Subgroups — C₃×#90337 #13060988

Order 1344.

392 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	C₃×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#6509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#6507	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6492	C₂	1	1	yes	maximal, characteristic
5	C₃×#6487	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6461	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#6461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#6459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#6453	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#6448	C₂	1	1	yes	maximal, characteristic
13	C₃×#6446	C₂	1	1	yes	maximal, characteristic
14	C₃×#6442	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#6442	C₂	1	1	yes	maximal, characteristic, complemented
16	#90337	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
21	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic
23	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
29	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
30	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
31	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
34	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
35	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
37	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
38	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
39	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
40	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
44	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
45	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
46	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
47	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
48	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
49	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic
50	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic
51	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic
52	C₇×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
53	#6509	C₂×C₃	1	1	yes	characteristic, complemented
54	#6507	C₂×C₃	1	1	yes	characteristic, complemented
55	#6492	C₂×C₃	1	1	yes	characteristic
56	#6487	C₂×C₃	1	1	yes	characteristic, complemented
57	#6461	C₂×C₃	1	1	yes	characteristic, complemented
58	#6461	C₂×C₃	1	1	yes	characteristic, complemented
59	#6459	C₂×C₃	1	1	yes	characteristic, complemented
60	#6453	C₂×C₃	1	1	yes	characteristic, complemented
61	#6452	C₂×C₃	1	1	yes	characteristic, complemented
62	#6451	C₂×C₃	1	1	yes	characteristic, complemented
63	#6448	C₂×C₃	1	1	yes	characteristic
64	#6446	C₂×C₃	1	1	yes	characteristic
65	#6442	C₂×C₃	1	1	yes	characteristic, complemented
66	#6442	C₂×C₃	1	1	yes	characteristic, complemented
67	C₃×#563	—	7	1	no	maximal, Hall
68	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
69	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
70	C₃×C₇×Q₈	—	4	1	no	—
71	C₂×C₃×C₄×C₇	—	4	1	no	—
72	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
78	C₃×C₂²⋊D₇	—	4	1	no	—
79	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
80	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
81	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
82	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
