Subgroups — C₂×C₇×#3093 #13237724

Order 1792.

2346 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#525	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3093	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#485	C₂	1	4	yes	maximal, complemented
5	C₂×C₇×#482	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#428	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#417	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#407	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
11	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
12	C₇×#525	—	2	4	no	—
13	C₇×#525	C₂²	1	8	yes	—
14	C₂×C₇×#123	—	2	1	no	—
15	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₇×#121	C₂²	1	2	yes	—
17	C₂×C₇×#120	—	2	1	no	—
18	C₂×C₄×C₇×D₄	—	2	2	no	—
19	C₂×C₇×#117	—	2	2	no	—
20	C₂×C₇×#117	—	2	4	no	—
21	C₂×C₇×#117	C₂²	1	1	yes	characteristic
22	C₂×C₇×#117	C₂²	1	4	yes	—
23	C₂×C₇×#117	C₂²	1	8	yes	complemented
24	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
26	C₂²×C₄²×C₇	—	2	1	no	—
27	C₇×#485	C₂²	1	32	yes	complemented
28	C₇×#482	C₂²	1	32	yes	complemented
29	C₇×#428	C₂²	1	16	yes	complemented
30	C₂×C₇×#107	C₂²	1	4	yes	complemented
31	C₂×C₇×#106	C₂²	1	4	yes	complemented
32	C₇×#417	C₂²	1	16	yes	complemented
33	C₂×C₇×#103	C₂²	1	4	yes	complemented
34	C₂×C₇×#102	C₂²	1	4	yes	complemented
35	C₇×#407	C₂²	1	8	yes	complemented
36	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	—
37	C₂×#3093	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂⁵×C₇	D₄	1	1	yes	characteristic
39	C₂×C₇×#41	—	2	2	no	—
40	C₂×C₇×#41	—	2	8	no	—
41	C₂×C₇×#41	C₂³	1	4	yes	—
42	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
43	C₂²×C₇×D₄	—	2	1	no	—
44	C₂²×C₇×D₄	—	2	2	no	—
45	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₇	—	2	8	no	—
47	C₂³×C₄×C₇	—	2	2	no	—
48	C₂³×C₄×C₇	—	2	1	no	—
49	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₇	D₄	1	2	yes	—
51	C₂³×C₄×C₇	D₄	1	4	yes	—
52	C₂³×C₄×C₇	C₂³	1	2	yes	—
53	C₂³×C₄×C₇	C₂³	1	4	yes	—
54	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
55	C₂×C₇×M₁₆	—	2	8	no	—
56	C₂×C₇×M₁₆	C₂³	1	8	yes	—
57	C₂²×C₇×C₈	C₂³	1	4	yes	—
58	C₇×#123	—	2	8	no	—
59	C₇×C₂²⋊Q₈	—	2	4	no	—
60	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
61	C₇×#121	—	2	4	no	—
62	C₇×#121	C₂³	1	8	yes	—
63	C₇×#120	—	2	8	no	—
64	C₄×C₇×D₄	—	2	16	no	—
65	C₇×#117	—	2	8	no	—
66	C₇×#117	—	2	16	no	—
67	C₇×#117	—	2	2	no	—
68	C₇×#117	C₂³	1	16	yes	—
69	C₇×#117	C₂³	1	4	yes	—
70	C₂×C₇×C₄⋊C₄	—	2	4	no	—
71	C₂×C₇×C₄⋊C₄	—	2	2	no	—
72	C₂×C₇×C₄⋊C₄	—	2	2	no	—
73	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
75	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
77	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
78	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₄²×C₇	—	2	4	no	—
82	C₂×C₄²×C₇	—	2	8	no	—
83	C₂×C₄²×C₇	—	2	1	no	—
