊Q₈	—	83	2	no	—
344	C₄⋊Q₈	—	83	2	no	—
345	C₄⋊Q₈	—	83	1	no	—
346	C₄⋊Q₈	—	83	1	no	—
347	C₄⋊Q₈	—	83	2	no	—
348	C₄⋊Q₈	—	83	2	no	—
349	C₄⋊Q₈	—	83	2	no	—
350	C₄⋊Q₈	—	83	1	no	—
351	C₄⋊Q₈	—	83	1	no	—
352	C₄⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
353	C₄⋊Q₈	C₂×D₈₃	1	2	yes	—
354	C₄⋊Q₈	C₂×D₈₃	1	1	yes	characteristic
355	#126	—	83	2	no	—
356	#126	—	83	1	no	—
357	#126	—	83	2	no	—
358	#126	—	83	2	no	—
359	#126	—	83	2	no	—
360	#126	—	83	1	no	—
361	#126	—	83	2	no	—
362	#125	—	83	1	no	—
363	#125	—	83	2	no	—
364	#125	—	83	2	no	—
365	#125	—	83	1	no	—
366	#125	—	83	2	no	—
367	#125	—	83	2	no	—
368	#125	C₂×D₈₃	1	1	yes	characteristic
369	#125	C₂×D₈₃	1	1	yes	characteristic
370	#125	C₂×D₈₃	1	2	yes	—
371	#124	—	83	2	no	—
372	#124	—	83	1	no	—
373	#124	—	83	2	no	—
374	#124	—	83	2	no	—
375	#124	—	83	1	no	—
376	#124	—	83	2	no	—
377	#123	—	83	2	no	—
378	#123	—	83	2	no	—
379	#123	—	83	1	no	—
380	#123	—	83	2	no	—
381	#123	—	83	2	no	—
382	#123	—	83	2	no	—
383	#123	—	83	2	no	—
384	#123	—	83	2	no	—
385	#123	—	83	1	no	—
386	#123	—	83	2	no	—
387	#123	—	83	2	no	—
388	C₂²⋊Q₈	—	83	2	no	—
389	C₂²⋊Q₈	—	83	2	no	—
390	C₂²⋊Q₈	—	83	2	no	—
391	C₂²⋊Q₈	—	83	1	no	—
392	C₂²⋊Q₈	—	83	1	no	—
393	C₂²⋊Q₈	—	83	2	no	—
394	C₂²⋊Q₈	—	83	2	no	—
395	C₂²⋊Q₈	—	83	2	no	—
396	C₂²⋊Q₈	—	83	2	no	—
397	C₂²⋊Q₈	—	83	2	no	—
398	C₂²⋊Q₈	—	83	2	no	—
399	C₂²⋊Q₈	—	83	1	no	—
400	C₂²⋊Q₈	—	83	2	no	—
401	C₂²⋊Q₈	—	83	1	no	—
402	C₂²⋊Q₈	—	83	2	no	—
403	C₂²⋊Q₈	C₂×D₈₃	1	2	yes	—
404	C₂²⋊Q₈	C₂×D₈₃	1	2	yes	—
405	#121	—	83	1	no	—
406	#121	—	83	1	no	—
407	#121	—	83	1	no	—
408	#121	—	83	1	no	—
409	#121	—	83	2	no	—
410	C₄×Q₈	—	83	1	no	—
411	C₄×Q₈	—	83	2	no	—
412	C₄×Q₈	—	83	1	no	—
413	C₄×Q₈	—	83	1	no	—
414	C₄×Q₈	—	83	1	no	—
415	C₄×D₄	—	83	1	no	—
416	C₄×D₄	—	83	1	no	—
417	C₄×D₄	—	83	2	no	—
418	C₄×D₄	—	83	2	no	—
419	C₄×D₄	—	83	1	no	—
420	C₄×D₄	—	83	1	no	—
421	C₄×D₄	—	83	1	no	—
422	C₄×D₄	—	83	1	no	—
423	#117	—	83	2	no	—
424	#117	—	83	2	no	—
425	#117	—	83	1	no	—
426	#117	—	83	1	no	—
427	#117	—	83	2	no	—
428	#117	—	83	2	no	—
429	#117	C₂×D₈₃	1	1	yes	characteristic
430	#117	C₂×D₈₃	1	1	yes	characteristic
431	C₂×C₄⋊C₄	—	83	2	no	—
432	C₂×C₄⋊C₄	—	83	1	no	—
433	C₂×C₄⋊C₄	—	83	1	no	—
434	C₂×C₄⋊C₄	—	83	2	no	—
435	C₂×C₄⋊C₄	—	83	1	no	—
436	C₂×C₄⋊C₄	C₂×D₈₃	1	1	yes	characteristic
437	C₂×C₄²	—	83	1	no	—
438	#41	—	332	4	no	—
439	#41	—	332	4	no	—
440	C₂×Q₈	—	332	4	no	—
441	C₂×Q₈	—	83	2	no	—
442	C₂×Q₈	—	83	2	no	—
443	C₂×Q₈	—	83	2	no	—
444	C₂×Q₈	—	83	2	no	—
445	C₂×Q₈	—	83	1	no	—
446	C₂×Q₈	—	83	1	no	—
447	C₂×Q₈	C₂²×D₈₃	1	2	yes	—
448	C₂×Q₈	C₂²×D₈₃	1	2	yes	—
449	C₂×D₄	—	83	2	no	—
450	C₂×D₄	—	83	1	no	—
451	C₂×D₄	—	83	1	no	—
452	C₂×D₄	—	83	2	no	—
453	C₂×D₄	—	83	1	no	—
454	C₂×D₄	—	83	2	no	—
455	C₂×D₄	—	83	1	no	—
456	C₂²×C₄	—	83	2	no	—
457	C₂²×C₄	—	83	2	no	—
458	C₂²×C₄	—	83	2	no	—
459	C₂²×C₄	—	83	1	no	—
460	C₂²×C₄	—	83	1	no	—
461	C₂²×C₄	—	83	1	no	—
462	C₂²×C₄	—	83	2	no	—
463	C₂²×C₄	—	83	2	no	—
464	C₂²×C₄	—	83	2	no	—
465	C₂²×C₄	—	83	1	no	—
466	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
467	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
468	C₄⋊C₄	—	83	2	no	—
469	C₄⋊C₄	—	83	1	no	—
470	C₄⋊C₄	—	83	1	no	—
471	C₄⋊C₄	—	83	2	no	—
472	C₄⋊C₄	—	83	1	no	—
473	C₄⋊C₄	—	83	2	no	—
474	C₄⋊C₄	—	83	2	no	—
475	C₄⋊C₄	—	83	2	no	—
476	C₄⋊C₄	—	83	2	no	—
477	C₄⋊C₄	—	83	2	no	—
478	C₄⋊C₄	—	83	1	no	—
479	C₄⋊C₄	—	83	2	no	—
480	C₄⋊C₄	—	83	2	no	—
481	C₄⋊C₄	—	83	2	no	—
482	C₄⋊C₄	—	83	1	no	—
483	C₄⋊C₄	—	83	1	no	—
484	C₄⋊C₄	—	83	2	no	—
485	C₄⋊C₄	—	83	1	no	—
486	C₄⋊C₄	—	83	1	no	—
