Subgroups — #468×D₁₀₉ #28372616

Order 13952.

544 conjugacy classes of subgroups.

The subgroup lattice has 420 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×M₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#121×D₁₀₉	C₂	1	1	yes	maximal, characteristic
5	#20295275	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295274	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295273	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295272	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295271	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295270	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295269	C₂	1	1	yes	maximal, characteristic, complemented
12	#107×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	#468×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₁₀₉	—	2	1	no	—
18	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
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×#13182013	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13182012	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13182012	C₂²	1	1	yes	characteristic, complemented
27	M₁₆×D₁₀₉	—	2	4	no	—
28	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
30	#16812679	C₂²	1	1	yes	characteristic, complemented
31	#16812678	C₂²	1	1	yes	characteristic, complemented
32	#16812677	—	2	1	no	—
33	#16812676	—	2	1	no	—
34	#16812675	C₂²	1	1	yes	characteristic, complemented
35	#16812674	C₂²	1	1	yes	characteristic
36	#16812673	C₂²	1	1	yes	characteristic
37	#16812672	—	2	1	no	—
38	#16812671	—	2	1	no	—
39	#16812670	C₂²	1	1	yes	characteristic
40	C₄⋊C₄×D₁₀₉	—	2	1	no	—
41	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
42	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
43	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
44	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
45	#16812633	C₂²	1	1	yes	characteristic, complemented
46	#16812632	C₂²	1	1	yes	characteristic, complemented
47	#16812632	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×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	#121×C₁₀₉	C₂²	1	1	yes	characteristic
58	#107×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	D₄	1	1	yes	characteristic
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	—	2	1	no	—
68	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
70	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
71	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
72	D₄×D₁₀₉	—	2	2	no	—
73	D₄×D₁₀₉	—	2	2	no	—
74	D₄×D₁₀₉	—	4	4	no	—
75	C₂²×Dic₁₀₉	D₄	1	1	yes	characteristic
76	C₂×C₄×D₁₀₉	—	2	2	no	—
77	C₂×C₄×D₁₀₉	—	2	2	no	—
78	C₂×C₄×D₁₀₉	—	2	1	no	—
79	C₂×C₄×D₁₀₉	—	2	1	no	—
