Subgroups — #13372244

Order 1792.

858 conjugacy classes of subgroups.

The subgroup lattice has 392 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	C₂×#89969	C₂	1	2	yes	maximal
3	#11739957	C₂	1	2	yes	maximal, complemented
4	#11729400	C₂	1	2	yes	maximal, complemented
5	#11728417	C₂	1	2	yes	maximal, complemented
6	#11728046	C₂	1	4	yes	maximal, complemented
7	#11727546	C₂	1	1	yes	maximal, characteristic, complemented
8	#11727511	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	C₂×#6511	C₂²	1	4	yes	—
12	C₄×C₇×Q₁₆	C₄	1	1	yes	characteristic, complemented
13	C₄×C₇×Q₁₆	C₄	1	1	yes	characteristic, complemented
14	C₄×C₇×SD₁₆	C₄	1	2	yes	complemented
15	C₄×C₇×SD₁₆	C₄	1	2	yes	complemented
16	C₄×C₇×D₈	C₄	1	1	yes	characteristic, complemented
17	C₄×C₇×D₈	C₄	1	1	yes	characteristic, complemented
18	C₇×#427	C₂²	1	1	yes	characteristic
19	C₇×#416	C₂²	1	2	yes	—
20	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
21	C₂×#6411	C₂²	1	4	yes	—
22	#89969	—	2	8	no	—
23	C₂×#6393	C₂²	1	2	yes	—
24	C₂×#6393	C₂²	1	2	yes	—
25	C₂×#6389	C₂²	1	2	yes	—
26	#89771	—	2	4	no	—
27	#89771	C₂²	1	4	yes	—
28	C₄×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
29	#89696	—	2	2	no	—
30	#89696	C₂²	1	2	yes	—
31	C₂×C₄⋊(C₇⋊C₈)	—	2	2	no	—
32	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
33	#89345	C₂²	1	2	yes	—
34	#89327	C₂²	1	4	yes	—
35	#22686	—	7	1	no	maximal, Sylow
36	C₂×C₇×#41	C₂³	1	2	yes	—
37	C₇×#135	D₄	1	4	yes	—
38	C₇×#135	Q₈	1	4	yes	—
39	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
40	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
41	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
44	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
45	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
46	C₄×C₇×D₄	—	2	2	no	—
47	C₄×C₇×D₄	—	2	2	no	—
48	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
49	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
50	C₇×#117	—	2	2	no	—
51	C₇×#117	C₂³	1	2	yes	—
52	C₂×C₄²×C₇	—	2	2	no	—
53	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
54	#6511	—	2	8	no	—
55	#6511	—	4	4	no	—
56	C₂×C₄⋊Dic₇	—	2	1	no	—
57	C₂×C₄×Dic₇	C₂³	1	2	yes	—
58	C₂×#1136	—	2	4	no	—
59	C₂×#1136	C₂³	1	4	yes	—
60	C₂²×C₇⋊C₈	—	2	4	no	—
61	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
62	C₇×#107	C₂×C₄	1	1	yes	characteristic
63	C₇×#107	C₂×C₄	1	1	yes	characteristic
64	C₇×#106	C₂×C₄	1	2	yes	—
65	C₇×#103	C₂×C₄	1	2	yes	—
66	C₇×#103	C₂×C₄	1	2	yes	—
67	C₇×#102	C₂×C₄	1	2	yes	—
68	C₇×#102	C₂×C₄	1	2	yes	—
69	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
70	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
71	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
73	#6411	—	2	8	no	—
74	C₇⋊#95	—	2	1	no	—
75	#6393	—	2	4	no	—
76	#6393	—	4	2	no	—
77	#6389	—	2	4	no	—
78	C₄⋊(C₇⋊C₈)	—	2	2	no	—
79	C₄⋊(C₇⋊C₈)	—	2	2	no	—
80	C₄⋊(C₇⋊C₈)	—	2	4	no	—
81	C₄⋊(C₇⋊C₈)	—	2	4	no	—
82	C₄⋊(C₇⋊C₈)	D₄	1	2	yes	—
83	C₄⋊(C₇⋊C₈)	D₄	1	2	yes	—
84	C₂×#444	—	7	2	no	—
85	C₄×#135	D₇	1	1	yes	characteristic
86	#2906	—	7	2	no	—
87	#1946	—	7	2	no	—
88	#1866	—	7	4	no	—
89	#1848	—	7	1	no	—
90	#1806	—	7	2	no	—
