Subgroups — #30874279

Order 17152.

858 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863518	C₂	1	2	yes	maximal
2	#22568777	C₂	1	2	yes	maximal, complemented
3	#22560963	C₂	1	2	yes	maximal, complemented
4	#22560486	C₂	1	4	yes	maximal, complemented
5	#22560381	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560229	C₂	1	2	yes	maximal, complemented
7	#22560076	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#14524050	C₂²	1	4	yes	—
10	#16863518	—	2	8	no	—
11	C₂×#14523979	C₂²	1	2	yes	—
12	C₂×#14523979	C₂²	1	2	yes	—
13	#16863423	—	2	4	no	—
14	#16863423	C₂²	1	4	yes	—
15	#16863420	—	2	2	no	—
16	#16863420	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
18	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#14523970	C₂²	1	4	yes	—
20	C₂×#14523953	C₂²	1	2	yes	—
21	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
22	#16863155	C₂²	1	4	yes	—
23	#16863150	C₂²	1	2	yes	—
24	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
25	C₄×#41×C₆₇	C₂²	1	2	yes	—
26	C₄×Q₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
27	C₄×Q₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
28	C₄×SD₁₆×C₆₇	C₄	1	2	yes	complemented
29	C₄×SD₁₆×C₆₇	C₄	1	2	yes	complemented
30	C₄×D₈×C₆₇	C₄	1	1	yes	characteristic, complemented
31	C₄×D₈×C₆₇	C₄	1	1	yes	characteristic, complemented
32	#427×C₆₇	C₂²	1	1	yes	characteristic
33	#416×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
35	#14524050	—	2	8	no	—
36	#14524050	—	4	4	no	—
37	C₂×#11761612	—	2	4	no	—
38	C₂×#11761612	C₂³	1	4	yes	—
39	C₂²×C₆₇⋊C₈	—	2	4	no	—
40	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
41	C₂×C₄⋊Dic₆₇	—	2	1	no	—
42	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
43	#14523979	—	2	4	no	—
44	#14523979	—	4	2	no	—
45	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
46	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
47	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
48	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
49	C₄⋊(C₆₇⋊C₈)	D₄	1	2	yes	—
50	C₄⋊(C₆₇⋊C₈)	D₄	1	2	yes	—
51	#14523970	—	2	8	no	—
52	#14523953	—	2	4	no	—
53	C₆₇⋊#95	—	2	1	no	—
54	C₂×#41×C₆₇	C₂³	1	2	yes	—
55	#135×C₆₇	D₄	1	4	yes	—
56	#135×C₆₇	Q₈	1	4	yes	—
57	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
58	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
59	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
62	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
63	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
64	C₄×D₄×C₆₇	—	2	2	no	—
65	C₄×D₄×C₆₇	—	2	2	no	—
66	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
67	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
68	#117×C₆₇	—	2	2	no	—
69	#117×C₆₇	C₂³	1	2	yes	—
70	C₂×C₄²×C₆₇	—	2	2	no	—
71	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
72	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
73	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
74	#106×C₆₇	C₂×C₄	1	2	yes	—
75	#103×C₆₇	C₂×C₄	1	2	yes	—
76	#103×C₆₇	C₂×C₄	1	2	yes	—
77	#102×C₆₇	C₂×C₄	1	2	yes	—
78	#102×C₆₇	C₂×C₄	1	2	yes	—
79	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
83	C₂²×Dic₆₇	—	2	2	no	—
84	#11761612	—	2	4	no	—
85	#11761612	—	2	4	no	—
86	#11761612	—	4	8	no	—
87	C₂×C₆₇⋊C₈	—	2	2	no	—
88	C₂×C₆₇⋊C₈	—	2	2	no	—
89	C₂×C₆₇⋊C₈	—	2	4	no	—
90	C₂×C₆₇⋊C₈	—	4	8	no	—