84	C₇×#107	C₂³	1	16	yes	complemented
85	C₇×#106	C₂³	1	16	yes	complemented
86	C₇×#103	C₂³	1	16	yes	complemented
87	C₇×#102	C₂³	1	16	yes	complemented
88	C₇×C₂²⋊C₈	C₂³	1	16	yes	—
89	C₂×#525	C₂×C₇	1	1	yes	characteristic
90	C₂²×#117	C₂×C₇	1	1	yes	characteristic, complemented
91	#3093	C₂×C₇	1	16	yes	direct product factor
92	C₂×#485	C₂×C₇	1	4	yes	complemented
93	C₂×#482	C₂×C₇	1	4	yes	complemented
94	C₂×#428	C₂×C₇	1	2	yes	complemented
95	C₂×#417	C₂×C₇	1	2	yes	complemented
96	C₂×#407	C₂×C₇	1	1	yes	characteristic, complemented
97	C₂⁴×C₇	—	2	4	no	—
98	C₂⁴×C₇	—	2	1	no	—
99	C₂⁴×C₇	—	4	4	no	—
100	C₂⁴×C₇	C₂×D₄	1	2	yes	—
101	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
102	C₂⁴×C₇	C₂×D₄	1	4	yes	—
103	C₇×#41	—	2	16	no	—
104	C₇×#41	—	4	8	no	—
105	C₂×C₇×Q₈	—	2	1	no	—
106	C₂×C₇×Q₈	—	2	4	no	—
107	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
108	C₂×C₇×D₄	—	2	8	no	—
109	C₂×C₇×D₄	—	2	4	no	—
110	C₂×C₇×D₄	—	2	1	no	—
111	C₂×C₇×D₄	—	2	4	no	—
112	C₂×C₇×D₄	—	4	8	no	—
113	C₂×C₇×D₄	—	4	4	no	—
114	C₂×C₇×D₄	C₂⁴	1	2	yes	—
115	C₂²×C₄×C₇	—	2	4	no	—
116	C₂²×C₄×C₇	—	2	8	no	—
117	C₂²×C₄×C₇	—	2	16	no	—
118	C₂²×C₄×C₇	—	2	8	no	—
119	C₂²×C₄×C₇	—	2	16	no	—
120	C₂²×C₄×C₇	—	2	8	no	—
121	C₂²×C₄×C₇	—	2	4	no	—
122	C₂²×C₄×C₇	—	2	2	no	—
123	C₂²×C₄×C₇	—	2	1	no	—
124	C₂²×C₄×C₇	—	2	4	no	—
125	C₂²×C₄×C₇	—	4	8	no	—
126	C₂²×C₄×C₇	—	4	4	no	—
127	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
129	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	#41	1	8	yes	—
134	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
137	C₇×M₁₆	—	2	16	no	—
138	C₂×C₇×C₈	—	2	8	no	—
139	C₂×C₇×C₈	C₂⁴	1	8	yes	—
140	C₇×C₄⋊C₄	—	2	8	no	—
141	C₇×C₄⋊C₄	—	2	4	no	—
142	C₇×C₄⋊C₄	—	2	8	no	—
143	C₇×C₄⋊C₄	—	2	2	no	—
144	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
145	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
146	C₇×C₂²⋊C₄	—	2	16	no	—
147	C₇×C₂²⋊C₄	—	2	4	no	—
148	C₇×C₂²⋊C₄	—	2	8	no	—
149	C₇×C₂²⋊C₄	—	2	8	no	—
150	C₄²×C₇	—	2	16	no	—
151	C₄²×C₇	—	2	4	no	—
152	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
153	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
154	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
155	#525	—	2	4	no	—
156	#525	C₂²×C₇	1	8	yes	—
157	C₂×#123	—	2	1	no	—
158	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
159	C₂×#121	C₂²×C₇	1	2	yes	—
160	C₂×#120	—	2	1	no	—
161	C₂×C₄×D₄	—	2	2	no	—
162	C₂×#117	—	2	2	no	—
163	C₂×#117	—	2	4	no	—
164	C₂×#117	C₂²×C₇	1	4	yes	—
165	C₂×#117	C₂²×C₇	1	1	yes	characteristic
166	C₂×#117	C₂²×C₇	1	8	yes	complemented
167	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
168	C₂²×C₂²⋊C₄	—	2	1	no	—
169	C₂²×C₄²	—	2	1	no	—
170	#485	C₂²×C₇	1	32	yes	complemented
171	#482	C₂²×C₇	1	32	yes	complemented
172	#428	C₂²×C₇	1	16	yes	complemented
173	C₂×#107	C₂²×C₇	1	4	yes	complemented
