Subgroups — C₂×#22581598 #31819854

Order 17792.

1900 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14555784	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#22581598	C₂	1	16	yes	maximal, direct product factor
4	C₂×#17984830	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#17984826	C₂	1	2	yes	maximal, complemented
6	C₂×#17984822	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#17984817	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#17984816	C₂	1	2	yes	maximal, complemented
9	C₂×#17984812	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×D₅₅₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×(C₂×D₁₃₉)⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₁₃₉	C₂²	1	2	yes	—
14	C₂×#14555784	—	2	8	no	—
15	C₂×#14555784	C₂²	1	8	yes	complemented
16	C₂²×Dic₂₇₈	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₅₅₆	C₂²	1	1	yes	characteristic
18	C₂²×D₅₅₆	C₂²	1	1	yes	characteristic
19	C₂²×D₅₅₆	C₂²	1	2	yes	complemented
20	C₂²×C₂²⋊D₁₃₉	C₂²	1	2	yes	—
21	C₂²×C₂²⋊D₁₃₉	C₂²	1	2	yes	complemented
22	C₂×D₄×D₁₃₉	—	2	8	no	—
23	C₂×D₄×D₁₃₉	C₂²	1	8	yes	complemented
24	C₂³×Dic₁₃₉	C₂²	1	2	yes	complemented
25	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
27	#17984830	C₂²	1	8	yes	complemented
28	#17984826	C₂²	1	16	yes	complemented
29	#17984822	C₂²	1	8	yes	complemented
30	#17984817	C₂²	1	8	yes	complemented
31	#17984816	C₂²	1	16	yes	complemented
32	#17984812	C₂²	1	16	yes	complemented
33	C₄×D₅₅₆	C₂²	1	8	yes	complemented
34	C₂×C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄⋊Dic₁₃₉	C₂²	1	2	yes	complemented
36	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	2	yes	—
38	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	2	yes	complemented
39	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	2	yes	complemented
40	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	2	yes	complemented
42	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	16	yes	complemented
43	C₂²×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₉	C₂²	1	2	yes	complemented
45	C₄×D₄×C₁₃₉	C₂²	1	8	yes	complemented
46	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
48	C₂×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
49	C₂³×D₁₃₉	—	2	8	no	—
50	C₂³×D₁₃₉	—	2	8	no	—
51	C₂³×D₁₃₉	—	4	4	no	—
52	C₂³×D₁₃₉	C₂³	1	2	yes	—
53	C₂³×D₁₃₉	C₂³	1	1	yes	characteristic
