Subgroups — C₇×#61469 #13238685

Order 1792.

1866 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3483	C₂	1	1	yes	maximal, characteristic
2	C₇×Q₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×Q₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3357	C₂	1	3	yes	maximal, complemented
8	C₇×#3333	C₂	1	3	yes	maximal, complemented
9	C₇×#3329	C₂	1	3	yes	maximal, complemented
10	C₇×#3278	C₂	1	3	yes	maximal, complemented
11	C₇×#3182	C₂	1	3	yes	maximal, complemented
12	C₇×#3116	C₂	1	3	yes	maximal, complemented
13	C₇×#3112	C₂	1	3	yes	maximal, complemented
14	C₇×#2971	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₇×#137	C₂	1	3	yes	maximal, complemented
16	C₂×C₇×#137	C₂²	1	3	yes	—
17	C₇×Q₈²	C₂²	1	1	yes	characteristic
18	C₇×Q₈²	C₂²	1	1	yes	characteristic
19	C₇×#557	—	2	1	no	—
20	C₇×#557	C₂²	1	1	yes	characteristic
21	C₇×#555	—	2	3	no	—
22	C₇×#555	C₂²	1	3	yes	—
23	C₇×#554	—	2	3	no	—
24	C₇×#554	C₂²	1	3	yes	—
25	C₇×#550	—	2	1	no	—
26	C₇×#550	C₂²	1	3	yes	—
27	C₇×#550	C₂²	1	1	yes	characteristic
28	C₇×D₄×Q₈	C₂²	1	3	yes	—
29	C₇×#533	—	2	3	no	—
30	C₇×#533	C₂²	1	3	yes	—
31	C₇×#532	—	2	3	no	—
32	C₇×#532	C₂²	1	3	yes	—
33	C₄×C₇×#41	—	2	1	no	—
34	C₄×C₇×#41	—	2	1	no	—
35	C₄×C₇×#41	C₂²	1	3	yes	—
36	C₄×C₇×#41	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×Q₈	C₂²	1	3	yes	—
38	C₇×#500	C₂²	1	3	yes	—
39	C₇×#492	C₂²	1	3	yes	—
40	C₇×#487	C₂²	1	3	yes	—
41	C₇×#486	C₂²	1	3	yes	—
42	C₇×#485	C₂²	1	6	yes	—
43	C₇×#480	C₂²	1	6	yes	—
44	C₇×#477	C₂²	1	3	yes	—
45	C₇×#477	C₂²	1	3	yes	—
46	C₇×#477	C₂²	1	3	yes	—
47	C₇×#476	C₂²	1	3	yes	—
48	C₇×#468	C₂²	1	6	yes	—
49	C₇×#468	C₂²	1	6	yes	—
50	C₇×#462	C₂²	1	3	yes	—
51	C₇×#461	C₂²	1	3	yes	—
52	C₇×#460	C₂²	1	3	yes	—
53	C₇×#460	C₂²	1	3	yes	—
54	C₇×#452	C₂²	1	6	yes	—
55	C₇×#448	C₂²	1	6	yes	—
56	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
57	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
58	C₇×#441	C₂²	1	1	yes	characteristic
59	C₇×#441	C₂²	1	3	yes	—
60	C₇×#440	C₂²	1	3	yes	—
61	C₇×#440	C₂²	1	6	yes	—
62	C₇×#440	C₂²	1	3	yes	—
63	C₄×C₇×Q₁₆	C₂²	1	3	yes	—
64	C₄×C₇×Q₁₆	C₂²	1	3	yes	—
65	C₄×C₇×SD₁₆	C₂²	1	3	yes	—
66	C₄×C₇×SD₁₆	C₂²	1	3	yes	—
67	C₇×#436	C₂²	1	3	yes	—
68	C₇×#436	C₂²	1	3	yes	—
69	C₇×#432	C₂²	1	3	yes	—
70	C₇×#428	C₂²	1	3	yes	—
71	C₇×#419	C₂²	1	3	yes	—
72	C₇×#417	C₂²	1	3	yes	—
73	C₄×C₇×M₁₆	C₂²	1	3	yes	—
74	#61469	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂×C₇×#41	—	2	1	no	—
