Subgroups — #30839719

Order 17152.

786 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863770	C₂	1	1	yes	maximal, characteristic, complemented
2	#22569689	C₂	1	1	yes	maximal, characteristic
3	#41×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559559	C₂	1	4	yes	maximal, complemented
5	#22559552	C₂	1	4	yes	maximal, complemented
6	#22558964	C₂	1	1	yes	maximal, characteristic, complemented
7	#22558894	C₂	1	1	yes	maximal, characteristic, complemented
8	#22558878	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14524068	—	2	1	no	—
11	C₂²×#11761615	—	2	2	no	—
12	C₂×#14524040	C₂²	1	1	yes	characteristic
13	#16863770	—	2	1	no	—
14	#16863770	—	2	1	no	—
15	#16863770	C₂²	1	4	yes	—
16	#16863596	—	2	1	no	—
17	#16863596	C₂²	1	2	yes	—
18	#16863591	—	2	1	no	—
19	#16863591	C₂²	1	2	yes	—
20	Q₈×C₆₇⋊C₈	C₂²	1	2	yes	complemented
21	D₄×C₆₇⋊C₈	—	2	2	no	—
22	D₄×C₆₇⋊C₈	C₂²	1	2	yes	complemented
23	#16863449	—	2	1	no	—
24	#16863449	C₂²	1	1	yes	characteristic
25	#16863420	C₂²	1	1	yes	characteristic
26	#16863400	—	2	1	no	—
27	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
28	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
29	#16863146	C₂²	1	4	yes	complemented
30	#16863142	C₂²	1	4	yes	complemented
31	#16863139	C₂²	1	4	yes	—
32	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
34	#477×C₆₇	—	2	1	no	—
35	#476×C₆₇	—	2	1	no	—
36	#475×C₆₇	C₂²	1	2	yes	complemented
37	#474×C₆₇	C₂²	1	2	yes	complemented
38	#428×C₆₇	—	2	1	no	—
39	#423×C₆₇	C₂²	1	1	yes	characteristic
40	#417×C₆₇	—	2	1	no	—
41	C₂²×D₂₆₈	—	2	1	no	—
42	C₂²×D₂₆₈	—	2	1	no	—
43	C₂²×D₂₆₈	—	2	1	no	—
44	#14524068	—	4	4	no	—
45	C₂×#11761615	—	2	4	no	—
46	C₂×#11761615	—	2	4	no	—
47	C₂×#11761615	—	2	2	no	—
48	C₂×#11761615	—	4	8	no	—
49	C₂×#11761613	—	2	2	no	—
50	C₂×#11761612	—	2	1	no	—
51	C₂²×C₆₇⋊C₈	—	2	2	no	—
52	C₂²×C₆₇⋊C₈	D₄	1	2	yes	—
53	#14524040	—	2	1	no	—
54	#14524040	—	2	1	no	—
55	#14524040	—	2	1	no	—
56	#14524040	C₂³	1	2	yes	—
57	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
58	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
59	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
60	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
61	#14523963	—	2	2	no	—
62	#14523963	—	2	2	no	—
63	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
64	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
65	C₄×C₆₇⋊C₈	—	2	2	no	—
66	C₄×C₆₇⋊C₈	—	2	1	no	—
67	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
68	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
69	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
70	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
71	C₂²×Q₈×C₆₇	—	2	1	no	—
72	C₂×M₁₆×C₆₇	—	2	1	no	—
