Subgroups — C₂×#20257528 #27123171

Order 12032.

7418 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257528	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689873	C₂	1	3	yes	maximal, complemented
3	C₂×#15689867	C₂	1	6	yes	maximal, complemented
4	C₂×#15689862	C₂	1	6	yes	maximal, complemented
5	C₂×#15689672	C₂	1	3	yes	maximal, complemented
6	C₂×#15689652	C₂	1	6	yes	maximal, complemented
7	C₂×#15689629	C₂	1	6	yes	maximal, complemented
8	C₂×C₄₇×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625354	C₂²	1	1	yes	characteristic, complemented
10	C₂²×#10625352	C₂²	1	3	yes	—
11	C₂⁴×Dic₄₇	C₂²	1	2	yes	complemented
12	#15689873	C₂²	1	48	yes	complemented
13	#15689867	C₂²	1	96	yes	complemented
14	#15689862	C₂²	1	96	yes	complemented
15	#15689672	C₂²	1	48	yes	complemented
16	C₂×#13094022	C₂²	1	3	yes	complemented
17	C₂×#13094020	C₂²	1	3	yes	—
18	#15689652	C₂²	1	96	yes	complemented
19	C₂×#13094017	C₂²	1	12	yes	complemented
20	C₂×#13094016	C₂²	1	6	yes	complemented
21	C₂×#13094012	C₂²	1	3	yes	complemented
22	#15689629	C₂²	1	96	yes	complemented
23	C₂×#13094008	C₂²	1	6	yes	complemented
24	C₂×#13094006	C₂²	1	12	yes	complemented
25	C₂×#13094005	C₂²	1	6	yes	—
26	C₂×#13094001	C₂²	1	12	yes	complemented
27	C₂×#13094000	C₂²	1	6	yes	complemented
28	C₂×#13093997	C₂²	1	12	yes	complemented
29	C₂×#13093996	C₂²	1	12	yes	—
30	C₂×#13093995	C₂²	1	6	yes	—
31	C₂×#13093993	C₂²	1	6	yes	complemented
32	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	complemented
33	C₂×D₄×Dic₄₇	C₂²	1	6	yes	—
34	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	12	yes	complemented
35	C₂×#13093980	C₂²	1	6	yes	complemented
36	C₂×C₄²×D₄₇	C₂²	1	3	yes	complemented
37	C₄₇×H(3,𝔽₄)	C₂²	1	16	yes	complemented
38	C₂×#124×C₄₇	C₂²	1	6	yes	—
39	C₂×#124×C₄₇	C₂²	1	3	yes	—
40	C₂×#120×C₄₇	C₂²	1	6	yes	—
41	C₂×#10625354	—	4	4	no	—
42	C₂×#10625354	C₂³	1	8	yes	complemented
43	C₂×#10625352	—	4	12	no	—
44	C₂×#10625352	C₂³	1	24	yes	—
45	C₂²×Dic₉₄	C₂³	1	3	yes	—
46	C₂²×D₁₈₈	C₂³	1	3	yes	—
47	C₂²×C₂²⋊D₄₇	C₂³	1	12	yes	—
48	C₂²×C₂²⋊D₄₇	C₂³	1	6	yes	—
49	C₂³×Dic₄₇	—	4	8	no	—
50	C₂³×Dic₄₇	C₂³	1	6	yes	—
51	C₂³×Dic₄₇	C₂³	1	6	yes	—
52	C₂³×Dic₄₇	C₂³	1	16	yes	complemented
53	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
54	C₂²×C₄×D₄₇	C₂³	1	6	yes	—
55	#13094022	C₂³	1	24	yes	complemented
56	#13094020	C₂³	1	24	yes	—
57	#13094017	C₂³	1	96	yes	complemented