54	C₂³×D₁₃₉	C₂³	1	8	yes	—
55	C₂³×D₁₃₉	C₂³	1	1	yes	characteristic
56	#14555784	—	2	32	no	—
57	C₂×Dic₂₇₈	—	2	4	no	—
58	C₂×Dic₂₇₈	C₂³	1	4	yes	complemented
59	C₂×D₅₅₆	—	2	4	no	—
60	C₂×D₅₅₆	—	2	4	no	—
61	C₂×D₅₅₆	—	4	4	no	—
62	C₂×D₅₅₆	C₂³	1	4	yes	—
63	C₂×D₅₅₆	C₂³	1	4	yes	—
64	C₂×D₅₅₆	C₂³	1	8	yes	complemented
65	C₂×C₂²⋊D₁₃₉	—	2	8	no	—
66	C₂×C₂²⋊D₁₃₉	—	2	8	no	—
67	C₂×C₂²⋊D₁₃₉	C₂³	1	8	yes	—
68	C₂×C₂²⋊D₁₃₉	C₂³	1	8	yes	complemented
69	D₄×D₁₃₉	—	2	32	no	—
70	C₂²×Dic₁₃₉	—	2	8	no	—
71	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
72	C₂²×Dic₁₃₉	C₂³	1	2	yes	—
73	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
74	C₂²×Dic₁₃₉	C₂³	1	8	yes	complemented
75	C₂×C₄×D₁₃₉	—	2	4	no	—
76	C₂×C₄×D₁₃₉	—	2	4	no	—
77	C₂×C₄×D₁₃₉	C₂³	1	4	yes	—
78	C₂×C₄×D₁₃₉	C₂³	1	4	yes	complemented
79	C₄⋊Dic₁₃₉	C₂³	1	4	yes	complemented
80	C₄⋊Dic₁₃₉	C₂³	1	8	yes	complemented
81	(C₂×D₁₃₉)⋊C₄	C₂³	1	4	yes	—
82	(C₂×D₁₃₉)⋊C₄	C₂³	1	8	yes	—
83	(C₂×D₁₃₉)⋊C₄	C₂³	1	8	yes	complemented
84	(C₂×D₁₃₉)⋊C₄	C₂³	1	8	yes	complemented
85	(C₂×D₁₃₉)⋊C₄	C₂³	1	4	yes	complemented
86	(C₂×D₁₃₉)⋊C₄	C₂³	1	8	yes	complemented
87	C₂⁴×C₁₃₉	C₂³	1	2	yes	—
88	C₂×D₄×C₁₃₉	D₄	1	8	yes	complemented
89	C₂×D₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂²×C₄×C₁₃₉	—	4	4	no	—
91	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₉	C₂³	1	8	yes	complemented
96	C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	complemented
97	C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	complemented
98	C₄²×C₁₃₉	C₂³	1	4	yes	complemented
99	C₂²×D₁₃₉	—	2	2	no	—
100	C₂²×D₁₃₉	—	2	2	no	—
101	C₂²×D₁₃₉	—	2	2	no	—
102	C₂²×D₁₃₉	—	2	16	no	—
103	C₂²×D₁₃₉	—	2	4	no	—
104	C₂²×D₁₃₉	—	2	2	no	—
105	C₂²×D₁₃₉	—	2	4	no	—
106	C₂²×D₁₃₉	—	2	2	no	—
107	C₂²×D₁₃₉	—	2	4	no	—
108	C₂²×D₁₃₉	—	2	16	no	—
109	C₂²×D₁₃₉	—	4	8	no	—
110	C₂²×D₁₃₉	—	4	32	no	—
111	C₂²×D₁₃₉	#41	1	4	yes	complemented
112	C₂²×D₁₃₉	C₂⁴	1	4	yes	—
113	C₂²×D₁₃₉	C₂⁴	1	2	yes	—
114	C₂²×D₁₃₉	C₂⁴	1	2	yes	—
115	Dic₂₇₈	—	2	8	no	—
116	D₅₅₆	—	2	8	no	—
117	D₅₅₆	—	2	8	no	—
118	D₅₅₆	—	4	8	no	—
119	C₂²⋊D₁₃₉	—	2	16	no	—
120	C₂²⋊D₁₃₉	—	2	16	no	—
121	C₂×Dic₁₃₉	—	2	2	no	—
122	C₂×Dic₁₃₉	—	2	2	no	—
123	C₂×Dic₁₃₉	—	2	4	no	—
124	C₂×Dic₁₃₉	—	2	16	no	—
125	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
126	C₂×Dic₁₃₉	C₂⁴	1	4	yes	—
127	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
128	C₄×D₁₃₉	—	2	8	no	—
129	C₄×D₁₃₉	—	2	8	no	—
