Subgroups — #26122136

Order 12032.

986 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
2	C₄×#13093983	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688883	C₂	1	4	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10625329	C₂²	1	2	yes	—
6	C₂×#13093983	C₂²	1	2	yes	—
7	#15689147	—	2	2	no	—
8	#15689147	C₄	1	4	yes	complemented
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
11	C₄×C₄⋊Dic₄₇	C₄	1	2	yes	complemented
12	C₄×C₄⋊Dic₄₇	C₄	1	2	yes	complemented
13	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
14	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
15	#15688969	—	2	1	no	—
16	C₄²×Dic₄₇	—	2	1	no	—
17	#15688883	—	2	8	no	—
18	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
19	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
20	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₄₇	—	2	2	no	—
22	C₄×C₄⋊C₄×C₄₇	C₄	1	4	yes	complemented
23	C₂×#95×C₄₇	—	2	1	no	—
24	C₂×#10625329	—	2	2	no	—
25	C₂×#10625329	—	2	4	no	—
26	C₂×#10625329	—	2	4	no	—
27	C₂×#10625329	C₂×C₄	1	4	yes	—
28	C₂²×C₄₇⋊C₈	—	2	2	no	—
29	#13093983	—	2	2	no	—
30	#13093983	—	2	2	no	—
31	#13093983	D₄	1	4	yes	—
32	#13093983	Q₈	1	4	yes	—
33	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
34	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄×Dic₄₇	—	2	2	no	—
36	C₂×C₄×Dic₄₇	—	2	2	no	—
37	C₂×C₄×Dic₄₇	—	2	2	no	—
38	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
39	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
40	C₄₇⋊#95	—	2	2	no	—
41	C₄₇⋊#95	—	2	2	no	—
42	C₂³×C₄×C₄₇	—	2	2	no	—
43	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
48	C₂×C₄²×C₄₇	—	2	4	no	—
49	C₂×C₄²×C₄₇	—	2	4	no	—
50	C₂×C₄²×C₄₇	—	2	2	no	—
51	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
52	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₇	D₄	1	2	yes	—
59	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
60	#95×C₄₇	—	2	4	no	—
61	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₇	—	2	4	no	—
63	C₂²×C₄×C₄₇	—	2	8	no	—
64	C₂²×C₄×C₄₇	—	2	4	no	—
65	C₂²×C₄×C₄₇	—	4	2	no	—
66	C₂²×C₄×C₄₇	—	4	4	no	—
67	C₂²×C₄×C₄₇	—	4	4	no	—
68	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
72	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
73	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
75	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
76	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
84	C₂²×C₄×C₄₇	#41	1	2	yes	—
85	C₂²×C₄×C₄₇	#41	1	2	yes	—
86	C₂²×Dic₄₇	—	2	4	no	—
87	C₄⋊C₄×C₄₇	—	2	16	no	—
88	C₄²×C₄₇	—	2	8	no	—
89	C₄²×C₄₇	—	4	2	no	—
90	C₄²×C₄₇	—	4	2	no	—
91	C₄²×C₄₇	C₄²	1	2	yes	—
92	C₄²×C₄₇	C₄²	1	2	yes	—
93	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
94	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
95	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
96	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
97	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
98	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
99	C₂²⋊Dic₄₇	—	2	4	no	—
100	C₂²⋊Dic₄₇	—	2	4	no	—
101	C₄⋊Dic₄₇	—	2	4	no	—
102	C₄⋊Dic₄₇	C₄⋊C₄	1	8	yes	complemented
103	C₄×Dic₄₇	—	2	4	no	—
104	C₄×Dic₄₇	—	2	4	no	—
105	C₄×Dic₄₇	—	4	4	no	—
106	C₄×Dic₄₇	—	4	4	no	—
107	#10625329	—	2	8	no	—
108	#10625329	—	4	2	no	—
109	#10625329	—	4	2	no	—
110	C₂×C₄₇⋊C₈	—	2	4	no	—
111	C₂×C₄₇⋊C₈	—	4	4	no	—
112	C₂³×C₄₇	—	2	2	no	—
113	C₂³×C₄₇	—	2	2	no	—
114	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₂³×C₄₇	#121	1	2	yes	—
118	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
119	C₂×C₄×C₄₇	—	2	2	no	—
120	C₂×C₄×C₄₇	—	2	2	no	—
121	C₂×C₄×C₄₇	—	2	2	no	—
122	C₂×C₄×C₄₇	—	2	4	no	—
123	C₂×C₄×C₄₇	—	2	4	no	—
124	C₂×C₄×C₄₇	—	2	8	no	—
125	C₂×C₄×C₄₇	—	4	2	no	—
126	C₂×C₄×C₄₇	—	4	2	no	—
127	C₂×C₄×C₄₇	—	4	16	no	—
128	C₂×C₄×C₄₇	—	4	4	no	—
129	C₂×C₄×C₄₇	—	4	4	no	—
