Subgroups — C₂×#20242875 #26198783

Order 12032.

758 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689403	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689201	C₂	1	1	yes	maximal, characteristic
4	#20242875	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688873	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688869	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688868	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#474	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625337	—	2	1	no	—
10	C₂²×#10625337	—	2	1	no	—
11	C₂²×#10625329	—	2	1	no	—
12	C₂×#13094024	C₂²	1	1	yes	characteristic
13	#15689502	—	2	2	no	—
14	#15689502	C₂²	1	4	yes	complemented
15	#15689403	—	2	2	no	—
16	#15689403	C₂²	1	4	yes	—
17	#15689201	—	2	2	no	—
18	#15689201	C₂²	1	4	yes	—
19	C₂×#13093957	—	2	1	no	—
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#13093945	—	2	1	no	—
23	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	#15688873	C₂²	1	4	yes	complemented
26	#15688869	C₂²	1	4	yes	complemented
27	#15688868	C₂²	1	4	yes	complemented
28	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#474	—	2	2	no	—
31	C₄₇×#474	C₂²	1	4	yes	—
32	C₂×#107×C₄₇	—	2	1	no	—
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#102×C₄₇	—	2	1	no	—
35	C₂²×Dic₉₄	—	2	1	no	—
36	C₂×#10625337	—	2	4	no	—
37	C₂×#10625337	—	2	4	no	—
38	C₂×#10625337	—	4	4	no	—
39	C₂×#10625337	—	4	4	no	—
40	C₂×#10625329	—	2	4	no	—
41	C₂×#10625329	—	4	4	no	—
42	C₂²×C₄₇⋊C₈	—	2	1	no	—
43	C₂²×C₄₇⋊C₈	—	2	1	no	—
44	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
46	#13094024	—	2	1	no	—
47	#13094024	—	2	1	no	—
48	#13094024	—	2	1	no	—
49	#13094024	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	—	2	1	no	—
51	C₂×C₄⋊Dic₄₇	—	2	1	no	—
52	#13093957	—	2	4	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
57	#13093945	—	2	4	no	—
58	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
59	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
60	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
61	C₂²×Q₈×C₄₇	—	2	1	no	—
62	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₇	—	2	1	no	—
64	C₂²×C₈×C₄₇	—	2	1	no	—
65	C₄⋊Q₈×C₄₇	—	2	1	no	—
66	C₄⋊Q₈×C₄₇	—	2	1	no	—
67	C₄⋊Q₈×C₄₇	—	2	1	no	—
68	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
69	C₄×D₄×C₄₇	—	2	1	no	—
70	C₄×D₄×C₄₇	—	2	1	no	—
71	C₄×D₄×C₄₇	D₄	1	2	yes	—
72	C₄×D₄×C₄₇	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	#107×C₄₇	—	2	4	no	—
79	C₄⋊C₈×C₄₇	—	2	1	no	—
80	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
81	#102×C₄₇	—	2	4	no	—
82	C₂⁴×C₄₇	—	2	1	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	4	1	no	—
85	C₂×Q₈×C₄₇	—	4	2	no	—
86	C₂×Q₈×C₄₇	—	4	2	no	—
87	C₂×D₄×C₄₇	—	2	1	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₇	—	2	1	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	4	2	no	—
95	C₂²×C₄×C₄₇	—	4	2	no	—
96	C₂²×C₄×C₄₇	—	4	1	no	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
100	C₂²×Dic₄₇	—	4	1	no	—
101	C₂×Dic₉₄	—	2	2	no	—
102	C₂×Dic₉₄	—	4	2	no	—
103	C₂×Dic₉₄	—	4	2	no	—
104	C₂×Dic₉₄	—	4	1	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	4	2	no	—
107	C₄⋊C₄×C₄₇	—	2	1	no	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	4	1	no	—
111	C₄⋊C₄×C₄₇	—	4	1	no	—
112	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
113	C₂²⋊C₄×C₄₇	—	2	2	no	—
114	C₂²⋊C₄×C₄₇	—	2	2	no	—
115	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₄₇	#41	1	1	yes	characteristic
118	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
119	#10625337	—	4	8	no	—
120	#10625337	—	4	8	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	4	1	no	—
124	C₄⋊Dic₄₇	—	4	1	no	—
125	#10625329	—	4	8	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	4	2	no	—
