Subgroups — C₂×C₇×#3352 #13238461

Order 1792.

1834 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#552	C₂	1	2	yes	maximal
2	C₇×#3352	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#484	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#485	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#479	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#470	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic
10	C₂×C₇×#428	C₂	1	2	yes	maximal, complemented
11	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
13	C₇×#552	—	2	8	no	—
14	C₇×#552	C₂²	1	16	yes	—
15	C₂×C₇×#126	—	2	2	no	—
16	C₂×C₇×#125	—	2	2	no	—
17	C₂×C₇×#125	C₂²	1	2	yes	—
18	C₂×C₇×#123	—	2	2	no	—
19	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
22	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₇×#117	—	2	2	no	—
24	C₂×C₇×#117	C₂²	1	2	yes	—
25	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
26	C₇×#499	C₂²	1	8	yes	complemented
27	C₇×#485	C₂²	1	16	yes	complemented
28	C₇×#484	C₂²	1	16	yes	complemented
29	C₇×#479	C₂²	1	16	yes	complemented
30	C₇×#470	C₂²	1	16	yes	complemented
31	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
32	C₇×#436	C₂²	1	8	yes	—
33	C₇×#428	C₂²	1	16	yes	complemented
34	C₂×C₇×#107	C₂²	1	1	yes	characteristic
35	C₂×C₇×#107	C₂²	1	1	yes	characteristic
36	C₂×C₇×#107	C₂²	1	1	yes	characteristic
37	C₂×C₇×#107	C₂²	1	2	yes	—
38	C₂×C₇×#106	C₂²	1	2	yes	—
39	C₂×C₇×#106	C₂²	1	2	yes	—
40	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₇×#103	C₂²	1	2	yes	—
42	C₂×C₇×#103	C₂²	1	2	yes	—
43	C₂×C₇×#103	C₂²	1	2	yes	—
44	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
46	C₂×#3352	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂²×C₇×Q₈	C₂³	1	2	yes	—
48	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₇	—	2	2	no	—
50	C₂³×C₄×C₇	C₂³	1	2	yes	—
51	C₂×C₇×Q₁₆	—	2	4	no	—
52	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
53	C₂×C₇×M₁₆	—	2	8	no	—
54	C₂×C₇×M₁₆	C₂³	1	8	yes	—
55	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₇×C₈	C₂³	1	2	yes	—
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₇×#126	—	2	16	no	—
59	C₇×#125	—	2	16	no	—
60	C₇×#125	—	2	4	no	—
61	C₇×#125	C₂³	1	8	yes	—
62	C₇×#123	—	2	16	no	—
63	C₇×C₂²⋊Q₈	—	2	4	no	—
64	C₇×C₂²⋊Q₈	—	2	4	no	—
65	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
66	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
67	C₄×C₇×Q₈	—	2	4	no	—
68	C₄×C₇×Q₈	C₂³	1	8	yes	—
69	C₄×C₇×D₄	D₄	1	4	yes	—
70	C₄×C₇×D₄	C₂³	1	4	yes	—
71	C₇×#117	—	2	4	no	—
72	C₇×#117	—	2	16	no	—
73	C₇×#117	C₂³	1	8	yes	—
74	C₂×C₇×C₄⋊C₄	—	2	2	no	—
75	C₂×C₇×C₄⋊C₄	—	2	4	no	—
76	C₂×C₇×C₄⋊C₄	—	2	2	no	—
77	C₂×C₇×C₄⋊C₄	—	2	2	no	—
78	C₂×C₇×C₄⋊C₄	—	2	2	no	—
79	C₂×C₇×C₄⋊C₄	—	2	2	no	—
80	C₂×C₇×C₄⋊C₄	—	2	2	no	—
81	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
82	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
83	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
90	C₂×C₄²×C₇	—	2	2	no	—
91	C₂×C₄²×C₇	—	2	2	no	—
92	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
93	C₇×#107	C₂³	1	8	yes	—
94	C₇×#107	C₂³	1	4	yes	—
95	C₇×#107	C₂³	1	4	yes	—
96	C₇×#107	C₂³	1	4	yes	—
97	C₇×#106	C₂³	1	8	yes	—
98	C₇×#106	C₂³	1	8	yes	—
99	C₇×C₄⋊C₈	C₂³	1	4	yes	—
100	C₇×#103	C₂³	1	8	yes	—
101	C₇×#103	C₂³	1	8	yes	—
102	C₇×#103	C₂³	1	8	yes	—
103	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
