Subgroups — C₇×#33856 #13211072

Order 1792.

652 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3416	C₂	1	2	yes	maximal, complemented
2	C₇×#3293	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3292	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2223	C₂	1	2	yes	maximal, complemented
6	C₇×#2214	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2213	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2194	C₂	1	2	yes	maximal, complemented
9	C₇×#2193	C₂	1	2	yes	maximal, complemented
10	C₇×#2178	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#578	—	2	1	no	—
13	C₇×#578	C₂²	1	2	yes	complemented
14	C₇×#576	—	2	1	no	—
15	C₇×#576	C₂²	1	2	yes	—
16	C₇×#510	—	2	2	no	—
17	C₇×#510	C₂²	1	2	yes	—
18	C₇×#509	—	2	2	no	—
19	C₇×#509	C₂²	1	2	yes	complemented
20	C₇×#508	—	2	2	no	—
21	C₇×#508	C₂²	1	1	yes	characteristic
22	C₂×C₇×SD₃₂	—	2	2	no	—
23	C₂×C₇×SD₃₂	C₂²	1	2	yes	complemented
24	C₂×C₇×SD₃₂	C₂²	1	2	yes	complemented
25	C₇×#504	C₂²	1	2	yes	complemented
26	C₇×#494	C₂²	1	1	yes	characteristic, complemented
27	C₇×#493	C₂²	1	1	yes	characteristic
28	C₇×#473	—	2	1	no	—
29	C₇×#473	C₂²	1	2	yes	complemented
30	C₇×#472	—	2	1	no	—
31	C₇×#472	C₂²	1	2	yes	—
32	C₇×#456	—	2	2	no	—
33	C₇×#453	—	2	2	no	—
34	C₇×#443	C₂²	1	1	yes	characteristic
35	C₇×#443	C₂²	1	1	yes	characteristic
36	C₇×#443	C₂²	1	1	yes	characteristic, complemented
37	C₇×#368	C₂²	1	1	yes	characteristic, complemented
38	C₇×#364	C₂²	1	1	yes	characteristic, complemented
39	C₇×#362	C₂²	1	2	yes	complemented
40	C₇×#361	C₂²	1	2	yes	complemented
41	C₇×#359	C₂²	1	1	yes	characteristic
42	C₇×#359	C₂²	1	1	yes	characteristic, complemented
43	C₇×#350	C₂²	1	2	yes	complemented
44	C₄×C₇×C₁₆	C₂²	1	1	yes	characteristic, complemented
45	#33856	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₇×2₋¹⁺⁴	—	2	2	no	—
47	C₇×H(5,𝔽₂)	—	2	2	no	—
48	C₇×#137	—	2	2	no	—
49	C₇×#137	—	2	2	no	—
50	C₇×#137	—	4	2	no	—
51	C₇×#137	—	4	2	no	—
52	C₇×AGL(1,ℤ/8)	—	2	2	no	—
53	C₇×AGL(1,ℤ/8)	—	2	2	no	—
54	C₇×AGL(1,ℤ/8)	—	4	2	no	—
55	C₇×AGL(1,ℤ/8)	—	4	2	no	—
56	C₇×#135	—	2	2	no	—
57	C₇×#135	—	2	2	no	—
58	C₇×#135	—	4	1	no	—
59	C₇×#135	—	4	1	no	—
60	C₇×#135	D₄	1	1	yes	characteristic
61	C₇×#135	C₂³	1	1	yes	characteristic
62	C₇×#135	C₂³	1	1	yes	characteristic
63	C₂×C₇×Q₁₆	—	2	2	no	—
64	C₂×C₇×Q₁₆	—	2	1	no	—
65	C₂×C₇×Q₁₆	—	4	1	no	—
66	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
