Subgroups — #440×D₁₀₉ #28371807

Order 13952.

544 conjugacy classes of subgroups.

The subgroup lattice has 376 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	C₄×Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic
4	#20295129	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295128	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295127	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295126	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295125	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295124	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295123	C₂	1	1	yes	maximal, characteristic, complemented
11	#107×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#103×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×D₁₀₉	C₂	1	1	yes	maximal, characteristic
14	#97×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#440×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	C₂²×C₄×D₁₀₉	—	2	1	no	—
19	C₂×#13182018	C₂²	1	1	yes	characteristic
20	C₂×#13182017	C₂²	1	1	yes	characteristic
21	C₂×#13182016	C₂²	1	1	yes	characteristic
22	SD₁₆×D₁₀₉	C₄	1	8	yes	complemented
23	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
24	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
25	Q₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
26	C₄×Dic₂₁₈	—	2	1	no	—
27	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
28	#16812664	—	2	1	no	—
29	#16812664	C₂²	1	1	yes	characteristic, complemented
30	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
31	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
32	#16812661	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊D₁₀₉	—	2	1	no	—
34	#16812659	—	2	1	no	—
35	C₄⋊C₄×D₁₀₉	—	2	1	no	—
36	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
37	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
38	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
39	C₄²×D₁₀₉	—	2	1	no	—
40	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
41	#16812633	C₂²	1	1	yes	characteristic, complemented
42	#16812632	C₂²	1	1	yes	characteristic, complemented
43	#16812632	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	#16812609	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	#107×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	#97×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	—	2	1	no	—
74	C₂×C₄×D₁₀₉	—	2	1	no	—
75	C₂×C₄×D₁₀₉	—	4	4	no	—
76	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
77	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
78	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
79	#13182018	C₂×C₄	1	4	yes	complemented
80	#13182017	C₂×C₄	1	4	yes	complemented
81	#13182016	C₂×C₄	1	4	yes	complemented
82	C₂×#11724784	C₂³	1	1	yes	characteristic
83	C₂×#11724784	C₂³	1	1	yes	characteristic
84	C₈×D₁₀₉	—	2	2	no	—
85	C₈×D₁₀₉	C₂×C₄	1	4	yes	complemented
86	C₄⋊Dic₁₀₉	—	2	1	no	—
87	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
88	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
89	#13182008	—	2	1	no	—
90	#13182008	—	2	1	no	—
91	#13182008	—	2	1	no	—
92	#13182008	—	2	1	no	—
93	C₂²⋊Dic₁₀₉	—	2	1	no	—
94	#13182006	—	2	1	no	—
95	#13182006	—	2	1	no	—
96	C₄×Dic₁₀₉	—	2	1	no	—
97	C₄×Dic₁₀₉	—	2	1	no	—
