Subgroups — #13324337

Order 1792.

630 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3168	C₂	1	1	yes	maximal, characteristic
2	#11740571	C₂	1	2	yes	maximal, complemented
3	#11729506	C₂	1	2	yes	maximal, complemented
4	#11728659	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₁₆×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728653	C₂	1	2	yes	maximal, complemented
7	SD₁₆×C₇⋊C₈	C₂	1	2	yes	maximal, complemented
8	#11728635	C₂	1	1	yes	maximal, characteristic, complemented
9	D₈×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#11727486	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#529	C₂²	1	2	yes	—
13	C₇×#499	C₄	1	1	yes	characteristic
14	C₇×#495	C₄	1	1	yes	characteristic
15	C₇×#488	C₄	1	2	yes	—
16	C₇×#467	C₄	1	1	yes	characteristic
17	C₇×#466	C₄	1	1	yes	characteristic
18	C₇×#465	C₄	1	2	yes	—
19	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
20	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
21	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
23	#89796	C₂²	1	2	yes	—
24	Q₈×C₇⋊C₈	C₂²	1	2	yes	—
25	#89784	C₂²	1	2	yes	—
26	#89783	—	2	2	no	—
27	D₄×C₇⋊C₈	—	2	2	no	—
28	D₄×C₇⋊C₈	C₂²	1	2	yes	—
29	#89772	—	2	2	no	—
30	#89769	—	2	2	no	—
31	#89698	C₂²	1	2	yes	—
32	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
34	Q₈⋊(C₇⋊C₈)	C₂²	1	2	yes	—
35	Q₈⋊(C₇⋊C₈)	C₂²	1	2	yes	—
36	D₄⋊(C₇⋊C₈)	C₂²	1	2	yes	—
37	D₄⋊(C₇⋊C₈)	C₂²	1	2	yes	—
38	#89253	C₂²	1	1	yes	characteristic
39	#89253	C₂²	1	1	yes	characteristic
40	#89252	C₂²	1	2	yes	—
41	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
42	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
43	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
44	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
45	#17959	—	7	1	no	maximal, Sylow
46	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
47	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
51	C₇×#126	—	2	2	no	—
52	C₇×#125	C₂×C₄	1	2	yes	—
53	C₇×#124	C₂×C₄	1	2	yes	—
54	C₇×#123	—	2	2	no	—
55	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
56	C₇×#121	C₂×C₄	1	2	yes	—
57	C₄×C₇×Q₈	C₂³	1	2	yes	—
58	C₄×C₇×D₄	—	2	2	no	—
59	C₄×C₇×D₄	C₂³	1	2	yes	—
60	C₇×#117	—	2	2	no	—
61	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
62	C₂×#1136	—	2	2	no	—
63	C₂²×C₇⋊C₈	—	2	1	no	—
64	C₂²×C₇⋊C₈	—	2	2	no	—
65	C₂²×C₇⋊C₈	D₄	1	1	yes	characteristic
66	C₂²×C₇⋊C₈	D₄	1	1	yes	characteristic
67	C₇×#107	C₂×C₄	1	1	yes	characteristic
68	C₇×#107	C₂×C₄	1	1	yes	characteristic
69	C₇×#106	C₂×C₄	1	2	yes	—
70	C₇×#103	C₂×C₄	1	2	yes	—
71	C₇×#103	C₂×C₄	1	2	yes	—
72	C₇×#102	C₂×C₄	1	2	yes	—
73	C₇×#102	C₂×C₄	1	2	yes	—
74	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
75	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
79	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
80	C₂²⋊(C₇⋊C₈)	—	2	2	no	—
81	C₄⋊(C₇⋊C₈)	—	2	2	no	—
82	C₄⋊(C₇⋊C₈)	—	2	2	no	—
83	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
84	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
85	#6377	—	2	2	no	—
