Subgroups — C₂×C₇×#2955 #13237395

Order 1792.

2666 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#575	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇×#131	C₂	1	2	yes	maximal, complemented
3	C₇×#2955	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#444	C₂	1	4	yes	maximal, complemented
5	C₂×C₇×#443	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#430	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#421	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×#41	C₂²	1	2	yes	—
10	C₇×#575	C₄	1	8	yes	complemented
11	C₇×#575	C₂²	1	8	yes	—
12	C₂×C₇×#137	C₄	1	4	yes	complemented
13	C₂×C₇×AGL(1,ℤ/8)	C₄	1	4	yes	complemented
14	C₂×C₇×#135	C₂²	1	4	yes	—
15	C₂×C₇×#131	—	2	2	no	—
16	C₂×C₇×#131	—	2	8	no	—
17	C₂×C₇×#131	—	2	2	no	—
18	C₂×C₇×#131	C₂²	1	4	yes	complemented
19	C₂×C₇×#131	C₂²	1	4	yes	complemented
20	C₂×C₇×#131	C₂²	1	16	yes	complemented
21	C₂²×C₇×M₁₆	—	2	2	no	—
22	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
23	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
24	C₂³×C₇×C₈	—	2	2	no	—
25	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×#117	C₂²	1	1	yes	characteristic
27	C₇×#444	C₂²	1	32	yes	complemented
28	C₇×#443	C₂²	1	32	yes	complemented
29	C₇×#430	C₂²	1	8	yes	complemented
30	C₂×C₇×#108	C₂²	1	4	yes	complemented
31	C₇×#421	C₂²	1	16	yes	complemented
32	C₂×C₇×#104	C₂²	1	8	yes	complemented
33	C₇×#405	C₂²	1	8	yes	complemented
34	C₂×C₇×#97	C₂²	1	2	yes	complemented
35	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
36	C₂×#2955	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×C₇×#41	—	2	2	no	—
38	C₂×C₇×#41	—	2	4	no	—
39	C₂×C₇×#41	—	2	2	no	—
40	C₂×C₇×#41	—	2	4	no	—
41	C₂×C₇×#41	C₂×C₄	1	4	yes	—
42	C₂×C₇×#41	C₂×C₄	1	8	yes	—
43	C₂×C₇×#41	C₂³	1	4	yes	—
44	C₂×C₇×#41	C₂³	1	8	yes	—
45	C₂²×C₇×Q₈	C₂×C₄	1	2	yes	—
46	C₂²×C₇×D₄	—	2	2	no	—
47	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₇	—	2	2	no	—
49	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
50	C₇×#137	C₂×C₄	1	32	yes	complemented
51	C₇×AGL(1,ℤ/8)	C₂×C₄	1	32	yes	complemented
52	C₇×#135	C₂×C₄	1	16	yes	—
53	C₇×#135	C₂³	1	16	yes	—
54	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	—
55	C₂×C₇×SD₁₆	C₂×C₄	1	8	yes	—
56	C₂×C₇×D₈	C₂×C₄	1	4	yes	—
57	C₇×#131	—	2	16	no	—
58	C₇×#131	—	2	16	no	—
59	C₇×#131	—	2	8	no	—
60	C₇×#131	—	2	8	no	—
61	C₇×#131	C₂³	1	16	yes	complemented
62	C₇×#131	C₂³	1	16	yes	complemented
63	C₂×C₇×M₁₆	—	2	2	no	—
64	C₂×C₇×M₁₆	—	2	4	no	—
65	C₂×C₇×M₁₆	—	2	4	no	—
66	C₂×C₇×M₁₆	—	2	4	no	—
67	C₂×C₇×M₁₆	—	2	16	no	—
68	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
69	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
70	C₂×C₇×M₁₆	C₂³	1	4	yes	—
71	C₂×C₇×M₁₆	C₂³	1	8	yes	—
72	C₂×C₇×M₁₆	C₂³	1	4	yes	—
73	C₂²×C₇×C₈	—	2	2	no	—
74	C₂²×C₇×C₈	—	2	4	no	—
