Subgroups — C₃×#90318 #13060973

Order 1344.

660 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	C₂×C₃×#1161	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6509	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6458	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#6457	C₂	1	2	yes	maximal, complemented
8	C₃×#6456	C₂	1	2	yes	maximal, complemented
9	C₃×#6455	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6445	C₂	1	2	yes	maximal, complemented
11	C₃×(C₂²⋊D₇)⋊C₄	C₂	1	2	yes	maximal, complemented
12	#90318	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	—
17	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
18	C₃×#1161	—	2	4	no	—
19	C₂×C₃×D₂₈	C₂²	1	2	yes	—
20	C₂×C₃×D₂₈	C₂²	1	2	yes	—
21	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₄×D₇	—	2	4	no	—
23	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄×D₇	C₂²	1	2	yes	complemented
28	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
32	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
33	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
34	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
35	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
36	C₃×Dic₇⋊C₄	C₂²	1	2	yes	complemented
37	C₃×C₄×Dic₇	C₂²	1	2	yes	complemented
38	C₂×#1161	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂²×C₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
40	C₇×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
41	#6509	C₂×C₃	1	1	yes	characteristic, complemented
42	#6493	C₂×C₃	1	1	yes	characteristic, complemented
43	#6458	C₂×C₃	1	1	yes	characteristic, complemented
44	#6457	C₂×C₃	1	2	yes	complemented
45	#6456	C₂×C₃	1	2	yes	complemented
46	#6455	C₂×C₃	1	1	yes	characteristic, complemented
47	#6445	C₂×C₃	1	2	yes	complemented
48	(C₂²⋊D₇)⋊C₄	C₂×C₃	1	2	yes	complemented
49	C₃×#525	—	7	1	no	maximal, Hall
50	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
51	C₂²×C₃×D₇	—	2	2	no	—
52	C₂²×C₃×D₇	—	2	2	no	—
53	C₂²×C₃×D₇	—	2	2	no	—
54	C₂²×C₃×D₇	C₂³	1	2	yes	—
55	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
56	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
57	C₃×C₇×Q₈	—	2	2	no	—
58	C₂×C₃×C₄×C₇	—	2	2	no	—
59	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
60	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
61	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
63	C₃×C₂²⋊D₇	—	2	4	no	—
64	C₂×C₃×Dic₇	—	2	2	no	—
65	C₂×C₃×Dic₇	C₂³	1	2	yes	—
66	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
68	C₃×D₂₈	—	2	4	no	—
69	C₃×D₂₈	—	2	4	no	—
70	C₃×D₂₈	—	2	2	no	—
71	C₃×C₄×D₇	—	2	2	no	—
72	C₃×C₄×D₇	—	2	2	no	—
73	C₃×C₄×D₇	—	2	2	no	—
74	C₃×C₄×D₇	—	2	4	no	—
75	C₃×C₄×D₇	D₄	1	4	yes	complemented
76	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
78	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
