Subgroups — C₄×#16863800 #30864564

Order 17152.

878 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863800	C₂	1	1	yes	maximal, characteristic
2	C₄×#14524042	C₂	1	2	yes	maximal
3	#22561168	C₂	1	2	yes	maximal
4	#22560943	C₂	1	1	yes	maximal, characteristic
5	#22560941	C₂	1	2	yes	maximal
6	#22560940	C₂	1	1	yes	maximal, characteristic
7	#22560367	C₂	1	1	yes	maximal, characteristic
8	C₄×#14523976	C₂	1	2	yes	maximal
9	C₄×#14523977	C₂	1	1	yes	maximal, characteristic
10	C₄×C₈×Dic₆₇	C₂	1	1	yes	maximal, characteristic
11	C₄×#107×C₆₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#14524042	C₂²	1	2	yes	—
13	C₂×C₄×Dic₁₃₄	—	2	2	no	—
14	#16863800	C₄	1	8	yes	direct product factor
15	C₂×#14523977	C₂²	1	1	yes	characteristic
16	C₂×#14523977	C₂²	1	1	yes	characteristic
17	C₂×#14523976	C₂²	1	2	yes	—
18	C₂×#14523976	C₂²	1	2	yes	—
19	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
24	#16863300	—	2	2	no	—
25	#16863295	C₂²	1	2	yes	—
26	#16863293	—	2	2	no	—
27	#16863292	C₂²	1	2	yes	—
28	#16863265	C₂²	1	2	yes	—
29	C₄×Dic₆₇⋊C₄	—	2	2	no	—
30	C₄×C₄⋊Dic₆₇	C₂²	1	2	yes	—
31	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
32	#16863159	C₂²	1	2	yes	—
33	#16863158	C₂²	1	2	yes	—
34	#16863158	C₂²	1	2	yes	—
35	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
39	#340×C₆₇	C₂²	1	2	yes	—
40	C₂²×Dic₁₃₄	—	2	2	no	—
41	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
42	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
43	#14524042	—	2	4	no	—
44	#14524042	C₂×C₄	1	8	yes	—
45	C₄×Dic₁₃₄	—	4	8	no	—
46	C₂×C₄⋊Dic₆₇	—	2	2	no	—
47	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
49	C₂×Dic₆₇⋊C₄	—	2	2	no	—
50	C₂×Dic₆₇⋊C₄	—	2	2	no	—
51	C₂×Dic₆₇⋊C₄	—	2	2	no	—
52	C₂×Dic₆₇⋊C₄	—	2	2	no	—
53	C₂×C₄×Dic₆₇	—	2	2	no	—
54	C₂×C₄×Dic₆₇	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₆₇	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₆₇	D₄	1	1	yes	characteristic
57	C₂×C₄×Dic₆₇	D₄	1	1	yes	characteristic
58	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
60	#14523977	—	2	2	no	—
61	#14523977	C₂×C₄	1	4	yes	—
62	#14523976	—	2	4	no	—
63	#14523976	C₂×C₄	1	8	yes	—
64	C₄×C₆₇⋊C₈	Q₈	1	4	yes	complemented
65	C₈×Dic₆₇	—	2	2	no	—
66	C₈×Dic₆₇	—	2	2	no	—
67	C₈×Dic₆₇	—	2	2	no	—
68	C₈×Dic₆₇	C₂×C₄	1	4	yes	—
69	C₆₇⋊#95	—	2	2	no	—
70	C₆₇⋊#95	—	2	2	no	—
71	C₆₇⋊#95	—	2	2	no	—
72	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₆₇	—	2	2	no	—
77	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
78	#107×C₆₇	—	2	2	no	—
79	#107×C₆₇	C₂×C₄	1	4	yes	—
80	C₄×C₈×C₆₇	Q₈	1	4	yes	complemented
