Subgroups — #30875544

Order 17152.

710 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22568875	C₂	1	2	yes	maximal, complemented
2	#22561103	C₂	1	1	yes	maximal, characteristic
3	#22561098	C₂	1	1	yes	maximal, characteristic
4	#22560859	C₂	1	2	yes	maximal, complemented
5	#22560859	C₂	1	2	yes	maximal, complemented
6	#22560384	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560229	C₂	1	2	yes	maximal, complemented
8	#22560095	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560090	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560081	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2943	C₂	1	1	yes	maximal, characteristic
12	#16863457	—	2	2	no	—
13	#16863457	—	2	2	no	—
14	#16863453	—	2	2	no	—
15	#16863449	—	2	2	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	#16863420	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#14523970	C₂²	1	2	yes	—
22	C₂×#14523970	C₂²	1	2	yes	—
23	#16863363	C₂²	1	2	yes	—
24	#16863363	C₂²	1	2	yes	—
25	#16863352	C₂²	1	2	yes	—
26	#16863352	C₂²	1	2	yes	—
27	C₂×#14523953	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
30	#16863155	C₂²	1	2	yes	—
31	#16863155	C₂²	1	2	yes	—
32	#16863150	C₂²	1	1	yes	characteristic
33	#16863150	C₂²	1	1	yes	characteristic
34	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
35	C₄×#41×C₆₇	C₂²	1	2	yes	—
36	#442×C₆₇	C₄	1	2	yes	complemented
37	#441×C₆₇	C₄	1	2	yes	complemented
38	#440×C₆₇	C₄	1	2	yes	complemented
39	#440×C₆₇	C₄	1	2	yes	complemented
40	#427×C₆₇	C₂²	1	1	yes	characteristic
41	#416×C₆₇	C₂²	1	2	yes	—
42	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#11761612	C₂³	1	2	yes	—
44	C₂×#11761612	C₂³	1	2	yes	—
45	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂×C₄⋊Dic₆₇	—	2	1	no	—
48	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
49	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
50	#14523979	—	2	2	no	—
51	#14523979	—	2	2	no	—
52	#14523979	—	4	2	no	—
53	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
54	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
55	C₄⋊(C₆₇⋊C₈)	D₄	1	2	yes	—
56	C₄⋊(C₆₇⋊C₈)	D₄	1	2	yes	—
57	#14523970	—	4	2	no	—
58	#14523970	—	4	2	no	—
59	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
60	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
62	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
63	#14523954	—	2	2	no	—
64	#14523954	—	2	2	no	—
65	#14523953	—	2	2	no	—
66	C₄×C₆₇⋊C₈	—	2	2	no	—
67	C₄×C₆₇⋊C₈	—	2	2	no	—
68	C₈×Dic₆₇	—	2	2	no	—
69	C₆₇⋊#95	—	2	1	no	—
70	C₂×#41×C₆₇	C₂³	1	2	yes	—
71	#135×C₆₇	—	2	2	no	—
72	#135×C₆₇	—	2	2	no	—
73	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
75	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
78	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
79	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
80	C₄×D₄×C₆₇	—	2	2	no	—
81	C₄×D₄×C₆₇	—	2	2	no	—
82	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
83	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
84	#117×C₆₇	—	2	2	no	—
85	#117×C₆₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₆₇	—	2	2	no	—
87	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
88	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