58	#13094016	C₂³	1	48	yes	complemented
59	#13094012	C₂³	1	24	yes	complemented
60	#13094008	C₂³	1	48	yes	complemented
61	#13094006	C₂³	1	96	yes	complemented
62	#13094005	C₂³	1	48	yes	—
63	#13094001	C₂³	1	96	yes	complemented
64	#13094000	C₂³	1	48	yes	complemented
65	#13093997	C₂³	1	96	yes	complemented
66	#13093996	C₂³	1	96	yes	—
67	#13093995	C₂³	1	48	yes	—
68	#13093993	C₂³	1	48	yes	complemented
69	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
70	D₄×Dic₄₇	C₂³	1	48	yes	—
71	(C₂²⋊D₄₇)⋊C₄	C₂³	1	96	yes	complemented
72	#13093980	C₂³	1	48	yes	complemented
73	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
74	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
75	C₂×Dic₄₇⋊C₄	C₂³	1	12	yes	—
76	C₂×Dic₄₇⋊C₄	C₂³	1	12	yes	—
77	C₂×C₂²⋊Dic₄₇	C₂³	1	6	yes	—
78	C₂×C₂²⋊Dic₄₇	C₂³	1	12	yes	—
79	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	12	yes	—
80	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
81	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
82	C₄²×D₄₇	C₂³	1	24	yes	complemented
83	C₂⁵×C₄₇	C₂³	1	2	yes	—
84	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
85	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₄₇	C₂³	1	6	yes	—
87	C₂²×D₄×C₄₇	C₂³	1	3	yes	—
88	#124×C₄₇	C₂³	1	48	yes	—
89	#124×C₄₇	C₂³	1	24	yes	—
90	#120×C₄₇	C₂³	1	48	yes	—
91	C₂×C₂²⋊C₄×C₄₇	C₂³	1	6	yes	—
92	C₂×C₂²⋊C₄×C₄₇	C₂³	1	12	yes	—
93	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
94	C₂⁴×C₄₇	—	4	8	no	—
95	C₂⁴×C₄₇	—	4	4	no	—
96	C₂⁴×C₄₇	C₂⁴	1	6	yes	—
97	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
98	C₂³×D₄₇	C₂⁴	1	3	yes	—
99	C₂×Q₈×C₄₇	—	4	4	no	—
100	C₂×Q₈×C₄₇	—	4	2	no	—
101	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
102	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
103	C₂×D₄×C₄₇	—	4	12	no	—
104	C₂×D₄×C₄₇	—	4	6	no	—
105	C₂×D₄×C₄₇	C₂⁴	1	24	yes	—
106	C₂×D₄×C₄₇	C₂⁴	1	12	yes	—
107	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
108	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
109	C₂×C₂²⋊D₄₇	—	4	24	no	—
110	C₂×C₂²⋊D₄₇	—	4	12	no	—
111	C₂×C₂²⋊D₄₇	C₂⁴	1	48	yes	—
112	C₂×C₂²⋊D₄₇	C₂⁴	1	24	yes	—
113	C₂²×Dic₄₇	—	2	24	no	—
114	C₂²×Dic₄₇	—	4	32	no	—
115	C₂²×Dic₄₇	—	4	12	no	—
116	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
117	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
118	C₂²×Dic₄₇	C₂⁴	1	24	yes	—
119	C₂²×Dic₄₇	C₂⁴	1	24	yes	—