83	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
84	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
85	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
86	C₃×C₄×D₇	—	4	1	no	—
87	C₃×Dic₁₄	—	4	1	no	—
88	C₃×Dic₁₄	—	4	1	no	—
89	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
93	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
95	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
99	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
101	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
102	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
103	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
104	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
108	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
109	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
110	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
111	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
112	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
118	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
122	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
123	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
124	C₃×C₄⋊Q₈	—	7	1	no	—
125	C₃×C₄⋊Q₈	—	7	1	no	—
126	C₃×#126	—	7	1	no	—
127	C₃×#126	—	7	1	no	—
128	C₃×#126	—	7	1	no	—
129	C₃×#126	—	7	1	no	—
130	C₃×#125	—	7	1	no	—
131	C₃×#125	—	7	1	no	—
132	C₃×#124	—	7	1	no	—
133	C₃×#123	—	7	1	no	—
134	C₃×#123	—	7	1	no	—
135	C₃×C₂²⋊Q₈	—	7	1	no	—
136	C₃×C₂²⋊Q₈	—	7	1	no	—
137	C₃×C₂²⋊Q₈	—	7	1	no	—
138	C₃×C₂²⋊Q₈	D₇	1	1	yes	characteristic, complemented
139	C₂²×C₃×C₇	—	2	1	no	—
140	C₂²×C₃×C₇	—	2	1	no	—
141	C₂²×C₃×C₇	—	2	1	no	—
142	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
143	C₂×C₃×D₇	—	2	1	no	—
144	C₂×C₃×D₇	—	2	1	no	—
145	C₂×C₃×D₇	—	2	1	no	—
146	C₃×C₄×C₇	—	2	1	no	—
147	C₃×C₄×C₇	—	2	1	no	—
148	C₃×C₄×C₇	—	2	1	no	—
149	C₃×C₄×C₇	—	2	1	no	—
150	C₃×C₄×C₇	—	2	1	no	—
151	C₃×C₄×C₇	—	2	1	no	—
152	C₃×Dic₇	—	2	1	no	—
153	C₃×Dic₇	—	2	1	no	—
154	C₃×Dic₇	—	2	1	no	—
155	C₃×Dic₇	—	2	1	no	—
156	C₃×Dic₇	—	2	1	no	—
157	C₃×Dic₇	—	2	1	no	—
158	C₃×Dic₇	—	2	1	no	—
159	#563	—	7	1	no	Sylow
160	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
161	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
162	C₇×Q₈	—	4	1	no	—
163	C₂×C₄×C₇	—	4	1	no	—
164	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
165	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
166	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
167	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
168	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
169	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
170	C₂²⋊D₇	—	4	1	no	—
171	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
172	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
173	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
174	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
175	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
176	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
177	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
178	C₄×D₇	—	4	1	no	—
179	Dic₁₄	—	4	1	no	—
180	Dic₁₄	—	4	1	no	—
181	C₂×C₃×Q₈	—	7	1	no	—
182	C₂×C₃×Q₈	—	7	1	no	—
183	C₂×C₃×Q₈	C₂×D₇	1	1	yes	characteristic
184	C₂×C₃×D₄	—	7	1	no	—
185	C₂²×C₃×C₄	—	7	1	no	—