130	C₂×C₄₇⋊C₈	—	4	2	no	—
131	C₂×C₄₇⋊C₈	D₈	1	4	yes	—
132	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
133	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	4	2	no	—
136	C₂³×C₄₇	—	4	2	no	—
137	C₂³×C₄₇	—	4	2	no	—
138	C₂³×C₄₇	#121	1	1	yes	characteristic
139	Q₈×C₄₇	—	4	2	no	—
140	Q₈×C₄₇	—	4	2	no	—
141	Q₈×C₄₇	—	8	2	no	—
142	D₄×C₄₇	—	2	2	no	—
143	D₄×C₄₇	—	2	2	no	—
144	D₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	8	2	no	—
153	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
154	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
157	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
158	C₂×C₄×C₄₇	#137	1	2	yes	—
159	C₂×C₄×C₄₇	#137	1	2	yes	—
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	8	2	no	—
165	Dic₉₄	—	4	2	no	—
166	Dic₉₄	—	4	2	no	—
167	Dic₉₄	—	8	2	no	—
168	C₈×C₄₇	—	4	2	no	—
169	C₄₇⋊C₈	—	2	2	no	—
170	C₄₇⋊C₈	—	4	2	no	—
171	C₄₇⋊C₈	—	4	2	no	—
172	C₄₇⋊C₈	C₂×D₈	1	4	yes	—
173	C₂×#1689	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	—	4	2	no	—
175	C₂²×C₄₇	—	4	2	no	—
176	C₂²×C₄₇	—	4	2	no	—
177	C₂²×C₄₇	—	8	4	no	—
178	C₂²×C₄₇	#459	1	2	yes	—
179	C₂²×C₄₇	#470	1	2	yes	—
180	C₂²×C₄₇	#473	1	2	yes	—
181	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
182	C₄×C₄₇	—	2	1	no	—
183	C₄×C₄₇	—	2	1	no	—
184	C₄×C₄₇	—	4	2	no	—
185	C₄×C₄₇	—	8	2	no	—
186	C₄×C₄₇	#459	1	2	yes	—
187	C₄×C₄₇	#470	1	2	yes	—
188	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
189	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
191	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
192	Dic₄₇	—	8	2	no	—
193	C₂×#494	—	47	1	no	—
194	C₂×#474	—	47	1	no	—
195	C₂×#474	D₄₇	1	1	yes	characteristic
196	C₂×#436	—	47	1	no	—
197	#1689	—	47	8	no	—
198	C₂×#334	—	47	1	no	—
199	C₂×#332	—	47	1	no	—
200	C₂×#332	—	47	1	no	—
201	C₂×C₄₇	—	8	2	no	—
202	C₂×C₄₇	#1689	1	4	yes	complemented
203	C₂×C₄₇	C₂×#459	1	1	yes	characteristic
204	C₂×C₄₇	C₂×#470	1	1	yes	characteristic
205	C₂×C₄₇	C₂×#473	1	1	yes	characteristic
206	C₂²×Q₁₆	—	94	1	no	—
207	C₂²×Q₁₆	—	94	1	no	—
208	C₂²×M₁₆	—	94	1	no	—
209	C₂×C₄⋊Q₈	—	47	1	no	—
210	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
211	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
212	#494	—	47	4	no	—
213	#494	—	94	2	no	—
214	#474	—	2	2	no	—
215	#474	—	47	4	no	—
216	#474	—	94	2	no	—
217	#474	C₂×D₄₇	1	4	yes	—
218	#436	—	47	4	no	—
219	#436	—	94	2	no	—
220	C₂×#107	—	2	1	no	—
221	C₂×#107	—	94	1	no	—
222	C₂×C₄⋊C₈	—	47	1	no	—
223	C₂×C₄⋊C₈	—	47	1	no	—
224	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
225	C₂×#102	—	2	1	no	—
226	C₂×#102	—	94	1	no	—
227	C₂×C₂²⋊C₈	—	94	1	no	—
228	C₂×C₄×C₈	—	47	1	no	—
229	#334	—	47	4	no	—
230	#332	—	47	4	no	—
231	#332	—	47	4	no	—
232	C₄₇	C₂×#1689	1	1	yes	characteristic, complemented, Sylow
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×Q₈	—	94	1	no	—
235	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
236	C₂³×C₄	—	2	1	no	—
237	C₂×Q₁₆	—	94	4	no	—
238	C₂×Q₁₆	—	94	4	no	—
239	C₂×Q₁₆	—	188	4	no	—
240	C₂×Q₁₆	—	188	4	no	—
241	C₂×M₁₆	—	94	4	no	—
242	C₂×M₁₆	—	188	4	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	47	1	no	—
245	C₂²×C₈	—	47	1	no	—
246	C₂²×C₈	—	94	1	no	—
247	C₂²×C₈	—	94	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	47	2	no	—
252	C₄⋊Q₈	—	94	1	no	—
253	C₄⋊Q₈	—	94	1	no	—
254	C₄⋊Q₈	—	94	1	no	—
255	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
259	C₄×D₄	C₂²×D₄₇	1	2	yes	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	94	1	no	—
263	C₂×C₄⋊C₄	—	94	1	no	—
264	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
267	#107	—	2	4	no	—
268	#107	—	94	4	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	47	2	no	—
271	C₄⋊C₈	—	47	2	no	—
272	C₄⋊C₈	—	94	1	no	—
273	C₄⋊C₈	—	94	1	no	—