73	C₄⋊Q₈×C₆₇	—	2	1	no	—
74	C₄⋊Q₈×C₆₇	—	2	1	no	—
75	C₄⋊Q₈×C₆₇	—	2	1	no	—
76	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
77	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
79	C₄×D₄×C₆₇	—	2	1	no	—
80	C₄×D₄×C₆₇	—	2	1	no	—
81	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
82	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
83	#117×C₆₇	—	2	1	no	—
84	#117×C₆₇	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
87	C₂×C₄²×C₆₇	—	2	1	no	—
88	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
89	#107×C₆₇	—	2	2	no	—
90	#106×C₆₇	—	2	2	no	—
91	C₄⋊C₈×C₆₇	—	2	1	no	—
92	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
93	#103×C₆₇	—	2	2	no	—
94	#102×C₆₇	—	2	2	no	—
95	C₂³×D₆₇	—	4	1	no	—
96	C₂×D₂₆₈	—	2	2	no	—
97	C₂×D₂₆₈	—	2	2	no	—
98	C₂×D₂₆₈	—	2	2	no	—
99	C₂×D₂₆₈	—	4	4	no	—
100	C₂×D₂₆₈	—	4	2	no	—
101	C₂×D₂₆₈	—	4	2	no	—
102	C₂×D₂₆₈	—	4	1	no	—
103	C₂×D₂₆₈	—	4	1	no	—
104	C₂×D₂₆₈	—	4	1	no	—
105	C₂×D₂₆₈	—	8	2	no	—
106	#11761615	—	4	8	no	—
107	#11761615	—	4	4	no	—
108	#11761615	—	4	8	no	—
109	#11761613	—	4	4	no	—
110	#11761612	—	4	2	no	—
111	C₂×C₆₇⋊C₈	—	2	4	no	—
112	C₂×C₆₇⋊C₈	—	2	2	no	—
113	C₂×C₆₇⋊C₈	—	2	2	no	—
114	C₂×C₆₇⋊C₈	—	4	4	no	—
115	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
116	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
117	#41×C₆₇	—	2	2	no	—
118	#41×C₆₇	SD₁₆	1	4	yes	complemented
119	C₂×Q₈×C₆₇	—	2	2	no	—
120	C₂×Q₈×C₆₇	—	4	4	no	—
121	C₂×Q₈×C₆₇	—	4	1	no	—
122	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
123	C₂×D₄×C₆₇	—	2	1	no	—
124	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₇	—	2	1	no	—
126	C₂²×C₄×C₆₇	—	2	1	no	—
127	C₂²×C₄×C₆₇	—	2	1	no	—
128	C₂²×C₄×C₆₇	—	4	1	no	—
129	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
132	M₁₆×C₆₇	—	4	2	no	—
133	C₂×C₈×C₆₇	—	2	2	no	—
134	C₄⋊C₄×C₆₇	—	2	1	no	—
135	C₄⋊C₄×C₆₇	—	2	1	no	—
136	C₄⋊C₄×C₆₇	—	2	2	no	—
137	C₄⋊C₄×C₆₇	—	2	2	no	—
138	C₄⋊C₄×C₆₇	—	4	1	no	—
139	C₄⋊C₄×C₆₇	—	4	1	no	—
140	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂²⋊C₄×C₆₇	—	2	1	no	—
143	C₂²⋊C₄×C₆₇	—	2	1	no	—
144	C₂²⋊C₄×C₆₇	—	2	1	no	—
145	C₄²×C₆₇	—	2	1	no	—
146	C₄²×C₆₇	—	2	1	no	—
147	C₄²×C₆₇	—	2	1	no	—
148	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₆₇	#41	1	1	yes	characteristic
151	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
152	C₂³×C₆₇	—	2	1	no	—
153	C₂³×C₆₇	#121	1	1	yes	characteristic
154	C₂²×D₆₇	—	4	2	no	—
155	C₂²×D₆₇	—	8	2	no	—
156	C₂²×D₆₇	—	8	2	no	—
157	C₂²×D₆₇	—	8	2	no	—
158	Q₈×C₆₇	—	2	1	no	—
159	Q₈×C₆₇	—	4	4	no	—
160	Q₈×C₆₇	—	8	2	no	—
161	Q₈×C₆₇	C₂×SD₁₆	1	2	yes	complemented
162	D₄×C₆₇	—	2	4	no	—
163	D₄×C₆₇	—	2	1	no	—
164	D₄×C₆₇	C₂×SD₁₆	1	2	yes	complemented
165	C₂×C₄×C₆₇	—	2	1	no	—
166	C₂×C₄×C₆₇	—	2	2	no	—