91	C₂×C₆₇⋊C₈	C₂×D₄	1	4	yes	—
92	C₄⋊Dic₆₇	—	4	2	no	—
93	C₄×Dic₆₇	—	2	2	no	—
94	C₄×Dic₆₇	—	2	2	no	—
95	#41×C₆₇	—	2	2	no	—
96	#41×C₆₇	—	2	2	no	—
97	#41×C₆₇	C₂×D₄	1	4	yes	—
98	#41×C₆₇	C₂×Q₈	1	4	yes	—
99	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
100	C₂×D₄×C₆₇	—	2	2	no	—
101	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₆₇	—	2	2	no	—
103	C₂²×C₄×C₆₇	—	2	2	no	—
104	C₂²×C₄×C₆₇	—	2	2	no	—
105	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
106	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
107	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
108	Q₁₆×C₆₇	C₄⋊C₄	1	4	yes	complemented
109	SD₁₆×C₆₇	C₄⋊C₄	1	8	yes	complemented
110	D₈×C₆₇	C₄⋊C₄	1	4	yes	complemented
111	C₂×C₈×C₆₇	—	2	1	no	—
112	C₂×C₈×C₆₇	—	2	1	no	—
113	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₆₇	C₂×Q₈	1	2	yes	—
119	C₄⋊C₄×C₆₇	—	2	2	no	—
120	C₄⋊C₄×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
122	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
123	C₂²⋊C₄×C₆₇	—	2	2	no	—
124	C₂²⋊C₄×C₆₇	—	2	2	no	—
125	C₂²⋊C₄×C₆₇	—	2	2	no	—
126	C₄²×C₆₇	—	2	2	no	—
127	C₄²×C₆₇	—	2	2	no	—
128	C₄²×C₆₇	—	2	2	no	—
129	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
133	C₂³×C₆₇	—	2	2	no	—
134	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
135	Q₈×C₆₇	—	2	2	no	—
136	Q₈×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
137	D₄×C₆₇	—	2	4	no	—
138	D₄×C₆₇	—	2	4	no	—
139	D₄×C₆₇	—	2	2	no	—
140	D₄×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
141	C₂×C₄×C₆₇	—	2	2	no	—
142	C₂×C₄×C₆₇	—	2	4	no	—
143	C₂×C₄×C₆₇	—	2	4	no	—
144	C₂×C₄×C₆₇	—	2	2	no	—
145	C₂×C₄×C₆₇	—	2	2	no	—
146	C₂×C₄×C₆₇	—	2	2	no	—
147	C₂×C₄×C₆₇	—	4	1	no	—
148	C₂×C₄×C₆₇	—	4	4	no	—
149	C₂×C₄×C₆₇	—	8	2	no	—
150	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
160	C₂×Dic₆₇	—	4	2	no	—
161	C₂×Dic₆₇	—	4	2	no	—
162	C₂×Dic₆₇	—	4	2	no	—
163	C₈×C₆₇	—	2	1	no	—
164	C₈×C₆₇	—	2	1	no	—
165	C₈×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
166	C₈×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
167	C₆₇⋊C₈	—	2	4	no	—
168	C₆₇⋊C₈	—	4	4	no	—
169	C₂²×C₆₇	—	2	1	no	—
170	C₂²×C₆₇	—	2	1	no	—
171	C₂²×C₆₇	—	2	4	no	—
172	C₂²×C₆₇	—	4	2	no	—
173	C₂²×C₆₇	—	4	2	no	—
174	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
175	C₂²×C₆₇	#547	1	1	yes	characteristic
176	C₂²×C₆₇	#554	1	1	yes	characteristic
177	C₄×C₆₇	—	2	4	no	—
178	C₄×C₆₇	—	2	1	no	—
179	C₄×C₆₇	—	2	1	no	—
180	C₄×C₆₇	—	2	1	no	—
181	C₄×C₆₇	—	4	2	no	—
182	C₄×C₆₇	—	4	2	no	—
183	C₄×C₆₇	#444	1	2	yes	complemented
184	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₄×C₆₇	#520	1	1	yes	characteristic
186	C₄×C₆₇	D₄²	1	1	yes	characteristic
187	C₄×C₆₇	D₄×Q₈	1	1	yes	characteristic
188	Dic₆₇	—	8	2	no	—
189	#22686	—	67	1	no	maximal, Sylow
190	C₂×C₆₇	—	2	1	no	—
191	C₂×C₆₇	—	2	1	no	—
192	C₂×C₆₇	—	4	4	no	—
193	C₂×C₆₇	D₄×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₆₇	C₂×#444	1	1	yes	characteristic
195	C₂×C₆₇	#2957	1	1	yes	characteristic
196	C₂×#444	—	67	2	no	—
197	C₄×#135	D₆₇	1	1	yes	characteristic
198	#2906	—	67	2	no	—
199	#1946	—	67	2	no	—
200	#1866	—	67	4	no	—
201	#1848	—	67	1	no	—
202	#1806	—	67	2	no	—
203	#1770	—	67	1	no	—
204	C₆₇	#22686	1	1	yes	characteristic, complemented, Sylow
205	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