80	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
81	#1161	—	2	4	no	—
82	C₂×D₂₈	C₂²×C₃	1	2	yes	—
83	C₂×D₂₈	C₂²×C₃	1	2	yes	—
84	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
85	C₂×C₄×D₇	—	2	4	no	—
86	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₄×D₇	C₂²×C₃	1	2	yes	complemented
91	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
92	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
93	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
94	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
95	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
96	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
97	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
98	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
99	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
100	C₄×Dic₇	C₂²×C₃	1	2	yes	complemented
101	C₂×C₃×#41	—	7	1	no	—
102	C₂³×C₃×C₄	—	7	1	no	—
103	C₃×#123	—	7	2	no	—
104	C₃×C₂²⋊Q₈	—	7	1	no	—
105	C₃×C₂²⋊Q₈	D₇	1	1	yes	characteristic, complemented
106	C₃×#121	—	7	1	no	—
107	C₃×#121	—	7	1	no	—
108	C₃×#120	—	7	2	no	—
109	C₃×C₄×D₄	—	7	2	no	—
110	C₃×C₄×D₄	—	7	2	no	—
111	C₃×#117	—	7	1	no	—
112	C₂²×C₃×C₇	—	2	1	no	—
113	C₂²×C₃×C₇	—	2	1	no	—
114	C₂²×C₃×C₇	#41	1	2	yes	complemented
115	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
116	C₂×C₃×D₇	—	2	8	no	—
117	C₂×C₃×D₇	—	2	1	no	—
118	C₂×C₃×D₇	—	2	1	no	—
119	C₂×C₃×D₇	—	2	1	no	—
120	C₂×C₃×D₇	—	2	1	no	—
121	C₂×C₃×D₇	—	2	2	no	—
122	C₂×C₃×D₇	—	2	2	no	—
123	C₂×C₃×D₇	—	2	2	no	—
124	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
125	C₂×C₃×D₇	#41	1	2	yes	complemented
126	C₃×C₄×C₇	—	2	1	no	—
127	C₃×C₄×C₇	—	2	2	no	—
128	C₃×C₄×C₇	—	2	2	no	—
129	C₃×C₄×C₇	C₂×D₄	1	2	yes	—
130	C₃×Dic₇	—	2	1	no	—
131	C₃×Dic₇	—	2	2	no	—
132	C₃×Dic₇	C₂×D₄	1	2	yes	—
133	#525	—	7	1	no	Sylow
134	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
135	C₂²×D₇	—	2	2	no	—
136	C₂²×D₇	—	2	2	no	—
137	C₂²×D₇	—	2	2	no	—
138	C₂²×D₇	C₂³×C₃	1	2	yes	—
139	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
140	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
141	C₇×Q₈	—	2	2	no	—
142	C₂×C₄×C₇	—	2	2	no	—
143	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
144	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
145	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
146	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
147	C₂²⋊D₇	—	2	4	no	—
148	C₂×Dic₇	—	2	2	no	—
149	C₂×Dic₇	C₂³×C₃	1	2	yes	—
150	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
151	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
152	D₂₈	—	2	4	no	—
153	D₂₈	—	2	4	no	—
154	D₂₈	—	2	2	no	—
155	C₄×D₇	—	2	2	no	—
156	C₄×D₇	—	2	2	no	—
157	C₄×D₇	—	2	2	no	—
158	C₄×D₇	—	2	4	no	—
159	C₄×D₇	C₃×D₄	1	4	yes	complemented
