Subgroups — C₄×D₄×D₂₁ #13061636

Order 1344.

852 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×D₂₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₂₁	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×Dic₂₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#4268	C₂	1	2	yes	maximal, complemented
6	#10621376	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄⋊C₄×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#10621364	C₂	1	2	yes	maximal, complemented
9	C₂²⋊C₄×D₂₁	C₂	1	2	yes	maximal, complemented
10	C₄×D₈₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×D₄×D₇	—	3	1	no	maximal, Hall
13	C₂³×D₂₁	C₂²	1	2	yes	—
14	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₇	C₂²	1	2	yes	complemented
16	C₂×#4268	C₂²	1	2	yes	—
17	C₂²×Dic₂₁	C₂²	1	2	yes	complemented
18	D₄×D₂₁	C₄	1	8	yes	direct product factor
19	C₂×D₈₄	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₂₁	—	2	8	no	—
21	C₂×C₄×D₂₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₂₁	C₂²	1	2	yes	—
23	C₂×C₄×D₂₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₂₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₂₁	C₂²	1	2	yes	complemented
26	C₂×C₄×D₂₁	C₂²	1	2	yes	complemented
27	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
29	C₃×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
30	#66636	C₂²	1	2	yes	complemented
31	#66631	C₂²	1	2	yes	complemented
32	#66631	C₂²	1	2	yes	complemented
33	C₄⋊Dic₂₁	C₂²	1	1	yes	characteristic, complemented
34	#66629	C₂²	1	2	yes	complemented
35	C₄×Dic₂₁	C₂²	1	1	yes	characteristic, complemented
36	C₄×Dic₂₁	C₂²	1	1	yes	characteristic, complemented
37	C₄×Dic₂₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×D₇	—	3	1	no	—
39	C₂²×C₄×D₇	—	3	2	no	—
40	C₄×C₇×D₄	D₃	1	1	yes	characteristic, complemented
41	D₄×Dic₇	—	3	1	no	—
42	C₄×C₂²⋊D₇	—	3	2	no	—
43	#6456	—	3	1	no	—
44	D₇×C₄⋊C₄	—	3	1	no	—
45	(C₂²⋊D₇)⋊C₄	—	3	2	no	—
46	D₇×C₂²⋊C₄	—	3	2	no	—
47	C₄×D₂₈	—	3	1	no	—
48	C₄²×D₇	—	3	1	no	—
49	C₄×D₃×D₄	—	7	1	no	maximal, Hall
50	C₂³×C₃×C₇	C₂³	1	2	yes	—
51	C₂²×D₂₁	—	2	4	no	—
52	C₂²×D₂₁	—	2	4	no	—
53	C₂²×D₂₁	C₂×C₄	1	8	yes	complemented
54	C₂²×D₂₁	C₂³	1	2	yes	—
55	C₂²×D₂₁	C₂³	1	1	yes	characteristic
