Subgroups — C₂×#20295835 #28377790

Order 13952.

1460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812747	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16812745	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295835	C₂	1	16	yes	maximal, direct product factor
4	C₂×#16812731	C₂	1	2	yes	maximal, complemented
5	C₂×#16812727	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16812726	C₂	1	2	yes	maximal, complemented
7	C₂×#16812722	C₂	1	2	yes	maximal, complemented
8	C₂×#16812719	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#13182016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×SD₁₆×D₁₀₉	C₂	1	2	yes	maximal, complemented
11	C₂×#16812707	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#16812747	—	2	4	no	—
14	#16812747	C₂²	1	8	yes	complemented
15	#16812745	—	2	4	no	—
16	#16812745	C₂²	1	8	yes	complemented
17	C₂×#13182030	—	2	1	no	—
18	C₂×#13182030	C₂²	1	2	yes	—
19	C₂×#13182030	C₂²	1	2	yes	complemented
20	C₂×#13182029	—	2	1	no	—
21	C₂×#13182029	—	2	2	no	—
22	C₂×#13182029	C₂²	1	1	yes	characteristic
23	C₂×#13182029	C₂²	1	1	yes	characteristic, complemented
24	C₂×Q₈×D₁₀₉	—	2	1	no	—
25	C₂×Q₈×D₁₀₉	C₂²	1	2	yes	complemented
26	C₂²×D₄₃₆	—	2	1	no	—
27	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₁₀₉	—	2	2	no	—
29	C₂×D₄×D₁₀₉	C₂²	1	2	yes	—
30	#16812731	C₂²	1	16	yes	complemented
31	#16812727	C₂²	1	8	yes	complemented
32	#16812726	C₂²	1	16	yes	complemented
33	#16812722	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	2	yes	complemented
39	C₂×#13182016	C₂²	1	2	yes	complemented
40	C₂×#13182016	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13182016	C₂²	1	8	yes	complemented
42	SD₁₆×D₁₀₉	C₂²	1	16	yes	complemented
43	C₂×D₈₇₂	C₂²	1	2	yes	complemented
44	C₂×#13182014	C₂²	1	1	yes	characteristic, 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
50	C₂²×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
51	#137×C₁₀₉	C₂²	1	8	yes	complemented
52	C₂×Q₁₆×C₁₀₉	C₂²	1	2	yes	complemented
53	C₂×SD₁₆×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	#13182030	—	2	8	no	—
58	#13182030	—	2	4	no	—
59	#13182030	—	2	4	no	—
60	#13182030	C₂³	1	8	yes	—
61	#13182030	C₂³	1	8	yes	complemented
62	#13182029	—	2	2	no	—
63	#13182029	—	2	16	no	—
64	#13182029	—	2	8	no	—
65	#13182029	D₄	1	4	yes	—
66	#13182029	C₂³	1	4	yes	—
