Subgroups — C₃×#90236 #13060889

Order 1344.

676 conjugacy classes of subgroups.

The subgroup lattice has 336 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	1	yes	maximal, characteristic
2	C₃×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₄×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₂²⋊D₇	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×(C₂×D₇)⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₃×#6456	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#6455	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×(C₂²⋊D₇)⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₃×D₇×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6435	C₂	1	1	yes	maximal, characteristic, complemented
12	#90236	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₇	C₂²	1	2	yes	—
14	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₇	C₂²	1	2	yes	complemented
16	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	—
17	C₂²×C₃×Dic₇	C₂²	1	2	yes	complemented
18	C₃×D₄×D₇	C₄	1	8	yes	complemented
19	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄×D₇	C₂²	1	2	yes	complemented
22	C₂×C₃×C₄×D₇	C₂²	1	2	yes	complemented
23	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
25	C₃×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₂²⋊Dic₇	C₂²	1	2	yes	complemented
27	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
29	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
31	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
32	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
33	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₄×Dic₇	C₂²	1	2	yes	complemented
36	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×D₄×D₇	C₂×C₃	1	1	yes	characteristic
38	C₄×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
39	D₄×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
40	C₄×C₂²⋊D₇	C₂×C₃	1	2	yes	complemented
41	C₂×(C₂×D₇)⋊C₄	C₂×C₃	1	2	yes	complemented
42	#6456	C₂×C₃	1	1	yes	characteristic, complemented
43	#6455	C₂×C₃	1	1	yes	characteristic, complemented
44	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	2	yes	complemented
45	D₇×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
46	C₄×D₂₈	C₂×C₃	1	1	yes	characteristic, complemented
47	#6435	C₂×C₃	1	1	yes	characteristic, complemented
48	C₃×#518	—	7	1	no	maximal, Hall
49	C₂³×C₃×C₇	C₂³	1	2	yes	—
50	C₂²×C₃×D₇	—	4	2	no	—
51	C₂²×C₃×D₇	—	4	2	no	—
52	C₂²×C₃×D₇	C₂×C₄	1	8	yes	complemented
53	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
54	C₂²×C₃×D₇	C₂³	1	2	yes	—
55	C₃×C₇×D₄	C₂×C₄	1	4	yes	complemented
56	C₂×C₃×C₄×C₇	—	4	2	no	—
57	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
58	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₃×C₂²⋊D₇	C₂×C₄	1	8	yes	complemented
62	C₂×C₃×Dic₇	—	4	2	no	—
63	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