56	C₃×C₇×D₄	C₂×C₄	1	4	yes	complemented
57	C₂×C₃×C₄×C₇	—	2	4	no	—
58	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
60	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
62	#4268	C₂×C₄	1	8	yes	complemented
63	C₂×Dic₂₁	—	2	4	no	—
64	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
65	C₂×Dic₂₁	C₂³	1	2	yes	—
66	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
67	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
68	D₈₄	C₂×C₄	1	4	yes	complemented
69	C₄×D₂₁	—	2	4	no	—
70	C₄×D₂₁	—	2	2	no	—
71	C₄×D₂₁	—	2	4	no	—
72	C₄×D₂₁	—	2	4	no	—
73	C₄×D₂₁	C₂×C₄	1	4	yes	complemented
74	C₄×D₂₁	D₄	1	4	yes	direct product factor
75	C₂³×D₇	—	3	2	no	—
76	C₂×C₇×D₄	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₄×C₇	C₂×D₃	1	2	yes	complemented
78	C₂×C₂²⋊D₇	—	3	2	no	—
79	C₂²×Dic₇	—	3	2	no	—
80	D₄×D₇	—	3	8	no	—
81	C₂×D₂₈	—	3	1	no	—
82	C₂×C₄×D₇	—	3	1	no	—
83	C₂×C₄×D₇	—	3	1	no	—
84	C₂×C₄×D₇	—	3	1	no	—
85	C₂×C₄×D₇	—	3	2	no	—
86	C₂×C₄×D₇	—	3	2	no	—
87	C₂×C₄×D₇	—	3	2	no	—
88	C₂×C₄×D₇	—	6	8	no	—
89	C₇×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
90	C₇×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
91	C₄²×C₇	C₂×D₃	1	1	yes	characteristic, complemented
92	C₂²⋊Dic₇	—	3	2	no	—
93	(C₂×D₇)⋊C₄	—	3	2	no	—
94	(C₂×D₇)⋊C₄	—	3	2	no	—
95	C₄⋊Dic₇	—	3	1	no	—
96	Dic₇⋊C₄	—	3	2	no	—
97	C₄×Dic₇	—	3	1	no	—
98	C₄×Dic₇	—	3	1	no	—
99	C₄×Dic₇	—	3	1	no	—
100	C₂×D₃×D₄	—	7	1	no	—
101	C₂²×C₄×D₃	—	7	2	no	—
102	C₃×C₄×D₄	D₇	1	1	yes	characteristic, complemented
103	D₄×Dic₃	—	7	1	no	—
104	C₄×#67	—	7	2	no	—
105	#893	—	7	1	no	—
106	D₃×C₄⋊C₄	—	7	1	no	—
107	#67⋊C₄	—	7	2	no	—
108	D₃×C₂²⋊C₄	—	7	2	no	—
109	C₄×D₁₂	—	7	1	no	—
110	C₄²×D₃	—	7	1	no	—
111	C₂²×C₃×C₇	—	2	2	no	—
112	C₂²×C₃×C₇	—	2	2	no	—
113	C₂²×C₃×C₇	C₂²×C₄	1	4	yes	complemented
114	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
115	C₂×D₂₁	—	2	2	no	—
116	C₂×D₂₁	—	2	2	no	—
117	C₂×D₂₁	—	2	16	no	—
118	C₂×D₂₁	C₂²×C₄	1	2	yes	—
119	C₂×D₂₁	C₂²×C₄	1	4	yes	complemented
120	C₂×D₂₁	C₂×D₄	1	2	yes	—
121	C₂×D₂₁	#41	1	2	yes	—
122	C₃×C₄×C₇	—	2	2	no	—
123	C₃×C₄×C₇	—	2	1	no	—
124	C₃×C₄×C₇	C₂²×C₄	1	2	yes	complemented
125	C₃×C₄×C₇	C₂×D₄	1	2	yes	complemented
126	Dic₂₁	—	2	2	no	—
127	Dic₂₁	—	2	1	no	—
128	Dic₂₁	C₂²×C₄	1	2	yes	complemented
