Subgroups — C₄×#66684 #13059467

Order 1344.

620 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#66684	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₇×#67	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#67⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
6	(C₂²⋊D₇)⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#10621094	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#4248	C₂	1	1	yes	maximal, characteristic, complemented
9	#10621004	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#4245	C₂	1	1	yes	maximal, characteristic, complemented
11	#10620962	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×D₃×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#10620956	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×Dic₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#10620887	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#1159	—	3	1	no	maximal, Hall
17	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
18	C₂²×Dic₂₁	C₂²	1	1	yes	characteristic
19	C₂²×Dic₂₁	C₂²	1	1	yes	characteristic
20	C₂×C₇×#67	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₃×C₇	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
24	C₂×#4248	C₂²	1	1	yes	characteristic
25	C₂×#4245	C₂²	1	1	yes	characteristic
26	C₂×D₃×Dic₇	C₂²	1	1	yes	characteristic
27	C₂×D₃×Dic₇	C₂²	1	1	yes	characteristic
28	#66684	C₄	1	8	yes	direct product factor
29	C₂×Dic₃×D₇	C₂²	1	1	yes	characteristic
30	C₂×Dic₃×D₇	C₂²	1	1	yes	characteristic
31	C₄×Dic₂₁	C₂²	1	1	yes	characteristic
32	C₄×Dic₂₁	C₂²	1	1	yes	characteristic
33	C₄×Dic₂₁	C₂²	1	1	yes	characteristic
34	C₄×Dic₂₁	C₂²	1	1	yes	characteristic
35	C₇×#217	C₂²	1	1	yes	characteristic
36	C₇×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₇×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₇×Dic₃	C₂²	1	1	yes	characteristic
39	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
40	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic
43	Dic₃⋊Dic₇	C₂²	1	1	yes	characteristic
44	#66577	C₂²	1	1	yes	characteristic
45	#66577	C₂²	1	1	yes	characteristic
46	Dic₇⋊Dic₃	C₂²	1	1	yes	characteristic
47	(C₂×D₃)⋊Dic₇	C₂²	1	1	yes	characteristic
48	(C₂×D₇)⋊Dic₃	C₂²	1	1	yes	characteristic
49	Dic₃×Dic₇	C₂²	1	1	yes	characteristic
50	Dic₃×Dic₇	C₂²	1	1	yes	characteristic
51	Dic₃×Dic₇	C₂²	1	1	yes	characteristic
52	Dic₃×Dic₇	C₂²	1	1	yes	characteristic
53	C₂×#1159	—	3	1	no	—
54	C₄×C₇×D₄	—	3	1	no	—
55	D₄×Dic₇	—	3	1	no	—
