Subgroups — C₃×#90327 #13060979

Order 1344.

456 conjugacy classes of subgroups.

The subgroup lattice has 408 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×C₄×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×Dic₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6459	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#6459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#6452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×(C₂²⋊D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₃×(C₂²⋊D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₃×#6441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#6441	C₂	1	1	yes	maximal, characteristic, complemented
16	#90327	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	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
21	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
25	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic
27	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
37	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
38	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×Dic₇⋊C₄	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	C₄×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic
56	C₂×Dic₇⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
57	#6459	C₂×C₃	1	1	yes	characteristic, complemented
58	#6459	C₂×C₃	1	1	yes	characteristic, complemented
59	D₇×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
60	#6452	C₂×C₃	1	1	yes	characteristic, complemented
61	#6452	C₂×C₃	1	1	yes	characteristic, complemented
62	#6450	C₂×C₃	1	1	yes	characteristic, complemented
63	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	1	yes	characteristic
64	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	1	yes	characteristic
65	#6441	C₂×C₃	1	1	yes	characteristic, complemented
66	#6441	C₂×C₃	1	1	yes	characteristic, complemented
67	C₃×#554	—	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	Q₈	1	4	yes	complemented
79	C₂×C₃×Dic₇	—	2	2	no	—
80	C₂×C₃×Dic₇	—	4	1	no	—
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	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
87	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
88	C₃×C₄×D₇	—	2	2	no	—
89	C₃×C₄×D₇	—	4	1	no	—
90	C₃×C₄×D₇	—	4	1	no	—
91	C₃×Dic₁₄	—	2	2	no	—
92	C₃×Dic₁₄	—	4	1	no	—
93	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
96	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
97	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
101	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
102	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
103	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
104	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
108	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
109	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
111	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
113	C₄⋊Dic₇	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	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