67	C₂×C₇×D₈	—	2	2	no	—
68	C₂×C₇×D₈	—	2	1	no	—
69	C₂×C₇×D₈	—	4	1	no	—
70	C₂×C₇×D₈	C₂³	1	2	yes	—
71	C₇×#131	—	2	1	no	—
72	C₇×#131	—	2	1	no	—
73	C₇×#131	C₂³	1	2	yes	—
74	C₇×C₄⋊Q₈	—	2	1	no	—
75	C₇×#127	—	2	1	no	—
76	C₇×Q₃₂	—	2	2	no	—
77	C₇×Q₃₂	D₄	1	1	yes	characteristic, complemented
78	C₇×SD₃₂	—	2	2	no	—
79	C₇×SD₃₂	—	2	2	no	—
80	C₇×SD₃₂	—	2	2	no	—
81	C₇×SD₃₂	—	2	2	no	—
82	C₇×SD₃₂	—	4	2	no	—
83	C₇×SD₃₂	D₄	1	1	yes	characteristic, complemented
84	C₇×SD₃₂	D₄	1	1	yes	characteristic, complemented
85	C₇×D₁₆	—	2	2	no	—
86	C₇×D₁₆	D₄	1	1	yes	characteristic, complemented
87	C₇×M₃₂	—	2	2	no	—
88	C₇×M₃₂	C₂³	1	2	yes	—
89	C₂×C₇×C₁₆	—	2	2	no	—
90	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
91	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
92	C₇×#108	D₄	1	1	yes	characteristic
93	C₇×#108	C₂³	1	1	yes	characteristic
94	C₇×#108	C₂³	1	1	yes	characteristic
95	C₇×#104	—	2	1	no	—
96	C₇×#104	—	2	1	no	—
97	C₇×#104	D₄	1	2	yes	—
98	C₇×#101	—	2	2	no	—
99	C₇×#100	—	2	2	no	—
100	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
101	#3416	C₂×C₇	1	2	yes	complemented
102	#3293	C₂×C₇	1	1	yes	characteristic, complemented
103	#3292	C₂×C₇	1	1	yes	characteristic, complemented
104	#2248	C₂×C₇	1	1	yes	characteristic, complemented
105	#2223	C₂×C₇	1	2	yes	complemented
106	#2214	C₂×C₇	1	1	yes	characteristic, complemented
107	#2213	C₂×C₇	1	1	yes	characteristic, complemented
108	#2194	C₂×C₇	1	2	yes	complemented
109	#2193	C₂×C₇	1	2	yes	complemented
110	#2178	C₂×C₇	1	1	yes	characteristic, complemented
111	#2170	C₂×C₇	1	1	yes	characteristic, complemented
112	C₇×#41	—	2	1	no	—
113	C₇×#41	—	2	1	no	—
114	C₇×#41	—	4	2	no	—
115	C₇×#41	—	4	2	no	—
116	C₇×#41	—	4	2	no	—
117	C₇×#41	—	4	2	no	—
118	C₇×#41	—	8	2	no	—
119	C₇×#41	C₂×D₄	1	2	yes	—
120	C₂×C₇×Q₈	—	2	2	no	—
121	C₂×C₇×Q₈	—	4	2	no	—
122	C₂×C₇×Q₈	—	4	2	no	—
123	C₂×C₇×D₄	—	2	2	no	—
124	C₂×C₇×D₄	—	4	2	no	—
125	C₂×C₇×D₄	—	4	2	no	—
126	C₂×C₇×D₄	—	8	1	no	—
127	C₂×C₇×D₄	—	8	2	no	—
128	C₇×Q₁₆	—	2	2	no	—
129	C₇×Q₁₆	—	2	2	no	—
130	C₇×Q₁₆	—	4	2	no	—
131	C₇×Q₁₆	—	4	2	no	—
132	C₇×Q₁₆	—	4	1	no	—
133	C₇×Q₁₆	—	4	1	no	—
134	C₇×Q₁₆	D₈	1	1	yes	characteristic
135	C₇×Q₁₆	C₂×D₄	1	1	yes	characteristic
136	C₇×Q₁₆	C₂×D₄	1	1	yes	characteristic
137	C₇×SD₁₆	—	2	1	no	—
138	C₇×SD₁₆	—	2	1	no	—
139	C₇×SD₁₆	—	4	2	no	—
140	C₇×SD₁₆	—	4	2	no	—
141	C₇×SD₁₆	—	4	2	no	—
142	C₇×SD₁₆	—	4	2	no	—
143	C₇×SD₁₆	D₈	1	2	yes	—
