Subgroups — D₃×C₇×#135 #13061483

Order 1344.

532 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₇×#41	C₂	1	2	yes	maximal, complemented
2	C₃×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#950	C₂	1	2	yes	maximal, complemented
4	C₇×#919	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#916	C₂	1	2	yes	maximal, complemented
7	D₃×C₇×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₇×#912	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#904	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×D₃×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#135	—	3	1	no	maximal, Hall
13	C₃×C₇×#41	C₂²	1	2	yes	complemented
14	C₇×#239	C₂²	1	2	yes	complemented
15	D₃×C₇×Q₈	C₂²	1	2	yes	—
16	C₇×#237	—	2	2	no	—
17	C₇×#237	C₂²	1	2	yes	complemented
18	D₃×C₇×D₄	—	2	2	no	—
19	D₃×C₇×D₄	C₂²	1	2	yes	—
20	C₇×#235	—	2	2	no	—
21	C₇×#235	C₂²	1	2	yes	complemented
22	C₂×C₄×D₃×C₇	—	2	2	no	—
23	C₂×C₄×D₃×C₇	C₂²	1	1	yes	characteristic
24	C₃×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₇×SD₁₆	C₂²	1	2	yes	complemented
26	C₃×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
28	C₇×#216	C₂²	1	2	yes	complemented
29	C₇×#215	C₂²	1	2	yes	complemented
30	C₇×#214	C₂²	1	2	yes	complemented
31	C₇×#213	C₂²	1	2	yes	complemented
32	C₂×C₇×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₇×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
34	C₇×D₂₄	C₂²	1	1	yes	characteristic, complemented
35	C₇×#204	C₂²	1	2	yes	complemented
36	D₃×C₇×C₈	C₂²	1	1	yes	characteristic
37	D₃×C₇×C₈	C₂²	1	1	yes	characteristic
38	D₃×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
39	D₃×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₇×#41	—	3	2	no	—
41	C₇×#135	—	3	2	no	—
42	C₇×#135	—	3	1	no	—
43	C₇×#135	—	3	2	no	—
44	C₇×#135	—	3	1	no	—
45	C₇×#135	—	3	1	no	—
46	C₇×#135	D₃	1	1	yes	characteristic, direct product factor
47	C₂×C₇×Q₁₆	—	3	1	no	—
48	C₂×C₇×SD₁₆	—	3	2	no	—
49	C₂×C₇×D₈	—	3	1	no	—
50	C₂²×C₇×C₈	—	3	1	no	—
51	D₃×#135	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
52	C₂²×D₃×C₇	—	2	2	no	—
53	C₂²×D₃×C₇	D₄	1	1	yes	characteristic
54	C₃×C₇×Q₈	C₂³	1	2	yes	—
55	C₃×C₇×D₄	—	2	2	no	—
56	C₃×C₇×D₄	C₂³	1	2	yes	—
57	C₂×C₃×C₄×C₇	—	2	2	no	—
58	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₇×#67	—	2	2	no	—
60	C₇×#67	—	2	2	no	—
