Subgroups — #463×D₁₀₉ #28372452

Order 13952.

564 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	#124×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295244	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295243	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295242	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295241	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295240	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295239	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295238	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄⋊C₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#103×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#102×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#463×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₀₉	—	2	1	no	—
20	C₂×#13182018	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13182017	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13182016	C₂²	1	1	yes	characteristic, complemented
23	SD₁₆×D₁₀₉	—	2	4	no	—
24	C₂×D₈₇₂	C₂²	1	1	yes	characteristic
25	C₂×#13182014	C₂²	1	1	yes	characteristic
26	C₂×#13182014	C₂²	1	1	yes	characteristic
27	D₈×D₁₀₉	—	2	4	no	—
28	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
30	#16812688	C₂²	1	1	yes	characteristic, complemented
31	#16812687	C₂²	1	1	yes	characteristic, complemented
32	#16812686	C₂²	1	1	yes	characteristic, complemented
33	#16812685	—	2	1	no	—
34	#16812685	—	2	1	no	—
35	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
36	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
37	#16812661	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₂²⋊D₁₀₉	—	2	1	no	—
39	#16812659	—	2	1	no	—
40	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
41	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
42	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
43	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
44	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
45	C₄⋊#11724784	C₂²	1	1	yes	characteristic, complemented
46	#16812628	C₂²	1	1	yes	characteristic, complemented
47	#16812628	C₂²	1	1	yes	characteristic, complemented
48	#16812624	C₂²	1	1	yes	characteristic, complemented
49	#16812623	C₂²	1	1	yes	characteristic, complemented
50	#16812622	C₂²	1	1	yes	characteristic, complemented
51	#16812621	C₂²	1	1	yes	characteristic, complemented
52	#16812620	C₂²	1	1	yes	characteristic, complemented
53	#16812619	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×D₈×C₁₀₉	C₂²	1	1	yes	characteristic
56	#124×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	#103×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
60	#102×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₀₉	—	2	1	no	—
62	C₂³×D₁₀₉	—	2	1	no	—
63	C₂×Dic₂₁₈	—	2	1	no	—
64	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
65	Q₈×D₁₀₉	—	2	2	no	—