67	#13182029	C₂³	1	4	yes	complemented
68	C₂×Dic₂₁₈	—	2	2	no	—
69	C₂×Dic₂₁₈	D₄	1	1	yes	characteristic
70	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
71	Q₈×D₁₀₉	—	2	4	no	—
72	Q₈×D₁₀₉	—	2	8	no	—
73	Q₈×D₁₀₉	C₂³	1	8	yes	complemented
74	C₂×D₄₃₆	—	2	2	no	—
75	C₂×D₄₃₆	—	2	2	no	—
76	C₂×D₄₃₆	—	2	1	no	—
77	C₂×D₄₃₆	—	2	2	no	—
78	C₂×D₄₃₆	—	2	8	no	—
79	C₂×D₄₃₆	D₄	1	1	yes	characteristic
80	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
81	C₂×D₄₃₆	C₂³	1	2	yes	—
82	C₂×D₄₃₆	C₂³	1	4	yes	—
83	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
84	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
85	C₂×C₂²⋊D₁₀₉	D₄	1	2	yes	—
86	D₄×D₁₀₉	—	2	16	no	—
87	D₄×D₁₀₉	—	2	4	no	—
88	D₄×D₁₀₉	C₂³	1	8	yes	—
89	C₂×C₄×D₁₀₉	—	2	2	no	—
90	C₂×C₄×D₁₀₉	—	2	1	no	—
91	C₂×C₄×D₁₀₉	—	2	2	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	8	yes	complemented
98	#13182016	C₂³	1	8	yes	complemented
99	#13182016	C₂³	1	4	yes	complemented
100	D₈₇₂	C₂³	1	8	yes	complemented
101	#13182014	C₂³	1	4	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	#41×C₁₀₉	—	2	2	no	—
108	#41×C₁₀₉	C₂³	1	4	yes	—
109	C₂×Q₈×C₁₀₉	—	2	1	no	—
110	C₂×Q₈×C₁₀₉	—	2	2	no	—
111	C₂×Q₈×C₁₀₉	C₂³	1	2	yes	—
112	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
113	C₂×Q₈×C₁₀₉	C₂³	1	4	yes	complemented
114	C₂×D₄×C₁₀₉	—	2	1	no	—
115	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₁₀₉	—	2	1	no	—
117	C₂²×C₄×C₁₀₉	—	2	1	no	—
118	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
119	Q₁₆×C₁₀₉	C₂³	1	8	yes	complemented
120	SD₁₆×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	C₂×D₄	1	1	yes	characteristic
125	C₂²×D₁₀₉	—	2	1	no	—
126	C₂²×D₁₀₉	—	2	2	no	—
127	C₂²×D₁₀₉	—	2	4	no	—
128	C₂²×D₁₀₉	—	2	8	no	—
129	C₂²×D₁₀₉	—	8	4	no	—
130	C₂²×D₁₀₉	—	8	2	no	—
131	C₂²×D₁₀₉	C₂×D₄	1	2	yes	—
132	Q₈×C₁₀₉	—	2	2	no	—
133	Q₈×C₁₀₉	—	2	4	no	—
134	Q₈×C₁₀₉	—	2	1	no	—
135	Q₈×C₁₀₉	C₂⁴	1	4	yes	—
136	Q₈×C₁₀₉	C₂⁴	1	2	yes	—
137	D₄×C₁₀₉	—	2	4	no	—
138	D₄×C₁₀₉	—	2	1	no	—
139	D₄×C₁₀₉	C₂⁴	1	2	yes	—
140	C₂×C₄×C₁₀₉	—	2	1	no	—
141	C₂×C₄×C₁₀₉	—	2	2	no	—
142	C₂×C₄×C₁₀₉	—	2	4	no	—
143	C₂×C₄×C₁₀₉	—	2	4	no	—
144	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
146	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
147	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
148	C₂²⋊D₁₀₉	—	2	4	no	—
149	C₂²⋊D₁₀₉	—	2	8	no	—
150	C₂²⋊D₁₀₉	C₂×D₄	1	8	yes	—
