Subgroups — #30838318

Order 17152.

620 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570795	C₂	1	1	yes	maximal, characteristic, complemented
2	#22570281	C₂	1	2	yes	maximal
3	C₈×#11761628	C₂	1	1	yes	maximal, characteristic
4	#22559640	C₂	1	2	yes	maximal, complemented
5	#22559633	C₂	1	2	yes	maximal, complemented
6	#22559604	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559599	C₂	1	1	yes	maximal, characteristic, complemented
8	#22559580	C₂	1	1	yes	maximal, characteristic, complemented
9	#22559575	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558873	C₂	1	2	yes	maximal, complemented
11	C₆₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863953	C₂²	1	2	yes	—
13	C₄×#11761628	C₂²	1	1	yes	characteristic
14	#16863801	C₂²	1	1	yes	characteristic
15	#16863776	C₂²	1	1	yes	characteristic
16	#16863747	C₂²	1	2	yes	—
17	#16863738	—	2	2	no	—
18	#16863682	C₂²	1	2	yes	—
19	#16863677	C₂²	1	2	yes	—
20	#16863637	—	2	1	no	—
21	#16863637	—	2	1	no	—
22	#16863607	C₂²	1	2	yes	—
23	#16863602	C₂²	1	2	yes	—
24	#16863560	—	2	2	no	—
25	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
27	C₄×Dic₂₆₈	—	2	1	no	—
28	C₄×Dic₂₆₈	—	2	1	no	—
29	C₄×Dic₂₆₈	—	2	2	no	—
30	C₄×#11761617	—	2	2	no	—
31	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
32	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
33	C₈×C₂²⋊D₆₇	—	2	1	no	—
34	C₈×C₂²⋊D₆₇	—	2	1	no	—
35	#16863449	C₂²	1	1	yes	characteristic
36	#16863447	—	2	1	no	—
37	C₄×C₈×D₆₇	—	2	1	no	—
38	#16863143	C₂²	1	2	yes	—
39	#16863143	C₂²	1	2	yes	—
40	#16863141	C₂²	1	2	yes	—
41	#16863141	C₂²	1	2	yes	—
42	#431×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
44	#335×C₆₇	C₂²	1	1	yes	characteristic
45	#335×C₆₇	C₂²	1	1	yes	characteristic
46	#334×C₆₇	C₂²	1	2	yes	—
47	C₂×#11761628	D₄	1	1	yes	characteristic
48	C₂×Dic₂₆₈	—	2	2	no	—
49	C₂×Dic₂₆₈	—	2	1	no	—
50	C₂×Dic₂₆₈	—	2	1	no	—
51	C₂×#11761617	—	2	2	no	—
52	C₂×C₈×D₆₇	—	2	1	no	—
53	C₂×C₈×D₆₇	—	2	1	no	—
54	#14524043	C₂³	1	2	yes	—
55	#14524043	C₂³	1	2	yes	—
56	#14524035	—	2	2	no	—
57	#14524022	—	2	2	no	—
58	#14524022	—	2	2	no	—
59	C₄×Dic₁₃₄	—	2	2	no	—
60	C₄×Dic₁₃₄	—	2	2	no	—
61	C₄×Dic₁₃₄	D₄	1	1	yes	characteristic
62	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
63	C₄×D₂₆₈	D₄	1	1	yes	characteristic
64	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
65	C₄×C₂²⋊D₆₇	—	2	1	no	—
66	C₄×C₂²⋊D₆₇	—	2	1	no	—
67	#14524002	—	2	2	no	—
68	#14524002	D₄	1	1	yes	characteristic
69	#14524000	—	2	1	no	—
70	C₄²×D₆₇	—	2	1	no	—
71	#14523977	—	2	2	no	—
72	#14523977	—	2	1	no	—
