Subgroups — #28371886

Order 13952.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 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
2	#20295502	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295498	C₂	1	1	yes	maximal, characteristic
4	#20295129	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295126	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295124	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295123	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#13182018	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₁₆×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295113	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295061	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295033	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295029	C₂	1	1	yes	maximal, characteristic
14	#20294980	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×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×#13182018	C₂²	1	1	yes	characteristic
19	C₂×#13182017	C₂²	1	1	yes	characteristic
20	C₂×#13182016	C₂²	1	1	yes	characteristic
21	SD₁₆×D₁₀₉	C₄	1	8	yes	complemented
22	C₂×#13182012	C₂²	1	1	yes	characteristic
23	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
24	Q₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
25	C₄×Dic₂₁₈	—	2	1	no	—
26	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
27	#16812664	—	2	1	no	—
28	#16812664	C₂²	1	1	yes	characteristic, complemented
29	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
30	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
31	#16812661	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊D₁₀₉	—	2	1	no	—
33	#16812659	—	2	1	no	—
34	#16812657	—	2	1	no	—
35	#16812657	C₂²	1	1	yes	characteristic
36	#16812657	C₂²	1	1	yes	characteristic
37	#16812656	—	2	1	no	—
38	#16812656	C₂²	1	1	yes	characteristic
39	C₂×#13182006	—	2	1	no	—
40	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
41	#16812632	C₂²	1	1	yes	characteristic, complemented
42	#16812632	C₂²	1	1	yes	characteristic, complemented
43	#16812631	C₂²	1	1	yes	characteristic, complemented
44	#16812624	C₂²	1	1	yes	characteristic, complemented
45	#16812623	C₂²	1	1	yes	characteristic, complemented
46	#16812622	C₂²	1	1	yes	characteristic, complemented
47	#16812621	C₂²	1	1	yes	characteristic
48	#16812620	C₂²	1	1	yes	characteristic
49	#16812619	C₂²	1	1	yes	characteristic
50	#16812610	C₂²	1	1	yes	characteristic, complemented
51	#16812609	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
54	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
55	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
