Subgroups — C₇×#22983 #13200199

Order 1792.

708 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3076	C₂	1	1	yes	maximal, characteristic
2	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2906	C₂	1	1	yes	maximal, characteristic
4	C₇×#1994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1946	C₂	1	2	yes	maximal, complemented
7	C₇×#1922	C₂	1	2	yes	maximal, complemented
8	C₇×#1866	C₂	1	2	yes	maximal
9	C₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1765	C₂	1	2	yes	maximal
11	C₄×C₇×#104	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#131	C₂²	1	2	yes	—
13	C₇×#533	C₂²	1	1	yes	characteristic
14	C₄×C₇×#41	C₂²	1	1	yes	characteristic
15	C₇×#479	C₄	1	2	yes	complemented
16	C₇×#478	C₄	1	2	yes	complemented
17	C₇×#477	C₄	1	1	yes	characteristic, complemented
18	C₇×#476	C₄	1	1	yes	characteristic, complemented
19	C₇×#475	C₄	1	1	yes	characteristic, complemented
20	C₇×#474	C₄	1	1	yes	characteristic, complemented
21	C₇×#446	—	2	2	no	—
22	C₇×#446	—	2	1	no	—
23	C₇×C₈×Q₈	—	2	1	no	—
24	C₂×C₇×#108	C₂²	1	2	yes	—
25	C₇×#427	C₂²	1	2	yes	—
26	C₇×#424	—	2	2	no	—
27	C₇×#424	C₂²	1	2	yes	—
28	C₇×#424	C₂²	1	2	yes	—
29	C₇×#423	—	2	1	no	—
30	C₇×#423	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₄⋊C₈	—	2	1	no	—
32	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×#104	C₂²	1	1	yes	characteristic
35	C₂×C₇×#104	C₂²	1	1	yes	characteristic
36	C₇×#416	C₂²	1	2	yes	—
37	C₇×#405	C₂²	1	2	yes	—
38	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₇×#97	C₂²	1	2	yes	—
40	C₄³×C₇	C₂²	1	1	yes	characteristic
41	C₇×#341	C₂²	1	2	yes	—
42	C₇×#339	C₂²	1	2	yes	—
43	C₇×#339	C₂²	1	2	yes	—
44	C₇×#339	C₂²	1	1	yes	characteristic
45	C₇×#339	C₂²	1	1	yes	characteristic
46	C₇×#336	C₂²	1	2	yes	—
47	#22983	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	C₂³	1	1	yes	characteristic
49	C₇×#131	—	2	4	no	—
50	C₇×#131	—	4	2	no	—
51	C₂×C₇×M₁₆	—	2	2	no	—
52	C₂×C₇×M₁₆	C₂³	1	2	yes	—
53	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
55	C₂²×C₇×C₈	—	2	2	no	—
56	C₂²×C₇×C₈	C₂³	1	2	yes	—
57	C₂²×C₇×C₈	C₂³	1	2	yes	—
58	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
59	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
60	C₇×#125	C₂×C₄	1	2	yes	—
61	C₇×C₂²⋊Q₈	—	2	1	no	—
62	C₇×C₂²⋊Q₈	—	2	1	no	—
63	C₄×C₇×Q₈	—	2	1	no	—
64	C₄×C₇×Q₈	—	2	1	no	—
65	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
66	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
67	C₄×C₇×D₄	—	2	1	no	—
68	C₄×C₇×D₄	—	2	1	no	—
69	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
70	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
71	C₇×#117	—	2	1	no	—
72	C₇×#117	C₂³	1	1	yes	characteristic
73	C₇×#117	C₂³	1	2	yes	—
74	C₂×C₄²×C₇	—	2	1	no	—
75	C₂×C₄²×C₇	—	2	1	no	—
76	C₂×C₄²×C₇	—	2	1	no	—
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₇×#108	—	4	2	no	—
81	C₇×#107	C₂×C₄	1	2	yes	—
82	C₇×#107	C₂×C₄	1	2	yes	—
83	C₇×#106	C₂×C₄	1	2	yes	—