144	C₇×D₈	—	2	2	no	—
145	C₇×D₈	—	2	2	no	—
146	C₇×D₈	—	4	2	no	—
147	C₇×D₈	—	4	2	no	—
148	C₇×D₈	—	4	1	no	—
149	C₇×D₈	—	4	1	no	—
150	C₇×D₈	D₈	1	1	yes	characteristic
151	C₇×D₈	C₂×D₄	1	1	yes	characteristic
152	C₇×D₈	C₂×D₄	1	1	yes	characteristic
153	C₇×M₁₆	—	2	2	no	—
154	C₇×M₁₆	—	2	1	no	—
155	C₇×M₁₆	—	2	1	no	—
156	C₇×M₁₆	—	4	1	no	—
157	C₇×M₁₆	—	4	1	no	—
158	C₇×M₁₆	C₂×D₄	1	2	yes	—
159	C₂×C₇×C₈	—	2	2	no	—
160	C₂×C₇×C₈	—	4	1	no	—
161	C₂×C₇×C₈	—	4	1	no	—
162	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
163	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
164	C₇×C₄⋊C₄	—	8	1	no	—
165	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
166	C₇×C₁₆	—	2	2	no	—
167	C₇×C₁₆	—	2	1	no	—
168	C₇×C₁₆	C₂×D₄	1	1	yes	characteristic
169	C₇×C₁₆	C₂×D₄	1	1	yes	characteristic
170	#578	—	2	1	no	—
171	#578	C₂²×C₇	1	2	yes	complemented
172	#576	—	2	1	no	—
173	#576	C₂²×C₇	1	2	yes	—
174	#510	—	2	2	no	—
175	#510	C₂²×C₇	1	2	yes	—
176	#509	—	2	2	no	—
177	#509	C₂²×C₇	1	2	yes	complemented
178	#508	—	2	2	no	—
179	#508	C₂²×C₇	1	1	yes	characteristic
180	C₂×SD₃₂	—	2	2	no	—
181	C₂×SD₃₂	C₂²×C₇	1	2	yes	complemented
182	C₂×SD₃₂	C₂²×C₇	1	2	yes	complemented
183	#504	C₂²×C₇	1	2	yes	complemented
184	#494	C₂²×C₇	1	1	yes	characteristic, complemented
185	#493	C₂²×C₇	1	1	yes	characteristic
186	#473	—	2	1	no	—
187	#473	C₂²×C₇	1	2	yes	complemented
188	#472	—	2	1	no	—
189	#472	C₂²×C₇	1	2	yes	—
190	#456	—	2	2	no	—
191	#453	—	2	2	no	—
192	#443	C₂²×C₇	1	1	yes	characteristic
193	#443	C₂²×C₇	1	1	yes	characteristic
194	#443	C₂²×C₇	1	1	yes	characteristic, complemented
195	#368	C₂²×C₇	1	1	yes	characteristic, complemented
196	#364	C₂²×C₇	1	1	yes	characteristic, complemented
197	#362	C₂²×C₇	1	2	yes	complemented
198	#361	C₂²×C₇	1	2	yes	complemented
199	#359	C₂²×C₇	1	1	yes	characteristic
200	#359	C₂²×C₇	1	1	yes	characteristic, complemented
201	#350	C₂²×C₇	1	2	yes	complemented
202	C₄×C₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
203	C₂³×C₇	—	4	2	no	—
204	C₂³×C₇	—	8	2	no	—
205	C₇×Q₈	—	2	1	no	—
206	C₇×Q₈	—	2	1	no	—
207	C₇×Q₈	—	4	2	no	—
208	C₇×Q₈	—	4	2	no	—
209	C₇×Q₈	—	8	2	no	—
210	C₇×Q₈	C₂×D₈	1	2	yes	—
211	C₇×D₄	—	2	2	no	—
212	C₇×D₄	—	2	1	no	—
213	C₇×D₄	—	2	1	no	—
214	C₇×D₄	—	4	1	no	—
215	C₇×D₄	—	4	1	no	—
216	C₇×D₄	—	4	2	no	—
217	C₇×D₄	—	4	2	no	—
218	C₇×D₄	—	8	2	no	—
219	C₇×D₄	—	8	2	no	—
220	C₇×D₄	—	8	2	no	—
221	C₇×D₄	—	16	2	no	—