56	#106×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	#103×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
58	#102×C₁₀₉	C₂²	1	1	yes	characteristic
59	C₄×C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₁₀₉	—	2	1	no	—
61	C₂×Dic₂₁₈	—	2	1	no	—
62	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
63	Q₈×D₁₀₉	—	2	2	no	—
64	Q₈×D₁₀₉	C₂×C₄	1	4	yes	complemented
65	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
67	D₄×D₁₀₉	—	2	2	no	—
68	D₄×D₁₀₉	C₂×C₄	1	4	yes	—
69	C₂²×Dic₁₀₉	—	2	1	no	—
70	C₂×C₄×D₁₀₉	—	2	1	no	—
71	C₂×C₄×D₁₀₉	—	2	1	no	—
72	C₂×C₄×D₁₀₉	—	2	1	no	—
73	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
74	#13182018	C₂×C₄	1	4	yes	complemented
75	#13182017	C₂×C₄	1	4	yes	complemented
76	#13182016	C₂×C₄	1	4	yes	complemented
77	#13182012	—	2	2	no	—
78	C₂×#11724784	C₂³	1	1	yes	characteristic
79	C₂×#11724784	C₂³	1	1	yes	characteristic
80	C₈×D₁₀₉	C₂×C₄	1	4	yes	complemented
81	C₄⋊Dic₁₀₉	—	2	1	no	—
82	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
83	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
84	#13182008	—	2	1	no	—
85	#13182008	—	2	1	no	—
86	#13182008	D₄	1	1	yes	characteristic
87	#13182008	D₄	1	1	yes	characteristic
88	C₂²⋊Dic₁₀₉	—	2	1	no	—
89	#13182006	—	2	1	no	—
90	#13182006	—	2	1	no	—
91	#13182006	—	2	1	no	—
92	#13182006	—	2	1	no	—
93	#13182006	D₄	1	1	yes	characteristic
94	#13182006	D₄	1	1	yes	characteristic
95	C₄×Dic₁₀₉	—	2	1	no	—
96	C₄×Dic₁₀₉	—	2	1	no	—
97	C₄×Dic₁₀₉	—	2	1	no	—
98	C₄×Dic₁₀₉	—	2	1	no	—
99	C₄×Dic₁₀₉	—	2	1	no	—
100	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
101	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
102	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₁₀₉	—	2	1	no	—
104	SD₁₆×C₁₀₉	C₂×C₄	1	4	yes	complemented
105	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
106	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
107	C₄⋊C₄×C₁₀₉	—	2	1	no	—
108	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
109	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
111	C₄²×C₁₀₉	—	2	1	no	—
112	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
113	C₂³×C₁₀₉	—	2	1	no	—
114	C₂²×D₁₀₉	—	2	1	no	—
115	C₂²×D₁₀₉	—	2	4	no	—
116	C₂²×D₁₀₉	—	8	1	no	—
117	C₂²×D₁₀₉	—	8	1	no	—
118	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
119	Q₈×C₁₀₉	—	2	1	no	—
120	Q₈×C₁₀₉	C₂²×C₄	1	2	yes	—
121	D₄×C₁₀₉	—	2	1	no	—
122	D₄×C₁₀₉	C₂²×C₄	1	2	yes	—
123	C₂×C₄×C₁₀₉	—	2	1	no	—
124	C₂×C₄×C₁₀₉	—	2	1	no	—
125	C₂×C₄×C₁₀₉	—	2	1	no	—
126	C₂×C₄×C₁₀₉	—	8	1	no	—
127	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
130	C₂²⋊D₁₀₉	—	2	4	no	—
131	C₂×Dic₁₀₉	—	2	1	no	—
132	C₂×Dic₁₀₉	—	2	1	no	—
133	C₂×Dic₁₀₉	—	2	1	no	—
134	C₂×Dic₁₀₉	—	8	1	no	—