126	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
127	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
128	C₃×C₄⋊Q₈	—	7	1	no	—
129	C₃×#125	—	7	1	no	—
130	C₃×#125	—	7	1	no	—
131	C₃×C₂²⋊Q₈	—	7	1	no	—
132	C₃×C₂²⋊Q₈	—	7	1	no	—
133	C₃×C₂²⋊Q₈	—	7	1	no	—
134	C₃×C₂²⋊Q₈	—	7	1	no	—
135	C₃×C₂²⋊Q₈	—	7	1	no	—
136	C₃×C₂²⋊Q₈	D₇	1	1	yes	characteristic, complemented
137	C₃×C₄×Q₈	—	7	1	no	—
138	C₃×C₄×D₄	—	7	1	no	—
139	C₃×C₄×D₄	—	7	1	no	—
140	C₃×C₄×D₄	—	7	1	no	—
141	C₂×C₃×C₄⋊C₄	—	7	1	no	—
142	C₂×C₃×C₄⋊C₄	—	7	1	no	—
143	C₂²×C₃×C₇	—	2	1	no	—
144	C₂²×C₃×C₇	—	2	1	no	—
145	C₂²×C₃×C₇	C₂×Q₈	1	2	yes	—
146	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
147	C₂×C₃×D₇	—	2	1	no	—
148	C₂×C₃×D₇	—	2	1	no	—
149	C₂×C₃×D₇	C₂×Q₈	1	2	yes	—
150	C₃×C₄×C₇	—	2	1	no	—
151	C₃×C₄×C₇	—	2	1	no	—
152	C₃×C₄×C₇	—	2	1	no	—
153	C₃×C₄×C₇	—	2	1	no	—
154	C₃×C₄×C₇	—	2	1	no	—
155	C₃×C₄×C₇	—	2	1	no	—
156	C₃×Dic₇	—	2	1	no	—
157	C₃×Dic₇	—	2	1	no	—
158	C₃×Dic₇	—	2	1	no	—
159	C₃×Dic₇	—	2	1	no	—
160	C₃×Dic₇	—	2	1	no	—
161	C₃×Dic₇	C₂×Q₈	1	2	yes	—
162	C₃×Dic₇	#41	1	2	yes	—
163	#554	—	7	1	no	Sylow
164	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
165	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
166	C₇×Q₈	—	4	1	no	—
167	C₂×C₄×C₇	—	4	1	no	—
168	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
169	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
171	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
172	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
173	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
174	C₂²⋊D₇	C₃×Q₈	1	4	yes	complemented
175	C₂×Dic₇	—	2	2	no	—
176	C₂×Dic₇	—	4	1	no	—
177	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
178	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
179	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
180	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
181	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
182	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
183	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
184	C₄×D₇	—	2	2	no	—
185	C₄×D₇	—	4	1	no	—
186	C₄×D₇	—	4	1	no	—
187	Dic₁₄	—	2	2	no	—
188	Dic₁₄	—	4	1	no	—
189	C₂×C₃×Q₈	—	7	1	no	—
190	C₂×C₃×Q₈	—	7	1	no	—
191	C₂×C₃×Q₈	C₂×D₇	1	1	yes	characteristic
192	C₂×C₃×D₄	—	7	1	no	—
193	C₂²×C₃×C₄	—	7	1	no	—
194	C₂²×C₃×C₄	—	7	1	no	—
195	C₂²×C₃×C₄	—	7	1	no	—
196	C₂²×C₃×C₄	—	7	1	no	—
197	C₂²×C₃×C₄	—	7	1	no	—
198	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
199	C₃×C₄⋊C₄	—	7	1	no	—
200	C₃×C₄⋊C₄	—	7	1	no	—
201	C₃×C₄⋊C₄	—	7	1	no	—
202	C₃×C₄⋊C₄	—	7	1	no	—
203	C₃×C₄⋊C₄	—	7	1	no	—
204	C₃×C₄⋊C₄	—	7	1	no	—
205	C₃×C₄⋊C₄	—	7	1	no	—
206	C₃×C₄⋊C₄	—	7	1	no	—
207	C₃×C₄⋊C₄	—	7	1	no	—
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	C₂×D₇	1	1	yes	characteristic
213	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
214	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
215	C₃×C₂²⋊C₄	—	7	1	no	—
