Subgroups — C₂×C₄×#14555784 #31819582

Order 17792.

1728 conjugacy classes of subgroups.

The subgroup lattice has 312 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
2	C₄×#14555784	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄×Dic₂₇₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#17984807	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×Dic₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×C₂²⋊D₁₃₉	C₂	1	2	yes	maximal, complemented
7	C₂×(C₂²⋊D₁₃₉)⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₂×#17984800	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#17984798	C₂	1	2	yes	maximal, complemented
10	C₂²×C₄×Dic₁₃₉	C₂	1	2	yes	maximal, complemented
11	C₂×C₄²×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#14555784	C₄	1	16	yes	direct product factor
14	C₂×#14555784	C₂²	1	8	yes	—
15	C₂²×Dic₂₇₈	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊D₁₃₉	C₂²	1	2	yes	—
17	C₂³×Dic₁₃₉	C₂²	1	2	yes	—
18	C₂³×Dic₁₃₉	C₂²	1	2	yes	—
19	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
22	C₄×Dic₂₇₈	C₂²	1	8	yes	complemented
23	#17984807	C₂²	1	8	yes	complemented
24	D₄×Dic₁₃₉	C₂²	1	8	yes	complemented
25	C₄×C₂²⋊D₁₃₉	C₂²	1	16	yes	complemented
26	(C₂²⋊D₁₃₉)⋊C₄	C₂²	1	16	yes	complemented
27	#17984800	C₂²	1	8	yes	complemented
28	#17984798	C₂²	1	16	yes	complemented
29	C₂×C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×Dic₁₃₉⋊C₄	C₂²	1	2	yes	—
31	C₂×Dic₁₃₉⋊C₄	C₂²	1	2	yes	—
32	C₂×C₂²⋊Dic₁₃₉	C₂²	1	2	yes	—
33	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	2	yes	—
34	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×Dic₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×Dic₁₃₉	C₂²	1	2	yes	—
40	C₂×C₄×Dic₁₃₉	C₂²	1	16	yes	complemented
41	C₄²×D₁₃₉	C₂²	1	8	yes	complemented
42	C₂²×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂³×C₄×C₁₃₉	C₂²	1	2	yes	—
44	C₄×D₄×C₁₃₉	C₂²	1	8	yes	complemented
45	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
47	C₂×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂³×D₁₃₉	C₂³	1	1	yes	characteristic
49	#14555784	C₂×C₄	1	64	yes	direct product factor
50	C₂×Dic₂₇₈	C₂×C₄	1	8	yes	complemented
51	C₂×Dic₂₇₈	C₂³	1	4	yes	—
52	C₂×C₂²⋊D₁₃₉	C₂×C₄	1	16	yes	complemented
53	C₂×C₂²⋊D₁₃₉	C₂³	1	8	yes	—
54	C₂²×Dic₁₃₉	—	2	8	no	—
55	C₂²×Dic₁₃₉	C₂×C₄	1	16	yes	complemented
56	C₂²×Dic₁₃₉	C₂³	1	2	yes	—
57	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
58	C₂²×Dic₁₃₉	C₂³	1	8	yes	—
