Subgroups — C₇×#33691 #13210907

Order 1792.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3173	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2955	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2239	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2238	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2230	C₂	1	2	yes	maximal, complemented
6	C₇×#2212	C₂	1	2	yes	maximal, complemented
7	C₇×#2191	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2190	C₂	1	1	yes	maximal, characteristic
9	C₇×AGL(1,ℤ/16)	C₂	1	2	yes	maximal, complemented
10	C₇×#2180	C₂	1	2	yes	maximal, complemented
11	C₇×#2166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#575	C₂²	1	1	yes	characteristic
13	C₂×C₇×#131	—	2	1	no	—
14	C₇×#542	—	2	1	no	—
15	C₇×#510	C₂²	1	2	yes	—
16	C₇×#509	C₂²	1	2	yes	—
17	C₇×#498	C₂²	1	1	yes	characteristic, complemented
18	C₇×#495	C₂²	1	1	yes	characteristic, complemented
19	C₇×#489	—	2	1	no	—
20	C₇×#470	C₂²	1	1	yes	characteristic
21	C₇×#469	C₂²	1	1	yes	characteristic
22	C₇×#465	—	2	1	no	—
23	C₇×#444	—	2	1	no	—
24	C₇×#444	C₂²	1	2	yes	—
25	C₇×#443	—	2	1	no	—
26	C₇×#443	C₂²	1	2	yes	—
27	C₇×#442	C₂²	1	1	yes	characteristic, complemented
28	C₇×#441	C₂²	1	1	yes	characteristic, complemented
29	C₄×C₇×SD₁₆	—	2	1	no	—
30	C₇×#430	C₂²	1	1	yes	characteristic
31	C₇×#421	—	2	1	no	—
32	C₇×#405	C₂²	1	1	yes	characteristic
33	C₇×#365	C₂²	1	2	yes	complemented
34	C₇×#365	C₂²	1	2	yes	complemented
35	C₇×#364	C₂²	1	2	yes	complemented
36	C₇×#362	C₂²	1	2	yes	complemented
37	C₇×#361	C₂²	1	2	yes	complemented
38	C₇×#360	C₂²	1	2	yes	—
39	C₇×#360	C₂²	1	2	yes	—
40	C₇×#349	C₂²	1	1	yes	characteristic
41	C₇×#349	C₂²	1	1	yes	characteristic
42	C₇×#347	C₂²	1	2	yes	complemented
43	#33691	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₇×#41	—	2	1	no	—
45	C₇×#137	—	2	2	no	—
46	C₇×AGL(1,ℤ/8)	—	2	2	no	—
47	C₇×#135	—	2	1	no	—
48	C₇×#135	C₂³	1	2	yes	—
49	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₇×SD₁₆	—	2	1	no	—
51	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
52	C₇×#131	—	2	2	no	—
53	C₇×#131	—	2	2	no	—
54	C₇×#131	—	4	1	no	—
55	C₇×#131	—	4	1	no	—
56	C₂×C₇×M₁₆	—	2	1	no	—
57	C₂×C₇×M₁₆	—	4	1	no	—
58	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
59	C₂²×C₇×C₈	—	4	1	no	—
60	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
61	C₇×C₄⋊Q₈	—	2	1	no	—
62	C₇×#126	—	4	1	no	—
63	C₇×#124	—	2	1	no	—
64	C₇×#124	—	4	1	no	—
65	C₇×#123	—	4	1	no	—
66	C₇×C₂²⋊Q₈	—	2	1	no	—
67	C₇×C₂²⋊Q₈	—	4	1	no	—
68	C₇×#121	—	2	1	no	—
