Subgroups — C₂×C₃×#6502 #13061135

Order 1344.

852 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₃×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₂²⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6502	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×(C₂×D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×Dic₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#6502	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂⁴×C₃×C₇	C₂²	1	1	yes	characteristic
11	C₂⁴×C₃×C₇	C₂²	1	1	yes	characteristic
12	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₇×D₄	—	2	4	no	—
14	C₂×C₃×C₇×D₄	C₂²	1	4	yes	complemented
15	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₂²⋊D₇	—	2	4	no	—
17	C₂×C₃×C₂²⋊D₇	—	2	4	no	—
18	C₂×C₃×C₂²⋊D₇	C₂²	1	4	yes	complemented
19	C₂×C₃×C₂²⋊D₇	C₂²	1	4	yes	complemented
20	C₂²×C₃×Dic₇	—	2	4	no	—
21	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
22	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
23	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
24	C₂²×C₃×Dic₇	C₂²	1	4	yes	complemented
25	C₃×C₂²⋊Dic₇	C₂²	1	4	yes	complemented
26	C₃×(C₂×D₇)⋊C₄	C₂²	1	4	yes	complemented
27	C₃×Dic₇⋊C₄	C₂²	1	4	yes	complemented
28	C₂²×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂²×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂²×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂³×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₂²⋊Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
33	#6502	C₂×C₃	1	8	yes	direct product factor
34	C₂×(C₂×D₇)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×Dic₇⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₃×#121	—	7	1	no	maximal, Hall
37	C₂³×C₃×C₇	—	2	2	no	—
38	C₂³×C₃×C₇	—	2	2	no	—
39	C₂³×C₃×C₇	—	2	2	no	—
40	C₂³×C₃×C₇	—	2	2	no	—
41	C₂³×C₃×C₇	—	2	2	no	—
42	C₂³×C₃×C₇	D₄	1	4	yes	complemented
43	C₂³×C₃×C₇	C₂³	1	2	yes	—
44	C₂³×C₃×C₇	C₂³	1	2	yes	—
45	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
46	C₂²×C₃×D₇	—	2	2	no	—
47	C₂²×C₃×D₇	—	2	2	no	—
48	C₂²×C₃×D₇	—	2	2	no	—
49	C₂²×C₃×D₇	C₂³	1	2	yes	—
50	C₃×C₇×D₄	—	2	8	no	—
51	C₂×C₃×C₄×C₇	—	2	2	no	—
52	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
53	C₃×C₂²⋊D₇	—	2	8	no	—
54	C₃×C₂²⋊D₇	—	2	8	no	—
55	C₂×C₃×Dic₇	—	2	2	no	—
56	C₂×C₃×Dic₇	—	2	2	no	—
57	C₂×C₃×Dic₇	—	2	8	no	—
58	C₂×C₃×Dic₇	D₄	1	4	yes	complemented
59	C₂×C₃×Dic₇	C₂³	1	2	yes	—
60	C₂×C₃×Dic₇	C₂³	1	2	yes	—
61	C₂×C₃×Dic₇	C₂³	1	2	yes	—
62	C₂⁴×C₇	C₂²×C₃	1	1	yes	characteristic
