Subgroups — #13247708

Order 1792.

552 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#89606	C₂	1	1	yes	maximal, characteristic
2	C₂×#89274	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#89254	C₂	1	1	yes	maximal, characteristic
4	#11727238	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#6383	C₂	1	1	yes	maximal, characteristic
6	C₇×#1279	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₇	—	2	1	no	—
9	C₂×C₄×D₂₈	C₂²	1	1	yes	characteristic
10	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
12	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×(C₂×D₇)⋊C₈	—	2	1	no	—
14	C₂×#6383	C₄	1	1	yes	characteristic
15	C₂×#6383	C₄	1	1	yes	characteristic
16	C₂×C₄⋊(C₇⋊C₈)	—	2	1	no	—
17	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
20	#89606	—	2	2	no	—
21	#89606	—	2	2	no	—
22	#89324	C₄	1	1	yes	characteristic
23	#89324	C₄	1	1	yes	characteristic
24	#89319	—	2	1	no	—
25	#89274	—	2	2	no	—
26	#89254	—	2	2	no	—
27	#8843	—	7	1	no	maximal, Sylow
28	C₂²×D₂₈	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×D₇	—	2	1	no	—
30	C₂²×C₇×C₈	—	2	1	no	—
31	C₂²×C₇×C₈	—	2	1	no	—
32	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
33	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₇	—	2	1	no	—
35	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
36	C₂×(C₂×D₇)⋊C₄	—	2	1	no	—
37	C₂×C₄⋊Dic₇	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₇⋊C₈	—	2	1	no	—
39	C₂²×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₇⋊C₈	D₄	1	1	yes	characteristic
42	C₂²×C₇⋊C₈	D₄	1	1	yes	characteristic
43	C₂×C₈×D₇	—	2	4	no	—
44	C₂×C₈×D₇	—	4	2	no	—
45	C₂×C₈×D₇	—	4	2	no	—
46	C₄×D₂₈	—	2	1	no	—
47	C₄×D₂₈	—	2	1	no	—
48	C₄×D₂₈	D₄	1	2	yes	—
49	C₄×D₂₈	Q₈	1	2	yes	—
50	C₇×C₄⋊C₈	—	2	1	no	—
51	C₇×C₄⋊C₈	D₄	1	2	yes	—
52	C₄×C₇×C₈	—	2	1	no	—
53	C₄×C₇×C₈	—	2	1	no	—
54	C₇×#95	—	2	1	no	—
55	(C₂×D₇)⋊C₈	—	2	4	no	—
56	#6383	—	2	2	no	—
57	#6383	C₈	1	4	yes	complemented
58	C₄⋊(C₇⋊C₈)	—	2	1	no	—
59	C₄⋊(C₇⋊C₈)	—	2	1	no	—
60	C₄⋊(C₇⋊C₈)	—	4	2	no	—
61	C₄×C₇⋊C₈	—	2	1	no	—
62	C₄×C₇⋊C₈	—	2	1	no	—
63	C₄×C₇⋊C₈	—	2	1	no	—
64	C₄×C₇⋊C₈	—	2	1	no	—
65	C₂×C₈×D₄	—	7	1	no	—
66	#1939	—	7	1	no	—
67	C₄×#102	—	7	1	no	—
68	C₂×#335	—	7	1	no	—
69	C₂×D₄⋊C₈	—	7	1	no	—
70	#1279	D₇	1	1	yes	characteristic, complemented
71	#1273	—	7	1	no	—
72	C₂³×D₇	—	2	1	no	—
73	C₂²×C₄×C₇	—	2	1	no	—
74	C₂²×C₄×C₇	—	2	1	no	—
75	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₇	#41	1	1	yes	characteristic