487	C₄⋊C₄	—	83	2	no	—
488	C₄⋊C₄	—	83	1	no	—
489	C₄⋊C₄	—	83	1	no	—
490	C₄⋊C₄	—	83	2	no	—
491	C₄⋊C₄	—	83	2	no	—
492	C₄⋊C₄	—	83	2	no	—
493	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
497	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
498	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
499	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
501	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
502	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
505	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
506	C₂²⋊C₄	—	83	2	no	—
507	C₂²⋊C₄	—	83	1	no	—
508	C₂²⋊C₄	—	83	1	no	—
509	C₂²⋊C₄	—	83	2	no	—
510	C₂²⋊C₄	—	83	1	no	—
511	C₂²⋊C₄	—	83	1	no	—
512	C₂²⋊C₄	—	83	2	no	—
513	C₂²⋊C₄	—	83	1	no	—
514	C₂²⋊C₄	—	83	2	no	—
515	C₂²⋊C₄	—	83	2	no	—
516	C₂²⋊C₄	—	83	2	no	—
517	C₂²⋊C₄	—	83	2	no	—
518	C₂²⋊C₄	—	83	1	no	—
519	C₂²⋊C₄	—	83	2	no	—
520	C₂²⋊C₄	—	83	2	no	—
521	C₂²⋊C₄	—	83	2	no	—
522	C₂²⋊C₄	—	83	2	no	—
523	C₂²⋊C₄	—	83	1	no	—
524	C₂²⋊C₄	—	83	2	no	—
525	C₂²⋊C₄	—	83	1	no	—
526	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
527	C₂²⋊C₄	C₂²×D₈₃	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
529	C₄²	—	83	1	no	—
530	C₄²	—	83	1	no	—
531	C₄²	—	83	1	no	—
532	C₄²	—	83	2	no	—
533	C₄²	—	83	2	no	—
534	C₄²	—	83	1	no	—
535	C₄²	—	83	2	no	—
536	C₄²	—	83	2	no	—
537	C₄²	C₂²×D₈₃	1	1	yes	characteristic
538	C₄²	C₂²×D₈₃	1	2	yes	—
539	C₄²	C₂²×D₈₃	1	1	yes	characteristic
540	C₂³	—	83	1	no	—
541	C₂³	—	83	2	no	—
542	C₂³	—	83	1	no	—
543	C₂³	C₂³×D₈₃	1	1	yes	characteristic
544	Q₈	—	4	2	no	—
545	Q₈	—	4	2	no	—
546	Q₈	—	332	2	no	—
547	Q₈	—	332	2	no	—
548	Q₈	—	332	2	no	—
549	Q₈	—	332	2	no	—
550	Q₈	—	166	2	no	—
551	Q₈	—	166	2	no	—
552	D₄	—	332	2	no	—
553	D₄	—	332	2	no	—
554	D₄	—	166	4	no	—
555	D₄	—	166	2	no	—
556	D₄	—	166	2	no	—
557	D₄	—	166	2	no	—
558	D₄	—	166	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	332	2	no	—
562	C₂×C₄	—	332	2	no	—
563	C₂×C₄	—	332	2	no	—
564	C₂×C₄	—	83	1	no	—
565	C₂×C₄	—	83	1	no	—
566	C₂×C₄	—	83	2	no	—
567	C₂×C₄	—	83	1	no	—
568	C₂×C₄	—	83	1	no	—
569	C₂×C₄	—	83	1	no	—
570	C₂×C₄	—	83	2	no	—
571	C₂×C₄	—	83	1	no	—
572	C₂×C₄	—	83	2	no	—
573	C₂×C₄	—	166	4	no	—
574	C₂×C₄	—	166	2	no	—
575	C₂×C₄	—	166	2	no	—
576	C₂×C₄	—	166	4	no	—
577	C₂×C₄	—	166	4	no	—
578	C₂×C₄	—	166	2	no	—
579	C₂×C₄	—	166	2	no	—
580	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
582	C₂×C₄	C₂³×D₈₃	1	2	yes	—
583	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₈₃	1	2	yes	—
585	C₂×C₄	C₂³×D₈₃	1	2	yes	—
586	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₈₃	1	2	yes	—
589	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	83	2	no	—
594	C₂²	—	166	1	no	—
595	C₂²	—	166	2	no	—
596	C₂²	—	166	2	no	—
597	C₂²	—	166	1	no	—
598	C₂²	—	166	1	no	—
599	C₂²	—	166	2	no	—
600	C₂²	—	166	1	no	—
601	C₂²	—	166	1	no	—
602	C₂²	C₂⁴×D₈₃	1	1	yes	characteristic
603	C₄	—	2	2	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	83	2	no	—
613	C₄	—	166	2	no	—
614	C₄	—	166	1	no	—
615	C₄	—	166	2	no	—
616	C₄	—	166	1	no	—
617	C₄	—	166	1	no	—
618	C₄	—	166	1	no	—
619	C₄	—	166	1	no	—
620	C₄	—	166	2	no	—
621	C₄	#14581840	1	2	yes	—
622	C₂	—	4	1	no	—
623	C₂	—	332	2	no	—
624	C₂	—	332	1	no	—
625	C₂	—	166	2	no	—
626	C₂	H(5,𝔽₂)×D₈₃	1	1	yes	characteristic
627	C₂	2₋¹⁺⁴×D₈₃	1	1	yes	characteristic
628	C₂	C₂×#14581840	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁵
Fitting	#544×C₈₃	C₂
hypercenter	#544	D₈₃
hypocenter	C₈₃	#3544
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ #544

