Subgroups — C₇×#23185 #13200401

Order 1792.

1238 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#493	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×D₈	C₂	1	2	yes	maximal, complemented
3	C₇×#2366	C₂	1	2	yes	maximal, complemented
4	C₇×#1982	C₂	1	2	yes	maximal, complemented
5	C₇×#1970	C₂	1	2	yes	maximal, complemented
6	C₇×#1879	C₂	1	4	yes	maximal, complemented
7	C₄×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×D₈	C₂²	1	2	yes	—
10	C₂²×C₇×D₈	C₂²	1	2	yes	—
11	C₂×C₇×#127	C₂²	1	2	yes	—
12	C₂×C₄×C₇×D₄	—	2	2	no	—
13	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
14	C₇×#493	C₄	1	8	yes	complemented
15	C₄×C₇×D₈	—	2	8	no	—
16	C₂×C₇×#107	C₂²	1	1	yes	characteristic
17	C₂×C₇×#107	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×#102	C₂²	1	4	yes	—
20	C₂×C₇×#102	C₂²	1	4	yes	—
21	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
23	C₇×#390	—	2	2	no	—
24	C₇×#390	C₂²	1	4	yes	—
25	C₇×#386	—	2	4	no	—
26	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
27	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₇×#340	C₂²	1	2	yes	—
29	C₇×#336	C₂²	1	2	yes	—
30	#23185	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂²×C₇×D₄	—	2	2	no	—
32	C₂²×C₇×D₄	—	2	2	no	—
33	C₂²×C₇×D₄	C₂³	1	4	yes	—
34	C₂³×C₄×C₇	—	2	4	no	—
35	C₂×C₇×D₈	—	2	4	no	—
36	C₂×C₇×D₈	—	2	4	no	—
37	C₂×C₇×D₈	—	4	2	no	—
38	C₂×C₇×D₈	—	4	2	no	—
39	C₂×C₇×D₈	C₂×C₄	1	8	yes	complemented
40	C₂×C₇×D₈	C₂×C₄	1	8	yes	complemented
41	C₂²×C₇×C₈	C₂³	1	2	yes	—
42	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
44	C₇×#127	—	2	4	no	—
45	C₇×#127	C₂×C₄	1	8	yes	complemented
46	C₄×C₇×D₄	—	2	8	no	—
47	C₄×C₇×D₄	—	4	4	no	—
48	C₄×C₇×D₄	—	4	8	no	—
49	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
50	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
51	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
52	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
53	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
54	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
55	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
56	C₂×C₄²×C₇	—	2	2	no	—
57	C₂×C₄²×C₇	C₂³	1	2	yes	—
58	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
59	C₇×#107	—	2	2	no	—
60	C₇×#107	D₄	1	4	yes	complemented
61	C₇×C₄⋊C₈	—	2	2	no	—
62	C₇×#102	—	2	8	no	—
63	C₇×#102	—	4	4	no	—
64	C₄×C₇×C₈	—	2	4	no	—
65	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
66	C₇×#95	—	2	2	no	—
67	C₇×#95	D₄	1	2	yes	—
68	C₂×#493	C₂×C₇	1	1	yes	characteristic
69	C₂×C₄×D₈	C₂×C₇	1	2	yes	complemented
70	#2366	C₂×C₇	1	2	yes	complemented
71	#1982	C₂×C₇	1	2	yes	complemented
72	#1970	C₂×C₇	1	2	yes	complemented
73	#1879	C₂×C₇	1	4	yes	complemented
74	C₄×#107	C₂×C₇	1	1	yes	characteristic, complemented
75	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
76	C₂⁴×C₇	—	2	4	no	—
77	C₂×C₇×D₄	—	2	8	no	—
78	C₂×C₇×D₄	—	2	8	no	—
79	C₂×C₇×D₄	—	2	4	no	—
80	C₂×C₇×D₄	—	2	4	no	—
81	C₂×C₇×D₄	—	2	4	no	—
82	C₂×C₇×D₄	—	2	4	no	—
83	C₂×C₇×D₄	—	2	4	no	—
84	C₂×C₇×D₄	—	4	4	no	—
85	C₂×C₇×D₄	—	4	4	no	—
86	C₂×C₇×D₄	—	8	2	no	—
87	C₂×C₇×D₄	—	8	2	no	—
88	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
89	C₂²×C₄×C₇	—	2	2	no	—
90	C₂²×C₄×C₇	—	2	2	no	—