76	C₂×C₇×#41	—	2	3	no	—
77	C₂×C₇×#41	D₄	1	1	yes	characteristic
78	C₂×C₇×#41	C₂³	1	3	yes	—
79	C₂²×C₇×Q₈	C₂³	1	3	yes	—
80	C₇×#137	—	2	12	no	—
81	C₂×C₇×Q₁₆	C₂³	1	3	yes	—
82	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₇×SD₁₆	C₂³	1	3	yes	—
84	C₂×C₇×SD₁₆	C₂³	1	3	yes	—
85	C₂×C₇×SD₁₆	C₂³	1	6	yes	—
86	C₂×C₇×M₁₆	C₂³	1	3	yes	—
87	C₂×C₇×M₁₆	C₂³	1	3	yes	—
88	C₇×C₄⋊Q₈	—	2	3	no	—
89	C₇×C₄⋊Q₈	—	2	3	no	—
90	C₇×C₄⋊Q₈	—	2	3	no	—
91	C₇×C₄⋊Q₈	C₂³	1	3	yes	—
92	C₇×C₄⋊Q₈	C₂³	1	3	yes	—
93	C₇×C₄⋊Q₈	C₂³	1	3	yes	—
94	C₇×#127	—	2	3	no	—
95	C₇×#127	C₂³	1	3	yes	—
96	C₇×#125	—	2	3	no	—
97	C₇×#125	—	2	3	no	—
98	C₇×#125	—	2	3	no	—
99	C₇×#124	—	2	6	no	—
100	C₇×#124	—	2	3	no	—
101	C₇×C₂²⋊Q₈	—	2	3	no	—
102	C₇×C₂²⋊Q₈	—	2	6	no	—
103	C₇×C₂²⋊Q₈	—	2	6	no	—
104	C₇×C₂²⋊Q₈	C₂³	1	6	yes	—
105	C₇×#121	—	2	3	no	—
106	C₇×#121	—	2	3	no	—
107	C₇×#121	—	2	3	no	—
108	C₇×#121	—	2	6	no	—
109	C₇×#121	C₂³	1	6	yes	—
110	C₄×C₇×Q₈	—	2	1	no	—
111	C₄×C₇×Q₈	—	2	1	no	—
112	C₄×C₇×Q₈	—	2	1	no	—
113	C₄×C₇×Q₈	—	2	3	no	—
114	C₄×C₇×Q₈	—	2	3	no	—
115	C₄×C₇×Q₈	—	2	3	no	—
116	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
117	C₄×C₇×Q₈	C₂³	1	3	yes	—
118	C₄×C₇×Q₈	C₂³	1	3	yes	—
119	C₄×C₇×Q₈	C₂³	1	3	yes	—
120	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
121	C₄×C₇×Q₈	C₂³	1	3	yes	—
122	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
123	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
124	C₄×C₇×D₄	—	2	3	no	—
125	C₄×C₇×D₄	—	2	3	no	—
126	C₄×C₇×D₄	—	2	3	no	—
127	C₄×C₇×D₄	—	2	3	no	—
128	C₄×C₇×D₄	—	2	3	no	—
129	C₄×C₇×D₄	—	2	3	no	—
130	C₄×C₇×D₄	D₄	1	3	yes	—
131	C₄×C₇×D₄	C₂³	1	3	yes	—
132	C₄×C₇×D₄	C₂³	1	3	yes	—
133	C₄×C₇×D₄	C₂³	1	3	yes	—
134	C₇×#117	—	2	3	no	—
135	C₇×#117	—	2	3	no	—
136	C₇×#117	—	2	3	no	—
137	C₇×#117	D₄	1	3	yes	—
138	C₇×#117	C₂³	1	3	yes	—
139	C₂×C₇×C₄⋊C₄	—	2	3	no	—
140	C₂×C₇×C₄⋊C₄	C₂³	1	3	yes	—
141	C₂×C₄²×C₇	—	2	3	no	—
142	C₂×C₄²×C₇	—	2	3	no	—
143	C₂×C₄²×C₇	C₂³	1	3	yes	—
144	C₇×#107	C₂³	1	3	yes	—
145	C₇×#107	C₂³	1	6	yes	—
146	C₇×#107	C₂³	1	3	yes	—
147	C₇×#106	C₂³	1	3	yes	—
148	C₇×#106	C₂³	1	1	yes	characteristic
149	C₇×C₄⋊C₈	C₂³	1	3	yes	—
150	C₇×C₄⋊C₈	C₂³	1	3	yes	—
151	C₇×#103	C₂³	1	3	yes	—
152	C₇×#103	C₂³	1	6	yes	—
153	C₇×#103	C₂³	1	3	yes	—
154	C₇×#103	C₂³	1	3	yes	—
155	C₇×#103	C₂³	1	3	yes	—
156	C₇×#103	C₂³	1	1	yes	characteristic
157	C₇×#103	C₂³	1	1	yes	characteristic
158	C₇×#102	C₂³	1	3	yes	—
159	C₇×#102	C₂³	1	6	yes	—
