Subgroups — C₃×#90344 #13060999

Order 1344.

692 conjugacy classes of subgroups.

The subgroup lattice has 384 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	C₂²×C₃×D₂₈	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×#6458	C₂	1	2	yes	maximal, complemented
7	C₃×#6457	C₂	1	2	yes	maximal, complemented
8	C₃×#6447	C₂	1	2	yes	maximal, complemented
9	C₃×#6445	C₂	1	2	yes	maximal, complemented
10	C₃×#6445	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	#90344	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
14	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic, complemented
15	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
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	C₃×D₄×D₇	—	2	4	no	—
22	C₂×C₃×D₂₈	—	2	4	no	—
23	C₂×C₃×D₂₈	C₂²	1	2	yes	—
24	C₂×C₃×D₂₈	C₂²	1	2	yes	complemented
25	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×D₂₈	C₂²	1	2	yes	complemented
27	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×C₄×D₇	C₂²	1	2	yes	complemented
29	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
32	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
33	C₃×(C₂×D₇)⋊C₄	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×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
37	C₃×Dic₇⋊C₄	C₂²	1	2	yes	complemented
38	C₂×D₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂²×D₂₈	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	#6458	C₂×C₃	1	2	yes	complemented
44	#6457	C₂×C₃	1	2	yes	complemented
45	#6447	C₂×C₃	1	2	yes	complemented
46	#6445	C₂×C₃	1	2	yes	complemented
47	#6445	C₂×C₃	1	1	yes	characteristic, complemented
48	D₇×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
49	C₃×#534	—	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	2	no	—
54	C₂²×C₃×D₇	—	4	2	no	—
55	C₂²×C₃×D₇	—	4	2	no	—
56	C₂²×C₃×D₇	—	4	2	no	—
57	C₂²×C₃×D₇	D₄	1	4	yes	complemented
58	C₂²×C₃×D₇	C₂³	1	2	yes	—
59	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
60	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
61	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
62	C₃×C₇×D₄	—	2	2	no	—
63	C₂×C₃×C₄×C₇	—	2	2	no	—
64	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
65	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
67	C₃×C₂²⋊D₇	—	2	2	no	—
68	C₃×C₂²⋊D₇	—	2	2	no	—
69	C₃×C₂²⋊D₇	—	4	2	no	—
70	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
71	C₂×C₃×Dic₇	C₂³	1	2	yes	—
72	C₃×D₂₈	—	2	4	no	—
73	C₃×D₂₈	—	2	4	no	—
74	C₃×D₂₈	—	2	2	no	—
75	C₃×D₂₈	—	4	2	no	—
76	C₃×C₄×D₇	—	2	2	no	—
77	C₃×C₄×D₇	—	4	2	no	—
78	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
79	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
80	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
81	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
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	D₄×D₇	—	2	4	no	—
87	C₂×D₂₈	—	2	4	no	—
88	C₂×D₂₈	C₂²×C₃	1	2	yes	—
89	C₂×D₂₈	C₂²×C₃	1	2	yes	complemented
90	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
91	C₂×D₂₈	C₂²×C₃	1	2	yes	complemented
92	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
93	C₂×C₄×D₇	C₂²×C₃	1	2	yes	complemented
94	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
95	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
96	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
97	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
98	(C₂×D₇)⋊C₄	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	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
102	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