89	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
90	#106×C₆₇	C₂×C₄	1	2	yes	—
91	#103×C₆₇	C₂×C₄	1	2	yes	—
92	#103×C₆₇	C₂×C₄	1	2	yes	—
93	#102×C₆₇	C₂×C₄	1	2	yes	—
94	#102×C₆₇	C₂×C₄	1	2	yes	—
95	#97×C₆₇	C₂×C₄	1	2	yes	—
96	#97×C₆₇	C₂×C₄	1	2	yes	—
97	C₂²×Dic₆₇	—	2	1	no	—
98	C₂²×Dic₆₇	—	2	1	no	—
99	#11761612	—	2	2	no	—
100	#11761612	—	2	2	no	—
101	#11761612	—	2	2	no	—
102	#11761612	—	2	2	no	—
103	C₂×C₆₇⋊C₈	—	2	1	no	—
104	C₂×C₆₇⋊C₈	—	2	1	no	—
105	C₂×C₆₇⋊C₈	—	2	1	no	—
106	C₂×C₆₇⋊C₈	—	2	1	no	—
107	C₂×C₆₇⋊C₈	—	2	2	no	—
108	C₂×C₆₇⋊C₈	—	2	2	no	—
109	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
110	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
111	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
112	C₄⋊Dic₆₇	—	4	2	no	—
113	C₄×Dic₆₇	—	2	1	no	—
114	C₄×Dic₆₇	—	2	1	no	—
115	C₄×Dic₆₇	—	2	1	no	—
116	C₄×Dic₆₇	—	2	1	no	—
117	#41×C₆₇	—	2	2	no	—
118	#41×C₆₇	—	2	2	no	—
119	#41×C₆₇	—	2	2	no	—
120	#41×C₆₇	—	2	2	no	—
121	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
122	C₂×D₄×C₆₇	—	2	2	no	—
123	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₆₇	—	2	2	no	—
125	C₂²×C₄×C₆₇	—	2	2	no	—
126	C₂²×C₄×C₆₇	—	2	2	no	—
127	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
128	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
129	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
130	Q₁₆×C₆₇	—	2	2	no	—
131	SD₁₆×C₆₇	—	2	4	no	—
132	D₈×C₆₇	—	2	2	no	—
133	C₂×C₈×C₆₇	—	2	1	no	—
134	C₂×C₈×C₆₇	—	2	1	no	—
135	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₆₇	#41	1	2	yes	—
139	C₂×C₈×C₆₇	#41	1	2	yes	—
140	C₄⋊C₄×C₆₇	—	2	2	no	—
141	C₄⋊C₄×C₆₇	—	2	2	no	—
142	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
143	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
144	C₂²⋊C₄×C₆₇	—	2	2	no	—
145	C₂²⋊C₄×C₆₇	—	2	2	no	—
146	C₂²⋊C₄×C₆₇	—	2	2	no	—
147	C₄²×C₆₇	—	2	2	no	—
148	C₄²×C₆₇	—	2	2	no	—
149	C₄²×C₆₇	—	2	2	no	—
150	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
151	C₄²×C₆₇	C₂×D₄	1	2	yes	—
152	C₂³×C₆₇	—	2	2	no	—
153	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
154	Q₈×C₆₇	—	2	2	no	—
155	Q₈×C₆₇	—	2	2	no	—
156	D₄×C₆₇	—	2	2	no	—
157	D₄×C₆₇	—	2	2	no	—
158	D₄×C₆₇	—	4	2	no	—
159	D₄×C₆₇	—	4	2	no	—
160	C₂×C₄×C₆₇	—	2	2	no	—
161	C₂×C₄×C₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	—	4	1	no	—
164	C₂×C₄×C₆₇	—	4	1	no	—
165	C₂×C₄×C₆₇	—	4	4	no	—
166	C₂×C₄×C₆₇	—	4	2	no	—
167	C₂×C₄×C₆₇	—	4	2	no	—
168	C₂×C₄×C₆₇	—	8	2	no	—
169	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
177	C₂×Dic₆₇	—	2	2	no	—
178	C₂×Dic₆₇	—	4	1	no	—
179	C₂×Dic₆₇	—	4	1	no	—
180	C₂×Dic₆₇	—	4	1	no	—
181	C₂×Dic₆₇	—	4	1	no	—
182	C₂×Dic₆₇	—	4	1	no	—
183	C₈×C₆₇	—	2	2	no	—
184	C₈×C₆₇	#117	1	2	yes	—
185	C₈×C₆₇	#117	1	2	yes	—
186	C₆₇⋊C₈	—	2	1	no	—
187	C₆₇⋊C₈	—	2	1	no	—
188	C₆₇⋊C₈	—	2	2	no	—
189	C₆₇⋊C₈	—	4	2	no	—
190	C₆₇⋊C₈	—	4	2	no	—
191	C₂²×C₆₇	—	2	1	no	—
192	C₂²×C₆₇	—	2	1	no	—
193	C₂²×C₆₇	—	4	2	no	—
194	C₂²×C₆₇	—	4	2	no	—
195	C₂²×C₆₇	—	4	2	no	—
196	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂²×C₆₇	#555	1	1	yes	characteristic
198	C₂²×C₆₇	#556	1	1	yes	characteristic
199	C₄×C₆₇	—	2	2	no	—
200	C₄×C₆₇	—	2	2	no	—
201	C₄×C₆₇	—	4	2	no	—
202	C₄×C₆₇	—	4	2	no	—
203	C₄×C₆₇	—	4	2	no	—
204	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