78	C₂²×Dic₇	—	2	1	no	—
79	C₂×D₂₈	—	2	1	no	—
80	C₂×D₂₈	—	2	1	no	—
81	C₂×D₂₈	—	2	1	no	—
82	C₂×D₂₈	C₄⋊C₄	1	2	yes	—
83	C₂×D₂₈	C₂×C₈	1	2	yes	—
84	C₂×D₂₈	M₁₆	1	2	yes	—
85	C₂×C₄×D₇	—	2	2	no	—
86	C₂×C₄×D₇	—	2	2	no	—
87	C₂×C₄×D₇	—	4	1	no	—
88	C₂×C₄×D₇	—	4	1	no	—
89	C₂×C₄×D₇	—	4	1	no	—
90	C₂×C₄×D₇	—	4	1	no	—
91	C₂×C₇×C₈	—	2	2	no	—
92	C₂×C₇×C₈	—	2	2	no	—
93	C₂×C₇×C₈	—	4	1	no	—
94	C₂×C₇×C₈	—	4	1	no	—
95	C₂×C₇×C₈	—	4	1	no	—
96	C₂×C₇×C₈	—	4	1	no	—
97	C₇×C₄⋊C₄	—	2	1	no	—
98	C₇×C₄⋊C₄	—	2	1	no	—
99	C₇×C₄⋊C₄	—	2	1	no	—
100	C₇×C₄⋊C₄	C₂×C₈	1	2	yes	complemented
101	C₄²×C₇	—	4	1	no	—
102	C₄²×C₇	—	4	1	no	—
103	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
106	C₄²×C₇	#41	1	1	yes	characteristic
107	(C₂×D₇)⋊C₄	—	2	2	no	—
108	(C₂×D₇)⋊C₄	—	2	2	no	—
109	C₄⋊Dic₇	—	2	1	no	—
110	C₄⋊Dic₇	C₄⋊C₄	1	2	yes	—
111	C₂×C₇⋊C₈	—	2	1	no	—
112	C₂×C₇⋊C₈	—	2	1	no	—
113	C₂×C₇⋊C₈	—	2	1	no	—
114	C₂×C₇⋊C₈	—	2	1	no	—
115	C₂×C₇⋊C₈	—	2	1	no	—
116	C₂×C₇⋊C₈	—	2	1	no	—
117	C₂×C₇⋊C₈	—	2	1	no	—
118	C₂×C₇⋊C₈	—	2	1	no	—
119	C₂×C₇⋊C₈	—	2	1	no	—
120	C₂×C₇⋊C₈	—	2	1	no	—
121	C₂×C₇⋊C₈	—	4	1	no	—
122	C₂×C₇⋊C₈	—	4	1	no	—
123	C₂×C₇⋊C₈	—	4	1	no	—
124	C₂×C₇⋊C₈	C₂×C₈	1	2	yes	complemented
125	C₂×C₇⋊C₈	D₈	1	2	yes	—
126	C₈×D₇	—	4	8	no	—
127	C₂³×C₈	—	14	1	no	—
128	C₂×C₄×D₄	—	7	1	no	—
129	C₈×D₄	—	14	2	no	—
130	C₈×D₄	—	14	2	no	—
131	C₂×C₄⋊C₈	—	7	1	no	—
132	C₂×C₄⋊C₈	—	14	1	no	—
133	C₂×C₄⋊C₈	C₂×D₇	1	1	yes	characteristic
134	C₂×#102	—	7	1	no	—
135	C₂×#102	—	7	1	no	—
136	C₂×C₂²⋊C₈	—	14	1	no	—
137	C₂×C₄×C₈	—	7	1	no	—
138	C₂×C₄×C₈	—	7	1	no	—
139	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
140	C₄×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
141	#340	—	7	1	no	—
142	#340	—	7	1	no	—
143	#336	—	14	1	no	—
144	#335	—	14	2	no	—
145	D₄⋊C₈	—	14	2	no	—
146	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
147	C₂²×D₇	—	2	2	no	—
148	C₂²×D₇	—	2	2	no	—
149	C₂²×D₇	—	2	2	no	—
150	C₂²×D₇	—	4	1	no	—
151	C₂²×D₇	—	4	1	no	—
152	C₂²×D₇	—	4	1	no	—
153	C₂²×D₇	—	4	1	no	—
154	C₂×C₄×C₇	—	2	1	no	—
155	C₂×C₄×C₇	—	2	1	no	—
156	C₂×C₄×C₇	—	2	2	no	—
157	C₂×C₄×C₇	—	4	1	no	—
158	C₂×C₄×C₇	—	4	1	no	—
159	C₂×C₄×C₇	—	4	1	no	—
160	C₂×C₄×C₇	—	4	1	no	—
161	C₂×C₄×C₇	—	4	1	no	—
162	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₇	#120	1	1	yes	characteristic
165	C₂×C₄×C₇	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₇	C₂²⋊Q₈	1	1	yes	characteristic
167	C₂×C₄×C₇	#123	1	1	yes	characteristic
