Subgroups — C₃×#90296 #13060949

Order 1344.

692 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×D₇	C₂	1	2	yes	maximal, complemented
2	C₃×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#6502	C₂	1	2	yes	maximal, complemented
4	C₃×#6500	C₂	1	2	yes	maximal, complemented
5	C₃×#6493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×(C₂×D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#6457	C₂	1	2	yes	maximal, complemented
8	C₃×#6446	C₂	1	2	yes	maximal, complemented
9	C₃×#6445	C₂	1	2	yes	maximal, complemented
10	#90296	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
12	C₂³×C₃×D₇	C₂²	1	2	yes	complemented
13	C₂×C₃×C₇×D₄	C₂²	1	2	yes	complemented
14	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	—
17	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
18	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
19	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
20	C₃×D₄×D₇	—	2	8	no	—
21	C₂×C₃×D₂₈	C₂²	1	2	yes	—
22	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₄×D₇	C₂²	1	2	yes	complemented
24	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
26	C₃×C₂²⋊Dic₇	C₂²	1	2	yes	complemented
27	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
28	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
29	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
30	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
31	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
32	C₃×Dic₇⋊C₄	C₂²	1	2	yes	complemented
33	C₂×D₄×D₇	C₂×C₃	1	2	yes	complemented
34	C₇×#121	C₂×C₃	1	1	yes	characteristic, complemented
35	#6502	C₂×C₃	1	2	yes	complemented
36	#6500	C₂×C₃	1	2	yes	complemented
37	#6493	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×(C₂×D₇)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
39	#6457	C₂×C₃	1	2	yes	complemented
40	#6446	C₂×C₃	1	2	yes	complemented
41	#6445	C₂×C₃	1	2	yes	complemented
42	C₃×#534	—	7	1	no	maximal, Hall
43	C₂³×C₃×C₇	C₂³	1	2	yes	—
44	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
45	C₂²×C₃×D₇	—	2	4	no	—
46	C₂²×C₃×D₇	—	4	1	no	—
47	C₂²×C₃×D₇	—	4	1	no	—
48	C₂²×C₃×D₇	—	4	2	no	—
49	C₂²×C₃×D₇	—	4	2	no	—
50	C₂²×C₃×D₇	D₄	1	4	yes	complemented
51	C₂²×C₃×D₇	C₂³	1	2	yes	—
52	C₂²×C₃×D₇	C₂³	1	2	yes	—
53	C₃×C₇×D₄	—	2	4	no	—
54	C₃×C₇×D₄	—	4	1	no	—
55	C₂×C₃×C₄×C₇	—	4	1	no	—
56	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
57	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₃×C₂²⋊D₇	—	2	4	no	—
60	C₃×C₂²⋊D₇	—	2	4	no	—
61	C₃×C₂²⋊D₇	—	4	2	no	—
62	C₂×C₃×Dic₇	—	4	1	no	—
63	C₂×C₃×Dic₇	C₂³	1	2	yes	—
64	C₂×C₃×Dic₇	C₂³	1	2	yes	—
65	C₃×D₂₈	—	2	4	no	—
66	C₃×D₂₈	—	4	1	no	—
67	C₃×C₄×D₇	—	2	4	no	—
68	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
69	C₂³×D₇	C₂²×C₃	1	2	yes	complemented
