Subgroups — #30825046

Order 17152.

572 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569326	C₂	1	1	yes	maximal, characteristic
2	#22568853	C₂	1	1	yes	maximal, characteristic
3	#22559000	C₂	1	1	yes	maximal, characteristic, complemented
4	#22558997	C₂	1	1	yes	maximal, characteristic, complemented
5	#22558995	C₂	1	1	yes	maximal, characteristic, complemented
6	#22558992	C₂	1	1	yes	maximal, characteristic, complemented
7	#22558990	C₂	1	1	yes	maximal, characteristic, complemented
8	#22558987	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558985	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558983	C₂	1	1	yes	maximal, characteristic, complemented
11	#22558977	C₂	1	1	yes	maximal, characteristic, complemented
12	#22558974	C₂	1	1	yes	maximal, characteristic, complemented
13	#22558970	C₂	1	1	yes	maximal, characteristic, complemented
14	#22558967	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2989	C₂	1	1	yes	maximal, characteristic
16	#16863527	—	2	1	no	—
17	#16863474	—	2	1	no	—
18	#16863468	—	2	1	no	—
19	#16863468	—	2	1	no	—
20	#16863457	C₄	1	2	yes	—
21	#16863457	C₄	1	2	yes	—
22	#16863453	C₂²	1	1	yes	characteristic
23	#16863453	C₂²	1	1	yes	characteristic
24	#16863449	C₂²	1	1	yes	characteristic
25	#16863449	C₂²	1	1	yes	characteristic
26	#16863449	C₂²	1	1	yes	characteristic
27	#16863449	C₂²	1	1	yes	characteristic
28	#16863449	C₂²	1	1	yes	characteristic
29	#16863423	C₄	1	2	yes	—
30	#16863420	C₂²	1	1	yes	characteristic
31	#16863420	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
33	#16863363	C₄	1	2	yes	—
34	C₄×#11761612	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
36	#16863148	C₂²	1	1	yes	characteristic
37	#16863148	C₂²	1	1	yes	characteristic
38	#16863148	C₂²	1	1	yes	characteristic
39	#16863148	C₂²	1	1	yes	characteristic
40	#16863148	C₂²	1	1	yes	characteristic
41	#16863148	C₂²	1	1	yes	characteristic
42	#16863148	C₂²	1	1	yes	characteristic
43	#16863148	C₂²	1	1	yes	characteristic
44	#16863148	C₂²	1	1	yes	characteristic
45	#16863148	C₂²	1	1	yes	characteristic
46	#16863146	C₂²	1	1	yes	characteristic
47	#16863146	C₂²	1	1	yes	characteristic
48	#16863146	C₂²	1	1	yes	characteristic
49	#16863146	C₂²	1	1	yes	characteristic
50	#16863146	C₂²	1	1	yes	characteristic
51	#16863146	C₂²	1	1	yes	characteristic
52	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
53	#446×C₆₇	—	2	1	no	—
54	#436×C₆₇	—	2	1	no	—
55	#435×C₆₇	—	2	1	no	—
56	#435×C₆₇	—	2	1	no	—
57	#432×C₆₇	C₂²	1	1	yes	characteristic
58	#432×C₆₇	C₂²	1	1	yes	characteristic
59	#431×C₆₇	C₂²	1	1	yes	characteristic
60	#423×C₆₇	C₂²	1	1	yes	characteristic
61	#423×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×#11761612	—	2	1	no	—
64	C₂×#11761612	—	2	1	no	—
65	C₂×#11761612	C₂×C₄	1	2	yes	—
66	C₂²×C₆₇⋊C₈	—	2	1	no	—
67	C₂²×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
68	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
69	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
70	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
71	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
72	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
73	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
74	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
75	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
77	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
78	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
