Subgroups — C₂×C₄×D₄×D₁₀₉ #28376199

Order 13952.

2528 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×D₁₀₉	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₄₃₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16812661	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×C₂²⋊D₁₀₉	C₂	1	2	yes	maximal, complemented
7	C₂×#16812659	C₂	1	2	yes	maximal, complemented
8	C₄×D₄×D₁₀₉	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₄⋊C₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂²⋊C₄×D₁₀₉	C₂	1	2	yes	maximal, complemented
11	C₂×C₄²×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₁₀₉	C₂²	1	2	yes	—
14	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊D₁₀₉	C₂²	1	2	yes	—
16	C₂×D₄×D₁₀₉	C₄	1	16	yes	direct product factor
17	C₂×D₄×D₁₀₉	C₂²	1	8	yes	—
18	C₂³×Dic₁₀₉	C₂²	1	2	yes	complemented
19	C₂²×C₄×D₁₀₉	—	2	16	no	—
20	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	—
22	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	complemented
25	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	complemented
26	C₂²×C₄×D₁₀₉	C₂²	1	16	yes	complemented
27	C₄×D₄₃₆	C₂²	1	8	yes	complemented
28	D₄×Dic₁₀₉	C₂²	1	8	yes	complemented
29	#16812661	C₂²	1	8	yes	complemented
30	C₄×C₂²⋊D₁₀₉	C₂²	1	16	yes	complemented
31	#16812659	C₂²	1	16	yes	complemented
32	C₂×C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×#13182008	C₂²	1	2	yes	complemented
34	C₄⋊C₄×D₁₀₉	C₂²	1	8	yes	complemented
35	C₂×C₂²⋊Dic₁₀₉	C₂²	1	2	yes	complemented
36	C₂×#13182006	C₂²	1	2	yes	complemented
37	C₂×#13182006	C₂²	1	2	yes	complemented
38	C₂²⋊C₄×D₁₀₉	C₂²	1	16	yes	complemented
39	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
42	C₄²×D₁₀₉	C₂²	1	8	yes	complemented
43	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
44	C₂³×C₄×C₁₀₉	C₂²	1	2	yes	complemented
45	C₄×D₄×C₁₀₉	C₂²	1	8	yes	complemented
46	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
48	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
49	C₂³×D₁₀₉	—	2	8	no	—
50	C₂³×D₁₀₉	—	2	8	no	—
51	C₂³×D₁₀₉	C₂×C₄	1	16	yes	complemented
52	C₂³×D₁₀₉	C₂³	1	8	yes	—
53	C₂³×D₁₀₉	C₂³	1	2	yes	—
54	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
55	C₂×D₄₃₆	C₂×C₄	1	8	yes	complemented
56	C₂×D₄₃₆	C₂³	1	4	yes	—