86	#6377	—	2	2	no	—
87	C₄×C₇⋊C₈	—	2	1	no	—
88	C₄×C₇⋊C₈	—	2	2	no	—
89	C₄×C₇⋊C₈	D₄	1	1	yes	characteristic
90	C₄×C₇⋊C₈	D₄	1	1	yes	characteristic
91	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
92	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
93	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
94	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
95	#3168	D₇	1	1	yes	characteristic
96	#2966	—	7	2	no	—
97	#1591	—	7	1	no	—
98	#1590	—	7	2	no	—
99	#1589	—	7	1	no	—
100	C₈×Q₁₆	—	7	1	no	—
101	C₈×SD₁₆	—	7	2	no	—
102	C₈×D₈	—	7	1	no	—
103	#1568	—	7	1	no	—
104	#1494	—	7	2	no	—
105	C₂×C₈²	—	7	1	no	—
106	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
107	C₂×C₇×D₄	—	2	2	no	—
108	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₇	—	2	2	no	—
110	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇	#41	1	1	yes	characteristic
113	C₇×Q₁₆	—	2	2	no	—
114	C₇×SD₁₆	—	2	4	no	—
115	C₇×D₈	—	2	2	no	—
116	C₂×C₇×C₈	—	2	2	no	—
117	C₂×C₇×C₈	—	2	2	no	—
118	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
122	C₇×C₄⋊C₄	—	2	2	no	—
123	C₇×C₄⋊C₄	—	2	2	no	—
124	C₇×C₄⋊C₄	—	2	2	no	—
125	C₇×C₄⋊C₄	—	2	2	no	—
126	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
127	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
128	C₇×C₂²⋊C₄	—	2	2	no	—
129	C₇×C₂²⋊C₄	—	2	2	no	—
130	C₇×C₂²⋊C₄	—	2	2	no	—
131	C₇×C₂²⋊C₄	—	2	2	no	—
132	C₇×C₂²⋊C₄	—	2	2	no	—
133	C₄²×C₇	—	2	2	no	—
134	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₇	#41	1	1	yes	characteristic
137	C₄²×C₇	C₂⁴	1	1	yes	characteristic
138	#1136	—	4	4	no	—
139	C₂×C₇⋊C₈	—	2	4	no	—
140	C₂×C₇⋊C₈	—	2	1	no	—
141	C₂×C₇⋊C₈	—	2	1	no	—
142	C₂×C₇⋊C₈	—	2	2	no	—
143	C₂×C₇⋊C₈	—	2	2	no	—
144	C₂×C₇⋊C₈	—	2	2	no	—
145	C₂×C₇⋊C₈	—	2	2	no	—
146	C₂×C₇⋊C₈	—	4	4	no	—
147	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
148	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
149	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
150	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
151	#529	C₂×D₇	1	2	yes	—
152	#499	Dic₇	1	1	yes	characteristic
153	#495	Dic₇	1	1	yes	characteristic
154	#488	Dic₇	1	2	yes	—
155	#467	Dic₇	1	1	yes	characteristic
156	#466	Dic₇	1	1	yes	characteristic
157	#465	Dic₇	1	2	yes	—
158	#446	—	7	2	no	—
159	C₈×Q₈	—	7	2	no	—
160	C₄×Q₁₆	C₂×D₇	1	1	yes	characteristic
161	C₄×SD₁₆	C₂×D₇	1	2	yes	—
162	C₄×D₈	C₂×D₇	1	1	yes	characteristic
163	#436	—	7	2	no	—
164	#435	—	14	2	no	—
165	C₈×D₄	—	7	2	no	—
166	C₈×D₄	—	14	2	no	—
167	#433	—	14	2	no	—
168	#432	—	7	2	no	—
169	#405	—	14	2	no	—
170	C₂×C₄×C₈	—	7	1	no	—
171	C₂×C₄×C₈	—	7	1	no	—
172	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
173	#335	—	7	1	no	—
174	#335	—	7	1	no	—
175	#334	—	7	2	no	—
176	Q₈⋊C₈	—	7	2	no	—
177	Q₈⋊C₈	—	7	2	no	—
178	D₄⋊C₈	—	7	2	no	—
179	D₄⋊C₈	—	7	2	no	—
180	C₈²	—	7	1	no	—
181	C₈²	—	7	1	no	—
182	C₈²	—	7	1	no	—
183	C₈²	—	7	1	no	—
184	C₂³×C₇	—	2	2	no	—
185	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
186	C₇×Q₈	—	2	2	no	—
187	C₇×Q₈	—	2	2	no	—