Complements

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

N	H ≅ G/N	type
1. #19128455	C₂	semidirect
2. #19128452	C₂	semidirect
3. #19128431	C₂	semidirect
4. #19128414	C₂	semidirect
5. #19128407	C₂	semidirect
6. #19128406	C₂	semidirect
7. #19128390	C₂	semidirect
8. #19128389	C₂	semidirect
9. #19128383	C₂	semidirect
10. #19128354	C₂	semidirect
11. #19128353	C₂	semidirect
12. #19128352	C₂	semidirect
13. #19128331	C₂	semidirect
14. #19128328	C₂	semidirect
15. #19128325	C₂	semidirect
16. #19128322	C₂	semidirect
17. #19128321	C₂	semidirect
18. #19128276	C₂	semidirect
19. #19128274	C₂	semidirect
20. C₄⋊Q₈×D₈₃	C₂	semidirect
21. #19128236	C₂	semidirect
22. #19128229	C₂	semidirect
23. #544×C₈₃	C₂	semidirect
315. C₈₃	#3544	semidirect
330. #544	D₈₃	semidirect

Maximal subgroups

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

subgroup	index
#19128455	2
#19128452	2
#19128431	2
#19128414	2
#19128407	2
#19128406	2
#19128390	2
#19128389	2
#19128383	2
#19128354	2
#19128353	2
#19128352	2
#19128331	2
#19128328	2
#19128325	2
#19128322	2
#19128321	2
#19128276	2
#19128274	2
C₄⋊Q₈×D₈₃	2
#19128236	2
#19128229	2
#544×C₈₃	2
#3544	83