Subgroups — C₃×#90283 #13060929

Order 1344.

668 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#1159	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6516	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6503	C₂	1	2	yes	maximal, complemented
6	C₃×#6502	C₂	1	2	yes	maximal, complemented
7	C₃×#6500	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#6448	C₂	1	2	yes	maximal, complemented
9	C₃×#6447	C₂	1	2	yes	maximal, complemented
10	C₃×#6445	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6440	C₂	1	1	yes	maximal, characteristic, complemented
12	#90283	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁴×C₃×C₇	C₂²	1	1	yes	characteristic
14	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₇×D₄	C₂²	1	2	yes	complemented
17	C₂×C₃×C₂²⋊D₇	—	2	4	no	—
18	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	—
20	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	—
21	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
23	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
24	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
25	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
26	C₃×#1159	—	2	4	no	—
27	C₂×C₃×D₂₈	C₂²	1	2	yes	complemented
28	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
32	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
33	C₃×C₂²⋊Dic₇	C₂²	1	2	yes	complemented
34	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
35	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
36	C₃×Dic₇⋊C₄	C₂²	1	2	yes	complemented
37	C₃×C₄×Dic₇	C₂²	1	2	yes	complemented
38	C₂²×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#1159	C₂×C₃	1	1	yes	characteristic, complemented
40	C₇×#120	C₂×C₃	1	1	yes	characteristic, complemented
41	#6516	C₂×C₃	1	1	yes	characteristic, complemented
42	#6503	C₂×C₃	1	2	yes	complemented
43	#6502	C₂×C₃	1	2	yes	complemented
44	#6500	C₂×C₃	1	1	yes	characteristic, complemented
45	#6448	C₂×C₃	1	2	yes	complemented
46	#6447	C₂×C₃	1	2	yes	complemented
47	#6445	C₂×C₃	1	1	yes	characteristic, complemented
48	#6440	C₂×C₃	1	1	yes	characteristic, complemented
49	C₃×#535	—	7	1	no	maximal, Hall
50	C₂³×C₃×C₇	—	2	2	no	—
51	C₂³×C₃×C₇	—	4	2	no	—
52	C₂³×C₃×C₇	C₂³	1	2	yes	—
53	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
54	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
55	C₂²×C₃×D₇	—	2	2	no	—
56	C₂²×C₃×D₇	—	4	2	no	—
57	C₂²×C₃×D₇	C₂³	1	2	yes	—
58	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
59	C₃×C₇×D₄	—	2	2	no	—
60	C₃×C₇×D₄	—	4	2	no	—
61	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
63	C₃×C₂²⋊D₇	—	2	2	no	—
64	C₃×C₂²⋊D₇	—	2	2	no	—
65	C₃×C₂²⋊D₇	—	2	4	no	—
66	C₃×C₂²⋊D₇	—	2	4	no	—
67	C₃×C₂²⋊D₇	—	4	2	no	—
68	C₃×C₂²⋊D₇	—	4	2	no	—
69	C₂×C₃×Dic₇	—	2	2	no	—
70	C₂×C₃×Dic₇	D₄	1	4	yes	complemented
71	C₂×C₃×Dic₇	C₂³	1	2	yes	—
72	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
