Subgroups — C₂×#11741355 #14218117

Order 1792.

2642 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×#90510	C₂	1	2	yes	maximal, complemented
3	C₂×#90008	C₂	1	2	yes	maximal, complemented
4	#11741355	C₂	1	16	yes	maximal, direct product factor
5	C₂×#89969	C₂	1	4	yes	maximal, complemented
6	C₂×#89968	C₂	1	4	yes	maximal, complemented
7	C₂²×#6393	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#89873	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×#41	C₂²	1	2	yes	—
10	C₂×C₇×#135	C₄	1	2	yes	complemented
11	C₂×C₇×#135	C₄	1	2	yes	complemented
12	C₂×C₇×#135	C₄	1	8	yes	complemented
13	C₂×C₇×#135	C₂²	1	2	yes	—
14	C₂×C₇×#135	C₂²	1	2	yes	—
15	C₂×C₇×#135	C₂²	1	8	yes	—
16	C₂²×C₇×Q₁₆	C₄	1	1	yes	characteristic, complemented
17	C₂²×C₇×SD₁₆	C₄	1	2	yes	complemented
18	C₂²×C₇×D₈	C₄	1	1	yes	characteristic, complemented
19	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
20	#90510	—	2	8	no	—
21	#90510	C₂²	1	16	yes	complemented
22	C₂×#6511	—	2	4	no	—
23	C₂×#6511	C₂²	1	8	yes	complemented
24	C₂×#6489	C₂²	1	1	yes	characteristic
25	C₂²×#1136	—	2	4	no	—
26	C₂²×#1136	C₂²	1	2	yes	—
27	C₂²×#1136	C₂²	1	1	yes	characteristic
28	#90008	C₂²	1	16	yes	complemented
29	C₂×#6411	C₂²	1	8	yes	complemented
30	#89969	C₂²	1	32	yes	complemented
31	#89968	C₂²	1	32	yes	complemented
32	C₂×#6393	C₂²	1	2	yes	complemented
33	C₂×#6393	C₂²	1	2	yes	complemented
34	C₂×#6393	C₂²	1	8	yes	complemented
35	#89873	C₂²	1	8	yes	complemented
36	C₂×#6389	C₂²	1	2	yes	complemented
37	C₂×C₈×Dic₇	C₂²	1	2	yes	complemented
38	C₂×#2957	—	7	1	no	maximal, Sylow
39	C₂×C₇×#41	—	2	2	no	—
40	C₂×C₇×#41	—	2	4	no	—
41	C₂×C₇×#41	—	2	2	no	—
42	C₂×C₇×#41	—	2	4	no	—
43	C₂×C₇×#41	C₂×C₄	1	4	yes	—
44	C₂×C₇×#41	C₂×C₄	1	8	yes	—
45	C₂×C₇×#41	C₂³	1	4	yes	—
46	C₂×C₇×#41	C₂³	1	8	yes	—
47	C₂²×C₇×Q₈	C₂×C₄	1	2	yes	—
48	C₂²×C₇×D₄	—	2	2	no	—
49	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₇	—	2	2	no	—
51	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
52	C₇×#135	C₂×C₄	1	8	yes	—
53	C₇×#135	C₂×C₄	1	8	yes	—
54	C₇×#135	C₂×C₄	1	16	yes	complemented
55	C₇×#135	C₂×C₄	1	16	yes	complemented
56	C₇×#135	C₂³	1	8	yes	—
57	C₇×#135	C₂³	1	8	yes	—
58	C₂×C₇×Q₁₆	C₂×C₄	1	2	yes	—
59	C₂×C₇×Q₁₆	C₂×C₄	1	2	yes	—
60	C₂×C₇×Q₁₆	C₂×C₄	1	8	yes	complemented
61	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
62	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
63	C₂×C₇×SD₁₆	C₂×C₄	1	16	yes	complemented
64	C₂×C₇×D₈	C₂×C₄	1	2	yes	—
