Subgroups — C₂₃×#61858 #19209484

Order 5888.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3388	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3387	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3376	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3369	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3364	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3244	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3242	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3125	C₂	1	2	yes	maximal
20	C₂₃×#3120	C₂	1	2	yes	maximal, complemented
21	C₂₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#3102	C₂	1	1	yes	maximal, characteristic
23	C₂₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#563	—	2	2	no	—
25	Q₈²×C₂₃	C₂²	1	2	yes	—
26	Q₈²×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#557	C₂²	1	1	yes	characteristic
28	C₂₃×#557	C₂²	1	1	yes	characteristic
29	C₂₃×#557	C₂²	1	1	yes	characteristic
30	C₂₃×#557	C₂²	1	2	yes	—
31	C₂₃×#556	—	2	1	no	—
32	C₂₃×#556	C₂²	1	1	yes	characteristic
33	C₂₃×#556	C₂²	1	2	yes	—
34	C₂₃×#554	—	2	2	no	—
35	C₂₃×#554	C₂²	1	2	yes	—
36	C₂₃×#554	C₂²	1	1	yes	characteristic
37	C₂₃×#552	—	2	1	no	—
38	D₄×Q₈×C₂₃	—	2	1	no	—
39	D₄×Q₈×C₂₃	—	2	1	no	—
40	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
42	C₂₃×#544	—	2	1	no	—
43	C₂₃×#544	—	2	2	no	—
44	C₂₃×#544	C₂²	1	2	yes	—
45	C₂₃×#542	C₂²	1	2	yes	—
46	C₂₃×#541	—	2	1	no	—
47	C₂₃×#541	—	2	2	no	—
48	C₂₃×#541	C₂²	1	2	yes	—
49	C₂₃×#533	—	2	1	no	—
50	C₂₃×#533	C₂²	1	1	yes	characteristic
51	C₂₃×#533	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
53	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
54	C₂₃×#529	C₂²	1	1	yes	characteristic
55	C₂₃×#520	C₂²	1	2	yes	—
56	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
57	C₂₃×#501	C₂²	1	2	yes	—
58	C₂₃×#501	C₂²	1	2	yes	—
59	C₂₃×#501	C₂²	1	2	yes	—
60	C₂₃×#499	C₂²	1	2	yes	—
61	C₂₃×#498	C₂²	1	1	yes	characteristic
62	C₂₃×#498	C₂²	1	1	yes	characteristic
63	C₂₃×#498	C₂²	1	2	yes	—
64	C₂₃×#491	C₂²	1	2	yes	—
65	C₂₃×#489	C₂²	1	2	yes	—
66	C₂₃×#489	C₂²	1	2	yes	—
67	C₂₃×#488	C₂²	1	2	yes	—
68	C₂₃×#487	C₂²	1	1	yes	characteristic
69	C₂₃×#487	C₂²	1	1	yes	characteristic
70	C₂₃×#487	C₂²	1	2	yes	—
71	C₂₃×#485	C₂²	1	1	yes	characteristic
72	C₂₃×#485	C₂²	1	2	yes	—
73	C₂₃×#484	C₂²	1	2	yes	—
74	C₂₃×#483	C₂²	1	2	yes	—
75	C₂₃×#483	C₂²	1	2	yes	—
76	C₂₃×#482	C₂²	1	1	yes	characteristic
77	C₂₃×#481	C₂²	1	2	yes	—
78	C₂₃×#479	C₂²	1	2	yes	—
79	C₂₃×#479	C₂²	1	2	yes	—
80	C₂₃×#479	C₂²	1	2	yes	—
81	C₂₃×#479	C₂²	1	1	yes	characteristic
82	C₂₃×#479	C₂²	1	2	yes	—
83	C₂₃×#478	C₂²	1	2	yes	—
84	C₂₃×#478	C₂²	1	1	yes	characteristic
85	C₂₃×#478	C₂²	1	2	yes	—
86	C₂₃×#477	C₂²	1	2	yes	—
87	C₂₃×#477	C₂²	1	1	yes	characteristic
88	C₂₃×#476	C₂²	1	2	yes	—
89	C₂₃×#476	C₂²	1	1	yes	characteristic
90	C₂₃×#476	C₂²	1	2	yes	—
91	C₂₃×#475	C₂²	1	2	yes	—
92	C₂₃×#475	C₂²	1	2	yes	—
93	C₂₃×#475	C₂²	1	1	yes	characteristic
94	C₂₃×#475	C₂²	1	1	yes	characteristic
95	C₂₃×#475	C₂²	1	2	yes	—
96	C₂₃×#475	C₂²	1	2	yes	—
97	C₂₃×#475	C₂²	1	2	yes	—
98	C₂₃×#474	C₂²	1	1	yes	characteristic
99	C₂₃×#474	C₂²	1	1	yes	characteristic
100	C₂₃×#464	C₂²	1	1	yes	characteristic
101	C₂₃×#464	C₂²	1	2	yes	—
102	C₂₃×#463	C₂²	1	1	yes	characteristic
103	C₂₃×#463	C₂²	1	2	yes	—
104	C₂₃×#462	C₂²	1	1	yes	characteristic
105	C₂₃×#462	C₂²	1	2	yes	—
106	C₂₃×#461	C₂²	1	1	yes	characteristic
107	C₂₃×#461	C₂²	1	2	yes	—
108	C₂₃×#452	C₂²	1	1	yes	characteristic
109	C₂₃×#452	C₂²	1	2	yes	—
110	C₂₃×#449	C₂²	1	1	yes	characteristic
111	C₂₃×#446	C₂²	1	1	yes	characteristic
112	C₂₃×#446	C₂²	1	2	yes	—
113	C₂₃×#446	C₂²	1	1	yes	characteristic
114	C₂₃×#446	C₂²	1	2	yes	—
115	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
117	C₂₃×#442	C₂²	1	2	yes	—
118	C₂₃×#441	C₂²	1	2	yes	—
119	C₂₃×#441	C₂²	1	2	yes	—
120	C₂₃×#441	C₂²	1	2	yes	—
121	C₂₃×#440	C₂²	1	2	yes	—
