Subgroups — #28372646

Order 13952.

548 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812726	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295539	C₂	1	1	yes	maximal, characteristic, complemented
4	#121×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295279	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295277	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295274	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295263	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295261	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295258	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295252	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295067	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295029	C₂	1	1	yes	maximal, characteristic, complemented
14	#20295026	C₂	1	1	yes	maximal, characteristic, complemented
15	#468×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13182030	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	#16812726	—	2	4	no	—
21	C₂×#13182016	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₈₇₂	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13182014	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13182013	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13182012	C₂²	1	1	yes	characteristic
26	C₂×#13182012	C₂²	1	1	yes	characteristic
27	M₁₆×D₁₀₉	—	2	4	no	—
28	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
30	#16812684	—	2	1	no	—
31	#16812675	C₂²	1	1	yes	characteristic, complemented
32	#16812674	C₂²	1	1	yes	characteristic
33	#16812674	C₂²	1	1	yes	characteristic, complemented
34	#16812673	C₂²	1	1	yes	characteristic
35	#16812673	C₂²	1	1	yes	characteristic, complemented
36	#16812672	—	2	1	no	—
37	#16812671	—	2	1	no	—
38	#16812670	C₂²	1	1	yes	characteristic
39	#16812669	—	2	1	no	—
40	#16812661	—	2	1	no	—
41	#16812659	—	2	1	no	—
42	#16812657	C₂²	1	1	yes	characteristic
43	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
44	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
45	#16812632	C₂²	1	1	yes	characteristic, complemented
46	#16812631	C₂²	1	1	yes	characteristic, complemented
47	#16812630	C₂²	1	1	yes	characteristic, complemented
48	#16812623	C₂²	1	1	yes	characteristic, complemented
49	#16812621	C₂²	1	1	yes	characteristic, complemented
50	#16812621	C₂²	1	1	yes	characteristic, complemented
51	#16812620	C₂²	1	1	yes	characteristic, complemented
52	#16812619	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	#13182030	—	2	2	no	—
64	#13182030	—	2	2	no	—
65	C₂×D₄₃₆	—	2	1	no	—
66	C₂×D₄₃₆	—	2	1	no	—
67	C₂×D₄₃₆	—	2	1	no	—
68	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
69	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
71	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
72	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
73	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
74	D₄×D₁₀₉	—	2	2	no	—
75	D₄×D₁₀₉	—	2	2	no	—
76	D₄×D₁₀₉	—	4	4	no	—
77	C₂²×Dic₁₀₉	D₄	1	1	yes	characteristic
78	C₂×C₄×D₁₀₉	—	2	2	no	—
79	C₂×C₄×D₁₀₉	—	2	2	no	—
80	C₂×C₄×D₁₀₉	—	2	1	no	—
81	C₂×C₄×D₁₀₉	—	2	1	no	—
82	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
83	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
84	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
85	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