98	C₄×Dic₁₀₉	—	2	1	no	—
99	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
100	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
101	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
103	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₀₉	—	2	1	no	—
105	SD₁₆×C₁₀₉	C₂×C₄	1	4	yes	complemented
106	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₁₀₉	—	2	1	no	—
109	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
111	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
112	C₄²×C₁₀₉	—	2	1	no	—
113	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
114	C₂³×C₁₀₉	—	2	1	no	—
115	C₂²×D₁₀₉	—	2	1	no	—
116	C₂²×D₁₀₉	—	2	4	no	—
117	C₂²×D₁₀₉	—	4	2	no	—
118	C₂²×D₁₀₉	—	4	2	no	—
119	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
120	Q₈×C₁₀₉	—	2	1	no	—
121	Q₈×C₁₀₉	C₂²×C₄	1	2	yes	complemented
122	D₄×C₁₀₉	—	2	1	no	—
123	D₄×C₁₀₉	C₂²×C₄	1	2	yes	—
124	C₂×C₄×C₁₀₉	—	2	1	no	—
125	C₂×C₄×C₁₀₉	—	2	1	no	—
126	C₂×C₄×C₁₀₉	—	2	1	no	—
127	C₂×C₄×C₁₀₉	—	4	2	no	—
128	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
131	C₂²⋊D₁₀₉	—	2	4	no	—
132	C₂×Dic₁₀₉	—	2	1	no	—
133	C₂×Dic₁₀₉	—	2	1	no	—
134	C₂×Dic₁₀₉	—	2	1	no	—
135	C₂×Dic₁₀₉	—	4	2	no	—
136	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
139	D₄₃₆	—	2	1	no	—
140	D₄₃₆	C₂²×C₄	1	2	yes	—
141	C₄×D₁₀₉	—	2	4	no	—
142	C₄×D₁₀₉	—	2	2	no	—
143	C₄×D₁₀₉	—	2	2	no	—
144	C₄×D₁₀₉	—	4	2	no	—
145	C₄×D₁₀₉	—	4	2	no	—
146	C₄×D₁₀₉	—	4	2	no	—
147	C₄×D₁₀₉	—	4	2	no	—
148	C₄×D₁₀₉	C₂²×C₄	1	2	yes	—
149	C₄×D₁₀₉	#41	1	2	yes	—
150	Dic₂₁₈	—	2	1	no	—
151	Dic₂₁₈	—	2	4	no	—
152	Dic₂₁₈	C₂²×C₄	1	2	yes	complemented
153	C₈×C₁₀₉	—	2	1	no	—
154	C₈×C₁₀₉	C₂²×C₄	1	2	yes	complemented
155	#11724784	—	2	1	no	—
156	#11724784	C₂²×C₄	1	2	yes	complemented
157	C₂²×C₁₀₉	—	2	2	no	—
158	C₂²×C₁₀₉	—	4	1	no	—
159	C₂²×C₁₀₉	—	4	1	no	—
160	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×D₁₀₉	—	2	2	no	—
162	C₂×D₁₀₉	—	4	1	no	—
163	C₂×D₁₀₉	—	4	1	no	—
164	C₂×D₁₀₉	—	4	8	no	—
165	C₂×D₁₀₉	C₄×D₄	1	2	yes	—
166	C₂×D₁₀₉	AGL(1,ℤ/8)	1	2	yes	—
167	C₂×D₁₀₉	#137	1	2	yes	—
168	C₄×C₁₀₉	—	2	2	no	—
169	C₄×C₁₀₉	—	2	1	no	—
170	C₄×C₁₀₉	—	2	1	no	—
171	C₄×C₁₀₉	—	4	1	no	—
172	C₄×C₁₀₉	—	4	1	no	—
173	C₄×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
174	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
175	Dic₁₀₉	—	2	2	no	—
176	Dic₁₀₉	—	2	1	no	—
177	Dic₁₀₉	—	2	1	no	—
178	Dic₁₀₉	—	4	1	no	—
179	Dic₁₀₉	—	4	1	no	—
180	Dic₁₀₉	C₄×D₄	1	2	yes	—
181	C₂×C₁₀₉	—	4	2	no	—
182	C₂×C₁₀₉	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂×C₁₀₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂×C₁₀₉	C₂×#137	1	1	yes	characteristic
185	D₁₀₉	—	4	2	no	—
186	D₁₀₉	#440	1	4	yes	direct product factor
187	C₂×#440	—	109	1	no	maximal, Sylow
188	C₁₀₉	C₂×#440	1	1	yes	characteristic, complemented, Sylow
189	C₂²×SD₁₆	—	109	1	no	—
190	C₂×C₄×Q₈	—	109	1	no	—
191	C₂×C₄×D₄	—	109	1	no	—
192	#440	—	109	1	no	—
193	#440	—	109	1	no	—
194	#440	—	109	1	no	—
195	#440	—	109	1	no	—
196	#440	—	109	1	no	—
197	#440	—	109	1	no	—
198	#440	—	109	1	no	—
199	#440	D₁₀₉	1	1	yes	characteristic, direct product factor
200	C₂×#107	—	109	1	no	—
201	C₂×#103	—	109	1	no	—
202	C₂×#102	—	109	1	no	—
203	C₂×#97	—	109	1	no	—
204	C₂²×Q₈	—	109	1	no	—
205	C₂²×D₄	—	109	1	no	—