167	C₂×C₄×C₆₇	—	2	4	no	—
168	C₂×C₄×C₆₇	—	2	2	no	—
169	C₂×C₄×C₆₇	—	2	1	no	—
170	C₂×C₄×C₆₇	—	2	1	no	—
171	C₂×C₄×C₆₇	—	4	2	no	—
172	C₂×C₄×C₆₇	—	4	2	no	—
173	C₂×C₄×C₆₇	—	4	2	no	—
174	C₂×C₄×C₆₇	—	8	2	no	—
175	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
176	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
177	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
178	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
179	C₂×C₄×C₆₇	#135	1	2	yes	—
180	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
183	D₂₆₈	—	4	2	no	—
184	D₂₆₈	—	4	2	no	—
185	D₂₆₈	—	4	4	no	—
186	D₂₆₈	—	8	2	no	—
187	D₂₆₈	—	8	2	no	—
188	D₂₆₈	—	8	2	no	—
189	D₂₆₈	—	8	2	no	—
190	C₈×C₆₇	—	4	2	no	—
191	C₆₇⋊C₈	—	2	2	no	—
192	C₆₇⋊C₈	—	4	2	no	—
193	C₆₇⋊C₈	—	4	2	no	—
194	C₆₇⋊C₈	AGL(1,ℤ/8)	1	4	yes	complemented
195	C₂²×C₆₇	—	2	1	no	—
196	C₂²×C₆₇	—	2	1	no	—
197	C₂²×C₆₇	—	2	2	no	—
198	C₂²×C₆₇	—	4	1	no	—
199	C₂²×C₆₇	—	4	1	no	—
200	C₂²×C₆₇	#465	1	2	yes	—
201	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
202	C₂×D₆₇	—	8	2	no	—
203	C₂×D₆₇	—	8	2	no	—
204	C₂×D₆₇	—	8	2	no	—
205	C₂×D₆₇	—	16	4	no	—
206	C₄×C₆₇	—	2	1	no	—
207	C₄×C₆₇	—	2	2	no	—
208	C₄×C₆₇	—	2	1	no	—
209	C₄×C₆₇	—	4	1	no	—
210	C₄×C₆₇	—	4	1	no	—
211	C₄×C₆₇	—	8	2	no	—
212	C₄×C₆₇	#465	1	2	yes	—
213	C₄×C₆₇	#471	1	2	yes	—
214	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
215	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
216	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
217	#19266	—	67	1	no	maximal, Sylow
218	C₂×C₆₇	—	2	2	no	—
219	C₂×C₆₇	—	4	2	no	—
220	C₂×C₆₇	#3038	1	1	yes	characteristic
221	C₂×C₆₇	C₂×#465	1	1	yes	characteristic
222	C₂×C₆₇	C₂×#471	1	1	yes	characteristic
223	D₆₇	—	16	2	no	—
224	C₂×#492	—	67	1	no	—
225	#3079	D₆₇	1	1	yes	characteristic, complemented
226	#3038	—	67	1	no	—
227	C₈×#41	—	67	1	no	—
228	#1666	—	67	4	no	—
229	#1665	—	67	4	no	—
230	#1566	—	67	1	no	—
231	#1549	—	67	1	no	—
232	#1545	—	67	1	no	—
233	C₆₇	#19266	1	1	yes	characteristic, complemented, Sylow
234	C₂×AGL(1,ℤ/8)	—	134	1	no	—
235	C₂²×SD₁₆	—	134	2	no	—
236	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
237	C₂×#127	—	67	1	no	—
238	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
239	#492	—	67	4	no	—
240	#492	—	134	1	no	—
241	#492	—	134	1	no	—
242	#477	—	2	1	no	—
243	#476	—	2	1	no	—
244	#475	C₂×D₆₇	1	2	yes	complemented
245	#474	C₂×D₆₇	1	2	yes	complemented
246	#460	—	67	2	no	—
247	#460	—	134	1	no	—
248	#459	—	67	2	no	—
249	#459	—	134	1	no	—
250	C₈×Q₈	—	67	2	no	—
251	C₈×D₄	—	67	2	no	—
252	C₈×D₄	—	134	2	no	—
253	#431	—	67	1	no	—
254	#431	—	134	1	no	—
255	#428	—	2	1	no	—
256	#423	—	67	1	no	—
257	#423	C₂×D₆₇	1	1	yes	characteristic
258	#418	—	134	1	no	—
259	#417	—	2	1	no	—
