Subgroups — C₃×#90520 #13061170

Order 1344.

668 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#6510	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6509	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6502	C₂	1	2	yes	maximal, complemented
6	C₃×#6500	C₂	1	2	yes	maximal, complemented
7	C₃×D₄×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#6493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#6492	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×(C₂×D₇)⋊C₄	C₂	1	2	yes	maximal, complemented
12	#90520	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₇	C₂²	1	2	yes	—
14	C₃×C₇×#41	—	2	4	no	—
15	C₂×C₃×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₇×D₄	C₂²	1	2	yes	complemented
18	C₂²×C₃×C₄×C₇	C₂²	1	2	yes	complemented
19	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	—
22	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
23	C₂²×C₃×Dic₇	C₂²	1	2	yes	complemented
24	C₃×D₄×D₇	—	2	4	no	—
25	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
27	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₂²⋊Dic₇	C₂²	1	2	yes	complemented
29	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
31	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
32	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
33	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
34	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
35	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₃×Dic₇⋊C₄	C₂²	1	2	yes	complemented
37	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₇×#41	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×D₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
40	#6510	C₂×C₃	1	1	yes	characteristic, complemented
41	#6509	C₂×C₃	1	1	yes	characteristic, complemented
42	#6502	C₂×C₃	1	2	yes	complemented
43	#6500	C₂×C₃	1	2	yes	complemented
44	D₄×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
45	#6493	C₂×C₃	1	1	yes	characteristic, complemented
46	#6492	C₂×C₃	1	2	yes	complemented
47	C₄×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×(C₂×D₇)⋊C₄	C₂×C₃	1	2	yes	complemented
49	C₃×#546	—	7	1	no	maximal, Hall
50	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
51	C₂³×C₃×C₇	C₂³	1	2	yes	—
52	C₂²×C₃×D₇	—	2	4	no	—
53	C₂²×C₃×D₇	—	2	4	no	—
54	C₂²×C₃×D₇	—	4	2	no	—
55	C₂²×C₃×D₇	C₂³	1	2	yes	—
56	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
57	C₃×C₇×Q₈	—	2	2	no	—
58	C₃×C₇×D₄	—	2	4	no	—
59	C₃×C₇×D₄	D₄	1	4	yes	complemented
60	C₂×C₃×C₄×C₇	—	2	4	no	—
61	C₂×C₃×C₄×C₇	—	2	2	no	—
62	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
64	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
65	C₃×C₂²⋊D₇	—	2	4	no	—
66	C₃×C₂²⋊D₇	—	2	2	no	—
67	C₃×C₂²⋊D₇	—	4	2	no	—
68	C₂×C₃×Dic₇	—	4	2	no	—
69	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
70	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
71	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