206	C₂³×C₄	—	218	1	no	—
207	C₂×SD₁₆	—	109	1	no	—
208	C₂×SD₁₆	—	109	1	no	—
209	C₂×SD₁₆	—	109	8	no	—
210	C₂×SD₁₆	—	109	1	no	—
211	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic
212	C₂²×C₈	—	109	1	no	—
213	C₂²×C₈	—	109	1	no	—
214	C₄×Q₈	—	109	1	no	—
215	C₄×Q₈	—	109	1	no	—
216	C₄×Q₈	—	109	1	no	—
217	C₄×Q₈	—	218	1	no	—
218	C₄×Q₈	—	218	1	no	—
219	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
220	C₄×D₄	—	109	1	no	—
221	C₄×D₄	—	109	1	no	—
222	C₄×D₄	—	109	1	no	—
223	C₄×D₄	—	218	1	no	—
224	C₄×D₄	—	218	1	no	—
225	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
226	C₂×C₄⋊C₄	—	109	1	no	—
227	C₂×C₄⋊C₄	—	109	1	no	—
228	C₂×C₄⋊C₄	—	218	1	no	—
229	C₂×C₂²⋊C₄	—	218	1	no	—
230	C₂×C₄²	—	109	1	no	—
231	C₂×C₄²	—	218	1	no	—
232	#107	—	109	1	no	—
233	#107	—	109	1	no	—
234	#107	—	109	1	no	—
235	#107	C₂×D₁₀₉	1	1	yes	characteristic, complemented
236	#103	—	109	1	no	—
237	#103	—	109	1	no	—
238	#103	—	109	1	no	—
239	#103	C₂×D₁₀₉	1	1	yes	characteristic, complemented
240	#102	—	109	1	no	—
241	#102	—	109	1	no	—
242	#102	—	109	1	no	—
243	#102	C₂×D₁₀₉	1	1	yes	characteristic
244	#97	—	109	1	no	—
245	#97	—	109	1	no	—
246	#97	—	109	1	no	—
247	#97	C₂×D₁₀₉	1	1	yes	characteristic, complemented
248	C₂⁴	—	218	1	no	—
249	C₂×Q₈	—	109	4	no	—
250	C₂×Q₈	—	109	1	no	—
251	C₂×Q₈	—	218	1	no	—
252	C₂×Q₈	—	218	2	no	—
253	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
254	C₂×D₄	—	109	4	no	—
255	C₂×D₄	—	109	1	no	—
256	C₂×D₄	—	218	2	no	—
257	C₂×D₄	—	218	1	no	—
258	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	109	1	no	—
261	C₂²×C₄	—	109	1	no	—
262	C₂²×C₄	—	109	1	no	—
263	C₂²×C₄	—	436	4	no	—
264	C₂²×C₄	—	218	1	no	—
265	C₂²×C₄	—	218	1	no	—
266	C₂²×C₄	—	218	1	no	—
267	C₂²×C₄	—	218	1	no	—
268	C₂²×C₄	—	218	1	no	—
269	C₂²×C₄	—	218	1	no	—
270	SD₁₆	—	109	4	no	—
271	SD₁₆	—	109	4	no	—
272	SD₁₆	—	109	4	no	—
273	SD₁₆	C₄×D₁₀₉	1	4	yes	complemented
274	C₂×C₈	—	109	1	no	—
275	C₂×C₈	—	109	4	no	—
276	C₂×C₈	—	109	1	no	—
277	C₂×C₈	—	218	2	no	—
278	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
279	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	109	1	no	—
282	C₄⋊C₄	—	109	1	no	—
283	C₄⋊C₄	—	218	1	no	—
284	C₄⋊C₄	—	218	1	no	—
285	C₄⋊C₄	—	218	1	no	—
286	C₄⋊C₄	—	218	1	no	—
287	C₄⋊C₄	—	218	1	no	—
288	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
289	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	218	1	no	—
292	C₂²⋊C₄	—	218	1	no	—
293	C₂²⋊C₄	—	218	1	no	—
294	C₄²	—	2	1	no	—
295	C₄²	—	109	1	no	—
296	C₄²	—	109	1	no	—
297	C₄²	—	109	1	no	—
298	C₄²	—	218	1	no	—
299	C₄²	—	218	1	no	—
300	C₄²	—	218	1	no	—
301	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
302	C₂³	—	2	1	no	—
303	C₂³	—	109	1	no	—
304	C₂³	—	436	2	no	—
305	C₂³	—	436	2	no	—
306	C₂³	—	218	4	no	—
307	C₂³	—	218	1	no	—
308	Q₈	—	2	1	no	—
309	Q₈	—	109	2	no	—
310	Q₈	—	218	4	no	—
311	Q₈	—	218	1	no	—
312	Q₈	C₂×C₄×D₁₀₉	1	2	yes	complemented
313	D₄	—	2	1	no	—
314	D₄	—	109	2	no	—
315	D₄	—	218	4	no	—
316	D₄	—	218	1	no	—
317	D₄	C₂×C₄×D₁₀₉	1	2	yes	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	109	1	no	—
323	C₂×C₄	—	109	2	no	—
324	C₂×C₄	—	109	2	no	—
325	C₂×C₄	—	109	1	no	—
326	C₂×C₄	—	109	1	no	—
327	C₂×C₄	—	436	2	no	—
328	C₂×C₄	—	436	2	no	—
329	C₂×C₄	—	436	2	no	—
330	C₂×C₄	—	436	2	no	—