135	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
136	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
138	D₄₃₆	—	2	1	no	—
139	D₄₃₆	C₂²×C₄	1	2	yes	—
140	C₄×D₁₀₉	—	2	4	no	—
141	C₄×D₁₀₉	—	8	1	no	—
142	C₄×D₁₀₉	—	8	1	no	—
143	C₄×D₁₀₉	C₂²×C₄	1	2	yes	—
144	C₄×D₁₀₉	#41	1	2	yes	—
145	Dic₂₁₈	—	2	1	no	—
146	Dic₂₁₈	—	2	4	no	—
147	Dic₂₁₈	C₂²×C₄	1	2	yes	—
148	C₈×C₁₀₉	—	2	1	no	—
149	C₈×C₁₀₉	C₂²×C₄	1	2	yes	—
150	#11724784	—	2	1	no	—
151	#11724784	C₂²×C₄	1	2	yes	—
152	C₂²×C₁₀₉	—	2	2	no	—
153	C₂²×C₁₀₉	—	4	1	no	—
154	C₂²×C₁₀₉	—	4	1	no	—
155	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
156	C₂×D₁₀₉	—	2	1	no	—
157	C₂×D₁₀₉	—	2	1	no	—
158	C₂×D₁₀₉	—	2	2	no	—
159	C₂×D₁₀₉	—	4	1	no	—
160	C₂×D₁₀₉	—	4	1	no	—
161	C₂×D₁₀₉	—	8	4	no	—
162	C₂×D₁₀₉	C₄×D₄	1	2	yes	—
163	C₄×C₁₀₉	—	2	2	no	—
164	C₄×C₁₀₉	—	2	1	no	—
165	C₄×C₁₀₉	—	2	1	no	—
166	C₄×C₁₀₉	—	4	1	no	—
167	C₄×C₁₀₉	—	4	1	no	—
168	C₄×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
169	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
170	Dic₁₀₉	—	2	2	no	—
171	Dic₁₀₉	—	2	1	no	—
172	Dic₁₀₉	—	2	1	no	—
173	Dic₁₀₉	—	4	1	no	—
174	Dic₁₀₉	—	4	1	no	—
175	Dic₁₀₉	C₄×D₄	1	2	yes	—
176	C₂×C₁₀₉	—	4	2	no	—
177	C₂×C₁₀₉	C₂×C₄×D₄	1	1	yes	characteristic
178	C₂×C₁₀₉	#577	1	1	yes	characteristic
179	C₂×C₁₀₉	#577	1	1	yes	characteristic
180	D₁₀₉	—	2	2	no	—
181	D₁₀₉	—	4	2	no	—
182	#2949	—	109	1	no	maximal, Sylow
183	C₁₀₉	#2949	1	1	yes	characteristic, complemented, Sylow
184	C₂²×SD₁₆	—	109	1	no	—
185	#519	—	109	1	no	—
186	#518	—	109	1	no	—
187	#440	—	109	1	no	—
188	#440	—	109	1	no	—
189	#440	—	109	1	no	—
190	#440	—	109	1	no	—
191	C₄×SD₁₆	—	109	1	no	—
192	C₄×SD₁₆	—	109	1	no	—
193	C₄×SD₁₆	—	109	1	no	—
194	C₄×SD₁₆	D₁₀₉	1	1	yes	characteristic, complemented
195	#427	—	109	1	no	—
196	#419	—	109	1	no	—
197	#418	—	109	1	no	—
198	#405	—	109	1	no	—
199	C₂²×Q₈	—	109	1	no	—
200	C₂²×D₄	—	109	1	no	—
201	C₂×SD₁₆	—	109	1	no	—
202	C₂×SD₁₆	—	109	1	no	—
203	C₂×SD₁₆	—	109	8	no	—
204	C₂×SD₁₆	—	109	1	no	—
205	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic
206	C₂×M₁₆	—	109	1	no	—
207	C₂²×C₈	—	109	1	no	—
208	C₄×Q₈	—	109	1	no	—
209	C₄×Q₈	—	109	1	no	—
210	C₄×Q₈	—	109	1	no	—
211	C₄×Q₈	—	218	1	no	—
212	C₄×Q₈	—	218	1	no	—
213	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
214	C₄×D₄	—	109	1	no	—
215	C₄×D₄	—	109	1	no	—
216	C₄×D₄	—	109	1	no	—
217	C₄×D₄	—	218	1	no	—
218	C₄×D₄	—	218	1	no	—
219	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
220	#117	—	109	1	no	—
221	#117	—	109	1	no	—
222	#117	—	109	1	no	—
223	#117	—	218	1	no	—
224	#117	—	218	1	no	—
225	C₂×C₂²⋊C₄	—	218	1	no	—
226	C₂×C₂²⋊C₄	—	218	1	no	—
227	#107	—	109	1	no	—
228	#107	—	109	1	no	—
229	#106	—	109	1	no	—
