Subgroups — C₃×#89437 #13055102

Order 1344.

572 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₂₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×(C₂×D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×(C₂×D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×(C₂×D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₇×#95	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₇⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
8	#89437	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
10	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
14	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
15	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₂₈	—	2	2	no	—
17	C₂×C₃×D₂₈	—	2	2	no	—
18	C₂×C₃×D₂₈	C₄	1	4	yes	complemented
19	C₂×C₃×C₄×D₇	—	2	2	no	—
20	C₂×C₃×C₄×D₇	—	2	2	no	—
21	C₂×C₃×C₄×D₇	—	2	2	no	—
22	C₃×(C₂×D₇)⋊C₄	—	2	2	no	—
23	C₃×(C₂×D₇)⋊C₄	—	2	2	no	—
24	C₃×(C₂×D₇)⋊C₄	—	2	2	no	—
25	C₂²×D₂₈	C₂×C₃	1	1	yes	characteristic
26	C₂²×C₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×(C₂×D₇)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×(C₂×D₇)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×(C₂×D₇)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
30	C₇×#95	C₂×C₃	1	1	yes	characteristic, complemented
31	C₇⋊#95	C₂×C₃	1	1	yes	characteristic, complemented
32	C₃×#386	—	7	1	no	maximal, Hall
33	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
34	C₂²×C₃×D₇	—	2	1	no	—
35	C₂²×C₃×D₇	—	2	1	no	—
36	C₂²×C₃×D₇	—	2	1	no	—
37	C₂²×C₃×D₇	—	2	1	no	—
38	C₂²×C₃×D₇	—	2	1	no	—
39	C₂²×C₃×D₇	—	2	1	no	—
40	C₂²×C₃×D₇	—	2	1	no	—
41	C₂²×C₃×D₇	—	2	1	no	—
42	C₂²×C₃×D₇	—	2	1	no	—
43	C₂²×C₃×D₇	—	2	1	no	—
44	C₂²×C₃×D₇	C₂×C₄	1	2	yes	—
45	C₂²×C₃×D₇	C₂×C₄	1	2	yes	complemented
46	C₂²×C₃×D₇	D₄	1	2	yes	—
47	C₂²×C₃×D₇	D₄	1	2	yes	—
48	C₂×C₃×C₄×C₇	—	2	1	no	—
49	C₂×C₃×C₄×C₇	—	2	1	no	—
50	C₂×C₃×C₄×C₇	—	2	1	no	—
51	C₂×C₃×C₄×C₇	—	2	1	no	—
52	C₂×C₃×C₄×C₇	—	2	1	no	—
53	C₂×C₃×C₄×C₇	—	2	1	no	—
54	C₂×C₃×C₄×C₇	—	2	1	no	—
55	C₂×C₃×C₄×C₇	C₂×C₄	1	2	yes	complemented
56	C₂×C₃×C₄×C₇	D₄	1	2	yes	complemented
57	C₂×C₃×Dic₇	—	2	1	no	—
58	C₂×C₃×Dic₇	—	2	1	no	—
59	C₂×C₃×Dic₇	—	2	1	no	—
60	C₂×C₃×Dic₇	—	2	1	no	—
61	C₂×C₃×Dic₇	—	2	1	no	—
62	C₂×C₃×Dic₇	D₄	1	2	yes	complemented
63	C₃×D₂₈	—	2	8	no	—
64	C₃×C₄×D₇	—	2	8	no	—
65	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
66	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
67	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
70	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
