Subgroups — C₇×#36625 #13213841

Order 1792.

3110 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
3	C₇×#2857	C₂	1	4	yes	maximal, complemented
4	C₇×#2855	C₂	1	4	yes	maximal, complemented
5	C₇×#2851	C₂	1	4	yes	maximal, complemented
6	C₇×#2848	C₂	1	4	yes	maximal
7	C₄×C₇×C₂²⋊Q₈	C₂	1	8	yes	maximal, complemented
8	C₇×#2296	C₂	1	2	yes	maximal, complemented
9	C₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2280	C₂	1	2	yes	maximal
11	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
13	C₇×#533	—	2	8	no	—
14	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
15	C₂×C₇×#125	C₂²	1	2	yes	complemented
16	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
17	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	—
18	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	complemented
19	C₂×C₇×#117	C₂²	1	2	yes	—
20	C₂×C₇×#117	C₂²	1	2	yes	—
21	C₂²×C₄²×C₇	—	2	8	no	—
22	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₇	C₂²	1	4	yes	—
24	C₂²×C₄²×C₇	C₂²	1	2	yes	—
25	C₂²×C₄²×C₇	C₂²	1	2	yes	—
26	C₂²×C₄²×C₇	C₂²	1	2	yes	—
27	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
28	C₇×#391	C₂²	1	8	yes	complemented
29	C₇×#389	C₂²	1	8	yes	complemented
30	C₇×#389	C₂²	1	8	yes	complemented
31	C₇×#387	C₂²	1	16	yes	complemented
32	C₇×#385	C₂²	1	8	yes	—
33	C₇×#385	C₂²	1	16	yes	—
34	C₇×#384	C₂²	1	2	yes	complemented
35	C₇×#382	C₂²	1	2	yes	complemented
36	C₇×#381	C₂²	1	4	yes	—
37	C₇×#380	C₂²	1	8	yes	—
38	C₇×#380	C₂²	1	4	yes	—
39	C₇×#380	C₂²	1	8	yes	—
40	C₇×#379	C₂²	1	4	yes	—
41	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	complemented
42	C₄×C₇×C₄⋊C₄	C₂²	1	8	yes	complemented
43	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
44	#36625	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂⁵×C₇	C₂³	1	1	yes	characteristic
46	C₂²×C₇×Q₈	C₂³	1	4	yes	—
47	C₂³×C₄×C₇	—	2	8	no	—
48	C₂³×C₄×C₇	—	2	4	no	—
49	C₂³×C₄×C₇	—	2	16	no	—
50	C₂³×C₄×C₇	—	2	4	no	—
51	C₂³×C₄×C₇	Q₈	1	8	yes	complemented
52	C₂³×C₄×C₇	C₂³	1	2	yes	—
53	C₂³×C₄×C₇	C₂³	1	4	yes	—
54	C₂³×C₄×C₇	C₂³	1	2	yes	—
55	C₂³×C₄×C₇	C₂³	1	2	yes	—
56	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₇	C₂³	1	2	yes	—
58	C₂³×C₄×C₇	C₂³	1	4	yes	—
59	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
60	C₇×C₄⋊Q₈	—	2	8	no	—
61	C₇×#125	—	2	8	no	—
62	C₇×C₂²⋊Q₈	—	2	16	no	—
63	C₇×C₂²⋊Q₈	—	2	32	no	—
64	C₄×C₇×Q₈	—	2	16	no	—
65	C₇×#117	—	2	8	no	—
66	C₇×#117	—	2	8	no	—
67	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
71	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
73	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
74	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
75	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
76	C₂×C₄²×C₇	—	2	8	no	—
77	C₂×C₄²×C₇	—	2	4	no	—
78	C₂×C₄²×C₇	—	2	16	no	—
79	C₂×C₄²×C₇	—	2	8	no	—
80	C₂×C₄²×C₇	—	2	8	no	—
81	C₂×C₄²×C₇	D₄	1	8	yes	—
82	C₂×C₄²×C₇	C₂³	1	4	yes	—
83	C₂×C₄²×C₇	C₂³	1	2	yes	—
84	C₂×C₄²×C₇	C₂³	1	4	yes	—
85	C₂×C₄²×C₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₇	C₂³	1	4	yes	—
87	C₂×C₄²×C₇	C₂³	1	4	yes	—
88	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₇	C₂³	1	2	yes	—