130	C₂³×C₁₃₉	—	2	4	no	—
131	C₂³×C₁₃₉	—	2	4	no	—
132	C₂³×C₁₃₉	C₂×D₄	1	8	yes	—
133	C₂³×C₁₃₉	C₂⁴	1	4	yes	—
134	C₂³×C₁₃₉	C₂⁴	1	1	yes	characteristic
135	D₄×C₁₃₉	C₂×D₄	1	16	yes	complemented
136	C₂×C₄×C₁₃₉	—	2	2	no	—
137	C₂×C₄×C₁₃₉	—	2	2	no	—
138	C₂×C₄×C₁₃₉	—	2	4	no	—
139	C₂×C₄×C₁₃₉	—	4	8	no	—
140	C₂×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
141	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
142	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
143	C₂×C₄×C₁₃₉	C₂⁴	1	4	yes	—
144	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
145	C₂²×C₁₃₉	—	2	16	no	—
146	C₂²×C₁₃₉	—	2	4	no	—
147	C₂²×C₁₃₉	—	2	4	no	—
148	C₂²×C₁₃₉	C₂²×D₄	1	8	yes	—
149	C₂²×C₁₃₉	C₂²×D₄	1	2	yes	—
150	C₂²×C₁₃₉	C₂×#41	1	2	yes	—
151	C₂²×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
152	C₂²×C₁₃₉	C₂⁵	1	1	yes	characteristic
153	C₂×D₁₃₉	—	2	8	no	—
154	C₂×D₁₃₉	—	2	2	no	—
155	C₂×D₁₃₉	—	2	2	no	—
156	C₂×D₁₃₉	—	2	2	no	—
157	C₂×D₁₃₉	—	2	4	no	—
158	C₂×D₁₃₉	—	2	2	no	—
159	C₂×D₁₃₉	—	2	4	no	—
160	C₂×D₁₃₉	—	2	2	no	—
161	C₂×D₁₃₉	—	2	4	no	—
162	C₂×D₁₃₉	—	4	32	no	—
163	C₂×D₁₃₉	—	4	4	no	—
164	C₂×D₁₃₉	—	4	8	no	—
165	C₂×D₁₃₉	C₂×#41	1	4	yes	complemented
166	C₄×C₁₃₉	—	2	2	no	—
167	C₄×C₁₃₉	—	2	2	no	—
168	C₄×C₁₃₉	—	2	4	no	—
169	C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
170	Dic₁₃₉	—	2	2	no	—
171	Dic₁₃₉	—	2	2	no	—
172	Dic₁₃₉	—	2	4	no	—
173	C₂×C₁₃₉	—	2	8	no	—
174	C₂×C₁₃₉	#546	1	4	yes	complemented
175	C₂×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
176	C₂×C₁₃₉	C₂²×#41	1	1	yes	characteristic
177	C₂×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
178	D₁₃₉	—	2	4	no	—
179	D₁₃₉	—	4	2	no	—
180	D₁₃₉	—	4	4	no	—
181	C₁₃₉	C₂×#546	1	1	yes	characteristic, complemented, Sylow
182	C₂×#546	—	139	1	no	maximal, Sylow
183	C₂²×#41	—	139	1	no	—
184	C₂³×D₄	—	139	1	no	—
185	#546	—	139	16	no	—
186	C₂×#124	—	139	1	no	—
187	C₂×#123	—	139	2	no	—
188	C₂×C₂²⋊Q₈	—	139	1	no	—
189	C₂×#121	—	139	2	no	—
190	C₂×#121	—	139	1	no	—
191	C₂×#120	—	139	2	no	—
192	C₂×C₄×D₄	—	139	1	no	—
193	C₂×C₄×D₄	D₁₃₉	1	1	yes	characteristic, complemented
194	C₂²×C₂²⋊C₄	—	139	2	no	—
195	C₂⁵	—	139	2	no	—
196	C₂×#41	—	278	8	no	—
197	C₂×#41	—	139	8	no	—
198	C₂²×Q₈	—	139	1	no	—
199	C₂²×D₄	—	278	8	no	—
200	C₂²×D₄	—	139	2	no	—
201	C₂²×D₄	—	139	2	no	—
202	C₂²×D₄	—	139	8	no	—
203	C₂²×D₄	—	139	1	no	—
204	C₂²×D₄	—	139	1	no	—
205	C₂²×D₄	—	139	2	no	—
