Subgroups — C₂×C₇×#3334 #13238441

Order 1792.

2374 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#547	C₂	1	2	yes	maximal, complemented
2	C₇×#3334	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#480	C₂	1	4	yes	maximal, complemented
5	C₂×C₇×#474	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#466	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×#107	C₂	1	2	yes	maximal, complemented
10	C₂²×C₇×#41	—	2	2	no	—
11	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
12	C₂³×C₇×C₈	C₂²	1	2	yes	—
13	C₇×#547	—	2	8	no	—
14	C₇×#547	C₂²	1	16	yes	complemented
15	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₇×#123	—	2	4	no	—
17	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
18	C₂×C₇×#121	C₂²	1	4	yes	—
19	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
20	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	—
22	C₇×#500	C₂²	1	8	yes	complemented
23	C₇×#480	C₂²	1	32	yes	complemented
24	C₇×#474	C₂²	1	16	yes	complemented
25	C₇×#466	C₂²	1	16	yes	complemented
26	C₄×C₇×D₈	C₂²	1	8	yes	complemented
27	C₇×C₈×D₄	C₂²	1	8	yes	complemented
28	C₂×C₇×#107	C₂²	1	2	yes	—
29	C₂×C₇×#107	C₂²	1	2	yes	—
30	C₂×C₇×#107	C₂²	1	1	yes	characteristic
31	C₂×C₇×#107	C₂²	1	4	yes	—
32	C₂×C₇×#107	C₂²	1	16	yes	complemented
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×#102	C₂²	1	2	yes	—
35	C₂×C₇×#102	C₂²	1	4	yes	—
36	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
38	C₂×#3334	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×C₇×#41	—	2	16	no	—
40	C₂×C₇×#41	—	4	16	no	—
41	C₂²×C₇×Q₈	—	2	2	no	—
42	C₂²×C₇×D₄	—	2	4	no	—
43	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
44	C₂²×C₇×D₄	C₂³	1	2	yes	—
45	C₂³×C₄×C₇	—	2	4	no	—
46	C₂³×C₄×C₇	—	2	2	no	—
47	C₂³×C₄×C₇	C₂³	1	2	yes	—
48	C₂×C₇×D₈	—	2	4	no	—
49	C₂×C₇×D₈	C₂³	1	4	yes	—
50	C₂²×C₇×C₈	—	2	8	no	—
51	C₂²×C₇×C₈	C₂³	1	8	yes	—
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂³	1	2	yes	—
54	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
55	C₇×C₄⋊Q₈	—	2	4	no	—
56	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
57	C₇×#123	—	2	32	no	—
58	C₇×C₂²⋊Q₈	—	2	16	no	—
59	C₇×#121	—	2	8	no	—
60	C₇×#121	C₂³	1	16	yes	—
61	C₄×C₇×D₄	—	2	4	no	—
62	C₄×C₇×D₄	D₄	1	4	yes	—
63	C₄×C₇×D₄	C₂³	1	8	yes	—
64	C₄×C₇×D₄	C₂³	1	4	yes	—
65	C₂×C₇×C₄⋊C₄	—	2	4	no	—
66	C₂×C₇×C₄⋊C₄	—	2	8	no	—
67	C₂×C₇×C₄⋊C₄	—	2	2	no	—
68	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
74	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₇×#107	C₂³	1	8	yes	—
77	C₇×#107	C₂³	1	16	yes	—
78	C₇×#107	C₂³	1	8	yes	—
79	C₇×#107	C₂³	1	4	yes	—
80	C₇×C₄⋊C₈	C₂³	1	4	yes	—
81	C₇×#102	C₂³	1	16	yes	—
82	C₇×#102	C₂³	1	8	yes	—
83	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