122	C₂₃×#440	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
124	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
125	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
128	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
129	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
130	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
131	C₂₃×#433	C₂²	1	2	yes	—
132	C₂₃×#433	C₂²	1	2	yes	—
133	C₂₃×#432	C₂²	1	1	yes	characteristic
134	C₂₃×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₂₃	—	2	1	no	—
137	C₂²×Q₈×C₂₃	—	2	1	no	—
138	C₂²×Q₈×C₂₃	—	2	1	no	—
139	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
145	C₂₃×C₄⋊Q₈	—	2	1	no	—
146	C₂₃×C₄⋊Q₈	—	2	1	no	—
147	C₂₃×C₄⋊Q₈	—	2	2	no	—
148	C₂₃×C₄⋊Q₈	—	2	2	no	—
149	C₂₃×C₄⋊Q₈	—	2	2	no	—
150	C₂₃×C₄⋊Q₈	—	2	2	no	—
151	C₂₃×C₄⋊Q₈	—	2	1	no	—
152	C₂₃×C₄⋊Q₈	—	2	2	no	—
153	C₂₃×C₄⋊Q₈	—	2	2	no	—
154	C₂₃×C₄⋊Q₈	—	2	1	no	—
155	C₂₃×C₄⋊Q₈	—	2	1	no	—
156	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
157	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
158	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₂₃×#126	—	2	2	no	—
168	C₂₃×#126	—	2	2	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#126	—	2	2	no	—
172	C₂₃×#126	—	2	2	no	—
173	C₂₃×#126	—	2	1	no	—
174	C₂₃×#125	—	2	2	no	—
175	C₂₃×#125	—	2	1	no	—
176	C₂₃×#125	—	2	2	no	—
177	C₂₃×#125	—	2	2	no	—
178	C₂₃×#125	—	2	2	no	—
179	C₂₃×#125	—	2	2	no	—
180	C₂₃×#125	—	2	2	no	—
181	C₂₃×#125	—	2	2	no	—
182	C₂₃×#125	—	2	2	no	—
183	C₂₃×#125	—	2	1	no	—
184	C₂₃×#125	D₄	1	2	yes	—
185	C₂₃×#125	C₂³	1	2	yes	—
186	C₂₃×#125	C₂³	1	2	yes	—
187	C₂₃×#125	C₂³	1	2	yes	—
188	C₂₃×#125	C₂³	1	1	yes	characteristic
189	C₂₃×#124	—	2	2	no	—
190	C₂₃×#124	C₂³	1	2	yes	—
191	C₂₃×#124	C₂³	1	1	yes	characteristic
192	C₂₃×#123	—	2	1	no	—
193	C₂₃×#123	—	2	2	no	—
194	C₂₃×C₂²⋊Q₈	—	2	1	no	—
195	C₂₃×C₂²⋊Q₈	—	2	2	no	—
196	C₂₃×C₂²⋊Q₈	—	2	1	no	—
197	C₂₃×C₂²⋊Q₈	—	2	2	no	—
198	C₂₃×C₂²⋊Q₈	—	2	1	no	—
199	C₂₃×C₂²⋊Q₈	—	2	1	no	—
200	C₂₃×C₂²⋊Q₈	—	2	1	no	—
201	C₂₃×C₂²⋊Q₈	—	2	2	no	—
202	C₂₃×C₂²⋊Q₈	—	2	2	no	—
203	C₂₃×C₂²⋊Q₈	—	2	2	no	—
204	C₂₃×C₂²⋊Q₈	—	2	2	no	—
205	C₂₃×C₂²⋊Q₈	—	2	2	no	—
206	C₂₃×C₂²⋊Q₈	—	2	2	no	—
207	C₂₃×C₂²⋊Q₈	—	2	2	no	—
208	C₂₃×C₂²⋊Q₈	—	2	2	no	—
209	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
212	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂₃×#121	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₂₃	—	2	1	no	—
216	C₄×Q₈×C₂₃	—	2	2	no	—
217	C₄×Q₈×C₂₃	—	2	1	no	—
218	C₄×Q₈×C₂₃	—	2	1	no	—
219	C₄×Q₈×C₂₃	—	2	1	no	—
220	C₄×Q₈×C₂₃	—	2	2	no	—
221	C₄×Q₈×C₂₃	—	2	1	no	—
222	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
225	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
227	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
229	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
230	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
234	C₄×D₄×C₂₃	—	2	1	no	—
235	C₄×D₄×C₂₃	—	2	1	no	—
236	C₄×D₄×C₂₃	—	2	1	no	—
237	C₄×D₄×C₂₃	—	2	2	no	—
238	C₄×D₄×C₂₃	—	2	2	no	—
239	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₂₃	C₂³	1	2	yes	—
241	C₄×D₄×C₂₃	C₂³	1	2	yes	—
242	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₂₃	C₂³	1	2	yes	—
245	C₂₃×#117	—	2	1	no	—
246	C₂₃×#117	—	2	2	no	—
247	C₂₃×#117	—	2	1	no	—
248	C₂₃×#117	—	2	2	no	—
249	C₂₃×#117	—	2	1	no	—
250	C₂₃×#117	—	2	1	no	—
251	C₂₃×#117	C₂³	1	1	yes	characteristic
252	C₂₃×#117	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
255	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
256	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
257	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
258	C₂×C₄²×C₂₃	—	2	1	no	—
259	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
260	C₂₃×#107	C₂³	1	1	yes	characteristic
261	C₂₃×#107	C₂³	1	2	yes	—
262	C₂₃×#107	C₂³	1	1	yes	characteristic
263	C₂₃×#107	C₂³	1	2	yes	—
264	C₂₃×#107	C₂³	1	2	yes	—
265	C₂₃×#106	C₂³	1	2	yes	—
