Subgroups — C₇×#60093 #13237309

Order 1792.

4852 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#585	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2901	C₂	1	16	yes	maximal, complemented
5	C₂×C₇×#421	C₂	1	12	yes	maximal, complemented
6	C₇×#585	—	2	4	no	—
7	C₇×#585	—	2	4	no	—
8	C₇×#585	C₄	1	8	yes	complemented
9	C₇×#585	C₂²	1	8	yes	—
10	C₂×C₇×2₋¹⁺⁴	—	2	1	no	—
11	C₂×C₇×2₋¹⁺⁴	C₄	1	4	yes	complemented
12	C₂×C₇×H(5,𝔽₂)	—	2	3	no	—
13	C₂×C₇×H(5,𝔽₂)	C₄	1	4	yes	complemented
14	C₂²×C₇×#41	—	2	4	no	—
15	C₂²×C₇×#41	C₂²	1	6	yes	—
16	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
17	C₇×#568	—	2	4	no	—
18	C₇×#568	C₂²	1	8	yes	complemented
19	C₂×C₇×#131	—	2	4	no	—
20	C₂²×C₇×M₁₆	C₂²	1	6	yes	complemented
21	C₇×#520	—	2	4	no	—
22	C₇×#519	—	2	1	no	—
23	C₇×#518	—	2	3	no	—
24	C₄×C₇×#41	C₂²	1	8	yes	complemented
25	C₂×C₇×#117	C₂²	1	6	yes	complemented
26	C₇×#421	C₂²	1	16	yes	complemented
27	C₇×#421	C₂²	1	48	yes	complemented
28	C₂×C₇×#104	C₂²	1	48	yes	complemented
29	#60093	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₇×2₋¹⁺⁴	—	2	16	no	—
31	C₇×2₋¹⁺⁴	—	2	8	no	—
32	C₇×2₋¹⁺⁴	—	2	8	no	—
33	C₇×2₋¹⁺⁴	C₂×C₄	1	32	yes	complemented
34	C₇×H(5,𝔽₂)	—	2	16	no	—
35	C₇×H(5,𝔽₂)	—	2	24	no	—
36	C₇×H(5,𝔽₂)	—	2	24	no	—
37	C₇×H(5,𝔽₂)	C₂×C₄	1	32	yes	complemented
38	C₂×C₇×#41	—	2	32	no	—
39	C₂×C₇×#41	—	2	32	no	—
40	C₂×C₇×#41	—	2	4	no	—
41	C₂×C₇×#41	—	2	12	no	—
42	C₂×C₇×#41	—	2	6	no	—
43	C₂×C₇×#41	—	2	6	no	—
44	C₂×C₇×#41	—	2	12	no	—
45	C₂×C₇×#41	—	2	12	no	—
46	C₂×C₇×#41	C₂×C₄	1	4	yes	—
47	C₂×C₇×#41	C₂×C₄	1	4	yes	—
48	C₂×C₇×#41	C₂×C₄	1	12	yes	complemented
49	C₂×C₇×#41	C₂×C₄	1	24	yes	complemented
50	C₂×C₇×#41	D₄	1	4	yes	—
51	C₂×C₇×#41	D₄	1	4	yes	—
52	C₂×C₇×#41	D₄	1	4	yes	—
53	C₂×C₇×#41	C₂³	1	4	yes	—
54	C₂×C₇×#41	C₂³	1	24	yes	—
55	C₂×C₇×#41	C₂³	1	4	yes	—
56	C₂²×C₇×Q₈	—	2	4	no	—
57	C₂²×C₇×Q₈	C₂×C₄	1	6	yes	complemented
58	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
59	C₂²×C₇×D₄	—	2	6	no	—
60	C₂²×C₇×D₄	—	2	12	no	—
61	C₂²×C₇×D₄	C₂×C₄	1	6	yes	complemented
62	C₂²×C₇×D₄	D₄	1	3	yes	—
63	C₂³×C₄×C₇	—	2	6	no	—
64	C₂³×C₄×C₇	C₂³	1	3	yes	—
65	C₇×#131	—	2	32	no	—
66	C₂×C₇×M₁₆	—	2	6	no	—
67	C₂×C₇×M₁₆	—	2	12	no	—
68	C₂×C₇×M₁₆	C₂³	1	4	yes	—
69	C₂×C₇×M₁₆	C₂³	1	24	yes	complemented
70	C₂²×C₇×C₈	—	2	6	no	—
71	C₄×C₇×Q₈	—	2	8	no	—
72	C₄×C₇×D₄	—	2	24	no	—
73	C₇×#117	—	2	6	no	—
74	C₇×#117	—	2	6	no	—
75	C₇×#117	C₂³	1	4	yes	—
76	C₇×#117	C₂³	1	12	yes	complemented
77	C₂×C₇×C₄⋊C₄	—	2	6	no	—
78	C₂×C₇×C₂²⋊C₄	—	2	6	no	—