230	#106	C₂×D₁₀₉	1	1	yes	characteristic, complemented
231	#103	—	109	1	no	—
232	#103	—	109	1	no	—
233	#103	—	109	1	no	—
234	#103	C₂×D₁₀₉	1	1	yes	characteristic, complemented
235	#102	—	109	1	no	—
236	#102	—	109	1	no	—
237	#102	—	109	1	no	—
238	#102	C₂×D₁₀₉	1	1	yes	characteristic
239	#97	—	109	1	no	—
240	#97	—	109	1	no	—
241	C₄×C₈	—	109	1	no	—
242	C₄×C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
243	C₂⁴	—	218	1	no	—
244	C₂×Q₈	—	109	4	no	—
245	C₂×Q₈	—	109	1	no	—
246	C₂×Q₈	—	218	1	no	—
247	C₂×Q₈	—	218	2	no	—
248	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
249	C₂×D₄	—	109	4	no	—
250	C₂×D₄	—	109	1	no	—
251	C₂×D₄	—	218	2	no	—
252	C₂×D₄	—	218	1	no	—
253	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	109	1	no	—
256	C₂²×C₄	—	218	1	no	—
257	C₂²×C₄	—	218	1	no	—
258	C₂²×C₄	—	218	1	no	—
259	C₂²×C₄	—	218	1	no	—
260	SD₁₆	—	109	4	no	—
261	SD₁₆	—	109	4	no	—
262	SD₁₆	—	109	4	no	—
263	SD₁₆	C₄×D₁₀₉	1	4	yes	complemented
264	M₁₆	—	218	2	no	—
265	C₂×C₈	—	109	1	no	—
266	C₂×C₈	—	109	4	no	—
267	C₂×C₈	—	109	1	no	—
268	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
269	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
270	C₄⋊C₄	—	2	1	no	—
271	C₄⋊C₄	—	109	1	no	—
272	C₄⋊C₄	—	109	1	no	—
273	C₄⋊C₄	—	109	1	no	—
274	C₄⋊C₄	—	109	1	no	—
275	C₄⋊C₄	—	218	1	no	—
276	C₄⋊C₄	—	218	1	no	—
277	C₄⋊C₄	—	218	1	no	—
278	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
279	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
280	C₂²⋊C₄	—	2	1	no	—
281	C₂²⋊C₄	—	109	1	no	—
282	C₂²⋊C₄	—	109	1	no	—
283	C₂²⋊C₄	—	218	1	no	—
284	C₂²⋊C₄	—	218	1	no	—
285	C₂²⋊C₄	—	218	1	no	—
286	C₂²⋊C₄	—	218	1	no	—
287	C₂²⋊C₄	—	218	1	no	—
288	C₄²	—	2	1	no	—
289	C₄²	—	109	1	no	—
290	C₄²	—	218	1	no	—
291	C₄²	—	218	1	no	—
292	C₄²	—	218	1	no	—
293	C₄²	—	218	1	no	—
294	C₄²	—	218	1	no	—
295	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
296	C₂³	—	2	1	no	—
297	C₂³	—	872	1	no	—
298	C₂³	—	872	1	no	—
299	C₂³	—	109	1	no	—
300	C₂³	—	218	4	no	—
301	C₂³	—	218	1	no	—
302	Q₈	—	2	1	no	—
303	Q₈	—	109	2	no	—
304	Q₈	—	218	4	no	—
305	Q₈	—	218	1	no	—
306	Q₈	C₂×C₄×D₁₀₉	1	2	yes	—
307	D₄	—	2	1	no	—
308	D₄	—	109	2	no	—
309	D₄	—	218	4	no	—
310	D₄	—	218	1	no	—
311	D₄	C₂×C₄×D₁₀₉	1	2	yes	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	8	1	no	—
316	C₂×C₄	—	872	1	no	—
317	C₂×C₄	—	872	1	no	—
318	C₂×C₄	—	872	1	no	—
319	C₂×C₄	—	109	1	no	—
320	C₂×C₄	—	109	2	no	—
321	C₂×C₄	—	109	2	no	—
322	C₂×C₄	—	109	1	no	—
323	C₂×C₄	—	109	1	no	—
324	C₂×C₄	—	218	4	no	—
325	C₂×C₄	—	218	1	no	—
326	C₂×C₄	—	218	1	no	—
327	C₂×C₄	—	218	1	no	—
328	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
329	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