61	C₇×#67	—	2	2	no	—
62	C₂×C₇×Dic₃	—	2	2	no	—
63	C₂×C₇×Dic₃	D₄	1	1	yes	characteristic
64	C₇×D₁₂	—	2	2	no	—
65	C₇×D₁₂	C₂³	1	2	yes	—
66	C₄×D₃×C₇	—	2	2	no	—
67	C₄×D₃×C₇	—	2	2	no	—
68	C₄×D₃×C₇	—	2	2	no	—
69	C₄×D₃×C₇	D₄	1	1	yes	characteristic
70	C₄×D₃×C₇	D₄	1	1	yes	characteristic
71	C₄×D₃×C₇	C₂³	1	1	yes	characteristic
72	C₄×D₃×C₇	C₂³	1	1	yes	characteristic
73	C₇×Dic₆	—	2	2	no	—
74	C₇×Dic₆	C₂³	1	2	yes	—
75	C₃×C₇×C₈	C₂³	1	1	yes	characteristic
76	C₃×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₇×C₃⋊C₈	C₂³	1	1	yes	characteristic
78	C₇×C₃⋊C₈	C₂³	1	1	yes	characteristic
79	C₇×#41	—	3	2	no	—
80	C₇×#41	—	3	2	no	—
81	C₇×#41	—	3	2	no	—
82	C₇×#41	—	6	2	no	—
83	C₇×#41	—	6	2	no	—
84	C₇×#41	C₂×D₃	1	2	yes	complemented
85	C₂×C₇×Q₈	—	3	2	no	—
86	C₂×C₇×D₄	—	3	2	no	—
87	C₂×C₇×D₄	—	6	2	no	—
88	C₂²×C₄×C₇	—	3	1	no	—
89	C₂²×C₄×C₇	—	6	2	no	—
90	C₇×Q₁₆	—	3	2	no	—
91	C₇×Q₁₆	—	3	1	no	—
92	C₇×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
93	C₇×SD₁₆	—	3	2	no	—
94	C₇×SD₁₆	—	3	2	no	—
95	C₇×SD₁₆	—	3	2	no	—
96	C₇×SD₁₆	C₂×D₃	1	2	yes	complemented
97	C₇×D₈	—	3	2	no	—
98	C₇×D₈	—	3	1	no	—
99	C₇×D₈	C₂×D₃	1	1	yes	characteristic, complemented
100	C₂×C₇×C₈	—	3	1	no	—
101	C₂×C₇×C₈	—	3	1	no	—
102	C₂×C₇×C₈	—	3	1	no	—
103	C₂×C₇×C₈	—	3	1	no	—
104	C₂×C₇×C₈	—	3	1	no	—
105	C₂×C₇×C₈	C₂×D₃	1	1	yes	characteristic, complemented
106	D₃×#41	C₂×C₇	1	2	yes	complemented
107	C₃×#135	C₂×C₇	1	1	yes	characteristic, complemented
108	#950	C₂×C₇	1	2	yes	complemented
109	#919	C₂×C₇	1	1	yes	characteristic, complemented
110	D₃×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
111	#916	C₂×C₇	1	2	yes	complemented
112	D₃×SD₁₆	C₂×C₇	1	2	yes	complemented
113	#912	C₂×C₇	1	1	yes	characteristic, complemented
114	D₃×D₈	C₂×C₇	1	1	yes	characteristic, complemented
115	#904	C₂×C₇	1	1	yes	characteristic, complemented
116	C₂×D₃×C₈	C₂×C₇	1	1	yes	characteristic, complemented
117	C₂²×C₃×C₇	—	2	2	no	—
118	C₂²×C₃×C₇	C₂×D₄	1	1	yes	characteristic
119	C₂×D₃×C₇	—	2	2	no	—
120	C₂×D₃×C₇	—	2	2	no	—
121	C₂×D₃×C₇	—	4	4	no	—
122	C₂×D₃×C₇	C₂×D₄	1	1	yes	characteristic
123	C₂×D₃×C₇	C₂×D₄	1	1	yes	characteristic
124	C₃×C₄×C₇	—	2	2	no	—
125	C₃×C₄×C₇	C₂×D₄	1	1	yes	characteristic
126	C₃×C₄×C₇	C₂⁴	1	1	yes	characteristic
127	C₇×Dic₃	—	2	2	no	—
128	C₇×Dic₃	C₂×D₄	1	1	yes	characteristic
