Subgroups — C₃×#90300 #13060953

Order 1344.

856 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×D₇	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6503	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6500	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#6458	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#6456	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6447	C₂	1	2	yes	maximal, complemented
11	C₃×#6445	C₂	1	2	yes	maximal, complemented
12	#90300	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₇	C₂²	1	2	yes	complemented
14	C₂³×C₃×D₇	C₂²	1	2	yes	complemented
15	C₂×C₃×C₇×D₄	C₂²	1	2	yes	complemented
16	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
20	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
21	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
22	C₃×D₄×D₇	—	2	8	no	—
23	C₃×D₄×D₇	—	2	4	no	—
24	C₂×C₃×D₂₈	—	2	4	no	—
25	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×D₂₈	C₂²	1	2	yes	complemented
27	C₂×C₃×D₂₈	C₂²	1	2	yes	complemented
28	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₄×D₇	C₂²	1	2	yes	complemented
30	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
33	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
34	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
36	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
37	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂×D₄×D₇	C₂×C₃	1	2	yes	complemented
41	C₂²×D₂₈	C₂×C₃	1	1	yes	characteristic, complemented
42	C₇×#121	C₂×C₃	1	1	yes	characteristic, complemented
43	#6503	C₂×C₃	1	1	yes	characteristic, complemented
44	#6500	C₂×C₃	1	2	yes	complemented
45	C₄×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
46	#6458	C₂×C₃	1	1	yes	characteristic, complemented
47	#6456	C₂×C₃	1	1	yes	characteristic, complemented
48	#6447	C₂×C₃	1	2	yes	complemented
49	#6445	C₂×C₃	1	2	yes	complemented
50	C₃×D₄²	—	7	1	no	maximal, Hall
51	C₂³×C₃×C₇	C₂³	1	2	yes	—
52	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
53	C₂²×C₃×D₇	—	2	4	no	—
54	C₂²×C₃×D₇	—	2	4	no	—
55	C₂²×C₃×D₇	—	2	4	no	—
56	C₂²×C₃×D₇	—	2	4	no	—
57	C₂²×C₃×D₇	—	4	2	no	—
58	C₂²×C₃×D₇	—	4	2	no	—
59	C₂²×C₃×D₇	C₂³	1	2	yes	—
60	C₂²×C₃×D₇	C₂³	1	2	yes	—
61	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
62	C₃×C₇×D₄	—	2	4	no	—
63	C₃×C₇×D₄	—	2	2	no	—
64	C₂×C₃×C₄×C₇	—	2	2	no	—
65	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
67	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
68	C₃×C₂²⋊D₇	—	2	4	no	—
69	C₃×C₂²⋊D₇	—	2	4	no	—
70	C₃×C₂²⋊D₇	—	4	2	no	—
71	C₃×C₂²⋊D₇	D₄	1	4	yes	complemented
72	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
73	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
