Subgroups — C₃×C₇×#551 #13061971

Order 1344.

496 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#126	C₂	1	2	yes	maximal, complemented
2	C₃×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×#123	C₂	1	2	yes	maximal, complemented
5	C₃×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
6	C₃×C₇×#120	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄×C₇×D₄	C₂	1	2	yes	maximal, complemented
8	C₃×C₇×#117	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×C₇×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₇×#551	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂⁴×C₃×C₇	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₃×C₇×D₄	C₂²	1	2	yes	—
14	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₇	C₂²	1	2	yes	—
16	C₂²×C₃×C₄×C₇	C₂²	1	2	yes	—
17	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
19	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
20	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
21	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
22	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
29	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₄²×C₇	C₂²	1	2	yes	complemented
32	C₇×#126	C₂×C₃	1	2	yes	complemented
33	C₇×#124	C₂×C₃	1	1	yes	characteristic, complemented
34	C₇×#123	C₂×C₃	1	1	yes	characteristic, complemented
35	C₇×#123	C₂×C₃	1	2	yes	complemented
36	C₇×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
37	C₇×#120	C₂×C₃	1	1	yes	characteristic
38	C₄×C₇×D₄	C₂×C₃	1	2	yes	complemented
39	C₇×#117	C₂×C₃	1	2	yes	complemented
40	C₂×C₇×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
41	C₃×#551	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂³×C₃×C₇	—	2	4	no	—
43	C₂³×C₃×C₇	—	4	1	no	—
44	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
45	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
46	C₂³×C₃×C₇	C₂³	1	2	yes	—
47	C₃×C₇×Q₈	—	4	1	no	—
48	C₃×C₇×D₄	—	2	4	no	—
49	C₃×C₇×D₄	—	4	1	no	—
50	C₂×C₃×C₄×C₇	—	2	4	no	—
51	C₂×C₃×C₄×C₇	—	4	2	no	—
52	C₂×C₃×C₄×C₇	—	4	1	no	—
53	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
54	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
55	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
56	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
58	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
59	C₂⁴×C₇	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
61	C₂×C₇×D₄	C₂²×C₃	1	2	yes	—
62	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₄×C₇	C₂²×C₃	1	2	yes	—
64	C₂²×C₄×C₇	C₂²×C₃	1	2	yes	—
65	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
66	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
67	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
68	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
69	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
70	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
71	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
72	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
73	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
74	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
75	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
76	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
77	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
78	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
