Subgroups — C₂²×C₇×#536 #13239896

Order 1792.

11406 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₇×#41	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#536	C₂	1	48	yes	maximal, direct product factor
4	C₂²×C₇×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
5	C₂²×C₇×#124	C₂	1	2	yes	maximal, complemented
6	C₂²×C₇×#123	C₂	1	4	yes	maximal, complemented
7	C₂²×C₇×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
8	C₂²×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×#41	—	2	16	no	—
10	C₂²×C₇×#41	C₂²	1	24	yes	—
11	C₂³×C₇×Q₈	—	2	16	no	—
12	C₂³×C₇×Q₈	C₂²	1	2	yes	—
13	C₂³×C₇×Q₈	C₂²	1	2	yes	—
14	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
15	C₂³×C₇×Q₈	C₂²	1	24	yes	complemented
16	C₂³×C₇×D₄	C₂²	1	2	yes	—
17	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
20	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
21	C₇×#536	C₂²	1	256	yes	direct product factor
22	C₂×C₇×C₄⋊Q₈	C₂²	1	48	yes	complemented
23	C₂×C₇×#124	C₂²	1	48	yes	complemented
24	C₂×C₇×#123	C₂²	1	96	yes	complemented
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	96	yes	complemented
26	C₂×C₇×#117	C₂²	1	24	yes	complemented
27	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₇×C₄⋊C₄	C₂²	1	8	yes	—
29	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
31	C₂²×C₄²×C₇	C₂²	1	2	yes	—
32	C₂²×#536	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂⁵×C₇	C₂³	1	2	yes	—
34	C₂⁵×C₇	C₂³	1	1	yes	characteristic
35	C₂×C₇×#41	—	2	192	no	—
36	C₂×C₇×#41	C₂³	1	64	yes	—
37	C₂²×C₇×Q₈	—	2	16	no	—
38	C₂²×C₇×Q₈	—	2	16	no	—
39	C₂²×C₇×Q₈	—	2	192	no	—
40	C₂²×C₇×Q₈	—	2	8	no	—
41	C₂²×C₇×Q₈	C₂³	1	24	yes	—
42	C₂²×C₇×Q₈	C₂³	1	24	yes	—
43	C₂²×C₇×Q₈	C₂³	1	12	yes	—
44	C₂²×C₇×Q₈	C₂³	1	64	yes	complemented
45	C₂²×C₇×D₄	—	2	16	no	—
46	C₂²×C₇×D₄	—	2	8	no	—
47	C₂²×C₇×D₄	C₂³	1	24	yes	—
48	C₂²×C₇×D₄	C₂³	1	12	yes	—
49	C₂³×C₄×C₇	—	2	16	no	—
50	C₂³×C₄×C₇	—	2	16	no	—
51	C₂³×C₄×C₇	D₄	1	16	yes	—
52	C₂³×C₄×C₇	C₂³	1	24	yes	—
53	C₂³×C₄×C₇	C₂³	1	24	yes	—
54	C₂³×C₄×C₇	C₂³	1	2	yes	—
55	C₂³×C₄×C₇	C₂³	1	4	yes	—
56	C₂³×C₄×C₇	C₂³	1	4	yes	—
57	C₂³×C₄×C₇	C₂³	1	12	yes	—
58	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
60	C₇×C₄⋊Q₈	C₂³	1	128	yes	complemented
61	C₇×#124	C₂³	1	128	yes	complemented
62	C₇×#123	C₂³	1	256	yes	complemented
63	C₇×C₂²⋊Q₈	C₂³	1	256	yes	complemented
64	C₇×#117	C₂³	1	64	yes	complemented
65	C₂×C₇×C₄⋊C₄	C₂³	1	24	yes	—
66	C₂×C₇×C₄⋊C₄	C₂³	1	96	yes	—
67	C₂×C₇×C₂²⋊C₄	C₂³	1	24	yes	—
68	C₂×C₇×C₂²⋊C₄	C₂³	1	96	yes	—
69	C₂×C₄²×C₇	C₂³	1	24	yes	—
