Subgroups — C₃×#90298 #13060951

Order 1344.

668 conjugacy classes of subgroups.

The subgroup lattice has 388 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, complemented
2	C₂×C₃×#1157	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6503	C₂	1	2	yes	maximal, complemented
5	C₃×#6501	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6500	C₂	1	2	yes	maximal, complemented
7	C₃×#6493	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#6458	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#6455	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6448	C₂	1	2	yes	maximal, complemented
11	C₃×#6445	C₂	1	2	yes	maximal, complemented
12	#90298	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	C₂×C₃×C₇×D₄	C₂²	1	2	yes	complemented
16	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	—
18	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
21	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
22	C₃×D₄×D₇	—	2	4	no	—
23	C₃×#1157	—	2	4	no	—
24	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×D₂₈	C₂²	1	2	yes	complemented
27	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
32	C₃×C₂²⋊Dic₇	C₂²	1	2	yes	complemented
33	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
34	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
35	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
36	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×Dic₇	C₂²	1	2	yes	complemented
38	C₂×D₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#1157	C₂×C₃	1	1	yes	characteristic, complemented
40	C₇×#121	C₂×C₃	1	1	yes	characteristic, complemented
41	#6503	C₂×C₃	1	2	yes	complemented
42	#6501	C₂×C₃	1	1	yes	characteristic, complemented
43	#6500	C₂×C₃	1	2	yes	complemented
44	#6493	C₂×C₃	1	1	yes	characteristic, complemented
45	#6458	C₂×C₃	1	1	yes	characteristic, complemented
46	#6455	C₂×C₃	1	1	yes	characteristic, complemented
47	#6448	C₂×C₃	1	2	yes	complemented
48	#6445	C₂×C₃	1	2	yes	complemented
49	C₃×#535	—	7	1	no	maximal, Hall
50	C₂³×C₃×C₇	C₂³	1	2	yes	—
51	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
52	C₂²×C₃×D₇	—	2	4	no	—
53	C₂²×C₃×D₇	—	4	2	no	—
54	C₂²×C₃×D₇	—	4	2	no	—
55	C₂²×C₃×D₇	C₂³	1	2	yes	—
56	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
57	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
58	C₃×C₇×D₄	—	2	2	no	—
59	C₃×C₇×D₄	—	4	2	no	—
60	C₂×C₃×C₄×C₇	—	2	2	no	—
61	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
64	C₃×C₂²⋊D₇	—	2	2	no	—
65	C₃×C₂²⋊D₇	—	2	2	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	C₂³	1	2	yes	—
70	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
71	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
72	C₃×D₂₈	—	2	2	no	—
73	C₃×D₂₈	—	2	2	no	—
74	C₃×D₂₈	—	4	2	no	—
75	C₃×C₄×D₇	—	2	2	no	—
76	C₃×C₄×D₇	D₄	1	4	yes	complemented
77	C₃×Dic₁₄	—	2	2	no	—
78	C₂³×D₇	C₂²×C₃	1	2	yes	—
79	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₇×D₄	C₂²×C₃	1	2	yes	complemented
81	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
82	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
83	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic, complemented
85	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
86	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
87	D₄×D₇	—	2	4	no	—
88	#1157	—	2	4	no	—
89	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
90	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
91	C₂×D₂₈	C₂²×C₃	1	2	yes	complemented
92	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