84	C₄×C₇×C₈	C₂³	1	4	yes	—
85	C₂×#547	C₂×C₇	1	2	yes	complemented
86	#3334	C₂×C₇	1	16	yes	direct product factor
87	C₂×#500	C₂×C₇	1	1	yes	characteristic, complemented
88	C₂×#480	C₂×C₇	1	4	yes	complemented
89	C₂×#474	C₂×C₇	1	2	yes	complemented
90	C₂×#466	C₂×C₇	1	2	yes	complemented
91	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
92	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
93	C₂²×#107	C₂×C₇	1	2	yes	complemented
94	C₂⁴×C₇	—	2	2	no	—
95	C₂⁴×C₇	C₂×D₄	1	2	yes	—
96	C₇×#41	—	4	64	no	—
97	C₂×C₇×Q₈	—	2	8	no	—
98	C₂×C₇×Q₈	—	4	8	no	—
99	C₂×C₇×D₄	—	2	16	no	—
100	C₂×C₇×D₄	—	2	2	no	—
101	C₂×C₇×D₄	—	2	4	no	—
102	C₂×C₇×D₄	—	2	4	no	—
103	C₂×C₇×D₄	—	4	16	no	—
104	C₂×C₇×D₄	D₈	1	8	yes	complemented
105	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
106	C₂×C₇×D₄	C₂⁴	1	4	yes	—
107	C₂²×C₄×C₇	—	2	4	no	—
108	C₂²×C₄×C₇	—	2	4	no	—
109	C₂²×C₄×C₇	—	2	16	no	—
110	C₂²×C₄×C₇	—	2	2	no	—
111	C₂²×C₄×C₇	—	2	4	no	—
112	C₂²×C₄×C₇	—	2	8	no	—
113	C₂²×C₄×C₇	—	4	16	no	—
114	C₂²×C₄×C₇	—	4	8	no	—
115	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
121	C₇×D₈	—	2	8	no	—
122	C₂×C₇×C₈	—	2	4	no	—
123	C₂×C₇×C₈	—	2	2	no	—
124	C₂×C₇×C₈	—	2	16	no	—
125	C₂×C₇×C₈	#41	1	4	yes	complemented
126	C₂×C₇×C₈	C₂⁴	1	2	yes	—
127	C₂×C₇×C₈	C₂⁴	1	4	yes	—
128	C₂×C₇×C₈	C₂⁴	1	2	yes	—
129	C₇×C₄⋊C₄	—	2	2	no	—
130	C₇×C₄⋊C₄	—	2	4	no	—
131	C₇×C₄⋊C₄	—	2	16	no	—
132	C₇×C₄⋊C₄	—	2	8	no	—
133	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
134	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
135	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
136	C₇×C₂²⋊C₄	—	2	8	no	—
137	C₇×C₂²⋊C₄	—	2	16	no	—
138	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
139	C₄²×C₇	C₂×D₄	1	2	yes	—
140	C₄²×C₇	C₂⁴	1	2	yes	—
141	C₂²×#41	—	2	2	no	—
142	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
143	C₂³×C₈	C₂²×C₇	1	2	yes	—
144	#547	—	2	8	no	—
145	#547	C₂²×C₇	1	16	yes	complemented
146	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
147	C₂×#123	—	2	4	no	—
148	C₂×C₂²⋊Q₈	—	2	2	no	—
149	C₂×#121	C₂²×C₇	1	4	yes	—
150	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
151	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
152	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	—
153	#500	C₂²×C₇	1	8	yes	complemented
154	#480	C₂²×C₇	1	32	yes	complemented
155	#474	C₂²×C₇	1	16	yes	complemented
156	#466	C₂²×C₇	1	16	yes	complemented
157	C₄×D₈	C₂²×C₇	1	8	yes	complemented
158	C₈×D₄	C₂²×C₇	1	8	yes	complemented
159	C₂×#107	C₂²×C₇	1	2	yes	—
160	C₂×#107	C₂²×C₇	1	4	yes	—
161	C₂×#107	C₂²×C₇	1	2	yes	—
162	C₂×#107	C₂²×C₇	1	1	yes	characteristic
163	C₂×#107	C₂²×C₇	1	16	yes	complemented
164	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