73	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
74	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
75	C₃×D₂₈	—	4	2	no	—
76	C₃×C₄×D₇	—	2	2	no	—
77	C₃×Dic₁₄	—	2	2	no	—
78	C₂⁴×C₇	C₂²×C₃	1	1	yes	characteristic
79	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₇×D₄	C₂²×C₃	1	2	yes	complemented
82	C₂×C₂²⋊D₇	—	2	4	no	—
83	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
85	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
86	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic, complemented
87	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
88	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
89	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
90	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
91	#1159	—	2	4	no	—
92	C₂×D₂₈	C₂²×C₃	1	2	yes	complemented
93	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
94	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic, complemented
95	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
97	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
98	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
99	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
100	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
101	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
102	C₄×Dic₇	C₂²×C₃	1	2	yes	complemented
103	C₂×C₃×#41	—	7	1	no	—
104	C₂²×C₃×D₄	—	7	1	no	—
105	C₃×#127	—	7	2	no	—
106	C₃×#124	—	7	2	no	—
107	C₃×#121	—	7	2	no	—
108	C₃×#121	—	7	2	no	—
109	C₃×#120	—	7	1	no	—
110	C₃×#120	—	7	1	no	—
111	C₃×#120	—	7	1	no	—
112	C₃×#120	D₇	1	1	yes	characteristic, complemented
113	C₃×#117	—	7	1	no	—
114	C₂²×C₃×C₇	—	2	2	no	—
115	C₂²×C₃×C₇	—	2	1	no	—
116	C₂²×C₃×C₇	—	2	2	no	—
117	C₂²×C₃×C₇	—	2	2	no	—
118	C₂²×C₃×C₇	—	2	2	no	—
119	C₂²×C₃×C₇	—	2	2	no	—
120	C₂²×C₃×C₇	—	4	4	no	—
121	C₂²×C₃×C₇	C₂×D₄	1	2	yes	—
122	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
123	C₂×C₃×D₇	—	2	1	no	—
124	C₂×C₃×D₇	—	2	2	no	—
125	C₂×C₃×D₇	—	2	2	no	—
126	C₂×C₃×D₇	—	2	2	no	—
127	C₂×C₃×D₇	—	2	2	no	—
128	C₂×C₃×D₇	—	4	4	no	—
129	C₃×C₄×C₇	—	2	1	no	—
130	C₃×C₄×C₇	—	2	2	no	—
131	C₃×Dic₇	—	2	1	no	—
132	C₃×Dic₇	—	2	2	no	—
133	C₃×Dic₇	C₂×D₄	1	2	yes	—
134	C₃×Dic₇	C₂×D₄	1	2	yes	—
135	#535	—	7	1	no	Sylow
136	C₂³×C₇	—	2	2	no	—
137	C₂³×C₇	—	4	2	no	—
138	C₂³×C₇	C₂³×C₃	1	2	yes	—
139	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
140	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
141	C₂²×D₇	—	2	2	no	—
142	C₂²×D₇	—	4	2	no	—
143	C₂²×D₇	C₂³×C₃	1	2	yes	—
144	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
145	C₇×D₄	—	2	2	no	—
146	C₇×D₄	—	4	2	no	—
147	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
148	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
149	C₂²⋊D₇	—	2	2	no	—
150	C₂²⋊D₇	—	2	2	no	—
151	C₂²⋊D₇	—	2	4	no	—
152	C₂²⋊D₇	—	2	4	no	—
153	C₂²⋊D₇	—	4	2	no	—
154	C₂²⋊D₇	—	4	2	no	—
155	C₂×Dic₇	—	2	2	no	—
156	C₂×Dic₇	C₃×D₄	1	4	yes	complemented