104	C₄×C₇×C₈	C₂³	1	4	yes	—
105	C₂×#552	C₂×C₇	1	2	yes	—
106	#3352	C₂×C₇	1	16	yes	direct product factor
107	C₂×#499	C₂×C₇	1	1	yes	characteristic, complemented
108	C₂×#484	C₂×C₇	1	2	yes	complemented
109	C₂×#485	C₂×C₇	1	2	yes	complemented
110	C₂×#479	C₂×C₇	1	2	yes	complemented
111	C₂×#470	C₂×C₇	1	2	yes	complemented
112	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
113	C₂×#436	C₂×C₇	1	1	yes	characteristic
114	C₂×#428	C₂×C₇	1	2	yes	complemented
115	C₂⁴×C₇	C₂×D₄	1	2	yes	—
116	C₂×C₇×Q₈	—	2	2	no	—
117	C₂×C₇×Q₈	—	2	4	no	—
118	C₂×C₇×Q₈	—	2	4	no	—
119	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
120	C₂×C₇×D₄	—	4	2	no	—
121	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₇	—	2	4	no	—
123	C₂²×C₄×C₇	—	2	4	no	—
124	C₂²×C₄×C₇	—	2	8	no	—
125	C₂²×C₄×C₇	—	2	2	no	—
126	C₂²×C₄×C₇	—	2	2	no	—
127	C₂²×C₄×C₇	—	2	2	no	—
128	C₂²×C₄×C₇	—	2	2	no	—
129	C₂²×C₄×C₇	—	4	8	no	—
130	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
136	C₇×Q₁₆	—	2	8	no	—
137	C₇×M₁₆	—	2	16	no	—
138	C₂×C₇×C₈	—	2	4	no	—
139	C₂×C₇×C₈	—	2	2	no	—
140	C₂×C₇×C₈	#41	1	4	yes	—
141	C₂×C₇×C₈	C₂⁴	1	2	yes	—
142	C₂×C₇×C₈	C₂⁴	1	4	yes	—
143	C₂×C₇×C₈	C₂⁴	1	2	yes	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	2	8	no	—
147	C₇×C₄⋊C₄	—	2	8	no	—
148	C₇×C₄⋊C₄	—	2	8	no	—
149	C₇×C₄⋊C₄	—	2	8	no	—
150	C₇×C₄⋊C₄	—	2	8	no	—
151	C₇×C₄⋊C₄	—	2	8	no	—
152	C₇×C₄⋊C₄	—	2	2	no	—
153	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
154	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
155	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
156	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
157	C₇×C₂²⋊C₄	—	2	8	no	—
158	C₇×C₂²⋊C₄	—	2	8	no	—
159	C₇×C₂²⋊C₄	—	2	8	no	—
160	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
161	C₄²×C₇	—	2	8	no	—
162	C₄²×C₇	—	2	8	no	—
163	C₄²×C₇	C₂×D₄	1	2	yes	—
164	C₄²×C₇	C₂⁴	1	2	yes	—
165	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
166	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
167	#552	—	2	8	no	—
168	#552	C₂²×C₇	1	16	yes	—
169	C₂×#126	—	2	2	no	—
170	C₂×#125	—	2	2	no	—
171	C₂×#125	C₂²×C₇	1	2	yes	—
172	C₂×#123	—	2	2	no	—
173	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
174	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
175	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
176	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
177	C₂×#117	—	2	2	no	—
178	C₂×#117	C₂²×C₇	1	2	yes	—
179	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
180	#499	C₂²×C₇	1	8	yes	complemented
181	#485	C₂²×C₇	1	16	yes	complemented
182	#484	C₂²×C₇	1	16	yes	complemented
183	#479	C₂²×C₇	1	16	yes	complemented
184	#470	C₂²×C₇	1	16	yes	complemented
185	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
186	#436	C₂²×C₇	1	8	yes	—
187	#428	C₂²×C₇	1	16	yes	complemented
188	C₂×#107	C₂²×C₇	1	2	yes	—
189	C₂×#107	C₂²×C₇	1	1	yes	characteristic
190	C₂×#107	C₂²×C₇	1	1	yes	characteristic
191	C₂×#107	C₂²×C₇	1	1	yes	characteristic
192	C₂×#106	C₂²×C₇	1	2	yes	—
193	C₂×#106	C₂²×C₇	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
195	C₂×#103	C₂²×C₇	1	2	yes	—
196	C₂×#103	C₂²×C₇	1	2	yes	—
197	C₂×#103	C₂²×C₇	1	2	yes	—
198	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
199	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
200	C₂³×C₇	—	2	4	no	—
201	C₂³×C₇	—	2	4	no	—
202	C₂³×C₇	—	2	4	no	—
203	C₂³×C₇	C₂²×D₄	1	4	yes	—