206	C₂²×D₄	C₂×D₁₃₉	1	1	yes	characteristic
207	C₂³×C₄	—	139	2	no	—
208	C₂³×C₄	—	139	1	no	—
209	C₂³×C₄	—	139	1	no	—
210	C₂³×C₄	C₂×D₁₃₉	1	2	yes	complemented
211	#124	—	139	8	no	—
212	#123	—	139	16	no	—
213	C₂²⋊Q₈	—	139	8	no	—
214	#121	—	139	16	no	—
215	#121	—	139	8	no	—
216	#120	—	139	16	no	—
217	C₄×D₄	—	139	8	no	—
218	C₄×D₄	C₂×D₁₃₉	1	8	yes	complemented
219	C₂×C₄⋊C₄	—	139	1	no	—
220	C₂×C₄⋊C₄	—	139	2	no	—
221	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic, complemented
222	C₂×C₂²⋊C₄	—	139	1	no	—
223	C₂×C₂²⋊C₄	—	139	2	no	—
224	C₂×C₂²⋊C₄	—	139	2	no	—
225	C₂×C₂²⋊C₄	—	139	2	no	—
226	C₂×C₂²⋊C₄	—	139	1	no	—
227	C₂×C₂²⋊C₄	—	139	2	no	—
228	C₂×C₂²⋊C₄	—	139	16	no	—
229	C₂×C₂²⋊C₄	C₂×D₁₃₉	1	2	yes	complemented
230	C₂×C₄²	C₂×D₁₃₉	1	1	yes	characteristic, complemented
231	C₂⁴	—	278	8	no	—
232	C₂⁴	—	278	8	no	—
233	C₂⁴	—	556	4	no	—
234	C₂⁴	—	139	2	no	—
235	C₂⁴	—	139	1	no	—
236	C₂⁴	—	139	8	no	—
237	C₂⁴	—	139	1	no	—
238	C₂⁴	C₂²×D₁₃₉	1	2	yes	—
239	#41	—	278	32	no	—
240	C₂×Q₈	—	278	4	no	—
241	C₂×Q₈	—	139	4	no	—
242	C₂×D₄	—	278	4	no	—
243	C₂×D₄	—	278	8	no	—
244	C₂×D₄	—	278	8	no	—
245	C₂×D₄	—	278	32	no	—
246	C₂×D₄	—	278	4	no	—
247	C₂×D₄	—	556	4	no	—
248	C₂×D₄	—	139	8	no	—
249	C₂×D₄	—	139	8	no	—
250	C₂×D₄	—	139	4	no	—
251	C₂×D₄	—	139	4	no	—
252	C₂×D₄	—	139	8	no	—
253	C₂×D₄	D₅₅₆	1	8	yes	complemented
254	C₂×D₄	C₂²×D₁₃₉	1	4	yes	—
255	C₂²×C₄	—	4	4	no	—
256	C₂²×C₄	—	278	8	no	—
257	C₂²×C₄	—	278	4	no	—
258	C₂²×C₄	—	278	4	no	—
259	C₂²×C₄	—	139	8	no	—
260	C₂²×C₄	—	139	1	no	—
261	C₂²×C₄	—	139	2	no	—
262	C₂²×C₄	—	139	1	no	—
263	C₂²×C₄	—	139	4	no	—
264	C₂²×C₄	—	139	4	no	—
265	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
266	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
267	C₂²×C₄	C₂²×D₁₃₉	1	2	yes	—
268	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
269	C₂²×C₄	C₂²×D₁₃₉	1	8	yes	complemented
270	C₄⋊C₄	—	139	4	no	—
271	C₄⋊C₄	—	139	8	no	—
272	C₄⋊C₄	C₂²×D₁₃₉	1	4	yes	complemented
273	C₂²⋊C₄	—	139	4	no	—
274	C₂²⋊C₄	—	139	8	no	—
275	C₂²⋊C₄	—	139	8	no	—
276	C₂²⋊C₄	—	139	8	no	—
277	C₂²⋊C₄	—	139	4	no	—
278	C₂²⋊C₄	—	139	8	no	—
279	C₂²⋊C₄	C₂²×D₁₃₉	1	8	yes	complemented
280	C₄²	C₂²×D₁₃₉	1	4	yes	complemented
281	C₂³	—	2	4	no	—
282	C₂³	—	2	4	no	—
283	C₂³	—	278	16	no	—
284	C₂³	—	278	2	no	—
285	C₂³	—	278	2	no	—
286	C₂³	—	278	2	no	—
287	C₂³	—	278	16	no	—
288	C₂³	—	278	4	no	—
289	C₂³	—	278	2	no	—