56	C₄×C₂²⋊D₇	—	3	1	no	—
57	C₄×C₂²⋊D₇	D₃	1	1	yes	characteristic, complemented
58	C₂×C₄×Dic₇	—	3	1	no	—
59	C₂×C₄×Dic₇	—	3	1	no	—
60	#6455	—	3	1	no	—
61	#6450	—	3	1	no	—
62	(C₂²⋊D₇)⋊C₄	—	3	1	no	—
63	(C₂²⋊D₇)⋊C₄	—	3	1	no	—
64	#6440	—	3	1	no	—
65	#6440	—	3	1	no	—
66	C₄²×D₇	—	3	1	no	—
67	C₄×Dic₁₄	—	3	1	no	—
68	C₄×#237	—	7	1	no	maximal, Hall
69	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
70	C₂²×D₃×C₇	C₂³	1	1	yes	characteristic
71	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₄×C₇	—	2	2	no	—
73	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
75	C₂×Dic₂₁	—	2	2	no	—
76	C₂×Dic₂₁	C₂×C₄	1	4	yes	complemented
77	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
78	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
79	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
80	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
81	C₇×#67	C₂×C₄	1	4	yes	complemented
82	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
83	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
85	C₄×D₃×C₇	—	2	2	no	—
86	C₃×C₂²⋊D₇	C₂×C₄	1	4	yes	complemented
87	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
88	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
89	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
90	C₃×C₄×D₇	—	2	2	no	—
91	#4248	C₂×C₄	1	4	yes	complemented
92	#4245	C₂×C₄	1	4	yes	complemented
93	D₃×Dic₇	—	2	2	no	—
94	D₃×Dic₇	C₂×C₄	1	4	yes	complemented
95	Dic₃×D₇	—	2	2	no	—
96	Dic₃×D₇	C₂×C₄	1	4	yes	complemented
97	C₂×C₇×D₄	—	3	1	no	—
98	C₂²×C₄×C₇	—	3	1	no	—
99	C₂²×C₄×C₇	C₂×D₃	1	1	yes	characteristic
100	C₂×C₂²⋊D₇	—	3	1	no	—
101	C₂×C₂²⋊D₇	C₂×D₃	1	1	yes	characteristic
102	C₂²×Dic₇	—	3	1	no	—
103	C₂²×Dic₇	—	3	1	no	—
104	C₂²×Dic₇	—	3	1	no	—
105	C₂²×Dic₇	—	3	1	no	—
106	#1159	—	3	8	no	—
107	C₂×C₄×D₇	—	3	1	no	—
108	C₂×C₄×D₇	—	3	1	no	—
109	C₂×C₄×D₇	C₂×D₃	1	1	yes	characteristic
110	C₂×Dic₁₄	—	3	1	no	—
111	C₇×C₄⋊C₄	—	3	1	no	—
112	C₇×C₂²⋊C₄	—	3	1	no	—
113	C₇×C₂²⋊C₄	—	3	1	no	—
114	C₄²×C₇	—	3	1	no	—
115	C₂²⋊Dic₇	—	3	1	no	—
116	C₂²⋊Dic₇	C₂×D₃	1	1	yes	characteristic
117	(C₂×D₇)⋊C₄	—	3	1	no	—
118	(C₂×D₇)⋊C₄	C₂×D₃	1	1	yes	characteristic
119	C₄⋊Dic₇	—	3	1	no	—
120	Dic₇⋊C₄	—	3	1	no	—
121	Dic₇⋊C₄	—	3	1	no	—
122	Dic₇⋊C₄	—	3	1	no	—
123	Dic₇⋊C₄	C₂×D₃	1	1	yes	characteristic
124	C₄×Dic₇	—	3	1	no	—
125	C₄×Dic₇	—	3	1	no	—
126	C₄×Dic₇	—	3	1	no	—
127	C₄×Dic₇	—	3	1	no	—
128	C₄×Dic₇	—	3	1	no	—
129	C₄×Dic₇	—	3	1	no	—
130	C₄×Dic₇	—	3	1	no	—
131	C₄×Dic₇	—	3	1	no	—
