Subgroups — #11737310

Order 896.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#6474	C₂	1	1	yes	maximal, characteristic
2	C₄×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#1159	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#442	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#89790	C₂	1	1	yes	maximal, characteristic, complemented
7	#89786	C₂	1	1	yes	maximal, characteristic, complemented
8	#89633	C₂	1	1	yes	maximal, characteristic, complemented
9	#89624	C₂	1	1	yes	maximal, characteristic, complemented
10	#89543	C₂	1	1	yes	maximal, characteristic, complemented
11	#89542	C₂	1	1	yes	maximal, characteristic, complemented
12	#89530	C₂	1	1	yes	maximal, characteristic, complemented
13	#89528	C₂	1	1	yes	maximal, characteristic, complemented
14	#89482	C₂	1	1	yes	maximal, characteristic, complemented
15	#89479	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#1159	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₇	—	2	1	no	—
19	C₂×C₇×D₈	C₂²	1	1	yes	characteristic
20	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
22	D₄×Dic₇	C₂²	1	1	yes	characteristic
23	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
24	C₂×#1142	C₂²	1	1	yes	characteristic
25	C₂×#1141	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊D₇	—	2	1	no	—
27	C₄×C₂²⋊D₇	—	2	1	no	—
28	C₂×C₄×Dic₇	—	2	1	no	—
29	#6474	C₄	1	8	yes	complemented
30	C₂×#1132	C₂²	1	1	yes	characteristic
31	C₂×#1131	C₂²	1	1	yes	characteristic
32	C₂×#1131	C₂²	1	1	yes	characteristic
33	#6456	C₂²	1	1	yes	characteristic
34	#6455	C₂²	1	1	yes	characteristic
35	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	#6450	C₂²	1	1	yes	characteristic, complemented
37	(C₂²⋊D₇)⋊C₄	—	2	1	no	—
38	(C₂²⋊D₇)⋊C₄	—	2	1	no	—
39	D₇×C₂²⋊C₄	—	2	1	no	—
40	#6440	—	2	1	no	—
41	C₄×D₂₈	C₂²	1	1	yes	characteristic
42	C₄²×D₇	C₂²	1	1	yes	characteristic
43	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
44	C₇×#106	C₂²	1	1	yes	characteristic, complemented
45	C₇×#102	C₂²	1	1	yes	characteristic
46	C₇×#102	C₂²	1	1	yes	characteristic, complemented
47	C₇×#97	C₂²	1	1	yes	characteristic, complemented
48	#6406	C₂²	1	1	yes	characteristic
49	#6406	C₂²	1	1	yes	characteristic, complemented
50	#6395	C₂²	1	1	yes	characteristic
51	#6392	C₂²	1	1	yes	characteristic, complemented
52	#6390	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
54	C₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
55	#6384	C₂²	1	1	yes	characteristic, complemented
56	#6383	C₂²	1	1	yes	characteristic
57	#6382	C₂²	1	1	yes	characteristic, complemented
58	#6381	C₂²	1	1	yes	characteristic, complemented
