Subgroups — C₇×D₄×#67 #13061519

Order 1344.

856 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×#67	C₂	1	2	yes	maximal, complemented
3	C₂×D₃×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#953	C₂	1	2	yes	maximal, complemented
5	C₇×#940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#939	C₂	1	2	yes	maximal, complemented
7	C₇×#938	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#937	C₂	1	2	yes	maximal, complemented
9	C₇×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#930	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×#67	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×D₄²	—	3	1	no	maximal, Hall
13	C₂⁴×C₃×C₇	C₂²	1	2	yes	complemented
14	C₂³×D₃×C₇	C₂²	1	2	yes	complemented
15	C₂×C₃×C₇×D₄	—	2	4	no	—
16	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₇×D₄	C₂²	1	2	yes	complemented
18	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₇×#67	—	2	8	no	—
21	C₂×C₇×#67	C₂²	1	1	yes	characteristic
22	C₂×C₇×#67	C₂²	1	2	yes	complemented
23	C₂×C₇×#67	C₂²	1	2	yes	complemented
24	C₂×C₇×#67	C₂²	1	2	yes	complemented
25	C₂×C₇×#67	C₂²	1	2	yes	complemented
26	C₂×C₇×#67	C₂²	1	2	yes	complemented
27	C₂²×C₇×Dic₃	C₂²	1	2	yes	complemented
28	D₃×C₇×D₄	—	2	4	no	—
29	C₂×C₇×D₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×D₃×C₇	C₂²	1	1	yes	characteristic, complemented
31	C₇×#217	C₂²	1	1	yes	characteristic, complemented
32	C₇×#217	C₂²	1	2	yes	complemented
33	C₇×#217	C₂²	1	2	yes	complemented
34	C₇×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₇×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₇×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
37	C₇×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₇×Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₇×D₄	—	3	2	no	—
40	C₂²×C₇×D₄	—	3	1	no	—
41	C₂²×C₇×D₄	D₃	1	1	yes	characteristic, complemented
42	C₇×#127	—	3	1	no	—
43	C₇×#121	—	3	1	no	—
44	C₇×#121	—	3	2	no	—
45	C₇×#121	—	3	1	no	—
46	C₇×#120	—	3	2	no	—
47	C₇×#120	—	3	2	no	—
48	C₄×C₇×D₄	—	3	1	no	—
49	C₄×C₇×D₄	—	3	1	no	—
50	D₄×#67	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
51	C₂³×C₃×C₇	—	2	4	no	—
52	C₂³×C₃×C₇	—	2	4	no	—
53	C₂³×C₃×C₇	—	4	2	no	—
54	C₂³×C₃×C₇	C₂³	1	2	yes	—
55	C₂³×C₃×C₇	C₂³	1	2	yes	—
56	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