174	C₂×#106	C₂²×C₇	1	4	yes	complemented
175	#417	C₂²×C₇	1	16	yes	complemented
176	C₂×#103	C₂²×C₇	1	4	yes	complemented
177	C₂×#102	C₂²×C₇	1	4	yes	complemented
178	#407	C₂²×C₇	1	8	yes	complemented
179	C₂×C₂²⋊C₈	C₂²×C₇	1	4	yes	—
180	C₂³×C₇	—	2	4	no	—
181	C₂³×C₇	—	2	8	no	—
182	C₂³×C₇	—	2	4	no	—
183	C₂³×C₇	—	2	4	no	—
184	C₂³×C₇	—	2	4	no	—
185	C₂³×C₇	—	2	2	no	—
186	C₂³×C₇	—	4	8	no	—
187	C₂³×C₇	—	4	16	no	—
188	C₂³×C₇	—	4	2	no	—
189	C₂³×C₇	—	4	4	no	—
190	C₂³×C₇	#123	1	4	yes	—
191	C₂³×C₇	C₂²×D₄	1	4	yes	—
192	C₂³×C₇	C₂²×D₄	1	2	yes	—
193	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
194	C₇×Q₈	—	2	4	no	—
195	C₇×Q₈	—	4	2	no	—
196	C₇×D₄	—	2	4	no	—
197	C₇×D₄	—	4	16	no	—
198	C₇×D₄	—	4	8	no	—
199	C₇×D₄	—	4	2	no	—
200	C₂×C₄×C₇	—	2	8	no	—
201	C₂×C₄×C₇	—	2	4	no	—
202	C₂×C₄×C₇	—	2	16	no	—
203	C₂×C₄×C₇	—	2	8	no	—
204	C₂×C₄×C₇	—	2	8	no	—
205	C₂×C₄×C₇	—	2	8	no	—
206	C₂×C₄×C₇	—	2	4	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	4	16	no	—
209	C₂×C₄×C₇	—	4	2	no	—
210	C₂×C₄×C₇	—	4	8	no	—
211	C₂×C₄×C₇	—	4	4	no	—
212	C₂×C₄×C₇	—	4	8	no	—
213	C₂×C₄×C₇	#123	1	4	yes	—
214	C₂×C₄×C₇	#123	1	8	yes	—
215	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
216	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇	C₂×#41	1	4	yes	—
219	C₂×C₄×C₇	C₂×#41	1	8	yes	—
220	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
221	C₇×C₈	—	2	8	no	—
222	C₂⁵	C₇×D₄	1	1	yes	characteristic
223	C₂×#41	—	2	2	no	—
224	C₂×#41	—	2	8	no	—
225	C₂×#41	C₂³×C₇	1	4	yes	—
226	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
227	C₂²×D₄	—	2	2	no	—
228	C₂²×D₄	—	2	1	no	—
229	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
230	C₂³×C₄	—	2	8	no	—
231	C₂³×C₄	—	2	2	no	—
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	C₇×D₄	1	2	yes	—
234	C₂³×C₄	C₇×D₄	1	4	yes	—
235	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₇	1	2	yes	—
237	C₂³×C₄	C₂³×C₇	1	4	yes	—
238	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
239	C₂×M₁₆	—	2	8	no	—
240	C₂×M₁₆	C₂³×C₇	1	8	yes	—
241	C₂²×C₈	C₂³×C₇	1	4	yes	—
242	#123	—	2	8	no	—
243	C₂²⋊Q₈	—	2	4	no	—
244	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
245	#121	—	2	4	no	—
246	#121	C₂³×C₇	1	8	yes	—
247	#120	—	2	8	no	—
248	C₄×D₄	—	2	16	no	—
249	#117	—	2	8	no	—
250	#117	—	2	16	no	—
251	#117	—	2	2	no	—
252	#117	C₂³×C₇	1	16	yes	—
253	#117	C₂³×C₇	1	4	yes	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	4	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
258	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
259	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	4	no	—
261	C₂×C₂²⋊C₄	—	2	8	no	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	—	2	4	no	—
266	C₂×C₄²	—	2	8	no	—
267	C₂×C₄²	—	2	1	no	—
268	#107	C₂³×C₇	1	16	yes	complemented
269	#106	C₂³×C₇	1	16	yes	complemented
270	#103	C₂³×C₇	1	16	yes	complemented
