Subgroups — C₂×#22581751 #31821149

Order 17792.

1484 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14555785	C₂	1	1	yes	maximal, characteristic, complemented
2	#22581751	C₂	1	16	yes	maximal, direct product factor
3	C₂×#17984873	C₂	1	2	yes	maximal, complemented
4	C₂×#17984872	C₂	1	2	yes	maximal, complemented
5	C₂×#17984868	C₂	1	2	yes	maximal, complemented
6	C₂×#17984867	C₂	1	2	yes	maximal, complemented
7	C₂×#17984862	C₂	1	4	yes	maximal, complemented
8	C₂²×#14555769	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14555785	—	2	1	no	—
11	C₂×#14555785	—	2	1	no	—
12	C₂×#14555785	—	2	4	no	—
13	C₂×#14555785	C₂²	1	2	yes	—
14	C₂×#14555785	C₂²	1	2	yes	complemented
15	C₂×#14555785	C₂²	1	8	yes	complemented
16	C₂²×Dic₂₇₈	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₅₅₆	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊D₁₃₉	—	2	1	no	—
19	C₂²×C₄×D₁₃₉	—	2	1	no	—
20	#17984873	C₂²	1	16	yes	complemented
21	#17984872	C₂²	1	16	yes	complemented
22	#17984868	C₂²	1	16	yes	complemented
23	#17984867	C₂²	1	16	yes	complemented
24	#17984862	C₂²	1	32	yes	complemented
25	C₂×#14555775	C₂²	1	4	yes	complemented
26	C₂×#14555773	C₂²	1	4	yes	complemented
27	C₂×#14555772	C₂²	1	4	yes	complemented
28	C₂×#14555770	C₂²	1	4	yes	complemented
29	C₂×#14555769	C₂²	1	2	yes	complemented
30	C₂×#14555769	C₂²	1	2	yes	complemented
31	C₂×#14555769	C₂²	1	8	yes	complemented
32	C₂²×C₁₃₉⋊C₈	C₂²	1	2	yes	complemented
33	C₂×#41×C₁₃₉	—	2	1	no	—
34	C₂×#41×C₁₃₉	—	2	1	no	—
35	C₂×#41×C₁₃₉	—	2	4	no	—
36	C₂×#41×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#41×C₁₃₉	C₂²	1	2	yes	complemented
38	C₂×#41×C₁₃₉	C₂²	1	8	yes	complemented
39	C₂²×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
40	C₂²×D₄×C₁₃₉	—	2	1	no	—
41	C₂²×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
42	C₂³×C₄×C₁₃₉	—	2	1	no	—
43	C₂³×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂³×D₁₃₉	—	2	1	no	—
45	#14555785	—	2	4	no	—
46	#14555785	—	2	8	no	—
47	#14555785	—	2	8	no	—
48	#14555785	—	2	4	no	—
49	#14555785	C₂³	1	8	yes	—
50	#14555785	C₂³	1	8	yes	complemented
51	C₂×Dic₂₇₈	—	2	1	no	—
52	C₂×Dic₂₇₈	—	2	2	no	—
53	C₂×Dic₂₇₈	C₂³	1	2	yes	—
54	C₂×Dic₂₇₈	C₂³	1	4	yes	complemented
55	C₂×D₅₅₆	—	2	1	no	—
56	C₂×D₅₅₆	—	2	2	no	—
57	C₂×D₅₅₆	C₂³	1	2	yes	—
58	C₂×D₅₅₆	C₂³	1	4	yes	complemented
59	C₂×C₂²⋊D₁₃₉	—	2	2	no	—
60	C₂×C₂²⋊D₁₃₉	—	2	2	no	—
61	C₂×C₂²⋊D₁₃₉	—	2	8	no	—
62	C₂²×Dic₁₃₉	—	2	1	no	—
63	C₂×C₄×D₁₃₉	—	2	2	no	—
64	C₂×C₄×D₁₃₉	—	2	8	no	—
65	C₂×C₄×D₁₃₉	—	2	2	no	—
66	#14555775	C₂³	1	16	yes	complemented
67	#14555773	C₂³	1	16	yes	complemented
68	#14555772	C₂³	1	16	yes	complemented
69	#14555770	C₂³	1	16	yes	complemented
70	#14555769	C₂³	1	8	yes	complemented
71	#14555769	C₂³	1	8	yes	complemented
72	C₂×C₁₃₉⋊C₈	C₂³	1	4	yes	—