79	C₂×C₄²×C₇	C₂³	1	12	yes	complemented
80	C₇×#104	C₂³	1	64	yes	complemented
81	C₂×#585	C₂×C₇	1	1	yes	characteristic
82	C₂×#568	C₂×C₇	1	1	yes	characteristic, complemented
83	#3428	C₂×C₇	1	1	yes	characteristic, complemented
84	#2901	C₂×C₇	1	16	yes	complemented
85	C₂×#421	C₂×C₇	1	12	yes	complemented
86	C₂⁴×C₇	—	2	6	no	—
87	C₂⁴×C₇	C₂×D₄	1	3	yes	—
88	C₇×#41	—	2	32	no	—
89	C₇×#41	—	2	96	no	—
90	C₇×#41	—	2	24	no	—
91	C₇×#41	—	2	24	no	—
92	C₇×#41	—	2	24	no	—
93	C₇×#41	—	2	4	no	—
94	C₇×#41	—	2	4	no	—
95	C₇×#41	—	2	24	no	—
96	C₇×#41	—	2	24	no	—
97	C₇×#41	C₂²⋊C₄	1	16	yes	—
98	C₇×#41	C₂²⋊C₄	1	16	yes	—
99	C₇×#41	C₂²×C₄	1	8	yes	—
100	C₇×#41	C₂²×C₄	1	48	yes	—
101	C₇×#41	C₂²×C₄	1	16	yes	—
102	C₇×#41	C₂×D₄	1	16	yes	—
103	C₇×#41	C₂⁴	1	8	yes	—
104	C₂×C₇×Q₈	—	2	32	no	—
105	C₂×C₇×Q₈	—	2	6	no	—
106	C₂×C₇×Q₈	—	2	12	no	—
107	C₂×C₇×Q₈	C₂²⋊C₄	1	4	yes	—
108	C₂×C₇×Q₈	C₂²⋊C₄	1	4	yes	—
109	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
110	C₂×C₇×Q₈	C₂²×C₄	1	24	yes	—
111	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
112	C₂×C₇×D₄	—	2	12	no	—
113	C₂×C₇×D₄	—	2	24	no	—
114	C₂×C₇×D₄	—	2	4	no	—
115	C₂×C₇×D₄	—	2	24	no	—
116	C₂×C₇×D₄	—	2	96	no	—
117	C₂×C₇×D₄	—	2	6	no	—
118	C₂×C₇×D₄	—	2	12	no	—
119	C₂×C₇×D₄	C₂²⋊C₄	1	12	yes	—
120	C₂×C₇×D₄	C₂²⋊C₄	1	12	yes	—
121	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
122	C₂×C₇×D₄	C₂²×C₄	1	24	yes	—
123	C₂×C₇×D₄	C₂×D₄	1	12	yes	—
124	C₂²×C₄×C₇	—	2	6	no	—
125	C₂²×C₄×C₇	—	2	12	no	—
126	C₂²×C₄×C₇	—	2	24	no	—
127	C₂²×C₄×C₇	—	2	4	no	—
128	C₂²×C₄×C₇	—	2	24	no	—
129	C₂²×C₄×C₇	—	2	12	no	—
130	C₂²×C₄×C₇	C₂²×C₄	1	6	yes	—
131	C₂²×C₄×C₇	C₂²×C₄	1	6	yes	—
132	C₂²×C₄×C₇	C₂×D₄	1	6	yes	—
133	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
134	C₂²×C₄×C₇	C₂×D₄	1	6	yes	—
135	C₂²×C₄×C₇	C₂×D₄	1	6	yes	—
136	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
137	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
138	C₇×M₁₆	—	2	4	no	—
139	C₇×M₁₆	—	2	24	no	—
140	C₇×M₁₆	C₂⁴	1	8	yes	—
141	C₂×C₇×C₈	—	2	4	no	—
142	C₂×C₇×C₈	—	2	24	no	—
143	C₇×C₄⋊C₄	—	2	4	no	—
144	C₇×C₄⋊C₄	—	2	12	no	—
145	C₇×C₂²⋊C₄	—	2	4	no	—
146	C₇×C₂²⋊C₄	—	2	12	no	—
147	C₄²×C₇	—	2	12	no	—
148	C₄²×C₇	C₂⁴	1	8	yes	—
149	#585	—	2	4	no	—
150	#585	—	2	4	no	—
151	#585	C₄×C₇	1	8	yes	complemented
152	#585	C₂²×C₇	1	8	yes	—
153	C₂×2₋¹⁺⁴	—	2	1	no	—
154	C₂×2₋¹⁺⁴	C₄×C₇	1	4	yes	complemented
155	C₂×H(5,𝔽₂)	—	2	3	no	—
156	C₂×H(5,𝔽₂)	C₄×C₇	1	4	yes	complemented
157	C₂²×#41	—	2	4	no	—
158	C₂²×#41	C₂²×C₇	1	6	yes	—
159	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