271	#102	C₂³×C₇	1	16	yes	complemented
272	C₂²⋊C₈	C₂³×C₇	1	16	yes	—
273	C₂²×C₇	—	2	8	no	—
274	C₂²×C₇	—	2	4	no	—
275	C₂²×C₇	—	2	4	no	—
276	C₂²×C₇	—	2	4	no	—
277	C₂²×C₇	—	2	4	no	—
278	C₂²×C₇	—	4	16	no	—
279	C₂²×C₇	—	4	8	no	—
280	C₂²×C₇	—	4	2	no	—
281	C₂²×C₇	—	4	4	no	—
282	C₂²×C₇	—	8	4	no	—
283	C₂²×C₇	C₂×#123	1	4	yes	—
284	C₂²×C₇	C₂×#123	1	2	yes	—
285	C₂²×C₇	#575	1	4	yes	—
286	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
287	C₄×C₇	—	2	4	no	—
288	C₄×C₇	—	4	2	no	—
289	C₄×C₇	—	4	8	no	—
290	C₄×C₇	—	4	4	no	—
291	C₄×C₇	C₂×#123	1	4	yes	—
292	C₄×C₇	C₂×#123	1	2	yes	—
293	C₄×C₇	C₂²×#41	1	2	yes	—
294	C₂⁴	—	2	4	no	—
295	C₂⁴	—	2	1	no	—
296	C₂⁴	—	4	4	no	—
297	C₂⁴	C₂×C₇×D₄	1	2	yes	—
298	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
299	C₂⁴	C₂×C₇×D₄	1	4	yes	—
300	#41	—	2	16	no	—
301	#41	—	4	8	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
305	C₂×D₄	—	2	8	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	4	8	no	—
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	C₂⁴×C₇	1	2	yes	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	16	no	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	—	2	16	no	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	4	8	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
325	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
326	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
327	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
328	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
330	C₂²×C₄	C₇×#41	1	8	yes	—
331	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
332	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
333	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
334	M₁₆	—	2	16	no	—
335	C₂×C₈	—	2	8	no	—
336	C₂×C₈	C₂⁴×C₇	1	8	yes	—
337	C₄⋊C₄	—	2	8	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
342	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
343	C₂²⋊C₄	—	2	16	no	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	2	8	no	—
346	C₂²⋊C₄	—	2	8	no	—
347	C₄²	—	2	16	no	—
348	C₄²	—	2	4	no	—
349	C₂×C₇	—	2	4	no	—
350	C₂×C₇	—	4	4	no	—
351	C₂×C₇	—	8	2	no	—
352	C₂×C₇	#3093	1	4	yes	direct product factor
353	C₂×C₇	C₂²×#123	1	1	yes	characteristic
354	C₂×C₇	C₂×#575	1	2	yes	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	4	8	no	—
362	C₂³	—	4	16	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	4	no	—
365	C₂³	C₇×#123	1	4	yes	—
366	C₂³	C₂²×C₇×D₄	1	4	yes	—
367	C₂³	C₂²×C₇×D₄	1	2	yes	—
368	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
369	Q₈	—	2	4	no	—
370	Q₈	—	4	2	no	—
371	D₄	—	2	4	no	—
372	D₄	—	4	16	no	—
373	D₄	—	4	8	no	—
374	D₄	—	4	2	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	16	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	16	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	8	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	8	no	—