160	C₇×#102	C₂³	1	3	yes	—
161	C₇×C₂²⋊C₈	C₂³	1	6	yes	—
162	C₇×#97	C₂³	1	1	yes	characteristic
163	C₇×#97	C₂³	1	3	yes	—
164	C₄×C₇×C₈	C₂³	1	3	yes	—
165	C₄×C₇×C₈	C₂³	1	3	yes	—
166	#3483	C₂×C₇	1	1	yes	characteristic
167	Q₈×#41	C₂×C₇	1	1	yes	characteristic, complemented
168	#3392	C₂×C₇	1	1	yes	characteristic, complemented
169	Q₈×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
170	#3363	C₂×C₇	1	1	yes	characteristic, complemented
171	#3362	C₂×C₇	1	1	yes	characteristic, complemented
172	#3357	C₂×C₇	1	3	yes	complemented
173	#3333	C₂×C₇	1	3	yes	complemented
174	#3329	C₂×C₇	1	3	yes	complemented
175	#3278	C₂×C₇	1	3	yes	complemented
176	#3182	C₂×C₇	1	3	yes	complemented
177	#3116	C₂×C₇	1	3	yes	complemented
178	#3112	C₂×C₇	1	3	yes	complemented
179	#2971	C₂×C₇	1	1	yes	characteristic, complemented
180	C₄×#137	C₂×C₇	1	3	yes	complemented
181	C₇×#41	—	2	4	no	—
182	C₇×#41	—	2	6	no	—
183	C₇×#41	—	4	3	no	—
184	C₇×#41	—	4	4	no	—
185	C₇×#41	—	8	6	no	—
186	C₂×C₇×Q₈	—	2	3	no	—
187	C₂×C₇×Q₈	—	2	3	no	—
188	C₂×C₇×Q₈	—	2	3	no	—
189	C₂×C₇×Q₈	—	2	6	no	—
190	C₂×C₇×Q₈	—	4	3	no	—
191	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
192	C₂×C₇×Q₈	C₂⁴	1	3	yes	—
193	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
194	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
195	C₂×C₇×D₄	—	2	3	no	—
196	C₂×C₇×D₄	—	2	6	no	—
197	C₂×C₇×D₄	—	2	3	no	—
198	C₂×C₇×D₄	—	2	3	no	—
199	C₂×C₇×D₄	C₂×D₄	1	3	yes	—
200	C₂×C₇×D₄	C₂⁴	1	3	yes	—
201	C₂²×C₄×C₇	—	2	3	no	—
202	C₂²×C₄×C₇	—	2	3	no	—
203	C₂²×C₄×C₇	—	2	3	no	—
204	C₂²×C₄×C₇	—	2	3	no	—
205	C₂²×C₄×C₇	—	2	3	no	—
206	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
207	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
208	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
209	C₇×Q₁₆	—	2	6	no	—
210	C₇×Q₁₆	#41	1	4	yes	complemented
211	C₇×SD₁₆	—	2	6	no	—
212	C₇×SD₁₆	—	2	6	no	—
213	C₇×SD₁₆	—	4	6	no	—
214	C₇×M₁₆	—	2	6	no	—
215	C₇×M₁₆	—	4	3	no	—
216	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
217	C₂×C₇×C₈	C₂⁴	1	3	yes	—
218	C₂×C₇×C₈	C₂⁴	1	3	yes	—
219	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
220	C₇×C₄⋊C₄	—	2	1	no	—
221	C₇×C₄⋊C₄	—	2	3	no	—
222	C₇×C₄⋊C₄	—	2	3	no	—
223	C₇×C₄⋊C₄	—	2	3	no	—
224	C₇×C₄⋊C₄	—	2	3	no	—
225	C₇×C₄⋊C₄	—	2	1	no	—
226	C₇×C₄⋊C₄	—	2	3	no	—
227	C₇×C₄⋊C₄	—	2	3	no	—
228	C₇×C₄⋊C₄	—	2	3	no	—
229	C₇×C₄⋊C₄	—	2	3	no	—
230	C₇×C₄⋊C₄	—	2	3	no	—
231	C₇×C₄⋊C₄	—	2	6	no	—
