Subgroups — C₂×#20295830 #28377784

Order 13952.

1512 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812745	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16812744	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295830	C₂	1	16	yes	maximal, direct product factor
4	C₂×#16812727	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16812726	C₂	1	2	yes	maximal, complemented
6	C₂×#16812723	C₂	1	2	yes	maximal, complemented
7	C₂×#16812720	C₂	1	2	yes	maximal, complemented
8	C₂×#16812719	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#13182014	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₈×D₁₀₉	C₂	1	2	yes	maximal, complemented
11	C₂×#16812707	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#16812745	—	2	4	no	—
14	#16812745	C₂²	1	8	yes	complemented
15	#16812744	—	2	4	no	—
16	#16812744	C₂²	1	8	yes	complemented
17	C₂×#13182030	C₂²	1	2	yes	complemented
18	C₂×#13182029	—	2	1	no	—
19	C₂×#13182029	C₂²	1	1	yes	characteristic
20	C₂×#13182029	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13182028	—	2	1	no	—
22	C₂×#13182028	C₂²	1	2	yes	complemented
23	C₂²×D₄₃₆	—	2	1	no	—
24	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₂²⋊D₁₀₉	—	2	2	no	—
26	C₂×D₄×D₁₀₉	—	2	1	no	—
27	C₂×D₄×D₁₀₉	—	2	2	no	—
28	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
29	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
30	#16812727	C₂²	1	8	yes	complemented
31	#16812726	C₂²	1	16	yes	complemented
32	#16812723	C₂²	1	16	yes	complemented
33	#16812720	C₂²	1	16	yes	complemented
34	#16812719	C₂²	1	8	yes	complemented
35	C₂×#13182019	C₂²	1	1	yes	characteristic, complemented
36	C₂×#13182018	C₂²	1	2	yes	complemented
37	C₂×#13182017	C₂²	1	1	yes	characteristic, complemented
38	C₂×#13182016	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₈₇₂	C₂²	1	2	yes	complemented
40	C₂×#13182014	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13182014	C₂²	1	2	yes	complemented
42	C₂×#13182014	C₂²	1	2	yes	complemented
43	C₂×#13182014	C₂²	1	8	yes	complemented
44	D₈×D₁₀₉	C₂²	1	16	yes	complemented
45	#16812707	C₂²	1	8	yes	complemented
46	C₂×#13182012	C₂²	1	2	yes	complemented
47	C₂²×#11724784	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₈×D₁₀₉	C₂²	1	2	yes	complemented
49	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
50	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
51	AGL(1,ℤ/8)×C₁₀₉	C₂²	1	8	yes	complemented
52	C₂×SD₁₆×C₁₀₉	C₂²	1	2	yes	complemented
53	C₂×D₈×C₁₀₉	C₂²	1	2	yes	complemented
54	C₂×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
55	C₂³×D₁₀₉	—	2	1	no	—
56	C₂³×D₁₀₉	—	2	2	no	—
57	C₂³×D₁₀₉	—	2	2	no	—
58	#13182030	—	2	4	no	—