74	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
75	C₃×D₂₈	—	2	4	no	—
76	C₃×D₂₈	—	2	4	no	—
77	C₃×D₂₈	—	2	2	no	—
78	C₃×D₂₈	D₄	1	4	yes	complemented
79	C₃×C₄×D₇	—	2	2	no	—
80	C₃×C₄×D₇	—	2	4	no	—
81	C₂³×D₇	C₂²×C₃	1	2	yes	complemented
82	C₂³×D₇	C₂²×C₃	1	2	yes	complemented
83	C₂×C₇×D₄	C₂²×C₃	1	2	yes	complemented
84	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
85	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
86	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
88	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
89	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
90	D₄×D₇	—	2	8	no	—
91	D₄×D₇	—	2	4	no	—
92	C₂×D₂₈	—	2	4	no	—
93	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
94	C₂×D₂₈	C₂²×C₃	1	2	yes	complemented
95	C₂×D₂₈	C₂²×C₃	1	2	yes	complemented
96	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
97	C₂×C₄×D₇	C₂²×C₃	1	2	yes	complemented
98	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
101	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
102	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
103	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
104	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
105	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₂²×C₃×D₄	—	7	2	no	—
108	C₂²×C₃×D₄	—	7	1	no	—
109	C₂²×C₃×D₄	—	7	1	no	—
110	C₃×#127	—	7	1	no	—
111	C₃×#121	—	7	1	no	—
112	C₃×#121	—	7	2	no	—
113	C₃×#121	D₇	1	1	yes	characteristic, complemented
114	C₃×#120	—	7	2	no	—
115	C₃×#120	—	7	2	no	—
116	C₃×C₄×D₄	—	7	1	no	—
117	C₃×C₄×D₄	—	7	1	no	—
118	C₂²×C₃×C₇	—	2	1	no	—
119	C₂²×C₃×C₇	—	2	1	no	—
120	C₂²×C₃×C₇	—	2	2	no	—
121	C₂²×C₃×C₇	—	2	2	no	—
122	C₂²×C₃×C₇	—	2	2	no	—
123	C₂²×C₃×C₇	C₂×D₄	1	2	yes	complemented
124	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
125	C₂×C₃×D₇	—	2	1	no	—
126	C₂×C₃×D₇	—	2	2	no	—
127	C₂×C₃×D₇	—	2	2	no	—
128	C₂×C₃×D₇	—	2	1	no	—
129	C₂×C₃×D₇	—	2	2	no	—
130	C₂×C₃×D₇	—	2	2	no	—
131	C₂×C₃×D₇	—	2	2	no	—
132	C₂×C₃×D₇	—	4	8	no	—
133	C₂×C₃×D₇	—	4	8	no	—
134	C₂×C₃×D₇	C₂×D₄	1	2	yes	complemented
135	C₂×C₃×D₇	C₂×D₄	1	4	yes	complemented
136	C₃×C₄×C₇	—	2	2	no	—
137	C₃×C₄×C₇	—	2	1	no	—
138	C₃×C₄×C₇	C₂×D₄	1	2	yes	complemented
139	C₃×Dic₇	—	2	1	no	—
140	C₃×Dic₇	—	2	1	no	—
141	C₃×Dic₇	C₂×D₄	1	2	yes	complemented
142	D₄²	—	7	1	no	Sylow
143	C₂³×C₇	C₂³×C₃	1	2	yes	—
144	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
145	C₂²×D₇	—	2	4	no	—
146	C₂²×D₇	—	2	4	no	—
147	C₂²×D₇	—	2	4	no	—
148	C₂²×D₇	—	2	4	no	—
149	C₂²×D₇	—	4	2	no	—
150	C₂²×D₇	—	4	2	no	—
151	C₂²×D₇	C₂³×C₃	1	2	yes	—
152	C₂²×D₇	C₂³×C₃	1	2	yes	—
153	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