70	C₂³×#41	C₂×C₇	1	1	yes	characteristic
71	C₂⁴×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
72	C₂×#536	C₂×C₇	1	48	yes	direct product factor
73	C₂²×C₄⋊Q₈	C₂×C₇	1	2	yes	complemented
74	C₂²×#124	C₂×C₇	1	2	yes	complemented
75	C₂²×#123	C₂×C₇	1	4	yes	complemented
76	C₂²×C₂²⋊Q₈	C₂×C₇	1	4	yes	complemented
77	C₂²×#117	C₂×C₇	1	1	yes	characteristic, complemented
78	C₂⁴×C₇	—	2	8	no	—
79	C₂⁴×C₇	—	2	8	no	—
80	C₂⁴×C₇	—	2	16	no	—
81	C₂⁴×C₇	C₂×D₄	1	8	yes	—
82	C₂⁴×C₇	C₂⁴	1	12	yes	—
83	C₂⁴×C₇	C₂⁴	1	6	yes	—
84	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
85	C₇×#41	—	2	256	no	—
86	C₂×C₇×Q₈	—	2	96	no	—
87	C₂×C₇×Q₈	—	2	96	no	—
88	C₂×C₇×Q₈	—	2	256	no	—
89	C₂×C₇×Q₈	—	2	48	no	—
90	C₂×C₇×Q₈	C₂⁴	1	32	yes	—
91	C₂×C₇×Q₈	C₂⁴	1	32	yes	—
92	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
93	C₂×C₇×D₄	—	2	96	no	—
94	C₂×C₇×D₄	—	2	48	no	—
95	C₂×C₇×D₄	C₂⁴	1	32	yes	—
96	C₂×C₇×D₄	C₂⁴	1	16	yes	—
97	C₂²×C₄×C₇	—	2	8	no	—
98	C₂²×C₄×C₇	—	2	96	no	—
99	C₂²×C₄×C₇	—	2	16	no	—
100	C₂²×C₄×C₇	—	2	16	no	—
101	C₂²×C₄×C₇	—	2	96	no	—
102	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
104	C₂²×C₄×C₇	C₂×D₄	1	96	yes	—
105	C₂²×C₄×C₇	C₂⁴	1	24	yes	—
106	C₂²×C₄×C₇	C₂⁴	1	24	yes	—
107	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
108	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
109	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
110	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
111	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
112	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
113	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
114	C₇×C₄⋊C₄	C₂⁴	1	128	yes	—
115	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
116	C₇×C₂²⋊C₄	C₂⁴	1	128	yes	—
117	C₄²×C₇	C₂⁴	1	32	yes	—
118	C₂²×#41	—	2	16	no	—
119	C₂²×#41	C₂²×C₇	1	24	yes	—
120	C₂³×Q₈	—	2	16	no	—
121	C₂³×Q₈	C₂²×C₇	1	2	yes	—
122	C₂³×Q₈	C₂²×C₇	1	2	yes	—
123	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
124	C₂³×Q₈	C₂²×C₇	1	24	yes	complemented
125	C₂³×D₄	C₂²×C₇	1	2	yes	—
126	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
127	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
128	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
129	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
130	#536	C₂²×C₇	1	256	yes	direct product factor
131	C₂×C₄⋊Q₈	C₂²×C₇	1	48	yes	complemented
132	C₂×#124	C₂²×C₇	1	48	yes	complemented
133	C₂×#123	C₂²×C₇	1	96	yes	complemented
134	C₂×C₂²⋊Q₈	C₂²×C₇	1	96	yes	complemented
