Subgroups — C₄×#16812744 #28376237

Order 13952.

1660 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812744	C₂	1	1	yes	maximal, characteristic
2	#20295507	C₂	1	2	yes	maximal, complemented
3	#20295505	C₂	1	4	yes	maximal, complemented
4	#20295501	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295499	C₂	1	4	yes	maximal, complemented
6	#20295498	C₂	1	4	yes	maximal, complemented
7	C₄×#13182029	C₂	1	2	yes	maximal, complemented
8	C₄×#13182028	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×C₂²⋊D₁₀₉	C₂	1	4	yes	maximal, complemented
10	C₄×D₄×D₁₀₉	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×D₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#16812744	C₄	1	16	yes	direct product factor
13	C₂×#13182029	C₂²	1	2	yes	—
14	C₂×#13182028	C₂²	1	4	yes	—
15	C₂²×C₂²⋊D₁₀₉	C₂²	1	4	yes	—
16	C₂×D₄×D₁₀₉	C₂²	1	4	yes	—
17	C₂²×C₄×D₁₀₉	C₂²	1	4	yes	complemented
18	C₄×Dic₂₁₈	C₂²	1	2	yes	complemented
19	C₄×Dic₂₁₈	C₂²	1	2	yes	complemented
20	#16812664	C₂²	1	4	yes	complemented
21	C₄×D₄₃₆	C₂²	1	2	yes	complemented
22	C₄×D₄₃₆	C₂²	1	2	yes	complemented
23	D₄×Dic₁₀₉	C₂²	1	4	yes	complemented
24	D₄×Dic₁₀₉	C₂²	1	4	yes	complemented
25	#16812661	C₂²	1	4	yes	complemented
26	C₄×C₂²⋊D₁₀₉	C₂²	1	8	yes	complemented
27	C₄×C₂²⋊D₁₀₉	C₂²	1	4	yes	complemented
28	C₄×C₂²⋊D₁₀₉	C₂²	1	8	yes	complemented
29	C₄×C₂²⋊D₁₀₉	C₂²	1	8	yes	complemented
30	C₄×C₂²⋊D₁₀₉	C₂²	1	4	yes	complemented
31	#16812659	C₂²	1	8	yes	complemented
32	#16812659	C₂²	1	8	yes	complemented
33	#16812658	C₂²	1	2	yes	complemented
34	#16812657	C₂²	1	4	yes	complemented
35	#16812656	C₂²	1	4	yes	complemented
36	#16812655	C₂²	1	8	yes	complemented
37	C₂×#13182008	C₂²	1	4	yes	complemented
38	C₄⋊C₄×D₁₀₉	C₂²	1	4	yes	complemented
39	C₂×C₂²⋊Dic₁₀₉	C₂²	1	4	yes	complemented
40	C₂×#13182006	C₂²	1	4	yes	complemented
41	C₂²⋊C₄×D₁₀₉	C₂²	1	8	yes	complemented
42	C₂×C₄×Dic₁₀₉	C₂²	1	4	yes	complemented
43	C₄²×D₁₀₉	C₂²	1	4	yes	complemented
44	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
45	C₂³×C₄×C₁₀₉	C₂²	1	2	yes	complemented
46	C₄×D₄×C₁₀₉	C₂²	1	4	yes	complemented
47	C₄×D₄×C₁₀₉	C₂²	1	4	yes	complemented
48	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
50	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
51	C₂³×D₁₀₉	C₂³	1	4	yes	—
52	#13182029	C₂×C₄	1	16	yes	complemented
53	#13182028	C₂×C₄	1	32	yes	complemented
54	C₂×Dic₂₁₈	C₂³	1	2	yes	—
55	C₂×D₄₃₆	C₂³	1	2	yes	—
56	C₂×C₂²⋊D₁₀₉	C₂×C₄	1	32	yes	complemented
57	C₂×C₂²⋊D₁₀₉	C₂³	1	8	yes	—
58	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
59	D₄×D₁₀₉	C₂×C₄	1	32	yes	complemented
60	C₂²×Dic₁₀₉	C₂³	1	4	yes	—
61	C₂²×Dic₁₀₉	C₂³	1	4	yes	—
62	C₂²×Dic₁₀₉	C₂³	1	4	yes	—
63	C₂×C₄×D₁₀₉	—	4	8	no	—