260	C₂×C₄×C₈	—	67	1	no	—
261	C₂×C₄×C₈	—	134	1	no	—
262	#334	—	67	4	no	—
263	#332	—	67	4	no	—
264	#331	—	67	4	no	—
265	C₂×#41	C₂²⋊D₆₇	1	1	yes	characteristic
266	C₂²×Q₈	—	2	1	no	—
267	C₂²×D₄	—	134	1	no	—
268	C₂²×D₄	—	134	1	no	—
269	C₂²×D₄	—	134	1	no	—
270	AGL(1,ℤ/8)	—	268	4	no	—
271	C₂×SD₁₆	—	268	8	no	—
272	C₂×SD₁₆	—	134	4	no	—
273	C₂×SD₁₆	—	134	4	no	—
274	C₂×SD₁₆	—	134	2	no	—
275	C₂×D₈	—	134	2	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	134	1	no	—
278	C₂²×C₈	—	67	2	no	—
279	C₂²×C₈	—	134	2	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
284	#127	—	67	2	no	—
285	#127	—	134	1	no	—
286	#127	—	134	1	no	—
287	#127	—	134	1	no	—
288	C₄×Q₈	C₂²⋊D₆₇	1	1	yes	characteristic
289	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	C₂²⋊D₆₇	1	1	yes	characteristic
293	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
294	#117	—	2	1	no	—
295	#117	C₂²⋊D₆₇	1	1	yes	characteristic
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
300	#107	—	2	2	no	—
301	#106	—	2	2	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	—	67	2	no	—
304	C₄⋊C₈	—	67	2	no	—
305	C₄⋊C₈	—	134	2	no	—
306	C₄⋊C₈	—	134	1	no	—
307	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
308	#103	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	134	2	no	—
311	#102	—	134	2	no	—
312	C₂²⋊C₈	—	134	2	no	—
313	C₂²⋊C₈	—	134	1	no	—
314	C₄×C₈	—	67	1	no	—
315	C₄×C₈	—	67	1	no	—
316	C₄×C₈	—	67	2	no	—
317	C₄×C₈	—	134	2	no	—
318	C₄×C₈	—	134	1	no	—
319	C₂⁴	—	268	1	no	—
320	#41	—	2	2	no	—
321	#41	#11761615	1	4	yes	complemented
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	4	4	no	—
324	C₂×Q₈	—	4	1	no	—
325	C₂×Q₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	268	4	no	—
328	C₂×D₄	—	268	1	no	—
329	C₂×D₄	—	268	1	no	—
330	C₂×D₄	—	268	1	no	—
331	C₂×D₄	—	268	2	no	—
332	C₂×D₄	—	268	2	no	—
333	C₂×D₄	—	536	2	no	—
334	C₂×D₄	—	134	2	no	—
335	C₂×D₄	—	134	2	no	—
336	C₂×D₄	—	134	2	no	—
337	C₂×D₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
344	C₂²×C₄	#11761627	1	1	yes	characteristic
345	SD₁₆	—	268	4	no	—
346	SD₁₆	—	268	8	no	—
347	SD₁₆	—	268	8	no	—
348	D₈	—	268	4	no	—
349	M₁₆	—	4	2	no	—
350	M₁₆	—	268	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	268	4	no	—
353	C₂×C₈	—	67	2	no	—
354	C₂×C₈	—	67	2	no	—
355	C₂×C₈	—	134	2	no	—
356	C₂×C₈	—	134	2	no	—
357	C₂×C₈	—	134	4	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
365	C₄⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	D₄×D₆₇	1	1	yes	characteristic
373	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
374	C₄²	#11761627	1	1	yes	characteristic
375	C₄²	C₂³×D₆₇	1	1	yes	characteristic
376	C₂³	—	2	1	no	—
377	C₂³	—	268	2	no	—
378	C₂³	—	536	2	no	—
379	C₂³	—	536	2	no	—