57	C₂×C₂²⋊D₁₀₉	C₂×C₄	1	16	yes	complemented
58	C₂×C₂²⋊D₁₀₉	C₂³	1	8	yes	—
59	D₄×D₁₀₉	C₂×C₄	1	64	yes	direct product factor
60	C₂²×Dic₁₀₉	—	2	8	no	—
61	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
62	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
63	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
64	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
65	C₂²×Dic₁₀₉	C₂³	1	8	yes	complemented
66	C₂×C₄×D₁₀₉	—	2	8	no	—
67	C₂×C₄×D₁₀₉	—	2	4	no	—
68	C₂×C₄×D₁₀₉	—	2	8	no	—
69	C₂×C₄×D₁₀₉	—	2	8	no	—
70	C₂×C₄×D₁₀₉	—	2	64	no	—
71	C₂×C₄×D₁₀₉	C₂×C₄	1	8	yes	complemented
72	C₂×C₄×D₁₀₉	D₄	1	8	yes	direct product factor
73	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
74	C₂×C₄×D₁₀₉	C₂³	1	8	yes	—
75	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
76	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
77	C₂×C₄×D₁₀₉	C₂³	1	8	yes	complemented
78	C₂×C₄×D₁₀₉	C₂³	1	8	yes	complemented
79	C₄⋊Dic₁₀₉	C₂³	1	4	yes	complemented
80	#13182008	C₂³	1	8	yes	complemented
81	C₂²⋊Dic₁₀₉	C₂³	1	8	yes	complemented
82	#13182006	C₂³	1	8	yes	complemented
83	#13182006	C₂³	1	8	yes	complemented
84	C₄×Dic₁₀₉	C₂³	1	4	yes	complemented
85	C₄×Dic₁₀₉	C₂³	1	4	yes	complemented
86	C₄×Dic₁₀₉	C₂³	1	4	yes	complemented
87	C₂⁴×C₁₀₉	C₂³	1	2	yes	—
88	C₂×D₄×C₁₀₉	C₂×C₄	1	8	yes	complemented
89	C₂×D₄×C₁₀₉	C₂³	1	4	yes	—
90	C₂²×C₄×C₁₀₉	—	2	8	no	—
91	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
93	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₀₉	C₂³	1	8	yes	complemented
96	C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
97	C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	complemented
98	C₄²×C₁₀₉	C₂³	1	4	yes	complemented
99	C₂³×C₁₀₉	—	2	4	no	—
100	C₂³×C₁₀₉	—	2	4	no	—
101	C₂³×C₁₀₉	C₂²×C₄	1	8	yes	complemented
102	C₂³×C₁₀₉	C₂⁴	1	4	yes	—
103	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
104	C₂²×D₁₀₉	—	2	4	no	—
105	C₂²×D₁₀₉	—	2	4	no	—
106	C₂²×D₁₀₉	—	2	64	no	—
107	C₂²×D₁₀₉	—	2	16	no	—
108	C₂²×D₁₀₉	—	2	16	no	—
109	C₂²×D₁₀₉	C₂²×C₄	1	4	yes	—
110	C₂²×D₁₀₉	C₂²×C₄	1	32	yes	complemented
111	C₂²×D₁₀₉	C₂²×C₄	1	8	yes	complemented
112	C₂²×D₁₀₉	C₂×D₄	1	4	yes	—
113	C₂²×D₁₀₉	#41	1	4	yes	—
114	C₂²×D₁₀₉	C₂⁴	1	4	yes	—
115	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