165	C₂×#102	C₂²×C₇	1	2	yes	—
166	C₂×#102	C₂²×C₇	1	4	yes	—
167	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
168	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
169	C₂³×C₇	—	2	4	no	—
170	C₂³×C₇	—	2	4	no	—
171	C₂³×C₇	—	2	4	no	—
172	C₂³×C₇	—	4	4	no	—
173	C₂³×C₇	—	4	4	no	—
174	C₂³×C₇	—	4	4	no	—
175	C₂³×C₇	C₂×D₈	1	8	yes	—
176	C₂³×C₇	C₂²×D₄	1	4	yes	—
177	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
178	C₇×Q₈	—	4	16	no	—
179	C₇×D₄	—	2	4	no	—
180	C₇×D₄	—	2	4	no	—
181	C₇×D₄	—	4	32	no	—
182	C₇×D₄	—	4	4	no	—
183	C₇×D₄	C₂×D₈	1	16	yes	complemented
184	C₂×C₄×C₇	—	2	4	no	—
185	C₂×C₄×C₇	—	2	2	no	—
186	C₂×C₄×C₇	—	2	8	no	—
187	C₂×C₄×C₇	—	2	4	no	—
188	C₂×C₄×C₇	—	2	4	no	—
189	C₂×C₄×C₇	—	2	4	no	—
190	C₂×C₄×C₇	—	2	8	no	—
191	C₂×C₄×C₇	—	4	4	no	—
192	C₂×C₄×C₇	—	4	8	no	—
193	C₂×C₄×C₇	—	4	32	no	—
194	C₂×C₄×C₇	—	4	16	no	—
195	C₂×C₄×C₇	C₂×D₈	1	4	yes	—
196	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
198	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₇	C₂×#41	1	2	yes	—
201	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
202	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
203	C₇×C₈	—	2	4	no	—
204	C₇×C₈	—	2	2	no	—
205	C₇×C₈	C₂×#41	1	4	yes	complemented
206	C₂×#41	—	2	16	no	—
207	C₂×#41	—	4	16	no	—
208	C₂²×Q₈	—	2	2	no	—
209	C₂²×D₄	—	2	4	no	—
210	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
211	C₂²×D₄	C₂³×C₇	1	2	yes	—
212	C₂³×C₄	—	2	4	no	—
213	C₂³×C₄	—	2	2	no	—
214	C₂³×C₄	C₂³×C₇	1	2	yes	—
215	C₂×D₈	—	2	4	no	—
216	C₂×D₈	C₂³×C₇	1	4	yes	—
217	C₂²×C₈	—	2	8	no	—
218	C₂²×C₈	C₂³×C₇	1	2	yes	—
219	C₂²×C₈	C₂³×C₇	1	8	yes	—
220	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
222	C₄⋊Q₈	—	2	4	no	—
223	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
224	#123	—	2	32	no	—
225	C₂²⋊Q₈	—	2	16	no	—
226	#121	—	2	8	no	—
227	#121	C₂³×C₇	1	16	yes	—
228	C₄×D₄	—	2	4	no	—
229	C₄×D₄	C₇×D₄	1	4	yes	—
230	C₄×D₄	C₂³×C₇	1	8	yes	—
231	C₄×D₄	C₂³×C₇	1	4	yes	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	8	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
237	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
238	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₂²⋊C₄	—	2	4	no	—
241	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
242	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
243	#107	C₂³×C₇	1	4	yes	—
244	#107	C₂³×C₇	1	8	yes	—
245	#107	C₂³×C₇	1	16	yes	—
246	#107	C₂³×C₇	1	8	yes	—
247	C₄⋊C₈	C₂³×C₇	1	4	yes	—
248	#102	C₂³×C₇	1	8	yes	—
249	#102	C₂³×C₇	1	16	yes	—
250	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
251	C₄×C₈	C₂³×C₇	1	4	yes	—
252	C₂²×C₇	—	2	16	no	—
253	C₂²×C₇	—	2	4	no	—
254	C₂²×C₇	—	2	4	no	—
255	C₂²×C₇	—	4	4	no	—
256	C₂²×C₇	—	4	4	no	—