80	C₂×C₄×D₁₀₉	—	2	1	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	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
85	#13182018	—	2	2	no	—
86	#13182017	—	2	2	no	—
87	#13182016	—	2	2	no	—
88	#13182013	—	2	2	no	—
89	#13182012	—	2	2	no	—
90	#13182012	—	2	2	no	—
91	C₂×#11724784	C₂³	1	1	yes	characteristic
92	C₂×#11724784	C₂³	1	1	yes	characteristic
93	C₈×D₁₀₉	—	2	2	no	—
94	C₈×D₁₀₉	D₄	1	4	yes	complemented
95	C₄⋊Dic₁₀₉	—	2	1	no	—
96	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
98	#13182008	—	2	1	no	—
99	#13182008	—	2	1	no	—
100	#13182008	—	2	1	no	—
101	#13182008	—	2	1	no	—
102	C₂²⋊Dic₁₀₉	—	2	1	no	—
103	C₂²⋊Dic₁₀₉	—	2	1	no	—
104	#13182006	—	2	1	no	—
105	#13182006	—	2	1	no	—
106	#13182006	—	2	1	no	—
107	#13182006	—	2	1	no	—
108	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₁₀₉	—	2	1	no	—
110	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
112	SD₁₆×C₁₀₉	—	2	2	no	—
113	M₁₆×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	—	2	1	no	—
117	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
118	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
120	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
121	C₂³×C₁₀₉	—	2	1	no	—
122	C₂³×C₁₀₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×D₁₀₉	—	2	2	no	—
124	C₂²×D₁₀₉	—	2	2	no	—
125	C₂²×D₁₀₉	—	2	2	no	—
126	C₂²×D₁₀₉	—	2	1	no	—
127	C₂²×D₁₀₉	—	4	2	no	—
128	C₂²×D₁₀₉	—	4	2	no	—
129	C₂²×D₁₀₉	—	4	2	no	—
130	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
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	—	4	2	no	—
137	C₂×C₄×C₁₀₉	—	2	1	no	—
138	C₂×C₄×C₁₀₉	—	2	1	no	—
139	C₂×C₄×C₁₀₉	—	2	1	no	—
140	C₂×C₄×C₁₀₉	—	2	1	no	—
141	C₂×C₄×C₁₀₉	—	2	1	no	—
142	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
144	C₂²⋊D₁₀₉	—	4	2	no	—
145	C₂²⋊D₁₀₉	—	4	2	no	—
146	C₂²⋊D₁₀₉	—	4	2	no	—
147	C₂×Dic₁₀₉	—	2	2	no	—
148	C₂×Dic₁₀₉	—	2	1	no	—
149	C₂×Dic₁₀₉	—	2	1	no	—
150	C₂×Dic₁₀₉	—	2	1	no	—
151	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
153	D₄₃₆	—	2	1	no	—
154	D₄₃₆	—	2	1	no	—
155	D₄₃₆	—	4	2	no	—
156	C₄×D₁₀₉	—	2	2	no	—
157	C₄×D₁₀₉	—	2	1	no	—
158	C₄×D₁₀₉	—	2	1	no	—
159	C₄×D₁₀₉	—	2	2	no	—
160	C₄×D₁₀₉	—	4	2	no	—
161	C₄×D₁₀₉	—	4	2	no	—
162	C₄×D₁₀₉	—	4	2	no	—
163	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
164	C₄×D₁₀₉	#41	1	2	yes	—
165	Dic₂₁₈	—	2	1	no	—
166	Dic₂₁₈	—	2	1	no	—
167	Dic₂₁₈	—	4	2	no	—
168	C₈×C₁₀₉	—	2	1	no	—
169	C₈×C₁₀₉	C₂×D₄	1	2	yes	complemented
170	#11724784	—	2	1	no	—
171	#11724784	C₂×D₄	1	2	yes	complemented
172	C₂²×C₁₀₉	—	2	1	no	—
173	C₂²×C₁₀₉	—	2	1	no	—
174	C₂²×C₁₀₉	—	2	1	no	—
175	C₂²×C₁₀₉	—	4	1	no	—
176	C₂²×C₁₀₉	—	4	1	no	—
177	C₂²×C₁₀₉	—	4	1	no	—
178	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×D₁₀₉	—	2	1	no	—
180	C₂×D₁₀₉	—	2	1	no	—