132	C₄×Dic₇	C₂×D₃	1	1	yes	characteristic
133	C₂×#237	—	7	1	no	—
134	C₃×C₄×D₄	—	7	1	no	—
135	D₄×Dic₃	—	7	1	no	—
136	C₄×#67	—	7	1	no	—
137	C₄×#67	D₇	1	1	yes	characteristic, complemented
138	C₂×C₄×Dic₃	—	7	1	no	—
139	C₂×C₄×Dic₃	—	7	1	no	—
140	#892	—	7	1	no	—
141	#887	—	7	1	no	—
142	#67⋊C₄	—	7	1	no	—
143	#67⋊C₄	—	7	1	no	—
144	#877	—	7	1	no	—
145	#877	—	7	1	no	—
146	C₄²×D₃	—	7	1	no	—
147	C₄×Dic₆	—	7	1	no	—
148	C₂²×C₃×C₇	—	2	1	no	—
149	C₂²×C₃×C₇	—	2	1	no	—
150	C₂²×C₃×C₇	C₂²×C₄	1	2	yes	—
151	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
152	C₂×D₃×C₇	—	2	1	no	—
153	C₂×D₃×C₇	—	2	1	no	—
154	C₂×D₃×C₇	C₂²×C₄	1	2	yes	—
155	C₂×C₃×D₇	—	2	1	no	—
156	C₂×C₃×D₇	—	2	1	no	—
157	C₂×C₃×D₇	C₂²×C₄	1	2	yes	—
158	C₃×C₄×C₇	—	2	1	no	—
159	C₃×C₄×C₇	#41	1	2	yes	complemented
160	Dic₂₁	—	2	1	no	—
161	Dic₂₁	C₂²×C₄	1	2	yes	—
162	Dic₂₁	C₂²×C₄	1	2	yes	—
163	Dic₂₁	#41	1	2	yes	complemented
164	C₃×Dic₇	—	2	1	no	—
165	C₃×Dic₇	—	2	1	no	—
166	C₃×Dic₇	C₂²×C₄	1	2	yes	—
167	C₇×Dic₃	—	2	1	no	—
168	C₇×Dic₃	—	2	1	no	—
169	C₇×Dic₃	C₂²×C₄	1	2	yes	—
170	C₄×#41	—	21	1	no	Sylow
171	C₂³×C₇	—	3	1	no	—
172	C₂³×C₇	C₂²×D₃	1	1	yes	characteristic
173	C₂²×D₇	C₂²×D₃	1	1	yes	characteristic
174	C₇×D₄	—	3	4	no	—
175	C₂×C₄×C₇	—	2	2	no	—
176	C₂×C₄×C₇	—	3	1	no	—
177	C₂×C₄×C₇	—	3	1	no	—
178	C₂×C₄×C₇	—	3	1	no	—
179	C₂×C₄×C₇	—	6	2	no	—
180	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
181	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
182	C₂²⋊D₇	—	3	4	no	—
183	C₂²⋊D₇	C₄×D₃	1	4	yes	complemented
184	C₂×Dic₇	—	3	4	no	—
185	C₂×Dic₇	—	3	1	no	—
186	C₂×Dic₇	—	3	1	no	—
187	C₂×Dic₇	—	3	1	no	—
188	C₂×Dic₇	—	3	4	no	—
189	C₂×Dic₇	—	3	1	no	—
190	C₂×Dic₇	—	6	2	no	—
191	C₂×Dic₇	—	6	2	no	—
192	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
193	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
194	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
195	C₄×D₇	—	2	2	no	—
196	C₄×D₇	—	3	4	no	—
197	C₄×D₇	—	6	2	no	—
198	Dic₁₄	—	3	4	no	—
199	C₂×C₃×D₄	—	7	1	no	—
200	C₂²×C₃×C₄	—	7	1	no	—
201	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
202	C₂×#67	—	7	1	no	—
203	C₂×#67	C₂×D₇	1	1	yes	characteristic
204	C₂²×Dic₃	—	7	1	no	—
205	C₂²×Dic₃	—	7	1	no	—
206	C₂²×Dic₃	—	7	1	no	—
207	C₂²×Dic₃	—	7	1	no	—
208	#237	—	7	8	no	—
209	C₂×C₄×D₃	—	7	1	no	—
210	C₂×C₄×D₃	—	7	1	no	—
211	C₂×C₄×D₃	C₂×D₇	1	1	yes	characteristic
212	C₂×Dic₆	—	7	1	no	—
213	C₃×C₄⋊C₄	—	7	1	no	—
214	C₃×C₂²⋊C₄	—	7	1	no	—
215	C₃×C₂²⋊C₄	—	7	1	no	—