81	#95×C₆₇	—	2	2	no	—
82	C₂×Dic₁₃₄	—	2	8	no	—
83	C₂×Dic₁₃₄	—	4	4	no	—
84	C₂×Dic₁₃₄	—	4	4	no	—
85	C₂²×Dic₆₇	—	2	2	no	—
86	C₂²×Dic₆₇	—	2	2	no	—
87	C₂²×Dic₆₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×Dic₆₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×Dic₆₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×Dic₆₇	C₂×D₄	1	1	yes	characteristic
91	C₂×C₆₇⋊C₈	—	2	1	no	—
92	C₂×C₆₇⋊C₈	—	2	1	no	—
93	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
94	C₂×C₆₇⋊C₈	C₂×Q₈	1	2	yes	—
95	C₂×C₆₇⋊C₈	C₂×Q₈	1	2	yes	—
96	C₂×C₆₇⋊C₈	#41	1	2	yes	—
97	C₄⋊Dic₆₇	—	2	2	no	—
98	C₄⋊Dic₆₇	—	2	2	no	—
99	C₄⋊Dic₆₇	—	2	2	no	—
100	C₄⋊Dic₆₇	—	4	4	no	—
101	C₄⋊Dic₆₇	C₂²×C₄	1	4	yes	—
102	Dic₆₇⋊C₄	—	2	8	no	—
103	Dic₆₇⋊C₄	—	4	4	no	—
104	Dic₆₇⋊C₄	—	4	4	no	—
105	Dic₆₇⋊C₄	—	4	4	no	—
106	C₄×Dic₆₇	—	2	1	no	—
107	C₄×Dic₆₇	—	2	1	no	—
108	C₄×Dic₆₇	—	2	2	no	—
109	C₄×Dic₆₇	—	2	2	no	—
110	C₄×Dic₆₇	—	4	4	no	—
111	C₄×Dic₆₇	D₈	1	4	yes	—
112	C₄×Dic₆₇	Q₁₆	1	4	yes	—
113	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
114	C₄×Dic₆₇	#41	1	2	yes	—
115	C₂²×C₄×C₆₇	—	2	2	no	—
116	C₂²×C₄×C₆₇	—	2	2	no	—
117	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₆₇	—	2	1	no	—
121	C₂×C₈×C₆₇	—	2	1	no	—
122	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₆₇	C₂×Q₈	1	2	yes	—
124	C₂×C₈×C₆₇	C₂×Q₈	1	2	yes	—
125	C₂×C₈×C₆₇	#41	1	2	yes	—
126	C₄⋊C₄×C₆₇	—	2	2	no	—
127	C₄⋊C₄×C₆₇	—	2	2	no	—
128	C₄⋊C₄×C₆₇	—	2	2	no	—
129	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
130	C₄²×C₆₇	—	4	4	no	—
131	C₄²×C₆₇	C₂×Q₈	1	2	yes	—
132	C₄²×C₆₇	C₂×Q₈	1	2	yes	—
133	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₆₇	—	2	1	no	—
135	C₂×C₄×C₆₇	—	2	1	no	—
136	C₂×C₄×C₆₇	—	2	4	no	—
137	C₂×C₄×C₆₇	—	4	2	no	—
138	C₂×C₄×C₆₇	—	4	2	no	—
139	C₂×C₄×C₆₇	—	4	2	no	—
140	C₂×C₄×C₆₇	—	4	2	no	—
141	C₂×C₄×C₆₇	—	4	2	no	—
142	C₂×C₄×C₆₇	C₄⋊Q₈	1	2	yes	—
143	C₂×C₄×C₆₇	C₄⋊Q₈	1	2	yes	—
144	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
145	C₂×C₄×C₆₇	C₂×Q₁₆	1	2	yes	—
146	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
152	C₂×Dic₆₇	—	2	1	no	—
153	C₂×Dic₆₇	—	2	1	no	—
154	C₂×Dic₆₇	—	2	1	no	—
155	C₂×Dic₆₇	—	2	1	no	—
156	C₂×Dic₆₇	—	2	4	no	—
157	C₂×Dic₆₇	—	4	2	no	—
158	C₂×Dic₆₇	—	4	2	no	—
159	C₂×Dic₆₇	—	4	2	no	—
160	C₂×Dic₆₇	—	4	2	no	—
161	C₂×Dic₆₇	—	4	2	no	—
162	C₂×Dic₆₇	C₄×D₄	1	2	yes	—
163	C₂×Dic₆₇	C₄×D₄	1	2	yes	—
164	C₂×Dic₆₇	C₂×D₈	1	2	yes	—
165	C₂×Dic₆₇	C₂×D₈	1	2	yes	—
166	C₂×Dic₆₇	C₂×Q₁₆	1	2	yes	—
167	C₂×Dic₆₇	C₂×Q₁₆	1	2	yes	—
168	C₂×Dic₆₇	#135	1	2	yes	—
169	C₂×Dic₆₇	#135	1	2	yes	—
170	Dic₁₃₄	—	4	16	no	—
171	C₈×C₆₇	—	2	2	no	—