380	C₂³	—	536	2	no	—
381	C₂³	#14524015	1	1	yes	characteristic
382	Q₈	—	2	1	no	—
383	Q₈	—	4	4	no	—
384	Q₈	—	8	2	no	—
385	Q₈	C₂×#11761615	1	2	yes	complemented
386	D₄	—	2	4	no	—
387	D₄	—	2	1	no	—
388	D₄	—	268	2	no	—
389	D₄	—	268	2	no	—
390	D₄	—	268	4	no	—
391	D₄	—	536	2	no	—
392	D₄	—	536	2	no	—
393	D₄	—	536	2	no	—
394	D₄	—	536	2	no	—
395	D₄	C₂×#11761615	1	2	yes	complemented
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	#14524015	1	1	yes	characteristic
407	C₂×C₄	#14524015	1	1	yes	characteristic
408	C₂×C₄	#14524015	1	1	yes	characteristic
409	C₂×C₄	C₂×#11761615	1	2	yes	—
410	C₂×C₄	#14524063	1	2	yes	—
411	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
413	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
414	C₈	—	4	2	no	—
415	C₈	—	268	2	no	—
416	C₈	—	268	2	no	—
417	C₈	—	67	4	no	—
418	C₈	—	134	2	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	536	2	no	—
425	C₂²	—	536	2	no	—
426	C₂²	—	536	2	no	—
427	C₂²	—	1072	4	no	—
428	C₂²	#16863627	1	2	yes	—
429	C₂²	C₂×#14524015	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	8	2	no	—
436	C₄	#16863627	1	2	yes	—
437	C₄	#16863661	1	2	yes	—
438	C₄	C₂²×#11761615	1	1	yes	characteristic
439	C₄	C₂×#14524063	1	1	yes	characteristic
440	C₄	AGL(1,ℤ/8)×D₆₇	1	2	yes	—
441	C₂	—	2	2	no	—
442	C₂	—	4	2	no	—
443	C₂	—	1072	2	no	—
444	C₂	#22569687	1	1	yes	characteristic
445	C₂	C₂×#16863627	1	1	yes	characteristic
446	C₂	C₂×#16863661	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14524015
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#3079	C₂
socle	C₂²×C₆₇	C₂×#121
prime radical	#22569689	C₂
hypercenter	#3079	D₆₇
hypocenter	C₆₇	#19266
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3079

Complements

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

N	H ≅ G/N	type
1. C₂×#16863770	C₂	semidirect
3. #41×C₆₇⋊C₈	C₂	semidirect
4. #22559559	C₂	semidirect
5. #22559552	C₂	semidirect
6. #22558964	C₂	semidirect
7. #22558894	C₂	semidirect
8. #22558878	C₂	semidirect
9. C₆₇×#3079	C₂	semidirect
20. Q₈×C₆₇⋊C₈	C₂²	semidirect
22. D₄×C₆₇⋊C₈	C₂²	semidirect
29. #16863146	C₂²	semidirect
30. #16863142	C₂²	semidirect
36. #475×C₆₇	C₂²	semidirect
37. #474×C₆₇	C₂²	semidirect
118. #41×C₆₇	SD₁₆	semidirect
161. Q₈×C₆₇	C₂×SD₁₆	semidirect
164. D₄×C₆₇	C₂×SD₁₆	semidirect
194. C₆₇⋊C₈	AGL(1,ℤ/8)	semidirect
225. #3079	D₆₇	semidirect
233. C₆₇	#19266	semidirect
244. #475	C₂×D₆₇	semidirect
245. #474	C₂×D₆₇	semidirect
321. #41	#11761615	semidirect
385. Q₈	C₂×#11761615	semidirect
395. D₄	C₂×#11761615	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863770	2
#22569689	2
#41×C₆₇⋊C₈	2
#22559559	2
#22559552	2
#22558964	2
#22558894	2
#22558878	2
C₆₇×#3079	2
#19266	67