157	C₂×Dic₇	C₂³×C₃	1	2	yes	—
158	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
159	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
160	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
161	D₂₈	—	4	2	no	—
162	C₄×D₇	—	2	2	no	—
163	Dic₁₄	—	2	2	no	—
164	C₂⁴×C₃	—	7	1	no	—
165	C₂⁴×C₃	C₂×D₇	1	1	yes	characteristic
166	C₃×#41	—	14	4	no	—
167	C₂×C₃×Q₈	—	7	1	no	—
168	C₂×C₃×D₄	—	7	1	no	—
169	C₂×C₃×D₄	—	7	2	no	—
170	C₂×C₃×D₄	—	7	2	no	—
171	C₂×C₃×D₄	—	7	1	no	—
172	C₂×C₃×D₄	—	7	2	no	—
173	C₂×C₃×D₄	—	7	2	no	—
174	C₂×C₃×D₄	—	7	2	no	—
175	C₂×C₃×D₄	—	14	4	no	—
176	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
177	C₂×C₃×D₄	C₂×D₇	1	2	yes	complemented
178	C₂²×C₃×C₄	—	7	1	no	—
179	C₂²×C₃×C₄	—	7	1	no	—
180	C₂²×C₃×C₄	—	7	1	no	—
181	C₃×C₄⋊C₄	—	7	2	no	—
182	C₃×C₂²⋊C₄	—	7	1	no	—
183	C₃×C₂²⋊C₄	—	7	2	no	—
184	C₃×C₂²⋊C₄	—	7	2	no	—
185	C₃×C₂²⋊C₄	—	7	2	no	—
186	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
187	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	complemented
188	C₃×C₄²	—	7	2	no	—
189	C₂×C₃×C₇	—	2	2	no	—
190	C₂×C₃×C₇	—	4	1	no	—
191	C₂×C₃×C₇	—	4	2	no	—
192	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₃×C₇	H(5,𝔽₂)	1	2	yes	—
194	C₃×D₇	—	4	1	no	—
195	C₃×D₇	—	4	2	no	—
196	C₂×#41	—	7	1	no	—
197	C₂²×D₄	—	7	1	no	—
198	#127	—	7	2	no	—
199	#124	—	7	2	no	—
200	#121	—	7	2	no	—
201	#121	—	7	2	no	—
202	#120	—	7	1	no	—
203	#120	—	7	1	no	—
204	#120	—	7	1	no	—
205	#120	C₃×D₇	1	1	yes	characteristic, complemented
206	#117	—	7	1	no	—
207	C₂²×C₇	—	2	2	no	—
208	C₂²×C₇	—	2	1	no	—
209	C₂²×C₇	—	2	2	no	—
210	C₂²×C₇	—	2	2	no	—
211	C₂²×C₇	—	2	2	no	—
212	C₂²×C₇	—	2	2	no	—
213	C₂²×C₇	—	4	4	no	—
214	C₂²×C₇	C₂×C₃×D₄	1	2	yes	—
215	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
216	C₂×D₇	—	2	1	no	—
217	C₂×D₇	—	2	2	no	—
218	C₂×D₇	—	2	2	no	—
219	C₂×D₇	—	2	2	no	—
220	C₂×D₇	—	2	2	no	—
221	C₂×D₇	—	4	4	no	—
222	C₄×C₇	—	2	1	no	—
223	C₄×C₇	—	2	2	no	—
224	Dic₇	—	2	1	no	—
225	Dic₇	—	2	2	no	—
226	Dic₇	C₂×C₃×D₄	1	2	yes	—
227	Dic₇	C₂×C₃×D₄	1	2	yes	—
228	C₂³×C₃	—	2	2	no	—
229	C₂³×C₃	—	4	2	no	—
230	C₂³×C₃	—	7	2	no	—
231	C₂³×C₃	—	7	1	no	—
232	C₂³×C₃	—	14	2	no	—
233	C₂³×C₃	—	28	2	no	—
234	C₂³×C₃	C₂²×D₇	1	2	yes	—
235	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
236	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
237	C₃×Q₈	—	14	2	no	—
238	C₃×D₄	—	2	2	no	—
239	C₃×D₄	—	4	2	no	—
240	C₃×D₄	—	14	4	no	—
241	C₃×D₄	—	14	4	no	—
242	C₃×D₄	—	14	2	no	—
243	C₃×D₄	—	14	2	no	—
244	C₃×D₄	—	28	2	no	—
245	C₃×D₄	—	28	2	no	—
246	C₃×D₄	—	28	2	no	—
247	C₂×C₃×C₄	—	7	4	no	—
248	C₂×C₃×C₄	—	7	1	no	—
249	C₂×C₃×C₄	—	7	1	no	—
250	C₂×C₃×C₄	—	7	2	no	—
251	C₂×C₃×C₄	—	7	1	no	—
252	C₂×C₃×C₄	—	14	2	no	—
253	C₂×C₃×C₄	—	14	2	no	—
254	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
255	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
256	C₃×C₇	#535	1	1	yes	characteristic, complemented, Hall
