Subgroups — C₇×#19897 #13197113

Order 1792.

638 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3392	C₂	1	1	yes	maximal, characteristic
2	C₇×#3387	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Q₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3278	C₂	1	1	yes	maximal, characteristic
5	C₇×#1705	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1691	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1686	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1672	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1666	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1653	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1651	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1631	C₂	1	1	yes	maximal, characteristic
13	C₇×#1623	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×C₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#137	—	2	1	no	—
17	C₇×Q₈²	C₂²	1	1	yes	characteristic
18	C₇×#557	C₂²	1	1	yes	characteristic
19	C₇×#550	C₂²	1	1	yes	characteristic
20	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
21	C₇×#501	—	2	1	no	—
22	C₇×#498	—	2	1	no	—
23	C₇×#498	C₂²	1	1	yes	characteristic
24	C₇×#498	C₂²	1	1	yes	characteristic
25	C₇×#498	C₂²	1	1	yes	characteristic
26	C₇×#492	—	2	1	no	—
27	C₇×#492	C₂²	1	1	yes	characteristic
28	C₇×#492	C₂²	1	1	yes	characteristic
29	C₇×#492	C₂²	1	1	yes	characteristic
30	C₇×#479	—	2	1	no	—
31	C₇×#477	C₂²	1	1	yes	characteristic
32	C₇×#476	—	2	1	no	—
33	C₇×#476	C₂²	1	1	yes	characteristic
34	C₇×#475	—	2	1	no	—
35	C₇×#475	—	2	1	no	—
36	C₇×#475	C₂²	1	1	yes	characteristic
37	C₇×#475	C₂²	1	1	yes	characteristic
38	C₇×#468	—	2	1	no	—
39	C₇×#462	C₂²	1	1	yes	characteristic
40	C₇×#461	—	2	1	no	—
41	C₇×#461	C₂²	1	1	yes	characteristic
42	C₇×#460	—	2	1	no	—
43	C₇×#460	C₂²	1	1	yes	characteristic
44	C₇×#460	C₂²	1	1	yes	characteristic
45	C₇×#452	—	2	1	no	—
46	C₇×#448	—	2	1	no	—
47	C₇×#446	C₂²	1	1	yes	characteristic
48	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
49	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
50	C₇×#441	—	2	1	no	—
51	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
52	C₄×C₇×SD₁₆	—	2	1	no	—
53	C₄×C₇×SD₁₆	—	2	1	no	—
54	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
55	C₇×#436	C₂²	1	1	yes	characteristic
56	C₇×#335	C₂²	1	1	yes	characteristic
57	C₇×#334	C₂²	1	1	yes	characteristic
58	C₇×#333	C₂²	1	1	yes	characteristic
59	C₇×#332	C₂²	1	1	yes	characteristic
60	C₇×#332	C₂²	1	1	yes	characteristic
61	C₇×#331	C₂²	1	1	yes	characteristic
62	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₇×C₈²	C₂²	1	1	yes	characteristic
67	#19897	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₇×#41	—	2	1	no	—
69	C₂²×C₇×Q₈	—	2	1	no	—
70	C₇×#137	—	4	4	no	—
71	C₂×C₇×Q₁₆	—	2	1	no	—
72	C₂×C₇×Q₁₆	D₄	1	1	yes	characteristic
73	C₂×C₇×SD₁₆	—	2	1	no	—
74	C₂×C₇×SD₁₆	—	2	1	no	—
75	C₂×C₇×SD₁₆	—	2	1	no	—
76	C₂×C₇×SD₁₆	—	2	1	no	—
