Subgroups — C₇×#18797 #13196013

Order 1792.

924 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3106	C₂	1	1	yes	maximal, characteristic
5	C₇×#1637	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1636	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1633	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1632	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1627	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1626	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1623	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1622	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1554	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1488	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1479	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×Q₈²	C₂²	1	1	yes	characteristic
17	C₇×#557	—	2	1	no	—
18	C₇×#557	C₂²	1	1	yes	characteristic
19	C₇×#554	—	2	2	no	—
20	C₇×#554	—	2	1	no	—
21	C₇×#554	—	2	1	no	—
22	C₇×#554	C₂²	1	1	yes	characteristic
23	C₇×D₄×Q₈	—	2	1	no	—
24	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
25	C₇×#533	—	2	2	no	—
26	C₇×#533	—	2	1	no	—
27	C₇×#533	—	2	1	no	—
28	C₇×#533	C₂²	1	1	yes	characteristic
29	C₇×#532	C₂²	1	1	yes	characteristic
30	C₄×C₇×#41	—	2	1	no	—
31	C₄×C₇×#41	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×Q₈	—	2	1	no	—
33	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
34	C₇×#494	C₂²	1	1	yes	characteristic
35	C₇×#492	C₂²	1	1	yes	characteristic
36	C₇×#487	C₂²	1	1	yes	characteristic
37	C₇×#486	C₂²	1	1	yes	characteristic
38	C₇×#482	—	2	1	no	—
39	C₇×#480	—	2	1	no	—
40	C₇×#477	C₂²	1	1	yes	characteristic
41	C₇×#477	C₂²	1	1	yes	characteristic
42	C₇×#477	C₂²	1	1	yes	characteristic
43	C₇×#476	C₂²	1	1	yes	characteristic
44	C₇×#464	—	2	2	no	—
45	C₇×#460	C₂²	1	1	yes	characteristic
46	C₇×#460	C₂²	1	1	yes	characteristic
47	C₇×#460	C₂²	1	1	yes	characteristic
48	C₇×#459	C₂²	1	1	yes	characteristic
49	C₇×#452	—	2	2	no	—
50	C₇×#449	—	2	1	no	—
51	C₇×#448	—	2	1	no	—
52	C₇×#440	—	2	1	no	—
53	C₇×#440	—	2	1	no	—
54	C₄×C₇×SD₁₆	—	2	1	no	—
55	C₄×C₇×D₈	—	2	1	no	—
56	C₇×#432	C₂²	1	1	yes	characteristic
57	C₇×#431	C₂²	1	1	yes	characteristic
58	C₇×#431	C₂²	1	1	yes	characteristic
59	C₇×#333	C₂²	1	1	yes	characteristic
60	C₇×#333	C₂²	1	1	yes	characteristic
61	C₇×#332	C₂²	1	1	yes	characteristic
62	C₇×#332	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×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
69	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	#18797	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂×C₇×#41	—	2	1	no	—
73	C₂×C₇×#41	D₄	1	1	yes	characteristic
74	C₂²×C₇×Q₈	—	2	1	no	—
