Subgroups — C₂×#20295498 #28376216

Order 13952.

1920 conjugacy classes of subgroups.

The subgroup lattice has 336 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	#20295498	C₂	1	16	yes	maximal, direct product factor
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	C₂×#16812657	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16812656	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#13182006	C₂	1	2	yes	maximal, complemented
11	C₂×C₂²⋊C₄×D₁₀₉	C₂	1	2	yes	maximal, 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	complemented
17	C₂×D₄×D₁₀₉	C₂²	1	8	yes	—
18	C₂³×Dic₁₀₉	C₂²	1	2	yes	complemented
19	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	complemented
21	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	complemented
22	C₄×D₄₃₆	C₂²	1	8	yes	complemented
23	D₄×Dic₁₀₉	C₂²	1	8	yes	complemented
24	#16812661	C₂²	1	8	yes	complemented
25	C₄×C₂²⋊D₁₀₉	C₂²	1	16	yes	complemented
26	#16812659	C₂²	1	16	yes	complemented
27	#16812657	C₂²	1	8	yes	complemented
28	#16812656	C₂²	1	8	yes	complemented
29	C₂×C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×#13182008	C₂²	1	1	yes	characteristic, complemented
31	C₂×#13182008	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂²⋊Dic₁₀₉	C₂²	1	2	yes	complemented
33	C₂×#13182006	C₂²	1	1	yes	characteristic
34	C₂×#13182006	C₂²	1	2	yes	—
35	C₂×#13182006	C₂²	1	1	yes	characteristic
36	C₂×#13182006	C₂²	1	2	yes	complemented
37	C₂×#13182006	C₂²	1	2	yes	complemented
38	C₂×#13182006	C₂²	1	16	yes	complemented
39	C₂²⋊C₄×D₁₀₉	C₂²	1	16	yes	complemented
40	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×Dic₁₀₉	C₂²	1	2	yes	complemented
42	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
43	C₂³×C₄×C₁₀₉	C₂²	1	2	yes	complemented
44	C₄×D₄×C₁₀₉	C₂²	1	8	yes	complemented
45	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
47	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
48	C₂³×D₁₀₉	—	4	4	no	—
49	C₂³×D₁₀₉	—	4	4	no	—
50	C₂³×D₁₀₉	C₂×C₄	1	16	yes	complemented
51	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
52	C₂³×D₁₀₉	C₂³	1	2	yes	—
53	C₂³×D₁₀₉	C₂³	1	8	yes	—
54	C₂×D₄₃₆	C₂×C₄	1	8	yes	complemented
55	C₂×D₄₃₆	C₂³	1	4	yes	—
56	C₂×C₂²⋊D₁₀₉	C₂×C₄	1	16	yes	complemented
57	C₂×C₂²⋊D₁₀₉	C₂³	1	8	yes	—
58	D₄×D₁₀₉	C₂×C₄	1	64	yes	complemented
59	C₂²×Dic₁₀₉	—	4	4	no	—
60	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
61	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
62	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
63	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
64	C₂²×Dic₁₀₉	C₂³	1	8	yes	complemented
65	C₂×C₄×D₁₀₉	—	4	4	no	—
66	C₂×C₄×D₁₀₉	—	4	4	no	—
67	C₂×C₄×D₁₀₉	C₂×C₄	1	8	yes	complemented
68	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