154	C₇×D₄	—	2	4	no	—
155	C₇×D₄	—	2	2	no	—
156	C₂×C₄×C₇	—	2	2	no	—
157	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
158	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
159	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
160	C₂²⋊D₇	—	2	4	no	—
161	C₂²⋊D₇	—	2	4	no	—
162	C₂²⋊D₇	—	4	2	no	—
163	C₂²⋊D₇	C₃×D₄	1	4	yes	complemented
164	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
165	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
166	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
167	D₂₈	—	2	4	no	—
168	D₂₈	—	2	4	no	—
169	D₂₈	—	2	2	no	—
170	D₂₈	C₃×D₄	1	4	yes	complemented
171	C₄×D₇	—	2	2	no	—
172	C₄×D₇	—	2	4	no	—
173	C₂⁴×C₃	—	7	2	no	—
174	C₂⁴×C₃	—	7	2	no	—
175	C₂×C₃×D₄	—	7	1	no	—
176	C₂×C₃×D₄	—	7	2	no	—
177	C₂×C₃×D₄	—	7	2	no	—
178	C₂×C₃×D₄	—	7	2	no	—
179	C₂×C₃×D₄	—	7	1	no	—
180	C₂×C₃×D₄	—	7	2	no	—
181	C₂×C₃×D₄	—	7	2	no	—
182	C₂×C₃×D₄	—	7	1	no	—
183	C₂×C₃×D₄	—	14	4	no	—
184	C₂×C₃×D₄	—	14	8	no	—
185	C₂×C₃×D₄	—	14	4	no	—
186	C₂×C₃×D₄	C₂×D₇	1	2	yes	complemented
187	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic, complemented
188	C₂²×C₃×C₄	—	7	2	no	—
189	C₂²×C₃×C₄	—	7	1	no	—
190	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic, complemented
191	C₃×C₄⋊C₄	—	7	1	no	—
192	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
193	C₃×C₂²⋊C₄	—	7	1	no	—
194	C₃×C₂²⋊C₄	—	7	2	no	—
195	C₃×C₂²⋊C₄	—	7	1	no	—
196	C₃×C₂²⋊C₄	—	7	2	no	—
197	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	complemented
198	C₃×C₄²	—	7	1	no	—
199	C₂×C₃×C₇	—	2	2	no	—
200	C₂×C₃×C₇	—	4	2	no	—
201	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
204	C₃×D₇	—	2	2	no	—
205	C₃×D₇	—	2	4	no	—
206	C₃×D₇	—	4	2	no	—
207	C₂²×D₄	—	7	2	no	—
208	C₂²×D₄	—	7	1	no	—
209	C₂²×D₄	—	7	1	no	—
210	#127	—	7	1	no	—
211	#121	—	7	1	no	—
212	#121	—	7	2	no	—
213	#121	C₃×D₇	1	1	yes	characteristic, complemented
214	#120	—	7	2	no	—
215	#120	—	7	2	no	—
216	C₄×D₄	—	7	1	no	—
217	C₄×D₄	—	7	1	no	—
218	C₂²×C₇	—	2	1	no	—
219	C₂²×C₇	—	2	1	no	—
220	C₂²×C₇	—	2	2	no	—
221	C₂²×C₇	—	2	2	no	—
222	C₂²×C₇	—	2	2	no	—
223	C₂²×C₇	C₂×C₃×D₄	1	2	yes	complemented
224	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
225	C₂×D₇	—	2	1	no	—
226	C₂×D₇	—	2	2	no	—
227	C₂×D₇	—	2	2	no	—
228	C₂×D₇	—	2	1	no	—
229	C₂×D₇	—	2	2	no	—
230	C₂×D₇	—	2	2	no	—
231	C₂×D₇	—	2	2	no	—
232	C₂×D₇	—	4	8	no	—
233	C₂×D₇	—	4	8	no	—
234	C₂×D₇	C₂×C₃×D₄	1	2	yes	complemented
235	C₂×D₇	C₂×C₃×D₄	1	4	yes	complemented
236	C₄×C₇	—	2	2	no	—
237	C₄×C₇	—	2	1	no	—
238	C₄×C₇	C₂×C₃×D₄	1	2	yes	complemented
239	Dic₇	—	2	1	no	—
240	Dic₇	—	2	1	no	—
241	Dic₇	C₂×C₃×D₄	1	2	yes	complemented
242	C₂³×C₃	—	7	2	no	—
243	C₂³×C₃	—	7	1	no	—
244	C₂³×C₃	—	7	2	no	—