75	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
76	C₂×C₇×Q₁₆	—	2	2	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	—	2	2	no	—
81	C₂×C₇×D₈	—	2	1	no	—
82	C₇×C₄⋊Q₈	—	2	2	no	—
83	C₇×C₄⋊Q₈	—	2	1	no	—
84	C₇×C₄⋊Q₈	—	2	2	no	—
85	C₇×C₄⋊Q₈	—	2	1	no	—
86	C₇×C₄⋊Q₈	—	2	1	no	—
87	C₇×C₄⋊Q₈	—	2	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	C₂³	1	1	yes	characteristic
92	C₇×#125	—	2	2	no	—
93	C₇×#125	—	2	2	no	—
94	C₇×#125	—	2	2	no	—
95	C₇×#125	—	2	1	no	—
96	C₇×#125	—	2	1	no	—
97	C₇×#125	—	2	1	no	—
98	C₇×#124	—	2	1	no	—
99	C₇×C₂²⋊Q₈	—	2	2	no	—
100	C₇×C₂²⋊Q₈	—	2	2	no	—
101	C₇×C₂²⋊Q₈	—	2	2	no	—
102	C₇×C₂²⋊Q₈	—	2	2	no	—
103	C₇×C₂²⋊Q₈	—	2	2	no	—
104	C₇×C₂²⋊Q₈	—	2	1	no	—
105	C₇×C₂²⋊Q₈	—	2	2	no	—
106	C₇×C₂²⋊Q₈	—	2	1	no	—
107	C₇×C₂²⋊Q₈	—	2	1	no	—
108	C₇×C₂²⋊Q₈	—	2	2	no	—
109	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
110	C₇×#121	—	2	1	no	—
111	C₇×#121	—	2	1	no	—
112	C₄×C₇×Q₈	—	2	2	no	—
113	C₄×C₇×Q₈	—	2	2	no	—
114	C₄×C₇×Q₈	—	2	2	no	—
115	C₄×C₇×Q₈	—	2	1	no	—
116	C₄×C₇×Q₈	—	2	1	no	—
117	C₄×C₇×Q₈	—	2	1	no	—
118	C₄×C₇×Q₈	—	2	1	no	—
119	C₄×C₇×Q₈	—	2	1	no	—
120	C₄×C₇×Q₈	—	2	1	no	—
121	C₄×C₇×Q₈	—	2	1	no	—
122	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
123	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
124	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
125	C₄×C₇×Q₈	D₄	1	2	yes	—
126	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
127	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
128	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
129	C₄×C₇×D₄	—	2	2	no	—
130	C₄×C₇×D₄	—	2	2	no	—
131	C₄×C₇×D₄	—	2	1	no	—
132	C₄×C₇×D₄	—	2	1	no	—
133	C₄×C₇×D₄	—	2	1	no	—
134	C₄×C₇×D₄	—	2	1	no	—
135	C₄×C₇×D₄	—	2	1	no	—
136	C₄×C₇×D₄	—	2	1	no	—
137	C₄×C₇×D₄	D₄	1	1	yes	characteristic
138	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
139	C₇×#117	—	2	2	no	—
140	C₇×#117	—	2	1	no	—
141	C₇×#117	—	2	1	no	—
142	C₇×#117	D₄	1	1	yes	characteristic
143	C₂×C₇×C₄⋊C₄	—	2	2	no	—
144	C₂×C₇×C₄⋊C₄	—	2	1	no	—
145	C₂×C₇×C₄⋊C₄	—	2	1	no	—
146	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
147	C₂×C₄²×C₇	—	2	2	no	—
148	C₂×C₄²×C₇	—	2	1	no	—
149	C₂×C₄²×C₇	—	2	1	no	—
150	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
151	C₇×#107	—	2	1	no	—
152	C₇×#107	—	2	1	no	—
153	C₇×#107	—	2	1	no	—
154	C₇×#106	—	2	1	no	—
155	C₇×C₄⋊C₈	—	2	1	no	—
156	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
157	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₇×#103	—	2	1	no	—
161	C₇×#103	—	2	1	no	—
162	C₇×#103	—	2	1	no	—
163	C₇×#103	—	2	2	no	—
164	C₇×#102	—	2	1	no	—
165	C₇×#102	—	2	1	no	—
166	C₇×#102	—	2	1	no	—
167	C₇×#102	—	2	1	no	—
168	C₇×#102	—	2	1	no	—
169	C₇×#102	—	2	2	no	—