151	C₂×Dic₁₀₉	—	2	1	no	—
152	C₂×Dic₁₀₉	C₂×D₄	1	2	yes	—
153	D₄₃₆	—	2	8	no	—
154	D₄₃₆	—	2	8	no	—
155	D₄₃₆	—	2	2	no	—
156	D₄₃₆	—	2	4	no	—
157	D₄₃₆	—	2	1	no	—
158	D₄₃₆	C₂×D₄	1	4	yes	—
159	D₄₃₆	C₂⁴	1	2	yes	—
160	D₄₃₆	C₂⁴	1	4	yes	—
161	C₄×D₁₀₉	—	2	8	no	—
162	C₄×D₁₀₉	—	2	4	no	—
163	C₄×D₁₀₉	—	2	8	no	—
164	C₄×D₁₀₉	—	2	8	no	—
165	C₄×D₁₀₉	C₂×D₄	1	4	yes	—
166	C₄×D₁₀₉	C₂⁴	1	4	yes	—
167	Dic₂₁₈	—	2	1	no	—
168	Dic₂₁₈	—	2	8	no	—
169	Dic₂₁₈	C₂×D₄	1	4	yes	—
170	Dic₂₁₈	C₂⁴	1	2	yes	—
171	C₈×C₁₀₉	C₂⁴	1	4	yes	—
172	#11724784	C₂⁴	1	2	yes	—
173	#11724784	C₂⁴	1	2	yes	—
174	C₂²×C₁₀₉	—	2	2	no	—
175	C₂²×C₁₀₉	—	2	2	no	—
176	C₂²×C₁₀₉	—	4	2	no	—
177	C₂²×C₁₀₉	C₂²×D₄	1	2	yes	—
178	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×D₁₀₉	—	2	4	no	—
180	C₂×D₁₀₉	—	2	2	no	—
181	C₂×D₁₀₉	—	2	4	no	—
182	C₂×D₁₀₉	—	4	2	no	—
183	C₂×D₁₀₉	—	4	4	no	—
184	C₂×D₁₀₉	—	8	8	no	—
185	C₂×D₁₀₉	—	8	4	no	—
186	C₂×D₁₀₉	C₂²×D₄	1	4	yes	—
187	C₄×C₁₀₉	—	2	4	no	—
188	C₄×C₁₀₉	—	2	2	no	—
189	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
190	C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
191	C₄×C₁₀₉	C₂⁵	1	1	yes	characteristic
192	Dic₁₀₉	—	2	2	no	—
193	Dic₁₀₉	C₂²×D₄	1	4	yes	—
194	C₂×C₁₀₉	—	2	2	no	—
195	C₂×C₁₀₉	—	4	2	no	—
196	C₂×C₁₀₉	#577	1	2	yes	complemented
197	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
198	D₁₀₉	—	2	4	no	—
199	D₁₀₉	—	4	2	no	—
200	D₁₀₉	—	4	4	no	—
201	C₂×#577	—	109	1	no	maximal, Sylow
202	C₁₀₉	C₂×#577	1	1	yes	characteristic, complemented, Sylow
203	C₂×2₋¹⁺⁴	—	109	1	no	—
204	C₂×H(5,𝔽₂)	—	109	1	no	—
205	#577	—	109	16	no	—
206	C₂×#137	—	109	2	no	—
207	C₂×#137	D₁₀₉	1	1	yes	characteristic, complemented
208	C₂×AGL(1,ℤ/8)	—	109	2	no	—
209	C₂×AGL(1,ℤ/8)	—	109	1	no	—
210	C₂×#135	—	109	1	no	—
211	C₂×#135	—	109	2	no	—
212	C₂²×SD₁₆	—	109	1	no	—
213	C₂²×SD₁₆	—	109	2	no	—
214	C₂×#131	—	109	1	no	—
215	2₋¹⁺⁴	—	109	8	no	—
216	2₋¹⁺⁴	—	218	4	no	—
217	H(5,𝔽₂)	—	109	8	no	—
218	H(5,𝔽₂)	—	218	4	no	—
219	C₂×#41	—	109	1	no	—
220	C₂×#41	—	109	2	no	—
221	C₂×#41	—	109	2	no	—
222	C₂×#41	—	109	1	no	—
223	C₂×#41	—	218	2	no	—
224	C₂×#41	—	218	1	no	—
225	C₂×#41	—	218	1	no	—
226	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic
227	C₂²×Q₈	—	109	2	no	—
228	C₂²×Q₈	—	218	1	no	—
229	C₂²×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
230	C₂²×D₄	—	109	2	no	—
231	C₂²×D₄	—	109	1	no	—
232	C₂²×D₄	—	218	1	no	—
