Subgroups — #30874288

Order 17152.

858 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863518	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863513	C₂	1	1	yes	maximal, characteristic
3	#22568777	C₂	1	2	yes	maximal, complemented
4	#22560963	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560958	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560486	C₂	1	2	yes	maximal, complemented
7	#22560486	C₂	1	2	yes	maximal, complemented
8	#22560384	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560229	C₂	1	2	yes	maximal, complemented
10	#22560081	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2943	C₂	1	1	yes	maximal, characteristic
12	C₂×#14524050	C₂²	1	2	yes	—
13	C₂×#14524050	C₂²	1	2	yes	—
14	#16863518	—	2	4	no	—
15	#16863513	—	2	4	no	—
16	C₂×#14523979	C₂²	1	1	yes	characteristic
17	C₂×#14523979	C₂²	1	1	yes	characteristic
18	C₂×#14523979	C₂²	1	2	yes	—
19	#16863423	—	2	2	no	—
20	#16863423	—	2	2	no	—
21	#16863423	C₂²	1	2	yes	—
22	#16863423	C₂²	1	2	yes	—
23	#16863420	—	2	2	no	—
24	#16863420	C₂²	1	2	yes	—
25	C₂×C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
26	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×#14523970	C₂²	1	2	yes	—
28	C₂×#14523970	C₂²	1	2	yes	—
29	C₂×#14523953	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
32	#16863155	C₂²	1	2	yes	—
33	#16863155	C₂²	1	2	yes	—
34	#16863150	C₂²	1	1	yes	characteristic
35	#16863150	C₂²	1	1	yes	characteristic
36	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
37	C₄×#41×C₆₇	C₂²	1	2	yes	—
38	#442×C₆₇	C₄	1	2	yes	complemented
39	#441×C₆₇	C₄	1	2	yes	complemented
40	#440×C₆₇	C₄	1	2	yes	complemented
41	#440×C₆₇	C₄	1	2	yes	complemented
42	#427×C₆₇	C₂²	1	1	yes	characteristic
43	#416×C₆₇	C₂²	1	2	yes	—
44	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
45	#14524050	—	2	4	no	—
46	#14524050	—	2	4	no	—
47	#14524050	—	4	2	no	—
48	#14524050	—	4	2	no	—
49	C₂×#11761612	—	2	2	no	—
50	C₂×#11761612	—	2	2	no	—
51	C₂×#11761612	C₂³	1	2	yes	—
52	C₂×#11761612	C₂³	1	2	yes	—
53	C₂²×C₆₇⋊C₈	—	2	2	no	—
54	C₂²×C₆₇⋊C₈	—	2	2	no	—
55	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊Dic₆₇	—	2	1	no	—
58	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
60	#14523979	—	2	2	no	—
61	#14523979	—	2	2	no	—
62	#14523979	—	4	2	no	—
63	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
64	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
65	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
66	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
67	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
68	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
69	C₄⋊(C₆₇⋊C₈)	D₄	1	2	yes	—
70	C₄⋊(C₆₇⋊C₈)	D₄	1	2	yes	—
71	#14523970	—	2	4	no	—
72	#14523970	—	2	4	no	—
73	#14523953	—	2	2	no	—
74	C₈×Dic₆₇	—	2	2	no	—
75	C₆₇⋊#95	—	2	1	no	—
76	C₂×#41×C₆₇	C₂³	1	2	yes	—
77	#135×C₆₇	D₄	1	4	yes	—