120	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
121	#10625354	—	4	16	no	—
122	#10625352	—	4	48	no	—
123	C₂×D₁₈₈	—	4	6	no	—
124	C₂×D₁₈₈	C₂⁴	1	12	yes	—
125	C₂×C₄×D₄₇	—	2	12	no	—
126	C₂×C₄×D₄₇	—	4	12	no	—
127	C₂×C₄×D₄₇	C₂⁴	1	12	yes	—
128	C₂×C₄×D₄₇	C₂⁴	1	24	yes	—
129	C₂×Dic₉₄	—	4	6	no	—
130	C₂×Dic₉₄	C₂⁴	1	12	yes	—
131	C₂²⋊C₄×C₄₇	C₂⁴	1	24	yes	—
132	C₂²⋊C₄×C₄₇	C₂⁴	1	48	yes	—
133	C₄²×C₄₇	C₂⁴	1	12	yes	—
134	C₂²⋊Dic₄₇	C₂⁴	1	24	yes	—
135	C₂²⋊Dic₄₇	C₂⁴	1	48	yes	—
136	(C₂×D₄₇)⋊C₄	C₂⁴	1	48	yes	—
137	C₄⋊Dic₄₇	C₂⁴	1	24	yes	—
138	C₄⋊Dic₄₇	C₂⁴	1	24	yes	—
139	Dic₄₇⋊C₄	C₂⁴	1	48	yes	—
140	Dic₄₇⋊C₄	C₂⁴	1	48	yes	—
141	C₄×Dic₄₇	C₂⁴	1	24	yes	—
142	C₄×Dic₄₇	C₂⁴	1	12	yes	—
143	C₂³×C₄₇	—	2	12	no	—
144	C₂³×C₄₇	—	2	24	no	—
145	C₂³×C₄₇	—	4	8	no	—
146	C₂³×C₄₇	—	4	16	no	—
147	C₂³×C₄₇	—	4	32	no	—
148	C₂³×C₄₇	C₂⁵	1	12	yes	—
149	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
150	C₂²×D₄₇	—	2	6	no	—
151	C₂²×D₄₇	—	2	12	no	—
152	C₂²×D₄₇	C₂⁵	1	6	yes	—
153	Q₈×C₄₇	—	4	4	no	—
154	Q₈×C₄₇	—	4	8	no	—
155	D₄×C₄₇	—	4	12	no	—
156	D₄×C₄₇	—	4	24	no	—
157	C₂×C₄×C₄₇	—	2	6	no	—
158	C₂×C₄×C₄₇	—	2	12	no	—
159	C₂×C₄×C₄₇	C₂⁵	1	6	yes	—
160	C₂×C₄×C₄₇	C₂⁵	1	12	yes	—
161	C₂²⋊D₄₇	—	4	24	no	—
162	C₂²⋊D₄₇	—	4	48	no	—
163	C₂×Dic₄₇	—	2	12	no	—
164	C₂×Dic₄₇	—	2	12	no	—
165	C₂×Dic₄₇	—	2	48	no	—
166	C₂×Dic₄₇	—	4	24	no	—
167	C₂×Dic₄₇	H(5,𝔽₂)	1	4	yes	—
168	C₂×Dic₄₇	C₂⁵	1	12	yes	—
169	C₂×Dic₄₇	C₂⁵	1	12	yes	—
170	C₂×Dic₄₇	C₂⁵	1	2	yes	—
171	D₁₈₈	—	4	12	no	—
172	C₄×D₄₇	—	2	24	no	—
173	C₄×D₄₇	—	4	24	no	—
174	Dic₉₄	—	4	12	no	—
175	C₂×#3529	—	47	1	no	maximal, Sylow
176	C₂²×C₄₇	—	2	12	no	—
177	C₂²×C₄₇	—	2	24	no	—
178	C₂²×C₄₇	—	4	32	no	—
179	C₂²×C₄₇	—	4	24	no	—
180	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
181	C₂²×C₄₇	#585	1	4	yes	—
182	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
183	C₂×D₄₇	—	2	6	no	—
184	C₂×D₄₇	—	2	12	no	—
185	C₂×D₄₇	—	4	12	no	—
186	C₄×C₄₇	—	2	6	no	—
187	C₄×C₄₇	—	2	12	no	—
188	Dic₄₇	—	2	12	no	—
189	Dic₄₇	—	2	12	no	—
190	Dic₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
191	#3529	—	47	32	no	—
192	C₂×#563	—	47	3	no	—
193	C₂×#562	—	47	6	no	—
194	C₂×H(3,𝔽₄)	D₄₇	1	1	yes	characteristic, complemented
195	C₂×#560	—	47	6	no	—
196	C₂×#532	—	47	3	no	—
197	C₂×#529	—	47	6	no	—
198	C₂×#525	—	47	6	no	—
199	C₂×C₄₇	—	4	12	no	—
200	C₂×C₄₇	#3529	1	4	yes	complemented
201	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄₇	C₂×#585	1	2	yes	—