63	C₂⁴×C₇	C₂²×C₃	1	1	yes	characteristic
64	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₇×D₄	—	2	4	no	—
66	C₂×C₇×D₄	C₂²×C₃	1	4	yes	complemented
67	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₂²⋊D₇	—	2	4	no	—
69	C₂×C₂²⋊D₇	—	2	4	no	—
70	C₂×C₂²⋊D₇	C₂²×C₃	1	4	yes	complemented
71	C₂×C₂²⋊D₇	C₂²×C₃	1	4	yes	complemented
72	C₂²×Dic₇	—	2	4	no	—
73	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
74	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
75	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
76	C₂²×Dic₇	C₂²×C₃	1	4	yes	complemented
77	C₂²⋊Dic₇	C₂²×C₃	1	4	yes	complemented
78	(C₂×D₇)⋊C₄	C₂²×C₃	1	4	yes	complemented
79	Dic₇⋊C₄	C₂²×C₃	1	4	yes	complemented
80	C₂²×C₃×D₄	—	7	1	no	—
81	C₂²×C₃×D₄	—	7	1	no	—
82	C₂²×C₃×D₄	D₇	1	1	yes	characteristic, complemented
83	C₂³×C₃×C₄	—	7	1	no	—
84	C₃×#121	—	7	8	no	—
85	C₂×C₃×C₄⋊C₄	—	7	1	no	—
86	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
87	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
88	C₂²×C₃×C₇	—	2	8	no	—
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	2	no	—
94	C₂²×C₃×C₇	—	4	4	no	—
95	C₂²×C₃×C₇	C₂×D₄	1	2	yes	—
96	C₂²×C₃×C₇	C₂×D₄	1	2	yes	—
97	C₂²×C₃×C₇	C₂×D₄	1	4	yes	complemented
98	C₂²×C₃×C₇	#41	1	2	yes	—
99	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
100	C₂×C₃×D₇	—	2	2	no	—
101	C₂×C₃×D₇	—	2	2	no	—
102	C₂×C₃×D₇	—	2	2	no	—
103	C₂×C₃×D₇	—	4	4	no	—
104	C₃×C₄×C₇	—	2	2	no	—
105	C₃×Dic₇	—	2	2	no	—
106	C₃×Dic₇	—	2	2	no	—
107	C₃×Dic₇	C₂×D₄	1	4	yes	complemented
108	C₂×#121	—	7	1	no	Sylow
109	C₂³×C₇	—	2	2	no	—
110	C₂³×C₇	—	2	2	no	—
111	C₂³×C₇	—	2	2	no	—
112	C₂³×C₇	—	2	2	no	—
113	C₂³×C₇	—	2	2	no	—
114	C₂³×C₇	C₃×D₄	1	4	yes	complemented
115	C₂³×C₇	C₂³×C₃	1	2	yes	—
116	C₂³×C₇	C₂³×C₃	1	2	yes	—
117	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
118	C₂²×D₇	—	2	2	no	—
119	C₂²×D₇	—	2	2	no	—
120	C₂²×D₇	—	2	2	no	—
121	C₂²×D₇	C₂³×C₃	1	2	yes	—
122	C₇×D₄	—	2	8	no	—
123	C₂×C₄×C₇	—	2	2	no	—
124	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
125	C₂²⋊D₇	—	2	8	no	—
126	C₂²⋊D₇	—	2	8	no	—
127	C₂×Dic₇	—	2	2	no	—
128	C₂×Dic₇	—	2	2	no	—
129	C₂×Dic₇	—	2	8	no	—
130	C₂×Dic₇	C₃×D₄	1	4	yes	complemented
131	C₂×Dic₇	C₂³×C₃	1	2	yes	—
132	C₂×Dic₇	C₂³×C₃	1	2	yes	—
133	C₂×Dic₇	C₂³×C₃	1	2	yes	—
134	C₂⁴×C₃	—	7	1	no	—
135	C₂⁴×C₃	C₂×D₇	1	1	yes	characteristic
136	C₂⁴×C₃	C₂×D₇	1	1	yes	characteristic
137	C₂×C₃×D₄	—	2	4	no	—
138	C₂×C₃×D₄	—	7	4	no	—
139	C₂×C₃×D₄	—	7	4	no	—
140	C₂×C₃×D₄	—	14	4	no	—
141	C₂×C₃×D₄	—	14	4	no	—