73	C₂×C₁₃₉⋊C₈	C₂³	1	8	yes	complemented
74	C₂⁴×C₁₃₉	—	2	1	no	—
75	C₂⁴×C₁₃₉	D₄	1	1	yes	characteristic
76	#41×C₁₃₉	—	2	4	no	—
77	#41×C₁₃₉	—	2	8	no	—
78	#41×C₁₃₉	—	2	8	no	—
79	#41×C₁₃₉	—	2	4	no	—
80	#41×C₁₃₉	C₂³	1	8	yes	—
81	#41×C₁₃₉	C₂³	1	8	yes	complemented
82	C₂×Q₈×C₁₃₉	—	2	1	no	—
83	C₂×Q₈×C₁₃₉	—	2	2	no	—
84	C₂×Q₈×C₁₃₉	C₂³	1	2	yes	—
85	C₂×Q₈×C₁₃₉	C₂³	1	4	yes	complemented
86	C₂×D₄×C₁₃₉	—	2	2	no	—
87	C₂×D₄×C₁₃₉	—	2	2	no	—
88	C₂×D₄×C₁₃₉	—	2	8	no	—
89	C₂×D₄×C₁₃₉	—	2	1	no	—
90	C₂×D₄×C₁₃₉	—	2	2	no	—
91	C₂×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂×D₄×C₁₃₉	C₂³	1	4	yes	complemented
93	C₂²×C₄×C₁₃₉	—	2	1	no	—
94	C₂²×C₄×C₁₃₉	—	2	2	no	—
95	C₂²×C₄×C₁₃₉	—	2	8	no	—
96	C₂²×C₄×C₁₃₉	—	2	2	no	—
97	C₂²×C₄×C₁₃₉	D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃₉	D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₉	D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₉	D₄	1	4	yes	—
101	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂²×D₁₃₉	—	2	2	no	—
106	C₂²×D₁₃₉	—	2	4	no	—
107	C₂²×D₁₃₉	—	4	4	no	—
108	Dic₂₇₈	—	2	2	no	—
109	Dic₂₇₈	—	2	4	no	—
110	Dic₂₇₈	C₂⁴	1	4	yes	—
111	D₅₅₆	—	2	2	no	—
112	D₅₅₆	—	2	4	no	—
113	D₅₅₆	C₂⁴	1	4	yes	—
114	C₂²⋊D₁₃₉	—	2	8	no	—
115	C₂²⋊D₁₃₉	—	2	8	no	—
116	C₂×Dic₁₃₉	—	2	2	no	—
117	C₂×Dic₁₃₉	—	2	4	no	—
118	C₄×D₁₃₉	—	2	8	no	—
119	C₄×D₁₃₉	—	2	8	no	—
120	C₁₃₉⋊C₈	C₂⁴	1	8	yes	—
121	C₂³×C₁₃₉	—	2	2	no	—
122	C₂³×C₁₃₉	—	2	4	no	—
123	C₂³×C₁₃₉	—	4	2	no	—
124	C₂³×C₁₃₉	—	4	4	no	—
125	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
126	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
127	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
128	C₂³×C₁₃₉	C₂×D₄	1	4	yes	—
129	Q₈×C₁₃₉	—	2	2	no	—
130	Q₈×C₁₃₉	—	2	4	no	—
131	Q₈×C₁₃₉	C₂⁴	1	4	yes	—
132	D₄×C₁₃₉	—	2	8	no	—
133	D₄×C₁₃₉	—	2	8	no	—
134	D₄×C₁₃₉	—	2	2	no	—
135	D₄×C₁₃₉	—	2	4	no	—
136	D₄×C₁₃₉	C₂⁴	1	4	yes	—
137	C₂×C₄×C₁₃₉	—	2	2	no	—
138	C₂×C₄×C₁₃₉	—	2	4	no	—
139	C₂×C₄×C₁₃₉	—	2	8	no	—
140	C₂×C₄×C₁₃₉	—	2	8	no	—
141	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
143	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
145	C₂×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
146	C₂×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
147	C₂×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
148	C₂×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
149	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
151	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
152	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
153	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
154	C₂²×C₁₃₉	—	2	2	no	—
155	C₂²×C₁₃₉	—	2	2	no	—
156	C₂²×C₁₃₉	—	2	2	no	—
157	C₂²×C₁₃₉	—	2	4	no	—
158	C₂²×C₁₃₉	—	4	4	no	—
159	C₂²×C₁₃₉	—	4	8	no	—
160	C₂²×C₁₃₉	—	4	4	no	—
161	C₂²×C₁₃₉	C₂²×D₄	1	2	yes	—
