Subgroups — C₃×#90347 #13060990

Order 1344.

660 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1159	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6459	C₂	1	2	yes	maximal, complemented
7	C₃×#6456	C₂	1	2	yes	maximal, complemented
8	C₃×#6447	C₂	1	2	yes	maximal, complemented
9	C₃×#6445	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×(C₂²⋊D₇)⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₃×#6440	C₂	1	1	yes	maximal, characteristic, complemented
12	#90347	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	—
17	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
20	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
21	C₃×#1159	—	2	4	no	—
22	C₂×C₃×D₂₈	C₂²	1	2	yes	—
23	C₂×C₃×C₄×D₇	—	2	4	no	—
24	C₂×C₃×C₄×D₇	C₂²	1	2	yes	—
25	C₂×C₃×C₄×D₇	C₂²	1	2	yes	—
26	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
29	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
31	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
32	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
33	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
34	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
35	C₃×Dic₇⋊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	C₂×#1159	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂²×C₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
40	C₇×#123	C₂×C₃	1	1	yes	characteristic, complemented
41	#6500	C₂×C₃	1	1	yes	characteristic, complemented
42	#6492	C₂×C₃	1	1	yes	characteristic, complemented
43	#6459	C₂×C₃	1	2	yes	complemented
44	#6456	C₂×C₃	1	2	yes	complemented
45	#6447	C₂×C₃	1	2	yes	complemented
46	#6445	C₂×C₃	1	1	yes	characteristic, complemented
47	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	2	yes	complemented
48	#6440	C₂×C₃	1	1	yes	characteristic, complemented
49	C₃×#525	—	7	1	no	maximal, Hall
50	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
51	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
52	C₂²×C₃×D₇	—	2	2	no	—
53	C₂²×C₃×D₇	—	2	4	no	—
54	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
55	C₂²×C₃×D₇	C₂³	1	2	yes	—
56	C₃×C₇×D₄	—	2	2	no	—
57	C₂×C₃×C₄×C₇	—	2	2	no	—
58	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
59	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
60	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₃×C₂²⋊D₇	—	2	2	no	—
62	C₃×C₂²⋊D₇	—	2	4	no	—
63	C₃×C₂²⋊D₇	—	2	2	no	—
64	C₂×C₃×Dic₇	—	2	2	no	—
65	C₂×C₃×Dic₇	D₄	1	4	yes	complemented
66	C₂×C₃×Dic₇	C₂³	1	2	yes	—
67	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
68	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
69	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
70	C₃×D₂₈	—	2	4	no	—
71	C₃×C₄×D₇	—	2	4	no	—
72	C₃×C₄×D₇	—	2	4	no	—
73	C₃×C₄×D₇	—	2	2	no	—
74	C₃×Dic₁₄	—	2	2	no	—
75	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
79	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic, complemented
81	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
82	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
83	#1159	—	2	4	no	—
84	C₂×D₂₈	C₂²×C₃	1	2	yes	—
85	C₂×C₄×D₇	—	2	4	no	—
86	C₂×C₄×D₇	C₂²×C₃	1	2	yes	—
87	C₂×C₄×D₇	C₂²×C₃	1	2	yes	—
88	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
89	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic, complemented
90	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