168	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₇	C₂×M₁₆	1	1	yes	characteristic
170	C₂×C₄×C₇	#131	1	1	yes	characteristic
171	C₂×C₄×C₇	#131	1	1	yes	characteristic
172	C₂×C₄×C₇	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₇	#135	1	1	yes	characteristic
174	C₂×C₄×C₇	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₂×C₄×C₇	#137	1	1	yes	characteristic
176	C₂×Dic₇	—	2	2	no	—
177	C₂×Dic₇	—	4	1	no	—
178	C₂×Dic₇	—	4	1	no	—
179	D₂₈	—	2	2	no	—
180	D₂₈	—	2	2	no	—
181	D₂₈	—	2	2	no	—
182	D₂₈	C₄⋊C₈	1	4	yes	complemented
183	C₄×D₇	—	4	2	no	—
184	C₄×D₇	—	4	2	no	—
185	C₄×D₇	—	4	2	no	—
186	C₄×D₇	—	4	2	no	—
187	C₇×C₈	—	4	2	no	—
188	C₇×C₈	—	4	2	no	—
189	C₇⋊C₈	—	2	2	no	—
190	C₇⋊C₈	—	2	2	no	—
191	C₇⋊C₈	—	4	1	no	—
192	C₇⋊C₈	—	4	1	no	—
193	C₇⋊C₈	—	8	1	no	—
194	C₂²×D₄	—	7	1	no	—
195	C₂³×C₄	—	14	1	no	—
196	C₂²×C₈	—	2	1	no	—
197	C₂²×C₈	—	2	1	no	—
198	C₂²×C₈	—	7	1	no	—
199	C₂²×C₈	—	7	1	no	—
200	C₂²×C₈	—	7	1	no	—
201	C₂²×C₈	—	7	1	no	—
202	C₂²×C₈	—	14	4	no	—
203	C₂²×C₈	—	14	1	no	—
204	C₂²×C₈	—	28	2	no	—
205	C₂²×C₈	—	28	2	no	—
206	C₄×D₄	—	7	2	no	—
207	C₄×D₄	—	7	2	no	—
208	C₄×D₄	—	14	1	no	—
209	C₄×D₄	—	14	1	no	—
210	C₂×C₄⋊C₄	—	7	1	no	—
211	C₂×C₄⋊C₄	C₄×D₇	1	1	yes	characteristic
212	C₂×C₄⋊C₄	C₄×D₇	1	1	yes	characteristic
213	C₂×C₂²⋊C₄	—	14	1	no	—
214	C₂×C₄²	—	2	1	no	—
215	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
216	C₄⋊C₈	—	2	1	no	—
217	C₄⋊C₈	—	14	1	no	—
218	C₄⋊C₈	—	14	1	no	—
219	C₄⋊C₈	—	28	2	no	—
220	C₄⋊C₈	D₂₈	1	2	yes	—
221	#102	—	7	4	no	—
222	#102	—	14	2	no	—
223	C₂²⋊C₈	—	14	4	no	—
224	C₄×C₈	—	2	1	no	—
225	C₄×C₈	—	2	1	no	—
226	C₄×C₈	—	14	1	no	—
227	C₄×C₈	—	14	1	no	—
228	C₄×C₈	—	14	1	no	—
229	C₄×C₈	—	14	1	no	—
230	#95	—	2	1	no	—
231	C₂²×C₇	#385	1	1	yes	characteristic
232	C₂²×C₇	C₈×D₄	1	1	yes	characteristic
233	C₂²×C₇	#435	1	1	yes	characteristic
234	C₂²×C₇	C₄×D₈	1	1	yes	characteristic
235	C₂²×C₇	#440	1	1	yes	characteristic
236	C₂²×C₇	#443	1	1	yes	characteristic
237	C₂²×C₇	#444	1	1	yes	characteristic
238	C₂×D₇	—	2	4	no	—
239	C₂×D₇	—	4	2	no	—
240	C₂×D₇	—	4	2	no	—
241	C₂×D₇	—	4	2	no	—
242	C₂×D₇	—	4	2	no	—
243	C₂×D₇	—	4	2	no	—
244	C₂×D₇	—	4	2	no	—
245	C₄×C₇	—	2	1	no	—
246	C₄×C₇	—	2	1	no	—
247	C₄×C₇	—	4	2	no	—
248	C₄×C₇	—	8	1	no	—
249	C₄×C₇	C₂×C₄⋊C₈	1	1	yes	characteristic
250	C₄×C₇	#424	1	1	yes	characteristic
251	C₄×C₇	C₈×D₄	1	1	yes	characteristic
252	C₄×C₇	#435	1	1	yes	characteristic
253	C₄×C₇	#447	1	1	yes	characteristic
254	C₄×C₇	#452	1	1	yes	characteristic