64	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
65	C₂×C₃×Dic₇	C₂³	1	2	yes	—
66	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
67	C₃×D₂₈	C₂×C₄	1	4	yes	complemented
68	C₃×C₄×D₇	—	4	2	no	—
69	C₃×C₄×D₇	—	4	2	no	—
70	C₃×C₄×D₇	C₂×C₄	1	4	yes	complemented
71	C₂³×D₇	C₂²×C₃	1	2	yes	—
72	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₄×C₇	C₂²×C₃	1	2	yes	complemented
74	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
75	C₂²×Dic₇	C₂²×C₃	1	2	yes	complemented
76	D₄×D₇	C₃×C₄	1	8	yes	complemented
77	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₄×D₇	C₂²×C₃	1	2	yes	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	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
84	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
85	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
88	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
89	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
90	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
91	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
92	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
93	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
94	C₄×Dic₇	C₂²×C₃	1	2	yes	complemented
95	C₂²×C₃×D₄	—	7	1	no	—
96	C₃×C₄×D₄	—	7	1	no	—
97	C₃×C₄×D₄	—	7	2	no	—
98	C₃×C₄×D₄	—	7	1	no	—
99	C₃×C₄×D₄	—	7	2	no	—
100	C₃×C₄×D₄	—	7	1	no	—
101	C₃×C₄×D₄	D₇	1	1	yes	characteristic, complemented
102	C₃×#117	—	7	1	no	—
103	C₃×#117	—	7	1	no	—
104	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
105	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
106	C₂²×C₃×C₇	—	2	2	no	—
107	C₂²×C₃×C₇	—	2	2	no	—
108	C₂²×C₃×C₇	C₂²×C₄	1	4	yes	—
109	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
110	C₂×C₃×D₇	—	2	2	no	—
111	C₂×C₃×D₇	—	2	2	no	—
112	C₂×C₃×D₇	—	2	1	no	—
113	C₂×C₃×D₇	—	2	1	no	—
114	C₂×C₃×D₇	—	4	8	no	—
115	C₂×C₃×D₇	C₂²×C₄	1	2	yes	—
116	C₂×C₃×D₇	C₂²×C₄	1	4	yes	—
117	C₃×C₄×C₇	—	2	1	no	—
118	C₃×C₄×C₇	—	2	2	no	—
119	C₃×C₄×C₇	—	2	1	no	—
120	C₃×C₄×C₇	C₂²×C₄	1	2	yes	—
121	C₃×Dic₇	—	2	1	no	—
122	C₃×Dic₇	—	2	2	no	—
123	C₃×Dic₇	—	2	1	no	—
124	C₃×Dic₇	C₂²×C₄	1	2	yes	—
125	#518	—	7	1	no	Sylow
126	C₂³×C₇	C₂³×C₃	1	2	yes	—
127	C₂²×D₇	—	4	2	no	—
128	C₂²×D₇	—	4	2	no	—
129	C₂²×D₇	C₂×C₃×C₄	1	8	yes	complemented
130	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
131	C₂²×D₇	C₂³×C₃	1	2	yes	—
132	C₇×D₄	C₂×C₃×C₄	1	4	yes	complemented
133	C₂×C₄×C₇	—	4	2	no	—
134	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
135	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
136	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
137	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
138	C₂²⋊D₇	C₂×C₃×C₄	1	8	yes	complemented
139	C₂×Dic₇	—	4	2	no	—
140	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
141	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