172	C₈×C₆₇	C₄×Q₈	1	4	yes	complemented
173	C₆₇⋊C₈	—	2	2	no	—
174	C₆₇⋊C₈	C₄×Q₈	1	4	yes	complemented
175	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
176	C₂²×C₆₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
177	C₂²×C₆₇	#532	1	1	yes	characteristic
178	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
179	C₂²×C₆₇	C₂²×Q₁₆	1	1	yes	characteristic
180	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
181	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
182	C₄×C₆₇	—	2	2	no	—
183	C₄×C₆₇	—	4	4	no	—
184	C₄×C₆₇	—	8	2	no	—
185	C₄×C₆₇	#500	1	4	yes	complemented
186	C₄×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
187	C₄×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
188	C₄×C₆₇	#533	1	1	yes	characteristic
189	C₄×C₆₇	#533	1	1	yes	characteristic
190	Dic₆₇	—	2	2	no	—
191	Dic₆₇	—	2	2	no	—
192	Dic₆₇	—	4	4	no	—
193	Dic₆₇	—	8	2	no	—
194	Dic₆₇	C₄×D₈	1	4	yes	—
195	Dic₆₇	C₄×Q₁₆	1	4	yes	—
196	C₄×#500	—	67	1	no	maximal, Sylow
197	C₂×C₆₇	C₄×C₄⋊Q₈	1	1	yes	characteristic
198	C₂×C₆₇	C₂×C₄×D₈	1	1	yes	characteristic
199	C₂×C₆₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
200	C₂×C₆₇	C₂×#500	1	1	yes	characteristic
201	C₂×C₆₇	#3160	1	1	yes	characteristic
202	C₂×C₆₇	#3169	1	1	yes	characteristic
203	C₂×C₆₇	#3170	1	1	yes	characteristic
204	C₂×#500	—	67	1	no	—
205	C₄×C₄⋊Q₈	—	67	2	no	—
206	#1990	—	67	2	no	—
207	#1942	—	67	1	no	—
208	#1942	—	67	1	no	—
209	#1942	—	67	2	no	—
210	#1845	—	67	1	no	—
211	C₄×#107	—	67	1	no	—
212	C₄×#107	—	67	2	no	—
213	C₄×#107	D₆₇	1	1	yes	characteristic
214	C₄²×C₈	—	67	1	no	—
215	C₆₇	C₄×#500	1	1	yes	characteristic, complemented, Sylow
216	C₂×C₄⋊Q₈	—	67	2	no	—
217	C₂×C₄×Q₈	—	134	2	no	—
218	#500	—	67	8	no	—
219	C₂×#107	—	67	1	no	—
220	C₂×#107	—	67	2	no	—
221	C₂×#107	—	67	1	no	—
222	C₂×#107	—	67	2	no	—
223	C₂×#107	C₂×D₆₇	1	1	yes	characteristic
224	C₂×#107	C₂×D₆₇	1	1	yes	characteristic
225	C₂×C₄×C₈	—	67	1	no	—
226	C₂×C₄×C₈	—	67	1	no	—
227	C₂×C₄×C₈	—	67	1	no	—
228	C₂×C₄×C₈	—	67	1	no	—
229	C₂×C₄×C₈	—	67	1	no	—
230	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
231	#391	—	134	2	no	—
232	#389	—	67	2	no	—
233	#389	—	67	2	no	—
234	#389	—	134	2	no	—
235	#384	—	67	2	no	—
236	C₄×C₄⋊C₄	—	67	2	no	—
237	C₄×C₄⋊C₄	—	134	2	no	—
238	C₄×C₄⋊C₄	C₂×D₆₇	1	2	yes	—
239	C₄³	—	67	1	no	—
240	#340	—	67	2	no	—
241	#340	—	67	2	no	—
242	#340	—	67	2	no	—
243	#340	C₂×D₆₇	1	2	yes	—
244	C₂²×Q₈	—	134	2	no	—
245	C₂²×C₈	—	67	1	no	—
246	C₂²×C₈	—	67	1	no	—
247	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
248	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