69	C₂×C₄×D₁₀₉	C₂³	1	8	yes	complemented
70	C₂×C₄×D₁₀₉	C₂³	1	8	yes	complemented
71	C₄⋊Dic₁₀₉	C₂³	1	4	yes	complemented
72	#13182008	C₂³	1	4	yes	complemented
73	#13182008	C₂³	1	4	yes	complemented
74	C₂²⋊Dic₁₀₉	C₂³	1	8	yes	complemented
75	#13182006	C₂³	1	4	yes	—
76	#13182006	C₂³	1	8	yes	—
77	#13182006	C₂³	1	4	yes	—
78	#13182006	C₂³	1	8	yes	complemented
79	#13182006	C₂³	1	8	yes	complemented
80	C₄×Dic₁₀₉	C₂³	1	4	yes	complemented
81	C₄×Dic₁₀₉	C₂³	1	8	yes	complemented
82	C₂⁴×C₁₀₉	C₂³	1	2	yes	—
83	C₂×D₄×C₁₀₉	C₂×C₄	1	8	yes	complemented
84	C₂×D₄×C₁₀₉	C₂³	1	4	yes	—
85	C₂²×C₄×C₁₀₉	—	4	4	no	—
86	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
89	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₀₉	C₂³	1	8	yes	complemented
91	C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
92	C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	complemented
93	C₄²×C₁₀₉	C₂³	1	4	yes	complemented
94	C₂³×C₁₀₉	—	2	4	no	—
95	C₂³×C₁₀₉	—	2	4	no	—
96	C₂³×C₁₀₉	C₂²×C₄	1	8	yes	—
97	C₂³×C₁₀₉	C₂⁴	1	4	yes	—
98	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
99	C₂²×D₁₀₉	—	2	4	no	—
100	C₂²×D₁₀₉	—	2	4	no	—
101	C₂²×D₁₀₉	—	2	2	no	—
102	C₂²×D₁₀₉	—	2	2	no	—
103	C₂²×D₁₀₉	—	4	32	no	—
104	C₂²×D₁₀₉	—	4	8	no	—
105	C₂²×D₁₀₉	—	4	8	no	—
106	C₂²×D₁₀₉	C₂²×C₄	1	4	yes	—
107	C₂²×D₁₀₉	C₂²×C₄	1	8	yes	—
108	C₂²×D₁₀₉	C₂²×C₄	1	32	yes	complemented
109	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
110	C₂²×D₁₀₉	C₂⁴	1	4	yes	—
111	D₄×C₁₀₉	C₂²×C₄	1	16	yes	complemented
112	C₂×C₄×C₁₀₉	—	2	2	no	—
113	C₂×C₄×C₁₀₉	—	2	4	no	—
114	C₂×C₄×C₁₀₉	—	2	2	no	—
115	C₂×C₄×C₁₀₉	—	4	8	no	—
116	C₂×C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
117	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
118	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
119	C₂×C₄×C₁₀₉	C₂⁴	1	4	yes	—
120	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
121	C₂²⋊D₁₀₉	C₂²×C₄	1	32	yes	complemented
122	C₂×Dic₁₀₉	—	2	2	no	—
123	C₂×Dic₁₀₉	—	2	4	no	—
124	C₂×Dic₁₀₉	—	2	2	no	—
125	C₂×Dic₁₀₉	—	4	8	no	—
126	C₂×Dic₁₀₉	C₂²×C₄	1	4	yes	—
127	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
128	C₂×Dic₁₀₉	C₂⁴	1	4	yes	—
129	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
130	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
131	D₄₃₆	C₂²×C₄	1	16	yes	complemented
132	C₄×D₁₀₉	—	4	8	no	—
133	C₄×D₁₀₉	—	4	8	no	—
134	C₄×D₁₀₉	C₂²×C₄	1	16	yes	complemented
135	C₂²×C₁₀₉	—	2	16	no	—
136	C₂²×C₁₀₉	—	2	4	no	—
137	C₂²×C₁₀₉	—	2	4	no	—
138	C₂²×C₁₀₉	C₂³×C₄	1	8	yes	—
139	C₂²×C₁₀₉	C₂³×C₄	1	2	yes	—
140	C₂²×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
141	C₂²×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
142	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
143	C₂×D₁₀₉	—	2	8	no	—
144	C₂×D₁₀₉	—	2	16	no	—
145	C₂×D₁₀₉	—	2	4	no	—