78	#135×C₆₇	Q₈	1	4	yes	—
79	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
80	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
81	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
84	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
85	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
86	C₄×D₄×C₆₇	—	2	2	no	—
87	C₄×D₄×C₆₇	—	2	2	no	—
88	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
89	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
90	#117×C₆₇	—	2	2	no	—
91	#117×C₆₇	C₂³	1	2	yes	—
92	C₂×C₄²×C₆₇	—	2	2	no	—
93	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
94	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
95	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
96	#106×C₆₇	C₂×C₄	1	2	yes	—
97	#103×C₆₇	C₂×C₄	1	2	yes	—
98	#103×C₆₇	C₂×C₄	1	2	yes	—
99	#102×C₆₇	C₂×C₄	1	2	yes	—
100	#102×C₆₇	C₂×C₄	1	2	yes	—
101	#97×C₆₇	C₂×C₄	1	2	yes	—
102	#97×C₆₇	C₂×C₄	1	2	yes	—
103	C₂²×Dic₆₇	—	2	1	no	—
104	C₂²×Dic₆₇	—	2	1	no	—
105	#11761612	—	2	2	no	—
106	#11761612	—	2	2	no	—
107	#11761612	—	2	2	no	—
108	#11761612	—	2	2	no	—
109	#11761612	—	4	4	no	—
110	#11761612	—	4	4	no	—
111	C₂×C₆₇⋊C₈	—	2	1	no	—
112	C₂×C₆₇⋊C₈	—	2	1	no	—
113	C₂×C₆₇⋊C₈	—	2	1	no	—
114	C₂×C₆₇⋊C₈	—	2	1	no	—
115	C₂×C₆₇⋊C₈	—	2	2	no	—
116	C₂×C₆₇⋊C₈	—	2	2	no	—
117	C₂×C₆₇⋊C₈	—	4	4	no	—
118	C₂×C₆₇⋊C₈	—	4	4	no	—
119	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
121	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
122	C₄⋊Dic₆₇	—	4	2	no	—
123	C₄×Dic₆₇	—	2	1	no	—
124	C₄×Dic₆₇	—	2	1	no	—
125	C₄×Dic₆₇	—	2	1	no	—
126	C₄×Dic₆₇	—	2	1	no	—
127	#41×C₆₇	—	2	2	no	—
128	#41×C₆₇	—	2	2	no	—
129	#41×C₆₇	C₂×D₄	1	4	yes	—
130	#41×C₆₇	C₂×Q₈	1	4	yes	—
131	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
132	C₂×D₄×C₆₇	—	2	2	no	—
133	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₆₇	—	2	2	no	—
135	C₂²×C₄×C₆₇	—	2	2	no	—
136	C₂²×C₄×C₆₇	—	2	2	no	—
137	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
138	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₆₇	C₄⋊C₄	1	4	yes	complemented
141	SD₁₆×C₆₇	C₄⋊C₄	1	8	yes	complemented
142	D₈×C₆₇	C₄⋊C₄	1	4	yes	complemented
143	C₂×C₈×C₆₇	—	2	1	no	—
144	C₂×C₈×C₆₇	—	2	1	no	—
145	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₆₇	C₂×Q₈	1	2	yes	—
150	C₄⋊C₄×C₆₇	—	2	2	no	—
151	C₄⋊C₄×C₆₇	—	2	2	no	—
152	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
153	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
154	C₂²⋊C₄×C₆₇	—	2	2	no	—
155	C₂²⋊C₄×C₆₇	—	2	2	no	—
156	C₂²⋊C₄×C₆₇	—	2	2	no	—
157	C₄²×C₆₇	—	2	2	no	—
158	C₄²×C₆₇	—	2	2	no	—
159	C₄²×C₆₇	—	2	2	no	—
160	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
161	C₄²×C₆₇	C₂×D₄	1	2	yes	—
162	C₂³×C₆₇	—	2	2	no	—
163	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
164	Q₈×C₆₇	—	2	2	no	—
165	Q₈×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
166	D₄×C₆₇	—	2	4	no	—