204	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
205	C₇×Q₈	—	2	4	no	—
206	C₇×Q₈	—	2	4	no	—
207	C₇×Q₈	—	4	4	no	—
208	C₇×D₄	—	4	4	no	—
209	C₂×C₄×C₇	—	2	4	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	2	8	no	—
213	C₂×C₄×C₇	—	2	4	no	—
214	C₂×C₄×C₇	—	2	4	no	—
215	C₂×C₄×C₇	—	2	4	no	—
216	C₂×C₄×C₇	—	2	4	no	—
217	C₂×C₄×C₇	—	2	4	no	—
218	C₂×C₄×C₇	—	2	4	no	—
219	C₂×C₄×C₇	—	4	16	no	—
220	C₂×C₄×C₇	—	4	4	no	—
221	C₂×C₄×C₇	—	4	4	no	—
222	C₂×C₄×C₇	—	4	4	no	—
223	C₂×C₄×C₇	—	4	4	no	—
224	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
226	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇	C₂×#41	1	2	yes	—
229	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
230	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
231	C₇×C₈	—	2	4	no	—
232	C₇×C₈	—	2	2	no	—
233	C₇×C₈	C₂×#41	1	4	yes	—
234	C₂²×Q₈	C₂³×C₇	1	2	yes	—
235	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	C₂³×C₇	1	2	yes	—
238	C₂×Q₁₆	—	2	4	no	—
239	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
240	C₂×M₁₆	—	2	8	no	—
241	C₂×M₁₆	C₂³×C₇	1	8	yes	—
242	C₂²×C₈	C₂³×C₇	1	2	yes	—
243	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
245	#126	—	2	16	no	—
246	#125	—	2	16	no	—
247	#125	—	2	4	no	—
248	#125	C₂³×C₇	1	8	yes	—
249	#123	—	2	16	no	—
250	C₂²⋊Q₈	—	2	4	no	—
251	C₂²⋊Q₈	—	2	4	no	—
252	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
253	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
254	C₄×Q₈	—	2	4	no	—
255	C₄×Q₈	C₂³×C₇	1	8	yes	—
256	C₄×D₄	C₇×D₄	1	4	yes	—
257	C₄×D₄	C₂³×C₇	1	4	yes	—
258	#117	—	2	4	no	—
259	#117	—	2	16	no	—
260	#117	C₂³×C₇	1	8	yes	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	4	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
272	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
280	#107	C₂³×C₇	1	4	yes	—
281	#107	C₂³×C₇	1	8	yes	—
282	#107	C₂³×C₇	1	4	yes	—
283	#107	C₂³×C₇	1	4	yes	—
284	#106	C₂³×C₇	1	8	yes	—
285	#106	C₂³×C₇	1	8	yes	—
286	C₄⋊C₈	C₂³×C₇	1	4	yes	—
287	#103	C₂³×C₇	1	8	yes	—
288	#103	C₂³×C₇	1	8	yes	—
289	#103	C₂³×C₇	1	8	yes	—
290	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
291	C₄×C₈	C₂³×C₇	1	4	yes	—
292	C₂²×C₇	—	2	4	no	—
293	C₂²×C₇	—	2	4	no	—
294	C₂²×C₇	—	2	4	no	—
295	C₂²×C₇	—	4	8	no	—
296	C₂²×C₇	#547	1	2	yes	—
297	C₂²×C₇	#575	1	2	yes	—
298	C₂²×C₇	#578	1	2	yes	—
299	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
300	C₄×C₇	—	2	4	no	—
301	C₄×C₇	—	2	2	no	—
302	C₄×C₇	—	2	2	no	—
303	C₄×C₇	—	4	4	no	—
304	C₄×C₇	—	4	4	no	—
305	C₄×C₇	—	4	4	no	—
306	C₄×C₇	—	4	4	no	—
307	C₄×C₇	#547	1	2	yes	—
308	C₄×C₇	C₂²×#41	1	1	yes	characteristic
309	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	C₂⁴	C₂×C₇×D₄	1	2	yes	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	8	no	—
324	C₂²×C₄	—	4	8	no	—
325	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
327	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
329	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
330	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
331	Q₁₆	—	2	8	no	—
332	M₁₆	—	2	16	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	C₇×#41	1	4	yes	—
336	C₂×C₈	C₂⁴×C₇	1	2	yes	—
337	C₂×C₈	C₂⁴×C₇	1	4	yes	—
338	C₂×C₈	C₂⁴×C₇	1	2	yes	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	8	no	—
342	C₄⋊C₄	—	2	8	no	—
343	C₄⋊C₄	—	2	8	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
349	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