69	C₄×C₇×Q₈	—	2	1	no	—
70	C₄×C₇×D₄	—	2	1	no	—
71	C₇×#117	D₄	1	1	yes	characteristic
72	C₇×Q₃₂	—	2	2	no	—
73	C₇×SD₃₂	—	2	2	no	—
74	C₇×SD₃₂	—	2	2	no	—
75	C₇×D₁₆	—	2	2	no	—
76	C₇×M₃₂	C₂³	1	2	yes	—
77	C₇×M₃₂	C₂³	1	2	yes	—
78	C₇×#108	—	2	1	no	—
79	C₇×#108	C₂³	1	2	yes	—
80	C₇×#106	—	2	1	no	—
81	C₇×#106	C₂³	1	1	yes	characteristic
82	C₇×#106	C₂³	1	1	yes	characteristic
83	C₇×#104	—	2	2	no	—
84	C₇×#104	—	2	2	no	—
85	C₇×#103	—	2	1	no	—
86	C₇×#103	—	2	1	no	—
87	C₇×#102	—	2	1	no	—
88	C₇×#102	—	2	1	no	—
89	C₇×#97	D₄	1	1	yes	characteristic
90	C₇×#97	C₂³	1	1	yes	characteristic
91	C₄×C₇×C₈	D₄	1	1	yes	characteristic
92	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
93	#3173	C₂×C₇	1	1	yes	characteristic, complemented
94	#2955	C₂×C₇	1	1	yes	characteristic, complemented
95	#2239	C₂×C₇	1	1	yes	characteristic, complemented
96	#2238	C₂×C₇	1	1	yes	characteristic, complemented
97	#2230	C₂×C₇	1	2	yes	complemented
98	#2212	C₂×C₇	1	2	yes	complemented
99	#2191	C₂×C₇	1	1	yes	characteristic, complemented
100	#2190	C₂×C₇	1	1	yes	characteristic
101	AGL(1,ℤ/16)	C₂×C₇	1	2	yes	complemented
102	#2180	C₂×C₇	1	2	yes	complemented
103	#2166	C₂×C₇	1	1	yes	characteristic, complemented
104	C₇×#41	—	2	2	no	—
105	C₇×#41	—	2	2	no	—
106	C₇×#41	—	4	1	no	—
107	C₇×#41	—	4	1	no	—
108	C₂×C₇×Q₈	—	2	1	no	—
109	C₂×C₇×Q₈	—	2	1	no	—
110	C₂×C₇×Q₈	—	4	1	no	—
111	C₂×C₇×D₄	—	2	1	no	—
112	C₂×C₇×D₄	—	2	1	no	—
113	C₂×C₇×D₄	—	4	1	no	—
114	C₂×C₇×D₄	—	4	1	no	—
115	C₂²×C₄×C₇	—	4	1	no	—
116	C₂²×C₄×C₇	—	4	1	no	—
117	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
118	C₇×Q₁₆	—	2	1	no	—
119	C₇×Q₁₆	—	2	2	no	—
120	C₇×Q₁₆	#41	1	2	yes	—
121	C₇×SD₁₆	—	2	2	no	—
122	C₇×SD₁₆	—	2	2	no	—
123	C₇×SD₁₆	—	4	1	no	—
124	C₇×SD₁₆	—	4	1	no	—
125	C₇×D₈	—	2	1	no	—
126	C₇×D₈	—	2	2	no	—
127	C₇×D₈	#41	1	2	yes	—
128	C₇×M₁₆	—	2	2	no	—
129	C₇×M₁₆	—	2	2	no	—
130	C₇×M₁₆	—	4	2	no	—
131	C₇×M₁₆	—	4	1	no	—
132	C₇×M₁₆	—	4	2	no	—
133	C₂×C₇×C₈	—	2	1	no	—
134	C₂×C₇×C₈	—	2	1	no	—
135	C₂×C₇×C₈	—	4	2	no	—
136	C₂×C₇×C₈	—	4	1	no	—
137	C₂×C₇×C₈	—	4	2	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	C₂⁴	1	1	yes	characteristic
142	C₇×C₄⋊C₄	—	2	1	no	—
143	C₇×C₄⋊C₄	—	2	1	no	—
144	C₇×C₄⋊C₄	—	2	1	no	—
145	C₇×C₄⋊C₄	—	4	1	no	—
146	C₇×C₄⋊C₄	—	4	1	no	—
147	C₇×C₄⋊C₄	—	4	1	no	—
148	C₇×C₂²⋊C₄	—	2	1	no	—
149	C₇×C₂²⋊C₄	—	4	1	no	—
150	C₇×C₂²⋊C₄	—	4	1	no	—
151	C₇×C₂²⋊C₄	—	4	1	no	—
152	C₇×C₂²⋊C₄	—	4	1	no	—
153	C₇×C₂²⋊C₄	—	4	1	no	—
154	C₄²×C₇	—	4	1	no	—
155	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
