Subgroups — C₂×#20244164 #26219799

Order 12032.

938 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093960	C₂	1	2	yes	maximal
2	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
4	#20244164	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688888	C₂	1	2	yes	maximal
6	C₂²×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	C₂²	1	2	yes	—
8	C₂²×#10625329	C₂²	1	1	yes	characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂×#13093960	—	2	8	no	—
11	C₂×#13093960	C₂²	1	8	yes	—
12	#15689147	—	2	2	no	—
13	#15689147	C₂²	1	4	yes	—
14	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
15	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
16	C₄×#10625329	—	2	2	no	—
17	C₄×#10625329	C₂²	1	4	yes	—
18	C₂×#13093935	—	2	1	no	—
19	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
20	#15688888	C₂²	1	8	yes	—
21	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
22	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₇	C₄	1	2	yes	—
24	C₂×C₄⋊C₈×C₄₇	C₄	1	4	yes	—
25	C₂×C₄⋊C₈×C₄₇	C₄	1	2	yes	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	4	yes	—
27	C₂×#10625329	—	2	1	no	—
28	C₂×#10625329	—	2	1	no	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	—	2	2	no	—
32	C₂×#10625329	—	2	4	no	—
33	C₂×#10625329	—	2	4	no	—
34	C₂×#10625329	D₄	1	4	yes	—
35	C₂×#10625329	Q₈	1	4	yes	—
36	C₂×#10625329	C₂³	1	4	yes	—
37	C₂×#10625329	C₂³	1	2	yes	—
38	C₂×#10625329	C₂³	1	2	yes	—
39	C₂²×C₄₇⋊C₈	—	2	1	no	—
40	C₂²×C₄₇⋊C₈	—	2	1	no	—
41	C₂²×C₄₇⋊C₈	—	2	2	no	—
42	#13093960	—	2	16	no	—
43	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
44	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
45	#13093935	—	2	4	no	—
46	C₄×C₄₇⋊C₈	—	2	4	no	—
47	C₂³×C₄×C₄₇	Q₈	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	Q₈	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₄₇	—	2	4	no	—
51	C₂²×C₈×C₄₇	—	2	4	no	—
52	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
53	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
55	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₇	D₄	1	2	yes	—
61	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
62	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
63	C₄⋊C₈×C₄₇	C₂×C₄	1	8	yes	—
64	C₄⋊C₈×C₄₇	C₂×C₄	1	8	yes	—
65	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	—	2	4	no	—
67	C₂²×C₄×C₄₇	—	4	2	no	—
68	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
83	C₂²×C₄×C₄₇	#41	1	2	yes	—
84	C₂²×C₄×C₄₇	#41	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
86	C₂×C₈×C₄₇	—	2	8	no	—
87	C₂×C₈×C₄₇	—	2	8	no	—
88	C₂×C₈×C₄₇	—	2	4	no	—
89	C₂×C₈×C₄₇	—	2	4	no	—
90	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
91	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
92	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
93	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
94	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
95	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
96	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
97	C₄²×C₄₇	C₂×D₄	1	2	yes	—
98	C₄²×C₄₇	C₂×D₄	1	2	yes	—
99	#10625329	—	2	4	no	—
100	#10625329	—	2	4	no	—
101	#10625329	—	2	2	no	—
102	#10625329	—	2	2	no	—
103	#10625329	—	2	4	no	—
104	#10625329	—	2	4	no	—
105	#10625329	—	4	4	no	—
106	#10625329	C₂×D₄	1	4	yes	—
107	#10625329	C₂×Q₈	1	4	yes	—
108	C₂×C₄₇⋊C₈	—	2	4	no	—
109	C₂×C₄₇⋊C₈	—	2	4	no	—
110	C₂×C₄₇⋊C₈	—	2	2	no	—
111	C₂×C₄₇⋊C₈	—	2	2	no	—
112	C₂×C₄₇⋊C₈	—	2	4	no	—
113	C₂×C₄₇⋊C₈	—	4	4	no	—
114	C₂³×C₄₇	—	2	2	no	—
115	C₂³×C₄₇	—	2	2	no	—
116	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂³×C₄₇	#125	1	2	yes	—
119	C₂³×C₄₇	C₄⋊Q₈	1	2	yes	—
120	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
121	C₂×C₄×C₄₇	—	2	2	no	—
122	C₂×C₄×C₄₇	—	2	2	no	—
123	C₂×C₄×C₄₇	—	2	2	no	—
124	C₂×C₄×C₄₇	—	2	4	no	—
125	C₂×C₄×C₄₇	—	2	4	no	—
126	C₂×C₄×C₄₇	—	4	2	no	—
127	C₂×C₄×C₄₇	—	4	2	no	—
128	C₂×C₄×C₄₇	#108	1	4	yes	complemented
129	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
130	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
132	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
136	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