146	C₂×D₁₀₉	—	2	4	no	—
147	C₂×D₁₀₉	—	2	2	no	—
148	C₂×D₁₀₉	—	2	2	no	—
149	C₂×D₁₀₉	—	4	32	no	—
150	C₂×D₁₀₉	C₂³×C₄	1	4	yes	—
151	C₂×D₁₀₉	C₂³×C₄	1	8	yes	—
152	C₄×C₁₀₉	—	2	2	no	—
153	C₄×C₁₀₉	—	2	4	no	—
154	C₄×C₁₀₉	—	2	2	no	—
155	C₄×C₁₀₉	C₂³×C₄	1	4	yes	—
156	Dic₁₀₉	—	2	2	no	—
157	Dic₁₀₉	—	2	4	no	—
158	Dic₁₀₉	—	2	2	no	—
159	Dic₁₀₉	C₂³×C₄	1	4	yes	—
160	C₂×C₁₀₉	—	2	8	no	—
161	C₂×C₁₀₉	#518	1	4	yes	complemented
162	C₂×C₁₀₉	C₂⁴×C₄	1	1	yes	characteristic
163	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
165	D₁₀₉	—	2	4	no	—
166	D₁₀₉	—	2	8	no	—
167	C₂×#518	—	109	1	no	maximal, Sylow
168	C₁₀₉	C₂×#518	1	1	yes	characteristic, complemented, Sylow
169	C₂³×D₄	—	109	1	no	—
170	#518	—	109	16	no	—
171	C₂×C₄×D₄	—	109	1	no	—
172	C₂×C₄×D₄	—	109	2	no	—
173	C₂×C₄×D₄	—	109	1	no	—
174	C₂×C₄×D₄	—	109	2	no	—
175	C₂×C₄×D₄	—	109	1	no	—
176	C₂×C₄×D₄	D₁₀₉	1	1	yes	characteristic, complemented
177	C₂×#117	—	109	1	no	—
178	C₂×#117	—	109	1	no	—
179	C₂²×C₂²⋊C₄	—	109	2	no	—
180	C₂²×C₂²⋊C₄	—	109	2	no	—
181	C₂⁵	—	109	2	no	—
182	C₂²×D₄	—	109	2	no	—
183	C₂²×D₄	—	109	16	no	—
184	C₂²×D₄	—	109	8	no	—
185	C₂²×D₄	—	109	1	no	—
186	C₂²×D₄	C₂×D₁₀₉	1	1	yes	characteristic
187	C₂³×C₄	—	109	1	no	—
188	C₂³×C₄	—	109	2	no	—
189	C₂³×C₄	—	109	2	no	—
190	C₂³×C₄	—	109	2	no	—
191	C₂³×C₄	C₂×D₁₀₉	1	2	yes	complemented
192	C₄×D₄	—	109	8	no	—
193	C₄×D₄	—	109	16	no	—
194	C₄×D₄	—	109	8	no	—
195	C₄×D₄	—	109	16	no	—
196	C₄×D₄	—	109	8	no	—
197	C₄×D₄	C₂×D₁₀₉	1	8	yes	complemented
198	#117	—	109	8	no	—
199	#117	—	109	8	no	—
200	C₂×C₄⋊C₄	—	109	1	no	—
201	C₂×C₄⋊C₄	—	109	1	no	—
202	C₂×C₄⋊C₄	—	109	1	no	—
203	C₂×C₄⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
204	C₂×C₂²⋊C₄	—	109	2	no	—
205	C₂×C₂²⋊C₄	—	109	2	no	—
206	C₂×C₂²⋊C₄	—	109	1	no	—
207	C₂×C₂²⋊C₄	—	109	1	no	—
208	C₂×C₂²⋊C₄	—	109	2	no	—
209	C₂×C₂²⋊C₄	—	109	2	no	—
210	C₂×C₂²⋊C₄	—	109	16	no	—
211	C₂×C₂²⋊C₄	—	109	16	no	—
212	C₂×C₂²⋊C₄	C₂×D₁₀₉	1	2	yes	complemented
213	C₂×C₄²	—	109	2	no	—
214	C₂×C₄²	—	109	1	no	—
215	C₂×C₄²	C₂×D₁₀₉	1	1	yes	characteristic, complemented
216	C₂⁴	—	109	16	no	—
217	C₂⁴	—	109	8	no	—
218	C₂⁴	—	109	1	no	—
219	C₂⁴	—	109	2	no	—
220	C₂⁴	—	436	4	no	—
221	C₂⁴	—	436	4	no	—
222	C₂⁴	C₂²×D₁₀₉	1	2	yes	—
223	C₂×D₄	—	109	16	no	—
224	C₂×D₄	—	109	8	no	—
225	C₂×D₄	—	109	64	no	—
226	C₂×D₄	—	109	8	no	—
227	C₂×D₄	—	109	4	no	—
228	C₂×D₄	C₄×D₁₀₉	1	8	yes	complemented
229	C₂×D₄	C₂²×D₁₀₉	1	4	yes	—
230	C₂²×C₄	—	4	4	no	—
231	C₂²×C₄	—	109	1	no	—
232	C₂²×C₄	—	109	8	no	—
233	C₂²×C₄	—	109	4	no	—
234	C₂²×C₄	—	109	8	no	—
235	C₂²×C₄	—	109	1	no	—
236	C₂²×C₄	—	109	1	no	—
237	C₂²×C₄	—	109	2	no	—
238	C₂²×C₄	—	109	8	no	—
239	C₂²×C₄	—	109	8	no	—
240	C₂²×C₄	—	436	4	no	—
241	C₂²×C₄	—	436	4	no	—
242	C₂²×C₄	—	436	4	no	—
243	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