73	#14523977	—	2	1	no	—
74	#14523975	—	2	2	no	—
75	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
77	Dic₆₇⋊C₈	—	2	1	no	—
78	Dic₆₇⋊C₈	—	2	1	no	—
79	#14523968	—	2	2	no	—
80	#14523968	—	2	2	no	—
81	#14523968	—	2	2	no	—
82	#14523968	—	2	2	no	—
83	#14523968	—	2	2	no	—
84	#14523965	—	2	2	no	—
85	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
86	(C₂×D₆₇)⋊C₈	—	2	1	no	—
87	(C₂×D₆₇)⋊C₈	—	2	1	no	—
88	C₄×C₆₇⋊C₈	—	2	1	no	—
89	C₈×Dic₆₇	—	2	1	no	—
90	C₈×Dic₆₇	—	2	1	no	—
91	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
95	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
96	C₂²⋊C₈×C₆₇	—	2	2	no	—
97	C₄×C₈×C₆₇	—	2	2	no	—
98	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
99	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
102	#11761628	—	2	2	no	—
103	#11761628	—	2	2	no	—
104	C₂×Dic₁₃₄	—	2	2	no	—
105	C₂×Dic₁₃₄	—	2	2	no	—
106	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
107	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
108	C₂×C₂²⋊D₆₇	—	2	1	no	—
109	C₂×C₄×D₆₇	—	2	1	no	—
110	C₂×C₄×D₆₇	—	2	1	no	—
111	C₂×C₄×D₆₇	—	2	1	no	—
112	Dic₂₆₈	—	4	2	no	—
113	Dic₂₆₈	—	4	4	no	—
114	Dic₂₆₈	—	4	2	no	—
115	#11761617	—	4	4	no	—
116	C₂×C₆₇⋊C₈	—	2	1	no	—
117	C₂×C₆₇⋊C₈	—	2	1	no	—
118	C₈×D₆₇	—	4	2	no	—
119	C₈×D₆₇	—	4	2	no	—
120	C₄⋊Dic₆₇	—	2	2	no	—
121	C₄⋊Dic₆₇	—	2	2	no	—
122	C₄⋊Dic₆₇	—	2	2	no	—
123	C₄⋊Dic₆₇	—	2	2	no	—
124	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
125	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
126	Dic₆₇⋊C₄	—	2	1	no	—
127	Dic₆₇⋊C₄	—	2	1	no	—
128	Dic₆₇⋊C₄	—	4	2	no	—
129	Dic₆₇⋊C₄	—	4	2	no	—
130	C₂²⋊Dic₆₇	—	2	1	no	—
131	C₂²⋊Dic₆₇	—	4	2	no	—
132	(C₂×D₆₇)⋊C₄	—	2	1	no	—
133	(C₂×D₆₇)⋊C₄	—	2	1	no	—
134	C₄×Dic₆₇	—	2	1	no	—
135	C₄×Dic₆₇	—	2	1	no	—
136	C₄×Dic₆₇	—	2	1	no	—
137	C₄×Dic₆₇	—	4	2	no	—
138	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
141	C₂×C₈×C₆₇	—	2	2	no	—
142	C₂×C₈×C₆₇	—	2	2	no	—
143	C₂×C₈×C₆₇	—	2	2	no	—
144	C₂×C₈×C₆₇	—	4	1	no	—
145	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₆₇	#41	1	1	yes	characteristic
152	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
153	C₂³×C₆₇	#121	1	1	yes	characteristic
154	C₂²×D₆₇	—	2	1	no	—
155	C₂×C₄×C₆₇	—	2	1	no	—
156	C₂×C₄×C₆₇	—	2	1	no	—
157	C₂×C₄×C₆₇	—	2	1	no	—
158	C₂×C₄×C₆₇	—	2	1	no	—
159	C₂×C₄×C₆₇	—	2	2	no	—
160	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
166	C₂²⋊D₆₇	—	2	4	no	—
167	C₂×Dic₆₇	—	2	1	no	—
168	C₂×Dic₆₇	—	2	1	no	—
169	C₂×Dic₆₇	—	2	1	no	—
170	C₂×Dic₆₇	—	4	2	no	—
171	C₂×Dic₆₇	—	4	2	no	—
172	D₂₆₈	—	2	1	no	—