255	C₄×C₇	#474	1	1	yes	characteristic
256	C₄×C₇	#478	1	1	yes	characteristic
257	Dic₇	—	4	2	no	—
258	C₂⁴	—	14	1	no	—
259	C₂×D₄	—	7	2	no	—
260	C₂×D₄	—	7	2	no	—
261	C₂×D₄	—	7	2	no	—
262	C₂×D₄	—	14	1	no	—
263	C₂×D₄	—	14	1	no	—
264	C₂×D₄	—	14	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	14	1	no	—
268	C₂²×C₄	—	14	2	no	—
269	C₂²×C₄	—	14	2	no	—
270	C₂²×C₄	—	28	1	no	—
271	C₂²×C₄	—	28	1	no	—
272	C₂²×C₄	—	28	1	no	—
273	C₂²×C₄	—	28	1	no	—
274	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
275	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
276	C₂²×C₄	#1159	1	1	yes	characteristic
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	4	1	no	—
280	C₂×C₈	—	4	1	no	—
281	C₂×C₈	—	4	1	no	—
282	C₂×C₈	—	4	1	no	—
283	C₂×C₈	—	7	2	no	—
284	C₂×C₈	—	7	2	no	—
285	C₂×C₈	—	14	1	no	—
286	C₂×C₈	—	14	1	no	—
287	C₂×C₈	—	14	1	no	—
288	C₂×C₈	—	14	1	no	—
289	C₂×C₈	—	14	1	no	—
290	C₂×C₈	—	14	1	no	—
291	C₂×C₈	—	14	1	no	—
292	C₂×C₈	—	14	1	no	—
293	C₂×C₈	—	14	1	no	—
294	C₂×C₈	—	14	1	no	—
295	C₂×C₈	—	28	8	no	—
296	C₂×C₈	—	28	1	no	—
297	C₂×C₈	—	28	1	no	—
298	C₂×C₈	—	28	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	7	2	no	—
303	C₄⋊C₄	—	14	1	no	—
304	C₄⋊C₄	C₈×D₇	1	2	yes	complemented
305	C₂²⋊C₄	—	14	2	no	—
306	C₂²⋊C₄	—	14	2	no	—
307	C₄²	—	4	1	no	—
308	C₄²	—	4	1	no	—
309	C₄²	C₂×D₂₈	1	1	yes	characteristic
310	C₄²	#1157	1	1	yes	characteristic
311	C₄²	D₄×D₇	1	1	yes	characteristic
312	C₄²	Q₈×D₇	1	1	yes	characteristic
313	C₂×C₇	C₈×D₈	1	1	yes	characteristic
314	C₂×C₇	SD₁₆⋊C₈	1	1	yes	characteristic
315	C₂×C₇	#1581	1	1	yes	characteristic
316	C₂×C₇	#1585	1	1	yes	characteristic
317	C₂×C₇	#1850	1	1	yes	characteristic
318	C₂×C₇	#1862	1	1	yes	characteristic
319	C₂×C₇	#1866	1	1	yes	characteristic
320	D₇	—	4	4	no	—
321	C₂³	—	14	2	no	—
322	C₂³	—	14	2	no	—
323	C₂³	—	14	2	no	—
324	C₂³	—	28	1	no	—
325	C₂³	—	28	1	no	—
326	C₂³	—	28	1	no	—
327	C₂³	—	28	1	no	—
328	C₂³	(C₂²⋊D₇)⋊C₄	1	1	yes	characteristic
329	D₄	—	7	4	no	—
330	D₄	—	14	2	no	—
331	D₄	—	14	2	no	—
332	D₄	—	14	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	14	2	no	—
342	C₂×C₄	—	28	1	no	—
343	C₂×C₄	—	28	1	no	—
344	C₂×C₄	—	28	2	no	—
345	C₂×C₄	—	28	2	no	—
346	C₂×C₄	—	28	2	no	—
347	C₂×C₄	—	28	2	no	—
348	C₂×C₄	C₄×D₂₈	1	1	yes	characteristic
349	C₂×C₄	#6445	1	1	yes	characteristic
350	C₂×C₄	#6446	1	1	yes	characteristic
351	C₂×C₄	D₇×C₄⋊C₄	1	1	yes	characteristic
352	C₂×C₄	#6459	1	1	yes	characteristic
353	C₂×C₄	#6460	1	1	yes	characteristic