59	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
60	C₂²×Dic₁₃₉	C₂³	1	2	yes	—
61	C₂²×Dic₁₃₉	C₂³	1	8	yes	—
62	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
63	C₂×C₄×D₁₃₉	—	2	4	no	—
64	C₂×C₄×D₁₃₉	—	2	4	no	—
65	C₂×C₄×D₁₃₉	C₂×C₄	1	8	yes	complemented
66	C₂×C₄×D₁₃₉	C₂³	1	4	yes	—
67	C₂×C₄×D₁₃₉	C₂³	1	4	yes	—
68	C₂×C₄×D₁₃₉	C₂³	1	4	yes	—
69	C₄⋊Dic₁₃₉	C₂³	1	4	yes	—
70	Dic₁₃₉⋊C₄	C₂³	1	8	yes	—
71	Dic₁₃₉⋊C₄	C₂³	1	8	yes	—
72	C₂²⋊Dic₁₃₉	C₂³	1	8	yes	—
73	(C₂×D₁₃₉)⋊C₄	C₂³	1	8	yes	—
74	C₄×Dic₁₃₉	C₂³	1	4	yes	—
75	C₄×Dic₁₃₉	C₂³	1	4	yes	—
76	C₄×Dic₁₃₉	C₂³	1	4	yes	—
77	C₄×Dic₁₃₉	C₂³	1	8	yes	—
78	C₄×Dic₁₃₉	C₂³	1	8	yes	—
79	C₄×Dic₁₃₉	C₂³	1	8	yes	—
80	C₂⁴×C₁₃₉	C₂³	1	2	yes	—
81	C₂×D₄×C₁₃₉	C₂×C₄	1	8	yes	complemented
82	C₂×D₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂²×C₄×C₁₃₉	—	2	8	no	—
84	C₂²×C₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₁₃₉	C₂³	1	8	yes	—
87	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
91	C₄²×C₁₃₉	C₂³	1	4	yes	—
92	C₂²×D₁₃₉	—	2	2	no	—
93	C₂²×D₁₃₉	—	2	2	no	—
94	C₂²×D₁₃₉	C₂²×C₄	1	4	yes	—
95	C₂²×D₁₃₉	C₂⁴	1	2	yes	—
96	Dic₂₇₈	C₂²×C₄	1	16	yes	complemented
97	C₂²⋊D₁₃₉	C₂²×C₄	1	32	yes	complemented
98	C₂×Dic₁₃₉	—	2	2	no	—
99	C₂×Dic₁₃₉	—	2	4	no	—
100	C₂×Dic₁₃₉	—	2	16	no	—
101	C₂×Dic₁₃₉	C₂²×C₄	1	4	yes	—
102	C₂×Dic₁₃₉	C₂²×C₄	1	8	yes	—
103	C₂×Dic₁₃₉	C₂²×C₄	1	32	yes	complemented
104	C₂×Dic₁₃₉	#41	1	4	yes	complemented
105	C₂×Dic₁₃₉	C₂⁴	1	4	yes	—
106	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
107	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
108	C₂×Dic₁₃₉	C₂⁴	1	4	yes	—
109	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
110	C₄×D₁₃₉	—	2	8	no	—
111	C₄×D₁₃₉	—	2	8	no	—
112	C₄×D₁₃₉	C₂²×C₄	1	16	yes	complemented
113	C₂³×C₁₃₉	—	2	4	no	—
114	C₂³×C₁₃₉	—	2	4	no	—
115	C₂³×C₁₃₉	C₂²×C₄	1	8	yes	—
116	C₂³×C₁₃₉	C₂⁴	1	4	yes	—
117	C₂³×C₁₃₉	C₂⁴	1	1	yes	characteristic
118	D₄×C₁₃₉	C₂²×C₄	1	16	yes	complemented
119	C₂×C₄×C₁₃₉	—	2	4	no	—
120	C₂×C₄×C₁₃₉	—	2	2	no	—
121	C₂×C₄×C₁₃₉	—	2	16	no	—
122	C₂×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
123	C₂×C₄×C₁₃₉	#41	1	4	yes	complemented
124	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
125	C₂×C₄×C₁₃₉	C₂⁴	1	4	yes	—
126	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
127	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
128	C₂²×C₁₃₉	—	2	16	no	—
129	C₂²×C₁₃₉	—	2	4	no	—
130	C₂²×C₁₃₉	—	2	4	no	—
131	C₂²×C₁₃₉	C₂³×C₄	1	8	yes	—