170	C₇×C₂²⋊C₈	—	2	1	no	—
171	C₇×C₂²⋊C₈	—	2	1	no	—
172	C₇×C₂²⋊C₈	—	2	1	no	—
173	C₇×#97	—	2	1	no	—
174	C₄×C₇×C₈	—	2	1	no	—
175	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
176	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
177	Q₈×#41	C₂×C₇	1	1	yes	characteristic, complemented
178	#3210	C₂×C₇	1	1	yes	characteristic, complemented
179	#3112	C₂×C₇	1	1	yes	characteristic, complemented
180	#3106	C₂×C₇	1	1	yes	characteristic
181	#1637	C₂×C₇	1	1	yes	characteristic, complemented
182	#1636	C₂×C₇	1	1	yes	characteristic, complemented
183	#1633	C₂×C₇	1	1	yes	characteristic, complemented
184	#1632	C₂×C₇	1	1	yes	characteristic, complemented
185	#1627	C₂×C₇	1	1	yes	characteristic, complemented
186	#1626	C₂×C₇	1	1	yes	characteristic, complemented
187	#1623	C₂×C₇	1	1	yes	characteristic, complemented
188	#1622	C₂×C₇	1	1	yes	characteristic, complemented
189	#1554	C₂×C₇	1	1	yes	characteristic, complemented
190	#1488	C₂×C₇	1	1	yes	characteristic, complemented
191	#1479	C₂×C₇	1	1	yes	characteristic, complemented
192	C₇×#41	—	2	2	no	—
193	C₇×#41	—	2	2	no	—
194	C₇×#41	—	8	2	no	—
195	C₂×C₇×Q₈	—	2	2	no	—
196	C₂×C₇×Q₈	—	2	2	no	—
197	C₂×C₇×Q₈	—	2	1	no	—
198	C₂×C₇×Q₈	—	2	1	no	—
199	C₂×C₇×Q₈	—	2	2	no	—
200	C₂×C₇×Q₈	—	2	1	no	—
201	C₂×C₇×Q₈	—	4	1	no	—
202	C₂×C₇×Q₈	—	4	2	no	—
203	C₂×C₇×Q₈	—	4	2	no	—
204	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
205	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
206	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
207	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
208	C₂×C₇×D₄	—	2	1	no	—
209	C₂×C₇×D₄	—	2	1	no	—
210	C₂×C₇×D₄	—	2	1	no	—
211	C₂×C₇×D₄	—	2	1	no	—
212	C₂×C₇×D₄	—	4	1	no	—
213	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₇	—	2	1	no	—
215	C₂²×C₄×C₇	—	2	2	no	—
216	C₂²×C₄×C₇	—	2	1	no	—
217	C₂²×C₄×C₇	—	2	2	no	—
218	C₂²×C₄×C₇	—	2	1	no	—
219	C₂²×C₄×C₇	—	2	1	no	—
220	C₂²×C₄×C₇	—	2	1	no	—
221	C₂²×C₄×C₇	—	4	1	no	—
222	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
225	C₇×Q₁₆	—	8	2	no	—
226	C₇×SD₁₆	—	4	2	no	—
227	C₇×SD₁₆	—	4	2	no	—
228	C₇×SD₁₆	—	4	2	no	—
229	C₇×SD₁₆	—	8	2	no	—
230	C₇×D₈	—	4	2	no	—
231	C₂×C₇×C₈	—	2	1	no	—
232	C₂×C₇×C₈	—	2	1	no	—
233	C₂×C₇×C₈	—	2	1	no	—
234	C₂×C₇×C₈	—	2	1	no	—
235	C₂×C₇×C₈	—	2	1	no	—
236	C₂×C₇×C₈	—	2	1	no	—
237	C₇×C₄⋊C₄	—	2	2	no	—
238	C₇×C₄⋊C₄	—	2	2	no	—
239	C₇×C₄⋊C₄	—	2	2	no	—
240	C₇×C₄⋊C₄	—	2	2	no	—
241	C₇×C₄⋊C₄	—	2	2	no	—
242	C₇×C₄⋊C₄	—	2	2	no	—
243	C₇×C₄⋊C₄	—	2	2	no	—
244	C₇×C₄⋊C₄	—	2	2	no	—
245	C₇×C₄⋊C₄	—	2	1	no	—
246	C₇×C₄⋊C₄	—	2	2	no	—
247	C₇×C₄⋊C₄	—	2	1	no	—
248	C₇×C₄⋊C₄	—	2	1	no	—
249	C₇×C₄⋊C₄	—	2	1	no	—
250	C₇×C₄⋊C₄	—	2	2	no	—
251	C₇×C₄⋊C₄	—	2	1	no	—