65	C₂×C₇×D₈	C₂×C₄	1	2	yes	—
66	C₂×C₇×D₈	C₂×C₄	1	8	yes	complemented
67	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
72	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇×C₈	C₂³	1	4	yes	—
75	C₂×C₂²⋊Dic₇	—	2	1	no	—
76	#6511	—	2	32	no	—
77	#6511	—	2	16	no	—
78	#6511	C₂³	1	32	yes	complemented
79	#6489	—	2	2	no	—
80	#6489	C₂³	1	4	yes	—
81	C₂×C₄⋊Dic₇	—	2	1	no	—
82	C₂×C₄×Dic₇	C₂³	1	2	yes	—
83	C₂×#1136	—	2	2	no	—
84	C₂×#1136	—	2	4	no	—
85	C₂×#1136	—	2	32	no	—
86	C₂×#1136	—	2	8	no	—
87	C₂×#1136	D₄	1	2	yes	—
88	C₂×#1136	D₄	1	2	yes	—
89	C₂×#1136	D₄	1	4	yes	—
90	C₂×#1136	C₂³	1	4	yes	—
91	C₂×#1136	C₂³	1	8	yes	—
92	C₂×#1136	C₂³	1	4	yes	—
93	C₂²×C₇⋊C₈	—	2	2	no	—
94	C₂²×C₇⋊C₈	—	2	8	no	—
95	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
96	#6411	C₂³	1	32	yes	complemented
97	#6393	C₂³	1	8	yes	complemented
98	#6393	C₂³	1	8	yes	complemented
99	#6389	C₂³	1	8	yes	complemented
100	C₈×Dic₇	C₂³	1	8	yes	complemented
101	C₂²×#135	D₇	1	1	yes	characteristic
102	C₂×#568	—	7	2	no	—
103	#2957	—	7	16	no	—
104	C₂×#444	—	7	4	no	—
105	C₂×#443	—	7	4	no	—
106	C₂²×#108	—	7	1	no	—
107	C₂×#421	—	7	2	no	—
108	C₂×#405	—	7	1	no	—
109	C₂⁴×C₇	—	2	2	no	—
110	C₂⁴×C₇	#41	1	1	yes	characteristic
111	C₇×#41	—	2	8	no	—
112	C₇×#41	—	2	8	no	—
113	C₇×#41	—	2	8	no	—
114	C₇×#41	—	2	8	no	—
115	C₇×#41	—	2	4	no	—
116	C₇×#41	—	2	4	no	—
117	C₇×#41	—	2	8	no	—
118	C₇×#41	C₂²×C₄	1	8	yes	—
119	C₇×#41	C₂²×C₄	1	16	yes	—
120	C₇×#41	C₂⁴	1	8	yes	—
121	C₂×C₇×Q₈	—	2	2	no	—
122	C₂×C₇×Q₈	—	2	4	no	—
123	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
124	C₂×C₇×Q₈	C₂²×C₄	1	8	yes	—
125	C₂×C₇×D₄	—	2	4	no	—
126	C₂×C₇×D₄	—	2	8	no	—
127	C₂×C₇×D₄	—	2	4	no	—
128	C₂×C₇×D₄	—	2	8	no	—
129	C₂×C₇×D₄	—	2	2	no	—
130	C₂×C₇×D₄	—	2	4	no	—
131	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
132	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
133	C₂²×C₄×C₇	—	2	2	no	—
134	C₂²×C₄×C₇	—	2	4	no	—
135	C₂²×C₄×C₇	—	2	8	no	—
136	C₂²×C₄×C₇	—	2	4	no	—
137	C₂²×C₄×C₇	—	2	8	no	—
138	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₇	#41	1	1	yes	characteristic
145	C₂²×C₄×C₇	#41	1	2	yes	—
146	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
148	C₂²×Dic₇	—	2	2	no	—
149	C₇×Q₁₆	C₂²×C₄	1	8	yes	—
150	C₇×Q₁₆	C₂²×C₄	1	8	yes	—
151	C₇×SD₁₆	C₂²×C₄	1	16	yes	—
152	C₇×SD₁₆	C₂²×C₄	1	16	yes	—
153	C₇×D₈	C₂²×C₄	1	8	yes	—
154	C₇×D₈	C₂²×C₄	1	8	yes	—
155	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
