Subgroups — C₇×#19889 #13197105

Order 1792.

710 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3391	C₂	1	1	yes	maximal, characteristic
2	C₇×Q₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3278	C₂	1	2	yes	maximal, complemented
4	C₇×#1706	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1685	C₂	1	2	yes	maximal, complemented
6	C₇×#1674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1668	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1641	C₂	1	2	yes	maximal, complemented
9	C₇×#1627	C₂	1	2	yes	maximal, complemented
10	C₇×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×C₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#137	—	2	2	no	—
13	C₇×#550	C₂²	1	2	yes	—
14	C₇×D₄×Q₈	C₂²	1	2	yes	—
15	C₇×#500	—	2	1	no	—
16	C₇×#500	C₂²	1	1	yes	characteristic
17	C₇×#493	—	2	1	no	—
18	C₇×#493	C₂²	1	1	yes	characteristic
19	C₇×#492	C₂²	1	2	yes	—
20	C₇×#486	C₂²	1	2	yes	—
21	C₇×#474	—	2	2	no	—
22	C₇×#474	C₂²	1	2	yes	—
23	C₇×#468	—	2	2	no	—
24	C₇×#462	C₂²	1	2	yes	—
25	C₇×#460	C₂²	1	2	yes	—
26	C₇×#459	—	2	2	no	—
27	C₇×#459	C₂²	1	2	yes	—
28	C₇×#452	—	2	2	no	—
29	C₇×#448	—	2	2	no	—
30	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
31	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
32	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
33	C₄×C₇×D₈	—	2	1	no	—
34	C₄×C₇×D₈	—	2	1	no	—
35	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
36	C₇×#436	C₂²	1	2	yes	—
37	C₇×#335	C₂²	1	1	yes	characteristic
38	C₇×#335	C₂²	1	1	yes	characteristic
39	C₇×#332	C₂²	1	2	yes	—
40	C₇×#331	C₂²	1	2	yes	—
41	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₇×D₄⋊C₈	C₂²	1	2	yes	—
44	C₇×C₈²	C₂²	1	1	yes	characteristic
45	#19889	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₇×#41	—	2	2	no	—
47	C₂²×C₇×Q₈	—	2	2	no	—
48	C₇×#137	—	4	8	no	—
49	C₂×C₇×Q₁₆	—	2	2	no	—
50	C₂×C₇×Q₁₆	D₄	1	1	yes	characteristic
51	C₂×C₇×SD₁₆	—	2	2	no	—
52	C₂×C₇×SD₁₆	—	2	2	no	—
53	C₂×C₇×SD₁₆	—	2	2	no	—
54	C₂×C₇×D₈	—	2	2	no	—
55	C₂×C₇×D₈	—	2	1	no	—
56	C₂×C₇×D₈	—	2	1	no	—
57	C₂×C₇×D₈	D₄	1	1	yes	characteristic
58	C₂×C₇×M₁₆	—	2	2	no	—
59	C₇×C₄⋊Q₈	—	2	2	no	—
60	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₇×#127	—	2	2	no	—
62	C₇×#127	C₂³	1	2	yes	—
63	C₇×C₂²⋊Q₈	—	2	2	no	—
64	C₇×C₂²⋊Q₈	—	4	2	no	—
65	C₇×#121	—	2	2	no	—
66	C₇×#121	—	4	2	no	—
67	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
68	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
69	C₄×C₇×D₄	—	2	2	no	—
70	C₄×C₇×D₄	—	2	2	no	—
71	C₄×C₇×D₄	C₂³	1	2	yes	—
72	C₇×#107	—	2	1	no	—
73	C₇×#107	—	2	1	no	—
74	C₇×#107	—	2	2	no	—
75	C₇×#107	D₄	1	1	yes	characteristic
76	C₇×#107	D₄	1	1	yes	characteristic
77	C₇×C₄⋊C₈	—	2	1	no	—
78	C₇×C₄⋊C₈	—	2	1	no	—
79	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₇×C₄⋊C₈	C₂³	1	2	yes	—
81	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
82	C₇×#103	—	2	2	no	—
83	C₇×#103	D₄	1	1	yes	characteristic
84	C₇×#103	D₄	1	1	yes	characteristic
85	C₇×#102	—	2	2	no	—
86	C₇×#102	—	2	2	no	—
87	C₇×#102	—	2	2	no	—
88	C₇×#102	—	4	2	no	—
89	C₇×#102	D₄	1	2	yes	—
90	C₇×C₂²⋊C₈	—	2	2	no	—
91	C₄×C₇×C₈	—	2	1	no	—
92	C₄×C₇×C₈	—	2	1	no	—
