Subgroups — #30874329

Order 17152.

862 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×#16863512	C₂	1	1	yes	maximal, characteristic
2	#22569086	C₂	1	1	yes	maximal, characteristic
3	#22569083	C₂	1	1	yes	maximal, characteristic
4	#22568808	C₂	1	2	yes	maximal, complemented
5	#22560995	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560438	C₂	1	2	yes	maximal, complemented
7	#22560432	C₂	1	2	yes	maximal, complemented
8	#22560367	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560272	C₂	1	2	yes	maximal, complemented
10	#22560089	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1952	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524065	C₂²	1	1	yes	characteristic
13	C₂×#14524051	C₂²	1	2	yes	—
14	#16863877	C₂²	1	2	yes	—
15	#16863876	C₂²	1	2	yes	—
16	#16863512	C₄	1	8	yes	complemented
17	#16863498	—	2	2	no	—
18	#16863495	—	2	2	no	—
19	C₄×Dic₂₆₈	—	2	1	no	—
20	#16863490	—	2	1	no	—
21	C₄×D₅₃₆	—	2	1	no	—
22	#16863478	—	2	1	no	—
23	C₂×#14523978	C₂²	1	1	yes	characteristic
24	#16863438	C₂²	1	2	yes	—
25	#16863437	—	2	2	no	—
26	#16863435	—	2	2	no	—
27	#16863432	C₂²	1	1	yes	characteristic
28	#16863431	—	2	2	no	—
29	C₂×#14523977	C₂²	1	1	yes	characteristic
30	C₂×#14523976	C₂²	1	2	yes	—
31	#107×D₆₇	—	2	2	no	—
32	C₂×#14523969	C₂²	1	2	yes	—
33	#16863398	C₂²	1	2	yes	—
34	#16863395	C₂²	1	2	yes	—
35	#16863351	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
37	#16863265	C₂²	1	2	yes	—
38	#16863164	C₂²	1	2	yes	—
39	#16863157	C₂²	1	1	yes	characteristic
40	#16863155	C₂²	1	1	yes	characteristic
41	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
42	#428×C₆₇	C₂²	1	2	yes	—
43	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
44	#405×C₆₇	C₂²	1	1	yes	characteristic
45	#343×C₆₇	C₂²	1	2	yes	—
46	C₂×#11761628	C₂³	1	2	yes	—
47	#14524065	C₂×C₄	1	4	yes	—
48	#14524065	Q₈	1	4	yes	—
49	C₂×Dic₂₆₈	D₄	1	1	yes	characteristic
50	C₂×#11761617	D₄	1	2	yes	—
51	C₂×D₅₃₆	D₄	1	1	yes	characteristic
52	#14524051	—	2	4	no	—
53	#14524051	C₂×C₄	1	8	yes	complemented
54	C₂×#11761612	C₂³	1	1	yes	characteristic
55	C₂×#11761611	—	2	2	no	—
56	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₆₇	—	2	2	no	—
58	C₄×Dic₁₃₄	—	2	2	no	—
59	#14524008	—	2	2	no	—
60	C₄×D₂₆₈	—	2	2	no	—
61	#14524005	—	2	2	no	—
62	C₄×C₂²⋊D₆₇	—	4	2	no	—
63	(C₂²⋊D₆₇)⋊C₄	—	4	2	no	—
64	#14524002	C₂³	1	1	yes	characteristic
65	#14524001	—	2	2	no	—
66	#14524001	—	2	2	no	—
67	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
68	C₂×Dic₆₇⋊C₄	—	4	2	no	—
69	C₄⋊C₄×D₆₇	—	2	2	no	—
70	C₄⋊C₄×D₆₇	—	2	2	no	—
71	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
72	#14523978	—	2	2	no	—
73	#14523977	—	2	2	no	—
74	#14523977	—	2	1	no	—
75	#14523977	—	2	1	no	—
76	#14523976	—	2	2	no	—
77	#14523976	—	2	2	no	—
78	#14523976	D₄	1	1	yes	characteristic
79	#14523976	D₄	1	1	yes	characteristic