233	C₂²×D₄	—	218	2	no	—
234	#137	—	109	16	no	—
235	#137	C₂×D₁₀₉	1	8	yes	complemented
236	AGL(1,ℤ/8)	—	109	16	no	—
237	AGL(1,ℤ/8)	—	109	8	no	—
238	#135	—	109	8	no	—
239	#135	—	109	16	no	—
240	C₂×Q₁₆	—	109	1	no	—
241	C₂×Q₁₆	C₂×D₁₀₉	1	2	yes	complemented
242	C₂×SD₁₆	—	109	2	no	—
243	C₂×SD₁₆	—	109	2	no	—
244	C₂×SD₁₆	—	109	1	no	—
245	C₂×SD₁₆	—	109	8	no	—
246	C₂×SD₁₆	—	109	1	no	—
247	C₂×SD₁₆	—	109	16	no	—
248	C₂×SD₁₆	—	109	2	no	—
249	C₂×SD₁₆	C₂×D₁₀₉	1	2	yes	complemented
250	C₂×D₈	—	109	1	no	—
251	C₂×D₈	—	109	2	no	—
252	#131	—	109	8	no	—
253	C₂×M₁₆	—	109	2	no	—
254	C₂×M₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
255	C₂²×C₈	—	109	1	no	—
256	C₂²×C₈	—	109	2	no	—
257	C₂⁴	—	218	2	no	—
258	C₂⁴	—	218	1	no	—
259	#41	—	2	2	no	—
260	#41	—	109	4	no	—
261	#41	—	109	4	no	—
262	#41	—	109	8	no	—
263	#41	—	109	8	no	—
264	#41	—	109	4	no	—
265	#41	—	218	16	no	—
266	#41	—	218	8	no	—
267	#41	—	218	4	no	—
268	#41	—	218	4	no	—
269	#41	—	218	8	no	—
270	#41	—	218	2	no	—
271	#41	C₂²×D₁₀₉	1	4	yes	—
272	C₂×Q₈	—	2	1	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	109	1	no	—
275	C₂×Q₈	—	109	8	no	—
276	C₂×Q₈	—	109	1	no	—
277	C₂×Q₈	—	218	2	no	—
278	C₂×Q₈	—	218	4	no	—
279	C₂×Q₈	—	218	8	no	—
280	C₂×Q₈	C₂²×D₁₀₉	1	2	yes	—
281	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
282	C₂×Q₈	C₂²×D₁₀₉	1	4	yes	complemented
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	109	2	no	—
285	C₂×D₄	—	109	8	no	—
286	C₂×D₄	—	109	1	no	—
287	C₂×D₄	—	109	1	no	—
288	C₂×D₄	—	109	2	no	—
289	C₂×D₄	—	109	4	no	—
290	C₂×D₄	—	218	8	no	—
291	C₂×D₄	—	218	2	no	—
292	C₂×D₄	—	218	2	no	—
293	C₂×D₄	—	218	4	no	—
294	C₂×D₄	—	218	2	no	—
295	C₂×D₄	—	218	16	no	—
296	C₂×D₄	—	218	1	no	—
297	C₂×D₄	—	218	1	no	—
298	C₂×D₄	—	218	2	no	—
299	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	109	2	no	—
303	C₂²×C₄	—	218	2	no	—
304	C₂²×C₄	—	218	2	no	—
305	C₂²×C₄	—	218	2	no	—
306	C₂²×C₄	—	218	1	no	—
307	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
308	Q₁₆	—	109	4	no	—
309	Q₁₆	C₂²×D₁₀₉	1	8	yes	complemented
310	SD₁₆	—	109	8	no	—
311	SD₁₆	—	109	8	no	—
312	SD₁₆	—	109	4	no	—
313	SD₁₆	—	109	4	no	—
314	SD₁₆	—	109	8	no	—
315	SD₁₆	C₂²×D₁₀₉	1	8	yes	complemented
316	D₈	—	109	4	no	—
317	D₈	—	109	8	no	—
318	M₁₆	—	109	8	no	—
319	M₁₆	C₂²×D₁₀₉	1	4	yes	complemented
320	C₂×C₈	—	109	1	no	—
321	C₂×C₈	—	109	1	no	—