86	#13182016	—	2	2	no	—
87	D₈₇₂	—	2	2	no	—
88	#13182014	—	2	2	no	—
89	#13182013	—	2	2	no	—
90	#13182012	—	2	2	no	—
91	#13182012	D₄	1	4	yes	complemented
92	C₂×#11724784	C₂³	1	1	yes	characteristic
93	C₂×#11724784	C₂³	1	1	yes	characteristic
94	C₈×D₁₀₉	—	2	2	no	—
95	C₈×D₁₀₉	—	2	2	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	C₂²⋊Dic₁₀₉	—	2	1	no	—
101	#13182006	—	2	1	no	—
102	#13182006	—	2	1	no	—
103	#13182006	—	2	1	no	—
104	#13182006	—	2	1	no	—
105	#13182006	—	2	1	no	—
106	#13182006	—	2	1	no	—
107	C₄×Dic₁₀₉	—	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	1	no	—
126	C₂²×D₁₀₉	—	2	1	no	—
127	C₂²×D₁₀₉	—	4	1	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	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
133	Q₈×C₁₀₉	—	2	1	no	—
134	Q₈×C₁₀₉	—	2	1	no	—
135	D₄×C₁₀₉	—	2	1	no	—
136	D₄×C₁₀₉	—	2	1	no	—
137	D₄×C₁₀₉	—	4	2	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	—	2	1	no	—
143	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
145	C₂²⋊D₁₀₉	—	4	2	no	—
146	C₂²⋊D₁₀₉	—	4	2	no	—
147	C₂²⋊D₁₀₉	—	4	2	no	—
148	C₂²⋊D₁₀₉	—	4	2	no	—
149	C₂×Dic₁₀₉	—	2	2	no	—
150	C₂×Dic₁₀₉	—	2	1	no	—
151	C₂×Dic₁₀₉	—	2	1	no	—
152	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
153	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
154	D₄₃₆	—	2	1	no	—
155	D₄₃₆	—	2	1	no	—
156	D₄₃₆	—	2	1	no	—
157	D₄₃₆	—	2	1	no	—
158	D₄₃₆	—	4	2	no	—
159	D₄₃₆	—	4	2	no	—
160	D₄₃₆	—	4	2	no	—
161	C₄×D₁₀₉	—	2	2	no	—
162	C₄×D₁₀₉	—	2	1	no	—
163	C₄×D₁₀₉	—	2	1	no	—
164	C₄×D₁₀₉	—	2	2	no	—
165	C₄×D₁₀₉	—	4	2	no	—
166	C₄×D₁₀₉	—	4	2	no	—
167	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
168	C₄×D₁₀₉	#41	1	2	yes	—
169	C₈×C₁₀₉	—	2	1	no	—
170	C₈×C₁₀₉	C₂×D₄	1	2	yes	complemented
171	#11724784	—	2	1	no	—
172	#11724784	C₂×D₄	1	2	yes	complemented
173	C₂²×C₁₀₉	—	2	1	no	—
174	C₂²×C₁₀₉	—	2	1	no	—
175	C₂²×C₁₀₉	—	2	1	no	—
176	C₂²×C₁₀₉	—	4	1	no	—
177	C₂²×C₁₀₉	—	4	1	no	—
178	C₂²×C₁₀₉	—	4	1	no	—
179	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
180	C₂×D₁₀₉	—	2	1	no	—
181	C₂×D₁₀₉	—	2	1	no	—
182	C₂×D₁₀₉	—	2	1	no	—
183	C₂×D₁₀₉	—	2	1	no	—
184	C₂×D₁₀₉	—	4	4	no	—
185	C₂×D₁₀₉	—	4	1	no	—
186	C₂×D₁₀₉	—	4	1	no	—
187	C₂×D₁₀₉	—	4	1	no	—
188	C₂×D₁₀₉	—	4	1	no	—
189	C₂×D₁₀₉	—	4	1	no	—
190	C₂×D₁₀₉	—	4	1	no	—
191	C₂×D₁₀₉	—	8	4	no	—
192	C₂×D₁₀₉	#121	1	2	yes	—
193	C₂×D₁₀₉	AGL(1,ℤ/8)	1	2	yes	complemented
194	C₄×C₁₀₉	—	2	1	no	—
195	C₄×C₁₀₉	—	4	1	no	—
196	C₄×C₁₀₉	—	4	1	no	—
197	C₄×C₁₀₉	—	4	1	no	—
198	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
199	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
200	Dic₁₀₉	—	2	1	no	—
201	Dic₁₀₉	—	4	1	no	—
202	Dic₁₀₉	—	4	1	no	—
203	Dic₁₀₉	#121	1	2	yes	—
204	C₂×C₁₀₉	—	4	1	no	—
205	C₂×C₁₀₉	—	8	1	no	—
206	C₂×C₁₀₉	C₂×#121	1	1	yes	characteristic
207	C₂×C₁₀₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
208	C₂×C₁₀₉	#575	1	1	yes	characteristic
209	D₁₀₉	—	2	2	no	—
210	D₁₀₉	—	2	2	no	—
211	D₁₀₉	—	8	1	no	—
212	D₁₀₉	—	8	1	no	—
213	#3055	—	109	1	no	maximal, Sylow
214	C₁₀₉	#3055	1	1	yes	characteristic, complemented, Sylow
215	C₂×AGL(1,ℤ/8)	—	109	1	no	—
216	C₂²×M₁₆	—	109	1	no	—
217	#525	—	109	1	no	—
218	C₂×#121	—	109	1	no	—
219	#469	—	109	1	no	—
220	#469	—	109	1	no	—
221	#468	—	109	1	no	—
222	#468	D₁₀₉	1	1	yes	characteristic, complemented
223	#466	—	109	1	no	—
224	#466	—	109	1	no	—