203	D₄₇	—	4	6	no	—
204	C₂²×#41	—	47	1	no	—
205	C₂²×#41	—	47	3	no	—
206	C₂⁴×C₄	—	47	2	no	—
207	#563	—	47	48	no	—
208	#562	—	47	96	no	—
209	H(3,𝔽₄)	C₂×D₄₇	1	16	yes	complemented
210	#560	—	47	96	no	—
211	#532	—	47	48	no	—
212	C₂×C₄⋊Q₈	—	47	3	no	—
213	C₂×#127	—	47	3	no	—
214	#529	—	47	96	no	—
215	C₂×#126	—	47	12	no	—
216	C₂×#125	—	47	6	no	—
217	C₂×#124	—	47	3	no	—
218	C₂×#124	C₂×D₄₇	1	6	yes	—
219	C₂×#124	C₂×D₄₇	1	3	yes	—
220	#525	—	47	96	no	—
221	C₂×#123	—	47	6	no	—
222	C₂×#123	—	47	6	no	—
223	C₂×#123	—	47	12	no	—
224	C₂×C₂²⋊Q₈	—	47	6	no	—
225	C₂×C₂²⋊Q₈	—	47	12	no	—
226	C₂×#121	—	47	12	no	—
227	C₂×#121	—	47	6	no	—
228	C₂×#121	—	47	12	no	—
229	C₂×#120	—	47	6	no	—
230	C₂×#120	C₂×D₄₇	1	6	yes	—
231	C₂×C₄×Q₈	—	47	2	no	—
232	C₂×C₄×D₄	—	47	6	no	—
233	C₂×C₄×D₄	—	47	12	no	—
234	C₂×#117	—	47	6	no	—
235	C₂²×C₄²	—	47	3	no	—
236	C₄₇	C₂×#3529	1	1	yes	characteristic, complemented, Sylow
237	C₂⁵	C₂²×D₄₇	1	2	yes	—
238	C₂×#41	—	47	8	no	—
239	C₂×#41	—	47	24	no	—
240	C₂×#41	—	188	12	no	—
241	C₂×#41	—	188	4	no	—
242	C₂²×Q₈	—	47	3	no	—
243	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
244	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
245	C₂²×D₄	—	47	12	no	—
246	C₂²×D₄	—	47	6	no	—
247	C₂²×D₄	—	47	3	no	—
248	C₂²×D₄	C₂²×D₄₇	1	6	yes	—
249	C₂²×D₄	C₂²×D₄₇	1	3	yes	—
250	C₂³×C₄	—	47	6	no	—
251	C₂³×C₄	—	47	6	no	—
252	C₂³×C₄	—	47	16	no	—
253	C₂³×C₄	—	47	3	no	—
254	C₂³×C₄	—	47	6	no	—
255	C₂³×C₄	—	188	8	no	—
256	C₄⋊Q₈	—	47	24	no	—
257	#127	—	47	24	no	—
258	#126	—	47	96	no	—
259	#125	—	47	48	no	—
260	#124	—	47	24	no	—
261	#124	C₂²×D₄₇	1	48	yes	—
262	#124	C₂²×D₄₇	1	24	yes	—
263	#123	—	47	48	no	—
264	#123	—	47	48	no	—
265	#123	—	47	96	no	—
266	C₂²⋊Q₈	—	47	48	no	—
267	C₂²⋊Q₈	—	47	96	no	—
268	#121	—	47	96	no	—
269	#121	—	47	48	no	—
270	#121	—	47	96	no	—
271	#120	—	47	48	no	—
272	#120	C₂²×D₄₇	1	48	yes	—
273	C₄×Q₈	—	47	16	no	—
274	C₄×D₄	—	47	48	no	—
275	C₄×D₄	—	47	96	no	—
276	#117	—	47	48	no	—
277	C₂×C₄⋊C₄	—	47	12	no	—
278	C₂×C₄⋊C₄	—	47	12	no	—
279	C₂×C₄⋊C₄	—	47	6	no	—
280	C₂×C₄⋊C₄	—	47	6	no	—
281	C₂×C₂²⋊C₄	—	47	6	no	—
282	C₂×C₂²⋊C₄	—	47	12	no	—
283	C₂×C₂²⋊C₄	—	47	12	no	—
284	C₂×C₂²⋊C₄	C₂²×D₄₇	1	6	yes	—
285	C₂×C₂²⋊C₄	C₂²×D₄₇	1	12	yes	—
286	C₂×C₄²	—	47	6	no	—
287	C₂×C₄²	—	47	3	no	—
288	C₂×C₄²	—	47	24	no	—
289	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
290	C₂⁴	—	4	4	no	—
291	C₂⁴	—	4	8	no	—