72	C₂×C₃×Dic₇	C₂³	1	2	yes	—
73	C₃×D₂₈	—	2	2	no	—
74	C₃×C₄×D₇	—	2	2	no	—
75	C₂³×D₇	C₂²×C₃	1	2	yes	—
76	C₇×#41	—	2	4	no	—
77	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
78	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₇×D₄	C₂²×C₃	1	2	yes	complemented
80	C₂²×C₄×C₇	C₂²×C₃	1	2	yes	complemented
81	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
82	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
84	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
85	C₂²×Dic₇	C₂²×C₃	1	2	yes	complemented
86	D₄×D₇	—	2	4	no	—
87	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
89	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
90	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
91	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
93	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
94	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
95	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
96	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
97	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
98	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
99	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₂×C₃×#41	D₇	1	1	yes	characteristic, complemented
101	C₂²×C₃×D₄	—	7	1	no	—
102	C₃×#124	—	7	1	no	—
103	C₃×#123	—	7	2	no	—
104	C₃×C₂²⋊Q₈	—	7	1	no	—
105	C₃×#121	—	7	2	no	—
106	C₃×#121	—	7	1	no	—
107	C₃×#120	—	7	2	no	—
108	C₃×C₄×D₄	—	7	1	no	—
109	C₃×C₄×D₄	—	7	1	no	—
110	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
111	C₂²×C₃×C₇	—	2	2	no	—
112	C₂²×C₃×C₇	—	2	2	no	—
113	C₂²×C₃×C₇	—	2	1	no	—
114	C₂²×C₃×C₇	—	2	1	no	—
115	C₂²×C₃×C₇	—	2	1	no	—
116	C₂²×C₃×C₇	C₂×D₄	1	4	yes	—
117	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
118	C₂×C₃×D₇	—	2	1	no	—
119	C₂×C₃×D₇	—	2	1	no	—
120	C₂×C₃×D₇	—	2	2	no	—
121	C₂×C₃×D₇	—	2	2	no	—
122	C₂×C₃×D₇	—	2	2	no	—
123	C₂×C₃×D₇	—	4	8	no	—
124	C₂×C₃×D₇	#41	1	2	yes	complemented
125	C₃×C₄×C₇	—	2	1	no	—
126	C₃×C₄×C₇	—	2	2	no	—
127	C₃×C₄×C₇	C₂×D₄	1	2	yes	—
128	C₃×Dic₇	—	2	1	no	—
129	C₃×Dic₇	—	2	1	no	—
130	C₃×Dic₇	—	2	1	no	—
131	C₃×Dic₇	—	2	2	no	—
132	#546	—	7	1	no	Sylow
133	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
134	C₂³×C₇	C₂³×C₃	1	2	yes	—
135	C₂²×D₇	—	2	4	no	—
136	C₂²×D₇	—	2	4	no	—
137	C₂²×D₇	—	4	2	no	—
138	C₂²×D₇	C₂³×C₃	1	2	yes	—
139	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
140	C₇×Q₈	—	2	2	no	—
141	C₇×D₄	—	2	4	no	—
142	C₇×D₄	C₃×D₄	1	4	yes	complemented
143	C₂×C₄×C₇	—	2	4	no	—
144	C₂×C₄×C₇	—	2	2	no	—
145	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
146	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
147	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
148	C₂²⋊D₇	—	2	4	no	—
149	C₂²⋊D₇	—	2	2	no	—
150	C₂²⋊D₇	—	4	2	no	—
151	C₂×Dic₇	—	4	2	no	—
152	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
153	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