257	C₂²×C₇	—	4	4	no	—
258	C₂²×C₇	—	8	8	no	—
259	C₂²×C₇	#547	1	2	yes	—
260	C₂²×C₇	C₂²×D₈	1	8	yes	—
261	C₂²×C₇	C₂²×D₈	1	2	yes	—
262	C₂²×C₇	#578	1	2	yes	—
263	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
264	C₄×C₇	—	2	4	no	—
265	C₄×C₇	—	2	2	no	—
266	C₄×C₇	—	4	4	no	—
267	C₄×C₇	—	4	8	no	—
268	C₄×C₇	#547	1	2	yes	—
269	C₄×C₇	C₂²×D₈	1	4	yes	—
270	C₄×C₇	C₂²×#41	1	1	yes	characteristic
271	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
272	C₂⁴	—	2	2	no	—
273	C₂⁴	C₂×C₇×D₄	1	2	yes	—
274	#41	—	4	64	no	—
275	C₂×Q₈	—	2	8	no	—
276	C₂×Q₈	—	4	8	no	—
277	C₂×D₄	—	2	16	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	4	16	no	—
282	C₂×D₄	C₇×D₈	1	8	yes	complemented
283	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
284	C₂×D₄	C₂⁴×C₇	1	4	yes	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	16	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	4	16	no	—
292	C₂²×C₄	—	4	8	no	—
293	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
295	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
296	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
297	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
298	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
299	D₈	—	2	8	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	16	no	—
303	C₂×C₈	C₇×#41	1	4	yes	complemented
304	C₂×C₈	C₂⁴×C₇	1	2	yes	—
305	C₂×C₈	C₂⁴×C₇	1	4	yes	—
306	C₂×C₈	C₂⁴×C₇	1	2	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	16	no	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
312	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
313	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
314	C₂²⋊C₄	—	2	8	no	—
315	C₂²⋊C₄	—	2	16	no	—
316	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
317	C₄²	C₂×C₇×D₄	1	2	yes	—
318	C₄²	C₂⁴×C₇	1	2	yes	—
319	C₂×C₇	—	2	8	no	—
320	C₂×C₇	—	8	4	no	—
321	C₂×C₇	#3334	1	4	yes	direct product factor
322	C₂×C₇	C₂×#547	1	1	yes	characteristic
323	C₂×C₇	C₂³×D₈	1	1	yes	characteristic
324	C₂×C₇	C₂×#578	1	1	yes	characteristic
325	C₂³	—	2	4	no	—
326	C₂³	—	2	4	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	4	4	no	—
329	C₂³	—	4	4	no	—
330	C₂³	—	4	4	no	—
331	C₂³	C₂×C₇×D₈	1	8	yes	—
332	C₂³	C₂²×C₇×D₄	1	4	yes	—
333	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
334	Q₈	—	4	16	no	—
335	D₄	—	2	4	no	—
336	D₄	—	2	4	no	—
337	D₄	—	4	32	no	—
338	D₄	—	4	4	no	—
339	D₄	C₂×C₇×D₈	1	16	yes	complemented
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	—	4	32	no	—
350	C₂×C₄	—	4	16	no	—
351	C₂×C₄	C₂×C₇×D₈	1	4	yes	—
352	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
353	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
354	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