84	C₇×#106	C₂×C₄	1	2	yes	—
85	C₇×C₄⋊C₈	—	2	2	no	—
86	C₇×C₄⋊C₈	—	2	2	no	—
87	C₇×C₄⋊C₈	—	2	2	no	—
88	C₇×C₄⋊C₈	—	2	2	no	—
89	C₇×C₄⋊C₈	—	2	1	no	—
90	C₇×C₄⋊C₈	—	2	1	no	—
91	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
93	C₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
94	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
95	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
96	C₇×C₄⋊C₈	D₄	1	2	yes	—
97	C₇×#104	—	2	2	no	—
98	C₇×#104	Q₈	1	4	yes	complemented
99	C₇×#103	C₂×C₄	1	2	yes	—
100	C₇×#103	C₂×C₄	1	2	yes	—
101	C₇×#102	C₂×C₄	1	2	yes	—
102	C₇×#102	C₂×C₄	1	2	yes	—
103	C₇×#97	—	2	2	no	—
104	C₇×#97	—	2	1	no	—
105	C₇×#97	—	4	2	no	—
106	C₄×C₇×C₈	—	2	2	no	—
107	C₄×C₇×C₈	—	2	1	no	—
108	#3076	C₂×C₇	1	1	yes	characteristic
109	#2962	C₂×C₇	1	1	yes	characteristic, complemented
110	#2906	C₂×C₇	1	1	yes	characteristic
111	#1994	C₂×C₇	1	1	yes	characteristic, complemented
112	#1950	C₂×C₇	1	1	yes	characteristic, complemented
113	#1946	C₂×C₇	1	2	yes	complemented
114	#1922	C₂×C₇	1	2	yes	complemented
115	#1866	C₂×C₇	1	2	yes	—
116	#1767	C₂×C₇	1	1	yes	characteristic, complemented
117	#1765	C₂×C₇	1	2	yes	—
118	C₄×#104	C₂×C₇	1	1	yes	characteristic
119	C₇×#41	—	2	1	no	—
120	C₇×#41	—	2	1	no	—
121	C₇×#41	C₂×Q₈	1	2	yes	—
122	C₇×#41	#41	1	2	yes	—
123	C₂×C₇×Q₈	—	2	1	no	—
124	C₂×C₇×Q₈	—	2	1	no	—
125	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₇×D₄	—	2	1	no	—
127	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	—	2	1	no	—
129	C₂²×C₄×C₇	—	2	1	no	—
130	C₂²×C₄×C₇	—	2	1	no	—
131	C₂²×C₄×C₇	—	2	1	no	—
132	C₂²×C₄×C₇	—	2	1	no	—
133	C₂²×C₄×C₇	#41	1	1	yes	characteristic
134	C₂²×C₄×C₇	#41	1	1	yes	characteristic
135	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
136	C₇×M₁₆	—	2	1	no	—
137	C₇×M₁₆	—	2	1	no	—
138	C₇×M₁₆	—	2	2	no	—
139	C₇×M₁₆	—	2	1	no	—
140	C₇×M₁₆	—	2	2	no	—
141	C₇×M₁₆	—	4	4	no	—
142	C₇×M₁₆	C₂×Q₈	1	2	yes	—
143	C₂×C₇×C₈	—	2	1	no	—
144	C₂×C₇×C₈	—	2	2	no	—
145	C₂×C₇×C₈	—	2	2	no	—
146	C₂×C₇×C₈	—	2	2	no	—
147	C₂×C₇×C₈	—	2	2	no	—
148	C₂×C₇×C₈	—	2	1	no	—
149	C₂×C₇×C₈	—	2	2	no	—
150	C₂×C₇×C₈	—	4	4	no	—
151	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
153	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
154	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
155	C₇×C₄⋊C₄	—	2	1	no	—
156	C₇×C₄⋊C₄	—	2	1	no	—
157	C₇×C₄⋊C₄	—	2	2	no	—
158	C₇×C₄⋊C₄	—	2	2	no	—
159	C₇×C₄⋊C₄	—	2	1	no	—
160	C₇×C₄⋊C₄	—	2	1	no	—
161	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
162	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
163	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
164	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
165	C₇×C₂²⋊C₄	—	2	1	no	—
166	C₇×C₂²⋊C₄	—	2	2	no	—
167	C₇×C₂²⋊C₄	—	2	1	no	—
168	C₇×C₂²⋊C₄	—	2	1	no	—
169	C₄²×C₇	—	2	1	no	—
170	C₄²×C₇	—	2	1	no	—
171	C₄²×C₇	—	2	2	no	—
172	C₄²×C₇	—	2	1	no	—
173	C₄²×C₇	—	2	1	no	—
174	C₄²×C₇	—	2	1	no	—
175	C₄²×C₇	—	2	1	no	—