116	D₄×C₁₀₉	C₂²×C₄	1	16	yes	complemented
117	C₂×C₄×C₁₀₉	—	2	4	no	—
118	C₂×C₄×C₁₀₉	—	2	2	no	—
119	C₂×C₄×C₁₀₉	—	2	16	no	—
120	C₂×C₄×C₁₀₉	C₂²×C₄	1	4	yes	complemented
121	C₂×C₄×C₁₀₉	C₂×D₄	1	4	yes	complemented
122	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
123	C₂×C₄×C₁₀₉	C₂⁴	1	4	yes	—
124	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
125	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
126	C₂²⋊D₁₀₉	C₂²×C₄	1	32	yes	complemented
127	C₂×Dic₁₀₉	—	2	4	no	—
128	C₂×Dic₁₀₉	—	2	2	no	—
129	C₂×Dic₁₀₉	—	2	16	no	—
130	C₂×Dic₁₀₉	C₂²×C₄	1	4	yes	complemented
131	C₂×Dic₁₀₉	C₂×D₄	1	4	yes	complemented
132	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
133	C₂×Dic₁₀₉	C₂⁴	1	4	yes	—
134	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
135	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
136	D₄₃₆	C₂²×C₄	1	16	yes	complemented
137	C₄×D₁₀₉	—	2	16	no	—
138	C₄×D₁₀₉	—	2	8	no	—
139	C₄×D₁₀₉	—	2	16	no	—
140	C₄×D₁₀₉	—	2	16	no	—
141	C₄×D₁₀₉	C₂²×C₄	1	16	yes	complemented
142	C₄×D₁₀₉	C₂×D₄	1	16	yes	direct product factor
143	C₂²×C₁₀₉	—	2	16	no	—
144	C₂²×C₁₀₉	—	2	4	no	—
145	C₂²×C₁₀₉	—	2	4	no	—
146	C₂²×C₁₀₉	C₂³×C₄	1	2	yes	—
147	C₂²×C₁₀₉	C₂³×C₄	1	8	yes	complemented
148	C₂²×C₁₀₉	C₂²×D₄	1	2	yes	—
149	C₂²×C₁₀₉	C₂×#41	1	2	yes	—
150	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
151	C₂×D₁₀₉	—	2	16	no	—
152	C₂×D₁₀₉	—	2	4	no	—
153	C₂×D₁₀₉	—	2	4	no	—
154	C₂×D₁₀₉	—	2	64	no	—
155	C₂×D₁₀₉	C₄×D₄	1	16	yes	direct product factor
156	C₂×D₁₀₉	C₂³×C₄	1	4	yes	—
157	C₂×D₁₀₉	C₂³×C₄	1	8	yes	complemented
158	C₂×D₁₀₉	C₂²×D₄	1	4	yes	—
159	C₂×D₁₀₉	C₂×#41	1	4	yes	—
160	C₄×C₁₀₉	—	2	4	no	—
161	C₄×C₁₀₉	—	2	2	no	—
162	C₄×C₁₀₉	C₂³×C₄	1	4	yes	complemented
163	C₄×C₁₀₉	C₂²×D₄	1	4	yes	complemented
164	Dic₁₀₉	—	2	4	no	—
165	Dic₁₀₉	—	2	2	no	—
166	Dic₁₀₉	C₂³×C₄	1	4	yes	complemented
167	Dic₁₀₉	C₂²×D₄	1	4	yes	complemented
168	C₂×C₁₀₉	—	2	8	no	—
169	C₂×C₁₀₉	C₂×C₄×D₄	1	4	yes	complemented
170	C₂×C₁₀₉	C₂⁴×C₄	1	1	yes	characteristic
171	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
172	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
173	D₁₀₉	—	2	8	no	—
174	D₁₀₉	C₂×C₄×D₄	1	8	yes	direct product factor
175	C₂²×C₄×D₄	—	109	1	no	maximal, Sylow
176	C₁₀₉	C₂²×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