59	#6377	C₂²	1	1	yes	characteristic, complemented
60	C₄×AGL(1,ℤ/8)	—	7	1	no	maximal, Sylow
61	C₂³×D₇	—	2	1	no	—
62	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
63	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₇	—	2	1	no	—
65	C₂²×C₄×C₇	—	2	1	no	—
66	C₂×C₂²⋊D₇	—	2	1	no	—
67	C₂×C₂²⋊D₇	—	2	1	no	—
68	C₂²×Dic₇	—	2	1	no	—
69	C₂²×Dic₇	—	2	1	no	—
70	C₂²×Dic₇	—	2	1	no	—
71	#1159	—	2	2	no	—
72	#1159	C₂×C₄	1	4	yes	complemented
73	D₄×D₇	—	2	2	no	—
74	D₄×D₇	C₂×C₄	1	4	yes	complemented
75	C₂×D₂₈	C₂³	1	1	yes	characteristic
76	C₂×C₄×D₇	—	2	1	no	—
77	C₂×C₄×D₇	—	2	1	no	—
78	C₂×C₄×D₇	—	2	1	no	—
79	C₂×C₄×D₇	—	4	4	no	—
80	C₂×C₄×D₇	D₄	1	1	yes	characteristic
81	C₂×C₄×D₇	D₄	1	1	yes	characteristic
82	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
83	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
84	C₇×D₈	C₂×C₄	1	4	yes	complemented
85	C₂×C₇×C₈	C₂³	1	1	yes	characteristic
86	C₂×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₇×C₂²⋊C₄	—	2	1	no	—
90	C₇×C₂²⋊C₄	—	2	1	no	—
91	C₄²×C₇	C₂³	1	1	yes	characteristic
92	C₂²⋊Dic₇	—	2	1	no	—
93	C₂²⋊Dic₇	—	2	1	no	—
94	#1142	C₂×C₄	1	4	yes	complemented
95	#1141	C₂×C₄	1	4	yes	complemented
96	(C₂×D₇)⋊C₄	—	2	1	no	—
97	(C₂×D₇)⋊C₄	—	2	1	no	—
98	(C₂×D₇)⋊C₄	—	2	1	no	—
99	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
100	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
101	Dic₇⋊C₄	—	2	1	no	—
102	Dic₇⋊C₄	—	2	1	no	—
103	Dic₇⋊C₄	—	2	1	no	—
104	C₄×Dic₇	—	2	1	no	—
105	C₄×Dic₇	—	2	1	no	—
106	C₄×Dic₇	—	2	1	no	—
107	C₄×Dic₇	D₄	1	1	yes	characteristic
108	C₄×Dic₇	D₄	1	1	yes	characteristic
109	C₄×Dic₇	C₂³	1	1	yes	characteristic
110	C₂×C₇⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×C₇⋊C₈	C₂³	1	1	yes	characteristic
112	#1132	C₂×C₄	1	4	yes	complemented
113	#1131	—	2	2	no	—
114	#1131	C₂×C₄	1	4	yes	complemented
115	C₂×AGL(1,ℤ/8)	—	7	1	no	—
116	C₄×#41	—	7	1	no	—
117	C₂×C₄×D₄	—	7	1	no	—
118	#442	—	7	1	no	—
119	#442	D₇	1	1	yes	characteristic, complemented
120	#440	—	7	1	no	—
121	#440	—	7	1	no	—
122	C₄×SD₁₆	—	7	1	no	—
123	C₄×SD₁₆	—	7	1	no	—
124	C₄×D₈	—	7	1	no	—
125	C₄×D₈	—	7	1	no	—
126	#428	—	7	1	no	—
127	#418	—	7	1	no	—
128	#417	—	7	1	no	—
129	C₄×M₁₆	—	7	1	no	—
130	C₂³×C₇	—	2	1	no	—
131	C₂³×C₇	—	2	1	no	—
132	C₂²×D₇	—	2	1	no	—
133	C₂²×D₇	—	2	4	no	—
134	C₂²×D₇	—	4	2	no	—
135	C₂²×D₇	—	4	2	no	—
136	C₂²×D₇	C₂×D₄	1	1	yes	characteristic
137	C₇×D₄	—	2	1	no	—
138	C₇×D₄	—	2	1	no	—
139	C₇×D₄	C₂²×C₄	1	2	yes	—
140	C₇×D₄	C₂²×C₄	1	2	yes	complemented
141	C₂×C₄×C₇	—	2	1	no	—
142	C₂×C₄×C₇	—	2	1	no	—
143	C₂×C₄×C₇	—	4	2	no	—
144	C₂×C₄×C₇	—	4	2	no	—