160	C₂⁴×C₃	—	7	1	no	—
161	C₃×#41	—	14	4	no	—
162	C₂×C₃×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
163	C₂×C₃×D₄	—	7	2	no	—
164	C₂×C₃×D₄	—	7	2	no	—
165	C₂×C₃×D₄	—	7	2	no	—
166	C₂×C₃×D₄	—	7	1	no	—
167	C₂²×C₃×C₄	—	7	1	no	—
168	C₂²×C₃×C₄	—	7	1	no	—
169	C₂²×C₃×C₄	—	7	1	no	—
170	C₂²×C₃×C₄	—	7	1	no	—
171	C₂²×C₃×C₄	—	7	1	no	—
172	C₂²×C₃×C₄	—	7	2	no	—
173	C₂²×C₃×C₄	—	14	4	no	—
174	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
175	C₃×C₄⋊C₄	—	7	2	no	—
176	C₃×C₄⋊C₄	—	7	1	no	—
177	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
178	C₃×C₄⋊C₄	C₂×D₇	1	2	yes	complemented
179	C₃×C₂²⋊C₄	—	7	2	no	—
180	C₃×C₂²⋊C₄	—	7	2	no	—
181	C₃×C₂²⋊C₄	—	7	2	no	—
182	C₃×C₂²⋊C₄	—	7	2	no	—
183	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	—
184	C₃×C₄²	—	7	2	no	—
185	C₂×C₃×C₇	—	2	2	no	—
186	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
188	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
189	C₃×D₇	—	2	2	no	—
190	C₃×D₇	—	2	2	no	—
191	C₃×D₇	—	4	2	no	—
192	C₂×#41	—	7	1	no	—
193	C₂³×C₄	—	7	1	no	—
194	#123	—	7	2	no	—
195	C₂²⋊Q₈	—	7	1	no	—
196	C₂²⋊Q₈	C₃×D₇	1	1	yes	characteristic, complemented
197	#121	—	7	1	no	—
198	#121	—	7	1	no	—
199	#120	—	7	2	no	—
200	C₄×D₄	—	7	2	no	—
201	C₄×D₄	—	7	2	no	—
202	#117	—	7	1	no	—
203	C₂²×C₇	—	2	1	no	—
204	C₂²×C₇	—	2	1	no	—
205	C₂²×C₇	C₃×#41	1	2	yes	complemented
206	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
207	C₂×D₇	—	2	8	no	—
208	C₂×D₇	—	2	1	no	—
209	C₂×D₇	—	2	1	no	—
210	C₂×D₇	—	2	1	no	—
211	C₂×D₇	—	2	1	no	—
212	C₂×D₇	—	2	2	no	—
213	C₂×D₇	—	2	2	no	—
214	C₂×D₇	—	2	2	no	—
215	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
216	C₂×D₇	C₃×#41	1	2	yes	complemented
217	C₄×C₇	—	2	1	no	—
218	C₄×C₇	—	2	2	no	—
219	C₄×C₇	—	2	2	no	—
220	C₄×C₇	C₂×C₃×D₄	1	2	yes	—
221	Dic₇	—	2	1	no	—
222	Dic₇	—	2	2	no	—
223	Dic₇	C₂×C₃×D₄	1	2	yes	—
224	C₂³×C₃	—	7	1	no	—
225	C₂³×C₃	—	7	1	no	—
226	C₂³×C₃	—	7	2	no	—
227	C₂³×C₃	—	14	2	no	—
228	C₂³×C₃	—	14	2	no	—
229	C₂³×C₃	—	14	2	no	—
230	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
231	C₃×Q₈	—	2	2	no	—
232	C₃×D₄	—	14	4	no	—
233	C₃×D₄	—	14	4	no	—
234	C₃×D₄	—	14	4	no	—
235	C₃×D₄	—	14	2	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	7	1	no	—
238	C₂×C₃×C₄	—	7	4	no	—
239	C₂×C₃×C₄	—	7	2	no	—
240	C₂×C₃×C₄	—	7	1	no	—
241	C₂×C₃×C₄	—	14	2	no	—
242	C₂×C₃×C₄	—	14	4	no	—
243	C₂×C₃×C₄	—	14	2	no	—
244	C₂×C₃×C₄	—	14	2	no	—
245	C₂×C₃×C₄	—	14	2	no	—
246	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
247	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
249	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
250	C₃×C₇	#525	1	1	yes	characteristic, complemented, Hall
251	C₂⁴	—	7	1	no	—
252	#41	—	14	4	no	—
253	C₂×Q₈	C₂×C₃×D₇	1	1	yes	characteristic, complemented
254	C₂×D₄	—	7	2	no	—
255	C₂×D₄	—	7	2	no	—