249	C₄⋊Q₈	—	67	8	no	—
250	C₄⋊Q₈	—	134	4	no	—
251	C₄×Q₈	—	268	8	no	—
252	C₂×C₄⋊C₄	—	67	2	no	—
253	C₂×C₄⋊C₄	—	67	2	no	—
254	C₂×C₄⋊C₄	—	134	2	no	—
255	C₂×C₄⋊C₄	—	134	2	no	—
256	C₂×C₄⋊C₄	—	134	2	no	—
257	C₂×C₄⋊C₄	—	134	2	no	—
258	C₂×C₄⋊C₄	—	134	2	no	—
259	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
260	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	67	1	no	—
263	C₂×C₄²	—	67	1	no	—
264	C₂×C₄²	—	67	1	no	—
265	C₂×C₄²	—	67	1	no	—
266	C₂×C₄²	—	67	1	no	—
267	C₂×C₄²	—	67	1	no	—
268	C₂×C₄²	—	134	2	no	—
269	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
270	#107	—	2	2	no	—
271	#107	—	67	4	no	—
272	#107	—	67	8	no	—
273	#107	—	134	4	no	—
274	#107	—	134	2	no	—
275	#107	C₄×D₆₇	1	4	yes	—
276	C₄×C₈	—	67	4	no	—
277	C₄×C₈	—	67	4	no	—
278	C₄×C₈	—	134	2	no	—
279	C₄×C₈	—	134	2	no	—
280	C₄×C₈	—	134	2	no	—
281	C₄×C₈	Dic₁₃₄	1	4	yes	complemented
282	#95	—	2	2	no	—
283	#95	—	134	2	no	—
284	#95	—	134	2	no	—
285	#95	—	134	2	no	—
286	C₂×Q₈	—	268	4	no	—
287	C₂×Q₈	—	268	4	no	—
288	C₂×Q₈	—	134	8	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	67	1	no	—
292	C₂²×C₄	—	67	1	no	—
293	C₂²×C₄	—	67	1	no	—
294	C₂²×C₄	—	67	1	no	—
295	C₂²×C₄	—	134	2	no	—
296	C₂²×C₄	—	134	2	no	—
297	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
298	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
299	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	67	2	no	—
303	C₂×C₈	—	67	2	no	—
304	C₂×C₈	—	67	2	no	—
305	C₂×C₈	—	67	2	no	—
306	C₂×C₈	—	134	1	no	—
307	C₂×C₈	—	134	1	no	—
308	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
309	C₂×C₈	C₂×Dic₁₃₄	1	2	yes	—
310	C₂×C₈	C₂×Dic₁₃₄	1	2	yes	—
311	C₂×C₈	#11761628	1	2	yes	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	268	4	no	—
316	C₄⋊C₄	—	268	4	no	—
317	C₄⋊C₄	—	268	4	no	—
318	C₄⋊C₄	—	268	4	no	—
319	C₄⋊C₄	—	67	4	no	—
320	C₄⋊C₄	—	134	8	no	—
321	C₄⋊C₄	—	134	2	no	—
322	C₄⋊C₄	—	134	2	no	—
323	C₄⋊C₄	—	134	2	no	—
324	C₄⋊C₄	C₂×C₄×D₆₇	1	4	yes	—
325	C₄²	—	4	4	no	—
326	C₄²	—	268	4	no	—
327	C₄²	—	67	4	no	—
328	C₄²	—	67	4	no	—
329	C₄²	—	67	2	no	—
330	C₄²	—	67	2	no	—
331	C₄²	—	134	2	no	—
332	C₄²	—	134	2	no	—
333	C₄²	—	134	1	no	—
334	C₄²	—	134	1	no	—
335	C₄²	Q₈×D₆₇	1	2	yes	—
336	C₄²	C₂×Dic₁₃₄	1	2	yes	—
337	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
338	Q₈	—	268	16	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	268	2	no	—
348	C₂×C₄	—	268	2	no	—
349	C₂×C₄	—	268	2	no	—
350	C₂×C₄	—	268	2	no	—
351	C₂×C₄	—	268	2	no	—
352	C₂×C₄	—	67	2	no	—
353	C₂×C₄	—	67	2	no	—
354	C₂×C₄	—	67	2	no	—
355	C₂×C₄	—	67	2	no	—
356	C₂×C₄	—	67	2	no	—