66	Q₈×D₁₀₉	—	2	2	no	—
67	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
68	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
70	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
71	D₄×D₁₀₉	—	2	2	no	—
72	D₄×D₁₀₉	—	2	2	no	—
73	D₄×D₁₀₉	—	2	2	no	—
74	D₄×D₁₀₉	D₄	1	4	yes	—
75	C₂²×Dic₁₀₉	—	2	1	no	—
76	C₂×C₄×D₁₀₉	—	2	1	no	—
77	C₂×C₄×D₁₀₉	—	2	1	no	—
78	C₂×C₄×D₁₀₉	—	2	1	no	—
79	C₂×C₄×D₁₀₉	—	2	1	no	—
80	C₂×C₄×D₁₀₉	—	4	4	no	—
81	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
82	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
83	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
84	#13182018	—	2	2	no	—
85	#13182017	—	2	2	no	—
86	#13182016	—	2	2	no	—
87	D₈₇₂	—	2	2	no	—
88	#13182014	—	2	2	no	—
89	#13182014	—	2	2	no	—
90	C₂×#11724784	C₂³	1	1	yes	characteristic
91	C₂×#11724784	C₂³	1	1	yes	characteristic
92	C₈×D₁₀₉	—	2	2	no	—
93	C₈×D₁₀₉	—	2	2	no	—
94	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
95	#13182008	—	2	1	no	—
96	C₂²⋊Dic₁₀₉	—	2	1	no	—
97	C₂²⋊Dic₁₀₉	—	2	1	no	—
98	C₂²⋊Dic₁₀₉	—	2	1	no	—
99	#13182006	—	2	1	no	—
100	#13182006	—	2	1	no	—
101	#13182006	—	2	1	no	—
102	#13182006	—	2	1	no	—
103	#13182006	—	2	1	no	—
104	#13182006	—	2	1	no	—
105	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
106	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
107	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₁₀₉	—	2	1	no	—
112	SD₁₆×C₁₀₉	—	2	2	no	—
113	D₈×C₁₀₉	—	2	2	no	—
114	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
117	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
118	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
119	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
120	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
121	C₂³×C₁₀₉	—	2	1	no	—
122	C₂³×C₁₀₉	—	2	1	no	—
123	C₂²×D₁₀₉	—	2	1	no	—
124	C₂²×D₁₀₉	—	2	4	no	—
125	C₂²×D₁₀₉	—	2	1	no	—
126	C₂²×D₁₀₉	—	4	2	no	—
127	C₂²×D₁₀₉	—	4	2	no	—
128	C₂²×D₁₀₉	—	4	2	no	—
129	C₂²×D₁₀₉	—	4	2	no	—
130	C₂²×D₁₀₉	—	4	2	no	—
131	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
132	Q₈×C₁₀₉	—	2	1	no	—
133	Q₈×C₁₀₉	—	2	1	no	—
134	D₄×C₁₀₉	—	2	1	no	—
135	D₄×C₁₀₉	—	2	1	no	—
136	D₄×C₁₀₉	—	2	1	no	—
137	D₄×C₁₀₉	C₂×D₄	1	2	yes	—
138	C₂×C₄×C₁₀₉	—	2	1	no	—
139	C₂×C₄×C₁₀₉	—	2	1	no	—
140	C₂×C₄×C₁₀₉	—	4	2	no	—
141	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
144	C₂²⋊D₁₀₉	—	2	4	no	—
145	C₂²⋊D₁₀₉	—	4	2	no	—
146	C₂×Dic₁₀₉	—	2	1	no	—
147	C₂×Dic₁₀₉	—	2	1	no	—
148	C₂×Dic₁₀₉	—	4	2	no	—
149	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
150	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
151	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
152	D₄₃₆	—	2	1	no	—
153	D₄₃₆	—	2	1	no	—
154	D₄₃₆	—	2	1	no	—
155	D₄₃₆	C₂×D₄	1	2	yes	—
156	C₄×D₁₀₉	—	2	2	no	—
157	C₄×D₁₀₉	—	2	2	no	—
158	C₄×D₁₀₉	—	4	2	no	—
159	C₄×D₁₀₉	—	4	2	no	—
160	C₄×D₁₀₉	—	4	2	no	—
161	C₄×D₁₀₉	—	4	2	no	—
162	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