94	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic, complemented
95	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
96	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
97	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
98	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
99	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
100	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
101	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, 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	1	no	—
108	C₃×#121	—	7	1	no	—
109	C₃×#121	—	7	1	no	—
110	C₃×#121	D₇	1	1	yes	characteristic, complemented
111	C₃×#120	—	7	2	no	—
112	C₃×#120	—	7	2	no	—
113	C₃×#117	—	7	1	no	—
114	C₂²×C₃×C₇	—	2	1	no	—
115	C₂²×C₃×C₇	—	2	2	no	—
116	C₂²×C₃×C₇	—	2	1	no	—
117	C₂²×C₃×C₇	—	2	2	no	—
118	C₂²×C₃×C₇	—	2	1	no	—
119	C₂²×C₃×C₇	—	2	2	no	—
120	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
121	C₂×C₃×D₇	—	2	1	no	—
122	C₂×C₃×D₇	—	2	1	no	—
123	C₂×C₃×D₇	—	2	1	no	—
124	C₂×C₃×D₇	—	2	2	no	—
125	C₂×C₃×D₇	—	2	1	no	—
126	C₂×C₃×D₇	—	2	2	no	—
127	C₂×C₃×D₇	—	2	1	no	—
128	C₂×C₃×D₇	—	2	2	no	—
129	C₂×C₃×D₇	—	4	8	no	—
130	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
131	C₃×C₄×C₇	—	2	1	no	—
132	C₃×C₄×C₇	—	2	2	no	—
133	C₃×C₄×C₇	C₂×D₄	1	2	yes	—
134	C₃×Dic₇	—	2	1	no	—
135	C₃×Dic₇	—	2	2	no	—
136	C₃×Dic₇	C₂×D₄	1	2	yes	—
137	#535	—	7	1	no	Sylow
138	C₂³×C₇	C₂³×C₃	1	2	yes	—
139	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
140	C₂²×D₇	—	2	4	no	—
141	C₂²×D₇	—	4	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	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
146	C₇×D₄	—	2	2	no	—
147	C₇×D₄	—	4	2	no	—
148	C₂×C₄×C₇	—	2	2	no	—
149	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
150	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
151	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
152	C₂²⋊D₇	—	2	2	no	—
153	C₂²⋊D₇	—	2	2	no	—
154	C₂²⋊D₇	—	2	4	no	—
155	C₂²⋊D₇	—	4	2	no	—
156	C₂²⋊D₇	—	4	2	no	—
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	D₂₈	—	2	2	no	—
161	D₂₈	—	2	2	no	—
162	D₂₈	—	4	2	no	—
163	C₄×D₇	—	2	2	no	—
164	C₄×D₇	C₃×D₄	1	4	yes	complemented
165	Dic₁₄	—	2	2	no	—
166	C₂⁴×C₃	—	7	2	no	—
167	C₃×#41	—	14	4	no	—
168	C₂×C₃×Q₈	—	7	1	no	—
169	C₂×C₃×D₄	—	7	1	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	1	no	—
175	C₂×C₃×D₄	—	7	1	no	—
176	C₂×C₃×D₄	—	7	2	no	—
177	C₂×C₃×D₄	—	14	4	no	—
178	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
179	C₂×C₃×D₄	C₂×D₇	1	2	yes	complemented
180	C₂²×C₃×C₄	—	7	1	no	—
181	C₂²×C₃×C₄	—	7	1	no	—
182	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic, complemented
183	C₃×C₄⋊C₄	—	7	1	no	—
184	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
185	C₃×C₂²⋊C₄	—	7	2	no	—
186	C₃×C₂²⋊C₄	—	7	2	no	—
187	C₃×C₂²⋊C₄	—	7	2	no	—
188	C₃×C₂²⋊C₄	—	7	2	no	—
189	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	complemented
190	C₃×C₄²	—	7	2	no	—
191	C₂×C₃×C₇	—	4	2	no	—
192	C₂×C₃×C₇	—	4	1	no	—
193	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
196	C₃×D₇	—	2	2	no	—
197	C₃×D₇	—	4	1	no	—
198	C₃×D₇	—	4	2	no	—
199	C₂×#41	—	7	1	no	—
200	C₂²×D₄	—	7	1	no	—
201	#127	—	7	2	no	—
202	#124	—	7	2	no	—
203	#121	—	7	1	no	—
204	#121	—	7	1	no	—
205	#121	—	7	1	no	—
206	#121	C₃×D₇	1	1	yes	characteristic, complemented
207	#120	—	7	2	no	—
208	#120	—	7	2	no	—
209	#117	—	7	1	no	—
210	C₂²×C₇	—	2	1	no	—
211	C₂²×C₇	—	2	2	no	—
212	C₂²×C₇	—	2	1	no	—
213	C₂²×C₇	—	2	2	no	—
214	C₂²×C₇	—	2	1	no	—
215	C₂²×C₇	—	2	2	no	—
216	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
217	C₂×D₇	—	2	1	no	—