91	C₂²×C₄×C₇	—	4	8	no	—
92	C₂²×C₄×C₇	—	4	8	no	—
93	C₂²×C₄×C₇	—	8	4	no	—
94	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
99	C₇×D₈	—	2	16	no	—
100	C₇×D₈	—	4	8	no	—
101	C₂×C₇×C₈	—	2	1	no	—
102	C₂×C₇×C₈	—	2	1	no	—
103	C₂×C₇×C₈	—	2	2	no	—
104	C₂×C₇×C₈	—	2	2	no	—
105	C₂×C₇×C₈	—	2	2	no	—
106	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
107	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
108	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
109	C₂×C₇×C₈	#41	1	2	yes	—
110	C₇×C₄⋊C₄	—	2	2	no	—
111	C₇×C₄⋊C₄	—	2	2	no	—
112	C₇×C₄⋊C₄	—	2	2	no	—
113	C₇×C₄⋊C₄	—	2	2	no	—
114	C₇×C₄⋊C₄	D₈	1	4	yes	complemented
115	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
116	C₇×C₂²⋊C₄	—	4	8	no	—
117	C₇×C₂²⋊C₄	—	4	8	no	—
118	C₇×C₂²⋊C₄	—	8	4	no	—
119	C₄²×C₇	—	2	2	no	—
120	C₄²×C₇	—	2	2	no	—
121	C₄²×C₇	—	4	4	no	—
122	C₄²×C₇	C₂²×C₄	1	2	yes	—
123	C₄²×C₇	#41	1	2	yes	—
124	C₂²×D₈	C₂²×C₇	1	2	yes	—
125	C₂²×D₈	C₂²×C₇	1	2	yes	—
126	C₂×#127	C₂²×C₇	1	2	yes	—
127	C₂×C₄×D₄	—	2	2	no	—
128	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
129	#493	C₄×C₇	1	8	yes	complemented
130	C₄×D₈	—	2	8	no	—
131	C₂×#107	C₂²×C₇	1	1	yes	characteristic
132	C₂×#107	C₂²×C₇	1	1	yes	characteristic
133	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
134	C₂×#102	C₂²×C₇	1	4	yes	—
135	C₂×#102	C₂²×C₇	1	4	yes	—
136	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
137	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
138	#390	—	2	2	no	—
139	#390	C₂²×C₇	1	4	yes	—
140	#386	—	2	4	no	—
141	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
142	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
143	#340	C₂²×C₇	1	2	yes	—
144	#336	C₂²×C₇	1	2	yes	—
145	C₂³×C₇	—	2	8	no	—
146	C₂³×C₇	—	4	4	no	—
147	C₂³×C₇	—	4	4	no	—
148	C₂³×C₇	—	4	4	no	—
149	C₂³×C₇	—	4	4	no	—
150	C₂³×C₇	—	4	4	no	—
151	C₂³×C₇	—	4	4	no	—
152	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
153	C₇×D₄	—	2	8	no	—
154	C₇×D₄	—	2	8	no	—
155	C₇×D₄	—	4	4	no	—
156	C₇×D₄	—	4	4	no	—
157	C₇×D₄	—	4	16	no	—
158	C₇×D₄	—	8	8	no	—
159	C₂×C₄×C₇	—	2	2	no	—
160	C₂×C₄×C₇	—	2	2	no	—
161	C₂×C₄×C₇	—	2	1	no	—
162	C₂×C₄×C₇	—	2	1	no	—
163	C₂×C₄×C₇	—	2	2	no	—
164	C₂×C₄×C₇	—	2	4	no	—
165	C₂×C₄×C₇	—	2	2	no	—
166	C₂×C₄×C₇	—	2	2	no	—
167	C₂×C₄×C₇	—	4	2	no	—
168	C₂×C₄×C₇	—	4	2	no	—
169	C₂×C₄×C₇	—	4	2	no	—
170	C₂×C₄×C₇	—	4	2	no	—
171	C₂×C₄×C₇	—	4	2	no	—
172	C₂×C₄×C₇	—	8	16	no	—
173	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₇	C₂×D₈	1	4	yes	—
176	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
177	C₂×C₄×C₇	#135	1	2	yes	—
178	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
184	C₇×C₈	—	2	2	no	—
185	C₇×C₈	—	4	2	no	—
186	C₇×C₈	C₄×D₄	1	4	yes	complemented
187	C₂²×D₄	—	2	2	no	—
188	C₂²×D₄	—	2	2	no	—
189	C₂²×D₄	C₂³×C₇	1	4	yes	—
190	C₂³×C₄	—	2	4	no	—
191	C₂×D₈	—	2	4	no	—
192	C₂×D₈	—	2	4	no	—
193	C₂×D₈	—	4	2	no	—
194	C₂×D₈	—	4	2	no	—
195	C₂×D₈	C₂×C₄×C₇	1	8	yes	complemented
196	C₂×D₈	C₂×C₄×C₇	1	8	yes	complemented
197	C₂²×C₈	C₂³×C₇	1	2	yes	—
198	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
199	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
200	#127	—	2	4	no	—
201	#127	C₂×C₄×C₇	1	8	yes	complemented