75	C₂²×C₇×C₈	—	2	16	no	—
76	C₂²×C₇×C₈	—	2	4	no	—
77	C₂²×C₇×C₈	D₄	1	2	yes	—
78	C₂²×C₇×C₈	D₄	1	4	yes	—
79	C₂²×C₇×C₈	D₄	1	2	yes	—
80	C₂²×C₇×C₈	C₂³	1	2	yes	—
81	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₇×C₈	C₂³	1	4	yes	—
83	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
84	C₇×#117	—	2	2	no	—
85	C₇×#117	C₂³	1	4	yes	—
86	C₂×C₇×C₄⋊C₄	—	2	1	no	—
87	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₄²×C₇	C₂³	1	2	yes	—
89	C₇×#108	C₂³	1	16	yes	complemented
90	C₇×#104	C₂³	1	32	yes	complemented
91	C₇×#97	C₂³	1	8	yes	complemented
92	C₄×C₇×C₈	C₂³	1	8	yes	complemented
93	C₂×#575	C₂×C₇	1	1	yes	characteristic
94	C₂²×#131	C₂×C₇	1	2	yes	complemented
95	#2955	C₂×C₇	1	16	yes	direct product factor
96	C₂×#444	C₂×C₇	1	4	yes	complemented
97	C₂×#443	C₂×C₇	1	4	yes	complemented
98	C₂×#430	C₂×C₇	1	1	yes	characteristic, complemented
99	C₂×#421	C₂×C₇	1	2	yes	complemented
100	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
101	C₂⁴×C₇	—	2	2	no	—
102	C₂⁴×C₇	#41	1	1	yes	characteristic
103	C₇×#41	—	2	8	no	—
104	C₇×#41	—	2	8	no	—
105	C₇×#41	—	2	8	no	—
106	C₇×#41	—	2	8	no	—
107	C₇×#41	—	2	4	no	—
108	C₇×#41	—	2	4	no	—
109	C₇×#41	—	2	8	no	—
110	C₇×#41	C₂²×C₄	1	8	yes	—
111	C₇×#41	C₂²×C₄	1	16	yes	—
112	C₇×#41	C₂⁴	1	8	yes	—
113	C₂×C₇×Q₈	—	2	2	no	—
114	C₂×C₇×Q₈	—	2	4	no	—
115	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
116	C₂×C₇×Q₈	C₂²×C₄	1	8	yes	—
117	C₂×C₇×D₄	—	2	4	no	—
118	C₂×C₇×D₄	—	2	8	no	—
119	C₂×C₇×D₄	—	2	4	no	—
120	C₂×C₇×D₄	—	2	8	no	—
121	C₂×C₇×D₄	—	2	2	no	—
122	C₂×C₇×D₄	—	2	4	no	—
123	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
124	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
125	C₂²×C₄×C₇	—	2	2	no	—
126	C₂²×C₄×C₇	—	2	4	no	—
127	C₂²×C₄×C₇	—	2	8	no	—
128	C₂²×C₄×C₇	—	2	4	no	—
129	C₂²×C₄×C₇	—	2	8	no	—
130	C₂²×C₄×C₇	—	2	2	no	—
131	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₇	#41	1	1	yes	characteristic
136	C₂²×C₄×C₇	#41	1	2	yes	—
137	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
139	C₇×Q₁₆	C₂²×C₄	1	16	yes	—
140	C₇×SD₁₆	C₂²×C₄	1	32	yes	—
141	C₇×D₈	C₂²×C₄	1	16	yes	—
142	C₇×M₁₆	—	2	8	no	—
143	C₇×M₁₆	—	2	4	no	—
144	C₇×M₁₆	—	2	16	no	—
145	C₇×M₁₆	—	2	16	no	—
146	C₇×M₁₆	C₂²×C₄	1	16	yes	—
147	C₇×M₁₆	C₂⁴	1	8	yes	—
148	C₂×C₇×C₈	—	2	4	no	—
149	C₂×C₇×C₈	—	2	8	no	—
150	C₂×C₇×C₈	—	2	16	no	—
151	C₂×C₇×C₈	—	2	16	no	—
152	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
153	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
154	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
155	C₂×C₇×C₈	C₂×D₄	1	8	yes	—
156	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₇×C₈	C₂×D₄	1	8	yes	—
158	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
159	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
160	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