135	C₂×#117	C₂²×C₇	1	24	yes	complemented
136	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
137	C₂²×C₄⋊C₄	C₂²×C₇	1	8	yes	—
138	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
139	C₂²×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
140	C₂²×C₄²	C₂²×C₇	1	2	yes	—
141	C₂³×C₇	—	2	32	no	—
142	C₂³×C₇	—	2	24	no	—
143	C₂³×C₇	—	2	24	no	—
144	C₂³×C₇	—	2	48	no	—
145	C₂³×C₇	—	4	32	no	—
146	C₂³×C₇	C₂²×D₄	1	24	yes	—
147	C₂³×C₇	C₂²×D₄	1	4	yes	—
148	C₂³×C₇	2₋¹⁺⁴	1	8	yes	—
149	C₂³×C₇	C₂⁵	1	8	yes	—
150	C₂³×C₇	C₂⁵	1	4	yes	—
151	C₂³×C₇	C₂⁵	1	3	yes	—
152	C₇×Q₈	—	2	64	no	—
153	C₇×Q₈	—	2	64	no	—
154	C₇×Q₈	—	2	32	no	—
155	C₇×D₄	—	2	64	no	—
156	C₇×D₄	—	2	32	no	—
157	C₂×C₄×C₇	—	2	24	no	—
158	C₂×C₄×C₇	—	2	64	no	—
159	C₂×C₄×C₇	—	2	48	no	—
160	C₂×C₄×C₇	—	2	48	no	—
161	C₂×C₄×C₇	—	2	64	no	—
162	C₂×C₄×C₇	C₂²×D₄	1	24	yes	—
163	C₂×C₄×C₇	C₂²×D₄	1	24	yes	—
164	C₂×C₄×C₇	C₂²×D₄	1	64	yes	—
165	C₂×C₄×C₇	C₂⁵	1	16	yes	—
166	C₂×C₄×C₇	C₂⁵	1	16	yes	—
167	C₂×C₄×C₇	C₂⁵	1	8	yes	—
168	C₂×C₄×C₇	C₂⁵	1	4	yes	—
169	C₂×C₄×C₇	C₂⁵	1	4	yes	—
170	C₂⁵	C₂³×C₇	1	2	yes	—
171	C₂⁵	C₂³×C₇	1	1	yes	characteristic
172	C₂×#41	—	2	192	no	—
173	C₂×#41	C₂³×C₇	1	64	yes	—
174	C₂²×Q₈	—	2	16	no	—
175	C₂²×Q₈	—	2	16	no	—
176	C₂²×Q₈	—	2	192	no	—
177	C₂²×Q₈	—	2	8	no	—
178	C₂²×Q₈	C₂³×C₇	1	24	yes	—
179	C₂²×Q₈	C₂³×C₇	1	24	yes	—
180	C₂²×Q₈	C₂³×C₇	1	12	yes	—
181	C₂²×Q₈	C₂³×C₇	1	64	yes	complemented
182	C₂²×D₄	—	2	16	no	—
183	C₂²×D₄	—	2	8	no	—
184	C₂²×D₄	C₂³×C₇	1	24	yes	—
185	C₂²×D₄	C₂³×C₇	1	12	yes	—
186	C₂³×C₄	—	2	16	no	—
187	C₂³×C₄	—	2	16	no	—
188	C₂³×C₄	C₇×D₄	1	16	yes	—
189	C₂³×C₄	C₂³×C₇	1	4	yes	—
190	C₂³×C₄	C₂³×C₇	1	4	yes	—
191	C₂³×C₄	C₂³×C₇	1	2	yes	—
192	C₂³×C₄	C₂³×C₇	1	24	yes	—
193	C₂³×C₄	C₂³×C₇	1	24	yes	—
194	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
195	C₂³×C₄	C₂³×C₇	1	12	yes	—
196	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
197	C₄⋊Q₈	C₂³×C₇	1	128	yes	complemented
198	#124	C₂³×C₇	1	128	yes	complemented
199	#123	C₂³×C₇	1	256	yes	complemented
200	C₂²⋊Q₈	C₂³×C₇	1	256	yes	complemented
201	#117	C₂³×C₇	1	64	yes	complemented
202	C₂×C₄⋊C₄	C₂³×C₇	1	24	yes	—
203	C₂×C₄⋊C₄	C₂³×C₇	1	96	yes	—
204	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
205	C₂×C₂²⋊C₄	C₂³×C₇	1	96	yes	—
206	C₂×C₄²	C₂³×C₇	1	24	yes	—
207	C₂²×C₇	—	2	8	no	—
208	C₂²×C₇	—	2	48	no	—
209	C₂²×C₇	—	2	8	no	—
210	C₂²×C₇	—	2	16	no	—
211	C₂²×C₇	—	4	48	no	—
212	C₂²×C₇	#536	1	16	yes	direct product factor
213	C₂²×C₇	C₂³×D₄	1	8	yes	—
214	C₂²×C₇	C₂³×D₄	1	6	yes	—
215	C₂²×C₇	C₂×2₋¹⁺⁴	1	12	yes	—