93	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
94	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
95	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
96	#3391	C₂×C₇	1	1	yes	characteristic
97	Q₈×D₈	C₂×C₇	1	1	yes	characteristic, complemented
98	#3278	C₂×C₇	1	2	yes	complemented
99	#1706	C₂×C₇	1	1	yes	characteristic, complemented
100	#1685	C₂×C₇	1	2	yes	complemented
101	#1674	C₂×C₇	1	1	yes	characteristic, complemented
102	#1668	C₂×C₇	1	1	yes	characteristic, complemented
103	#1641	C₂×C₇	1	2	yes	complemented
104	#1627	C₂×C₇	1	2	yes	complemented
105	#1589	C₂×C₇	1	1	yes	characteristic, complemented
106	C₈×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
107	C₇×#41	—	4	4	no	—
108	C₇×#41	—	8	2	no	—
109	C₂×C₇×Q₈	—	2	2	no	—
110	C₂×C₇×Q₈	—	4	2	no	—
111	C₂×C₇×Q₈	—	4	4	no	—
112	C₂×C₇×Q₈	—	8	2	no	—
113	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
114	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
115	C₂×C₇×D₄	—	2	2	no	—
116	C₂×C₇×D₄	—	2	2	no	—
117	C₂×C₇×D₄	—	2	2	no	—
118	C₂×C₇×D₄	—	4	2	no	—
119	C₂×C₇×D₄	—	4	2	no	—
120	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₇	—	2	2	no	—
122	C₂²×C₄×C₇	—	4	2	no	—
123	C₂²×C₄×C₇	—	4	2	no	—
124	C₇×Q₁₆	—	4	4	no	—
125	C₇×Q₁₆	D₈	1	4	yes	complemented
126	C₇×SD₁₆	—	4	4	no	—
127	C₇×SD₁₆	—	4	4	no	—
128	C₇×SD₁₆	—	8	2	no	—
129	C₇×D₈	—	2	2	no	—
130	C₇×D₈	—	4	2	no	—
131	C₇×D₈	—	8	1	no	—
132	C₇×D₈	—	8	2	no	—
133	C₇×M₁₆	—	4	4	no	—
134	C₂×C₇×C₈	—	2	1	no	—
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	—	2	2	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
139	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
140	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
141	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
142	C₇×C₄⋊C₄	—	2	1	no	—
143	C₇×C₄⋊C₄	—	2	1	no	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	4	2	no	—
147	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
148	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
149	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
150	C₇×C₂²⋊C₄	—	2	2	no	—
151	C₇×C₂²⋊C₄	—	4	2	no	—
152	C₇×C₂²⋊C₄	—	4	2	no	—
153	C₄²×C₇	—	2	1	no	—
154	C₄²×C₇	—	2	1	no	—
155	C₄²×C₇	C₂⁴	1	1	yes	characteristic
156	C₂×#137	—	2	2	no	—
157	#550	C₂²×C₇	1	2	yes	—
158	D₄×Q₈	C₂²×C₇	1	2	yes	—
159	#500	—	2	1	no	—
160	#500	C₂²×C₇	1	1	yes	characteristic
161	#493	—	2	1	no	—
162	#493	C₂²×C₇	1	1	yes	characteristic
163	#492	C₂²×C₇	1	2	yes	—
164	#486	C₂²×C₇	1	2	yes	—
165	#474	—	2	2	no	—
166	#474	C₂²×C₇	1	2	yes	—
167	#468	—	2	2	no	—
168	#462	C₂²×C₇	1	2	yes	—
169	#460	C₂²×C₇	1	2	yes	—
170	#459	—	2	2	no	—
171	#459	C₂²×C₇	1	2	yes	—
172	#452	—	2	2	no	—
173	#448	—	2	2	no	—
174	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
175	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
176	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
177	C₄×D₈	—	2	1	no	—
178	C₄×D₈	—	2	1	no	—
179	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
180	#436	C₂²×C₇	1	2	yes	—
181	#335	C₂²×C₇	1	1	yes	characteristic
182	#335	C₂²×C₇	1	1	yes	characteristic
183	#332	C₂²×C₇	1	2	yes	—
184	#331	C₂²×C₇	1	2	yes	—
185	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
