Subgroups — C₃×#90331 #13060969

Order 1344.

432 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#6510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#6507	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6461	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#6459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#6459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#6457	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6455	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#6450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#6448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#6448	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#6447	C₂	1	1	yes	maximal, characteristic
15	C₃×#6442	C₂	1	1	yes	maximal, characteristic, complemented
16	#90331	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
24	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic
26	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
32	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
33	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
34	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
35	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
42	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
44	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
45	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
46	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
47	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
48	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic
49	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic
50	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic
51	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic
52	C₇×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
53	#6510	C₂×C₃	1	1	yes	characteristic, complemented
54	#6507	C₂×C₃	1	1	yes	characteristic, complemented
55	#6492	C₂×C₃	1	1	yes	characteristic, complemented
56	C₄×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
57	#6461	C₂×C₃	1	1	yes	characteristic, complemented
58	#6459	C₂×C₃	1	1	yes	characteristic, complemented
59	#6459	C₂×C₃	1	1	yes	characteristic, complemented
60	#6457	C₂×C₃	1	1	yes	characteristic, complemented
61	#6455	C₂×C₃	1	1	yes	characteristic, complemented
62	#6450	C₂×C₃	1	1	yes	characteristic, complemented
63	#6448	C₂×C₃	1	1	yes	characteristic, complemented
64	#6448	C₂×C₃	1	1	yes	characteristic, complemented
65	#6447	C₂×C₃	1	1	yes	characteristic
66	#6442	C₂×C₃	1	1	yes	characteristic, complemented
67	C₃×#542	—	7	1	no	maximal, Hall
68	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
69	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
70	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
71	C₃×C₇×Q₈	—	4	1	no	—
72	C₂×C₃×C₄×C₇	—	4	1	no	—
73	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
79	C₃×C₂²⋊D₇	—	2	2	no	—
80	C₃×C₂²⋊D₇	—	4	1	no	—
81	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
82	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
83	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
84	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
85	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
86	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
87	C₃×D₂₈	—	4	1	no	—
88	C₃×C₄×D₇	—	2	2	no	—
89	C₃×C₄×D₇	—	4	1	no	—
90	C₃×Dic₁₄	—	2	2	no	—
91	C₃×Dic₁₄	—	4	1	no	—