322	C₂×C₈	—	109	4	no	—
323	C₂×C₈	—	109	8	no	—
324	C₂×C₈	C₂²×D₁₀₉	1	2	yes	—
325	C₂³	—	2	1	no	—
326	C₂³	—	872	2	no	—
327	C₂³	—	872	4	no	—
328	C₂³	—	109	2	no	—
329	C₂³	—	218	8	no	—
330	C₂³	—	218	4	no	—
331	C₂³	—	218	1	no	—
332	C₂³	—	218	2	no	—
333	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
334	Q₈	—	2	2	no	—
335	Q₈	—	2	4	no	—
336	Q₈	—	2	1	no	—
337	Q₈	—	109	4	no	—
338	Q₈	—	109	2	no	—
339	Q₈	—	218	8	no	—
340	Q₈	—	218	1	no	—
341	Q₈	C₂³×D₁₀₉	1	4	yes	—
342	Q₈	C₂³×D₁₀₉	1	2	yes	—
343	D₄	—	2	4	no	—
344	D₄	—	2	1	no	—
345	D₄	—	109	8	no	—
346	D₄	—	109	4	no	—
347	D₄	—	109	2	no	—
348	D₄	—	109	4	no	—
349	D₄	—	218	8	no	—
350	D₄	—	218	8	no	—
351	D₄	—	218	8	no	—
352	D₄	—	218	4	no	—
353	D₄	—	218	4	no	—
354	D₄	—	218	2	no	—
355	D₄	—	218	1	no	—
356	D₄	C₂³×D₁₀₉	1	2	yes	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	109	2	no	—
362	C₂×C₄	—	109	4	no	—
363	C₂×C₄	—	109	4	no	—
364	C₂×C₄	—	218	8	no	—
365	C₂×C₄	—	218	8	no	—
366	C₂×C₄	—	218	8	no	—
367	C₂×C₄	—	218	1	no	—
368	C₂×C₄	—	218	4	no	—
369	C₂×C₄	D₄×D₁₀₉	1	2	yes	—
370	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
371	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
372	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
373	C₈	—	109	2	no	—
374	C₈	—	109	2	no	—
375	C₈	C₂³×D₁₀₉	1	4	yes	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	872	4	no	—
380	C₂²	—	872	8	no	—
381	C₂²	—	109	4	no	—
382	C₂²	—	436	4	no	—
383	C₂²	—	436	2	no	—
384	C₂²	—	218	2	no	—
385	C₂²	—	218	4	no	—
386	C₂²	—	218	4	no	—
387	C₂²	C₂×D₄×D₁₀₉	1	2	yes	—
388	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	2	4	no	—
391	C₄	—	109	4	no	—
392	C₄	—	218	2	no	—
393	C₄	C₂×D₄×D₁₀₉	1	2	yes	—
394	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
395	C₄	C₂⁴×D₁₀₉	1	1	yes	characteristic
396	C₂	—	2	2	no	—
397	C₂	—	4	2	no	—
398	C₂	—	436	4	no	—
399	C₂	—	436	2	no	—
400	C₂	—	218	4	no	—
401	C₂	#20295835	1	2	yes	direct product factor
402	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×#137×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
hypercenter	C₂×#137	D₁₀₉
hypocenter	C₁₀₉	C₂×#577
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#137

Complements

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

N	H ≅ G/N	type
1. C₂×#16812747	C₂	semidirect
2. C₂×#16812745	C₂	semidirect
3. #20295835	C₂	direct (N × H)
4. C₂×#16812731	C₂	semidirect