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	C₂×D₇	1	1	yes	characteristic
220	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
221	C₃×C₄²	—	7	1	no	—
222	C₃×C₄²	—	7	1	no	—
223	C₃×C₄²	—	7	1	no	—
224	C₂×C₃×C₇	—	2	2	no	—
225	C₂×C₃×C₇	C₂²×Q₈	1	1	yes	characteristic
226	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
227	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
228	C₃×D₇	—	2	2	no	—
229	C₄⋊Q₈	—	7	1	no	—
230	#125	—	7	1	no	—
231	#125	—	7	1	no	—
232	C₂²⋊Q₈	—	7	1	no	—
233	C₂²⋊Q₈	—	7	1	no	—
234	C₂²⋊Q₈	—	7	1	no	—
235	C₂²⋊Q₈	—	7	1	no	—
236	C₂²⋊Q₈	—	7	1	no	—
237	C₂²⋊Q₈	C₃×D₇	1	1	yes	characteristic, complemented
238	C₄×Q₈	—	7	1	no	—
239	C₄×D₄	—	7	1	no	—
240	C₄×D₄	—	7	1	no	—
241	C₄×D₄	—	7	1	no	—
242	C₂×C₄⋊C₄	—	7	1	no	—
243	C₂×C₄⋊C₄	—	7	1	no	—
244	C₂²×C₇	—	2	1	no	—
245	C₂²×C₇	—	2	1	no	—
246	C₂²×C₇	C₂×C₃×Q₈	1	2	yes	—
247	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
248	C₂×D₇	—	2	1	no	—
249	C₂×D₇	—	2	1	no	—
250	C₂×D₇	C₂×C₃×Q₈	1	2	yes	—
251	C₄×C₇	—	2	1	no	—
252	C₄×C₇	—	2	1	no	—
253	C₄×C₇	—	2	1	no	—
254	C₄×C₇	—	2	1	no	—
255	C₄×C₇	—	2	1	no	—
256	C₄×C₇	—	2	1	no	—
257	Dic₇	—	2	1	no	—
258	Dic₇	—	2	1	no	—
259	Dic₇	—	2	1	no	—
260	Dic₇	—	2	1	no	—
261	Dic₇	—	2	1	no	—
262	Dic₇	C₂×C₃×Q₈	1	2	yes	—
263	Dic₇	C₃×#41	1	2	yes	—
264	C₂³×C₃	—	7	1	no	—
265	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
266	C₃×Q₈	—	4	1	no	—
267	C₃×Q₈	—	14	2	no	—
268	C₃×Q₈	—	28	1	no	—
269	C₃×D₄	—	7	4	no	—
270	C₂×C₃×C₄	—	4	1	no	—
271	C₂×C₃×C₄	—	7	1	no	—
272	C₂×C₃×C₄	—	7	1	no	—
273	C₂×C₃×C₄	—	7	1	no	—
274	C₂×C₃×C₄	—	7	1	no	—
275	C₂×C₃×C₄	—	7	1	no	—
276	C₂×C₃×C₄	—	7	1	no	—
277	C₂×C₃×C₄	—	7	1	no	—
278	C₂×C₃×C₄	—	14	2	no	—
279	C₂×C₃×C₄	—	14	2	no	—
280	C₂×C₃×C₄	—	28	1	no	—
281	C₂×C₃×C₄	—	28	1	no	—
282	C₂×C₃×C₄	—	28	1	no	—
283	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
289	C₃×C₇	#554	1	1	yes	characteristic, complemented, Hall
290	C₂×Q₈	—	7	1	no	—
291	C₂×Q₈	—	7	1	no	—
292	C₂×Q₈	C₂×C₃×D₇	1	1	yes	characteristic
293	C₂×D₄	—	7	1	no	—
294	C₂²×C₄	—	7	1	no	—
295	C₂²×C₄	—	7	1	no	—
296	C₂²×C₄	—	7	1	no	—
297	C₂²×C₄	—	7	1	no	—
298	C₂²×C₄	—	7	1	no	—
299	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
300	C₄⋊C₄	—	7	1	no	—
301	C₄⋊C₄	—	7	1	no	—
302	C₄⋊C₄	—	7	1	no	—
303	C₄⋊C₄	—	7	1	no	—
304	C₄⋊C₄	—	7	1	no	—
305	C₄⋊C₄	—	7	1	no	—
306	C₄⋊C₄	—	7	1	no	—
307	C₄⋊C₄	—	7	1	no	—
308	C₄⋊C₄	—	7	1	no	—
309	C₄⋊C₄	—	7	1	no	—
310	C₄⋊C₄	—	7	1	no	—
311	C₄⋊C₄	—	7	1	no	—
312	C₄⋊C₄	—	7	1	no	—
313	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
314	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
315	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
316	C₂²⋊C₄	—	7	1	no	—
317	C₂²⋊C₄	—	7	1	no	—
318	C₂²⋊C₄	—	7	1	no	—
319	C₂²⋊C₄	—	7	1	no	—
320	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
321	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
322	C₄²	—	7	1	no	—
323	C₄²	—	7	1	no	—
324	C₄²	—	7	1	no	—
325	C₂×C₇	—	2	2	no	—
326	C₂×C₇	C₂²×C₃×Q₈	1	1	yes	characteristic
327	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