290	C₂³	—	278	4	no	—
291	C₂³	—	278	2	no	—
292	C₂³	—	278	4	no	—
293	C₂³	—	556	8	no	—
294	C₂³	—	556	32	no	—
295	C₂³	—	139	4	no	—
296	C₂³	—	139	2	no	—
297	C₂³	—	139	4	no	—
298	C₂³	—	139	2	no	—
299	C₂³	C₂×D₅₅₆	1	8	yes	—
300	C₂³	C₂³×D₁₃₉	1	4	yes	—
301	C₂³	C₂³×D₁₃₉	1	1	yes	characteristic
302	Q₈	—	278	8	no	—
303	D₄	—	278	8	no	—
304	D₄	—	278	16	no	—
305	D₄	—	278	16	no	—
306	D₄	—	278	8	no	—
307	D₄	—	556	8	no	—
308	D₄	C₂×D₅₅₆	1	16	yes	complemented
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	8	no	—
313	C₂×C₄	—	278	2	no	—
314	C₂×C₄	—	278	2	no	—
315	C₂×C₄	—	278	4	no	—
316	C₂×C₄	—	278	16	no	—
317	C₂×C₄	—	278	8	no	—
318	C₂×C₄	—	278	8	no	—
319	C₂×C₄	—	139	2	no	—
320	C₂×C₄	—	139	4	no	—
321	C₂×C₄	—	139	2	no	—
322	C₂×C₄	C₂×D₅₅₆	1	4	yes	—
323	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
324	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
325	C₂×C₄	C₂³×D₁₃₉	1	4	yes	—
326	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	16	no	—
330	C₂²	—	278	2	no	—
331	C₂²	—	278	2	no	—
332	C₂²	—	278	8	no	—
333	C₂²	—	278	2	no	—
334	C₂²	—	278	4	no	—
335	C₂²	—	278	2	no	—
336	C₂²	—	278	4	no	—
337	C₂²	—	278	2	no	—
338	C₂²	—	278	4	no	—
339	C₂²	—	556	32	no	—
340	C₂²	—	556	8	no	—
341	C₂²	—	556	4	no	—
342	C₂²	—	139	4	no	—
343	C₂²	C₂²×D₅₅₆	1	8	yes	—
344	C₂²	C₂²×D₅₅₆	1	2	yes	—
345	C₂²	#41×D₁₃₉	1	2	yes	—
346	C₂²	#17984887	1	2	yes	—
347	C₂²	C₂⁴×D₁₃₉	1	1	yes	characteristic
348	C₄	—	2	2	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	4	no	—
351	C₄	—	278	2	no	—
352	C₄	—	278	2	no	—
353	C₄	—	278	4	no	—
354	C₄	C₂²×D₅₅₆	1	4	yes	—
355	C₂	—	2	8	no	—
356	C₂	—	278	4	no	—
357	C₂	—	556	4	no	—
358	C₂	—	556	2	no	—
359	C₂	#22581598	1	4	yes	direct product factor
360	C₂	C₂³×D₅₅₆	1	1	yes	characteristic
361	C₂	C₂×#41×D₁₃₉	1	1	yes	characteristic
362	C₂	C₂×#17984887	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₃₉
commutator, cosocle	C₂²×C₁₃₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃₉
Fitting	C₂×C₄×D₄×C₁₃₉	C₂
socle	C₂³×C₁₃₉	C₂⁴
hypercenter	C₂×C₄×D₄	D₁₃₉
hypocenter	C₁₃₉	C₂×#546
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#14555784	C₂	semidirect
2. C₂²×D₄×D₁₃₉	C₂	semidirect
3. #22581598	C₂	direct (N × H)
4. C₂×#17984830	C₂	semidirect
5. C₂×#17984826	C₂	semidirect
6. C₂×#17984822	C₂	semidirect
7. C₂×#17984817	C₂	semidirect
8. C₂×#17984816	C₂	semidirect
9. C₂×#17984812	C₂	semidirect