257	C₂⁴	—	7	1	no	—
258	C₂⁴	C₂×C₃×D₇	1	1	yes	characteristic
259	#41	—	14	4	no	—
260	C₂×Q₈	—	7	1	no	—
261	C₂×D₄	—	7	1	no	—
262	C₂×D₄	—	7	2	no	—
263	C₂×D₄	—	7	2	no	—
264	C₂×D₄	—	7	1	no	—
265	C₂×D₄	—	7	2	no	—
266	C₂×D₄	—	7	2	no	—
267	C₂×D₄	—	7	2	no	—
268	C₂×D₄	—	14	4	no	—
269	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
270	C₂×D₄	C₂×C₃×D₇	1	2	yes	complemented
271	C₂²×C₄	—	7	1	no	—
272	C₂²×C₄	—	7	1	no	—
273	C₂²×C₄	—	7	1	no	—
274	C₄⋊C₄	—	7	2	no	—
275	C₂²⋊C₄	—	7	1	no	—
276	C₂²⋊C₄	—	7	2	no	—
277	C₂²⋊C₄	—	7	2	no	—
278	C₂²⋊C₄	—	7	2	no	—
279	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
280	C₂²⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
281	C₄²	—	7	2	no	—
282	C₂×C₇	—	2	2	no	—
283	C₂×C₇	—	4	2	no	—
284	C₂×C₇	—	4	1	no	—
285	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
286	C₂×C₇	C₃×H(5,𝔽₂)	1	2	yes	—
287	D₇	—	4	2	no	—
288	D₇	—	4	1	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	2	no	—
292	C₂²×C₃	—	2	2	no	—
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	4	4	no	—
296	C₂²×C₃	—	14	1	no	—
297	C₂²×C₃	—	14	2	no	—
298	C₂²×C₃	—	14	2	no	—
299	C₂²×C₃	—	14	2	no	—
300	C₂²×C₃	—	14	2	no	—
301	C₂²×C₃	—	28	4	no	—
302	C₂²×C₃	D₄×D₇	1	2	yes	—
303	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	—	7	2	no	—
307	C₃×C₄	—	7	2	no	—
308	C₃×C₄	—	14	1	no	—
309	C₃×C₄	—	14	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	4	2	no	—
312	C₂³	—	7	2	no	—
313	C₂³	—	7	1	no	—
314	C₂³	—	14	2	no	—
315	C₂³	—	28	2	no	—
316	C₂³	C₂²×C₃×D₇	1	2	yes	—
317	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
318	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
319	Q₈	—	14	2	no	—
320	D₄	—	2	2	no	—
321	D₄	—	4	2	no	—
322	D₄	—	14	4	no	—
323	D₄	—	14	4	no	—
324	D₄	—	14	2	no	—
325	D₄	—	14	2	no	—
326	D₄	—	28	2	no	—
327	D₄	—	28	2	no	—
328	D₄	—	28	2	no	—
329	C₂×C₄	—	7	4	no	—
330	C₂×C₄	—	7	1	no	—
331	C₂×C₄	—	7	1	no	—
332	C₂×C₄	—	7	2	no	—
333	C₂×C₄	—	7	1	no	—
334	C₂×C₄	—	14	2	no	—
335	C₂×C₄	—	14	2	no	—
336	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
337	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
338	C₇	C₃×#535	1	1	yes	characteristic, complemented, Sylow
339	C₂×C₃	—	2	2	no	—
340	C₂×C₃	—	4	2	no	—
341	C₂×C₃	—	4	1	no	—
342	C₂×C₃	—	28	2	no	—
343	C₂×C₃	—	28	1	no	—
344	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
345	C₂×C₃	#6548	1	2	yes	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	4	no	—
353	C₂²	—	14	1	no	—
354	C₂²	—	14	2	no	—
355	C₂²	—	14	2	no	—
356	C₂²	—	14	2	no	—
357	C₂²	—	14	2	no	—
358	C₂²	—	28	4	no	—
359	C₂²	C₃×D₄×D₇	1	2	yes	—
360	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	2	no	—
363	C₄	—	7	2	no	—
364	C₄	—	7	2	no	—
365	C₄	—	14	1	no	—
366	C₄	—	14	2	no	—
367	C₃	#90283	1	1	yes	characteristic, direct product factor, Sylow
368	C₂	—	2	2	no	—
369	C₂	—	4	2	no	—
370	C₂	—	4	1	no	—
371	C₂	—	28	2	no	—
372	C₂	—	28	1	no	—