64	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
65	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
66	C₂×C₄×D₁₀₉	C₂³	1	8	yes	—
67	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
68	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
69	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
70	#13182008	C₂³	1	8	yes	—
71	#13182008	C₂³	1	4	yes	—
72	#13182008	C₂³	1	4	yes	—
73	C₂²⋊Dic₁₀₉	C₂³	1	8	yes	—
74	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	—
75	#13182006	C₂³	1	4	yes	—
76	#13182006	C₂³	1	8	yes	—
77	#13182006	C₂³	1	4	yes	—
78	C₄×Dic₁₀₉	C₂³	1	4	yes	—
79	C₄×Dic₁₀₉	C₂³	1	4	yes	—
80	C₄×Dic₁₀₉	C₂³	1	4	yes	—
81	C₄×Dic₁₀₉	C₂³	1	8	yes	—
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	4	yes	—
88	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
90	C₂²×C₄×C₁₀₉	C₂³	1	4	yes	—
91	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
92	C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
93	C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	—
94	C₄²×C₁₀₉	C₂³	1	2	yes	—
95	C₄²×C₁₀₉	C₂³	1	2	yes	—
96	C₂³×C₁₀₉	—	4	2	no	—
97	C₂³×C₁₀₉	—	4	2	no	—
98	C₂³×C₁₀₉	C₂²×C₄	1	8	yes	complemented
99	C₂³×C₁₀₉	C₂⁴	1	4	yes	—
100	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
101	C₂²×D₁₀₉	—	4	4	no	—
102	C₂²×D₁₀₉	—	4	4	no	—
103	C₂²×D₁₀₉	C₂²×C₄	1	16	yes	complemented
104	C₂²×D₁₀₉	C₂⁴	1	4	yes	—
105	D₄×C₁₀₉	C₂²×C₄	1	16	yes	complemented
106	C₂×C₄×C₁₀₉	—	2	2	no	—
107	C₂×C₄×C₁₀₉	—	2	8	no	—
108	C₂×C₄×C₁₀₉	—	4	2	no	—
109	C₂×C₄×C₁₀₉	—	4	4	no	—
110	C₂×C₄×C₁₀₉	—	4	1	no	—
111	C₂×C₄×C₁₀₉	C₂²×C₄	1	4	yes	complemented
112	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
113	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
114	C₂×C₄×C₁₀₉	C₂⁴	1	4	yes	—
115	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
116	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
117	C₂²⋊D₁₀₉	C₂²×C₄	1	32	yes	complemented
118	C₂²⋊D₁₀₉	C₂²×C₄	1	16	yes	complemented
119	C₂×Dic₁₀₉	—	4	4	no	—
120	C₂×Dic₁₀₉	—	4	4	no	—
121	C₂×Dic₁₀₉	C₂²×C₄	1	16	yes	complemented
122	C₂×Dic₁₀₉	C₂⁴	1	4	yes	—
123	C₂×Dic₁₀₉	C₂⁴	1	4	yes	—
124	C₂×Dic₁₀₉	C₂⁴	1	4	yes	—
125	D₄₃₆	C₂²×C₄	1	8	yes	complemented
126	C₄×D₁₀₉	—	2	8	no	—
127	C₄×D₁₀₉	—	4	8	no	—
128	C₄×D₁₀₉	—	4	4	no	—
129	C₄×D₁₀₉	C₂²×C₄	1	16	yes	complemented
130	Dic₂₁₈	C₂²×C₄	1	8	yes	complemented
131	C₂²×C₁₀₉	—	2	4	no	—
132	C₂²×C₁₀₉	—	2	1	no	—
133	C₂²×C₁₀₉	—	2	4	no	—
134	C₂²×C₁₀₉	—	2	1	no	—
135	C₂²×C₁₀₉	—	4	8	no	—
136	C₂²×C₁₀₉	C₂³×C₄	1	8	yes	—
137	C₂²×C₁₀₉	C₂³×C₄	1	2	yes	—
138	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
139	C₂×D₁₀₉	—	2	4	no	—
140	C₂×D₁₀₉	—	2	4	no	—
141	C₂×D₁₀₉	—	4	16	no	—
142	C₂×D₁₀₉	C₂³×C₄	1	8	yes	—
143	C₄×C₁₀₉	—	2	4	no	—