245	C₂³×C₃	—	14	4	no	—
246	C₂³×C₃	—	14	4	no	—
247	C₂³×C₃	—	14	4	no	—
248	C₂³×C₃	—	14	4	no	—
249	C₂³×C₃	—	28	2	no	—
250	C₂³×C₃	—	28	2	no	—
251	C₂³×C₃	C₂²×D₇	1	2	yes	—
252	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
253	C₃×D₄	—	2	4	no	—
254	C₃×D₄	—	2	2	no	—
255	C₃×D₄	—	7	4	no	—
256	C₃×D₄	—	7	4	no	—
257	C₃×D₄	—	14	4	no	—
258	C₃×D₄	—	14	4	no	—
259	C₃×D₄	—	14	4	no	—
260	C₃×D₄	—	14	4	no	—
261	C₃×D₄	—	14	2	no	—
262	C₃×D₄	—	28	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	7	1	no	—
265	C₂×C₃×C₄	—	7	1	no	—
266	C₂×C₃×C₄	—	7	1	no	—
267	C₂×C₃×C₄	—	14	4	no	—
268	C₂×C₃×C₄	—	14	2	no	—
269	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
270	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
272	C₃×C₇	D₄²	1	1	yes	characteristic, complemented, Hall
273	C₂⁴	—	7	2	no	—
274	C₂⁴	—	7	2	no	—
275	C₂×D₄	—	7	1	no	—
276	C₂×D₄	—	7	2	no	—
277	C₂×D₄	—	7	2	no	—
278	C₂×D₄	—	7	2	no	—
279	C₂×D₄	—	7	1	no	—
280	C₂×D₄	—	7	2	no	—
281	C₂×D₄	—	7	2	no	—
282	C₂×D₄	—	7	1	no	—
283	C₂×D₄	—	14	4	no	—
284	C₂×D₄	—	14	8	no	—
285	C₂×D₄	—	14	4	no	—
286	C₂×D₄	C₂×C₃×D₇	1	2	yes	complemented
287	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
288	C₂²×C₄	—	7	2	no	—
289	C₂²×C₄	—	7	1	no	—
290	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
291	C₄⋊C₄	—	7	1	no	—
292	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
293	C₂²⋊C₄	—	7	1	no	—
294	C₂²⋊C₄	—	7	2	no	—
295	C₂²⋊C₄	—	7	1	no	—
296	C₂²⋊C₄	—	7	2	no	—
297	C₂²⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
298	C₄²	—	7	1	no	—
299	C₂×C₇	—	2	2	no	—
300	C₂×C₇	—	4	2	no	—
301	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
302	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
303	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
304	D₇	—	2	2	no	—
305	D₇	—	2	4	no	—
306	D₇	—	4	2	no	—
307	C₂²×C₃	—	2	1	no	—
308	C₂²×C₃	—	2	1	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	7	2	no	—
313	C₂²×C₃	—	7	4	no	—
314	C₂²×C₃	—	14	2	no	—
315	C₂²×C₃	—	14	1	no	—
316	C₂²×C₃	—	14	2	no	—
317	C₂²×C₃	—	14	1	no	—
318	C₂²×C₃	—	14	2	no	—
319	C₂²×C₃	—	14	2	no	—
320	C₂²×C₃	—	14	2	no	—
321	C₂²×C₃	—	28	8	no	—
322	C₂²×C₃	—	28	8	no	—
323	C₂²×C₃	D₄×D₇	1	2	yes	complemented
324	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	7	2	no	—
328	C₃×C₄	—	14	1	no	—
329	C₃×C₄	—	14	1	no	—
330	C₃×C₄	D₄×D₇	1	2	yes	complemented
331	C₂³	—	7	2	no	—
332	C₂³	—	7	1	no	—
333	C₂³	—	7	2	no	—
334	C₂³	—	14	4	no	—
335	C₂³	—	14	4	no	—
336	C₂³	—	14	4	no	—
337	C₂³	—	14	4	no	—
338	C₂³	—	28	2	no	—
339	C₂³	—	28	2	no	—
340	C₂³	C₂²×C₃×D₇	1	2	yes	—
341	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
342	D₄	—	2	4	no	—
343	D₄	—	2	2	no	—
344	D₄	—	7	4	no	—
345	D₄	—	7	4	no	—