328	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
329	D₇	—	2	2	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	2	1	no	—
332	C₂²×C₃	—	7	2	no	—
333	C₂²×C₃	—	14	1	no	—
334	C₂²×C₃	—	14	1	no	—
335	C₂²×C₃	Q₈×D₇	1	2	yes	—
336	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	—	2	1	no	—
343	C₃×C₄	—	7	2	no	—
344	C₃×C₄	—	7	2	no	—
345	C₃×C₄	—	14	1	no	—
346	C₃×C₄	—	14	1	no	—
347	C₃×C₄	—	14	1	no	—
348	C₃×C₄	—	14	1	no	—
349	C₃×C₄	—	14	1	no	—
350	C₂³	—	7	1	no	—
351	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
352	Q₈	—	4	1	no	—
353	Q₈	—	14	2	no	—
354	Q₈	—	28	1	no	—
355	D₄	—	7	4	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	7	1	no	—
358	C₂×C₄	—	7	1	no	—
359	C₂×C₄	—	7	1	no	—
360	C₂×C₄	—	7	1	no	—
361	C₂×C₄	—	7	1	no	—
362	C₂×C₄	—	7	1	no	—
363	C₂×C₄	—	7	1	no	—
364	C₂×C₄	—	14	2	no	—
365	C₂×C₄	—	14	2	no	—
366	C₂×C₄	—	28	1	no	—
367	C₂×C₄	—	28	1	no	—
368	C₂×C₄	—	28	1	no	—
369	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
375	C₇	C₃×#554	1	1	yes	characteristic, complemented, Sylow
376	C₂×C₃	—	2	2	no	—
377	C₂×C₃	—	14	2	no	—
378	C₂×C₃	#6548	1	1	yes	characteristic
379	C₂×C₃	C₂×Q₈×D₇	1	1	yes	characteristic
380	C₂×C₃	D₇×#41	1	1	yes	characteristic
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	7	2	no	—
384	C₂²	—	14	1	no	—
385	C₂²	—	14	1	no	—
386	C₂²	C₃×Q₈×D₇	1	2	yes	—
387	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	7	2	no	—
395	C₄	—	7	2	no	—
396	C₄	—	14	1	no	—
397	C₄	—	14	1	no	—
398	C₄	—	14	1	no	—
399	C₄	—	14	1	no	—
400	C₄	—	14	1	no	—
401	C₃	#90327	1	1	yes	characteristic, direct product factor, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	14	2	no	—
404	C₂	C₃×#6548	1	1	yes	characteristic
405	C₂	C₂×C₃×Q₈×D₇	1	1	yes	characteristic
406	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	C₂×C₃×C₂²⋊D₇	C₂²
hypercenter	C₃×C₂²⋊Q₈	D₇
hypocenter	C₇	C₃×#554
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. C₂×C₃×Dic₇⋊C₄	C₂	semidirect
6. C₃×#6459	C₂	semidirect
7. C₃×#6459	C₂	semidirect
8. C₃×D₇×C₄⋊C₄	C₂	semidirect
9. C₃×#6452	C₂	semidirect
10. C₃×#6452	C₂	semidirect
11. C₃×#6450	C₂	semidirect
14. C₃×#6441	C₂	semidirect
15. C₃×#6441	C₂	semidirect
16. #90327	C₃	direct (N × H)
52. C₇×C₂²⋊Q₈	C₂×C₃	semidirect
53. #6509	C₂×C₃	semidirect
54. #6507	C₂×C₃	semidirect
56. C₂×Dic₇⋊C₄	C₂×C₃	semidirect
57. #6459	C₂×C₃	semidirect
58. #6459	C₂×C₃	semidirect
59. D₇×C₄⋊C₄	C₂×C₃	semidirect
60. #6452	C₂×C₃	semidirect
61. #6452	C₂×C₃	semidirect
62. #6450	C₂×C₃	semidirect
65. #6441	C₂×C₃	semidirect
66. #6441	C₂×C₃	semidirect
78. C₃×C₂²⋊D₇	Q₈	semidirect
136. C₃×C₂²⋊Q₈	D₇	semidirect
174. C₂²⋊D₇	C₃×Q₈	semidirect
237. C₂²⋊Q₈	C₃×D₇	semidirect
289. C₃×C₇	#554	semidirect
375. C₇	C₃×#554	semidirect
401. C₃	#90327	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×C₄×C₂²⋊D₇	2
C₂×C₃×Dic₇⋊C₄	2
C₃×#6459	2
C₃×D₇×C₄⋊C₄	2
C₃×#6452	2
C₃×#6450	2
C₃×(C₂²⋊D₇)⋊C₄	2
C₃×#6441	2
#90327	3
C₃×#554	7

Subgroups — C3×#90327 #13060979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90327 #13060979