162	C₂²×C₁₃₉	C₂²×D₄	1	2	yes	—
163	C₂²×C₁₃₉	C₂²×D₄	1	2	yes	—
164	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
165	C₂×D₁₃₉	—	2	4	no	—
166	C₂×D₁₃₉	—	4	8	no	—
167	C₂×D₁₃₉	—	4	4	no	—
168	C₄×C₁₃₉	—	2	4	no	—
169	C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
170	C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
171	C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
172	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
173	C₄×C₁₃₉	C₂⁵	1	1	yes	characteristic
174	Dic₁₃₉	—	2	4	no	—
175	C₂×C₁₃₉	—	2	2	no	—
176	C₂×C₁₃₉	—	2	2	no	—
177	C₂×C₁₃₉	—	2	2	no	—
178	C₂×C₁₃₉	—	4	4	no	—
179	C₂×C₁₃₉	#575	1	2	yes	complemented
180	C₂×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
181	D₁₃₉	—	4	4	no	—
182	C₁₃₉	C₂×#575	1	1	yes	characteristic, complemented, Sylow
183	C₂×#575	—	139	1	no	maximal, Sylow
184	C₂²×#41	—	139	1	no	—
185	C₂²×#41	D₁₃₉	1	1	yes	characteristic, complemented
186	#575	—	139	16	no	—
187	C₂×#137	—	139	2	no	—
188	C₂×#137	—	139	2	no	—
189	C₂×AGL(1,ℤ/8)	—	139	2	no	—
190	C₂×AGL(1,ℤ/8)	—	139	2	no	—
191	C₂×#135	—	139	4	no	—
192	C₂²×M₁₆	—	139	1	no	—
193	C₂×#41	—	2	1	no	—
194	C₂×#41	—	2	4	no	—
195	C₂×#41	—	2	1	no	—
196	C₂×#41	—	278	1	no	—
197	C₂×#41	—	278	4	no	—
198	C₂×#41	—	278	1	no	—
199	C₂×#41	—	139	2	no	—
200	C₂×#41	—	139	2	no	—
201	C₂×#41	—	139	8	no	—
202	C₂×#41	C₂×D₁₃₉	1	2	yes	—
203	C₂×#41	C₂×D₁₃₉	1	2	yes	complemented
204	C₂×#41	C₂×D₁₃₉	1	8	yes	complemented
205	C₂²×Q₈	—	139	1	no	—
206	C₂²×Q₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
207	C₂²×D₄	—	2	1	no	—
208	C₂²×D₄	—	278	1	no	—
209	C₂²×D₄	—	139	1	no	—
210	C₂²×D₄	C₂×D₁₃₉	1	1	yes	characteristic, complemented
211	C₂³×C₄	—	2	1	no	—
212	C₂³×C₄	—	278	1	no	—
213	C₂³×C₄	C₂×D₁₃₉	1	1	yes	characteristic
214	#137	—	139	16	no	—
215	#137	—	139	16	no	—
216	AGL(1,ℤ/8)	—	139	16	no	—
217	AGL(1,ℤ/8)	—	139	16	no	—
218	#135	—	139	32	no	—
219	C₂×Q₁₆	—	139	4	no	—
220	C₂×SD₁₆	—	139	4	no	—
221	C₂×SD₁₆	—	139	4	no	—
222	C₂×D₈	—	139	4	no	—
223	C₂×M₁₆	—	139	2	no	—
224	C₂×M₁₆	—	139	2	no	—
225	C₂×M₁₆	—	139	8	no	—
226	C₂²×C₈	—	139	2	no	—
227	C₂⁴	—	2	1	no	—
228	C₂⁴	—	278	1	no	—
229	C₂⁴	C₂²⋊D₁₃₉	1	1	yes	characteristic
230	#41	—	2	4	no	—
231	#41	—	2	8	no	—
232	#41	—	2	8	no	—
233	#41	—	2	4	no	—
234	#41	—	278	8	no	—
235	#41	—	278	4	no	—
236	#41	—	278	4	no	—
237	#41	—	278	8	no	—
238	#41	—	139	8	no	—
239	#41	—	139	8	no	—
240	#41	C₂²×D₁₃₉	1	8	yes	—
241	#41	C₂²×D₁₃₉	1	8	yes	complemented
242	C₂×Q₈	—	2	1	no	—
243	C₂×Q₈	—	2	2	no	—
244	C₂×Q₈	—	278	1	no	—
245	C₂×Q₈	—	278	2	no	—
246	C₂×Q₈	—	139	2	no	—
247	C₂×Q₈	—	139	4	no	—
248	C₂×Q₈	C₂²×D₁₃₉	1	2	yes	—
249	C₂×Q₈	C₂²×D₁₃₉	1	4	yes	complemented
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	1	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	278	2	no	—
256	C₂×D₄	—	278	2	no	—