142	C₂×Dic₇	C₂³×C₃	1	2	yes	—
143	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
144	D₂₈	C₂×C₃×C₄	1	4	yes	complemented
145	C₄×D₇	—	4	2	no	—
146	C₄×D₇	—	4	2	no	—
147	C₄×D₇	C₂×C₃×C₄	1	4	yes	complemented
148	C₂⁴×C₃	—	7	2	no	—
149	C₂×C₃×D₄	—	7	2	no	—
150	C₂×C₃×D₄	—	7	8	no	—
151	C₂×C₃×D₄	—	7	1	no	—
152	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
153	C₂²×C₃×C₄	—	7	1	no	—
154	C₂²×C₃×C₄	—	7	2	no	—
155	C₂²×C₃×C₄	—	7	2	no	—
156	C₂²×C₃×C₄	—	7	2	no	—
157	C₂²×C₃×C₄	C₂×D₇	1	2	yes	complemented
158	C₃×C₄⋊C₄	—	7	1	no	—
159	C₃×C₄⋊C₄	—	7	1	no	—
160	C₃×C₄⋊C₄	—	7	1	no	—
161	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
162	C₃×C₂²⋊C₄	—	7	2	no	—
163	C₃×C₂²⋊C₄	—	7	2	no	—
164	C₃×C₂²⋊C₄	—	7	1	no	—
165	C₃×C₂²⋊C₄	—	7	1	no	—
166	C₃×C₂²⋊C₄	—	7	2	no	—
167	C₃×C₂²⋊C₄	—	7	2	no	—
168	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	complemented
169	C₃×C₄²	—	7	2	no	—
170	C₃×C₄²	—	7	1	no	—
171	C₃×C₄²	C₂×D₇	1	1	yes	characteristic, complemented
172	C₂×C₃×C₇	—	2	4	no	—
173	C₂×C₃×C₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
176	C₃×D₇	—	2	2	no	—
177	C₃×D₇	—	2	4	no	—
178	C₂²×D₄	—	7	1	no	—
179	C₄×D₄	—	7	1	no	—
180	C₄×D₄	—	7	2	no	—
181	C₄×D₄	—	7	1	no	—
182	C₄×D₄	—	7	2	no	—
183	C₄×D₄	—	7	1	no	—
184	C₄×D₄	C₃×D₇	1	1	yes	characteristic, complemented
185	#117	—	7	1	no	—
186	#117	—	7	1	no	—
187	C₂×C₂²⋊C₄	—	7	2	no	—
188	C₂×C₂²⋊C₄	—	7	2	no	—
189	C₂²×C₇	—	2	2	no	—
190	C₂²×C₇	—	2	2	no	—
191	C₂²×C₇	C₂²×C₃×C₄	1	4	yes	—
192	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
193	C₂×D₇	—	2	2	no	—
194	C₂×D₇	—	2	2	no	—
195	C₂×D₇	—	2	1	no	—
196	C₂×D₇	—	2	1	no	—
197	C₂×D₇	—	4	8	no	—
198	C₂×D₇	C₂²×C₃×C₄	1	2	yes	—
199	C₂×D₇	C₂²×C₃×C₄	1	4	yes	—
200	C₄×C₇	—	2	1	no	—
201	C₄×C₇	—	2	2	no	—
202	C₄×C₇	—	2	1	no	—
203	C₄×C₇	C₂²×C₃×C₄	1	2	yes	—
204	Dic₇	—	2	1	no	—
205	Dic₇	—	2	2	no	—
206	Dic₇	—	2	1	no	—
207	Dic₇	C₂²×C₃×C₄	1	2	yes	—
208	C₂³×C₃	—	7	1	no	—
209	C₂³×C₃	—	7	2	no	—
210	C₂³×C₃	—	7	8	no	—
211	C₂³×C₃	—	28	2	no	—
212	C₂³×C₃	—	28	2	no	—
213	C₂³×C₃	C₂²×D₇	1	2	yes	—
214	C₃×D₄	—	7	8	no	—
215	C₃×D₄	—	7	4	no	—
216	C₃×D₄	C₄×D₇	1	4	yes	complemented
217	C₂×C₃×C₄	—	4	2	no	—
218	C₂×C₃×C₄	—	7	1	no	—
219	C₂×C₃×C₄	—	7	4	no	—
220	C₂×C₃×C₄	—	7	1	no	—
221	C₂×C₃×C₄	—	7	1	no	—
222	C₂×C₃×C₄	—	7	2	no	—
223	C₂×C₃×C₄	—	28	2	no	—
224	C₂×C₃×C₄	—	28	2	no	—
225	C₂×C₃×C₄	—	28	2	no	—
226	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
227	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
230	C₃×C₇	#518	1	1	yes	characteristic, complemented, Hall
231	C₂⁴	—	7	2	no	—
232	C₂×D₄	—	7	2	no	—
233	C₂×D₄	—	7	8	no	—
234	C₂×D₄	—	7	1	no	—
235	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
236	C₂²×C₄	—	7	1	no	—
237	C₂²×C₄	—	7	2	no	—
238	C₂²×C₄	—	7	2	no	—
239	C₂²×C₄	—	7	2	no	—
240	C₂²×C₄	C₂×C₃×D₇	1	2	yes	complemented
241	C₄⋊C₄	—	7	1	no	—