354	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
355	C₂×C₄	#6464	1	1	yes	characteristic
356	C₂×C₄	D₇×M₁₆	1	1	yes	characteristic
357	C₂×C₄	#6470	1	1	yes	characteristic
358	C₂×C₄	D₇×D₈	1	1	yes	characteristic
359	C₂×C₄	#6477	1	1	yes	characteristic
360	C₂×C₄	#6479	1	1	yes	characteristic
361	C₂×C₄	#6481	1	1	yes	characteristic
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₈	—	14	2	no	—
365	C₈	—	14	2	no	—
366	C₈	—	28	1	no	—
367	C₈	—	28	1	no	—
368	C₈	—	56	1	no	—
369	C₇	#8843	1	1	yes	characteristic, complemented, Sylow
370	C₂²	—	14	4	no	—
371	C₂²	—	28	2	no	—
372	C₂²	—	28	2	no	—
373	C₂²	—	28	2	no	—
374	C₂²	—	28	2	no	—
375	C₂²	—	28	2	no	—
376	C₂²	—	28	2	no	—
377	C₂²	#89440	1	1	yes	characteristic
378	C₂²	(C₂²⋊D₇)⋊C₈	1	1	yes	characteristic
379	C₂²	#89500	1	1	yes	characteristic
380	C₂²	#89528	1	1	yes	characteristic
381	C₂²	#89589	1	1	yes	characteristic
382	C₂²	#89595	1	1	yes	characteristic
383	C₂²	#89596	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	8	1	no	—
388	C₄	—	28	2	no	—
389	C₄	C₈×D₂₈	1	1	yes	characteristic
390	C₄	#89478	1	1	yes	characteristic
391	C₄	#89545	1	1	yes	characteristic
392	C₄	#89582	1	1	yes	characteristic
393	C₄	D₇×C₄⋊C₈	1	1	yes	characteristic
394	C₄	#89611	1	1	yes	characteristic
395	C₄	#89643	1	1	yes	characteristic
396	C₄	#89662	1	1	yes	characteristic
397	C₂	—	28	4	no	—
398	C₂	#11725902	1	1	yes	characteristic
399	C₂	#11725907	1	1	yes	characteristic
400	C₂	#11725968	1	1	yes	characteristic
401	C₂	#11725974	1	1	yes	characteristic
402	C₂	#11726420	1	1	yes	characteristic
403	C₂	#11726528	1	1	yes	characteristic
404	C₂	#11726648	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₇
commutator	C₂×C₄×C₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₇
Fitting	C₇×#1279	C₂
socle	C₂³×C₇	C₄×D₄
prime radical	C₂²×D₂₈	C₂×C₄
cosocle	C₂×C₄²×C₇	C₂³
hypercenter	#1279	D₇
hypocenter	C₇	#8843
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
2. C₂×#89274	C₂	semidirect
4. #11727238	C₂	semidirect
6. C₇×#1279	C₂	semidirect
7. C₇⋊#1273	C₂	semidirect
57. #6383	C₈	semidirect
70. #1279	D₇	semidirect
100. C₇×C₄⋊C₄	C₂×C₈	semidirect
124. C₂×C₇⋊C₈	C₂×C₈	semidirect
182. D₂₈	C₄⋊C₈	semidirect
304. C₄⋊C₄	C₈×D₇	semidirect
369. C₇	#8843	semidirect

Maximal subgroups

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

subgroup	index
C₂×#89606	2
C₂×#89274	2
C₂×#89254	2
#11727238	2
C₄×#6383	2
C₇×#1279	2
C₇⋊#1273	2
#8843	7