Subgroups — C₂×C₇×#3283 #13238259

Order 1792.

2806 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#135	C₂	1	2	yes	maximal, complemented
2	C₂×C₇×#547	C₂	1	2	yes	maximal, complemented
3	C₇×#3283	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#467	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#461	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#452	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₇×#41	C₂²	1	4	yes	—
11	C₂×C₇×#135	—	2	16	no	—
12	C₂×C₇×#135	C₂²	1	16	yes	complemented
13	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
15	C₂²×C₇×SD₁₆	C₂²	1	4	yes	—
16	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
17	C₂³×C₇×C₈	C₂²	1	2	yes	—
18	C₇×#547	—	2	8	no	—
19	C₇×#547	C₂²	1	16	yes	complemented
20	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₇×#123	—	2	4	no	—
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
23	C₂×C₇×#121	—	2	2	no	—
24	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
25	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
26	C₂²×C₇×C₄⋊C₄	—	2	2	no	—
27	C₇×#494	C₂²	1	8	yes	complemented
28	C₇×#467	C₂²	1	16	yes	complemented
29	C₇×#461	C₂²	1	16	yes	complemented
30	C₇×#452	C₂²	1	32	yes	complemented
31	C₄×C₇×D₈	C₂²	1	8	yes	complemented
32	C₇×C₈×D₄	C₂²	1	8	yes	complemented
33	C₂×C₇×#107	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×#103	C₂²	1	4	yes	—
36	C₂×C₇×#102	C₂²	1	2	yes	—
37	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
39	C₂×#3283	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂×C₇×#41	—	2	8	no	—
41	C₂×C₇×#41	—	2	16	no	—
42	C₂×C₇×#41	—	4	8	no	—
43	C₂×C₇×#41	C₂³	1	16	yes	—
44	C₂²×C₇×Q₈	C₂³	1	4	yes	—
45	C₂²×C₇×D₄	—	2	4	no	—
46	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
47	C₂²×C₇×D₄	C₂³	1	2	yes	—
48	C₂³×C₄×C₇	—	2	4	no	—
49	C₂³×C₄×C₇	—	2	2	no	—
50	C₂³×C₄×C₇	C₂³	1	2	yes	—
51	C₇×#135	—	2	64	no	—
52	C₂×C₇×Q₁₆	—	2	8	no	—
53	C₂×C₇×Q₁₆	—	4	4	no	—
54	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
55	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
56	C₂×C₇×SD₁₆	—	2	16	no	—
57	C₂×C₇×SD₁₆	C₂³	1	16	yes	—
58	C₂×C₇×D₈	D₄	1	8	yes	complemented
59	C₂×C₇×D₈	C₂³	1	4	yes	—
60	C₂²×C₇×C₈	—	2	8	no	—
61	C₂²×C₇×C₈	C₂³	1	8	yes	—
62	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇×C₈	C₂³	1	2	yes	—
64	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
65	C₇×C₄⋊Q₈	—	2	4	no	—
66	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
67	C₇×#123	—	2	32	no	—
68	C₇×C₂²⋊Q₈	—	2	8	no	—
69	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
70	C₇×#121	—	2	16	no	—
71	C₄×C₇×D₄	—	2	4	no	—
72	C₄×C₇×D₄	D₄	1	4	yes	—
73	C₄×C₇×D₄	C₂³	1	8	yes	—
74	C₄×C₇×D₄	C₂³	1	4	yes	—
75	C₂×C₇×C₄⋊C₄	—	2	2	no	—
76	C₂×C₇×C₄⋊C₄	—	2	4	no	—
77	C₂×C₇×C₄⋊C₄	—	2	2	no	—
78	C₂×C₇×C₄⋊C₄	—	2	16	no	—
79	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
82	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