176	C₄²×C₇	—	4	2	no	—
177	C₄²×C₇	—	4	2	no	—
178	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₇	C₂×Q₈	1	2	yes	—
183	C₂×#131	C₂²×C₇	1	2	yes	—
184	#533	C₂²×C₇	1	1	yes	characteristic
185	C₄×#41	C₂²×C₇	1	1	yes	characteristic
186	#479	C₄×C₇	1	2	yes	complemented
187	#478	C₄×C₇	1	2	yes	complemented
188	#477	C₄×C₇	1	1	yes	characteristic, complemented
189	#476	C₄×C₇	1	1	yes	characteristic, complemented
190	#475	C₄×C₇	1	1	yes	characteristic, complemented
191	#474	C₄×C₇	1	1	yes	characteristic, complemented
192	#446	—	2	2	no	—
193	#446	—	2	1	no	—
194	C₈×Q₈	—	2	1	no	—
195	C₂×#108	C₂²×C₇	1	2	yes	—
196	#427	C₂²×C₇	1	2	yes	—
197	#424	—	2	2	no	—
198	#424	C₂²×C₇	1	2	yes	—
199	#424	C₂²×C₇	1	2	yes	—
200	#423	—	2	1	no	—
201	#423	C₂²×C₇	1	1	yes	characteristic
202	C₂×C₄⋊C₈	—	2	1	no	—
203	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
204	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
205	C₂×#104	C₂²×C₇	1	1	yes	characteristic
206	C₂×#104	C₂²×C₇	1	1	yes	characteristic
207	#416	C₂²×C₇	1	2	yes	—
208	#405	C₂²×C₇	1	2	yes	—
209	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
210	C₂×#97	C₂²×C₇	1	2	yes	—
211	C₄³	C₂²×C₇	1	1	yes	characteristic
212	#341	C₂²×C₇	1	2	yes	—
213	#339	C₂²×C₇	1	2	yes	—
214	#339	C₂²×C₇	1	1	yes	characteristic
215	#339	C₂²×C₇	1	1	yes	characteristic
216	#339	C₂²×C₇	1	2	yes	—
217	#336	C₂²×C₇	1	2	yes	—
218	C₂³×C₇	—	2	1	no	—
219	C₂³×C₇	C₂×#41	1	1	yes	characteristic
220	C₇×Q₈	—	2	1	no	—
221	C₇×Q₈	—	4	2	no	—
222	C₇×Q₈	—	8	1	no	—
223	C₇×Q₈	C₄×Q₈	1	2	yes	—
224	C₇×D₄	—	2	2	no	—
225	C₇×D₄	—	2	2	no	—
226	C₇×D₄	—	2	1	no	—
227	C₇×D₄	C₄×Q₈	1	2	yes	—
228	C₂×C₄×C₇	—	2	1	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	2	2	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	2	1	no	—
234	C₂×C₄×C₇	—	2	1	no	—
235	C₂×C₄×C₇	—	2	2	no	—
236	C₂×C₄×C₇	—	2	2	no	—
237	C₂×C₄×C₇	—	2	2	no	—
238	C₂×C₄×C₇	—	4	1	no	—
239	C₂×C₄×C₇	—	4	1	no	—
240	C₂×C₄×C₇	—	4	1	no	—
241	C₂×C₄×C₇	—	4	1	no	—
242	C₂×C₄×C₇	—	4	1	no	—
243	C₂×C₄×C₇	—	4	2	no	—
244	C₂×C₄×C₇	—	8	1	no	—
245	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
250	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
252	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
255	C₇×C₈	—	2	2	no	—
256	C₇×C₈	—	2	2	no	—
257	C₇×C₈	—	2	2	no	—
258	C₇×C₈	—	2	2	no	—
259	C₇×C₈	—	2	2	no	—
260	C₇×C₈	—	4	2	no	—
261	C₇×C₈	—	4	1	no	—
262	C₂×#41	C₂³×C₇	1	1	yes	characteristic
263	#131	—	2	4	no	—
264	#131	—	4	2	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	C₂³×C₇	1	2	yes	—
267	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
268	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	C₂³×C₇	1	2	yes	—
271	C₂²×C₈	C₂³×C₇	1	2	yes	—
272	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
273	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
274	#125	C₂×C₄×C₇	1	2	yes	—
275	C₂²⋊Q₈	—	2	1	no	—
276	C₂²⋊Q₈	—	2	1	no	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×Q₈	—	2	1	no	—