160	#568	—	2	4	no	—
161	#568	C₂²×C₇	1	8	yes	complemented
162	C₂×#131	—	2	4	no	—
163	C₂²×M₁₆	C₂²×C₇	1	6	yes	complemented
164	#520	—	2	4	no	—
165	#519	—	2	1	no	—
166	#518	—	2	3	no	—
167	C₄×#41	C₂²×C₇	1	8	yes	complemented
168	C₂×#117	C₂²×C₇	1	6	yes	complemented
169	#421	C₂²×C₇	1	16	yes	complemented
170	#421	C₂²×C₇	1	48	yes	complemented
171	C₂×#104	C₂²×C₇	1	48	yes	complemented
172	C₂³×C₇	—	2	4	no	—
173	C₂³×C₇	—	2	24	no	—
174	C₂³×C₇	—	8	3	no	—
175	C₂³×C₇	—	8	12	no	—
176	C₂³×C₇	C₂×C₂²⋊C₄	1	6	yes	—
177	C₂³×C₇	C₂×C₂²⋊C₄	1	6	yes	—
178	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
179	C₂³×C₇	C₂²×D₄	1	6	yes	—
180	C₇×Q₈	—	2	24	no	—
181	C₇×Q₈	—	2	4	no	—
182	C₇×Q₈	C₂×C₂²⋊C₄	1	16	yes	—
183	C₇×Q₈	C₂³×C₄	1	8	yes	—
184	C₇×D₄	—	2	48	no	—
185	C₇×D₄	—	2	8	no	—
186	C₇×D₄	—	2	8	no	—
187	C₇×D₄	—	2	24	no	—
188	C₇×D₄	—	2	4	no	—
189	C₇×D₄	C₂×C₂²⋊C₄	1	48	yes	—
190	C₇×D₄	C₂³×C₄	1	8	yes	—
191	C₂×C₄×C₇	—	2	4	no	—
192	C₂×C₄×C₇	—	2	24	no	—
193	C₂×C₄×C₇	—	2	8	no	—
194	C₂×C₄×C₇	—	2	48	no	—
195	C₂×C₄×C₇	—	2	8	no	—
196	C₂×C₄×C₇	—	2	8	no	—
197	C₂×C₄×C₇	—	8	12	no	—
198	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	6	yes	—
199	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	12	yes	—
200	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	12	yes	—
201	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	6	yes	—
202	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₇	C₂³×C₄	1	12	yes	—
205	C₂×C₄×C₇	C₂²×D₄	1	6	yes	—
206	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₇	C₂²×D₄	1	12	yes	—
209	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
211	C₇×C₈	—	2	8	no	—
212	2₋¹⁺⁴	—	2	16	no	—
213	2₋¹⁺⁴	—	2	8	no	—
214	2₋¹⁺⁴	—	2	8	no	—
215	2₋¹⁺⁴	C₂×C₄×C₇	1	32	yes	complemented
216	H(5,𝔽₂)	—	2	16	no	—
217	H(5,𝔽₂)	—	2	24	no	—
218	H(5,𝔽₂)	—	2	24	no	—
219	H(5,𝔽₂)	C₂×C₄×C₇	1	32	yes	complemented
220	C₂×#41	—	2	32	no	—
221	C₂×#41	—	2	32	no	—
222	C₂×#41	—	2	4	no	—
223	C₂×#41	—	2	12	no	—
224	C₂×#41	—	2	6	no	—
225	C₂×#41	—	2	6	no	—
226	C₂×#41	—	2	12	no	—
227	C₂×#41	—	2	12	no	—
228	C₂×#41	C₂×C₄×C₇	1	4	yes	—
229	C₂×#41	C₂×C₄×C₇	1	4	yes	—
230	C₂×#41	C₂×C₄×C₇	1	12	yes	complemented
231	C₂×#41	C₂×C₄×C₇	1	24	yes	complemented
232	C₂×#41	C₇×D₄	1	4	yes	—
233	C₂×#41	C₇×D₄	1	4	yes	—
234	C₂×#41	C₇×D₄	1	4	yes	—
235	C₂×#41	C₂³×C₇	1	4	yes	—
236	C₂×#41	C₂³×C₇	1	24	yes	—
237	C₂×#41	C₂³×C₇	1	4	yes	—
238	C₂²×Q₈	—	2	4	no	—
239	C₂²×Q₈	C₂×C₄×C₇	1	6	yes	complemented
240	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