266	C₂₃×#106	C₂³	1	2	yes	—
267	C₂₃×#106	C₂³	1	1	yes	characteristic
268	C₂₃×#106	C₂³	1	2	yes	—
269	C₂₃×#106	C₂³	1	1	yes	characteristic
270	C₂₃×#106	C₂³	1	2	yes	—
271	C₂₃×#106	C₂³	1	2	yes	—
272	C₂₃×#106	C₂³	1	2	yes	—
273	C₂₃×#106	C₂³	1	2	yes	—
274	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
279	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
280	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₂₃×#103	C₂³	1	1	yes	characteristic
283	C₂₃×#103	C₂³	1	2	yes	—
284	C₂₃×#103	C₂³	1	2	yes	—
285	C₂₃×#103	C₂³	1	1	yes	characteristic
286	C₂₃×#103	C₂³	1	2	yes	—
287	C₂₃×#103	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	2	yes	—
289	C₂₃×#103	C₂³	1	1	yes	characteristic
290	C₂₃×#103	C₂³	1	2	yes	—
291	C₂₃×#103	C₂³	1	2	yes	—
292	C₂₃×#103	C₂³	1	2	yes	—
293	C₂₃×#103	C₂³	1	2	yes	—
294	C₂₃×#103	C₂³	1	2	yes	—
295	C₂₃×#102	C₂³	1	1	yes	characteristic
296	C₂₃×#102	C₂³	1	1	yes	characteristic
297	C₂₃×#102	C₂³	1	1	yes	characteristic
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×#97	C₂³	1	2	yes	—
306	C₂₃×#97	C₂³	1	2	yes	—
307	C₂₃×#97	C₂³	1	2	yes	—
308	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	2	yes	—
311	C₄×C₈×C₂₃	C₂³	1	2	yes	—
312	#41×C₂₃	—	2	2	no	—
313	#41×C₂₃	—	2	2	no	—
314	C₂×Q₈×C₂₃	—	2	1	no	—
315	C₂×Q₈×C₂₃	—	2	1	no	—
316	C₂×Q₈×C₂₃	—	2	1	no	—
317	C₂×Q₈×C₂₃	—	2	2	no	—
318	C₂×Q₈×C₂₃	—	2	2	no	—
319	C₂×Q₈×C₂₃	—	2	2	no	—
320	C₂×Q₈×C₂₃	—	2	2	no	—
321	C₂×Q₈×C₂₃	—	8	2	no	—
322	C₂×Q₈×C₂₃	—	8	2	no	—
323	C₂×Q₈×C₂₃	—	8	2	no	—
324	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
327	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₂₃	—	2	1	no	—
331	C₂×D₄×C₂₃	—	2	1	no	—
332	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₂₃	—	2	1	no	—
335	C₂²×C₄×C₂₃	—	2	2	no	—
336	C₂²×C₄×C₂₃	—	2	1	no	—
337	C₂²×C₄×C₂₃	—	2	1	no	—
338	C₂²×C₄×C₂₃	—	2	1	no	—
339	C₂²×C₄×C₂₃	—	2	2	no	—
340	C₂²×C₄×C₂₃	—	2	2	no	—
341	C₂²×C₄×C₂₃	—	2	2	no	—
342	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
345	Q₁₆×C₂₃	—	2	2	no	—
346	Q₁₆×C₂₃	—	2	4	no	—
347	SD₁₆×C₂₃	—	2	2	no	—
348	SD₁₆×C₂₃	—	2	2	no	—
349	SD₁₆×C₂₃	—	2	4	no	—
350	D₈×C₂₃	—	2	2	no	—
351	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
353	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
356	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₂₃	—	2	2	no	—
358	C₄⋊C₄×C₂₃	—	2	2	no	—
359	C₄⋊C₄×C₂₃	—	2	1	no	—
360	C₄⋊C₄×C₂₃	—	2	2	no	—
361	C₄⋊C₄×C₂₃	—	2	2	no	—
362	C₄⋊C₄×C₂₃	—	2	1	no	—
363	C₄⋊C₄×C₂₃	—	2	1	no	—
364	C₄⋊C₄×C₂₃	—	2	2	no	—
365	C₄⋊C₄×C₂₃	—	2	2	no	—
366	C₄⋊C₄×C₂₃	—	2	2	no	—
367	C₄⋊C₄×C₂₃	—	2	1	no	—
368	C₄⋊C₄×C₂₃	—	2	1	no	—
369	C₄⋊C₄×C₂₃	—	2	1	no	—
370	C₄⋊C₄×C₂₃	—	2	2	no	—
371	C₄⋊C₄×C₂₃	—	2	1	no	—
372	C₄⋊C₄×C₂₃	—	2	1	no	—
373	C₄⋊C₄×C₂₃	—	2	1	no	—
374	C₄⋊C₄×C₂₃	—	2	2	no	—
375	C₄⋊C₄×C₂₃	—	2	2	no	—
376	C₄⋊C₄×C₂₃	—	2	2	no	—
377	C₄⋊C₄×C₂₃	—	2	2	no	—
378	C₄⋊C₄×C₂₃	—	2	2	no	—
379	C₄⋊C₄×C₂₃	—	2	2	no	—
380	C₄⋊C₄×C₂₃	—	2	1	no	—
381	C₄⋊C₄×C₂₃	—	2	2	no	—
382	C₄⋊C₄×C₂₃	—	2	2	no	—
383	C₄⋊C₄×C₂₃	—	2	2	no	—
384	C₄⋊C₄×C₂₃	—	2	2	no	—
385	C₄⋊C₄×C₂₃	—	2	2	no	—
386	C₄⋊C₄×C₂₃	—	2	2	no	—
387	C₄⋊C₄×C₂₃	—	2	1	no	—
388	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
389	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
390	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
404	C₂²⋊C₄×C₂₃	—	2	2	no	—
405	C₂²⋊C₄×C₂₃	—	2	1	no	—
406	C₂²⋊C₄×C₂₃	—	2	1	no	—
407	C₂²⋊C₄×C₂₃	—	2	1	no	—
408	C₂²⋊C₄×C₂₃	—	2	1	no	—
409	C₂²⋊C₄×C₂₃	—	2	1	no	—
410	C₂²⋊C₄×C₂₃	—	2	2	no	—
411	C₂²⋊C₄×C₂₃	—	2	2	no	—
412	C₂²⋊C₄×C₂₃	—	2	1	no	—
413	C₂²⋊C₄×C₂₃	—	2	1	no	—
414	C₂²⋊C₄×C₂₃	—	2	2	no	—
415	C₂²⋊C₄×C₂₃	—	2	2	no	—
416	C₂²⋊C₄×C₂₃	—	2	1	no	—
417	C₂²⋊C₄×C₂₃	—	2	2	no	—
418	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
419	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
420	C₄²×C₂₃	—	2	1	no	—
421	C₄²×C₂₃	—	2	1	no	—
422	C₄²×C₂₃	—	2	1	no	—
423	C₄²×C₂₃	—	2	2	no	—
424	C₄²×C₂₃	—	2	2	no	—