257	C₂×D₄	—	278	8	no	—
258	C₂×D₄	—	278	1	no	—
259	C₂×D₄	—	278	2	no	—
260	C₂×D₄	—	139	2	no	—
261	C₂×D₄	—	139	4	no	—
262	C₂×D₄	C₂²×D₁₃₉	1	2	yes	—
263	C₂×D₄	C₂²×D₁₃₉	1	4	yes	complemented
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	278	1	no	—
269	C₂²×C₄	—	278	2	no	—
270	C₂²×C₄	—	278	8	no	—
271	C₂²×C₄	—	278	2	no	—
272	C₂²×C₄	C₂²⋊D₁₃₉	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊D₁₃₉	1	4	yes	—
274	C₂²×C₄	C₂²⋊D₁₃₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊D₁₃₉	1	1	yes	characteristic
276	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
277	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
278	C₂²×C₄	C₂²×D₁₃₉	1	4	yes	—
279	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
280	Q₁₆	—	139	16	no	—
281	SD₁₆	—	139	16	no	—
282	SD₁₆	—	139	16	no	—
283	D₈	—	139	16	no	—
284	M₁₆	—	139	8	no	—
285	M₁₆	—	139	8	no	—
286	C₂×C₈	—	139	4	no	—
287	C₂×C₈	—	139	8	no	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	4	2	no	—
291	C₂³	—	4	4	no	—
292	C₂³	—	278	4	no	—
293	C₂³	—	278	2	no	—
294	C₂³	—	556	4	no	—
295	C₂³	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
296	C₂³	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
297	C₂³	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
298	C₂³	C₂×C₂²⋊D₁₃₉	1	4	yes	—
299	Q₈	—	2	2	no	—
300	Q₈	—	2	4	no	—
301	Q₈	—	278	4	no	—
302	Q₈	—	278	2	no	—
303	Q₈	—	139	4	no	—
304	Q₈	C₂³×D₁₃₉	1	4	yes	—
305	D₄	—	2	8	no	—
306	D₄	—	2	8	no	—
307	D₄	—	2	2	no	—
308	D₄	—	2	4	no	—
309	D₄	—	278	8	no	—
310	D₄	—	278	8	no	—
311	D₄	—	278	4	no	—
312	D₄	—	278	2	no	—
313	D₄	—	139	4	no	—
314	D₄	C₂³×D₁₃₉	1	4	yes	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	278	4	no	—
320	C₂×C₄	—	278	2	no	—
321	C₂×C₄	—	278	8	no	—
322	C₂×C₄	—	278	8	no	—
323	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
324	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	4	yes	—
325	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
326	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	4	yes	—
327	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	2	yes	—
328	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	2	yes	—
329	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	2	yes	—
330	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	4	yes	—
331	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
332	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
333	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
334	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
335	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
336	C₈	—	139	8	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	4	8	no	—
343	C₂²	—	4	4	no	—
344	C₂²	—	278	4	no	—
345	C₂²	—	556	8	no	—
346	C₂²	—	556	4	no	—
347	C₂²	C₂²×C₂²⋊D₁₃₉	1	2	yes	—