79	C₄²×C₇	C₂²×C₃	1	2	yes	complemented
80	C₃×#126	C₂×C₇	1	2	yes	complemented
81	C₃×#124	C₂×C₇	1	1	yes	characteristic, complemented
82	C₃×#123	C₂×C₇	1	1	yes	characteristic, complemented
83	C₃×#123	C₂×C₇	1	2	yes	complemented
84	C₃×C₂²⋊Q₈	C₂×C₇	1	2	yes	complemented
85	C₃×#120	C₂×C₇	1	1	yes	characteristic
86	C₃×C₄×D₄	C₂×C₇	1	2	yes	complemented
87	C₃×#117	C₂×C₇	1	2	yes	complemented
88	C₂×C₃×C₂²⋊C₄	C₂×C₇	1	2	yes	complemented
89	C₂²×C₃×C₇	—	2	2	no	—
90	C₂²×C₃×C₇	—	2	2	no	—
91	C₂²×C₃×C₇	—	2	2	no	—
92	C₂²×C₃×C₇	—	2	2	no	—
93	C₂²×C₃×C₇	—	2	1	no	—
94	C₂²×C₃×C₇	—	2	1	no	—
95	C₂²×C₃×C₇	—	4	4	no	—
96	C₂²×C₃×C₇	#41	1	4	yes	—
97	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
98	C₃×C₄×C₇	—	2	2	no	—
99	C₃×C₄×C₇	—	2	2	no	—
100	C₃×C₄×C₇	—	2	2	no	—
101	C₃×C₄×C₇	—	2	2	no	—
102	C₃×C₄×C₇	—	2	2	no	—
103	C₃×C₄×C₇	—	2	1	no	—
104	#551	C₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
105	C₂³×C₇	—	2	4	no	—
106	C₂³×C₇	—	4	1	no	—
107	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
108	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
109	C₂³×C₇	C₂³×C₃	1	2	yes	—
110	C₇×Q₈	—	4	1	no	—
111	C₇×D₄	—	2	4	no	—
112	C₇×D₄	—	4	1	no	—
113	C₂×C₄×C₇	—	2	4	no	—
114	C₂×C₄×C₇	—	4	2	no	—
115	C₂×C₄×C₇	—	4	1	no	—
116	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
117	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
118	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
119	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
120	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
121	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
122	C₂⁴×C₃	C₂²×C₇	1	1	yes	characteristic
123	C₂×C₃×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
124	C₂×C₃×D₄	C₂²×C₇	1	2	yes	—
125	C₂×C₃×D₄	C₂²×C₇	1	1	yes	characteristic
126	C₂²×C₃×C₄	C₂²×C₇	1	2	yes	—
127	C₂²×C₃×C₄	C₂²×C₇	1	2	yes	—
128	C₂²×C₃×C₄	C₂²×C₇	1	1	yes	characteristic, complemented
129	C₃×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
130	C₃×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
131	C₃×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
132	C₃×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
133	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
134	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
135	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
136	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
137	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
138	C₃×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
139	C₃×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
140	C₃×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
141	C₃×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
142	C₃×C₄²	C₂²×C₇	1	2	yes	complemented
143	C₂×C₃×C₇	—	2	4	no	—
144	C₂×C₃×C₇	—	4	1	no	—
145	C₂×C₃×C₇	—	4	1	no	—
146	C₂×C₃×C₇	C₂×#41	1	2	yes	—
147	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
148	#126	C₂×C₃×C₇	1	2	yes	complemented
149	#124	C₂×C₃×C₇	1	1	yes	characteristic, complemented
150	#123	C₂×C₃×C₇	1	1	yes	characteristic, complemented
151	#123	C₂×C₃×C₇	1	2	yes	complemented
152	C₂²⋊Q₈	C₂×C₃×C₇	1	2	yes	complemented
153	#120	C₂×C₃×C₇	1	1	yes	characteristic
154	C₄×D₄	C₂×C₃×C₇	1	2	yes	complemented
155	#117	C₂×C₃×C₇	1	2	yes	complemented
156	C₂×C₂²⋊C₄	C₂×C₃×C₇	1	2	yes	complemented