129	Dic₂₁	C₂×D₄	1	2	yes	complemented
130	C₂×C₄×D₄	—	21	1	no	Sylow
131	C₂³×C₇	C₂²×D₃	1	2	yes	—
132	C₂²×D₇	—	3	1	no	—
133	C₂²×D₇	—	3	8	no	—
134	C₂²×D₇	—	3	2	no	—
135	C₂²×D₇	—	6	4	no	—
136	C₂²×D₇	—	6	4	no	—
137	C₇×D₄	C₄×D₃	1	4	yes	complemented
138	C₂×C₄×C₇	—	2	4	no	—
139	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
140	C₂×C₄×C₇	C₂²×D₃	1	2	yes	—
141	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
142	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
143	C₂²⋊D₇	—	3	8	no	—
144	C₂×Dic₇	—	3	1	no	—
145	C₂×Dic₇	—	3	1	no	—
146	C₂×Dic₇	—	3	1	no	—
147	C₂×Dic₇	—	3	2	no	—
148	C₂×Dic₇	—	6	4	no	—
149	D₂₈	—	3	4	no	—
150	C₄×D₇	—	3	4	no	—
151	C₄×D₇	—	3	4	no	—
152	C₄×D₇	—	6	4	no	—
153	C₄×D₇	—	6	4	no	—
154	C₄×D₇	—	6	2	no	—
155	C₄×D₇	—	6	4	no	—
156	C₂³×D₃	—	7	2	no	—
157	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂×D₇	1	2	yes	complemented
159	C₂×#67	—	7	2	no	—
160	C₂²×Dic₃	—	7	2	no	—
161	D₃×D₄	—	7	8	no	—
162	C₂×D₁₂	—	7	1	no	—
163	C₂×C₄×D₃	—	7	1	no	—
164	C₂×C₄×D₃	—	7	1	no	—
165	C₂×C₄×D₃	—	7	1	no	—
166	C₂×C₄×D₃	—	7	2	no	—
167	C₂×C₄×D₃	—	7	2	no	—
168	C₂×C₄×D₃	—	7	2	no	—
169	C₂×C₄×D₃	—	14	8	no	—
170	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
171	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	complemented
172	C₃×C₄²	C₂×D₇	1	1	yes	characteristic, complemented
173	#217	—	7	2	no	—
174	(C₂×D₃)⋊C₄	—	7	2	no	—
175	(C₂×D₃)⋊C₄	—	7	2	no	—
176	C₄⋊Dic₃	—	7	1	no	—
177	Dic₃⋊C₄	—	7	2	no	—
178	C₄×Dic₃	—	7	1	no	—
179	C₄×Dic₃	—	7	1	no	—
180	C₄×Dic₃	—	7	1	no	—
181	C₂×C₃×C₇	—	2	4	no	—
182	C₂×C₃×C₇	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
185	D₂₁	—	2	4	no	—
186	D₂₁	C₄×D₄	1	4	yes	direct product factor
187	C₂²×D₄	—	21	1	no	—
188	C₂³×C₄	—	21	2	no	—
189	C₄×D₄	—	21	1	no	—
190	C₄×D₄	—	21	2	no	—
191	C₄×D₄	—	21	1	no	—
192	C₄×D₄	—	21	2	no	—
193	C₄×D₄	—	21	1	no	—
194	C₄×D₄	D₂₁	1	1	yes	characteristic, direct product factor
195	C₂×C₄⋊C₄	—	21	1	no	—
196	C₂×C₂²⋊C₄	—	21	2	no	—
197	C₂×C₄²	—	21	1	no	—
198	C₂²×C₇	—	2	2	no	—
199	C₂²×C₇	—	2	2	no	—
200	C₂²×C₇	C₂×C₄×D₃	1	4	yes	complemented
201	C₂²×C₇	C₂³×D₃	1	1	yes	characteristic
202	C₂×D₇	—	3	2	no	—
203	C₂×D₇	—	3	2	no	—
204	C₂×D₇	—	3	2	no	—
205	C₂×D₇	—	3	4	no	—