232	C₇×C₄⋊C₄	C₂×D₄	1	3	yes	—
233	C₇×C₄⋊C₄	C₂×D₄	1	3	yes	—
234	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
235	C₇×C₄⋊C₄	C₂⁴	1	3	yes	—
236	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
237	C₇×C₄⋊C₄	C₂⁴	1	3	yes	—
238	C₇×C₂²⋊C₄	—	2	6	no	—
239	C₇×C₂²⋊C₄	—	2	3	no	—
240	C₇×C₂²⋊C₄	—	2	6	no	—
241	C₇×C₂²⋊C₄	—	2	3	no	—
242	C₇×C₂²⋊C₄	—	2	3	no	—
243	C₇×C₂²⋊C₄	C₂×D₄	1	6	yes	—
244	C₄²×C₇	—	2	1	no	—
245	C₄²×C₇	—	2	1	no	—
246	C₄²×C₇	—	2	3	no	—
247	C₄²×C₇	—	2	3	no	—
248	C₄²×C₇	—	2	3	no	—
249	C₄²×C₇	—	2	3	no	—
250	C₄²×C₇	—	2	3	no	—
251	C₄²×C₇	C₂×D₄	1	3	yes	—
252	C₄²×C₇	C₂×D₄	1	3	yes	—
253	C₄²×C₇	C₂⁴	1	3	yes	—
254	C₄²×C₇	C₂⁴	1	1	yes	characteristic
255	C₂×#137	C₂²×C₇	1	3	yes	—
256	Q₈²	C₂²×C₇	1	1	yes	characteristic
257	Q₈²	C₂²×C₇	1	1	yes	characteristic
258	#557	—	2	1	no	—
259	#557	C₂²×C₇	1	1	yes	characteristic
260	#555	—	2	3	no	—
261	#555	C₂²×C₇	1	3	yes	—
262	#554	—	2	3	no	—
263	#554	C₂²×C₇	1	3	yes	—
264	#550	—	2	1	no	—
265	#550	C₂²×C₇	1	3	yes	—
266	#550	C₂²×C₇	1	1	yes	characteristic
267	D₄×Q₈	C₂²×C₇	1	3	yes	—
268	#533	—	2	3	no	—
269	#533	C₂²×C₇	1	3	yes	—
270	#532	—	2	3	no	—
271	#532	C₂²×C₇	1	3	yes	—
272	C₄×#41	—	2	1	no	—
273	C₄×#41	—	2	1	no	—
274	C₄×#41	C₂²×C₇	1	3	yes	—
275	C₄×#41	C₂²×C₇	1	1	yes	characteristic
276	C₂×C₄×Q₈	C₂²×C₇	1	3	yes	—
277	#500	C₂²×C₇	1	3	yes	—
278	#492	C₂²×C₇	1	3	yes	—
279	#487	C₂²×C₇	1	3	yes	—
280	#486	C₂²×C₇	1	3	yes	—
281	#485	C₂²×C₇	1	6	yes	—
282	#480	C₂²×C₇	1	6	yes	—
283	#477	C₂²×C₇	1	3	yes	—
284	#477	C₂²×C₇	1	3	yes	—
285	#477	C₂²×C₇	1	3	yes	—
286	#476	C₂²×C₇	1	3	yes	—
287	#468	C₂²×C₇	1	6	yes	—
288	#468	C₂²×C₇	1	6	yes	—
289	#462	C₂²×C₇	1	3	yes	—
290	#461	C₂²×C₇	1	3	yes	—
291	#460	C₂²×C₇	1	3	yes	—
292	#460	C₂²×C₇	1	3	yes	—
293	#452	C₂²×C₇	1	6	yes	—
294	#448	C₂²×C₇	1	6	yes	—
295	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
296	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
297	#441	C₂²×C₇	1	3	yes	—
298	#441	C₂²×C₇	1	1	yes	characteristic
299	#440	C₂²×C₇	1	3	yes	—
300	#440	C₂²×C₇	1	6	yes	—
301	#440	C₂²×C₇	1	3	yes	—
302	C₄×Q₁₆	C₂²×C₇	1	3	yes	—
303	C₄×Q₁₆	C₂²×C₇	1	3	yes	—
304	C₄×SD₁₆	C₂²×C₇	1	3	yes	—
305	C₄×SD₁₆	C₂²×C₇	1	3	yes	—
306	#436	C₂²×C₇	1	3	yes	—
307	#436	C₂²×C₇	1	3	yes	—
308	#432	C₂²×C₇	1	3	yes	—
309	#428	C₂²×C₇	1	3	yes	—
310	#419	C₂²×C₇	1	3	yes	—
311	#417	C₂²×C₇	1	3	yes	—
312	C₄×M₁₆	C₂²×C₇	1	3	yes	—
313	C₂³×C₇	—	2	3	no	—
314	C₂³×C₇	C₂²×D₄	1	3	yes	—