158	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
161	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
162	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
163	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
164	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
165	C₂×C₇×C₈	C₂⁴	1	2	yes	—
166	C₂×C₇×C₈	C₂⁴	1	2	yes	—
167	C₂²⋊Dic₇	—	2	4	no	—
168	C₄⋊Dic₇	—	2	4	no	—
169	C₄×Dic₇	—	2	2	no	—
170	C₄×Dic₇	C₂⁴	1	4	yes	—
171	#1136	—	2	8	no	—
172	#1136	—	2	4	no	—
173	#1136	—	2	32	no	—
174	#1136	C₂×D₄	1	8	yes	—
175	#1136	C₂×D₄	1	8	yes	—
176	#1136	C₂⁴	1	8	yes	—
177	C₂×C₇⋊C₈	—	2	4	no	—
178	C₂×C₇⋊C₈	—	2	8	no	—
179	C₂×C₇⋊C₈	—	2	32	no	—
180	C₂×C₇⋊C₈	C₂×D₄	1	4	yes	—
181	C₂×C₇⋊C₈	C₂×D₄	1	4	yes	—
182	C₂×C₇⋊C₈	C₂⁴	1	4	yes	—
183	C₂²×#41	C₂×D₇	1	2	yes	—
184	C₂×#135	Dic₇	1	2	yes	complemented
185	C₂×#135	Dic₇	1	2	yes	complemented
186	C₂×#135	Dic₇	1	8	yes	complemented
187	C₂×#135	C₂×D₇	1	2	yes	—
188	C₂×#135	C₂×D₇	1	2	yes	—
189	C₂×#135	C₂×D₇	1	8	yes	—
190	C₂²×Q₁₆	Dic₇	1	1	yes	characteristic, complemented
191	C₂²×SD₁₆	Dic₇	1	2	yes	complemented
192	C₂²×D₈	Dic₇	1	1	yes	characteristic, complemented
193	#568	—	7	16	no	—
194	#568	—	14	8	no	—
195	C₂×#131	—	7	8	no	—
196	C₂×#131	—	14	4	no	—
197	C₂²×M₁₆	—	7	1	no	—
198	C₂²×M₁₆	—	7	2	no	—
199	C₂²×M₁₆	—	14	4	no	—
200	C₂³×C₈	C₂×D₇	1	1	yes	characteristic
201	C₂×#117	—	7	1	no	—
202	#444	—	7	32	no	—
203	#443	—	7	32	no	—
204	C₂×#108	—	7	2	no	—
205	C₂×#108	—	7	2	no	—
206	C₂×#108	—	7	8	no	—
207	#421	—	7	16	no	—
208	C₂×#104	—	7	8	no	—
209	#405	—	7	8	no	—
210	C₂×#97	—	7	2	no	—
211	C₂×C₄×C₈	—	7	2	no	—
212	C₂³×C₇	—	2	4	no	—
213	C₂³×C₇	—	2	8	no	—
214	C₂³×C₇	—	4	2	no	—
215	C₂³×C₇	—	8	4	no	—
216	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
217	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
218	C₂³×C₇	C₄×D₄	1	2	yes	—
219	C₂³×C₇	C₂×#41	1	1	yes	characteristic
220	C₂³×C₇	C₂×#41	1	2	yes	—
221	C₇×Q₈	—	2	4	no	—
222	C₇×Q₈	—	2	8	no	—
223	C₇×Q₈	C₂³×C₄	1	8	yes	—
224	C₇×D₄	—	2	8	no	—
225	C₇×D₄	—	2	16	no	—
226	C₇×D₄	—	2	8	no	—
227	C₇×D₄	—	2	4	no	—
228	C₇×D₄	—	2	8	no	—
229	C₇×D₄	C₂³×C₄	1	8	yes	—
230	C₂×C₄×C₇	—	2	8	no	—
231	C₂×C₄×C₇	—	2	4	no	—
232	C₂×C₄×C₇	—	2	8	no	—
233	C₂×C₄×C₇	—	2	16	no	—
234	C₂×C₄×C₇	—	2	8	no	—
235	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
236	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
238	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
240	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