388	C₂×C₄	C₇×#123	1	4	yes	—
389	C₂×C₄	C₇×#123	1	8	yes	—
390	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
391	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
392	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
393	C₂×C₄	C₂×C₇×#41	1	4	yes	—
394	C₂×C₄	C₂×C₇×#41	1	8	yes	—
395	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
396	C₈	—	2	8	no	—
397	C₇	C₂×#3093	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²	—	2	4	no	—
399	C₂²	—	2	8	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	4	16	no	—
404	C₂²	—	4	8	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	4	no	—
408	C₂²	C₂×C₇×#123	1	4	yes	—
409	C₂²	C₂×C₇×#123	1	2	yes	—
410	C₂²	C₇×#575	1	4	yes	—
411	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	4	8	no	—
414	C₄	—	4	4	no	—
415	C₄	—	4	2	no	—
416	C₄	C₂×C₇×#123	1	4	yes	—
417	C₄	C₂×C₇×#123	1	2	yes	—
418	C₄	C₂²×C₇×#41	1	2	yes	—
419	C₂	—	2	4	no	—
420	C₂	—	4	4	no	—
421	C₂	—	8	2	no	—
422	C₂	C₇×#3093	1	4	yes	direct product factor
423	C₂	C₂²×C₇×#123	1	1	yes	characteristic
424	C₂	C₂×C₇×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂⁴×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₇×#117	C₂	semidirect
3. C₇×#3093	C₂	direct (N × H)
4. C₂×C₇×#485	C₂	semidirect
5. C₂×C₇×#482	C₂	semidirect
6. C₂×C₇×#428	C₂	semidirect
7. C₂×C₇×#417	C₂	semidirect
8. C₂×C₇×#407	C₂	semidirect
23. C₂×C₇×#117	C₂²	semidirect
27. C₇×#485	C₂²	semidirect
28. C₇×#482	C₂²	semidirect
29. C₇×#428	C₂²	semidirect
30. C₂×C₇×#107	C₂²	semidirect
31. C₂×C₇×#106	C₂²	semidirect
32. C₇×#417	C₂²	semidirect
33. C₂×C₇×#103	C₂²	semidirect
34. C₂×C₇×#102	C₂²	semidirect
35. C₇×#407	C₂²	semidirect
37. C₂×#3093	C₇	direct (N × H)
84. C₇×#107	C₂³	semidirect
85. C₇×#106	C₂³	semidirect
86. C₇×#103	C₂³	semidirect
87. C₇×#102	C₂³	semidirect
90. C₂²×#117	C₂×C₇	semidirect
91. #3093	C₂×C₇	direct (N × H)
92. C₂×#485	C₂×C₇	semidirect
93. C₂×#482	C₂×C₇	semidirect
94. C₂×#428	C₂×C₇	semidirect
95. C₂×#417	C₂×C₇	semidirect
96. C₂×#407	C₂×C₇	semidirect
166. C₂×#117	C₂²×C₇	semidirect
170. #485	C₂²×C₇	semidirect
171. #482	C₂²×C₇	semidirect
172. #428	C₂²×C₇	semidirect
173. C₂×#107	C₂²×C₇	semidirect
174. C₂×#106	C₂²×C₇	semidirect
175. #417	C₂²×C₇	semidirect
176. C₂×#103	C₂²×C₇	semidirect
177. C₂×#102	C₂²×C₇	semidirect
178. #407	C₂²×C₇	semidirect
268. #107	C₂³×C₇	semidirect
269. #106	C₂³×C₇	semidirect
270. #103	C₂³×C₇	semidirect
271. #102	C₂³×C₇	semidirect
352. C₂×C₇	#3093	direct (N × H)
397. C₇	C₂×#3093	direct (N × H)
422. C₂	C₇×#3093	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×#525	2
C₂²×C₇×#117	2
C₇×#3093	2
C₂×C₇×#485	2
C₂×C₇×#482	2
C₂×C₇×#428	2
C₂×C₇×#417	2
C₂×C₇×#407	2
C₂×#3093	7

Subgroups — C2×C7×#3093 #13237724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3093 #13237724