Subgroups — C₇×#22802 #13200018

Order 1792.

722 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic
2	C₇×#2925	C₂	1	2	yes	maximal, complemented
3	C₇×#1974	C₂	1	2	yes	maximal
4	C₇×#1929	C₂	1	4	yes	maximal, complemented
5	C₇×#1848	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1806	C₂	1	2	yes	maximal, complemented
7	C₇×#1772	C₂	1	2	yes	maximal, complemented
8	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#135	C₂²	1	1	yes	characteristic
10	C₄×C₇×#41	C₂²	1	2	yes	—
11	C₄×C₇×Q₁₆	C₄	1	1	yes	characteristic, complemented
12	C₄×C₇×Q₁₆	C₄	1	1	yes	characteristic, complemented
13	C₄×C₇×SD₁₆	C₄	1	2	yes	complemented
14	C₄×C₇×SD₁₆	C₄	1	2	yes	complemented
15	C₄×C₇×D₈	C₄	1	1	yes	characteristic, complemented
16	C₄×C₇×D₈	C₄	1	1	yes	characteristic, complemented
17	C₇×#433	—	2	4	no	—
18	C₇×#432	—	2	2	no	—
19	C₇×#431	—	2	2	no	—
20	C₂×C₇×#108	C₂²	1	2	yes	—
21	C₂×C₇×#108	C₂²	1	2	yes	—
22	C₇×#427	C₂²	1	1	yes	characteristic
23	C₇×#423	C₂²	1	2	yes	—
24	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#104	C₂²	1	4	yes	—
26	C₇×#416	C₂²	1	2	yes	—
27	C₇×#408	C₂²	1	4	yes	—
28	C₇×#405	C₂²	1	4	yes	—
29	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₇×#339	C₂²	1	4	yes	—
33	C₇×#336	C₂²	1	2	yes	—
34	#22802	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂×C₇×#41	C₂³	1	2	yes	—
36	C₇×#135	—	2	2	no	—
37	C₇×#135	—	2	2	no	—
38	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
39	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
40	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₇×M₁₆	C₂³	1	4	yes	—
42	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₇×C₈	C₂³	1	2	yes	—
44	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
45	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
46	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
47	C₄×C₇×D₄	—	2	2	no	—
48	C₄×C₇×D₄	—	2	2	no	—
49	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
50	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
51	C₇×#117	—	2	2	no	—
52	C₇×#117	C₂³	1	2	yes	—
53	C₂×C₇×C₄⋊C₄	—	2	1	no	—
54	C₂×C₄²×C₇	—	2	2	no	—
55	C₂×C₄²×C₇	C₂³	1	2	yes	—
56	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
57	C₇×#108	—	2	4	no	—
58	C₇×#108	—	4	2	no	—
59	C₇×#107	C₂×C₄	1	1	yes	characteristic
60	C₇×#107	C₂×C₄	1	1	yes	characteristic
61	C₇×#106	C₂×C₄	1	2	yes	—
62	C₇×C₄⋊C₈	—	2	2	no	—
63	C₇×C₄⋊C₈	—	2	2	no	—
64	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
65	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
66	C₇×C₄⋊C₈	D₄	1	2	yes	—
67	C₇×#104	—	4	4	no	—
68	C₇×#103	C₂×C₄	1	2	yes	—
69	C₇×#103	C₂×C₄	1	2	yes	—
70	C₇×#102	C₂×C₄	1	2	yes	—
71	C₇×#102	C₂×C₄	1	2	yes	—
72	C₇×C₂²⋊C₈	—	2	4	no	—
73	C₇×C₂²⋊C₈	—	2	4	no	—
74	C₇×#97	—	2	4	no	—
75	C₄×C₇×C₈	—	2	4	no	—
76	C₄×C₇×C₈	—	2	4	no	—
77	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
78	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
79	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
80	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
81	C₇×#95	—	2	1	no	—
82	C₄×#135	C₂×C₇	1	1	yes	characteristic
83	#2925	C₂×C₇	1	2	yes	complemented