315	C₇×Q₈	—	2	1	no	—
316	C₇×Q₈	—	2	1	no	—
317	C₇×Q₈	—	2	3	no	—
318	C₇×Q₈	—	2	3	no	—
319	C₇×Q₈	—	4	6	no	—
320	C₇×Q₈	—	8	3	no	—
321	C₇×Q₈	—	8	3	no	—
322	C₇×Q₈	#137	1	4	yes	complemented
323	C₇×Q₈	C₂×#41	1	2	yes	—
324	C₇×Q₈	C₂×#41	1	2	yes	—
325	C₇×D₄	—	2	6	no	—
326	C₇×D₄	—	2	3	no	—
327	C₇×D₄	—	2	3	no	—
328	C₇×D₄	—	4	6	no	—
329	C₇×D₄	—	4	6	no	—
330	C₇×D₄	—	8	3	no	—
331	C₇×D₄	—	8	6	no	—
332	C₂×C₄×C₇	—	2	1	no	—
333	C₂×C₄×C₇	—	2	1	no	—
334	C₂×C₄×C₇	—	2	6	no	—
335	C₂×C₄×C₇	—	2	3	no	—
336	C₂×C₄×C₇	—	2	3	no	—
337	C₂×C₄×C₇	—	2	1	no	—
338	C₂×C₄×C₇	—	2	1	no	—
339	C₂×C₄×C₇	—	2	3	no	—
340	C₂×C₄×C₇	—	2	3	no	—
341	C₂×C₄×C₇	—	2	3	no	—
342	C₂×C₄×C₇	—	4	3	no	—
343	C₂×C₄×C₇	—	4	6	no	—
344	C₂×C₄×C₇	—	4	6	no	—
345	C₂×C₄×C₇	—	4	6	no	—
346	C₂×C₄×C₇	—	4	6	no	—
347	C₂×C₄×C₇	—	8	3	no	—
348	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
351	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
352	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
353	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
354	C₇×C₈	—	2	3	no	—
355	C₇×C₈	—	2	1	no	—
356	C₇×C₈	—	2	3	no	—
357	C₇×C₈	C₂×#41	1	2	yes	—
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	3	no	—
360	C₂×#41	C₇×D₄	1	1	yes	characteristic
361	C₂×#41	C₂³×C₇	1	3	yes	—
362	C₂²×Q₈	C₂³×C₇	1	3	yes	—
363	#137	—	2	12	no	—
364	C₂×Q₁₆	C₂³×C₇	1	3	yes	—
365	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
366	C₂×SD₁₆	C₂³×C₇	1	3	yes	—
367	C₂×SD₁₆	C₂³×C₇	1	3	yes	—
368	C₂×SD₁₆	C₂³×C₇	1	6	yes	—
369	C₂×M₁₆	C₂³×C₇	1	3	yes	—
370	C₂×M₁₆	C₂³×C₇	1	3	yes	—
371	C₄⋊Q₈	—	2	3	no	—
372	C₄⋊Q₈	—	2	3	no	—
373	C₄⋊Q₈	—	2	3	no	—
374	C₄⋊Q₈	C₂³×C₇	1	3	yes	—
375	C₄⋊Q₈	C₂³×C₇	1	3	yes	—
376	C₄⋊Q₈	C₂³×C₇	1	3	yes	—
377	#127	—	2	3	no	—
378	#127	C₂³×C₇	1	3	yes	—
379	#125	—	2	3	no	—
380	#125	—	2	3	no	—
381	#125	—	2	3	no	—
382	#124	—	2	6	no	—
383	#124	—	2	3	no	—
384	C₂²⋊Q₈	—	2	3	no	—
385	C₂²⋊Q₈	—	2	6	no	—
386	C₂²⋊Q₈	—	2	6	no	—
387	C₂²⋊Q₈	C₂³×C₇	1	6	yes	—
388	#121	—	2	3	no	—
389	#121	—	2	3	no	—
390	#121	—	2	3	no	—
391	#121	—	2	6	no	—
392	#121	C₂³×C₇	1	6	yes	—
393	C₄×Q₈	—	2	1	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	—	2	1	no	—
396	C₄×Q₈	—	2	3	no	—
397	C₄×Q₈	—	2	3	no	—
398	C₄×Q₈	—	2	3	no	—
399	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
400	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
401	C₄×Q₈	C₂³×C₇	1	3	yes	—
402	C₄×Q₈	C₂³×C₇	1	3	yes	—
403	C₄×Q₈	C₂³×C₇	1	3	yes	—