279	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
280	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
284	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
285	#117	—	2	1	no	—
286	#117	C₂³×C₇	1	1	yes	characteristic
287	#117	C₂³×C₇	1	2	yes	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
294	#108	—	4	2	no	—
295	#107	C₂×C₄×C₇	1	2	yes	—
296	#107	C₂×C₄×C₇	1	2	yes	—
297	#106	C₂×C₄×C₇	1	2	yes	—
298	#106	C₂×C₄×C₇	1	2	yes	—
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
306	C₄⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
307	C₄⋊C₈	C₂×C₄×C₇	1	2	yes	—
308	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
309	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
310	C₄⋊C₈	C₇×D₄	1	2	yes	—
311	#104	—	2	2	no	—
312	#104	C₇×Q₈	1	4	yes	complemented
313	#103	C₂×C₄×C₇	1	2	yes	—
314	#103	C₂×C₄×C₇	1	2	yes	—
315	#102	C₂×C₄×C₇	1	2	yes	—
316	#102	C₂×C₄×C₇	1	2	yes	—
317	#97	—	2	2	no	—
318	#97	—	2	1	no	—
319	#97	—	4	2	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₂²×C₇	—	2	1	no	—
323	C₂²×C₇	—	2	1	no	—
324	C₂²×C₇	—	2	2	no	—
325	C₂²×C₇	—	4	1	no	—
326	C₂²×C₇	—	4	1	no	—
327	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
328	C₂²×C₇	#552	1	1	yes	characteristic
329	C₂²×C₇	#554	1	1	yes	characteristic
330	C₄×C₇	—	2	2	no	—
331	C₄×C₇	—	2	1	no	—
332	C₄×C₇	—	2	1	no	—
333	C₄×C₇	—	2	1	no	—
334	C₄×C₇	—	4	2	no	—
335	C₄×C₇	—	4	2	no	—
336	C₄×C₇	—	4	1	no	—
337	C₄×C₇	—	4	2	no	—
338	C₄×C₇	—	4	1	no	—
339	C₄×C₇	—	4	2	no	—
340	C₄×C₇	#444	1	2	yes	—
341	C₄×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
342	C₄×C₇	#520	1	1	yes	characteristic
343	C₄×C₇	#546	1	1	yes	characteristic
344	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
345	#41	—	2	1	no	—
346	#41	—	2	1	no	—
347	#41	C₂×C₇×Q₈	1	2	yes	—
348	#41	C₇×#41	1	2	yes	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	C₇×#41	1	1	yes	characteristic
360	C₂²×C₄	C₇×#41	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
362	M₁₆	—	2	1	no	—
363	M₁₆	—	2	1	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	2	1	no	—
366	M₁₆	—	2	2	no	—
367	M₁₆	—	4	4	no	—
368	M₁₆	C₂×C₇×Q₈	1	2	yes	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	4	4	no	—
377	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
378	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
379	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
380	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
388	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
389	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
390	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	4	2	no	—
403	C₄²	—	4	2	no	—
404	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
405	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
406	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
407	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
408	C₄²	C₂×C₇×Q₈	1	2	yes	—