177	C₂³×D₄	—	109	1	no	—
178	C₂⁴×C₄	—	109	2	no	—
179	C₂×C₄×D₄	—	109	1	no	—
180	C₂×C₄×D₄	—	109	2	no	—
181	C₂×C₄×D₄	—	109	16	no	—
182	C₂×C₄×D₄	—	109	1	no	—
183	C₂×C₄×D₄	—	109	2	no	—
184	C₂×C₄×D₄	—	109	1	no	—
185	C₂×C₄×D₄	D₁₀₉	1	1	yes	characteristic, direct product factor
186	C₂²×C₄⋊C₄	—	109	1	no	—
187	C₂²×C₂²⋊C₄	—	109	2	no	—
188	C₂²×C₄²	—	109	1	no	—
189	C₂⁵	—	109	2	no	—
190	C₂²×D₄	—	109	2	no	—
191	C₂²×D₄	—	109	16	no	—
192	C₂²×D₄	—	109	8	no	—
193	C₂²×D₄	—	109	1	no	—
194	C₂²×D₄	C₂×D₁₀₉	1	1	yes	characteristic
195	C₂³×C₄	—	109	1	no	—
196	C₂³×C₄	—	109	1	no	—
197	C₂³×C₄	—	109	2	no	—
198	C₂³×C₄	—	109	1	no	—
199	C₂³×C₄	—	109	2	no	—
200	C₂³×C₄	—	109	2	no	—
201	C₂³×C₄	—	109	2	no	—
202	C₂³×C₄	—	109	16	no	—
203	C₂³×C₄	—	218	16	no	—
204	C₂³×C₄	C₂×D₁₀₉	1	2	yes	complemented
205	C₄×D₄	—	109	8	no	—
206	C₄×D₄	—	109	16	no	—
207	C₄×D₄	—	109	8	no	—
208	C₄×D₄	—	109	16	no	—
209	C₄×D₄	—	109	8	no	—
210	C₄×D₄	C₂×D₁₀₉	1	8	yes	direct product factor
211	C₂×C₄⋊C₄	—	109	2	no	—
212	C₂×C₄⋊C₄	—	109	1	no	—
213	C₂×C₄⋊C₄	—	109	8	no	—
214	C₂×C₄⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
215	C₂×C₂²⋊C₄	—	109	2	no	—
216	C₂×C₂²⋊C₄	—	109	2	no	—
217	C₂×C₂²⋊C₄	—	109	2	no	—
218	C₂×C₂²⋊C₄	—	109	16	no	—
219	C₂×C₂²⋊C₄	C₂×D₁₀₉	1	2	yes	complemented
220	C₂×C₄²	—	109	1	no	—
221	C₂×C₄²	—	109	1	no	—
222	C₂×C₄²	—	109	1	no	—
223	C₂×C₄²	—	109	8	no	—
224	C₂×C₄²	C₂×D₁₀₉	1	1	yes	characteristic, complemented
225	C₂⁴	—	109	1	no	—
226	C₂⁴	—	109	16	no	—
227	C₂⁴	—	109	8	no	—
228	C₂⁴	—	109	2	no	—
229	C₂⁴	—	218	8	no	—
230	C₂⁴	—	218	8	no	—
231	C₂⁴	C₂²×D₁₀₉	1	2	yes	—
232	C₂×D₄	—	109	16	no	—
233	C₂×D₄	—	109	8	no	—
234	C₂×D₄	—	109	64	no	—
235	C₂×D₄	—	109	8	no	—
236	C₂×D₄	—	109	4	no	—
237	C₂×D₄	C₄×D₁₀₉	1	8	yes	direct product factor
238	C₂×D₄	C₂²×D₁₀₉	1	4	yes	—
239	C₂²×C₄	—	2	8	no	—
240	C₂²×C₄	—	109	1	no	—
241	C₂²×C₄	—	109	1	no	—
242	C₂²×C₄	—	109	8	no	—
243	C₂²×C₄	—	109	8	no	—
244	C₂²×C₄	—	109	4	no	—
245	C₂²×C₄	—	109	4	no	—
246	C₂²×C₄	—	109	1	no	—
247	C₂²×C₄	—	109	2	no	—
248	C₂²×C₄	—	109	8	no	—
249	C₂²×C₄	—	109	4	no	—
250	C₂²×C₄	—	109	8	no	—
251	C₂²×C₄	—	109	8	no	—
252	C₂²×C₄	—	109	8	no	—
253	C₂²×C₄	—	218	8	no	—
254	C₂²×C₄	—	218	64	no	—
255	C₂²×C₄	—	218	4	no	—
256	C₂²×C₄	—	218	8	no	—
257	C₂²×C₄	—	218	8	no	—