91	C₇×#95	C₂³	1	16	yes	—
92	C₇×#95	C₂³	1	8	yes	—
93	C₇×#95	C₂³	1	16	yes	—
94	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
95	C₂³×C₄²	C₂×C₇	1	1	yes	characteristic
96	#2857	C₂×C₇	1	4	yes	complemented
97	#2855	C₂×C₇	1	4	yes	complemented
98	#2851	C₂×C₇	1	4	yes	complemented
99	#2848	C₂×C₇	1	4	yes	—
100	C₄×C₂²⋊Q₈	C₂×C₇	1	8	yes	complemented
101	#2296	C₂×C₇	1	2	yes	complemented
102	#2285	C₂×C₇	1	1	yes	characteristic, complemented
103	#2280	C₂×C₇	1	2	yes	—
104	C₂⁴×C₇	—	2	2	no	—
105	C₂⁴×C₇	—	2	8	no	—
106	C₂⁴×C₇	—	2	2	no	—
107	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
108	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
109	C₂⁴×C₇	C₂⁴	1	2	yes	—
110	C₂×C₇×Q₈	—	2	8	no	—
111	C₂×C₇×Q₈	—	2	16	no	—
112	C₂²×C₄×C₇	—	2	64	no	—
113	C₂²×C₄×C₇	—	2	4	no	—
114	C₂²×C₄×C₇	—	2	2	no	—
115	C₂²×C₄×C₇	—	2	8	no	—
116	C₂²×C₄×C₇	—	2	2	no	—
117	C₂²×C₄×C₇	—	2	32	no	—
118	C₂²×C₄×C₇	—	2	8	no	—
119	C₂²×C₄×C₇	—	2	4	no	—
120	C₂²×C₄×C₇	—	2	4	no	—
121	C₂²×C₄×C₇	—	2	8	no	—
122	C₂²×C₄×C₇	—	2	8	no	—
123	C₂²×C₄×C₇	—	2	8	no	—
124	C₂²×C₄×C₇	—	2	4	no	—
125	C₂²×C₄×C₇	—	2	4	no	—
126	C₂²×C₄×C₇	—	2	8	no	—
127	C₂²×C₄×C₇	—	2	8	no	—
128	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
129	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
131	C₂²×C₄×C₇	C₂×Q₈	1	8	yes	—
132	C₂²×C₄×C₇	C₂×Q₈	1	8	yes	—
133	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
134	C₂²×C₄×C₇	#41	1	16	yes	—
135	C₂²×C₄×C₇	#41	1	4	yes	—
136	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
137	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
138	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
144	C₇×C₄⋊C₄	—	2	8	no	—
145	C₇×C₄⋊C₄	—	2	16	no	—
146	C₇×C₄⋊C₄	—	2	8	no	—
147	C₇×C₄⋊C₄	—	2	8	no	—
148	C₇×C₄⋊C₄	—	2	16	no	—
149	C₇×C₄⋊C₄	—	2	32	no	—
150	C₇×C₂²⋊C₄	—	2	8	no	—
151	C₇×C₂²⋊C₄	—	2	8	no	—
152	C₇×C₂²⋊C₄	—	2	32	no	—
153	C₄²×C₇	—	2	8	no	—
154	C₄²×C₇	—	2	4	no	—
155	C₄²×C₇	—	2	4	no	—
156	C₄²×C₇	—	2	8	no	—
157	C₄²×C₇	—	2	8	no	—
158	C₄²×C₇	—	2	8	no	—
159	C₄²×C₇	C₂×D₄	1	8	yes	—
160	C₄²×C₇	C₂×D₄	1	4	yes	—
161	C₄²×C₇	C₂×D₄	1	4	yes	—
162	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
163	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
164	#533	—	2	8	no	—
165	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
166	C₂×#125	C₂²×C₇	1	2	yes	complemented
167	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
168	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	—
169	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	complemented
170	C₂×#117	C₂²×C₇	1	2	yes	—
171	C₂×#117	C₂²×C₇	1	2	yes	—
172	C₂²×C₄²	—	2	8	no	—
173	C₂²×C₄²	C₂²×C₇	1	2	yes	—
174	C₂²×C₄²	C₂²×C₇	1	2	yes	—
175	C₂²×C₄²	C₂²×C₇	1	2	yes	—
176	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
177	C₂²×C₄²	C₂²×C₇	1	4	yes	—
178	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
179	#391	C₂²×C₇	1	8	yes	complemented
180	#389	C₂²×C₇	1	8	yes	complemented
181	#389	C₂²×C₇	1	8	yes	complemented
182	#387	C₂²×C₇	1	16	yes	complemented
183	#385	C₂²×C₇	1	16	yes	—
184	#385	C₂²×C₇	1	8	yes	—
185	#384	C₂²×C₇	1	2	yes	complemented