225	#465	—	109	1	no	—
226	#465	—	109	1	no	—
227	#428	—	109	1	no	—
228	#418	—	109	1	no	—
229	#417	—	109	1	no	—
230	C₂×#41	—	109	1	no	—
231	C₂²×D₄	—	109	1	no	—
232	C₂²×D₄	—	218	1	no	—
233	C₂³×C₄	—	109	1	no	—
234	AGL(1,ℤ/8)	—	218	4	no	—
235	C₂×SD₁₆	—	109	1	no	—
236	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
237	C₂×D₈	—	109	1	no	—
238	C₂×D₈	—	109	1	no	—
239	C₂×M₁₆	—	109	1	no	—
240	C₂×M₁₆	—	109	1	no	—
241	C₂×M₁₆	—	109	1	no	—
242	C₂×M₁₆	—	218	4	no	—
243	C₂×M₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
244	C₂²×C₈	—	109	1	no	—
245	C₂²×C₈	—	109	1	no	—
246	#123	—	218	1	no	—
247	C₂²⋊Q₈	—	109	1	no	—
248	C₂²⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
249	#121	—	109	1	no	—
250	#121	—	109	1	no	—
251	#121	—	109	1	no	—
252	#121	—	109	1	no	—
253	#121	—	109	1	no	—
254	#121	—	218	1	no	—
255	#121	—	218	1	no	—
256	#121	C₂×D₁₀₉	1	1	yes	characteristic
257	#120	—	218	1	no	—
258	C₄×D₄	—	218	1	no	—
259	C₄×D₄	—	218	1	no	—
260	#117	—	109	1	no	—
261	C₂×C₄⋊C₄	—	109	1	no	—
262	C₂×C₂²⋊C₄	—	218	1	no	—
263	#107	—	109	1	no	—
264	#107	C₂×D₁₀₉	1	1	yes	characteristic, complemented
265	#106	—	109	1	no	—
266	#106	—	109	1	no	—
267	#103	—	109	1	no	—
268	#103	C₂×D₁₀₉	1	1	yes	characteristic, complemented
269	#102	—	109	1	no	—
270	#102	—	109	1	no	—
271	#102	—	109	1	no	—
272	#102	—	109	1	no	—
273	#102	—	109	1	no	—
274	#102	C₂×D₁₀₉	1	1	yes	characteristic, complemented
275	C₂⁴	—	109	1	no	—
276	C₂⁴	—	218	1	no	—
277	#41	—	218	2	no	—
278	#41	—	218	2	no	—
279	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	109	1	no	—
282	C₂×D₄	—	109	1	no	—
283	C₂×D₄	—	436	4	no	—
284	C₂×D₄	—	218	1	no	—
285	C₂×D₄	—	218	1	no	—
286	C₂×D₄	—	218	1	no	—
287	C₂×D₄	—	218	2	no	—
288	C₂×D₄	—	218	2	no	—
289	C₂×D₄	—	218	1	no	—
290	C₂×D₄	—	218	1	no	—
291	C₂×D₄	—	218	1	no	—
292	C₂×D₄	—	218	1	no	—
293	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
294	C₂²×C₄	—	109	1	no	—
295	C₂²×C₄	—	109	1	no	—
296	C₂²×C₄	—	109	1	no	—
297	C₂²×C₄	—	109	1	no	—
298	C₂²×C₄	—	109	1	no	—
299	C₂²×C₄	—	218	1	no	—
300	C₂²×C₄	—	218	2	no	—
301	C₂²×C₄	—	218	2	no	—
302	C₂²×C₄	—	218	1	no	—
303	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
304	SD₁₆	—	2	2	no	—
305	SD₁₆	—	218	2	no	—
306	D₈	—	218	2	no	—
307	D₈	—	218	2	no	—
308	M₁₆	—	2	2	no	—
309	M₁₆	—	109	4	no	—
310	M₁₆	—	218	2	no	—
311	M₁₆	—	218	2	no	—
312	C₂×C₈	—	109	1	no	—
313	C₂×C₈	—	109	1	no	—
314	C₂×C₈	—	218	2	no	—
315	C₂×C₈	—	218	2	no	—
316	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
317	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	109	1	no	—
320	C₄⋊C₄	—	109	1	no	—
321	C₄⋊C₄	—	218	1	no	—
322	C₄⋊C₄	—	218	1	no	—
323	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
324	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
325	C₂²⋊C₄	—	2	1	no	—
326	C₂²⋊C₄	—	2	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	C₂²⋊C₄	—	218	1	no	—
332	C₂²⋊C₄	—	218	1	no	—
333	C₂²⋊C₄	—	218	1	no	—
334	C₄²	—	218	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	109	1	no	—
337	C₂³	—	109	1	no	—
338	C₂³	—	436	1	no	—
339	C₂³	—	436	2	no	—
340	C₂³	—	436	2	no	—
341	C₂³	—	436	2	no	—
342	C₂³	—	218	2	no	—
343	C₂³	—	218	2	no	—
344	C₂³	—	218	1	no	—
345	C₂³	—	218	1	no	—
346	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
347	Q₈	—	2	1	no	—
348	Q₈	—	2	1	no	—
349	D₄	—	2	1	no	—
350	D₄	—	2	1	no	—
351	D₄	—	4	2	no	—
