Subgroups — #26122135

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	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688882	C₂	1	4	yes	maximal
4	C₄×#117×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10625329	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
7	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
8	#15689147	—	2	2	no	—
9	#15689147	C₄	1	4	yes	complemented
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
12	C₄×C₄⋊Dic₄₇	—	2	2	no	—
13	C₄×C₄⋊Dic₄₇	C₄	1	4	yes	complemented
14	C₂×C₄₇⋊#95	—	2	1	no	—
15	#15688882	—	2	8	no	—
16	C₂×#117×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₄₇	C₄	1	2	yes	complemented
19	C₄×C₄⋊C₄×C₄₇	C₄	1	2	yes	complemented
20	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
21	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
22	C₄₇×#376	—	2	1	no	—
23	C₄³×C₄₇	—	2	1	no	—
24	C₂³×Dic₄₇	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	4	no	—
27	C₂×#10625329	—	2	4	no	—
28	C₂×#10625329	C₂×C₄	1	4	yes	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	8	no	—
31	C₂×C₄⋊Dic₄₇	—	2	4	no	—
32	C₂×C₄×Dic₄₇	—	2	4	no	—
33	C₂×C₄×Dic₄₇	—	2	4	no	—
34	C₂×C₄×Dic₄₇	—	2	2	no	—
35	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
36	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
37	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
38	C₄₇⋊#95	—	2	4	no	—
39	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	#117×C₄₇	—	2	2	no	—
43	#117×C₄₇	—	2	2	no	—
44	#117×C₄₇	D₄	1	4	yes	—
45	#117×C₄₇	Q₈	1	4	yes	—
46	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
47	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₄²×C₄₇	—	2	2	no	—
49	C₂×C₄²×C₄₇	—	2	2	no	—
50	C₂×C₄²×C₄₇	—	2	2	no	—
51	C₂×C₄²×C₄₇	C₂×C₄	1	2	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	D₄	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	Q₈	1	2	yes	—
59	#95×C₄₇	—	2	2	no	—
60	#95×C₄₇	—	2	2	no	—
61	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₇	—	2	4	no	—
63	C₂²×C₄×C₄₇	—	2	4	no	—
64	C₂²×C₄×C₄₇	—	4	2	no	—
65	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₄×C₄₇	C₂²⋊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	C₂²×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	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₄₇	#41	1	2	yes	—
82	C₂²×C₄×C₄₇	#41	1	2	yes	—
83	C₂²×Dic₄₇	—	2	8	no	—
84	C₂²×Dic₄₇	—	2	4	no	—
85	C₂²×Dic₄₇	—	4	4	no	—
86	C₂²×Dic₄₇	—	4	4	no	—
87	C₄⋊C₄×C₄₇	—	2	4	no	—
88	C₄⋊C₄×C₄₇	C₄⋊C₄	1	8	yes	complemented
89	C₂²⋊C₄×C₄₇	—	2	4	no	—
90	C₂²⋊C₄×C₄₇	—	2	4	no	—
91	C₄²×C₄₇	—	2	4	no	—
92	C₄²×C₄₇	—	2	4	no	—
93	C₄²×C₄₇	—	4	4	no	—
94	C₄²×C₄₇	—	4	4	no	—
95	C₄²×C₄₇	C₄²	1	2	yes	—
96	C₄²×C₄₇	C₄²	1	2	yes	—
97	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
98	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
99	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
100	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
101	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
102	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
103	C₄⋊Dic₄₇	—	2	16	no	—
104	C₄×Dic₄₇	—	2	8	no	—
105	C₄×Dic₄₇	—	4	2	no	—
106	C₄×Dic₄₇	—	4	2	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	4	no	—
128	C₂×C₄×C₄₇	—	4	4	no	—
129	C₂×C₄×C₄₇	#95	1	2	yes	—
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	#104	1	4	yes	—
134	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
135	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₇	C₂×C₄⋊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	#117	1	2	yes	—
140	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
142	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
143	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
144	C₂×C₄×C₄₇	#121	1	2	yes	—
145	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
146	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#125	1	2	yes	—
149	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
151	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
152	C₂×Dic₄₇	—	2	8	no	—
153	C₂×Dic₄₇	—	4	16	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	D₄₇	1	1	yes	characteristic
185	C₂×C₄×C₄⋊C₄	—	47	1	no	—
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	C₂×D₄₇	1	2	yes	—
196	C₂²×C₄⋊C₄	—	94	1	no	—
197	C₂²×C₄²	—	47	2	no	—
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	—	47	4	no	—
204	C₄×C₄⋊C₄	—	94	2	no	—
205	C₄×C₄⋊C₄	Dic₄₇	1	2	yes	complemented
206	C₄×C₄⋊C₄	Dic₄₇	1	2	yes	complemented