70	C₂×C₇×D₄	C₂²×C₃	1	2	yes	complemented
71	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
72	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
73	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
74	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
75	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
76	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
77	D₄×D₇	—	2	8	no	—
78	C₂×D₂₈	C₂²×C₃	1	2	yes	—
79	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
80	C₂×C₄×D₇	C₂²×C₃	1	2	yes	complemented
81	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
82	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
83	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
84	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
85	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
86	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
87	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
88	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
89	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
90	C₂²×C₃×D₄	—	7	2	no	—
91	C₃×#123	—	7	2	no	—
92	C₃×#123	—	7	2	no	—
93	C₃×#121	—	7	2	no	—
94	C₃×#121	—	7	1	no	—
95	C₃×#121	D₇	1	1	yes	characteristic, complemented
96	C₃×#120	—	7	2	no	—
97	C₃×#120	—	7	2	no	—
98	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
99	C₂²×C₃×C₇	—	2	1	no	—
100	C₂²×C₃×C₇	—	2	1	no	—
101	C₂²×C₃×C₇	—	2	2	no	—
102	C₂²×C₃×C₇	—	2	2	no	—
103	C₂²×C₃×C₇	—	2	2	no	—
104	C₂²×C₃×C₇	C₂×D₄	1	2	yes	—
105	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
106	C₂×C₃×D₇	—	2	2	no	—
107	C₂×C₃×D₇	—	2	2	no	—
108	C₂×C₃×D₇	—	2	2	no	—
109	C₂×C₃×D₇	—	2	2	no	—
110	C₂×C₃×D₇	—	2	2	no	—
111	C₂×C₃×D₇	—	4	4	no	—
112	C₂×C₃×D₇	—	4	8	no	—
113	C₂×C₃×D₇	C₂×D₄	1	4	yes	—
114	C₃×C₄×C₇	—	2	2	no	—
115	C₃×C₄×C₇	—	2	1	no	—
116	C₃×C₄×C₇	—	2	1	no	—
117	C₃×Dic₇	—	2	2	no	—
118	C₃×Dic₇	—	2	2	no	—
119	#534	—	7	1	no	Sylow
120	C₂³×C₇	C₂³×C₃	1	2	yes	—
121	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
122	C₂²×D₇	—	2	4	no	—
123	C₂²×D₇	—	4	1	no	—
124	C₂²×D₇	—	4	1	no	—
125	C₂²×D₇	—	4	2	no	—
126	C₂²×D₇	—	4	2	no	—
127	C₂²×D₇	C₃×D₄	1	4	yes	complemented
128	C₂²×D₇	C₂³×C₃	1	2	yes	—
129	C₂²×D₇	C₂³×C₃	1	2	yes	—
130	C₇×D₄	—	2	4	no	—
131	C₇×D₄	—	4	1	no	—
132	C₂×C₄×C₇	—	4	1	no	—
133	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
134	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
135	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
136	C₂²⋊D₇	—	2	4	no	—
137	C₂²⋊D₇	—	2	4	no	—
138	C₂²⋊D₇	—	4	2	no	—
139	C₂×Dic₇	—	4	1	no	—
140	C₂×Dic₇	C₂³×C₃	1	2	yes	—
141	C₂×Dic₇	C₂³×C₃	1	2	yes	—
142	D₂₈	—	2	4	no	—
143	D₂₈	—	4	1	no	—
144	C₄×D₇	—	2	4	no	—
145	C₂⁴×C₃	—	7	1	no	—
146	C₂⁴×C₃	—	7	2	no	—
147	C₂×C₃×D₄	—	7	2	no	—
148	C₂×C₃×D₄	—	7	2	no	—
149	C₂×C₃×D₄	—	7	2	no	—