352	D₄	—	436	2	no	—
353	D₄	—	436	2	no	—
354	D₄	—	436	2	no	—
355	D₄	—	436	2	no	—
356	D₄	—	436	2	no	—
357	D₄	—	436	2	no	—
358	D₄	—	436	2	no	—
359	D₄	—	218	1	no	—
360	D₄	—	218	1	no	—
361	D₄	—	218	1	no	—
362	D₄	—	218	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	109	1	no	—
369	C₂×C₄	—	109	2	no	—
370	C₂×C₄	—	109	2	no	—
371	C₂×C₄	—	109	1	no	—
372	C₂×C₄	—	436	2	no	—
373	C₂×C₄	—	436	2	no	—
374	C₂×C₄	—	218	2	no	—
375	C₂×C₄	—	218	2	no	—
376	C₂×C₄	—	218	2	no	—
377	C₂×C₄	—	218	1	no	—
378	C₂×C₄	—	218	1	no	—
379	C₂×C₄	—	218	1	no	—
380	C₂×C₄	—	218	1	no	—
381	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
382	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	109	2	no	—
385	C₈	—	218	1	no	—
386	C₈	D₄×D₁₀₉	1	2	yes	complemented
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	872	4	no	—
394	C₂²	—	109	2	no	—
395	C₂²	—	109	2	no	—
396	C₂²	—	436	4	no	—
397	C₂²	—	436	1	no	—
398	C₂²	—	436	1	no	—
399	C₂²	—	436	1	no	—
400	C₂²	—	436	1	no	—
401	C₂²	—	436	1	no	—
402	C₂²	—	436	1	no	—
403	C₂²	—	218	1	no	—
404	C₂²	—	218	1	no	—
405	C₂²	—	218	1	no	—
406	C₂²	—	218	1	no	—
407	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	109	2	no	—
413	C₄	—	436	1	no	—
414	C₄	—	436	1	no	—
415	C₄	—	218	1	no	—
416	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
417	C₄	#41×D₁₀₉	1	1	yes	characteristic
418	C₂	—	4	1	no	—
419	C₂	—	8	1	no	—
420	C₂	—	872	1	no	—
421	C₂	—	872	1	no	—
422	C₂	—	218	2	no	—
423	C₂	—	218	2	no	—
424	C₂	#121×D₁₀₉	1	1	yes	characteristic
425	C₂	AGL(1,ℤ/8)×D₁₀₉	1	1	yes	characteristic
426	C₂	#20295825	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
hypercenter	#468	D₁₀₉
hypocenter	C₁₀₉	#3055
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×#16812726	C₂	semidirect
2. C₂×M₁₆×D₁₀₉	C₂	semidirect
3. #20295539	C₂	semidirect
4. #121×D₁₀₉	C₂	semidirect
5. #20295279	C₂	semidirect
6. #20295277	C₂	semidirect
7. #20295274	C₂	semidirect
8. #20295263	C₂	semidirect
9. #20295261	C₂	semidirect
10. #20295258	C₂	semidirect
11. #20295252	C₂	semidirect
12. #20295067	C₂	semidirect
13. #20295029	C₂	semidirect
14. #20295026	C₂	semidirect
15. #468×C₁₀₉	C₂	semidirect
21. C₂×#13182016	C₂²	semidirect
22. C₂×D₈₇₂	C₂²	semidirect
23. C₂×#13182014	C₂²	semidirect
24. C₂×#13182013	C₂²	semidirect
28. C₂×C₈×D₁₀₉	C₂²	semidirect
29. C₂×C₈×D₁₀₉	C₂²	semidirect
31. #16812675	C₂²	semidirect
33. #16812674	C₂²	semidirect
35. #16812673	C₂²	semidirect
45. #16812632	C₂²	semidirect
46. #16812631	C₂²	semidirect
47. #16812630	C₂²	semidirect
48. #16812623	C₂²	semidirect
49. #16812621	C₂²	semidirect
50. #16812621	C₂²	semidirect
51. #16812620	C₂²	semidirect
52. #16812619	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
91. #13182012	D₄	semidirect
170. C₈×C₁₀₉	C₂×D₄	semidirect
172. #11724784	C₂×D₄	semidirect
193. C₂×D₁₀₉	AGL(1,ℤ/8)	semidirect
214. C₁₀₉	#3055	semidirect
222. #468	D₁₀₉	semidirect
236. C₂×SD₁₆	C₂×D₁₀₉	semidirect
243. C₂×M₁₆	C₂×D₁₀₉	semidirect
248. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
264. #107	C₂×D₁₀₉	semidirect
268. #103	C₂×D₁₀₉	semidirect
274. #102	C₂×D₁₀₉	semidirect
386. 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×#16812726	2
C₂×M₁₆×D₁₀₉	2
#20295539	2
#121×D₁₀₉	2
#20295279	2
#20295277	2
#20295274	2
#20295263	2
#20295261	2
#20295258	2
#20295252	2
#20295067	2
#20295029	2
#20295026	2
#468×C₁₀₉	2
#3055	109