207	C₄×C₂²⋊C₄	—	2	1	no	—
208	C₄×C₂²⋊C₄	—	2	1	no	—
209	#376	—	2	1	no	—
210	C₂×#95	—	94	1	no	—
211	C₄³	—	2	1	no	—
212	#339	—	94	8	no	—
213	C₄₇	#10852	1	1	yes	characteristic, complemented, Sylow
214	C₂³×C₄	—	94	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	—	2	2	no	—
224	#117	—	2	2	no	—
225	#117	Dic₉₄	1	4	yes	—
226	#117	D₁₈₈	1	4	yes	—
227	C₂×C₄⋊C₄	—	94	8	no	—
228	C₂×C₄⋊C₄	—	94	4	no	—
229	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
230	C₂×C₂²⋊C₄	—	2	2	no	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	—	47	4	no	—
235	C₂×C₄²	—	94	4	no	—
236	C₂×C₄²	—	94	4	no	—
237	C₂×C₄²	—	94	2	no	—
238	C₂×C₄²	Dic₉₄	1	2	yes	—
239	C₂×C₄²	C₄×D₄₇	1	2	yes	—
240	C₂×C₄²	C₄×D₄₇	1	2	yes	—
241	C₂×C₄²	D₁₈₈	1	2	yes	—
242	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
243	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
244	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
245	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
246	C₄⋊C₈	—	94	4	no	—
247	C₄⋊C₈	—	94	4	no	—
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	#95	—	94	4	no	—
251	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	—	94	8	no	—
256	C₂²×C₄	—	94	4	no	—
257	C₂²×C₄	—	188	4	no	—
258	C₂²×C₄	—	188	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	2	yes	—
262	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
263	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
266	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
267	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
268	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
269	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
273	C₂²×C₄	#10625350	1	2	yes	—
274	C₂²×C₄	#10625350	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	4	no	—
283	C₄⋊C₄	—	94	16	no	—
284	C₄⋊C₄	C₄⋊Dic₄₇	1	8	yes	complemented
285	C₂²⋊C₄	—	2	4	no	—
286	C₂²⋊C₄	—	2	4	no	—
287	C₄²	—	2	4	no	—
288	C₄²	—	2	4	no	—
289	C₄²	—	4	4	no	—
290	C₄²	—	4	4	no	—
291	C₄²	—	94	8	no	—
292	C₄²	—	188	2	no	—
293	C₄²	—	188	2	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	#13093998	1	2	yes	—
308	C₂³	#13094003	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	4	no	—
319	C₂×C₄	—	94	8	no	—
320	C₂×C₄	—	188	4	no	—
321	C₂×C₄	—	188	16	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	#13093951	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	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
332	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
333	C₂×C₄	#13093983	1	2	yes	—
334	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
335	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
336	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
337	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
338	C₂×C₄	#13093998	1	2	yes	—
339	C₂×C₄	#13094003	1	2	yes	—
340	C₂×C₄	#13094012	1	1	yes	characteristic
341	C₂×C₄	#13094012	1	1	yes	characteristic
342	C₂×C₄	#13094016	1	2	yes	—
343	C₂×C₄	#13094021	1	1	yes	characteristic
344	C₂×C₄	#13094024	1	2	yes	—
345	C₂×C₄	#13094024	1	1	yes	characteristic
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	#15688983	1	2	yes	—
355	C₂²	#15689021	1	2	yes	—
356	C₂²	#15689025	1	1	yes	characteristic
357	C₂²	#15689029	1	1	yes	characteristic
358	C₂²	C₂×#13093951	1	2	yes	—
359	C₂²	#15689140	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	#15688882	1	4	yes	complemented
366	C₄	C₄×C₄⋊Dic₄₇	1	2	yes	—
367	C₄	#15688989	1	1	yes	characteristic
368	C₄	#15688993	1	1	yes	characteristic
369	C₄	#15689021	1	2	yes	—
370	C₄	#15689025	1	1	yes	characteristic
371	C₄	#15689029	1	1	yes	characteristic
372	C₂	—	2	1	no	—
373	C₂	—	2	2	no	—
374	C₂	—	2	1	no	—
375	C₂	#20241618	1	1	yes	characteristic
376	C₂	C₂×#15688882	1	1	yes	characteristic
377	C₂	#20243097	1	1	yes	characteristic
378	C₂	#20243408	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄×#117×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₄×#117	D₄₇
hypocenter	C₄₇	#10852
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
9. #15689147	C₄	semidirect
13. C₄×C₄⋊Dic₄₇	C₄	semidirect
18. C₄×C₄⋊C₄×C₄₇	C₄	semidirect
19. C₄×C₄⋊C₄×C₄₇	C₄	semidirect
88. C₄⋊C₄×C₄₇	C₄⋊C₄	semidirect
175. C₄×C₄₇	#339	semidirect
205. C₄×C₄⋊C₄	Dic₄₇	semidirect
206. C₄×C₄⋊C₄	Dic₄₇	semidirect
213. C₄₇	#10852	semidirect
284. C₄⋊C₄	C₄⋊Dic₄₇	semidirect
365. C₄	#15688882	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
C₂×C₄×C₄⋊Dic₄₇	2
C₂×#15688882	2
C₄×#117×C₄₇	2
#10852	47