Subgroups — #464×D₁₀₉ #28372472

Order 13952.

500 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×SD₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	#124×D₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295251	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295250	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295249	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295248	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295247	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295246	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295245	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
15	#464×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
19	C₂×Dic₄₃₆	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13182019	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13182019	C₂²	1	1	yes	characteristic, complemented
22	Q₁₆×D₁₀₉	—	2	4	no	—
23	C₂×#13182018	C₂²	1	1	yes	characteristic
24	C₂×#13182017	C₂²	1	1	yes	characteristic
25	C₂×#13182016	C₂²	1	1	yes	characteristic
26	SD₁₆×D₁₀₉	—	2	4	no	—
27	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
29	#16812688	C₂²	1	1	yes	characteristic
30	#16812687	C₂²	1	1	yes	characteristic
31	#16812686	C₂²	1	1	yes	characteristic
32	#16812685	—	2	1	no	—
33	#16812685	—	2	1	no	—
34	Q₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
35	C₄×Dic₂₁₈	—	2	1	no	—
36	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
37	#16812664	—	2	1	no	—
38	#16812664	C₂²	1	1	yes	characteristic, complemented
39	C₄⋊C₄×D₁₀₉	—	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	C₄²×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
52	#16812620	C₂²	1	1	yes	characteristic
53	#16812619	C₂²	1	1	yes	characteristic
54	C₂×Q₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
56	#124×C₁₀₉	C₂²	1	1	yes	characteristic
57	C₄×Q₈×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
61	C₂³×D₁₀₉	—	2	1	no	—
62	C₂×Dic₂₁₈	—	2	1	no	—
63	C₂×Dic₂₁₈	—	2	1	no	—
64	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
65	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
66	Q₈×D₁₀₉	—	2	2	no	—
67	Q₈×D₁₀₉	—	2	2	no	—
68	Q₈×D₁₀₉	—	2	2	no	—
69	Q₈×D₁₀₉	D₄	1	4	yes	—
70	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
72	D₄×D₁₀₉	—	2	2	no	—
73	D₄×D₁₀₉	—	2	2	no	—
74	C₂×C₄×D₁₀₉	—	2	1	no	—
75	C₂×C₄×D₁₀₉	—	2	1	no	—
76	C₂×C₄×D₁₀₉	—	2	1	no	—
77	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
78	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
79	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
80	Dic₄₃₆	—	2	2	no	—
81	#13182019	—	2	2	no	—
82	#13182019	—	2	2	no	—
83	#13182018	—	2	2	no	—
84	#13182017	—	2	2	no	—
85	#13182016	—	2	2	no	—
86	C₂×#11724784	C₂³	1	1	yes	characteristic
87	C₂×#11724784	C₂³	1	1	yes	characteristic
88	C₈×D₁₀₉	—	2	2	no	—
89	C₈×D₁₀₉	—	2	2	no	—
90	C₄⋊Dic₁₀₉	—	2	1	no	—
91	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
92	#13182008	—	2	1	no	—
93	#13182008	—	2	1	no	—
94	#13182008	—	2	1	no	—
95	C₂²⋊Dic₁₀₉	—	2	1	no	—
96	C₂²⋊Dic₁₀₉	—	2	1	no	—
97	#13182006	—	2	1	no	—
98	#13182006	—	2	1	no	—
99	#13182006	—	2	1	no	—
100	#13182006	—	2	1	no	—