91	#1770	—	7	1	no	—
92	C₇×#41	—	2	2	no	—
93	C₇×#41	—	2	2	no	—
94	C₇×#41	C₂×D₄	1	4	yes	—
95	C₇×#41	C₂×Q₈	1	4	yes	—
96	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
97	C₂×C₇×D₄	—	2	2	no	—
98	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₇	—	2	2	no	—
100	C₂²×C₄×C₇	—	2	2	no	—
101	C₂²×C₄×C₇	—	2	2	no	—
102	C₂²×C₄×C₇	#41	1	1	yes	characteristic
103	C₂²×C₄×C₇	#41	1	1	yes	characteristic
104	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₇	—	2	2	no	—
106	C₇×Q₁₆	C₄⋊C₄	1	4	yes	complemented
107	C₇×SD₁₆	C₄⋊C₄	1	8	yes	complemented
108	C₇×D₈	C₄⋊C₄	1	4	yes	complemented
109	C₂×C₇×C₈	—	2	1	no	—
110	C₂×C₇×C₈	—	2	1	no	—
111	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
116	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
117	C₇×C₄⋊C₄	—	2	2	no	—
118	C₇×C₄⋊C₄	—	2	2	no	—
119	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
120	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
121	C₇×C₂²⋊C₄	—	2	2	no	—
122	C₇×C₂²⋊C₄	—	2	2	no	—
123	C₇×C₂²⋊C₄	—	2	2	no	—
124	C₄²×C₇	—	2	2	no	—
125	C₄²×C₇	—	2	2	no	—
126	C₄²×C₇	—	2	2	no	—
127	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
131	C₄⋊Dic₇	—	4	2	no	—
132	C₄×Dic₇	—	2	2	no	—
133	C₄×Dic₇	—	2	2	no	—
134	#1136	—	2	4	no	—
135	#1136	—	2	4	no	—
136	#1136	—	4	8	no	—
137	C₂×C₇⋊C₈	—	2	2	no	—
138	C₂×C₇⋊C₈	—	2	2	no	—
139	C₂×C₇⋊C₈	—	2	4	no	—
140	C₂×C₇⋊C₈	—	4	8	no	—
141	C₂×C₇⋊C₈	C₂×D₄	1	4	yes	—
142	C₂×#135	C₂×D₇	1	1	yes	characteristic
143	C₂×#131	—	7	4	no	—
144	C₄×#41	C₂×D₇	1	2	yes	—
145	#444	—	14	8	no	—
146	C₄×Q₁₆	Dic₇	1	1	yes	characteristic, complemented
147	C₄×Q₁₆	Dic₇	1	1	yes	characteristic, complemented
148	C₄×SD₁₆	Dic₇	1	2	yes	complemented
149	C₄×SD₁₆	Dic₇	1	2	yes	complemented
150	C₄×D₈	Dic₇	1	1	yes	characteristic, complemented
151	C₄×D₈	Dic₇	1	1	yes	characteristic, complemented
152	C₂×#108	—	7	2	no	—
153	C₂×#108	—	7	2	no	—
154	#427	C₂×D₇	1	1	yes	characteristic
155	#424	—	7	4	no	—
156	#424	—	14	4	no	—
157	#423	—	7	2	no	—
158	#423	—	14	2	no	—
159	C₂×C₄⋊C₈	—	7	1	no	—
160	C₂×C₄⋊C₈	—	14	2	no	—
161	C₂×#104	—	7	4	no	—
162	#416	C₂×D₇	1	2	yes	—
163	C₂×#97	—	7	2	no	—
164	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
165	C₄×C₄⋊C₄	—	7	1	no	—
166	#339	—	7	4	no	—
167	#336	—	7	2	no	—
168	C₂³×C₇	—	2	2	no	—
169	C₂³×C₇	C₂×#41	1	1	yes	characteristic
170	C₇×Q₈	—	2	2	no	—
171	C₇×Q₈	C₂×C₄⋊C₄	1	4	yes	—
172	C₇×D₄	—	2	4	no	—
173	C₇×D₄	—	2	4	no	—
174	C₇×D₄	—	2	2	no	—
175	C₇×D₄	C₂×C₄⋊C₄	1	4	yes	—
176	C₂×C₄×C₇	—	2	2	no	—
177	C₂×C₄×C₇	—	2	4	no	—
178	C₂×C₄×C₇	—	2	4	no	—
179	C₂×C₄×C₇	—	2	2	no	—
180	C₂×C₄×C₇	—	2	2	no	—
181	C₂×C₄×C₇	—	2	2	no	—
182	C₂×C₄×C₇	—	4	1	no	—
183	C₂×C₄×C₇	—	4	4	no	—
184	C₂×C₄×C₇	—	8	2	no	—
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	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
195	C₂×Dic₇	—	4	2	no	—
196	C₂×Dic₇	—	4	2	no	—
197	C₂×Dic₇	—	4	2	no	—
198	C₇×C₈	—	2	1	no	—
199	C₇×C₈	—	2	1	no	—
200	C₇×C₈	C₂×C₄⋊C₄	1	2	yes	—
201	C₇×C₈	C₂×C₄⋊C₄	1	2	yes	—
202	C₇⋊C₈	—	2	4	no	—
203	C₇⋊C₈	—	4	4	no	—
204	C₂×#41	C₂²×D₇	1	2	yes	—
205	#135	Dic₁₄	1	4	yes	—
206	#135	D₂₈	1	4	yes	—
207	C₂×Q₁₆	C₂×Dic₇	1	1	yes	characteristic