10. C₂×C₄×D₅₅₆	C₂	semidirect
11. C₂²×(C₂×D₁₃₉)⋊C₄	C₂	semidirect
12. C₂×C₄×D₄×C₁₃₉	C₂	semidirect
15. C₂×#14555784	C₂²	semidirect
16. C₂²×Dic₂₇₈	C₂²	semidirect
19. C₂²×D₅₅₆	C₂²	semidirect
21. C₂²×C₂²⋊D₁₃₉	C₂²	semidirect
23. C₂×D₄×D₁₃₉	C₂²	semidirect
24. C₂³×Dic₁₃₉	C₂²	semidirect
26. C₂²×C₄×D₁₃₉	C₂²	semidirect
27. #17984830	C₂²	semidirect
28. #17984826	C₂²	semidirect
29. #17984822	C₂²	semidirect
30. #17984817	C₂²	semidirect
31. #17984816	C₂²	semidirect
32. #17984812	C₂²	semidirect
33. C₄×D₅₅₆	C₂²	semidirect
34. C₂×C₄⋊Dic₁₃₉	C₂²	semidirect
35. C₂×C₄⋊Dic₁₃₉	C₂²	semidirect
38. C₂×(C₂×D₁₃₉)⋊C₄	C₂²	semidirect
39. C₂×(C₂×D₁₃₉)⋊C₄	C₂²	semidirect
40. C₂×(C₂×D₁₃₉)⋊C₄	C₂²	semidirect
41. C₂×(C₂×D₁₃₉)⋊C₄	C₂²	semidirect
42. C₂×(C₂×D₁₃₉)⋊C₄	C₂²	semidirect
44. C₂³×C₄×C₁₃₉	C₂²	semidirect
45. C₄×D₄×C₁₃₉	C₂²	semidirect
46. C₂×C₄⋊C₄×C₁₃₉	C₂²	semidirect
47. C₂×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
48. C₂×C₄²×C₁₃₉	C₂²	semidirect
58. C₂×Dic₂₇₈	C₂³	semidirect
64. C₂×D₅₅₆	C₂³	semidirect
68. C₂×C₂²⋊D₁₃₉	C₂³	semidirect
74. C₂²×Dic₁₃₉	C₂³	semidirect
78. C₂×C₄×D₁₃₉	C₂³	semidirect
79. C₄⋊Dic₁₃₉	C₂³	semidirect
80. C₄⋊Dic₁₃₉	C₂³	semidirect
83. (C₂×D₁₃₉)⋊C₄	C₂³	semidirect
84. (C₂×D₁₃₉)⋊C₄	C₂³	semidirect
85. (C₂×D₁₃₉)⋊C₄	C₂³	semidirect
86. (C₂×D₁₃₉)⋊C₄	C₂³	semidirect
88. C₂×D₄×C₁₃₉	D₄	semidirect
95. C₂²×C₄×C₁₃₉	C₂³	semidirect
96. C₄⋊C₄×C₁₃₉	C₂³	semidirect
97. C₂²⋊C₄×C₁₃₉	C₂³	semidirect
98. C₄²×C₁₃₉	C₂³	semidirect
111. C₂²×D₁₃₉	#41	semidirect
135. D₄×C₁₃₉	C₂×D₄	semidirect
165. C₂×D₁₃₉	C₂×#41	semidirect
174. C₂×C₁₃₉	#546	semidirect
181. C₁₃₉	C₂×#546	semidirect
193. C₂×C₄×D₄	D₁₃₉	semidirect
210. C₂³×C₄	C₂×D₁₃₉	semidirect
218. C₄×D₄	C₂×D₁₃₉	semidirect
221. C₂×C₄⋊C₄	C₂×D₁₃₉	semidirect
229. C₂×C₂²⋊C₄	C₂×D₁₃₉	semidirect
230. C₂×C₄²	C₂×D₁₃₉	semidirect
253. C₂×D₄	D₅₅₆	semidirect
269. C₂²×C₄	C₂²×D₁₃₉	semidirect
272. C₄⋊C₄	C₂²×D₁₃₉	semidirect
279. C₂²⋊C₄	C₂²×D₁₃₉	semidirect
280. C₄²	C₂²×D₁₃₉	semidirect
308. D₄	C₂×D₅₅₆	semidirect
359. C₂	#22581598	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×#14555784	2
C₂²×D₄×D₁₃₉	2
#22581598	2
C₂×#17984830	2
C₂×#17984826	2
C₂×#17984822	2
C₂×#17984817	2
C₂×#17984816	2
C₂×#17984812	2
C₂×C₄×D₅₅₆	2
C₂²×(C₂×D₁₃₉)⋊C₄	2
C₂×C₄×D₄×C₁₃₉	2
C₂×#546	139

Subgroups — C2×#22581598 #31819854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22581598 #31819854