157	C₇×C₁₆	—	2	2	no	—
158	C₇×C₁₆	—	2	2	no	—
159	#575	C₂²×C₇	1	1	yes	characteristic
160	C₂×#131	—	2	1	no	—
161	#542	—	2	1	no	—
162	#510	C₂²×C₇	1	2	yes	—
163	#509	C₂²×C₇	1	2	yes	—
164	#498	C₂²×C₇	1	1	yes	characteristic, complemented
165	#495	C₂²×C₇	1	1	yes	characteristic, complemented
166	#489	—	2	1	no	—
167	#470	C₂²×C₇	1	1	yes	characteristic
168	#469	C₂²×C₇	1	1	yes	characteristic
169	#465	—	2	1	no	—
170	#444	—	2	1	no	—
171	#444	C₂²×C₇	1	2	yes	—
172	#443	—	2	1	no	—
173	#443	C₂²×C₇	1	2	yes	—
174	#442	C₂²×C₇	1	1	yes	characteristic, complemented
175	#441	C₂²×C₇	1	1	yes	characteristic, complemented
176	C₄×SD₁₆	—	2	1	no	—
177	#430	C₂²×C₇	1	1	yes	characteristic
178	#421	—	2	1	no	—
179	#405	C₂²×C₇	1	1	yes	characteristic
180	#365	C₂²×C₇	1	2	yes	complemented
181	#365	C₂²×C₇	1	2	yes	complemented
182	#364	C₂²×C₇	1	2	yes	complemented
183	#362	C₂²×C₇	1	2	yes	complemented
184	#361	C₂²×C₇	1	2	yes	complemented
185	#360	C₂²×C₇	1	2	yes	—
186	#360	C₂²×C₇	1	2	yes	—
187	#349	C₂²×C₇	1	1	yes	characteristic
188	#349	C₂²×C₇	1	1	yes	characteristic
189	#347	C₂²×C₇	1	2	yes	complemented
190	C₂³×C₇	—	4	1	no	—
191	C₂³×C₇	—	4	1	no	—
192	C₂³×C₇	AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₇×Q₈	—	2	2	no	—
194	C₇×Q₈	—	4	1	no	—
195	C₇×Q₈	—	4	1	no	—
196	C₇×Q₈	—	4	1	no	—
197	C₇×Q₈	—	16	1	no	—
198	C₇×D₄	—	2	2	no	—
199	C₇×D₄	—	4	1	no	—
200	C₇×D₄	—	4	2	no	—
201	C₇×D₄	—	4	2	no	—
202	C₇×D₄	—	4	1	no	—
203	C₇×D₄	—	4	1	no	—
204	C₇×D₄	—	16	1	no	—
205	C₂×C₄×C₇	—	2	1	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	1	no	—
208	C₂×C₄×C₇	—	2	1	no	—
209	C₂×C₄×C₇	—	4	2	no	—
210	C₂×C₄×C₇	—	4	1	no	—
211	C₂×C₄×C₇	—	4	2	no	—
212	C₂×C₄×C₇	—	4	1	no	—
213	C₂×C₄×C₇	—	4	1	no	—
214	C₂×C₄×C₇	—	4	1	no	—
215	C₂×C₄×C₇	—	16	1	no	—
216	C₂×C₄×C₇	AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
218	C₇×C₈	—	2	1	no	—
219	C₇×C₈	—	2	1	no	—
220	C₇×C₈	—	4	2	no	—
221	C₇×C₈	AGL(1,ℤ/8)	1	1	yes	characteristic
222	C₇×C₈	AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₇×C₈	C₂×#41	1	2	yes	—
224	C₂×#41	—	2	1	no	—
225	#137	—	2	2	no	—
226	AGL(1,ℤ/8)	—	2	2	no	—
227	#135	—	2	1	no	—
228	#135	C₂³×C₇	1	2	yes	—
229	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
230	C₂×SD₁₆	—	2	1	no	—
231	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
232	#131	—	2	2	no	—
233	#131	—	2	2	no	—
234	#131	—	4	1	no	—
235	#131	—	4	1	no	—
236	C₂×M₁₆	—	2	1	no	—
237	C₂×M₁₆	—	4	1	no	—
238	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
239	C₂²×C₈	—	4	1	no	—
240	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