256	C₂×D₄	—	7	2	no	—
257	C₂×D₄	—	7	1	no	—
258	C₂²×C₄	—	7	1	no	—
259	C₂²×C₄	—	7	1	no	—
260	C₂²×C₄	—	7	1	no	—
261	C₂²×C₄	—	7	2	no	—
262	C₂²×C₄	—	7	1	no	—
263	C₂²×C₄	—	7	1	no	—
264	C₂²×C₄	—	14	4	no	—
265	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
266	C₄⋊C₄	—	7	2	no	—
267	C₄⋊C₄	—	7	1	no	—
268	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
269	C₄⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
270	C₂²⋊C₄	—	7	2	no	—
271	C₂²⋊C₄	—	7	2	no	—
272	C₂²⋊C₄	—	7	2	no	—
273	C₂²⋊C₄	—	7	2	no	—
274	C₂²⋊C₄	C₂×C₃×D₇	1	2	yes	—
275	C₄²	—	7	2	no	—
276	C₂×C₇	—	2	2	no	—
277	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
278	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
279	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
280	D₇	—	2	2	no	—
281	D₇	—	2	2	no	—
282	D₇	—	4	2	no	—
283	C₂²×C₃	—	2	1	no	—
284	C₂²×C₃	—	2	1	no	—
285	C₂²×C₃	—	7	2	no	—
286	C₂²×C₃	—	7	2	no	—
287	C₂²×C₃	—	14	8	no	—
288	C₂²×C₃	—	14	1	no	—
289	C₂²×C₃	—	14	1	no	—
290	C₂²×C₃	—	14	1	no	—
291	C₂²×C₃	—	14	1	no	—
292	C₂²×C₃	—	14	2	no	—
293	C₂²×C₃	—	14	2	no	—
294	C₂²×C₃	—	14	2	no	—
295	C₂²×C₃	#1161	1	2	yes	complemented
296	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	2	2	no	—
300	C₃×C₄	—	7	2	no	—
301	C₃×C₄	—	14	1	no	—
302	C₃×C₄	—	14	2	no	—
303	C₃×C₄	D₄×D₇	1	2	yes	—
304	C₂³	—	7	1	no	—
305	C₂³	—	7	1	no	—
306	C₂³	—	7	2	no	—
307	C₂³	—	14	2	no	—
308	C₂³	—	14	2	no	—
309	C₂³	—	14	2	no	—
310	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
311	Q₈	—	2	2	no	—
312	D₄	—	14	4	no	—
313	D₄	—	14	4	no	—
314	D₄	—	14	4	no	—
315	D₄	—	14	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	7	1	no	—
318	C₂×C₄	—	7	4	no	—
319	C₂×C₄	—	7	2	no	—
320	C₂×C₄	—	7	1	no	—
321	C₂×C₄	—	14	2	no	—
322	C₂×C₄	—	14	4	no	—
323	C₂×C₄	—	14	2	no	—
324	C₂×C₄	—	14	2	no	—
325	C₂×C₄	—	14	2	no	—
326	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
327	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
328	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
329	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
330	C₇	C₃×#525	1	1	yes	characteristic, complemented, Sylow
331	C₂×C₃	—	2	2	no	—
332	C₂×C₃	—	14	2	no	—
333	C₂×C₃	—	14	2	no	—
334	C₂×C₃	—	28	2	no	—
335	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
336	C₂×C₃	C₂×#1161	1	1	yes	characteristic
337	C₂×C₃	D₇×#41	1	1	yes	characteristic
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	7	2	no	—
341	C₂²	—	7	2	no	—
342	C₂²	—	14	8	no	—
343	C₂²	—	14	1	no	—
344	C₂²	—	14	1	no	—
345	C₂²	—	14	1	no	—
346	C₂²	—	14	1	no	—
347	C₂²	—	14	2	no	—
348	C₂²	—	14	2	no	—
349	C₂²	—	14	2	no	—
350	C₂²	C₃×#1161	1	2	yes	complemented
351	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	7	2	no	—
356	C₄	—	14	1	no	—
357	C₄	—	14	2	no	—
358	C₄	C₃×D₄×D₇	1	2	yes	—
359	C₃	#90318	1	1	yes	characteristic, direct product factor, Sylow