330	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
331	C₈	—	2	1	no	—
332	C₈	—	109	2	no	—
333	C₈	—	218	1	no	—
334	C₈	C₂×C₄×D₁₀₉	1	2	yes	—
335	C₂²	—	2	2	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	872	4	no	—
339	C₂²	—	109	2	no	—
340	C₂²	—	436	1	no	—
341	C₂²	—	436	1	no	—
342	C₂²	—	218	2	no	—
343	C₂²	—	218	1	no	—
344	C₂²	—	218	1	no	—
345	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
346	C₄	—	2	2	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	4	1	no	—
350	C₄	—	4	1	no	—
351	C₄	—	109	2	no	—
352	C₄	—	436	1	no	—
353	C₄	—	436	1	no	—
354	C₄	—	218	2	no	—
355	C₄	—	218	1	no	—
356	C₄	—	218	1	no	—
357	C₄	C₂²×C₄×D₁₀₉	1	1	yes	characteristic
358	C₄	#41×D₁₀₉	1	1	yes	characteristic
359	C₂	—	4	2	no	—
360	C₂	—	436	2	no	—
361	C₂	—	218	2	no	—
362	C₂	C₄×D₄×D₁₀₉	1	1	yes	characteristic
363	C₂	#20295832	1	1	yes	characteristic
364	C₂	#20295833	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator	C₄×C₁₀₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	C₄×SD₁₆×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	C₂×D₄×D₁₀₉	C₂²
cosocle	C₂×C₄×C₁₀₉	C₂⁴
hypercenter	C₄×SD₁₆	D₁₀₉
hypocenter	C₁₀₉	#2949
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. #20295502	C₂	semidirect
4. #20295129	C₂	semidirect
5. #20295126	C₂	semidirect
6. #20295124	C₂	semidirect
7. #20295123	C₂	semidirect
8. C₄×#13182018	C₂	semidirect
9. SD₁₆×Dic₁₀₉	C₂	semidirect
10. #20295113	C₂	semidirect
11. #20295061	C₂	semidirect
12. #20295033	C₂	semidirect
14. #20294980	C₂	semidirect
15. C₄×SD₁₆×C₁₀₉	C₂	semidirect
21. SD₁₆×D₁₀₉	C₄	semidirect
24. Q₈×Dic₁₀₉	C₂²	semidirect
26. C₄×Dic₂₁₈	C₂²	semidirect
28. #16812664	C₂²	semidirect
41. #16812632	C₂²	semidirect
42. #16812632	C₂²	semidirect
43. #16812631	C₂²	semidirect
44. #16812624	C₂²	semidirect
45. #16812623	C₂²	semidirect
46. #16812622	C₂²	semidirect
50. #16812610	C₂²	semidirect
51. #16812609	C₂²	semidirect
52. C₈×Dic₁₀₉	C₂²	semidirect
54. C₄×Q₈×C₁₀₉	C₂²	semidirect
56. #106×C₁₀₉	C₂²	semidirect
57. #103×C₁₀₉	C₂²	semidirect
59. C₄×C₈×C₁₀₉	C₂²	semidirect
64. Q₈×D₁₀₉	C₂×C₄	semidirect
74. #13182018	C₂×C₄	semidirect
75. #13182017	C₂×C₄	semidirect
76. #13182016	C₂×C₄	semidirect
80. C₈×D₁₀₉	C₂×C₄	semidirect
104. SD₁₆×C₁₀₉	C₂×C₄	semidirect
183. C₁₀₉	#2949	semidirect
194. C₄×SD₁₆	D₁₀₉	semidirect
213. C₄×Q₈	C₂×D₁₀₉	semidirect
230. #106	C₂×D₁₀₉	semidirect
234. #103	C₂×D₁₀₉	semidirect
242. C₄×C₈	C₂×D₁₀₉	semidirect
263. SD₁₆	C₄×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
#20295502	2
#20295498	2
#20295129	2
#20295126	2
#20295124	2
#20295123	2
C₄×#13182018	2
SD₁₆×Dic₁₀₉	2
#20295113	2
#20295061	2
#20295033	2
#20295029	2
#20294980	2
C₄×SD₁₆×C₁₀₉	2
#2949	109