130	C₂×C₄×C₄₇	#95	1	2	yes	—
131	C₂×C₄×C₄₇	#95	1	2	yes	—
132	C₂×C₄×C₄₇	#95	1	2	yes	—
133	C₂×C₄×C₄₇	#95	1	2	yes	—
134	C₂×C₄×C₄₇	#104	1	4	yes	—
135	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
136	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	#117	1	2	yes	—
141	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
142	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
144	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
145	C₂×C₄×C₄₇	#121	1	2	yes	—
146	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#125	1	2	yes	—
150	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
153	C₂×Dic₄₇	—	2	8	no	—
154	C₂×Dic₄₇	—	4	4	no	—
155	C₂×Dic₄₇	—	4	4	no	—
156	C₄₇⋊C₈	—	4	4	no	—
157	#10852	—	47	1	no	maximal, Sylow
158	C₂²×C₄₇	—	2	4	no	—
159	C₂²×C₄₇	—	2	4	no	—
160	C₂²×C₄₇	—	2	1	no	—
161	C₂²×C₄₇	—	2	1	no	—
162	C₂²×C₄₇	—	2	1	no	—
163	C₂²×C₄₇	—	2	1	no	—
164	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
165	C₂²×C₄₇	#380	1	2	yes	—
166	C₂²×C₄₇	#389	1	2	yes	—
167	C₂²×C₄₇	#390	1	1	yes	characteristic
168	C₂²×C₄₇	#391	1	1	yes	characteristic
169	C₂²×C₄₇	C₂×#104	1	2	yes	—
170	C₂²×C₄₇	#421	1	2	yes	—
171	C₄×C₄₇	—	2	2	no	—
172	C₄×C₄₇	—	2	2	no	—
173	C₄×C₄₇	—	2	2	no	—
174	C₄×C₄₇	—	4	8	no	—
175	C₄×C₄₇	#339	1	4	yes	complemented
176	C₄×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
177	C₄×C₄₇	#382	1	1	yes	characteristic
178	C₄×C₄₇	#384	1	1	yes	characteristic
179	C₄×C₄₇	#389	1	2	yes	—
180	C₄×C₄₇	#390	1	1	yes	characteristic
181	C₄×C₄₇	#391	1	1	yes	characteristic
182	Dic₄₇	—	4	8	no	—
183	C₂×#423	—	47	1	no	—
184	C₄×#117	—	47	1	no	—
185	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
186	C₂×#339	—	47	4	no	—
187	C₂×C₄₇	—	2	1	no	—
188	C₂×C₄₇	—	2	2	no	—
189	C₂×C₄₇	—	2	1	no	—
190	C₂×C₄₇	C₄⋊#95	1	1	yes	characteristic
191	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
192	C₂×C₄₇	#1733	1	1	yes	characteristic
193	C₂×C₄₇	#1806	1	4	yes	—
194	C₂²×M₁₆	—	47	2	no	—
195	C₂×#117	—	47	2	no	—
196	C₂²×C₄⋊C₄	—	2	1	no	—
197	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
198	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
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	C₄×C₄⋊C₄	—	2	2	no	—
204	C₄×C₄⋊C₄	—	47	2	no	—
205	C₄×C₄⋊C₄	—	47	2	no	—
206	C₄×C₄⋊C₄	Dic₄₇	1	4	yes	complemented
207	C₄×C₂²⋊C₄	—	94	1	no	—
208	C₄×C₂²⋊C₄	—	94	1	no	—
209	#376	—	94	1	no	—
210	C₂×#95	—	2	1	no	—
211	C₄³	—	94	1	no	—
212	#339	—	94	8	no	—
213	C₄₇	#10852	1	1	yes	characteristic, complemented, Sylow
214	C₂³×C₄	—	2	2	no	—
215	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
216	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
217	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
218	C₂×M₁₆	—	47	4	no	—
219	C₂×M₁₆	—	94	2	no	—
220	C₂×M₁₆	—	94	4	no	—
221	C₂×M₁₆	—	94	4	no	—
222	C₂²×C₈	—	94	2	no	—
223	#117	—	47	4	no	—
224	#117	—	47	4	no	—
225	#117	—	94	2	no	—
226	#117	—	94	2	no	—
227	C₂×C₄⋊C₄	—	2	8	no	—
228	C₂×C₄⋊C₄	—	2	4	no	—
229	C₂×C₄⋊C₄	—	47	4	no	—
230	C₂×C₂²⋊C₄	—	94	2	no	—
231	C₂×C₄²	—	2	4	no	—
232	C₂×C₄²	—	2	4	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	—	94	2	no	—
235	C₂×C₄²	—	94	2	no	—
236	C₂×C₄²	—	94	2	no	—
237	C₂×C₄²	Dic₉₄	1	2	yes	—
238	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
239	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
240	C₂×C₄²	C₄×D₄₇	1	2	yes	—
241	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
242	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
243	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
244	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
245	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
246	C₄⋊C₈	—	94	4	no	—
247	C₄⋊C₈	—	94	4	no	—
248	#95	—	2	4	no	—
249	#95	—	94	2	no	—
250	#95	—	94	2	no	—
251	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	—	4	4	no	—