80	#14523975	—	2	2	no	—
81	#14523974	D₄	1	1	yes	characteristic
82	#14523974	D₄	1	1	yes	characteristic
83	#14523969	C₂×C₄	1	8	yes	complemented
84	#14523968	—	2	2	no	—
85	#14523966	—	2	2	no	—
86	#14523965	—	2	2	no	—
87	#14523963	—	2	2	no	—
88	#14523953	—	2	1	no	—
89	C₈×Dic₆₇	—	2	1	no	—
90	C₈×Dic₆₇	C₂×C₄	1	4	yes	complemented
91	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
93	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	#117×C₆₇	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
96	#108×C₆₇	C₂×C₄	1	4	yes	complemented
97	#107×C₆₇	—	2	1	no	—
98	#107×C₆₇	—	2	1	no	—
99	#107×C₆₇	—	2	2	no	—
100	#106×C₆₇	—	2	2	no	—
101	#97×C₆₇	—	2	1	no	—
102	C₄×C₈×C₆₇	—	2	1	no	—
103	#11761628	—	2	2	no	—
104	#11761628	—	2	2	no	—
105	#11761628	C₂²×C₄	1	4	yes	—
106	#11761628	C₂×Q₈	1	4	yes	—
107	C₂×Dic₁₃₄	C₂×D₄	1	2	yes	—
108	C₂×D₂₆₈	C₂×D₄	1	2	yes	—
109	C₂×C₂²⋊D₆₇	—	2	2	no	—
110	C₂²×Dic₆₇	—	2	1	no	—
111	C₂²×Dic₆₇	—	2	2	no	—
112	C₂×C₄×D₆₇	—	2	2	no	—
113	C₂×C₄×D₆₇	—	4	2	no	—
114	C₂×C₄×D₆₇	—	4	2	no	—
115	Dic₂₆₈	C₄⋊C₄	1	4	yes	complemented
116	#11761617	C₄⋊C₄	1	8	yes	complemented
117	D₅₃₆	C₄⋊C₄	1	4	yes	complemented
118	#11761612	—	2	1	no	—
119	#11761612	—	2	1	no	—
120	#11761611	—	2	8	no	—
121	C₂×C₆₇⋊C₈	—	2	1	no	—
122	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
123	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
124	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
125	C₂×C₆₇⋊C₈	#41	1	2	yes	—
126	C₈×D₆₇	—	2	8	no	—
127	C₄⋊Dic₆₇	—	2	2	no	—
128	C₄⋊Dic₆₇	—	2	2	no	—
129	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
130	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
131	Dic₆₇⋊C₄	—	4	2	no	—
132	Dic₆₇⋊C₄	—	4	2	no	—
133	Dic₆₇⋊C₄	—	8	4	no	—
134	C₂²⋊Dic₆₇	—	2	1	no	—
135	(C₂×D₆₇)⋊C₄	—	4	2	no	—
136	(C₂×D₆₇)⋊C₄	—	4	2	no	—
137	C₄×Dic₆₇	—	2	1	no	—
138	C₄×Dic₆₇	—	2	1	no	—
139	C₄×Dic₆₇	—	4	2	no	—
140	C₄×Dic₆₇	—	4	2	no	—
141	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₆₇	—	2	2	no	—
143	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
144	M₁₆×C₆₇	—	2	2	no	—
145	M₁₆×C₆₇	—	2	1	no	—
146	M₁₆×C₆₇	—	2	1	no	—
147	M₁₆×C₆₇	C₂²×C₄	1	4	yes	—
148	C₂×C₈×C₆₇	—	2	2	no	—
149	C₂×C₈×C₆₇	—	2	1	no	—
150	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₆₇	C₂×Q₈	1	2	yes	—
154	C₄⋊C₄×C₆₇	—	2	2	no	—
155	C₄⋊C₄×C₆₇	—	2	2	no	—
156	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
157	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
158	C₂²⋊C₄×C₆₇	—	2	1	no	—
159	C₄²×C₆₇	—	2	1	no	—
160	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	2	1	no	—
163	C₂×C₄×C₆₇	—	2	1	no	—
164	C₂×C₄×C₆₇	—	4	2	no	—
165	C₂×C₄×C₆₇	—	8	2	no	—
166	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂²⋊D₆₇	—	2	4	no	—
173	C₂²⋊D₆₇	—	2	4	no	—
174	C₂×Dic₆₇	—	2	2	no	—
175	C₂×Dic₆₇	—	2	2	no	—
176	C₂×Dic₆₇	—	2	2	no	—
177	C₂×Dic₆₇	—	2	2	no	—
178	C₂×Dic₆₇	—	2	1	no	—