57	C₂²×D₃×C₇	—	2	4	no	—
58	C₂²×D₃×C₇	—	2	4	no	—
59	C₂²×D₃×C₇	—	4	2	no	—
60	C₂²×D₃×C₇	C₂³	1	2	yes	—
61	C₂²×D₃×C₇	C₂³	1	1	yes	characteristic
62	C₃×C₇×D₄	—	2	4	no	—
63	C₃×C₇×D₄	—	2	2	no	—
64	C₃×C₇×D₄	D₄	1	4	yes	complemented
65	C₂×C₃×C₄×C₇	—	2	2	no	—
66	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
68	C₇×#67	—	2	4	no	—
69	C₇×#67	—	2	4	no	—
70	C₇×#67	—	2	4	no	—
71	C₇×#67	—	2	4	no	—
72	C₇×#67	—	4	2	no	—
73	C₇×#67	D₄	1	4	yes	direct product factor
74	C₂×C₇×Dic₃	—	2	4	no	—
75	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
76	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
77	C₂×C₇×Dic₃	C₂³	1	2	yes	—
78	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
79	C₇×D₁₂	—	2	2	no	—
80	C₄×D₃×C₇	—	2	2	no	—
81	C₂⁴×C₇	—	3	2	no	—
82	C₂⁴×C₇	C₂×D₃	1	2	yes	complemented
83	C₂×C₇×D₄	—	2	4	no	—
84	C₂×C₇×D₄	—	3	1	no	—
85	C₂×C₇×D₄	—	3	2	no	—
86	C₂×C₇×D₄	—	3	2	no	—
87	C₂×C₇×D₄	—	3	2	no	—
88	C₂×C₇×D₄	—	3	2	no	—
89	C₂×C₇×D₄	—	3	2	no	—
90	C₂×C₇×D₄	—	3	1	no	—
91	C₂×C₇×D₄	—	6	8	no	—
92	C₂×C₇×D₄	—	6	4	no	—
93	C₂×C₇×D₄	C₂×D₃	1	1	yes	characteristic
94	C₂×C₇×D₄	C₂×D₃	1	2	yes	complemented
95	C₂×C₇×D₄	C₂×D₃	1	1	yes	characteristic, complemented
96	C₂²×C₄×C₇	—	3	2	no	—
97	C₂²×C₄×C₇	—	3	1	no	—
98	C₂²×C₄×C₇	C₂×D₃	1	1	yes	characteristic, complemented
99	C₇×C₄⋊C₄	—	3	1	no	—
100	C₇×C₄⋊C₄	—	3	1	no	—
101	C₇×C₂²⋊C₄	—	3	1	no	—
102	C₇×C₂²⋊C₄	—	3	2	no	—
103	C₇×C₂²⋊C₄	—	3	2	no	—
104	C₇×C₂²⋊C₄	—	3	1	no	—
105	C₇×C₂²⋊C₄	—	3	2	no	—
106	C₄²×C₇	—	3	1	no	—
107	C₂²×C₃×D₄	C₂×C₇	1	1	yes	characteristic, complemented
108	C₂²×#67	C₂×C₇	1	2	yes	complemented
109	C₂×D₃×D₄	C₂×C₇	1	1	yes	characteristic, complemented
110	#953	C₂×C₇	1	2	yes	complemented
111	#940	C₂×C₇	1	1	yes	characteristic, complemented
112	#939	C₂×C₇	1	2	yes	complemented
113	#938	C₂×C₇	1	1	yes	characteristic, complemented
114	#937	C₂×C₇	1	2	yes	complemented
115	D₄×Dic₃	C₂×C₇	1	1	yes	characteristic, complemented
116	#930	C₂×C₇	1	1	yes	characteristic, complemented
117	C₄×#67	C₂×C₇	1	1	yes	characteristic, complemented
118	C₂²×C₃×C₇	—	2	2	no	—
119	C₂²×C₃×C₇	—	2	1	no	—
120	C₂²×C₃×C₇	—	2	2	no	—
121	C₂²×C₃×C₇	—	2	1	no	—
122	C₂²×C₃×C₇	—	2	2	no	—
123	C₂²×C₃×C₇	—	2	2	no	—
124	C₂²×C₃×C₇	—	2	2	no	—
125	C₂²×C₃×C₇	—	4	8	no	—
126	C₂²×C₃×C₇	C₂×D₄	1	2	yes	complemented
127	C₂²×C₃×C₇	C₂×D₄	1	4	yes	complemented