129	C₇×Dic₃	C₂×D₄	1	1	yes	characteristic
130	C₂×#135	—	3	1	no	Sylow
131	C₂³×C₇	—	3	1	no	—
132	C₂³×C₇	—	6	2	no	—
133	C₇×Q₈	—	3	2	no	—
134	C₇×Q₈	—	6	2	no	—
135	C₇×Q₈	C₂²×D₃	1	2	yes	—
136	C₇×D₄	—	2	2	no	—
137	C₇×D₄	—	3	2	no	—
138	C₇×D₄	—	6	2	no	—
139	C₇×D₄	—	6	2	no	—
140	C₇×D₄	—	6	2	no	—
141	C₇×D₄	—	6	2	no	—
142	C₇×D₄	C₂²×D₃	1	2	yes	—
143	C₂×C₄×C₇	—	2	2	no	—
144	C₂×C₄×C₇	—	3	1	no	—
145	C₂×C₄×C₇	—	3	1	no	—
146	C₂×C₄×C₇	—	3	1	no	—
147	C₂×C₄×C₇	—	3	1	no	—
148	C₂×C₄×C₇	—	3	1	no	—
149	C₂×C₄×C₇	—	6	2	no	—
150	C₂×C₄×C₇	—	6	2	no	—
151	C₂×C₄×C₇	—	6	2	no	—
152	C₂×C₄×C₇	—	6	2	no	—
153	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
154	C₇×C₈	—	3	1	no	—
155	C₇×C₈	—	3	1	no	—
156	C₇×C₈	C₂²×D₃	1	1	yes	characteristic
157	C₇×C₈	C₂²×D₃	1	1	yes	characteristic
158	C₃×#41	C₂²×C₇	1	2	yes	complemented
159	#239	C₂²×C₇	1	2	yes	complemented
160	D₃×Q₈	C₂²×C₇	1	2	yes	—
161	#237	—	2	2	no	—
162	#237	C₂²×C₇	1	2	yes	complemented
163	D₃×D₄	—	2	2	no	—
164	D₃×D₄	C₂²×C₇	1	2	yes	—
165	#235	—	2	2	no	—
166	#235	C₂²×C₇	1	2	yes	complemented
167	C₂×C₄×D₃	—	2	2	no	—
168	C₂×C₄×D₃	C₂²×C₇	1	1	yes	characteristic
169	C₃×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
170	C₃×SD₁₆	C₂²×C₇	1	2	yes	complemented
171	C₃×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
172	C₂×C₃×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
173	#216	C₂²×C₇	1	2	yes	complemented
174	#215	C₂²×C₇	1	2	yes	complemented
175	#214	C₂²×C₇	1	2	yes	complemented
176	#213	C₂²×C₇	1	2	yes	complemented
177	C₂×C₃⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
178	Dic₁₂	C₂²×C₇	1	1	yes	characteristic, complemented
179	D₂₄	C₂²×C₇	1	1	yes	characteristic, complemented
180	#204	C₂²×C₇	1	2	yes	complemented
181	D₃×C₈	C₂²×C₇	1	1	yes	characteristic
182	D₃×C₈	C₂²×C₇	1	1	yes	characteristic
183	D₃×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
184	D₃×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
185	C₂×C₃×C₇	—	2	1	no	—
186	C₂×C₃×C₇	—	4	2	no	—
187	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
188	D₃×C₇	—	2	1	no	—
189	D₃×C₇	—	4	2	no	—
190	D₃×C₇	#135	1	2	yes	direct product factor
191	C₂×#41	—	3	2	no	—
192	#135	—	3	2	no	—
193	#135	—	3	1	no	—
194	#135	—	3	2	no	—
195	#135	—	3	1	no	—
196	#135	—	3	1	no	—
197	#135	D₃×C₇	1	1	yes	characteristic, direct product factor
