Subgroups — #13243448

Order 1792.

714 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic
2	C₄×#6489	C₂	1	1	yes	maximal, characteristic
3	C₂×#89697	C₂	1	1	yes	maximal, characteristic
4	#11725483	C₂	1	4	yes	maximal
5	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
6	C₂×#6489	C₄	1	2	yes	—
7	C₇×#431	—	2	1	no	—
8	C₇×#431	—	2	1	no	—
9	C₇×#431	—	2	1	no	—
10	C₇×#431	—	2	1	no	—
11	C₂×C₇×C₄⋊C₈	C₄	1	2	yes	complemented
12	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
13	C₂×C₄×C₇×C₈	C₄	1	2	yes	complemented
14	C₄×C₂²⋊Dic₇	C₄	1	2	yes	—
15	C₄×C₂²⋊Dic₇	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	2	yes	—
17	C₄×C₄⋊Dic₇	—	2	1	no	—
18	C₄×C₄⋊Dic₇	—	2	1	no	—
19	#89704	—	2	1	no	—
20	C₄²×Dic₇	—	2	1	no	—
21	#89697	—	2	1	no	—
22	#89697	—	2	1	no	—
23	#89697	C₄	1	2	yes	complemented
24	#89697	C₄	1	2	yes	complemented
25	C₂×C₄⋊(C₇⋊C₈)	—	2	1	no	—
26	C₂×C₄×C₇⋊C₈	—	2	1	no	—
27	#7924	—	7	1	no	maximal, Sylow
28	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
31	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
32	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₇	Q₈	1	1	yes	characteristic
43	C₂×C₄²×C₇	Q₈	1	1	yes	characteristic
44	C₂×C₂²⋊Dic₇	C₂×C₄	1	4	yes	—
45	#6489	—	2	4	no	—
46	#6489	C₈	1	8	yes	complemented
47	C₂×C₄⋊Dic₇	—	2	2	no	—
48	C₂×C₄×Dic₇	—	2	2	no	—
49	C₂×C₄×Dic₇	—	2	2	no	—
50	C₂×C₄×Dic₇	—	2	2	no	—
51	C₂²×C₇⋊C₈	—	2	2	no	—
52	C₇×C₄⋊C₈	—	2	2	no	—
53	C₇×C₄⋊C₈	—	2	2	no	—
54	C₇×C₂²⋊C₈	—	2	2	no	—
55	C₇×C₂²⋊C₈	—	2	2	no	—
56	C₄×C₇×C₈	—	2	2	no	—
57	C₄×C₇×C₈	—	2	2	no	—
58	C₇⋊#95	—	2	2	no	—
59	C₇⋊#95	—	2	2	no	—
60	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	4	yes	—
62	C₄⋊(C₇⋊C₈)	—	2	2	no	—
63	C₄⋊(C₇⋊C₈)	—	2	2	no	—
64	C₄×C₇⋊C₈	—	2	2	no	—
65	C₄×C₇⋊C₈	—	2	2	no	—
66	C₂×#431	—	7	1	no	—
67	C₂×#431	D₇	1	1	yes	characteristic
68	C₄×#117	—	7	1	no	—
69	#1282	—	7	4	no	—
70	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₇	—	4	2	no	—
72	C₂²×C₄×C₇	—	4	2	no	—
73	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
74	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
75	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₇	C₂×C₈	1	4	yes	—
86	C₂²×C₄×C₇	M₁₆	1	4	yes	—
87	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
93	C₂²×Dic₇	—	2	4	no	—
94	C₂×C₇×C₈	—	2	4	no	—
95	C₂×C₇×C₈	—	4	4	no	—
96	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₇	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₇	C₄⋊C₄	1	1	yes	characteristic
112	C₂²⋊Dic₇	—	2	4	no	—
113	C₂²⋊Dic₇	C₂×C₈	1	8	yes	—
114	C₄⋊Dic₇	—	2	8	no	—
115	C₄×Dic₇	—	2	8	no	—
116	C₄×Dic₇	—	4	4	no	—
117	C₄×Dic₇	—	4	4	no	—
118	C₂×C₇⋊C₈	—	2	4	no	—
119	C₂×C₇⋊C₈	—	4	4	no	—
120	C₂×#117	—	7	2	no	—