84	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
85	C₇×#107	C₂³	1	4	yes	—
86	C₇×C₄⋊C₈	C₂³	1	4	yes	—
87	C₇×#103	C₂³	1	16	yes	—
88	C₇×#102	C₂³	1	8	yes	—
89	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
90	C₄×C₇×C₈	C₂³	1	4	yes	—
91	C₂²×#135	C₂×C₇	1	2	yes	complemented
92	C₂×#547	C₂×C₇	1	2	yes	complemented
93	#3283	C₂×C₇	1	16	yes	direct product factor
94	C₂×#494	C₂×C₇	1	1	yes	characteristic, complemented
95	C₂×#467	C₂×C₇	1	2	yes	complemented
96	C₂×#461	C₂×C₇	1	2	yes	complemented
97	C₂×#452	C₂×C₇	1	4	yes	complemented
98	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
99	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
100	C₂⁴×C₇	—	2	2	no	—
101	C₂⁴×C₇	C₂×D₄	1	2	yes	—
102	C₇×#41	—	2	32	no	—
103	C₇×#41	—	4	16	no	—
104	C₇×#41	—	4	32	no	—
105	C₂×C₇×Q₈	—	2	4	no	—
106	C₂×C₇×Q₈	—	2	8	no	—
107	C₂×C₇×Q₈	—	2	8	no	—
108	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
109	C₂×C₇×D₄	—	2	16	no	—
110	C₂×C₇×D₄	—	2	4	no	—
111	C₂×C₇×D₄	—	2	2	no	—
112	C₂×C₇×D₄	—	2	4	no	—
113	C₂×C₇×D₄	—	4	16	no	—
114	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
115	C₂×C₇×D₄	C₂×D₄	1	8	yes	—
116	C₂×C₇×D₄	C₂⁴	1	4	yes	—
117	C₂²×C₄×C₇	—	2	4	no	—
118	C₂²×C₄×C₇	—	2	4	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	2	4	no	—
121	C₂²×C₄×C₇	—	2	8	no	—
122	C₂²×C₄×C₇	—	2	16	no	—
123	C₂²×C₄×C₇	—	4	16	no	—
124	C₂²×C₄×C₇	—	4	8	no	—
125	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
131	C₇×Q₁₆	—	2	16	no	—
132	C₇×Q₁₆	—	4	8	no	—
133	C₇×SD₁₆	—	2	32	no	—
134	C₇×D₈	C₂×D₄	1	16	yes	complemented
135	C₂×C₇×C₈	—	2	4	no	—
136	C₂×C₇×C₈	—	2	2	no	—
137	C₂×C₇×C₈	—	2	16	no	—
138	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
139	C₂×C₇×C₈	C₂⁴	1	2	yes	—
140	C₂×C₇×C₈	C₂⁴	1	4	yes	—
141	C₂×C₇×C₈	C₂⁴	1	2	yes	—
142	C₇×C₄⋊C₄	—	2	8	no	—
143	C₇×C₄⋊C₄	—	2	16	no	—
144	C₇×C₄⋊C₄	—	2	8	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
147	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
148	C₇×C₂²⋊C₄	—	2	16	no	—
149	C₇×C₂²⋊C₄	—	2	8	no	—
150	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
151	C₄²×C₇	C₂×D₄	1	2	yes	—
152	C₄²×C₇	C₂⁴	1	2	yes	—
153	C₂²×#41	C₂²×C₇	1	4	yes	—
154	C₂×#135	—	2	16	no	—
155	C₂×#135	C₂²×C₇	1	16	yes	complemented
156	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
157	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
158	C₂²×SD₁₆	C₂²×C₇	1	4	yes	—
159	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
160	C₂³×C₈	C₂²×C₇	1	2	yes	—
161	#547	—	2	8	no	—
162	#547	C₂²×C₇	1	16	yes	complemented
163	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
164	C₂×#123	—	2	4	no	—
165	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
166	C₂×#121	—	2	2	no	—
167	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
168	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
169	C₂²×C₄⋊C₄	—	2	2	no	—
170	#494	C₂²×C₇	1	8	yes	complemented