145	C₂×C₄×C₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄×C₇	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
148	C₂²⋊D₇	—	2	4	no	—
149	C₂²⋊D₇	—	2	4	no	—
150	C₂×Dic₇	—	2	1	no	—
151	C₂×Dic₇	—	2	4	no	—
152	C₂×Dic₇	—	2	1	no	—
153	C₂×Dic₇	—	2	1	no	—
154	C₂×Dic₇	—	4	2	no	—
155	C₂×Dic₇	—	4	2	no	—
156	C₂×Dic₇	C₂×D₄	1	1	yes	characteristic
157	C₂×Dic₇	C₂×D₄	1	1	yes	characteristic
158	C₂×Dic₇	C₂×D₄	1	1	yes	characteristic
159	D₂₈	—	2	1	no	—
160	D₂₈	C₂²×C₄	1	2	yes	—
161	C₄×D₇	—	2	2	no	—
162	C₄×D₇	—	4	1	no	—
163	C₄×D₇	—	4	2	no	—
164	C₄×D₇	—	4	2	no	—
165	C₄×D₇	—	4	2	no	—
166	C₄×D₇	C₂²×C₄	1	2	yes	—
167	C₄×D₇	#41	1	2	yes	—
168	Dic₁₄	—	2	1	no	—
169	Dic₁₄	C₂²×C₄	1	2	yes	complemented
170	C₇×C₈	—	2	1	no	—
171	C₇×C₈	C₂²×C₄	1	2	yes	complemented
172	C₇⋊C₈	—	2	1	no	—
173	C₇⋊C₈	C₂²×C₄	1	2	yes	complemented
174	C₂×#41	—	7	1	no	—
175	C₂²×D₄	—	7	1	no	—
176	C₂³×C₄	—	14	1	no	—
177	AGL(1,ℤ/8)	—	7	8	no	—
178	C₂×SD₁₆	—	7	1	no	—
179	C₂×SD₁₆	—	7	1	no	—
180	C₂×D₈	—	7	1	no	—
181	C₂×D₈	C₂×D₇	1	1	yes	characteristic
182	C₂×M₁₆	—	7	1	no	—
183	C₂×M₁₆	—	7	1	no	—
184	C₄×Q₈	—	7	1	no	—
185	C₄×Q₈	—	7	1	no	—
186	C₄×D₄	—	7	1	no	—
187	C₄×D₄	—	7	1	no	—
188	C₄×D₄	—	7	1	no	—
189	C₄×D₄	—	7	1	no	—
190	C₄×D₄	—	14	1	no	—
191	C₄×D₄	—	14	1	no	—
192	C₄×D₄	—	14	1	no	—
193	C₄×D₄	—	14	1	no	—
194	C₄×D₄	C₂×D₇	1	1	yes	characteristic
195	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
196	#117	—	7	1	no	—
197	#117	—	14	1	no	—
198	C₂×C₄⋊C₄	—	7	1	no	—
199	C₂×C₂²⋊C₄	—	14	1	no	—
200	C₂×C₄²	—	7	1	no	—
201	C₂×C₄²	—	14	1	no	—
202	#107	—	7	1	no	—
203	#107	—	7	1	no	—
204	#106	—	7	1	no	—
205	#106	C₂×D₇	1	1	yes	characteristic, complemented
206	#103	—	7	1	no	—
207	#103	—	7	1	no	—
208	#102	—	7	1	no	—
209	#102	—	7	1	no	—
210	#102	—	7	1	no	—
211	#102	—	7	1	no	—
212	#102	C₂×D₇	1	1	yes	characteristic
213	#102	C₂×D₇	1	1	yes	characteristic, complemented
214	#97	—	7	1	no	—
215	#97	C₂×D₇	1	1	yes	characteristic, complemented
216	C₄×C₈	—	7	1	no	—
217	C₄×C₈	—	7	1	no	—
218	C₂²×C₇	—	2	2	no	—
219	C₂²×C₇	—	2	2	no	—
220	C₂²×C₇	—	4	1	no	—
221	C₂²×C₇	—	4	1	no	—
222	C₂²×C₇	—	4	1	no	—
223	C₂²×C₇	—	4	1	no	—
224	C₂²×C₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×D₇	—	2	1	no	—
226	C₂×D₇	—	2	1	no	—
227	C₂×D₇	—	2	2	no	—
228	C₂×D₇	—	4	8	no	—
229	C₂×D₇	—	4	1	no	—
230	C₂×D₇	—	4	1	no	—
231	C₂×D₇	C₄×D₄	1	2	yes	—
232	C₄×C₇	—	2	1	no	—
233	C₄×C₇	—	2	1	no	—
234	C₄×C₇	—	4	1	no	—
235	C₄×C₇	—	4	1	no	—
236	C₄×C₇	C₂³×C₄	1	1	yes	characteristic
237	C₄×C₇	C₂×#41	1	1	yes	characteristic
238	Dic₇	—	2	2	no	—
239	Dic₇	—	2	1	no	—
240	Dic₇	—	4	1	no	—
241	Dic₇	—	4	1	no	—
242	Dic₇	C₄×D₄	1	2	yes	—