5. C₂×#16812727	C₂	semidirect
6. C₂×#16812726	C₂	semidirect
7. C₂×#16812722	C₂	semidirect
8. C₂×#16812719	C₂	semidirect
9. C₂²×#13182016	C₂	semidirect
10. C₂×SD₁₆×D₁₀₉	C₂	semidirect
11. C₂×#16812707	C₂	semidirect
12. C₂×#137×C₁₀₉	C₂	semidirect
14. #16812747	C₂²	semidirect
16. #16812745	C₂²	semidirect
19. C₂×#13182030	C₂²	semidirect
23. C₂×#13182029	C₂²	semidirect
25. C₂×Q₈×D₁₀₉	C₂²	semidirect
30. #16812731	C₂²	semidirect
31. #16812727	C₂²	semidirect
32. #16812726	C₂²	semidirect
33. #16812722	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×#13182016	C₂²	semidirect
40. C₂×#13182016	C₂²	semidirect
41. C₂×#13182016	C₂²	semidirect
42. SD₁₆×D₁₀₉	C₂²	semidirect
43. C₂×D₈₇₂	C₂²	semidirect
44. C₂×#13182014	C₂²	semidirect
45. #16812707	C₂²	semidirect
46. C₂×#13182012	C₂²	semidirect
47. C₂²×#11724784	C₂²	semidirect
48. C₂×C₈×D₁₀₉	C₂²	semidirect
50. C₂²×Q₈×C₁₀₉	C₂²	semidirect
51. #137×C₁₀₉	C₂²	semidirect
52. C₂×Q₁₆×C₁₀₉	C₂²	semidirect
53. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
54. C₂×M₁₆×C₁₀₉	C₂²	semidirect
61. #13182030	C₂³	semidirect
67. #13182029	C₂³	semidirect
73. Q₈×D₁₀₉	C₂³	semidirect
94. #13182019	C₂³	semidirect
95. #13182018	C₂³	semidirect
96. #13182017	C₂³	semidirect
97. #13182016	C₂³	semidirect
98. #13182016	C₂³	semidirect
99. #13182016	C₂³	semidirect
100. D₈₇₂	C₂³	semidirect
101. #13182014	C₂³	semidirect
102. #13182012	C₂³	semidirect
105. C₂×#11724784	C₂³	semidirect
106. C₈×D₁₀₉	C₂³	semidirect
113. C₂×Q₈×C₁₀₉	C₂³	semidirect
119. Q₁₆×C₁₀₉	C₂³	semidirect
120. SD₁₆×C₁₀₉	C₂³	semidirect
121. M₁₆×C₁₀₉	C₂³	semidirect
196. C₂×C₁₀₉	#577	semidirect
202. C₁₀₉	C₂×#577	semidirect
207. C₂×#137	D₁₀₉	semidirect
229. C₂²×Q₈	C₂×D₁₀₉	semidirect
235. #137	C₂×D₁₀₉	semidirect
241. C₂×Q₁₆	C₂×D₁₀₉	semidirect
249. C₂×SD₁₆	C₂×D₁₀₉	semidirect
254. C₂×M₁₆	C₂×D₁₀₉	semidirect
282. C₂×Q₈	C₂²×D₁₀₉	semidirect
309. Q₁₆	C₂²×D₁₀₉	semidirect
315. SD₁₆	C₂²×D₁₀₉	semidirect
319. M₁₆	C₂²×D₁₀₉	semidirect
401. C₂	#20295835	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×#16812747	2
C₂×#16812745	2
#20295835	2
C₂×#16812731	2
C₂×#16812727	2
C₂×#16812726	2
C₂×#16812722	2
C₂×#16812719	2
C₂²×#13182016	2
C₂×SD₁₆×D₁₀₉	2
C₂×#16812707	2
C₂×#137×C₁₀₉	2
C₂×#577	109

Subgroups — C2×#20295835 #28377790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20295835 #28377790