241	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
242	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
243	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
246	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₇	C₂×#41	1	2	yes	—
252	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
253	C₂×Dic₇	—	2	4	no	—
254	C₂×Dic₇	—	4	4	no	—
255	C₇×C₈	C₂³×C₄	1	2	yes	—
256	C₇×C₈	C₂³×C₄	1	2	yes	—
257	C₇×C₈	C₂³×C₄	1	2	yes	—
258	C₇×C₈	C₂³×C₄	1	2	yes	—
259	C₇⋊C₈	—	2	8	no	—
260	C₇⋊C₈	C₂²×D₄	1	8	yes	—
261	C₂×#41	—	2	2	no	—
262	C₂×#41	—	2	4	no	—
263	C₂×#41	—	2	2	no	—
264	C₂×#41	—	2	4	no	—
265	C₂×#41	C₂×Dic₇	1	4	yes	—
266	C₂×#41	C₂×Dic₇	1	8	yes	—
267	C₂×#41	C₂²×D₇	1	4	yes	—
268	C₂×#41	C₂²×D₇	1	8	yes	—
269	C₂²×Q₈	C₂×Dic₇	1	2	yes	—
270	C₂²×D₄	—	2	2	no	—
271	C₂²×D₄	C₂×Dic₇	1	2	yes	—
272	C₂³×C₄	—	2	2	no	—
273	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
274	#135	C₂×Dic₇	1	8	yes	—
275	#135	C₂×Dic₇	1	8	yes	—
276	#135	C₂×Dic₇	1	16	yes	complemented
277	#135	C₂×Dic₇	1	16	yes	complemented
278	#135	C₂²×D₇	1	8	yes	—
279	#135	C₂²×D₇	1	8	yes	—
280	C₂×Q₁₆	C₂×Dic₇	1	2	yes	—
281	C₂×Q₁₆	C₂×Dic₇	1	2	yes	—
282	C₂×Q₁₆	C₂×Dic₇	1	8	yes	complemented
283	C₂×SD₁₆	C₂×Dic₇	1	4	yes	—
284	C₂×SD₁₆	C₂×Dic₇	1	4	yes	—
285	C₂×SD₁₆	C₂×Dic₇	1	16	yes	complemented
286	C₂×D₈	C₂×Dic₇	1	2	yes	—
287	C₂×D₈	C₂×Dic₇	1	2	yes	—
288	C₂×D₈	C₂×Dic₇	1	8	yes	complemented
289	#131	—	7	32	no	—
290	#131	—	14	16	no	—
291	#131	—	14	32	no	—
292	C₂×M₁₆	—	7	2	no	—
293	C₂×M₁₆	—	7	2	no	—
294	C₂×M₁₆	—	7	4	no	—
295	C₂×M₁₆	—	7	4	no	—
296	C₂×M₁₆	—	7	4	no	—
297	C₂×M₁₆	—	7	8	no	—
298	C₂×M₁₆	—	14	8	no	—
299	C₂×M₁₆	—	14	32	no	—
300	C₂×M₁₆	—	14	2	no	—
301	C₂×M₁₆	—	14	4	no	—
302	C₂²×C₈	—	7	2	no	—
303	C₂²×C₈	—	14	8	no	—
304	C₂²×C₈	—	14	2	no	—
305	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
306	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
307	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
308	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
309	C₂²×C₈	C₂×Dic₇	1	4	yes	—
310	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
311	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
312	C₂²×C₈	C₂²×D₇	1	4	yes	—
313	#117	—	7	4	no	—
314	#117	—	14	2	no	—
315	C₂×C₄⋊C₄	—	14	1	no	—
316	C₂×C₂²⋊C₄	—	14	1	no	—
317	C₂×C₄²	—	7	2	no	—
318	#108	—	7	8	no	—
319	#108	—	7	8	no	—
320	#104	—	7	32	no	—
321	#97	—	7	8	no	—
322	C₄×C₈	—	7	8	no	—
323	C₂²×C₇	—	2	2	no	—
324	C₂²×C₇	—	2	2	no	—