132	C₂²×C₁₃₉	C₂³×C₄	1	2	yes	—
133	C₂²×C₁₃₉	C₂×#41	1	2	yes	—
134	C₂²×C₁₃₉	C₂×#41	1	2	yes	—
135	C₂²×C₁₃₉	C₂⁵	1	1	yes	characteristic
136	C₂×D₁₃₉	—	2	8	no	—
137	C₂×D₁₃₉	—	2	2	no	—
138	C₂×D₁₃₉	—	2	2	no	—
139	C₂×D₁₃₉	C₂³×C₄	1	4	yes	—
140	C₄×C₁₃₉	—	2	4	no	—
141	C₄×C₁₃₉	—	2	2	no	—
142	C₄×C₁₃₉	C₂³×C₄	1	4	yes	—
143	C₄×C₁₃₉	C₂×#41	1	4	yes	complemented
144	Dic₁₃₉	—	2	2	no	—
145	Dic₁₃₉	—	2	4	no	—
146	Dic₁₃₉	C₂³×C₄	1	4	yes	—
147	Dic₁₃₉	C₂³×C₄	1	8	yes	—
148	Dic₁₃₉	C₂×#41	1	4	yes	complemented
149	C₂×C₁₃₉	—	2	8	no	—
150	C₂×C₁₃₉	C₄×#41	1	4	yes	complemented
151	C₂×C₁₃₉	C₂⁴×C₄	1	1	yes	characteristic
152	C₂×C₁₃₉	C₂²×#41	1	1	yes	characteristic
153	C₂×C₁₃₉	C₂²×#41	1	1	yes	characteristic
154	D₁₃₉	—	2	4	no	—
155	C₁₃₉	C₂×C₄×#41	1	1	yes	characteristic, complemented, Sylow
156	C₂×C₄×#41	—	139	1	no	maximal, Sylow
157	C₂²×#41	—	139	1	no	—
158	C₄×#41	—	139	16	no	—
159	C₂×C₄×Q₈	—	139	1	no	—
160	C₂×C₄×Q₈	—	139	1	no	—
161	C₂×C₄×D₄	—	139	1	no	—
162	C₂×C₄×D₄	—	139	2	no	—
163	C₂×C₄×D₄	—	139	2	no	—
164	C₂×C₄×D₄	D₁₃₉	1	1	yes	characteristic, complemented
165	C₂×#117	—	139	1	no	—
166	C₂×#117	—	139	2	no	—
167	C₂²×C₄²	—	139	2	no	—
168	C₂²×C₄²	—	139	1	no	—
169	C₂×#41	—	139	16	no	—
170	C₂×#41	—	139	8	no	—
171	C₂²×Q₈	—	139	1	no	—
172	C₂²×D₄	—	139	2	no	—
173	C₂²×D₄	C₂×D₁₃₉	1	1	yes	characteristic
174	C₂³×C₄	—	139	2	no	—
175	C₂³×C₄	—	139	1	no	—
176	C₂³×C₄	—	139	1	no	—
177	C₂³×C₄	—	139	2	no	—
178	C₂³×C₄	—	139	1	no	—
179	C₂³×C₄	C₂×D₁₃₉	1	2	yes	—
180	C₄×Q₈	—	139	8	no	—
181	C₄×Q₈	—	139	8	no	—
182	C₄×D₄	—	139	8	no	—
183	C₄×D₄	—	139	16	no	—
184	C₄×D₄	—	139	16	no	—
185	C₄×D₄	C₂×D₁₃₉	1	8	yes	complemented
186	#117	—	139	8	no	—
187	#117	—	139	16	no	—
188	C₂×C₄⋊C₄	—	139	2	no	—
189	C₂×C₄⋊C₄	—	139	2	no	—
190	C₂×C₄⋊C₄	—	139	1	no	—
191	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
192	C₂×C₂²⋊C₄	—	139	2	no	—
193	C₂×C₂²⋊C₄	—	139	2	no	—
194	C₂×C₂²⋊C₄	C₂×D₁₃₉	1	2	yes	—
195	C₂×C₄²	—	139	2	no	—
196	C₂×C₄²	—	139	1	no	—
197	C₂×C₄²	—	139	1	no	—
198	C₂×C₄²	—	139	2	no	—
199	C₂×C₄²	—	139	16	no	—
200	C₂×C₄²	—	139	2	no	—
201	C₂×C₄²	—	139	1	no	—
202	C₂×C₄²	—	139	8	no	—
203	C₂×C₄²	C₂×D₁₃₉	1	1	yes	characteristic
204	C₂⁴	—	139	1	no	—
205	C₂⁴	C₂²×D₁₃₉	1	2	yes	—
206	#41	—	139	64	no	—
207	C₂×Q₈	—	139	8	no	—
208	C₂×Q₈	—	139	4	no	—
209	C₂×D₄	—	139	16	no	—
210	C₂×D₄	—	139	8	no	—
211	C₂×D₄	C₄×D₁₃₉	1	8	yes	complemented
212	C₂×D₄	C₂²×D₁₃₉	1	4	yes	—
213	C₂²×C₄	—	2	8	no	—
214	C₂²×C₄	—	278	4	no	—