186	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
187	C₃×C₄⋊C₄	—	7	1	no	—
188	C₃×C₄⋊C₄	—	7	1	no	—
189	C₃×C₄⋊C₄	—	7	1	no	—
190	C₃×C₄⋊C₄	—	7	1	no	—
191	C₃×C₄⋊C₄	—	7	1	no	—
192	C₃×C₄⋊C₄	—	7	1	no	—
193	C₃×C₄⋊C₄	—	7	1	no	—
194	C₃×C₄⋊C₄	—	7	1	no	—
195	C₃×C₄⋊C₄	—	7	1	no	—
196	C₃×C₄⋊C₄	—	7	1	no	—
197	C₃×C₄⋊C₄	—	7	1	no	—
198	C₃×C₄⋊C₄	—	7	1	no	—
199	C₃×C₄⋊C₄	—	7	1	no	—
200	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
201	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
202	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
203	C₃×C₂²⋊C₄	—	7	1	no	—
204	C₃×C₂²⋊C₄	—	7	1	no	—
205	C₃×C₂²⋊C₄	—	7	1	no	—
206	C₃×C₂²⋊C₄	—	7	1	no	—
207	C₃×C₂²⋊C₄	—	7	1	no	—
208	C₃×C₂²⋊C₄	—	7	1	no	—
209	C₃×C₂²⋊C₄	—	7	1	no	—
210	C₃×C₂²⋊C₄	—	7	1	no	—
211	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
212	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
213	C₃×C₄²	—	7	1	no	—
214	C₃×C₄²	—	7	1	no	—
215	C₃×C₄²	—	7	1	no	—
216	C₂×C₃×C₇	—	4	1	no	—
217	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₃×C₇	2₋¹⁺⁴	1	1	yes	characteristic
219	C₂×C₃×C₇	2₋¹⁺⁴	1	1	yes	characteristic
220	C₃×D₇	—	4	1	no	—
221	C₄⋊Q₈	—	7	1	no	—
222	C₄⋊Q₈	—	7	1	no	—
223	#126	—	7	1	no	—
224	#126	—	7	1	no	—
225	#126	—	7	1	no	—
226	#126	—	7	1	no	—
227	#125	—	7	1	no	—
228	#125	—	7	1	no	—
229	#124	—	7	1	no	—
230	#123	—	7	1	no	—
231	#123	—	7	1	no	—
232	C₂²⋊Q₈	—	7	1	no	—
233	C₂²⋊Q₈	—	7	1	no	—
234	C₂²⋊Q₈	—	7	1	no	—
235	C₂²⋊Q₈	C₃×D₇	1	1	yes	characteristic, complemented
236	C₂²×C₇	—	2	1	no	—
237	C₂²×C₇	—	2	1	no	—
238	C₂²×C₇	—	2	1	no	—
239	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
240	C₂×D₇	—	2	1	no	—
241	C₂×D₇	—	2	1	no	—
242	C₂×D₇	—	2	1	no	—
243	C₄×C₇	—	2	1	no	—
244	C₄×C₇	—	2	1	no	—
245	C₄×C₇	—	2	1	no	—
246	C₄×C₇	—	2	1	no	—
247	C₄×C₇	—	2	1	no	—
248	C₄×C₇	—	2	1	no	—
249	Dic₇	—	2	1	no	—
250	Dic₇	—	2	1	no	—
251	Dic₇	—	2	1	no	—
252	Dic₇	—	2	1	no	—
253	Dic₇	—	2	1	no	—
254	Dic₇	—	2	1	no	—
255	Dic₇	—	2	1	no	—
256	C₂³×C₃	—	7	1	no	—
257	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
258	C₃×Q₈	—	4	1	no	—
259	C₃×Q₈	—	28	1	no	—
260	C₃×Q₈	—	28	1	no	—
261	C₃×D₄	—	28	1	no	—
262	C₂×C₃×C₄	—	4	1	no	—
263	C₂×C₃×C₄	—	7	1	no	—
264	C₂×C₃×C₄	—	7	1	no	—
265	C₂×C₃×C₄	—	7	1	no	—
266	C₂×C₃×C₄	—	7	1	no	—
267	C₂×C₃×C₄	—	7	1	no	—
268	C₂×C₃×C₄	—	7	1	no	—
269	C₂×C₃×C₄	—	7	1	no	—
270	C₂×C₃×C₄	—	28	1	no	—
271	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
277	C₃×C₇	#563	1	1	yes	characteristic, complemented, Hall
278	C₂×Q₈	—	7	1	no	—
279	C₂×Q₈	—	7	1	no	—
280	C₂×Q₈	C₂×C₃×D₇	1	1	yes	characteristic
281	C₂×D₄	—	7	1	no	—
282	C₂²×C₄	—	7	1	no	—
283	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
284	C₄⋊C₄	—	7	1	no	—
285	C₄⋊C₄	—	7	1	no	—
286	C₄⋊C₄	—	7	1	no	—
287	C₄⋊C₄	—	7	1	no	—
288	C₄⋊C₄	—	7	1	no	—
289	C₄⋊C₄	—	7	1	no	—
290	C₄⋊C₄	—	7	1	no	—
291	C₄⋊C₄	—	7	1	no	—
292	C₄⋊C₄	—	7	1	no	—
293	C₄⋊C₄	—	7	1	no	—
294	C₄⋊C₄	—	7	1	no	—
295	C₄⋊C₄	—	7	1	no	—
296	C₄⋊C₄	—	7	1	no	—
297	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
298	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
299	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
300	C₂²⋊C₄	—	7	1	no	—
301	C₂²⋊C₄	—	7	1	no	—
302	C₂²⋊C₄	—	7	1	no	—
303	C₂²⋊C₄	—	7	1	no	—
304	C₂²⋊C₄	—	7	1	no	—
305	C₂²⋊C₄	—	7	1	no	—
306	C₂²⋊C₄	—	7	1	no	—
307	C₂²⋊C₄	—	7	1	no	—
308	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