241	C₄⋊Q₈	—	2	1	no	—
242	#126	—	4	1	no	—
243	#124	—	2	1	no	—
244	#124	—	4	1	no	—
245	#123	—	4	1	no	—
246	C₂²⋊Q₈	—	2	1	no	—
247	C₂²⋊Q₈	—	4	1	no	—
248	#121	—	2	1	no	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	#117	C₇×D₄	1	1	yes	characteristic
252	Q₃₂	—	2	2	no	—
253	SD₃₂	—	2	2	no	—
254	SD₃₂	—	2	2	no	—
255	D₁₆	—	2	2	no	—
256	M₃₂	C₂³×C₇	1	2	yes	—
257	M₃₂	C₂³×C₇	1	2	yes	—
258	#108	—	2	1	no	—
259	#108	C₂³×C₇	1	2	yes	—
260	#106	—	2	1	no	—
261	#106	C₂³×C₇	1	1	yes	characteristic
262	#106	C₂³×C₇	1	1	yes	characteristic
263	#104	—	2	2	no	—
264	#104	—	2	2	no	—
265	#103	—	2	1	no	—
266	#103	—	2	1	no	—
267	#102	—	2	1	no	—
268	#102	—	2	1	no	—
269	#97	C₇×D₄	1	1	yes	characteristic
270	#97	C₂³×C₇	1	1	yes	characteristic
271	C₄×C₈	C₇×D₄	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
273	C₂²×C₇	—	2	1	no	—
274	C₂²×C₇	—	4	1	no	—
275	C₂²×C₇	—	4	2	no	—
276	C₂²×C₇	—	8	1	no	—
277	C₂²×C₇	—	8	1	no	—
278	C₂²×C₇	—	8	2	no	—
279	C₂²×C₇	—	8	1	no	—
280	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
281	C₄×C₇	—	2	1	no	—
282	C₄×C₇	—	4	1	no	—
283	C₄×C₇	—	4	1	no	—
284	C₄×C₇	—	4	2	no	—
285	C₄×C₇	—	8	1	no	—
286	C₄×C₇	—	8	1	no	—
287	C₄×C₇	—	8	1	no	—
288	C₄×C₇	#525	1	1	yes	characteristic
289	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
290	#41	—	2	2	no	—
291	#41	—	2	2	no	—
292	#41	—	4	1	no	—
293	#41	—	4	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
304	Q₁₆	—	2	1	no	—
305	Q₁₆	—	2	2	no	—
306	Q₁₆	C₇×#41	1	2	yes	—
307	SD₁₆	—	2	2	no	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	4	1	no	—
310	SD₁₆	—	4	1	no	—
311	D₈	—	2	1	no	—
312	D₈	—	2	2	no	—
313	D₈	C₇×#41	1	2	yes	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	4	2	no	—
317	M₁₆	—	4	1	no	—
318	M₁₆	—	4	2	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
325	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
326	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
327	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	1	no	—
340	C₄²	—	4	1	no	—
341	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
342	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
343	C₁₆	—	2	2	no	—
344	C₁₆	—	2	2	no	—
345	C₂×C₇	—	2	1	no	—
346	C₂×C₇	—	4	1	no	—
347	C₂×C₇	—	8	2	no	—
348	C₂×C₇	—	16	1	no	—
349	C₂×C₇	#3109	1	1	yes	characteristic
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
353	Q₈	—	2	2	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	16	1	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	1	no	—