208	C₂×SD₁₆	C₂×Dic₇	1	2	yes	—
209	C₂×D₈	C₂×Dic₇	1	1	yes	characteristic
210	#131	—	14	8	no	—
211	#131	—	28	4	no	—
212	C₂×M₁₆	—	7	4	no	—
213	C₂×M₁₆	—	14	4	no	—
214	C₂²×C₈	—	7	2	no	—
215	C₂²×C₈	—	14	4	no	—
216	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
217	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
218	C₄×Q₈	C₂×Dic₇	1	2	yes	—
219	C₄×Q₈	C₂×Dic₇	1	2	yes	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	—	2	2	no	—
222	C₄×D₄	C₂×Dic₇	1	2	yes	—
223	C₄×D₄	C₂×Dic₇	1	2	yes	—
224	#117	—	2	2	no	—
225	#117	C₂²×D₇	1	2	yes	—
226	C₂×C₄⋊C₄	—	14	1	no	—
227	C₂×C₄²	—	2	2	no	—
228	C₂×C₄²	—	7	2	no	—
229	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
230	#108	—	14	4	no	—
231	#108	—	28	2	no	—
232	#107	C₂×Dic₇	1	1	yes	characteristic
233	#107	C₂×Dic₇	1	1	yes	characteristic
234	#106	C₂×Dic₇	1	2	yes	—
235	C₄⋊C₈	—	7	2	no	—
236	C₄⋊C₈	—	7	2	no	—
237	C₄⋊C₈	—	14	4	no	—
238	C₄⋊C₈	—	14	4	no	—
239	C₄⋊C₈	—	14	2	no	—
240	C₄⋊C₈	—	14	2	no	—
241	#104	—	14	8	no	—
242	#103	C₂×Dic₇	1	2	yes	—
243	#103	C₂×Dic₇	1	2	yes	—
244	#102	C₂×Dic₇	1	2	yes	—
245	#102	C₂×Dic₇	1	2	yes	—
246	#97	—	14	4	no	—
247	C₄×C₈	C₂×Dic₇	1	1	yes	characteristic
248	C₄×C₈	C₂×Dic₇	1	1	yes	characteristic
249	C₄×C₈	C₂×Dic₇	1	1	yes	characteristic
250	C₄×C₈	C₂×Dic₇	1	1	yes	characteristic
251	#95	—	14	1	no	—
252	C₂²×C₇	—	2	1	no	—
253	C₂²×C₇	—	2	1	no	—
254	C₂²×C₇	—	2	4	no	—
255	C₂²×C₇	—	4	2	no	—
256	C₂²×C₇	—	4	2	no	—
257	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂²×C₇	#547	1	1	yes	characteristic
259	C₂²×C₇	#554	1	1	yes	characteristic
260	C₄×C₇	—	2	4	no	—
261	C₄×C₇	—	2	1	no	—
262	C₄×C₇	—	2	1	no	—
263	C₄×C₇	—	2	1	no	—
264	C₄×C₇	—	4	2	no	—
265	C₄×C₇	—	4	2	no	—
266	C₄×C₇	#444	1	2	yes	complemented
267	C₄×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
268	C₄×C₇	#520	1	1	yes	characteristic
269	C₄×C₇	D₄²	1	1	yes	characteristic
270	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
271	Dic₇	—	8	2	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	#41	C₂×Dic₁₄	1	4	yes	—
275	#41	C₂×D₂₈	1	4	yes	—
276	C₂×Q₈	C₂²×Dic₇	1	2	yes	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	C₂²×Dic₇	1	2	yes	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	14	2	no	—
283	C₂²×C₄	#1159	1	1	yes	characteristic
284	C₂²×C₄	#1159	1	1	yes	characteristic
285	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
286	Q₁₆	C₄⋊Dic₇	1	4	yes	complemented
287	SD₁₆	C₄⋊Dic₇	1	8	yes	complemented
288	D₈	C₄⋊Dic₇	1	4	yes	complemented
289	M₁₆	—	14	4	no	—
290	M₁₆	—	14	4	no	—
291	M₁₆	—	28	8	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	7	4	no	—
295	C₂×C₈	—	14	2	no	—
296	C₂×C₈	—	14	2	no	—
297	C₂×C₈	—	14	4	no	—
298	C₂×C₈	—	28	8	no	—
299	C₂×C₈	C₂×Dic₁₄	1	2	yes	—
300	C₂×C₈	C₂×D₂₈	1	2	yes	—
301	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
302	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
303	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
304	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	28	2	no	—
308	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
309	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	14	2	no	—