121	C₂²×C₄²	C₂×D₇	1	1	yes	characteristic
122	#431	—	2	1	no	—
123	#431	—	2	1	no	—
124	#431	—	2	1	no	—
125	#431	—	2	1	no	—
126	#431	—	7	2	no	—
127	#431	—	7	2	no	—
128	#431	—	14	1	no	—
129	#431	—	14	1	no	—
130	C₂×C₄⋊C₈	—	14	1	no	—
131	C₂×C₄⋊C₈	Dic₇	1	2	yes	complemented
132	C₂×C₂²⋊C₈	—	7	2	no	—
133	C₂×C₂²⋊C₈	C₂×D₇	1	2	yes	—
134	C₂×C₄×C₈	—	14	1	no	—
135	C₂×C₄×C₈	Dic₇	1	2	yes	complemented
136	C₄×C₄⋊C₄	—	14	1	no	—
137	C₄×C₄⋊C₄	—	14	1	no	—
138	C₄×C₂²⋊C₄	—	7	2	no	—
139	C₄×C₂²⋊C₄	—	7	2	no	—
140	#376	—	14	1	no	—
141	C₄³	—	14	1	no	—
142	C₂³×C₇	—	4	1	no	—
143	C₂³×C₇	—	4	1	no	—
144	C₂³×C₇	C₂×C₄²	1	1	yes	characteristic
145	C₂³×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂³×C₇	C₂²×C₈	1	2	yes	—
148	C₂³×C₇	C₂×M₁₆	1	2	yes	—
149	C₂×C₄×C₇	—	2	2	no	—
150	C₂×C₄×C₇	—	2	2	no	—
151	C₂×C₄×C₇	—	2	2	no	—
152	C₂×C₄×C₇	—	2	2	no	—
153	C₂×C₄×C₇	—	2	2	no	—
154	C₂×C₄×C₇	—	2	2	no	—
155	C₂×C₄×C₇	—	4	1	no	—
156	C₂×C₄×C₇	—	4	1	no	—
157	C₂×C₄×C₇	—	4	1	no	—
158	C₂×C₄×C₇	—	4	1	no	—
159	C₂×C₄×C₇	—	4	1	no	—
160	C₂×C₄×C₇	—	4	1	no	—
161	C₂×C₄×C₇	#95	1	1	yes	characteristic
162	C₂×C₄×C₇	#95	1	1	yes	characteristic
163	C₂×C₄×C₇	#95	1	1	yes	characteristic
164	C₂×C₄×C₇	#95	1	1	yes	characteristic
165	C₂×C₄×C₇	#95	1	1	yes	characteristic
166	C₂×C₄×C₇	#95	1	1	yes	characteristic
167	C₂×C₄×C₇	#95	1	1	yes	characteristic
168	C₂×C₄×C₇	#95	1	1	yes	characteristic
169	C₂×C₄×C₇	C₄×C₈	1	2	yes	—
170	C₂×C₄×C₇	C₄×C₈	1	2	yes	—
171	C₂×C₄×C₇	#97	1	2	yes	—
172	C₂×C₄×C₇	#97	1	2	yes	—
173	C₂×C₄×C₇	C₂²⋊C₈	1	4	yes	—
174	C₂×C₄×C₇	C₂²⋊C₈	1	4	yes	—
175	C₂×C₄×C₇	C₄⋊C₈	1	4	yes	—
176	C₂×C₄×C₇	C₄⋊C₈	1	4	yes	—
177	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×Dic₇	—	2	8	no	—
182	C₂×Dic₇	—	4	4	no	—
183	C₂×Dic₇	—	4	4	no	—
184	C₇×C₈	—	4	4	no	—
185	C₇⋊C₈	—	4	4	no	—
186	C₂³×C₄	C₄×D₇	1	1	yes	characteristic
187	C₂³×C₄	C₄×D₇	1	1	yes	characteristic
188	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
189	C₂²×C₈	—	14	2	no	—
190	C₂²×C₈	C₂×Dic₇	1	4	yes	—
191	#117	—	7	8	no	—
192	#117	—	14	4	no	—
193	C₂×C₄⋊C₄	—	14	2	no	—
194	C₂×C₂²⋊C₄	—	7	4	no	—
195	C₂×C₄²	—	14	2	no	—
196	C₂×C₄²	—	14	2	no	—
197	C₂×C₄²	—	14	2	no	—
198	C₂×C₄²	Dic₁₄	1	1	yes	characteristic
199	C₂×C₄²	Dic₁₄	1	1	yes	characteristic
200	C₂×C₄²	C₄×D₇	1	1	yes	characteristic
201	C₂×C₄²	C₄×D₇	1	1	yes	characteristic
202	C₂×C₄²	D₂₈	1	1	yes	characteristic
203	C₂×C₄²	D₂₈	1	1	yes	characteristic
204	C₂×C₄²	C₂×Dic₇	1	1	yes	characteristic
205	C₂×C₄²	C₂×Dic₇	1	1	yes	characteristic
206	C₂×C₄²	C₂²⋊D₇	1	1	yes	characteristic
207	C₂×C₄²	C₂²⋊D₇	1	1	yes	characteristic
208	C₂×C₄²	C₂²⋊D₇	1	1	yes	characteristic
209	C₂×C₄²	C₂²⋊D₇	1	1	yes	characteristic
210	C₄⋊C₈	—	2	2	no	—
211	C₄⋊C₈	—	2	2	no	—
212	C₄⋊C₈	—	14	2	no	—