71	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
72	C₂×D₂₈	—	2	2	no	—
73	C₂×D₂₈	—	2	2	no	—
74	C₂×D₂₈	C₃×C₄	1	4	yes	complemented
75	C₂×C₄×D₇	—	2	2	no	—
76	C₂×C₄×D₇	—	2	2	no	—
77	C₂×C₄×D₇	—	2	2	no	—
78	(C₂×D₇)⋊C₄	—	2	2	no	—
79	(C₂×D₇)⋊C₄	—	2	2	no	—
80	(C₂×D₇)⋊C₄	—	2	2	no	—
81	C₂²×C₃×D₄	—	7	1	no	—
82	C₂³×C₃×C₄	—	7	1	no	—
83	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
84	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
85	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
86	C₃×#95	—	7	1	no	—
87	C₃×#95	D₇	1	1	yes	characteristic, complemented
88	C₂²×C₃×C₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₃×C₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₃×C₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₃×C₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₃×C₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₃×C₇	#41	1	1	yes	characteristic
94	C₂²×C₃×C₇	#41	1	1	yes	characteristic
95	C₂×C₃×D₇	—	2	2	no	—
96	C₂×C₃×D₇	—	2	2	no	—
97	C₂×C₃×D₇	—	2	2	no	—
98	C₂×C₃×D₇	—	2	2	no	—
99	C₂×C₃×D₇	—	2	2	no	—
100	C₂×C₃×D₇	—	2	2	no	—
101	C₂×C₃×D₇	—	2	2	no	—
102	C₂×C₃×D₇	—	2	2	no	—
103	C₂×C₃×D₇	—	2	2	no	—
104	C₂×C₃×D₇	—	4	1	no	—
105	C₂×C₃×D₇	—	4	1	no	—
106	C₂×C₃×D₇	—	4	1	no	—
107	C₂×C₃×D₇	—	4	1	no	—
108	C₂×C₃×D₇	C₂²⋊C₄	1	4	yes	complemented
109	C₃×C₄×C₇	—	2	2	no	—
110	C₃×C₄×C₇	—	2	2	no	—
111	C₃×C₄×C₇	—	4	1	no	—
112	C₃×Dic₇	—	2	2	no	—
113	C₃×Dic₇	—	4	1	no	—
114	#386	—	7	1	no	Sylow
115	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
116	C₂²×D₇	—	2	1	no	—
117	C₂²×D₇	—	2	1	no	—
118	C₂²×D₇	—	2	1	no	—
119	C₂²×D₇	—	2	1	no	—
120	C₂²×D₇	—	2	1	no	—
121	C₂²×D₇	—	2	1	no	—
122	C₂²×D₇	—	2	1	no	—
123	C₂²×D₇	—	2	1	no	—
124	C₂²×D₇	—	2	1	no	—
125	C₂²×D₇	—	2	1	no	—
126	C₂²×D₇	C₂×C₃×C₄	1	2	yes	—
127	C₂²×D₇	C₂×C₃×C₄	1	2	yes	complemented
128	C₂²×D₇	C₃×D₄	1	2	yes	—
129	C₂²×D₇	C₃×D₄	1	2	yes	—
130	C₂×C₄×C₇	—	2	1	no	—
131	C₂×C₄×C₇	—	2	1	no	—
132	C₂×C₄×C₇	—	2	1	no	—
133	C₂×C₄×C₇	—	2	1	no	—
134	C₂×C₄×C₇	—	2	1	no	—
135	C₂×C₄×C₇	—	2	1	no	—
136	C₂×C₄×C₇	—	2	1	no	—
137	C₂×C₄×C₇	C₂×C₃×C₄	1	2	yes	complemented
138	C₂×C₄×C₇	C₃×D₄	1	2	yes	complemented
139	C₂×Dic₇	—	2	1	no	—
140	C₂×Dic₇	—	2	1	no	—
141	C₂×Dic₇	—	2	1	no	—
142	C₂×Dic₇	—	2	1	no	—
143	C₂×Dic₇	—	2	1	no	—
144	C₂×Dic₇	C₃×D₄	1	2	yes	complemented
145	D₂₈	—	2	8	no	—
146	C₄×D₇	—	2	8	no	—
147	C₂⁴×C₃	—	7	1	no	—
148	C₂⁴×C₃	—	7	1	no	—
149	C₂×C₃×D₄	—	7	4	no	—
150	C₂×C₃×D₄	—	14	2	no	—
151	C₂×C₃×D₄	—	14	2	no	—
152	C₂²×C₃×C₄	—	7	1	no	—
153	C₂²×C₃×C₄	—	7	1	no	—
154	C₂²×C₃×C₄	—	14	2	no	—