252	C₇×C₄⋊C₄	—	2	1	no	—
253	C₇×C₄⋊C₄	—	2	1	no	—
254	C₇×C₄⋊C₄	—	2	1	no	—
255	C₇×C₄⋊C₄	—	2	1	no	—
256	C₇×C₄⋊C₄	—	2	1	no	—
257	C₇×C₄⋊C₄	—	2	1	no	—
258	C₇×C₄⋊C₄	—	2	1	no	—
259	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
260	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
261	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
262	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
263	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
264	C₇×C₂²⋊C₄	—	2	2	no	—
265	C₇×C₂²⋊C₄	—	2	2	no	—
266	C₇×C₂²⋊C₄	—	2	2	no	—
267	C₇×C₂²⋊C₄	—	2	1	no	—
268	C₇×C₂²⋊C₄	—	2	1	no	—
269	C₇×C₂²⋊C₄	—	2	1	no	—
270	C₇×C₂²⋊C₄	—	4	1	no	—
271	C₇×C₂²⋊C₄	—	4	1	no	—
272	C₄²×C₇	—	2	2	no	—
273	C₄²×C₇	—	2	2	no	—
274	C₄²×C₇	—	2	1	no	—
275	C₄²×C₇	—	2	2	no	—
276	C₄²×C₇	—	2	1	no	—
277	C₄²×C₇	—	2	1	no	—
278	C₄²×C₇	—	2	1	no	—
279	C₄²×C₇	—	2	1	no	—
280	C₄²×C₇	—	2	1	no	—
281	C₄²×C₇	—	2	1	no	—
282	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₇	C₂⁴	1	1	yes	characteristic
286	Q₈²	C₂²×C₇	1	1	yes	characteristic
287	#557	—	2	1	no	—
288	#557	C₂²×C₇	1	1	yes	characteristic
289	#554	—	2	2	no	—
290	#554	—	2	1	no	—
291	#554	—	2	1	no	—
292	#554	C₂²×C₇	1	1	yes	characteristic
293	D₄×Q₈	—	2	1	no	—
294	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
295	#533	—	2	2	no	—
296	#533	—	2	1	no	—
297	#533	—	2	1	no	—
298	#533	C₂²×C₇	1	1	yes	characteristic
299	#532	C₂²×C₇	1	1	yes	characteristic
300	C₄×#41	—	2	1	no	—
301	C₄×#41	C₂²×C₇	1	1	yes	characteristic
302	C₂×C₄×Q₈	—	2	1	no	—
303	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
304	#494	C₂²×C₇	1	1	yes	characteristic
305	#492	C₂²×C₇	1	1	yes	characteristic
306	#487	C₂²×C₇	1	1	yes	characteristic
307	#486	C₂²×C₇	1	1	yes	characteristic
308	#482	—	2	1	no	—
309	#480	—	2	1	no	—
310	#477	C₂²×C₇	1	1	yes	characteristic
311	#477	C₂²×C₇	1	1	yes	characteristic
312	#477	C₂²×C₇	1	1	yes	characteristic
313	#476	C₂²×C₇	1	1	yes	characteristic
314	#464	—	2	2	no	—
315	#460	C₂²×C₇	1	1	yes	characteristic
316	#460	C₂²×C₇	1	1	yes	characteristic
317	#460	C₂²×C₇	1	1	yes	characteristic
318	#459	C₂²×C₇	1	1	yes	characteristic
319	#452	—	2	2	no	—
320	#449	—	2	1	no	—
321	#448	—	2	1	no	—
322	#440	—	2	1	no	—
323	#440	—	2	1	no	—
324	C₄×SD₁₆	—	2	1	no	—
325	C₄×D₈	—	2	1	no	—
326	#432	C₂²×C₇	1	1	yes	characteristic
327	#431	C₂²×C₇	1	1	yes	characteristic
328	#431	C₂²×C₇	1	1	yes	characteristic
329	#333	C₂²×C₇	1	1	yes	characteristic
330	#333	C₂²×C₇	1	1	yes	characteristic
331	#332	C₂²×C₇	1	1	yes	characteristic
332	#332	C₂²×C₇	1	1	yes	characteristic
333	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
334	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