186	Q₈⋊C₈	C₂²×C₇	1	1	yes	characteristic
187	D₄⋊C₈	C₂²×C₇	1	2	yes	—
188	C₈²	C₂²×C₇	1	1	yes	characteristic
189	C₂³×C₇	—	2	2	no	—
190	C₂³×C₇	—	4	2	no	—
191	C₇×Q₈	—	2	1	no	—
192	C₇×Q₈	—	2	1	no	—
193	C₇×Q₈	—	4	2	no	—
194	C₇×Q₈	—	4	2	no	—
195	C₇×Q₈	—	8	4	no	—
196	C₇×Q₈	C₂×D₈	1	2	yes	—
197	C₇×Q₈	C₂×D₈	1	2	yes	—
198	C₇×D₄	—	2	2	no	—
199	C₇×D₄	—	2	2	no	—
200	C₇×D₄	—	4	2	no	—
201	C₇×D₄	—	4	2	no	—
202	C₇×D₄	—	4	2	no	—
203	C₇×D₄	—	4	2	no	—
204	C₇×D₄	—	8	4	no	—
205	C₇×D₄	—	8	2	no	—
206	C₇×D₄	—	16	2	no	—
207	C₂×C₄×C₇	—	2	1	no	—
208	C₂×C₄×C₇	—	2	1	no	—
209	C₂×C₄×C₇	—	2	1	no	—
210	C₂×C₄×C₇	—	2	1	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	4	2	no	—
213	C₂×C₄×C₇	—	4	2	no	—
214	C₂×C₄×C₇	—	4	2	no	—
215	C₂×C₄×C₇	—	8	4	no	—
216	C₂×C₄×C₇	—	8	4	no	—
217	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
220	C₇×C₈	—	2	1	no	—
221	C₇×C₈	—	2	1	no	—
222	C₇×C₈	—	4	1	no	—
223	C₇×C₈	—	4	2	no	—
224	C₇×C₈	—	4	1	no	—
225	C₇×C₈	—	4	1	no	—
226	C₇×C₈	C₂×D₈	1	2	yes	—
227	C₇×C₈	#137	1	2	yes	complemented
228	C₂×#41	—	2	2	no	—
229	C₂²×Q₈	—	2	2	no	—
230	#137	—	4	8	no	—
231	C₂×Q₁₆	—	2	2	no	—
232	C₂×Q₁₆	C₇×D₄	1	1	yes	characteristic
233	C₂×SD₁₆	—	2	2	no	—
234	C₂×SD₁₆	—	2	2	no	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×D₈	—	2	2	no	—
237	C₂×D₈	—	2	1	no	—
238	C₂×D₈	—	2	1	no	—
239	C₂×D₈	C₇×D₄	1	1	yes	characteristic
240	C₂×M₁₆	—	2	2	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
243	#127	—	2	2	no	—
244	#127	C₂³×C₇	1	2	yes	—
245	C₂²⋊Q₈	—	2	2	no	—
246	C₂²⋊Q₈	—	4	2	no	—
247	#121	—	2	2	no	—
248	#121	—	4	2	no	—
249	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
250	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	C₂³×C₇	1	2	yes	—
254	#107	—	2	1	no	—
255	#107	—	2	1	no	—
256	#107	—	2	2	no	—
257	#107	C₇×D₄	1	1	yes	characteristic
258	#107	C₇×D₄	1	1	yes	characteristic
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	C₂³×C₇	1	2	yes	—
262	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
263	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
264	#103	—	2	2	no	—
265	#103	C₇×D₄	1	1	yes	characteristic
266	#103	C₇×D₄	1	1	yes	characteristic
267	#102	—	2	2	no	—
268	#102	—	2	2	no	—
269	#102	—	2	2	no	—
270	#102	—	4	2	no	—
271	#102	C₇×D₄	1	2	yes	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₄×C₈	—	2	1	no	—
274	C₄×C₈	—	2	1	no	—
275	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
276	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
278	C₂²×C₇	—	4	2	no	—
279	C₂²×C₇	—	4	2	no	—
280	C₂²×C₇	—	4	2	no	—
281	C₂²×C₇	—	8	2	no	—
282	C₂²×C₇	—	8	2	no	—
283	C₂²×C₇	—	8	2	no	—
284	C₂²×C₇	D₄²	1	1	yes	characteristic
285	C₄×C₇	—	2	2	no	—
286	C₄×C₇	—	2	2	no	—
287	C₄×C₇	—	2	1	no	—
288	C₄×C₇	—	4	2	no	—
289	C₄×C₇	—	4	1	no	—
290	C₄×C₇	—	4	1	no	—
291	C₄×C₇	—	8	2	no	—
292	C₄×C₇	C₂²×D₈	1	1	yes	characteristic
293	C₄×C₇	C₂×#137	1	1	yes	characteristic
294	C₄×C₇	#576	1	1	yes	characteristic
295	C₄×C₇	#577	1	1	yes	characteristic
296	#41	—	4	4	no	—
297	#41	—	8	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	—	4	4	no	—
301	C₂×Q₈	—	8	2	no	—
302	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