179	C₂×Dic₆₇	—	2	1	no	—
180	C₂×Dic₆₇	—	4	2	no	—
181	C₂×Dic₆₇	—	8	2	no	—
182	D₂₆₈	—	2	2	no	—
183	D₂₆₈	C₂×C₄⋊C₄	1	4	yes	—
184	C₄×D₆₇	—	2	4	no	—
185	C₄×D₆₇	—	2	4	no	—
186	C₄×D₆₇	—	16	2	no	—
187	C₄×D₆₇	—	16	2	no	—
188	Dic₁₃₄	—	2	2	no	—
189	Dic₁₃₄	C₂×C₄⋊C₄	1	4	yes	—
190	C₈×C₆₇	—	2	4	no	—
191	C₈×C₆₇	—	4	1	no	—
192	C₈×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
193	C₈×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
194	C₆₇⋊C₈	—	4	1	no	—
195	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
196	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
197	C₂²×C₆₇	—	2	1	no	—
198	C₂²×C₆₇	—	2	1	no	—
199	C₂²×C₆₇	#520	1	1	yes	characteristic
200	C₂²×C₆₇	D₄²	1	1	yes	characteristic
201	C₂²×C₆₇	#554	1	1	yes	characteristic
202	C₂×D₆₇	—	2	4	no	—
203	C₂×D₆₇	—	4	2	no	—
204	C₂×D₆₇	—	4	2	no	—
205	C₄×C₆₇	—	4	1	no	—
206	C₄×C₆₇	—	4	1	no	—
207	C₄×C₆₇	—	8	2	no	—
208	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
209	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
210	C₄×C₆₇	#547	1	1	yes	characteristic
211	C₄×C₆₇	D₄×Q₈	1	1	yes	characteristic
212	Dic₆₇	—	2	4	no	—
213	Dic₆₇	—	2	4	no	—
214	Dic₆₇	—	4	1	no	—
215	Dic₆₇	—	4	1	no	—
216	Dic₆₇	—	8	2	no	—
217	#22692	—	67	1	no	maximal, Sylow
218	C₂×C₆₇	—	2	1	no	—
219	C₂×C₆₇	—	2	1	no	—
220	C₂×C₆₇	D₄×C₄⋊C₄	1	1	yes	characteristic
221	C₂×C₆₇	#3292	1	1	yes	characteristic
222	C₂×C₆₇	#3293	1	1	yes	characteristic
223	D₆₇	—	4	4	no	—
224	C₂×#443	—	67	1	no	—
225	#2951	—	67	1	no	—
226	#2951	—	67	1	no	—
227	#2913	—	67	2	no	—
228	#1952	—	67	1	no	—
229	#1952	D₆₇	1	1	yes	characteristic, complemented
230	#1859	—	67	2	no	—
231	#1859	—	67	2	no	—
232	#1845	—	67	1	no	—
233	#1816	—	67	2	no	—
234	#1772	—	67	1	no	—
235	C₆₇	#22692	1	1	yes	characteristic, complemented, Sylow
236	C₂×#135	—	67	1	no	—
237	C₂×#131	—	67	2	no	—
238	#520	—	67	2	no	—
239	#520	—	67	2	no	—
240	#443	—	67	8	no	—
241	#440	—	134	2	no	—
242	#440	—	134	2	no	—
243	C₄×Q₁₆	—	134	1	no	—
244	C₄×Q₁₆	—	134	1	no	—
245	C₄×D₈	—	134	1	no	—
246	C₄×D₈	—	134	1	no	—
247	C₂×#108	—	67	1	no	—
248	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
249	#428	—	67	2	no	—
250	#428	—	134	2	no	—
251	#428	—	134	2	no	—
252	#428	C₂×D₆₇	1	2	yes	—
253	#427	—	67	1	no	—
254	#427	—	134	2	no	—
255	C₂×#107	—	67	1	no	—
256	C₂×#107	—	67	2	no	—
257	C₂×#107	—	134	2	no	—
258	C₂×#107	C₂×D₆₇	1	1	yes	characteristic
259	C₂×#104	—	67	2	no	—
260	#417	—	67	2	no	—
261	#417	—	67	2	no	—
262	#405	—	67	1	no	—
263	#405	C₂×D₆₇	1	1	yes	characteristic
264	C₂×C₄×C₈	—	67	1	no	—
265	#384	—	67	2	no	—
266	#343	—	67	2	no	—
267	#343	C₂×D₆₇	1	2	yes	—
268	#339	—	67	1	no	—
269	#339	—	67	1	no	—
270	C₂×#41	—	67	2	no	—
271	#135	—	67	4	no	—
272	#135	—	67	4	no	—
273	C₂×Q₁₆	—	67	1	no	—
274	C₂×SD₁₆	—	67	2	no	—
275	C₂×D₈	—	67	1	no	—
276	#131	—	67	8	no	—
277	#131	—	134	4	no	—
278	C₂×M₁₆	—	67	1	no	—
279	C₂×M₁₆	—	134	2	no	—