215	C₂²×C₄	—	278	8	no	—
216	C₂²×C₄	—	278	4	no	—
217	C₂²×C₄	—	139	2	no	—
218	C₂²×C₄	—	139	1	no	—
219	C₂²×C₄	—	139	8	no	—
220	C₂²×C₄	—	139	4	no	—
221	C₂²×C₄	—	139	4	no	—
222	C₂²×C₄	—	139	16	no	—
223	C₂²×C₄	—	139	1	no	—
224	C₂²×C₄	—	139	1	no	—
225	C₂²×C₄	—	139	2	no	—
226	C₂²×C₄	—	139	8	no	—
227	C₂²×C₄	—	139	8	no	—
228	C₂²×C₄	—	139	4	no	—
229	C₂²×C₄	C₂²×D₁₃₉	1	2	yes	—
230	C₂²×C₄	C₂²×D₁₃₉	1	8	yes	—
231	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
232	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
233	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
234	C₄⋊C₄	—	139	8	no	—
235	C₄⋊C₄	—	139	8	no	—
236	C₄⋊C₄	—	139	4	no	—
237	C₄⋊C₄	C₂²×D₁₃₉	1	4	yes	—
238	C₂²⋊C₄	—	139	8	no	—
239	C₂²⋊C₄	—	139	8	no	—
240	C₂²⋊C₄	C₂²×D₁₃₉	1	8	yes	—
241	C₄²	—	139	4	no	—
242	C₄²	—	139	8	no	—
243	C₄²	—	139	4	no	—
244	C₄²	—	139	4	no	—
245	C₄²	—	139	8	no	—
246	C₄²	—	139	8	no	—
247	C₄²	C₂²×D₁₃₉	1	4	yes	—
248	C₂³	—	2	4	no	—
249	C₂³	—	2	4	no	—
250	C₂³	—	278	2	no	—
251	C₂³	—	278	2	no	—
252	C₂³	—	139	4	no	—
253	C₂³	—	139	2	no	—
254	C₂³	C₂×C₄×D₁₃₉	1	8	yes	—
255	C₂³	C₂³×D₁₃₉	1	4	yes	—
256	C₂³	C₂³×D₁₃₉	1	1	yes	characteristic
257	Q₈	—	139	16	no	—
258	D₄	—	139	32	no	—
259	D₄	C₂×C₄×D₁₃₉	1	16	yes	complemented
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	2	4	no	—
262	C₂×C₄	—	2	16	no	—
263	C₂×C₄	—	278	8	no	—
264	C₂×C₄	—	278	4	no	—
265	C₂×C₄	—	278	2	no	—
266	C₂×C₄	—	278	16	no	—
267	C₂×C₄	—	278	8	no	—
268	C₂×C₄	—	139	4	no	—
269	C₂×C₄	—	139	2	no	—
270	C₂×C₄	—	139	4	no	—
271	C₂×C₄	—	139	8	no	—
272	C₂×C₄	—	139	32	no	—
273	C₂×C₄	—	139	4	no	—
274	C₂×C₄	—	139	2	no	—
275	C₂×C₄	—	139	2	no	—
276	C₂×C₄	—	139	4	no	—
277	C₂×C₄	—	139	16	no	—
278	C₂×C₄	C₂×C₄×D₁₃₉	1	4	yes	—
279	C₂×C₄	#14555784	1	4	yes	direct product factor
280	C₂×C₄	C₂³×D₁₃₉	1	4	yes	—
281	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
282	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
283	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
284	C₂²	—	2	4	no	—
285	C₂²	—	2	4	no	—
286	C₂²	—	2	16	no	—
287	C₂²	—	278	2	no	—
288	C₂²	—	278	2	no	—
289	C₂²	—	278	8	no	—
290	C₂²	—	139	4	no	—
291	C₂²	C₂²×C₄×D₁₃₉	1	8	yes	—
292	C₂²	C₂²×C₄×D₁₃₉	1	2	yes	—
293	C₂²	#41×D₁₃₉	1	2	yes	—
294	C₂²	C₂×#14555784	1	2	yes	—
295	C₂²	C₂⁴×D₁₃₉	1	1	yes	characteristic
296	C₄	—	2	2	no	—
297	C₄	—	2	4	no	—
298	C₄	—	278	4	no	—
299	C₄	—	278	2	no	—
300	C₄	—	139	4	no	—
301	C₄	—	139	8	no	—
302	C₄	—	139	4	no	—
303	C₄	C₂²×C₄×D₁₃₉	1	4	yes	—