292	C₂⁴	—	47	3	no	—
293	C₂⁴	C₂³×D₄₇	1	6	yes	—
294	C₂⁴	C₂³×D₄₇	1	8	yes	—
295	#41	—	188	48	no	—
296	#41	—	188	16	no	—
297	C₂×Q₈	—	4	4	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	47	12	no	—
300	C₂×Q₈	—	188	6	no	—
301	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
302	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
303	C₂×D₄	—	4	12	no	—
304	C₂×D₄	—	4	6	no	—
305	C₂×D₄	—	47	48	no	—
306	C₂×D₄	—	47	24	no	—
307	C₂×D₄	—	47	12	no	—
308	C₂×D₄	—	188	6	no	—
309	C₂×D₄	—	188	24	no	—
310	C₂×D₄	—	188	12	no	—
311	C₂×D₄	C₂³×D₄₇	1	24	yes	—
312	C₂×D₄	C₂³×D₄₇	1	12	yes	—
313	C₂²×C₄	—	47	1	no	—
314	C₂²×C₄	—	47	24	no	—
315	C₂²×C₄	—	47	6	no	—
316	C₂²×C₄	—	47	6	no	—
317	C₂²×C₄	—	47	24	no	—
318	C₂²×C₄	—	47	12	no	—
319	C₂²×C₄	—	47	24	no	—
320	C₂²×C₄	—	94	12	no	—
321	C₂²×C₄	—	94	24	no	—
322	C₂²×C₄	—	188	12	no	—
323	C₂²×C₄	—	188	32	no	—
324	C₂²×C₄	—	188	12	no	—
325	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
326	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
327	C₄⋊C₄	—	47	48	no	—
328	C₄⋊C₄	—	47	48	no	—
329	C₄⋊C₄	—	47	24	no	—
330	C₄⋊C₄	—	47	24	no	—
331	C₂²⋊C₄	—	47	24	no	—
332	C₂²⋊C₄	—	47	48	no	—
333	C₂²⋊C₄	—	47	48	no	—
334	C₂²⋊C₄	C₂³×D₄₇	1	24	yes	—
335	C₂²⋊C₄	C₂³×D₄₇	1	48	yes	—
336	C₄²	—	47	24	no	—
337	C₄²	—	47	12	no	—
338	C₄²	C₂³×D₄₇	1	12	yes	—
339	C₂³	—	2	12	no	—
340	C₂³	—	2	24	no	—
341	C₂³	—	4	8	no	—
342	C₂³	—	4	16	no	—
343	C₂³	—	4	32	no	—
344	C₂³	—	47	6	no	—
345	C₂³	—	94	6	no	—
346	C₂³	—	94	12	no	—
347	C₂³	C₂⁴×D₄₇	1	12	yes	—
348	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
349	Q₈	—	4	8	no	—
350	Q₈	—	4	4	no	—
351	Q₈	—	188	12	no	—
352	D₄	—	4	24	no	—
353	D₄	—	4	12	no	—
354	D₄	—	188	12	no	—
355	D₄	—	188	48	no	—
356	D₄	—	188	24	no	—
357	C₂×C₄	—	2	6	no	—
358	C₂×C₄	—	2	12	no	—
359	C₂×C₄	—	47	4	no	—
360	C₂×C₄	—	47	2	no	—
361	C₂×C₄	—	47	12	no	—
362	C₂×C₄	—	47	12	no	—
363	C₂×C₄	—	94	24	no	—
364	C₂×C₄	—	94	48	no	—
365	C₂×C₄	—	94	12	no	—
366	C₂×C₄	—	94	12	no	—
367	C₂×C₄	—	188	24	no	—
368	C₂×C₄	—	188	24	no	—
369	C₂×C₄	C₂⁴×D₄₇	1	12	yes	—
370	C₂×C₄	C₂⁴×D₄₇	1	6	yes	—
371	C₂²	—	2	12	no	—
372	C₂²	—	2	24	no	—
373	C₂²	—	4	32	no	—
374	C₂²	—	4	24	no	—
375	C₂²	—	94	6	no	—
376	C₂²	—	94	12	no	—
377	C₂²	—	188	12	no	—
378	C₂²	H(5,𝔽₂)×D₄₇	1	2	yes	—
379	C₂²	#15689958	1	4	yes	—
380	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
381	C₄	—	2	6	no	—
382	C₄	—	2	12	no	—