150	C₂×C₃×D₄	—	7	2	no	—
151	C₂×C₃×D₄	—	7	1	no	—
152	C₂×C₃×D₄	—	14	8	no	—
153	C₂×C₃×D₄	C₂×D₇	1	2	yes	complemented
154	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic, complemented
155	C₂²×C₃×C₄	—	7	1	no	—
156	C₂²×C₃×C₄	—	7	2	no	—
157	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic, complemented
158	C₃×C₄⋊C₄	—	7	2	no	—
159	C₃×C₄⋊C₄	—	7	1	no	—
160	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
161	C₃×C₂²⋊C₄	—	7	2	no	—
162	C₃×C₂²⋊C₄	—	7	2	no	—
163	C₃×C₂²⋊C₄	—	7	2	no	—
164	C₃×C₂²⋊C₄	—	7	2	no	—
165	C₃×C₂²⋊C₄	—	7	2	no	—
166	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	complemented
167	C₂×C₃×C₇	—	2	2	no	—
168	C₂×C₃×C₇	—	4	2	no	—
169	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
172	C₃×D₇	—	2	4	no	—
173	C₃×D₇	—	4	2	no	—
174	C₂²×D₄	—	7	2	no	—
175	#123	—	7	2	no	—
176	#123	—	7	2	no	—
177	#121	—	7	2	no	—
178	#121	—	7	1	no	—
179	#121	C₃×D₇	1	1	yes	characteristic, complemented
180	#120	—	7	2	no	—
181	#120	—	7	2	no	—
182	C₂×C₂²⋊C₄	—	7	1	no	—
183	C₂²×C₇	—	2	1	no	—
184	C₂²×C₇	—	2	1	no	—
185	C₂²×C₇	—	2	2	no	—
186	C₂²×C₇	—	2	2	no	—
187	C₂²×C₇	—	2	2	no	—
188	C₂²×C₇	C₂×C₃×D₄	1	2	yes	—
189	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
190	C₂×D₇	—	2	2	no	—
191	C₂×D₇	—	2	2	no	—
192	C₂×D₇	—	2	2	no	—
193	C₂×D₇	—	2	2	no	—
194	C₂×D₇	—	2	2	no	—
195	C₂×D₇	—	4	4	no	—
196	C₂×D₇	—	4	8	no	—
197	C₂×D₇	C₂×C₃×D₄	1	4	yes	—
198	C₄×C₇	—	2	2	no	—
199	C₄×C₇	—	2	1	no	—
200	C₄×C₇	—	2	1	no	—
201	Dic₇	—	2	2	no	—
202	Dic₇	—	2	2	no	—
203	C₂³×C₃	—	7	2	no	—
204	C₂³×C₃	—	7	4	no	—
205	C₂³×C₃	—	7	2	no	—
206	C₂³×C₃	—	14	4	no	—
207	C₂³×C₃	—	28	1	no	—
208	C₂³×C₃	—	28	1	no	—
209	C₂³×C₃	—	28	2	no	—
210	C₂³×C₃	—	28	2	no	—
211	C₂³×C₃	C₂²×D₇	1	2	yes	—
212	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
213	C₃×D₄	—	2	4	no	—
214	C₃×D₄	—	4	1	no	—
215	C₃×D₄	—	14	4	no	—
216	C₃×D₄	—	14	4	no	—
217	C₃×D₄	—	14	4	no	—
218	C₃×D₄	—	28	1	no	—
219	C₃×D₄	—	28	2	no	—
220	C₂×C₃×C₄	—	4	1	no	—
221	C₂×C₃×C₄	—	7	2	no	—
222	C₂×C₃×C₄	—	7	2	no	—
223	C₂×C₃×C₄	—	14	4	no	—
224	C₂×C₃×C₄	—	28	1	no	—
225	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
228	C₃×C₇	#534	1	1	yes	characteristic, complemented, Hall
229	C₂⁴	—	7	1	no	—
230	C₂⁴	—	7	2	no	—
231	C₂×D₄	—	7	2	no	—
232	C₂×D₄	—	7	2	no	—
233	C₂×D₄	—	7	2	no	—
234	C₂×D₄	—	7	2	no	—
235	C₂×D₄	—	7	1	no	—
236	C₂×D₄	—	14	8	no	—
237	C₂×D₄	C₂×C₃×D₇	1	2	yes	complemented
238	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
239	C₂²×C₄	—	7	1	no	—
240	C₂²×C₄	—	7	2	no	—
241	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
242	C₄⋊C₄	—	7	2	no	—
243	C₄⋊C₄	—	7	1	no	—
244	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
245	C₂²⋊C₄	—	7	2	no	—
246	C₂²⋊C₄	—	7	2	no	—
247	C₂²⋊C₄	—	7	2	no	—
248	C₂²⋊C₄	—	7	2	no	—
249	C₂²⋊C₄	—	7	2	no	—