173	D₂₆₈	#135	1	2	yes	—
174	C₄×D₆₇	—	2	4	no	—
175	C₄×D₆₇	—	4	1	no	—
176	C₄×D₆₇	—	4	1	no	—
177	C₄×D₆₇	—	4	2	no	—
178	Dic₁₃₄	—	2	1	no	—
179	Dic₁₃₄	—	4	2	no	—
180	Dic₁₃₄	—	4	2	no	—
181	Dic₁₃₄	—	4	2	no	—
182	Dic₁₃₄	—	4	2	no	—
183	Dic₁₃₄	#135	1	2	yes	—
184	C₈×C₆₇	—	2	1	no	—
185	C₈×C₆₇	—	2	1	no	—
186	C₈×C₆₇	—	2	1	no	—
187	C₈×C₆₇	—	4	2	no	—
188	C₈×C₆₇	—	4	2	no	—
189	C₈×C₆₇	#135	1	2	yes	—
190	C₆₇⋊C₈	—	4	1	no	—
191	C₆₇⋊C₈	—	4	1	no	—
192	C₂²×C₆₇	—	2	1	no	—
193	C₂²×C₆₇	—	2	1	no	—
194	C₂²×C₆₇	—	2	1	no	—
195	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
196	C₂×D₆₇	—	2	2	no	—
197	C₂×D₆₇	—	4	1	no	—
198	C₂×D₆₇	—	4	1	no	—
199	C₄×C₆₇	—	2	1	no	—
200	C₄×C₆₇	—	2	1	no	—
201	C₄×C₆₇	—	2	1	no	—
202	C₄×C₆₇	#473	1	2	yes	—
203	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
204	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
205	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
206	C₄×C₆₇	#575	1	1	yes	characteristic
207	Dic₆₇	—	2	2	no	—
208	Dic₆₇	—	4	1	no	—
209	Dic₆₇	—	4	1	no	—
210	Dic₆₇	—	8	2	no	—
211	Dic₆₇	—	8	2	no	—
212	#19129	—	67	1	no	maximal, Sylow
213	C₂×C₆₇	—	4	1	no	—
214	C₂×C₆₇	#3035	1	1	yes	characteristic
215	C₂×C₆₇	#3050	1	1	yes	characteristic
216	C₂×C₆₇	C₂×#473	1	1	yes	characteristic
217	D₆₇	—	4	2	no	—
218	#3170	—	67	1	no	—
219	#3107	—	67	2	no	—
220	C₈×#41	—	67	1	no	—
221	#1680	—	67	2	no	—
222	#1679	—	67	2	no	—
223	#1674	—	67	1	no	—
224	#1673	—	67	1	no	—
225	#1670	—	67	1	no	—
226	#1669	—	67	1	no	—
227	#1564	D₆₇	1	1	yes	characteristic, complemented
228	#1544	—	67	2	no	—
229	C₆₇	#19129	1	1	yes	characteristic, complemented, Sylow
230	#533	—	67	2	no	—
231	C₄×#41	—	67	1	no	—
232	#500	—	67	1	no	—
233	#494	—	67	1	no	—
234	#487	—	67	2	no	—
235	#485	—	134	2	no	—
236	#475	—	67	2	no	—
237	#474	—	67	2	no	—
238	#467	—	134	1	no	—
239	#467	—	134	1	no	—
240	#462	—	67	2	no	—
241	#461	—	67	2	no	—
242	#452	—	134	2	no	—
243	C₈×Q₈	—	67	1	no	—
244	C₈×Q₈	—	67	1	no	—
245	C₄×Q₁₆	—	134	2	no	—
246	C₄×Q₁₆	—	134	1	no	—
247	C₄×Q₁₆	—	134	1	no	—
248	C₄×SD₁₆	—	134	2	no	—
249	C₈×D₄	—	67	1	no	—
250	C₈×D₄	—	67	1	no	—
251	C₈×D₄	—	134	1	no	—
252	C₈×D₄	—	134	1	no	—
253	#431	—	67	1	no	—
254	#431	—	134	1	no	—
255	#431	C₂×D₆₇	1	2	yes	—
256	C₂×C₄×C₈	—	134	1	no	—
257	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
258	#335	C₂×D₆₇	1	1	yes	characteristic
259	#335	C₂×D₆₇	1	1	yes	characteristic
260	#334	C₂×D₆₇	1	2	yes	—
261	#332	—	67	2	no	—
262	#332	—	67	2	no	—
263	#332	—	67	2	no	—
264	#332	—	67	2	no	—
265	C₂×#41	—	67	1	no	—
266	C₂×Q₁₆	—	134	2	no	—
267	C₂×Q₁₆	—	134	1	no	—