77	C₂×C₇×SD₁₆	—	2	1	no	—
78	C₂×C₇×SD₁₆	—	2	1	no	—
79	C₂×C₇×SD₁₆	—	2	1	no	—
80	C₂×C₇×SD₁₆	—	4	1	no	—
81	C₂×C₇×SD₁₆	D₄	1	1	yes	characteristic
82	C₂×C₇×M₁₆	—	2	1	no	—
83	C₇×C₄⋊Q₈	—	2	1	no	—
84	C₇×C₄⋊Q₈	—	2	1	no	—
85	C₇×C₄⋊Q₈	—	2	1	no	—
86	C₇×C₄⋊Q₈	—	2	1	no	—
87	C₇×C₄⋊Q₈	—	4	1	no	—
88	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₇×#127	—	2	1	no	—
92	C₇×#127	C₂³	1	1	yes	characteristic
93	C₇×#125	—	2	1	no	—
94	C₇×#125	—	4	1	no	—
95	C₇×C₂²⋊Q₈	—	2	1	no	—
96	C₇×C₂²⋊Q₈	—	4	1	no	—
97	C₇×#121	—	2	1	no	—
98	C₇×#121	—	4	1	no	—
99	C₄×C₇×Q₈	—	2	1	no	—
100	C₄×C₇×Q₈	—	2	1	no	—
101	C₄×C₇×Q₈	—	2	1	no	—
102	C₄×C₇×Q₈	—	2	1	no	—
103	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
104	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
105	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
106	C₄×C₇×D₄	—	2	1	no	—
107	C₄×C₇×D₄	—	2	1	no	—
108	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
109	C₇×#107	—	2	1	no	—
110	C₇×#107	D₄	1	1	yes	characteristic
111	C₇×#106	—	2	1	no	—
112	C₇×#106	—	2	1	no	—
113	C₇×#106	—	2	1	no	—
114	C₇×#106	—	2	1	no	—
115	C₇×#106	—	2	1	no	—
116	C₇×#106	—	2	1	no	—
117	C₇×#106	—	2	1	no	—
118	C₇×#106	—	4	1	no	—
119	C₇×#106	D₄	1	1	yes	characteristic
120	C₇×C₄⋊C₈	—	2	1	no	—
121	C₇×C₄⋊C₈	—	2	1	no	—
122	C₇×C₄⋊C₈	—	2	1	no	—
123	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
124	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
125	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
126	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
127	C₇×#103	—	2	1	no	—
128	C₇×#103	—	2	1	no	—
129	C₇×#103	—	2	1	no	—
130	C₇×#103	—	2	1	no	—
131	C₇×#103	—	2	1	no	—
132	C₇×#103	D₄	1	1	yes	characteristic
133	C₇×#103	D₄	1	1	yes	characteristic
134	C₇×#103	D₄	1	1	yes	characteristic
135	C₇×#102	—	2	1	no	—
136	C₇×#102	—	2	1	no	—
137	C₇×#102	—	2	1	no	—
138	C₇×#102	D₄	1	1	yes	characteristic
139	C₇×C₂²⋊C₈	—	2	1	no	—
140	C₇×#97	—	2	1	no	—
141	C₄×C₇×C₈	—	2	1	no	—
142	C₄×C₇×C₈	—	2	1	no	—
143	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
145	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
146	#3392	C₂×C₇	1	1	yes	characteristic
147	#3387	C₂×C₇	1	1	yes	characteristic, complemented
148	Q₈×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
149	#3278	C₂×C₇	1	1	yes	characteristic
150	#1705	C₂×C₇	1	1	yes	characteristic, complemented
151	#1691	C₂×C₇	1	1	yes	characteristic, complemented
152	#1686	C₂×C₇	1	1	yes	characteristic, complemented
153	#1672	C₂×C₇	1	1	yes	characteristic, complemented
154	#1666	C₂×C₇	1	1	yes	characteristic, complemented
155	#1653	C₂×C₇	1	1	yes	characteristic, complemented
156	#1651	C₂×C₇	1	1	yes	characteristic, complemented
157	#1631	C₂×C₇	1	1	yes	characteristic
158	#1623	C₂×C₇	1	1	yes	characteristic, complemented
159	#1590	C₂×C₇	1	1	yes	characteristic, complemented
160	C₈×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
161	C₇×#41	—	4	2	no	—