205	C₄×C₆₇	#520	1	1	yes	characteristic
206	C₄×C₆₇	#547	1	1	yes	characteristic
207	C₄×C₆₇	#550	1	1	yes	characteristic
208	Dic₆₇	—	4	2	no	—
209	Dic₆₇	—	8	1	no	—
210	#22804	—	67	1	no	maximal, Sylow
211	C₂×C₆₇	—	2	1	no	—
212	C₂×C₆₇	—	2	1	no	—
213	C₂×C₆₇	—	8	2	no	—
214	C₂×C₆₇	#2354	1	1	yes	characteristic
215	C₂×C₆₇	#2955	1	1	yes	characteristic
216	C₂×C₆₇	#2956	1	1	yes	characteristic
217	#2943	D₆₇	1	1	yes	characteristic
218	#2925	—	67	2	no	—
219	#1975	—	67	1	no	—
220	#1974	—	67	1	no	—
221	#1929	—	67	2	no	—
222	#1929	—	67	2	no	—
223	#1849	—	67	1	no	—
224	#1806	—	67	2	no	—
225	#1773	—	67	1	no	—
226	#1772	—	67	1	no	—
227	#1771	—	67	1	no	—
228	C₆₇	#22804	1	1	yes	characteristic, complemented, Sylow
229	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
230	C₄×#41	C₂×D₆₇	1	2	yes	—
231	#442	Dic₆₇	1	2	yes	complemented
232	#441	Dic₆₇	1	2	yes	complemented
233	#440	Dic₆₇	1	2	yes	complemented
234	#440	Dic₆₇	1	2	yes	complemented
235	#433	—	134	2	no	—
236	#433	—	134	2	no	—
237	#432	—	134	2	no	—
238	#431	—	134	2	no	—
239	C₂×#108	—	67	2	no	—
240	C₂×#108	—	67	1	no	—
241	C₂×#108	—	67	1	no	—
242	#427	C₂×D₆₇	1	1	yes	characteristic
243	#423	—	67	2	no	—
244	C₂×C₄⋊C₈	—	67	1	no	—
245	C₂×#104	—	67	2	no	—
246	C₂×#104	—	67	2	no	—
247	#416	C₂×D₆₇	1	2	yes	—
248	#408	—	67	2	no	—
249	#408	—	67	2	no	—
250	#405	—	67	2	no	—
251	#405	—	67	2	no	—
252	C₂×#97	—	67	1	no	—
253	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
254	C₂×C₄×C₈	—	67	1	no	—
255	C₄×C₄⋊C₄	—	67	1	no	—
256	#339	—	67	2	no	—
257	#339	—	67	2	no	—
258	#336	—	67	1	no	—
259	#336	—	67	1	no	—
260	C₂×#41	C₂²×D₆₇	1	2	yes	—
261	#135	—	2	2	no	—
262	#135	—	2	2	no	—
263	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic
264	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	—
265	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
266	C₂×M₁₆	—	67	2	no	—
267	C₂×M₁₆	—	67	2	no	—
268	C₂²×C₈	—	67	1	no	—
269	C₂²×C₈	—	67	1	no	—
270	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
271	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
272	C₄×Q₈	C₂×Dic₆₇	1	2	yes	—
273	C₄×Q₈	C₂×Dic₆₇	1	2	yes	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
277	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
278	#117	—	2	2	no	—
279	#117	C₂²×D₆₇	1	2	yes	—
280	C₂×C₄⋊C₄	—	134	1	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	—	67	1	no	—
283	C₂×C₄²	—	67	1	no	—
284	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
285	#108	—	268	2	no	—
286	#108	—	134	2	no	—
287	#108	—	134	2	no	—
288	#107	C₂×Dic₆₇	1	1	yes	characteristic
289	#107	C₂×Dic₆₇	1	1	yes	characteristic
290	#106	C₂×Dic₆₇	1	2	yes	—
291	C₄⋊C₈	—	67	2	no	—
292	C₄⋊C₈	—	67	2	no	—
293	C₄⋊C₈	—	134	2	no	—
294	C₄⋊C₈	—	134	2	no	—
295	#104	—	268	2	no	—
296	#104	—	268	2	no	—
297	#103	C₂×Dic₆₇	1	2	yes	—
298	#103	C₂×Dic₆₇	1	2	yes	—
299	#102	C₂×Dic₆₇	1	2	yes	—
300	#102	C₂×Dic₆₇	1	2	yes	—
301	C₂²⋊C₈	—	134	2	no	—
302	C₂²⋊C₈	—	134	2	no	—
303	C₂²⋊C₈	—	134	2	no	—
304	C₂²⋊C₈	—	134	2	no	—
305	#97	—	134	2	no	—
306	#97	—	134	2	no	—
307	#97	—	134	2	no	—
308	#97	C₂×Dic₆₇	1	2	yes	—
309	#97	C₂×Dic₆₇	1	2	yes	—
310	C₄×C₈	—	134	2	no	—
311	C₄×C₈	—	134	2	no	—
312	C₄×C₈	—	134	2	no	—
313	#95	—	134	1	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	134	1	no	—