206	C₂×D₇	—	6	16	no	—
207	C₂×D₇	—	6	2	no	—
208	C₂×D₇	—	6	2	no	—
209	C₄×C₇	—	2	2	no	—
210	C₄×C₇	—	2	1	no	—
211	C₄×C₇	C₂×C₄×D₃	1	2	yes	complemented
212	C₄×C₇	D₃×D₄	1	2	yes	complemented
213	Dic₇	—	3	2	no	—
214	Dic₇	—	3	2	no	—
215	Dic₇	—	6	2	no	—
216	Dic₇	—	6	1	no	—
217	C₂³×C₃	C₂²×D₇	1	2	yes	—
218	C₂²×D₃	—	7	1	no	—
219	C₂²×D₃	—	7	8	no	—
220	C₂²×D₃	—	7	2	no	—
221	C₂²×D₃	—	14	4	no	—
222	C₂²×D₃	—	14	4	no	—
223	C₃×D₄	C₄×D₇	1	4	yes	complemented
224	C₂×C₃×C₄	—	2	4	no	—
225	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
227	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
229	#67	—	7	8	no	—
230	C₂×Dic₃	—	7	1	no	—
231	C₂×Dic₃	—	7	1	no	—
232	C₂×Dic₃	—	7	1	no	—
233	C₂×Dic₃	—	7	2	no	—
234	C₂×Dic₃	—	14	4	no	—
235	D₁₂	—	7	4	no	—
236	C₄×D₃	—	7	4	no	—
237	C₄×D₃	—	7	4	no	—
238	C₄×D₃	—	14	4	no	—
239	C₄×D₃	—	14	2	no	—
240	C₄×D₃	—	14	4	no	—
241	C₄×D₃	—	14	4	no	—
242	C₃×C₇	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Hall
243	C₂⁴	—	21	2	no	—
244	C₂×D₄	—	21	2	no	—
245	C₂×D₄	—	21	8	no	—
246	C₂×D₄	—	21	1	no	—
247	C₂×D₄	C₂×D₂₁	1	1	yes	characteristic
248	C₂²×C₄	—	21	1	no	—
249	C₂²×C₄	—	21	1	no	—
250	C₂²×C₄	—	21	2	no	—
251	C₂²×C₄	—	21	1	no	—
252	C₂²×C₄	—	21	2	no	—
253	C₂²×C₄	—	21	2	no	—
254	C₂²×C₄	—	21	2	no	—
255	C₂²×C₄	—	42	8	no	—
256	C₂²×C₄	C₂×D₂₁	1	2	yes	complemented
257	C₄⋊C₄	—	21	2	no	—
258	C₄⋊C₄	—	21	1	no	—
259	C₄⋊C₄	C₂×D₂₁	1	1	yes	characteristic, complemented
260	C₂²⋊C₄	—	21	2	no	—
261	C₂²⋊C₄	—	21	2	no	—
262	C₂²⋊C₄	—	21	2	no	—
263	C₂²⋊C₄	C₂×D₂₁	1	2	yes	complemented
264	C₄²	—	21	1	no	—
265	C₄²	—	21	1	no	—
266	C₄²	—	21	1	no	—
267	C₄²	C₂×D₂₁	1	1	yes	characteristic, complemented
268	C₂×C₇	—	2	4	no	—
269	C₂×C₇	C₂²×C₄×D₃	1	1	yes	characteristic
270	C₂×C₇	C₂×D₃×D₄	1	1	yes	characteristic
271	C₂×C₇	D₃×#41	1	1	yes	characteristic
272	D₇	—	3	4	no	—
273	D₇	—	6	4	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	2	no	—
276	C₂²×C₃	C₂×C₄×D₇	1	4	yes	complemented
277	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
278	C₂×D₃	—	7	2	no	—
279	C₂×D₃	—	7	2	no	—
280	C₂×D₃	—	7	2	no	—
281	C₂×D₃	—	7	4	no	—
282	C₂×D₃	—	14	16	no	—
283	C₂×D₃	—	14	2	no	—
284	C₂×D₃	—	14	2	no	—
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	—	2	1	no	—