425	C₄²×C₂₃	—	2	2	no	—
426	C₄²×C₂₃	—	2	1	no	—
427	C₄²×C₂₃	—	2	2	no	—
428	C₄²×C₂₃	—	2	2	no	—
429	C₄²×C₂₃	—	2	2	no	—
430	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
432	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
433	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
434	C₄²×C₂₃	C₂⁴	1	2	yes	—
435	C₄²×C₂₃	C₂⁴	1	2	yes	—
436	#61858	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
437	C₂³×C₂₃	—	2	1	no	—
438	C₂³×C₂₃	—	2	1	no	—
439	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
440	Q₈×C₂₃	—	2	2	no	—
441	Q₈×C₂₃	—	2	2	no	—
442	Q₈×C₂₃	—	2	1	no	—
443	Q₈×C₂₃	—	2	1	no	—
444	Q₈×C₂₃	—	2	2	no	—
445	Q₈×C₂₃	—	2	1	no	—
446	Q₈×C₂₃	—	2	2	no	—
447	Q₈×C₂₃	—	4	2	no	—
448	Q₈×C₂₃	—	4	2	no	—
449	Q₈×C₂₃	—	4	2	no	—
450	Q₈×C₂₃	—	8	1	no	—
451	Q₈×C₂₃	—	8	2	no	—
452	Q₈×C₂₃	—	8	2	no	—
453	Q₈×C₂₃	—	8	2	no	—
454	Q₈×C₂₃	—	8	2	no	—
455	Q₈×C₂₃	2₋¹⁺⁴	1	2	yes	—
456	D₄×C₂₃	—	2	4	no	—
457	D₄×C₂₃	—	2	1	no	—
458	D₄×C₂₃	—	2	1	no	—
459	D₄×C₂₃	—	2	1	no	—
460	D₄×C₂₃	—	8	1	no	—
461	D₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
462	C₂×C₄×C₂₃	—	2	4	no	—
463	C₂×C₄×C₂₃	—	2	1	no	—
464	C₂×C₄×C₂₃	—	2	2	no	—
465	C₂×C₄×C₂₃	—	2	1	no	—
466	C₂×C₄×C₂₃	—	2	1	no	—
467	C₂×C₄×C₂₃	—	2	2	no	—
468	C₂×C₄×C₂₃	—	2	1	no	—
469	C₂×C₄×C₂₃	—	2	1	no	—
470	C₂×C₄×C₂₃	—	2	1	no	—
471	C₂×C₄×C₂₃	—	2	1	no	—
472	C₂×C₄×C₂₃	—	2	2	no	—
473	C₂×C₄×C₂₃	—	2	1	no	—
474	C₂×C₄×C₂₃	—	2	2	no	—
475	C₂×C₄×C₂₃	—	2	2	no	—
476	C₂×C₄×C₂₃	—	4	1	no	—
477	C₂×C₄×C₂₃	—	4	2	no	—
478	C₂×C₄×C₂₃	—	4	2	no	—
479	C₂×C₄×C₂₃	—	4	2	no	—
480	C₂×C₄×C₂₃	—	8	2	no	—
481	C₂×C₄×C₂₃	—	8	2	no	—
482	C₂×C₄×C₂₃	—	8	2	no	—
483	C₂×C₄×C₂₃	—	8	2	no	—
484	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
494	C₈×C₂₃	—	2	1	no	—
495	C₈×C₂₃	—	2	1	no	—
496	C₈×C₂₃	—	2	1	no	—
497	C₈×C₂₃	—	2	2	no	—
498	C₈×C₂₃	—	2	1	no	—
499	C₈×C₂₃	—	2	2	no	—
500	#3555	C₂×C₂₃	1	1	yes	characteristic, complemented
501	#3503	C₂×C₂₃	1	1	yes	characteristic, complemented
502	#3388	C₂×C₂₃	1	2	yes	complemented
503	#3387	C₂×C₂₃	1	1	yes	characteristic, complemented
504	#3387	C₂×C₂₃	1	2	yes	complemented
505	#3384	C₂×C₂₃	1	1	yes	characteristic, complemented
506	#3381	C₂×C₂₃	1	1	yes	characteristic, complemented
507	Q₈×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
508	#3376	C₂×C₂₃	1	2	yes	complemented
509	#3374	C₂×C₂₃	1	1	yes	characteristic, complemented
510	#3369	C₂×C₂₃	1	2	yes	complemented
511	#3367	C₂×C₂₃	1	1	yes	characteristic, complemented
512	#3364	C₂×C₂₃	1	1	yes	characteristic, complemented
513	#3359	C₂×C₂₃	1	1	yes	characteristic, complemented
514	#3244	C₂×C₂₃	1	2	yes	complemented
515	#3242	C₂×C₂₃	1	2	yes	complemented
516	#3239	C₂×C₂₃	1	1	yes	characteristic, complemented
517	#3229	C₂×C₂₃	1	1	yes	characteristic, complemented
518	#3125	C₂×C₂₃	1	2	yes	—
519	#3120	C₂×C₂₃	1	2	yes	complemented
520	#3116	C₂×C₂₃	1	1	yes	characteristic, complemented
521	#3102	C₂×C₂₃	1	1	yes	characteristic
522	#2985	C₂×C₂₃	1	1	yes	characteristic, complemented
523	C₂²×C₂₃	—	2	1	no	—
524	C₂²×C₂₃	—	2	1	no	—
525	C₂²×C₂₃	—	2	2	no	—
526	C₂²×C₂₃	—	2	1	no	—
527	C₂²×C₂₃	—	4	1	no	—
528	C₂²×C₂₃	—	4	1	no	—
529	C₂²×C₂₃	—	4	1	no	—
530	C₂²×C₂₃	—	4	1	no	—
531	C₂²×C₂₃	—	4	1	no	—
532	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
533	C₄×C₂₃	—	2	1	no	—
534	C₄×C₂₃	—	2	1	no	—
535	C₄×C₂₃	—	2	2	no	—
536	C₄×C₂₃	—	2	2	no	—
537	C₄×C₂₃	—	2	1	no	—
538	C₄×C₂₃	—	2	2	no	—
539	C₄×C₂₃	—	2	1	no	—
540	C₄×C₂₃	—	2	2	no	—
541	C₄×C₂₃	—	2	2	no	—
542	C₄×C₂₃	—	4	1	no	—
543	C₄×C₂₃	—	4	2	no	—
544	C₄×C₂₃	—	4	1	no	—
545	C₄×C₂₃	—	4	2	no	—
546	C₄×C₂₃	—	4	1	no	—
547	C₄×C₂₃	—	4	1	no	—
548	C₄×C₂₃	—	4	1	no	—
549	C₄×C₂₃	—	4	2	no	—
550	C₄×C₂₃	—	4	2	no	—
551	C₄×C₂₃	#577	1	2	yes	—
552	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
554	#563	—	2	2	no	—
555	Q₈²	C₂²×C₂₃	1	2	yes	—
556	Q₈²	C₂²×C₂₃	1	1	yes	characteristic
557	#557	C₂²×C₂₃	1	1	yes	characteristic
558	#557	C₂²×C₂₃	1	1	yes	characteristic