243	Dic₇	AGL(1,ℤ/8)	1	2	yes	complemented
244	C₂⁴	—	14	1	no	—
245	#41	—	7	4	no	—
246	#41	—	14	2	no	—
247	C₂×Q₈	—	7	1	no	—
248	C₂×D₄	—	7	4	no	—
249	C₂×D₄	—	7	1	no	—
250	C₂×D₄	—	14	2	no	—
251	C₂×D₄	—	14	1	no	—
252	C₂×D₄	—	14	1	no	—
253	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
254	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	7	1	no	—
258	C₂²×C₄	—	7	1	no	—
259	C₂²×C₄	—	7	1	no	—
260	C₂²×C₄	—	14	1	no	—
261	C₂²×C₄	—	14	1	no	—
262	C₂²×C₄	—	14	1	no	—
263	C₂²×C₄	—	14	1	no	—
264	C₂²×C₄	—	14	1	no	—
265	C₂²×C₄	—	14	1	no	—
266	C₂²×C₄	—	28	4	no	—
267	SD₁₆	—	7	4	no	—
268	SD₁₆	—	7	4	no	—
269	D₈	—	7	4	no	—
270	D₈	C₄×D₇	1	4	yes	complemented
271	M₁₆	—	7	4	no	—
272	M₁₆	—	14	2	no	—
273	C₂×C₈	—	7	1	no	—
274	C₂×C₈	—	7	1	no	—
275	C₂×C₈	C₂²×D₇	1	1	yes	characteristic
276	C₂×C₈	C₂²×D₇	1	1	yes	characteristic
277	C₄⋊C₄	—	7	1	no	—
278	C₄⋊C₄	—	7	1	no	—
279	C₄⋊C₄	—	14	1	no	—
280	C₄⋊C₄	—	14	1	no	—
281	C₄⋊C₄	—	14	1	no	—
282	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
283	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
284	C₂²⋊C₄	—	2	1	no	—
285	C₂²⋊C₄	—	2	1	no	—
286	C₂²⋊C₄	—	14	1	no	—
287	C₂²⋊C₄	—	14	1	no	—
288	C₂²⋊C₄	—	14	1	no	—
289	C₂²⋊C₄	—	14	1	no	—
290	C₂²⋊C₄	—	14	1	no	—
291	C₄²	—	7	1	no	—
292	C₄²	—	7	1	no	—
293	C₄²	—	7	1	no	—
294	C₄²	—	14	1	no	—
295	C₄²	—	14	1	no	—
296	C₄²	—	14	1	no	—
297	C₄²	C₂²×D₇	1	1	yes	characteristic
298	C₂×C₇	—	4	2	no	—
299	C₂×C₇	—	4	2	no	—
300	C₂×C₇	C₂×C₄×D₄	1	1	yes	characteristic
301	C₂×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
302	C₂×C₇	#575	1	1	yes	characteristic
303	D₇	—	2	2	no	—
304	D₇	—	4	2	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	7	1	no	—
308	C₂³	—	14	4	no	—
309	C₂³	—	14	1	no	—
310	C₂³	—	28	2	no	—
311	C₂³	—	28	2	no	—
312	Q₈	—	7	2	no	—
313	Q₈	—	14	1	no	—
314	D₄	—	2	1	no	—
315	D₄	—	2	1	no	—
316	D₄	—	7	2	no	—
317	D₄	—	14	4	no	—
318	D₄	—	14	4	no	—
319	D₄	—	14	1	no	—
320	D₄	C₂×C₄×D₇	1	2	yes	—
321	D₄	C₂×C₄×D₇	1	2	yes	complemented
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	7	1	no	—
327	C₂×C₄	—	7	1	no	—
328	C₂×C₄	—	7	2	no	—
329	C₂×C₄	—	7	2	no	—
330	C₂×C₄	—	7	1	no	—
331	C₂×C₄	—	14	2	no	—
332	C₂×C₄	—	14	4	no	—
333	C₂×C₄	—	14	1	no	—
334	C₂×C₄	—	14	1	no	—
335	C₂×C₄	—	14	1	no	—
336	C₂×C₄	—	28	1	no	—
337	C₂×C₄	—	28	2	no	—
338	C₂×C₄	—	28	2	no	—
339	C₂×C₄	—	28	2	no	—
340	C₂×C₄	—	28	2	no	—
341	C₂×C₄	—	28	2	no	—
342	C₂×C₄	D₄×D₇	1	1	yes	characteristic
343	C₂×C₄	D₄×D₇	1	1	yes	characteristic
344	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
345	C₈	—	2	1	no	—
346	C₈	—	7	2	no	—
347	C₈	—	14	1	no	—
348	C₈	C₂×C₄×D₇	1	2	yes	complemented