213	C₄⋊C₈	—	14	2	no	—
214	C₂²⋊C₈	—	2	2	no	—
215	C₂²⋊C₈	—	2	2	no	—
216	C₂²⋊C₈	—	7	4	no	—
217	C₂²⋊C₈	—	14	2	no	—
218	C₄×C₈	—	2	2	no	—
219	C₄×C₈	—	2	2	no	—
220	C₄×C₈	—	14	2	no	—
221	C₄×C₈	—	14	2	no	—
222	#95	—	14	2	no	—
223	#95	—	14	2	no	—
224	C₂²×C₇	—	2	1	no	—
225	C₂²×C₇	—	2	1	no	—
226	C₂²×C₇	—	2	1	no	—
227	C₂²×C₇	—	2	1	no	—
228	C₂²×C₇	—	2	1	no	—
229	C₂²×C₇	—	2	1	no	—
230	C₂²×C₇	—	4	2	no	—
231	C₂²×C₇	—	4	2	no	—
232	C₂²×C₇	C₂×#95	1	1	yes	characteristic
233	C₂²×C₇	C₂×C₄×C₈	1	1	yes	characteristic
234	C₂²×C₇	C₂×#97	1	1	yes	characteristic
235	C₂²×C₇	C₂×C₂²⋊C₈	1	2	yes	—
236	C₂²×C₇	C₂×C₄⋊C₈	1	2	yes	—
237	C₄×C₇	—	2	1	no	—
238	C₄×C₇	—	2	1	no	—
239	C₄×C₇	—	2	1	no	—
240	C₄×C₇	—	2	1	no	—
241	C₄×C₇	—	2	1	no	—
242	C₄×C₇	—	2	1	no	—
243	C₄×C₇	#336	1	2	yes	—
244	C₄×C₇	#336	1	2	yes	—
245	C₄×C₇	#336	1	2	yes	—
246	C₄×C₇	#336	1	2	yes	—
247	C₄×C₇	#344	1	2	yes	—
248	C₄×C₇	#410	1	2	yes	—
249	Dic₇	—	4	8	no	—
250	C₂⁴	C₂×C₄×D₇	1	1	yes	characteristic
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	14	4	no	—
254	C₂²×C₄	C₈×D₇	1	4	yes	—
255	C₂²×C₄	#1131	1	4	yes	—
256	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
257	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
258	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
259	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
260	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	Dic₇⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	(C₂×D₇)⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	(C₂×D₇)⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	(C₂×D₇)⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	(C₂×D₇)⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	C₂×Dic₁₄	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₂₈	1	1	yes	characteristic
271	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	4	4	no	—
276	C₂×C₈	—	14	4	no	—
277	C₂×C₈	—	28	4	no	—
278	C₄⋊C₄	—	14	8	no	—
279	C₂²⋊C₄	—	7	8	no	—
280	C₂²⋊C₄	—	14	4	no	—
281	C₄²	—	14	8	no	—
282	C₄²	—	28	4	no	—
283	C₄²	—	28	4	no	—
284	C₄²	Dic₇⋊C₄	1	1	yes	characteristic
285	C₄²	Dic₇⋊C₄	1	1	yes	characteristic
286	C₄²	Dic₇⋊C₄	1	1	yes	characteristic
287	C₄²	Dic₇⋊C₄	1	1	yes	characteristic
288	C₄²	C₄⋊Dic₇	1	1	yes	characteristic
289	C₄²	C₄⋊Dic₇	1	1	yes	characteristic
290	C₄²	C₄⋊Dic₇	1	1	yes	characteristic
291	C₄²	C₄⋊Dic₇	1	1	yes	characteristic
292	C₄²	(C₂×D₇)⋊C₄	1	1	yes	characteristic
293	C₄²	(C₂×D₇)⋊C₄	1	1	yes	characteristic
294	C₄²	(C₂×D₇)⋊C₄	1	1	yes	characteristic
295	C₄²	(C₂×D₇)⋊C₄	1	1	yes	characteristic
296	C₄²	C₂²⋊Dic₇	1	1	yes	characteristic
297	C₄²	C₂²⋊Dic₇	1	1	yes	characteristic
298	C₄²	C₂²⋊Dic₇	1	1	yes	characteristic
299	C₄²	C₂²⋊Dic₇	1	1	yes	characteristic
