Subgroups — C₃×#90328 #13060981

Order 1344.

496 conjugacy classes of subgroups.

The subgroup lattice has 444 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×#6510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#6509	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×(C₂×D₇)⋊C₄	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×#6457	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#6457	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6456	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6455	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#6449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#6445	C₂	1	1	yes	maximal, characteristic
14	C₃×D₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#6440	C₂	1	1	yes	maximal, characteristic, complemented
16	#90328	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
21	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
22	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₂²⋊Dic₇	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×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
46	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
52	C₇×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
53	#6510	C₂×C₃	1	1	yes	characteristic, complemented
54	#6509	C₂×C₃	1	1	yes	characteristic, complemented
55	C₄×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×(C₂×D₇)⋊C₄	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	#6457	C₂×C₃	1	1	yes	characteristic, complemented
60	#6457	C₂×C₃	1	1	yes	characteristic, complemented
61	#6456	C₂×C₃	1	1	yes	characteristic, complemented
62	#6455	C₂×C₃	1	1	yes	characteristic, complemented
63	#6449	C₂×C₃	1	1	yes	characteristic, complemented
64	#6445	C₂×C₃	1	1	yes	characteristic
65	D₇×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
66	#6440	C₂×C₃	1	1	yes	characteristic, complemented
67	C₃×#551	—	7	1	no	maximal, Hall
68	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
69	C₂²×C₃×D₇	—	2	2	no	—
70	C₂²×C₃×D₇	—	2	2	no	—
71	C₂²×C₃×D₇	—	4	1	no	—
72	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
73	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
74	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
75	C₃×C₇×Q₈	—	4	1	no	—
76	C₂×C₃×C₄×C₇	—	4	1	no	—
77	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
83	C₃×C₂²⋊D₇	—	2	2	no	—
84	C₂×C₃×Dic₇	—	2	2	no	—
85	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
86	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
87	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
88	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
89	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
90	C₃×D₂₈	—	2	2	no	—
91	C₃×D₂₈	—	4	1	no	—
92	C₃×C₄×D₇	—	2	2	no	—
93	C₃×C₄×D₇	—	4	1	no	—
94	C₃×C₄×D₇	—	4	1	no	—
95	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
97	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
99	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