161	C₂×C₇×C₈	C₂⁴	1	4	yes	—
162	C₂×C₇×C₈	C₂⁴	1	2	yes	—
163	C₂×C₇×C₈	C₂⁴	1	2	yes	—
164	C₇×C₄⋊C₄	—	2	4	no	—
165	C₇×C₂²⋊C₄	—	2	4	no	—
166	C₄²×C₇	—	2	2	no	—
167	C₄²×C₇	C₂⁴	1	4	yes	—
168	C₂²×#41	C₂²×C₇	1	2	yes	—
169	#575	C₄×C₇	1	8	yes	complemented
170	#575	C₂²×C₇	1	8	yes	—
171	C₂×#137	C₄×C₇	1	4	yes	complemented
172	C₂×AGL(1,ℤ/8)	C₄×C₇	1	4	yes	complemented
173	C₂×#135	C₂²×C₇	1	4	yes	—
174	C₂×#131	—	2	2	no	—
175	C₂×#131	—	2	2	no	—
176	C₂×#131	—	2	8	no	—
177	C₂×#131	C₂²×C₇	1	4	yes	complemented
178	C₂×#131	C₂²×C₇	1	4	yes	complemented
179	C₂×#131	C₂²×C₇	1	16	yes	complemented
180	C₂²×M₁₆	—	2	2	no	—
181	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
182	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
183	C₂³×C₈	—	2	2	no	—
184	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
185	C₂×#117	C₂²×C₇	1	1	yes	characteristic
186	#444	C₂²×C₇	1	32	yes	complemented
187	#443	C₂²×C₇	1	32	yes	complemented
188	#430	C₂²×C₇	1	8	yes	complemented
189	C₂×#108	C₂²×C₇	1	4	yes	complemented
190	#421	C₂²×C₇	1	16	yes	complemented
191	C₂×#104	C₂²×C₇	1	8	yes	complemented
192	#405	C₂²×C₇	1	8	yes	complemented
193	C₂×#97	C₂²×C₇	1	2	yes	complemented
194	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
195	C₂³×C₇	—	2	8	no	—
196	C₂³×C₇	—	2	4	no	—
197	C₂³×C₇	—	4	2	no	—
198	C₂³×C₇	—	4	8	no	—
199	C₂³×C₇	C₄×D₄	1	2	yes	—
200	C₂³×C₇	C₄×D₄	1	2	yes	—
201	C₂³×C₇	C₂×#41	1	1	yes	characteristic
202	C₂³×C₇	C₂×#41	1	2	yes	—
203	C₇×Q₈	—	2	8	no	—
204	C₇×Q₈	—	2	4	no	—
205	C₇×Q₈	C₂³×C₄	1	8	yes	—
206	C₇×D₄	—	2	16	no	—
207	C₇×D₄	—	2	8	no	—
208	C₇×D₄	—	2	8	no	—
209	C₇×D₄	—	2	8	no	—
210	C₇×D₄	—	2	4	no	—
211	C₇×D₄	C₂³×C₄	1	8	yes	—
212	C₂×C₄×C₇	—	2	8	no	—
213	C₂×C₄×C₇	—	2	4	no	—
214	C₂×C₄×C₇	—	2	8	no	—
215	C₂×C₄×C₇	—	2	16	no	—
216	C₂×C₄×C₇	—	2	8	no	—
217	C₂×C₄×C₇	—	2	4	no	—
218	C₂×C₄×C₇	—	4	4	no	—
219	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
221	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
222	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
223	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
226	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
228	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₇	C₂×#41	1	2	yes	—
231	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
232	C₇×C₈	—	2	8	no	—
233	C₇×C₈	C₂³×C₄	1	8	yes	—
234	C₇×C₈	C₂²×D₄	1	2	yes	—
235	C₇×C₈	C₂²×D₄	1	4	yes	—
236	C₇×C₈	C₂²×D₄	1	2	yes	—
237	C₂×#41	—	2	2	no	—
238	C₂×#41	—	2	4	no	—
239	C₂×#41	—	2	2	no	—
240	C₂×#41	—	2	4	no	—
241	C₂×#41	C₂×C₄×C₇	1	4	yes	—
242	C₂×#41	C₂×C₄×C₇	1	8	yes	—
243	C₂×#41	C₂³×C₇	1	4	yes	—
244	C₂×#41	C₂³×C₇	1	8	yes	—
245	C₂²×Q₈	C₂×C₄×C₇	1	2	yes	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
250	#137	C₂×C₄×C₇	1	32	yes	complemented
251	AGL(1,ℤ/8)	C₂×C₄×C₇	1	32	yes	complemented