206	C₂×#131	—	67	4	no	—
207	C₄×#41	C₂×D₆₇	1	2	yes	—
208	#444	—	134	8	no	—
209	C₄×Q₁₆	Dic₆₇	1	1	yes	characteristic, complemented
210	C₄×Q₁₆	Dic₆₇	1	1	yes	characteristic, complemented
211	C₄×SD₁₆	Dic₆₇	1	2	yes	complemented
212	C₄×SD₁₆	Dic₆₇	1	2	yes	complemented
213	C₄×D₈	Dic₆₇	1	1	yes	characteristic, complemented
214	C₄×D₈	Dic₆₇	1	1	yes	characteristic, complemented
215	C₂×#108	—	67	2	no	—
216	C₂×#108	—	67	2	no	—
217	#427	C₂×D₆₇	1	1	yes	characteristic
218	#424	—	67	4	no	—
219	#424	—	134	4	no	—
220	#423	—	67	2	no	—
221	#423	—	134	2	no	—
222	C₂×C₄⋊C₈	—	67	1	no	—
223	C₂×C₄⋊C₈	—	134	2	no	—
224	C₂×#104	—	67	4	no	—
225	#416	C₂×D₆₇	1	2	yes	—
226	C₂×#97	—	67	2	no	—
227	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
228	C₄×C₄⋊C₄	—	67	1	no	—
229	#339	—	67	4	no	—
230	#336	—	67	2	no	—
231	C₂×#41	C₂²×D₆₇	1	2	yes	—
232	#135	Dic₁₃₄	1	4	yes	—
233	#135	D₂₆₈	1	4	yes	—
234	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic
235	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	—
236	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
237	#131	—	268	4	no	—
238	#131	—	134	8	no	—
239	C₂×M₁₆	—	67	4	no	—
240	C₂×M₁₆	—	134	4	no	—
241	C₂²×C₈	—	67	2	no	—
242	C₂²×C₈	—	134	4	no	—
243	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
244	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
245	C₄×Q₈	C₂×Dic₆₇	1	2	yes	—
246	C₄×Q₈	C₂×Dic₆₇	1	2	yes	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	2	no	—
249	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
250	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
251	#117	—	2	2	no	—
252	#117	C₂²×D₆₇	1	2	yes	—
253	C₂×C₄⋊C₄	—	134	1	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	67	2	no	—
256	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
257	#108	—	268	2	no	—
258	#108	—	134	4	no	—
259	#107	C₂×Dic₆₇	1	1	yes	characteristic
260	#107	C₂×Dic₆₇	1	1	yes	characteristic
261	#106	C₂×Dic₆₇	1	2	yes	—
262	C₄⋊C₈	—	67	2	no	—
263	C₄⋊C₈	—	67	2	no	—
264	C₄⋊C₈	—	134	4	no	—
265	C₄⋊C₈	—	134	4	no	—
266	C₄⋊C₈	—	134	2	no	—
267	C₄⋊C₈	—	134	2	no	—
268	#104	—	134	8	no	—
269	#103	C₂×Dic₆₇	1	2	yes	—
270	#103	C₂×Dic₆₇	1	2	yes	—
271	#102	C₂×Dic₆₇	1	2	yes	—
272	#102	C₂×Dic₆₇	1	2	yes	—
273	#97	—	134	4	no	—
274	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
275	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
276	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
277	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
278	#95	—	134	1	no	—
279	#41	—	2	2	no	—
280	#41	—	2	2	no	—
281	#41	C₂×D₂₆₈	1	4	yes	—
282	#41	C₂×Dic₁₃₄	1	4	yes	—
283	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	134	2	no	—
290	C₂²×C₄	#11761627	1	1	yes	characteristic
291	C₂²×C₄	#11761627	1	1	yes	characteristic
292	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
293	Q₁₆	C₄⋊Dic₆₇	1	4	yes	complemented
294	SD₁₆	C₄⋊Dic₆₇	1	8	yes	complemented
295	D₈	C₄⋊Dic₆₇	1	4	yes	complemented
296	M₁₆	—	268	8	no	—
297	M₁₆	—	134	4	no	—
298	M₁₆	—	134	4	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	268	8	no	—
302	C₂×C₈	—	67	4	no	—
303	C₂×C₈	—	134	4	no	—
304	C₂×C₈	—	134	2	no	—
305	C₂×C₈	—	134	2	no	—
306	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
307	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
308	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