128	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
129	C₂×D₃×C₇	—	2	1	no	—
130	C₂×D₃×C₇	—	2	1	no	—
131	C₂×D₃×C₇	—	2	2	no	—
132	C₂×D₃×C₇	—	2	2	no	—
133	C₂×D₃×C₇	—	2	2	no	—
134	C₂×D₃×C₇	—	4	8	no	—
135	C₂×D₃×C₇	C₂×D₄	1	2	yes	complemented
136	C₃×C₄×C₇	—	2	1	no	—
137	C₃×C₄×C₇	C₂×D₄	1	2	yes	complemented
138	C₇×Dic₃	—	2	1	no	—
139	C₇×Dic₃	—	2	2	no	—
140	C₇×Dic₃	—	2	1	no	—
141	C₇×Dic₃	C₂×D₄	1	2	yes	complemented
142	D₄²	—	3	1	no	Sylow
143	C₂³×C₇	—	2	4	no	—
144	C₂³×C₇	—	2	4	no	—
145	C₂³×C₇	—	3	1	no	—
146	C₂³×C₇	—	3	2	no	—
147	C₂³×C₇	—	4	2	no	—
148	C₂³×C₇	—	6	4	no	—
149	C₂³×C₇	—	6	4	no	—
150	C₂³×C₇	—	12	2	no	—
151	C₂³×C₇	C₂²×D₃	1	2	yes	—
152	C₂³×C₇	C₂²×D₃	1	1	yes	characteristic
153	C₂³×C₇	C₂²×D₃	1	2	yes	—
154	C₇×D₄	—	2	4	no	—
155	C₇×D₄	—	2	2	no	—
156	C₇×D₄	—	3	4	no	—
157	C₇×D₄	—	6	4	no	—
158	C₇×D₄	—	6	4	no	—
159	C₇×D₄	—	6	4	no	—
160	C₇×D₄	—	6	4	no	—
161	C₇×D₄	—	6	2	no	—
162	C₇×D₄	—	12	2	no	—
163	C₇×D₄	#67	1	4	yes	direct product factor
164	C₂×C₄×C₇	—	2	2	no	—
165	C₂×C₄×C₇	—	3	1	no	—
166	C₂×C₄×C₇	—	3	1	no	—
167	C₂×C₄×C₇	—	3	2	no	—
168	C₂×C₄×C₇	—	3	1	no	—
169	C₂×C₄×C₇	—	6	4	no	—
170	C₂×C₄×C₇	—	6	2	no	—
171	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
172	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
173	C₂⁴×C₃	C₂²×C₇	1	2	yes	complemented
174	C₂³×D₃	C₂²×C₇	1	2	yes	complemented
175	C₂×C₃×D₄	—	2	4	no	—
176	C₂×C₃×D₄	C₂²×C₇	1	1	yes	characteristic
177	C₂×C₃×D₄	C₂²×C₇	1	2	yes	complemented
178	C₂×C₃×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
179	C₂²×C₃×C₄	C₂²×C₇	1	1	yes	characteristic, complemented
180	C₂×#67	—	2	8	no	—
181	C₂×#67	C₂²×C₇	1	1	yes	characteristic
182	C₂×#67	C₂²×C₇	1	2	yes	complemented
183	C₂×#67	C₂²×C₇	1	2	yes	complemented
184	C₂×#67	C₂²×C₇	1	2	yes	complemented
185	C₂×#67	C₂²×C₇	1	2	yes	complemented
186	C₂×#67	C₂²×C₇	1	2	yes	complemented
187	C₂²×Dic₃	C₂²×C₇	1	2	yes	complemented
188	D₃×D₄	—	2	4	no	—
189	C₂×D₁₂	C₂²×C₇	1	1	yes	characteristic, complemented
190	C₂×C₄×D₃	C₂²×C₇	1	1	yes	characteristic, complemented
191	#217	C₂²×C₇	1	1	yes	characteristic, complemented
192	#217	C₂²×C₇	1	2	yes	complemented
193	#217	C₂²×C₇	1	2	yes	complemented
194	(C₂×D₃)⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
195	(C₂×D₃)⋊C₄	C₂²×C₇	1	2	yes	complemented
196	C₄⋊Dic₃	C₂²×C₇	1	1	yes	characteristic, complemented