144	C₄×C₁₀₉	—	2	1	no	—
145	C₄×C₁₀₉	—	2	2	no	—
146	C₄×C₁₀₉	C₂³×C₄	1	4	yes	—
147	C₄×C₁₀₉	H(5,𝔽₂)	1	2	yes	complemented
148	Dic₁₀₉	—	2	4	no	—
149	Dic₁₀₉	—	2	4	no	—
150	Dic₁₀₉	C₂³×C₄	1	8	yes	—
151	C₂×C₁₀₉	—	2	8	no	—
152	C₂×C₁₀₉	—	2	2	no	—
153	C₂×C₁₀₉	C₂⁴×C₄	1	1	yes	characteristic
154	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
155	C₂×C₁₀₉	#585	1	1	yes	characteristic
156	D₁₀₉	—	2	8	no	—
157	C₄×H(5,𝔽₂)	—	109	1	no	maximal, Sylow
158	C₁₀₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
159	C₂×H(5,𝔽₂)	—	109	1	no	—
160	#520	—	109	4	no	—
161	#520	—	109	2	no	—
162	#518	—	109	1	no	—
163	#518	—	109	4	no	—
164	#518	—	109	4	no	—
165	C₄×#41	—	109	4	no	—
166	C₄×#41	—	109	2	no	—
167	C₂×C₄×D₄	—	109	4	no	—
168	C₂×C₄×D₄	—	109	4	no	—
169	C₂×C₄×D₄	D₁₀₉	1	1	yes	characteristic, complemented
170	H(5,𝔽₂)	—	109	16	no	—
171	C₂×#41	—	109	4	no	—
172	C₂×#41	—	109	2	no	—
173	C₂²×D₄	—	109	4	no	—
174	C₂²×D₄	—	109	4	no	—
175	C₂²×D₄	C₂×D₁₀₉	1	1	yes	characteristic
176	C₂³×C₄	—	109	4	no	—
177	C₂³×C₄	C₂×D₁₀₉	1	2	yes	complemented
178	C₄×Q₈	—	109	4	no	—
179	C₄×Q₈	—	109	2	no	—
180	C₄×Q₈	—	109	2	no	—
181	C₄×D₄	—	109	4	no	—
182	C₄×D₄	—	109	4	no	—
183	C₄×D₄	—	109	8	no	—
184	C₄×D₄	—	109	4	no	—
185	C₄×D₄	—	109	8	no	—
186	C₄×D₄	—	109	8	no	—
187	C₄×D₄	—	109	4	no	—
188	C₄×D₄	—	109	4	no	—
189	C₄×D₄	—	109	8	no	—
190	C₄×D₄	—	109	8	no	—
191	C₄×D₄	—	109	2	no	—
192	C₄×D₄	—	109	2	no	—
193	C₄×D₄	C₂×D₁₀₉	1	4	yes	complemented
194	C₄×D₄	C₂×D₁₀₉	1	4	yes	complemented
195	#117	—	109	2	no	—
196	#117	—	109	4	no	—
197	#117	—	109	8	no	—
198	#117	—	109	4	no	—
199	C₂×C₄⋊C₄	—	109	4	no	—
200	C₂×C₄⋊C₄	—	109	4	no	—
201	C₂×C₄⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
202	C₂×C₂²⋊C₄	—	109	4	no	—
203	C₂×C₂²⋊C₄	—	109	4	no	—
204	C₂×C₂²⋊C₄	—	109	8	no	—
205	C₂×C₂²⋊C₄	C₂×D₁₀₉	1	2	yes	complemented
206	C₂×C₄²	—	109	4	no	—
207	C₂×C₄²	—	109	4	no	—
208	C₂×C₄²	C₂×D₁₀₉	1	1	yes	characteristic, complemented
209	C₂⁴	—	109	4	no	—
210	C₂⁴	C₂²×D₁₀₉	1	2	yes	—
211	#41	—	109	32	no	—
212	#41	—	109	16	no	—
213	C₂×Q₈	—	109	2	no	—
214	C₂×D₄	—	109	32	no	—
215	C₂×D₄	—	109	4	no	—
216	C₂×D₄	—	109	8	no	—
217	C₂×D₄	—	109	32	no	—
218	C₂×D₄	—	109	2	no	—
219	C₂×D₄	C₄×D₁₀₉	1	8	yes	complemented
220	C₂×D₄	C₂²×D₁₀₉	1	4	yes	—
221	C₂²×C₄	—	4	4	no	—
222	C₂²×C₄	—	109	4	no	—
223	C₂²×C₄	—	109	4	no	—
224	C₂²×C₄	—	109	4	no	—
225	C₂²×C₄	—	109	4	no	—
226	C₂²×C₄	—	109	4	no	—
227	C₂²×C₄	—	109	8	no	—
228	C₂²×C₄	—	109	4	no	—
229	C₂²×C₄	—	436	8	no	—
230	C₂²×C₄	C₂²×D₁₀₉	1	4	yes	—
231	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
232	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
233	C₂²×C₄	C₂²×D₁₀₉	1	4	yes	—
234	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