84	#1974	C₂×C₇	1	2	yes	—
85	#1929	C₂×C₇	1	4	yes	complemented
86	#1848	C₂×C₇	1	1	yes	characteristic, complemented
87	#1806	C₂×C₇	1	2	yes	complemented
88	#1772	C₂×C₇	1	2	yes	complemented
89	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
90	C₇×#41	—	2	2	no	—
91	C₇×#41	—	2	2	no	—
92	C₇×#41	—	2	2	no	—
93	C₇×#41	—	2	2	no	—
94	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
95	C₂×C₇×D₄	—	2	2	no	—
96	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₇	—	2	2	no	—
98	C₂²×C₄×C₇	—	2	2	no	—
99	C₂²×C₄×C₇	—	2	2	no	—
100	C₂²×C₄×C₇	—	2	2	no	—
101	C₂²×C₄×C₇	#41	1	1	yes	characteristic
102	C₂²×C₄×C₇	#41	1	1	yes	characteristic
103	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
104	C₇×Q₁₆	—	2	2	no	—
105	C₇×SD₁₆	—	2	4	no	—
106	C₇×D₈	—	2	2	no	—
107	C₇×M₁₆	—	2	4	no	—
108	C₇×M₁₆	—	2	4	no	—
109	C₂×C₇×C₈	—	2	2	no	—
110	C₂×C₇×C₈	—	2	1	no	—
111	C₂×C₇×C₈	—	2	1	no	—
112	C₂×C₇×C₈	—	2	2	no	—
113	C₂×C₇×C₈	—	2	4	no	—
114	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
119	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
120	C₂×C₇×C₈	#41	1	2	yes	—
121	C₂×C₇×C₈	#41	1	2	yes	—
122	C₇×C₄⋊C₄	—	2	4	no	—
123	C₇×C₄⋊C₄	—	2	2	no	—
124	C₇×C₄⋊C₄	—	2	2	no	—
125	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
126	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
127	C₇×C₂²⋊C₄	—	2	2	no	—
128	C₇×C₂²⋊C₄	—	2	2	no	—
129	C₇×C₂²⋊C₄	—	2	2	no	—
130	C₄²×C₇	—	2	2	no	—
131	C₄²×C₇	—	2	2	no	—
132	C₄²×C₇	—	2	2	no	—
133	C₄²×C₇	—	2	2	no	—
134	C₄²×C₇	—	2	2	no	—
135	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
139	C₂×#135	C₂²×C₇	1	1	yes	characteristic
140	C₄×#41	C₂²×C₇	1	2	yes	—
141	C₄×Q₁₆	C₄×C₇	1	1	yes	characteristic, complemented
142	C₄×Q₁₆	C₄×C₇	1	1	yes	characteristic, complemented
143	C₄×SD₁₆	C₄×C₇	1	2	yes	complemented
144	C₄×SD₁₆	C₄×C₇	1	2	yes	complemented
145	C₄×D₈	C₄×C₇	1	1	yes	characteristic, complemented
146	C₄×D₈	C₄×C₇	1	1	yes	characteristic, complemented
147	#433	—	2	4	no	—
148	#432	—	2	2	no	—
149	#431	—	2	2	no	—
150	C₂×#108	C₂²×C₇	1	2	yes	—
151	C₂×#108	C₂²×C₇	1	2	yes	—
152	#427	C₂²×C₇	1	1	yes	characteristic
153	#423	C₂²×C₇	1	2	yes	—
154	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
155	C₂×#104	C₂²×C₇	1	4	yes	—
156	#416	C₂²×C₇	1	2	yes	—
157	#408	C₂²×C₇	1	4	yes	—
158	#405	C₂²×C₇	1	4	yes	—
159	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
160	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
161	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
162	#339	C₂²×C₇	1	4	yes	—
163	#336	C₂²×C₇	1	2	yes	—
164	C₂³×C₇	—	2	2	no	—
165	C₂³×C₇	C₂×#41	1	1	yes	characteristic
166	C₇×Q₈	—	2	2	no	—
167	C₇×Q₈	—	2	2	no	—
168	C₇×D₄	—	2	2	no	—
169	C₇×D₄	—	2	2	no	—
170	C₇×D₄	—	4	2	no	—
171	C₇×D₄	—	4	2	no	—
172	C₂×C₄×C₇	—	2	2	no	—
173	C₂×C₄×C₇	—	2	4	no	—
174	C₂×C₄×C₇	—	2	2	no	—
175	C₂×C₄×C₇	—	2	2	no	—
176	C₂×C₄×C₇	—	2	2	no	—
177	C₂×C₄×C₇	—	4	1	no	—
178	C₂×C₄×C₇	—	4	2	no	—
179	C₂×C₄×C₇	—	4	2	no	—
180	C₂×C₄×C₇	—	4	2	no	—
181	C₂×C₄×C₇	—	4	2	no	—
182	C₂×C₄×C₇	—	4	4	no	—
183	C₂×C₄×C₇	—	8	2	no	—
184	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
194	C₇×C₈	—	2	1	no	—