197	Dic₃⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
198	C₄×Dic₃	C₂²×C₇	1	1	yes	characteristic, complemented
199	C₂×C₃×C₇	—	2	4	no	—
200	C₂×C₃×C₇	—	2	2	no	—
201	C₂×C₃×C₇	—	4	2	no	—
202	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
205	D₃×C₇	—	2	2	no	—
206	D₃×C₇	—	4	2	no	—
207	C₂²×D₄	—	3	2	no	—
208	C₂²×D₄	—	3	1	no	—
209	C₂²×D₄	D₃×C₇	1	1	yes	characteristic, complemented
210	#127	—	3	1	no	—
211	#121	—	3	1	no	—
212	#121	—	3	2	no	—
213	#121	—	3	1	no	—
214	#120	—	3	2	no	—
215	#120	—	3	2	no	—
216	C₄×D₄	—	3	1	no	—
217	C₄×D₄	—	3	1	no	—
218	C₂²×C₇	—	2	2	no	—
219	C₂²×C₇	—	2	1	no	—
220	C₂²×C₇	—	2	2	no	—
221	C₂²×C₇	—	2	1	no	—
222	C₂²×C₇	—	2	2	no	—
223	C₂²×C₇	—	2	2	no	—
224	C₂²×C₇	—	2	2	no	—
225	C₂²×C₇	—	3	2	no	—
226	C₂²×C₇	—	4	8	no	—
227	C₂²×C₇	—	6	1	no	—
228	C₂²×C₇	—	6	1	no	—
229	C₂²×C₇	—	6	2	no	—
230	C₂²×C₇	—	6	2	no	—
231	C₂²×C₇	—	6	2	no	—
232	C₂²×C₇	—	12	8	no	—
233	C₂²×C₇	D₃×D₄	1	2	yes	complemented
234	C₂²×C₇	C₂×#67	1	4	yes	complemented
235	C₂²×C₇	C₂³×D₃	1	1	yes	characteristic
236	C₄×C₇	—	2	1	no	—
237	C₄×C₇	—	3	2	no	—
238	C₄×C₇	—	6	2	no	—
239	C₄×C₇	—	6	1	no	—
240	C₄×C₇	—	6	1	no	—
241	C₄×C₇	C₂×#67	1	2	yes	complemented
242	C₂³×C₃	—	2	4	no	—
243	C₂³×C₃	—	2	4	no	—
244	C₂³×C₃	—	4	2	no	—
245	C₂³×C₃	C₂³×C₇	1	2	yes	—
246	C₂³×C₃	C₂³×C₇	1	2	yes	—
247	C₂³×C₃	C₂³×C₇	1	1	yes	characteristic
248	C₂²×D₃	—	2	4	no	—
249	C₂²×D₃	—	2	4	no	—
250	C₂²×D₃	—	4	2	no	—
251	C₂²×D₃	C₂³×C₇	1	2	yes	—
252	C₂²×D₃	C₂³×C₇	1	1	yes	characteristic
253	C₃×D₄	—	2	4	no	—
254	C₃×D₄	—	2	2	no	—
255	C₃×D₄	C₇×D₄	1	4	yes	complemented
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂³×C₇	1	1	yes	characteristic
259	#67	—	2	4	no	—
260	#67	—	2	4	no	—
261	#67	—	2	4	no	—
262	#67	—	2	4	no	—
263	#67	—	4	2	no	—
264	#67	C₇×D₄	1	4	yes	direct product factor
265	C₂×Dic₃	—	2	4	no	—
266	C₂×Dic₃	C₂³×C₇	1	1	yes	characteristic
267	C₂×Dic₃	C₂³×C₇	1	1	yes	characteristic
268	C₂×Dic₃	C₂³×C₇	1	2	yes	—
269	C₂×Dic₃	C₂³×C₇	1	1	yes	characteristic
270	D₁₂	—	2	2	no	—
271	C₄×D₃	—	2	2	no	—
272	C₃×C₇	D₄²	1	1	yes	characteristic, complemented, Hall
273	C₂⁴	—	3	2	no	—
274	C₂⁴	C₂×D₃×C₇	1	2	yes	complemented
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	3	1	no	—
277	C₂×D₄	—	3	2	no	—
278	C₂×D₄	—	3	2	no	—
279	C₂×D₄	—	3	2	no	—
280	C₂×D₄	—	3	2	no	—