250	C₂²⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
251	C₂×C₇	—	2	2	no	—
252	C₂×C₇	—	4	2	no	—
253	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
254	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
255	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
256	D₇	—	2	4	no	—
257	D₇	—	4	2	no	—
258	C₂²×C₃	—	2	1	no	—
259	C₂²×C₃	—	2	1	no	—
260	C₂²×C₃	—	2	2	no	—
261	C₂²×C₃	—	2	2	no	—
262	C₂²×C₃	—	2	2	no	—
263	C₂²×C₃	—	7	4	no	—
264	C₂²×C₃	—	14	2	no	—
265	C₂²×C₃	—	14	2	no	—
266	C₂²×C₃	—	14	2	no	—
267	C₂²×C₃	—	14	2	no	—
268	C₂²×C₃	—	14	2	no	—
269	C₂²×C₃	—	28	4	no	—
270	C₂²×C₃	—	28	8	no	—
271	C₂²×C₃	D₄×D₇	1	2	yes	—
272	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
273	C₃×C₄	—	2	2	no	—
274	C₃×C₄	—	2	1	no	—
275	C₃×C₄	—	2	1	no	—
276	C₃×C₄	—	14	2	no	—
277	C₃×C₄	—	14	2	no	—
278	C₂³	—	7	2	no	—
279	C₂³	—	7	4	no	—
280	C₂³	—	7	2	no	—
281	C₂³	—	14	4	no	—
282	C₂³	—	28	1	no	—
283	C₂³	—	28	1	no	—
284	C₂³	—	28	2	no	—
285	C₂³	—	28	2	no	—
286	C₂³	C₂²×C₃×D₇	1	2	yes	—
287	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
288	D₄	—	2	4	no	—
289	D₄	—	4	1	no	—
290	D₄	—	14	4	no	—
291	D₄	—	14	4	no	—
292	D₄	—	14	4	no	—
293	D₄	—	28	1	no	—
294	D₄	—	28	2	no	—
295	C₂×C₄	—	4	1	no	—
296	C₂×C₄	—	7	2	no	—
297	C₂×C₄	—	7	2	no	—
298	C₂×C₄	—	14	4	no	—
299	C₂×C₄	—	28	1	no	—
300	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
301	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
302	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
303	C₇	C₃×#534	1	1	yes	characteristic, complemented, Sylow
304	C₂×C₃	—	2	2	no	—
305	C₂×C₃	—	4	2	no	—
306	C₂×C₃	—	14	4	no	—
307	C₂×C₃	—	28	2	no	—
308	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
309	C₂×C₃	#6548	1	1	yes	characteristic
310	C₂×C₃	#6553	1	1	yes	characteristic
311	C₂²	—	2	1	no	—
312	C₂²	—	2	1	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	7	4	no	—
317	C₂²	—	14	2	no	—
318	C₂²	—	14	2	no	—
319	C₂²	—	14	2	no	—
320	C₂²	—	14	2	no	—
321	C₂²	—	14	2	no	—
322	C₂²	—	28	4	no	—
323	C₂²	—	28	8	no	—
324	C₂²	C₃×D₄×D₇	1	2	yes	—
325	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
326	C₄	—	2	2	no	—
327	C₄	—	2	1	no	—
328	C₄	—	2	1	no	—
329	C₄	—	14	2	no	—
330	C₄	—	14	2	no	—
331	C₃	#90296	1	1	yes	characteristic, direct product factor, Sylow
332	C₂	—	2	2	no	—
333	C₂	—	4	2	no	—
334	C₂	—	14	4	no	—
335	C₂	—	28	2	no	—
336	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
337	C₂	C₃×#6548	1	1	yes	characteristic
338	C₂	C₃×#6553	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×#121	C₂
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₃×#121	D₇
hypocenter	C₇	C₃×#534
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄×D₇	C₂	semidirect
2. C₃×C₇×#121	C₂	semidirect
3. C₃×#6502	C₂	semidirect