357	C₂×C₄	—	67	2	no	—
358	C₂×C₄	—	67	2	no	—
359	C₂×C₄	—	67	2	no	—
360	C₂×C₄	—	134	4	no	—
361	C₂×C₄	—	134	1	no	—
362	C₂×C₄	—	134	1	no	—
363	C₂×C₄	—	134	1	no	—
364	C₂×C₄	—	134	1	no	—
365	C₂×C₄	#14524042	1	2	yes	—
366	C₂×C₄	#14524042	1	2	yes	—
367	C₂×C₄	D₈×D₆₇	1	2	yes	—
368	C₂×C₄	Q₁₆×D₆₇	1	2	yes	—
369	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
370	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
371	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
372	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
373	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
374	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	67	4	no	—
377	C₈	—	134	2	no	—
378	C₈	C₄×Dic₁₃₄	1	4	yes	complemented
379	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
380	C₂²	C₂×#14524042	1	1	yes	characteristic
381	C₂²	#16863943	1	1	yes	characteristic
382	C₂²	C₂×D₈×D₆₇	1	1	yes	characteristic
383	C₂²	C₂×Q₁₆×D₆₇	1	1	yes	characteristic
384	C₂²	#135×D₆₇	1	1	yes	characteristic
385	C₂²	#135×D₆₇	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	4	4	no	—
388	C₄	—	8	2	no	—
389	C₄	—	268	4	no	—
390	C₄	—	536	2	no	—
391	C₄	—	67	4	no	—
392	C₄	—	67	4	no	—
393	C₄	—	134	2	no	—
394	C₄	—	134	2	no	—
395	C₄	#16863800	1	4	yes	direct product factor
396	C₄	C₄×Q₈×D₆₇	1	1	yes	characteristic
397	C₄	C₂×C₄×Dic₁₃₄	1	1	yes	characteristic
398	C₄	#16863949	1	1	yes	characteristic
399	C₄	#16863950	1	1	yes	characteristic
400	C₂	C₄×#14524042	1	1	yes	characteristic
401	C₂	C₄×D₈×D₆₇	1	1	yes	characteristic
402	C₂	C₄×Q₁₆×D₆₇	1	1	yes	characteristic
403	C₂	C₂×#16863800	1	1	yes	characteristic
404	C₂	#22570721	1	1	yes	characteristic
405	C₂	#22570785	1	1	yes	characteristic
406	C₂	#22570792	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₄×#107×C₆₇	C₂
socle, prime radical	C₂³×C₆₇	C₂²×D₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₄×#107	D₆₇
hypocenter	C₆₇	C₄×#500
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
14. #16863800	C₄	direct (N × H)
64. C₄×C₆₇⋊C₈	Q₈	semidirect
80. C₄×C₈×C₆₇	Q₈	semidirect
172. C₈×C₆₇	C₄×Q₈	semidirect
174. C₆₇⋊C₈	C₄×Q₈	semidirect
185. C₄×C₆₇	#500	semidirect
215. C₆₇	C₄×#500	semidirect
281. C₄×C₈	Dic₁₃₄	semidirect
378. C₈	C₄×Dic₁₃₄	semidirect
395. C₄	#16863800	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×#16863800	2
C₄×#14524042	2
#22561168	2
#22560943	2
#22560941	2
#22560940	2
#22560367	2
C₄×#14523976	2
C₄×#14523977	2
C₄×C₈×Dic₆₇	2
C₄×#107×C₆₇	2
C₄×#500	67

Subgroups — C4×#16863800 #30864564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16863800 #30864564