167	D₄×C₆₇	—	2	4	no	—
168	D₄×C₆₇	—	2	2	no	—
169	D₄×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
170	C₂×C₄×C₆₇	—	2	2	no	—
171	C₂×C₄×C₆₇	—	2	4	no	—
172	C₂×C₄×C₆₇	—	2	4	no	—
173	C₂×C₄×C₆₇	—	2	2	no	—
174	C₂×C₄×C₆₇	—	2	2	no	—
175	C₂×C₄×C₆₇	—	4	1	no	—
176	C₂×C₄×C₆₇	—	4	1	no	—
177	C₂×C₄×C₆₇	—	4	4	no	—
178	C₂×C₄×C₆₇	—	8	2	no	—
179	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
187	C₂×Dic₆₇	—	2	2	no	—
188	C₂×Dic₆₇	—	4	1	no	—
189	C₂×Dic₆₇	—	4	1	no	—
190	C₂×Dic₆₇	—	4	1	no	—
191	C₂×Dic₆₇	—	4	1	no	—
192	C₂×Dic₆₇	—	4	1	no	—
193	C₈×C₆₇	—	2	2	no	—
194	C₈×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
195	C₈×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
196	C₆₇⋊C₈	—	2	1	no	—
197	C₆₇⋊C₈	—	2	2	no	—
198	C₆₇⋊C₈	—	2	1	no	—
199	C₆₇⋊C₈	—	4	2	no	—
200	C₆₇⋊C₈	—	4	2	no	—
201	C₂²×C₆₇	—	2	1	no	—
202	C₂²×C₆₇	—	2	1	no	—
203	C₂²×C₆₇	—	2	4	no	—
204	C₂²×C₆₇	—	4	2	no	—
205	C₂²×C₆₇	—	4	2	no	—
206	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂²×C₆₇	#547	1	1	yes	characteristic
208	C₂²×C₆₇	#554	1	1	yes	characteristic
209	C₄×C₆₇	—	2	4	no	—
210	C₄×C₆₇	—	2	2	no	—
211	C₄×C₆₇	—	2	2	no	—
212	C₄×C₆₇	—	4	2	no	—
213	C₄×C₆₇	—	4	2	no	—
214	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
215	C₄×C₆₇	#520	1	1	yes	characteristic
216	C₄×C₆₇	D₄²	1	1	yes	characteristic
217	C₄×C₆₇	D₄×Q₈	1	1	yes	characteristic
218	Dic₆₇	—	4	2	no	—
219	Dic₆₇	—	8	1	no	—
220	#22687	—	67	1	no	maximal, Sylow
221	C₂×C₆₇	—	2	1	no	—
222	C₂×C₆₇	—	2	1	no	—
223	C₂×C₆₇	—	4	4	no	—
224	C₂×C₆₇	D₄×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₆₇	#2955	1	1	yes	characteristic
226	C₂×C₆₇	#2956	1	1	yes	characteristic
227	C₂×#444	—	67	1	no	—
228	C₂×#443	—	67	1	no	—
229	#2943	D₆₇	1	1	yes	characteristic
230	#2906	—	67	2	no	—
231	#1946	—	67	1	no	—
232	#1945	—	67	1	no	—
233	#1866	—	67	2	no	—
234	#1866	—	67	2	no	—
235	#1849	—	67	1	no	—
236	#1806	—	67	2	no	—
237	#1771	—	67	1	no	—
238	C₆₇	#22687	1	1	yes	characteristic, complemented, Sylow
239	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
240	C₂×#131	—	67	2	no	—
241	C₂×#131	—	67	2	no	—
242	C₄×#41	C₂×D₆₇	1	2	yes	—
243	#444	—	134	4	no	—
244	#443	—	134	4	no	—
245	#442	Dic₆₇	1	2	yes	complemented
246	#441	Dic₆₇	1	2	yes	complemented
247	#440	Dic₆₇	1	2	yes	complemented
248	#440	Dic₆₇	1	2	yes	complemented
249	C₂×#108	—	67	2	no	—
250	C₂×#108	—	67	1	no	—
251	C₂×#108	—	67	1	no	—
252	#427	C₂×D₆₇	1	1	yes	characteristic
253	#424	—	67	2	no	—
254	#424	—	67	2	no	—
255	#424	—	134	2	no	—
256	#424	—	134	2	no	—
257	#423	—	67	2	no	—
258	#423	—	134	2	no	—
259	C₂×C₄⋊C₈	—	67	1	no	—
260	C₂×C₄⋊C₈	—	134	2	no	—
261	C₂×#104	—	67	2	no	—
262	C₂×#104	—	67	2	no	—
263	#416	C₂×D₆₇	1	2	yes	—
264	C₂×#97	—	67	1	no	—
265	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
266	C₂×C₄×C₈	—	67	1	no	—
267	C₄×C₄⋊C₄	—	67	1	no	—
268	#339	—	67	2	no	—
269	#339	—	67	2	no	—
270	#336	—	67	1	no	—