244	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
245	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
246	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
247	C₂²×C₄	C₂²×D₁₀₉	1	8	yes	complemented
248	C₄⋊C₄	—	109	4	no	—
249	C₄⋊C₄	—	109	4	no	—
250	C₄⋊C₄	—	109	4	no	—
251	C₄⋊C₄	C₂²×D₁₀₉	1	4	yes	complemented
252	C₂²⋊C₄	—	109	8	no	—
253	C₂²⋊C₄	—	109	8	no	—
254	C₂²⋊C₄	—	109	4	no	—
255	C₂²⋊C₄	—	109	4	no	—
256	C₂²⋊C₄	—	109	8	no	—
257	C₂²⋊C₄	—	109	8	no	—
258	C₂²⋊C₄	C₂²×D₁₀₉	1	8	yes	complemented
259	C₄²	—	109	8	no	—
260	C₄²	—	109	4	no	—
261	C₄²	C₂²×D₁₀₉	1	4	yes	complemented
262	C₂³	—	2	4	no	—
263	C₂³	—	2	4	no	—
264	C₂³	—	109	32	no	—
265	C₂³	—	109	4	no	—
266	C₂³	—	109	8	no	—
267	C₂³	—	109	2	no	—
268	C₂³	—	109	4	no	—
269	C₂³	—	436	32	no	—
270	C₂³	—	436	8	no	—
271	C₂³	—	436	8	no	—
272	C₂³	—	218	4	no	—
273	C₂³	—	218	2	no	—
274	C₂³	—	218	4	no	—
275	C₂³	—	218	2	no	—
276	C₂³	C₂×C₄×D₁₀₉	1	8	yes	—
277	C₂³	C₂³×D₁₀₉	1	4	yes	—
278	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
279	D₄	—	109	32	no	—
280	D₄	—	109	16	no	—
281	D₄	C₂×C₄×D₁₀₉	1	16	yes	complemented
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	4	8	no	—
286	C₂×C₄	—	109	4	no	—
287	C₂×C₄	—	109	2	no	—
288	C₂×C₄	—	109	16	no	—
289	C₂×C₄	—	109	2	no	—
290	C₂×C₄	—	109	4	no	—
291	C₂×C₄	—	109	2	no	—
292	C₂×C₄	—	436	8	no	—
293	C₂×C₄	—	436	8	no	—
294	C₂×C₄	—	436	8	no	—
295	C₂×C₄	—	218	2	no	—
296	C₂×C₄	—	218	4	no	—
297	C₂×C₄	—	218	2	no	—
298	C₂×C₄	C₂×C₄×D₁₀₉	1	4	yes	—
299	C₂×C₄	C₂³×D₁₀₉	1	4	yes	—
300	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
301	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
302	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
303	C₂²	—	2	16	no	—
304	C₂²	—	2	4	no	—
305	C₂²	—	2	4	no	—
306	C₂²	—	109	4	no	—
307	C₂²	—	109	8	no	—
308	C₂²	—	436	32	no	—
309	C₂²	—	218	8	no	—
310	C₂²	—	218	16	no	—
311	C₂²	—	218	4	no	—
312	C₂²	—	218	2	no	—
313	C₂²	—	218	4	no	—
314	C₂²	—	218	2	no	—
315	C₂²	C₂²×C₄×D₁₀₉	1	8	yes	—
316	C₂²	C₂²×C₄×D₁₀₉	1	2	yes	—
317	C₂²	#16812744	1	2	yes	—
318	C₂²	#16812745	1	2	yes	—
319	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
320	C₄	—	2	2	no	—
321	C₄	—	2	4	no	—
322	C₄	—	2	2	no	—
323	C₄	—	109	4	no	—
324	C₄	—	218	2	no	—
325	C₄	—	218	4	no	—
326	C₄	—	218	2	no	—
327	C₄	C₂²×C₄×D₁₀₉	1	4	yes	—
328	C₂	—	2	8	no	—
329	C₂	—	218	4	no	—
330	C₂	—	218	8	no	—
331	C₂	#20295498	1	4	yes	direct product factor
332	C₂	C₂³×C₄×D₁₀₉	1	1	yes	characteristic
333	C₂	C₂×#16812744	1	1	yes	characteristic
334	C₂	C₂×#16812745	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×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	C₂×#518
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #20295498	C₂	direct (N × H)