154	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
155	C₂×Dic₇	C₂³×C₃	1	2	yes	—
156	D₂₈	—	2	2	no	—
157	C₄×D₇	—	2	2	no	—
158	C₂⁴×C₃	—	7	2	no	—
159	C₃×#41	—	2	4	no	—
160	C₂×C₃×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
161	C₂×C₃×D₄	—	7	1	no	—
162	C₂×C₃×D₄	—	7	2	no	—
163	C₂×C₃×D₄	—	7	2	no	—
164	C₂×C₃×D₄	—	7	1	no	—
165	C₂×C₃×D₄	—	14	4	no	—
166	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
167	C₂×C₃×D₄	C₂×D₇	1	2	yes	complemented
168	C₂²×C₃×C₄	—	7	2	no	—
169	C₂²×C₃×C₄	—	7	1	no	—
170	C₂²×C₃×C₄	C₂×D₇	1	2	yes	complemented
171	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic, complemented
172	C₃×C₄⋊C₄	—	7	1	no	—
173	C₃×C₄⋊C₄	—	7	2	no	—
174	C₃×C₄⋊C₄	—	7	1	no	—
175	C₃×C₂²⋊C₄	—	7	2	no	—
176	C₃×C₂²⋊C₄	—	7	1	no	—
177	C₃×C₂²⋊C₄	—	7	1	no	—
178	C₃×C₂²⋊C₄	—	7	2	no	—
179	C₃×C₂²⋊C₄	—	7	2	no	—
180	C₃×C₂²⋊C₄	—	7	2	no	—
181	C₃×C₂²⋊C₄	—	7	2	no	—
182	C₃×C₄²	—	7	1	no	—
183	C₂×C₃×C₇	—	2	4	no	—
184	C₂×C₃×C₇	—	4	1	no	—
185	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
188	C₃×D₇	—	2	2	no	—
189	C₃×D₇	—	4	2	no	—
190	C₂×#41	C₃×D₇	1	1	yes	characteristic, complemented
191	C₂²×D₄	—	7	1	no	—
192	#124	—	7	1	no	—
193	#123	—	7	2	no	—
194	C₂²⋊Q₈	—	7	1	no	—
195	#121	—	7	2	no	—
196	#121	—	7	1	no	—
197	#120	—	7	2	no	—
198	C₄×D₄	—	7	1	no	—
199	C₄×D₄	—	7	1	no	—
200	C₂×C₂²⋊C₄	—	7	2	no	—
201	C₂²×C₇	—	2	2	no	—
202	C₂²×C₇	—	2	2	no	—
203	C₂²×C₇	—	2	1	no	—
204	C₂²×C₇	—	2	1	no	—
205	C₂²×C₇	—	2	1	no	—
206	C₂²×C₇	C₂×C₃×D₄	1	4	yes	—
207	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
208	C₂×D₇	—	2	1	no	—
209	C₂×D₇	—	2	1	no	—
210	C₂×D₇	—	2	2	no	—
211	C₂×D₇	—	2	2	no	—
212	C₂×D₇	—	2	2	no	—
213	C₂×D₇	—	4	8	no	—
214	C₂×D₇	C₃×#41	1	2	yes	complemented
215	C₄×C₇	—	2	1	no	—
216	C₄×C₇	—	2	2	no	—
217	C₄×C₇	C₂×C₃×D₄	1	2	yes	—
218	Dic₇	—	2	1	no	—
219	Dic₇	—	2	1	no	—
220	Dic₇	—	2	1	no	—
221	Dic₇	—	2	2	no	—
222	C₂³×C₃	—	7	1	no	—
223	C₂³×C₃	—	7	2	no	—
224	C₂³×C₃	—	14	4	no	—
225	C₂³×C₃	—	14	4	no	—
226	C₂³×C₃	—	28	2	no	—
227	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
228	C₂³×C₃	C₂²×D₇	1	2	yes	—
229	C₃×Q₈	—	2	2	no	—
230	C₃×D₄	—	2	4	no	—
231	C₃×D₄	—	14	2	no	—
232	C₃×D₄	—	14	4	no	—
233	C₃×D₄	—	14	2	no	—
234	C₃×D₄	—	28	2	no	—
235	C₃×D₄	C₂²⋊D₇	1	4	yes	complemented
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	7	1	no	—
239	C₂×C₃×C₄	—	7	1	no	—
240	C₂×C₃×C₄	—	7	2	no	—
241	C₂×C₃×C₄	—	7	1	no	—
242	C₂×C₃×C₄	—	14	2	no	—
243	C₂×C₃×C₄	—	28	2	no	—
244	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
246	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
247	C₃×C₇	#546	1	1	yes	characteristic, complemented, Hall
248	C₂⁴	—	7	2	no	—
249	#41	—	2	4	no	—
250	C₂×Q₈	C₂×C₃×D₇	1	1	yes	characteristic, complemented
251	C₂×D₄	—	7	1	no	—
252	C₂×D₄	—	7	2	no	—
253	C₂×D₄	—	7	2	no	—
254	C₂×D₄	—	7	1	no	—
255	C₂×D₄	—	14	4	no	—
256	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
257	C₂×D₄	C₂×C₃×D₇	1	2	yes	complemented