91	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
93	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
94	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
95	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
96	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
97	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
98	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
99	C₄×Dic₇	C₂²×C₃	1	2	yes	complemented
100	C₂×C₃×#41	—	7	1	no	—
101	C₂³×C₃×C₄	—	7	1	no	—
102	C₃×#123	—	7	1	no	—
103	C₃×#123	D₇	1	1	yes	characteristic, complemented
104	C₃×C₂²⋊Q₈	—	7	2	no	—
105	C₃×#121	—	7	2	no	—
106	C₃×#120	—	7	1	no	—
107	C₃×#120	—	7	1	no	—
108	C₃×C₄×D₄	—	7	2	no	—
109	C₃×C₄×D₄	—	7	2	no	—
110	C₃×#117	—	7	1	no	—
111	C₂²×C₃×C₇	—	2	2	no	—
112	C₂²×C₃×C₇	—	2	1	no	—
113	C₂²×C₃×C₇	—	2	2	no	—
114	C₂²×C₃×C₇	C₂×D₄	1	2	yes	—
115	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
116	C₂×C₃×D₇	—	2	8	no	—
117	C₂×C₃×D₇	—	2	2	no	—
118	C₂×C₃×D₇	—	2	2	no	—
119	C₂×C₃×D₇	—	2	1	no	—
120	C₂×C₃×D₇	—	2	2	no	—
121	C₂×C₃×D₇	#41	1	4	yes	complemented
122	C₃×C₄×C₇	—	2	1	no	—
123	C₃×C₄×C₇	—	2	2	no	—
124	C₃×C₄×C₇	—	2	2	no	—
125	C₃×Dic₇	—	2	1	no	—
126	C₃×Dic₇	—	2	2	no	—
127	C₃×Dic₇	C₂×D₄	1	2	yes	—
128	C₃×Dic₇	C₂×D₄	1	2	yes	—
129	#525	—	7	1	no	Sylow
130	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
131	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
132	C₂²×D₇	—	2	2	no	—
133	C₂²×D₇	—	2	4	no	—
134	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
135	C₂²×D₇	C₂³×C₃	1	2	yes	—
136	C₇×D₄	—	2	2	no	—
137	C₂×C₄×C₇	—	2	2	no	—
138	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
139	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
140	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
141	C₂²⋊D₇	—	2	2	no	—
142	C₂²⋊D₇	—	2	4	no	—
143	C₂²⋊D₇	—	2	2	no	—
144	C₂×Dic₇	—	2	2	no	—
145	C₂×Dic₇	C₃×D₄	1	4	yes	complemented
146	C₂×Dic₇	C₂³×C₃	1	2	yes	—
147	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
148	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
149	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
150	D₂₈	—	2	4	no	—
151	C₄×D₇	—	2	4	no	—
152	C₄×D₇	—	2	4	no	—
153	C₄×D₇	—	2	2	no	—
154	Dic₁₄	—	2	2	no	—
155	C₂⁴×C₃	—	7	1	no	—
156	C₃×#41	—	14	4	no	—
157	C₂×C₃×Q₈	—	7	1	no	—
158	C₂×C₃×D₄	—	7	2	no	—
159	C₂×C₃×D₄	—	7	1	no	—
160	C₂×C₃×D₄	—	7	1	no	—
161	C₂×C₃×D₄	—	7	2	no	—
162	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
163	C₂²×C₃×C₄	—	7	1	no	—
164	C₂²×C₃×C₄	—	7	1	no	—
165	C₂²×C₃×C₄	—	7	2	no	—
166	C₂²×C₃×C₄	—	7	2	no	—
167	C₂²×C₃×C₄	—	7	1	no	—
168	C₂²×C₃×C₄	—	14	4	no	—
169	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
170	C₃×C₄⋊C₄	—	7	2	no	—
171	C₃×C₄⋊C₄	—	7	2	no	—
172	C₃×C₄⋊C₄	C₂×D₇	1	2	yes	complemented
173	C₃×C₂²⋊C₄	—	7	1	no	—
174	C₃×C₂²⋊C₄	—	7	2	no	—
175	C₃×C₂²⋊C₄	—	7	2	no	—
176	C₃×C₂²⋊C₄	—	7	2	no	—
177	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
178	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	complemented
179	C₃×C₄²	—	7	2	no	—
180	C₂×C₃×C₇	—	2	2	no	—
181	C₂×C₃×C₇	—	4	1	no	—
182	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₃×C₇	C₂×#41	1	2	yes	—
184	C₃×D₇	—	2	4	no	—
185	C₃×D₇	—	4	1	no	—
186	C₂×#41	—	7	1	no	—
187	C₂³×C₄	—	7	1	no	—
188	#123	—	7	1	no	—
189	#123	C₃×D₇	1	1	yes	characteristic, complemented
190	C₂²⋊Q₈	—	7	2	no	—