242	C₄⋊C₄	—	7	1	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	1	no	—
248	C₂²⋊C₄	—	7	1	no	—
249	C₂²⋊C₄	—	7	2	no	—
250	C₂²⋊C₄	—	7	2	no	—
251	C₂²⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
252	C₄²	—	7	2	no	—
253	C₄²	—	7	1	no	—
254	C₄²	C₂×C₃×D₇	1	1	yes	characteristic, complemented
255	C₂×C₇	—	2	4	no	—
256	C₂×C₇	C₂³×C₃×C₄	1	1	yes	characteristic
257	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
258	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
259	D₇	—	2	2	no	—
260	D₇	—	2	4	no	—
261	C₂²×C₃	—	2	2	no	—
262	C₂²×C₃	—	2	2	no	—
263	C₂²×C₃	—	7	2	no	—
264	C₂²×C₃	—	7	4	no	—
265	C₂²×C₃	—	14	2	no	—
266	C₂²×C₃	—	14	1	no	—
267	C₂²×C₃	—	14	2	no	—
268	C₂²×C₃	—	14	1	no	—
269	C₂²×C₃	—	28	8	no	—
270	C₂²×C₃	C₂×C₄×D₇	1	4	yes	—
271	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
272	C₃×C₄	—	2	1	no	—
273	C₃×C₄	—	2	2	no	—
274	C₃×C₄	—	2	1	no	—
275	C₃×C₄	—	7	2	no	—
276	C₃×C₄	—	14	1	no	—
277	C₃×C₄	—	14	2	no	—
278	C₃×C₄	—	14	1	no	—
279	C₃×C₄	C₂×C₄×D₇	1	2	yes	—
280	C₂³	—	7	1	no	—
281	C₂³	—	7	2	no	—
282	C₂³	—	7	8	no	—
283	C₂³	—	28	2	no	—
284	C₂³	—	28	2	no	—
285	C₂³	C₂²×C₃×D₇	1	2	yes	—
286	D₄	—	7	8	no	—
287	D₄	—	7	4	no	—
288	D₄	C₃×C₄×D₇	1	4	yes	complemented
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	7	1	no	—
291	C₂×C₄	—	7	4	no	—
292	C₂×C₄	—	7	1	no	—
293	C₂×C₄	—	7	2	no	—
294	C₂×C₄	—	7	1	no	—
295	C₂×C₄	—	28	2	no	—
296	C₂×C₄	—	28	2	no	—
297	C₂×C₄	—	28	2	no	—
298	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
299	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
300	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
301	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
302	C₇	C₃×#518	1	1	yes	characteristic, complemented, Sylow
303	C₂×C₃	—	2	4	no	—
304	C₂×C₃	—	14	2	no	—
305	C₂×C₃	—	14	4	no	—
306	C₂×C₃	C₂²×C₄×D₇	1	1	yes	characteristic
307	C₂×C₃	#6548	1	1	yes	characteristic
308	C₂×C₃	#6553	1	1	yes	characteristic
309	C₂²	—	2	2	no	—
310	C₂²	—	2	2	no	—
311	C₂²	—	7	2	no	—
312	C₂²	—	7	4	no	—
313	C₂²	—	14	2	no	—
314	C₂²	—	14	1	no	—
315	C₂²	—	14	2	no	—
316	C₂²	—	14	1	no	—
317	C₂²	—	28	8	no	—
318	C₂²	C₂×C₃×C₄×D₇	1	4	yes	—
319	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
320	C₄	—	2	1	no	—
321	C₄	—	2	2	no	—
322	C₄	—	2	1	no	—
323	C₄	—	7	2	no	—
324	C₄	—	14	1	no	—
325	C₄	—	14	2	no	—
326	C₄	—	14	1	no	—
327	C₄	C₂×C₃×C₄×D₇	1	2	yes	—
328	C₃	#90236	1	1	yes	characteristic, direct product factor, Sylow
329	C₂	—	2	4	no	—
330	C₂	—	14	2	no	—
331	C₂	—	14	4	no	—
332	C₂	C₂²×C₃×C₄×D₇	1	1	yes	characteristic
333	C₂	C₃×#6548	1	1	yes	characteristic
334	C₂	C₃×#6553	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₇
commutator	C₂×C₇	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×D₇
Fitting	C₃×C₄×C₇×D₄	C₂
socle	C₂²×C₃×C₇	C₂⁴
prime radical	C₂×C₃×D₄×D₇	C₂
cosocle	C₂²×C₇	C₂⁴×C₃
hypercenter	C₃×C₄×D₄	D₇