335	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
336	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
337	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
338	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
339	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
340	D₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
341	C₂³×C₇	—	2	1	no	—
342	C₂³×C₇	—	4	1	no	—
343	C₂³×C₇	#120	1	1	yes	characteristic
344	C₇×Q₈	—	2	1	no	—
345	C₇×Q₈	—	2	1	no	—
346	C₇×Q₈	—	2	1	no	—
347	C₇×Q₈	—	2	1	no	—
348	C₇×Q₈	—	4	2	no	—
349	C₇×Q₈	—	4	2	no	—
350	C₇×Q₈	—	4	4	no	—
351	C₇×Q₈	—	4	2	no	—
352	C₇×Q₈	—	4	1	no	—
353	C₇×Q₈	—	4	1	no	—
354	C₇×Q₈	—	8	2	no	—
355	C₇×Q₈	#135	1	2	yes	—
356	C₇×Q₈	#137	1	2	yes	—
357	C₇×D₄	—	2	4	no	—
358	C₇×D₄	—	2	1	no	—
359	C₇×D₄	—	4	2	no	—
360	C₇×D₄	—	4	1	no	—
361	C₇×D₄	—	4	1	no	—
362	C₇×D₄	—	4	1	no	—
363	C₇×D₄	—	4	1	no	—
364	C₇×D₄	—	8	2	no	—
365	C₇×D₄	#137	1	2	yes	—
366	C₂×C₄×C₇	—	2	4	no	—
367	C₂×C₄×C₇	—	2	1	no	—
368	C₂×C₄×C₇	—	2	1	no	—
369	C₂×C₄×C₇	—	2	1	no	—
370	C₂×C₄×C₇	—	2	1	no	—
371	C₂×C₄×C₇	—	2	1	no	—
372	C₂×C₄×C₇	—	2	1	no	—
373	C₂×C₄×C₇	—	2	1	no	—
374	C₂×C₄×C₇	—	2	1	no	—
375	C₂×C₄×C₇	—	2	2	no	—
376	C₂×C₄×C₇	—	2	2	no	—
377	C₂×C₄×C₇	—	2	1	no	—
378	C₂×C₄×C₇	—	2	1	no	—
379	C₂×C₄×C₇	—	2	1	no	—
380	C₂×C₄×C₇	—	4	1	no	—
381	C₂×C₄×C₇	—	4	2	no	—
382	C₂×C₄×C₇	—	4	4	no	—
383	C₂×C₄×C₇	—	4	1	no	—
384	C₂×C₄×C₇	—	4	1	no	—
385	C₂×C₄×C₇	—	4	1	no	—
386	C₂×C₄×C₇	—	8	1	no	—
387	C₂×C₄×C₇	—	8	2	no	—
388	C₂×C₄×C₇	—	8	1	no	—
389	C₂×C₄×C₇	—	8	2	no	—
390	C₂×C₄×C₇	#120	1	1	yes	characteristic
391	C₂×C₄×C₇	#120	1	1	yes	characteristic
392	C₂×C₄×C₇	#120	1	1	yes	characteristic
393	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
396	C₇×C₈	—	4	1	no	—
397	C₇×C₈	—	4	1	no	—
398	C₇×C₈	—	4	1	no	—
399	C₇×C₈	—	4	1	no	—
400	C₇×C₈	—	4	1	no	—
401	C₇×C₈	—	4	1	no	—
402	C₂×#41	—	2	1	no	—
403	C₂×#41	C₇×D₄	1	1	yes	characteristic
404	C₂²×Q₈	—	2	1	no	—
405	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
406	C₂×Q₁₆	—	2	2	no	—
407	C₂×SD₁₆	—	2	1	no	—
408	C₂×SD₁₆	—	2	1	no	—
409	C₂×SD₁₆	—	2	1	no	—
410	C₂×SD₁₆	—	2	2	no	—
411	C₂×D₈	—	2	1	no	—
412	C₄⋊Q₈	—	2	2	no	—
413	C₄⋊Q₈	—	2	1	no	—
414	C₄⋊Q₈	—	2	2	no	—
415	C₄⋊Q₈	—	2	1	no	—
416	C₄⋊Q₈	—	2	1	no	—
417	C₄⋊Q₈	—	2	1	no	—
418	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
419	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
420	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
421	#127	C₂³×C₇	1	1	yes	characteristic
422	#125	—	2	2	no	—
423	#125	—	2	2	no	—
424	#125	—	2	2	no	—
425	#125	—	2	1	no	—
426	#125	—	2	1	no	—
427	#125	—	2	1	no	—
428	#124	—	2	1	no	—
429	C₂²⋊Q₈	—	2	2	no	—
430	C₂²⋊Q₈	—	2	2	no	—
431	C₂²⋊Q₈	—	2	2	no	—
432	C₂²⋊Q₈	—	2	2	no	—