280	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
281	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
282	C₂²×C₈	—	67	1	no	—
283	C₂²×C₈	—	134	2	no	—
284	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
285	C₄×Q₈	—	134	2	no	—
286	C₄×Q₈	—	134	2	no	—
287	C₄×D₄	—	268	2	no	—
288	C₄×D₄	—	268	2	no	—
289	C₄×D₄	—	134	2	no	—
290	C₄×D₄	—	134	2	no	—
291	#117	—	67	1	no	—
292	#117	—	134	2	no	—
293	#117	—	134	2	no	—
294	#117	C₂²×D₆₇	1	1	yes	characteristic
295	C₂×C₄⋊C₄	—	268	2	no	—
296	C₂×C₄⋊C₄	—	67	2	no	—
297	C₂×C₄⋊C₄	—	134	2	no	—
298	C₂×C₄⋊C₄	—	134	2	no	—
299	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
300	C₂×C₄²	—	67	1	no	—
301	#108	—	134	2	no	—
302	#108	C₄×D₆₇	1	4	yes	complemented
303	#107	—	2	1	no	—
304	#107	—	2	1	no	—
305	#107	—	2	2	no	—
306	#107	—	67	1	no	—
307	#107	—	67	1	no	—
308	#107	—	134	2	no	—
309	#107	—	134	2	no	—
310	#107	—	134	2	no	—
311	#107	—	134	1	no	—
312	#107	—	134	1	no	—
313	#106	—	2	2	no	—
314	#106	—	67	1	no	—
315	#106	—	67	1	no	—
316	#106	—	134	2	no	—
317	#104	—	67	8	no	—
318	#103	—	134	2	no	—
319	#103	—	134	2	no	—
320	#102	—	134	2	no	—
321	#102	—	134	2	no	—
322	#97	—	2	1	no	—
323	#97	—	134	1	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	67	4	no	—
326	C₄×C₈	—	134	1	no	—
327	#41	—	67	4	no	—
328	#41	—	67	4	no	—
329	#41	—	134	2	no	—
330	#41	—	134	2	no	—
331	C₂×Q₈	—	67	2	no	—
332	C₂×D₄	—	67	2	no	—
333	C₂×D₄	—	134	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	268	2	no	—
336	C₂²×C₄	—	268	2	no	—
337	C₂²×C₄	—	134	2	no	—
338	C₂²×C₄	—	134	1	no	—
339	C₂²×C₄	—	134	2	no	—
340	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
341	Q₁₆	—	67	4	no	—
342	SD₁₆	—	67	8	no	—
343	D₈	—	67	4	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	1	no	—
346	M₁₆	—	2	1	no	—
347	M₁₆	—	134	8	no	—
348	M₁₆	—	134	1	no	—
349	M₁₆	—	134	1	no	—
350	M₁₆	C₂×C₄×D₆₇	1	4	yes	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	67	2	no	—
354	C₂×C₈	—	67	1	no	—
355	C₂×C₈	—	67	1	no	—
356	C₂×C₈	—	67	2	no	—
357	C₂×C₈	—	134	8	no	—
358	C₂×C₈	—	134	1	no	—
359	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
360	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
361	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
362	C₂×C₈	Q₈×D₆₇	1	2	yes	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	268	2	no	—
366	C₄⋊C₄	—	268	2	no	—
367	C₄⋊C₄	—	536	4	no	—
368	C₄⋊C₄	—	67	1	no	—
369	C₄⋊C₄	—	67	1	no	—
370	C₄⋊C₄	—	134	2	no	—
371	C₄⋊C₄	—	134	2	no	—
372	C₄⋊C₄	D₄×D₆₇	1	1	yes	characteristic
373	C₄⋊C₄	D₄×D₆₇	1	1	yes	characteristic
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	268	2	no	—
376	C₂²⋊C₄	—	268	2	no	—
377	C₂²⋊C₄	—	134	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	268	2	no	—
380	C₄²	—	268	2	no	—
381	C₄²	—	67	2	no	—
382	C₄²	—	134	1	no	—
383	C₄²	—	134	1	no	—
384	C₂³	—	134	2	no	—