162	C₇×#41	—	8	1	no	—
163	C₂×C₇×Q₈	—	2	1	no	—
164	C₂×C₇×Q₈	—	2	1	no	—
165	C₂×C₇×Q₈	—	2	1	no	—
166	C₂×C₇×Q₈	—	4	1	no	—
167	C₂×C₇×Q₈	—	4	1	no	—
168	C₂×C₇×Q₈	—	4	2	no	—
169	C₂×C₇×Q₈	—	8	1	no	—
170	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
172	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
173	C₂×C₇×D₄	—	2	1	no	—
174	C₂×C₇×D₄	—	2	1	no	—
175	C₂×C₇×D₄	—	2	1	no	—
176	C₂×C₇×D₄	—	4	1	no	—
177	C₂×C₇×D₄	—	4	1	no	—
178	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₇	—	2	1	no	—
180	C₂²×C₄×C₇	—	4	1	no	—
181	C₂²×C₄×C₇	—	4	1	no	—
182	C₇×Q₁₆	—	4	2	no	—
183	C₇×Q₁₆	SD₁₆	1	4	yes	complemented
184	C₇×SD₁₆	—	2	2	no	—
185	C₇×SD₁₆	—	4	2	no	—
186	C₇×SD₁₆	—	4	2	no	—
187	C₇×SD₁₆	—	4	2	no	—
188	C₇×SD₁₆	—	8	1	no	—
189	C₇×SD₁₆	—	8	1	no	—
190	C₇×SD₁₆	—	8	2	no	—
191	C₇×SD₁₆	—	8	1	no	—
192	C₇×SD₁₆	—	8	1	no	—
193	C₇×M₁₆	—	4	2	no	—
194	C₂×C₇×C₈	—	2	1	no	—
195	C₂×C₇×C₈	—	2	1	no	—
196	C₂×C₇×C₈	—	2	1	no	—
197	C₂×C₇×C₈	—	2	1	no	—
198	C₂×C₇×C₈	—	2	1	no	—
199	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
200	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
201	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
202	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
203	C₇×C₄⋊C₄	—	2	1	no	—
204	C₇×C₄⋊C₄	—	2	1	no	—
205	C₇×C₄⋊C₄	—	2	1	no	—
206	C₇×C₄⋊C₄	—	2	1	no	—
207	C₇×C₄⋊C₄	—	2	1	no	—
208	C₇×C₄⋊C₄	—	2	1	no	—
209	C₇×C₄⋊C₄	—	2	1	no	—
210	C₇×C₄⋊C₄	—	2	1	no	—
211	C₇×C₄⋊C₄	—	2	1	no	—
212	C₇×C₄⋊C₄	—	4	1	no	—
213	C₇×C₄⋊C₄	—	4	1	no	—
214	C₇×C₄⋊C₄	—	4	1	no	—
215	C₇×C₄⋊C₄	—	4	1	no	—
216	C₇×C₄⋊C₄	—	4	1	no	—
217	C₇×C₄⋊C₄	—	4	1	no	—
218	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
219	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
220	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
221	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
222	C₇×C₂²⋊C₄	—	2	1	no	—
223	C₇×C₂²⋊C₄	—	4	1	no	—
224	C₇×C₂²⋊C₄	—	4	1	no	—
225	C₄²×C₇	—	2	1	no	—
226	C₄²×C₇	—	2	1	no	—
227	C₄²×C₇	—	2	1	no	—
228	C₄²×C₇	—	4	1	no	—
229	C₄²×C₇	—	4	1	no	—
230	C₄²×C₇	C₂⁴	1	1	yes	characteristic
231	C₂×#137	—	2	1	no	—
232	Q₈²	C₂²×C₇	1	1	yes	characteristic
233	#557	C₂²×C₇	1	1	yes	characteristic
234	#550	C₂²×C₇	1	1	yes	characteristic
235	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
236	#501	—	2	1	no	—
237	#498	—	2	1	no	—
238	#498	C₂²×C₇	1	1	yes	characteristic
239	#498	C₂²×C₇	1	1	yes	characteristic
240	#498	C₂²×C₇	1	1	yes	characteristic
241	#492	—	2	1	no	—
242	#492	C₂²×C₇	1	1	yes	characteristic
243	#492	C₂²×C₇	1	1	yes	characteristic
244	#492	C₂²×C₇	1	1	yes	characteristic
245	#479	—	2	1	no	—
246	#477	C₂²×C₇	1	1	yes	characteristic
247	#476	—	2	1	no	—
248	#476	C₂²×C₇	1	1	yes	characteristic
249	#475	—	2	1	no	—
250	#475	—	2	1	no	—
251	#475	C₂²×C₇	1	1	yes	characteristic
252	#475	C₂²×C₇	1	1	yes	characteristic
253	#468	—	2	1	no	—
254	#462	C₂²×C₇	1	1	yes	characteristic
255	#461	—	2	1	no	—
256	#461	C₂²×C₇	1	1	yes	characteristic