559	#557	C₂²×C₂₃	1	1	yes	characteristic
560	#557	C₂²×C₂₃	1	2	yes	—
561	#556	—	2	1	no	—
562	#556	C₂²×C₂₃	1	1	yes	characteristic
563	#556	C₂²×C₂₃	1	2	yes	—
564	#554	—	2	2	no	—
565	#554	C₂²×C₂₃	1	2	yes	—
566	#554	C₂²×C₂₃	1	1	yes	characteristic
567	#552	—	2	1	no	—
568	D₄×Q₈	—	2	1	no	—
569	D₄×Q₈	—	2	1	no	—
570	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
571	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
572	#544	—	2	1	no	—
573	#544	—	2	2	no	—
574	#544	C₂²×C₂₃	1	2	yes	—
575	#542	C₂²×C₂₃	1	2	yes	—
576	#541	—	2	1	no	—
577	#541	—	2	2	no	—
578	#541	C₂²×C₂₃	1	2	yes	—
579	#533	—	2	1	no	—
580	#533	C₂²×C₂₃	1	1	yes	characteristic
581	#533	C₂²×C₂₃	1	1	yes	characteristic
582	C₂×C₄⋊Q₈	—	2	1	no	—
583	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
584	#529	C₂²×C₂₃	1	1	yes	characteristic
585	#520	C₂²×C₂₃	1	2	yes	—
586	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
587	#501	C₂²×C₂₃	1	2	yes	—
588	#501	C₂²×C₂₃	1	2	yes	—
589	#501	C₂²×C₂₃	1	2	yes	—
590	#499	C₂²×C₂₃	1	2	yes	—
591	#498	C₂²×C₂₃	1	1	yes	characteristic
592	#498	C₂²×C₂₃	1	2	yes	—
593	#498	C₂²×C₂₃	1	1	yes	characteristic
594	#491	C₂²×C₂₃	1	2	yes	—
595	#489	C₂²×C₂₃	1	2	yes	—
596	#489	C₂²×C₂₃	1	2	yes	—
597	#488	C₂²×C₂₃	1	2	yes	—
598	#487	C₂²×C₂₃	1	1	yes	characteristic
599	#487	C₂²×C₂₃	1	2	yes	—
600	#487	C₂²×C₂₃	1	1	yes	characteristic
601	#485	C₂²×C₂₃	1	1	yes	characteristic
602	#485	C₂²×C₂₃	1	2	yes	—
603	#484	C₂²×C₂₃	1	2	yes	—
604	#483	C₂²×C₂₃	1	2	yes	—
605	#483	C₂²×C₂₃	1	2	yes	—
606	#482	C₂²×C₂₃	1	1	yes	characteristic
607	#481	C₂²×C₂₃	1	2	yes	—
608	#479	C₂²×C₂₃	1	1	yes	characteristic
609	#479	C₂²×C₂₃	1	2	yes	—
610	#479	C₂²×C₂₃	1	2	yes	—
611	#479	C₂²×C₂₃	1	2	yes	—
612	#479	C₂²×C₂₃	1	2	yes	—
613	#478	C₂²×C₂₃	1	1	yes	characteristic
614	#478	C₂²×C₂₃	1	2	yes	—
615	#478	C₂²×C₂₃	1	2	yes	—
616	#477	C₂²×C₂₃	1	2	yes	—
617	#477	C₂²×C₂₃	1	1	yes	characteristic
618	#476	C₂²×C₂₃	1	2	yes	—
619	#476	C₂²×C₂₃	1	1	yes	characteristic
620	#476	C₂²×C₂₃	1	2	yes	—
621	#475	C₂²×C₂₃	1	1	yes	characteristic
622	#475	C₂²×C₂₃	1	2	yes	—
623	#475	C₂²×C₂₃	1	2	yes	—
624	#475	C₂²×C₂₃	1	2	yes	—
625	#475	C₂²×C₂₃	1	1	yes	characteristic
626	#475	C₂²×C₂₃	1	2	yes	—
627	#475	C₂²×C₂₃	1	2	yes	—
628	#474	C₂²×C₂₃	1	1	yes	characteristic
629	#474	C₂²×C₂₃	1	1	yes	characteristic
630	#464	C₂²×C₂₃	1	1	yes	characteristic
631	#464	C₂²×C₂₃	1	2	yes	—
632	#463	C₂²×C₂₃	1	1	yes	characteristic
633	#463	C₂²×C₂₃	1	2	yes	—
634	#462	C₂²×C₂₃	1	1	yes	characteristic
635	#462	C₂²×C₂₃	1	2	yes	—
636	#461	C₂²×C₂₃	1	1	yes	characteristic
637	#461	C₂²×C₂₃	1	2	yes	—
638	#452	C₂²×C₂₃	1	1	yes	characteristic
639	#452	C₂²×C₂₃	1	2	yes	—
640	#449	C₂²×C₂₃	1	1	yes	characteristic
641	#446	C₂²×C₂₃	1	1	yes	characteristic
642	#446	C₂²×C₂₃	1	2	yes	—
643	#446	C₂²×C₂₃	1	1	yes	characteristic
644	#446	C₂²×C₂₃	1	2	yes	—
645	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
646	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
647	#442	C₂²×C₂₃	1	2	yes	—
648	#441	C₂²×C₂₃	1	2	yes	—
649	#441	C₂²×C₂₃	1	2	yes	—
650	#441	C₂²×C₂₃	1	2	yes	—
651	#440	C₂²×C₂₃	1	2	yes	—
652	#440	C₂²×C₂₃	1	2	yes	—
653	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
654	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
655	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
656	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
657	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
658	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
659	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
660	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
661	#433	C₂²×C₂₃	1	2	yes	—
662	#433	C₂²×C₂₃	1	2	yes	—
663	#432	C₂²×C₂₃	1	1	yes	characteristic
664	#431	C₂²×C₂₃	1	1	yes	characteristic
665	C₂×C₂₃	—	4	1	no	—
666	C₂×C₂₃	—	4	2	no	—
667	C₂×C₂₃	—	8	1	no	—
668	C₂×C₂₃	#3486	1	1	yes	characteristic