222	C₇×D₄	C₂×D₈	1	2	yes	—
223	C₂×C₄×C₇	—	2	1	no	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	4	1	no	—
227	C₂×C₄×C₇	—	4	2	no	—
228	C₂×C₄×C₇	—	8	2	no	—
229	C₂×C₄×C₇	—	8	2	no	—
230	C₂×C₄×C₇	—	8	2	no	—
231	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
232	C₇×C₈	—	2	2	no	—
233	C₇×C₈	—	4	1	no	—
234	C₇×C₈	—	4	1	no	—
235	C₇×C₈	C₂×D₈	1	1	yes	characteristic
236	C₇×C₈	C₂×D₈	1	1	yes	characteristic
237	C₇×C₈	C₂²×D₄	1	1	yes	characteristic
238	C₇×C₈	H(5,𝔽₂)	1	1	yes	characteristic
239	2₋¹⁺⁴	—	2	2	no	—
240	H(5,𝔽₂)	—	2	2	no	—
241	#137	—	2	2	no	—
242	#137	—	2	2	no	—
243	#137	—	4	2	no	—
244	#137	—	4	2	no	—
245	AGL(1,ℤ/8)	—	2	2	no	—
246	AGL(1,ℤ/8)	—	2	2	no	—
247	AGL(1,ℤ/8)	—	4	2	no	—
248	AGL(1,ℤ/8)	—	4	2	no	—
249	#135	—	2	2	no	—
250	#135	—	2	2	no	—
251	#135	—	4	1	no	—
252	#135	—	4	1	no	—
253	#135	C₇×D₄	1	1	yes	characteristic
254	#135	C₂³×C₇	1	1	yes	characteristic
255	#135	C₂³×C₇	1	1	yes	characteristic
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	—	2	1	no	—
258	C₂×Q₁₆	—	4	1	no	—
259	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
260	C₂×D₈	—	2	2	no	—
261	C₂×D₈	—	2	1	no	—
262	C₂×D₈	—	4	1	no	—
263	C₂×D₈	C₂³×C₇	1	2	yes	—
264	#131	—	2	1	no	—
265	#131	—	2	1	no	—
266	#131	C₂³×C₇	1	2	yes	—
267	C₄⋊Q₈	—	2	1	no	—
268	#127	—	2	1	no	—
269	Q₃₂	—	2	2	no	—
270	Q₃₂	C₇×D₄	1	1	yes	characteristic, complemented
271	SD₃₂	—	2	2	no	—
272	SD₃₂	—	2	2	no	—
273	SD₃₂	—	2	2	no	—
274	SD₃₂	—	2	2	no	—
275	SD₃₂	—	4	2	no	—
276	SD₃₂	C₇×D₄	1	1	yes	characteristic, complemented
277	SD₃₂	C₇×D₄	1	1	yes	characteristic, complemented
278	D₁₆	—	2	2	no	—
279	D₁₆	C₇×D₄	1	1	yes	characteristic, complemented
280	M₃₂	—	2	2	no	—
281	M₃₂	C₂³×C₇	1	2	yes	—
282	C₂×C₁₆	—	2	2	no	—
283	C₂×C₁₆	C₂³×C₇	1	1	yes	characteristic
284	C₂×C₁₆	C₂³×C₇	1	1	yes	characteristic
285	#108	C₇×D₄	1	1	yes	characteristic
286	#108	C₂³×C₇	1	1	yes	characteristic
287	#108	C₂³×C₇	1	1	yes	characteristic
288	#104	—	2	1	no	—
289	#104	—	2	1	no	—
290	#104	C₇×D₄	1	2	yes	—
291	#101	—	2	2	no	—
292	#100	—	2	2	no	—
293	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
294	C₂²×C₇	—	2	2	no	—
295	C₂²×C₇	—	4	1	no	—
296	C₂²×C₇	—	4	1	no	—
297	C₂²×C₇	—	8	2	no	—
298	C₂²×C₇	—	16	2	no	—
299	C₂²×C₇	—	32	2	no	—
300	C₂²×C₇	#576	1	1	yes	characteristic
301	C₄×C₇	—	2	2	no	—
302	C₄×C₇	—	2	2	no	—
303	C₄×C₇	—	4	1	no	—
304	C₄×C₇	—	4	1	no	—
305	C₄×C₇	—	8	2	no	—
306	C₄×C₇	D₄²	1	1	yes	characteristic