155	C₂²×C₃×C₄	—	14	2	no	—
156	C₂²×C₃×C₄	—	14	2	no	—
157	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
160	C₃×C₂²⋊C₄	—	14	2	no	—
161	C₃×C₂²⋊C₄	—	14	2	no	—
162	C₃×C₂²⋊C₄	—	14	2	no	—
163	C₂×C₃×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₃×C₇	C₄×D₄	1	1	yes	characteristic
165	C₂×C₃×C₇	C₄×D₄	1	1	yes	characteristic
166	C₂×C₃×C₇	#120	1	1	yes	characteristic
167	C₂×C₃×C₇	#121	1	1	yes	characteristic
168	C₂×C₃×C₇	#121	1	1	yes	characteristic
169	C₂×C₃×C₇	#123	1	1	yes	characteristic
170	C₃×D₇	—	2	4	no	—
171	C₃×D₇	—	4	2	no	—
172	C₂²×D₄	—	7	1	no	—
173	C₂³×C₄	—	7	1	no	—
174	C₂×C₂²⋊C₄	—	7	1	no	—
175	C₂×C₂²⋊C₄	—	7	1	no	—
176	C₂×C₂²⋊C₄	—	7	1	no	—
177	#95	—	7	1	no	—
178	#95	C₃×D₇	1	1	yes	characteristic, complemented
179	C₂²×C₇	C₂²×C₃×C₄	1	1	yes	characteristic
180	C₂²×C₇	C₂×C₃×D₄	1	1	yes	characteristic
181	C₂²×C₇	C₂×C₃×D₄	1	1	yes	characteristic
182	C₂²×C₇	C₂×C₃×D₄	1	1	yes	characteristic
183	C₂²×C₇	C₂×C₃×D₄	1	1	yes	characteristic
184	C₂²×C₇	C₃×#41	1	1	yes	characteristic
185	C₂²×C₇	C₃×#41	1	1	yes	characteristic
186	C₂×D₇	—	2	2	no	—
187	C₂×D₇	—	2	2	no	—
188	C₂×D₇	—	2	2	no	—
189	C₂×D₇	—	2	2	no	—
190	C₂×D₇	—	2	2	no	—
191	C₂×D₇	—	2	2	no	—
192	C₂×D₇	—	2	2	no	—
193	C₂×D₇	—	2	2	no	—
194	C₂×D₇	—	2	2	no	—
195	C₂×D₇	—	4	1	no	—
196	C₂×D₇	—	4	1	no	—
197	C₂×D₇	—	4	1	no	—
198	C₂×D₇	—	4	1	no	—
199	C₂×D₇	C₃×C₂²⋊C₄	1	4	yes	complemented
200	C₄×C₇	—	2	2	no	—
201	C₄×C₇	—	2	2	no	—
202	C₄×C₇	—	4	1	no	—
203	Dic₇	—	2	2	no	—
204	Dic₇	—	4	1	no	—
205	C₂³×C₃	—	7	2	no	—
206	C₂³×C₃	—	7	2	no	—
207	C₂³×C₃	—	7	2	no	—
208	C₂³×C₃	—	7	2	no	—
209	C₂³×C₃	—	14	1	no	—
210	C₂³×C₃	—	14	1	no	—
211	C₂³×C₃	—	14	1	no	—
212	C₂³×C₃	—	14	1	no	—
213	C₂³×C₃	—	14	1	no	—
214	C₂³×C₃	—	14	1	no	—
215	C₂³×C₃	—	14	1	no	—
216	C₂³×C₃	—	14	1	no	—
217	C₂³×C₃	—	14	1	no	—
218	C₂³×C₃	—	14	1	no	—
219	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
220	C₃×D₄	—	14	8	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	2	1	no	—
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	1	no	—
228	C₂×C₃×C₄	—	7	2	no	—
229	C₂×C₃×C₄	—	14	8	no	—
230	C₂×C₃×C₄	—	14	1	no	—
231	C₂×C₃×C₄	—	14	1	no	—
232	C₂×C₃×C₄	—	14	1	no	—
233	C₂×C₃×C₄	—	14	1	no	—
234	C₂×C₃×C₄	—	14	1	no	—
235	C₂×C₃×C₄	C₄×D₇	1	2	yes	complemented
236	C₂×C₃×C₄	D₂₈	1	2	yes	complemented
237	C₃×C₇	#386	1	1	yes	characteristic, complemented, Hall
238	C₂⁴	—	7	1	no	—
239	C₂⁴	—	7	1	no	—
240	C₂×D₄	—	7	4	no	—
241	C₂×D₄	—	14	2	no	—
242	C₂×D₄	—	14	2	no	—
243	C₂²×C₄	—	7	1	no	—
244	C₂²×C₄	—	7	1	no	—
245	C₂²×C₄	—	14	2	no	—
246	C₂²×C₄	—	14	2	no	—
247	C₂²×C₄	—	14	2	no	—