669	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
670	C₂×C₂₃	#3586	1	1	yes	characteristic
671	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
672	C₂²×Q₈	—	2	1	no	—
673	C₂²×Q₈	—	2	1	no	—
674	C₂²×Q₈	—	2	1	no	—
675	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
676	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
677	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
678	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
679	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
680	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
681	C₄⋊Q₈	—	2	1	no	—
682	C₄⋊Q₈	—	2	1	no	—
683	C₄⋊Q₈	—	2	2	no	—
684	C₄⋊Q₈	—	2	2	no	—
685	C₄⋊Q₈	—	2	2	no	—
686	C₄⋊Q₈	—	2	2	no	—
687	C₄⋊Q₈	—	2	2	no	—
688	C₄⋊Q₈	—	2	2	no	—
689	C₄⋊Q₈	—	2	1	no	—
690	C₄⋊Q₈	—	2	1	no	—
691	C₄⋊Q₈	—	2	1	no	—
692	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
693	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
694	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
695	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
696	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
699	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
701	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
702	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	1	no	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	1	no	—
717	#125	—	2	2	no	—
718	#125	—	2	2	no	—
719	#125	—	2	1	no	—
720	#125	D₄×C₂₃	1	2	yes	—
721	#125	C₂³×C₂₃	1	1	yes	characteristic
722	#125	C₂³×C₂₃	1	2	yes	—
723	#125	C₂³×C₂₃	1	2	yes	—
724	#125	C₂³×C₂₃	1	2	yes	—
725	#124	—	2	2	no	—
726	#124	C₂³×C₂₃	1	1	yes	characteristic
727	#124	C₂³×C₂₃	1	2	yes	—
728	#123	—	2	1	no	—
729	#123	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	1	no	—
735	C₂²⋊Q₈	—	2	1	no	—
736	C₂²⋊Q₈	—	2	1	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
746	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
747	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
748	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
749	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
750	#121	C₂³×C₂₃	1	1	yes	characteristic
751	C₄×Q₈	—	2	2	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	2	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
759	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
760	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
761	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
762	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
763	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
764	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
765	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
766	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
767	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
769	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
776	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
777	C₄×D₄	C₂³×C₂₃	1	2	yes	—
778	C₄×D₄	C₂³×C₂₃	1	2	yes	—
779	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
780	C₄×D₄	C₂³×C₂₃	1	2	yes	—
781	#117	—	2	1	no	—
782	#117	—	2	2	no	—
783	#117	—	2	2	no	—
784	#117	—	2	1	no	—
785	#117	—	2	1	no	—
786	#117	—	2	1	no	—
787	#117	C₂³×C₂₃	1	1	yes	characteristic
788	#117	C₂³×C₂₃	1	2	yes	—
789	C₂×C₄⋊C₄	—	2	1	no	—
790	C₂×C₄⋊C₄	—	2	2	no	—
791	C₂×C₄⋊C₄	—	2	2	no	—
792	C₂×C₄⋊C₄	—	2	1	no	—
793	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
794	C₂×C₄²	—	2	1	no	—
795	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
796	#107	C₂³×C₂₃	1	1	yes	characteristic
797	#107	C₂³×C₂₃	1	2	yes	—
798	#107	C₂³×C₂₃	1	1	yes	characteristic
799	#107	C₂³×C₂₃	1	2	yes	—
800	#107	C₂³×C₂₃	1	2	yes	—
801	#106	C₂³×C₂₃	1	2	yes	—
802	#106	C₂³×C₂₃	1	2	yes	—
803	#106	C₂³×C₂₃	1	1	yes	characteristic
804	#106	C₂³×C₂₃	1	2	yes	—
805	#106	C₂³×C₂₃	1	1	yes	characteristic
806	#106	C₂³×C₂₃	1	2	yes	—
807	#106	C₂³×C₂₃	1	2	yes	—