258	C₂²×C₄	—	7	2	no	—
259	C₂²×C₄	—	7	1	no	—
260	C₂²×C₄	C₂×C₃×D₇	1	2	yes	complemented
261	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
262	C₄⋊C₄	—	7	1	no	—
263	C₄⋊C₄	—	7	2	no	—
264	C₄⋊C₄	—	7	1	no	—
265	C₂²⋊C₄	—	7	2	no	—
266	C₂²⋊C₄	—	7	1	no	—
267	C₂²⋊C₄	—	7	1	no	—
268	C₂²⋊C₄	—	7	2	no	—
269	C₂²⋊C₄	—	7	2	no	—
270	C₂²⋊C₄	—	7	2	no	—
271	C₂²⋊C₄	—	7	2	no	—
272	C₄²	—	7	1	no	—
273	C₂×C₇	—	2	4	no	—
274	C₂×C₇	—	4	1	no	—
275	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
276	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
277	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
278	D₇	—	2	2	no	—
279	D₇	—	4	2	no	—
280	C₂²×C₃	—	2	2	no	—
281	C₂²×C₃	—	2	2	no	—
282	C₂²×C₃	—	2	1	no	—
283	C₂²×C₃	—	2	1	no	—
284	C₂²×C₃	—	2	1	no	—
285	C₂²×C₃	—	7	2	no	—
286	C₂²×C₃	—	14	1	no	—
287	C₂²×C₃	—	14	1	no	—
288	C₂²×C₃	—	14	2	no	—
289	C₂²×C₃	—	14	2	no	—
290	C₂²×C₃	—	14	2	no	—
291	C₂²×C₃	—	28	8	no	—
292	C₂²×C₃	C₂×C₂²⋊D₇	1	4	yes	—
293	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
294	C₃×C₄	—	2	1	no	—
295	C₃×C₄	—	2	2	no	—
296	C₃×C₄	—	14	1	no	—
297	C₃×C₄	—	14	1	no	—
298	C₃×C₄	—	14	2	no	—
299	C₃×C₄	—	14	1	no	—
300	C₃×C₄	C₂×C₂²⋊D₇	1	2	yes	—
301	C₂³	—	7	1	no	—
302	C₂³	—	7	2	no	—
303	C₂³	—	14	4	no	—
304	C₂³	—	14	4	no	—
305	C₂³	—	28	2	no	—
306	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
307	C₂³	C₂²×C₃×D₇	1	2	yes	—
308	Q₈	—	2	2	no	—
309	D₄	—	2	4	no	—
310	D₄	—	14	2	no	—
311	D₄	—	14	4	no	—
312	D₄	—	14	2	no	—
313	D₄	—	28	2	no	—
314	D₄	C₃×C₂²⋊D₇	1	4	yes	complemented
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	7	1	no	—
318	C₂×C₄	—	7	1	no	—
319	C₂×C₄	—	7	2	no	—
320	C₂×C₄	—	7	1	no	—
321	C₂×C₄	—	14	2	no	—
322	C₂×C₄	—	28	2	no	—
323	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
324	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
325	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
326	C₇	C₃×#546	1	1	yes	characteristic, complemented, Sylow
327	C₂×C₃	—	2	4	no	—
328	C₂×C₃	—	4	1	no	—
329	C₂×C₃	—	14	2	no	—
330	C₂×C₃	—	28	2	no	—
331	C₂×C₃	D₇×#41	1	1	yes	characteristic
332	C₂×C₃	#6553	1	1	yes	characteristic
333	C₂×C₃	C₂²×C₂²⋊D₇	1	1	yes	characteristic
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	7	2	no	—
340	C₂²	—	14	1	no	—
341	C₂²	—	14	1	no	—
342	C₂²	—	14	2	no	—
343	C₂²	—	14	2	no	—
344	C₂²	—	14	2	no	—
345	C₂²	—	28	8	no	—
346	C₂²	C₂×C₃×C₂²⋊D₇	1	4	yes	—
347	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	2	no	—
350	C₄	—	14	1	no	—
351	C₄	—	14	1	no	—
352	C₄	—	14	2	no	—
353	C₄	—	14	1	no	—
354	C₄	C₂×C₃×C₂²⋊D₇	1	2	yes	—
355	C₃	#90520	1	1	yes	characteristic, direct product factor, Sylow
356	C₂	—	2	4	no	—
357	C₂	—	4	1	no	—
358	C₂	—	14	2	no	—
359	C₂	—	28	2	no	—
360	C₂	C₃×D₇×#41	1	1	yes	characteristic
361	C₂	C₃×#6553	1	1	yes	characteristic
362	C₂	C₂²×C₃×C₂²⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₇
commutator, cosocle	C₂²×C₇	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₇