274	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
275	#102	—	2	4	no	—
276	#102	—	94	4	no	—
277	C₂²⋊C₈	—	94	4	no	—
278	C₄×C₈	—	47	2	no	—
279	C₄×C₈	—	47	2	no	—
280	C₂⁴	—	2	1	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	—	94	2	no	—
286	C₂×Q₈	—	188	2	no	—
287	C₂×Q₈	—	188	2	no	—
288	C₂×Q₈	—	188	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	188	1	no	—
300	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
301	C₂²×C₄	#10625352	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
303	Q₁₆	—	188	8	no	—
304	Q₁₆	—	188	8	no	—
305	M₁₆	—	188	8	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	—	47	4	no	—
309	C₂×C₈	—	47	2	no	—
310	C₂×C₈	—	47	2	no	—
311	C₂×C₈	—	94	2	no	—
312	C₂×C₈	—	94	2	no	—
313	C₂×C₈	—	94	2	no	—
314	C₂×C₈	—	188	2	no	—
315	C₂×C₈	—	188	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	94	2	no	—
322	C₄⋊C₄	—	94	2	no	—
323	C₄⋊C₄	—	188	1	no	—
324	C₄⋊C₄	—	188	1	no	—
325	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₄²	D₄×D₄₇	1	1	yes	characteristic
329	C₄²	#10625352	1	1	yes	characteristic
330	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
331	C₄²	C₂³×D₄₇	1	1	yes	characteristic
332	C₂³	—	2	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	#13093996	1	1	yes	characteristic
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	8	2	no	—
340	Q₈	—	376	2	no	—
341	Q₈	—	188	2	no	—
342	Q₈	—	188	2	no	—
343	D₄	—	2	2	no	—
344	D₄	—	2	2	no	—
345	D₄	—	4	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	8	2	no	—
354	C₂×C₄	—	376	2	no	—
355	C₂×C₄	—	188	2	no	—
356	C₂×C₄	#13093996	1	1	yes	characteristic
357	C₂×C₄	#13093996	1	1	yes	characteristic
358	C₂×C₄	#13093996	1	1	yes	characteristic
359	C₂×C₄	D₈×D₄₇	1	2	yes	—
360	C₂×C₄	#13094048	1	2	yes	—
361	C₂×C₄	#13094054	1	2	yes	—
362	C₂×C₄	#13094055	1	2	yes	—
363	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
364	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
365	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
366	C₈	—	4	2	no	—
367	C₈	—	47	4	no	—
368	C₈	—	94	2	no	—
369	C₈	—	188	2	no	—
370	C₈	—	188	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	8	4	no	—
375	C₂²	#15689316	1	2	yes	—
376	C₂²	#15689379	1	2	yes	—
377	C₂²	#15689396	1	2	yes	—
378	C₂²	C₂×#13093996	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	4	2	no	—
382	C₄	—	8	2	no	—
383	C₄	—	376	2	no	—
384	C₄	#15689316	1	2	yes	—
385	C₄	#15689379	1	2	yes	—
386	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
387	C₄	C₂×#13094048	1	1	yes	characteristic
388	C₄	C₂×#13094054	1	1	yes	characteristic
389	C₄	C₂×#13094055	1	1	yes	characteristic
390	C₂	—	8	2	no	—
391	C₂	#20242875	1	4	yes	direct product factor
392	C₂	C₂×#15689316	1	1	yes	characteristic
393	C₂	C₂×#15689379	1	1	yes	characteristic
394	C₂	C₂×#15689396	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#474	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂²×D₄×C₄₇	D₄
hypercenter	C₂×#474	D₄₇
hypocenter	C₄₇	C₂×#1689
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#474

Complements

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

N	H ≅ G/N	type
1. C₂×#15689502	C₂	semidirect
4. #20242875	C₂	direct (N × H)
5. C₂×#15688873	C₂	semidirect
6. C₂×#15688869	C₂	semidirect
7. C₂×#15688868	C₂	semidirect
14. #15689502	C₂²	semidirect
25. #15688873	C₂²	semidirect
26. #15688869	C₂²	semidirect
27. #15688868	C₂²	semidirect
202. C₂×C₄₇	#1689	semidirect
232. C₄₇	C₂×#1689	semidirect
391. C₂	#20242875	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×#15689502	2
C₂×#15689403	2
C₂×#15689201	2
#20242875	2
C₂×#15688873	2
C₂×#15688869	2
C₂×#15688868	2
C₂×C₄₇×#474	2
C₂×#1689	47

Subgroups — C2×#20242875 #26198783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242875 #26198783