202	C₄×D₄	—	2	8	no	—
203	C₄×D₄	—	4	4	no	—
204	C₄×D₄	—	4	8	no	—
205	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
208	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
209	C₂×C₂²⋊C₄	—	2	4	no	—
210	C₂×C₂²⋊C₄	—	2	4	no	—
211	C₂×C₂²⋊C₄	—	2	4	no	—
212	C₂×C₄²	—	2	2	no	—
213	C₂×C₄²	C₂³×C₇	1	2	yes	—
214	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
215	#107	—	2	2	no	—
216	#107	C₇×D₄	1	4	yes	complemented
217	C₄⋊C₈	—	2	2	no	—
218	#102	—	2	8	no	—
219	#102	—	4	4	no	—
220	C₄×C₈	—	2	4	no	—
221	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
222	#95	—	2	2	no	—
223	#95	C₇×D₄	1	2	yes	—
224	C₂²×C₇	—	4	8	no	—
225	C₂²×C₇	—	4	8	no	—
226	C₂²×C₇	—	4	8	no	—
227	C₂²×C₇	—	8	4	no	—
228	C₂²×C₇	—	8	4	no	—
229	C₂²×C₇	—	8	4	no	—
230	C₂²×C₇	—	8	4	no	—
231	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
232	C₂²×C₇	D₄²	1	1	yes	characteristic
233	C₂²×C₇	#550	1	1	yes	characteristic
234	C₂²×C₇	C₂²×D₈	1	1	yes	characteristic
235	C₂²×C₇	C₂×#135	1	1	yes	characteristic
236	C₂²×C₇	#576	1	1	yes	characteristic
237	C₂²×C₇	#576	1	1	yes	characteristic
238	C₄×C₇	—	2	2	no	—
239	C₄×C₇	—	2	4	no	—
240	C₄×C₇	—	4	4	no	—
241	C₄×C₇	—	4	2	no	—
242	C₄×C₇	—	8	2	no	—
243	C₄×C₇	C₄×D₈	1	4	yes	complemented
244	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
245	C₄×C₇	#518	1	1	yes	characteristic
246	C₄×C₇	#550	1	1	yes	characteristic
247	C₄×C₇	#559	1	1	yes	characteristic
248	C₂⁴	—	2	4	no	—
249	C₂×D₄	—	2	8	no	—
250	C₂×D₄	—	2	8	no	—
251	C₂×D₄	—	2	4	no	—
252	C₂×D₄	—	2	4	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	2	4	no	—
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	—	4	4	no	—
257	C₂×D₄	—	4	4	no	—
258	C₂×D₄	—	8	2	no	—
259	C₂×D₄	—	8	2	no	—
260	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	4	8	no	—
264	C₂²×C₄	—	4	8	no	—
265	C₂²×C₄	—	8	4	no	—
266	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
267	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
269	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
270	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
271	D₈	—	2	16	no	—
272	D₈	—	4	8	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
279	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
280	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
281	C₂×C₈	C₇×#41	1	2	yes	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	C₇×D₈	1	4	yes	complemented
287	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
288	C₂²⋊C₄	—	4	8	no	—
289	C₂²⋊C₄	—	4	8	no	—
290	C₂²⋊C₄	—	8	4	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	4	4	no	—
294	C₄²	C₂²×C₄×C₇	1	2	yes	—
295	C₄²	C₇×#41	1	2	yes	—
296	C₂×C₇	—	8	8	no	—
297	C₂×C₇	#2366	1	1	yes	characteristic
298	C₂×C₇	C₂×C₄×D₈	1	1	yes	characteristic
299	C₂×C₇	#2948	1	1	yes	characteristic
300	C₂×C₇	D₄×D₈	1	1	yes	characteristic
301	C₂×C₇	#3287	1	1	yes	characteristic
302	C₂×C₇	#3391	1	1	yes	characteristic
303	C₂×C₇	#3396	1	1	yes	characteristic
304	C₂³	—	2	8	no	—
305	C₂³	—	4	4	no	—
306	C₂³	—	4	4	no	—
307	C₂³	—	4	4	no	—
308	C₂³	—	4	4	no	—
309	C₂³	—	4	4	no	—
310	C₂³	—	4	4	no	—
311	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
312	D₄	—	2	8	no	—
313	D₄	—	2	8	no	—
314	D₄	—	4	4	no	—
315	D₄	—	4	4	no	—