257	#460	—	2	1	no	—
258	#460	C₂²×C₇	1	1	yes	characteristic
259	#460	C₂²×C₇	1	1	yes	characteristic
260	#452	—	2	1	no	—
261	#448	—	2	1	no	—
262	#446	C₂²×C₇	1	1	yes	characteristic
263	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
264	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
265	#441	—	2	1	no	—
266	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
267	C₄×SD₁₆	—	2	1	no	—
268	C₄×SD₁₆	—	2	1	no	—
269	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
270	#436	C₂²×C₇	1	1	yes	characteristic
271	#335	C₂²×C₇	1	1	yes	characteristic
272	#334	C₂²×C₇	1	1	yes	characteristic
273	#333	C₂²×C₇	1	1	yes	characteristic
274	#332	C₂²×C₇	1	1	yes	characteristic
275	#332	C₂²×C₇	1	1	yes	characteristic
276	#331	C₂²×C₇	1	1	yes	characteristic
277	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
278	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
279	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
280	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
281	C₈²	C₂²×C₇	1	1	yes	characteristic
282	C₂³×C₇	—	2	1	no	—
283	C₂³×C₇	—	4	1	no	—
284	C₇×Q₈	—	2	1	no	—
285	C₇×Q₈	—	2	1	no	—
286	C₇×Q₈	—	2	1	no	—
287	C₇×Q₈	—	2	1	no	—
288	C₇×Q₈	—	4	1	no	—
289	C₇×Q₈	—	4	1	no	—
290	C₇×Q₈	—	4	1	no	—
291	C₇×Q₈	—	4	1	no	—
292	C₇×Q₈	—	8	2	no	—
293	C₇×Q₈	—	8	1	no	—
294	C₇×Q₈	—	16	1	no	—
295	C₇×Q₈	C₂×SD₁₆	1	2	yes	—
296	C₇×Q₈	C₂×SD₁₆	1	2	yes	—
297	C₇×D₄	—	2	1	no	—
298	C₇×D₄	—	2	1	no	—
299	C₇×D₄	—	4	1	no	—
300	C₇×D₄	—	4	1	no	—
301	C₇×D₄	—	4	1	no	—
302	C₇×D₄	—	4	1	no	—
303	C₇×D₄	—	8	2	no	—
304	C₇×D₄	—	8	1	no	—
305	C₇×D₄	—	16	1	no	—
306	C₂×C₄×C₇	—	2	1	no	—
307	C₂×C₄×C₇	—	2	1	no	—
308	C₂×C₄×C₇	—	2	1	no	—
309	C₂×C₄×C₇	—	2	1	no	—
310	C₂×C₄×C₇	—	2	1	no	—
311	C₂×C₄×C₇	—	2	1	no	—
312	C₂×C₄×C₇	—	2	1	no	—
313	C₂×C₄×C₇	—	4	1	no	—
314	C₂×C₄×C₇	—	4	1	no	—
315	C₂×C₄×C₇	—	4	1	no	—
316	C₂×C₄×C₇	—	4	1	no	—
317	C₂×C₄×C₇	—	4	1	no	—
318	C₂×C₄×C₇	—	8	2	no	—
319	C₂×C₄×C₇	—	8	2	no	—
320	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
323	C₇×C₈	—	2	2	no	—
324	C₇×C₈	—	2	1	no	—
325	C₇×C₈	—	2	1	no	—
326	C₇×C₈	—	4	1	no	—
327	C₇×C₈	—	4	1	no	—
328	C₇×C₈	—	4	1	no	—
329	C₇×C₈	—	4	1	no	—
330	C₇×C₈	C₂×SD₁₆	1	2	yes	—
331	C₇×C₈	#137	1	2	yes	complemented
332	C₂×#41	—	2	1	no	—
333	C₂²×Q₈	—	2	1	no	—
334	#137	—	4	4	no	—
335	C₂×Q₁₆	—	2	1	no	—
336	C₂×Q₁₆	C₇×D₄	1	1	yes	characteristic
337	C₂×SD₁₆	—	2	1	no	—
338	C₂×SD₁₆	—	2	1	no	—
339	C₂×SD₁₆	—	2	1	no	—
340	C₂×SD₁₆	—	2	1	no	—
341	C₂×SD₁₆	—	2	1	no	—
342	C₂×SD₁₆	—	2	1	no	—
343	C₂×SD₁₆	—	2	1	no	—
344	C₂×SD₁₆	—	4	1	no	—
345	C₂×SD₁₆	C₇×D₄	1	1	yes	characteristic
346	C₂×M₁₆	—	2	1	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	—	2	1	no	—
349	C₄⋊Q₈	—	2	1	no	—
350	C₄⋊Q₈	—	2	1	no	—
351	C₄⋊Q₈	—	4	1	no	—
352	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
353	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
354	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