252	#135	C₂×C₄×C₇	1	16	yes	—
253	#135	C₂³×C₇	1	16	yes	—
254	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	—
255	C₂×SD₁₆	C₂×C₄×C₇	1	8	yes	—
256	C₂×D₈	C₂×C₄×C₇	1	4	yes	—
257	#131	—	2	16	no	—
258	#131	—	2	16	no	—
259	#131	—	2	8	no	—
260	#131	—	2	8	no	—
261	#131	C₂³×C₇	1	16	yes	complemented
262	#131	C₂³×C₇	1	16	yes	complemented
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	4	no	—
265	C₂×M₁₆	—	2	4	no	—
266	C₂×M₁₆	—	2	4	no	—
267	C₂×M₁₆	—	2	16	no	—
268	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
269	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
270	C₂×M₁₆	C₂³×C₇	1	4	yes	—
271	C₂×M₁₆	C₂³×C₇	1	8	yes	—
272	C₂×M₁₆	C₂³×C₇	1	4	yes	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	4	no	—
275	C₂²×C₈	—	2	16	no	—
276	C₂²×C₈	—	2	4	no	—
277	C₂²×C₈	C₇×D₄	1	2	yes	—
278	C₂²×C₈	C₇×D₄	1	2	yes	—
279	C₂²×C₈	C₇×D₄	1	4	yes	—
280	C₂²×C₈	C₂³×C₇	1	2	yes	—
281	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₇	1	4	yes	—
284	#117	—	2	2	no	—
285	#117	C₂³×C₇	1	4	yes	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₄²	C₂³×C₇	1	2	yes	—
289	#108	C₂³×C₇	1	16	yes	complemented
290	#104	C₂³×C₇	1	32	yes	complemented
291	#97	C₂³×C₇	1	8	yes	complemented
292	C₄×C₈	C₂³×C₇	1	8	yes	complemented
293	C₂²×C₇	—	2	2	no	—
294	C₂²×C₇	—	2	4	no	—
295	C₂²×C₇	—	2	8	no	—
296	C₂²×C₇	—	4	2	no	—
297	C₂²×C₇	—	4	2	no	—
298	C₂²×C₇	—	4	16	no	—
299	C₂²×C₇	—	4	8	no	—
300	C₂²×C₇	C₂×C₄×D₄	1	4	yes	—
301	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
304	C₄×C₇	—	2	8	no	—
305	C₄×C₇	—	4	4	no	—
306	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
307	C₄×C₇	C₂×C₄×D₄	1	4	yes	—
308	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
309	C₄×C₇	C₂⁴×C₄	1	1	yes	characteristic
310	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
311	C₂⁴	—	2	2	no	—
312	C₂⁴	C₇×#41	1	1	yes	characteristic
313	#41	—	2	8	no	—
314	#41	—	2	8	no	—
315	#41	—	2	8	no	—
316	#41	—	2	8	no	—
317	#41	—	2	4	no	—
318	#41	—	2	4	no	—
319	#41	—	2	8	no	—
320	#41	C₂²×C₄×C₇	1	8	yes	—
321	#41	C₂²×C₄×C₇	1	16	yes	—
322	#41	C₂⁴×C₇	1	8	yes	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
326	C₂×Q₈	C₂²×C₄×C₇	1	8	yes	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	8	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
334	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	8	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
342	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
343	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
344	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
345	C₂²×C₄	C₇×#41	1	1	yes	characteristic
346	C₂²×C₄	C₇×#41	1	2	yes	—
347	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
349	Q₁₆	C₂²×C₄×C₇	1	16	yes	—
350	SD₁₆	C₂²×C₄×C₇	1	32	yes	—
351	D₈	C₂²×C₄×C₇	1	16	yes	—
352	M₁₆	—	2	8	no	—