79	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
80	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
81	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
82	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
83	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
84	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
85	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
86	#14523954	—	2	1	no	—
87	#14523954	—	2	1	no	—
88	#14523954	C₂×C₄	1	2	yes	—
89	C₄×C₆₇⋊C₈	—	2	1	no	—
90	C₄×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
91	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
92	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
93	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
94	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
95	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
96	C₂×M₁₆×C₆₇	—	2	1	no	—
97	C₂×M₁₆×C₆₇	—	2	1	no	—
98	C₂²×C₈×C₆₇	—	2	1	no	—
99	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
100	C₄×Q₈×C₆₇	Q₈	1	1	yes	characteristic
101	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
102	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
103	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
104	C₄×D₄×C₆₇	Q₈	1	1	yes	characteristic
105	C₄×D₄×C₆₇	Q₈	1	1	yes	characteristic
106	C₄×D₄×C₆₇	Q₈	1	1	yes	characteristic
107	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
108	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
109	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₆₇	—	2	1	no	—
114	C₄⋊C₈×C₆₇	—	2	1	no	—
115	C₄⋊C₈×C₆₇	—	2	1	no	—
116	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
117	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
118	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
119	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
120	C₂²⋊C₈×C₆₇	—	2	1	no	—
121	C₂²⋊C₈×C₆₇	—	2	1	no	—
122	C₂²⋊C₈×C₆₇	—	2	1	no	—
123	#97×C₆₇	—	2	1	no	—
124	#97×C₆₇	—	2	1	no	—
125	C₄×C₈×C₆₇	—	2	1	no	—
126	#11761612	—	4	2	no	—
127	#11761612	—	8	1	no	—
128	#11761612	—	8	1	no	—
129	C₂×C₆₇⋊C₈	—	2	1	no	—
130	C₂×C₆₇⋊C₈	—	2	1	no	—
131	C₂×C₆₇⋊C₈	—	2	1	no	—
132	C₂×C₆₇⋊C₈	—	2	1	no	—
133	C₂×C₆₇⋊C₈	—	4	2	no	—
134	C₂×C₆₇⋊C₈	—	8	1	no	—
135	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
136	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
138	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
139	#41×C₆₇	—	4	2	no	—
140	C₂×Q₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
141	C₂×D₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
142	C₂×D₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
143	C₂×D₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
151	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
152	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
153	M₁₆×C₆₇	—	8	1	no	—
154	M₁₆×C₆₇	—	8	1	no	—
155	C₂×C₈×C₆₇	—	2	1	no	—
156	C₂×C₈×C₆₇	—	2	1	no	—
157	C₂×C₈×C₆₇	—	2	1	no	—
158	C₂×C₈×C₆₇	—	2	1	no	—
159	C₂×C₈×C₆₇	—	8	1	no	—
160	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
161	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
162	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
163	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
164	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
165	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
166	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
167	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