331	C₂×C₄	—	436	2	no	—
332	C₂×C₄	—	218	2	no	—
333	C₂×C₄	—	218	2	no	—
334	C₂×C₄	—	218	4	no	—
335	C₂×C₄	—	218	1	no	—
336	C₂×C₄	—	218	1	no	—
337	C₂×C₄	—	218	1	no	—
338	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
339	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
340	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
341	C₈	—	2	1	no	—
342	C₈	—	109	2	no	—
343	C₈	—	218	1	no	—
344	C₈	C₂×C₄×D₁₀₉	1	2	yes	complemented
345	C₂²	—	2	2	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	109	2	no	—
349	C₂²	—	109	2	no	—
350	C₂²	—	109	2	no	—
351	C₂²	—	436	8	no	—
352	C₂²	—	436	1	no	—
353	C₂²	—	436	1	no	—
354	C₂²	—	218	2	no	—
355	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	109	2	no	—
362	C₄	—	436	1	no	—
363	C₄	—	436	1	no	—
364	C₄	—	218	2	no	—
365	C₄	—	218	1	no	—
366	C₄	—	218	1	no	—
367	C₄	C₂²×C₄×D₁₀₉	1	1	yes	characteristic
368	C₄	#41×D₁₀₉	1	1	yes	characteristic
369	C₂	—	4	2	no	—
370	C₂	—	109	4	no	—
371	C₂	—	436	2	no	—
372	C₂	C₄×D₄×D₁₀₉	1	1	yes	characteristic
373	C₂	AGL(1,ℤ/8)×D₁₀₉	1	1	yes	characteristic
374	C₂	#137×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator	C₄×C₁₀₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	#440×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	C₂×D₄×D₁₀₉	C₂²
cosocle	C₂×C₄×C₁₀₉	C₂⁴
hypercenter	#440	D₁₀₉
hypocenter	C₁₀₉	C₂×#440
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #440

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×D₁₀₉	C₂	semidirect
4. #20295129	C₂	semidirect
5. #20295128	C₂	semidirect
6. #20295127	C₂	semidirect
7. #20295126	C₂	semidirect
8. #20295125	C₂	semidirect
9. #20295124	C₂	semidirect
10. #20295123	C₂	semidirect
11. #107×D₁₀₉	C₂	semidirect
12. #103×D₁₀₉	C₂	semidirect
14. #97×D₁₀₉	C₂	semidirect
15. #440×C₁₀₉	C₂	semidirect
22. SD₁₆×D₁₀₉	C₄	semidirect
25. Q₈×Dic₁₀₉	C₂²	semidirect
27. C₄×Dic₂₁₈	C₂²	semidirect
29. #16812664	C₂²	semidirect
41. #16812633	C₂²	semidirect
42. #16812632	C₂²	semidirect
43. #16812632	C₂²	semidirect
44. #16812624	C₂²	semidirect
45. #16812623	C₂²	semidirect
46. #16812622	C₂²	semidirect
50. #16812610	C₂²	semidirect
51. #16812609	C₂²	semidirect
52. #16812609	C₂²	semidirect
54. C₄×Q₈×C₁₀₉	C₂²	semidirect
56. #107×C₁₀₉	C₂²	semidirect
57. #103×C₁₀₉	C₂²	semidirect
59. #97×C₁₀₉	C₂²	semidirect
64. Q₈×D₁₀₉	C₂×C₄	semidirect
79. #13182018	C₂×C₄	semidirect
80. #13182017	C₂×C₄	semidirect
81. #13182016	C₂×C₄	semidirect
85. C₈×D₁₀₉	C₂×C₄	semidirect
105. SD₁₆×C₁₀₉	C₂×C₄	semidirect
121. Q₈×C₁₀₉	C₂²×C₄	semidirect
152. Dic₂₁₈	C₂²×C₄	semidirect
154. C₈×C₁₀₉	C₂²×C₄	semidirect
156. #11724784	C₂²×C₄	semidirect
186. D₁₀₉	#440	direct (N × H)
188. C₁₀₉	C₂×#440	semidirect
199. #440	D₁₀₉	direct (N × H)
219. C₄×Q₈	C₂×D₁₀₉	semidirect
235. #107	C₂×D₁₀₉	semidirect
239. #103	C₂×D₁₀₉	semidirect
247. #97	C₂×D₁₀₉	semidirect
273. SD₁₆	C₄×D₁₀₉	semidirect
312. Q₈	C₂×C₄×D₁₀₉	semidirect
344. C₈	C₂×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
C₄×Q₈×D₁₀₉	2
C₄×D₄×D₁₀₉	2
#20295129	2
#20295128	2
#20295127	2
#20295126	2
#20295125	2
#20295124	2
#20295123	2
#107×D₁₀₉	2
#103×D₁₀₉	2
#102×D₁₀₉	2
#97×D₁₀₉	2
#440×C₁₀₉	2
C₂×#440	109

Subgroups — #440×D109 #28371807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #440×D₁₀₉ #28371807