216	C₃×C₄²	—	7	1	no	—
217	#217	—	7	1	no	—
218	#217	C₂×D₇	1	1	yes	characteristic
219	(C₂×D₃)⋊C₄	—	7	1	no	—
220	(C₂×D₃)⋊C₄	C₂×D₇	1	1	yes	characteristic
221	C₄⋊Dic₃	—	7	1	no	—
222	Dic₃⋊C₄	—	7	1	no	—
223	Dic₃⋊C₄	—	7	1	no	—
224	Dic₃⋊C₄	—	7	1	no	—
225	Dic₃⋊C₄	C₂×D₇	1	1	yes	characteristic
226	C₄×Dic₃	—	7	1	no	—
227	C₄×Dic₃	—	7	1	no	—
228	C₄×Dic₃	—	7	1	no	—
229	C₄×Dic₃	—	7	1	no	—
230	C₄×Dic₃	—	7	1	no	—
231	C₄×Dic₃	—	7	1	no	—
232	C₄×Dic₃	—	7	1	no	—
233	C₄×Dic₃	—	7	1	no	—
234	C₄×Dic₃	C₂×D₇	1	1	yes	characteristic
235	C₂×C₃×C₇	—	2	2	no	—
236	C₂×C₃×C₇	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
238	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
239	C₃×D₇	—	2	2	no	—
240	D₃×C₇	—	2	2	no	—
241	C₂×#41	—	21	1	no	—
242	C₄×Q₈	—	21	1	no	—
243	C₄×Q₈	—	21	1	no	—
244	C₄×D₄	—	3	1	no	—
245	C₄×D₄	—	7	1	no	—
246	C₄×D₄	—	21	1	no	—
247	C₄×D₄	—	21	1	no	—
248	C₄×D₄	—	21	1	no	—
249	C₄×D₄	—	21	1	no	—
250	#117	—	21	1	no	—
251	#117	—	21	1	no	—
252	#117	—	21	1	no	—
253	C₂×C₄²	—	21	1	no	—
254	C₂×C₄²	—	21	1	no	—
255	C₂×C₄²	—	21	1	no	—
256	C₂²×C₇	—	2	1	no	—
257	C₂²×C₇	—	2	1	no	—
258	C₂²×C₇	—	3	2	no	—
259	C₂²×C₇	—	6	1	no	—
260	C₂²×C₇	—	6	1	no	—
261	C₂²×C₇	C₂×C₄×D₃	1	2	yes	—
262	C₂²×C₇	C₂³×D₃	1	1	yes	characteristic
263	C₂×D₇	—	2	1	no	—
264	C₂×D₇	—	2	1	no	—
265	C₂×D₇	C₂×C₄×D₃	1	2	yes	—
266	C₄×C₇	—	2	1	no	—
267	C₄×C₇	—	3	2	no	—
268	C₄×C₇	—	6	1	no	—
269	C₄×C₇	—	6	1	no	—
270	C₄×C₇	#237	1	2	yes	complemented
271	Dic₇	—	2	1	no	—
272	Dic₇	—	2	1	no	—
273	Dic₇	—	3	2	no	—
274	Dic₇	—	3	2	no	—
275	Dic₇	—	3	2	no	—
276	Dic₇	—	6	1	no	—
277	Dic₇	C₂×C₄×D₃	1	2	yes	—
278	C₂³×C₃	—	7	1	no	—
279	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
280	C₂²×D₃	C₂²×D₇	1	1	yes	characteristic
281	C₃×D₄	—	7	4	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	7	1	no	—
284	C₂×C₃×C₄	—	7	1	no	—
285	C₂×C₃×C₄	—	7	1	no	—
286	C₂×C₃×C₄	—	14	2	no	—
287	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
289	#67	—	7	4	no	—
290	#67	C₄×D₇	1	4	yes	complemented
291	C₂×Dic₃	—	7	4	no	—
292	C₂×Dic₃	—	7	1	no	—
293	C₂×Dic₃	—	7	1	no	—
294	C₂×Dic₃	—	7	1	no	—
295	C₂×Dic₃	—	7	4	no	—
296	C₂×Dic₃	—	7	1	no	—
297	C₂×Dic₃	—	14	2	no	—
298	C₂×Dic₃	—	14	2	no	—
299	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
300	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
301	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
302	C₄×D₃	—	2	2	no	—
303	C₄×D₃	—	7	4	no	—
304	C₄×D₃	—	14	2	no	—
305	Dic₆	—	7	4	no	—