100	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
101	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
105	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
111	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
118	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
120	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
121	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
124	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
125	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
126	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
128	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
130	C₃×#126	—	7	1	no	—
131	C₃×#126	—	7	1	no	—
132	C₃×#124	—	7	1	no	—
133	C₃×#123	—	7	1	no	—
134	C₃×#123	—	7	1	no	—
135	C₃×#123	—	7	1	no	—
136	C₃×C₂²⋊Q₈	—	7	1	no	—
137	C₃×C₂²⋊Q₈	D₇	1	1	yes	characteristic, complemented
138	C₃×#120	—	7	1	no	—
139	C₃×C₄×D₄	—	7	1	no	—
140	C₃×C₄×D₄	—	7	1	no	—
141	C₃×#117	—	7	1	no	—
142	C₃×#117	—	7	1	no	—
143	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
144	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
145	C₂²×C₃×C₇	—	2	1	no	—
146	C₂²×C₃×C₇	—	2	1	no	—
147	C₂²×C₃×C₇	#41	1	2	yes	—
148	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
149	C₂×C₃×D₇	—	2	1	no	—
150	C₂×C₃×D₇	—	2	1	no	—
151	C₂×C₃×D₇	—	2	1	no	—
152	C₂×C₃×D₇	—	2	1	no	—
153	C₂×C₃×D₇	—	2	1	no	—
154	C₂×C₃×D₇	—	2	1	no	—
155	C₂×C₃×D₇	—	2	1	no	—
156	C₂×C₃×D₇	—	2	1	no	—
157	C₂×C₃×D₇	—	4	4	no	—
158	C₂×C₃×D₇	#41	1	2	yes	—
159	C₃×C₄×C₇	—	2	1	no	—
160	C₃×C₄×C₇	—	2	1	no	—
161	C₃×C₄×C₇	—	2	1	no	—
162	C₃×C₄×C₇	—	2	1	no	—
163	C₃×C₄×C₇	—	2	1	no	—
164	C₃×C₄×C₇	—	2	1	no	—
165	C₃×Dic₇	—	2	1	no	—
166	C₃×Dic₇	—	2	1	no	—
167	C₃×Dic₇	—	2	1	no	—
168	C₃×Dic₇	—	2	1	no	—
169	C₃×Dic₇	—	2	1	no	—
170	#551	—	7	1	no	Sylow
171	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
172	C₂²×D₇	—	2	2	no	—
173	C₂²×D₇	—	2	2	no	—
174	C₂²×D₇	—	4	1	no	—
175	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
176	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
177	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
178	C₇×Q₈	—	4	1	no	—
179	C₂×C₄×C₇	—	4	1	no	—
180	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
184	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
186	C₂²⋊D₇	—	2	2	no	—
187	C₂×Dic₇	—	2	2	no	—
188	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
189	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
190	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
191	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
192	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
193	D₂₈	—	2	2	no	—
194	D₂₈	—	4	1	no	—
195	C₄×D₇	—	2	2	no	—
196	C₄×D₇	—	4	1	no	—
197	C₄×D₇	—	4	1	no	—
198	C₂⁴×C₃	—	7	1	no	—
199	C₂×C₃×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
200	C₂×C₃×D₄	—	7	1	no	—
201	C₂×C₃×D₄	—	7	1	no	—
202	C₂×C₃×D₄	—	7	1	no	—
203	C₂²×C₃×C₄	—	7	1	no	—
204	C₂²×C₃×C₄	—	7	1	no	—
205	C₂²×C₃×C₄	—	7	1	no	—
206	C₂²×C₃×C₄	—	7	1	no	—
207	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