171	#467	C₂²×C₇	1	16	yes	complemented
172	#461	C₂²×C₇	1	16	yes	complemented
173	#452	C₂²×C₇	1	32	yes	complemented
174	C₄×D₈	C₂²×C₇	1	8	yes	complemented
175	C₈×D₄	C₂²×C₇	1	8	yes	complemented
176	C₂×#107	C₂²×C₇	1	1	yes	characteristic
177	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
178	C₂×#103	C₂²×C₇	1	4	yes	—
179	C₂×#102	C₂²×C₇	1	2	yes	—
180	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
181	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
182	C₂³×C₇	—	2	4	no	—
183	C₂³×C₇	—	2	8	no	—
184	C₂³×C₇	—	2	4	no	—
185	C₂³×C₇	—	2	4	no	—
186	C₂³×C₇	—	2	4	no	—
187	C₂³×C₇	—	4	4	no	—
188	C₂³×C₇	—	4	4	no	—
189	C₂³×C₇	C₂²×D₄	1	4	yes	—
190	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
191	C₇×Q₈	—	2	8	no	—
192	C₇×Q₈	—	2	8	no	—
193	C₇×Q₈	—	4	8	no	—
194	C₇×D₄	—	2	8	no	—
195	C₇×D₄	—	2	8	no	—
196	C₇×D₄	—	2	4	no	—
197	C₇×D₄	—	4	32	no	—
198	C₇×D₄	C₂²×D₄	1	8	yes	—
199	C₂×C₄×C₇	—	2	4	no	—
200	C₂×C₄×C₇	—	2	2	no	—
201	C₂×C₄×C₇	—	2	8	no	—
202	C₂×C₄×C₇	—	2	4	no	—
203	C₂×C₄×C₇	—	2	4	no	—
204	C₂×C₄×C₇	—	2	4	no	—
205	C₂×C₄×C₇	—	2	8	no	—
206	C₂×C₄×C₇	—	4	32	no	—
207	C₂×C₄×C₇	—	4	8	no	—
208	C₂×C₄×C₇	—	4	4	no	—
209	C₂×C₄×C₇	—	4	16	no	—
210	C₂×C₄×C₇	#135	1	4	yes	complemented
211	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
213	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
217	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
218	C₇×C₈	—	2	4	no	—
219	C₇×C₈	—	2	2	no	—
220	C₇×C₈	C₂²×D₄	1	4	yes	—
221	C₂×#41	—	2	8	no	—
222	C₂×#41	—	2	16	no	—
223	C₂×#41	—	4	8	no	—
224	C₂×#41	C₂³×C₇	1	16	yes	—
225	C₂²×Q₈	C₂³×C₇	1	4	yes	—
226	C₂²×D₄	—	2	4	no	—
227	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
228	C₂²×D₄	C₂³×C₇	1	2	yes	—
229	C₂³×C₄	—	2	2	no	—
230	C₂³×C₄	—	2	4	no	—
231	C₂³×C₄	C₂³×C₇	1	2	yes	—
232	#135	—	2	64	no	—
233	C₂×Q₁₆	—	2	8	no	—
234	C₂×Q₁₆	—	4	4	no	—
235	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
236	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
237	C₂×SD₁₆	—	2	16	no	—
238	C₂×SD₁₆	C₂³×C₇	1	16	yes	—
239	C₂×D₈	C₇×D₄	1	8	yes	complemented
240	C₂×D₈	C₂³×C₇	1	4	yes	—
241	C₂²×C₈	—	2	8	no	—
242	C₂²×C₈	C₂³×C₇	1	2	yes	—
243	C₂²×C₈	C₂³×C₇	1	8	yes	—
244	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
246	C₄⋊Q₈	—	2	4	no	—
247	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
248	#123	—	2	32	no	—
249	C₂²⋊Q₈	—	2	8	no	—
250	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
251	#121	—	2	16	no	—
252	C₄×D₄	—	2	4	no	—
253	C₄×D₄	C₇×D₄	1	4	yes	—
254	C₄×D₄	C₂³×C₇	1	8	yes	—
255	C₄×D₄	C₂³×C₇	1	4	yes	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	16	no	—
260	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
265	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
266	#107	C₂³×C₇	1	4	yes	—
267	C₄⋊C₈	C₂³×C₇	1	4	yes	—
268	#103	C₂³×C₇	1	16	yes	—
269	#102	C₂³×C₇	1	8	yes	—
270	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