356	C₂×C₄	C₂×C₇×#41	1	2	yes	—
357	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
358	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
359	C₈	—	2	4	no	—
360	C₈	—	2	2	no	—
361	C₈	C₂×C₇×#41	1	4	yes	complemented
362	C₇	C₂×#3334	1	1	yes	characteristic, direct product factor, Sylow
363	C₂²	—	2	4	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	16	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	8	8	no	—
370	C₂²	C₇×#547	1	2	yes	—
371	C₂²	C₂²×C₇×D₈	1	8	yes	—
372	C₂²	C₂²×C₇×D₈	1	2	yes	—
373	C₂²	C₇×#578	1	2	yes	—
374	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
375	C₄	—	2	2	no	—
376	C₄	—	2	4	no	—
377	C₄	—	4	4	no	—
378	C₄	—	4	8	no	—
379	C₄	C₇×#547	1	2	yes	—
380	C₄	C₂²×C₇×D₈	1	4	yes	—
381	C₄	C₂²×C₇×#41	1	1	yes	characteristic
382	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
383	C₂	—	2	8	no	—
384	C₂	—	8	4	no	—
385	C₂	C₇×#3334	1	4	yes	direct product factor
386	C₂	C₂×C₇×#547	1	1	yes	characteristic
387	C₂	C₂³×C₇×D₈	1	1	yes	characteristic
388	C₂	C₂×C₇×#578	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#547	C₂	semidirect
2. C₇×#3334	C₂	direct (N × H)
3. C₂×C₇×#500	C₂	semidirect
4. C₂×C₇×#480	C₂	semidirect
5. C₂×C₇×#474	C₂	semidirect
6. C₂×C₇×#466	C₂	semidirect
7. C₂×C₄×C₇×D₈	C₂	semidirect
8. C₂×C₇×C₈×D₄	C₂	semidirect
9. C₂²×C₇×#107	C₂	semidirect
14. C₇×#547	C₂²	semidirect
22. C₇×#500	C₂²	semidirect
23. C₇×#480	C₂²	semidirect
24. C₇×#474	C₂²	semidirect
25. C₇×#466	C₂²	semidirect
26. C₄×C₇×D₈	C₂²	semidirect
27. C₇×C₈×D₄	C₂²	semidirect
32. C₂×C₇×#107	C₂²	semidirect
38. C₂×#3334	C₇	direct (N × H)
85. C₂×#547	C₂×C₇	semidirect
86. #3334	C₂×C₇	direct (N × H)
87. C₂×#500	C₂×C₇	semidirect
88. C₂×#480	C₂×C₇	semidirect
89. C₂×#474	C₂×C₇	semidirect
90. C₂×#466	C₂×C₇	semidirect
91. C₂×C₄×D₈	C₂×C₇	semidirect
92. C₂×C₈×D₄	C₂×C₇	semidirect
93. C₂²×#107	C₂×C₇	semidirect
104. C₂×C₇×D₄	D₈	semidirect
125. C₂×C₇×C₈	#41	semidirect
145. #547	C₂²×C₇	semidirect
153. #500	C₂²×C₇	semidirect
154. #480	C₂²×C₇	semidirect
155. #474	C₂²×C₇	semidirect
156. #466	C₂²×C₇	semidirect
157. C₄×D₈	C₂²×C₇	semidirect
158. C₈×D₄	C₂²×C₇	semidirect
163. C₂×#107	C₂²×C₇	semidirect
183. C₇×D₄	C₂×D₈	semidirect
205. C₇×C₈	C₂×#41	semidirect
282. C₂×D₄	C₇×D₈	semidirect
303. C₂×C₈	C₇×#41	semidirect
321. C₂×C₇	#3334	direct (N × H)
339. D₄	C₂×C₇×D₈	semidirect
361. C₈	C₂×C₇×#41	semidirect
362. C₇	C₂×#3334	direct (N × H)
385. C₂	C₇×#3334	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×#547	2
C₇×#3334	2
C₂×C₇×#500	2
C₂×C₇×#480	2
C₂×C₇×#474	2
C₂×C₇×#466	2
C₂×C₄×C₇×D₈	2
C₂×C₇×C₈×D₄	2
C₂²×C₇×#107	2
C₂×#3334	7

Subgroups — C2×C7×#3334 #13238441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3334 #13238441