409	C₂×C₇	—	2	1	no	—
410	C₂×C₇	—	2	1	no	—
411	C₂×C₇	—	4	2	no	—
412	C₂×C₇	#2360	1	1	yes	characteristic
413	C₂×C₇	C₂×#444	1	1	yes	characteristic
414	C₂×C₇	#2956	1	1	yes	characteristic
415	C₂³	—	2	1	no	—
416	C₂³	C₂×C₇×#41	1	1	yes	characteristic
417	Q₈	—	2	1	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	8	1	no	—
420	Q₈	C₄×C₇×Q₈	1	2	yes	—
421	D₄	—	2	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	1	no	—
424	D₄	C₄×C₇×Q₈	1	2	yes	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	8	1	no	—
442	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
443	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
444	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
445	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
446	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
447	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
448	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
449	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
450	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
452	C₈	—	2	2	no	—
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	2	2	no	—
457	C₈	—	4	2	no	—
458	C₈	—	4	1	no	—
459	C₇	#22983	1	1	yes	characteristic, direct product factor, Sylow
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
466	C₂²	C₇×#552	1	1	yes	characteristic
467	C₂²	C₇×#554	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	1	no	—
477	C₄	—	4	2	no	—
478	C₄	C₇×#444	1	2	yes	—
479	C₄	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
480	C₄	C₇×#520	1	1	yes	characteristic
481	C₄	C₇×#546	1	1	yes	characteristic
482	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	4	2	no	—
486	C₂	C₇×#2360	1	1	yes	characteristic
487	C₂	C₂×C₇×#444	1	1	yes	characteristic
488	C₂	C₇×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×C₇×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2962	C₂	semidirect
4. C₇×#1994	C₂	semidirect
5. C₇×#1950	C₂	semidirect
6. C₇×#1946	C₂	semidirect
7. C₇×#1922	C₂	semidirect
9. C₇×#1767	C₂	semidirect
15. C₇×#479	C₄	semidirect
16. C₇×#478	C₄	semidirect
17. C₇×#477	C₄	semidirect
18. C₇×#476	C₄	semidirect
19. C₇×#475	C₄	semidirect
20. C₇×#474	C₄	semidirect
47. #22983	C₇	direct (N × H)
98. C₇×#104	Q₈	semidirect
109. #2962	C₂×C₇	semidirect
111. #1994	C₂×C₇	semidirect
112. #1950	C₂×C₇	semidirect
113. #1946	C₂×C₇	semidirect
114. #1922	C₂×C₇	semidirect
116. #1767	C₂×C₇	semidirect
186. #479	C₄×C₇	semidirect
187. #478	C₄×C₇	semidirect
188. #477	C₄×C₇	semidirect
189. #476	C₄×C₇	semidirect
190. #475	C₄×C₇	semidirect
191. #474	C₄×C₇	semidirect
312. #104	C₇×Q₈	semidirect
459. C₇	#22983	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×#3076	2
C₇×#2962	2
C₇×#2906	2
C₇×#1994	2
C₇×#1950	2
C₇×#1946	2
C₇×#1922	2
C₇×#1866	2
C₇×#1767	2
C₇×#1765	2
C₄×C₇×#104	2
#22983	7

Subgroups — C7×#22983 #13200199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22983 #13200199