218	C₂×D₇	—	2	1	no	—
219	C₂×D₇	—	2	1	no	—
220	C₂×D₇	—	2	2	no	—
221	C₂×D₇	—	2	1	no	—
222	C₂×D₇	—	2	2	no	—
223	C₂×D₇	—	2	1	no	—
224	C₂×D₇	—	2	2	no	—
225	C₂×D₇	—	4	8	no	—
226	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
227	C₄×C₇	—	2	1	no	—
228	C₄×C₇	—	2	2	no	—
229	C₄×C₇	C₂×C₃×D₄	1	2	yes	—
230	Dic₇	—	2	1	no	—
231	Dic₇	—	2	2	no	—
232	Dic₇	C₂×C₃×D₄	1	2	yes	—
233	C₂³×C₃	—	7	1	no	—
234	C₂³×C₃	—	7	2	no	—
235	C₂³×C₃	—	7	1	no	—
236	C₂³×C₃	—	14	4	no	—
237	C₂³×C₃	—	28	2	no	—
238	C₂³×C₃	—	28	2	no	—
239	C₂³×C₃	C₂²×D₇	1	2	yes	—
240	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
241	C₃×Q₈	—	14	2	no	—
242	C₃×D₄	—	2	2	no	—
243	C₃×D₄	—	4	2	no	—
244	C₃×D₄	—	14	2	no	—
245	C₃×D₄	—	14	4	no	—
246	C₃×D₄	—	14	2	no	—
247	C₃×D₄	—	14	2	no	—
248	C₃×D₄	—	14	2	no	—
249	C₃×D₄	—	28	2	no	—
250	C₃×D₄	—	28	2	no	—
251	C₃×D₄	—	28	2	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	7	1	no	—
254	C₂×C₃×C₄	—	7	4	no	—
255	C₂×C₃×C₄	—	7	2	no	—
256	C₂×C₃×C₄	—	7	1	no	—
257	C₂×C₃×C₄	—	14	2	no	—
258	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
259	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
261	C₃×C₇	#535	1	1	yes	characteristic, complemented, Hall
262	C₂⁴	—	7	2	no	—
263	#41	—	14	4	no	—
264	C₂×Q₈	—	7	1	no	—
265	C₂×D₄	—	7	1	no	—
266	C₂×D₄	—	7	2	no	—
267	C₂×D₄	—	7	1	no	—
268	C₂×D₄	—	7	2	no	—
269	C₂×D₄	—	7	2	no	—
270	C₂×D₄	—	7	1	no	—
271	C₂×D₄	—	7	1	no	—
272	C₂×D₄	—	7	2	no	—
273	C₂×D₄	—	14	4	no	—
274	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
275	C₂×D₄	C₂×C₃×D₇	1	2	yes	complemented
276	C₂²×C₄	—	7	1	no	—
277	C₂²×C₄	—	7	1	no	—
278	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
279	C₄⋊C₄	—	7	1	no	—
280	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
281	C₂²⋊C₄	—	7	2	no	—
282	C₂²⋊C₄	—	7	2	no	—
283	C₂²⋊C₄	—	7	2	no	—
284	C₂²⋊C₄	—	7	2	no	—
285	C₂²⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
286	C₄²	—	7	2	no	—
287	C₂×C₇	—	4	2	no	—
288	C₂×C₇	—	4	1	no	—
289	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
290	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
291	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
292	D₇	—	2	2	no	—
293	D₇	—	4	2	no	—
294	D₇	—	4	1	no	—
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	—	2	2	no	—
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	2	no	—
301	C₂²×C₃	—	7	2	no	—
302	C₂²×C₃	—	14	1	no	—
303	C₂²×C₃	—	14	1	no	—
304	C₂²×C₃	—	14	1	no	—
305	C₂²×C₃	—	14	2	no	—
306	C₂²×C₃	—	14	1	no	—
307	C₂²×C₃	—	14	2	no	—
308	C₂²×C₃	—	14	1	no	—
309	C₂²×C₃	—	14	2	no	—
310	C₂²×C₃	—	28	8	no	—
311	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	7	2	no	—
315	C₃×C₄	—	14	1	no	—
316	C₃×C₄	—	14	2	no	—
317	C₃×C₄	D₄×D₇	1	2	yes	—
318	C₂³	—	7	1	no	—
319	C₂³	—	7	2	no	—
320	C₂³	—	7	1	no	—
321	C₂³	—	14	4	no	—
322	C₂³	—	28	2	no	—
323	C₂³	—	28	2	no	—
324	C₂³	C₂²×C₃×D₇	1	2	yes	—
325	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
326	Q₈	—	14	2	no	—
327	D₄	—	2	2	no	—
328	D₄	—	4	2	no	—
329	D₄	—	14	2	no	—
330	D₄	—	14	4	no	—
331	D₄	—	14	2	no	—
332	D₄	—	14	2	no	—
333	D₄	—	14	2	no	—
334	D₄	—	28	2	no	—
335	D₄	—	28	2	no	—
336	D₄	—	28	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	7	1	no	—
339	C₂×C₄	—	7	4	no	—
340	C₂×C₄	—	7	2	no	—
341	C₂×C₄	—	7	1	no	—
342	C₂×C₄	—	14	2	no	—
343	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
344	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
346	C₇	C₃×#535	1	1	yes	characteristic, complemented, Sylow
347	C₂×C₃	—	4	2	no	—
348	C₂×C₃	—	4	1	no	—
349	C₂×C₃	—	14	2	no	—
350	C₂×C₃	—	28	2	no	—
351	C₂×C₃	—	28	1	no	—