241	C₂²×D₄	—	2	6	no	—
242	C₂²×D₄	—	2	12	no	—
243	C₂²×D₄	C₂×C₄×C₇	1	6	yes	complemented
244	C₂²×D₄	C₇×D₄	1	3	yes	—
245	C₂³×C₄	—	2	6	no	—
246	C₂³×C₄	C₂³×C₇	1	3	yes	—
247	#131	—	2	32	no	—
248	C₂×M₁₆	—	2	6	no	—
249	C₂×M₁₆	—	2	12	no	—
250	C₂×M₁₆	C₂³×C₇	1	4	yes	—
251	C₂×M₁₆	C₂³×C₇	1	24	yes	complemented
252	C₂²×C₈	—	2	6	no	—
253	C₄×Q₈	—	2	8	no	—
254	C₄×D₄	—	2	24	no	—
255	#117	—	2	6	no	—
256	#117	—	2	6	no	—
257	#117	C₂³×C₇	1	4	yes	—
258	#117	C₂³×C₇	1	12	yes	complemented
259	C₂×C₄⋊C₄	—	2	6	no	—
260	C₂×C₂²⋊C₄	—	2	6	no	—
261	C₂×C₄²	C₂³×C₇	1	12	yes	complemented
262	#104	C₂³×C₇	1	64	yes	complemented
263	C₂²×C₇	—	2	8	no	—
264	C₂²×C₇	—	4	6	no	—
265	C₂²×C₇	—	4	6	no	—
266	C₂²×C₇	—	4	1	no	—
267	C₂²×C₇	—	4	6	no	—
268	C₂²×C₇	—	4	8	no	—
269	C₂²×C₇	—	8	24	no	—
270	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
271	C₂²×C₇	C₂²×C₂²⋊C₄	1	12	yes	—
272	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
273	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
274	C₄×C₇	—	2	8	no	—
275	C₄×C₇	—	4	8	no	—
276	C₄×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
277	C₄×C₇	C₂²×C₂²⋊C₄	1	12	yes	—
278	C₄×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
279	C₄×C₇	C₂⁴×C₄	1	1	yes	characteristic
280	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
281	C₂⁴	—	2	6	no	—
282	C₂⁴	C₂×C₇×D₄	1	3	yes	—
283	#41	—	2	32	no	—
284	#41	—	2	96	no	—
285	#41	—	2	24	no	—
286	#41	—	2	24	no	—
287	#41	—	2	24	no	—
288	#41	—	2	4	no	—
289	#41	—	2	24	no	—
290	#41	—	2	4	no	—
291	#41	—	2	24	no	—
292	#41	C₇×C₂²⋊C₄	1	16	yes	—
293	#41	C₇×C₂²⋊C₄	1	16	yes	—
294	#41	C₂²×C₄×C₇	1	8	yes	—
295	#41	C₂²×C₄×C₇	1	48	yes	—
296	#41	C₂²×C₄×C₇	1	16	yes	—
297	#41	C₂×C₇×D₄	1	16	yes	—
298	#41	C₂⁴×C₇	1	8	yes	—
299	C₂×Q₈	—	2	32	no	—
300	C₂×Q₈	—	2	6	no	—
301	C₂×Q₈	—	2	12	no	—
302	C₂×Q₈	C₇×C₂²⋊C₄	1	4	yes	—
303	C₂×Q₈	C₇×C₂²⋊C₄	1	4	yes	—
304	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
305	C₂×Q₈	C₂²×C₄×C₇	1	24	yes	—
306	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
307	C₂×D₄	—	2	12	no	—
308	C₂×D₄	—	2	24	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	24	no	—
311	C₂×D₄	—	2	96	no	—
312	C₂×D₄	—	2	6	no	—
313	C₂×D₄	—	2	12	no	—
314	C₂×D₄	C₇×C₂²⋊C₄	1	12	yes	—
315	C₂×D₄	C₇×C₂²⋊C₄	1	12	yes	—
316	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
317	C₂×D₄	C₂²×C₄×C₇	1	24	yes	—
318	C₂×D₄	C₂×C₇×D₄	1	12	yes	—
319	C₂²×C₄	—	2	6	no	—
320	C₂²×C₄	—	2	12	no	—
321	C₂²×C₄	—	2	24	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	24	no	—