59	#13182030	C₂³	1	8	yes	complemented
60	#13182029	—	2	2	no	—
61	#13182029	—	2	8	no	—
62	#13182029	D₄	1	4	yes	—
63	#13182029	C₂³	1	4	yes	—
64	#13182029	C₂³	1	4	yes	complemented
65	#13182028	—	2	4	no	—
66	#13182028	—	2	8	no	—
67	#13182028	C₂³	1	8	yes	complemented
68	C₂×Dic₂₁₈	D₄	1	1	yes	characteristic
69	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
70	C₂×D₄₃₆	—	2	2	no	—
71	C₂×D₄₃₆	—	2	1	no	—
72	C₂×D₄₃₆	—	2	2	no	—
73	C₂×D₄₃₆	—	2	8	no	—
74	C₂×D₄₃₆	D₄	1	1	yes	characteristic
75	C₂×D₄₃₆	C₂³	1	2	yes	—
76	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
77	C₂×D₄₃₆	C₂³	1	4	yes	complemented
78	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
79	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
80	C₂×C₂²⋊D₁₀₉	—	2	16	no	—
81	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
82	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
83	C₂×C₂²⋊D₁₀₉	D₄	1	2	yes	—
84	D₄×D₁₀₉	—	2	16	no	—
85	D₄×D₁₀₉	—	2	8	no	—
86	D₄×D₁₀₉	—	2	4	no	—
87	D₄×D₁₀₉	—	2	4	no	—
88	D₄×D₁₀₉	C₂³	1	8	yes	complemented
89	D₄×D₁₀₉	C₂³	1	8	yes	complemented
90	C₂²×Dic₁₀₉	—	2	2	no	—
91	C₂×C₄×D₁₀₉	—	2	1	no	—
92	C₂×C₄×D₁₀₉	—	2	2	no	—
93	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
94	#13182019	C₂³	1	4	yes	complemented
95	#13182018	C₂³	1	8	yes	complemented
96	#13182017	C₂³	1	4	yes	complemented
97	#13182016	C₂³	1	4	yes	complemented
98	D₈₇₂	C₂³	1	8	yes	complemented
99	#13182014	C₂³	1	4	yes	complemented
100	#13182014	C₂³	1	8	yes	complemented
101	#13182014	C₂³	1	8	yes	complemented
102	#13182012	C₂³	1	8	yes	complemented
103	C₂×#11724784	C₂³	1	1	yes	characteristic
104	C₂×#11724784	C₂³	1	1	yes	characteristic
105	C₂×#11724784	C₂³	1	4	yes	complemented
106	C₈×D₁₀₉	C₂³	1	8	yes	complemented
107	C₂⁴×C₁₀₉	—	2	1	no	—
108	#41×C₁₀₉	—	2	2	no	—
109	#41×C₁₀₉	C₂³	1	4	yes	complemented
110	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
111	C₂×D₄×C₁₀₉	—	2	1	no	—
112	C₂×D₄×C₁₀₉	—	2	1	no	—
113	C₂×D₄×C₁₀₉	—	2	2	no	—
114	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
115	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
116	C₂×D₄×C₁₀₉	C₂³	1	4	yes	complemented
117	C₂²×C₄×C₁₀₉	—	2	1	no	—
118	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
119	SD₁₆×C₁₀₉	C₂³	1	8	yes	complemented
120	D₈×C₁₀₉	C₂³	1	8	yes	complemented
121	M₁₆×C₁₀₉	C₂³	1	4	yes	complemented
122	C₂×C₈×C₁₀₉	C₂³	1	2	yes	—
123	C₂³×C₁₀₉	—	2	1	no	—
124	C₂³×C₁₀₉	—	2	2	no	—
125	C₂³×C₁₀₉	—	2	4	no	—
126	C₂³×C₁₀₉	—	8	2	no	—
127	C₂³×C₁₀₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×D₁₀₉	—	2	1	no	—
129	C₂²×D₁₀₉	—	2	2	no	—
130	C₂²×D₁₀₉	—	2	4	no	—
131	C₂²×D₁₀₉	—	2	8	no	—
132	C₂²×D₁₀₉	—	2	8	no	—
133	C₂²×D₁₀₉	—	8	4	no	—