186	#382	C₂²×C₇	1	2	yes	complemented
187	#381	C₂²×C₇	1	4	yes	—
188	#380	C₂²×C₇	1	4	yes	—
189	#380	C₂²×C₇	1	8	yes	—
190	#380	C₂²×C₇	1	8	yes	—
191	#379	C₂²×C₇	1	4	yes	—
192	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	complemented
193	C₄×C₄⋊C₄	C₂²×C₇	1	8	yes	complemented
194	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
195	C₂³×C₇	—	2	16	no	—
196	C₂³×C₇	—	2	16	no	—
197	C₂³×C₇	—	2	8	no	—
198	C₂³×C₇	—	2	16	no	—
199	C₂³×C₇	—	2	2	no	—
200	C₂³×C₇	—	2	2	no	—
201	C₂³×C₇	—	2	4	no	—
202	C₂³×C₇	—	2	4	no	—
203	C₂³×C₇	C₂²×D₄	1	2	yes	—
204	C₂³×C₇	C₂²×Q₈	1	2	yes	—
205	C₂³×C₇	C₂²×Q₈	1	4	yes	—
206	C₂³×C₇	C₂×#41	1	2	yes	—
207	C₂³×C₇	C₂×#41	1	8	yes	—
208	C₂³×C₇	C₂⁵	1	1	yes	characteristic
209	C₇×Q₈	—	4	16	no	—
210	C₂×C₄×C₇	—	2	32	no	—
211	C₂×C₄×C₇	—	2	16	no	—
212	C₂×C₄×C₇	—	2	8	no	—
213	C₂×C₄×C₇	—	2	2	no	—
214	C₂×C₄×C₇	—	2	4	no	—
215	C₂×C₄×C₇	—	2	2	no	—
216	C₂×C₄×C₇	—	2	4	no	—
217	C₂×C₄×C₇	—	2	4	no	—
218	C₂×C₄×C₇	—	2	16	no	—
219	C₂×C₄×C₇	—	2	16	no	—
220	C₂×C₄×C₇	—	2	16	no	—
221	C₂×C₄×C₇	—	2	32	no	—
222	C₂×C₄×C₇	—	2	8	no	—
223	C₂×C₄×C₇	—	2	8	no	—
224	C₂×C₄×C₇	—	2	16	no	—
225	C₂×C₄×C₇	—	2	16	no	—
226	C₂×C₄×C₇	C₂²⋊Q₈	1	16	yes	complemented
227	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
228	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
231	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
232	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
233	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
234	C₂×C₄×C₇	C₂×#41	1	8	yes	—
235	C₂×C₄×C₇	C₂×#41	1	2	yes	—
236	C₂×C₄×C₇	C₂×#41	1	2	yes	—
237	C₂×C₄×C₇	C₂×#41	1	8	yes	—
238	C₂⁵	C₂³×C₇	1	1	yes	characteristic
239	C₂²×Q₈	C₂³×C₇	1	4	yes	—
240	C₂³×C₄	—	2	8	no	—
241	C₂³×C₄	—	2	4	no	—
242	C₂³×C₄	—	2	16	no	—
243	C₂³×C₄	—	2	4	no	—
244	C₂³×C₄	C₇×Q₈	1	8	yes	complemented
245	C₂³×C₄	C₂³×C₇	1	2	yes	—
246	C₂³×C₄	C₂³×C₇	1	4	yes	—
247	C₂³×C₄	C₂³×C₇	1	2	yes	—
248	C₂³×C₄	C₂³×C₇	1	2	yes	—
249	C₂³×C₄	C₂³×C₇	1	2	yes	—
250	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₇	1	4	yes	—
252	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
253	C₄⋊Q₈	—	2	8	no	—
254	#125	—	2	8	no	—
255	C₂²⋊Q₈	—	2	16	no	—
256	C₂²⋊Q₈	—	2	32	no	—
257	C₄×Q₈	—	2	16	no	—
258	#117	—	2	8	no	—
259	#117	—	2	8	no	—
260	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
261	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
262	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
263	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
265	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
266	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
267	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
269	C₂×C₄²	—	2	8	no	—
270	C₂×C₄²	—	2	4	no	—
271	C₂×C₄²	—	2	16	no	—
272	C₂×C₄²	—	2	8	no	—
273	C₂×C₄²	—	2	8	no	—
274	C₂×C₄²	C₇×D₄	1	8	yes	—
275	C₂×C₄²	C₂³×C₇	1	4	yes	—
276	C₂×C₄²	C₂³×C₇	1	4	yes	—
277	C₂×C₄²	C₂³×C₇	1	2	yes	—
278	C₂×C₄²	C₂³×C₇	1	4	yes	—
279	C₂×C₄²	C₂³×C₇	1	2	yes	—
280	C₂×C₄²	C₂³×C₇	1	4	yes	—
281	C₂×C₄²	C₂³×C₇	1	2	yes	—
282	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
284	#95	C₂³×C₇	1	16	yes	—