208	C₃×C₄⋊C₄	—	7	1	no	—
209	C₃×C₄⋊C₄	—	7	1	no	—
210	C₃×C₄⋊C₄	—	7	1	no	—
211	C₃×C₄⋊C₄	—	7	1	no	—
212	C₃×C₄⋊C₄	—	7	1	no	—
213	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
214	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
215	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
216	C₃×C₂²⋊C₄	—	7	1	no	—
217	C₃×C₂²⋊C₄	—	7	1	no	—
218	C₃×C₂²⋊C₄	—	7	1	no	—
219	C₃×C₂²⋊C₄	—	7	1	no	—
220	C₃×C₂²⋊C₄	—	7	1	no	—
221	C₃×C₂²⋊C₄	—	7	1	no	—
222	C₃×C₂²⋊C₄	—	7	1	no	—
223	C₃×C₂²⋊C₄	—	7	1	no	—
224	C₃×C₂²⋊C₄	—	7	1	no	—
225	C₃×C₂²⋊C₄	—	7	1	no	—
226	C₃×C₂²⋊C₄	—	7	1	no	—
227	C₃×C₂²⋊C₄	—	7	1	no	—
228	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
229	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
230	C₃×C₄²	—	7	1	no	—
231	C₃×C₄²	—	7	1	no	—
232	C₃×C₄²	—	7	1	no	—
233	C₂×C₃×C₇	—	2	2	no	—
234	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
235	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
236	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
237	C₃×D₇	—	2	2	no	—
238	C₃×D₇	—	4	1	no	—
239	C₃×D₇	—	4	1	no	—
240	#126	—	7	1	no	—
241	#126	—	7	1	no	—
242	#124	—	7	1	no	—
243	#123	—	7	1	no	—
244	#123	—	7	1	no	—
245	#123	—	7	1	no	—
246	C₂²⋊Q₈	—	7	1	no	—
247	C₂²⋊Q₈	C₃×D₇	1	1	yes	characteristic, complemented
248	#120	—	7	1	no	—
249	C₄×D₄	—	7	1	no	—
250	C₄×D₄	—	7	1	no	—
251	#117	—	7	1	no	—
252	#117	—	7	1	no	—
253	C₂×C₂²⋊C₄	—	7	1	no	—
254	C₂×C₂²⋊C₄	—	7	1	no	—
255	C₂²×C₇	—	2	1	no	—
256	C₂²×C₇	—	2	1	no	—
257	C₂²×C₇	C₃×#41	1	2	yes	—
258	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
259	C₂×D₇	—	2	1	no	—
260	C₂×D₇	—	2	1	no	—
261	C₂×D₇	—	2	1	no	—
262	C₂×D₇	—	2	1	no	—
263	C₂×D₇	—	2	1	no	—
264	C₂×D₇	—	2	1	no	—
265	C₂×D₇	—	2	1	no	—
266	C₂×D₇	—	2	1	no	—
267	C₂×D₇	—	4	4	no	—
268	C₂×D₇	C₃×#41	1	2	yes	—
269	C₄×C₇	—	2	1	no	—
270	C₄×C₇	—	2	1	no	—
271	C₄×C₇	—	2	1	no	—
272	C₄×C₇	—	2	1	no	—
273	C₄×C₇	—	2	1	no	—
274	C₄×C₇	—	2	1	no	—
275	Dic₇	—	2	1	no	—
276	Dic₇	—	2	1	no	—
277	Dic₇	—	2	1	no	—
278	Dic₇	—	2	1	no	—
279	Dic₇	—	2	1	no	—
280	C₂³×C₃	—	7	1	no	—
281	C₂³×C₃	—	7	1	no	—
282	C₂³×C₃	—	7	1	no	—
283	C₂³×C₃	—	14	2	no	—
284	C₂³×C₃	—	14	2	no	—
285	C₂³×C₃	—	28	1	no	—
286	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
287	C₃×Q₈	—	4	1	no	—
288	C₃×D₄	—	14	2	no	—
289	C₃×D₄	—	14	2	no	—
290	C₃×D₄	—	28	1	no	—
291	C₂×C₃×C₄	—	4	1	no	—
292	C₂×C₃×C₄	—	7	1	no	—
293	C₂×C₃×C₄	—	7	1	no	—
294	C₂×C₃×C₄	—	7	1	no	—
295	C₂×C₃×C₄	—	7	1	no	—
296	C₂×C₃×C₄	—	7	1	no	—
297	C₂×C₃×C₄	—	14	2	no	—
298	C₂×C₃×C₄	—	14	2	no	—
299	C₂×C₃×C₄	—	28	1	no	—
300	C₂×C₃×C₄	—	28	1	no	—
301	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
305	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
306	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
307	C₃×C₇	#551	1	1	yes	characteristic, complemented, Hall
308	C₂⁴	—	7	1	no	—
309	C₂×Q₈	C₂×C₃×D₇	1	1	yes	characteristic, complemented
310	C₂×D₄	—	7	1	no	—
311	C₂×D₄	—	7	1	no	—
312	C₂×D₄	—	7	1	no	—
313	C₂²×C₄	—	7	1	no	—
314	C₂²×C₄	—	7	1	no	—
315	C₂²×C₄	—	7	1	no	—