216	C₂²×C₇	C₂⁶	1	1	yes	characteristic
217	C₄×C₇	—	2	8	no	—
218	C₄×C₇	—	2	16	no	—
219	C₄×C₇	—	2	16	no	—
220	C₄×C₇	C₂³×D₄	1	8	yes	—
221	C₄×C₇	C₂³×D₄	1	8	yes	—
222	C₂⁴	—	2	8	no	—
223	C₂⁴	—	2	8	no	—
224	C₂⁴	—	2	16	no	—
225	C₂⁴	C₂×C₇×D₄	1	8	yes	—
226	C₂⁴	C₂⁴×C₇	1	12	yes	—
227	C₂⁴	C₂⁴×C₇	1	6	yes	—
228	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
229	#41	—	2	256	no	—
230	C₂×Q₈	—	2	96	no	—
231	C₂×Q₈	—	2	96	no	—
232	C₂×Q₈	—	2	256	no	—
233	C₂×Q₈	—	2	48	no	—
234	C₂×Q₈	C₂⁴×C₇	1	32	yes	—
235	C₂×Q₈	C₂⁴×C₇	1	32	yes	—
236	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
237	C₂×D₄	—	2	96	no	—
238	C₂×D₄	—	2	48	no	—
239	C₂×D₄	C₂⁴×C₇	1	32	yes	—
240	C₂×D₄	C₂⁴×C₇	1	16	yes	—
241	C₂²×C₄	—	2	8	no	—
242	C₂²×C₄	—	2	96	no	—
243	C₂²×C₄	—	2	16	no	—
244	C₂²×C₄	—	2	16	no	—
245	C₂²×C₄	—	2	96	no	—
246	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
247	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
248	C₂²×C₄	C₂×C₇×D₄	1	96	yes	—
249	C₂²×C₄	C₂⁴×C₇	1	24	yes	—
250	C₂²×C₄	C₂⁴×C₇	1	24	yes	—
251	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
252	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
253	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
254	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
255	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
256	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
257	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
258	C₄⋊C₄	C₂⁴×C₇	1	128	yes	—
259	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
260	C₂²⋊C₄	C₂⁴×C₇	1	128	yes	—
261	C₄²	C₂⁴×C₇	1	32	yes	—
262	C₂×C₇	—	2	8	no	—
263	C₂×C₇	—	4	8	no	—
264	C₂×C₇	C₂×#536	1	12	yes	direct product factor
265	C₂×C₇	C₂⁴×D₄	1	1	yes	characteristic
266	C₂×C₇	C₂²×2₋¹⁺⁴	1	2	yes	—
267	C₂³	—	2	24	no	—
268	C₂³	—	2	32	no	—
269	C₂³	—	2	24	no	—
270	C₂³	—	2	48	no	—
271	C₂³	—	4	32	no	—
272	C₂³	C₂²×C₇×D₄	1	24	yes	—
273	C₂³	C₂²×C₇×D₄	1	4	yes	—
274	C₂³	C₇×2₋¹⁺⁴	1	8	yes	—
275	C₂³	C₂⁵×C₇	1	8	yes	—
276	C₂³	C₂⁵×C₇	1	4	yes	—
277	C₂³	C₂⁵×C₇	1	3	yes	—
278	Q₈	—	2	64	no	—
279	Q₈	—	2	64	no	—
280	Q₈	—	2	32	no	—
281	D₄	—	2	64	no	—
282	D₄	—	2	32	no	—
283	C₂×C₄	—	2	24	no	—
284	C₂×C₄	—	2	64	no	—
285	C₂×C₄	—	2	48	no	—
286	C₂×C₄	—	2	48	no	—
287	C₂×C₄	—	2	64	no	—
288	C₂×C₄	C₂²×C₇×D₄	1	24	yes	—
289	C₂×C₄	C₂²×C₇×D₄	1	24	yes	—
290	C₂×C₄	C₂²×C₇×D₄	1	64	yes	—
291	C₂×C₄	C₂⁵×C₇	1	16	yes	—
292	C₂×C₄	C₂⁵×C₇	1	16	yes	—
293	C₂×C₄	C₂⁵×C₇	1	8	yes	—
294	C₂×C₄	C₂⁵×C₇	1	4	yes	—
295	C₂×C₄	C₂⁵×C₇	1	4	yes	—
296	C₇	C₂²×#536	1	1	yes	characteristic, direct product factor, Sylow