137	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
138	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
139	C₂×C₄×C₄₇	#121	1	2	yes	—
140	C₂×C₄×C₄₇	#121	1	2	yes	—
141	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
142	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₄₇	#125	1	2	yes	—
144	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
145	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₈×C₄₇	—	2	8	no	—
152	C₄₇⋊C₈	—	2	4	no	—
153	C₄₇⋊C₈	—	2	4	no	—
154	C₄₇⋊C₈	—	4	4	no	—
155	C₂×#1950	—	47	1	no	maximal, Sylow
156	C₂²×C₄₇	—	2	1	no	—
157	C₂²×C₄₇	—	2	1	no	—
158	C₂²×C₄₇	—	2	1	no	—
159	C₂²×C₄₇	—	2	1	no	—
160	C₂²×C₄₇	—	2	4	no	—
161	C₂²×C₄₇	—	2	4	no	—
162	C₂²×C₄₇	#389	1	2	yes	—
163	C₂²×C₄₇	#389	1	2	yes	—
164	C₂²×C₄₇	C₂×#108	1	2	yes	—
165	C₂²×C₄₇	#430	1	2	yes	—
166	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
167	C₂²×C₄₇	C₂×#125	1	1	yes	characteristic
168	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
169	C₄×C₄₇	—	2	2	no	—
170	C₄×C₄₇	—	2	2	no	—
171	C₄×C₄₇	—	2	2	no	—
172	C₄×C₄₇	#389	1	2	yes	—
173	C₄×C₄₇	#389	1	2	yes	—
174	C₄×C₄₇	C₂×#108	1	4	yes	complemented
175	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
176	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
177	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
178	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
179	C₂²×#108	—	47	2	no	—
180	C₂×#423	—	47	1	no	—
181	C₂²×C₄⋊C₈	D₄₇	1	1	yes	characteristic
182	C₂×C₄×M₁₆	—	47	1	no	—
183	#1950	—	47	8	no	—
184	C₂×#341	—	47	2	no	—
185	C₂×C₄₇	—	2	1	no	—
186	C₂×C₄₇	—	2	1	no	—
187	C₂×C₄₇	—	2	2	no	—
188	C₂×C₄₇	#1950	1	4	yes	complemented
189	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
190	C₂×C₄₇	C₂²×#108	1	1	yes	characteristic
191	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
192	C₂²×M₁₆	—	47	1	no	—
193	C₂²×M₁₆	—	47	1	no	—
194	C₂²×M₁₆	—	47	2	no	—
195	C₂³×C₈	C₂×D₄₇	1	2	yes	—
196	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
197	C₂×#108	—	47	8	no	—
198	C₂×#108	—	94	8	no	—
199	#423	—	47	4	no	—
200	#423	—	94	2	no	—
201	C₂×C₄⋊C₈	—	94	1	no	—
202	C₂×C₄⋊C₈	—	94	1	no	—
203	C₂×C₄⋊C₈	Dic₄₇	1	2	yes	—
204	C₂×C₄⋊C₈	Dic₄₇	1	4	yes	—
205	C₂×C₄⋊C₈	Dic₄₇	1	2	yes	—
206	C₂×C₄⋊C₈	C₂×D₄₇	1	4	yes	—
207	C₄×M₁₆	—	47	4	no	—
208	C₄×M₁₆	—	94	2	no	—
209	C₂×#97	—	94	1	no	—
210	C₂×C₄×C₈	—	94	1	no	—
211	#341	—	47	8	no	—
212	C₄₇	C₂×#1950	1	1	yes	characteristic, complemented, Sylow
213	C₂³×C₄	Dic₉₄	1	1	yes	characteristic
214	C₂³×C₄	Dic₉₄	1	1	yes	characteristic
215	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
216	C₂×M₁₆	—	47	4	no	—
217	C₂×M₁₆	—	47	4	no	—
218	C₂×M₁₆	—	47	2	no	—
219	C₂×M₁₆	—	47	2	no	—
220	C₂×M₁₆	—	47	4	no	—
221	C₂×M₁₆	—	94	1	no	—
222	C₂×M₁₆	—	94	1	no	—
223	C₂×M₁₆	—	94	2	no	—
224	C₂×M₁₆	—	94	2	no	—
225	C₂×M₁₆	—	94	2	no	—
226	C₂×M₁₆	—	94	4	no	—
227	C₂×M₁₆	—	94	4	no	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	—	94	1	no	—
231	C₂²×C₈	—	94	1	no	—
232	C₂²×C₈	—	94	2	no	—
233	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
234	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
235	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
236	C₂×C₄²	Dic₉₄	1	2	yes	—
237	C₂×C₄²	D₁₈₈	1	2	yes	—
238	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
239	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
240	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
241	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
242	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
244	#108	—	94	16	no	—
245	C₄⋊C₈	—	94	4	no	—
246	C₄⋊C₈	—	94	4	no	—
247	C₄⋊C₈	C₂×Dic₄₇	1	8	yes	—
248	C₄⋊C₈	C₂×Dic₄₇	1	8	yes	—
249	#97	—	94	4	no	—
250	C₄×C₈	—	94	4	no	—
251	C₂⁴	C₂×Dic₉₄	1	1	yes	characteristic
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
255	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
256	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
257	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
258	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
259	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
260	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
261	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