163	C₄×D₁₀₉	#41	1	2	yes	—
164	Dic₂₁₈	—	2	1	no	—
165	Dic₂₁₈	—	2	1	no	—
166	Dic₂₁₈	—	4	2	no	—
167	C₈×C₁₀₉	—	2	1	no	—
168	C₈×C₁₀₉	—	2	1	no	—
169	#11724784	—	2	1	no	—
170	#11724784	—	2	1	no	—
171	C₂²×C₁₀₉	—	2	2	no	—
172	C₂²×C₁₀₉	—	4	1	no	—
173	C₂²×C₁₀₉	—	4	1	no	—
174	C₂²×C₁₀₉	—	4	1	no	—
175	C₂²×C₁₀₉	—	4	1	no	—
176	C₂²×C₁₀₉	—	4	1	no	—
177	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×D₁₀₉	—	2	2	no	—
179	C₂×D₁₀₉	—	4	1	no	—
180	C₂×D₁₀₉	—	4	1	no	—
181	C₂×D₁₀₉	—	4	8	no	—
182	C₂×D₁₀₉	—	4	1	no	—
183	C₂×D₁₀₉	—	4	1	no	—
184	C₂×D₁₀₉	—	4	1	no	—
185	C₂×D₁₀₉	—	8	4	no	—
186	C₂×D₁₀₉	#121	1	2	yes	—
187	C₂×D₁₀₉	#135	1	2	yes	—
188	C₂×D₁₀₉	AGL(1,ℤ/8)	1	2	yes	—
189	C₄×C₁₀₉	—	2	1	no	—
190	C₄×C₁₀₉	—	2	1	no	—
191	C₄×C₁₀₉	—	4	1	no	—
192	C₄×C₁₀₉	—	4	1	no	—
193	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
194	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
195	Dic₁₀₉	—	2	1	no	—
196	Dic₁₀₉	—	2	1	no	—
197	Dic₁₀₉	—	4	1	no	—
198	Dic₁₀₉	—	4	1	no	—
199	Dic₁₀₉	#121	1	2	yes	—
200	C₂×C₁₀₉	—	4	2	no	—
201	C₂×C₁₀₉	—	8	1	no	—
202	C₂×C₁₀₉	C₂×#121	1	1	yes	characteristic
203	C₂×C₁₀₉	C₂×#135	1	1	yes	characteristic
204	C₂×C₁₀₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
205	D₁₀₉	—	4	2	no	—
206	D₁₀₉	—	8	1	no	—
207	D₁₀₉	#463	1	4	yes	direct product factor
208	C₂×#463	—	109	1	no	maximal, Sylow
209	C₁₀₉	C₂×#463	1	1	yes	characteristic, complemented, Sylow
210	C₂²×SD₁₆	—	109	1	no	—
211	C₂²×D₈	—	109	1	no	—
212	C₂×#124	—	109	1	no	—
213	C₂×C₄×D₄	—	109	1	no	—
214	#463	—	109	1	no	—
215	#463	—	109	1	no	—
216	#463	—	109	1	no	—
217	#463	—	109	1	no	—
218	#463	—	109	1	no	—
219	#463	—	109	1	no	—
220	#463	—	109	1	no	—
221	#463	D₁₀₉	1	1	yes	characteristic, direct product factor
222	C₂×C₄⋊C₈	—	109	1	no	—
223	C₂×#103	—	109	1	no	—
224	C₂×#102	—	109	1	no	—
225	C₂²×Q₈	—	109	1	no	—
226	C₂²×D₄	—	109	1	no	—
227	C₂²×D₄	—	109	1	no	—
228	C₂³×C₄	—	218	1	no	—
229	C₂×SD₁₆	—	109	1	no	—
230	C₂×SD₁₆	—	109	1	no	—
231	C₂×SD₁₆	—	109	1	no	—
232	C₂×SD₁₆	—	218	4	no	—
233	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
234	C₂×D₈	—	109	1	no	—
235	C₂×D₈	—	109	1	no	—
236	C₂×D₈	—	109	1	no	—
237	C₂×D₈	—	218	4	no	—
238	C₂×D₈	C₂×D₁₀₉	1	1	yes	characteristic
239	C₂²×C₈	—	109	1	no	—
240	C₂²×C₈	—	109	1	no	—
241	#124	—	109	1	no	—
242	#124	—	109	1	no	—
243	#124	—	109	1	no	—
244	#124	—	218	1	no	—
245	#124	—	218	1	no	—
246	#124	C₂×D₁₀₉	1	1	yes	characteristic, complemented
247	C₄×D₄	—	109	1	no	—
248	C₄×D₄	—	109	1	no	—
249	C₄×D₄	—	109	1	no	—
250	C₄×D₄	—	218	1	no	—
251	C₄×D₄	—	218	1	no	—
252	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
253	C₂×C₄⋊C₄	—	109	1	no	—
254	C₂×C₂²⋊C₄	—	218	1	no	—
255	C₂×C₂²⋊C₄	—	218	1	no	—
256	C₂×C₂²⋊C₄	—	218	1	no	—
257	C₂×C₄²	—	109	1	no	—
258	C₄⋊C₈	—	109	1	no	—
259	C₄⋊C₈	—	109	1	no	—
260	C₄⋊C₈	—	109	1	no	—
261	C₄⋊C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
262	#103	—	109	1	no	—