303	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	4	2	no	—
313	Q₁₆	—	4	4	no	—
314	Q₁₆	C₇×D₈	1	4	yes	complemented
315	SD₁₆	—	4	4	no	—
316	SD₁₆	—	4	4	no	—
317	SD₁₆	—	8	2	no	—
318	D₈	—	2	2	no	—
319	D₈	—	4	2	no	—
320	D₈	—	8	1	no	—
321	D₈	—	8	2	no	—
322	M₁₆	—	4	4	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
328	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
329	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
330	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
337	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
338	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	C₂⁴×C₇	1	1	yes	characteristic
345	C₂×C₇	—	8	2	no	—
346	C₂×C₇	—	16	2	no	—
347	C₂×C₇	#3278	1	1	yes	characteristic
348	C₂×C₇	D₄×D₈	1	1	yes	characteristic
349	C₂×C₇	#3290	1	1	yes	characteristic
350	C₂³	—	2	2	no	—
351	C₂³	—	4	2	no	—
352	Q₈	—	2	1	no	—
353	Q₈	—	2	1	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	8	4	no	—
357	Q₈	C₂×C₇×D₈	1	2	yes	—
358	Q₈	C₂×C₇×D₈	1	2	yes	—
359	D₄	—	2	2	no	—
360	D₄	—	2	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	8	4	no	—
366	D₄	—	8	2	no	—
367	D₄	—	16	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	8	4	no	—
377	C₂×C₄	—	8	4	no	—
378	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
380	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
381	C₈	—	2	1	no	—
382	C₈	—	2	1	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	1	no	—
387	C₈	C₂×C₇×D₈	1	2	yes	—
388	C₈	C₇×#137	1	2	yes	complemented
389	C₇	#19889	1	1	yes	characteristic, direct product factor, Sylow
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	C₇×D₄²	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	1	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	8	2	no	—
404	C₄	C₂²×C₇×D₈	1	1	yes	characteristic
405	C₄	C₂×C₇×#137	1	1	yes	characteristic
406	C₄	C₇×#576	1	1	yes	characteristic
407	C₄	C₇×#577	1	1	yes	characteristic
408	C₂	—	8	2	no	—
409	C₂	—	16	2	no	—
410	C₂	C₇×#3278	1	1	yes	characteristic
411	C₂	C₇×D₄×D₈	1	1	yes	characteristic
412	C₂	C₇×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#3391	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×Q₈×D₈	C₂	semidirect
3. C₇×#3278	C₂	semidirect
4. C₇×#1706	C₂	semidirect
5. C₇×#1685	C₂	semidirect
6. C₇×#1674	C₂	semidirect
7. C₇×#1668	C₂	semidirect
8. C₇×#1641	C₂	semidirect
9. C₇×#1627	C₂	semidirect
10. C₇×#1589	C₂	semidirect
11. C₇×C₈×Q₁₆	C₂	semidirect
45. #19889	C₇	direct (N × H)
97. Q₈×D₈	C₂×C₇	semidirect
98. #3278	C₂×C₇	semidirect
99. #1706	C₂×C₇	semidirect
100. #1685	C₂×C₇	semidirect
101. #1674	C₂×C₇	semidirect
102. #1668	C₂×C₇	semidirect
103. #1641	C₂×C₇	semidirect
104. #1627	C₂×C₇	semidirect
105. #1589	C₂×C₇	semidirect
106. C₈×Q₁₆	C₂×C₇	semidirect
125. C₇×Q₁₆	D₈	semidirect
227. C₇×C₈	#137	semidirect
314. Q₁₆	C₇×D₈	semidirect
388. C₈	C₇×#137	semidirect
389. C₇	#19889	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3391	2
C₇×Q₈×D₈	2
C₇×#3278	2
C₇×#1706	2
C₇×#1685	2
C₇×#1674	2
C₇×#1668	2
C₇×#1641	2
C₇×#1627	2
C₇×#1589	2
C₇×C₈×Q₁₆	2
#19889	7

Subgroups — C7×#19889 #13197105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19889 #13197105