325	C₂²×C₇	—	2	2	no	—
326	C₂²×C₇	—	2	8	no	—
327	C₂²×C₇	—	4	2	no	—
328	C₂²×C₇	—	4	2	no	—
329	C₂²×C₇	—	4	8	no	—
330	C₂²×C₇	—	8	8	no	—
331	C₂²×C₇	C₂×C₄×D₄	1	2	yes	—
332	C₂²×C₇	C₂×C₄×D₄	1	2	yes	—
333	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
334	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
335	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
336	C₄×C₇	—	2	8	no	—
337	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
338	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
339	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
340	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
341	C₄×C₇	C₂⁴×C₄	1	1	yes	characteristic
342	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
343	Dic₇	—	4	4	no	—
344	C₂⁴	—	2	2	no	—
345	C₂⁴	#1159	1	1	yes	characteristic
346	#41	—	2	8	no	—
347	#41	—	2	8	no	—
348	#41	—	2	8	no	—
349	#41	—	2	4	no	—
350	#41	—	2	8	no	—
351	#41	—	2	4	no	—
352	#41	—	2	8	no	—
353	#41	C₂²×Dic₇	1	8	yes	—
354	#41	C₂²×Dic₇	1	16	yes	—
355	#41	C₂³×D₇	1	8	yes	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	C₂²×Dic₇	1	4	yes	—
359	C₂×Q₈	C₂²×Dic₇	1	8	yes	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	8	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	C₂²×Dic₇	1	4	yes	—
367	C₂×D₄	C₂²×Dic₇	1	8	yes	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	2	8	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	14	2	no	—
374	C₂²×C₄	D₄×D₇	1	2	yes	—
375	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
376	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
377	C₂²×C₄	#1159	1	1	yes	characteristic
378	C₂²×C₄	#1159	1	2	yes	—
379	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
380	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
381	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
382	C₂²×C₄	C₂³×D₇	1	2	yes	—
383	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
384	Q₁₆	C₂²×Dic₇	1	8	yes	—
385	Q₁₆	C₂²×Dic₇	1	8	yes	—
386	SD₁₆	C₂²×Dic₇	1	16	yes	—
387	SD₁₆	C₂²×Dic₇	1	16	yes	—
388	D₈	C₂²×Dic₇	1	8	yes	—
389	D₈	C₂²×Dic₇	1	8	yes	—
390	M₁₆	—	7	8	no	—
391	M₁₆	—	7	8	no	—
392	M₁₆	—	7	8	no	—
393	M₁₆	—	14	32	no	—
394	M₁₆	—	14	8	no	—
395	M₁₆	—	14	4	no	—
396	C₂×C₈	—	7	4	no	—
397	C₂×C₈	—	7	4	no	—
398	C₂×C₈	—	7	4	no	—
399	C₂×C₈	—	14	32	no	—
400	C₂×C₈	—	14	8	no	—
401	C₂×C₈	—	14	4	no	—
402	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
403	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