92	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
96	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
99	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
100	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
101	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
102	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
103	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
104	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
107	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
108	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
111	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
117	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
118	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
124	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
125	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
126	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
127	C₃×C₄⋊Q₈	—	7	1	no	—
128	C₃×#126	—	7	1	no	—
129	C₃×#126	—	7	1	no	—
130	C₃×#124	—	7	1	no	—
131	C₃×#124	—	7	1	no	—
132	C₃×#124	—	7	1	no	—
133	C₃×#123	—	7	1	no	—
134	C₃×#123	—	7	1	no	—
135	C₃×C₂²⋊Q₈	—	7	1	no	—
136	C₃×C₂²⋊Q₈	—	7	1	no	—
137	C₃×C₂²⋊Q₈	D₇	1	1	yes	characteristic, complemented
138	C₃×#121	—	7	1	no	—
139	C₃×C₄×Q₈	—	7	1	no	—
140	C₃×C₄×D₄	—	7	1	no	—
141	C₃×#117	—	7	1	no	—
142	C₂²×C₃×C₇	—	2	1	no	—
143	C₂²×C₃×C₇	—	2	1	no	—
144	C₂²×C₃×C₇	—	2	1	no	—
145	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
146	C₂×C₃×D₇	—	2	1	no	—
147	C₂×C₃×D₇	—	2	1	no	—
148	C₂×C₃×D₇	—	2	1	no	—
149	C₂×C₃×D₇	—	2	1	no	—
150	C₂×C₃×D₇	—	2	1	no	—
151	C₂×C₃×D₇	—	2	1	no	—
152	C₃×C₄×C₇	—	2	1	no	—
153	C₃×C₄×C₇	—	2	1	no	—
154	C₃×C₄×C₇	—	2	1	no	—
155	C₃×C₄×C₇	—	2	1	no	—
156	C₃×C₄×C₇	—	2	1	no	—
157	C₃×C₄×C₇	—	2	1	no	—
158	C₃×Dic₇	—	2	1	no	—
159	C₃×Dic₇	—	2	1	no	—
160	C₃×Dic₇	—	2	1	no	—
161	C₃×Dic₇	—	2	1	no	—
162	C₃×Dic₇	—	2	1	no	—
163	C₃×Dic₇	#41	1	2	yes	—
164	#542	—	7	1	no	Sylow
165	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
166	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
167	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
168	C₇×Q₈	—	4	1	no	—
169	C₂×C₄×C₇	—	4	1	no	—
170	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
171	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
172	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
173	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
174	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
175	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
176	C₂²⋊D₇	—	2	2	no	—
177	C₂²⋊D₇	—	4	1	no	—
178	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
179	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
180	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
181	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
182	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
183	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
184	D₂₈	—	4	1	no	—
185	C₄×D₇	—	2	2	no	—
186	C₄×D₇	—	4	1	no	—
187	Dic₁₄	—	2	2	no	—
188	Dic₁₄	—	4	1	no	—
189	C₂×C₃×Q₈	—	7	1	no	—
190	C₂×C₃×Q₈	—	7	1	no	—
191	C₂×C₃×Q₈	C₂×D₇	1	1	yes	characteristic
192	C₂×C₃×D₄	—	7	1	no	—
193	C₂×C₃×D₄	—	7	1	no	—
194	C₂×C₃×D₄	—	7	1	no	—
195	C₂²×C₃×C₄	—	7	1	no	—
196	C₂²×C₃×C₄	—	7	1	no	—
197	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
198	C₃×C₄⋊C₄	—	7	1	no	—
199	C₃×C₄⋊C₄	—	7	1	no	—
200	C₃×C₄⋊C₄	—	7	1	no	—
201	C₃×C₄⋊C₄	—	7	1	no	—