103	C₂²×C₃×D₄	—	7	1	no	—
104	C₂²×C₃×D₄	—	7	1	no	—
105	C₃×#123	—	7	1	no	—
106	C₃×#123	—	7	2	no	—
107	C₃×#123	D₇	1	1	yes	characteristic, complemented
108	C₃×#121	—	7	2	no	—
109	C₃×#121	—	7	2	no	—
110	C₃×#120	—	7	1	no	—
111	C₃×#120	—	7	2	no	—
112	C₃×#120	—	7	1	no	—
113	C₂×C₃×C₂²⋊C₄	—	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	C₂×D₄	1	2	yes	—
118	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
119	C₂×C₃×D₇	—	2	2	no	—
120	C₂×C₃×D₇	—	2	2	no	—
121	C₂×C₃×D₇	—	2	2	no	—
122	C₂×C₃×D₇	—	2	1	no	—
123	C₂×C₃×D₇	—	2	2	no	—
124	C₂×C₃×D₇	—	2	2	no	—
125	C₂×C₃×D₇	—	2	2	no	—
126	C₂×C₃×D₇	—	4	4	no	—
127	C₂×C₃×D₇	—	4	4	no	—
128	C₂×C₃×D₇	—	4	4	no	—
129	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
134	C₃×Dic₇	—	2	1	no	—
135	C₃×Dic₇	—	2	2	no	—
136	#534	—	7	1	no	Sylow
137	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
138	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
139	C₂²×D₇	—	2	2	no	—
140	C₂²×D₇	—	2	2	no	—
141	C₂²×D₇	—	4	2	no	—
142	C₂²×D₇	—	4	2	no	—
143	C₂²×D₇	—	4	2	no	—
144	C₂²×D₇	C₃×D₄	1	4	yes	complemented
145	C₂²×D₇	C₂³×C₃	1	2	yes	—
146	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
147	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
148	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
149	C₇×D₄	—	2	2	no	—
150	C₂×C₄×C₇	—	2	2	no	—
151	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
152	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
153	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
154	C₂²⋊D₇	—	2	2	no	—
155	C₂²⋊D₇	—	2	2	no	—
156	C₂²⋊D₇	—	4	2	no	—
157	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
158	C₂×Dic₇	C₂³×C₃	1	2	yes	—
159	D₂₈	—	2	4	no	—
160	D₂₈	—	2	4	no	—
161	D₂₈	—	2	2	no	—
162	D₂₈	—	4	2	no	—
163	C₄×D₇	—	2	2	no	—
164	C₄×D₇	—	4	2	no	—
165	C₂⁴×C₃	—	7	1	no	—
166	C₂⁴×C₃	—	7	1	no	—
167	C₂⁴×C₃	—	7	1	no	—
168	C₂×C₃×D₄	—	7	1	no	—
169	C₂×C₃×D₄	—	7	1	no	—
170	C₂×C₃×D₄	—	7	2	no	—
171	C₂×C₃×D₄	—	7	2	no	—
172	C₂×C₃×D₄	—	7	1	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	—	14	4	no	—
177	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
178	C₂²×C₃×C₄	—	7	1	no	—
179	C₂²×C₃×C₄	—	7	2	no	—
180	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic, complemented
181	C₃×C₄⋊C₄	—	7	2	no	—
182	C₃×C₄⋊C₄	C₂×D₇	1	2	yes	complemented
183	C₃×C₂²⋊C₄	—	7	1	no	—
184	C₃×C₂²⋊C₄	—	7	2	no	—
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	C₂×D₇	1	1	yes	characteristic, complemented
189	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	complemented
190	C₂×C₃×C₇	—	2	2	no	—
191	C₂×C₃×C₇	—	4	1	no	—
192	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₃×C₇	H(5,𝔽₂)	1	2	yes	—
194	C₃×D₇	—	2	2	no	—
195	C₃×D₇	—	2	2	no	—
196	C₃×D₇	—	4	2	no	—
197	C₃×D₇	—	4	1	no	—
198	C₂²×D₄	—	7	1	no	—
199	C₂²×D₄	—	7	1	no	—
200	#123	—	7	1	no	—
201	#123	—	7	2	no	—
202	#123	C₃×D₇	1	1	yes	characteristic, complemented
203	#121	—	7	2	no	—
204	#121	—	7	2	no	—
205	#120	—	7	1	no	—
206	#120	—	7	2	no	—
207	#120	—	7	1	no	—
208	C₂×C₂²⋊C₄	—	7	1	no	—
209	C₂²×C₇	—	2	2	no	—
210	C₂²×C₇	—	2	1	no	—
211	C₂²×C₇	—	2	2	no	—
212	C₂²×C₇	C₂×C₃×D₄	1	2	yes	—
213	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
214	C₂×D₇	—	2	2	no	—
215	C₂×D₇	—	2	2	no	—
216	C₂×D₇	—	2	2	no	—
217	C₂×D₇	—	2	1	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	C₂×D₇	—	4	4	no	—
223	C₂×D₇	—	4	4	no	—
224	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
225	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
226	C₄×C₇	—	2	1	no	—
227	C₄×C₇	—	2	2	no	—
228	C₄×C₇	—	2	2	no	—