181	C₂×D₁₀₉	—	2	1	no	—
182	C₂×D₁₀₉	—	4	4	no	—
183	C₂×D₁₀₉	—	4	1	no	—
184	C₂×D₁₀₉	—	4	1	no	—
185	C₂×D₁₀₉	—	4	1	no	—
186	C₂×D₁₀₉	—	8	4	no	—
187	C₂×D₁₀₉	#121	1	2	yes	—
188	C₂×D₁₀₉	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×D₁₀₉	#137	1	2	yes	—
190	C₄×C₁₀₉	—	2	1	no	—
191	C₄×C₁₀₉	—	4	1	no	—
192	C₄×C₁₀₉	—	4	1	no	—
193	C₄×C₁₀₉	—	4	1	no	—
194	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
195	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
196	Dic₁₀₉	—	2	1	no	—
197	Dic₁₀₉	—	4	1	no	—
198	Dic₁₀₉	—	4	1	no	—
199	Dic₁₀₉	—	4	1	no	—
200	Dic₁₀₉	#121	1	2	yes	—
201	C₂×C₁₀₉	—	4	1	no	—
202	C₂×C₁₀₉	—	8	1	no	—
203	C₂×C₁₀₉	C₂×#121	1	1	yes	characteristic
204	C₂×C₁₀₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
205	C₂×C₁₀₉	C₂×#137	1	1	yes	characteristic
206	D₁₀₉	—	4	1	no	—
207	D₁₀₉	—	8	1	no	—
208	D₁₀₉	#468	1	4	yes	direct product factor
209	C₂×#468	—	109	1	no	maximal, Sylow
210	C₁₀₉	C₂×#468	1	1	yes	characteristic, complemented, Sylow
211	C₂²×SD₁₆	—	109	1	no	—
212	C₂²×M₁₆	—	109	1	no	—
213	C₂×C₂²⋊Q₈	—	109	1	no	—
214	C₂×#121	—	109	1	no	—
215	#468	—	109	1	no	—
216	#468	—	109	1	no	—
217	#468	—	109	1	no	—
218	#468	—	109	1	no	—
219	#468	—	109	1	no	—
220	#468	—	109	1	no	—
221	#468	—	109	1	no	—
222	#468	D₁₀₉	1	1	yes	characteristic, direct product factor
223	C₂×#107	—	109	1	no	—
224	C₂×#103	—	109	1	no	—
225	C₂×#102	—	109	1	no	—
226	C₂²×Q₈	—	109	1	no	—
227	C₂²×D₄	—	109	1	no	—
228	C₂²×D₄	—	218	1	no	—
229	C₂³×C₄	—	109	1	no	—
230	C₂×SD₁₆	—	109	1	no	—
231	C₂×SD₁₆	—	109	1	no	—
232	C₂×SD₁₆	—	109	1	no	—
233	C₂×SD₁₆	—	218	4	no	—
234	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
235	C₂×M₁₆	—	109	1	no	—
236	C₂×M₁₆	—	109	1	no	—
237	C₂×M₁₆	—	109	1	no	—
238	C₂×M₁₆	—	218	4	no	—
239	C₂×M₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
240	C₂²×C₈	—	109	1	no	—
241	C₂²×C₈	—	109	1	no	—
242	C₂²⋊Q₈	—	109	1	no	—
243	C₂²⋊Q₈	—	109	1	no	—
244	C₂²⋊Q₈	—	109	1	no	—
245	C₂²⋊Q₈	—	218	1	no	—
246	C₂²⋊Q₈	—	218	1	no	—
247	C₂²⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
248	#121	—	109	1	no	—
249	#121	—	109	1	no	—
250	#121	—	109	1	no	—
251	#121	—	218	1	no	—
252	#121	—	218	1	no	—
253	#121	C₂×D₁₀₉	1	1	yes	characteristic
254	C₂×C₄⋊C₄	—	109	1	no	—
255	C₂×C₄⋊C₄	—	109	1	no	—
256	C₂×C₄⋊C₄	—	218	1	no	—
257	C₂×C₂²⋊C₄	—	218	1	no	—
258	C₂×C₂²⋊C₄	—	218	1	no	—
259	#107	—	109	1	no	—
260	#107	—	109	1	no	—
261	#107	—	109	1	no	—
262	#107	C₂×D₁₀₉	1	1	yes	characteristic, complemented
263	#103	—	109	1	no	—
264	#103	—	109	1	no	—
265	#103	—	109	1	no	—
266	#103	C₂×D₁₀₉	1	1	yes	characteristic, complemented
267	#102	—	109	1	no	—
268	#102	—	109	1	no	—
269	#102	—	109	1	no	—
270	#102	C₂×D₁₀₉	1	1	yes	characteristic, complemented
271	C₂⁴	—	109	1	no	—