Fitting	C₂×C₃×C₇×#41	C₂
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₂×C₃×#41	D₇
hypocenter	C₇	C₃×#546
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₇×#41	C₂	semidirect
2. C₂×C₃×D₄×D₇	C₂	semidirect
3. C₃×#6510	C₂	semidirect
4. C₃×#6509	C₂	semidirect
5. C₃×#6502	C₂	semidirect
6. C₃×#6500	C₂	semidirect
7. C₃×D₄×Dic₇	C₂	semidirect
8. C₃×#6493	C₂	semidirect
9. C₃×#6492	C₂	semidirect
10. C₃×C₄×C₂²⋊D₇	C₂	semidirect
11. C₂×C₃×(C₂×D₇)⋊C₄	C₂	semidirect
12. #90520	C₃	direct (N × H)
15. C₂×C₃×C₇×Q₈	C₂²	semidirect
17. C₂×C₃×C₇×D₄	C₂²	semidirect
18. C₂²×C₃×C₄×C₇	C₂²	semidirect
19. C₂²×C₃×C₄×C₇	C₂²	semidirect
22. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
23. C₂²×C₃×Dic₇	C₂²	semidirect
27. C₃×C₂²⋊Dic₇	C₂²	semidirect
28. C₃×C₂²⋊Dic₇	C₂²	semidirect
31. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
32. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
33. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
34. C₃×C₄⋊Dic₇	C₂²	semidirect
35. C₃×Dic₇⋊C₄	C₂²	semidirect
36. C₃×Dic₇⋊C₄	C₂²	semidirect
37. C₃×C₄×Dic₇	C₂²	semidirect
38. C₂×C₇×#41	C₂×C₃	semidirect
39. C₂×D₄×D₇	C₂×C₃	semidirect
40. #6510	C₂×C₃	semidirect
41. #6509	C₂×C₃	semidirect
42. #6502	C₂×C₃	semidirect
43. #6500	C₂×C₃	semidirect
44. D₄×Dic₇	C₂×C₃	semidirect
45. #6493	C₂×C₃	semidirect
46. #6492	C₂×C₃	semidirect
47. C₄×C₂²⋊D₇	C₂×C₃	semidirect
48. C₂×(C₂×D₇)⋊C₄	C₂×C₃	semidirect
59. C₃×C₇×D₄	D₄	semidirect
77. C₂×C₇×Q₈	C₂²×C₃	semidirect
79. C₂×C₇×D₄	C₂²×C₃	semidirect
80. C₂²×C₄×C₇	C₂²×C₃	semidirect
81. C₂²×C₄×C₇	C₂²×C₃	semidirect
84. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
85. C₂²×Dic₇	C₂²×C₃	semidirect
89. C₂²⋊Dic₇	C₂²×C₃	semidirect
90. C₂²⋊Dic₇	C₂²×C₃	semidirect
93. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
94. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
95. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
96. C₄⋊Dic₇	C₂²×C₃	semidirect
97. Dic₇⋊C₄	C₂²×C₃	semidirect
98. Dic₇⋊C₄	C₂²×C₃	semidirect
99. C₄×Dic₇	C₂²×C₃	semidirect
100. C₂×C₃×#41	D₇	semidirect
124. C₂×C₃×D₇	#41	semidirect
142. C₇×D₄	C₃×D₄	semidirect
160. C₂×C₃×Q₈	C₂×D₇	semidirect
167. C₂×C₃×D₄	C₂×D₇	semidirect
170. C₂²×C₃×C₄	C₂×D₇	semidirect
171. C₂²×C₃×C₄	C₂×D₇	semidirect
190. C₂×#41	C₃×D₇	semidirect
214. C₂×D₇	C₃×#41	semidirect
235. C₃×D₄	C₂²⋊D₇	semidirect
247. C₃×C₇	#546	semidirect
250. C₂×Q₈	C₂×C₃×D₇	semidirect
257. C₂×D₄	C₂×C₃×D₇	semidirect
260. C₂²×C₄	C₂×C₃×D₇	semidirect
261. C₂²×C₄	C₂×C₃×D₇	semidirect
314. D₄	C₃×C₂²⋊D₇	semidirect
326. C₇	C₃×#546	semidirect
355. C₃	#90520	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×#41	2
C₂×C₃×D₄×D₇	2
C₃×#6510	2
C₃×#6509	2
C₃×#6502	2
C₃×#6500	2
C₃×D₄×Dic₇	2
C₃×#6493	2
C₃×#6492	2
C₃×C₄×C₂²⋊D₇	2
C₂×C₃×(C₂×D₇)⋊C₄	2
#90520	3
C₃×#546	7

Subgroups — C3×#90520 #13061170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90520 #13061170