248	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
249	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
250	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
251	C₂²⋊C₄	—	14	2	no	—
252	C₂²⋊C₄	—	14	2	no	—
253	C₂²⋊C₄	—	14	2	no	—
254	C₂×C₇	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₇	C₃×C₄×D₄	1	1	yes	characteristic
256	C₂×C₇	C₃×C₄×D₄	1	1	yes	characteristic
257	C₂×C₇	C₃×#120	1	1	yes	characteristic
258	C₂×C₇	C₃×#121	1	1	yes	characteristic
259	C₂×C₇	C₃×#121	1	1	yes	characteristic
260	C₂×C₇	C₃×#123	1	1	yes	characteristic
261	D₇	—	2	4	no	—
262	D₇	—	4	2	no	—
263	C₂²×C₃	—	7	4	no	—
264	C₂²×C₃	—	14	2	no	—
265	C₂²×C₃	—	14	2	no	—
266	C₂²×C₃	—	14	2	no	—
267	C₂²×C₃	—	14	2	no	—
268	C₂²×C₃	—	14	2	no	—
269	C₂²×C₃	—	14	2	no	—
270	C₂²×C₃	—	14	2	no	—
271	C₂²×C₃	—	14	2	no	—
272	C₂²×C₃	—	14	2	no	—
273	C₂²×C₃	—	28	1	no	—
274	C₂²×C₃	—	28	1	no	—
275	C₂²×C₃	—	28	1	no	—
276	C₂²×C₃	—	28	1	no	—
277	C₂²×C₃	C₂×C₄×D₇	1	1	yes	characteristic
278	C₂²×C₃	C₂×D₂₈	1	1	yes	characteristic
279	C₂²×C₃	#1157	1	1	yes	characteristic
280	C₂²×C₃	D₄×D₇	1	1	yes	characteristic
281	C₂²×C₃	D₄×D₇	1	1	yes	characteristic
282	C₂²×C₃	D₄×D₇	1	1	yes	characteristic
283	C₂²×C₃	#1161	1	1	yes	characteristic
284	C₃×C₄	—	2	2	no	—
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	—	4	1	no	—
287	C₃×C₄	—	14	2	no	—
288	C₃×C₄	—	28	1	no	—
289	C₂³	—	7	2	no	—
290	C₂³	—	7	2	no	—
291	C₂³	—	7	2	no	—
292	C₂³	—	7	2	no	—
293	C₂³	—	14	1	no	—
294	C₂³	—	14	1	no	—
295	C₂³	—	14	1	no	—
296	C₂³	—	14	1	no	—
297	C₂³	—	14	1	no	—
298	C₂³	—	14	1	no	—
299	C₂³	—	14	1	no	—
300	C₂³	—	14	1	no	—
301	C₂³	—	14	1	no	—
302	C₂³	—	14	1	no	—
303	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
304	D₄	—	14	8	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	7	2	no	—
313	C₂×C₄	—	14	8	no	—
314	C₂×C₄	—	14	1	no	—
315	C₂×C₄	—	14	1	no	—
316	C₂×C₄	—	14	1	no	—
317	C₂×C₄	—	14	1	no	—
318	C₂×C₄	—	14	1	no	—
319	C₂×C₄	C₃×C₄×D₇	1	2	yes	complemented
320	C₂×C₄	C₃×D₂₈	1	2	yes	complemented
321	C₇	C₃×#386	1	1	yes	characteristic, complemented, Sylow
322	C₂×C₃	—	14	4	no	—
323	C₂×C₃	—	28	2	no	—
324	C₂×C₃	C₄×D₂₈	1	1	yes	characteristic
325	C₂×C₃	D₇×C₂²⋊C₄	1	1	yes	characteristic
326	C₂×C₃	#6445	1	1	yes	characteristic
327	C₂×C₃	#6447	1	1	yes	characteristic
328	C₂×C₃	#6456	1	1	yes	characteristic
329	C₂×C₃	#6457	1	1	yes	characteristic
330	C₂×C₃	#6458	1	1	yes	characteristic
331	C₂²	—	7	4	no	—
332	C₂²	—	14	2	no	—
333	C₂²	—	14	2	no	—
334	C₂²	—	14	2	no	—
335	C₂²	—	14	2	no	—
336	C₂²	—	14	2	no	—
337	C₂²	—	14	2	no	—