271	C₄×C₈	C₂³×C₇	1	4	yes	—
272	C₂²×C₇	—	2	4	no	—
273	C₂²×C₇	—	2	8	no	—
274	C₂²×C₇	—	2	4	no	—
275	C₂²×C₇	—	2	4	no	—
276	C₂²×C₇	—	4	8	no	—
277	C₂²×C₇	—	4	16	no	—
278	C₂²×C₇	—	4	4	no	—
279	C₂²×C₇	—	4	4	no	—
280	C₂²×C₇	D₄²	1	2	yes	—
281	C₂²×C₇	C₂×#135	1	2	yes	—
282	C₂²×C₇	#578	1	2	yes	—
283	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
284	C₄×C₇	—	2	4	no	—
285	C₄×C₇	—	2	2	no	—
286	C₄×C₇	—	4	8	no	—
287	C₄×C₇	—	4	4	no	—
288	C₄×C₇	D₄²	1	2	yes	—
289	C₄×C₇	C₂×#135	1	4	yes	complemented
290	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
291	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
292	C₂⁴	—	2	2	no	—
293	C₂⁴	C₂×C₇×D₄	1	2	yes	—
294	#41	—	2	32	no	—
295	#41	—	4	16	no	—
296	#41	—	4	32	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	—	2	8	no	—
299	C₂×Q₈	—	2	8	no	—
300	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
301	C₂×D₄	—	2	16	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	4	16	no	—
306	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
307	C₂×D₄	C₂×C₇×D₄	1	8	yes	—
308	C₂×D₄	C₂⁴×C₇	1	4	yes	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	16	no	—
315	C₂²×C₄	—	4	16	no	—
316	C₂²×C₄	—	4	8	no	—
317	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
319	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
320	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
323	Q₁₆	—	2	16	no	—
324	Q₁₆	—	4	8	no	—
325	SD₁₆	—	2	32	no	—
326	D₈	C₂×C₇×D₄	1	16	yes	complemented
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	16	no	—
330	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
331	C₂×C₈	C₂⁴×C₇	1	2	yes	—
332	C₂×C₈	C₂⁴×C₇	1	4	yes	—
333	C₂×C₈	C₂⁴×C₇	1	2	yes	—
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	2	16	no	—
336	C₄⋊C₄	—	2	8	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
339	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
340	C₂²⋊C₄	—	2	16	no	—
341	C₂²⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
343	C₄²	C₂×C₇×D₄	1	2	yes	—
344	C₄²	C₂⁴×C₇	1	2	yes	—
345	C₂×C₇	—	4	4	no	—
346	C₂×C₇	—	4	8	no	—
347	C₂×C₇	#3283	1	4	yes	direct product factor
348	C₂×C₇	C₂×D₄²	1	1	yes	characteristic
349	C₂×C₇	C₂²×#135	1	1	yes	characteristic
350	C₂×C₇	C₂×#578	1	1	yes	characteristic
351	C₂³	—	2	4	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	4	no	—
358	C₂³	C₂²×C₇×D₄	1	4	yes	—
359	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
360	Q₈	—	2	8	no	—
361	Q₈	—	2	8	no	—
362	Q₈	—	4	8	no	—
363	D₄	—	2	4	no	—
364	D₄	—	2	8	no	—
365	D₄	—	2	8	no	—
366	D₄	—	4	32	no	—
367	D₄	C₂²×C₇×D₄	1	8	yes	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	4	32	no	—
376	C₂×C₄	—	4	8	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	16	no	—
379	C₂×C₄	C₇×#135	1	4	yes	complemented
380	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
381	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