349	C₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	7	2	no	—
357	C₂²	—	14	1	no	—
358	C₂²	—	14	1	no	—
359	C₂²	—	14	2	no	—
360	C₂²	—	28	8	no	—
361	C₂²	—	28	1	no	—
362	C₂²	—	28	1	no	—
363	C₂²	C₂×D₄×D₇	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	7	2	no	—
369	C₄	—	7	2	no	—
370	C₄	—	14	1	no	—
371	C₄	—	14	2	no	—
372	C₄	—	28	1	no	—
373	C₄	—	28	1	no	—
374	C₄	C₂²×C₄×D₇	1	1	yes	characteristic
375	C₄	D₇×#41	1	1	yes	characteristic
376	C₂	—	4	2	no	—
377	C₂	—	4	2	no	—
378	C₂	—	14	2	no	—
379	C₂	—	28	2	no	—
380	C₂	C₄×D₄×D₇	1	1	yes	characteristic
381	C₂	D₇×AGL(1,ℤ/8)	1	1	yes	characteristic
382	C₂	#90464	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₇
commutator	C₄×C₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₇
Fitting	C₇×#442	C₂
socle	C₂²×C₇	C₂²×D₄
prime radical	C₂×#6474	C₂
cosocle	C₂×C₄×C₇	C₂⁴
hypercenter	#442	D₇
hypocenter	C₇	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #442

Complements

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

N	H ≅ G/N	type
2. C₄×D₄×D₇	C₂	semidirect
3. C₄×#1159	C₂	semidirect
4. C₇×#442	C₂	semidirect
5. D₈×Dic₇	C₂	semidirect
6. #89790	C₂	semidirect
7. #89786	C₂	semidirect
8. #89633	C₂	semidirect
9. #89624	C₂	semidirect
10. #89543	C₂	semidirect
11. #89542	C₂	semidirect
12. #89530	C₂	semidirect
13. #89528	C₂	semidirect
14. #89482	C₂	semidirect
15. #89479	C₂	semidirect
21. C₄×C₇×D₄	C₂²	semidirect
23. D₄×Dic₇	C₂²	semidirect
29. #6474	C₄	semidirect
36. #6450	C₂²	semidirect
43. C₄×Dic₁₄	C₂²	semidirect
44. C₇×#106	C₂²	semidirect
46. C₇×#102	C₂²	semidirect
47. C₇×#97	C₂²	semidirect
49. #6406	C₂²	semidirect
51. #6392	C₂²	semidirect
52. #6390	C₂²	semidirect
53. C₈×Dic₇	C₂²	semidirect
54. C₈×Dic₇	C₂²	semidirect
55. #6384	C₂²	semidirect
57. #6382	C₂²	semidirect
58. #6381	C₂²	semidirect
59. #6377	C₂²	semidirect
72. #1159	C₂×C₄	semidirect
74. D₄×D₇	C₂×C₄	semidirect
84. C₇×D₈	C₂×C₄	semidirect
94. #1142	C₂×C₄	semidirect
95. #1141	C₂×C₄	semidirect
112. #1132	C₂×C₄	semidirect
114. #1131	C₂×C₄	semidirect
119. #442	D₇	semidirect
140. C₇×D₄	C₂²×C₄	semidirect
169. Dic₁₄	C₂²×C₄	semidirect
171. C₇×C₈	C₂²×C₄	semidirect
173. C₇⋊C₈	C₂²×C₄	semidirect
195. C₄×D₄	C₂×D₇	semidirect
205. #106	C₂×D₇	semidirect
213. #102	C₂×D₇	semidirect
215. #97	C₂×D₇	semidirect
243. Dic₇	AGL(1,ℤ/8)	semidirect
270. D₈	C₄×D₇	semidirect
321. D₄	C₂×C₄×D₇	semidirect
348. C₈	C₂×C₄×D₇	semidirect
349. C₇	C₄×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₂×#6474	2
C₄×D₄×D₇	2
C₄×#1159	2
C₇×#442	2
D₈×Dic₇	2
#89790	2
#89786	2
#89633	2
#89624	2
#89543	2
#89542	2
#89530	2
#89528	2
#89482	2
#89479	2
C₄×AGL(1,ℤ/8)	7