433	C₂²⋊Q₈	—	2	2	no	—
434	C₂²⋊Q₈	—	2	1	no	—
435	C₂²⋊Q₈	—	2	2	no	—
436	C₂²⋊Q₈	—	2	1	no	—
437	C₂²⋊Q₈	—	2	1	no	—
438	C₂²⋊Q₈	—	2	2	no	—
439	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
440	#121	—	2	1	no	—
441	#121	—	2	1	no	—
442	C₄×Q₈	—	2	2	no	—
443	C₄×Q₈	—	2	2	no	—
444	C₄×Q₈	—	2	2	no	—
445	C₄×Q₈	—	2	1	no	—
446	C₄×Q₈	—	2	1	no	—
447	C₄×Q₈	—	2	1	no	—
448	C₄×Q₈	—	2	1	no	—
449	C₄×Q₈	—	2	1	no	—
450	C₄×Q₈	—	2	1	no	—
451	C₄×Q₈	—	2	1	no	—
452	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
453	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
454	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
455	C₄×Q₈	C₇×D₄	1	2	yes	—
456	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
457	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
458	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
459	C₄×D₄	—	2	2	no	—
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	—	2	1	no	—
462	C₄×D₄	—	2	1	no	—
463	C₄×D₄	—	2	1	no	—
464	C₄×D₄	—	2	1	no	—
465	C₄×D₄	—	2	1	no	—
466	C₄×D₄	—	2	1	no	—
467	C₄×D₄	C₇×D₄	1	1	yes	characteristic
468	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
469	#117	—	2	2	no	—
470	#117	—	2	1	no	—
471	#117	—	2	1	no	—
472	#117	C₇×D₄	1	1	yes	characteristic
473	C₂×C₄⋊C₄	—	2	2	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
477	C₂×C₄²	—	2	2	no	—
478	C₂×C₄²	—	2	1	no	—
479	C₂×C₄²	—	2	1	no	—
480	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
481	#107	—	2	1	no	—
482	#107	—	2	1	no	—
483	#107	—	2	1	no	—
484	#106	—	2	1	no	—
485	C₄⋊C₈	—	2	1	no	—
486	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
487	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
488	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
489	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
490	#103	—	2	1	no	—
491	#103	—	2	1	no	—
492	#103	—	2	1	no	—
493	#103	—	2	2	no	—
494	#102	—	2	1	no	—
495	#102	—	2	1	no	—
496	#102	—	2	1	no	—
497	#102	—	2	1	no	—
498	#102	—	2	1	no	—
499	#102	—	2	2	no	—
500	C₂²⋊C₈	—	2	1	no	—
501	C₂²⋊C₈	—	2	1	no	—
502	C₂²⋊C₈	—	2	1	no	—
503	#97	—	2	1	no	—
504	C₄×C₈	—	2	1	no	—
505	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
506	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
507	C₂²×C₇	—	2	1	no	—
508	C₂²×C₇	—	2	1	no	—
509	C₂²×C₇	—	2	2	no	—
510	C₂²×C₇	—	2	1	no	—
511	C₂²×C₇	—	4	1	no	—
512	C₂²×C₇	—	4	1	no	—
513	C₂²×C₇	—	8	1	no	—
514	C₂²×C₇	—	8	1	no	—
515	C₂²×C₇	—	8	1	no	—
516	C₂²×C₇	C₂×#120	1	1	yes	characteristic
517	C₄×C₇	—	2	1	no	—
518	C₄×C₇	—	2	2	no	—
519	C₄×C₇	—	2	1	no	—
520	C₄×C₇	—	2	2	no	—
521	C₄×C₇	—	2	1	no	—
522	C₄×C₇	—	2	1	no	—
523	C₄×C₇	—	4	1	no	—
524	C₄×C₇	—	4	2	no	—
525	C₄×C₇	—	4	1	no	—
526	C₄×C₇	—	4	1	no	—