281	C₂×D₄	—	3	2	no	—
282	C₂×D₄	—	3	1	no	—
283	C₂×D₄	—	6	8	no	—
284	C₂×D₄	—	6	4	no	—
285	C₂×D₄	C₂×D₃×C₇	1	1	yes	characteristic
286	C₂×D₄	C₂×D₃×C₇	1	2	yes	complemented
287	C₂×D₄	C₂×D₃×C₇	1	1	yes	characteristic, complemented
288	C₂²×C₄	—	3	2	no	—
289	C₂²×C₄	—	3	1	no	—
290	C₂²×C₄	C₂×D₃×C₇	1	1	yes	characteristic, complemented
291	C₄⋊C₄	—	3	1	no	—
292	C₄⋊C₄	—	3	1	no	—
293	C₂²⋊C₄	—	3	1	no	—
294	C₂²⋊C₄	—	3	2	no	—
295	C₂²⋊C₄	—	3	2	no	—
296	C₂²⋊C₄	—	3	1	no	—
297	C₂²⋊C₄	—	3	2	no	—
298	C₄²	—	3	1	no	—
299	C₂×C₇	—	2	2	no	—
300	C₂×C₇	—	2	4	no	—
301	C₂×C₇	—	4	2	no	—
302	C₂×C₇	—	6	2	no	—
303	C₂×C₇	—	12	2	no	—
304	C₂×C₇	C₂×D₃×D₄	1	1	yes	characteristic
305	C₂×C₇	#1004	1	1	yes	characteristic
306	C₂×C₇	C₂²×#67	1	1	yes	characteristic
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	2	1	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	2	no	—
314	C₂²×C₃	—	4	8	no	—
315	C₂²×C₃	C₂×C₇×D₄	1	2	yes	complemented
316	C₂²×C₃	C₂×C₇×D₄	1	4	yes	complemented
317	C₂²×C₃	C₂⁴×C₇	1	1	yes	characteristic
318	C₂×D₃	—	2	1	no	—
319	C₂×D₃	—	2	1	no	—
320	C₂×D₃	—	2	2	no	—
321	C₂×D₃	—	2	2	no	—
322	C₂×D₃	—	2	2	no	—
323	C₂×D₃	—	4	8	no	—
324	C₂×D₃	C₂×C₇×D₄	1	2	yes	complemented
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	C₂×C₇×D₄	1	2	yes	complemented
327	Dic₃	—	2	1	no	—
328	Dic₃	—	2	2	no	—
329	Dic₃	—	2	1	no	—
330	Dic₃	C₂×C₇×D₄	1	2	yes	complemented
331	C₂³	—	2	4	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	3	1	no	—
334	C₂³	—	3	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	6	4	no	—
337	C₂³	—	6	4	no	—
338	C₂³	—	12	2	no	—
339	C₂³	C₂²×D₃×C₇	1	2	yes	—
340	C₂³	C₂²×D₃×C₇	1	1	yes	characteristic
341	C₂³	C₂²×D₃×C₇	1	2	yes	—
342	D₄	—	2	4	no	—
343	D₄	—	2	2	no	—
344	D₄	—	3	4	no	—
345	D₄	—	6	4	no	—
346	D₄	—	6	4	no	—
347	D₄	—	6	4	no	—
348	D₄	—	6	4	no	—
349	D₄	—	6	2	no	—
350	D₄	—	12	2	no	—
351	D₄	C₇×#67	1	4	yes	direct product factor
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	3	1	no	—
354	C₂×C₄	—	3	1	no	—
355	C₂×C₄	—	3	2	no	—
356	C₂×C₄	—	3	1	no	—
357	C₂×C₄	—	6	4	no	—
358	C₂×C₄	—	6	2	no	—
359	C₂×C₄	C₂²×D₃×C₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₃×C₇	1	1	yes	characteristic
361	C₇	D₄×#67	1	1	yes	characteristic, direct product factor, Sylow
362	C₂×C₃	—	2	4	no	—
363	C₂×C₃	—	2	2	no	—
364	C₂×C₃	—	4	2	no	—