338	C₂²	—	14	2	no	—
339	C₂²	—	14	2	no	—
340	C₂²	—	14	2	no	—
341	C₂²	—	28	1	no	—
342	C₂²	—	28	1	no	—
343	C₂²	—	28	1	no	—
344	C₂²	—	28	1	no	—
345	C₂²	C₂×C₃×C₄×D₇	1	1	yes	characteristic
346	C₂²	C₂×C₃×D₂₈	1	1	yes	characteristic
347	C₂²	C₃×#1157	1	1	yes	characteristic
348	C₂²	C₃×D₄×D₇	1	1	yes	characteristic
349	C₂²	C₃×D₄×D₇	1	1	yes	characteristic
350	C₂²	C₃×D₄×D₇	1	1	yes	characteristic
351	C₂²	C₃×#1161	1	1	yes	characteristic
352	C₄	—	2	2	no	—
353	C₄	—	2	2	no	—
354	C₄	—	4	1	no	—
355	C₄	—	14	2	no	—
356	C₄	—	28	1	no	—
357	C₃	#89437	1	1	yes	characteristic, direct product factor, Sylow
358	C₂	—	14	4	no	—
359	C₂	—	28	2	no	—
360	C₂	C₃×C₄×D₂₈	1	1	yes	characteristic
361	C₂	C₃×D₇×C₂²⋊C₄	1	1	yes	characteristic
362	C₂	C₃×#6445	1	1	yes	characteristic
363	C₂	C₃×#6447	1	1	yes	characteristic
364	C₂	C₃×#6456	1	1	yes	characteristic
365	C₂	C₃×#6457	1	1	yes	characteristic
366	C₂	C₃×#6458	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂²×D₇
commutator	C₂²×C₇	C₂²×C₃×C₄
Frattini	C₂³	C₂²×C₃×D₇
Fitting	C₃×C₇×#95	C₂
socle	C₂³×C₃×C₇	C₂³
prime radical	C₂²×C₃×D₂₈	C₂
cosocle	C₂³×C₇	C₂³×C₃
hypercenter	C₃×#95	D₇
hypocenter	C₇	C₃×#386
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#95

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₄×D₇	C₂	semidirect
3. C₂×C₃×(C₂×D₇)⋊C₄	C₂	semidirect
4. C₂×C₃×(C₂×D₇)⋊C₄	C₂	semidirect
5. C₂×C₃×(C₂×D₇)⋊C₄	C₂	semidirect
6. C₃×C₇×#95	C₂	semidirect
7. C₃×C₇⋊#95	C₂	semidirect
8. #89437	C₃	direct (N × H)
18. C₂×C₃×D₂₈	C₄	semidirect
26. C₂²×C₄×D₇	C₂×C₃	semidirect
27. C₂×(C₂×D₇)⋊C₄	C₂×C₃	semidirect
28. C₂×(C₂×D₇)⋊C₄	C₂×C₃	semidirect
29. C₂×(C₂×D₇)⋊C₄	C₂×C₃	semidirect
30. C₇×#95	C₂×C₃	semidirect
31. C₇⋊#95	C₂×C₃	semidirect
45. C₂²×C₃×D₇	C₂×C₄	semidirect
55. C₂×C₃×C₄×C₇	C₂×C₄	semidirect
56. C₂×C₃×C₄×C₇	D₄	semidirect
62. C₂×C₃×Dic₇	D₄	semidirect
74. C₂×D₂₈	C₃×C₄	semidirect
87. C₃×#95	D₇	semidirect
108. C₂×C₃×D₇	C₂²⋊C₄	semidirect
127. C₂²×D₇	C₂×C₃×C₄	semidirect
137. C₂×C₄×C₇	C₂×C₃×C₄	semidirect
138. C₂×C₄×C₇	C₃×D₄	semidirect
144. C₂×Dic₇	C₃×D₄	semidirect
178. #95	C₃×D₇	semidirect
199. C₂×D₇	C₃×C₂²⋊C₄	semidirect
235. C₂×C₃×C₄	C₄×D₇	semidirect
236. C₂×C₃×C₄	D₂₈	semidirect
237. C₃×C₇	#386	semidirect
319. C₂×C₄	C₃×C₄×D₇	semidirect
320. C₂×C₄	C₃×D₂₈	semidirect
321. C₇	C₃×#386	semidirect
357. C₃	#89437	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₂₈	2
C₂²×C₃×C₄×D₇	2
C₂×C₃×(C₂×D₇)⋊C₄	2
C₃×C₇×#95	2
C₃×C₇⋊#95	2
#89437	3
C₃×#386	7

Subgroups — C3×#89437 #13055102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#89437 #13055102