195	C₇×C₈	—	2	1	no	—
196	C₇×C₈	—	2	2	no	—
197	C₇×C₈	—	2	2	no	—
198	C₇×C₈	—	4	4	no	—
199	C₇×C₈	#117	1	2	yes	—
200	C₇×C₈	#117	1	2	yes	—
201	C₂×#41	C₂³×C₇	1	2	yes	—
202	#135	—	2	2	no	—
203	#135	—	2	2	no	—
204	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
205	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
206	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
207	C₂×M₁₆	C₂³×C₇	1	4	yes	—
208	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
209	C₂²×C₈	C₂³×C₇	1	2	yes	—
210	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
211	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
212	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
213	C₄×D₄	—	2	2	no	—
214	C₄×D₄	—	2	2	no	—
215	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
216	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
217	#117	—	2	2	no	—
218	#117	C₂³×C₇	1	2	yes	—
219	C₂×C₄⋊C₄	—	2	1	no	—
220	C₂×C₄²	—	2	2	no	—
221	C₂×C₄²	C₂³×C₇	1	2	yes	—
222	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
223	#108	—	2	4	no	—
224	#108	—	4	2	no	—
225	#107	C₂×C₄×C₇	1	1	yes	characteristic
226	#107	C₂×C₄×C₇	1	1	yes	characteristic
227	#106	C₂×C₄×C₇	1	2	yes	—
228	C₄⋊C₈	—	2	2	no	—
229	C₄⋊C₈	—	2	2	no	—
230	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
231	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
232	C₄⋊C₈	C₇×D₄	1	2	yes	—
233	#104	—	4	4	no	—
234	#103	C₂×C₄×C₇	1	2	yes	—
235	#103	C₂×C₄×C₇	1	2	yes	—
236	#102	C₂×C₄×C₇	1	2	yes	—
237	#102	C₂×C₄×C₇	1	2	yes	—
238	C₂²⋊C₈	—	2	4	no	—
239	C₂²⋊C₈	—	2	4	no	—
240	#97	—	2	4	no	—
241	C₄×C₈	—	2	4	no	—
242	C₄×C₈	—	2	4	no	—
243	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
244	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
245	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
246	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
247	#95	—	2	1	no	—
248	C₂²×C₇	—	2	1	no	—
249	C₂²×C₇	—	2	1	no	—
250	C₂²×C₇	—	4	2	no	—
251	C₂²×C₇	—	4	2	no	—
252	C₂²×C₇	—	4	2	no	—
253	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂²×C₇	#555	1	1	yes	characteristic
255	C₂²×C₇	#556	1	1	yes	characteristic
256	C₄×C₇	—	2	1	no	—
257	C₄×C₇	—	2	1	no	—
258	C₄×C₇	—	2	1	no	—
259	C₄×C₇	—	4	4	no	—
260	C₄×C₇	—	4	2	no	—
261	C₄×C₇	—	4	2	no	—
262	C₄×C₇	—	4	2	no	—
263	C₄×C₇	#443	1	2	yes	—
264	C₄×C₇	C₂×#117	1	1	yes	characteristic
265	C₄×C₇	#520	1	1	yes	characteristic
266	C₄×C₇	#547	1	1	yes	characteristic
267	C₄×C₇	#550	1	1	yes	characteristic
268	#41	—	2	2	no	—
269	#41	—	2	2	no	—
270	#41	—	2	2	no	—
271	#41	—	2	2	no	—
272	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	C₇×#41	1	1	yes	characteristic
280	C₂²×C₄	C₇×#41	1	1	yes	characteristic
281	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
282	Q₁₆	—	2	2	no	—
283	SD₁₆	—	2	4	no	—
284	D₈	—	2	2	no	—
285	M₁₆	—	2	4	no	—
286	M₁₆	—	2	4	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
293	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
294	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
295	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
296	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