306	C₃×C₇	C₄×#41	1	1	yes	characteristic, complemented, Hall
307	#41	—	21	8	no	—
308	C₂×Q₈	—	21	1	no	—
309	C₂×D₄	—	3	1	no	—
310	C₂×D₄	—	7	1	no	—
311	C₂×D₄	—	21	1	no	—
312	C₂²×C₄	—	3	1	no	—
313	C₂²×C₄	—	7	1	no	—
314	C₂²×C₄	—	21	1	no	—
315	C₂²×C₄	—	21	1	no	—
316	C₂²×C₄	—	21	1	no	—
317	C₂²×C₄	—	21	1	no	—
318	C₂²×C₄	—	21	1	no	—
319	C₂²×C₄	—	21	1	no	—
320	C₂²×C₄	D₃×D₇	1	1	yes	characteristic
321	C₄⋊C₄	—	3	1	no	—
322	C₄⋊C₄	—	7	1	no	—
323	C₄⋊C₄	—	21	1	no	—
324	C₄⋊C₄	—	21	1	no	—
325	C₄⋊C₄	—	21	1	no	—
326	C₄⋊C₄	—	21	1	no	—
327	C₂²⋊C₄	—	3	1	no	—
328	C₂²⋊C₄	—	3	1	no	—
329	C₂²⋊C₄	—	7	1	no	—
330	C₂²⋊C₄	—	7	1	no	—
331	C₂²⋊C₄	—	21	1	no	—
332	C₂²⋊C₄	—	21	1	no	—
333	C₄²	—	3	1	no	—
334	C₄²	—	7	1	no	—
335	C₄²	—	21	1	no	—
336	C₄²	—	21	1	no	—
337	C₄²	—	21	1	no	—
338	C₄²	—	21	1	no	—
339	C₄²	—	21	1	no	—
340	C₄²	—	21	1	no	—
341	C₄²	—	21	1	no	—
342	C₄²	—	21	1	no	—
343	C₂×C₇	—	2	2	no	—
344	C₂×C₇	—	6	2	no	—
345	C₂×C₇	C₂²×C₄×D₃	1	1	yes	characteristic
346	C₂×C₇	C₂×#237	1	1	yes	characteristic
347	C₂×C₇	D₃×#41	1	1	yes	characteristic
348	D₇	—	2	2	no	—
349	C₂²×C₃	—	2	1	no	—
350	C₂²×C₃	—	2	1	no	—
351	C₂²×C₃	—	7	2	no	—
352	C₂²×C₃	—	14	1	no	—
353	C₂²×C₃	—	14	1	no	—
354	C₂²×C₃	C₂×C₄×D₇	1	2	yes	—
355	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
356	C₂×D₃	—	2	1	no	—
357	C₂×D₃	—	2	1	no	—
358	C₂×D₃	C₂×C₄×D₇	1	2	yes	—
359	C₃×C₄	—	2	1	no	—
360	C₃×C₄	—	7	2	no	—
361	C₃×C₄	—	14	1	no	—
362	C₃×C₄	—	14	1	no	—
363	C₃×C₄	#1159	1	2	yes	complemented
364	Dic₃	—	2	1	no	—
365	Dic₃	—	2	1	no	—
366	Dic₃	—	7	2	no	—
367	Dic₃	—	7	2	no	—
368	Dic₃	—	7	2	no	—
369	Dic₃	—	14	1	no	—
370	Dic₃	C₂×C₄×D₇	1	2	yes	—
371	C₂³	—	3	1	no	—
372	C₂³	—	7	1	no	—
373	C₂³	C₂×D₃×D₇	1	1	yes	characteristic
374	Q₈	—	21	4	no	—
375	D₄	—	3	4	no	—
376	D₄	—	7	4	no	—
377	D₄	—	21	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	3	1	no	—
380	C₂×C₄	—	3	1	no	—
381	C₂×C₄	—	3	1	no	—
382	C₂×C₄	—	6	2	no	—
383	C₂×C₄	—	7	1	no	—
384	C₂×C₄	—	7	1	no	—
385	C₂×C₄	—	7	1	no	—
386	C₂×C₄	—	14	2	no	—
387	C₂×C₄	—	21	4	no	—
388	C₂×C₄	—	21	4	no	—
389	C₂×C₄	—	21	4	no	—
390	C₂×C₄	—	21	1	no	—
391	C₂×C₄	—	21	1	no	—
392	C₂×C₄	—	21	1	no	—
393	C₂×C₄	—	21	1	no	—
394	C₂×C₄	—	42	2	no	—
395	C₂×C₄	—	42	2	no	—
396	C₂×C₄	—	42	2	no	—
397	C₂×C₄	C₂×D₃×D₇	1	1	yes	characteristic
398	C₂×C₄	C₂×D₃×D₇	1	1	yes	characteristic
399	C₇	C₄×#237	1	1	yes	characteristic, complemented, Sylow
400	C₂×C₃	—	2	2	no	—
401	C₂×C₃	—	14	2	no	—
402	C₂×C₃	C₂²×C₄×D₇	1	1	yes	characteristic
403	C₂×C₃	C₂×#1159	1	1	yes	characteristic