198	C₂×Q₁₆	—	3	1	no	—
199	C₂×SD₁₆	—	3	2	no	—
200	C₂×D₈	—	3	1	no	—
201	C₂²×C₈	—	3	1	no	—
202	C₂²×C₇	—	2	2	no	—
203	C₂²×C₇	—	3	1	no	—
204	C₂²×C₇	—	3	1	no	—
205	C₂²×C₇	—	6	2	no	—
206	C₂²×C₇	—	6	2	no	—
207	C₂²×C₇	—	12	4	no	—
208	C₂²×C₇	D₃×D₄	1	1	yes	characteristic
209	C₄×C₇	—	2	2	no	—
210	C₄×C₇	—	3	1	no	—
211	C₄×C₇	—	3	1	no	—
212	C₄×C₇	—	6	2	no	—
213	C₄×C₇	D₃×D₄	1	1	yes	characteristic
214	C₄×C₇	C₂³×D₃	1	1	yes	characteristic
215	C₂²×D₃	—	2	2	no	—
216	C₂²×D₃	C₇×D₄	1	1	yes	characteristic
217	C₃×Q₈	C₂³×C₇	1	2	yes	—
218	C₃×D₄	—	2	2	no	—
219	C₃×D₄	C₂³×C₇	1	2	yes	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
222	#67	—	2	2	no	—
223	#67	—	2	2	no	—
224	#67	—	2	2	no	—
225	C₂×Dic₃	—	2	2	no	—
226	C₂×Dic₃	C₇×D₄	1	1	yes	characteristic
227	D₁₂	—	2	2	no	—
228	D₁₂	C₂³×C₇	1	2	yes	—
229	C₄×D₃	—	2	2	no	—
230	C₄×D₃	—	2	2	no	—
231	C₄×D₃	—	2	2	no	—
232	C₄×D₃	C₇×D₄	1	1	yes	characteristic
233	C₄×D₃	C₇×D₄	1	1	yes	characteristic
234	C₄×D₃	C₂³×C₇	1	1	yes	characteristic
235	C₄×D₃	C₂³×C₇	1	1	yes	characteristic
236	Dic₆	—	2	2	no	—
237	Dic₆	C₂³×C₇	1	2	yes	—
238	C₃×C₈	C₂³×C₇	1	1	yes	characteristic
239	C₃×C₈	C₂³×C₇	1	1	yes	characteristic
240	C₃⋊C₈	C₂³×C₇	1	1	yes	characteristic
241	C₃⋊C₈	C₂³×C₇	1	1	yes	characteristic
242	C₃×C₇	C₂×#135	1	1	yes	characteristic, complemented, Hall
243	#41	—	3	2	no	—
244	#41	—	3	2	no	—
245	#41	—	3	2	no	—
246	#41	—	6	2	no	—
247	#41	—	6	2	no	—
248	#41	C₂×D₃×C₇	1	2	yes	complemented
249	C₂×Q₈	—	3	2	no	—
250	C₂×D₄	—	3	2	no	—
251	C₂×D₄	—	6	2	no	—
252	C₂²×C₄	—	3	1	no	—
253	C₂²×C₄	—	6	2	no	—
254	Q₁₆	—	3	2	no	—
255	Q₁₆	—	3	1	no	—
256	Q₁₆	C₂×D₃×C₇	1	1	yes	characteristic, complemented
257	SD₁₆	—	3	2	no	—
258	SD₁₆	—	3	2	no	—
259	SD₁₆	—	3	2	no	—
260	SD₁₆	C₂×D₃×C₇	1	2	yes	complemented
261	D₈	—	3	2	no	—
262	D₈	—	3	1	no	—
263	D₈	C₂×D₃×C₇	1	1	yes	characteristic, complemented
264	C₂×C₈	—	3	1	no	—
265	C₂×C₈	—	3	1	no	—
266	C₂×C₈	—	3	1	no	—
267	C₂×C₈	—	3	1	no	—
268	C₂×C₈	—	3	1	no	—
269	C₂×C₈	C₂×D₃×C₇	1	1	yes	characteristic, complemented
270	C₂×C₇	—	2	1	no	—
271	C₂×C₇	—	3	2	no	—
272	C₂×C₇	—	4	2	no	—
273	C₂×C₇	—	6	1	no	—
274	C₂×C₇	—	12	2	no	—
275	C₂×C₇	C₂×D₃×D₄	1	1	yes	characteristic
276	C₂²×C₃	—	2	2	no	—
277	C₂²×C₃	C₂×C₇×D₄	1	1	yes	characteristic
278	C₂×D₃	—	2	2	no	—
279	C₂×D₃	—	2	2	no	—
280	C₂×D₃	—	4	4	no	—