404	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
405	C₄×Q₈	C₂³×C₇	1	3	yes	—
406	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
407	C₄×D₄	—	2	3	no	—
408	C₄×D₄	—	2	3	no	—
409	C₄×D₄	—	2	3	no	—
410	C₄×D₄	—	2	3	no	—
411	C₄×D₄	—	2	3	no	—
412	C₄×D₄	—	2	3	no	—
413	C₄×D₄	C₇×D₄	1	3	yes	—
414	C₄×D₄	C₂³×C₇	1	3	yes	—
415	C₄×D₄	C₂³×C₇	1	3	yes	—
416	C₄×D₄	C₂³×C₇	1	3	yes	—
417	#117	—	2	3	no	—
418	#117	—	2	3	no	—
419	#117	—	2	3	no	—
420	#117	C₇×D₄	1	3	yes	—
421	#117	C₂³×C₇	1	3	yes	—
422	C₂×C₄⋊C₄	—	2	3	no	—
423	C₂×C₄⋊C₄	C₂³×C₇	1	3	yes	—
424	C₂×C₄²	—	2	3	no	—
425	C₂×C₄²	—	2	3	no	—
426	C₂×C₄²	C₂³×C₇	1	3	yes	—
427	#107	C₂³×C₇	1	3	yes	—
428	#107	C₂³×C₇	1	3	yes	—
429	#107	C₂³×C₇	1	6	yes	—
430	#106	C₂³×C₇	1	1	yes	characteristic
431	#106	C₂³×C₇	1	3	yes	—
432	C₄⋊C₈	C₂³×C₇	1	3	yes	—
433	C₄⋊C₈	C₂³×C₇	1	3	yes	—
434	#103	C₂³×C₇	1	1	yes	characteristic
435	#103	C₂³×C₇	1	3	yes	—
436	#103	C₂³×C₇	1	1	yes	characteristic
437	#103	C₂³×C₇	1	3	yes	—
438	#103	C₂³×C₇	1	3	yes	—
439	#103	C₂³×C₇	1	3	yes	—
440	#103	C₂³×C₇	1	6	yes	—
441	#102	C₂³×C₇	1	3	yes	—
442	#102	C₂³×C₇	1	3	yes	—
443	#102	C₂³×C₇	1	6	yes	—
444	C₂²⋊C₈	C₂³×C₇	1	6	yes	—
445	#97	C₂³×C₇	1	1	yes	characteristic
446	#97	C₂³×C₇	1	3	yes	—
447	C₄×C₈	C₂³×C₇	1	3	yes	—
448	C₄×C₈	C₂³×C₇	1	3	yes	—
449	C₂²×C₇	—	2	3	no	—
450	C₂²×C₇	—	2	3	no	—
451	C₂²×C₇	—	2	3	no	—
452	C₂²×C₇	—	4	3	no	—
453	C₂²×C₇	—	4	3	no	—
454	C₂²×C₇	—	4	3	no	—
455	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
456	C₄×C₇	—	2	1	no	—
457	C₄×C₇	—	2	3	no	—
458	C₄×C₇	—	2	3	no	—
459	C₄×C₇	—	2	2	no	—
460	C₄×C₇	—	2	2	no	—
461	C₄×C₇	—	2	1	no	—
462	C₄×C₇	—	4	3	no	—
463	C₄×C₇	—	4	1	no	—
464	C₄×C₇	—	4	3	no	—
465	C₄×C₇	—	4	3	no	—
466	C₄×C₇	—	4	1	no	—
467	C₄×C₇	C₂×#137	1	6	yes	—
468	C₄×C₇	C₂²×#41	1	1	yes	characteristic
469	C₄×C₇	#585	1	1	yes	characteristic
470	#41	—	2	4	no	—
471	#41	—	2	6	no	—
472	#41	—	4	3	no	—
473	#41	—	4	4	no	—
474	#41	—	8	6	no	—
475	C₂×Q₈	—	2	3	no	—
476	C₂×Q₈	—	2	3	no	—
477	C₂×Q₈	—	2	3	no	—
478	C₂×Q₈	—	2	6	no	—
479	C₂×Q₈	—	4	3	no	—
480	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
481	C₂×Q₈	C₂⁴×C₇	1	3	yes	—
482	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
483	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
484	C₂×D₄	—	2	3	no	—
485	C₂×D₄	—	2	6	no	—
486	C₂×D₄	—	2	3	no	—
487	C₂×D₄	—	2	3	no	—
488	C₂×D₄	C₂×C₇×D₄	1	3	yes	—
489	C₂×D₄	C₂⁴×C₇	1	3	yes	—
490	C₂²×C₄	—	2	3	no	—
491	C₂²×C₄	—	2	3	no	—