365	C₂×C₃	C₂²×C₇×D₄	1	1	yes	characteristic
366	C₂×C₃	C₂²×C₇×D₄	1	1	yes	characteristic
367	C₂×C₃	C₇×H(5,𝔽₂)	1	1	yes	characteristic
368	D₃	—	2	2	no	—
369	D₃	—	4	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	3	2	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	6	1	no	—
380	C₂²	—	6	1	no	—
381	C₂²	—	6	2	no	—
382	C₂²	—	6	2	no	—
383	C₂²	—	6	2	no	—
384	C₂²	—	12	8	no	—
385	C₂²	D₃×C₇×D₄	1	2	yes	complemented
386	C₂²	C₂×C₇×#67	1	4	yes	complemented
387	C₂²	C₂³×D₃×C₇	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	3	2	no	—
390	C₄	—	6	2	no	—
391	C₄	—	6	1	no	—
392	C₄	—	6	1	no	—
393	C₄	C₂×C₇×#67	1	2	yes	complemented
394	C₃	C₇×D₄²	1	1	yes	characteristic, complemented, Sylow
395	C₂	—	2	2	no	—
396	C₂	—	2	4	no	—
397	C₂	—	4	2	no	—
398	C₂	—	6	2	no	—
399	C₂	—	12	2	no	—
400	C₂	C₂×D₃×C₇×D₄	1	1	yes	characteristic
401	C₂	C₇×#1004	1	1	yes	characteristic
402	C₂	C₂²×C₇×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₇	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₇
Frattini	C₂²	C₂³×D₃×C₇
Fitting	C₂²×C₃×C₇×D₄	C₂
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₂²×C₇×D₄	D₃
hypocenter	C₃	C₇×D₄²
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₇ ◁ C₂²×C₇×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₇×D₄	C₂	semidirect
2. C₂²×C₇×#67	C₂	semidirect
3. C₂×D₃×C₇×D₄	C₂	semidirect
4. C₇×#953	C₂	semidirect
5. C₇×#940	C₂	semidirect
6. C₇×#939	C₂	semidirect
7. C₇×#938	C₂	semidirect
8. C₇×#937	C₂	semidirect
9. C₇×D₄×Dic₃	C₂	semidirect
10. C₇×#930	C₂	semidirect
11. C₄×C₇×#67	C₂	semidirect
13. C₂⁴×C₃×C₇	C₂²	semidirect
14. C₂³×D₃×C₇	C₂²	semidirect
17. C₂×C₃×C₇×D₄	C₂²	semidirect
18. C₂×C₃×C₇×D₄	C₂²	semidirect
19. C₂²×C₃×C₄×C₇	C₂²	semidirect
22. C₂×C₇×#67	C₂²	semidirect
23. C₂×C₇×#67	C₂²	semidirect
24. C₂×C₇×#67	C₂²	semidirect
25. C₂×C₇×#67	C₂²	semidirect
26. C₂×C₇×#67	C₂²	semidirect
27. C₂²×C₇×Dic₃	C₂²	semidirect
29. C₂×C₇×D₁₂	C₂²	semidirect
30. C₂×C₄×D₃×C₇	C₂²	semidirect
31. C₇×#217	C₂²	semidirect
32. C₇×#217	C₂²	semidirect
33. C₇×#217	C₂²	semidirect
34. C₇×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₇×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₇×C₄⋊Dic₃	C₂²	semidirect
37. C₇×Dic₃⋊C₄	C₂²	semidirect
38. C₄×C₇×Dic₃	C₂²	semidirect
41. C₂²×C₇×D₄	D₃	semidirect
50. D₄×#67	C₇	direct (N × H)