285	#95	C₂³×C₇	1	8	yes	—
286	#95	C₂³×C₇	1	16	yes	—
287	C₂²×C₇	—	2	32	no	—
288	C₂²×C₇	—	2	4	no	—
289	C₂²×C₇	—	2	4	no	—
290	C₂²×C₇	—	2	8	no	—
291	C₂²×C₇	—	2	4	no	—
292	C₂²×C₇	—	2	4	no	—
293	C₂²×C₇	—	2	4	no	—
294	C₂²×C₇	—	2	8	no	—
295	C₂²×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
296	C₂²×C₇	#533	1	8	yes	complemented
297	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
298	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
299	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
300	C₂²×C₇	C₂²×#41	1	4	yes	—
301	C₄×C₇	—	2	4	no	—
302	C₄×C₇	—	2	4	no	—
303	C₄×C₇	—	2	8	no	—
304	C₄×C₇	—	4	8	no	—
305	C₄×C₇	—	4	8	no	—
306	C₄×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
307	C₄×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
308	C₄×C₇	#525	1	8	yes	—
309	C₂⁴	—	2	2	no	—
310	C₂⁴	—	2	8	no	—
311	C₂⁴	—	2	2	no	—
312	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
313	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
314	C₂⁴	C₂⁴×C₇	1	2	yes	—
315	C₂×Q₈	—	2	8	no	—
316	C₂×Q₈	—	2	16	no	—
317	C₂²×C₄	—	2	64	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	32	no	—
323	C₂²×C₄	—	2	8	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
334	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
335	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
336	C₂²×C₄	C₂×C₇×Q₈	1	8	yes	—
337	C₂²×C₄	C₂×C₇×Q₈	1	8	yes	—
338	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
339	C₂²×C₄	C₇×#41	1	16	yes	—
340	C₂²×C₄	C₇×#41	1	4	yes	—
341	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
342	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
343	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
346	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
347	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	16	no	—
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	—	2	8	no	—
353	C₄⋊C₄	—	2	16	no	—
354	C₄⋊C₄	—	2	32	no	—
355	C₂²⋊C₄	—	2	8	no	—
356	C₂²⋊C₄	—	2	8	no	—
357	C₂²⋊C₄	—	2	32	no	—
358	C₄²	—	2	8	no	—
359	C₄²	—	2	4	no	—
360	C₄²	—	2	4	no	—
361	C₄²	—	2	8	no	—
362	C₄²	—	2	8	no	—
363	C₄²	—	2	8	no	—
364	C₄²	C₂×C₇×D₄	1	8	yes	—
365	C₄²	C₂×C₇×D₄	1	4	yes	—
366	C₄²	C₂×C₇×D₄	1	4	yes	—
367	C₂×C₇	—	2	4	no	—
368	C₂×C₇	—	2	8	no	—
369	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
370	C₂×C₇	C₂×#525	1	2	yes	—
371	C₂×C₇	C₂×#533	1	2	yes	—
372	C₂×C₇	#3444	1	2	yes	—
373	C₂³	—	2	16	no	—
374	C₂³	—	2	16	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	2	8	no	—
380	C₂³	—	2	16	no	—
381	C₂³	C₂²×C₇×D₄	1	2	yes	—
382	C₂³	C₂²×C₇×Q₈	1	2	yes	—
383	C₂³	C₂²×C₇×Q₈	1	4	yes	—
384	C₂³	C₂×C₇×#41	1	2	yes	—
385	C₂³	C₂×C₇×#41	1	8	yes	—
386	C₂³	C₂⁵×C₇	1	1	yes	characteristic
387	Q₈	—	4	16	no	—
388	C₂×C₄	—	2	32	no	—
389	C₂×C₄	—	2	16	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	16	no	—
397	C₂×C₄	—	2	16	no	—
398	C₂×C₄	—	2	16	no	—
399	C₂×C₄	—	2	32	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	16	no	—
403	C₂×C₄	—	2	16	no	—
404	C₂×C₄	C₇×C₂²⋊Q₈	1	16	yes	complemented
405	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
406	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