316	D₄	—	4	16	no	—
317	D₄	—	8	8	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	8	16	no	—
332	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
333	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
334	C₂×C₄	C₂×C₇×D₈	1	4	yes	—
335	C₂×C₄	C₂×C₇×D₈	1	2	yes	—
336	C₂×C₄	C₇×#135	1	2	yes	—
337	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
338	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
339	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
340	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
341	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
342	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
343	C₈	—	2	2	no	—
344	C₈	—	4	2	no	—
345	C₈	C₄×C₇×D₄	1	4	yes	complemented
346	C₇	#23185	1	1	yes	characteristic, direct product factor, Sylow
347	C₂²	—	4	8	no	—
348	C₂²	—	4	8	no	—
349	C₂²	—	4	8	no	—
350	C₂²	—	8	4	no	—
351	C₂²	—	8	4	no	—
352	C₂²	—	8	4	no	—
353	C₂²	—	8	4	no	—
354	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
355	C₂²	C₇×D₄²	1	1	yes	characteristic
356	C₂²	C₇×#550	1	1	yes	characteristic
357	C₂²	C₂²×C₇×D₈	1	1	yes	characteristic
358	C₂²	C₂×C₇×#135	1	1	yes	characteristic
359	C₂²	C₇×#576	1	1	yes	characteristic
360	C₂²	C₇×#576	1	1	yes	characteristic
361	C₄	—	2	2	no	—
362	C₄	—	2	4	no	—
363	C₄	—	4	4	no	—
364	C₄	—	4	2	no	—
365	C₄	—	8	2	no	—
366	C₄	C₄×C₇×D₈	1	4	yes	complemented
367	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
368	C₄	C₇×#518	1	1	yes	characteristic
369	C₄	C₇×#550	1	1	yes	characteristic
370	C₄	C₇×#559	1	1	yes	characteristic
371	C₂	—	8	8	no	—
372	C₂	C₇×#2366	1	1	yes	characteristic
373	C₂	C₂×C₄×C₇×D₈	1	1	yes	characteristic
374	C₂	C₇×#2948	1	1	yes	characteristic
375	C₂	C₇×D₄×D₈	1	1	yes	characteristic
376	C₂	C₇×#3287	1	1	yes	characteristic
377	C₂	C₇×#3391	1	1	yes	characteristic
378	C₂	C₇×#3396	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#493	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₇×D₈	C₂	semidirect
3. C₇×#2366	C₂	semidirect
4. C₇×#1982	C₂	semidirect
5. C₇×#1970	C₂	semidirect
6. C₇×#1879	C₂	semidirect
7. C₄×C₇×#107	C₂	semidirect
8. C₇×C₈×C₄⋊C₄	C₂	semidirect
14. C₇×#493	C₄	semidirect
30. #23185	C₇	direct (N × H)
39. C₂×C₇×D₈	C₂×C₄	semidirect
40. C₂×C₇×D₈	C₂×C₄	semidirect
45. C₇×#127	C₂×C₄	semidirect
60. C₇×#107	D₄	semidirect
65. C₄×C₇×C₈	C₂×C₄	semidirect
69. C₂×C₄×D₈	C₂×C₇	semidirect
70. #2366	C₂×C₇	semidirect
71. #1982	C₂×C₇	semidirect
72. #1970	C₂×C₇	semidirect
73. #1879	C₂×C₇	semidirect
74. C₄×#107	C₂×C₇	semidirect
75. C₈×C₄⋊C₄	C₂×C₇	semidirect
114. C₇×C₄⋊C₄	D₈	semidirect
129. #493	C₄×C₇	semidirect
186. C₇×C₈	C₄×D₄	semidirect
195. C₂×D₈	C₂×C₄×C₇	semidirect
196. C₂×D₈	C₂×C₄×C₇	semidirect
201. #127	C₂×C₄×C₇	semidirect
216. #107	C₇×D₄	semidirect
221. C₄×C₈	C₂×C₄×C₇	semidirect
243. C₄×C₇	C₄×D₈	semidirect
286. C₄⋊C₄	C₇×D₈	semidirect
345. C₈	C₄×C₇×D₄	semidirect
346. C₇	#23185	direct (N × H)
366. C₄	C₄×C₇×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#493	2
C₂×C₄×C₇×D₈	2
C₇×#2366	2
C₇×#1982	2
C₇×#1970	2
C₇×#1879	2
C₄×C₇×#107	2
C₇×C₈×C₄⋊C₄	2
#23185	7

Subgroups — C7×#23185 #13200401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23185 #13200401