235	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
236	C₄⋊C₄	—	109	8	no	—
237	C₄⋊C₄	—	109	4	no	—
238	C₄⋊C₄	—	109	4	no	—
239	C₄⋊C₄	—	109	2	no	—
240	C₄⋊C₄	—	109	2	no	—
241	C₄⋊C₄	C₂²×D₁₀₉	1	4	yes	—
242	C₂²⋊C₄	—	109	4	no	—
243	C₂²⋊C₄	—	109	8	no	—
244	C₂²⋊C₄	—	109	8	no	—
245	C₂²⋊C₄	—	109	4	no	—
246	C₂²⋊C₄	—	109	4	no	—
247	C₂²⋊C₄	C₂²×D₁₀₉	1	8	yes	—
248	C₄²	—	109	8	no	—
249	C₄²	—	109	4	no	—
250	C₄²	—	109	4	no	—
251	C₄²	—	109	4	no	—
252	C₄²	C₂²×D₁₀₉	1	2	yes	—
253	C₄²	C₂²×D₁₀₉	1	2	yes	—
254	C₂³	—	4	2	no	—
255	C₂³	—	4	2	no	—
256	C₂³	—	109	16	no	—
257	C₂³	—	109	4	no	—
258	C₂³	—	436	4	no	—
259	C₂³	—	436	4	no	—
260	C₂³	C₂×C₄×D₁₀₉	1	8	yes	complemented
261	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
262	C₂³	C₂³×D₁₀₉	1	4	yes	—
263	Q₈	—	109	8	no	—
264	D₄	—	109	32	no	—
265	D₄	—	109	16	no	—
266	D₄	—	109	8	no	—
267	D₄	C₂×C₄×D₁₀₉	1	16	yes	complemented
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	8	no	—
270	C₂×C₄	—	4	4	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	—	4	1	no	—
273	C₂×C₄	—	109	16	no	—
274	C₂×C₄	—	109	4	no	—
275	C₂×C₄	—	109	16	no	—
276	C₂×C₄	—	109	4	no	—
277	C₂×C₄	—	109	4	no	—
278	C₂×C₄	—	436	8	no	—
279	C₂×C₄	—	436	4	no	—
280	C₂×C₄	—	436	4	no	—
281	C₂×C₄	—	436	4	no	—
282	C₂×C₄	—	218	8	no	—
283	C₂×C₄	C₂×C₄×D₁₀₉	1	4	yes	complemented
284	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
285	C₂×C₄	C₂³×D₁₀₉	1	4	yes	—
286	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
287	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
288	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
289	C₂²	—	2	1	no	—
290	C₂²	—	2	4	no	—
291	C₂²	—	2	1	no	—
292	C₂²	—	2	4	no	—
293	C₂²	—	4	8	no	—
294	C₂²	—	109	8	no	—
295	C₂²	—	436	16	no	—
296	C₂²	—	218	4	no	—
297	C₂²	—	218	4	no	—
298	C₂²	C₂²×C₄×D₁₀₉	1	8	yes	—
299	C₂²	C₂²×C₄×D₁₀₉	1	2	yes	—
300	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
301	C₄	—	2	1	no	—
302	C₄	—	2	4	no	—
303	C₄	—	2	2	no	—
304	C₄	—	109	8	no	—
305	C₄	—	218	4	no	—
306	C₄	—	218	4	no	—
307	C₄	C₂²×C₄×D₁₀₉	1	4	yes	—
308	C₄	#16812744	1	2	yes	direct product factor
309	C₂	—	2	2	no	—
310	C₂	—	2	8	no	—
311	C₂	—	218	8	no	—
312	C₂	C₂³×C₄×D₁₀₉	1	1	yes	characteristic
313	C₂	C₂×#16812744	1	1	yes	characteristic
314	C₂	#20295862	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₀₉
commutator	C₂×C₁₀₉	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₁₀₉
Fitting	C₂×C₄×D₄×C₁₀₉	C₂
socle, cosocle	C₂²×C₁₀₉	C₂⁵
prime radical	C₂×#16812744	C₂
hypercenter	C₂×C₄×D₄	D₁₀₉
hypocenter	C₁₀₉	C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #20295507	C₂	semidirect
3. #20295505	C₂	semidirect
4. #20295501	C₂	semidirect
5. #20295499	C₂	semidirect