281	C₂×D₃	C₂×C₇×D₄	1	1	yes	characteristic
282	C₂×D₃	C₂×C₇×D₄	1	1	yes	characteristic
283	C₃×C₄	—	2	2	no	—
284	C₃×C₄	C₂×C₇×D₄	1	1	yes	characteristic
285	C₃×C₄	C₂⁴×C₇	1	1	yes	characteristic
286	Dic₃	—	2	2	no	—
287	Dic₃	C₂×C₇×D₄	1	1	yes	characteristic
288	Dic₃	C₂×C₇×D₄	1	1	yes	characteristic
289	C₂³	—	3	1	no	—
290	C₂³	—	6	2	no	—
291	Q₈	—	3	2	no	—
292	Q₈	—	6	2	no	—
293	Q₈	C₂²×D₃×C₇	1	2	yes	—
294	D₄	—	2	2	no	—
295	D₄	—	3	2	no	—
296	D₄	—	6	2	no	—
297	D₄	—	6	2	no	—
298	D₄	—	6	2	no	—
299	D₄	—	6	2	no	—
300	D₄	C₂²×D₃×C₇	1	2	yes	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	3	1	no	—
303	C₂×C₄	—	3	1	no	—
304	C₂×C₄	—	3	1	no	—
305	C₂×C₄	—	3	1	no	—
306	C₂×C₄	—	3	1	no	—
307	C₂×C₄	—	6	2	no	—
308	C₂×C₄	—	6	2	no	—
309	C₂×C₄	—	6	2	no	—
310	C₂×C₄	—	6	2	no	—
311	C₂×C₄	C₂²×D₃×C₇	1	1	yes	characteristic
312	C₈	—	3	1	no	—
313	C₈	—	3	1	no	—
314	C₈	C₂²×D₃×C₇	1	1	yes	characteristic
315	C₈	C₂²×D₃×C₇	1	1	yes	characteristic
316	C₇	D₃×#135	1	1	yes	characteristic, direct product factor, Sylow
317	C₂×C₃	—	2	1	no	—
318	C₂×C₃	—	4	2	no	—
319	C₂×C₃	C₂²×C₇×D₄	1	1	yes	characteristic
320	D₃	—	2	1	no	—
321	D₃	—	4	2	no	—
322	D₃	C₇×#135	1	2	yes	direct product factor
323	C₂²	—	2	2	no	—
324	C₂²	—	3	1	no	—
325	C₂²	—	3	1	no	—
326	C₂²	—	6	2	no	—
327	C₂²	—	6	2	no	—
328	C₂²	—	12	4	no	—
329	C₂²	D₃×C₇×D₄	1	1	yes	characteristic
330	C₄	—	2	2	no	—
331	C₄	—	3	1	no	—
332	C₄	—	3	1	no	—
333	C₄	—	6	2	no	—
334	C₄	D₃×C₇×D₄	1	1	yes	characteristic
335	C₄	C₂³×D₃×C₇	1	1	yes	characteristic
336	C₃	C₂×C₇×#135	1	1	yes	characteristic, complemented, Sylow
337	C₂	—	2	1	no	—
338	C₂	—	3	2	no	—
339	C₂	—	4	2	no	—
340	C₂	—	6	1	no	—
341	C₂	—	12	2	no	—
342	C₂	C₂×D₃×C₇×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₇	D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁴×C₇
Frattini	C₄	C₂³×D₃×C₇
Fitting	C₃×C₇×#135	C₂
socle	C₂×C₃×C₇	C₂²×D₄
hypercenter	C₇×#135	D₃
hypocenter	C₃	C₂×C₇×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₇ ◁ C₂×C₄×C₇ ◁ C₇×#135

Complements

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

N	H ≅ G/N	type
1. D₃×C₇×#41	C₂	semidirect
2. C₃×C₇×#135	C₂	semidirect
3. C₇×#950	C₂	semidirect
4. C₇×#919	C₂	semidirect
5. D₃×C₇×Q₁₆	C₂	semidirect
6. C₇×#916	C₂	semidirect
7. D₃×C₇×SD₁₆	C₂	semidirect
8. C₇×#912	C₂	semidirect