527	C₄×C₇	—	4	2	no	—
528	C₄×C₇	—	4	1	no	—
529	C₄×C₇	—	4	1	no	—
530	C₄×C₇	—	8	1	no	—
531	C₄×C₇	C₂×#135	1	1	yes	characteristic
532	C₄×C₇	C₂×#137	1	1	yes	characteristic
533	C₄×C₇	C₂×#137	1	1	yes	characteristic
534	C₄×C₇	#575	1	1	yes	characteristic
535	#41	—	2	2	no	—
536	#41	—	2	2	no	—
537	#41	—	8	2	no	—
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	2	2	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	2	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	4	1	no	—
545	C₂×Q₈	—	4	2	no	—
546	C₂×Q₈	—	4	2	no	—
547	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
548	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
549	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
550	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	4	1	no	—
556	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	4	1	no	—
565	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
566	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
567	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
568	Q₁₆	—	8	2	no	—
569	SD₁₆	—	4	2	no	—
570	SD₁₆	—	4	2	no	—
571	SD₁₆	—	4	2	no	—
572	SD₁₆	—	8	2	no	—
573	D₈	—	4	2	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
603	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
604	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
605	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
606	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	1	no	—
611	C₂²⋊C₄	—	2	1	no	—
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	4	1	no	—
614	C₂²⋊C₄	—	4	1	no	—
615	C₄²	—	2	2	no	—
616	C₄²	—	2	2	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	2	2	no	—
619	C₄²	—	2	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	2	1	no	—
622	C₄²	—	2	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
626	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
627	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
628	C₄²	C₂⁴×C₇	1	1	yes	characteristic
629	C₂×C₇	—	4	1	no	—
630	C₂×C₇	—	4	2	no	—
631	C₂×C₇	—	16	1	no	—
632	C₂×C₇	#3002	1	1	yes	characteristic
633	C₂×C₇	#3004	1	1	yes	characteristic
634	C₂×C₇	#3021	1	1	yes	characteristic
635	C₂³	—	2	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	C₇×#120	1	1	yes	characteristic
638	Q₈	—	2	1	no	—
639	Q₈	—	2	1	no	—
640	Q₈	—	2	1	no	—
641	Q₈	—	2	1	no	—
642	Q₈	—	4	2	no	—
643	Q₈	—	4	2	no	—
644	Q₈	—	4	4	no	—
645	Q₈	—	4	2	no	—
646	Q₈	—	4	1	no	—
647	Q₈	—	4	1	no	—
648	Q₈	—	8	2	no	—
649	Q₈	C₇×#135	1	2	yes	—
650	Q₈	C₇×#137	1	2	yes	—
651	D₄	—	2	4	no	—
652	D₄	—	2	1	no	—
653	D₄	—	4	2	no	—
654	D₄	—	4	1	no	—
655	D₄	—	4	1	no	—
656	D₄	—	4	1	no	—
657	D₄	—	4	1	no	—
658	D₄	—	8	2	no	—