360	C₂	—	2	2	no	—
361	C₂	—	14	2	no	—
362	C₂	—	14	2	no	—
363	C₂	—	28	2	no	—
364	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
365	C₂	C₂×C₃×#1161	1	1	yes	characteristic
366	C₂	C₃×D₇×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₇
commutator, cosocle	C₂²×C₇	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₇
Fitting	C₃×C₇×C₂²⋊Q₈	C₂
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₃×C₂²⋊Q₈	D₇
hypocenter	C₇	C₃×#525
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#1161	C₂	semidirect
2. C₂²×C₃×C₄×D₇	C₂	semidirect
3. C₃×C₇×C₂²⋊Q₈	C₂	semidirect
4. C₃×#6509	C₂	semidirect
5. C₃×#6493	C₂	semidirect
6. C₃×#6458	C₂	semidirect
7. C₃×#6457	C₂	semidirect
8. C₃×#6456	C₂	semidirect
9. C₃×#6455	C₂	semidirect
10. C₃×#6445	C₂	semidirect
11. C₃×(C₂²⋊D₇)⋊C₄	C₂	semidirect
12. #90318	C₃	direct (N × H)
14. C₂×C₃×C₇×Q₈	C₂²	semidirect
21. C₂×C₃×D₂₈	C₂²	semidirect
27. C₂×C₃×C₄×D₇	C₂²	semidirect
28. C₃×C₇×C₄⋊C₄	C₂²	semidirect
29. C₃×C₇×C₄⋊C₄	C₂²	semidirect
33. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
34. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
35. C₃×C₄⋊Dic₇	C₂²	semidirect
36. C₃×Dic₇⋊C₄	C₂²	semidirect
37. C₃×C₄×Dic₇	C₂²	semidirect
38. C₂×#1161	C₂×C₃	semidirect
39. C₂²×C₄×D₇	C₂×C₃	semidirect
40. C₇×C₂²⋊Q₈	C₂×C₃	semidirect
41. #6509	C₂×C₃	semidirect
42. #6493	C₂×C₃	semidirect
43. #6458	C₂×C₃	semidirect
44. #6457	C₂×C₃	semidirect
45. #6456	C₂×C₃	semidirect
46. #6455	C₂×C₃	semidirect
47. #6445	C₂×C₃	semidirect
48. (C₂²⋊D₇)⋊C₄	C₂×C₃	semidirect
75. C₃×C₄×D₇	D₄	semidirect
77. C₂×C₇×Q₈	C₂²×C₃	semidirect
84. C₂×D₂₈	C₂²×C₃	semidirect
90. C₂×C₄×D₇	C₂²×C₃	semidirect
91. C₇×C₄⋊C₄	C₂²×C₃	semidirect
92. C₇×C₄⋊C₄	C₂²×C₃	semidirect
96. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
97. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
98. C₄⋊Dic₇	C₂²×C₃	semidirect
99. Dic₇⋊C₄	C₂²×C₃	semidirect
100. C₄×Dic₇	C₂²×C₃	semidirect
105. C₃×C₂²⋊Q₈	D₇	semidirect
114. C₂²×C₃×C₇	#41	semidirect
125. C₂×C₃×D₇	#41	semidirect
159. C₄×D₇	C₃×D₄	semidirect
162. C₂×C₃×Q₈	C₂×D₇	semidirect
177. C₃×C₄⋊C₄	C₂×D₇	semidirect
178. C₃×C₄⋊C₄	C₂×D₇	semidirect
196. C₂²⋊Q₈	C₃×D₇	semidirect
205. C₂²×C₇	C₃×#41	semidirect
216. C₂×D₇	C₃×#41	semidirect
250. C₃×C₇	#525	semidirect
253. C₂×Q₈	C₂×C₃×D₇	semidirect
268. C₄⋊C₄	C₂×C₃×D₇	semidirect
269. C₄⋊C₄	C₂×C₃×D₇	semidirect
295. C₂²×C₃	#1161	semidirect
330. C₇	C₃×#525	semidirect
350. C₂²	C₃×#1161	semidirect
359. C₃	#90318	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#1161	2
C₂²×C₃×C₄×D₇	2
C₃×C₇×C₂²⋊Q₈	2
C₃×#6509	2
C₃×#6493	2
C₃×#6458	2
C₃×#6457	2
C₃×#6456	2
C₃×#6455	2
C₃×#6445	2
C₃×(C₂²⋊D₇)⋊C₄	2
#90318	3
C₃×#525	7

Subgroups — C3×#90318 #13060973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90318 #13060973