346	D₄	—	14	4	no	—
347	D₄	—	14	4	no	—
348	D₄	—	14	4	no	—
349	D₄	—	14	4	no	—
350	D₄	—	14	2	no	—
351	D₄	—	28	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	7	1	no	—
354	C₂×C₄	—	7	1	no	—
355	C₂×C₄	—	7	1	no	—
356	C₂×C₄	—	14	4	no	—
357	C₂×C₄	—	14	2	no	—
358	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
359	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
361	C₇	C₃×D₄²	1	1	yes	characteristic, complemented, Sylow
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	—	4	2	no	—
364	C₂×C₃	—	14	4	no	—
365	C₂×C₃	—	14	2	no	—
366	C₂×C₃	—	28	2	no	—
367	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
368	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
369	C₂×C₃	#6553	1	1	yes	characteristic
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	7	2	no	—
376	C₂²	—	7	4	no	—
377	C₂²	—	14	2	no	—
378	C₂²	—	14	1	no	—
379	C₂²	—	14	2	no	—
380	C₂²	—	14	1	no	—
381	C₂²	—	14	2	no	—
382	C₂²	—	14	2	no	—
383	C₂²	—	14	2	no	—
384	C₂²	—	28	8	no	—
385	C₂²	—	28	8	no	—
386	C₂²	C₃×D₄×D₇	1	2	yes	complemented
387	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	2	no	—
390	C₄	—	7	2	no	—
391	C₄	—	14	1	no	—
392	C₄	—	14	1	no	—
393	C₄	C₃×D₄×D₇	1	2	yes	complemented
394	C₃	#90300	1	1	yes	characteristic, direct product factor, Sylow
395	C₂	—	2	2	no	—
396	C₂	—	4	2	no	—
397	C₂	—	14	4	no	—
398	C₂	—	14	2	no	—
399	C₂	—	28	2	no	—
400	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
401	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
402	C₂	C₃×#6553	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×#121	C₂
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₃×#121	D₇
hypocenter	C₇	C₃×D₄²
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄×D₇	C₂	semidirect
2. C₂×C₃×D₄×D₇	C₂	semidirect
3. C₂²×C₃×D₂₈	C₂	semidirect
4. C₃×C₇×#121	C₂	semidirect
5. C₃×#6503	C₂	semidirect
6. C₃×#6500	C₂	semidirect
7. C₃×C₄×C₂²⋊D₇	C₂	semidirect
8. C₃×#6458	C₂	semidirect
9. C₃×#6456	C₂	semidirect
10. C₃×#6447	C₂	semidirect
11. C₃×#6445	C₂	semidirect
12. #90300	C₃	direct (N × H)
13. C₂³×C₃×D₇	C₂²	semidirect
14. C₂³×C₃×D₇	C₂²	semidirect
15. C₂×C₃×C₇×D₄	C₂²	semidirect
16. C₂×C₃×C₇×D₄	C₂²	semidirect
17. C₂²×C₃×C₄×C₇	C₂²	semidirect
19. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
20. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
21. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
26. C₂×C₃×D₂₈	C₂²	semidirect
27. C₂×C₃×D₂₈	C₂²	semidirect
28. C₂×C₃×D₂₈	C₂²	semidirect
29. C₂×C₃×C₄×D₇	C₂²	semidirect
30. C₂×C₃×C₄×D₇	C₂²	semidirect
31. C₃×C₇×C₄⋊C₄	C₂²	semidirect
32. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
33. C₃×C₂²⋊Dic₇	C₂²	semidirect
34. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
35. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
36. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
37. C₃×Dic₇⋊C₄	C₂²	semidirect
38. C₃×C₄×Dic₇	C₂²	semidirect
39. C₂×D₄×D₇	C₂×C₃	semidirect
40. C₂×D₄×D₇	C₂×C₃	semidirect
41. C₂²×D₂₈	C₂×C₃	semidirect
42. C₇×#121	C₂×C₃	semidirect
43. #6503	C₂×C₃	semidirect
44. #6500	C₂×C₃	semidirect
45. C₄×C₂²⋊D₇	C₂×C₃	semidirect
46. #6458	C₂×C₃	semidirect
47. #6456	C₂×C₃	semidirect
48. #6447	C₂×C₃	semidirect
49. #6445	C₂×C₃	semidirect
71. C₃×C₂²⋊D₇	D₄	semidirect
78. C₃×D₂₈	D₄	semidirect
81. C₂³×D₇	C₂²×C₃	semidirect
82. C₂³×D₇	C₂²×C₃	semidirect
83. C₂×C₇×D₄	C₂²×C₃	semidirect
84. C₂×C₇×D₄	C₂²×C₃	semidirect
85. C₂²×C₄×C₇	C₂²×C₃	semidirect
87. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
88. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
89. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
94. C₂×D₂₈	C₂²×C₃	semidirect
95. C₂×D₂₈	C₂²×C₃	semidirect
96. C₂×D₂₈	C₂²×C₃	semidirect
97. C₂×C₄×D₇	C₂²×C₃	semidirect
98. C₂×C₄×D₇	C₂²×C₃	semidirect
99. C₇×C₄⋊C₄	C₂²×C₃	semidirect
100. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
101. C₂²⋊Dic₇	C₂²×C₃	semidirect
102. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
103. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
104. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
105. Dic₇⋊C₄	C₂²×C₃	semidirect
106. C₄×Dic₇	C₂²×C₃	semidirect
113. C₃×#121	D₇	semidirect
123. C₂²×C₃×C₇	C₂×D₄	semidirect
134. C₂×C₃×D₇	C₂×D₄	semidirect
135. C₂×C₃×D₇	C₂×D₄	semidirect
138. C₃×C₄×C₇	C₂×D₄	semidirect
141. C₃×Dic₇	C₂×D₄	semidirect
163. C₂²⋊D₇	C₃×D₄	semidirect
170. D₂₈	C₃×D₄	semidirect
186. C₂×C₃×D₄	C₂×D₇	semidirect
187. C₂×C₃×D₄	C₂×D₇	semidirect
190. C₂²×C₃×C₄	C₂×D₇	semidirect
192. C₃×C₄⋊C₄	C₂×D₇	semidirect
197. C₃×C₂²⋊C₄	C₂×D₇	semidirect
213. #121	C₃×D₇	semidirect
223. C₂²×C₇	C₂×C₃×D₄	semidirect
234. C₂×D₇	C₂×C₃×D₄	semidirect
235. C₂×D₇	C₂×C₃×D₄	semidirect
238. C₄×C₇	C₂×C₃×D₄	semidirect
241. Dic₇	C₂×C₃×D₄	semidirect
272. C₃×C₇	D₄²	semidirect
286. C₂×D₄	C₂×C₃×D₇	semidirect
287. C₂×D₄	C₂×C₃×D₇	semidirect
290. C₂²×C₄	C₂×C₃×D₇	semidirect
292. C₄⋊C₄	C₂×C₃×D₇	semidirect
297. C₂²⋊C₄	C₂×C₃×D₇	semidirect
323. C₂²×C₃	D₄×D₇	semidirect
330. C₃×C₄	D₄×D₇	semidirect
361. C₇	C₃×D₄²	semidirect
386. C₂²	C₃×D₄×D₇	semidirect
393. C₄	C₃×D₄×D₇	semidirect
394. C₃	#90300	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×D₄×D₇	2
C₂²×C₃×D₂₈	2
C₃×C₇×#121	2
C₃×#6503	2
C₃×#6500	2
C₃×C₄×C₂²⋊D₇	2
C₃×#6458	2
C₃×#6456	2
C₃×#6447	2
C₃×#6445	2
#90300	3
C₃×D₄²	7

Subgroups — C3×#90300 #13060953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90300 #13060953