272	C₂⁴	—	218	1	no	—
273	C₂×Q₈	—	109	1	no	—
274	C₂×Q₈	—	218	1	no	—
275	C₂×Q₈	—	218	2	no	—
276	C₂×Q₈	—	218	2	no	—
277	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	109	1	no	—
280	C₂×D₄	—	436	4	no	—
281	C₂×D₄	—	218	1	no	—
282	C₂×D₄	—	218	2	no	—
283	C₂×D₄	—	218	2	no	—
284	C₂×D₄	—	218	1	no	—
285	C₂×D₄	—	218	1	no	—
286	C₂×D₄	—	218	1	no	—
287	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
288	C₂²×C₄	—	109	1	no	—
289	C₂²×C₄	—	109	1	no	—
290	C₂²×C₄	—	109	1	no	—
291	C₂²×C₄	—	109	1	no	—
292	C₂²×C₄	—	109	1	no	—
293	C₂²×C₄	—	218	2	no	—
294	C₂²×C₄	—	218	2	no	—
295	C₂²×C₄	—	218	1	no	—
296	C₂²×C₄	—	218	1	no	—
297	C₂²×C₄	—	218	1	no	—
298	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
299	SD₁₆	—	2	2	no	—
300	SD₁₆	—	218	2	no	—
301	SD₁₆	—	218	2	no	—
302	SD₁₆	—	218	2	no	—
303	M₁₆	—	2	2	no	—
304	M₁₆	—	218	2	no	—
305	M₁₆	—	218	2	no	—
306	M₁₆	—	218	2	no	—
307	C₂×C₈	—	109	1	no	—
308	C₂×C₈	—	109	4	no	—
309	C₂×C₈	—	109	1	no	—
310	C₂×C₈	—	218	2	no	—
311	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
312	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	109	1	no	—
315	C₄⋊C₄	—	109	1	no	—
316	C₄⋊C₄	—	218	1	no	—
317	C₄⋊C₄	—	218	1	no	—
318	C₄⋊C₄	—	218	1	no	—
319	C₄⋊C₄	—	218	1	no	—
320	C₄⋊C₄	—	218	1	no	—
321	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
322	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
323	C₂²⋊C₄	—	2	1	no	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	—	218	1	no	—
326	C₂²⋊C₄	—	218	1	no	—
327	C₂²⋊C₄	—	218	1	no	—
328	C₂²⋊C₄	—	218	1	no	—
329	C₂²⋊C₄	—	218	1	no	—
330	C₂²⋊C₄	—	218	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	109	1	no	—
333	C₂³	—	109	1	no	—
334	C₂³	—	436	2	no	—
335	C₂³	—	436	2	no	—
336	C₂³	—	436	2	no	—
337	C₂³	—	218	2	no	—
338	C₂³	—	218	2	no	—
339	C₂³	—	218	2	no	—
340	C₂³	—	218	1	no	—
341	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
342	Q₈	—	2	1	no	—
343	Q₈	—	2	1	no	—
344	Q₈	—	436	2	no	—
345	Q₈	—	218	1	no	—
346	Q₈	—	218	1	no	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	4	2	no	—
350	D₄	—	436	2	no	—
351	D₄	—	436	2	no	—
352	D₄	—	436	2	no	—
353	D₄	—	436	2	no	—
354	D₄	—	218	1	no	—
355	D₄	—	218	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	—	109	1	no	—
362	C₂×C₄	—	109	2	no	—
363	C₂×C₄	—	109	2	no	—
364	C₂×C₄	—	109	1	no	—
365	C₂×C₄	—	436	2	no	—
366	C₂×C₄	—	436	2	no	—
367	C₂×C₄	—	436	2	no	—
368	C₂×C₄	—	218	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	—	218	1	no	—
374	C₂×C₄	—	218	1	no	—
375	C₂×C₄	—	218	1	no	—
376	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
378	C₈	—	2	1	no	—
379	C₈	—	109	2	no	—
380	C₈	—	218	1	no	—
381	C₈	D₄×D₁₀₉	1	2	yes	complemented
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	872	4	no	—