324	C₂²×C₄	—	2	12	no	—
325	C₂²×C₄	C₂²×C₄×C₇	1	6	yes	—
326	C₂²×C₄	C₂²×C₄×C₇	1	6	yes	—
327	C₂²×C₄	C₂×C₇×D₄	1	6	yes	—
328	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
329	C₂²×C₄	C₂×C₇×D₄	1	6	yes	—
330	C₂²×C₄	C₂×C₇×D₄	1	6	yes	—
331	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
332	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
333	M₁₆	—	2	4	no	—
334	M₁₆	—	2	24	no	—
335	M₁₆	C₂⁴×C₇	1	8	yes	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	2	24	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	12	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	12	no	—
342	C₄²	—	2	12	no	—
343	C₄²	C₂⁴×C₇	1	8	yes	—
344	C₂×C₇	—	2	1	no	—
345	C₂×C₇	—	2	1	no	—
346	C₂×C₇	—	2	1	no	—
347	C₂×C₇	—	2	12	no	—
348	C₂×C₇	—	4	8	no	—
349	C₂×C₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
350	C₂³	—	2	4	no	—
351	C₂³	—	2	24	no	—
352	C₂³	—	8	3	no	—
353	C₂³	—	8	12	no	—
354	C₂³	C₂×C₇×C₂²⋊C₄	1	6	yes	—
355	C₂³	C₂×C₇×C₂²⋊C₄	1	6	yes	—
356	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
357	C₂³	C₂²×C₇×D₄	1	6	yes	—
358	Q₈	—	2	24	no	—
359	Q₈	—	2	4	no	—
360	Q₈	C₂×C₇×C₂²⋊C₄	1	16	yes	—
361	Q₈	C₂³×C₄×C₇	1	8	yes	—
362	D₄	—	2	8	no	—
363	D₄	—	2	48	no	—
364	D₄	—	2	8	no	—
365	D₄	—	2	24	no	—
366	D₄	—	2	4	no	—
367	D₄	C₂×C₇×C₂²⋊C₄	1	48	yes	—
368	D₄	C₂³×C₄×C₇	1	8	yes	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	24	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	48	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	8	12	no	—
376	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	6	yes	—
377	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	12	yes	—
378	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	12	yes	—
379	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	6	yes	—
380	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
381	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
382	C₂×C₄	C₂³×C₄×C₇	1	12	yes	—
383	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₇×D₄	1	12	yes	—
385	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
386	C₂×C₄	C₂²×C₇×D₄	1	6	yes	—
387	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
388	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
389	C₈	—	2	8	no	—
390	C₇	#60093	1	1	yes	characteristic, direct product factor, Sylow
391	C₂²	—	2	8	no	—
392	C₂²	—	4	6	no	—
393	C₂²	—	4	6	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	6	no	—
396	C₂²	—	4	8	no	—
397	C₂²	—	8	24	no	—
398	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