142	C₂×C₃×D₄	C₂×D₇	1	4	yes	complemented
143	C₂²×C₃×C₄	—	7	1	no	—
144	C₂²×C₃×C₄	—	7	4	no	—
145	C₂²×C₃×C₄	—	7	1	no	—
146	C₂²×C₃×C₄	—	7	1	no	—
147	C₂²×C₃×C₄	—	14	4	no	—
148	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
149	C₃×C₄⋊C₄	—	7	4	no	—
150	C₃×C₂²⋊C₄	—	7	4	no	—
151	C₃×C₂²⋊C₄	—	7	4	no	—
152	C₂×C₃×C₇	—	2	4	no	—
153	C₂×C₃×C₇	—	4	2	no	—
154	C₂×C₃×C₇	#121	1	4	yes	complemented
155	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
158	C₃×D₇	—	4	2	no	—
159	C₂²×D₄	—	7	1	no	—
160	C₂²×D₄	—	7	1	no	—
161	C₂²×D₄	C₃×D₇	1	1	yes	characteristic, complemented
162	C₂³×C₄	—	7	1	no	—
163	#121	—	7	8	no	—
164	C₂×C₄⋊C₄	—	7	1	no	—
165	C₂×C₂²⋊C₄	—	7	1	no	—
166	C₂×C₂²⋊C₄	—	7	1	no	—
167	C₂²×C₇	—	2	8	no	—
168	C₂²×C₇	—	2	2	no	—
169	C₂²×C₇	—	2	2	no	—
170	C₂²×C₇	—	2	2	no	—
171	C₂²×C₇	—	2	2	no	—
172	C₂²×C₇	—	2	2	no	—
173	C₂²×C₇	—	4	4	no	—
174	C₂²×C₇	C₂×C₃×D₄	1	2	yes	—
175	C₂²×C₇	C₂×C₃×D₄	1	2	yes	—
176	C₂²×C₇	C₂×C₃×D₄	1	4	yes	complemented
177	C₂²×C₇	C₃×#41	1	2	yes	—
178	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
179	C₂×D₇	—	2	2	no	—
180	C₂×D₇	—	2	2	no	—
181	C₂×D₇	—	2	2	no	—
182	C₂×D₇	—	4	4	no	—
183	C₄×C₇	—	2	2	no	—
184	Dic₇	—	2	2	no	—
185	Dic₇	—	2	2	no	—
186	Dic₇	C₂×C₃×D₄	1	4	yes	complemented
187	C₂³×C₃	—	2	2	no	—
188	C₂³×C₃	—	2	2	no	—
189	C₂³×C₃	—	2	2	no	—
190	C₂³×C₃	—	2	2	no	—
191	C₂³×C₃	—	2	2	no	—
192	C₂³×C₃	—	7	2	no	—
193	C₂³×C₃	—	14	2	no	—
194	C₂³×C₃	—	14	2	no	—
195	C₂³×C₃	—	14	2	no	—
196	C₂³×C₃	C₂²⋊D₇	1	4	yes	complemented
197	C₂³×C₃	C₂²×D₇	1	2	yes	—
198	C₂³×C₃	C₂²×D₇	1	2	yes	—
199	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
200	C₃×D₄	—	2	8	no	—
201	C₃×D₄	—	14	8	no	—
202	C₃×D₄	—	14	8	no	—
203	C₂×C₃×C₄	—	2	2	no	—
204	C₂×C₃×C₄	—	7	4	no	—
205	C₂×C₃×C₄	—	7	2	no	—
206	C₂×C₃×C₄	—	7	2	no	—
207	C₂×C₃×C₄	—	7	2	no	—
208	C₂×C₃×C₄	—	14	8	no	—
209	C₂×C₃×C₄	—	14	2	no	—
210	C₂×C₃×C₄	—	14	2	no	—
211	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
212	C₃×C₇	C₂×#121	1	1	yes	characteristic, complemented, Hall
213	C₂⁴	—	7	1	no	—
214	C₂⁴	C₂×C₃×D₇	1	1	yes	characteristic
215	C₂⁴	C₂×C₃×D₇	1	1	yes	characteristic
216	C₂×D₄	—	2	4	no	—
217	C₂×D₄	—	7	4	no	—
218	C₂×D₄	—	7	4	no	—
219	C₂×D₄	—	14	4	no	—
220	C₂×D₄	—	14	4	no	—
221	C₂×D₄	C₂×C₃×D₇	1	4	yes	complemented
222	C₂²×C₄	—	7	1	no	—
223	C₂²×C₄	—	7	1	no	—
224	C₂²×C₄	—	7	1	no	—
225	C₂²×C₄	—	7	4	no	—
226	C₂²×C₄	—	14	4	no	—
227	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
228	C₄⋊C₄	—	7	4	no	—
229	C₂²⋊C₄	—	7	4	no	—
230	C₂²⋊C₄	—	7	4	no	—
231	C₂×C₇	—	2	4	no	—