355	#127	—	2	1	no	—
356	#127	C₂³×C₇	1	1	yes	characteristic
357	#125	—	2	1	no	—
358	#125	—	4	1	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	—	4	1	no	—
361	#121	—	2	1	no	—
362	#121	—	4	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
368	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
369	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
373	#107	—	2	1	no	—
374	#107	C₇×D₄	1	1	yes	characteristic
375	#106	—	2	1	no	—
376	#106	—	2	1	no	—
377	#106	—	2	1	no	—
378	#106	—	2	1	no	—
379	#106	—	2	1	no	—
380	#106	—	2	1	no	—
381	#106	—	2	1	no	—
382	#106	—	4	1	no	—
383	#106	C₇×D₄	1	1	yes	characteristic
384	C₄⋊C₈	—	2	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
388	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
389	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
390	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
391	#103	—	2	1	no	—
392	#103	—	2	1	no	—
393	#103	—	2	1	no	—
394	#103	—	2	1	no	—
395	#103	—	2	1	no	—
396	#103	C₇×D₄	1	1	yes	characteristic
397	#103	C₇×D₄	1	1	yes	characteristic
398	#103	C₇×D₄	1	1	yes	characteristic
399	#102	—	2	1	no	—
400	#102	—	2	1	no	—
401	#102	—	2	1	no	—
402	#102	C₇×D₄	1	1	yes	characteristic
403	C₂²⋊C₈	—	2	1	no	—
404	#97	—	2	1	no	—
405	C₄×C₈	—	2	1	no	—
406	C₄×C₈	—	2	1	no	—
407	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
408	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
409	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
410	C₂²×C₇	—	4	1	no	—
411	C₂²×C₇	—	4	1	no	—
412	C₂²×C₇	—	4	1	no	—
413	C₂²×C₇	—	8	1	no	—
414	C₂²×C₇	—	8	1	no	—
415	C₂²×C₇	—	8	1	no	—
416	C₂²×C₇	D₄²	1	1	yes	characteristic
417	C₄×C₇	—	2	2	no	—
418	C₄×C₇	—	2	2	no	—
419	C₄×C₇	—	2	1	no	—
420	C₄×C₇	—	4	1	no	—
421	C₄×C₇	—	4	1	no	—
422	C₄×C₇	—	4	1	no	—
423	C₄×C₇	—	4	1	no	—
424	C₄×C₇	—	4	1	no	—
425	C₄×C₇	—	8	1	no	—
426	C₄×C₇	—	8	1	no	—
427	C₄×C₇	—	8	1	no	—
428	C₄×C₇	C₂²×SD₁₆	1	1	yes	characteristic
429	C₄×C₇	C₂×#137	1	1	yes	characteristic
430	C₄×C₇	#577	1	1	yes	characteristic
431	C₄×C₇	#577	1	1	yes	characteristic
432	#41	—	4	2	no	—
433	#41	—	8	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	4	1	no	—
438	C₂×Q₈	—	4	1	no	—
439	C₂×Q₈	—	4	2	no	—
440	C₂×Q₈	—	8	1	no	—
441	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
442	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
443	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	4	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	Q₁₆	—	4	2	no	—
454	Q₁₆	C₇×SD₁₆	1	4	yes	complemented
455	SD₁₆	—	2	2	no	—
456	SD₁₆	—	4	2	no	—
457	SD₁₆	—	4	2	no	—
458	SD₁₆	—	4	2	no	—
459	SD₁₆	—	8	1	no	—
460	SD₁₆	—	8	1	no	—
461	SD₁₆	—	8	2	no	—
462	SD₁₆	—	8	1	no	—
463	SD₁₆	—	8	1	no	—
464	M₁₆	—	4	2	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
471	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
472	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
473	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