134	C₂²×D₁₀₉	—	8	4	no	—
135	C₂²×D₁₀₉	—	8	2	no	—
136	C₂²×D₁₀₉	C₂×D₄	1	2	yes	—
137	Q₈×C₁₀₉	—	2	1	no	—
138	Q₈×C₁₀₉	C₂⁴	1	2	yes	—
139	D₄×C₁₀₉	—	2	4	no	—
140	D₄×C₁₀₉	—	2	2	no	—
141	D₄×C₁₀₉	—	2	4	no	—
142	D₄×C₁₀₉	—	2	1	no	—
143	D₄×C₁₀₉	C₂⁴	1	2	yes	—
144	D₄×C₁₀₉	C₂⁴	1	4	yes	—
145	C₂×C₄×C₁₀₉	—	2	1	no	—
146	C₂×C₄×C₁₀₉	—	2	4	no	—
147	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
149	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
150	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
151	C₂²⋊D₁₀₉	—	2	4	no	—
152	C₂²⋊D₁₀₉	—	2	8	no	—
153	C₂²⋊D₁₀₉	—	2	8	no	—
154	C₂²⋊D₁₀₉	—	2	8	no	—
155	C₂²⋊D₁₀₉	C₂×D₄	1	8	yes	—
156	C₂×Dic₁₀₉	—	2	1	no	—
157	C₂×Dic₁₀₉	—	2	8	no	—
158	C₂×Dic₁₀₉	C₂×D₄	1	2	yes	—
159	D₄₃₆	—	2	8	no	—
160	D₄₃₆	—	2	1	no	—
161	D₄₃₆	—	2	2	no	—
162	D₄₃₆	—	2	4	no	—
163	D₄₃₆	C₂×D₄	1	4	yes	—
164	D₄₃₆	C₂⁴	1	4	yes	—
165	D₄₃₆	C₂⁴	1	2	yes	—
166	C₄×D₁₀₉	—	2	4	no	—
167	C₄×D₁₀₉	—	2	8	no	—
168	C₄×D₁₀₉	C₂×D₄	1	4	yes	—
169	C₄×D₁₀₉	C₂⁴	1	4	yes	—
170	Dic₂₁₈	—	2	1	no	—
171	Dic₂₁₈	C₂×D₄	1	4	yes	—
172	Dic₂₁₈	C₂⁴	1	2	yes	—
173	C₈×C₁₀₉	C₂⁴	1	4	yes	—
174	#11724784	C₂⁴	1	2	yes	—
175	#11724784	C₂⁴	1	2	yes	—
176	C₂²×C₁₀₉	—	2	2	no	—
177	C₂²×C₁₀₉	—	2	4	no	—
178	C₂²×C₁₀₉	—	2	2	no	—
179	C₂²×C₁₀₉	—	4	2	no	—
180	C₂²×C₁₀₉	—	4	4	no	—
181	C₂²×C₁₀₉	—	8	4	no	—
182	C₂²×C₁₀₉	C₂²×D₄	1	2	yes	—
183	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×D₁₀₉	—	2	4	no	—
185	C₂×D₁₀₉	—	2	4	no	—
186	C₂×D₁₀₉	—	2	2	no	—
187	C₂×D₁₀₉	—	4	2	no	—
188	C₂×D₁₀₉	—	4	4	no	—
189	C₂×D₁₀₉	—	8	8	no	—
190	C₂×D₁₀₉	—	8	8	no	—
191	C₂×D₁₀₉	—	8	4	no	—
192	C₂×D₁₀₉	C₂²×D₄	1	4	yes	—
193	C₄×C₁₀₉	—	2	2	no	—
194	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
195	C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
196	C₄×C₁₀₉	C₂⁵	1	1	yes	characteristic
197	Dic₁₀₉	—	2	2	no	—
198	Dic₁₀₉	C₂²×D₄	1	4	yes	—
199	C₂×C₁₀₉	—	2	2	no	—
200	C₂×C₁₀₉	—	4	2	no	—
201	C₂×C₁₀₉	—	4	4	no	—
202	C₂×C₁₀₉	#576	1	2	yes	complemented
203	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
204	D₁₀₉	—	2	4	no	—
205	D₁₀₉	—	4	4	no	—
206	D₁₀₉	—	4	2	no	—
207	C₂×#576	—	109	1	no	maximal, Sylow
208	C₁₀₉	C₂×#576	1	1	yes	characteristic, complemented, Sylow
209	C₂×H(5,𝔽₂)	—	109	1	no	—
210	C₂×H(5,𝔽₂)	—	109	1	no	—
211	#576	—	109	16	no	—
212	C₂×AGL(1,ℤ/8)	—	109	2	no	—
213	C₂×AGL(1,ℤ/8)	—	109	2	no	—
214	C₂×AGL(1,ℤ/8)	—	109	1	no	—
215	C₂×AGL(1,ℤ/8)	D₁₀₉	1	1	yes	characteristic, complemented
216	C₂×#135	—	109	1	no	—
217	C₂×#135	—	109	2	no	—
218	C₂²×D₈	—	109	1	no	—
219	C₂²×D₈	—	109	2	no	—
220	C₂×#131	—	109	1	no	—
221	H(5,𝔽₂)	—	109	8	no	—
222	H(5,𝔽₂)	—	109	8	no	—
223	H(5,𝔽₂)	—	218	4	no	—
224	H(5,𝔽₂)	—	218	4	no	—
225	C₂×#41	—	109	1	no	—