258	C₂²×C₄	—	218	8	no	—
259	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
260	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
261	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
262	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
263	C₂²×C₄	C₂²×D₁₀₉	1	8	yes	complemented
264	C₄⋊C₄	—	109	8	no	—
265	C₄⋊C₄	—	109	4	no	—
266	C₄⋊C₄	C₂²×D₁₀₉	1	4	yes	complemented
267	C₂²⋊C₄	—	109	8	no	—
268	C₂²⋊C₄	—	109	8	no	—
269	C₂²⋊C₄	—	109	8	no	—
270	C₂²⋊C₄	C₂²×D₁₀₉	1	8	yes	complemented
271	C₄²	—	109	4	no	—
272	C₄²	—	109	4	no	—
273	C₄²	—	109	4	no	—
274	C₄²	C₂²×D₁₀₉	1	4	yes	complemented
275	C₂³	—	2	4	no	—
276	C₂³	—	2	4	no	—
277	C₂³	—	109	4	no	—
278	C₂³	—	109	4	no	—
279	C₂³	—	109	4	no	—
280	C₂³	—	109	2	no	—
281	C₂³	—	109	8	no	—
282	C₂³	—	109	32	no	—
283	C₂³	—	109	4	no	—
284	C₂³	—	218	16	no	—
285	C₂³	—	218	64	no	—
286	C₂³	—	218	16	no	—
287	C₂³	—	218	4	no	—
288	C₂³	—	218	4	no	—
289	C₂³	C₂×C₄×D₁₀₉	1	8	yes	complemented
290	C₂³	C₂³×D₁₀₉	1	4	yes	—
291	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
292	D₄	—	109	32	no	—
293	D₄	—	109	16	no	—
294	D₄	C₂×C₄×D₁₀₉	1	16	yes	direct product factor
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	16	no	—
298	C₂×C₄	—	109	4	no	—
299	C₂×C₄	—	109	4	no	—
300	C₂×C₄	—	109	2	no	—
301	C₂×C₄	—	109	2	no	—
302	C₂×C₄	—	109	16	no	—
303	C₂×C₄	—	109	16	no	—
304	C₂×C₄	—	109	2	no	—
305	C₂×C₄	—	109	4	no	—
306	C₂×C₄	—	218	16	no	—
307	C₂×C₄	—	218	16	no	—
308	C₂×C₄	—	218	8	no	—
309	C₂×C₄	—	218	16	no	—
310	C₂×C₄	—	218	4	no	—
311	C₂×C₄	—	218	2	no	—
312	C₂×C₄	—	218	16	no	—
313	C₂×C₄	C₂×C₄×D₁₀₉	1	4	yes	complemented
314	C₂×C₄	D₄×D₁₀₉	1	4	yes	direct product factor
315	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
316	C₂×C₄	C₂³×D₁₀₉	1	4	yes	—
317	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
318	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
319	C₂²	—	2	16	no	—
320	C₂²	—	2	4	no	—
321	C₂²	—	2	4	no	—
322	C₂²	—	109	16	no	—
323	C₂²	—	109	4	no	—
324	C₂²	—	109	4	no	—
325	C₂²	—	109	4	no	—
326	C₂²	—	109	8	no	—
327	C₂²	—	218	64	no	—
328	C₂²	—	218	16	no	—
329	C₂²	—	218	4	no	—
330	C₂²	—	218	4	no	—
331	C₂²	C₂²×C₄×D₁₀₉	1	2	yes	—
332	C₂²	C₂²×C₄×D₁₀₉	1	8	yes	complemented
333	C₂²	C₂×D₄×D₁₀₉	1	2	yes	—
334	C₂²	#41×D₁₀₉	1	2	yes	—