287	C₃×C₄	C₂×C₄×D₇	1	2	yes	complemented
288	C₃×C₄	D₄×D₇	1	2	yes	complemented
289	Dic₃	—	7	2	no	—
290	Dic₃	—	7	2	no	—
291	Dic₃	—	14	2	no	—
292	Dic₃	—	14	1	no	—
293	C₂³	—	21	1	no	—
294	C₂³	—	21	8	no	—
295	C₂³	—	21	2	no	—
296	C₂³	—	42	4	no	—
297	C₂³	—	42	4	no	—
298	C₂³	C₂²×D₂₁	1	2	yes	—
299	D₄	—	21	8	no	—
300	D₄	—	21	4	no	—
301	D₄	C₄×D₂₁	1	4	yes	direct product factor
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	21	1	no	—
304	C₂×C₄	—	21	1	no	—
305	C₂×C₄	—	21	4	no	—
306	C₂×C₄	—	21	4	no	—
307	C₂×C₄	—	21	1	no	—
308	C₂×C₄	—	21	2	no	—
309	C₂×C₄	—	42	4	no	—
310	C₂×C₄	—	42	4	no	—
311	C₂×C₄	—	42	2	no	—
312	C₂×C₄	—	42	4	no	—
313	C₂×C₄	—	42	4	no	—
314	C₂×C₄	C₂²×D₂₁	1	1	yes	characteristic
315	C₂×C₄	C₂²×D₂₁	1	2	yes	—
316	C₂×C₄	C₂²×D₂₁	1	1	yes	characteristic
317	C₂×C₄	C₂²×D₂₁	1	1	yes	characteristic
318	C₇	C₄×D₃×D₄	1	1	yes	characteristic, complemented, Sylow
319	C₂×C₃	—	2	4	no	—
320	C₂×C₃	C₂²×C₄×D₇	1	1	yes	characteristic
321	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
322	C₂×C₃	D₇×#41	1	1	yes	characteristic
323	D₃	—	7	4	no	—
324	D₃	—	14	4	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	21	2	no	—
328	C₂²	—	21	2	no	—
329	C₂²	—	21	2	no	—
330	C₂²	—	21	4	no	—
331	C₂²	—	42	16	no	—
332	C₂²	—	42	2	no	—
333	C₂²	—	42	2	no	—
334	C₂²	C₂×C₄×D₂₁	1	4	yes	complemented
335	C₂²	C₂³×D₂₁	1	1	yes	characteristic
336	C₄	—	2	2	no	—
337	C₄	—	2	1	no	—
338	C₄	—	21	2	no	—
339	C₄	—	21	2	no	—
340	C₄	—	42	2	no	—
341	C₄	—	42	1	no	—
342	C₄	C₂×C₄×D₂₁	1	2	yes	complemented
343	C₄	D₄×D₂₁	1	2	yes	direct product factor
344	C₃	C₄×D₄×D₇	1	1	yes	characteristic, complemented, Sylow
345	C₂	—	2	4	no	—
346	C₂	—	21	4	no	—
347	C₂	—	42	4	no	—
348	C₂	C₂²×C₄×D₂₁	1	1	yes	characteristic
349	C₂	C₂×D₄×D₂₁	1	1	yes	characteristic
350	C₂	#41×D₂₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₁
commutator	C₂×C₃×C₇	C₂³×C₄
Frattini	C₂²	C₂³×D₂₁
Fitting	C₃×C₄×C₇×D₄	C₂
socle, cosocle	C₂²×C₃×C₇	C₂⁴
prime radical	C₂×D₄×D₂₁	C₂
hypercenter	C₄×D₄	D₂₁
hypocenter	C₃×C₇	C₂×C₄×D₄
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₂₁	C₂	semidirect
3. C₃×C₄×C₇×D₄	C₂	semidirect
4. D₄×Dic₂₁	C₂	semidirect
5. C₄×#4268	C₂	semidirect
6. #10621376	C₂	semidirect
7. C₄⋊C₄×D₂₁	C₂	semidirect