348	C₂²	C₂²×C₂²⋊D₁₃₉	1	2	yes	—
349	C₂²	C₂²×C₂²⋊D₁₃₉	1	2	yes	—
350	C₂²	C₂²×C₂²⋊D₁₃₉	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	278	4	no	—
353	C₄	C₂²×C₂²⋊D₁₃₉	1	2	yes	—
354	C₄	C₂²×C₂²⋊D₁₃₉	1	2	yes	—
355	C₄	C₂²×C₂²⋊D₁₃₉	1	2	yes	—
356	C₄	C₂²×C₂²⋊D₁₃₉	1	1	yes	characteristic
357	C₄	C₂⁴×D₁₃₉	1	1	yes	characteristic
358	C₂	—	2	2	no	—
359	C₂	—	2	2	no	—
360	C₂	—	2	2	no	—
361	C₂	—	4	4	no	—
362	C₂	—	556	4	no	—
363	C₂	#22581751	1	2	yes	direct product factor
364	C₂	C₂³×C₂²⋊D₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₃₉
commutator, cosocle	C₄×C₁₃₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₃₉
Fitting	C₂²×#41×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
hypercenter	C₂²×#41	D₁₃₉
hypocenter	C₁₃₉	C₂×#575
LCS	G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×#14555785	C₂	semidirect
2. #22581751	C₂	direct (N × H)
3. C₂×#17984873	C₂	semidirect
4. C₂×#17984872	C₂	semidirect
5. C₂×#17984868	C₂	semidirect
6. C₂×#17984867	C₂	semidirect
7. C₂×#17984862	C₂	semidirect
8. C₂²×#14555769	C₂	semidirect
9. C₂²×#41×C₁₃₉	C₂	semidirect
14. C₂×#14555785	C₂²	semidirect
15. C₂×#14555785	C₂²	semidirect
16. C₂²×Dic₂₇₈	C₂²	semidirect
17. C₂²×D₅₅₆	C₂²	semidirect
20. #17984873	C₂²	semidirect
21. #17984872	C₂²	semidirect
22. #17984868	C₂²	semidirect
23. #17984867	C₂²	semidirect
24. #17984862	C₂²	semidirect
25. C₂×#14555775	C₂²	semidirect
26. C₂×#14555773	C₂²	semidirect
27. C₂×#14555772	C₂²	semidirect
28. C₂×#14555770	C₂²	semidirect
29. C₂×#14555769	C₂²	semidirect
30. C₂×#14555769	C₂²	semidirect
31. C₂×#14555769	C₂²	semidirect
32. C₂²×C₁₃₉⋊C₈	C₂²	semidirect
37. C₂×#41×C₁₃₉	C₂²	semidirect
38. C₂×#41×C₁₃₉	C₂²	semidirect
39. C₂²×Q₈×C₁₃₉	C₂²	semidirect
41. C₂²×D₄×C₁₃₉	C₂²	semidirect
50. #14555785	C₂³	semidirect
54. C₂×Dic₂₇₈	C₂³	semidirect
58. C₂×D₅₅₆	C₂³	semidirect
66. #14555775	C₂³	semidirect
67. #14555773	C₂³	semidirect
68. #14555772	C₂³	semidirect
69. #14555770	C₂³	semidirect
70. #14555769	C₂³	semidirect
71. #14555769	C₂³	semidirect
73. C₂×C₁₃₉⋊C₈	C₂³	semidirect
81. #41×C₁₃₉	C₂³	semidirect
85. C₂×Q₈×C₁₃₉	C₂³	semidirect
92. C₂×D₄×C₁₃₉	C₂³	semidirect
179. C₂×C₁₃₉	#575	semidirect
182. C₁₃₉	C₂×#575	semidirect
185. C₂²×#41	D₁₃₉	semidirect
203. C₂×#41	C₂×D₁₃₉	semidirect
204. C₂×#41	C₂×D₁₃₉	semidirect
206. C₂²×Q₈	C₂×D₁₃₉	semidirect
210. C₂²×D₄	C₂×D₁₃₉	semidirect
241. #41	C₂²×D₁₃₉	semidirect
249. C₂×Q₈	C₂²×D₁₃₉	semidirect
263. C₂×D₄	C₂²×D₁₃₉	semidirect
363. C₂	#22581751	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×#14555785	2
#22581751	2
C₂×#17984873	2
C₂×#17984872	2
C₂×#17984868	2
C₂×#17984867	2
C₂×#17984862	2
C₂²×#14555769	2
C₂²×#41×C₁₃₉	2
C₂×#575	139

Subgroups — C2×#22581751 #31821149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22581751 #31821149