373	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
374	C₂	C₃×#6548	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂³×D₇
commutator, cosocle	C₂²×C₇	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₇
Fitting	C₃×C₇×#120	C₂
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₃×#120	D₇
hypocenter	C₇	C₃×#535
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#120

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₂²⋊D₇	C₂	semidirect
2. C₂×C₃×#1159	C₂	semidirect
3. C₃×C₇×#120	C₂	semidirect
4. C₃×#6516	C₂	semidirect
5. C₃×#6503	C₂	semidirect
6. C₃×#6502	C₂	semidirect
7. C₃×#6500	C₂	semidirect
8. C₃×#6448	C₂	semidirect
9. C₃×#6447	C₂	semidirect
10. C₃×#6445	C₂	semidirect
11. C₃×#6440	C₂	semidirect
12. #90283	C₃	direct (N × H)
16. C₂×C₃×C₇×D₄	C₂²	semidirect
21. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
22. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
23. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
25. C₂²×C₃×Dic₇	C₂²	semidirect
27. C₂×C₃×D₂₈	C₂²	semidirect
28. C₂×C₃×C₄×D₇	C₂²	semidirect
29. C₂×C₃×Dic₁₄	C₂²	semidirect
31. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
33. C₃×C₂²⋊Dic₇	C₂²	semidirect
34. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
35. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
36. C₃×Dic₇⋊C₄	C₂²	semidirect
37. C₃×C₄×Dic₇	C₂²	semidirect
38. C₂²×C₂²⋊D₇	C₂×C₃	semidirect
39. C₂×#1159	C₂×C₃	semidirect
40. C₇×#120	C₂×C₃	semidirect
41. #6516	C₂×C₃	semidirect
42. #6503	C₂×C₃	semidirect
43. #6502	C₂×C₃	semidirect
44. #6500	C₂×C₃	semidirect
45. #6448	C₂×C₃	semidirect
46. #6447	C₂×C₃	semidirect
47. #6445	C₂×C₃	semidirect
48. #6440	C₂×C₃	semidirect
70. C₂×C₃×Dic₇	D₄	semidirect
81. C₂×C₇×D₄	C₂²×C₃	semidirect
86. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
87. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
88. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
90. C₂²×Dic₇	C₂²×C₃	semidirect
92. C₂×D₂₈	C₂²×C₃	semidirect
93. C₂×C₄×D₇	C₂²×C₃	semidirect
94. C₂×Dic₁₄	C₂²×C₃	semidirect
96. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
98. C₂²⋊Dic₇	C₂²×C₃	semidirect
99. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
100. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
101. Dic₇⋊C₄	C₂²×C₃	semidirect
102. C₄×Dic₇	C₂²×C₃	semidirect
112. C₃×#120	D₇	semidirect
156. C₂×Dic₇	C₃×D₄	semidirect
177. C₂×C₃×D₄	C₂×D₇	semidirect
187. C₃×C₂²⋊C₄	C₂×D₇	semidirect
205. #120	C₃×D₇	semidirect
256. C₃×C₇	#535	semidirect
270. C₂×D₄	C₂×C₃×D₇	semidirect
280. C₂²⋊C₄	C₂×C₃×D₇	semidirect
338. C₇	C₃×#535	semidirect
367. C₃	#90283	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×C₂²⋊D₇	2
C₂×C₃×#1159	2
C₃×C₇×#120	2
C₃×#6516	2
C₃×#6503	2
C₃×#6502	2
C₃×#6500	2
C₃×#6448	2
C₃×#6447	2
C₃×#6445	2
C₃×#6440	2
#90283	3
C₃×#535	7

Subgroups — C3×#90283 #13060929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90283 #13060929