101	C₄×Dic₁₀₉	—	2	1	no	—
102	C₄×Dic₁₀₉	—	2	1	no	—
103	C₄×Dic₁₀₉	—	2	1	no	—
104	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
105	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
106	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
107	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	Q₁₆×C₁₀₉	—	2	2	no	—
111	SD₁₆×C₁₀₉	—	2	2	no	—
112	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₁₀₉	—	2	1	no	—
115	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
116	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
117	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
118	C₄²×C₁₀₉	—	2	1	no	—
119	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
120	C₂³×C₁₀₉	—	2	1	no	—
121	C₂²×D₁₀₉	—	2	1	no	—
122	C₂²×D₁₀₉	—	4	2	no	—
123	C₂²×D₁₀₉	—	4	2	no	—
124	C₂²×D₁₀₉	—	4	2	no	—
125	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
126	Q₈×C₁₀₉	—	2	1	no	—
127	Q₈×C₁₀₉	—	2	1	no	—
128	Q₈×C₁₀₉	—	2	1	no	—
129	Q₈×C₁₀₉	C₂×D₄	1	2	yes	—
130	D₄×C₁₀₉	—	2	1	no	—
131	D₄×C₁₀₉	—	2	1	no	—
132	C₂×C₄×C₁₀₉	—	2	1	no	—
133	C₂×C₄×C₁₀₉	—	2	1	no	—
134	C₂×C₄×C₁₀₉	—	2	1	no	—
135	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
138	C₂²⋊D₁₀₉	—	4	2	no	—
139	C₂×Dic₁₀₉	—	2	1	no	—
140	C₂×Dic₁₀₉	—	2	1	no	—
141	C₂×Dic₁₀₉	—	2	1	no	—
142	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
143	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
144	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
145	D₄₃₆	—	2	1	no	—
146	D₄₃₆	—	2	1	no	—
147	C₄×D₁₀₉	—	2	4	no	—
148	C₄×D₁₀₉	—	2	2	no	—
149	C₄×D₁₀₉	—	2	2	no	—
150	C₄×D₁₀₉	—	4	2	no	—
151	C₄×D₁₀₉	—	4	2	no	—
152	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
153	C₄×D₁₀₉	#41	1	2	yes	—
154	Dic₂₁₈	—	2	1	no	—
155	Dic₂₁₈	—	2	4	no	—
156	Dic₂₁₈	—	2	1	no	—
157	Dic₂₁₈	—	2	1	no	—
158	Dic₂₁₈	—	4	2	no	—
159	Dic₂₁₈	C₂×D₄	1	2	yes	—
160	C₈×C₁₀₉	—	2	1	no	—
161	C₈×C₁₀₉	—	2	1	no	—
162	#11724784	—	2	1	no	—
163	#11724784	—	2	1	no	—
164	C₂²×C₁₀₉	—	4	1	no	—
165	C₂²×C₁₀₉	—	4	1	no	—
166	C₂²×C₁₀₉	—	4	1	no	—
167	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×D₁₀₉	—	4	1	no	—
169	C₂×D₁₀₉	—	4	1	no	—
170	C₂×D₁₀₉	—	4	1	no	—
171	C₂×D₁₀₉	—	8	4	no	—
172	C₂×D₁₀₉	#121	1	2	yes	—
173	C₂×D₁₀₉	#135	1	2	yes	—
174	C₂×D₁₀₉	#137	1	2	yes	—
175	C₄×C₁₀₉	—	2	2	no	—
176	C₄×C₁₀₉	—	2	1	no	—
177	C₄×C₁₀₉	—	2	1	no	—
178	C₄×C₁₀₉	—	4	1	no	—
179	C₄×C₁₀₉	—	4	1	no	—
180	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
181	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
182	Dic₁₀₉	—	2	2	no	—
183	Dic₁₀₉	—	2	1	no	—
184	Dic₁₀₉	—	2	1	no	—
185	Dic₁₀₉	—	4	1	no	—
186	Dic₁₀₉	—	4	1	no	—
187	Dic₁₀₉	#121	1	2	yes	—
188	C₂×C₁₀₉	—	8	1	no	—
189	C₂×C₁₀₉	C₂×#121	1	1	yes	characteristic
190	C₂×C₁₀₉	C₂×#135	1	1	yes	characteristic
191	C₂×C₁₀₉	C₂×#137	1	1	yes	characteristic
192	D₁₀₉	—	8	1	no	—
193	D₁₀₉	#464	1	4	yes	direct product factor
194	C₂×#464	—	109	1	no	maximal, Sylow
195	C₁₀₉	C₂×#464	1	1	yes	characteristic, complemented, Sylow
196	C₂²×Q₁₆	—	109	1	no	—
197	C₂²×SD₁₆	—	109	1	no	—
198	C₂×#124	—	109	1	no	—
199	C₂×C₄×Q₈	—	109	1	no	—
200	#464	—	109	1	no	—
201	#464	—	109	1	no	—
202	#464	—	109	1	no	—
203	#464	—	109	1	no	—