317	C₄²	—	14	2	no	—
318	C₄²	D₄×D₇	1	1	yes	characteristic
319	C₄²	D₄×D₇	1	1	yes	characteristic
320	C₄²	C₂²×Dic₇	1	1	yes	characteristic
321	C₄²	C₂²×Dic₇	1	1	yes	characteristic
322	C₂×C₇	—	2	1	no	—
323	C₂×C₇	—	2	1	no	—
324	C₂×C₇	—	4	4	no	—
325	C₂×C₇	D₄×C₄⋊C₄	1	1	yes	characteristic
326	C₂×C₇	C₂×#444	1	1	yes	characteristic
327	C₂×C₇	#2957	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	C₂×#1159	1	1	yes	characteristic
330	Q₈	—	2	2	no	—
331	Q₈	C₂×C₄⋊Dic₇	1	4	yes	—
332	D₄	—	2	4	no	—
333	D₄	—	2	4	no	—
334	D₄	—	2	2	no	—
335	D₄	C₂×C₄⋊Dic₇	1	4	yes	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	28	2	no	—
346	C₂×C₄	—	28	2	no	—
347	C₂×C₄	—	28	2	no	—
348	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
349	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
350	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
351	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
352	C₂×C₄	C₂²×Dic₁₄	1	1	yes	characteristic
353	C₂×C₄	C₂²×D₂₈	1	1	yes	characteristic
354	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
355	C₂×C₄	#6553	1	1	yes	characteristic
356	C₂×C₄	#6554	1	1	yes	characteristic
357	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	14	4	no	—
361	C₈	—	28	4	no	—
362	C₈	C₂×C₄⋊Dic₇	1	2	yes	—
363	C₈	C₂×C₄⋊Dic₇	1	2	yes	—
364	C₇	#22686	1	1	yes	characteristic, complemented, Sylow
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	#90234	1	1	yes	characteristic
371	C₂²	#90246	1	1	yes	characteristic
372	C₂²	C₂×D₄×Dic₇	1	1	yes	characteristic
373	C₄	—	2	4	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	56	2	no	—
380	C₄	#89969	1	2	yes	complemented
381	C₄	D₄×Dic₁₄	1	1	yes	characteristic
382	C₄	D₄×D₂₈	1	1	yes	characteristic
383	C₄	C₂²×C₄⋊Dic₇	1	1	yes	characteristic
384	C₄	#90518	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	4	4	no	—
388	C₂	D₄×C₄⋊Dic₇	1	1	yes	characteristic
389	C₂	C₂×#89969	1	1	yes	characteristic
390	C₂	#11741355	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇
Fitting	C₄×C₇×#135	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×C₇×#135	C₂²
cosocle	C₂²×C₄×C₇	C₂⁴
hypercenter	C₄×#135	D₇
hypocenter	C₇	#22686
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
3. #11739957	C₂	semidirect
4. #11729400	C₂	semidirect
5. #11728417	C₂	semidirect
6. #11728046	C₂	semidirect
7. #11727546	C₂	semidirect
8. #11727511	C₂	semidirect
12. C₄×C₇×Q₁₆	C₄	semidirect
13. C₄×C₇×Q₁₆	C₄	semidirect
14. C₄×C₇×SD₁₆	C₄	semidirect
15. C₄×C₇×SD₁₆	C₄	semidirect
16. C₄×C₇×D₈	C₄	semidirect
17. C₄×C₇×D₈	C₄	semidirect
106. C₇×Q₁₆	C₄⋊C₄	semidirect
107. C₇×SD₁₆	C₄⋊C₄	semidirect
108. C₇×D₈	C₄⋊C₄	semidirect
146. C₄×Q₁₆	Dic₇	semidirect
147. C₄×Q₁₆	Dic₇	semidirect
148. C₄×SD₁₆	Dic₇	semidirect
149. C₄×SD₁₆	Dic₇	semidirect
150. C₄×D₈	Dic₇	semidirect
151. C₄×D₈	Dic₇	semidirect
266. C₄×C₇	#444	semidirect
286. Q₁₆	C₄⋊Dic₇	semidirect
287. SD₁₆	C₄⋊Dic₇	semidirect
288. D₈	C₄⋊Dic₇	semidirect
364. C₇	#22686	semidirect
380. C₄	#89969	semidirect

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
C₂×#89969	2
#11739957	2
#11729400	2
#11728417	2
#11728046	2
#11727546	2
#11727511	2
#22686	7