300	C₂×C₇	—	2	2	no	—
301	C₂×C₇	—	2	1	no	—
302	C₂×C₇	—	2	1	no	—
303	C₂×C₇	—	2	2	no	—
304	C₂×C₇	C₂×#336	1	1	yes	characteristic
305	C₂×C₇	#1740	1	1	yes	characteristic
306	C₂×C₇	C₂×#344	1	1	yes	characteristic
307	C₂³	—	4	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	C₂×C₈×D₇	1	2	yes	—
310	C₂³	C₂×#1131	1	2	yes	—
311	C₂³	C₂×C₄×Dic₇	1	1	yes	characteristic
312	C₂³	C₂×Dic₇⋊C₄	1	1	yes	characteristic
313	C₂³	C₂×(C₂×D₇)⋊C₄	1	1	yes	characteristic
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	14	8	no	—
327	C₂×C₄	—	28	4	no	—
328	C₂×C₄	—	28	4	no	—
329	C₂×C₄	C₈×Dic₇	1	2	yes	—
330	C₂×C₄	C₈×Dic₇	1	2	yes	—
331	C₂×C₄	Dic₇⋊C₈	1	4	yes	—
332	C₂×C₄	Dic₇⋊C₈	1	4	yes	—
333	C₂×C₄	#6389	1	2	yes	—
334	C₂×C₄	#6389	1	2	yes	—
335	C₂×C₄	(C₂×D₇)⋊C₈	1	4	yes	—
336	C₂×C₄	(C₂×D₇)⋊C₈	1	4	yes	—
337	C₂×C₄	C₇⋊#95	1	1	yes	characteristic
338	C₂×C₄	C₇⋊#95	1	1	yes	characteristic
339	C₂×C₄	C₇⋊#95	1	1	yes	characteristic
340	C₂×C₄	C₇⋊#95	1	1	yes	characteristic
341	C₂×C₄	C₇⋊#95	1	1	yes	characteristic
342	C₂×C₄	C₇⋊#95	1	1	yes	characteristic
343	C₂×C₄	C₇⋊#95	1	1	yes	characteristic
344	C₂×C₄	C₇⋊#95	1	1	yes	characteristic
345	C₂×C₄	C₂×Dic₇⋊C₄	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄⋊Dic₇	1	1	yes	characteristic
347	C₂×C₄	C₂×(C₂×D₇)⋊C₄	1	1	yes	characteristic
348	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
349	C₈	—	4	4	no	—
350	C₈	—	28	4	no	—
351	C₇	#7924	1	1	yes	characteristic, complemented, Sylow
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	C₂×C₈×Dic₇	1	1	yes	characteristic
361	C₂²	C₂×Dic₇⋊C₈	1	2	yes	—
362	C₂²	C₂×#6389	1	1	yes	characteristic
363	C₂²	C₂×(C₂×D₇)⋊C₈	1	2	yes	—
364	C₂²	C₂×C₇⋊#95	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	28	8	no	—
372	C₄	#89345	1	2	yes	—
373	C₄	#89345	1	2	yes	—
374	C₄	#89345	1	2	yes	—
375	C₄	#89345	1	2	yes	—
376	C₄	#89351	1	2	yes	—
377	C₄	#90012	1	2	yes	—
378	C₂	—	2	2	no	—
379	C₂	—	2	1	no	—
380	C₂	—	2	2	no	—
381	C₂	—	2	1	no	—
382	C₂	#11729346	1	1	yes	characteristic
383	C₂	C₂×#89345	1	1	yes	characteristic
384	C₂	C₂×#89351	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²⋊Dic₇
commutator	C₂²×C₇	C₂×C₄×C₈
Frattini	C₂³×C₄	C₂²×D₇
Fitting	C₂×C₇×#431	C₂
socle	C₂²×C₇	C₂×#95
prime radical	C₂⁴×C₇	C₂²×C₄
cosocle	C₂³×C₄×C₇	C₂³
hypercenter	C₂×#431	D₇
hypocenter	C₇	#7924
LCS	G ▷ C₂²×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
11. C₂×C₇×C₄⋊C₈	C₄	semidirect
13. C₂×C₄×C₇×C₈	C₄	semidirect
23. #89697	C₄	semidirect
24. #89697	C₄	semidirect
46. #6489	C₈	semidirect
131. C₂×C₄⋊C₈	Dic₇	semidirect
135. C₂×C₄×C₈	Dic₇	semidirect
351. C₇	#7924	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#431	2
C₄×#6489	2
C₂×#89697	2
#11725483	2
#7924	7