226	C₂×#41	—	109	2	no	—
227	C₂×#41	—	109	2	no	—
228	C₂×#41	—	109	1	no	—
229	C₂×#41	—	218	1	no	—
230	C₂×#41	—	218	1	no	—
231	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic, complemented
232	C₂²×D₄	—	109	2	no	—
233	C₂²×D₄	—	109	2	no	—
234	C₂²×D₄	—	109	1	no	—
235	C₂²×D₄	—	218	1	no	—
236	C₂²×D₄	—	218	2	no	—
237	C₂²×D₄	—	218	1	no	—
238	C₂²×D₄	—	218	2	no	—
239	C₂²×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
240	AGL(1,ℤ/8)	—	109	16	no	—
241	AGL(1,ℤ/8)	—	109	16	no	—
242	AGL(1,ℤ/8)	—	109	8	no	—
243	AGL(1,ℤ/8)	C₂×D₁₀₉	1	8	yes	complemented
244	#135	—	109	8	no	—
245	#135	—	109	16	no	—
246	C₂×Q₁₆	—	109	1	no	—
247	C₂×SD₁₆	—	109	1	no	—
248	C₂×SD₁₆	—	109	1	no	—
249	C₂×SD₁₆	—	109	2	no	—
250	C₂×SD₁₆	C₂×D₁₀₉	1	2	yes	complemented
251	C₂×D₈	—	109	2	no	—
252	C₂×D₈	—	109	1	no	—
253	C₂×D₈	—	109	2	no	—
254	C₂×D₈	—	109	8	no	—
255	C₂×D₈	—	109	16	no	—
256	C₂×D₈	—	109	2	no	—
257	C₂×D₈	C₂×D₁₀₉	1	2	yes	complemented
258	#131	—	109	8	no	—
259	C₂×M₁₆	—	109	2	no	—
260	C₂×M₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
261	C₂²×C₈	—	109	1	no	—
262	C₂²×C₈	—	109	2	no	—
263	C₂⁴	—	2	1	no	—
264	C₂⁴	—	218	2	no	—
265	C₂⁴	—	218	2	no	—
266	C₂⁴	—	218	1	no	—
267	#41	—	2	2	no	—
268	#41	—	109	4	no	—
269	#41	—	109	4	no	—
270	#41	—	109	8	no	—
271	#41	—	109	8	no	—
272	#41	—	109	4	no	—
273	#41	—	218	8	no	—
274	#41	—	218	4	no	—
275	#41	—	218	4	no	—
276	#41	—	218	8	no	—
277	#41	—	218	2	no	—
278	#41	C₂²×D₁₀₉	1	4	yes	complemented
279	C₂×Q₈	—	109	1	no	—
280	C₂×Q₈	—	109	1	no	—
281	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	109	2	no	—
286	C₂×D₄	—	109	8	no	—
287	C₂×D₄	—	109	8	no	—
288	C₂×D₄	—	109	1	no	—
289	C₂×D₄	—	109	2	no	—
290	C₂×D₄	—	109	1	no	—
291	C₂×D₄	—	109	4	no	—
292	C₂×D₄	—	218	8	no	—
293	C₂×D₄	—	218	2	no	—
294	C₂×D₄	—	218	4	no	—
295	C₂×D₄	—	218	4	no	—
296	C₂×D₄	—	218	2	no	—
297	C₂×D₄	—	218	2	no	—
298	C₂×D₄	—	218	16	no	—
299	C₂×D₄	—	218	8	no	—
300	C₂×D₄	—	218	16	no	—
301	C₂×D₄	—	218	2	no	—
302	C₂×D₄	—	218	1	no	—
303	C₂×D₄	—	218	1	no	—
304	C₂×D₄	—	218	2	no	—
305	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
306	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
307	C₂×D₄	C₂²×D₁₀₉	1	4	yes	complemented
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	109	2	no	—
310	C₂²×C₄	—	218	2	no	—
311	C₂²×C₄	—	218	2	no	—
312	C₂²×C₄	—	218	1	no	—
313	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
314	Q₁₆	—	109	4	no	—
315	SD₁₆	—	109	4	no	—
316	SD₁₆	—	109	4	no	—
317	SD₁₆	—	109	8	no	—
318	SD₁₆	C₂²×D₁₀₉	1	8	yes	complemented
319	D₈	—	109	8	no	—
320	D₈	—	109	4	no	—
321	D₈	—	109	8	no	—
322	D₈	—	109	8	no	—
323	D₈	C₂²×D₁₀₉	1	8	yes	complemented
324	M₁₆	—	109	8	no	—