168	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
169	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
170	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
171	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
172	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
179	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
180	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
181	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
182	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
185	Q₈×C₆₇	—	4	1	no	—
186	D₄×C₆₇	—	4	1	no	—
187	D₄×C₆₇	—	4	1	no	—
188	D₄×C₆₇	—	4	1	no	—
189	C₂×C₄×C₆₇	—	2	2	no	—
190	C₂×C₄×C₆₇	—	2	2	no	—
191	C₂×C₄×C₆₇	—	2	2	no	—
192	C₂×C₄×C₆₇	—	2	1	no	—
193	C₂×C₄×C₆₇	—	2	1	no	—
194	C₂×C₄×C₆₇	—	2	1	no	—
195	C₂×C₄×C₆₇	—	2	1	no	—
196	C₂×C₄×C₆₇	—	2	1	no	—
197	C₂×C₄×C₆₇	—	2	1	no	—
198	C₂×C₄×C₆₇	—	4	1	no	—
199	C₂×C₄×C₆₇	—	4	1	no	—
200	C₂×C₄×C₆₇	—	4	1	no	—
201	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
213	C₈×C₆₇	—	4	1	no	—
214	C₈×C₆₇	—	4	1	no	—
215	C₈×C₆₇	—	4	1	no	—
216	C₈×C₆₇	—	4	1	no	—
217	C₆₇⋊C₈	—	2	2	no	—
218	C₆₇⋊C₈	—	2	2	no	—
219	C₆₇⋊C₈	—	2	2	no	—
220	C₆₇⋊C₈	—	2	2	no	—
221	C₆₇⋊C₈	—	4	1	no	—
222	C₆₇⋊C₈	—	4	1	no	—
223	C₆₇⋊C₈	—	4	1	no	—
224	C₆₇⋊C₈	—	4	1	no	—
225	C₂²×C₆₇	—	2	1	no	—
226	C₂²×C₆₇	—	2	1	no	—
227	C₂²×C₆₇	—	2	1	no	—
228	C₂²×C₆₇	—	2	1	no	—
229	C₂²×C₆₇	—	2	1	no	—
230	C₂²×C₆₇	—	2	1	no	—
231	C₂²×C₆₇	—	2	1	no	—
232	C₂²×C₆₇	—	2	1	no	—
233	C₂²×C₆₇	—	2	1	no	—
234	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
235	C₄×C₆₇	—	2	1	no	—
236	C₄×C₆₇	—	2	1	no	—
237	C₄×C₆₇	—	2	1	no	—
238	C₄×C₆₇	—	2	1	no	—
239	C₄×C₆₇	—	2	1	no	—
240	C₄×C₆₇	—	2	1	no	—
241	C₄×C₆₇	—	2	1	no	—
242	C₄×C₆₇	—	2	1	no	—
243	C₄×C₆₇	—	2	1	no	—
244	C₄×C₆₇	—	2	1	no	—
245	C₄×C₆₇	#568	1	2	yes	—
246	C₄×C₆₇	#576	1	1	yes	characteristic
247	C₄×C₆₇	#578	1	1	yes	characteristic
248	#17825	—	67	1	no	maximal, Sylow
249	C₂×C₆₇	—	4	1	no	—
250	C₂×C₆₇	—	4	1	no	—
251	C₂×C₆₇	—	4	1	no	—
252	C₂×C₆₇	#2905	1	1	yes	characteristic
253	C₂×C₆₇	#2913	1	1	yes	characteristic
254	C₂×C₆₇	#2916	1	1	yes	characteristic
255	#2989	—	67	1	no	—
256	#2989	D₆₇	1	1	yes	characteristic
257	#2922	—	67	1	no	—
258	#1574	—	67	1	no	—
259	#1574	—	67	1	no	—
260	#1573	—	67	1	no	—
261	#1573	—	67	1	no	—
262	#1572	—	67	1	no	—
263	#1572	—	67	1	no	—
264	#1571	—	67	1	no	—
265	#1571	—	67	1	no	—
266	#1569	—	67	1	no	—
267	#1569	—	67	1	no	—
268	#1568	—	67	1	no	—
269	#1567	—	67	1	no	—
270	C₆₇	#17825	1	1	yes	characteristic, complemented, Sylow
271	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
272	#446	—	2	1	no	—
273	#446	—	134	1	no	—
274	#436	—	2	1	no	—
275	#436	—	134	1	no	—
276	#435	—	2	1	no	—
277	#435	—	2	1	no	—
278	#435	—	134	1	no	—
279	#435	—	134	1	no	—
280	#433	—	67	2	no	—
281	#433	—	67	2	no	—
282	#432	—	67	1	no	—
283	#432	—	67	1	no	—
284	#432	C₂×D₆₇	1	1	yes	characteristic
285	#432	C₂×D₆₇	1	1	yes	characteristic
286	#431	—	67	1	no	—
287	#431	—	67	1	no	—
288	#431	—	67	1	no	—
289	#431	—	67	1	no	—
290	#431	—	67	1	no	—
291	#431	C₂×D₆₇	1	1	yes	characteristic
292	#424	—	67	2	no	—
293	#423	—	67	1	no	—
294	#423	—	67	1	no	—
295	#423	C₂×D₆₇	1	1	yes	characteristic
296	#423	C₂×D₆₇	1	1	yes	characteristic
297	C₂×C₄⋊C₈	—	67	1	no	—
298	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
299	#408	—	67	2	no	—
300	C₄×M₁₆	—	67	1	no	—
301	C₂×C₄×C₈	—	67	1	no	—
302	#335	—	67	1	no	—
303	#335	—	67	1	no	—
304	#335	—	67	1	no	—
305	#335	—	67	1	no	—