325	C₂²×C₄	—	134	1	no	—
326	C₂²×C₄	#11761627	1	1	yes	characteristic
327	C₂²×C₄	#11761627	1	1	yes	characteristic
328	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
329	Q₁₆	—	2	2	no	—
330	SD₁₆	—	2	4	no	—
331	D₈	—	2	2	no	—
332	M₁₆	—	134	2	no	—
333	M₁₆	—	134	2	no	—
334	M₁₆	—	134	2	no	—
335	M₁₆	—	134	2	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	67	1	no	—
339	C₂×C₈	—	67	2	no	—
340	C₂×C₈	—	67	1	no	—
341	C₂×C₈	—	134	2	no	—
342	C₂×C₈	—	134	2	no	—
343	C₂×C₈	—	134	1	no	—
344	C₂×C₈	—	134	1	no	—
345	C₂×C₈	—	134	1	no	—
346	C₂×C₈	—	134	1	no	—
347	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
348	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
349	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
350	C₂×C₈	#11761628	1	2	yes	—
351	C₂×C₈	#11761628	1	2	yes	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	268	2	no	—
355	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
356	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	134	1	no	—
364	C₄²	—	134	1	no	—
365	C₄²	—	134	1	no	—
366	C₄²	—	134	1	no	—
367	C₄²	C₂²×Dic₆₇	1	2	yes	—
368	C₄²	D₄×D₆₇	1	2	yes	—
369	C₂³	—	2	2	no	—
370	C₂³	C₂×#11761627	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	268	1	no	—
387	C₂×C₄	—	268	1	no	—
388	C₂×C₄	—	268	1	no	—
389	C₂×C₄	—	268	1	no	—
390	C₂×C₄	—	268	1	no	—
391	C₂×C₄	—	134	2	no	—
392	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
393	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
394	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
395	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
396	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
397	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
398	C₂×C₄	#14524089	1	1	yes	characteristic
399	C₂×C₄	#14524090	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	268	2	no	—
402	C₈	—	268	2	no	—
403	C₈	—	134	1	no	—
404	C₈	—	134	2	no	—
405	C₈	—	134	1	no	—
406	C₈	#14524002	1	2	yes	—
407	C₈	#14524002	1	2	yes	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
414	C₂²	#16864111	1	1	yes	characteristic
415	C₂²	#16864116	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	268	2	no	—
422	C₄	—	536	1	no	—
423	C₄	C₂×#14524002	1	1	yes	characteristic
424	C₄	#16863879	1	1	yes	characteristic
425	C₄	#16864051	1	1	yes	characteristic
426	C₄	#16864067	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	8	2	no	—
430	C₂	#22563158	1	1	yes	characteristic
431	C₂	#22569112	1	1	yes	characteristic
432	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	#22804
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
1. #22568875	C₂	semidirect
4. #22560859	C₂	semidirect
5. #22560859	C₂	semidirect
6. #22560384	C₂	semidirect
7. #22560229	C₂	semidirect
8. #22560095	C₂	semidirect
9. #22560090	C₂	semidirect
10. #22560081	C₂	semidirect
36. #442×C₆₇	C₄	semidirect
37. #441×C₆₇	C₄	semidirect
38. #440×C₆₇	C₄	semidirect
39. #440×C₆₇	C₄	semidirect
228. C₆₇	#22804	semidirect
231. #442	Dic₆₇	semidirect
232. #441	Dic₆₇	semidirect
233. #440	Dic₆₇	semidirect
234. #440	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22568875	2
#22561103	2
#22561098	2
#22560859	2
#22560384	2
#22560229	2
#22560095	2
#22560090	2
#22560081	2
C₆₇×#2943	2
#22804	67