188	C₇×D₄	—	2	2	no	—
189	C₇×D₄	—	2	2	no	—
190	C₇×D₄	—	4	4	no	—
191	C₂×C₄×C₇	—	2	2	no	—
192	C₂×C₄×C₇	—	2	1	no	—
193	C₂×C₄×C₇	—	2	1	no	—
194	C₂×C₄×C₇	—	2	1	no	—
195	C₂×C₄×C₇	—	2	1	no	—
196	C₂×C₄×C₇	—	2	2	no	—
197	C₂×C₄×C₇	—	2	2	no	—
198	C₂×C₄×C₇	—	2	2	no	—
199	C₂×C₄×C₇	—	4	2	no	—
200	C₂×C₄×C₇	—	4	2	no	—
201	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
207	C₇×C₈	—	2	1	no	—
208	C₇×C₈	—	2	1	no	—
209	C₇×C₈	#131	1	2	yes	—
210	C₇×C₈	#131	1	2	yes	—
211	C₇⋊C₈	—	2	2	no	—
212	C₇⋊C₈	—	2	2	no	—
213	C₇⋊C₈	—	2	1	no	—
214	C₇⋊C₈	—	2	1	no	—
215	C₇⋊C₈	—	4	2	no	—
216	C₇⋊C₈	—	4	2	no	—
217	C₇⋊C₈	#135	1	2	yes	—
218	C₇⋊C₈	#135	1	2	yes	—
219	C₂×Q₁₆	C₂×Dic₇	1	1	yes	characteristic
220	C₂×SD₁₆	C₂×Dic₇	1	2	yes	—
221	C₂×D₈	C₂×Dic₇	1	1	yes	characteristic
222	C₂×M₁₆	—	14	2	no	—
223	C₂²×C₈	—	7	1	no	—
224	C₂²×C₈	—	7	1	no	—
225	C₂²×C₈	—	14	2	no	—
226	C₂²×C₈	—	14	1	no	—
227	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
228	C₂²×C₈	C₂×Dic₇	1	1	yes	characteristic
229	#126	—	2	2	no	—
230	#125	C₂×Dic₇	1	2	yes	—
231	#124	C₂×Dic₇	1	2	yes	—
232	#123	—	2	2	no	—
233	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
234	#121	C₂×Dic₇	1	2	yes	—
235	C₄×Q₈	C₂²×D₇	1	2	yes	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	C₂²×D₇	1	2	yes	—
238	#117	—	2	2	no	—
239	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
240	#107	C₂×Dic₇	1	1	yes	characteristic
241	#107	C₂×Dic₇	1	1	yes	characteristic
242	#106	C₂×Dic₇	1	2	yes	—
243	C₄⋊C₈	—	7	2	no	—
244	C₄⋊C₈	—	7	2	no	—
245	C₄⋊C₈	—	14	2	no	—
246	C₄⋊C₈	—	14	2	no	—
247	#103	C₂×Dic₇	1	2	yes	—
248	#103	C₂×Dic₇	1	2	yes	—
249	#102	C₂×Dic₇	1	2	yes	—
250	#102	C₂×Dic₇	1	2	yes	—
251	C₂²⋊C₈	—	14	2	no	—
252	C₂²⋊C₈	—	14	2	no	—
253	C₂²⋊C₈	—	14	2	no	—
254	#97	—	14	2	no	—
255	#97	—	14	2	no	—
256	C₄×C₈	—	7	1	no	—
257	C₄×C₈	—	7	1	no	—
258	C₄×C₈	—	7	1	no	—
259	C₄×C₈	—	7	1	no	—
260	C₄×C₈	—	7	1	no	—
261	C₄×C₈	—	7	1	no	—
262	C₄×C₈	—	14	2	no	—
263	C₄×C₈	—	14	1	no	—
264	C₄×C₈	C₂×Dic₇	1	1	yes	characteristic
265	C₄×C₈	C₂×Dic₇	1	1	yes	characteristic
266	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
267	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
268	C₂²×C₇	—	2	1	no	—
269	C₂²×C₇	—	2	1	no	—
270	C₂²×C₇	—	4	2	no	—
271	C₂²×C₇	—	4	2	no	—
272	C₂²×C₇	—	4	2	no	—
273	C₂²×C₇	#443	1	2	yes	—
274	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
275	C₄×C₇	—	2	1	no	—
276	C₄×C₇	—	2	1	no	—
277	C₄×C₇	—	2	1	no	—
278	C₄×C₇	—	2	1	no	—
279	C₄×C₇	—	4	2	no	—
280	C₄×C₇	—	4	2	no	—
281	C₄×C₇	—	4	2	no	—
282	C₄×C₇	C₂×#131	1	1	yes	characteristic
283	C₄×C₇	C₂×#131	1	1	yes	characteristic
284	C₄×C₇	C₂×#135	1	1	yes	characteristic
285	C₄×C₇	C₂×#135	1	1	yes	characteristic
286	C₂×Q₈	C₂²×Dic₇	1	2	yes	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	C₂²×Dic₇	1	2	yes	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
291	C₂²×C₄	#1159	1	1	yes	characteristic
292	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
293	Q₁₆	—	2	2	no	—
294	SD₁₆	—	2	4	no	—
295	D₈	—	2	2	no	—