157	C₂²×C₇	—	2	2	no	—
158	C₂²×C₇	—	2	2	no	—
159	C₂²×C₇	—	2	2	no	—
160	C₂²×C₇	—	2	2	no	—
161	C₂²×C₇	—	2	1	no	—
162	C₂²×C₇	—	2	1	no	—
163	C₂²×C₇	—	4	4	no	—
164	C₂²×C₇	C₃×#41	1	4	yes	—
165	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
166	C₄×C₇	—	2	2	no	—
167	C₄×C₇	—	2	2	no	—
168	C₄×C₇	—	2	2	no	—
169	C₄×C₇	—	2	2	no	—
170	C₄×C₇	—	2	2	no	—
171	C₄×C₇	—	2	1	no	—
172	C₂³×C₃	—	2	4	no	—
173	C₂³×C₃	—	4	1	no	—
174	C₂³×C₃	C₂³×C₇	1	1	yes	characteristic
175	C₂³×C₃	C₂³×C₇	1	1	yes	characteristic
176	C₂³×C₃	C₂³×C₇	1	2	yes	—
177	C₃×Q₈	—	4	1	no	—
178	C₃×D₄	—	2	4	no	—
179	C₃×D₄	—	4	1	no	—
180	C₂×C₃×C₄	—	2	4	no	—
181	C₂×C₃×C₄	—	4	2	no	—
182	C₂×C₃×C₄	—	4	1	no	—
183	C₂×C₃×C₄	C₂³×C₇	1	2	yes	—
184	C₂×C₃×C₄	C₂³×C₇	1	2	yes	—
185	C₂×C₃×C₄	C₂³×C₇	1	2	yes	—
186	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
187	C₂×C₃×C₄	C₂³×C₇	1	2	yes	—
188	C₂×C₃×C₄	C₂³×C₇	1	2	yes	—
189	C₃×C₇	#551	1	1	yes	characteristic, direct product factor, Hall
190	C₂⁴	C₂²×C₃×C₇	1	1	yes	characteristic
191	C₂×Q₈	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
192	C₂×D₄	C₂²×C₃×C₇	1	2	yes	—
193	C₂×D₄	C₂²×C₃×C₇	1	1	yes	characteristic
194	C₂²×C₄	C₂²×C₃×C₇	1	2	yes	—
195	C₂²×C₄	C₂²×C₃×C₇	1	2	yes	—
196	C₂²×C₄	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
197	C₄⋊C₄	C₂²×C₃×C₇	1	2	yes	complemented
198	C₄⋊C₄	C₂²×C₃×C₇	1	2	yes	complemented
199	C₄⋊C₄	C₂²×C₃×C₇	1	2	yes	complemented
200	C₄⋊C₄	C₂²×C₃×C₇	1	2	yes	complemented
201	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	—
202	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	—
203	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	—
204	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	—
205	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	—
206	C₂²⋊C₄	C₂²×C₃×C₇	1	1	yes	characteristic
207	C₂²⋊C₄	C₂²×C₃×C₇	1	2	yes	complemented
208	C₂²⋊C₄	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
209	C₄²	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
210	C₄²	C₂²×C₃×C₇	1	2	yes	complemented
211	C₂×C₇	—	2	4	no	—
212	C₂×C₇	—	4	1	no	—
213	C₂×C₇	—	4	1	no	—
214	C₂×C₇	C₂×C₃×#41	1	2	yes	—
215	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
216	C₂²×C₃	—	2	2	no	—
217	C₂²×C₃	—	2	2	no	—
218	C₂²×C₃	—	2	2	no	—
219	C₂²×C₃	—	2	2	no	—
220	C₂²×C₃	—	2	1	no	—
221	C₂²×C₃	—	2	1	no	—
222	C₂²×C₃	—	4	4	no	—
223	C₂²×C₃	C₇×#41	1	4	yes	—
224	C₂²×C₃	C₂⁴×C₇	1	1	yes	characteristic
225	C₃×C₄	—	2	2	no	—
226	C₃×C₄	—	2	2	no	—
227	C₃×C₄	—	2	2	no	—
228	C₃×C₄	—	2	2	no	—
229	C₃×C₄	—	2	2	no	—
230	C₃×C₄	—	2	1	no	—
231	C₂³	—	2	4	no	—
232	C₂³	—	4	1	no	—
233	C₂³	C₂³×C₃×C₇	1	1	yes	characteristic
234	C₂³	C₂³×C₃×C₇	1	1	yes	characteristic
235	C₂³	C₂³×C₃×C₇	1	2	yes	—
236	Q₈	—	4	1	no	—
237	D₄	—	2	4	no	—
238	D₄	—	4	1	no	—
239	C₂×C₄	—	2	4	no	—
240	C₂×C₄	—	4	2	no	—
241	C₂×C₄	—	4	1	no	—
242	C₂×C₄	C₂³×C₃×C₇	1	2	yes	—
243	C₂×C₄	C₂³×C₃×C₇	1	2	yes	—
244	C₂×C₄	C₂³×C₃×C₇	1	2	yes	—
245	C₂×C₄	C₂³×C₃×C₇	1	1	yes	characteristic
246	C₂×C₄	C₂³×C₃×C₇	1	2	yes	—
247	C₂×C₄	C₂³×C₃×C₇	1	2	yes	—
248	C₇	C₃×#551	1	1	yes	characteristic, direct product factor, Sylow
249	C₂×C₃	—	2	4	no	—
250	C₂×C₃	—	4	1	no	—
251	C₂×C₃	—	4	1	no	—
252	C₂×C₃	C₂×C₇×#41	1	2	yes	—
253	C₂×C₃	C₇×H(5,𝔽₂)	1	1	yes	characteristic
254	C₂²	—	2	2	no	—
255	C₂²	—	2	2	no	—
256	C₂²	—	2	2	no	—
257	C₂²	—	2	2	no	—
258	C₂²	—	2	1	no	—
259	C₂²	—	2	1	no	—
260	C₂²	—	4	4	no	—