325	M₁₆	C₂²×D₁₀₉	1	4	yes	complemented
326	C₂×C₈	—	109	1	no	—
327	C₂×C₈	—	109	1	no	—
328	C₂×C₈	—	109	4	no	—
329	C₂×C₈	—	109	8	no	—
330	C₂×C₈	C₂²×D₁₀₉	1	2	yes	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	8	2	no	—
335	C₂³	—	872	2	no	—
336	C₂³	—	872	4	no	—
337	C₂³	—	872	4	no	—
338	C₂³	—	109	2	no	—
339	C₂³	—	218	8	no	—
340	C₂³	—	218	8	no	—
341	C₂³	—	218	4	no	—
342	C₂³	—	218	2	no	—
343	C₂³	—	218	1	no	—
344	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
345	Q₈	—	2	1	no	—
346	Q₈	—	109	4	no	—
347	Q₈	—	109	2	no	—
348	Q₈	—	218	1	no	—
349	Q₈	C₂³×D₁₀₉	1	2	yes	—
350	D₄	—	2	4	no	—
351	D₄	—	2	2	no	—
352	D₄	—	2	4	no	—
353	D₄	—	2	1	no	—
354	D₄	—	109	8	no	—
355	D₄	—	109	4	no	—
356	D₄	—	109	4	no	—
357	D₄	—	109	2	no	—
358	D₄	—	218	8	no	—
359	D₄	—	218	8	no	—
360	D₄	—	218	8	no	—
361	D₄	—	218	8	no	—
362	D₄	—	218	4	no	—
363	D₄	—	218	4	no	—
364	D₄	—	218	1	no	—
365	D₄	—	218	2	no	—
366	D₄	C₂³×D₁₀₉	1	4	yes	—
367	D₄	C₂³×D₁₀₉	1	2	yes	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	109	2	no	—
371	C₂×C₄	—	109	4	no	—
372	C₂×C₄	—	109	4	no	—
373	C₂×C₄	—	218	8	no	—
374	C₂×C₄	—	218	8	no	—
375	C₂×C₄	—	218	1	no	—
376	C₂×C₄	—	218	4	no	—
377	C₂×C₄	D₄×D₁₀₉	1	2	yes	—
378	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
379	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
380	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
381	C₈	—	109	2	no	—
382	C₈	—	109	2	no	—
383	C₈	C₂³×D₁₀₉	1	4	yes	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	8	4	no	—
390	C₂²	—	872	4	no	—
391	C₂²	—	872	8	no	—
392	C₂²	—	872	8	no	—
393	C₂²	—	109	4	no	—
394	C₂²	—	436	4	no	—
395	C₂²	—	436	2	no	—
396	C₂²	—	218	4	no	—
397	C₂²	—	218	2	no	—
398	C₂²	—	218	4	no	—
399	C₂²	C₂×D₄×D₁₀₉	1	2	yes	—
400	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	109	4	no	—
403	C₄	—	218	2	no	—
404	C₄	C₂×D₄×D₁₀₉	1	2	yes	—
405	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
406	C₄	C₂⁴×D₁₀₉	1	1	yes	characteristic
407	C₂	—	2	2	no	—
408	C₂	—	4	4	no	—
409	C₂	—	4	2	no	—
410	C₂	—	436	4	no	—
411	C₂	—	436	2	no	—
412	C₂	—	218	4	no	—
413	C₂	#20295830	1	2	yes	direct product factor
414	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₄×C₁₀₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₀₉
Fitting	C₂×AGL(1,ℤ/8)×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₁₀₉
hypocenter	C₁₀₉	C₂×#576
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×#16812745	C₂	semidirect
2. C₂×#16812744	C₂	semidirect
3. #20295830	C₂	direct (N × H)
4. C₂×#16812727	C₂	semidirect
5. C₂×#16812726	C₂	semidirect
6. C₂×#16812723	C₂	semidirect
7. C₂×#16812720	C₂	semidirect
8. C₂×#16812719	C₂	semidirect