382	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
383	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
385	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
386	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
387	C₈	—	2	4	no	—
388	C₈	—	2	2	no	—
389	C₈	C₂²×C₇×D₄	1	4	yes	—
390	C₇	C₂×#3283	1	1	yes	characteristic, direct product factor, Sylow
391	C₂²	—	2	4	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	2	4	no	—
394	C₂²	—	2	8	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	8	no	—
398	C₂²	—	4	16	no	—
399	C₂²	C₇×D₄²	1	2	yes	—
400	C₂²	C₂×C₇×#135	1	2	yes	—
401	C₂²	C₇×#578	1	2	yes	—
402	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
403	C₄	—	2	2	no	—
404	C₄	—	2	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	8	no	—
407	C₄	C₇×D₄²	1	2	yes	—
408	C₄	C₂×C₇×#135	1	4	yes	complemented
409	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
410	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
411	C₂	—	4	4	no	—
412	C₂	—	4	8	no	—
413	C₂	C₇×#3283	1	4	yes	direct product factor
414	C₂	C₂×C₇×D₄²	1	1	yes	characteristic
415	C₂	C₂²×C₇×#135	1	1	yes	characteristic
416	C₂	C₂×C₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
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
1. C₂²×C₇×#135	C₂	semidirect
2. C₂×C₇×#547	C₂	semidirect
3. C₇×#3283	C₂	direct (N × H)
4. C₂×C₇×#494	C₂	semidirect
5. C₂×C₇×#467	C₂	semidirect
6. C₂×C₇×#461	C₂	semidirect
7. C₂×C₇×#452	C₂	semidirect
8. C₂×C₄×C₇×D₈	C₂	semidirect
9. C₂×C₇×C₈×D₄	C₂	semidirect
12. C₂×C₇×#135	C₂²	semidirect
19. C₇×#547	C₂²	semidirect
27. C₇×#494	C₂²	semidirect
28. C₇×#467	C₂²	semidirect
29. C₇×#461	C₂²	semidirect
30. C₇×#452	C₂²	semidirect
31. C₄×C₇×D₈	C₂²	semidirect
32. C₇×C₈×D₄	C₂²	semidirect
39. C₂×#3283	C₇	direct (N × H)
58. C₂×C₇×D₈	D₄	semidirect
91. C₂²×#135	C₂×C₇	semidirect
92. C₂×#547	C₂×C₇	semidirect
93. #3283	C₂×C₇	direct (N × H)
94. C₂×#494	C₂×C₇	semidirect
95. C₂×#467	C₂×C₇	semidirect
96. C₂×#461	C₂×C₇	semidirect
97. C₂×#452	C₂×C₇	semidirect
98. C₂×C₄×D₈	C₂×C₇	semidirect
99. C₂×C₈×D₄	C₂×C₇	semidirect
134. C₇×D₈	C₂×D₄	semidirect
155. C₂×#135	C₂²×C₇	semidirect
162. #547	C₂²×C₇	semidirect
170. #494	C₂²×C₇	semidirect
171. #467	C₂²×C₇	semidirect
172. #461	C₂²×C₇	semidirect
173. #452	C₂²×C₇	semidirect
174. C₄×D₈	C₂²×C₇	semidirect
175. C₈×D₄	C₂²×C₇	semidirect
210. C₂×C₄×C₇	#135	semidirect
239. C₂×D₈	C₇×D₄	semidirect
289. C₄×C₇	C₂×#135	semidirect
326. D₈	C₂×C₇×D₄	semidirect
347. C₂×C₇	#3283	direct (N × H)
379. C₂×C₄	C₇×#135	semidirect
390. C₇	C₂×#3283	direct (N × H)
408. C₄	C₂×C₇×#135	semidirect
413. C₂	C₇×#3283	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×#135	2
C₂×C₇×#547	2
C₇×#3283	2
C₂×C₇×#494	2
C₂×C₇×#467	2
C₂×C₇×#461	2
C₂×C₇×#452	2
C₂×C₄×C₇×D₈	2
C₂×C₇×C₈×D₄	2
C₂×#3283	7

Subgroups — C2×C7×#3283 #13238259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3283 #13238259