808	#106	C₂³×C₂₃	1	2	yes	—
809	#106	C₂³×C₂₃	1	2	yes	—
810	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
811	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
815	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
816	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
817	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
818	#103	C₂³×C₂₃	1	1	yes	characteristic
819	#103	C₂³×C₂₃	1	2	yes	—
820	#103	C₂³×C₂₃	1	2	yes	—
821	#103	C₂³×C₂₃	1	1	yes	characteristic
822	#103	C₂³×C₂₃	1	2	yes	—
823	#103	C₂³×C₂₃	1	1	yes	characteristic
824	#103	C₂³×C₂₃	1	2	yes	—
825	#103	C₂³×C₂₃	1	1	yes	characteristic
826	#103	C₂³×C₂₃	1	2	yes	—
827	#103	C₂³×C₂₃	1	2	yes	—
828	#103	C₂³×C₂₃	1	2	yes	—
829	#103	C₂³×C₂₃	1	2	yes	—
830	#103	C₂³×C₂₃	1	2	yes	—
831	#102	C₂³×C₂₃	1	1	yes	characteristic
832	#102	C₂³×C₂₃	1	1	yes	characteristic
833	#102	C₂³×C₂₃	1	1	yes	characteristic
834	#102	C₂³×C₂₃	1	2	yes	—
835	#102	C₂³×C₂₃	1	2	yes	—
836	#102	C₂³×C₂₃	1	1	yes	characteristic
837	#102	C₂³×C₂₃	1	2	yes	—
838	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
839	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
840	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
841	#97	C₂³×C₂₃	1	2	yes	—
842	#97	C₂³×C₂₃	1	2	yes	—
843	#97	C₂³×C₂₃	1	2	yes	—
844	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
845	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
846	C₄×C₈	C₂³×C₂₃	1	2	yes	—
847	C₄×C₈	C₂³×C₂₃	1	2	yes	—
848	C₂₃	#61858	1	1	yes	characteristic, direct product factor, Sylow
849	#41	—	2	2	no	—
850	#41	—	2	2	no	—
851	C₂×Q₈	—	2	1	no	—
852	C₂×Q₈	—	2	1	no	—
853	C₂×Q₈	—	2	1	no	—
854	C₂×Q₈	—	2	2	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	2	no	—
858	C₂×Q₈	—	8	2	no	—
859	C₂×Q₈	—	8	2	no	—
860	C₂×Q₈	—	8	2	no	—
861	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
862	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
863	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
864	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
865	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
866	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
867	C₂×D₄	—	2	1	no	—
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
870	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
880	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
882	Q₁₆	—	2	2	no	—
883	Q₁₆	—	2	4	no	—
884	SD₁₆	—	2	2	no	—
885	SD₁₆	—	2	2	no	—
886	SD₁₆	—	2	4	no	—
887	D₈	—	2	2	no	—
888	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
889	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
890	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
891	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
892	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
893	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
926	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
927	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
928	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
929	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
930	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
931	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
932	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
933	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
936	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
938	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
939	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	1	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	1	no	—
946	C₂²⋊C₄	—	2	1	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
956	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
957	C₄²	—	2	1	no	—
958	C₄²	—	2	1	no	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	2	no	—
967	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
968	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