399	C₂²	C₂²×C₇×C₂²⋊C₄	1	12	yes	—
400	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
401	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
402	C₄	—	2	8	no	—
403	C₄	—	4	8	no	—
404	C₄	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
405	C₄	C₂²×C₇×C₂²⋊C₄	1	12	yes	—
406	C₄	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
407	C₄	C₂⁴×C₄×C₇	1	1	yes	characteristic
408	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	12	no	—
413	C₂	—	4	8	no	—
414	C₂	C₂³×C₇×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₇	C₂³×D₄
commutator	C₄	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂×C₇	C₂³×C₂²⋊C₄
prime radical	C₂×C₇×#585	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇ ◁ C₂²×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#568	C₂	semidirect
3. C₇×#3428	C₂	semidirect
4. C₇×#2901	C₂	semidirect
5. C₂×C₇×#421	C₂	semidirect
8. C₇×#585	C₄	semidirect
11. C₂×C₇×2₋¹⁺⁴	C₄	semidirect
13. C₂×C₇×H(5,𝔽₂)	C₄	semidirect
18. C₇×#568	C₂²	semidirect
20. C₂²×C₇×M₁₆	C₂²	semidirect
24. C₄×C₇×#41	C₂²	semidirect
25. C₂×C₇×#117	C₂²	semidirect
26. C₇×#421	C₂²	semidirect
27. C₇×#421	C₂²	semidirect
28. C₂×C₇×#104	C₂²	semidirect
29. #60093	C₇	direct (N × H)
33. C₇×2₋¹⁺⁴	C₂×C₄	semidirect
37. C₇×H(5,𝔽₂)	C₂×C₄	semidirect
48. C₂×C₇×#41	C₂×C₄	semidirect
49. C₂×C₇×#41	C₂×C₄	semidirect
57. C₂²×C₇×Q₈	C₂×C₄	semidirect
61. C₂²×C₇×D₄	C₂×C₄	semidirect
69. C₂×C₇×M₁₆	C₂³	semidirect
76. C₇×#117	C₂³	semidirect
79. C₂×C₄²×C₇	C₂³	semidirect
80. C₇×#104	C₂³	semidirect
82. C₂×#568	C₂×C₇	semidirect
83. #3428	C₂×C₇	semidirect
84. #2901	C₂×C₇	semidirect
85. C₂×#421	C₂×C₇	semidirect
151. #585	C₄×C₇	semidirect
154. C₂×2₋¹⁺⁴	C₄×C₇	semidirect
156. C₂×H(5,𝔽₂)	C₄×C₇	semidirect
161. #568	C₂²×C₇	semidirect
163. C₂²×M₁₆	C₂²×C₇	semidirect
167. C₄×#41	C₂²×C₇	semidirect
168. C₂×#117	C₂²×C₇	semidirect
169. #421	C₂²×C₇	semidirect
170. #421	C₂²×C₇	semidirect
171. C₂×#104	C₂²×C₇	semidirect
215. 2₋¹⁺⁴	C₂×C₄×C₇	semidirect
219. H(5,𝔽₂)	C₂×C₄×C₇	semidirect
230. C₂×#41	C₂×C₄×C₇	semidirect
231. C₂×#41	C₂×C₄×C₇	semidirect
239. C₂²×Q₈	C₂×C₄×C₇	semidirect
243. C₂²×D₄	C₂×C₄×C₇	semidirect
251. C₂×M₁₆	C₂³×C₇	semidirect
258. #117	C₂³×C₇	semidirect
261. C₂×C₄²	C₂³×C₇	semidirect
262. #104	C₂³×C₇	semidirect
390. C₇	#60093	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×#585	2
C₂×C₇×#568	2
C₇×#3428	2
C₇×#2901	2
C₂×C₇×#421	2
#60093	7

Subgroups — C7×#60093 #13237309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60093 #13237309