229	Dic₇	—	2	1	no	—
230	Dic₇	—	2	2	no	—
231	C₂³×C₃	—	7	1	no	—
232	C₂³×C₃	—	7	1	no	—
233	C₂³×C₃	—	7	4	no	—
234	C₂³×C₃	—	7	2	no	—
235	C₂³×C₃	—	7	1	no	—
236	C₂³×C₃	—	14	2	no	—
237	C₂³×C₃	—	14	2	no	—
238	C₂³×C₃	—	28	2	no	—
239	C₂³×C₃	—	28	2	no	—
240	C₂³×C₃	—	28	2	no	—
241	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
242	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
243	C₃×D₄	—	2	2	no	—
244	C₃×D₄	—	14	4	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	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	7	2	no	—
253	C₂×C₃×C₄	—	7	1	no	—
254	C₂×C₃×C₄	—	14	2	no	—
255	C₂×C₃×C₄	—	28	2	no	—
256	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
257	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
259	C₃×C₇	#534	1	1	yes	characteristic, complemented, Hall
260	C₂⁴	—	7	1	no	—
261	C₂⁴	—	7	1	no	—
262	C₂⁴	—	7	1	no	—
263	C₂×D₄	—	7	1	no	—
264	C₂×D₄	—	7	1	no	—
265	C₂×D₄	—	7	2	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	—	14	4	no	—
271	C₂×D₄	—	14	4	no	—
272	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
273	C₂²×C₄	—	7	1	no	—
274	C₂²×C₄	—	7	2	no	—
275	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
276	C₄⋊C₄	—	7	2	no	—
277	C₄⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
278	C₂²⋊C₄	—	7	1	no	—
279	C₂²⋊C₄	—	7	2	no	—
280	C₂²⋊C₄	—	7	2	no	—
281	C₂²⋊C₄	—	7	2	no	—
282	C₂²⋊C₄	—	7	2	no	—
283	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
284	C₂²⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
285	C₂×C₇	—	2	2	no	—
286	C₂×C₇	—	4	1	no	—
287	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
288	C₂×C₇	C₃×H(5,𝔽₂)	1	2	yes	—
289	D₇	—	2	2	no	—
290	D₇	—	2	2	no	—
291	D₇	—	4	2	no	—
292	D₇	—	4	1	no	—
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	7	2	no	—
297	C₂²×C₃	—	7	2	no	—
298	C₂²×C₃	—	14	2	no	—
299	C₂²×C₃	—	14	2	no	—
300	C₂²×C₃	—	14	2	no	—
301	C₂²×C₃	—	14	1	no	—
302	C₂²×C₃	—	14	2	no	—
303	C₂²×C₃	—	14	2	no	—
304	C₂²×C₃	—	14	2	no	—
305	C₂²×C₃	—	28	4	no	—
306	C₂²×C₃	—	28	4	no	—
307	C₂²×C₃	—	28	4	no	—
308	C₂²×C₃	D₄×D₇	1	2	yes	—
309	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
310	C₃×C₄	—	2	2	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	14	1	no	—
314	C₃×C₄	—	14	2	no	—
315	C₂³	—	7	1	no	—
316	C₂³	—	7	1	no	—
317	C₂³	—	7	4	no	—
318	C₂³	—	7	2	no	—
319	C₂³	—	7	1	no	—
320	C₂³	—	14	2	no	—
321	C₂³	—	14	2	no	—
322	C₂³	—	28	2	no	—
323	C₂³	—	28	2	no	—
324	C₂³	—	28	2	no	—
325	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
326	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
327	D₄	—	2	2	no	—
328	D₄	—	14	4	no	—
329	D₄	—	14	4	no	—
330	D₄	—	14	2	no	—
331	D₄	—	14	2	no	—
332	D₄	—	14	2	no	—
333	D₄	—	28	2	no	—
334	D₄	—	28	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	7	2	no	—
337	C₂×C₄	—	7	1	no	—
338	C₂×C₄	—	14	2	no	—
339	C₂×C₄	—	28	2	no	—
340	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
341	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
342	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
343	C₇	C₃×#534	1	1	yes	characteristic, complemented, Sylow
344	C₂×C₃	—	2	2	no	—
345	C₂×C₃	—	4	1	no	—
346	C₂×C₃	—	14	2	no	—
347	C₂×C₃	—	14	2	no	—
348	C₂×C₃	—	28	2	no	—
349	C₂×C₃	—	28	1	no	—
350	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
351	C₂×C₃	#6553	1	2	yes	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	7	2	no	—
356	C₂²	—	7	2	no	—
357	C₂²	—	14	2	no	—
358	C₂²	—	14	2	no	—
359	C₂²	—	14	2	no	—
360	C₂²	—	14	1	no	—
361	C₂²	—	14	2	no	—
362	C₂²	—	14	2	no	—
363	C₂²	—	14	2	no	—
364	C₂²	—	28	4	no	—
365	C₂²	—	28	4	no	—