383	C₄	—	47	4	no	—
384	C₄	—	94	12	no	—
385	C₄	—	94	12	no	—
386	C₂	—	4	12	no	—
387	C₂	—	188	6	no	—
388	C₂	#20257528	1	4	yes	direct product factor
389	C₂	C₂×H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
390	C₂	C₂×#15689958	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×H(3,𝔽₄)	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×H(3,𝔽₄)	D₄₇
hypocenter	C₄₇	C₂×#3529
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. #20257528	C₂	direct (N × H)
2. C₂×#15689873	C₂	semidirect
3. C₂×#15689867	C₂	semidirect
4. C₂×#15689862	C₂	semidirect
5. C₂×#15689672	C₂	semidirect
6. C₂×#15689652	C₂	semidirect
7. C₂×#15689629	C₂	semidirect
8. C₂×C₄₇×H(3,𝔽₄)	C₂	semidirect
9. C₂²×#10625354	C₂²	semidirect
11. C₂⁴×Dic₄₇	C₂²	semidirect
12. #15689873	C₂²	semidirect
13. #15689867	C₂²	semidirect
14. #15689862	C₂²	semidirect
15. #15689672	C₂²	semidirect
16. C₂×#13094022	C₂²	semidirect
18. #15689652	C₂²	semidirect
19. C₂×#13094017	C₂²	semidirect
20. C₂×#13094016	C₂²	semidirect
21. C₂×#13094012	C₂²	semidirect
22. #15689629	C₂²	semidirect
23. C₂×#13094008	C₂²	semidirect
24. C₂×#13094006	C₂²	semidirect
26. C₂×#13094001	C₂²	semidirect
27. C₂×#13094000	C₂²	semidirect
28. C₂×#13093997	C₂²	semidirect
31. C₂×#13093993	C₂²	semidirect
32. C₂×Q₈×Dic₄₇	C₂²	semidirect
34. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
35. C₂×#13093980	C₂²	semidirect
36. C₂×C₄²×D₄₇	C₂²	semidirect
37. C₄₇×H(3,𝔽₄)	C₂²	semidirect
42. C₂×#10625354	C₂³	semidirect
52. C₂³×Dic₄₇	C₂³	semidirect
55. #13094022	C₂³	semidirect
57. #13094017	C₂³	semidirect
58. #13094016	C₂³	semidirect
59. #13094012	C₂³	semidirect
60. #13094008	C₂³	semidirect
61. #13094006	C₂³	semidirect
63. #13094001	C₂³	semidirect
64. #13094000	C₂³	semidirect
65. #13093997	C₂³	semidirect
68. #13093993	C₂³	semidirect
69. Q₈×Dic₄₇	C₂³	semidirect
71. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
72. #13093980	C₂³	semidirect
82. C₄²×D₄₇	C₂³	semidirect
194. C₂×H(3,𝔽₄)	D₄₇	semidirect
200. C₂×C₄₇	#3529	semidirect
209. H(3,𝔽₄)	C₂×D₄₇	semidirect
236. C₄₇	C₂×#3529	semidirect
388. C₂	#20257528	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20257528	2
C₂×#15689873	2
C₂×#15689867	2
C₂×#15689862	2
C₂×#15689672	2
C₂×#15689652	2
C₂×#15689629	2
C₂×C₄₇×H(3,𝔽₄)	2
C₂×#3529	47

Subgroups — C2×#20257528 #27123171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257528 #27123171