309	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
310	C₄²	—	7	1	no	—
311	C₄²	—	7	1	no	—
312	C₄²	—	7	1	no	—
313	C₂×C₇	—	4	1	no	—
314	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×C₇	C₃×2₋¹⁺⁴	1	1	yes	characteristic
316	C₂×C₇	C₃×2₋¹⁺⁴	1	1	yes	characteristic
317	D₇	—	4	1	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	—	2	1	no	—
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	14	1	no	—
322	C₂²×C₃	—	14	1	no	—
323	C₂²×C₃	—	14	1	no	—
324	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	2	1	no	—
330	C₃×C₄	—	2	1	no	—
331	C₃×C₄	—	14	1	no	—
332	C₃×C₄	—	14	1	no	—
333	C₃×C₄	—	14	1	no	—
334	C₃×C₄	—	14	1	no	—
335	C₃×C₄	—	14	1	no	—
336	C₃×C₄	—	14	1	no	—
337	C₃×C₄	—	14	1	no	—
338	C₂³	—	7	1	no	—
339	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
340	Q₈	—	4	1	no	—
341	Q₈	—	28	1	no	—
342	Q₈	—	28	1	no	—
343	D₄	—	28	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	7	1	no	—
346	C₂×C₄	—	7	1	no	—
347	C₂×C₄	—	7	1	no	—
348	C₂×C₄	—	7	1	no	—
349	C₂×C₄	—	7	1	no	—
350	C₂×C₄	—	7	1	no	—
351	C₂×C₄	—	7	1	no	—
352	C₂×C₄	—	28	1	no	—
353	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
359	C₇	C₃×#563	1	1	yes	characteristic, complemented, Sylow
360	C₂×C₃	—	4	1	no	—
361	C₂×C₃	—	28	1	no	—
362	C₂×C₃	#6548	1	1	yes	characteristic
363	C₂×C₃	#6551	1	1	yes	characteristic
364	C₂×C₃	#6554	1	1	yes	characteristic
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	14	1	no	—
369	C₂²	—	14	1	no	—
370	C₂²	—	14	1	no	—
371	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	14	1	no	—
379	C₄	—	14	1	no	—
380	C₄	—	14	1	no	—
381	C₄	—	14	1	no	—
382	C₄	—	14	1	no	—
383	C₄	—	14	1	no	—
384	C₄	—	14	1	no	—
385	C₃	#90337	1	1	yes	characteristic, direct product factor, Sylow
386	C₂	—	4	1	no	—
387	C₂	—	28	1	no	—
388	C₂	C₃×#6548	1	1	yes	characteristic
389	C₂	C₃×#6551	1	1	yes	characteristic
390	C₂	C₃×#6554	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₇
commutator, cosocle	C₂²×C₇	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₇
Fitting	C₃×C₇×C₂²⋊Q₈	C₂
socle	C₂²×C₃×C₇	C₂⁴
prime radical	C₂×C₃×C₂²⋊D₇	C₂²
hypercenter	C₃×C₂²⋊Q₈	D₇
hypocenter	C₇	C₃×#563
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₂²⋊Q₈	C₂	semidirect
2. C₃×#6509	C₂	semidirect
3. C₃×#6507	C₂	semidirect
5. C₃×#6487	C₂	semidirect
6. C₃×#6461	C₂	semidirect
7. C₃×#6461	C₂	semidirect
8. C₃×#6459	C₂	semidirect
9. C₃×#6453	C₂	semidirect
10. C₃×#6452	C₂	semidirect
11. C₃×#6451	C₂	semidirect
14. C₃×#6442	C₂	semidirect
15. C₃×#6442	C₂	semidirect
16. #90337	C₃	direct (N × H)
52. C₇×C₂²⋊Q₈	C₂×C₃	semidirect
53. #6509	C₂×C₃	semidirect
54. #6507	C₂×C₃	semidirect
56. #6487	C₂×C₃	semidirect
57. #6461	C₂×C₃	semidirect
58. #6461	C₂×C₃	semidirect
59. #6459	C₂×C₃	semidirect
60. #6453	C₂×C₃	semidirect
61. #6452	C₂×C₃	semidirect
62. #6451	C₂×C₃	semidirect
65. #6442	C₂×C₃	semidirect
66. #6442	C₂×C₃	semidirect
138. C₃×C₂²⋊Q₈	D₇	semidirect
235. C₂²⋊Q₈	C₃×D₇	semidirect
277. C₃×C₇	#563	semidirect
359. C₇	C₃×#563	semidirect
385. C₃	#90337	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₂²⋊Q₈	2
C₃×#6509	2
C₃×#6507	2
C₃×#6492	2
C₃×#6487	2
C₃×#6461	2
C₃×#6459	2
C₃×#6453	2
C₃×#6452	2
C₃×#6451	2
C₃×#6448	2
C₃×#6446	2
C₃×#6442	2
#90337	3
C₃×#563	7

Subgroups — C3×#90337 #13060988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90337 #13060988