8. #10621364	C₂	semidirect
9. C₂²⋊C₄×D₂₁	C₂	semidirect
10. C₄×D₈₄	C₂	semidirect
11. C₄²×D₂₁	C₂	semidirect
15. C₂²×C₃×C₄×C₇	C₂²	semidirect
17. C₂²×Dic₂₁	C₂²	semidirect
18. D₄×D₂₁	C₄	direct (N × H)
25. C₂×C₄×D₂₁	C₂²	semidirect
26. C₂×C₄×D₂₁	C₂²	semidirect
27. C₃×C₇×C₄⋊C₄	C₂²	semidirect
28. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
29. C₃×C₄²×C₇	C₂²	semidirect
30. #66636	C₂²	semidirect
31. #66631	C₂²	semidirect
32. #66631	C₂²	semidirect
33. C₄⋊Dic₂₁	C₂²	semidirect
34. #66629	C₂²	semidirect
35. C₄×Dic₂₁	C₂²	semidirect
36. C₄×Dic₂₁	C₂²	semidirect
37. C₄×Dic₂₁	C₂²	semidirect
40. C₄×C₇×D₄	D₃	semidirect
53. C₂²×D₂₁	C₂×C₄	semidirect
56. C₃×C₇×D₄	C₂×C₄	semidirect
62. #4268	C₂×C₄	semidirect
68. D₈₄	C₂×C₄	semidirect
73. C₄×D₂₁	C₂×C₄	semidirect
74. C₄×D₂₁	D₄	direct (N × H)
77. C₂²×C₄×C₇	C₂×D₃	semidirect
89. C₇×C₄⋊C₄	C₂×D₃	semidirect
90. C₇×C₂²⋊C₄	C₂×D₃	semidirect
91. C₄²×C₇	C₂×D₃	semidirect
102. C₃×C₄×D₄	D₇	semidirect
113. C₂²×C₃×C₇	C₂²×C₄	semidirect
119. C₂×D₂₁	C₂²×C₄	semidirect
124. C₃×C₄×C₇	C₂²×C₄	semidirect
125. C₃×C₄×C₇	C₂×D₄	semidirect
128. Dic₂₁	C₂²×C₄	semidirect
129. Dic₂₁	C₂×D₄	semidirect
137. C₇×D₄	C₄×D₃	semidirect
158. C₂²×C₃×C₄	C₂×D₇	semidirect
170. C₃×C₄⋊C₄	C₂×D₇	semidirect
171. C₃×C₂²⋊C₄	C₂×D₇	semidirect
172. C₃×C₄²	C₂×D₇	semidirect
186. D₂₁	C₄×D₄	direct (N × H)
194. C₄×D₄	D₂₁	direct (N × H)
200. C₂²×C₇	C₂×C₄×D₃	semidirect
211. C₄×C₇	C₂×C₄×D₃	semidirect
212. C₄×C₇	D₃×D₄	semidirect
223. C₃×D₄	C₄×D₇	semidirect
242. C₃×C₇	C₂×C₄×D₄	semidirect
256. C₂²×C₄	C₂×D₂₁	semidirect
259. C₄⋊C₄	C₂×D₂₁	semidirect
263. C₂²⋊C₄	C₂×D₂₁	semidirect
267. C₄²	C₂×D₂₁	semidirect
276. C₂²×C₃	C₂×C₄×D₇	semidirect
287. C₃×C₄	C₂×C₄×D₇	semidirect
288. C₃×C₄	D₄×D₇	semidirect
301. D₄	C₄×D₂₁	direct (N × H)
318. C₇	C₄×D₃×D₄	semidirect
334. C₂²	C₂×C₄×D₂₁	semidirect
342. C₄	C₂×C₄×D₂₁	semidirect
343. C₄	D₄×D₂₁	direct (N × H)
344. C₃	C₄×D₄×D₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×D₂₁	2
C₂²×C₄×D₂₁	2
C₃×C₄×C₇×D₄	2
D₄×Dic₂₁	2
C₄×#4268	2
#10621376	2
C₄⋊C₄×D₂₁	2
#10621364	2
C₂²⋊C₄×D₂₁	2
C₄×D₈₄	2
C₄²×D₂₁	2
C₄×D₄×D₇	3
C₄×D₃×D₄	7

Subgroups — C4×D4×D21 #13061636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₄×D₂₁ #13061636