271	#336	—	67	1	no	—
272	C₂×#41	C₂²×D₆₇	1	2	yes	—
273	#135	Dic₁₃₄	1	4	yes	—
274	#135	D₂₆₈	1	4	yes	—
275	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic
276	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	—
277	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
278	#131	—	268	2	no	—
279	#131	—	268	2	no	—
280	#131	—	134	4	no	—
281	#131	—	134	4	no	—
282	C₂×M₁₆	—	67	2	no	—
283	C₂×M₁₆	—	67	2	no	—
284	C₂×M₁₆	—	134	2	no	—
285	C₂×M₁₆	—	134	2	no	—
286	C₂²×C₈	—	67	1	no	—
287	C₂²×C₈	—	67	1	no	—
288	C₂²×C₈	—	134	2	no	—
289	C₂²×C₈	—	134	2	no	—
290	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
291	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
292	C₄×Q₈	C₂×Dic₆₇	1	2	yes	—
293	C₄×Q₈	C₂×Dic₆₇	1	2	yes	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
297	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
298	#117	—	2	2	no	—
299	#117	C₂²×D₆₇	1	2	yes	—
300	C₂×C₄⋊C₄	—	134	1	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	67	1	no	—
303	C₂×C₄²	—	67	1	no	—
304	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
305	#108	—	268	2	no	—
306	#108	—	134	2	no	—
307	#108	—	134	2	no	—
308	#107	C₂×Dic₆₇	1	1	yes	characteristic
309	#107	C₂×Dic₆₇	1	1	yes	characteristic
310	#106	C₂×Dic₆₇	1	2	yes	—
311	C₄⋊C₈	—	67	2	no	—
312	C₄⋊C₈	—	67	2	no	—
313	C₄⋊C₈	—	134	2	no	—
314	C₄⋊C₈	—	134	2	no	—
315	C₄⋊C₈	—	134	2	no	—
316	C₄⋊C₈	—	134	2	no	—
317	C₄⋊C₈	—	134	2	no	—
318	C₄⋊C₈	—	134	2	no	—
319	#104	—	134	4	no	—
320	#104	—	134	4	no	—
321	#103	C₂×Dic₆₇	1	2	yes	—
322	#103	C₂×Dic₆₇	1	2	yes	—
323	#102	C₂×Dic₆₇	1	2	yes	—
324	#102	C₂×Dic₆₇	1	2	yes	—
325	#97	—	134	2	no	—
326	#97	C₂×Dic₆₇	1	2	yes	—
327	#97	C₂×Dic₆₇	1	2	yes	—
328	C₄×C₈	—	134	2	no	—
329	#95	—	134	1	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	C₂×D₂₆₈	1	4	yes	—
333	#41	C₂×Dic₁₃₄	1	4	yes	—
334	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	134	1	no	—
341	C₂²×C₄	—	134	1	no	—
342	C₂²×C₄	#11761627	1	1	yes	characteristic
343	C₂²×C₄	#11761627	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
345	Q₁₆	C₄⋊Dic₆₇	1	4	yes	complemented
346	SD₁₆	C₄⋊Dic₆₇	1	8	yes	complemented
347	D₈	C₄⋊Dic₆₇	1	4	yes	complemented
348	M₁₆	—	268	4	no	—
349	M₁₆	—	268	4	no	—
350	M₁₆	—	134	2	no	—
351	M₁₆	—	134	2	no	—
352	M₁₆	—	134	2	no	—
353	M₁₆	—	134	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	268	4	no	—
357	C₂×C₈	—	268	4	no	—
358	C₂×C₈	—	67	1	no	—
359	C₂×C₈	—	67	2	no	—
360	C₂×C₈	—	67	1	no	—
361	C₂×C₈	—	134	2	no	—
362	C₂×C₈	—	134	2	no	—
363	C₂×C₈	—	134	1	no	—
364	C₂×C₈	—	134	1	no	—
365	C₂×C₈	—	134	1	no	—
366	C₂×C₈	—	134	1	no	—
367	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
368	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
369	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
370	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
371	C₂×C₈	C₂×Dic₁₃₄	1	2	yes	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	268	2	no	—