335	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
336	C₄	—	2	4	no	—
337	C₄	—	2	2	no	—
338	C₄	—	109	4	no	—
339	C₄	—	109	4	no	—
340	C₄	—	218	4	no	—
341	C₄	—	218	2	no	—
342	C₄	C₂²×C₄×D₁₀₉	1	4	yes	complemented
343	C₄	C₂×D₄×D₁₀₉	1	4	yes	direct product factor
344	C₂	—	2	8	no	—
345	C₂	—	109	8	no	—
346	C₂	—	218	8	no	—
347	C₂	C₄×D₄×D₁₀₉	1	4	yes	direct product factor
348	C₂	C₂³×C₄×D₁₀₉	1	1	yes	characteristic
349	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic
350	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₀₉
commutator	C₂×C₁₀₉	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₁₀₉
Fitting	C₂×C₄×D₄×C₁₀₉	C₂
socle	C₂³×C₁₀₉	C₂⁴
prime radical	C₂²×D₄×D₁₀₉	C₂
cosocle	C₂²×C₁₀₉	C₂⁵
hypercenter	C₂×C₄×D₄	D₁₀₉
hypocenter	C₁₀₉	C₂²×C₄×D₄
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄×D₁₀₉	C₂	semidirect
3. C₂×C₄×D₄₃₆	C₂	semidirect
4. C₂×D₄×Dic₁₀₉	C₂	semidirect
5. C₂×#16812661	C₂	semidirect
6. C₂×C₄×C₂²⋊D₁₀₉	C₂	semidirect
7. C₂×#16812659	C₂	semidirect
8. C₄×D₄×D₁₀₉	C₂	direct (N × H)
9. C₂×C₄⋊C₄×D₁₀₉	C₂	semidirect
10. C₂×C₂²⋊C₄×D₁₀₉	C₂	semidirect
11. C₂×C₄²×D₁₀₉	C₂	semidirect
12. C₂×C₄×D₄×C₁₀₉	C₂	semidirect
16. C₂×D₄×D₁₀₉	C₄	direct (N × H)
18. C₂³×Dic₁₀₉	C₂²	semidirect
24. C₂²×C₄×D₁₀₉	C₂²	semidirect
25. C₂²×C₄×D₁₀₉	C₂²	semidirect
26. C₂²×C₄×D₁₀₉	C₂²	semidirect
27. C₄×D₄₃₆	C₂²	semidirect
28. D₄×Dic₁₀₉	C₂²	semidirect
29. #16812661	C₂²	semidirect
30. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
31. #16812659	C₂²	semidirect
32. C₂×C₄⋊Dic₁₀₉	C₂²	semidirect
33. C₂×#13182008	C₂²	semidirect
34. C₄⋊C₄×D₁₀₉	C₂²	semidirect
35. C₂×C₂²⋊Dic₁₀₉	C₂²	semidirect
36. C₂×#13182006	C₂²	semidirect
37. C₂×#13182006	C₂²	semidirect
38. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
39. C₂×C₄×Dic₁₀₉	C₂²	semidirect
40. C₂×C₄×Dic₁₀₉	C₂²	semidirect
41. C₂×C₄×Dic₁₀₉	C₂²	semidirect
42. C₄²×D₁₀₉	C₂²	semidirect
44. C₂³×C₄×C₁₀₉	C₂²	semidirect
45. C₄×D₄×C₁₀₉	C₂²	semidirect
46. C₂×C₄⋊C₄×C₁₀₉	C₂²	semidirect
47. C₂×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
48. C₂×C₄²×C₁₀₉	C₂²	semidirect
51. C₂³×D₁₀₉	C₂×C₄	semidirect
55. C₂×D₄₃₆	C₂×C₄	semidirect
57. C₂×C₂²⋊D₁₀₉	C₂×C₄	semidirect
59. D₄×D₁₀₉	C₂×C₄	direct (N × H)
65. C₂²×Dic₁₀₉	C₂³	semidirect
71. C₂×C₄×D₁₀₉	C₂×C₄	semidirect