232	C₂×C₇	—	4	2	no	—
233	C₂×C₇	C₃×#121	1	4	yes	complemented
234	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
235	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
236	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
237	D₇	—	4	2	no	—
238	C₂²×C₃	—	2	8	no	—
239	C₂²×C₃	—	2	2	no	—
240	C₂²×C₃	—	2	2	no	—
241	C₂²×C₃	—	2	2	no	—
242	C₂²×C₃	—	2	2	no	—
243	C₂²×C₃	—	2	2	no	—
244	C₂²×C₃	—	4	4	no	—
245	C₂²×C₃	—	14	2	no	—
246	C₂²×C₃	—	14	2	no	—
247	C₂²×C₃	—	14	2	no	—
248	C₂²×C₃	—	28	4	no	—
249	C₂²×C₃	D₄×D₇	1	2	yes	—
250	C₂²×C₃	#1159	1	2	yes	—
251	C₂²×C₃	C₂×C₂²⋊D₇	1	2	yes	—
252	C₂²×C₃	C₂×C₂²⋊D₇	1	4	yes	complemented
253	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
254	C₃×C₄	—	2	2	no	—
255	C₃×C₄	—	7	4	no	—
256	C₃×C₄	—	14	2	no	—
257	C₃×C₄	—	14	2	no	—
258	C₂³	—	2	2	no	—
259	C₂³	—	2	2	no	—
260	C₂³	—	2	2	no	—
261	C₂³	—	2	2	no	—
262	C₂³	—	2	2	no	—
263	C₂³	—	7	2	no	—
264	C₂³	—	14	2	no	—
265	C₂³	—	14	2	no	—
266	C₂³	—	14	2	no	—
267	C₂³	C₃×C₂²⋊D₇	1	4	yes	complemented
268	C₂³	C₂²×C₃×D₇	1	2	yes	—
269	C₂³	C₂²×C₃×D₇	1	2	yes	—
270	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
271	D₄	—	2	8	no	—
272	D₄	—	14	8	no	—
273	D₄	—	14	8	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	7	4	no	—
276	C₂×C₄	—	7	2	no	—
277	C₂×C₄	—	7	2	no	—
278	C₂×C₄	—	7	2	no	—
279	C₂×C₄	—	14	8	no	—
280	C₂×C₄	—	14	2	no	—
281	C₂×C₄	—	14	2	no	—
282	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
283	C₇	C₂×C₃×#121	1	1	yes	characteristic, complemented, Sylow
284	C₂×C₃	—	2	4	no	—
285	C₂×C₃	—	4	2	no	—
286	C₂×C₃	—	28	2	no	—
287	C₂×C₃	#6502	1	4	yes	direct product factor
288	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
289	C₂×C₃	C₂×#1159	1	1	yes	characteristic
290	C₂×C₃	C₂²×C₂²⋊D₇	1	1	yes	characteristic
291	C₂²	—	2	8	no	—
292	C₂²	—	2	2	no	—
293	C₂²	—	2	2	no	—
294	C₂²	—	2	2	no	—
295	C₂²	—	2	2	no	—
296	C₂²	—	2	2	no	—
297	C₂²	—	4	4	no	—
298	C₂²	—	14	2	no	—
299	C₂²	—	14	2	no	—
300	C₂²	—	14	2	no	—
301	C₂²	—	28	4	no	—
302	C₂²	C₃×D₄×D₇	1	2	yes	—
303	C₂²	C₃×#1159	1	2	yes	—
304	C₂²	C₂×C₃×C₂²⋊D₇	1	2	yes	—
305	C₂²	C₂×C₃×C₂²⋊D₇	1	4	yes	complemented
306	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
307	C₄	—	2	2	no	—
308	C₄	—	7	4	no	—
309	C₄	—	14	2	no	—
310	C₄	—	14	2	no	—
311	C₃	C₂×#6502	1	1	yes	characteristic, direct product factor, Sylow
312	C₂	—	2	4	no	—
313	C₂	—	4	2	no	—
314	C₂	—	28	2	no	—
315	C₂	C₃×#6502	1	4	yes	direct product factor
316	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