262	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
265	C₂²×C₄	D₄×D₄₇	1	2	yes	—
266	C₂²×C₄	#10625352	1	2	yes	—
267	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
268	C₂²×C₄	#10625354	1	2	yes	—
269	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
270	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
271	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
272	M₁₆	—	47	4	no	—
273	M₁₆	—	47	4	no	—
274	M₁₆	—	94	4	no	—
275	M₁₆	—	94	4	no	—
276	M₁₆	—	94	2	no	—
277	M₁₆	—	94	2	no	—
278	M₁₆	—	94	4	no	—
279	M₁₆	—	94	4	no	—
280	M₁₆	—	188	4	no	—
281	C₂×C₈	—	2	8	no	—
282	C₂×C₈	—	2	8	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	94	4	no	—
286	C₂×C₈	—	94	4	no	—
287	C₂×C₈	—	94	2	no	—
288	C₂×C₈	—	94	2	no	—
289	C₂×C₈	—	94	4	no	—
290	C₂×C₈	—	188	4	no	—
291	C₂×C₈	C₂²×Dic₄₇	1	8	yes	—
292	C₄²	C₄⋊Dic₄₇	1	2	yes	—
293	C₄²	C₄⋊Dic₄₇	1	2	yes	—
294	C₄²	C₄⋊Dic₄₇	1	2	yes	—
295	C₄²	C₄⋊Dic₄₇	1	2	yes	—
296	C₄²	C₂×D₁₈₈	1	2	yes	—
297	C₄²	C₂×D₁₈₈	1	2	yes	—
298	C₄²	C₂²×Dic₄₇	1	2	yes	—
299	C₄²	C₂²×Dic₄₇	1	2	yes	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
303	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
304	C₂³	#13094015	1	2	yes	—
305	C₂³	#13094023	1	2	yes	—
306	C₂³	C₂²×Dic₉₄	1	1	yes	characteristic
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	#13093960	1	4	yes	complemented
315	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
316	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
317	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
318	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
319	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
320	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
321	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
322	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
323	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
324	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
325	C₂×C₄	#13093999	1	2	yes	—
326	C₂×C₄	#13093999	1	2	yes	—
327	C₂×C₄	#13094004	1	2	yes	—
328	C₂×C₄	#13094004	1	2	yes	—
329	C₂×C₄	#13094015	1	2	yes	—
330	C₂×C₄	#13094023	1	2	yes	—
331	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
332	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
334	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
335	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
336	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
337	C₈	—	2	8	no	—
338	C₈	—	94	4	no	—
339	C₈	—	94	4	no	—
340	C₈	—	188	4	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	#15689022	1	2	yes	—
348	C₂²	#15689022	1	2	yes	—
349	C₂²	C₂×#13093960	1	2	yes	—
350	C₂²	#15689172	1	2	yes	—
351	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
352	C₂²	C₂×#13094015	1	1	yes	characteristic
353	C₂²	C₂×#13094023	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	#15689022	1	2	yes	—
358	C₄	#15689022	1	2	yes	—
359	C₄	C₂×#13093960	1	4	yes	complemented
360	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
361	C₄	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
362	C₄	C₂×#13093999	1	1	yes	characteristic
363	C₄	C₂×#13094004	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	2	1	no	—
366	C₂	—	2	1	no	—
367	C₂	#20244164	1	4	yes	direct product factor
368	C₂	C₂×#15689022	1	1	yes	characteristic
369	C₂	C₂²×#13093960	1	1	yes	characteristic
370	C₂	C₂×#15689172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×C₄⋊C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₄⋊C₄
prime radical	C₂⁴×C₄₇	C₂×Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×C₄⋊C₈	D₄₇
hypocenter	C₄₇	C₂×#1950
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
4. #20244164	C₂	direct (N × H)
128. C₂×C₄×C₄₇	#108	semidirect
174. C₄×C₄₇	C₂×#108	semidirect
188. C₂×C₄₇	#1950	semidirect
212. C₄₇	C₂×#1950	semidirect
314. C₂×C₄	#13093960	semidirect
359. C₄	C₂×#13093960	semidirect
367. C₂	#20244164	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×#13093960	2
C₂×#15689147	2
C₂×C₄×#10625329	2
#20244164	2
C₂×#15688888	2
C₂²×C₄⋊C₈×C₄₇	2
C₂×#1950	47

Subgroups — C2×#20244164 #26219799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244164 #26219799