9. C₂²×#13182014	C₂	semidirect
10. C₂×D₈×D₁₀₉	C₂	semidirect
11. C₂×#16812707	C₂	semidirect
12. C₂×AGL(1,ℤ/8)×C₁₀₉	C₂	semidirect
14. #16812745	C₂²	semidirect
16. #16812744	C₂²	semidirect
17. C₂×#13182030	C₂²	semidirect
20. C₂×#13182029	C₂²	semidirect
22. C₂×#13182028	C₂²	semidirect
24. C₂²×D₄₃₆	C₂²	semidirect
28. C₂×D₄×D₁₀₉	C₂²	semidirect
29. C₂×D₄×D₁₀₉	C₂²	semidirect
30. #16812727	C₂²	semidirect
31. #16812726	C₂²	semidirect
32. #16812723	C₂²	semidirect
33. #16812720	C₂²	semidirect
34. #16812719	C₂²	semidirect
35. C₂×#13182019	C₂²	semidirect
36. C₂×#13182018	C₂²	semidirect
37. C₂×#13182017	C₂²	semidirect
38. C₂×#13182016	C₂²	semidirect
39. C₂×D₈₇₂	C₂²	semidirect
40. C₂×#13182014	C₂²	semidirect
41. C₂×#13182014	C₂²	semidirect
42. C₂×#13182014	C₂²	semidirect
43. C₂×#13182014	C₂²	semidirect
44. D₈×D₁₀₉	C₂²	semidirect
45. #16812707	C₂²	semidirect
46. C₂×#13182012	C₂²	semidirect
47. C₂²×#11724784	C₂²	semidirect
48. C₂×C₈×D₁₀₉	C₂²	semidirect
49. C₂×#41×C₁₀₉	C₂²	semidirect
50. C₂²×D₄×C₁₀₉	C₂²	semidirect
51. AGL(1,ℤ/8)×C₁₀₉	C₂²	semidirect
52. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
53. C₂×D₈×C₁₀₉	C₂²	semidirect
54. C₂×M₁₆×C₁₀₉	C₂²	semidirect
59. #13182030	C₂³	semidirect
64. #13182029	C₂³	semidirect
67. #13182028	C₂³	semidirect
77. C₂×D₄₃₆	C₂³	semidirect
88. D₄×D₁₀₉	C₂³	semidirect
89. D₄×D₁₀₉	C₂³	semidirect
94. #13182019	C₂³	semidirect
95. #13182018	C₂³	semidirect
96. #13182017	C₂³	semidirect
97. #13182016	C₂³	semidirect
98. D₈₇₂	C₂³	semidirect
99. #13182014	C₂³	semidirect
100. #13182014	C₂³	semidirect
101. #13182014	C₂³	semidirect
102. #13182012	C₂³	semidirect
105. C₂×#11724784	C₂³	semidirect
106. C₈×D₁₀₉	C₂³	semidirect
109. #41×C₁₀₉	C₂³	semidirect
116. C₂×D₄×C₁₀₉	C₂³	semidirect
119. SD₁₆×C₁₀₉	C₂³	semidirect
120. D₈×C₁₀₉	C₂³	semidirect
121. M₁₆×C₁₀₉	C₂³	semidirect
202. C₂×C₁₀₉	#576	semidirect
208. C₁₀₉	C₂×#576	semidirect
215. C₂×AGL(1,ℤ/8)	D₁₀₉	semidirect
231. C₂×#41	C₂×D₁₀₉	semidirect
239. C₂²×D₄	C₂×D₁₀₉	semidirect
243. AGL(1,ℤ/8)	C₂×D₁₀₉	semidirect
250. C₂×SD₁₆	C₂×D₁₀₉	semidirect
257. C₂×D₈	C₂×D₁₀₉	semidirect
260. C₂×M₁₆	C₂×D₁₀₉	semidirect
278. #41	C₂²×D₁₀₉	semidirect
307. C₂×D₄	C₂²×D₁₀₉	semidirect
318. SD₁₆	C₂²×D₁₀₉	semidirect
323. D₈	C₂²×D₁₀₉	semidirect
325. M₁₆	C₂²×D₁₀₉	semidirect
413. C₂	#20295830	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×#16812745	2
C₂×#16812744	2
#20295830	2
C₂×#16812727	2
C₂×#16812726	2
C₂×#16812723	2
C₂×#16812720	2
C₂×#16812719	2
C₂²×#13182014	2
C₂×D₈×D₁₀₉	2
C₂×#16812707	2
C₂×AGL(1,ℤ/8)×C₁₀₉	2
C₂×#576	109

Subgroups — C2×#20295830 #28377784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20295830 #28377784