366	C₂²	—	28	4	no	—
367	C₂²	C₃×D₄×D₇	1	2	yes	—
368	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	2	no	—
372	C₄	—	14	1	no	—
373	C₄	—	14	2	no	—
374	C₃	#90344	1	1	yes	characteristic, direct product factor, Sylow
375	C₂	—	2	2	no	—
376	C₂	—	4	1	no	—
377	C₂	—	14	2	no	—
378	C₂	—	14	2	no	—
379	C₂	—	28	2	no	—
380	C₂	—	28	1	no	—
381	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
382	C₂	C₃×#6553	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×#534
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×D₄×D₇	C₂	semidirect
2. C₂²×C₃×D₂₈	C₂	semidirect
3. C₃×C₇×#123	C₂	semidirect
4. C₃×#6500	C₂	semidirect
5. C₃×#6492	C₂	semidirect
6. C₃×#6458	C₂	semidirect
7. C₃×#6457	C₂	semidirect
8. C₃×#6447	C₂	semidirect
9. C₃×#6445	C₂	semidirect
10. C₃×#6445	C₂	semidirect
11. C₃×D₇×C₂²⋊C₄	C₂	semidirect
12. #90344	C₃	direct (N × H)
14. C₂³×C₃×D₇	C₂²	semidirect
15. C₂³×C₃×D₇	C₂²	semidirect
17. C₂²×C₃×C₄×C₇	C₂²	semidirect
19. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
20. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
24. C₂×C₃×D₂₈	C₂²	semidirect
25. C₂×C₃×D₂₈	C₂²	semidirect
26. C₂×C₃×D₂₈	C₂²	semidirect
27. C₂×C₃×C₄×D₇	C₂²	semidirect
28. C₂×C₃×C₄×D₇	C₂²	semidirect
29. C₃×C₇×C₄⋊C₄	C₂²	semidirect
30. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
31. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
32. C₃×C₂²⋊Dic₇	C₂²	semidirect
33. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
34. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
35. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
36. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
37. C₃×Dic₇⋊C₄	C₂²	semidirect
38. C₂×D₄×D₇	C₂×C₃	semidirect
39. C₂²×D₂₈	C₂×C₃	semidirect
40. C₇×#123	C₂×C₃	semidirect
41. #6500	C₂×C₃	semidirect
42. #6492	C₂×C₃	semidirect
43. #6458	C₂×C₃	semidirect
44. #6457	C₂×C₃	semidirect
45. #6447	C₂×C₃	semidirect
46. #6445	C₂×C₃	semidirect
47. #6445	C₂×C₃	semidirect
48. D₇×C₂²⋊C₄	C₂×C₃	semidirect
57. C₂²×C₃×D₇	D₄	semidirect
79. C₂³×D₇	C₂²×C₃	semidirect
80. C₂³×D₇	C₂²×C₃	semidirect
82. C₂²×C₄×C₇	C₂²×C₃	semidirect
84. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
85. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
89. C₂×D₂₈	C₂²×C₃	semidirect
90. C₂×D₂₈	C₂²×C₃	semidirect
91. C₂×D₂₈	C₂²×C₃	semidirect
92. C₂×C₄×D₇	C₂²×C₃	semidirect
93. C₂×C₄×D₇	C₂²×C₃	semidirect
94. C₇×C₄⋊C₄	C₂²×C₃	semidirect
95. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
96. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
97. C₂²⋊Dic₇	C₂²×C₃	semidirect
98. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
99. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
100. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
101. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
102. Dic₇⋊C₄	C₂²×C₃	semidirect
107. C₃×#123	D₇	semidirect
144. C₂²×D₇	C₃×D₄	semidirect
180. C₂²×C₃×C₄	C₂×D₇	semidirect
182. C₃×C₄⋊C₄	C₂×D₇	semidirect
188. C₃×C₂²⋊C₄	C₂×D₇	semidirect
189. C₃×C₂²⋊C₄	C₂×D₇	semidirect
202. #123	C₃×D₇	semidirect
259. C₃×C₇	#534	semidirect
275. C₂²×C₄	C₂×C₃×D₇	semidirect
277. C₄⋊C₄	C₂×C₃×D₇	semidirect
283. C₂²⋊C₄	C₂×C₃×D₇	semidirect
284. C₂²⋊C₄	C₂×C₃×D₇	semidirect
343. C₇	C₃×#534	semidirect
374. C₃	#90344	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
C₂²×C₃×D₂₈	2
C₃×C₇×#123	2
C₃×#6500	2
C₃×#6492	2
C₃×#6458	2
C₃×#6457	2
C₃×#6447	2
C₃×#6445	2
C₃×D₇×C₂²⋊C₄	2
#90344	3
C₃×#534	7

Subgroups — C3×#90344 #13060999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90344 #13060999