204	#464	—	109	1	no	—
205	#464	—	109	1	no	—
206	#464	—	109	1	no	—
207	#464	D₁₀₉	1	1	yes	characteristic, direct product factor
208	C₂×C₄⋊C₈	—	109	1	no	—
209	C₂×#103	—	109	1	no	—
210	C₂×#102	—	109	1	no	—
211	C₂²×Q₈	—	109	1	no	—
212	C₂²×Q₈	—	109	1	no	—
213	C₂²×D₄	—	109	1	no	—
214	C₂×Q₁₆	—	109	1	no	—
215	C₂×Q₁₆	—	109	1	no	—
216	C₂×Q₁₆	—	109	1	no	—
217	C₂×Q₁₆	—	218	4	no	—
218	C₂×Q₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
219	C₂×SD₁₆	—	109	1	no	—
220	C₂×SD₁₆	—	109	1	no	—
221	C₂×SD₁₆	—	109	1	no	—
222	C₂×SD₁₆	—	218	4	no	—
223	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic
224	C₂²×C₈	—	109	1	no	—
225	C₂²×C₈	—	109	1	no	—
226	#124	—	109	1	no	—
227	#124	—	109	1	no	—
228	#124	—	109	1	no	—
229	#124	—	218	1	no	—
230	#124	—	218	1	no	—
231	#124	C₂×D₁₀₉	1	1	yes	characteristic
232	C₄×Q₈	—	109	1	no	—
233	C₄×Q₈	—	109	1	no	—
234	C₄×Q₈	—	109	1	no	—
235	C₄×Q₈	—	218	1	no	—
236	C₄×Q₈	—	218	1	no	—
237	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
238	C₂×C₄⋊C₄	—	109	1	no	—
239	C₂×C₄⋊C₄	—	218	1	no	—
240	C₂×C₂²⋊C₄	—	218	1	no	—
241	C₂×C₂²⋊C₄	—	218	1	no	—
242	C₂×C₄²	—	109	1	no	—
243	C₂×C₄²	—	218	1	no	—
244	C₄⋊C₈	—	109	1	no	—
245	C₄⋊C₈	—	109	1	no	—
246	C₄⋊C₈	—	109	1	no	—
247	C₄⋊C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
248	#103	—	109	1	no	—
249	#103	—	109	1	no	—
250	#103	—	109	1	no	—
251	#103	C₂×D₁₀₉	1	1	yes	characteristic, complemented
252	#102	—	109	1	no	—
253	#102	—	109	1	no	—
254	#102	—	109	1	no	—
255	#102	C₂×D₁₀₉	1	1	yes	characteristic
256	C₂⁴	—	218	1	no	—
257	C₂×Q₈	—	109	4	no	—
258	C₂×Q₈	—	109	1	no	—
259	C₂×Q₈	—	109	1	no	—
260	C₂×Q₈	—	218	1	no	—
261	C₂×Q₈	—	218	1	no	—
262	C₂×Q₈	—	218	2	no	—
263	C₂×Q₈	—	218	2	no	—
264	C₂×Q₈	—	218	2	no	—
265	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
266	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
267	C₂×D₄	—	109	1	no	—
268	C₂×D₄	—	218	2	no	—
269	C₂×D₄	—	218	2	no	—
270	C₂×D₄	—	218	1	no	—
271	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
272	C₂²×C₄	—	109	1	no	—
273	C₂²×C₄	—	109	1	no	—
274	C₂²×C₄	—	109	1	no	—
275	C₂²×C₄	—	218	1	no	—
276	C₂²×C₄	—	218	1	no	—
277	C₂²×C₄	—	218	1	no	—
278	Q₁₆	—	2	2	no	—
279	Q₁₆	—	218	2	no	—
280	Q₁₆	—	218	2	no	—
281	Q₁₆	—	218	2	no	—
282	SD₁₆	—	2	2	no	—
283	SD₁₆	—	218	2	no	—
284	SD₁₆	—	218	2	no	—
285	SD₁₆	—	218	2	no	—
286	C₂×C₈	—	109	1	no	—
287	C₂×C₈	—	109	1	no	—
288	C₂×C₈	—	218	2	no	—
289	C₂×C₈	—	218	2	no	—
290	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
291	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	109	1	no	—
294	C₄⋊C₄	—	218	1	no	—
295	C₄⋊C₄	—	218	1	no	—
296	C₄⋊C₄	—	218	1	no	—
297	C₄⋊C₄	—	218	1	no	—
298	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
299	C₂²⋊C₄	—	2	1	no	—
300	C₂²⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	218	1	no	—
302	C₂²⋊C₄	—	218	1	no	—
303	C₂²⋊C₄	—	218	1	no	—
304	C₂²⋊C₄	—	218	1	no	—
305	C₂²⋊C₄	—	218	1	no	—
306	C₂²⋊C₄	—	218	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	109	1	no	—
309	C₄²	—	109	1	no	—
310	C₄²	—	109	1	no	—
311	C₄²	—	218	1	no	—
312	C₄²	—	218	1	no	—
313	C₄²	—	218	1	no	—
314	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