6. #20295498	C₂	semidirect
7. C₄×#13182029	C₂	semidirect
8. C₄×#13182028	C₂	semidirect
9. C₂×C₄×C₂²⋊D₁₀₉	C₂	semidirect
10. C₄×D₄×D₁₀₉	C₂	semidirect
11. C₂×C₄×D₄×C₁₀₉	C₂	semidirect
12. #16812744	C₄	direct (N × H)
17. C₂²×C₄×D₁₀₉	C₂²	semidirect
18. C₄×Dic₂₁₈	C₂²	semidirect
19. C₄×Dic₂₁₈	C₂²	semidirect
20. #16812664	C₂²	semidirect
21. C₄×D₄₃₆	C₂²	semidirect
22. C₄×D₄₃₆	C₂²	semidirect
23. D₄×Dic₁₀₉	C₂²	semidirect
24. D₄×Dic₁₀₉	C₂²	semidirect
25. #16812661	C₂²	semidirect
26. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
27. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
28. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
29. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
30. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
31. #16812659	C₂²	semidirect
32. #16812659	C₂²	semidirect
33. #16812658	C₂²	semidirect
34. #16812657	C₂²	semidirect
35. #16812656	C₂²	semidirect
36. #16812655	C₂²	semidirect
37. C₂×#13182008	C₂²	semidirect
38. C₄⋊C₄×D₁₀₉	C₂²	semidirect
39. C₂×C₂²⋊Dic₁₀₉	C₂²	semidirect
40. C₂×#13182006	C₂²	semidirect
41. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
42. C₂×C₄×Dic₁₀₉	C₂²	semidirect
43. C₄²×D₁₀₉	C₂²	semidirect
45. C₂³×C₄×C₁₀₉	C₂²	semidirect
46. C₄×D₄×C₁₀₉	C₂²	semidirect
47. C₄×D₄×C₁₀₉	C₂²	semidirect
48. C₂×C₄⋊C₄×C₁₀₉	C₂²	semidirect
49. C₂×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
50. C₂×C₄²×C₁₀₉	C₂²	semidirect
52. #13182029	C₂×C₄	semidirect
53. #13182028	C₂×C₄	semidirect
56. C₂×C₂²⋊D₁₀₉	C₂×C₄	semidirect
59. D₄×D₁₀₉	C₂×C₄	semidirect
83. C₂×D₄×C₁₀₉	C₂×C₄	semidirect
98. C₂³×C₁₀₉	C₂²×C₄	semidirect
103. C₂²×D₁₀₉	C₂²×C₄	semidirect
105. D₄×C₁₀₉	C₂²×C₄	semidirect
111. C₂×C₄×C₁₀₉	C₂²×C₄	semidirect
117. C₂²⋊D₁₀₉	C₂²×C₄	semidirect
118. C₂²⋊D₁₀₉	C₂²×C₄	semidirect
121. C₂×Dic₁₀₉	C₂²×C₄	semidirect
125. D₄₃₆	C₂²×C₄	semidirect
129. C₄×D₁₀₉	C₂²×C₄	semidirect
130. Dic₂₁₈	C₂²×C₄	semidirect
147. C₄×C₁₀₉	H(5,𝔽₂)	semidirect
158. C₁₀₉	C₄×H(5,𝔽₂)	semidirect
169. C₂×C₄×D₄	D₁₀₉	semidirect
177. C₂³×C₄	C₂×D₁₀₉	semidirect
193. C₄×D₄	C₂×D₁₀₉	semidirect
194. C₄×D₄	C₂×D₁₀₉	semidirect
201. C₂×C₄⋊C₄	C₂×D₁₀₉	semidirect
205. C₂×C₂²⋊C₄	C₂×D₁₀₉	semidirect
208. C₂×C₄²	C₂×D₁₀₉	semidirect
219. C₂×D₄	C₄×D₁₀₉	semidirect
260. C₂³	C₂×C₄×D₁₀₉	semidirect
267. D₄	C₂×C₄×D₁₀₉	semidirect
283. C₂×C₄	C₂×C₄×D₁₀₉	semidirect
308. C₄	#16812744	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16812744	2
#20295507	2
#20295505	2
#20295501	2
#20295499	2
#20295498	2
C₄×#13182029	2
C₄×#13182028	2
C₂×C₄×C₂²⋊D₁₀₉	2
C₄×D₄×D₁₀₉	2
C₂×C₄×D₄×C₁₀₉	2
C₄×H(5,𝔽₂)	109

Subgroups — C4×#16812744 #28376237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16812744 #28376237