263	#103	—	109	1	no	—
264	#103	—	109	1	no	—
265	#103	C₂×D₁₀₉	1	1	yes	characteristic, complemented
266	#102	—	109	1	no	—
267	#102	—	109	1	no	—
268	#102	—	109	1	no	—
269	#102	C₂×D₁₀₉	1	1	yes	characteristic, complemented
270	C₂⁴	—	218	1	no	—
271	C₂⁴	—	218	1	no	—
272	C₂×Q₈	—	109	1	no	—
273	C₂×Q₈	—	218	1	no	—
274	C₂×Q₈	—	218	2	no	—
275	C₂×Q₈	—	218	2	no	—
276	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
277	C₂×D₄	—	109	4	no	—
278	C₂×D₄	—	109	1	no	—
279	C₂×D₄	—	109	1	no	—
280	C₂×D₄	—	218	2	no	—
281	C₂×D₄	—	218	2	no	—
282	C₂×D₄	—	218	2	no	—
283	C₂×D₄	—	218	1	no	—
284	C₂×D₄	—	218	1	no	—
285	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
286	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	109	1	no	—
289	C₂²×C₄	—	109	1	no	—
290	C₂²×C₄	—	109	1	no	—
291	C₂²×C₄	—	436	4	no	—
292	C₂²×C₄	—	218	1	no	—
293	C₂²×C₄	—	218	1	no	—
294	C₂²×C₄	—	218	1	no	—
295	C₂²×C₄	—	218	1	no	—
296	C₂²×C₄	—	218	1	no	—
297	SD₁₆	—	2	2	no	—
298	SD₁₆	—	218	2	no	—
299	SD₁₆	—	218	2	no	—
300	SD₁₆	—	218	2	no	—
301	D₈	—	2	2	no	—
302	D₈	—	218	2	no	—
303	D₈	—	218	2	no	—
304	D₈	—	218	2	no	—
305	C₂×C₈	—	109	1	no	—
306	C₂×C₈	—	109	1	no	—
307	C₂×C₈	—	218	2	no	—
308	C₂×C₈	—	218	2	no	—
309	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
310	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
311	C₄⋊C₄	—	109	1	no	—
312	C₄⋊C₄	—	218	1	no	—
313	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
314	C₂²⋊C₄	—	2	1	no	—
315	C₂²⋊C₄	—	2	1	no	—
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	218	1	no	—
318	C₂²⋊C₄	—	218	1	no	—
319	C₂²⋊C₄	—	218	1	no	—
320	C₂²⋊C₄	—	218	1	no	—
321	C₂²⋊C₄	—	218	1	no	—
322	C₂²⋊C₄	—	218	1	no	—
323	C₂²⋊C₄	—	218	1	no	—
324	C₂²⋊C₄	—	218	1	no	—
325	C₂²⋊C₄	—	218	1	no	—
326	C₄²	—	109	1	no	—
327	C₄²	—	109	1	no	—
328	C₄²	—	109	1	no	—
329	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	109	1	no	—
333	C₂³	—	436	2	no	—
334	C₂³	—	436	2	no	—
335	C₂³	—	436	2	no	—
336	C₂³	—	436	2	no	—
337	C₂³	—	436	2	no	—
338	C₂³	—	218	4	no	—
339	C₂³	—	218	1	no	—
340	C₂³	—	218	1	no	—
341	Q₈	—	2	1	no	—
342	Q₈	—	2	1	no	—
343	Q₈	—	436	2	no	—
344	Q₈	—	218	1	no	—
345	Q₈	—	218	1	no	—
346	D₄	—	2	1	no	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	109	2	no	—
350	D₄	—	436	2	no	—
351	D₄	—	218	4	no	—
352	D₄	—	218	1	no	—
353	D₄	—	218	1	no	—
354	D₄	—	218	1	no	—
355	D₄	D₄×D₁₀₉	1	2	yes	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	109	1	no	—
360	C₂×C₄	—	109	2	no	—
361	C₂×C₄	—	109	2	no	—
362	C₂×C₄	—	109	1	no	—
363	C₂×C₄	—	109	1	no	—
364	C₂×C₄	—	436	2	no	—
365	C₂×C₄	—	436	2	no	—
366	C₂×C₄	—	436	2	no	—
367	C₂×C₄	—	436	2	no	—
368	C₂×C₄	—	436	2	no	—
369	C₂×C₄	—	218	2	no	—
370	C₂×C₄	—	218	2	no	—
371	C₂×C₄	—	218	1	no	—
372	C₂×C₄	—	218	1	no	—
373	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
374	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
375	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	—	218	1	no	—