9. D₃×C₇×D₈	C₂	semidirect
10. C₇×#904	C₂	semidirect
11. C₂×D₃×C₇×C₈	C₂	semidirect
13. C₃×C₇×#41	C₂²	semidirect
14. C₇×#239	C₂²	semidirect
17. C₇×#237	C₂²	semidirect
21. C₇×#235	C₂²	semidirect
24. C₃×C₇×Q₁₆	C₂²	semidirect
25. C₃×C₇×SD₁₆	C₂²	semidirect
26. C₃×C₇×D₈	C₂²	semidirect
27. C₂×C₃×C₇×C₈	C₂²	semidirect
28. C₇×#216	C₂²	semidirect
29. C₇×#215	C₂²	semidirect
30. C₇×#214	C₂²	semidirect
31. C₇×#213	C₂²	semidirect
32. C₂×C₇×C₃⋊C₈	C₂²	semidirect
33. C₇×Dic₁₂	C₂²	semidirect
34. C₇×D₂₄	C₂²	semidirect
35. C₇×#204	C₂²	semidirect
38. D₃×C₇×C₈	C₂²	semidirect
39. D₃×C₇×C₈	C₂²	semidirect
46. C₇×#135	D₃	direct (N × H)
51. D₃×#135	C₇	direct (N × H)
84. C₇×#41	C₂×D₃	semidirect
92. C₇×Q₁₆	C₂×D₃	semidirect
96. C₇×SD₁₆	C₂×D₃	semidirect
99. C₇×D₈	C₂×D₃	semidirect
105. C₂×C₇×C₈	C₂×D₃	semidirect
106. D₃×#41	C₂×C₇	semidirect
107. C₃×#135	C₂×C₇	semidirect
108. #950	C₂×C₇	semidirect
109. #919	C₂×C₇	semidirect
110. D₃×Q₁₆	C₂×C₇	semidirect
111. #916	C₂×C₇	semidirect
112. D₃×SD₁₆	C₂×C₇	semidirect
113. #912	C₂×C₇	semidirect
114. D₃×D₈	C₂×C₇	semidirect
115. #904	C₂×C₇	semidirect
116. C₂×D₃×C₈	C₂×C₇	semidirect
158. C₃×#41	C₂²×C₇	semidirect
159. #239	C₂²×C₇	semidirect
162. #237	C₂²×C₇	semidirect
166. #235	C₂²×C₇	semidirect
169. C₃×Q₁₆	C₂²×C₇	semidirect
170. C₃×SD₁₆	C₂²×C₇	semidirect
171. C₃×D₈	C₂²×C₇	semidirect
172. C₂×C₃×C₈	C₂²×C₇	semidirect
173. #216	C₂²×C₇	semidirect
174. #215	C₂²×C₇	semidirect
175. #214	C₂²×C₇	semidirect
176. #213	C₂²×C₇	semidirect
177. C₂×C₃⋊C₈	C₂²×C₇	semidirect
178. Dic₁₂	C₂²×C₇	semidirect
179. D₂₄	C₂²×C₇	semidirect
180. #204	C₂²×C₇	semidirect
183. D₃×C₈	C₂²×C₇	semidirect
184. D₃×C₈	C₂²×C₇	semidirect
190. D₃×C₇	#135	direct (N × H)
197. #135	D₃×C₇	direct (N × H)
242. C₃×C₇	C₂×#135	semidirect
248. #41	C₂×D₃×C₇	semidirect
256. Q₁₆	C₂×D₃×C₇	semidirect
260. SD₁₆	C₂×D₃×C₇	semidirect
263. D₈	C₂×D₃×C₇	semidirect
269. C₂×C₈	C₂×D₃×C₇	semidirect
316. C₇	D₃×#135	direct (N × H)
322. D₃	C₇×#135	direct (N × H)
336. C₃	C₂×C₇×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₃×C₇×#41	2
C₃×C₇×#135	2
C₇×#950	2
C₇×#919	2
D₃×C₇×Q₁₆	2
C₇×#916	2
D₃×C₇×SD₁₆	2
C₇×#912	2
D₃×C₇×D₈	2
C₇×#904	2
C₂×D₃×C₇×C₈	2
C₂×C₇×#135	3
D₃×#135	7

Subgroups — D3×C7×#135 #13061483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×#135 #13061483