317	C₂	C₂×C₃×#1159	1	1	yes	characteristic
318	C₂	C₂²×C₃×C₂²⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂²×D₇
commutator, cosocle	C₂²×C₇	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₇
Fitting	C₂²×C₃×C₇×D₄	C₂
socle	C₂³×C₃×C₇	C₂³
hypercenter	C₂²×C₃×D₄	D₇
hypocenter	C₇	C₂×C₃×#121
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₇×D₄	C₂	semidirect
2. C₂²×C₃×C₂²⋊D₇	C₂	semidirect
3. C₂²×C₃×C₂²⋊D₇	C₂	semidirect
4. C₂³×C₃×Dic₇	C₂	semidirect
5. C₂×C₃×C₂²⋊Dic₇	C₂	semidirect
6. C₃×#6502	C₂	direct (N × H)
7. C₂×C₃×(C₂×D₇)⋊C₄	C₂	semidirect
8. C₂×C₃×Dic₇⋊C₄	C₂	semidirect
9. C₂×#6502	C₃	direct (N × H)
14. C₂×C₃×C₇×D₄	C₂²	semidirect
18. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
19. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
24. C₂²×C₃×Dic₇	C₂²	semidirect
25. C₃×C₂²⋊Dic₇	C₂²	semidirect
26. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
27. C₃×Dic₇⋊C₄	C₂²	semidirect
28. C₂²×C₇×D₄	C₂×C₃	semidirect
29. C₂²×C₂²⋊D₇	C₂×C₃	semidirect
30. C₂²×C₂²⋊D₇	C₂×C₃	semidirect
31. C₂³×Dic₇	C₂×C₃	semidirect
32. C₂×C₂²⋊Dic₇	C₂×C₃	semidirect
33. #6502	C₂×C₃	direct (N × H)
34. C₂×(C₂×D₇)⋊C₄	C₂×C₃	semidirect
35. C₂×Dic₇⋊C₄	C₂×C₃	semidirect
42. C₂³×C₃×C₇	D₄	semidirect
58. C₂×C₃×Dic₇	D₄	semidirect
66. C₂×C₇×D₄	C₂²×C₃	semidirect
70. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
71. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
76. C₂²×Dic₇	C₂²×C₃	semidirect
77. C₂²⋊Dic₇	C₂²×C₃	semidirect
78. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
79. Dic₇⋊C₄	C₂²×C₃	semidirect
82. C₂²×C₃×D₄	D₇	semidirect
97. C₂²×C₃×C₇	C₂×D₄	semidirect
107. C₃×Dic₇	C₂×D₄	semidirect
114. C₂³×C₇	C₃×D₄	semidirect
130. C₂×Dic₇	C₃×D₄	semidirect
142. C₂×C₃×D₄	C₂×D₇	semidirect
154. C₂×C₃×C₇	#121	semidirect
161. C₂²×D₄	C₃×D₇	semidirect
176. C₂²×C₇	C₂×C₃×D₄	semidirect
186. Dic₇	C₂×C₃×D₄	semidirect
196. C₂³×C₃	C₂²⋊D₇	semidirect
212. C₃×C₇	C₂×#121	semidirect
221. C₂×D₄	C₂×C₃×D₇	semidirect
233. C₂×C₇	C₃×#121	semidirect
252. C₂²×C₃	C₂×C₂²⋊D₇	semidirect
267. C₂³	C₃×C₂²⋊D₇	semidirect
283. C₇	C₂×C₃×#121	semidirect
287. C₂×C₃	#6502	direct (N × H)
305. C₂²	C₂×C₃×C₂²⋊D₇	semidirect
311. C₃	C₂×#6502	direct (N × H)
315. C₂	C₃×#6502	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₇×D₄	2
C₂²×C₃×C₂²⋊D₇	2
C₂³×C₃×Dic₇	2
C₂×C₃×C₂²⋊Dic₇	2
C₃×#6502	2
C₂×C₃×(C₂×D₇)⋊C₄	2
C₂×C₃×Dic₇⋊C₄	2
C₂×#6502	3
C₂×C₃×#121	7

Subgroups — C2×C3×#6502 #13061135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#6502 #13061135