379	C₈	—	218	1	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	872	4	no	—
387	C₂²	—	109	2	no	—
388	C₂²	—	109	2	no	—
389	C₂²	—	109	2	no	—
390	C₂²	—	436	8	no	—
391	C₂²	—	436	1	no	—
392	C₂²	—	436	1	no	—
393	C₂²	—	436	1	no	—
394	C₂²	—	436	1	no	—
395	C₂²	—	436	1	no	—
396	C₂²	—	218	2	no	—
397	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	109	2	no	—
403	C₄	—	436	1	no	—
404	C₄	—	436	1	no	—
405	C₄	—	218	1	no	—
406	C₄	—	218	1	no	—
407	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
408	C₄	#41×D₁₀₉	1	1	yes	characteristic
409	C₂	—	4	2	no	—
410	C₂	—	8	1	no	—
411	C₂	—	872	1	no	—
412	C₂	—	109	4	no	—
413	C₂	—	436	2	no	—
414	C₂	#121×D₁₀₉	1	1	yes	characteristic
415	C₂	#135×D₁₀₉	1	1	yes	characteristic
416	C₂	AGL(1,ℤ/8)×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₂×C₄×C₁₀₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	#463×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	C₂×D₈×D₁₀₉	C₂
hypercenter	#463	D₁₀₉
hypocenter	C₁₀₉	C₂×#463
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #463

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×D₁₀₉	C₂	semidirect
3. #124×D₁₀₉	C₂	semidirect
4. C₄×D₄×D₁₀₉	C₂	semidirect
5. #20295244	C₂	semidirect
6. #20295243	C₂	semidirect
7. #20295242	C₂	semidirect
8. #20295241	C₂	semidirect
9. #20295240	C₂	semidirect
10. #20295239	C₂	semidirect
11. #20295238	C₂	semidirect
12. C₄⋊C₈×D₁₀₉	C₂	semidirect
13. #103×D₁₀₉	C₂	semidirect
14. #102×D₁₀₉	C₂	semidirect
15. #463×C₁₀₉	C₂	semidirect
20. C₂×#13182018	C₂²	semidirect
21. C₂×#13182017	C₂²	semidirect
22. C₂×#13182016	C₂²	semidirect
30. #16812688	C₂²	semidirect
31. #16812687	C₂²	semidirect
32. #16812686	C₂²	semidirect
35. C₄×D₄₃₆	C₂²	semidirect
36. D₄×Dic₁₀₉	C₂²	semidirect
37. #16812661	C₂²	semidirect
45. C₄⋊#11724784	C₂²	semidirect
46. #16812628	C₂²	semidirect
47. #16812628	C₂²	semidirect
48. #16812624	C₂²	semidirect
49. #16812623	C₂²	semidirect
50. #16812622	C₂²	semidirect
51. #16812621	C₂²	semidirect
52. #16812620	C₂²	semidirect
53. #16812619	C₂²	semidirect
54. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
56. #124×C₁₀₉	C₂²	semidirect
57. C₄×D₄×C₁₀₉	C₂²	semidirect
58. C₄⋊C₈×C₁₀₉	C₂²	semidirect
59. #103×C₁₀₉	C₂²	semidirect
60. #102×C₁₀₉	C₂²	semidirect
207. D₁₀₉	#463	direct (N × H)
209. C₁₀₉	C₂×#463	semidirect
221. #463	D₁₀₉	direct (N × H)
233. C₂×SD₁₆	C₂×D₁₀₉	semidirect
246. #124	C₂×D₁₀₉	semidirect
252. C₄×D₄	C₂×D₁₀₉	semidirect
261. C₄⋊C₈	C₂×D₁₀₉	semidirect
265. #103	C₂×D₁₀₉	semidirect
269. #102	C₂×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×D₁₀₉	2
C₂×D₈×D₁₀₉	2
#124×D₁₀₉	2
C₄×D₄×D₁₀₉	2
#20295244	2
#20295243	2
#20295242	2
#20295241	2
#20295240	2
#20295239	2
#20295238	2
C₄⋊C₈×D₁₀₉	2
#103×D₁₀₉	2
#102×D₁₀₉	2
#463×C₁₀₉	2
C₂×#463	109

Subgroups — #463×D109 #28372452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #463×D₁₀₉ #28372452