257	C₂²×C₄	—	4	4	no	—
258	C₂²×C₄	—	94	4	no	—
259	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
260	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
261	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
266	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
267	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
271	C₂²×C₄	D₄×D₄₇	1	2	yes	—
272	C₂²×C₄	#10625352	1	2	yes	—
273	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
274	C₂²×C₄	#10625354	1	2	yes	—
275	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
277	M₁₆	—	94	8	no	—
278	M₁₆	—	188	2	no	—
279	M₁₆	—	188	2	no	—
280	C₂×C₈	—	94	4	no	—
281	C₂×C₈	—	188	4	no	—
282	C₄⋊C₄	—	2	16	no	—
283	C₄⋊C₄	—	47	8	no	—
284	C₄⋊C₄	—	94	4	no	—
285	C₂²⋊C₄	—	94	4	no	—
286	C₂²⋊C₄	—	94	4	no	—
287	C₄²	—	2	8	no	—
288	C₄²	—	4	2	no	—
289	C₄²	—	4	2	no	—
290	C₄²	—	94	4	no	—
291	C₄²	—	94	4	no	—
292	C₄²	—	188	4	no	—
293	C₄²	—	188	4	no	—
294	C₄²	C₄×Dic₄₇	1	2	yes	—
295	C₄²	C₄×Dic₄₇	1	2	yes	—
296	C₄²	Dic₄₇⋊C₄	1	2	yes	—
297	C₄²	Dic₄₇⋊C₄	1	2	yes	—
298	C₄²	C₄⋊Dic₄₇	1	2	yes	—
299	C₄²	C₄⋊Dic₄₇	1	2	yes	—
300	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
301	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
305	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
306	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
307	C₂³	#13093995	1	2	yes	—
308	C₂³	#13094000	1	2	yes	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	16	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	94	8	no	—
321	C₂×C₄	—	188	4	no	—
322	C₂×C₄	—	188	4	no	—
323	C₂×C₄	C₄₇⋊#95	1	2	yes	—
324	C₂×C₄	C₄₇⋊#95	1	2	yes	—
325	C₂×C₄	C₄₇⋊#95	1	2	yes	—
326	C₂×C₄	C₄₇⋊#95	1	2	yes	—
327	C₂×C₄	#13093952	1	4	yes	—
328	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
329	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
331	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
333	C₂×C₄	#13093982	1	2	yes	—
334	C₂×C₄	#13093986	1	2	yes	—
335	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
336	C₂×C₄	#13093989	1	2	yes	—
337	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
338	C₂×C₄	#13093999	1	2	yes	—
339	C₂×C₄	#13094004	1	2	yes	—
340	C₂×C₄	#13094011	1	1	yes	characteristic
341	C₂×C₄	#13094013	1	1	yes	characteristic
342	C₂×C₄	#13094015	1	2	yes	—
343	C₂×C₄	#13094020	1	1	yes	characteristic
344	C₂×C₄	#13094022	1	1	yes	characteristic
345	C₂×C₄	#13094023	1	2	yes	—
346	C₈	—	188	4	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	2	4	no	—
353	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
354	C₂²	#15688980	1	2	yes	—
355	C₂²	#15689019	1	2	yes	—
356	C₂²	#15689026	1	1	yes	characteristic
357	C₂²	#15689030	1	1	yes	characteristic
358	C₂²	C₂×#13093952	1	2	yes	—
359	C₂²	#15689141	1	2	yes	—
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	4	8	no	—
364	C₄	—	188	8	no	—
365	C₄	#15688883	1	4	yes	complemented
366	C₄	C₄⋊C₄×Dic₄₇	1	2	yes	—
367	C₄	#15688988	1	1	yes	characteristic
368	C₄	#15688992	1	1	yes	characteristic
369	C₄	#15689022	1	2	yes	—
370	C₄	#15689024	1	1	yes	characteristic
371	C₄	#15689028	1	1	yes	characteristic
372	C₂	—	2	1	no	—
373	C₂	—	2	2	no	—
374	C₂	—	2	1	no	—
375	C₂	#20241617	1	1	yes	characteristic
376	C₂	C₂×#15688883	1	1	yes	characteristic
377	C₂	#20243098	1	1	yes	characteristic
378	C₂	#20243409	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#10852
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
8. #15689147	C₄	semidirect
11. C₄×C₄⋊Dic₄₇	C₄	semidirect
12. C₄×C₄⋊Dic₄₇	C₄	semidirect
22. C₄×C₄⋊C₄×C₄₇	C₄	semidirect
102. C₄⋊Dic₄₇	C₄⋊C₄	semidirect
175. C₄×C₄₇	#339	semidirect
206. C₄×C₄⋊C₄	Dic₄₇	semidirect
213. C₄₇	#10852	semidirect
365. C₄	#15688883	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689147	2
C₄×#13093983	2
C₂×#15688883	2
C₂×C₄×C₄⋊C₄×C₄₇	2
#10852	47