350	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
351	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
352	C₂²⋊C₄	—	2	8	no	—
353	C₂²⋊C₄	—	2	8	no	—
354	C₂²⋊C₄	—	2	8	no	—
355	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
356	C₄²	—	2	8	no	—
357	C₄²	—	2	8	no	—
358	C₄²	C₂×C₇×D₄	1	2	yes	—
359	C₄²	C₂⁴×C₇	1	2	yes	—
360	C₂×C₇	—	4	4	no	—
361	C₂×C₇	#3352	1	4	yes	direct product factor
362	C₂×C₇	C₂×#547	1	1	yes	characteristic
363	C₂×C₇	C₂×#575	1	1	yes	characteristic
364	C₂×C₇	C₂×#578	1	1	yes	characteristic
365	C₂³	—	2	4	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	4	no	—
368	C₂³	C₂²×C₇×D₄	1	4	yes	—
369	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	2	4	no	—
372	Q₈	—	4	4	no	—
373	D₄	—	4	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	4	16	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
390	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
391	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
392	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
393	C₂×C₄	C₂×C₇×#41	1	2	yes	—
394	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
395	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
396	C₈	—	2	4	no	—
397	C₈	—	2	2	no	—
398	C₈	C₂×C₇×#41	1	4	yes	—
399	C₇	C₂×#3352	1	1	yes	characteristic, direct product factor, Sylow
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	4	8	no	—
404	C₂²	C₇×#547	1	2	yes	—
405	C₂²	C₇×#575	1	2	yes	—
406	C₂²	C₇×#578	1	2	yes	—
407	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	2	4	no	—
411	C₄	—	4	4	no	—
412	C₄	—	4	4	no	—
413	C₄	—	4	4	no	—
414	C₄	—	4	4	no	—
415	C₄	C₇×#547	1	2	yes	—
416	C₄	C₂²×C₇×#41	1	1	yes	characteristic
417	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
418	C₂	—	4	4	no	—
419	C₂	C₇×#3352	1	4	yes	direct product factor
420	C₂	C₂×C₇×#547	1	1	yes	characteristic
421	C₂	C₂×C₇×#575	1	1	yes	characteristic
422	C₂	C₂×C₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂²×C₇×D₄	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3352	C₂	direct (N × H)
3. C₂×C₇×#499	C₂	semidirect
4. C₂×C₇×#484	C₂	semidirect
5. C₂×C₇×#485	C₂	semidirect
6. C₂×C₇×#479	C₂	semidirect
7. C₂×C₇×#470	C₂	semidirect
8. C₂×C₄×C₇×Q₁₆	C₂	semidirect
10. C₂×C₇×#428	C₂	semidirect
26. C₇×#499	C₂²	semidirect
27. C₇×#485	C₂²	semidirect
28. C₇×#484	C₂²	semidirect
29. C₇×#479	C₂²	semidirect
30. C₇×#470	C₂²	semidirect
31. C₄×C₇×Q₁₆	C₂²	semidirect
33. C₇×#428	C₂²	semidirect
46. C₂×#3352	C₇	direct (N × H)
106. #3352	C₂×C₇	direct (N × H)
107. C₂×#499	C₂×C₇	semidirect
108. C₂×#484	C₂×C₇	semidirect
109. C₂×#485	C₂×C₇	semidirect
110. C₂×#479	C₂×C₇	semidirect
111. C₂×#470	C₂×C₇	semidirect
112. C₂×C₄×Q₁₆	C₂×C₇	semidirect
114. C₂×#428	C₂×C₇	semidirect
180. #499	C₂²×C₇	semidirect
181. #485	C₂²×C₇	semidirect
182. #484	C₂²×C₇	semidirect
183. #479	C₂²×C₇	semidirect
184. #470	C₂²×C₇	semidirect
185. C₄×Q₁₆	C₂²×C₇	semidirect
187. #428	C₂²×C₇	semidirect
361. C₂×C₇	#3352	direct (N × H)
399. C₇	C₂×#3352	direct (N × H)
419. C₂	C₇×#3352	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×C₇×#552	2
C₇×#3352	2
C₂×C₇×#499	2
C₂×C₇×#484	2
C₂×C₇×#485	2
C₂×C₇×#479	2
C₂×C₇×#470	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₇×#436	2
C₂×C₇×#428	2
C₂×#3352	7

Subgroups — C2×C7×#3352 #13238461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3352 #13238461