306	#335	—	67	1	no	—
307	#335	—	67	1	no	—
308	#335	—	67	1	no	—
309	#335	—	67	1	no	—
310	#335	—	67	1	no	—
311	#335	—	67	1	no	—
312	#334	—	67	1	no	—
313	#334	—	67	1	no	—
314	#334	—	67	1	no	—
315	#334	—	67	1	no	—
316	#334	—	67	1	no	—
317	#334	—	67	1	no	—
318	C₂×#41	C₄×D₆₇	1	1	yes	characteristic
319	C₂×M₁₆	—	2	1	no	—
320	C₂×M₁₆	—	2	1	no	—
321	C₂×M₁₆	—	67	2	no	—
322	C₂×M₁₆	—	134	1	no	—
323	C₂×M₁₆	—	134	1	no	—
324	C₂²×C₈	—	2	1	no	—
325	C₂²×C₈	—	67	2	no	—
326	C₂²×C₈	—	134	1	no	—
327	C₄×Q₈	Dic₁₃₄	1	1	yes	characteristic
328	C₄×Q₈	C₂²⋊D₆₇	1	1	yes	characteristic
329	C₄×D₄	Dic₁₃₄	1	1	yes	characteristic
330	C₄×D₄	Dic₁₃₄	1	1	yes	characteristic
331	C₄×D₄	Dic₁₃₄	1	1	yes	characteristic
332	C₄×D₄	C₂²⋊D₆₇	1	1	yes	characteristic
333	C₄×D₄	C₂²⋊D₆₇	1	1	yes	characteristic
334	C₄×D₄	C₂²⋊D₆₇	1	1	yes	characteristic
335	#117	C₄×D₆₇	1	1	yes	characteristic
336	#117	C₄×D₆₇	1	1	yes	characteristic
337	#117	C₄×D₆₇	1	1	yes	characteristic
338	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
339	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
340	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	—	2	1	no	—
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	—	67	2	no	—
345	C₄⋊C₈	—	67	2	no	—
346	C₄⋊C₈	—	67	2	no	—
347	C₄⋊C₈	—	67	2	no	—
348	C₄⋊C₈	—	67	1	no	—
349	C₄⋊C₈	—	67	1	no	—
350	C₄⋊C₈	—	67	1	no	—
351	C₄⋊C₈	—	67	1	no	—
352	C₄⋊C₈	—	134	1	no	—
353	C₄⋊C₈	—	134	1	no	—
354	C₄⋊C₈	—	134	1	no	—
355	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
356	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
357	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
358	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
359	C₂²⋊C₈	—	2	1	no	—
360	C₂²⋊C₈	—	2	1	no	—
361	C₂²⋊C₈	—	2	1	no	—
362	C₂²⋊C₈	—	67	2	no	—
363	C₂²⋊C₈	—	67	2	no	—
364	C₂²⋊C₈	—	67	2	no	—
365	C₂²⋊C₈	—	67	2	no	—
366	C₂²⋊C₈	—	134	1	no	—
367	C₂²⋊C₈	—	134	1	no	—
368	C₂²⋊C₈	—	134	1	no	—
369	#97	—	2	1	no	—
370	#97	—	2	1	no	—
371	#97	—	67	2	no	—
372	#97	—	134	1	no	—
373	#97	—	134	1	no	—
374	C₄×C₈	—	2	1	no	—
375	C₄×C₈	—	67	2	no	—
376	C₄×C₈	—	67	1	no	—
377	C₄×C₈	—	67	1	no	—
378	C₄×C₈	—	67	1	no	—
379	C₄×C₈	—	67	1	no	—
380	C₄×C₈	—	134	1	no	—
381	#41	—	4	2	no	—
382	C₂×Q₈	Dic₆₇⋊C₄	1	1	yes	characteristic
383	C₂×D₄	Dic₆₇⋊C₄	1	1	yes	characteristic
384	C₂×D₄	Dic₆₇⋊C₄	1	1	yes	characteristic
385	C₂×D₄	Dic₆₇⋊C₄	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
392	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
393	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
394	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
395	M₁₆	—	8	1	no	—
396	M₁₆	—	8	1	no	—
397	M₁₆	—	268	2	no	—
398	M₁₆	—	536	1	no	—
399	M₁₆	—	536	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	8	1	no	—
405	C₂×C₈	—	268	2	no	—
406	C₂×C₈	—	536	1	no	—
407	C₂×C₈	—	67	2	no	—
408	C₂×C₈	—	67	2	no	—
409	C₂×C₈	—	67	2	no	—
410	C₂×C₈	—	67	2	no	—
411	C₂×C₈	—	134	1	no	—
412	C₂×C₈	—	134	1	no	—
413	C₂×C₈	—	134	1	no	—
414	C₂×C₈	—	134	1	no	—
415	C₄⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
416	C₄⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
417	C₄⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
418	C₄⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
419	C₄⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
420	C₄⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
421	C₂²⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
422	C₂²⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