315	C₂³	—	2	1	no	—
316	C₂³	—	109	1	no	—
317	C₂³	—	436	2	no	—
318	C₂³	—	436	2	no	—
319	C₂³	—	436	2	no	—
320	C₂³	—	218	1	no	—
321	Q₈	—	2	1	no	—
322	Q₈	—	2	1	no	—
323	Q₈	—	2	1	no	—
324	Q₈	—	109	2	no	—
325	Q₈	—	436	2	no	—
326	Q₈	—	218	4	no	—
327	Q₈	—	218	1	no	—
328	Q₈	—	218	1	no	—
329	Q₈	—	218	1	no	—
330	Q₈	D₄×D₁₀₉	1	2	yes	—
331	D₄	—	2	1	no	—
332	D₄	—	2	1	no	—
333	D₄	—	436	2	no	—
334	D₄	—	218	1	no	—
335	D₄	—	218	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	109	1	no	—
340	C₂×C₄	—	109	2	no	—
341	C₂×C₄	—	109	2	no	—
342	C₂×C₄	—	109	1	no	—
343	C₂×C₄	—	109	1	no	—
344	C₂×C₄	—	436	2	no	—
345	C₂×C₄	—	436	2	no	—
346	C₂×C₄	—	218	2	no	—
347	C₂×C₄	—	218	2	no	—
348	C₂×C₄	—	218	4	no	—
349	C₂×C₄	—	218	1	no	—
350	C₂×C₄	—	218	1	no	—
351	C₂×C₄	—	218	1	no	—
352	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
353	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
354	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	218	1	no	—
358	C₈	—	218	1	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	872	4	no	—
363	C₂²	—	109	2	no	—
364	C₂²	—	109	2	no	—
365	C₂²	—	109	2	no	—
366	C₂²	—	436	1	no	—
367	C₂²	—	436	1	no	—
368	C₂²	—	436	1	no	—
369	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	1	no	—
375	C₄	—	109	2	no	—
376	C₄	—	436	1	no	—
377	C₄	—	436	1	no	—
378	C₄	—	218	2	no	—
379	C₄	—	218	1	no	—
380	C₄	—	218	1	no	—
381	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
382	C₄	#41×D₁₀₉	1	1	yes	characteristic
383	C₂	—	8	1	no	—
384	C₂	—	872	1	no	—
385	C₂	—	109	4	no	—
386	C₂	#121×D₁₀₉	1	1	yes	characteristic
387	C₂	#135×D₁₀₉	1	1	yes	characteristic
388	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	#464×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	C₂×D₄×D₁₀₉	C₂²
hypercenter	#464	D₁₀₉
hypocenter	C₁₀₉	C₂×#464
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #464

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×D₁₀₉	C₂	semidirect
4. C₄×Q₈×D₁₀₉	C₂	semidirect
5. #20295251	C₂	semidirect
6. #20295250	C₂	semidirect
7. #20295249	C₂	semidirect
8. #20295248	C₂	semidirect
9. #20295247	C₂	semidirect
10. #20295246	C₂	semidirect
11. #20295245	C₂	semidirect
12. C₄⋊C₈×D₁₀₉	C₂	semidirect
13. #103×D₁₀₉	C₂	semidirect
15. #464×C₁₀₉	C₂	semidirect
19. C₂×Dic₄₃₆	C₂²	semidirect
20. C₂×#13182019	C₂²	semidirect
21. C₂×#13182019	C₂²	semidirect
34. Q₈×Dic₁₀₉	C₂²	semidirect
36. C₄×Dic₂₁₈	C₂²	semidirect
38. #16812664	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
54. C₂×Q₁₆×C₁₀₉	C₂²	semidirect
57. C₄×Q₈×C₁₀₉	C₂²	semidirect
58. C₄⋊C₈×C₁₀₉	C₂²	semidirect
59. #103×C₁₀₉	C₂²	semidirect
193. D₁₀₉	#464	direct (N × H)
195. C₁₀₉	C₂×#464	semidirect
207. #464	D₁₀₉	direct (N × H)
218. C₂×Q₁₆	C₂×D₁₀₉	semidirect
237. C₄×Q₈	C₂×D₁₀₉	semidirect
247. C₄⋊C₈	C₂×D₁₀₉	semidirect
251. #103	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×Q₁₆×D₁₀₉	2
C₂×SD₁₆×D₁₀₉	2
#124×D₁₀₉	2
C₄×Q₈×D₁₀₉	2
#20295251	2
#20295250	2
#20295249	2
#20295248	2
#20295247	2
#20295246	2
#20295245	2
C₄⋊C₈×D₁₀₉	2
#103×D₁₀₉	2
#102×D₁₀₉	2
#464×C₁₀₉	2
C₂×#464	109

Subgroups — #464×D109 #28372472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #464×D₁₀₉ #28372472