492	C₂²×C₄	—	2	3	no	—
493	C₂²×C₄	—	2	3	no	—
494	C₂²×C₄	—	2	3	no	—
495	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
496	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
497	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
498	Q₁₆	—	2	6	no	—
499	Q₁₆	C₇×#41	1	4	yes	complemented
500	SD₁₆	—	2	6	no	—
501	SD₁₆	—	2	6	no	—
502	SD₁₆	—	4	6	no	—
503	M₁₆	—	2	6	no	—
504	M₁₆	—	4	3	no	—
505	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
506	C₂×C₈	C₂⁴×C₇	1	3	yes	—
507	C₂×C₈	C₂⁴×C₇	1	3	yes	—
508	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	3	no	—
511	C₄⋊C₄	—	2	3	no	—
512	C₄⋊C₄	—	2	3	no	—
513	C₄⋊C₄	—	2	3	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	3	no	—
516	C₄⋊C₄	—	2	3	no	—
517	C₄⋊C₄	—	2	3	no	—
518	C₄⋊C₄	—	2	3	no	—
519	C₄⋊C₄	—	2	3	no	—
520	C₄⋊C₄	—	2	6	no	—
521	C₄⋊C₄	C₂×C₇×D₄	1	3	yes	—
522	C₄⋊C₄	C₂×C₇×D₄	1	3	yes	—
523	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
524	C₄⋊C₄	C₂⁴×C₇	1	3	yes	—
525	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
526	C₄⋊C₄	C₂⁴×C₇	1	3	yes	—
527	C₂²⋊C₄	—	2	6	no	—
528	C₂²⋊C₄	—	2	3	no	—
529	C₂²⋊C₄	—	2	6	no	—
530	C₂²⋊C₄	—	2	3	no	—
531	C₂²⋊C₄	—	2	3	no	—
532	C₂²⋊C₄	C₂×C₇×D₄	1	6	yes	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	3	no	—
536	C₄²	—	2	3	no	—
537	C₄²	—	2	3	no	—
538	C₄²	—	2	3	no	—
539	C₄²	—	2	3	no	—
540	C₄²	C₂×C₇×D₄	1	3	yes	—
541	C₄²	C₂×C₇×D₄	1	3	yes	—
542	C₄²	C₂⁴×C₇	1	3	yes	—
543	C₄²	C₂⁴×C₇	1	1	yes	characteristic
544	C₂×C₇	—	4	3	no	—
545	C₂×C₇	—	8	3	no	—
546	C₂×C₇	D₄×#41	1	1	yes	characteristic
547	C₂×C₇	C₂²×#137	1	1	yes	characteristic
548	C₂×C₇	#3585	1	1	yes	characteristic
549	C₂³	—	2	3	no	—
550	C₂³	C₂²×C₇×D₄	1	3	yes	—
551	Q₈	—	2	1	no	—
552	Q₈	—	2	1	no	—
553	Q₈	—	2	3	no	—
554	Q₈	—	2	3	no	—
555	Q₈	—	4	6	no	—
556	Q₈	—	8	3	no	—
557	Q₈	—	8	3	no	—
558	Q₈	C₇×#137	1	4	yes	complemented
559	Q₈	C₂×C₇×#41	1	2	yes	—
560	Q₈	C₂×C₇×#41	1	2	yes	—
561	D₄	—	2	3	no	—
562	D₄	—	2	3	no	—
563	D₄	—	2	6	no	—
564	D₄	—	4	6	no	—
565	D₄	—	4	6	no	—
566	D₄	—	8	3	no	—
567	D₄	—	8	6	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	3	no	—
571	C₂×C₄	—	2	3	no	—
572	C₂×C₄	—	2	6	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	3	no	—
576	C₂×C₄	—	2	3	no	—
577	C₂×C₄	—	2	3	no	—
578	C₂×C₄	—	4	3	no	—
579	C₂×C₄	—	4	6	no	—
580	C₂×C₄	—	4	6	no	—
581	C₂×C₄	—	4	6	no	—
582	C₂×C₄	—	4	6	no	—
583	C₂×C₄	—	8	3	no	—
584	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