404	C₂×C₃	D₇×#41	1	1	yes	characteristic
405	D₃	—	2	2	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	3	2	no	—
409	C₂²	—	6	1	no	—
410	C₂²	—	6	1	no	—
411	C₂²	—	7	2	no	—
412	C₂²	—	14	1	no	—
413	C₂²	—	14	1	no	—
414	C₂²	C₄×D₃×D₇	1	2	yes	—
415	C₂²	C₂²×D₃×D₇	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	3	2	no	—
418	C₄	—	6	1	no	—
419	C₄	—	6	1	no	—
420	C₄	—	7	2	no	—
421	C₄	—	14	1	no	—
422	C₄	—	14	1	no	—
423	C₄	—	21	2	no	—
424	C₄	—	21	2	no	—
425	C₄	—	21	2	no	—
426	C₄	—	42	1	no	—
427	C₄	#66684	1	2	yes	direct product factor
428	C₃	C₄×#1159	1	1	yes	characteristic, complemented, Sylow
429	C₂	—	2	2	no	—
430	C₂	—	6	2	no	—
431	C₂	—	14	2	no	—
432	C₂	C₂×C₄×D₃×D₇	1	1	yes	characteristic
433	C₂	#10621563	1	1	yes	characteristic
434	C₂	C₂×#66684	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×D₇
commutator	C₂×C₃×C₇	C₂³×C₄
Frattini	C₂²	C₂²×D₃×D₇
Fitting	C₂²×C₃×C₄×C₇	C₂²
socle, cosocle	C₂²×C₃×C₇	C₂⁴
prime radical	C₂×#66684	C₂
hypercenter	C₂²×C₄	D₃×D₇
hypocenter	C₃×C₇	C₄×#41
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Dic₂₁	C₂	semidirect
3. C₄×C₇×#67	C₂	semidirect
4. C₃×C₄×C₂²⋊D₇	C₂	semidirect
5. #67⋊Dic₇	C₂	semidirect
6. (C₂²⋊D₇)⋊Dic₃	C₂	semidirect
7. #10621094	C₂	semidirect
8. C₄×#4248	C₂	semidirect
9. #10621004	C₂	semidirect
10. C₄×#4245	C₂	semidirect
11. #10620962	C₂	semidirect
12. C₄×D₃×Dic₇	C₂	semidirect
13. #10620956	C₂	semidirect
14. C₄×Dic₃×D₇	C₂	semidirect
15. #10620887	C₂	semidirect
28. #66684	C₄	direct (N × H)
57. C₄×C₂²⋊D₇	D₃	semidirect
76. C₂×Dic₂₁	C₂×C₄	semidirect
81. C₇×#67	C₂×C₄	semidirect
86. C₃×C₂²⋊D₇	C₂×C₄	semidirect
91. #4248	C₂×C₄	semidirect
92. #4245	C₂×C₄	semidirect
94. D₃×Dic₇	C₂×C₄	semidirect
96. Dic₃×D₇	C₂×C₄	semidirect
137. C₄×#67	D₇	semidirect
159. C₃×C₄×C₇	#41	semidirect
163. Dic₂₁	#41	semidirect
183. C₂²⋊D₇	C₄×D₃	semidirect
270. C₄×C₇	#237	semidirect
290. #67	C₄×D₇	semidirect
306. C₃×C₇	C₄×#41	semidirect
363. C₃×C₄	#1159	semidirect
399. C₇	C₄×#237	semidirect
427. C₄	#66684	direct (N × H)
428. C₃	C₄×#1159	semidirect

Maximal subgroups

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

subgroup	index
C₂×#66684	2
C₂×C₄×Dic₂₁	2
C₄×C₇×#67	2
C₃×C₄×C₂²⋊D₇	2
#67⋊Dic₇	2
(C₂²⋊D₇)⋊Dic₃	2
#10621094	2
C₄×#4248	2
#10621004	2
C₄×#4245	2
#10620962	2
C₄×D₃×Dic₇	2
#10620956	2
C₄×Dic₃×D₇	2
#10620887	2
C₄×#1159	3
C₄×#237	7

Subgroups — C4×#66684 #13059467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#66684 #13059467