316	C₂²×C₄	—	7	1	no	—
317	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
318	C₄⋊C₄	—	7	1	no	—
319	C₄⋊C₄	—	7	1	no	—
320	C₄⋊C₄	—	7	1	no	—
321	C₄⋊C₄	—	7	1	no	—
322	C₄⋊C₄	—	7	1	no	—
323	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
324	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
325	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
326	C₂²⋊C₄	—	7	1	no	—
327	C₂²⋊C₄	—	7	1	no	—
328	C₂²⋊C₄	—	7	1	no	—
329	C₂²⋊C₄	—	7	1	no	—
330	C₂²⋊C₄	—	7	1	no	—
331	C₂²⋊C₄	—	7	1	no	—
332	C₂²⋊C₄	—	7	1	no	—
333	C₂²⋊C₄	—	7	1	no	—
334	C₂²⋊C₄	—	7	1	no	—
335	C₂²⋊C₄	—	7	1	no	—
336	C₂²⋊C₄	—	7	1	no	—
337	C₂²⋊C₄	—	7	1	no	—
338	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
339	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
340	C₄²	—	7	1	no	—
341	C₄²	—	7	1	no	—
342	C₄²	—	7	1	no	—
343	C₂×C₇	—	2	2	no	—
344	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
345	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
346	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
347	D₇	—	2	2	no	—
348	D₇	—	4	1	no	—
349	D₇	—	4	1	no	—
350	C₂²×C₃	—	2	1	no	—
351	C₂²×C₃	—	2	1	no	—
352	C₂²×C₃	—	7	2	no	—
353	C₂²×C₃	—	14	1	no	—
354	C₂²×C₃	—	14	1	no	—
355	C₂²×C₃	—	14	1	no	—
356	C₂²×C₃	—	14	1	no	—
357	C₂²×C₃	—	14	1	no	—
358	C₂²×C₃	—	14	1	no	—
359	C₂²×C₃	—	14	1	no	—
360	C₂²×C₃	—	14	1	no	—
361	C₂²×C₃	—	28	4	no	—
362	C₂²×C₃	#1161	1	2	yes	—
363	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	2	1	no	—
366	C₃×C₄	—	2	1	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	2	1	no	—
369	C₃×C₄	—	2	1	no	—
370	C₃×C₄	—	14	1	no	—
371	C₃×C₄	—	14	1	no	—
372	C₃×C₄	—	14	1	no	—
373	C₃×C₄	—	14	1	no	—
374	C₃×C₄	—	14	1	no	—
375	C₂³	—	7	1	no	—
376	C₂³	—	7	1	no	—
377	C₂³	—	7	1	no	—
378	C₂³	—	14	2	no	—
379	C₂³	—	14	2	no	—
380	C₂³	—	28	1	no	—
381	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
382	Q₈	—	4	1	no	—
383	D₄	—	14	2	no	—
384	D₄	—	14	2	no	—
385	D₄	—	28	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	7	1	no	—
388	C₂×C₄	—	7	1	no	—
389	C₂×C₄	—	7	1	no	—
390	C₂×C₄	—	7	1	no	—
391	C₂×C₄	—	7	1	no	—
392	C₂×C₄	—	14	2	no	—
393	C₂×C₄	—	14	2	no	—
394	C₂×C₄	—	28	1	no	—
395	C₂×C₄	—	28	1	no	—
396	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
402	C₇	C₃×#551	1	1	yes	characteristic, complemented, Sylow
403	C₂×C₃	—	2	2	no	—
404	C₂×C₃	—	14	2	no	—
405	C₂×C₃	—	28	1	no	—
406	C₂×C₃	—	28	1	no	—
407	C₂×C₃	#6548	1	1	yes	characteristic
408	C₂×C₃	C₂×#1161	1	1	yes	characteristic
409	C₂×C₃	D₇×#41	1	1	yes	characteristic
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	7	2	no	—
413	C₂²	—	14	1	no	—
414	C₂²	—	14	1	no	—
415	C₂²	—	14	1	no	—
416	C₂²	—	14	1	no	—
417	C₂²	—	14	1	no	—
418	C₂²	—	14	1	no	—
419	C₂²	—	14	1	no	—
420	C₂²	—	14	1	no	—
421	C₂²	—	28	4	no	—
422	C₂²	C₃×#1161	1	2	yes	—
423	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	14	1	no	—
431	C₄	—	14	1	no	—
432	C₄	—	14	1	no	—
433	C₄	—	14	1	no	—
434	C₄	—	14	1	no	—
435	C₃	#90328	1	1	yes	characteristic, direct product factor, Sylow
436	C₂	—	2	2	no	—
437	C₂	—	14	2	no	—