364	D₄	—	16	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	16	1	no	—
376	C₂×C₄	C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
378	C₈	—	2	1	no	—
379	C₈	—	2	1	no	—
380	C₈	—	4	2	no	—
381	C₈	C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
382	C₈	C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
383	C₈	C₂×C₇×#41	1	2	yes	—
384	C₇	#33691	1	1	yes	characteristic, direct product factor, Sylow
385	C₂²	—	2	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	1	no	—
392	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	2	no	—
397	C₄	—	8	1	no	—
398	C₄	—	8	1	no	—
399	C₄	—	8	1	no	—
400	C₄	C₇×#525	1	1	yes	characteristic
401	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
402	C₂	—	2	1	no	—
403	C₂	—	4	1	no	—
404	C₂	—	8	2	no	—
405	C₂	—	16	1	no	—
406	C₂	C₇×#3109	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇	#3109
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₇
prime radical	C₇×#2190	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇ ◁ C₂×C₄×C₇ ◁ C₇×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3173	C₂	semidirect
2. C₇×#2955	C₂	semidirect
3. C₇×#2239	C₂	semidirect
4. C₇×#2238	C₂	semidirect
5. C₇×#2230	C₂	semidirect
6. C₇×#2212	C₂	semidirect
7. C₇×#2191	C₂	semidirect
9. C₇×AGL(1,ℤ/16)	C₂	semidirect
10. C₇×#2180	C₂	semidirect
11. C₇×#2166	C₂	semidirect
17. C₇×#498	C₂²	semidirect
18. C₇×#495	C₂²	semidirect
27. C₇×#442	C₂²	semidirect
28. C₇×#441	C₂²	semidirect
33. C₇×#365	C₂²	semidirect
34. C₇×#365	C₂²	semidirect
35. C₇×#364	C₂²	semidirect
36. C₇×#362	C₂²	semidirect
37. C₇×#361	C₂²	semidirect
42. C₇×#347	C₂²	semidirect
43. #33691	C₇	direct (N × H)
93. #3173	C₂×C₇	semidirect
94. #2955	C₂×C₇	semidirect
95. #2239	C₂×C₇	semidirect
96. #2238	C₂×C₇	semidirect
97. #2230	C₂×C₇	semidirect
98. #2212	C₂×C₇	semidirect
99. #2191	C₂×C₇	semidirect
101. AGL(1,ℤ/16)	C₂×C₇	semidirect
102. #2180	C₂×C₇	semidirect
103. #2166	C₂×C₇	semidirect
164. #498	C₂²×C₇	semidirect
165. #495	C₂²×C₇	semidirect
174. #442	C₂²×C₇	semidirect
175. #441	C₂²×C₇	semidirect
180. #365	C₂²×C₇	semidirect
181. #365	C₂²×C₇	semidirect
182. #364	C₂²×C₇	semidirect
183. #362	C₂²×C₇	semidirect
184. #361	C₂²×C₇	semidirect
189. #347	C₂²×C₇	semidirect
384. C₇	#33691	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×#3173	2
C₇×#2955	2
C₇×#2239	2
C₇×#2238	2
C₇×#2230	2
C₇×#2212	2
C₇×#2191	2
C₇×#2190	2
C₇×AGL(1,ℤ/16)	2
C₇×#2180	2
C₇×#2166	2
#33691	7

Subgroups — C7×#33691 #13210907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#33691 #13210907