72. C₂×C₄×D₁₀₉	D₄	direct (N × H)
77. C₂×C₄×D₁₀₉	C₂³	semidirect
78. C₂×C₄×D₁₀₉	C₂³	semidirect
79. C₄⋊Dic₁₀₉	C₂³	semidirect
80. #13182008	C₂³	semidirect
81. C₂²⋊Dic₁₀₉	C₂³	semidirect
82. #13182006	C₂³	semidirect
83. #13182006	C₂³	semidirect
84. C₄×Dic₁₀₉	C₂³	semidirect
85. C₄×Dic₁₀₉	C₂³	semidirect
86. C₄×Dic₁₀₉	C₂³	semidirect
88. C₂×D₄×C₁₀₉	C₂×C₄	semidirect
95. C₂²×C₄×C₁₀₉	C₂³	semidirect
96. C₄⋊C₄×C₁₀₉	C₂³	semidirect
97. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
98. C₄²×C₁₀₉	C₂³	semidirect
101. C₂³×C₁₀₉	C₂²×C₄	semidirect
110. C₂²×D₁₀₉	C₂²×C₄	semidirect
111. C₂²×D₁₀₉	C₂²×C₄	semidirect
116. D₄×C₁₀₉	C₂²×C₄	semidirect
120. C₂×C₄×C₁₀₉	C₂²×C₄	semidirect
121. C₂×C₄×C₁₀₉	C₂×D₄	semidirect
126. C₂²⋊D₁₀₉	C₂²×C₄	semidirect
130. C₂×Dic₁₀₉	C₂²×C₄	semidirect
131. C₂×Dic₁₀₉	C₂×D₄	semidirect
136. D₄₃₆	C₂²×C₄	semidirect
141. C₄×D₁₀₉	C₂²×C₄	semidirect
142. C₄×D₁₀₉	C₂×D₄	direct (N × H)
147. C₂²×C₁₀₉	C₂³×C₄	semidirect
155. C₂×D₁₀₉	C₄×D₄	direct (N × H)
157. C₂×D₁₀₉	C₂³×C₄	semidirect
162. C₄×C₁₀₉	C₂³×C₄	semidirect
163. C₄×C₁₀₉	C₂²×D₄	semidirect
166. Dic₁₀₉	C₂³×C₄	semidirect
167. Dic₁₀₉	C₂²×D₄	semidirect
169. C₂×C₁₀₉	C₂×C₄×D₄	semidirect
174. D₁₀₉	C₂×C₄×D₄	direct (N × H)
176. C₁₀₉	C₂²×C₄×D₄	semidirect
185. C₂×C₄×D₄	D₁₀₉	direct (N × H)
204. C₂³×C₄	C₂×D₁₀₉	semidirect
210. C₄×D₄	C₂×D₁₀₉	direct (N × H)
214. C₂×C₄⋊C₄	C₂×D₁₀₉	semidirect
219. C₂×C₂²⋊C₄	C₂×D₁₀₉	semidirect
224. C₂×C₄²	C₂×D₁₀₉	semidirect
237. C₂×D₄	C₄×D₁₀₉	direct (N × H)
263. C₂²×C₄	C₂²×D₁₀₉	semidirect
266. C₄⋊C₄	C₂²×D₁₀₉	semidirect
270. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
274. C₄²	C₂²×D₁₀₉	semidirect
289. C₂³	C₂×C₄×D₁₀₉	semidirect
294. D₄	C₂×C₄×D₁₀₉	direct (N × H)
313. C₂×C₄	C₂×C₄×D₁₀₉	semidirect
314. C₂×C₄	D₄×D₁₀₉	direct (N × H)
332. C₂²	C₂²×C₄×D₁₀₉	semidirect
342. C₄	C₂²×C₄×D₁₀₉	semidirect
343. C₄	C₂×D₄×D₁₀₉	direct (N × H)
347. C₂	C₄×D₄×D₁₀₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×D₄×D₁₀₉	2
C₂³×C₄×D₁₀₉	2
C₂×C₄×D₄₃₆	2
C₂×D₄×Dic₁₀₉	2
C₂×#16812661	2
C₂×C₄×C₂²⋊D₁₀₉	2
C₂×#16812659	2
C₄×D₄×D₁₀₉	2
C₂×C₄⋊C₄×D₁₀₉	2
C₂×C₂²⋊C₄×D₁₀₉	2
C₂×C₄²×D₁₀₉	2
C₂×C₄×D₄×C₁₀₉	2
C₂²×C₄×D₄	109

Subgroups — C2×C4×D4×D109 #28376199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×D₄×D₁₀₉ #28376199