659	D₄	C₇×#137	1	2	yes	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	2	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	8	1	no	—
681	C₂×C₄	—	8	2	no	—
682	C₂×C₄	—	8	1	no	—
683	C₂×C₄	—	8	2	no	—
684	C₂×C₄	C₇×#120	1	1	yes	characteristic
685	C₂×C₄	C₇×#120	1	1	yes	characteristic
686	C₂×C₄	C₇×#120	1	1	yes	characteristic
687	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
688	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
689	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
690	C₈	—	4	1	no	—
691	C₈	—	4	1	no	—
692	C₈	—	4	1	no	—
693	C₈	—	4	1	no	—
694	C₈	—	4	1	no	—
695	C₈	—	4	1	no	—
696	C₇	#18797	1	1	yes	characteristic, direct product factor, Sylow
697	C₂²	—	2	1	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	8	1	no	—
704	C₂²	—	8	1	no	—
705	C₂²	—	8	1	no	—
706	C₂²	C₂×C₇×#120	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	2	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	2	no	—
711	C₄	—	2	1	no	—
712	C₄	—	2	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	1	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	1	no	—
720	C₄	—	8	1	no	—
721	C₄	C₂×C₇×#135	1	1	yes	characteristic
722	C₄	C₂×C₇×#137	1	1	yes	characteristic
723	C₄	C₂×C₇×#137	1	1	yes	characteristic
724	C₄	C₇×#575	1	1	yes	characteristic
725	C₂	—	4	1	no	—
726	C₂	—	4	2	no	—
727	C₂	—	16	1	no	—
728	C₂	C₇×#3002	1	1	yes	characteristic
729	C₂	C₇×#3004	1	1	yes	characteristic
730	C₂	C₇×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#3106	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×Q₈×#41	C₂	semidirect
2. C₇×#3210	C₂	semidirect
3. C₇×#3112	C₂	semidirect
5. C₇×#1637	C₂	semidirect
6. C₇×#1636	C₂	semidirect
7. C₇×#1633	C₂	semidirect
8. C₇×#1632	C₂	semidirect
9. C₇×#1627	C₂	semidirect
10. C₇×#1626	C₂	semidirect
11. C₇×#1623	C₂	semidirect
12. C₇×#1622	C₂	semidirect
13. C₇×#1554	C₂	semidirect
14. C₇×#1488	C₂	semidirect
15. C₇×#1479	C₂	semidirect
71. #18797	C₇	direct (N × H)
177. Q₈×#41	C₂×C₇	semidirect
178. #3210	C₂×C₇	semidirect
179. #3112	C₂×C₇	semidirect
181. #1637	C₂×C₇	semidirect
182. #1636	C₂×C₇	semidirect
183. #1633	C₂×C₇	semidirect
184. #1632	C₂×C₇	semidirect
185. #1627	C₂×C₇	semidirect
186. #1626	C₂×C₇	semidirect
187. #1623	C₂×C₇	semidirect
188. #1622	C₂×C₇	semidirect
189. #1554	C₂×C₇	semidirect
190. #1488	C₂×C₇	semidirect
191. #1479	C₂×C₇	semidirect
696. C₇	#18797	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×Q₈×#41	2
C₇×#3210	2
C₇×#3112	2
C₇×#3106	2
C₇×#1637	2
C₇×#1636	2
C₇×#1633	2
C₇×#1632	2
C₇×#1627	2
C₇×#1626	2
C₇×#1623	2
C₇×#1622	2
C₇×#1554	2
C₇×#1488	2
C₇×#1479	2
#18797	7

Subgroups — C7×#18797 #13196013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#18797 #13196013