261	C₂²	C₃×C₇×#41	1	4	yes	—
262	C₂²	C₂⁴×C₃×C₇	1	1	yes	characteristic
263	C₄	—	2	2	no	—
264	C₄	—	2	2	no	—
265	C₄	—	2	2	no	—
266	C₄	—	2	2	no	—
267	C₄	—	2	2	no	—
268	C₄	—	2	1	no	—
269	C₃	C₇×#551	1	1	yes	characteristic, direct product factor, Sylow
270	C₂	—	2	4	no	—
271	C₂	—	4	1	no	—
272	C₂	—	4	1	no	—
273	C₂	C₂×C₃×C₇×#41	1	2	yes	—
274	C₂	C₃×C₇×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃×C₇
prime radical	C₃×C₇×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×#126	C₂	semidirect
2. C₃×C₇×#124	C₂	semidirect
3. C₃×C₇×#123	C₂	semidirect
4. C₃×C₇×#123	C₂	semidirect
5. C₃×C₇×C₂²⋊Q₈	C₂	semidirect
7. C₃×C₄×C₇×D₄	C₂	semidirect
8. C₃×C₇×#117	C₂	semidirect
9. C₂×C₃×C₇×C₂²⋊C₄	C₂	semidirect
10. C₇×#551	C₃	direct (N × H)
12. C₂×C₃×C₇×Q₈	C₂²	semidirect
17. C₂²×C₃×C₄×C₇	C₂²	semidirect
18. C₃×C₇×C₄⋊C₄	C₂²	semidirect
19. C₃×C₇×C₄⋊C₄	C₂²	semidirect
20. C₃×C₇×C₄⋊C₄	C₂²	semidirect
21. C₃×C₇×C₄⋊C₄	C₂²	semidirect
28. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
29. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
30. C₃×C₄²×C₇	C₂²	semidirect
31. C₃×C₄²×C₇	C₂²	semidirect
32. C₇×#126	C₂×C₃	semidirect
33. C₇×#124	C₂×C₃	semidirect
34. C₇×#123	C₂×C₃	semidirect
35. C₇×#123	C₂×C₃	semidirect
36. C₇×C₂²⋊Q₈	C₂×C₃	semidirect
38. C₄×C₇×D₄	C₂×C₃	semidirect
39. C₇×#117	C₂×C₃	semidirect
40. C₂×C₇×C₂²⋊C₄	C₂×C₃	semidirect
41. C₃×#551	C₇	direct (N × H)
60. C₂×C₇×Q₈	C₂²×C₃	semidirect
65. C₂²×C₄×C₇	C₂²×C₃	semidirect
66. C₇×C₄⋊C₄	C₂²×C₃	semidirect
67. C₇×C₄⋊C₄	C₂²×C₃	semidirect
68. C₇×C₄⋊C₄	C₂²×C₃	semidirect
69. C₇×C₄⋊C₄	C₂²×C₃	semidirect
76. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
77. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
78. C₄²×C₇	C₂²×C₃	semidirect
79. C₄²×C₇	C₂²×C₃	semidirect
80. C₃×#126	C₂×C₇	semidirect
81. C₃×#124	C₂×C₇	semidirect
82. C₃×#123	C₂×C₇	semidirect
83. C₃×#123	C₂×C₇	semidirect
84. C₃×C₂²⋊Q₈	C₂×C₇	semidirect
86. C₃×C₄×D₄	C₂×C₇	semidirect
87. C₃×#117	C₂×C₇	semidirect
88. C₂×C₃×C₂²⋊C₄	C₂×C₇	semidirect
104. #551	C₃×C₇	direct (N × H)
123. C₂×C₃×Q₈	C₂²×C₇	semidirect
128. C₂²×C₃×C₄	C₂²×C₇	semidirect
129. C₃×C₄⋊C₄	C₂²×C₇	semidirect
130. C₃×C₄⋊C₄	C₂²×C₇	semidirect
131. C₃×C₄⋊C₄	C₂²×C₇	semidirect
132. C₃×C₄⋊C₄	C₂²×C₇	semidirect
139. C₃×C₂²⋊C₄	C₂²×C₇	semidirect
140. C₃×C₂²⋊C₄	C₂²×C₇	semidirect
141. C₃×C₄²	C₂²×C₇	semidirect
142. C₃×C₄²	C₂²×C₇	semidirect
148. #126	C₂×C₃×C₇	semidirect
149. #124	C₂×C₃×C₇	semidirect
150. #123	C₂×C₃×C₇	semidirect
151. #123	C₂×C₃×C₇	semidirect
152. C₂²⋊Q₈	C₂×C₃×C₇	semidirect
154. C₄×D₄	C₂×C₃×C₇	semidirect
155. #117	C₂×C₃×C₇	semidirect
156. C₂×C₂²⋊C₄	C₂×C₃×C₇	semidirect
189. C₃×C₇	#551	direct (N × H)
191. C₂×Q₈	C₂²×C₃×C₇	semidirect
196. C₂²×C₄	C₂²×C₃×C₇	semidirect
197. C₄⋊C₄	C₂²×C₃×C₇	semidirect
198. C₄⋊C₄	C₂²×C₃×C₇	semidirect
199. C₄⋊C₄	C₂²×C₃×C₇	semidirect
200. C₄⋊C₄	C₂²×C₃×C₇	semidirect
207. C₂²⋊C₄	C₂²×C₃×C₇	semidirect
208. C₂²⋊C₄	C₂²×C₃×C₇	semidirect
209. C₄²	C₂²×C₃×C₇	semidirect
210. C₄²	C₂²×C₃×C₇	semidirect
248. C₇	C₃×#551	direct (N × H)
269. C₃	C₇×#551	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×#126	2
C₃×C₇×#124	2
C₃×C₇×#123	2
C₃×C₇×C₂²⋊Q₈	2
C₃×C₇×#120	2
C₃×C₄×C₇×D₄	2
C₃×C₇×#117	2
C₂×C₃×C₇×C₂²⋊C₄	2
C₇×#551	3
C₃×#551	7

Subgroups — C3×C7×#551 #13061971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×#551 #13061971