404	C₂×C₈	C₂²×Dic₇	1	4	yes	—
405	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
406	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
407	C₂×C₈	C₂²×Dic₇	1	4	yes	—
408	C₂×C₈	C₂²×Dic₇	1	2	yes	—
409	C₂×C₈	C₂²×Dic₇	1	2	yes	—
410	C₂×C₈	C₂²×Dic₇	1	4	yes	—
411	C₂×C₈	C₂²×Dic₇	1	4	yes	—
412	C₂×C₈	C₂³×D₇	1	2	yes	—
413	C₂×C₈	C₂³×D₇	1	2	yes	—
414	C₄⋊C₄	—	14	4	no	—
415	C₂²⋊C₄	—	14	4	no	—
416	C₄²	—	7	4	no	—
417	C₄²	—	14	2	no	—
418	C₂×C₇	—	2	1	no	—
419	C₂×C₇	—	2	2	no	—
420	C₂×C₇	—	2	1	no	—
421	C₂×C₇	—	2	2	no	—
422	C₂×C₇	—	4	8	no	—
423	C₂×C₇	#2957	1	2	yes	complemented
424	C₂×C₇	C₂²×C₄×D₄	1	1	yes	characteristic
425	C₂³	—	2	4	no	—
426	C₂³	—	2	8	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	8	4	no	—
429	C₂³	D₄×Dic₇	1	1	yes	characteristic
430	C₂³	D₄×Dic₇	1	1	yes	characteristic
431	C₂³	D₄×Dic₇	1	2	yes	—
432	C₂³	C₂×#1159	1	1	yes	characteristic
433	C₂³	C₂×#1159	1	2	yes	—
434	Q₈	—	2	4	no	—
435	Q₈	—	2	8	no	—
436	Q₈	C₂³×Dic₇	1	8	yes	—
437	D₄	—	2	8	no	—
438	D₄	—	2	16	no	—
439	D₄	—	2	8	no	—
440	D₄	—	2	4	no	—
441	D₄	—	2	8	no	—
442	D₄	C₂³×Dic₇	1	8	yes	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	16	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	14	4	no	—
449	C₂×C₄	—	28	4	no	—
450	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
451	C₂×C₄	D₄×Dic₇	1	2	yes	—
452	C₂×C₄	D₄×Dic₇	1	2	yes	—
453	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
454	C₂×C₄	D₄×Dic₇	1	2	yes	—
455	C₂×C₄	D₄×Dic₇	1	2	yes	—
456	C₂×C₄	D₄×Dic₇	1	2	yes	—
457	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
458	C₂×C₄	C₂×D₄×D₇	1	2	yes	—
459	C₂×C₄	C₂×D₄×D₇	1	2	yes	—
460	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
461	C₂×C₄	C₂×#1159	1	1	yes	characteristic
462	C₂×C₄	C₂×#1159	1	2	yes	—
463	C₂×C₄	C₂³×Dic₇	1	2	yes	—
464	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
465	C₂×C₄	C₂³×Dic₇	1	2	yes	—
466	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
467	C₂×C₄	C₂⁴×D₇	1	1	yes	characteristic
468	C₈	—	7	8	no	—
469	C₈	—	14	8	no	—
470	C₈	C₂³×Dic₇	1	2	yes	—
471	C₈	C₂³×Dic₇	1	2	yes	—
472	C₈	C₂³×Dic₇	1	2	yes	—
473	C₈	C₂³×Dic₇	1	2	yes	—
474	C₇	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	8	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	8	no	—
482	C₂²	—	8	8	no	—
483	C₂²	C₂×D₄×Dic₇	1	2	yes	—
484	C₂²	C₂×D₄×Dic₇	1	1	yes	characteristic
485	C₂²	C₂×D₄×Dic₇	1	2	yes	—
486	C₂²	C₂×D₄×Dic₇	1	1	yes	characteristic
487	C₂²	C₂²×#1159	1	1	yes	characteristic