385	C₂³	#14524089	1	1	yes	characteristic
386	Q₈	—	67	4	no	—
387	Q₈	—	134	2	no	—
388	D₄	—	67	4	no	—
389	D₄	—	134	4	no	—
390	D₄	—	134	4	no	—
391	D₄	—	134	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	—	268	2	no	—
397	C₂×C₄	—	536	2	no	—
398	C₂×C₄	—	1072	2	no	—
399	C₂×C₄	—	1072	2	no	—
400	C₂×C₄	—	134	1	no	—
401	C₂×C₄	—	134	1	no	—
402	C₂×C₄	—	134	2	no	—
403	C₂×C₄	—	134	2	no	—
404	C₂×C₄	—	134	2	no	—
405	C₂×C₄	—	134	2	no	—
406	C₂×C₄	—	134	4	no	—
407	C₂×C₄	—	134	4	no	—
408	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
409	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
410	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
411	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
412	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
413	C₂×C₄	#14524091	1	1	yes	characteristic
414	C₈	—	2	4	no	—
415	C₈	—	4	1	no	—
416	C₈	—	268	1	no	—
417	C₈	—	67	2	no	—
418	C₈	—	67	2	no	—
419	C₈	C₄⋊C₄×D₆₇	1	2	yes	—
420	C₈	C₄⋊C₄×D₆₇	1	2	yes	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	268	2	no	—
424	C₂²	—	268	2	no	—
425	C₂²	—	134	4	no	—
426	C₂²	#16863878	1	1	yes	characteristic
427	C₂²	#16864030	1	1	yes	characteristic
428	C₂²	#16864102	1	1	yes	characteristic
429	C₄	—	4	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	8	2	no	—
432	C₄	—	268	1	no	—
433	C₄	—	268	1	no	—
434	C₄	—	536	2	no	—
435	C₄	—	134	4	no	—
436	C₄	—	134	4	no	—
437	C₄	C₂×C₄⋊C₄×D₆₇	1	1	yes	characteristic
438	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
439	C₄	#16864048	1	1	yes	characteristic
440	C₄	#16864061	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	268	4	no	—
444	C₂	#22563110	1	1	yes	characteristic
445	C₂	#22572007	1	1	yes	characteristic
446	C₂	#22572012	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16864030
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1952	C₂
socle	C₂²×C₆₇	D₄²
prime radical	C₂×#14524065	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1952	D₆₇
hypocenter	C₆₇	#22692
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1952

Complements

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

N	H ≅ G/N	type
4. #22568808	C₂	semidirect
5. #22560995	C₂	semidirect
6. #22560438	C₂	semidirect
7. #22560432	C₂	semidirect
8. #22560367	C₂	semidirect
9. #22560272	C₂	semidirect
10. #22560089	C₂	semidirect
11. C₆₇×#1952	C₂	semidirect
16. #16863512	C₄	semidirect
53. #14524051	C₂×C₄	semidirect
83. #14523969	C₂×C₄	semidirect
90. C₈×Dic₆₇	C₂×C₄	semidirect
96. #108×C₆₇	C₂×C₄	semidirect
115. Dic₂₆₈	C₄⋊C₄	semidirect
116. #11761617	C₄⋊C₄	semidirect
117. D₅₃₆	C₄⋊C₄	semidirect
229. #1952	D₆₇	semidirect
235. C₆₇	#22692	semidirect
302. #108	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863512	2
#22569086	2
#22569083	2
#22568808	2
#22560995	2
#22560438	2
#22560432	2
#22560367	2
#22560272	2
#22560089	2
C₆₇×#1952	2
#22692	67