268	C₂×Q₁₆	—	134	1	no	—
269	C₂×SD₁₆	—	134	2	no	—
270	C₂²×C₈	—	134	1	no	—
271	C₂²×C₈	—	134	1	no	—
272	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
273	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
274	C₄⋊Q₈	—	67	2	no	—
275	C₄⋊Q₈	—	67	2	no	—
276	#125	—	134	2	no	—
277	C₂²⋊Q₈	—	134	2	no	—
278	C₂²⋊Q₈	—	134	2	no	—
279	C₄×Q₈	—	67	1	no	—
280	C₄×Q₈	—	67	1	no	—
281	C₄×Q₈	—	134	2	no	—
282	C₄×Q₈	—	134	2	no	—
283	C₄×D₄	—	67	1	no	—
284	C₄×D₄	—	67	1	no	—
285	C₄×D₄	—	134	1	no	—
286	C₄×D₄	—	134	1	no	—
287	#117	—	67	1	no	—
288	#117	—	134	2	no	—
289	#117	—	134	1	no	—
290	C₂×C₄²	—	134	1	no	—
291	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
292	#107	—	134	2	no	—
293	#107	—	134	1	no	—
294	#107	—	134	1	no	—
295	#106	—	134	2	no	—
296	C₄⋊C₈	—	67	1	no	—
297	C₄⋊C₈	—	67	1	no	—
298	C₄⋊C₈	—	134	1	no	—
299	C₄⋊C₈	—	134	1	no	—
300	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
301	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
302	#103	—	134	2	no	—
303	#103	—	134	2	no	—
304	#103	—	134	2	no	—
305	#103	—	134	2	no	—
306	#103	—	134	2	no	—
307	#102	—	134	2	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	134	1	no	—
310	C₂²⋊C₈	—	134	1	no	—
311	C₂²⋊C₈	—	134	1	no	—
312	C₄×C₈	—	2	2	no	—
313	C₄×C₈	—	134	1	no	—
314	C₄×C₈	—	134	1	no	—
315	C₄×C₈	—	134	1	no	—
316	C₄×C₈	D₂₆₈	1	1	yes	characteristic
317	C₄×C₈	D₂₆₈	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
320	#41	—	134	2	no	—
321	#41	—	134	2	no	—
322	C₂×Q₈	—	67	1	no	—
323	C₂×Q₈	—	134	2	no	—
324	C₂×Q₈	—	134	2	no	—
325	C₂×D₄	—	67	1	no	—
326	C₂×D₄	—	134	1	no	—
327	C₂²×C₄	—	134	1	no	—
328	C₂²×C₄	—	134	1	no	—
329	C₂²×C₄	—	134	1	no	—
330	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
332	C₂²×C₄	#11761629	1	1	yes	characteristic
333	Q₁₆	—	268	2	no	—
334	Q₁₆	—	268	4	no	—
335	Q₁₆	—	268	2	no	—
336	SD₁₆	—	268	4	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	268	2	no	—
342	C₂×C₈	—	268	2	no	—
343	C₂×C₈	—	134	1	no	—
344	C₂×C₈	—	134	1	no	—
345	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
346	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
347	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
348	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
349	C₄⋊C₄	—	268	2	no	—
350	C₄⋊C₄	—	268	2	no	—
351	C₄⋊C₄	—	67	1	no	—
352	C₄⋊C₄	—	67	1	no	—
353	C₄⋊C₄	—	134	2	no	—
354	C₄⋊C₄	—	134	2	no	—
355	C₄⋊C₄	—	134	2	no	—
356	C₄⋊C₄	—	134	2	no	—
357	C₄⋊C₄	—	134	1	no	—
358	C₄⋊C₄	—	134	1	no	—
359	C₂²⋊C₄	—	268	2	no	—
360	C₂²⋊C₄	—	134	1	no	—
361	C₂²⋊C₄	—	134	1	no	—