353	M₁₆	—	2	4	no	—
354	M₁₆	—	2	16	no	—
355	M₁₆	—	2	16	no	—
356	M₁₆	C₂²×C₄×C₇	1	16	yes	—
357	M₁₆	C₂⁴×C₇	1	8	yes	—
358	C₂×C₈	—	2	4	no	—
359	C₂×C₈	—	2	8	no	—
360	C₂×C₈	—	2	16	no	—
361	C₂×C₈	—	2	16	no	—
362	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
363	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
364	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
365	C₂×C₈	C₂×C₇×D₄	1	8	yes	—
366	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
367	C₂×C₈	C₂×C₇×D₄	1	8	yes	—
368	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
369	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
370	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
371	C₂×C₈	C₂⁴×C₇	1	4	yes	—
372	C₂×C₈	C₂⁴×C₇	1	2	yes	—
373	C₂×C₈	C₂⁴×C₇	1	2	yes	—
374	C₄⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₄²	—	2	2	no	—
377	C₄²	C₂⁴×C₇	1	4	yes	—
378	C₂×C₇	—	2	1	no	—
379	C₂×C₇	—	2	4	no	—
380	C₂×C₇	—	2	1	no	—
381	C₂×C₇	—	4	8	no	—
382	C₂×C₇	#2955	1	2	yes	direct product factor
383	C₂×C₇	C₂²×C₄×D₄	1	1	yes	characteristic
384	C₂³	—	2	8	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	8	no	—
388	C₂³	C₄×C₇×D₄	1	2	yes	—
389	C₂³	C₄×C₇×D₄	1	2	yes	—
390	C₂³	C₂×C₇×#41	1	1	yes	characteristic
391	C₂³	C₂×C₇×#41	1	2	yes	—
392	Q₈	—	2	8	no	—
393	Q₈	—	2	4	no	—
394	Q₈	C₂³×C₄×C₇	1	8	yes	—
395	D₄	—	2	8	no	—
396	D₄	—	2	16	no	—
397	D₄	—	2	8	no	—
398	D₄	—	2	8	no	—
399	D₄	—	2	4	no	—
400	D₄	C₂³×C₄×C₇	1	8	yes	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	16	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
409	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
410	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
411	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
412	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
413	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
414	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
415	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
417	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
418	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
419	C₂×C₄	C₂×C₇×#41	1	2	yes	—
420	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
421	C₈	—	2	8	no	—
422	C₈	C₂³×C₄×C₇	1	8	yes	—
423	C₈	C₂²×C₇×D₄	1	2	yes	—
424	C₈	C₂²×C₇×D₄	1	4	yes	—
425	C₈	C₂²×C₇×D₄	1	2	yes	—
426	C₇	C₂×#2955	1	1	yes	characteristic, direct product factor, Sylow
427	C₂²	—	2	2	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	8	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	16	no	—
433	C₂²	—	4	8	no	—
434	C₂²	C₂×C₄×C₇×D₄	1	4	yes	—
435	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
436	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
437	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
438	C₄	—	2	8	no	—
439	C₄	—	4	4	no	—