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. C₂×#16812657	C₂	semidirect
9. C₂×#16812656	C₂	semidirect
10. C₂²×#13182006	C₂	semidirect
11. C₂×C₂²⋊C₄×D₁₀₉	C₂	semidirect
12. C₂×C₄×D₄×C₁₀₉	C₂	semidirect
16. C₂×D₄×D₁₀₉	C₄	semidirect
18. C₂³×Dic₁₀₉	C₂²	semidirect
20. C₂²×C₄×D₁₀₉	C₂²	semidirect
21. C₂²×C₄×D₁₀₉	C₂²	semidirect
22. C₄×D₄₃₆	C₂²	semidirect
23. D₄×Dic₁₀₉	C₂²	semidirect
24. #16812661	C₂²	semidirect
25. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
26. #16812659	C₂²	semidirect
27. #16812657	C₂²	semidirect
28. #16812656	C₂²	semidirect
29. C₂×C₄⋊Dic₁₀₉	C₂²	semidirect
30. C₂×#13182008	C₂²	semidirect
31. C₂×#13182008	C₂²	semidirect
32. C₂×C₂²⋊Dic₁₀₉	C₂²	semidirect
36. C₂×#13182006	C₂²	semidirect
37. C₂×#13182006	C₂²	semidirect
38. C₂×#13182006	C₂²	semidirect
39. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
40. C₂×C₄×Dic₁₀₉	C₂²	semidirect
41. C₂×C₄×Dic₁₀₉	C₂²	semidirect
43. C₂³×C₄×C₁₀₉	C₂²	semidirect
44. C₄×D₄×C₁₀₉	C₂²	semidirect
45. C₂×C₄⋊C₄×C₁₀₉	C₂²	semidirect
46. C₂×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
47. C₂×C₄²×C₁₀₉	C₂²	semidirect
50. C₂³×D₁₀₉	C₂×C₄	semidirect
54. C₂×D₄₃₆	C₂×C₄	semidirect
56. C₂×C₂²⋊D₁₀₉	C₂×C₄	semidirect
58. D₄×D₁₀₉	C₂×C₄	semidirect
64. C₂²×Dic₁₀₉	C₂³	semidirect
67. C₂×C₄×D₁₀₉	C₂×C₄	semidirect
69. C₂×C₄×D₁₀₉	C₂³	semidirect
70. C₂×C₄×D₁₀₉	C₂³	semidirect
71. C₄⋊Dic₁₀₉	C₂³	semidirect
72. #13182008	C₂³	semidirect
73. #13182008	C₂³	semidirect
74. C₂²⋊Dic₁₀₉	C₂³	semidirect
78. #13182006	C₂³	semidirect
79. #13182006	C₂³	semidirect
80. C₄×Dic₁₀₉	C₂³	semidirect
81. C₄×Dic₁₀₉	C₂³	semidirect
83. C₂×D₄×C₁₀₉	C₂×C₄	semidirect
90. C₂²×C₄×C₁₀₉	C₂³	semidirect
91. C₄⋊C₄×C₁₀₉	C₂³	semidirect
92. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
93. C₄²×C₁₀₉	C₂³	semidirect
108. C₂²×D₁₀₉	C₂²×C₄	semidirect
111. D₄×C₁₀₉	C₂²×C₄	semidirect
121. C₂²⋊D₁₀₉	C₂²×C₄	semidirect
131. D₄₃₆	C₂²×C₄	semidirect
134. C₄×D₁₀₉	C₂²×C₄	semidirect
161. C₂×C₁₀₉	#518	semidirect
168. C₁₀₉	C₂×#518	semidirect
176. C₂×C₄×D₄	D₁₀₉	semidirect
191. C₂³×C₄	C₂×D₁₀₉	semidirect
197. C₄×D₄	C₂×D₁₀₉	semidirect
203. C₂×C₄⋊C₄	C₂×D₁₀₉	semidirect
212. C₂×C₂²⋊C₄	C₂×D₁₀₉	semidirect
215. C₂×C₄²	C₂×D₁₀₉	semidirect
228. C₂×D₄	C₄×D₁₀₉	semidirect
247. C₂²×C₄	C₂²×D₁₀₉	semidirect
251. C₄⋊C₄	C₂²×D₁₀₉	semidirect
258. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
261. C₄²	C₂²×D₁₀₉	semidirect
281. D₄	C₂×C₄×D₁₀₉	semidirect
331. C₂	#20295498	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
#20295498	2
C₂×C₄×D₄₃₆	2
C₂×D₄×Dic₁₀₉	2
C₂×#16812661	2
C₂×C₄×C₂²⋊D₁₀₉	2
C₂×#16812659	2
C₂×#16812657	2
C₂×#16812656	2
C₂²×#13182006	2
C₂×C₂²⋊C₄×D₁₀₉	2
C₂×C₄×D₄×C₁₀₉	2
C₂×#518	109

Subgroups — C2×#20295498 #28376216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20295498 #28376216