490	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
491	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
492	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	4	1	no	—
500	C₄²	—	4	1	no	—
501	C₄²	C₂⁴×C₇	1	1	yes	characteristic
502	C₂×C₇	—	8	1	no	—
503	C₂×C₇	—	16	1	no	—
504	C₂×C₇	#3278	1	1	yes	characteristic
505	C₂×C₇	D₄×SD₁₆	1	1	yes	characteristic
506	C₂×C₇	#3291	1	1	yes	characteristic
507	C₂³	—	2	1	no	—
508	C₂³	—	4	1	no	—
509	Q₈	—	2	1	no	—
510	Q₈	—	2	1	no	—
511	Q₈	—	2	1	no	—
512	Q₈	—	2	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	8	2	no	—
518	Q₈	—	8	1	no	—
519	Q₈	—	16	1	no	—
520	Q₈	C₂×C₇×SD₁₆	1	2	yes	—
521	Q₈	C₂×C₇×SD₁₆	1	2	yes	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	8	2	no	—
529	D₄	—	8	1	no	—
530	D₄	—	16	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
546	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
547	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
548	C₈	—	2	2	no	—
549	C₈	—	2	1	no	—
550	C₈	—	2	1	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	C₂×C₇×SD₁₆	1	2	yes	—
556	C₈	C₇×#137	1	2	yes	complemented
557	C₇	#19897	1	1	yes	characteristic, direct product factor, Sylow
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	C₇×D₄²	1	1	yes	characteristic
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	1	no	—
576	C₄	C₂²×C₇×SD₁₆	1	1	yes	characteristic
577	C₄	C₂×C₇×#137	1	1	yes	characteristic
578	C₄	C₇×#577	1	1	yes	characteristic
579	C₄	C₇×#577	1	1	yes	characteristic
580	C₂	—	8	1	no	—
581	C₂	—	16	1	no	—
582	C₂	C₇×#3278	1	1	yes	characteristic
583	C₂	C₇×D₄×SD₁₆	1	1	yes	characteristic
584	C₂	C₇×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#550	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3387	C₂	semidirect
3. C₇×Q₈×SD₁₆	C₂	semidirect
5. C₇×#1705	C₂	semidirect
6. C₇×#1691	C₂	semidirect
7. C₇×#1686	C₂	semidirect
8. C₇×#1672	C₂	semidirect
9. C₇×#1666	C₂	semidirect
10. C₇×#1653	C₂	semidirect
11. C₇×#1651	C₂	semidirect
13. C₇×#1623	C₂	semidirect
14. C₇×#1590	C₂	semidirect
15. C₇×C₈×Q₁₆	C₂	semidirect
67. #19897	C₇	direct (N × H)
147. #3387	C₂×C₇	semidirect
148. Q₈×SD₁₆	C₂×C₇	semidirect
150. #1705	C₂×C₇	semidirect
151. #1691	C₂×C₇	semidirect
152. #1686	C₂×C₇	semidirect
153. #1672	C₂×C₇	semidirect
154. #1666	C₂×C₇	semidirect
155. #1653	C₂×C₇	semidirect
156. #1651	C₂×C₇	semidirect
158. #1623	C₂×C₇	semidirect
159. #1590	C₂×C₇	semidirect
160. C₈×Q₁₆	C₂×C₇	semidirect
183. C₇×Q₁₆	SD₁₆	semidirect
331. C₇×C₈	#137	semidirect
454. Q₁₆	C₇×SD₁₆	semidirect
556. C₈	C₇×#137	semidirect
557. C₇	#19897	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3392	2
C₇×#3387	2
C₇×Q₈×SD₁₆	2
C₇×#3278	2
C₇×#1705	2
C₇×#1691	2
C₇×#1686	2
C₇×#1672	2
C₇×#1666	2
C₇×#1653	2
C₇×#1651	2
C₇×#1631	2
C₇×#1623	2
C₇×#1590	2
C₇×C₈×Q₁₆	2
#19897	7

Subgroups — C7×#19897 #13197113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19897 #13197113