440	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
441	C₄	C₂×C₄×C₇×D₄	1	4	yes	—
442	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
443	C₄	C₂⁴×C₄×C₇	1	1	yes	characteristic
444	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	4	no	—
447	C₂	—	2	1	no	—
448	C₂	—	4	8	no	—
449	C₂	C₇×#2955	1	2	yes	direct product factor
450	C₂	C₂²×C₄×C₇×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇×C₈	C₂×D₄
commutator	C₄	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×C₇×#575	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇×C₈ ◁ C₂³×C₇×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₇×#131	C₂	semidirect
3. C₇×#2955	C₂	direct (N × H)
4. C₂×C₇×#444	C₂	semidirect
5. C₂×C₇×#443	C₂	semidirect
6. C₂×C₇×#430	C₂	semidirect
7. C₂×C₇×#421	C₂	semidirect
8. C₂×C₇×#405	C₂	semidirect
10. C₇×#575	C₄	semidirect
12. C₂×C₇×#137	C₄	semidirect
13. C₂×C₇×AGL(1,ℤ/8)	C₄	semidirect
18. C₂×C₇×#131	C₂²	semidirect
19. C₂×C₇×#131	C₂²	semidirect
20. C₂×C₇×#131	C₂²	semidirect
27. C₇×#444	C₂²	semidirect
28. C₇×#443	C₂²	semidirect
29. C₇×#430	C₂²	semidirect
30. C₂×C₇×#108	C₂²	semidirect
31. C₇×#421	C₂²	semidirect
32. C₂×C₇×#104	C₂²	semidirect
33. C₇×#405	C₂²	semidirect
34. C₂×C₇×#97	C₂²	semidirect
35. C₂×C₄×C₇×C₈	C₂²	semidirect
36. C₂×#2955	C₇	direct (N × H)
50. C₇×#137	C₂×C₄	semidirect
51. C₇×AGL(1,ℤ/8)	C₂×C₄	semidirect
61. C₇×#131	C₂³	semidirect
62. C₇×#131	C₂³	semidirect
89. C₇×#108	C₂³	semidirect
90. C₇×#104	C₂³	semidirect
91. C₇×#97	C₂³	semidirect
92. C₄×C₇×C₈	C₂³	semidirect
94. C₂²×#131	C₂×C₇	semidirect
95. #2955	C₂×C₇	direct (N × H)
96. C₂×#444	C₂×C₇	semidirect
97. C₂×#443	C₂×C₇	semidirect
98. C₂×#430	C₂×C₇	semidirect
99. C₂×#421	C₂×C₇	semidirect
100. C₂×#405	C₂×C₇	semidirect
169. #575	C₄×C₇	semidirect
171. C₂×#137	C₄×C₇	semidirect
172. C₂×AGL(1,ℤ/8)	C₄×C₇	semidirect
177. C₂×#131	C₂²×C₇	semidirect
178. C₂×#131	C₂²×C₇	semidirect
179. C₂×#131	C₂²×C₇	semidirect
186. #444	C₂²×C₇	semidirect
187. #443	C₂²×C₇	semidirect
188. #430	C₂²×C₇	semidirect
189. C₂×#108	C₂²×C₇	semidirect
190. #421	C₂²×C₇	semidirect
191. C₂×#104	C₂²×C₇	semidirect
192. #405	C₂²×C₇	semidirect
193. C₂×#97	C₂²×C₇	semidirect
194. C₂×C₄×C₈	C₂²×C₇	semidirect
250. #137	C₂×C₄×C₇	semidirect
251. AGL(1,ℤ/8)	C₂×C₄×C₇	semidirect
261. #131	C₂³×C₇	semidirect
262. #131	C₂³×C₇	semidirect
289. #108	C₂³×C₇	semidirect
290. #104	C₂³×C₇	semidirect
291. #97	C₂³×C₇	semidirect
292. C₄×C₈	C₂³×C₇	semidirect
382. C₂×C₇	#2955	direct (N × H)
426. C₇	C₂×#2955	direct (N × H)
449. C₂	C₇×#2955	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#575	2
C₂²×C₇×#131	2
C₇×#2955	2
C₂×C₇×#444	2
C₂×C₇×#443	2
C₂×C₇×#430	2
C₂×C₇×#421	2
C₂×C₇×#405	2
C₂×#2955	7

Subgroups — C2×C7×#2955 #13237395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2955 #13237395