191	#121	—	7	2	no	—
192	#120	—	7	1	no	—
193	#120	—	7	1	no	—
194	C₄×D₄	—	7	2	no	—
195	C₄×D₄	—	7	2	no	—
196	#117	—	7	1	no	—
197	C₂²×C₇	—	2	2	no	—
198	C₂²×C₇	—	2	1	no	—
199	C₂²×C₇	—	2	2	no	—
200	C₂²×C₇	C₂×C₃×D₄	1	2	yes	—
201	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
202	C₂×D₇	—	2	8	no	—
203	C₂×D₇	—	2	2	no	—
204	C₂×D₇	—	2	2	no	—
205	C₂×D₇	—	2	1	no	—
206	C₂×D₇	—	2	2	no	—
207	C₂×D₇	C₃×#41	1	4	yes	complemented
208	C₄×C₇	—	2	1	no	—
209	C₄×C₇	—	2	2	no	—
210	C₄×C₇	—	2	2	no	—
211	Dic₇	—	2	1	no	—
212	Dic₇	—	2	2	no	—
213	Dic₇	C₂×C₃×D₄	1	2	yes	—
214	Dic₇	C₂×C₃×D₄	1	2	yes	—
215	C₂³×C₃	—	7	2	no	—
216	C₂³×C₃	—	7	1	no	—
217	C₂³×C₃	—	14	4	no	—
218	C₂³×C₃	—	14	2	no	—
219	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
220	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
221	C₃×Q₈	—	14	2	no	—
222	C₃×D₄	—	2	2	no	—
223	C₃×D₄	—	14	4	no	—
224	C₃×D₄	—	14	2	no	—
225	C₃×D₄	—	14	4	no	—
226	C₃×D₄	—	14	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	7	4	no	—
229	C₂×C₃×C₄	—	7	1	no	—
230	C₂×C₃×C₄	—	7	1	no	—
231	C₂×C₃×C₄	—	7	2	no	—
232	C₂×C₃×C₄	—	7	1	no	—
233	C₂×C₃×C₄	—	14	4	no	—
234	C₂×C₃×C₄	—	14	4	no	—
235	C₂×C₃×C₄	—	14	2	no	—
236	C₂×C₃×C₄	—	14	2	no	—
237	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
238	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
240	C₃×C₇	#525	1	1	yes	characteristic, complemented, Hall
241	C₂⁴	—	7	1	no	—
242	#41	—	14	4	no	—
243	C₂×Q₈	—	7	1	no	—
244	C₂×D₄	—	7	2	no	—
245	C₂×D₄	—	7	1	no	—
246	C₂×D₄	—	7	1	no	—
247	C₂×D₄	—	7	2	no	—
248	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
249	C₂²×C₄	—	7	1	no	—
250	C₂²×C₄	—	7	1	no	—
251	C₂²×C₄	—	7	2	no	—
252	C₂²×C₄	—	7	1	no	—
253	C₂²×C₄	—	7	2	no	—
254	C₂²×C₄	—	14	4	no	—
255	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
256	C₄⋊C₄	—	7	2	no	—
257	C₄⋊C₄	—	7	2	no	—
258	C₄⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
259	C₂²⋊C₄	—	7	1	no	—
260	C₂²⋊C₄	—	7	2	no	—
261	C₂²⋊C₄	—	7	2	no	—
262	C₂²⋊C₄	—	7	2	no	—
263	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
264	C₂²⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
265	C₄²	—	7	2	no	—
266	C₂×C₇	—	2	2	no	—
267	C₂×C₇	—	4	1	no	—
268	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
269	C₂×C₇	C₂×C₃×#41	1	2	yes	—
270	D₇	—	2	4	no	—
271	D₇	—	4	1	no	—
272	C₂²×C₃	—	2	2	no	—
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	7	4	no	—
276	C₂²×C₃	—	14	8	no	—
277	C₂²×C₃	—	14	2	no	—
278	C₂²×C₃	—	14	2	no	—
279	C₂²×C₃	—	14	1	no	—
280	C₂²×C₃	—	14	2	no	—
281	C₂²×C₃	D₄×D₇	1	2	yes	—
282	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
283	C₃×C₄	—	2	2	no	—
284	C₃×C₄	—	2	1	no	—
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	—	7	2	no	—
287	C₃×C₄	—	7	2	no	—
288	C₃×C₄	—	14	1	no	—
289	C₃×C₄	—	14	2	no	—
290	C₂³	—	7	2	no	—
291	C₂³	—	7	1	no	—
292	C₂³	—	14	4	no	—
293	C₂³	—	14	2	no	—
294	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
295	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
296	Q₈	—	14	2	no	—
297	D₄	—	2	2	no	—
298	D₄	—	14	4	no	—
299	D₄	—	14	2	no	—
300	D₄	—	14	4	no	—
301	D₄	—	14	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	7	4	no	—
304	C₂×C₄	—	7	1	no	—
305	C₂×C₄	—	7	1	no	—
306	C₂×C₄	—	7	2	no	—
307	C₂×C₄	—	7	1	no	—
308	C₂×C₄	—	14	4	no	—
309	C₂×C₄	—	14	4	no	—
310	C₂×C₄	—	14	2	no	—
311	C₂×C₄	—	14	2	no	—