64. C₃×C₇×D₄	D₄	semidirect
73. C₇×#67	D₄	direct (N × H)
82. C₂⁴×C₇	C₂×D₃	semidirect
94. C₂×C₇×D₄	C₂×D₃	semidirect
95. C₂×C₇×D₄	C₂×D₃	semidirect
98. C₂²×C₄×C₇	C₂×D₃	semidirect
107. C₂²×C₃×D₄	C₂×C₇	semidirect
108. C₂²×#67	C₂×C₇	semidirect
109. C₂×D₃×D₄	C₂×C₇	semidirect
110. #953	C₂×C₇	semidirect
111. #940	C₂×C₇	semidirect
112. #939	C₂×C₇	semidirect
113. #938	C₂×C₇	semidirect
114. #937	C₂×C₇	semidirect
115. D₄×Dic₃	C₂×C₇	semidirect
116. #930	C₂×C₇	semidirect
117. C₄×#67	C₂×C₇	semidirect
126. C₂²×C₃×C₇	C₂×D₄	semidirect
127. C₂²×C₃×C₇	C₂×D₄	semidirect
135. C₂×D₃×C₇	C₂×D₄	semidirect
137. C₃×C₄×C₇	C₂×D₄	semidirect
141. C₇×Dic₃	C₂×D₄	semidirect
163. C₇×D₄	#67	direct (N × H)
173. C₂⁴×C₃	C₂²×C₇	semidirect
174. C₂³×D₃	C₂²×C₇	semidirect
177. C₂×C₃×D₄	C₂²×C₇	semidirect
178. C₂×C₃×D₄	C₂²×C₇	semidirect
179. C₂²×C₃×C₄	C₂²×C₇	semidirect
182. C₂×#67	C₂²×C₇	semidirect
183. C₂×#67	C₂²×C₇	semidirect
184. C₂×#67	C₂²×C₇	semidirect
185. C₂×#67	C₂²×C₇	semidirect
186. C₂×#67	C₂²×C₇	semidirect
187. C₂²×Dic₃	C₂²×C₇	semidirect
189. C₂×D₁₂	C₂²×C₇	semidirect
190. C₂×C₄×D₃	C₂²×C₇	semidirect
191. #217	C₂²×C₇	semidirect
192. #217	C₂²×C₇	semidirect
193. #217	C₂²×C₇	semidirect
194. (C₂×D₃)⋊C₄	C₂²×C₇	semidirect
195. (C₂×D₃)⋊C₄	C₂²×C₇	semidirect
196. C₄⋊Dic₃	C₂²×C₇	semidirect
197. Dic₃⋊C₄	C₂²×C₇	semidirect
198. C₄×Dic₃	C₂²×C₇	semidirect
209. C₂²×D₄	D₃×C₇	semidirect
233. C₂²×C₇	D₃×D₄	semidirect
234. C₂²×C₇	C₂×#67	semidirect
241. C₄×C₇	C₂×#67	semidirect
255. C₃×D₄	C₇×D₄	semidirect
264. #67	C₇×D₄	direct (N × H)
272. C₃×C₇	D₄²	semidirect
274. C₂⁴	C₂×D₃×C₇	semidirect
286. C₂×D₄	C₂×D₃×C₇	semidirect
287. C₂×D₄	C₂×D₃×C₇	semidirect
290. C₂²×C₄	C₂×D₃×C₇	semidirect
315. C₂²×C₃	C₂×C₇×D₄	semidirect
316. C₂²×C₃	C₂×C₇×D₄	semidirect
324. C₂×D₃	C₂×C₇×D₄	semidirect
326. C₃×C₄	C₂×C₇×D₄	semidirect
330. Dic₃	C₂×C₇×D₄	semidirect
351. D₄	C₇×#67	direct (N × H)
361. C₇	D₄×#67	direct (N × H)
385. C₂²	D₃×C₇×D₄	semidirect
386. C₂²	C₂×C₇×#67	semidirect
393. C₄	C₂×C₇×#67	semidirect
394. C₃	C₇×D₄²	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₇×D₄	2
C₂²×C₇×#67	2
C₂×D₃×C₇×D₄	2
C₇×#953	2
C₇×#940	2
C₇×#939	2
C₇×#938	2
C₇×#937	2
C₇×D₄×Dic₃	2
C₇×#930	2
C₄×C₇×#67	2
C₇×D₄²	3
D₄×#67	7

Subgroups — C7×D4×#67 #13061519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₄×#67 #13061519