296	M₁₆	—	28	4	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	7	1	no	—
300	C₂×C₈	—	7	1	no	—
301	C₂×C₈	—	7	1	no	—
302	C₂×C₈	—	7	1	no	—
303	C₂×C₈	—	14	2	no	—
304	C₂×C₈	—	14	2	no	—
305	C₂×C₈	—	14	4	no	—
306	C₂×C₈	—	14	1	no	—
307	C₂×C₈	—	14	1	no	—
308	C₂×C₈	—	14	2	no	—
309	C₂×C₈	—	14	2	no	—
310	C₂×C₈	—	28	4	no	—
311	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
312	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
313	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
314	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
320	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	D₄×D₇	1	1	yes	characteristic
328	C₄²	#1159	1	1	yes	characteristic
329	C₄²	C₂²×Dic₇	1	1	yes	characteristic
330	C₄²	C₂³×D₇	1	1	yes	characteristic
331	C₂×C₇	—	2	2	no	—
332	C₂×C₇	—	8	2	no	—
333	C₂×C₇	#2931	1	1	yes	characteristic
334	C₂×C₇	C₄×#135	1	1	yes	characteristic
335	C₂×C₇	C₂×#443	1	1	yes	characteristic
336	C₂³	—	2	2	no	—
337	C₂³	D₄×Dic₇	1	1	yes	characteristic
338	Q₈	—	2	2	no	—
339	Q₈	—	2	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	2	2	no	—
342	D₄	—	4	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
354	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
355	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
356	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
357	C₂×C₄	C₂×#1159	1	1	yes	characteristic
358	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	7	2	no	—
362	C₈	—	7	2	no	—
363	C₈	—	14	2	no	—
364	C₈	—	14	2	no	—
365	C₈	—	14	1	no	—
366	C₈	—	14	1	no	—
367	C₈	—	28	2	no	—
368	C₈	—	28	2	no	—
369	C₈	#6511	1	2	yes	—
370	C₈	#6511	1	2	yes	—
371	C₇	#17959	1	1	yes	characteristic, complemented, Sylow
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	#89968	1	2	yes	—
378	C₂²	C₂×D₄×Dic₇	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	D₇×#135	1	1	yes	characteristic
387	C₄	D₇×#135	1	1	yes	characteristic
388	C₄	C₂×#6511	1	1	yes	characteristic
389	C₄	C₂×#6511	1	1	yes	characteristic
390	C₂	—	2	2	no	—
391	C₂	—	8	2	no	—
392	C₂	#11740720	1	1	yes	characteristic
393	C₂	Dic₇×#135	1	1	yes	characteristic
394	C₂	C₂×#89968	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₇×#3168	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#466	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#3168	D₇
hypocenter	C₇	#17959
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3168

Complements

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

N	H ≅ G/N	type
2. #11740571	C₂	semidirect
3. #11729506	C₂	semidirect
4. #11728659	C₂	semidirect
5. Q₁₆×C₇⋊C₈	C₂	semidirect
6. #11728653	C₂	semidirect
7. SD₁₆×C₇⋊C₈	C₂	semidirect
8. #11728635	C₂	semidirect
9. D₈×C₇⋊C₈	C₂	semidirect
10. #11727486	C₂	semidirect
11. C₂×C₈×C₇⋊C₈	C₂	semidirect
371. C₇	#17959	semidirect

Maximal subgroups

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

subgroup	index
C₇×#3168	2
#11740571	2
#11729506	2
#11728659	2
Q₁₆×C₇⋊C₈	2
#11728653	2
SD₁₆×C₇⋊C₈	2
#11728635	2
D₈×C₇⋊C₈	2
#11727486	2
C₂×C₈×C₇⋊C₈	2
#17959	7