307	C₄×C₇	C₂²×D₈	1	1	yes	characteristic
308	#41	—	2	1	no	—
309	#41	—	2	1	no	—
310	#41	—	4	2	no	—
311	#41	—	4	2	no	—
312	#41	—	4	2	no	—
313	#41	—	4	2	no	—
314	#41	—	8	2	no	—
315	#41	C₂×C₇×D₄	1	2	yes	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	4	2	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	8	1	no	—
323	C₂×D₄	—	8	2	no	—
324	Q₁₆	—	2	2	no	—
325	Q₁₆	—	2	2	no	—
326	Q₁₆	—	4	2	no	—
327	Q₁₆	—	4	2	no	—
328	Q₁₆	—	4	1	no	—
329	Q₁₆	—	4	1	no	—
330	Q₁₆	C₇×D₈	1	1	yes	characteristic
331	Q₁₆	C₂×C₇×D₄	1	1	yes	characteristic
332	Q₁₆	C₂×C₇×D₄	1	1	yes	characteristic
333	SD₁₆	—	2	1	no	—
334	SD₁₆	—	2	1	no	—
335	SD₁₆	—	4	2	no	—
336	SD₁₆	—	4	2	no	—
337	SD₁₆	—	4	2	no	—
338	SD₁₆	—	4	2	no	—
339	SD₁₆	C₇×D₈	1	2	yes	—
340	D₈	—	2	2	no	—
341	D₈	—	2	2	no	—
342	D₈	—	4	2	no	—
343	D₈	—	4	2	no	—
344	D₈	—	4	1	no	—
345	D₈	—	4	1	no	—
346	D₈	C₇×D₈	1	1	yes	characteristic
347	D₈	C₂×C₇×D₄	1	1	yes	characteristic
348	D₈	C₂×C₇×D₄	1	1	yes	characteristic
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	1	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	4	1	no	—
353	M₁₆	—	4	1	no	—
354	M₁₆	C₂×C₇×D₄	1	2	yes	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
359	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
360	C₄⋊C₄	—	8	1	no	—
361	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
362	C₁₆	—	2	2	no	—
363	C₁₆	—	2	1	no	—
364	C₁₆	C₂×C₇×D₄	1	1	yes	characteristic
365	C₁₆	C₂×C₇×D₄	1	1	yes	characteristic
366	C₂×C₇	—	2	1	no	—
367	C₂×C₇	—	4	2	no	—
368	C₂×C₇	—	8	1	no	—
369	C₂×C₇	—	8	1	no	—
370	C₂×C₇	—	16	2	no	—
371	C₂×C₇	D₄×D₈	1	1	yes	characteristic
372	C₂³	—	4	2	no	—
373	C₂³	—	8	2	no	—
374	Q₈	—	2	1	no	—
375	Q₈	—	2	1	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	8	2	no	—
379	Q₈	C₂×C₇×D₈	1	2	yes	—
380	D₄	—	2	2	no	—
381	D₄	—	2	1	no	—
382	D₄	—	2	1	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	16	2	no	—
391	D₄	C₂×C₇×D₈	1	2	yes	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	4	1	no	—
403	C₈	—	4	1	no	—
404	C₈	C₂×C₇×D₈	1	1	yes	characteristic
405	C₈	C₂×C₇×D₈	1	1	yes	characteristic
406	C₈	C₂²×C₇×D₄	1	1	yes	characteristic
407	C₈	C₇×H(5,𝔽₂)	1	1	yes	characteristic
408	C₇	#33856	1	1	yes	characteristic, direct product factor, Sylow
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	16	2	no	—
414	C₂²	—	32	2	no	—
415	C₂²	C₇×#576	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	8	2	no	—