375	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
376	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	134	1	no	—
384	C₄²	—	134	1	no	—
385	C₄²	—	134	1	no	—
386	C₄²	—	134	1	no	—
387	C₄²	C₂²×Dic₆₇	1	2	yes	—
388	C₄²	D₄×D₆₇	1	2	yes	—
389	C₂³	—	2	2	no	—
390	C₂³	C₂×#11761627	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	C₂×C₄⋊Dic₆₇	1	4	yes	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	2	2	no	—
396	D₄	C₂×C₄⋊Dic₆₇	1	4	yes	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	—	268	1	no	—
407	C₂×C₄	—	268	1	no	—
408	C₂×C₄	—	268	1	no	—
409	C₂×C₄	—	268	1	no	—
410	C₂×C₄	—	268	1	no	—
411	C₂×C₄	—	134	2	no	—
412	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
413	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
414	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
417	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
418	C₂×C₄	#14524089	1	1	yes	characteristic
419	C₂×C₄	#14524090	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	268	2	no	—
422	C₈	—	268	2	no	—
423	C₈	—	134	1	no	—
424	C₈	—	134	2	no	—
425	C₈	—	134	1	no	—
426	C₈	C₂×C₄⋊Dic₆₇	1	2	yes	—
427	C₈	C₂×C₄⋊Dic₆₇	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
434	C₂²	#16864050	1	1	yes	characteristic
435	C₂²	#16864103	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	268	2	no	—
442	C₄	—	536	1	no	—
443	C₄	C₂²×C₄⋊Dic₆₇	1	1	yes	characteristic
444	C₄	#16863879	1	1	yes	characteristic
445	C₄	D₄×D₂₆₈	1	1	yes	characteristic
446	C₄	D₄×Dic₁₃₄	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	4	4	no	—
450	C₂	D₄×C₄⋊Dic₆₇	1	1	yes	characteristic
451	C₂	#22569112	1	1	yes	characteristic
452	C₂	#22569119	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#2943	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#135×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#2943	D₆₇
hypocenter	C₆₇	#22687
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2943

Complements

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

N	H ≅ G/N	type
3. #22568777	C₂	semidirect
4. #22560963	C₂	semidirect
5. #22560958	C₂	semidirect
6. #22560486	C₂	semidirect
7. #22560486	C₂	semidirect
8. #22560384	C₂	semidirect
9. #22560229	C₂	semidirect
10. #22560081	C₂	semidirect
38. #442×C₆₇	C₄	semidirect
39. #441×C₆₇	C₄	semidirect
40. #440×C₆₇	C₄	semidirect
41. #440×C₆₇	C₄	semidirect
140. Q₁₆×C₆₇	C₄⋊C₄	semidirect
141. SD₁₆×C₆₇	C₄⋊C₄	semidirect
142. D₈×C₆₇	C₄⋊C₄	semidirect
238. C₆₇	#22687	semidirect
245. #442	Dic₆₇	semidirect
246. #441	Dic₆₇	semidirect
247. #440	Dic₆₇	semidirect
248. #440	Dic₆₇	semidirect
345. Q₁₆	C₄⋊Dic₆₇	semidirect
346. SD₁₆	C₄⋊Dic₆₇	semidirect
347. D₈	C₄⋊Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863518	2
C₂×#16863513	2
#22568777	2
#22560963	2
#22560958	2
#22560486	2
#22560384	2
#22560229	2
#22560081	2
C₆₇×#2943	2
#22687	67