297	C₂²	—	2	8	no	—
298	C₂²	—	2	48	no	—
299	C₂²	—	2	8	no	—
300	C₂²	—	2	16	no	—
301	C₂²	—	4	48	no	—
302	C₂²	C₇×#536	1	16	yes	direct product factor
303	C₂²	C₂³×C₇×D₄	1	8	yes	—
304	C₂²	C₂³×C₇×D₄	1	6	yes	—
305	C₂²	C₂×C₇×2₋¹⁺⁴	1	12	yes	—
306	C₂²	C₂⁶×C₇	1	1	yes	characteristic
307	C₄	—	2	8	no	—
308	C₄	—	2	16	no	—
309	C₄	—	2	16	no	—
310	C₄	C₂³×C₇×D₄	1	8	yes	—
311	C₄	C₂³×C₇×D₄	1	8	yes	—
312	C₂	—	2	8	no	—
313	C₂	—	4	8	no	—
314	C₂	C₂×C₇×#536	1	12	yes	direct product factor
315	C₂	C₂⁴×C₇×D₄	1	1	yes	characteristic
316	C₂	C₂²×C₇×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
prime radical	C₂³×C₇×#41	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₇×Q₈	C₂	semidirect
3. C₂×C₇×#536	C₂	direct (N × H)
4. C₂²×C₇×C₄⋊Q₈	C₂	semidirect
5. C₂²×C₇×#124	C₂	semidirect
6. C₂²×C₇×#123	C₂	semidirect
7. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
8. C₂²×C₇×#117	C₂	semidirect
15. C₂³×C₇×Q₈	C₂²	semidirect
21. C₇×#536	C₂²	direct (N × H)
22. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₇×#124	C₂²	semidirect
24. C₂×C₇×#123	C₂²	semidirect
25. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₇×#117	C₂²	semidirect
32. C₂²×#536	C₇	direct (N × H)
44. C₂²×C₇×Q₈	C₂³	semidirect
60. C₇×C₄⋊Q₈	C₂³	semidirect
61. C₇×#124	C₂³	semidirect
62. C₇×#123	C₂³	semidirect
63. C₇×C₂²⋊Q₈	C₂³	semidirect
64. C₇×#117	C₂³	semidirect
71. C₂⁴×Q₈	C₂×C₇	semidirect
72. C₂×#536	C₂×C₇	direct (N × H)
73. C₂²×C₄⋊Q₈	C₂×C₇	semidirect
74. C₂²×#124	C₂×C₇	semidirect
75. C₂²×#123	C₂×C₇	semidirect
76. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
77. C₂²×#117	C₂×C₇	semidirect
124. C₂³×Q₈	C₂²×C₇	semidirect
130. #536	C₂²×C₇	direct (N × H)
131. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
132. C₂×#124	C₂²×C₇	semidirect
133. C₂×#123	C₂²×C₇	semidirect
134. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
135. C₂×#117	C₂²×C₇	semidirect
181. C₂²×Q₈	C₂³×C₇	semidirect
197. C₄⋊Q₈	C₂³×C₇	semidirect
198. #124	C₂³×C₇	semidirect
199. #123	C₂³×C₇	semidirect
200. C₂²⋊Q₈	C₂³×C₇	semidirect
201. #117	C₂³×C₇	semidirect
212. C₂²×C₇	#536	direct (N × H)
264. C₂×C₇	C₂×#536	direct (N × H)
296. C₇	C₂²×#536	direct (N × H)
302. C₂²	C₇×#536	direct (N × H)
314. C₂	C₂×C₇×#536	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₇×#41	2
C₂⁴×C₇×Q₈	2
C₂×C₇×#536	2
C₂²×C₇×C₄⋊Q₈	2
C₂²×C₇×#124	2
C₂²×C₇×#123	2
C₂²×C₇×C₂²⋊Q₈	2
C₂²×C₇×#117	2
C₂²×#536	7

Subgroups — C22×C7×#536 #13239896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×#536 #13239896