969	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
970	C₄²	C₂⁴×C₂₃	1	2	yes	—
971	C₄²	C₂⁴×C₂₃	1	2	yes	—
972	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
973	C₂³	—	2	1	no	—
974	C₂³	—	2	1	no	—
975	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
976	Q₈	—	2	2	no	—
977	Q₈	—	2	2	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	2	1	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	2	1	no	—
982	Q₈	—	2	2	no	—
983	Q₈	—	4	2	no	—
984	Q₈	—	4	2	no	—
985	Q₈	—	4	2	no	—
986	Q₈	—	8	2	no	—
987	Q₈	—	8	2	no	—
988	Q₈	—	8	2	no	—
989	Q₈	—	8	1	no	—
990	Q₈	—	8	2	no	—
991	Q₈	C₂₃×2₋¹⁺⁴	1	2	yes	—
992	D₄	—	2	4	no	—
993	D₄	—	2	1	no	—
994	D₄	—	2	1	no	—
995	D₄	—	2	1	no	—
996	D₄	—	8	1	no	—
997	D₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
998	C₂×C₄	—	2	4	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	4	2	no	—
1015	C₂×C₄	—	4	2	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	—	8	2	no	—
1019	C₂×C₄	—	8	2	no	—
1020	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1022	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1025	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1026	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1027	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1028	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1029	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	1	no	—
1033	C₈	—	2	2	no	—
1034	C₈	—	2	1	no	—
1035	C₈	—	2	2	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1046	C₄	—	2	1	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	2	2	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	4	2	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	1	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	1	no	—
1064	C₄	C₂₃×#577	1	2	yes	—
1065	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1066	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1067	C₂	—	4	1	no	—
1068	C₂	—	4	2	no	—
1069	C₂	—	8	1	no	—
1070	C₂	C₂₃×#3486	1	1	yes	characteristic
1071	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1072	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#449	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3555	C₂	semidirect
2. C₂₃×#3503	C₂	semidirect
3. C₂₃×#3388	C₂	semidirect
4. C₂₃×#3387	C₂	semidirect
5. C₂₃×#3387	C₂	semidirect
6. C₂₃×#3384	C₂	semidirect
7. C₂₃×#3381	C₂	semidirect
8. Q₈×SD₁₆×C₂₃	C₂	semidirect
9. C₂₃×#3376	C₂	semidirect
10. C₂₃×#3374	C₂	semidirect
11. C₂₃×#3369	C₂	semidirect
12. C₂₃×#3367	C₂	semidirect
13. C₂₃×#3364	C₂	semidirect
14. C₂₃×#3359	C₂	semidirect
15. C₂₃×#3244	C₂	semidirect
16. C₂₃×#3242	C₂	semidirect
17. C₂₃×#3239	C₂	semidirect
18. C₂₃×#3229	C₂	semidirect
20. C₂₃×#3120	C₂	semidirect
21. C₂₃×#3116	C₂	semidirect
23. C₂₃×#2985	C₂	semidirect
436. #61858	C₂₃	direct (N × H)
500. #3555	C₂×C₂₃	semidirect
501. #3503	C₂×C₂₃	semidirect
502. #3388	C₂×C₂₃	semidirect
503. #3387	C₂×C₂₃	semidirect
504. #3387	C₂×C₂₃	semidirect
505. #3384	C₂×C₂₃	semidirect
506. #3381	C₂×C₂₃	semidirect
507. Q₈×SD₁₆	C₂×C₂₃	semidirect
508. #3376	C₂×C₂₃	semidirect
509. #3374	C₂×C₂₃	semidirect
510. #3369	C₂×C₂₃	semidirect
511. #3367	C₂×C₂₃	semidirect
512. #3364	C₂×C₂₃	semidirect
513. #3359	C₂×C₂₃	semidirect
514. #3244	C₂×C₂₃	semidirect
515. #3242	C₂×C₂₃	semidirect
516. #3239	C₂×C₂₃	semidirect
517. #3229	C₂×C₂₃	semidirect
519. #3120	C₂×C₂₃	semidirect
520. #3116	C₂×C₂₃	semidirect
522. #2985	C₂×C₂₃	semidirect
848. C₂₃	#61858	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3555	2
C₂₃×#3503	2
C₂₃×#3388	2
C₂₃×#3387	2
C₂₃×#3384	2
C₂₃×#3381	2
Q₈×SD₁₆×C₂₃	2
C₂₃×#3376	2
C₂₃×#3374	2
C₂₃×#3369	2
C₂₃×#3367	2
C₂₃×#3364	2
C₂₃×#3359	2
C₂₃×#3244	2
C₂₃×#3242	2
C₂₃×#3239	2
C₂₃×#3229	2
C₂₃×#3125	2
C₂₃×#3120	2
C₂₃×#3116	2
C₂₃×#3102	2
C₂₃×#2985	2
#61858	23

Subgroups — C23×#61858 #19209484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61858 #19209484