202	C₃×C₄⋊C₄	—	7	1	no	—
203	C₃×C₄⋊C₄	—	7	1	no	—
204	C₃×C₄⋊C₄	—	7	1	no	—
205	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
206	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
207	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
208	C₃×C₂²⋊C₄	—	7	1	no	—
209	C₃×C₂²⋊C₄	—	7	1	no	—
210	C₃×C₂²⋊C₄	—	7	1	no	—
211	C₃×C₂²⋊C₄	—	7	1	no	—
212	C₃×C₂²⋊C₄	—	7	1	no	—
213	C₃×C₂²⋊C₄	—	7	1	no	—
214	C₃×C₂²⋊C₄	—	7	1	no	—
215	C₃×C₂²⋊C₄	—	7	1	no	—
216	C₃×C₂²⋊C₄	—	7	1	no	—
217	C₃×C₂²⋊C₄	—	7	1	no	—
218	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
219	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
220	C₃×C₄²	—	7	1	no	—
221	C₃×C₄²	—	7	1	no	—
222	C₃×C₄²	—	7	1	no	—
223	C₃×C₄²	—	7	1	no	—
224	C₂×C₃×C₇	—	4	1	no	—
225	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
226	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₃×C₇	2₋¹⁺⁴	1	1	yes	characteristic
228	C₃×D₇	—	4	1	no	—
229	C₃×D₇	—	4	1	no	—
230	C₄⋊Q₈	—	7	1	no	—
231	#126	—	7	1	no	—
232	#126	—	7	1	no	—
233	#124	—	7	1	no	—
234	#124	—	7	1	no	—
235	#124	—	7	1	no	—
236	#123	—	7	1	no	—
237	#123	—	7	1	no	—
238	C₂²⋊Q₈	—	7	1	no	—
239	C₂²⋊Q₈	—	7	1	no	—
240	C₂²⋊Q₈	C₃×D₇	1	1	yes	characteristic, complemented
241	#121	—	7	1	no	—
242	C₄×Q₈	—	7	1	no	—
243	C₄×D₄	—	7	1	no	—
244	#117	—	7	1	no	—
245	C₂²×C₇	—	2	1	no	—
246	C₂²×C₇	—	2	1	no	—
247	C₂²×C₇	—	2	1	no	—
248	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
249	C₂×D₇	—	2	1	no	—
250	C₂×D₇	—	2	1	no	—
251	C₂×D₇	—	2	1	no	—
252	C₂×D₇	—	2	1	no	—
253	C₂×D₇	—	2	1	no	—
254	C₂×D₇	—	2	1	no	—
255	C₄×C₇	—	2	1	no	—
256	C₄×C₇	—	2	1	no	—
257	C₄×C₇	—	2	1	no	—
258	C₄×C₇	—	2	1	no	—
259	C₄×C₇	—	2	1	no	—
260	C₄×C₇	—	2	1	no	—
261	Dic₇	—	2	1	no	—
262	Dic₇	—	2	1	no	—
263	Dic₇	—	2	1	no	—
264	Dic₇	—	2	1	no	—
265	Dic₇	—	2	1	no	—
266	Dic₇	C₃×#41	1	2	yes	—
267	C₂³×C₃	—	7	1	no	—
268	C₂³×C₃	—	7	1	no	—
269	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
270	C₃×Q₈	—	4	1	no	—
271	C₃×Q₈	—	14	2	no	—
272	C₃×Q₈	—	28	1	no	—
273	C₃×D₄	—	14	2	no	—
274	C₃×D₄	—	28	1	no	—
275	C₃×D₄	—	28	1	no	—
276	C₂×C₃×C₄	—	4	1	no	—
277	C₂×C₃×C₄	—	7	1	no	—
278	C₂×C₃×C₄	—	7	1	no	—
279	C₂×C₃×C₄	—	7	1	no	—
280	C₂×C₃×C₄	—	7	1	no	—
281	C₂×C₃×C₄	—	7	1	no	—
282	C₂×C₃×C₄	—	7	1	no	—
283	C₂×C₃×C₄	—	14	2	no	—
284	C₂×C₃×C₄	—	28	1	no	—
285	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
291	C₃×C₇	#542	1	1	yes	characteristic, complemented, Hall
292	C₂×Q₈	—	7	1	no	—
293	C₂×Q₈	—	7	1	no	—
294	C₂×Q₈	C₂×C₃×D₇	1	1	yes	characteristic
295	C₂×D₄	—	7	1	no	—
296	C₂×D₄	—	7	1	no	—
297	C₂×D₄	—	7	1	no	—
298	C₂²×C₄	—	7	1	no	—
299	C₂²×C₄	—	7	1	no	—
300	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
301	C₄⋊C₄	—	7	1	no	—
302	C₄⋊C₄	—	7	1	no	—
303	C₄⋊C₄	—	7	1	no	—
304	C₄⋊C₄	—	7	1	no	—
305	C₄⋊C₄	—	7	1	no	—
306	C₄⋊C₄	—	7	1	no	—
307	C₄⋊C₄	—	7	1	no	—
308	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
309	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
310	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
311	C₂²⋊C₄	—	7	1	no	—
312	C₂²⋊C₄	—	7	1	no	—
313	C₂²⋊C₄	—	7	1	no	—
314	C₂²⋊C₄	—	7	1	no	—
315	C₂²⋊C₄	—	7	1	no	—
316	C₂²⋊C₄	—	7	1	no	—
317	C₂²⋊C₄	—	7	1	no	—
318	C₂²⋊C₄	—	7	1	no	—
319	C₂²⋊C₄	—	7	1	no	—
320	C₂²⋊C₄	—	7	1	no	—
321	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
322	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
323	C₄²	—	7	1	no	—
324	C₄²	—	7	1	no	—
325	C₄²	—	7	1	no	—
326	C₄²	—	7	1	no	—
327	C₂×C₇	—	4	1	no	—