309	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
310	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
311	C₂×C₈	C₂×Dic₁₃₄	1	2	yes	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	268	2	no	—
315	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
316	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	134	2	no	—
324	C₄²	—	134	2	no	—
325	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
326	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
327	C₄²	D₄×D₆₇	1	1	yes	characteristic
328	C₄²	D₄×D₆₇	1	1	yes	characteristic
329	C₂³	—	2	2	no	—
330	C₂³	C₂×#11761627	1	1	yes	characteristic
331	Q₈	—	2	2	no	—
332	Q₈	C₂×C₄⋊Dic₆₇	1	4	yes	—
333	D₄	—	2	4	no	—
334	D₄	—	2	4	no	—
335	D₄	—	2	2	no	—
336	D₄	C₂×C₄⋊Dic₆₇	1	4	yes	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	—	268	2	no	—
347	C₂×C₄	—	268	2	no	—
348	C₂×C₄	—	268	2	no	—
349	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
350	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
351	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
352	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
353	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
354	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
356	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
357	C₂×C₄	#14524089	1	1	yes	characteristic
358	C₂×C₄	#14524090	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	268	4	no	—
362	C₈	—	134	4	no	—
363	C₈	C₂×C₄⋊Dic₆₇	1	2	yes	—
364	C₈	C₂×C₄⋊Dic₆₇	1	2	yes	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
371	C₂²	#16864050	1	1	yes	characteristic
372	C₂²	#16864103	1	1	yes	characteristic
373	C₄	—	2	4	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	536	2	no	—
380	C₄	#16863518	1	2	yes	complemented
381	C₄	C₂²×C₄⋊Dic₆₇	1	1	yes	characteristic
382	C₄	#16863879	1	1	yes	characteristic
383	C₄	D₄×D₂₆₈	1	1	yes	characteristic
384	C₄	D₄×Dic₁₃₄	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	4	4	no	—
388	C₂	D₄×C₄⋊Dic₆₇	1	1	yes	characteristic
389	C₂	C₂×#16863518	1	1	yes	characteristic
390	C₂	#22569126	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	C₄×#135×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#135×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₄×#135	D₆₇
hypocenter	C₆₇	#22686
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
2. #22568777	C₂	semidirect
3. #22560963	C₂	semidirect
4. #22560486	C₂	semidirect
5. #22560381	C₂	semidirect
6. #22560229	C₂	semidirect
7. #22560076	C₂	semidirect
26. C₄×Q₁₆×C₆₇	C₄	semidirect
27. C₄×Q₁₆×C₆₇	C₄	semidirect
28. C₄×SD₁₆×C₆₇	C₄	semidirect
29. C₄×SD₁₆×C₆₇	C₄	semidirect
30. C₄×D₈×C₆₇	C₄	semidirect
31. C₄×D₈×C₆₇	C₄	semidirect
108. Q₁₆×C₆₇	C₄⋊C₄	semidirect
109. SD₁₆×C₆₇	C₄⋊C₄	semidirect
110. D₈×C₆₇	C₄⋊C₄	semidirect
183. C₄×C₆₇	#444	semidirect
204. C₆₇	#22686	semidirect
209. C₄×Q₁₆	Dic₆₇	semidirect
210. C₄×Q₁₆	Dic₆₇	semidirect
211. C₄×SD₁₆	Dic₆₇	semidirect
212. C₄×SD₁₆	Dic₆₇	semidirect
213. C₄×D₈	Dic₆₇	semidirect
214. C₄×D₈	Dic₆₇	semidirect
293. Q₁₆	C₄⋊Dic₆₇	semidirect
294. SD₁₆	C₄⋊Dic₆₇	semidirect
295. D₈	C₄⋊Dic₆₇	semidirect
380. C₄	#16863518	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863518	2
#22568777	2
#22560963	2
#22560486	2
#22560381	2
#22560229	2
#22560076	2
C₄×#135×C₆₇	2
#22686	67