362	C₂²⋊C₄	—	134	1	no	—
363	C₄²	—	268	2	no	—
364	C₄²	—	134	1	no	—
365	C₄²	—	134	1	no	—
366	C₄²	—	134	1	no	—
367	C₄²	D₄×D₆₇	1	1	yes	characteristic
368	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
369	C₄²	#11761629	1	1	yes	characteristic
370	C₄²	C₂³×D₆₇	1	1	yes	characteristic
371	C₂³	—	134	1	no	—
372	C₂³	#14524018	1	1	yes	characteristic
373	Q₈	—	268	2	no	—
374	Q₈	—	268	2	no	—
375	Q₈	—	268	2	no	—
376	Q₈	—	268	2	no	—
377	Q₈	—	67	2	no	—
378	Q₈	—	134	1	no	—
379	D₄	—	67	2	no	—
380	D₄	—	134	4	no	—
381	D₄	—	134	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	268	1	no	—
388	C₂×C₄	—	268	2	no	—
389	C₂×C₄	—	268	1	no	—
390	C₂×C₄	—	268	2	no	—
391	C₂×C₄	—	268	2	no	—
392	C₂×C₄	—	134	4	no	—
393	C₂×C₄	—	134	1	no	—
394	C₂×C₄	—	134	1	no	—
395	C₂×C₄	—	134	1	no	—
396	C₂×C₄	#14524018	1	1	yes	characteristic
397	C₂×C₄	#14524018	1	1	yes	characteristic
398	C₂×C₄	#14524018	1	1	yes	characteristic
399	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
401	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	2	no	—
407	C₈	—	268	1	no	—
408	C₈	—	268	1	no	—
409	C₈	#14524065	1	2	yes	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	268	1	no	—
414	C₂²	—	268	1	no	—
415	C₂²	—	134	2	no	—
416	C₂²	C₂×#14524018	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	268	1	no	—
421	C₄	—	268	1	no	—
422	C₄	—	536	2	no	—
423	C₄	—	536	2	no	—
424	C₄	—	134	2	no	—
425	C₄	#16863672	1	2	yes	—
426	C₄	#135×D₆₇	1	1	yes	characteristic
427	C₄	#135×D₆₇	1	1	yes	characteristic
428	C₄	C₂×#14524065	1	1	yes	characteristic
429	C₄	#16864196	1	1	yes	characteristic
430	C₂	—	4	1	no	—
431	C₂	—	268	2	no	—
432	C₂	#22569666	1	1	yes	characteristic
433	C₂	#22569791	1	1	yes	characteristic
434	C₂	C₂×#16863672	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524018
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#1564	C₂
socle	C₂²×C₆₇	C₂×#121
prime radical	C₂×#11761628	D₄
hypercenter	#1564	D₆₇
hypocenter	C₆₇	#19129
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
1. #22570795	C₂	semidirect
4. #22559640	C₂	semidirect
5. #22559633	C₂	semidirect
6. #22559604	C₂	semidirect
7. #22559599	C₂	semidirect
8. #22559580	C₂	semidirect
9. #22559575	C₂	semidirect
10. #22558873	C₂	semidirect
11. C₆₇×#1564	C₂	semidirect
227. #1564	D₆₇	semidirect
229. C₆₇	#19129	semidirect

Maximal subgroups

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

subgroup	index
#22570795	2
#22570281	2
C₈×#11761628	2
#22559640	2
#22559633	2
#22559604	2
#22559599	2
#22559580	2
#22559575	2
#22558873	2
C₆₇×#1564	2
#19129	67