407	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
408	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
409	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
410	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
411	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
412	C₂×C₄	C₂×C₇×#41	1	8	yes	—
413	C₂×C₄	C₂×C₇×#41	1	2	yes	—
414	C₂×C₄	C₂×C₇×#41	1	2	yes	—
415	C₂×C₄	C₂×C₇×#41	1	8	yes	—
416	C₇	#36625	1	1	yes	characteristic, direct product factor, Sylow
417	C₂²	—	2	32	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	8	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	2	8	no	—
425	C₂²	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
426	C₂²	C₇×#533	1	8	yes	complemented
427	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
428	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
429	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
430	C₂²	C₂²×C₇×#41	1	4	yes	—
431	C₄	—	2	4	no	—
432	C₄	—	2	4	no	—
433	C₄	—	2	8	no	—
434	C₄	—	4	8	no	—
435	C₄	—	4	8	no	—
436	C₄	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
437	C₄	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
438	C₄	C₇×#525	1	8	yes	—
439	C₂	—	2	4	no	—
440	C₂	—	2	8	no	—
441	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
442	C₂	C₂×C₇×#525	1	2	yes	—
443	C₂	C₂×C₇×#533	1	2	yes	—
444	C₂	C₇×#3444	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#533	C₂	semidirect
3. C₇×#2857	C₂	semidirect
4. C₇×#2855	C₂	semidirect
5. C₇×#2851	C₂	semidirect
7. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
8. C₇×#2296	C₂	semidirect
9. C₇×#2285	C₂	semidirect
14. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
15. C₂×C₇×#125	C₂²	semidirect
18. C₂×C₄×C₇×Q₈	C₂²	semidirect
28. C₇×#391	C₂²	semidirect
29. C₇×#389	C₂²	semidirect
30. C₇×#389	C₂²	semidirect
31. C₇×#387	C₂²	semidirect
34. C₇×#384	C₂²	semidirect
35. C₇×#382	C₂²	semidirect
41. C₄×C₇×C₄⋊C₄	C₂²	semidirect
42. C₄×C₇×C₄⋊C₄	C₂²	semidirect
44. #36625	C₇	direct (N × H)
51. C₂³×C₄×C₇	Q₈	semidirect
94. C₂×#533	C₂×C₇	semidirect
96. #2857	C₂×C₇	semidirect
97. #2855	C₂×C₇	semidirect
98. #2851	C₂×C₇	semidirect
100. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
101. #2296	C₂×C₇	semidirect
102. #2285	C₂×C₇	semidirect
165. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
166. C₂×#125	C₂²×C₇	semidirect
169. C₂×C₄×Q₈	C₂²×C₇	semidirect
179. #391	C₂²×C₇	semidirect
180. #389	C₂²×C₇	semidirect
181. #389	C₂²×C₇	semidirect
182. #387	C₂²×C₇	semidirect
185. #384	C₂²×C₇	semidirect
186. #382	C₂²×C₇	semidirect
192. C₄×C₄⋊C₄	C₂²×C₇	semidirect
193. C₄×C₄⋊C₄	C₂²×C₇	semidirect
226. C₂×C₄×C₇	C₂²⋊Q₈	semidirect
244. C₂³×C₄	C₇×Q₈	semidirect
296. C₂²×C₇	#533	semidirect
404. C₂×C₄	C₇×C₂²⋊Q₈	semidirect
416. C₇	#36625	direct (N × H)
426. C₂²	C₇×#533	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#533	2
C₂³×C₄²×C₇	2
C₇×#2857	2
C₇×#2855	2
C₇×#2851	2
C₇×#2848	2
C₄×C₇×C₂²⋊Q₈	2
C₇×#2296	2
C₇×#2285	2
C₇×#2280	2
#36625	7

Subgroups — C7×#36625 #13213841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36625 #13213841