304	C₄	C₂×#14555784	1	4	yes	direct product factor
305	C₂	—	2	8	no	—
306	C₂	—	278	4	no	—
307	C₂	C₄×#14555784	1	4	yes	direct product factor
308	C₂	C₂³×C₄×D₁₃₉	1	1	yes	characteristic
309	C₂	C₂×#41×D₁₃₉	1	1	yes	characteristic
310	C₂	C₂²×#14555784	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₃₉
commutator	C₂×C₁₃₉	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₁₃₉
Fitting	C₂×C₄×D₄×C₁₃₉	C₂
socle	C₂³×C₁₃₉	C₂⁴
prime radical	C₂²×#14555784	C₂
cosocle	C₂²×C₁₃₉	C₂⁵
hypercenter	C₂×C₄×D₄	D₁₃₉
hypocenter	C₁₃₉	C₂×C₄×#41
LCS	G ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₄×#14555784	C₂	direct (N × H)
3. C₂×C₄×Dic₂₇₈	C₂	semidirect
4. C₂×#17984807	C₂	semidirect
5. C₂×D₄×Dic₁₃₉	C₂	semidirect
6. C₂×C₄×C₂²⋊D₁₃₉	C₂	semidirect
7. C₂×(C₂²⋊D₁₃₉)⋊C₄	C₂	semidirect
8. C₂×#17984800	C₂	semidirect
9. C₂×#17984798	C₂	semidirect
10. C₂²×C₄×Dic₁₃₉	C₂	semidirect
11. C₂×C₄²×D₁₃₉	C₂	semidirect
12. C₂×C₄×D₄×C₁₃₉	C₂	semidirect
13. C₂×#14555784	C₄	direct (N × H)
22. C₄×Dic₂₇₈	C₂²	semidirect
23. #17984807	C₂²	semidirect
24. D₄×Dic₁₃₉	C₂²	semidirect
25. C₄×C₂²⋊D₁₃₉	C₂²	semidirect
26. (C₂²⋊D₁₃₉)⋊C₄	C₂²	semidirect
27. #17984800	C₂²	semidirect
28. #17984798	C₂²	semidirect
40. C₂×C₄×Dic₁₃₉	C₂²	semidirect
41. C₄²×D₁₃₉	C₂²	semidirect
44. C₄×D₄×C₁₃₉	C₂²	semidirect
49. #14555784	C₂×C₄	direct (N × H)
50. C₂×Dic₂₇₈	C₂×C₄	semidirect
52. C₂×C₂²⋊D₁₃₉	C₂×C₄	semidirect
55. C₂²×Dic₁₃₉	C₂×C₄	semidirect
65. C₂×C₄×D₁₃₉	C₂×C₄	semidirect
81. C₂×D₄×C₁₃₉	C₂×C₄	semidirect
96. Dic₂₇₈	C₂²×C₄	semidirect
97. C₂²⋊D₁₃₉	C₂²×C₄	semidirect
103. C₂×Dic₁₃₉	C₂²×C₄	semidirect
104. C₂×Dic₁₃₉	#41	semidirect
112. C₄×D₁₃₉	C₂²×C₄	semidirect
118. D₄×C₁₃₉	C₂²×C₄	semidirect
123. C₂×C₄×C₁₃₉	#41	semidirect
143. C₄×C₁₃₉	C₂×#41	semidirect
148. Dic₁₃₉	C₂×#41	semidirect
150. C₂×C₁₃₉	C₄×#41	semidirect
155. C₁₃₉	C₂×C₄×#41	semidirect
164. C₂×C₄×D₄	D₁₃₉	semidirect
185. C₄×D₄	C₂×D₁₃₉	semidirect
211. C₂×D₄	C₄×D₁₃₉	semidirect
259. D₄	C₂×C₄×D₁₃₉	semidirect
279. C₂×C₄	#14555784	direct (N × H)
304. C₄	C₂×#14555784	direct (N × H)
307. C₂	C₄×#14555784	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
C₄×#14555784	2
C₂×C₄×Dic₂₇₈	2
C₂×#17984807	2
C₂×D₄×Dic₁₃₉	2
C₂×C₄×C₂²⋊D₁₃₉	2
C₂×(C₂²⋊D₁₃₉)⋊C₄	2
C₂×#17984800	2
C₂×#17984798	2
C₂²×C₄×Dic₁₃₉	2
C₂×C₄²×D₁₃₉	2
C₂×C₄×D₄×C₁₃₉	2
C₂×C₄×#41	139

Subgroups — C2×C4×#14555784 #31819582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#14555784 #31819582