hypocenter	C₇	C₃×#518
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₇×D₄	C₂	semidirect
3. C₃×D₄×Dic₇	C₂	semidirect
4. C₃×C₄×C₂²⋊D₇	C₂	semidirect
5. C₂×C₃×(C₂×D₇)⋊C₄	C₂	semidirect
6. C₃×#6456	C₂	semidirect
7. C₃×#6455	C₂	semidirect
8. C₃×(C₂²⋊D₇)⋊C₄	C₂	semidirect
9. C₃×D₇×C₂²⋊C₄	C₂	semidirect
10. C₃×C₄×D₂₈	C₂	semidirect
11. C₃×#6435	C₂	semidirect
12. #90236	C₃	direct (N × H)
15. C₂²×C₃×C₄×C₇	C₂²	semidirect
17. C₂²×C₃×Dic₇	C₂²	semidirect
18. C₃×D₄×D₇	C₄	semidirect
21. C₂×C₃×C₄×D₇	C₂²	semidirect
22. C₂×C₃×C₄×D₇	C₂²	semidirect
23. C₃×C₇×C₄⋊C₄	C₂²	semidirect
24. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
25. C₃×C₄²×C₇	C₂²	semidirect
26. C₃×C₂²⋊Dic₇	C₂²	semidirect
30. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
31. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
32. C₃×C₄⋊Dic₇	C₂²	semidirect
33. C₃×Dic₇⋊C₄	C₂²	semidirect
34. C₃×Dic₇⋊C₄	C₂²	semidirect
35. C₃×C₄×Dic₇	C₂²	semidirect
36. C₃×C₄×Dic₇	C₂²	semidirect
38. C₄×C₇×D₄	C₂×C₃	semidirect
39. D₄×Dic₇	C₂×C₃	semidirect
40. C₄×C₂²⋊D₇	C₂×C₃	semidirect
41. C₂×(C₂×D₇)⋊C₄	C₂×C₃	semidirect
42. #6456	C₂×C₃	semidirect
43. #6455	C₂×C₃	semidirect
44. (C₂²⋊D₇)⋊C₄	C₂×C₃	semidirect
45. D₇×C₂²⋊C₄	C₂×C₃	semidirect
46. C₄×D₂₈	C₂×C₃	semidirect
47. #6435	C₂×C₃	semidirect
52. C₂²×C₃×D₇	C₂×C₄	semidirect
55. C₃×C₇×D₄	C₂×C₄	semidirect
61. C₃×C₂²⋊D₇	C₂×C₄	semidirect
67. C₃×D₂₈	C₂×C₄	semidirect
70. C₃×C₄×D₇	C₂×C₄	semidirect
73. C₂²×C₄×C₇	C₂²×C₃	semidirect
75. C₂²×Dic₇	C₂²×C₃	semidirect
76. D₄×D₇	C₃×C₄	semidirect
79. C₂×C₄×D₇	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. C₄²×C₇	C₂²×C₃	semidirect
84. C₂²⋊Dic₇	C₂²×C₃	semidirect
88. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
89. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
90. C₄⋊Dic₇	C₂²×C₃	semidirect
91. Dic₇⋊C₄	C₂²×C₃	semidirect
92. Dic₇⋊C₄	C₂²×C₃	semidirect
93. C₄×Dic₇	C₂²×C₃	semidirect
94. C₄×Dic₇	C₂²×C₃	semidirect
101. C₃×C₄×D₄	D₇	semidirect
129. C₂²×D₇	C₂×C₃×C₄	semidirect
132. C₇×D₄	C₂×C₃×C₄	semidirect
138. C₂²⋊D₇	C₂×C₃×C₄	semidirect
144. D₂₈	C₂×C₃×C₄	semidirect
147. C₄×D₇	C₂×C₃×C₄	semidirect
157. C₂²×C₃×C₄	C₂×D₇	semidirect
161. C₃×C₄⋊C₄	C₂×D₇	semidirect
168. C₃×C₂²⋊C₄	C₂×D₇	semidirect
171. C₃×C₄²	C₂×D₇	semidirect
184. C₄×D₄	C₃×D₇	semidirect
216. C₃×D₄	C₄×D₇	semidirect
230. C₃×C₇	#518	semidirect
240. C₂²×C₄	C₂×C₃×D₇	semidirect
244. C₄⋊C₄	C₂×C₃×D₇	semidirect
251. C₂²⋊C₄	C₂×C₃×D₇	semidirect
254. C₄²	C₂×C₃×D₇	semidirect
288. D₄	C₃×C₄×D₇	semidirect
302. C₇	C₃×#518	semidirect
328. C₃	#90236	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×C₄×C₇×D₄	2
C₃×D₄×Dic₇	2
C₃×C₄×C₂²⋊D₇	2
C₂×C₃×(C₂×D₇)⋊C₄	2
C₃×#6456	2
C₃×#6455	2
C₃×(C₂²⋊D₇)⋊C₄	2
C₃×D₇×C₂²⋊C₄	2
C₃×C₄×D₂₈	2
C₃×#6435	2
#90236	3
C₃×#518	7

Subgroups — C3×#90236 #13060889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90236 #13060889