423	C₂²⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
424	C₂²⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
425	C₂²⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
426	C₂²⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
427	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
428	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
429	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
430	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
431	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
432	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
433	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
434	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
435	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
436	C₄²	C₂³×D₆₇	1	1	yes	characteristic
437	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
438	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
439	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
440	Q₈	—	4	1	no	—
441	D₄	—	4	1	no	—
442	D₄	—	4	1	no	—
443	D₄	—	4	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
457	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
458	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
459	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
460	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
461	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
462	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
463	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
464	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
465	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
467	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
468	C₈	—	4	1	no	—
469	C₈	—	4	1	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	1	no	—
472	C₈	—	268	1	no	—
473	C₈	—	268	1	no	—
474	C₈	—	268	1	no	—
475	C₈	—	268	1	no	—
476	C₈	—	134	2	no	—
477	C₈	—	134	2	no	—
478	C₈	—	134	2	no	—
479	C₈	—	134	2	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	C₂²×Dic₆₇⋊C₄	1	1	yes	characteristic
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	#16864162	1	2	yes	—
501	C₄	#16864199	1	1	yes	characteristic
502	C₄	#16864211	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	4	1	no	—
505	C₂	—	4	1	no	—
506	C₂	#22568772	1	1	yes	characteristic
507	C₂	#22568807	1	1	yes	characteristic
508	C₂	#22568818	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#2989	C₂
socle	C₂²×C₆₇	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₆₇	C₂×C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#2989	D₆₇
hypocenter	C₆₇	#17825
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2989

Complements

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

N	H ≅ G/N	type
3. #22559000	C₂	semidirect
4. #22558997	C₂	semidirect
5. #22558995	C₂	semidirect
6. #22558992	C₂	semidirect
7. #22558990	C₂	semidirect
8. #22558987	C₂	semidirect
9. #22558985	C₂	semidirect
10. #22558983	C₂	semidirect
11. #22558977	C₂	semidirect
12. #22558974	C₂	semidirect
13. #22558970	C₂	semidirect
14. #22558967	C₂	semidirect
270. C₆₇	#17825	semidirect

Maximal subgroups

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

subgroup	index
#22569326	2
#22568853	2
#22559000	2
#22558997	2
#22558995	2
#22558992	2
#22558990	2
#22558987	2
#22558985	2
#22558983	2
#22558977	2
#22558974	2
#22558970	2
#22558967	2
C₆₇×#2989	2
#17825	67