389	C₂²	—	109	2	no	—
390	C₂²	—	109	2	no	—
391	C₂²	—	109	2	no	—
392	C₂²	—	436	4	no	—
393	C₂²	—	436	1	no	—
394	C₂²	—	436	1	no	—
395	C₂²	—	436	1	no	—
396	C₂²	—	218	1	no	—
397	C₂²	—	218	1	no	—
398	C₂²	—	218	1	no	—
399	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	109	2	no	—
405	C₄	—	436	1	no	—
406	C₄	—	436	1	no	—
407	C₄	—	436	1	no	—
408	C₄	—	218	1	no	—
409	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
410	C₄	#41×D₁₀₉	1	1	yes	characteristic
411	C₂	—	4	1	no	—
412	C₂	—	8	1	no	—
413	C₂	—	872	1	no	—
414	C₂	—	109	4	no	—
415	C₂	—	436	1	no	—
416	C₂	#121×D₁₀₉	1	1	yes	characteristic
417	C₂	AGL(1,ℤ/8)×D₁₀₉	1	1	yes	characteristic
418	C₂	#137×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	#468×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	#121×D₁₀₉	C₂
hypercenter	#468	D₁₀₉
hypocenter	C₁₀₉	C₂×#468
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #468

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×D₁₀₉	C₂	semidirect
2. C₂×M₁₆×D₁₀₉	C₂	semidirect
3. C₂²⋊Q₈×D₁₀₉	C₂	semidirect
5. #20295275	C₂	semidirect
6. #20295274	C₂	semidirect
7. #20295273	C₂	semidirect
8. #20295272	C₂	semidirect
9. #20295271	C₂	semidirect
10. #20295270	C₂	semidirect
11. #20295269	C₂	semidirect
12. #107×D₁₀₉	C₂	semidirect
13. #103×D₁₀₉	C₂	semidirect
14. #102×D₁₀₉	C₂	semidirect
15. #468×C₁₀₉	C₂	semidirect
20. C₂×#13182018	C₂²	semidirect
21. C₂×#13182017	C₂²	semidirect
22. C₂×#13182016	C₂²	semidirect
24. C₂×#13182013	C₂²	semidirect
25. C₂×#13182012	C₂²	semidirect
26. C₂×#13182012	C₂²	semidirect
30. #16812679	C₂²	semidirect
31. #16812678	C₂²	semidirect
34. #16812675	C₂²	semidirect
45. #16812633	C₂²	semidirect
46. #16812632	C₂²	semidirect
47. #16812632	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
55. C₂×M₁₆×C₁₀₉	C₂²	semidirect
56. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
58. #107×C₁₀₉	C₂²	semidirect
59. #103×C₁₀₉	C₂²	semidirect
60. #102×C₁₀₉	C₂²	semidirect
94. C₈×D₁₀₉	D₄	semidirect
169. C₈×C₁₀₉	C₂×D₄	semidirect
171. #11724784	C₂×D₄	semidirect
208. D₁₀₉	#468	direct (N × H)
210. C₁₀₉	C₂×#468	semidirect
222. #468	D₁₀₉	direct (N × H)
234. C₂×SD₁₆	C₂×D₁₀₉	semidirect
239. C₂×M₁₆	C₂×D₁₀₉	semidirect
247. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
262. #107	C₂×D₁₀₉	semidirect
266. #103	C₂×D₁₀₉	semidirect
270. #102	C₂×D₁₀₉	semidirect
381. C₈	D₄×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×M₁₆×D₁₀₉	2
C₂²⋊Q₈×D₁₀₉	2
#121×D₁₀₉	2
#20295275	2
#20295274	2
#20295273	2
#20295272	2
#20295271	2
#20295270	2
#20295269	2
#107×D₁₀₉	2
#103×D₁₀₉	2
#102×D₁₀₉	2
#468×C₁₀₉	2
C₂×#468	109

Subgroups — #468×D109 #28372616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #468×D₁₀₉ #28372616