421	C₄	C₇×D₄²	1	1	yes	characteristic
422	C₄	C₂²×C₇×D₈	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	8	1	no	—
426	C₂	—	8	1	no	—
427	C₂	—	16	2	no	—
428	C₂	C₇×D₄×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇	D₄×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇ ◁ C₂×C₄×C₇ ◁ C₇×#443 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3416	C₂	semidirect
2. C₇×#3293	C₂	semidirect
3. C₇×#3292	C₂	semidirect
4. C₇×#2248	C₂	semidirect
5. C₇×#2223	C₂	semidirect
6. C₇×#2214	C₂	semidirect
7. C₇×#2213	C₂	semidirect
8. C₇×#2194	C₂	semidirect
9. C₇×#2193	C₂	semidirect
10. C₇×#2178	C₂	semidirect
11. C₇×#2170	C₂	semidirect
13. C₇×#578	C₂²	semidirect
19. C₇×#509	C₂²	semidirect
23. C₂×C₇×SD₃₂	C₂²	semidirect
24. C₂×C₇×SD₃₂	C₂²	semidirect
25. C₇×#504	C₂²	semidirect
26. C₇×#494	C₂²	semidirect
29. C₇×#473	C₂²	semidirect
36. C₇×#443	C₂²	semidirect
37. C₇×#368	C₂²	semidirect
38. C₇×#364	C₂²	semidirect
39. C₇×#362	C₂²	semidirect
40. C₇×#361	C₂²	semidirect
42. C₇×#359	C₂²	semidirect
43. C₇×#350	C₂²	semidirect
44. C₄×C₇×C₁₆	C₂²	semidirect
45. #33856	C₇	direct (N × H)
77. C₇×Q₃₂	D₄	semidirect
83. C₇×SD₃₂	D₄	semidirect
84. C₇×SD₃₂	D₄	semidirect
86. C₇×D₁₆	D₄	semidirect
101. #3416	C₂×C₇	semidirect
102. #3293	C₂×C₇	semidirect
103. #3292	C₂×C₇	semidirect
104. #2248	C₂×C₇	semidirect
105. #2223	C₂×C₇	semidirect
106. #2214	C₂×C₇	semidirect
107. #2213	C₂×C₇	semidirect
108. #2194	C₂×C₇	semidirect
109. #2193	C₂×C₇	semidirect
110. #2178	C₂×C₇	semidirect
111. #2170	C₂×C₇	semidirect
171. #578	C₂²×C₇	semidirect
177. #509	C₂²×C₇	semidirect
181. C₂×SD₃₂	C₂²×C₇	semidirect
182. C₂×SD₃₂	C₂²×C₇	semidirect
183. #504	C₂²×C₇	semidirect
184. #494	C₂²×C₇	semidirect
187. #473	C₂²×C₇	semidirect
194. #443	C₂²×C₇	semidirect
195. #368	C₂²×C₇	semidirect
196. #364	C₂²×C₇	semidirect
197. #362	C₂²×C₇	semidirect
198. #361	C₂²×C₇	semidirect
200. #359	C₂²×C₇	semidirect
201. #350	C₂²×C₇	semidirect
202. C₄×C₁₆	C₂²×C₇	semidirect
270. Q₃₂	C₇×D₄	semidirect
276. SD₃₂	C₇×D₄	semidirect
277. SD₃₂	C₇×D₄	semidirect
279. D₁₆	C₇×D₄	semidirect
408. C₇	#33856	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×#3416	2
C₇×#3293	2
C₇×#3292	2
C₇×#2248	2
C₇×#2223	2
C₇×#2214	2
C₇×#2213	2
C₇×#2194	2
C₇×#2193	2
C₇×#2178	2
C₇×#2170	2
#33856	7

Subgroups — C7×#33856 #13211072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#33856 #13211072