585	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
586	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
587	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
588	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
589	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
590	C₈	—	2	3	no	—
591	C₈	—	2	1	no	—
592	C₈	—	2	3	no	—
593	C₈	C₂×C₇×#41	1	2	yes	—
594	C₇	#61469	1	1	yes	characteristic, direct product factor, Sylow
595	C₂²	—	2	3	no	—
596	C₂²	—	2	3	no	—
597	C₂²	—	2	3	no	—
598	C₂²	—	4	3	no	—
599	C₂²	—	4	3	no	—
600	C₂²	—	4	3	no	—
601	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	3	no	—
605	C₄	—	2	3	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	3	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	3	no	—
612	C₄	—	4	3	no	—
613	C₄	C₂×C₇×#137	1	6	yes	—
614	C₄	C₂²×C₇×#41	1	1	yes	characteristic
615	C₄	C₇×#585	1	1	yes	characteristic
616	C₂	—	4	3	no	—
617	C₂	—	8	3	no	—
618	C₂	C₇×D₄×#41	1	1	yes	characteristic
619	C₂	C₂²×C₇×#137	1	1	yes	characteristic
620	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3483	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×Q₈×#41	C₂	semidirect
3. C₇×#3392	C₂	semidirect
4. C₇×Q₈×Q₁₆	C₂	semidirect
5. C₇×#3363	C₂	semidirect
6. C₇×#3362	C₂	semidirect
7. C₇×#3357	C₂	semidirect
8. C₇×#3333	C₂	semidirect
9. C₇×#3329	C₂	semidirect
10. C₇×#3278	C₂	semidirect
11. C₇×#3182	C₂	semidirect
12. C₇×#3116	C₂	semidirect
13. C₇×#3112	C₂	semidirect
14. C₇×#2971	C₂	semidirect
15. C₄×C₇×#137	C₂	semidirect
74. #61469	C₇	direct (N × H)
167. Q₈×#41	C₂×C₇	semidirect
168. #3392	C₂×C₇	semidirect
169. Q₈×Q₁₆	C₂×C₇	semidirect
170. #3363	C₂×C₇	semidirect
171. #3362	C₂×C₇	semidirect
172. #3357	C₂×C₇	semidirect
173. #3333	C₂×C₇	semidirect
174. #3329	C₂×C₇	semidirect
175. #3278	C₂×C₇	semidirect
176. #3182	C₂×C₇	semidirect
177. #3116	C₂×C₇	semidirect
178. #3112	C₂×C₇	semidirect
179. #2971	C₂×C₇	semidirect
180. C₄×#137	C₂×C₇	semidirect
210. C₇×Q₁₆	#41	semidirect
322. C₇×Q₈	#137	semidirect
499. Q₁₆	C₇×#41	semidirect
558. Q₈	C₇×#137	semidirect
594. C₇	#61469	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×#3483	2
C₇×Q₈×#41	2
C₇×#3392	2
C₇×Q₈×Q₁₆	2
C₇×#3363	2
C₇×#3362	2
C₇×#3357	2
C₇×#3333	2
C₇×#3329	2
C₇×#3278	2
C₇×#3182	2
C₇×#3116	2
C₇×#3112	2
C₇×#2971	2
C₄×C₇×#137	2
#61469	7

Subgroups — C7×#61469 #13238685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61469 #13238685