4. C₃×#6500	C₂	semidirect
5. C₃×#6493	C₂	semidirect
6. C₂×C₃×(C₂×D₇)⋊C₄	C₂	semidirect
7. C₃×#6457	C₂	semidirect
8. C₃×#6446	C₂	semidirect
9. C₃×#6445	C₂	semidirect
10. #90296	C₃	direct (N × H)
12. C₂³×C₃×D₇	C₂²	semidirect
13. C₂×C₃×C₇×D₄	C₂²	semidirect
14. C₂×C₃×C₇×D₄	C₂²	semidirect
15. C₂²×C₃×C₄×C₇	C₂²	semidirect
17. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
18. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
19. C₂²×C₃×Dic₇	C₂²	semidirect
22. C₂×C₃×D₂₈	C₂²	semidirect
23. C₂×C₃×C₄×D₇	C₂²	semidirect
24. C₃×C₇×C₄⋊C₄	C₂²	semidirect
25. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
26. C₃×C₂²⋊Dic₇	C₂²	semidirect
27. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
28. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
29. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
30. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
31. C₃×C₄⋊Dic₇	C₂²	semidirect
32. C₃×Dic₇⋊C₄	C₂²	semidirect
33. C₂×D₄×D₇	C₂×C₃	semidirect
34. C₇×#121	C₂×C₃	semidirect
35. #6502	C₂×C₃	semidirect
36. #6500	C₂×C₃	semidirect
37. #6493	C₂×C₃	semidirect
38. C₂×(C₂×D₇)⋊C₄	C₂×C₃	semidirect
39. #6457	C₂×C₃	semidirect
40. #6446	C₂×C₃	semidirect
41. #6445	C₂×C₃	semidirect
50. C₂²×C₃×D₇	D₄	semidirect
69. C₂³×D₇	C₂²×C₃	semidirect
70. C₂×C₇×D₄	C₂²×C₃	semidirect
71. C₂×C₇×D₄	C₂²×C₃	semidirect
72. C₂²×C₄×C₇	C₂²×C₃	semidirect
74. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
75. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
76. C₂²×Dic₇	C₂²×C₃	semidirect
79. C₂×D₂₈	C₂²×C₃	semidirect
80. C₂×C₄×D₇	C₂²×C₃	semidirect
81. C₇×C₄⋊C₄	C₂²×C₃	semidirect
82. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
83. C₂²⋊Dic₇	C₂²×C₃	semidirect
84. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
85. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
86. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
87. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
88. C₄⋊Dic₇	C₂²×C₃	semidirect
89. Dic₇⋊C₄	C₂²×C₃	semidirect
95. C₃×#121	D₇	semidirect
127. C₂²×D₇	C₃×D₄	semidirect
153. C₂×C₃×D₄	C₂×D₇	semidirect
154. C₂×C₃×D₄	C₂×D₇	semidirect
157. C₂²×C₃×C₄	C₂×D₇	semidirect
160. C₃×C₄⋊C₄	C₂×D₇	semidirect
166. C₃×C₂²⋊C₄	C₂×D₇	semidirect
179. #121	C₃×D₇	semidirect
228. C₃×C₇	#534	semidirect
237. C₂×D₄	C₂×C₃×D₇	semidirect
238. C₂×D₄	C₂×C₃×D₇	semidirect
241. C₂²×C₄	C₂×C₃×D₇	semidirect
244. C₄⋊C₄	C₂×C₃×D₇	semidirect
250. C₂²⋊C₄	C₂×C₃×D₇	semidirect
303. C₇	C₃×#534	semidirect
331. C₃	#90296	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×D₄×D₇	2
C₃×C₇×#121	2
C₃×#6502	2
C₃×#6500	2
C₃×#6493	2
C₂×C₃×(C₂×D₇)⋊C₄	2
C₃×#6457	2
C₃×#6446	2
C₃×#6445	2
#90296	3
C₃×#534	7

Subgroups — C3×#90296 #13060949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90296 #13060949