312	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
313	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
314	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
315	C₇	C₃×#525	1	1	yes	characteristic, complemented, Sylow
316	C₂×C₃	—	2	2	no	—
317	C₂×C₃	—	4	1	no	—
318	C₂×C₃	—	14	4	no	—
319	C₂×C₃	—	28	1	no	—
320	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
321	C₂×C₃	D₇×#41	1	2	yes	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	7	4	no	—
326	C₂²	—	14	8	no	—
327	C₂²	—	14	2	no	—
328	C₂²	—	14	2	no	—
329	C₂²	—	14	1	no	—
330	C₂²	—	14	2	no	—
331	C₂²	C₃×D₄×D₇	1	2	yes	—
332	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
333	C₄	—	2	2	no	—
334	C₄	—	2	1	no	—
335	C₄	—	2	2	no	—
336	C₄	—	7	2	no	—
337	C₄	—	7	2	no	—
338	C₄	—	14	1	no	—
339	C₄	—	14	2	no	—
340	C₃	#90347	1	1	yes	characteristic, direct product factor, Sylow
341	C₂	—	2	2	no	—
342	C₂	—	4	1	no	—
343	C₂	—	14	4	no	—
344	C₂	—	28	1	no	—
345	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
346	C₂	C₃×D₇×#41	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×#123	C₂
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₃×#123	D₇
hypocenter	C₇	C₃×#525
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#1159	C₂	semidirect
2. C₂²×C₃×C₄×D₇	C₂	semidirect
3. C₃×C₇×#123	C₂	semidirect
4. C₃×#6500	C₂	semidirect
5. C₃×#6492	C₂	semidirect
6. C₃×#6459	C₂	semidirect
7. C₃×#6456	C₂	semidirect
8. C₃×#6447	C₂	semidirect
9. C₃×#6445	C₂	semidirect
10. C₃×(C₂²⋊D₇)⋊C₄	C₂	semidirect
11. C₃×#6440	C₂	semidirect
12. #90347	C₃	direct (N × H)
18. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
20. C₂²×C₃×Dic₇	C₂²	semidirect
26. C₂×C₃×C₄×D₇	C₂²	semidirect
27. C₂×C₃×Dic₁₄	C₂²	semidirect
28. C₃×C₇×C₄⋊C₄	C₂²	semidirect
30. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
34. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
35. C₃×Dic₇⋊C₄	C₂²	semidirect
36. C₃×Dic₇⋊C₄	C₂²	semidirect
37. C₃×C₄×Dic₇	C₂²	semidirect
38. C₂×#1159	C₂×C₃	semidirect
39. C₂²×C₄×D₇	C₂×C₃	semidirect
40. C₇×#123	C₂×C₃	semidirect
41. #6500	C₂×C₃	semidirect
42. #6492	C₂×C₃	semidirect
43. #6459	C₂×C₃	semidirect
44. #6456	C₂×C₃	semidirect
45. #6447	C₂×C₃	semidirect
46. #6445	C₂×C₃	semidirect
47. (C₂²⋊D₇)⋊C₄	C₂×C₃	semidirect
48. #6440	C₂×C₃	semidirect
65. C₂×C₃×Dic₇	D₄	semidirect
80. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
82. C₂²×Dic₇	C₂²×C₃	semidirect
88. C₂×C₄×D₇	C₂²×C₃	semidirect
89. C₂×Dic₁₄	C₂²×C₃	semidirect
90. C₇×C₄⋊C₄	C₂²×C₃	semidirect
92. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
96. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
97. Dic₇⋊C₄	C₂²×C₃	semidirect
98. Dic₇⋊C₄	C₂²×C₃	semidirect
99. C₄×Dic₇	C₂²×C₃	semidirect
103. C₃×#123	D₇	semidirect
121. C₂×C₃×D₇	#41	semidirect
145. C₂×Dic₇	C₃×D₄	semidirect
172. C₃×C₄⋊C₄	C₂×D₇	semidirect
178. C₃×C₂²⋊C₄	C₂×D₇	semidirect
189. #123	C₃×D₇	semidirect
207. C₂×D₇	C₃×#41	semidirect
240. C₃×C₇	#525	semidirect
258. C₄⋊C₄	C₂×C₃×D₇	semidirect
264. C₂²⋊C₄	C₂×C₃×D₇	semidirect
315. C₇	C₃×#525	semidirect
340. C₃	#90347	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×#1159	2
C₂²×C₃×C₄×D₇	2
C₃×C₇×#123	2
C₃×#6500	2
C₃×#6492	2
C₃×#6459	2
C₃×#6456	2
C₃×#6447	2
C₃×#6445	2
C₃×(C₂²⋊D₇)⋊C₄	2
C₃×#6440	2
#90347	3
C₃×#525	7

Subgroups — C3×#90347 #13060990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90347 #13060990