488	C₄	—	2	8	no	—
489	C₄	—	28	4	no	—
490	C₄	C₂×D₄×Dic₇	1	2	yes	—
491	C₄	C₂×D₄×Dic₇	1	1	yes	characteristic
492	C₄	C₂×D₄×Dic₇	1	1	yes	characteristic
493	C₄	C₂×D₄×Dic₇	1	2	yes	—
494	C₄	C₂²×D₄×D₇	1	1	yes	characteristic
495	C₄	C₂⁴×Dic₇	1	1	yes	characteristic
496	C₂	—	2	1	no	—
497	C₂	—	2	2	no	—
498	C₂	—	2	1	no	—
499	C₂	—	2	2	no	—
500	C₂	—	4	8	no	—
501	C₂	#11741355	1	2	yes	direct product factor
502	C₂	C₂²×D₄×Dic₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇
commutator	C₄×C₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇
Fitting, prime radical	C₂²×C₇×#135	C₂
socle	C₂²×C₇	C₂×C₄×D₄
cosocle	C₂×C₄×C₇	C₂⁵
hypercenter	C₂²×#135	D₇
hypocenter	C₇	C₂×#2957
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
2. C₂×#90510	C₂	semidirect
3. C₂×#90008	C₂	semidirect
4. #11741355	C₂	direct (N × H)
5. C₂×#89969	C₂	semidirect
6. C₂×#89968	C₂	semidirect
7. C₂²×#6393	C₂	semidirect
8. C₂×#89873	C₂	semidirect
10. C₂×C₇×#135	C₄	semidirect
11. C₂×C₇×#135	C₄	semidirect
12. C₂×C₇×#135	C₄	semidirect
16. C₂²×C₇×Q₁₆	C₄	semidirect
17. C₂²×C₇×SD₁₆	C₄	semidirect
18. C₂²×C₇×D₈	C₄	semidirect
21. #90510	C₂²	semidirect
23. C₂×#6511	C₂²	semidirect
28. #90008	C₂²	semidirect
29. C₂×#6411	C₂²	semidirect
30. #89969	C₂²	semidirect
31. #89968	C₂²	semidirect
32. C₂×#6393	C₂²	semidirect
33. C₂×#6393	C₂²	semidirect
34. C₂×#6393	C₂²	semidirect
35. #89873	C₂²	semidirect
36. C₂×#6389	C₂²	semidirect
37. C₂×C₈×Dic₇	C₂²	semidirect
54. C₇×#135	C₂×C₄	semidirect
55. C₇×#135	C₂×C₄	semidirect
60. C₂×C₇×Q₁₆	C₂×C₄	semidirect
63. C₂×C₇×SD₁₆	C₂×C₄	semidirect
66. C₂×C₇×D₈	C₂×C₄	semidirect
78. #6511	C₂³	semidirect
96. #6411	C₂³	semidirect
97. #6393	C₂³	semidirect
98. #6393	C₂³	semidirect
99. #6389	C₂³	semidirect
100. C₈×Dic₇	C₂³	semidirect
184. C₂×#135	Dic₇	semidirect
185. C₂×#135	Dic₇	semidirect
186. C₂×#135	Dic₇	semidirect
190. C₂²×Q₁₆	Dic₇	semidirect
191. C₂²×SD₁₆	Dic₇	semidirect
192. C₂²×D₈	Dic₇	semidirect
276. #135	C₂×Dic₇	semidirect
277. #135	C₂×Dic₇	semidirect
282. C₂×Q₁₆	C₂×Dic₇	semidirect
285. C₂×SD₁₆	C₂×Dic₇	semidirect
288. C₂×D₈	C₂×Dic₇	semidirect
423. C₂×C₇	#2957	semidirect
474. C₇	C₂×#2957	semidirect
501. C₂	#11741355	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×#135	2
C₂×#90510	2
C₂×#90008	2
#11741355	2
C₂×#89969	2
C₂×#89968	2
C₂²×#6393	2
C₂×#89873	2
C₂×#2957	7

Subgroups — C2×#11741355 #14218117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11741355 #14218117