328	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
329	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₇	C₃×2₋¹⁺⁴	1	1	yes	characteristic
331	D₇	—	4	1	no	—
332	D₇	—	4	1	no	—
333	C₂²×C₃	—	2	1	no	—
334	C₂²×C₃	—	2	1	no	—
335	C₂²×C₃	—	2	1	no	—
336	C₂²×C₃	—	14	1	no	—
337	C₂²×C₃	—	14	1	no	—
338	C₂²×C₃	—	14	1	no	—
339	C₂²×C₃	—	14	1	no	—
340	C₂²×C₃	—	14	1	no	—
341	C₂²×C₃	—	14	1	no	—
342	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	2	1	no	—
345	C₃×C₄	—	2	1	no	—
346	C₃×C₄	—	2	1	no	—
347	C₃×C₄	—	2	1	no	—
348	C₃×C₄	—	2	1	no	—
349	C₃×C₄	—	7	2	no	—
350	C₃×C₄	—	14	1	no	—
351	C₃×C₄	—	14	1	no	—
352	C₃×C₄	—	14	1	no	—
353	C₃×C₄	—	14	1	no	—
354	C₃×C₄	—	14	1	no	—
355	C₂³	—	7	1	no	—
356	C₂³	—	7	1	no	—
357	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
358	Q₈	—	4	1	no	—
359	Q₈	—	14	2	no	—
360	Q₈	—	28	1	no	—
361	D₄	—	14	2	no	—
362	D₄	—	28	1	no	—
363	D₄	—	28	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	7	1	no	—
366	C₂×C₄	—	7	1	no	—
367	C₂×C₄	—	7	1	no	—
368	C₂×C₄	—	7	1	no	—
369	C₂×C₄	—	7	1	no	—
370	C₂×C₄	—	7	1	no	—
371	C₂×C₄	—	14	2	no	—
372	C₂×C₄	—	28	1	no	—
373	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
379	C₇	C₃×#542	1	1	yes	characteristic, complemented, Sylow
380	C₂×C₃	—	4	1	no	—
381	C₂×C₃	—	28	1	no	—
382	C₂×C₃	—	28	1	no	—
383	C₂×C₃	#6548	1	1	yes	characteristic
384	C₂×C₃	#6551	1	1	yes	characteristic
385	C₂×C₃	D₇×#41	1	1	yes	characteristic
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	14	1	no	—
390	C₂²	—	14	1	no	—
391	C₂²	—	14	1	no	—
392	C₂²	—	14	1	no	—
393	C₂²	—	14	1	no	—
394	C₂²	—	14	1	no	—
395	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	7	2	no	—
403	C₄	—	14	1	no	—
404	C₄	—	14	1	no	—
405	C₄	—	14	1	no	—
406	C₄	—	14	1	no	—
407	C₄	—	14	1	no	—
408	C₃	#90331	1	1	yes	characteristic, direct product factor, Sylow
409	C₂	—	4	1	no	—
410	C₂	—	28	1	no	—
411	C₂	—	28	1	no	—
412	C₂	C₃×#6548	1	1	yes	characteristic
413	C₂	C₃×#6551	1	1	yes	characteristic
414	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
prime radical	C₃×#6447	C₂
hypercenter	C₃×C₂²⋊Q₈	D₇
hypocenter	C₇	C₃×#542
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. C₃×C₇×C₂²⋊Q₈	C₂	semidirect
2. C₃×#6510	C₂	semidirect
3. C₃×#6507	C₂	semidirect
4. C₃×#6492	C₂	semidirect
5. C₃×C₄×C₂²⋊D₇	C₂	semidirect
6. C₃×#6461	C₂	semidirect
7. C₃×#6459	C₂	semidirect
8. C₃×#6459	C₂	semidirect
9. C₃×#6457	C₂	semidirect
10. C₃×#6455	C₂	semidirect
11. C₃×#6450	C₂	semidirect
12. C₃×#6448	C₂	semidirect
13. C₃×#6448	C₂	semidirect
15. C₃×#6442	C₂	semidirect
16. #90331	C₃	direct (N × H)
52. C₇×C₂²⋊Q₈	C₂×C₃	semidirect
53. #6510	C₂×C₃	semidirect
54. #6507	C₂×C₃	semidirect
55. #6492	C₂×C₃	semidirect
56. C₄×C₂²⋊D₇	C₂×C₃	semidirect
57. #6461	C₂×C₃	semidirect
58. #6459	C₂×C₃	semidirect
59. #6459	C₂×C₃	semidirect
60. #6457	C₂×C₃	semidirect
61. #6455	C₂×C₃	semidirect
62. #6450	C₂×C₃	semidirect
63. #6448	C₂×C₃	semidirect
64. #6448	C₂×C₃	semidirect
66. #6442	C₂×C₃	semidirect
137. C₃×C₂²⋊Q₈	D₇	semidirect
240. C₂²⋊Q₈	C₃×D₇	semidirect
291. C₃×C₇	#542	semidirect
379. C₇	C₃×#542	semidirect
408. C₃	#90331	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₂²⋊Q₈	2
C₃×#6510	2
C₃×#6507	2
C₃×#6492	2
C₃×C₄×C₂²⋊D₇	2
C₃×#6461	2
C₃×#6459	2
C₃×#6457	2
C₃×#6455	2
C₃×#6450	2
C₃×#6448	2
C₃×#6447	2
C₃×#6442	2
#90331	3
C₃×#542	7

Subgroups — C3×#90331 #13060969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90331 #13060969