297	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
298	C₂×C₈	C₇×#41	1	2	yes	—
299	C₂×C₈	C₇×#41	1	2	yes	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
304	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
314	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
315	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
316	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
317	C₂×C₇	—	2	1	no	—
318	C₂×C₇	—	2	1	no	—
319	C₂×C₇	—	8	2	no	—
320	C₂×C₇	#2354	1	1	yes	characteristic
321	C₂×C₇	C₂×#443	1	1	yes	characteristic
322	C₂×C₇	#2957	1	1	yes	characteristic
323	C₂³	—	2	2	no	—
324	C₂³	C₂×C₇×#41	1	1	yes	characteristic
325	Q₈	—	2	2	no	—
326	Q₈	—	2	2	no	—
327	D₄	—	2	2	no	—
328	D₄	—	2	2	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
344	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
345	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
346	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
347	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
348	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
349	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
350	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
351	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	2	2	no	—
356	C₈	—	2	2	no	—
357	C₈	—	4	4	no	—
358	C₈	C₇×#117	1	2	yes	—
359	C₈	C₇×#117	1	2	yes	—
360	C₇	#22802	1	1	yes	characteristic, direct product factor, Sylow
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
367	C₂²	C₇×#555	1	1	yes	characteristic
368	C₂²	C₇×#556	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	2	no	—
374	C₄	—	4	2	no	—
375	C₄	—	4	2	no	—
376	C₄	C₇×#443	1	2	yes	—
377	C₄	C₂×C₇×#117	1	1	yes	characteristic
378	C₄	C₇×#520	1	1	yes	characteristic
379	C₄	C₇×#547	1	1	yes	characteristic
380	C₄	C₇×#550	1	1	yes	characteristic
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	8	2	no	—
384	C₂	C₇×#2354	1	1	yes	characteristic
385	C₂	C₂×C₇×#443	1	1	yes	characteristic
386	C₂	C₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×C₇×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2925	C₂	semidirect
4. C₇×#1929	C₂	semidirect
5. C₇×#1848	C₂	semidirect
6. C₇×#1806	C₂	semidirect
7. C₇×#1772	C₂	semidirect
8. C₇×C₈×C₄⋊C₄	C₂	semidirect
11. C₄×C₇×Q₁₆	C₄	semidirect
12. C₄×C₇×Q₁₆	C₄	semidirect
13. C₄×C₇×SD₁₆	C₄	semidirect
14. C₄×C₇×SD₁₆	C₄	semidirect
15. C₄×C₇×D₈	C₄	semidirect
16. C₄×C₇×D₈	C₄	semidirect
34. #22802	C₇	direct (N × H)
83. #2925	C₂×C₇	semidirect
85. #1929	C₂×C₇	semidirect
86. #1848	C₂×C₇	semidirect
87. #1806	C₂×C₇	semidirect
88. #1772	C₂×C₇	semidirect
89. C₈×C₄⋊C₄	C₂×C₇	semidirect
141. C₄×Q₁₆	C₄×C₇	semidirect
142. C₄×Q₁₆	C₄×C₇	semidirect
143. C₄×SD₁₆	C₄×C₇	semidirect
144. C₄×SD₁₆	C₄×C₇	semidirect
145. C₄×D₈	C₄×C₇	semidirect
146. C₄×D₈	C₄×C₇	semidirect
360. C₇	#22802	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₇×#135	2
C₇×#2925	2
C₇×#1974	2
C₇×#1929	2
C₇×#1848	2
C₇×#1806	2
C₇×#1772	2
C₇×C₈×C₄⋊C₄	2
#22802	7

Subgroups — C7×#22802 #13200018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22802 #13200018