438	C₂	—	28	1	no	—
439	C₂	—	28	1	no	—
440	C₂	C₃×#6548	1	1	yes	characteristic
441	C₂	C₂×C₃×#1161	1	1	yes	characteristic
442	C₂	C₃×D₇×#41	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	C₃×#6445	C₂
hypercenter	C₃×C₂²⋊Q₈	D₇
hypocenter	C₇	C₃×#551
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×#6510	C₂	semidirect
3. C₃×#6509	C₂	semidirect
4. C₃×C₄×C₂²⋊D₇	C₂	semidirect
5. C₂×C₃×(C₂×D₇)⋊C₄	C₂	semidirect
6. C₃×#6461	C₂	semidirect
7. C₃×#6461	C₂	semidirect
8. C₃×#6457	C₂	semidirect
9. C₃×#6457	C₂	semidirect
10. C₃×#6456	C₂	semidirect
11. C₃×#6455	C₂	semidirect
12. C₃×#6449	C₂	semidirect
14. C₃×D₇×C₂²⋊C₄	C₂	semidirect
15. C₃×#6440	C₂	semidirect
16. #90328	C₃	direct (N × H)
18. C₂×C₃×C₇×Q₈	C₂²	semidirect
26. C₂×C₃×C₄×D₇	C₂²	semidirect
27. C₃×C₇×C₄⋊C₄	C₂²	semidirect
28. C₃×C₇×C₄⋊C₄	C₂²	semidirect
29. C₃×C₇×C₄⋊C₄	C₂²	semidirect
41. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
42. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
43. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
44. C₃×C₄⋊Dic₇	C₂²	semidirect
45. C₃×C₄⋊Dic₇	C₂²	semidirect
46. C₃×Dic₇⋊C₄	C₂²	semidirect
47. C₃×Dic₇⋊C₄	C₂²	semidirect
48. C₃×Dic₇⋊C₄	C₂²	semidirect
49. C₃×C₄×Dic₇	C₂²	semidirect
50. C₃×C₄×Dic₇	C₂²	semidirect
51. C₃×C₄×Dic₇	C₂²	semidirect
52. C₇×C₂²⋊Q₈	C₂×C₃	semidirect
53. #6510	C₂×C₃	semidirect
54. #6509	C₂×C₃	semidirect
55. C₄×C₂²⋊D₇	C₂×C₃	semidirect
56. C₂×(C₂×D₇)⋊C₄	C₂×C₃	semidirect
57. #6461	C₂×C₃	semidirect
58. #6461	C₂×C₃	semidirect
59. #6457	C₂×C₃	semidirect
60. #6457	C₂×C₃	semidirect
61. #6456	C₂×C₃	semidirect
62. #6455	C₂×C₃	semidirect
63. #6449	C₂×C₃	semidirect
65. D₇×C₂²⋊C₄	C₂×C₃	semidirect
66. #6440	C₂×C₃	semidirect
96. C₂×C₇×Q₈	C₂²×C₃	semidirect
104. C₂×C₄×D₇	C₂²×C₃	semidirect
105. C₇×C₄⋊C₄	C₂²×C₃	semidirect
106. C₇×C₄⋊C₄	C₂²×C₃	semidirect
107. C₇×C₄⋊C₄	C₂²×C₃	semidirect
119. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
120. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
121. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
122. C₄⋊Dic₇	C₂²×C₃	semidirect
123. C₄⋊Dic₇	C₂²×C₃	semidirect
124. Dic₇⋊C₄	C₂²×C₃	semidirect
125. Dic₇⋊C₄	C₂²×C₃	semidirect
126. Dic₇⋊C₄	C₂²×C₃	semidirect
127. C₄×Dic₇	C₂²×C₃	semidirect
128. C₄×Dic₇	C₂²×C₃	semidirect
129. C₄×Dic₇	C₂²×C₃	semidirect
137. C₃×C₂²⋊Q₈	D₇	semidirect
199. C₂×C₃×Q₈	C₂×D₇	semidirect
213. C₃×C₄⋊C₄	C₂×D₇	semidirect
214. C₃×C₄⋊C₄	C₂×D₇	semidirect
215. C₃×C₄⋊C₄	C₂×D₇	semidirect
247. C₂²⋊Q₈	C₃×D₇	semidirect
307. C₃×C₇	#551	semidirect
309. C₂×Q₈	C₂×C₃×D₇	semidirect
323. C₄⋊C₄	C₂×C₃×D₇	semidirect
324. C₄⋊C₄	C₂×C₃×D₇	semidirect
325. C₄⋊C₄	C₂×C₃×D₇	semidirect
402. C₇	C₃×#551	semidirect
435. C₃	#90328	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×#6510	2
C₃×#6509	2
C₃×C₄×C₂²⋊D₇	2
C₂×C₃×(C₂×D₇)⋊C₄	2
C₃×#6461	2
C₃×#6457	2
C₃×#6456	2
C₃×#6455	2
C₃×#6449	2
C₃×#6445	2
C₃×D₇×C₂²⋊C₄	2
C₃×#6440	2
#90328	3
C₃×#551	7

Subgroups — C3×#90328 #13060981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90328 #13060981