352	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
353	C₂×C₃	#6548	1	1	yes	characteristic
354	C₂×C₃	#6553	1	1	yes	characteristic
355	C₂²	—	2	1	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	7	2	no	—
362	C₂²	—	14	1	no	—
363	C₂²	—	14	1	no	—
364	C₂²	—	14	1	no	—
365	C₂²	—	14	2	no	—
366	C₂²	—	14	1	no	—
367	C₂²	—	14	2	no	—
368	C₂²	—	14	1	no	—
369	C₂²	—	14	2	no	—
370	C₂²	—	28	8	no	—
371	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	2	no	—
374	C₄	—	7	2	no	—
375	C₄	—	14	1	no	—
376	C₄	—	14	2	no	—
377	C₄	C₃×D₄×D₇	1	2	yes	—
378	C₃	#90298	1	1	yes	characteristic, direct product factor, Sylow
379	C₂	—	4	2	no	—
380	C₂	—	4	1	no	—
381	C₂	—	14	2	no	—
382	C₂	—	28	2	no	—
383	C₂	—	28	1	no	—
384	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
385	C₂	C₃×#6548	1	1	yes	characteristic
386	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×#535
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. C₂×C₃×#1157	C₂	semidirect
3. C₃×C₇×#121	C₂	semidirect
4. C₃×#6503	C₂	semidirect
5. C₃×#6501	C₂	semidirect
6. C₃×#6500	C₂	semidirect
7. C₃×#6493	C₂	semidirect
8. C₃×#6458	C₂	semidirect
9. C₃×#6455	C₂	semidirect
10. C₃×#6448	C₂	semidirect
11. C₃×#6445	C₂	semidirect
12. #90298	C₃	direct (N × H)
15. C₂×C₃×C₇×D₄	C₂²	semidirect
16. C₂²×C₃×C₄×C₇	C₂²	semidirect
19. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
20. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
21. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
26. C₂×C₃×D₂₈	C₂²	semidirect
28. C₂×C₃×C₄×D₇	C₂²	semidirect
29. C₂×C₃×Dic₁₄	C₂²	semidirect
30. C₃×C₇×C₄⋊C₄	C₂²	semidirect
31. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
32. C₃×C₂²⋊Dic₇	C₂²	semidirect
34. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
35. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
36. C₃×C₄⋊Dic₇	C₂²	semidirect
37. C₃×C₄×Dic₇	C₂²	semidirect
38. C₂×D₄×D₇	C₂×C₃	semidirect
39. C₂×#1157	C₂×C₃	semidirect
40. C₇×#121	C₂×C₃	semidirect
41. #6503	C₂×C₃	semidirect
42. #6501	C₂×C₃	semidirect
43. #6500	C₂×C₃	semidirect
44. #6493	C₂×C₃	semidirect
45. #6458	C₂×C₃	semidirect
46. #6455	C₂×C₃	semidirect
47. #6448	C₂×C₃	semidirect
48. #6445	C₂×C₃	semidirect
76. C₃×C₄×D₇	D₄	semidirect
80. C₂×C₇×D₄	C₂²×C₃	semidirect
81. C₂²×C₄×C₇	C₂²×C₃	semidirect
84. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
85. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
86. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
91. C₂×D₂₈	C₂²×C₃	semidirect
93. C₂×C₄×D₇	C₂²×C₃	semidirect
94. C₂×Dic₁₄	C₂²×C₃	semidirect
95. C₇×C₄⋊C₄	C₂²×C₃	semidirect
96. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
97. C₂²⋊Dic₇	C₂²×C₃	semidirect
99. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
100. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
101. C₄⋊Dic₇	C₂²×C₃	semidirect
102. C₄×Dic₇	C₂²×C₃	semidirect
110. C₃×#121	D₇	semidirect
164. C₄×D₇	C₃×D₄	semidirect
179. C₂×C₃×D₄	C₂×D₇	semidirect
182. C₂²×C₃×C₄	C₂×D₇	semidirect
184. C₃×C₄⋊C₄	C₂×D₇	semidirect
189. C₃×C₂²⋊C₄	C₂×D₇	semidirect
206. #121	C₃×D₇	semidirect
261. C₃×C₇	#535	semidirect
275. C₂×D₄	C₂×C₃×D₇	semidirect
278. C₂²×C₄	C₂×C₃×D₇	semidirect
280. C₄⋊C₄	C₂×C₃×D₇	semidirect
285. C₂²⋊C₄	C₂×C₃×D₇	semidirect
346. C₇	C₃×#535	semidirect
378. C₃	#90298	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
C₂×C₃×#1157	2
C₃×C₇×#121	2
C₃×#6503	2
C₃×#6501	2
C₃×#6500	2
C₃×#6493	2
C₃×#6458	2
C₃×#6455	2
C₃×#6448	2
C₃×#6445	2
#90298	3
C₃×#535	7

Subgroups — C3×#90298 #13060951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90298 #13060951